TSTP Solution File: GRP308-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP308-1 : 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.xRzAE8QwIg true
% Computer : n010.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 01:51:08 EDT 2023
% Result : Unsatisfiable 2.09s 0.91s
% Output : Refutation 2.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15 % Problem : GRP308-1 : TPTP v8.1.2. Released v2.5.0.
% 0.13/0.16 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.xRzAE8QwIg true
% 0.14/0.37 % Computer : n010.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Tue Aug 29 01:11:04 EDT 2023
% 0.14/0.38 % CPUTime :
% 0.14/0.38 % Running portfolio for 300 s
% 0.14/0.38 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.38 % Number of cores: 8
% 0.14/0.38 % Python version: Python 3.6.8
% 0.14/0.38 % Running in FO mode
% 0.22/0.63 % Total configuration time : 435
% 0.22/0.63 % Estimated wc time : 1092
% 0.22/0.63 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.68 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.22/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.22/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.22/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 2.09/0.91 % Solved by fo/fo7.sh.
% 2.09/0.91 % done 387 iterations in 0.126s
% 2.09/0.91 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 2.09/0.91 % SZS output start Refutation
% 2.09/0.91 thf(sk_c2_type, type, sk_c2: $i).
% 2.09/0.91 thf(sk_c6_type, type, sk_c6: $i).
% 2.09/0.91 thf(sk_c5_type, type, sk_c5: $i).
% 2.09/0.91 thf(sk_c4_type, type, sk_c4: $i).
% 2.09/0.91 thf(identity_type, type, identity: $i).
% 2.09/0.91 thf(multiply_type, type, multiply: $i > $i > $i).
% 2.09/0.91 thf(sk_c7_type, type, sk_c7: $i).
% 2.09/0.91 thf(inverse_type, type, inverse: $i > $i).
% 2.09/0.91 thf(sk_c3_type, type, sk_c3: $i).
% 2.09/0.91 thf(sk_c1_type, type, sk_c1: $i).
% 2.09/0.91 thf(sk_c8_type, type, sk_c8: $i).
% 2.09/0.91 thf(prove_this_37, conjecture,
% 2.09/0.91 (~( ( ( multiply @ X5 @ sk_c8 ) != ( sk_c6 ) ) |
% 2.09/0.91 ( ( inverse @ X5 ) != ( sk_c6 ) ) |
% 2.09/0.91 ( ( inverse @ X2 ) != ( sk_c7 ) ) |
% 2.09/0.91 ( ( multiply @ X2 @ sk_c7 ) != ( sk_c6 ) ) |
% 2.09/0.91 ( ( inverse @ X1 ) != ( sk_c8 ) ) |
% 2.09/0.91 ( ( multiply @ X1 @ sk_c8 ) != ( sk_c7 ) ) |
% 2.09/0.91 ( ( inverse @ X4 ) != ( sk_c8 ) ) |
% 2.09/0.91 ( ( multiply @ X4 @ sk_c8 ) != ( X3 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c8 @ X3 ) != ( sk_c7 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c6 @ sk_c7 ) != ( sk_c8 ) ) |
% 2.09/0.91 ( ( inverse @ sk_c8 ) != ( sk_c6 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c8 @ sk_c7 ) != ( sk_c6 ) ) ))).
% 2.09/0.91 thf(zf_stmt_0, negated_conjecture,
% 2.09/0.91 (( ( multiply @ X5 @ sk_c8 ) != ( sk_c6 ) ) |
% 2.09/0.91 ( ( inverse @ X5 ) != ( sk_c6 ) ) | ( ( inverse @ X2 ) != ( sk_c7 ) ) |
% 2.09/0.91 ( ( multiply @ X2 @ sk_c7 ) != ( sk_c6 ) ) |
% 2.09/0.91 ( ( inverse @ X1 ) != ( sk_c8 ) ) |
% 2.09/0.91 ( ( multiply @ X1 @ sk_c8 ) != ( sk_c7 ) ) |
% 2.09/0.91 ( ( inverse @ X4 ) != ( sk_c8 ) ) |
% 2.09/0.91 ( ( multiply @ X4 @ sk_c8 ) != ( X3 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c8 @ X3 ) != ( sk_c7 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c6 @ sk_c7 ) != ( sk_c8 ) ) |
% 2.09/0.91 ( ( inverse @ sk_c8 ) != ( sk_c6 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c8 @ sk_c7 ) != ( sk_c6 ) )),
% 2.09/0.91 inference('cnf.neg', [status(esa)], [prove_this_37])).
% 2.09/0.91 thf(zip_derived_cl39, plain,
% 2.09/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 2.09/0.91 (((multiply @ X0 @ sk_c8) != (sk_c6))
% 2.09/0.91 | ((inverse @ X0) != (sk_c6))
% 2.09/0.91 | ((inverse @ X1) != (sk_c7))
% 2.09/0.91 | ((multiply @ X1 @ sk_c7) != (sk_c6))
% 2.09/0.91 | ((inverse @ X2) != (sk_c8))
% 2.09/0.91 | ((multiply @ X2 @ sk_c8) != (sk_c7))
% 2.09/0.91 | ((inverse @ X3) != (sk_c8))
% 2.09/0.91 | ((multiply @ X3 @ sk_c8) != (X4))
% 2.09/0.91 | ((multiply @ sk_c8 @ X4) != (sk_c7))
% 2.09/0.91 | ((multiply @ sk_c6 @ sk_c7) != (sk_c8))
% 2.09/0.91 | ((inverse @ sk_c8) != (sk_c6))
% 2.09/0.91 | ((multiply @ sk_c8 @ sk_c7) != (sk_c6)))),
% 2.09/0.91 inference('cnf', [status(esa)], [zf_stmt_0])).
% 2.09/0.91 thf(zip_derived_cl40, plain,
% 2.09/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 2.09/0.91 (((multiply @ X0 @ sk_c8) != (multiply @ sk_c8 @ sk_c7))
% 2.09/0.91 | ((inverse @ X0) != (multiply @ sk_c8 @ sk_c7))
% 2.09/0.91 | ((inverse @ X1) != (sk_c7))
% 2.09/0.91 | ((multiply @ X1 @ sk_c7) != (multiply @ sk_c8 @ sk_c7))
% 2.09/0.91 | ((inverse @ X2) != (sk_c8))
% 2.09/0.91 | ((multiply @ X2 @ sk_c8) != (sk_c7))
% 2.09/0.91 | ((inverse @ X3) != (sk_c8))
% 2.09/0.91 | ((multiply @ X3 @ sk_c8) != (X4))
% 2.09/0.91 | ((multiply @ sk_c8 @ X4) != (sk_c7))
% 2.09/0.91 | ((multiply @ (multiply @ sk_c8 @ sk_c7) @ sk_c7) != (sk_c8))
% 2.09/0.91 | ((inverse @ sk_c8) != (sk_c6))
% 2.09/0.91 | ((multiply @ sk_c8 @ sk_c7) != (sk_c6)))),
% 2.09/0.91 inference('local_rewriting', [status(thm)], [zip_derived_cl39])).
% 2.09/0.91 thf(associativity, axiom,
% 2.09/0.91 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 2.09/0.91 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 2.09/0.91 thf(zip_derived_cl2, plain,
% 2.09/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.09/0.91 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 2.09/0.91 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 2.09/0.91 inference('cnf', [status(esa)], [associativity])).
% 2.09/0.91 thf(zip_derived_cl56, plain,
% 2.09/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 2.09/0.91 (((multiply @ X0 @ sk_c8) != (multiply @ sk_c8 @ sk_c7))
% 2.09/0.91 | ((inverse @ X0) != (multiply @ sk_c8 @ sk_c7))
% 2.09/0.91 | ((inverse @ X1) != (sk_c7))
% 2.09/0.91 | ((multiply @ X1 @ sk_c7) != (multiply @ sk_c8 @ sk_c7))
% 2.09/0.91 | ((inverse @ X2) != (sk_c8))
% 2.09/0.91 | ((multiply @ X2 @ sk_c8) != (sk_c7))
% 2.09/0.91 | ((inverse @ X3) != (sk_c8))
% 2.09/0.91 | ((multiply @ X3 @ sk_c8) != (X4))
% 2.09/0.91 | ((multiply @ sk_c8 @ X4) != (sk_c7))
% 2.09/0.91 | ((multiply @ sk_c8 @ (multiply @ sk_c7 @ sk_c7)) != (sk_c8))
% 2.09/0.91 | ((inverse @ sk_c8) != (sk_c6))
% 2.09/0.91 | ((multiply @ sk_c8 @ sk_c7) != (sk_c6)))),
% 2.09/0.91 inference('demod', [status(thm)], [zip_derived_cl40, zip_derived_cl2])).
% 2.09/0.91 thf(prove_this_8, conjecture,
% 2.09/0.91 (~( ( ( inverse @ sk_c3 ) = ( sk_c8 ) ) |
% 2.09/0.91 ( ( inverse @ sk_c8 ) = ( sk_c6 ) ) ))).
% 2.09/0.91 thf(zf_stmt_1, negated_conjecture,
% 2.09/0.91 (( ( inverse @ sk_c3 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c8 ) = ( sk_c6 ) )),
% 2.09/0.91 inference('cnf.neg', [status(esa)], [prove_this_8])).
% 2.09/0.91 thf(zip_derived_cl10, plain,
% 2.09/0.91 ((((inverse @ sk_c3) = (sk_c8)) | ((inverse @ sk_c8) = (sk_c6)))),
% 2.09/0.91 inference('cnf', [status(esa)], [zf_stmt_1])).
% 2.09/0.91 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 2.09/0.91 thf(zip_derived_cl1, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.91 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.91 thf(zip_derived_cl41, plain,
% 2.09/0.91 ((((multiply @ sk_c8 @ sk_c3) = (identity))
% 2.09/0.91 | ((inverse @ sk_c8) = (sk_c6)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl1])).
% 2.09/0.91 thf(zip_derived_cl1, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.91 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.91 thf(zip_derived_cl2, plain,
% 2.09/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.09/0.91 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 2.09/0.91 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 2.09/0.91 inference('cnf', [status(esa)], [associativity])).
% 2.09/0.91 thf(zip_derived_cl60, plain,
% 2.09/0.91 (![X0 : $i, X1 : $i]:
% 2.09/0.91 ((multiply @ identity @ X0)
% 2.09/0.91 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 2.09/0.91 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 2.09/0.91 thf(zip_derived_cl0, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 2.09/0.91 inference('cnf', [status(esa)], [left_identity])).
% 2.09/0.91 thf(zip_derived_cl97, plain,
% 2.09/0.91 (![X0 : $i, X1 : $i]:
% 2.09/0.91 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.09/0.91 inference('demod', [status(thm)], [zip_derived_cl60, zip_derived_cl0])).
% 2.09/0.91 thf(zip_derived_cl119, plain,
% 2.09/0.91 ((((sk_c3) = (multiply @ (inverse @ sk_c8) @ identity))
% 2.09/0.91 | ((inverse @ sk_c8) = (sk_c6)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl97])).
% 2.09/0.91 thf(prove_this_7, conjecture,
% 2.09/0.91 (~( ( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 2.09/0.91 ( ( inverse @ sk_c8 ) = ( sk_c6 ) ) ))).
% 2.09/0.91 thf(zf_stmt_2, negated_conjecture,
% 2.09/0.91 (( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 2.09/0.91 ( ( inverse @ sk_c8 ) = ( sk_c6 ) )),
% 2.09/0.91 inference('cnf.neg', [status(esa)], [prove_this_7])).
% 2.09/0.91 thf(zip_derived_cl9, plain,
% 2.09/0.91 ((((multiply @ sk_c3 @ sk_c8) = (sk_c7)) | ((inverse @ sk_c8) = (sk_c6)))),
% 2.09/0.91 inference('cnf', [status(esa)], [zf_stmt_2])).
% 2.09/0.91 thf(zip_derived_cl175, plain,
% 2.09/0.91 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c8)
% 2.09/0.91 = (sk_c7))
% 2.09/0.91 | ((inverse @ sk_c8) = (sk_c6))
% 2.09/0.91 | ((inverse @ sk_c8) = (sk_c6)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl119, zip_derived_cl9])).
% 2.09/0.91 thf(zip_derived_cl2, plain,
% 2.09/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.09/0.91 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 2.09/0.91 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 2.09/0.91 inference('cnf', [status(esa)], [associativity])).
% 2.09/0.91 thf(zip_derived_cl0, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 2.09/0.91 inference('cnf', [status(esa)], [left_identity])).
% 2.09/0.91 thf(zip_derived_cl1, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.91 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.91 thf(zip_derived_cl183, plain,
% 2.09/0.91 ((((identity) = (sk_c7))
% 2.09/0.91 | ((inverse @ sk_c8) = (sk_c6))
% 2.09/0.91 | ((inverse @ sk_c8) = (sk_c6)))),
% 2.09/0.91 inference('demod', [status(thm)],
% 2.09/0.91 [zip_derived_cl175, zip_derived_cl2, zip_derived_cl0,
% 2.09/0.91 zip_derived_cl1])).
% 2.09/0.91 thf(zip_derived_cl184, plain,
% 2.09/0.91 ((((inverse @ sk_c8) = (sk_c6)) | ((identity) = (sk_c7)))),
% 2.09/0.91 inference('simplify', [status(thm)], [zip_derived_cl183])).
% 2.09/0.91 thf(prove_this_32, conjecture,
% 2.09/0.91 (~( ( ( inverse @ sk_c3 ) = ( sk_c8 ) ) |
% 2.09/0.91 ( ( inverse @ sk_c1 ) = ( sk_c8 ) ) ))).
% 2.09/0.91 thf(zf_stmt_3, negated_conjecture,
% 2.09/0.91 (( ( inverse @ sk_c3 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c8 ) )),
% 2.09/0.91 inference('cnf.neg', [status(esa)], [prove_this_32])).
% 2.09/0.91 thf(zip_derived_cl34, plain,
% 2.09/0.91 ((((inverse @ sk_c3) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c8)))),
% 2.09/0.91 inference('cnf', [status(esa)], [zf_stmt_3])).
% 2.09/0.91 thf(zip_derived_cl1, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.91 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.91 thf(zip_derived_cl47, plain,
% 2.09/0.91 ((((multiply @ sk_c8 @ sk_c1) = (identity))
% 2.09/0.91 | ((inverse @ sk_c3) = (sk_c8)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl34, zip_derived_cl1])).
% 2.09/0.91 thf(zip_derived_cl97, plain,
% 2.09/0.91 (![X0 : $i, X1 : $i]:
% 2.09/0.91 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.09/0.91 inference('demod', [status(thm)], [zip_derived_cl60, zip_derived_cl0])).
% 2.09/0.91 thf(zip_derived_cl128, plain,
% 2.09/0.91 ((((sk_c1) = (multiply @ (inverse @ sk_c8) @ identity))
% 2.09/0.91 | ((inverse @ sk_c3) = (sk_c8)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl47, zip_derived_cl97])).
% 2.09/0.91 thf(prove_this_26, conjecture,
% 2.09/0.91 (~( ( ( inverse @ sk_c3 ) = ( sk_c8 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c2 ) ) ))).
% 2.09/0.91 thf(zf_stmt_4, negated_conjecture,
% 2.09/0.91 (( ( inverse @ sk_c3 ) = ( sk_c8 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c2 ) )),
% 2.09/0.91 inference('cnf.neg', [status(esa)], [prove_this_26])).
% 2.09/0.91 thf(zip_derived_cl28, plain,
% 2.09/0.91 ((((inverse @ sk_c3) = (sk_c8)) | ((multiply @ sk_c1 @ sk_c8) = (sk_c2)))),
% 2.09/0.91 inference('cnf', [status(esa)], [zf_stmt_4])).
% 2.09/0.91 thf(zip_derived_cl377, plain,
% 2.09/0.91 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c8)
% 2.09/0.91 = (sk_c2))
% 2.09/0.91 | ((inverse @ sk_c3) = (sk_c8))
% 2.09/0.91 | ((inverse @ sk_c3) = (sk_c8)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl128, zip_derived_cl28])).
% 2.09/0.91 thf(zip_derived_cl2, plain,
% 2.09/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.09/0.91 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 2.09/0.91 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 2.09/0.91 inference('cnf', [status(esa)], [associativity])).
% 2.09/0.91 thf(zip_derived_cl0, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 2.09/0.91 inference('cnf', [status(esa)], [left_identity])).
% 2.09/0.91 thf(zip_derived_cl1, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.91 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.91 thf(zip_derived_cl395, plain,
% 2.09/0.91 ((((identity) = (sk_c2))
% 2.09/0.91 | ((inverse @ sk_c3) = (sk_c8))
% 2.09/0.91 | ((inverse @ sk_c3) = (sk_c8)))),
% 2.09/0.91 inference('demod', [status(thm)],
% 2.09/0.91 [zip_derived_cl377, zip_derived_cl2, zip_derived_cl0,
% 2.09/0.91 zip_derived_cl1])).
% 2.09/0.91 thf(zip_derived_cl396, plain,
% 2.09/0.91 ((((inverse @ sk_c3) = (sk_c8)) | ((identity) = (sk_c2)))),
% 2.09/0.91 inference('simplify', [status(thm)], [zip_derived_cl395])).
% 2.09/0.91 thf(prove_this_20, conjecture,
% 2.09/0.91 (~( ( ( inverse @ sk_c3 ) = ( sk_c8 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c8 @ sk_c2 ) = ( sk_c7 ) ) ))).
% 2.09/0.91 thf(zf_stmt_5, negated_conjecture,
% 2.09/0.91 (( ( inverse @ sk_c3 ) = ( sk_c8 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c8 @ sk_c2 ) = ( sk_c7 ) )),
% 2.09/0.91 inference('cnf.neg', [status(esa)], [prove_this_20])).
% 2.09/0.91 thf(zip_derived_cl22, plain,
% 2.09/0.91 ((((inverse @ sk_c3) = (sk_c8)) | ((multiply @ sk_c8 @ sk_c2) = (sk_c7)))),
% 2.09/0.91 inference('cnf', [status(esa)], [zf_stmt_5])).
% 2.09/0.91 thf(zip_derived_cl404, plain,
% 2.09/0.91 ((((multiply @ sk_c8 @ identity) = (sk_c7))
% 2.09/0.91 | ((inverse @ sk_c3) = (sk_c8))
% 2.09/0.91 | ((inverse @ sk_c3) = (sk_c8)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl396, zip_derived_cl22])).
% 2.09/0.91 thf(zip_derived_cl412, plain,
% 2.09/0.91 ((((inverse @ sk_c3) = (sk_c8))
% 2.09/0.91 | ((multiply @ sk_c8 @ identity) = (sk_c7)))),
% 2.09/0.91 inference('simplify', [status(thm)], [zip_derived_cl404])).
% 2.09/0.91 thf(zip_derived_cl1, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.91 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.91 thf(zip_derived_cl97, plain,
% 2.09/0.91 (![X0 : $i, X1 : $i]:
% 2.09/0.91 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.09/0.91 inference('demod', [status(thm)], [zip_derived_cl60, zip_derived_cl0])).
% 2.09/0.91 thf(zip_derived_cl117, plain,
% 2.09/0.91 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl97])).
% 2.09/0.91 thf(zip_derived_cl415, plain,
% 2.09/0.91 ((((sk_c3) = (multiply @ (inverse @ sk_c8) @ identity))
% 2.09/0.91 | ((multiply @ sk_c8 @ identity) = (sk_c7)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl412, zip_derived_cl117])).
% 2.09/0.91 thf(zip_derived_cl117, plain,
% 2.09/0.91 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl97])).
% 2.09/0.91 thf(zip_derived_cl97, plain,
% 2.09/0.91 (![X0 : $i, X1 : $i]:
% 2.09/0.91 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.09/0.91 inference('demod', [status(thm)], [zip_derived_cl60, zip_derived_cl0])).
% 2.09/0.91 thf(zip_derived_cl97, plain,
% 2.09/0.91 (![X0 : $i, X1 : $i]:
% 2.09/0.91 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.09/0.91 inference('demod', [status(thm)], [zip_derived_cl60, zip_derived_cl0])).
% 2.09/0.91 thf(zip_derived_cl114, plain,
% 2.09/0.91 (![X0 : $i, X1 : $i]:
% 2.09/0.91 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl97, zip_derived_cl97])).
% 2.09/0.91 thf(zip_derived_cl639, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl117, zip_derived_cl114])).
% 2.09/0.91 thf(zip_derived_cl639, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl117, zip_derived_cl114])).
% 2.09/0.91 thf(zip_derived_cl677, plain,
% 2.09/0.91 ((((sk_c3) = (inverse @ sk_c8)) | ((sk_c8) = (sk_c7)))),
% 2.09/0.91 inference('demod', [status(thm)],
% 2.09/0.91 [zip_derived_cl415, zip_derived_cl639, zip_derived_cl639])).
% 2.09/0.91 thf(prove_this_31, conjecture,
% 2.09/0.91 (~( ( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 2.09/0.91 ( ( inverse @ sk_c1 ) = ( sk_c8 ) ) ))).
% 2.09/0.91 thf(zf_stmt_6, negated_conjecture,
% 2.09/0.91 (( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 2.09/0.91 ( ( inverse @ sk_c1 ) = ( sk_c8 ) )),
% 2.09/0.91 inference('cnf.neg', [status(esa)], [prove_this_31])).
% 2.09/0.91 thf(zip_derived_cl33, plain,
% 2.09/0.91 ((((multiply @ sk_c3 @ sk_c8) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c8)))),
% 2.09/0.91 inference('cnf', [status(esa)], [zf_stmt_6])).
% 2.09/0.91 thf(zip_derived_cl639, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl117, zip_derived_cl114])).
% 2.09/0.91 thf(zip_derived_cl117, plain,
% 2.09/0.91 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl97])).
% 2.09/0.91 thf(zip_derived_cl683, plain,
% 2.09/0.91 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl639, zip_derived_cl117])).
% 2.09/0.91 thf(zip_derived_cl855, plain,
% 2.09/0.91 ((((sk_c1) = (inverse @ sk_c8)) | ((multiply @ sk_c3 @ sk_c8) = (sk_c7)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl33, zip_derived_cl683])).
% 2.09/0.91 thf(prove_this_25, conjecture,
% 2.09/0.91 (~( ( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c2 ) ) ))).
% 2.09/0.91 thf(zf_stmt_7, negated_conjecture,
% 2.09/0.91 (( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c2 ) )),
% 2.09/0.91 inference('cnf.neg', [status(esa)], [prove_this_25])).
% 2.09/0.91 thf(zip_derived_cl27, plain,
% 2.09/0.91 ((((multiply @ sk_c3 @ sk_c8) = (sk_c7))
% 2.09/0.91 | ((multiply @ sk_c1 @ sk_c8) = (sk_c2)))),
% 2.09/0.91 inference('cnf', [status(esa)], [zf_stmt_7])).
% 2.09/0.91 thf(zip_derived_cl1128, plain,
% 2.09/0.91 ((((multiply @ (inverse @ sk_c8) @ sk_c8) = (sk_c2))
% 2.09/0.91 | ((multiply @ sk_c3 @ sk_c8) = (sk_c7))
% 2.09/0.91 | ((multiply @ sk_c3 @ sk_c8) = (sk_c7)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl855, zip_derived_cl27])).
% 2.09/0.91 thf(zip_derived_cl1, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.91 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.91 thf(zip_derived_cl1146, plain,
% 2.09/0.91 ((((identity) = (sk_c2))
% 2.09/0.91 | ((multiply @ sk_c3 @ sk_c8) = (sk_c7))
% 2.09/0.91 | ((multiply @ sk_c3 @ sk_c8) = (sk_c7)))),
% 2.09/0.91 inference('demod', [status(thm)], [zip_derived_cl1128, zip_derived_cl1])).
% 2.09/0.91 thf(zip_derived_cl1147, plain,
% 2.09/0.91 ((((multiply @ sk_c3 @ sk_c8) = (sk_c7)) | ((identity) = (sk_c2)))),
% 2.09/0.91 inference('simplify', [status(thm)], [zip_derived_cl1146])).
% 2.09/0.91 thf(prove_this_19, conjecture,
% 2.09/0.91 (~( ( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c8 @ sk_c2 ) = ( sk_c7 ) ) ))).
% 2.09/0.91 thf(zf_stmt_8, negated_conjecture,
% 2.09/0.91 (( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c8 @ sk_c2 ) = ( sk_c7 ) )),
% 2.09/0.91 inference('cnf.neg', [status(esa)], [prove_this_19])).
% 2.09/0.91 thf(zip_derived_cl21, plain,
% 2.09/0.91 ((((multiply @ sk_c3 @ sk_c8) = (sk_c7))
% 2.09/0.91 | ((multiply @ sk_c8 @ sk_c2) = (sk_c7)))),
% 2.09/0.91 inference('cnf', [status(esa)], [zf_stmt_8])).
% 2.09/0.91 thf(zip_derived_cl1167, plain,
% 2.09/0.91 ((((multiply @ sk_c8 @ identity) = (sk_c7))
% 2.09/0.91 | ((multiply @ sk_c3 @ sk_c8) = (sk_c7))
% 2.09/0.91 | ((multiply @ sk_c3 @ sk_c8) = (sk_c7)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl1147, zip_derived_cl21])).
% 2.09/0.91 thf(zip_derived_cl639, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl117, zip_derived_cl114])).
% 2.09/0.91 thf(zip_derived_cl1176, plain,
% 2.09/0.91 ((((sk_c8) = (sk_c7))
% 2.09/0.91 | ((multiply @ sk_c3 @ sk_c8) = (sk_c7))
% 2.09/0.91 | ((multiply @ sk_c3 @ sk_c8) = (sk_c7)))),
% 2.09/0.91 inference('demod', [status(thm)], [zip_derived_cl1167, zip_derived_cl639])).
% 2.09/0.91 thf(zip_derived_cl1177, plain,
% 2.09/0.91 ((((multiply @ sk_c3 @ sk_c8) = (sk_c7)) | ((sk_c8) = (sk_c7)))),
% 2.09/0.91 inference('simplify', [status(thm)], [zip_derived_cl1176])).
% 2.09/0.91 thf(zip_derived_cl1397, plain,
% 2.09/0.91 ((((multiply @ (inverse @ sk_c8) @ sk_c8) = (sk_c7))
% 2.09/0.91 | ((sk_c8) = (sk_c7))
% 2.09/0.91 | ((sk_c8) = (sk_c7)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl677, zip_derived_cl1177])).
% 2.09/0.91 thf(zip_derived_cl1, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.91 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.91 thf(zip_derived_cl1401, plain,
% 2.09/0.91 ((((identity) = (sk_c7)) | ((sk_c8) = (sk_c7)) | ((sk_c8) = (sk_c7)))),
% 2.09/0.91 inference('demod', [status(thm)], [zip_derived_cl1397, zip_derived_cl1])).
% 2.09/0.91 thf(zip_derived_cl1402, plain,
% 2.09/0.91 ((((sk_c8) = (sk_c7)) | ((identity) = (sk_c7)))),
% 2.09/0.91 inference('simplify', [status(thm)], [zip_derived_cl1401])).
% 2.09/0.91 thf(prove_this_14, conjecture,
% 2.09/0.91 (~( ( ( inverse @ sk_c3 ) = ( sk_c8 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c8 ) ) ))).
% 2.09/0.91 thf(zf_stmt_9, negated_conjecture,
% 2.09/0.91 (( ( inverse @ sk_c3 ) = ( sk_c8 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c8 ) )),
% 2.09/0.91 inference('cnf.neg', [status(esa)], [prove_this_14])).
% 2.09/0.91 thf(zip_derived_cl16, plain,
% 2.09/0.91 ((((inverse @ sk_c3) = (sk_c8)) | ((multiply @ sk_c6 @ sk_c7) = (sk_c8)))),
% 2.09/0.91 inference('cnf', [status(esa)], [zf_stmt_9])).
% 2.09/0.91 thf(zip_derived_cl1, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.91 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.91 thf(zip_derived_cl50, plain,
% 2.09/0.91 ((((multiply @ sk_c8 @ sk_c3) = (identity))
% 2.09/0.91 | ((multiply @ sk_c6 @ sk_c7) = (sk_c8)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl16, zip_derived_cl1])).
% 2.09/0.91 thf(zip_derived_cl97, plain,
% 2.09/0.91 (![X0 : $i, X1 : $i]:
% 2.09/0.91 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.09/0.91 inference('demod', [status(thm)], [zip_derived_cl60, zip_derived_cl0])).
% 2.09/0.91 thf(zip_derived_cl121, plain,
% 2.09/0.91 ((((sk_c3) = (multiply @ (inverse @ sk_c8) @ identity))
% 2.09/0.91 | ((multiply @ sk_c6 @ sk_c7) = (sk_c8)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl97])).
% 2.09/0.91 thf(prove_this_13, conjecture,
% 2.09/0.91 (~( ( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c8 ) ) ))).
% 2.09/0.91 thf(zf_stmt_10, negated_conjecture,
% 2.09/0.91 (( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c8 ) )),
% 2.09/0.91 inference('cnf.neg', [status(esa)], [prove_this_13])).
% 2.09/0.91 thf(zip_derived_cl15, plain,
% 2.09/0.91 ((((multiply @ sk_c3 @ sk_c8) = (sk_c7))
% 2.09/0.91 | ((multiply @ sk_c6 @ sk_c7) = (sk_c8)))),
% 2.09/0.91 inference('cnf', [status(esa)], [zf_stmt_10])).
% 2.09/0.91 thf(zip_derived_cl597, plain,
% 2.09/0.91 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c8)
% 2.09/0.91 = (sk_c7))
% 2.09/0.91 | ((multiply @ sk_c6 @ sk_c7) = (sk_c8))
% 2.09/0.91 | ((multiply @ sk_c6 @ sk_c7) = (sk_c8)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl15])).
% 2.09/0.91 thf(zip_derived_cl2, plain,
% 2.09/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.09/0.91 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 2.09/0.91 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 2.09/0.91 inference('cnf', [status(esa)], [associativity])).
% 2.09/0.91 thf(zip_derived_cl0, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 2.09/0.91 inference('cnf', [status(esa)], [left_identity])).
% 2.09/0.91 thf(zip_derived_cl1, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.91 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.91 thf(zip_derived_cl606, plain,
% 2.09/0.91 ((((identity) = (sk_c7))
% 2.09/0.91 | ((multiply @ sk_c6 @ sk_c7) = (sk_c8))
% 2.09/0.91 | ((multiply @ sk_c6 @ sk_c7) = (sk_c8)))),
% 2.09/0.91 inference('demod', [status(thm)],
% 2.09/0.91 [zip_derived_cl597, zip_derived_cl2, zip_derived_cl0,
% 2.09/0.91 zip_derived_cl1])).
% 2.09/0.91 thf(zip_derived_cl607, plain,
% 2.09/0.91 ((((multiply @ sk_c6 @ sk_c7) = (sk_c8)) | ((identity) = (sk_c7)))),
% 2.09/0.91 inference('simplify', [status(thm)], [zip_derived_cl606])).
% 2.09/0.91 thf(zip_derived_cl1414, plain,
% 2.09/0.91 ((((multiply @ sk_c6 @ sk_c8) = (sk_c8))
% 2.09/0.91 | ((identity) = (sk_c7))
% 2.09/0.91 | ((identity) = (sk_c7)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl1402, zip_derived_cl607])).
% 2.09/0.91 thf(zip_derived_cl1422, plain,
% 2.09/0.91 ((((identity) = (sk_c7)) | ((multiply @ sk_c6 @ sk_c8) = (sk_c8)))),
% 2.09/0.91 inference('simplify', [status(thm)], [zip_derived_cl1414])).
% 2.09/0.91 thf(zip_derived_cl1501, plain,
% 2.09/0.91 ((((multiply @ (inverse @ sk_c8) @ sk_c8) = (sk_c8))
% 2.09/0.91 | ((identity) = (sk_c7))
% 2.09/0.91 | ((identity) = (sk_c7)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl184, zip_derived_cl1422])).
% 2.09/0.91 thf(zip_derived_cl1, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.91 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.91 thf(zip_derived_cl1509, plain,
% 2.09/0.91 ((((identity) = (sk_c8))
% 2.09/0.91 | ((identity) = (sk_c7))
% 2.09/0.91 | ((identity) = (sk_c7)))),
% 2.09/0.91 inference('demod', [status(thm)], [zip_derived_cl1501, zip_derived_cl1])).
% 2.09/0.91 thf(zip_derived_cl1510, plain,
% 2.09/0.91 ((((identity) = (sk_c7)) | ((identity) = (sk_c8)))),
% 2.09/0.91 inference('simplify', [status(thm)], [zip_derived_cl1509])).
% 2.09/0.91 thf(zip_derived_cl1402, plain,
% 2.09/0.91 ((((sk_c8) = (sk_c7)) | ((identity) = (sk_c7)))),
% 2.09/0.91 inference('simplify', [status(thm)], [zip_derived_cl1401])).
% 2.09/0.91 thf(zip_derived_cl1419, plain,
% 2.09/0.91 ((((sk_c8) != (identity)) | ((identity) = (sk_c7)))),
% 2.09/0.91 inference('eq_fact', [status(thm)], [zip_derived_cl1402])).
% 2.09/0.91 thf(zip_derived_cl1518, plain, (((identity) = (sk_c7))),
% 2.09/0.91 inference('clc', [status(thm)], [zip_derived_cl1510, zip_derived_cl1419])).
% 2.09/0.91 thf(zip_derived_cl639, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl117, zip_derived_cl114])).
% 2.09/0.91 thf(zip_derived_cl1518, plain, (((identity) = (sk_c7))),
% 2.09/0.91 inference('clc', [status(thm)], [zip_derived_cl1510, zip_derived_cl1419])).
% 2.09/0.91 thf(zip_derived_cl639, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl117, zip_derived_cl114])).
% 2.09/0.91 thf(zip_derived_cl1518, plain, (((identity) = (sk_c7))),
% 2.09/0.91 inference('clc', [status(thm)], [zip_derived_cl1510, zip_derived_cl1419])).
% 2.09/0.91 thf(zip_derived_cl1518, plain, (((identity) = (sk_c7))),
% 2.09/0.91 inference('clc', [status(thm)], [zip_derived_cl1510, zip_derived_cl1419])).
% 2.09/0.91 thf(zip_derived_cl639, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl117, zip_derived_cl114])).
% 2.09/0.91 thf(zip_derived_cl1518, plain, (((identity) = (sk_c7))),
% 2.09/0.91 inference('clc', [status(thm)], [zip_derived_cl1510, zip_derived_cl1419])).
% 2.09/0.91 thf(zip_derived_cl639, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl117, zip_derived_cl114])).
% 2.09/0.91 thf(zip_derived_cl1518, plain, (((identity) = (sk_c7))),
% 2.09/0.91 inference('clc', [status(thm)], [zip_derived_cl1510, zip_derived_cl1419])).
% 2.09/0.91 thf(zip_derived_cl1518, plain, (((identity) = (sk_c7))),
% 2.09/0.91 inference('clc', [status(thm)], [zip_derived_cl1510, zip_derived_cl1419])).
% 2.09/0.91 thf(zip_derived_cl1518, plain, (((identity) = (sk_c7))),
% 2.09/0.91 inference('clc', [status(thm)], [zip_derived_cl1510, zip_derived_cl1419])).
% 2.09/0.91 thf(zip_derived_cl1518, plain, (((identity) = (sk_c7))),
% 2.09/0.91 inference('clc', [status(thm)], [zip_derived_cl1510, zip_derived_cl1419])).
% 2.09/0.91 thf(zip_derived_cl0, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 2.09/0.91 inference('cnf', [status(esa)], [left_identity])).
% 2.09/0.91 thf(zip_derived_cl639, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl117, zip_derived_cl114])).
% 2.09/0.91 thf(zip_derived_cl1518, plain, (((identity) = (sk_c7))),
% 2.09/0.91 inference('clc', [status(thm)], [zip_derived_cl1510, zip_derived_cl1419])).
% 2.09/0.91 thf(zip_derived_cl639, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl117, zip_derived_cl114])).
% 2.09/0.91 thf(zip_derived_cl1556, plain,
% 2.09/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 2.09/0.91 (((multiply @ X0 @ sk_c8) != (sk_c8))
% 2.09/0.91 | ((inverse @ X0) != (sk_c8))
% 2.09/0.91 | ((inverse @ X1) != (identity))
% 2.09/0.91 | ((X1) != (sk_c8))
% 2.09/0.91 | ((inverse @ X2) != (sk_c8))
% 2.09/0.91 | ((multiply @ X2 @ sk_c8) != (identity))
% 2.09/0.91 | ((inverse @ X3) != (sk_c8))
% 2.09/0.91 | ((multiply @ X3 @ sk_c8) != (X4))
% 2.09/0.91 | ((multiply @ sk_c8 @ X4) != (identity))
% 2.09/0.91 | ((sk_c8) != (sk_c8))
% 2.09/0.91 | ((inverse @ sk_c8) != (sk_c6))
% 2.09/0.91 | ((sk_c8) != (sk_c6)))),
% 2.09/0.91 inference('demod', [status(thm)],
% 2.09/0.91 [zip_derived_cl56, zip_derived_cl1518, zip_derived_cl639,
% 2.09/0.91 zip_derived_cl1518, zip_derived_cl639, zip_derived_cl1518,
% 2.09/0.91 zip_derived_cl1518, zip_derived_cl639, zip_derived_cl1518,
% 2.09/0.91 zip_derived_cl639, zip_derived_cl1518, zip_derived_cl1518,
% 2.09/0.91 zip_derived_cl1518, zip_derived_cl1518, zip_derived_cl0,
% 2.09/0.91 zip_derived_cl639, zip_derived_cl1518, zip_derived_cl639])).
% 2.09/0.91 thf(zip_derived_cl1557, plain,
% 2.09/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 2.09/0.91 (((sk_c8) != (sk_c6))
% 2.09/0.91 | ((inverse @ sk_c8) != (sk_c6))
% 2.09/0.91 | ((multiply @ sk_c8 @ X4) != (identity))
% 2.09/0.91 | ((multiply @ X3 @ sk_c8) != (X4))
% 2.09/0.91 | ((inverse @ X3) != (sk_c8))
% 2.09/0.91 | ((multiply @ X2 @ sk_c8) != (identity))
% 2.09/0.91 | ((inverse @ X2) != (sk_c8))
% 2.09/0.91 | ((X1) != (sk_c8))
% 2.09/0.91 | ((inverse @ X1) != (identity))
% 2.09/0.91 | ((inverse @ X0) != (sk_c8))
% 2.09/0.91 | ((multiply @ X0 @ sk_c8) != (sk_c8)))),
% 2.09/0.91 inference('simplify', [status(thm)], [zip_derived_cl1556])).
% 2.09/0.91 thf(prove_this_33, conjecture,
% 2.09/0.91 (~( ( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c6 ) ) |
% 2.09/0.91 ( ( inverse @ sk_c1 ) = ( sk_c8 ) ) ))).
% 2.09/0.91 thf(zf_stmt_11, negated_conjecture,
% 2.09/0.91 (( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c6 ) ) |
% 2.09/0.91 ( ( inverse @ sk_c1 ) = ( sk_c8 ) )),
% 2.09/0.91 inference('cnf.neg', [status(esa)], [prove_this_33])).
% 2.09/0.91 thf(zip_derived_cl35, plain,
% 2.09/0.91 ((((multiply @ sk_c4 @ sk_c7) = (sk_c6)) | ((inverse @ sk_c1) = (sk_c8)))),
% 2.09/0.91 inference('cnf', [status(esa)], [zf_stmt_11])).
% 2.09/0.91 thf(zip_derived_cl1, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.91 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.91 thf(zip_derived_cl53, plain,
% 2.09/0.91 ((((multiply @ sk_c8 @ sk_c1) = (identity))
% 2.09/0.91 | ((multiply @ sk_c4 @ sk_c7) = (sk_c6)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl1])).
% 2.09/0.91 thf(zip_derived_cl97, plain,
% 2.09/0.91 (![X0 : $i, X1 : $i]:
% 2.09/0.91 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.09/0.91 inference('demod', [status(thm)], [zip_derived_cl60, zip_derived_cl0])).
% 2.09/0.91 thf(zip_derived_cl131, plain,
% 2.09/0.91 ((((sk_c1) = (multiply @ (inverse @ sk_c8) @ identity))
% 2.09/0.91 | ((multiply @ sk_c4 @ sk_c7) = (sk_c6)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl53, zip_derived_cl97])).
% 2.09/0.91 thf(prove_this_27, conjecture,
% 2.09/0.91 (~( ( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c6 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c2 ) ) ))).
% 2.09/0.91 thf(zf_stmt_12, negated_conjecture,
% 2.09/0.91 (( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c6 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c2 ) )),
% 2.09/0.91 inference('cnf.neg', [status(esa)], [prove_this_27])).
% 2.09/0.91 thf(zip_derived_cl29, plain,
% 2.09/0.91 ((((multiply @ sk_c4 @ sk_c7) = (sk_c6))
% 2.09/0.91 | ((multiply @ sk_c1 @ sk_c8) = (sk_c2)))),
% 2.09/0.91 inference('cnf', [status(esa)], [zf_stmt_12])).
% 2.09/0.91 thf(zip_derived_cl462, plain,
% 2.09/0.91 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c8)
% 2.09/0.91 = (sk_c2))
% 2.09/0.91 | ((multiply @ sk_c4 @ sk_c7) = (sk_c6))
% 2.09/0.91 | ((multiply @ sk_c4 @ sk_c7) = (sk_c6)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl131, zip_derived_cl29])).
% 2.09/0.91 thf(zip_derived_cl2, plain,
% 2.09/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.09/0.91 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 2.09/0.91 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 2.09/0.91 inference('cnf', [status(esa)], [associativity])).
% 2.09/0.91 thf(zip_derived_cl0, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 2.09/0.91 inference('cnf', [status(esa)], [left_identity])).
% 2.09/0.91 thf(zip_derived_cl1, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.91 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.91 thf(zip_derived_cl480, plain,
% 2.09/0.91 ((((identity) = (sk_c2))
% 2.09/0.91 | ((multiply @ sk_c4 @ sk_c7) = (sk_c6))
% 2.09/0.91 | ((multiply @ sk_c4 @ sk_c7) = (sk_c6)))),
% 2.09/0.91 inference('demod', [status(thm)],
% 2.09/0.91 [zip_derived_cl462, zip_derived_cl2, zip_derived_cl0,
% 2.09/0.91 zip_derived_cl1])).
% 2.09/0.91 thf(zip_derived_cl481, plain,
% 2.09/0.91 ((((multiply @ sk_c4 @ sk_c7) = (sk_c6)) | ((identity) = (sk_c2)))),
% 2.09/0.91 inference('simplify', [status(thm)], [zip_derived_cl480])).
% 2.09/0.91 thf(zip_derived_cl1518, plain, (((identity) = (sk_c7))),
% 2.09/0.91 inference('clc', [status(thm)], [zip_derived_cl1510, zip_derived_cl1419])).
% 2.09/0.91 thf(zip_derived_cl639, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl117, zip_derived_cl114])).
% 2.09/0.91 thf(zip_derived_cl1566, plain,
% 2.09/0.91 ((((sk_c4) = (sk_c6)) | ((identity) = (sk_c2)))),
% 2.09/0.91 inference('demod', [status(thm)],
% 2.09/0.91 [zip_derived_cl481, zip_derived_cl1518, zip_derived_cl639])).
% 2.09/0.91 thf(prove_this_21, conjecture,
% 2.09/0.91 (~( ( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c6 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c8 @ sk_c2 ) = ( sk_c7 ) ) ))).
% 2.09/0.91 thf(zf_stmt_13, negated_conjecture,
% 2.09/0.91 (( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c6 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c8 @ sk_c2 ) = ( sk_c7 ) )),
% 2.09/0.91 inference('cnf.neg', [status(esa)], [prove_this_21])).
% 2.09/0.91 thf(zip_derived_cl23, plain,
% 2.09/0.91 ((((multiply @ sk_c4 @ sk_c7) = (sk_c6))
% 2.09/0.91 | ((multiply @ sk_c8 @ sk_c2) = (sk_c7)))),
% 2.09/0.91 inference('cnf', [status(esa)], [zf_stmt_13])).
% 2.09/0.91 thf(zip_derived_cl1518, plain, (((identity) = (sk_c7))),
% 2.09/0.91 inference('clc', [status(thm)], [zip_derived_cl1510, zip_derived_cl1419])).
% 2.09/0.91 thf(zip_derived_cl639, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl117, zip_derived_cl114])).
% 2.09/0.91 thf(zip_derived_cl1518, plain, (((identity) = (sk_c7))),
% 2.09/0.91 inference('clc', [status(thm)], [zip_derived_cl1510, zip_derived_cl1419])).
% 2.09/0.91 thf(zip_derived_cl1536, plain,
% 2.09/0.91 ((((sk_c4) = (sk_c6)) | ((multiply @ sk_c8 @ sk_c2) = (identity)))),
% 2.09/0.91 inference('demod', [status(thm)],
% 2.09/0.91 [zip_derived_cl23, zip_derived_cl1518, zip_derived_cl639,
% 2.09/0.91 zip_derived_cl1518])).
% 2.09/0.91 thf(zip_derived_cl1770, plain,
% 2.09/0.91 ((((multiply @ sk_c8 @ identity) = (identity))
% 2.09/0.91 | ((sk_c4) = (sk_c6))
% 2.09/0.91 | ((sk_c4) = (sk_c6)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl1566, zip_derived_cl1536])).
% 2.09/0.91 thf(zip_derived_cl639, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl117, zip_derived_cl114])).
% 2.09/0.91 thf(zip_derived_cl1775, plain,
% 2.09/0.91 ((((sk_c8) = (identity)) | ((sk_c4) = (sk_c6)) | ((sk_c4) = (sk_c6)))),
% 2.09/0.91 inference('demod', [status(thm)], [zip_derived_cl1770, zip_derived_cl639])).
% 2.09/0.91 thf(zip_derived_cl1776, plain,
% 2.09/0.91 ((((sk_c4) = (sk_c6)) | ((sk_c8) = (identity)))),
% 2.09/0.91 inference('simplify', [status(thm)], [zip_derived_cl1775])).
% 2.09/0.91 thf(prove_this_34, conjecture,
% 2.09/0.91 (~( ( ( inverse @ sk_c4 ) = ( sk_c7 ) ) |
% 2.09/0.91 ( ( inverse @ sk_c1 ) = ( sk_c8 ) ) ))).
% 2.09/0.91 thf(zf_stmt_14, negated_conjecture,
% 2.09/0.91 (( ( inverse @ sk_c4 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c8 ) )),
% 2.09/0.91 inference('cnf.neg', [status(esa)], [prove_this_34])).
% 2.09/0.91 thf(zip_derived_cl36, plain,
% 2.09/0.91 ((((inverse @ sk_c4) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c8)))),
% 2.09/0.91 inference('cnf', [status(esa)], [zf_stmt_14])).
% 2.09/0.91 thf(zip_derived_cl1, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.91 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.91 thf(zip_derived_cl48, plain,
% 2.09/0.91 ((((multiply @ sk_c8 @ sk_c1) = (identity))
% 2.09/0.91 | ((inverse @ sk_c4) = (sk_c7)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl36, zip_derived_cl1])).
% 2.09/0.91 thf(zip_derived_cl97, plain,
% 2.09/0.91 (![X0 : $i, X1 : $i]:
% 2.09/0.91 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.09/0.91 inference('demod', [status(thm)], [zip_derived_cl60, zip_derived_cl0])).
% 2.09/0.91 thf(zip_derived_cl129, plain,
% 2.09/0.91 ((((sk_c1) = (multiply @ (inverse @ sk_c8) @ identity))
% 2.09/0.91 | ((inverse @ sk_c4) = (sk_c7)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl48, zip_derived_cl97])).
% 2.09/0.91 thf(prove_this_28, conjecture,
% 2.09/0.91 (~( ( ( inverse @ sk_c4 ) = ( sk_c7 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c2 ) ) ))).
% 2.09/0.91 thf(zf_stmt_15, negated_conjecture,
% 2.09/0.91 (( ( inverse @ sk_c4 ) = ( sk_c7 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c2 ) )),
% 2.09/0.91 inference('cnf.neg', [status(esa)], [prove_this_28])).
% 2.09/0.91 thf(zip_derived_cl30, plain,
% 2.09/0.91 ((((inverse @ sk_c4) = (sk_c7)) | ((multiply @ sk_c1 @ sk_c8) = (sk_c2)))),
% 2.09/0.91 inference('cnf', [status(esa)], [zf_stmt_15])).
% 2.09/0.91 thf(zip_derived_cl267, plain,
% 2.09/0.91 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c8)
% 2.09/0.91 = (sk_c2))
% 2.09/0.91 | ((inverse @ sk_c4) = (sk_c7))
% 2.09/0.91 | ((inverse @ sk_c4) = (sk_c7)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl129, zip_derived_cl30])).
% 2.09/0.91 thf(zip_derived_cl2, plain,
% 2.09/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.09/0.91 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 2.09/0.91 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 2.09/0.91 inference('cnf', [status(esa)], [associativity])).
% 2.09/0.91 thf(zip_derived_cl0, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 2.09/0.91 inference('cnf', [status(esa)], [left_identity])).
% 2.09/0.91 thf(zip_derived_cl1, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.91 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.91 thf(zip_derived_cl285, plain,
% 2.09/0.91 ((((identity) = (sk_c2))
% 2.09/0.91 | ((inverse @ sk_c4) = (sk_c7))
% 2.09/0.91 | ((inverse @ sk_c4) = (sk_c7)))),
% 2.09/0.91 inference('demod', [status(thm)],
% 2.09/0.91 [zip_derived_cl267, zip_derived_cl2, zip_derived_cl0,
% 2.09/0.91 zip_derived_cl1])).
% 2.09/0.91 thf(zip_derived_cl286, plain,
% 2.09/0.91 ((((inverse @ sk_c4) = (sk_c7)) | ((identity) = (sk_c2)))),
% 2.09/0.91 inference('simplify', [status(thm)], [zip_derived_cl285])).
% 2.09/0.91 thf(prove_this_22, conjecture,
% 2.09/0.91 (~( ( ( inverse @ sk_c4 ) = ( sk_c7 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c8 @ sk_c2 ) = ( sk_c7 ) ) ))).
% 2.09/0.91 thf(zf_stmt_16, negated_conjecture,
% 2.09/0.91 (( ( inverse @ sk_c4 ) = ( sk_c7 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c8 @ sk_c2 ) = ( sk_c7 ) )),
% 2.09/0.91 inference('cnf.neg', [status(esa)], [prove_this_22])).
% 2.09/0.91 thf(zip_derived_cl24, plain,
% 2.09/0.91 ((((inverse @ sk_c4) = (sk_c7)) | ((multiply @ sk_c8 @ sk_c2) = (sk_c7)))),
% 2.09/0.91 inference('cnf', [status(esa)], [zf_stmt_16])).
% 2.09/0.91 thf(zip_derived_cl294, plain,
% 2.09/0.91 ((((multiply @ sk_c8 @ identity) = (sk_c7))
% 2.09/0.91 | ((inverse @ sk_c4) = (sk_c7))
% 2.09/0.91 | ((inverse @ sk_c4) = (sk_c7)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl286, zip_derived_cl24])).
% 2.09/0.91 thf(zip_derived_cl300, plain,
% 2.09/0.91 ((((inverse @ sk_c4) = (sk_c7))
% 2.09/0.91 | ((multiply @ sk_c8 @ identity) = (sk_c7)))),
% 2.09/0.91 inference('simplify', [status(thm)], [zip_derived_cl294])).
% 2.09/0.91 thf(zip_derived_cl117, plain,
% 2.09/0.91 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl97])).
% 2.09/0.91 thf(zip_derived_cl346, plain,
% 2.09/0.91 ((((sk_c4) = (multiply @ (inverse @ sk_c7) @ identity))
% 2.09/0.91 | ((multiply @ sk_c8 @ identity) = (sk_c7)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl300, zip_derived_cl117])).
% 2.09/0.91 thf(zip_derived_cl639, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl117, zip_derived_cl114])).
% 2.09/0.91 thf(zip_derived_cl639, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl117, zip_derived_cl114])).
% 2.09/0.91 thf(zip_derived_cl674, plain,
% 2.09/0.91 ((((sk_c4) = (inverse @ sk_c7)) | ((sk_c8) = (sk_c7)))),
% 2.09/0.91 inference('demod', [status(thm)],
% 2.09/0.91 [zip_derived_cl346, zip_derived_cl639, zip_derived_cl639])).
% 2.09/0.91 thf(zip_derived_cl1518, plain, (((identity) = (sk_c7))),
% 2.09/0.91 inference('clc', [status(thm)], [zip_derived_cl1510, zip_derived_cl1419])).
% 2.09/0.91 thf(zip_derived_cl0, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 2.09/0.91 inference('cnf', [status(esa)], [left_identity])).
% 2.09/0.91 thf(zip_derived_cl97, plain,
% 2.09/0.91 (![X0 : $i, X1 : $i]:
% 2.09/0.91 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.09/0.91 inference('demod', [status(thm)], [zip_derived_cl60, zip_derived_cl0])).
% 2.09/0.91 thf(zip_derived_cl116, plain,
% 2.09/0.91 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl97])).
% 2.09/0.91 thf(zip_derived_cl97, plain,
% 2.09/0.91 (![X0 : $i, X1 : $i]:
% 2.09/0.91 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.09/0.91 inference('demod', [status(thm)], [zip_derived_cl60, zip_derived_cl0])).
% 2.09/0.91 thf(zip_derived_cl171, plain,
% 2.09/0.91 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ identity)) @ X0))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl116, zip_derived_cl97])).
% 2.09/0.91 thf(zip_derived_cl1, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.91 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.91 thf(zip_derived_cl626, plain, (((inverse @ identity) = (identity))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl171, zip_derived_cl1])).
% 2.09/0.91 thf(zip_derived_cl1518, plain, (((identity) = (sk_c7))),
% 2.09/0.91 inference('clc', [status(thm)], [zip_derived_cl1510, zip_derived_cl1419])).
% 2.09/0.91 thf(zip_derived_cl1577, plain,
% 2.09/0.91 ((((sk_c4) = (identity)) | ((sk_c8) = (identity)))),
% 2.09/0.91 inference('demod', [status(thm)],
% 2.09/0.91 [zip_derived_cl674, zip_derived_cl1518, zip_derived_cl626,
% 2.09/0.91 zip_derived_cl1518])).
% 2.09/0.91 thf(zip_derived_cl1784, plain,
% 2.09/0.91 ((((sk_c6) = (identity))
% 2.09/0.91 | ((sk_c8) = (identity))
% 2.09/0.91 | ((sk_c8) = (identity)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl1776, zip_derived_cl1577])).
% 2.09/0.91 thf(zip_derived_cl1786, plain,
% 2.09/0.91 ((((sk_c8) = (identity)) | ((sk_c6) = (identity)))),
% 2.09/0.91 inference('simplify', [status(thm)], [zip_derived_cl1784])).
% 2.09/0.91 thf(prove_this_4, conjecture,
% 2.09/0.91 (~( ( ( inverse @ sk_c4 ) = ( sk_c7 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c6 ) ) ))).
% 2.09/0.91 thf(zf_stmt_17, negated_conjecture,
% 2.09/0.91 (( ( inverse @ sk_c4 ) = ( sk_c7 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c6 ) )),
% 2.09/0.91 inference('cnf.neg', [status(esa)], [prove_this_4])).
% 2.09/0.91 thf(zip_derived_cl6, plain,
% 2.09/0.91 ((((inverse @ sk_c4) = (sk_c7)) | ((multiply @ sk_c8 @ sk_c7) = (sk_c6)))),
% 2.09/0.91 inference('cnf', [status(esa)], [zf_stmt_17])).
% 2.09/0.91 thf(zip_derived_cl1, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.91 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.91 thf(zip_derived_cl45, plain,
% 2.09/0.91 ((((multiply @ sk_c7 @ sk_c4) = (identity))
% 2.09/0.91 | ((multiply @ sk_c8 @ sk_c7) = (sk_c6)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1])).
% 2.09/0.91 thf(zip_derived_cl97, plain,
% 2.09/0.91 (![X0 : $i, X1 : $i]:
% 2.09/0.91 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.09/0.91 inference('demod', [status(thm)], [zip_derived_cl60, zip_derived_cl0])).
% 2.09/0.91 thf(zip_derived_cl134, plain,
% 2.09/0.91 ((((sk_c4) = (multiply @ (inverse @ sk_c7) @ identity))
% 2.09/0.91 | ((multiply @ sk_c8 @ sk_c7) = (sk_c6)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl45, zip_derived_cl97])).
% 2.09/0.91 thf(prove_this_3, conjecture,
% 2.09/0.91 (~( ( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c6 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c6 ) ) ))).
% 2.09/0.91 thf(zf_stmt_18, negated_conjecture,
% 2.09/0.91 (( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c6 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c6 ) )),
% 2.09/0.91 inference('cnf.neg', [status(esa)], [prove_this_3])).
% 2.09/0.91 thf(zip_derived_cl5, plain,
% 2.09/0.91 ((((multiply @ sk_c4 @ sk_c7) = (sk_c6))
% 2.09/0.91 | ((multiply @ sk_c8 @ sk_c7) = (sk_c6)))),
% 2.09/0.91 inference('cnf', [status(esa)], [zf_stmt_18])).
% 2.09/0.91 thf(zip_derived_cl419, plain,
% 2.09/0.91 ((((multiply @ (multiply @ (inverse @ sk_c7) @ identity) @ sk_c7)
% 2.09/0.91 = (sk_c6))
% 2.09/0.91 | ((multiply @ sk_c8 @ sk_c7) = (sk_c6))
% 2.09/0.91 | ((multiply @ sk_c8 @ sk_c7) = (sk_c6)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl134, zip_derived_cl5])).
% 2.09/0.91 thf(zip_derived_cl2, plain,
% 2.09/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.09/0.91 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 2.09/0.91 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 2.09/0.91 inference('cnf', [status(esa)], [associativity])).
% 2.09/0.91 thf(zip_derived_cl0, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 2.09/0.91 inference('cnf', [status(esa)], [left_identity])).
% 2.09/0.91 thf(zip_derived_cl1, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.91 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.91 thf(zip_derived_cl429, plain,
% 2.09/0.91 ((((identity) = (sk_c6))
% 2.09/0.91 | ((multiply @ sk_c8 @ sk_c7) = (sk_c6))
% 2.09/0.91 | ((multiply @ sk_c8 @ sk_c7) = (sk_c6)))),
% 2.09/0.91 inference('demod', [status(thm)],
% 2.09/0.91 [zip_derived_cl419, zip_derived_cl2, zip_derived_cl0,
% 2.09/0.91 zip_derived_cl1])).
% 2.09/0.91 thf(zip_derived_cl430, plain,
% 2.09/0.91 ((((multiply @ sk_c8 @ sk_c7) = (sk_c6)) | ((identity) = (sk_c6)))),
% 2.09/0.91 inference('simplify', [status(thm)], [zip_derived_cl429])).
% 2.09/0.91 thf(zip_derived_cl441, plain,
% 2.09/0.91 ((((multiply @ sk_c8 @ sk_c7) != (identity)) | ((identity) = (sk_c6)))),
% 2.09/0.91 inference('eq_fact', [status(thm)], [zip_derived_cl430])).
% 2.09/0.91 thf(zip_derived_cl1518, plain, (((identity) = (sk_c7))),
% 2.09/0.91 inference('clc', [status(thm)], [zip_derived_cl1510, zip_derived_cl1419])).
% 2.09/0.91 thf(zip_derived_cl639, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl117, zip_derived_cl114])).
% 2.09/0.91 thf(zip_derived_cl1564, plain,
% 2.09/0.91 ((((sk_c8) != (identity)) | ((identity) = (sk_c6)))),
% 2.09/0.91 inference('demod', [status(thm)],
% 2.09/0.91 [zip_derived_cl441, zip_derived_cl1518, zip_derived_cl639])).
% 2.09/0.91 thf(zip_derived_cl1787, plain, (((sk_c6) = (identity))),
% 2.09/0.91 inference('clc', [status(thm)], [zip_derived_cl1786, zip_derived_cl1564])).
% 2.09/0.91 thf(zip_derived_cl1787, plain, (((sk_c6) = (identity))),
% 2.09/0.91 inference('clc', [status(thm)], [zip_derived_cl1786, zip_derived_cl1564])).
% 2.09/0.91 thf(zip_derived_cl1816, plain,
% 2.09/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 2.09/0.91 (((sk_c8) != (identity))
% 2.09/0.91 | ((inverse @ sk_c8) != (identity))
% 2.09/0.91 | ((multiply @ sk_c8 @ X4) != (identity))
% 2.09/0.91 | ((multiply @ X3 @ sk_c8) != (X4))
% 2.09/0.91 | ((inverse @ X3) != (sk_c8))
% 2.09/0.91 | ((multiply @ X2 @ sk_c8) != (identity))
% 2.09/0.91 | ((inverse @ X2) != (sk_c8))
% 2.09/0.91 | ((X1) != (sk_c8))
% 2.09/0.91 | ((inverse @ X1) != (identity))
% 2.09/0.91 | ((inverse @ X0) != (sk_c8))
% 2.09/0.91 | ((multiply @ X0 @ sk_c8) != (sk_c8)))),
% 2.09/0.91 inference('demod', [status(thm)],
% 2.09/0.91 [zip_derived_cl1557, zip_derived_cl1787, zip_derived_cl1787])).
% 2.09/0.91 thf(zip_derived_cl1817, plain,
% 2.09/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 2.09/0.91 (((sk_c8) != (identity))
% 2.09/0.91 | ((inverse @ identity) != (identity))
% 2.09/0.91 | ((multiply @ identity @ X4) != (identity))
% 2.09/0.91 | ((multiply @ X3 @ identity) != (X4))
% 2.09/0.91 | ((inverse @ X3) != (identity))
% 2.09/0.91 | ((multiply @ X2 @ identity) != (identity))
% 2.09/0.91 | ((inverse @ X2) != (identity))
% 2.09/0.91 | ((X1) != (identity))
% 2.09/0.91 | ((inverse @ X1) != (identity))
% 2.09/0.91 | ((inverse @ X0) != (identity))
% 2.09/0.91 | ((multiply @ X0 @ identity) != (identity)))),
% 2.09/0.91 inference('local_rewriting', [status(thm)], [zip_derived_cl1816])).
% 2.09/0.91 thf(zip_derived_cl626, plain, (((inverse @ identity) = (identity))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl171, zip_derived_cl1])).
% 2.09/0.91 thf(zip_derived_cl0, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 2.09/0.91 inference('cnf', [status(esa)], [left_identity])).
% 2.09/0.91 thf(zip_derived_cl639, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl117, zip_derived_cl114])).
% 2.09/0.91 thf(zip_derived_cl639, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl117, zip_derived_cl114])).
% 2.09/0.91 thf(zip_derived_cl639, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl117, zip_derived_cl114])).
% 2.09/0.91 thf(zip_derived_cl1818, plain,
% 2.09/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 2.09/0.91 (((sk_c8) != (identity))
% 2.09/0.91 | ((identity) != (identity))
% 2.09/0.91 | ((X4) != (identity))
% 2.09/0.91 | ((X3) != (X4))
% 2.09/0.91 | ((inverse @ X3) != (identity))
% 2.09/0.91 | ((X2) != (identity))
% 2.09/0.91 | ((inverse @ X2) != (identity))
% 2.09/0.91 | ((X1) != (identity))
% 2.09/0.91 | ((inverse @ X1) != (identity))
% 2.09/0.91 | ((inverse @ X0) != (identity))
% 2.09/0.91 | ((X0) != (identity)))),
% 2.09/0.91 inference('demod', [status(thm)],
% 2.09/0.91 [zip_derived_cl1817, zip_derived_cl626, zip_derived_cl0,
% 2.09/0.91 zip_derived_cl639, zip_derived_cl639, zip_derived_cl639])).
% 2.09/0.91 thf(zip_derived_cl1819, plain,
% 2.09/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 2.09/0.91 (((X0) != (identity))
% 2.09/0.91 | ((inverse @ X0) != (identity))
% 2.09/0.91 | ((inverse @ X1) != (identity))
% 2.09/0.91 | ((X1) != (identity))
% 2.09/0.91 | ((inverse @ X2) != (identity))
% 2.09/0.91 | ((X2) != (identity))
% 2.09/0.91 | ((inverse @ X3) != (identity))
% 2.09/0.91 | ((X3) != (X4))
% 2.09/0.91 | ((X4) != (identity))
% 2.09/0.91 | ((sk_c8) != (identity)))),
% 2.09/0.91 inference('simplify', [status(thm)], [zip_derived_cl1818])).
% 2.09/0.91 thf(zip_derived_cl1828, plain,
% 2.09/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.09/0.91 (((sk_c8) != (identity))
% 2.09/0.91 | ((X0) != (identity))
% 2.09/0.91 | ((inverse @ X0) != (identity))
% 2.09/0.91 | ((X1) != (identity))
% 2.09/0.91 | ((inverse @ X1) != (identity))
% 2.09/0.91 | ((X2) != (identity))
% 2.09/0.91 | ((inverse @ X2) != (identity))
% 2.09/0.91 | ((inverse @ X3) != (identity))
% 2.09/0.91 | ((X3) != (identity)))),
% 2.09/0.91 inference('eq_res', [status(thm)], [zip_derived_cl1819])).
% 2.09/0.91 thf(prove_this_11, conjecture,
% 2.09/0.91 (~( ( ( inverse @ sk_c5 ) = ( sk_c6 ) ) |
% 2.09/0.91 ( ( inverse @ sk_c8 ) = ( sk_c6 ) ) ))).
% 2.09/0.91 thf(zf_stmt_19, negated_conjecture,
% 2.09/0.91 (( ( inverse @ sk_c5 ) = ( sk_c6 ) ) | ( ( inverse @ sk_c8 ) = ( sk_c6 ) )),
% 2.09/0.91 inference('cnf.neg', [status(esa)], [prove_this_11])).
% 2.09/0.91 thf(zip_derived_cl13, plain,
% 2.09/0.91 ((((inverse @ sk_c5) = (sk_c6)) | ((inverse @ sk_c8) = (sk_c6)))),
% 2.09/0.91 inference('cnf', [status(esa)], [zf_stmt_19])).
% 2.09/0.91 thf(zip_derived_cl1, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.91 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.91 thf(zip_derived_cl43, plain,
% 2.09/0.91 ((((multiply @ sk_c6 @ sk_c5) = (identity))
% 2.09/0.91 | ((inverse @ sk_c8) = (sk_c6)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl1])).
% 2.09/0.91 thf(zip_derived_cl1787, plain, (((sk_c6) = (identity))),
% 2.09/0.91 inference('clc', [status(thm)], [zip_derived_cl1786, zip_derived_cl1564])).
% 2.09/0.91 thf(zip_derived_cl0, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 2.09/0.91 inference('cnf', [status(esa)], [left_identity])).
% 2.09/0.91 thf(zip_derived_cl1787, plain, (((sk_c6) = (identity))),
% 2.09/0.91 inference('clc', [status(thm)], [zip_derived_cl1786, zip_derived_cl1564])).
% 2.09/0.91 thf(zip_derived_cl1796, plain,
% 2.09/0.91 ((((sk_c5) = (identity)) | ((inverse @ sk_c8) = (identity)))),
% 2.09/0.91 inference('demod', [status(thm)],
% 2.09/0.91 [zip_derived_cl43, zip_derived_cl1787, zip_derived_cl0,
% 2.09/0.91 zip_derived_cl1787])).
% 2.09/0.91 thf(prove_this_6, conjecture,
% 2.09/0.91 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c6 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c6 ) ) ))).
% 2.09/0.91 thf(zf_stmt_20, negated_conjecture,
% 2.09/0.91 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c6 ) ) |
% 2.09/0.91 ( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c6 ) )),
% 2.09/0.91 inference('cnf.neg', [status(esa)], [prove_this_6])).
% 2.09/0.91 thf(zip_derived_cl8, plain,
% 2.09/0.91 ((((multiply @ sk_c5 @ sk_c8) = (sk_c6))
% 2.09/0.91 | ((multiply @ sk_c8 @ sk_c7) = (sk_c6)))),
% 2.09/0.91 inference('cnf', [status(esa)], [zf_stmt_20])).
% 2.09/0.91 thf(zip_derived_cl1518, plain, (((identity) = (sk_c7))),
% 2.09/0.91 inference('clc', [status(thm)], [zip_derived_cl1510, zip_derived_cl1419])).
% 2.09/0.91 thf(zip_derived_cl639, plain,
% 2.09/0.91 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl117, zip_derived_cl114])).
% 2.09/0.91 thf(zip_derived_cl1524, plain,
% 2.09/0.91 ((((multiply @ sk_c5 @ sk_c8) = (sk_c6)) | ((sk_c8) = (sk_c6)))),
% 2.09/0.91 inference('demod', [status(thm)],
% 2.09/0.91 [zip_derived_cl8, zip_derived_cl1518, zip_derived_cl639])).
% 2.09/0.91 thf(zip_derived_cl1787, plain, (((sk_c6) = (identity))),
% 2.09/0.91 inference('clc', [status(thm)], [zip_derived_cl1786, zip_derived_cl1564])).
% 2.09/0.91 thf(zip_derived_cl1787, plain, (((sk_c6) = (identity))),
% 2.09/0.91 inference('clc', [status(thm)], [zip_derived_cl1786, zip_derived_cl1564])).
% 2.09/0.91 thf(zip_derived_cl1944, plain,
% 2.09/0.91 ((((multiply @ sk_c5 @ sk_c8) = (identity)) | ((sk_c8) = (identity)))),
% 2.09/0.91 inference('demod', [status(thm)],
% 2.09/0.91 [zip_derived_cl1524, zip_derived_cl1787, zip_derived_cl1787])).
% 2.09/0.91 thf(zip_derived_cl1947, plain,
% 2.09/0.91 ((((multiply @ identity @ sk_c8) = (identity))
% 2.09/0.91 | ((inverse @ sk_c8) = (identity))
% 2.09/0.91 | ((sk_c8) = (identity)))),
% 2.09/0.91 inference('sup+', [status(thm)], [zip_derived_cl1796, zip_derived_cl1944])).
% 2.09/0.92 thf(zip_derived_cl0, plain,
% 2.09/0.92 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 2.09/0.92 inference('cnf', [status(esa)], [left_identity])).
% 2.09/0.92 thf(zip_derived_cl1949, plain,
% 2.09/0.92 ((((sk_c8) = (identity))
% 2.09/0.92 | ((inverse @ sk_c8) = (identity))
% 2.09/0.92 | ((sk_c8) = (identity)))),
% 2.09/0.92 inference('demod', [status(thm)], [zip_derived_cl1947, zip_derived_cl0])).
% 2.09/0.92 thf(zip_derived_cl1950, plain,
% 2.09/0.92 ((((inverse @ sk_c8) = (identity)) | ((sk_c8) = (identity)))),
% 2.09/0.92 inference('simplify', [status(thm)], [zip_derived_cl1949])).
% 2.09/0.92 thf(zip_derived_cl683, plain,
% 2.09/0.92 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 2.09/0.92 inference('sup+', [status(thm)], [zip_derived_cl639, zip_derived_cl117])).
% 2.09/0.92 thf(zip_derived_cl2001, plain,
% 2.09/0.92 ((((sk_c8) = (inverse @ identity)) | ((sk_c8) = (identity)))),
% 2.09/0.92 inference('sup+', [status(thm)], [zip_derived_cl1950, zip_derived_cl683])).
% 2.09/0.92 thf(zip_derived_cl626, plain, (((inverse @ identity) = (identity))),
% 2.09/0.92 inference('sup+', [status(thm)], [zip_derived_cl171, zip_derived_cl1])).
% 2.09/0.92 thf(zip_derived_cl2004, plain,
% 2.09/0.92 ((((sk_c8) = (identity)) | ((sk_c8) = (identity)))),
% 2.09/0.92 inference('demod', [status(thm)], [zip_derived_cl2001, zip_derived_cl626])).
% 2.09/0.92 thf(zip_derived_cl2005, plain, (((sk_c8) = (identity))),
% 2.09/0.92 inference('simplify', [status(thm)], [zip_derived_cl2004])).
% 2.09/0.92 thf(zip_derived_cl2025, plain,
% 2.09/0.92 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.09/0.92 (((identity) != (identity))
% 2.09/0.92 | ((X0) != (identity))
% 2.09/0.92 | ((inverse @ X0) != (identity))
% 2.09/0.92 | ((X1) != (identity))
% 2.09/0.92 | ((inverse @ X1) != (identity))
% 2.09/0.92 | ((X2) != (identity))
% 2.09/0.92 | ((inverse @ X2) != (identity))
% 2.09/0.92 | ((inverse @ X3) != (identity))
% 2.09/0.92 | ((X3) != (identity)))),
% 2.09/0.92 inference('demod', [status(thm)],
% 2.09/0.92 [zip_derived_cl1828, zip_derived_cl2005])).
% 2.09/0.92 thf(zip_derived_cl2026, plain,
% 2.09/0.92 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.09/0.92 (((X3) != (identity))
% 2.09/0.92 | ((inverse @ X3) != (identity))
% 2.09/0.92 | ((inverse @ X2) != (identity))
% 2.09/0.92 | ((X2) != (identity))
% 2.09/0.92 | ((inverse @ X1) != (identity))
% 2.09/0.92 | ((X1) != (identity))
% 2.09/0.92 | ((inverse @ X0) != (identity))
% 2.09/0.92 | ((X0) != (identity)))),
% 2.09/0.92 inference('simplify', [status(thm)], [zip_derived_cl2025])).
% 2.09/0.92 thf(zip_derived_cl2049, plain,
% 2.09/0.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.09/0.92 (((X0) != (identity))
% 2.09/0.92 | ((inverse @ X0) != (identity))
% 2.09/0.92 | ((X1) != (identity))
% 2.09/0.92 | ((inverse @ X1) != (identity))
% 2.09/0.92 | ((X2) != (identity))
% 2.09/0.92 | ((inverse @ X2) != (identity))
% 2.09/0.92 | ((inverse @ identity) != (identity)))),
% 2.09/0.92 inference('eq_res', [status(thm)], [zip_derived_cl2026])).
% 2.09/0.92 thf(zip_derived_cl626, plain, (((inverse @ identity) = (identity))),
% 2.09/0.92 inference('sup+', [status(thm)], [zip_derived_cl171, zip_derived_cl1])).
% 2.09/0.92 thf(zip_derived_cl2050, plain,
% 2.09/0.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.09/0.92 (((X0) != (identity))
% 2.09/0.92 | ((inverse @ X0) != (identity))
% 2.09/0.92 | ((X1) != (identity))
% 2.09/0.92 | ((inverse @ X1) != (identity))
% 2.09/0.92 | ((X2) != (identity))
% 2.09/0.92 | ((inverse @ X2) != (identity))
% 2.09/0.92 | ((identity) != (identity)))),
% 2.09/0.92 inference('demod', [status(thm)], [zip_derived_cl2049, zip_derived_cl626])).
% 2.09/0.92 thf(zip_derived_cl2051, plain,
% 2.09/0.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.09/0.92 (((inverse @ X2) != (identity))
% 2.09/0.92 | ((X2) != (identity))
% 2.09/0.92 | ((inverse @ X1) != (identity))
% 2.09/0.92 | ((X1) != (identity))
% 2.09/0.92 | ((inverse @ X0) != (identity))
% 2.09/0.92 | ((X0) != (identity)))),
% 2.09/0.92 inference('simplify', [status(thm)], [zip_derived_cl2050])).
% 2.09/0.92 thf(zip_derived_cl2052, plain,
% 2.09/0.92 (![X0 : $i, X1 : $i]:
% 2.09/0.92 (((X0) != (identity))
% 2.09/0.92 | ((inverse @ X0) != (identity))
% 2.09/0.92 | ((X1) != (identity))
% 2.09/0.92 | ((inverse @ X1) != (identity))
% 2.09/0.92 | ((inverse @ identity) != (identity)))),
% 2.09/0.92 inference('eq_res', [status(thm)], [zip_derived_cl2051])).
% 2.09/0.92 thf(zip_derived_cl626, plain, (((inverse @ identity) = (identity))),
% 2.09/0.92 inference('sup+', [status(thm)], [zip_derived_cl171, zip_derived_cl1])).
% 2.09/0.92 thf(zip_derived_cl2053, plain,
% 2.09/0.92 (![X0 : $i, X1 : $i]:
% 2.09/0.92 (((X0) != (identity))
% 2.09/0.92 | ((inverse @ X0) != (identity))
% 2.09/0.92 | ((X1) != (identity))
% 2.09/0.92 | ((inverse @ X1) != (identity))
% 2.09/0.92 | ((identity) != (identity)))),
% 2.09/0.92 inference('demod', [status(thm)], [zip_derived_cl2052, zip_derived_cl626])).
% 2.09/0.92 thf(zip_derived_cl2054, plain,
% 2.09/0.92 (![X0 : $i, X1 : $i]:
% 2.09/0.92 (((inverse @ X1) != (identity))
% 2.09/0.92 | ((X1) != (identity))
% 2.09/0.92 | ((inverse @ X0) != (identity))
% 2.09/0.92 | ((X0) != (identity)))),
% 2.09/0.92 inference('simplify', [status(thm)], [zip_derived_cl2053])).
% 2.09/0.92 thf(zip_derived_cl2055, plain,
% 2.09/0.92 (![X0 : $i]:
% 2.09/0.92 (((X0) != (identity))
% 2.09/0.92 | ((inverse @ X0) != (identity))
% 2.09/0.92 | ((inverse @ identity) != (identity)))),
% 2.09/0.92 inference('eq_res', [status(thm)], [zip_derived_cl2054])).
% 2.09/0.92 thf(zip_derived_cl626, plain, (((inverse @ identity) = (identity))),
% 2.09/0.92 inference('sup+', [status(thm)], [zip_derived_cl171, zip_derived_cl1])).
% 2.09/0.92 thf(zip_derived_cl2056, plain,
% 2.09/0.92 (![X0 : $i]:
% 2.09/0.92 (((X0) != (identity))
% 2.09/0.92 | ((inverse @ X0) != (identity))
% 2.09/0.92 | ((identity) != (identity)))),
% 2.09/0.92 inference('demod', [status(thm)], [zip_derived_cl2055, zip_derived_cl626])).
% 2.09/0.92 thf(zip_derived_cl2057, plain,
% 2.09/0.92 (![X0 : $i]: (((inverse @ X0) != (identity)) | ((X0) != (identity)))),
% 2.09/0.92 inference('simplify', [status(thm)], [zip_derived_cl2056])).
% 2.09/0.92 thf(zip_derived_cl2058, plain, (((inverse @ identity) != (identity))),
% 2.09/0.92 inference('eq_res', [status(thm)], [zip_derived_cl2057])).
% 2.09/0.92 thf(zip_derived_cl626, plain, (((inverse @ identity) = (identity))),
% 2.09/0.92 inference('sup+', [status(thm)], [zip_derived_cl171, zip_derived_cl1])).
% 2.09/0.92 thf(zip_derived_cl2059, plain, (((identity) != (identity))),
% 2.09/0.92 inference('demod', [status(thm)], [zip_derived_cl2058, zip_derived_cl626])).
% 2.09/0.92 thf(zip_derived_cl2060, plain, ($false),
% 2.09/0.92 inference('simplify', [status(thm)], [zip_derived_cl2059])).
% 2.09/0.92
% 2.09/0.92 % SZS output end Refutation
% 2.09/0.92
% 2.09/0.92
% 2.09/0.92 % Terminating...
% 2.75/1.05 % Runner terminated.
% 2.75/1.05 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------