TSTP Solution File: GRP302-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP302-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.bSafkPvO7t true
% Computer : n016.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 01:51:07 EDT 2023
% Result : Unsatisfiable 1.01s 0.98s
% Output : Refutation 1.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : GRP302-1 : TPTP v8.1.2. Released v2.5.0.
% 0.07/0.15 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.bSafkPvO7t true
% 0.14/0.36 % Computer : n016.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Aug 28 21:35:45 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Running portfolio for 300 s
% 0.14/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.37 % Running in FO mode
% 0.52/0.62 % Total configuration time : 435
% 0.52/0.62 % Estimated wc time : 1092
% 0.52/0.62 % Estimated cpu time (7 cpus) : 156.0
% 0.87/0.72 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.87/0.72 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.87/0.73 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.99/0.75 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.99/0.79 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.99/0.81 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.99/0.84 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 1.01/0.98 % Solved by fo/fo7.sh.
% 1.01/0.98 % done 337 iterations in 0.195s
% 1.01/0.98 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.01/0.98 % SZS output start Refutation
% 1.01/0.98 thf(sk_c4_type, type, sk_c4: $i).
% 1.01/0.98 thf(sk_c6_type, type, sk_c6: $i).
% 1.01/0.98 thf(sk_c5_type, type, sk_c5: $i).
% 1.01/0.98 thf(sk_c3_type, type, sk_c3: $i).
% 1.01/0.98 thf(identity_type, type, identity: $i).
% 1.01/0.98 thf(multiply_type, type, multiply: $i > $i > $i).
% 1.01/0.98 thf(sk_c7_type, type, sk_c7: $i).
% 1.01/0.98 thf(inverse_type, type, inverse: $i > $i).
% 1.01/0.98 thf(sk_c1_type, type, sk_c1: $i).
% 1.01/0.98 thf(sk_c2_type, type, sk_c2: $i).
% 1.01/0.98 thf(sk_c8_type, type, sk_c8: $i).
% 1.01/0.98 thf(prove_this_9, conjecture,
% 1.01/0.98 (~( ( ( inverse @ sk_c3 ) = ( sk_c8 ) ) |
% 1.01/0.98 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) ) ))).
% 1.01/0.98 thf(zf_stmt_0, negated_conjecture,
% 1.01/0.98 (( ( inverse @ sk_c3 ) = ( sk_c8 ) ) |
% 1.01/0.98 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) )),
% 1.01/0.98 inference('cnf.neg', [status(esa)], [prove_this_9])).
% 1.01/0.98 thf(zip_derived_cl11, plain,
% 1.01/0.98 ((((inverse @ sk_c3) = (sk_c8)) | ((multiply @ sk_c1 @ sk_c7) = (sk_c8)))),
% 1.01/0.98 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.01/0.98 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 1.01/0.98 thf(zip_derived_cl1, plain,
% 1.01/0.98 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.01/0.98 inference('cnf', [status(esa)], [left_inverse])).
% 1.01/0.98 thf(zip_derived_cl1, plain,
% 1.01/0.98 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.01/0.98 inference('cnf', [status(esa)], [left_inverse])).
% 1.01/0.98 thf(associativity, axiom,
% 1.01/0.98 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 1.01/0.98 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 1.01/0.98 thf(zip_derived_cl2, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.01/0.98 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.01/0.98 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.01/0.98 inference('cnf', [status(esa)], [associativity])).
% 1.01/0.98 thf(zip_derived_cl80, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i]:
% 1.01/0.98 ((multiply @ identity @ X0)
% 1.01/0.98 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 1.01/0.98 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 1.01/0.98 thf(zip_derived_cl0, plain,
% 1.01/0.98 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.01/0.98 inference('cnf', [status(esa)], [left_identity])).
% 1.01/0.98 thf(zip_derived_cl97, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i]:
% 1.01/0.98 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.01/0.98 inference('demod', [status(thm)], [zip_derived_cl80, zip_derived_cl0])).
% 1.01/0.98 thf(zip_derived_cl116, plain,
% 1.01/0.98 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl97])).
% 1.01/0.98 thf(zip_derived_cl351, plain,
% 1.01/0.98 ((((sk_c3) = (multiply @ (inverse @ sk_c8) @ identity))
% 1.01/0.98 | ((multiply @ sk_c1 @ sk_c7) = (sk_c8)))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl116])).
% 1.01/0.98 thf(prove_this_10, conjecture,
% 1.01/0.98 (~( ( ( multiply @ sk_c3 @ sk_c7 ) = ( sk_c8 ) ) |
% 1.01/0.98 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) ) ))).
% 1.01/0.98 thf(zf_stmt_1, negated_conjecture,
% 1.01/0.98 (( ( multiply @ sk_c3 @ sk_c7 ) = ( sk_c8 ) ) |
% 1.01/0.98 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) )),
% 1.01/0.98 inference('cnf.neg', [status(esa)], [prove_this_10])).
% 1.01/0.98 thf(zip_derived_cl12, plain,
% 1.01/0.98 ((((multiply @ sk_c3 @ sk_c7) = (sk_c8))
% 1.01/0.98 | ((multiply @ sk_c1 @ sk_c7) = (sk_c8)))),
% 1.01/0.98 inference('cnf', [status(esa)], [zf_stmt_1])).
% 1.01/0.98 thf(zip_derived_cl406, plain,
% 1.01/0.98 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c7)
% 1.01/0.98 = (sk_c8))
% 1.01/0.98 | ((multiply @ sk_c1 @ sk_c7) = (sk_c8))
% 1.01/0.98 | ((multiply @ sk_c1 @ sk_c7) = (sk_c8)))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl351, zip_derived_cl12])).
% 1.01/0.98 thf(zip_derived_cl2, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.01/0.98 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.01/0.98 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.01/0.98 inference('cnf', [status(esa)], [associativity])).
% 1.01/0.98 thf(zip_derived_cl0, plain,
% 1.01/0.98 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.01/0.98 inference('cnf', [status(esa)], [left_identity])).
% 1.01/0.98 thf(zip_derived_cl412, plain,
% 1.01/0.98 ((((multiply @ (inverse @ sk_c8) @ sk_c7) = (sk_c8))
% 1.01/0.98 | ((multiply @ sk_c1 @ sk_c7) = (sk_c8))
% 1.01/0.98 | ((multiply @ sk_c1 @ sk_c7) = (sk_c8)))),
% 1.01/0.98 inference('demod', [status(thm)],
% 1.01/0.98 [zip_derived_cl406, zip_derived_cl2, zip_derived_cl0])).
% 1.01/0.98 thf(zip_derived_cl413, plain,
% 1.01/0.98 ((((multiply @ sk_c1 @ sk_c7) = (sk_c8))
% 1.01/0.98 | ((multiply @ (inverse @ sk_c8) @ sk_c7) = (sk_c8)))),
% 1.01/0.98 inference('simplify', [status(thm)], [zip_derived_cl412])).
% 1.01/0.98 thf(prove_this_5, conjecture,
% 1.01/0.98 (~( ( ( inverse @ sk_c5 ) = ( sk_c4 ) ) |
% 1.01/0.98 ( ( inverse @ sk_c1 ) = ( sk_c8 ) ) ))).
% 1.01/0.98 thf(zf_stmt_2, negated_conjecture,
% 1.01/0.98 (( ( inverse @ sk_c5 ) = ( sk_c4 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c8 ) )),
% 1.01/0.98 inference('cnf.neg', [status(esa)], [prove_this_5])).
% 1.01/0.98 thf(zip_derived_cl7, plain,
% 1.01/0.98 ((((inverse @ sk_c5) = (sk_c4)) | ((inverse @ sk_c1) = (sk_c8)))),
% 1.01/0.98 inference('cnf', [status(esa)], [zf_stmt_2])).
% 1.01/0.98 thf(prove_this_6, conjecture,
% 1.01/0.98 (~( ( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 1.01/0.98 ( ( inverse @ sk_c1 ) = ( sk_c8 ) ) ))).
% 1.01/0.98 thf(zf_stmt_3, negated_conjecture,
% 1.01/0.98 (( ( inverse @ sk_c4 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c8 ) )),
% 1.01/0.98 inference('cnf.neg', [status(esa)], [prove_this_6])).
% 1.01/0.98 thf(zip_derived_cl8, plain,
% 1.01/0.98 ((((inverse @ sk_c4) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c8)))),
% 1.01/0.98 inference('cnf', [status(esa)], [zf_stmt_3])).
% 1.01/0.98 thf(zip_derived_cl38, plain,
% 1.01/0.98 ((((inverse @ (inverse @ sk_c5)) = (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8)))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl8])).
% 1.01/0.98 thf(zip_derived_cl39, plain,
% 1.01/0.98 ((((inverse @ sk_c1) = (sk_c8))
% 1.01/0.98 | ((inverse @ (inverse @ sk_c5)) = (sk_c8)))),
% 1.01/0.98 inference('simplify', [status(thm)], [zip_derived_cl38])).
% 1.01/0.98 thf(zip_derived_cl116, plain,
% 1.01/0.98 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl97])).
% 1.01/0.98 thf(zip_derived_cl346, plain,
% 1.01/0.98 ((((sk_c5) = (multiply @ sk_c8 @ identity))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8)))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl39, zip_derived_cl116])).
% 1.01/0.98 thf(zip_derived_cl116, plain,
% 1.01/0.98 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl97])).
% 1.01/0.98 thf(zip_derived_cl97, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i]:
% 1.01/0.98 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.01/0.98 inference('demod', [status(thm)], [zip_derived_cl80, zip_derived_cl0])).
% 1.01/0.98 thf(zip_derived_cl97, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i]:
% 1.01/0.98 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.01/0.98 inference('demod', [status(thm)], [zip_derived_cl80, zip_derived_cl0])).
% 1.01/0.98 thf(zip_derived_cl113, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i]:
% 1.01/0.98 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl97, zip_derived_cl97])).
% 1.01/0.98 thf(zip_derived_cl463, plain,
% 1.01/0.98 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl116, zip_derived_cl113])).
% 1.01/0.98 thf(zip_derived_cl497, plain,
% 1.01/0.98 ((((sk_c5) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c8)))),
% 1.01/0.98 inference('demod', [status(thm)], [zip_derived_cl346, zip_derived_cl463])).
% 1.01/0.98 thf(prove_this_7, conjecture,
% 1.01/0.98 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c4 ) ) |
% 1.01/0.98 ( ( inverse @ sk_c1 ) = ( sk_c8 ) ) ))).
% 1.01/0.98 thf(zf_stmt_4, negated_conjecture,
% 1.01/0.98 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c4 ) ) |
% 1.01/0.98 ( ( inverse @ sk_c1 ) = ( sk_c8 ) )),
% 1.01/0.98 inference('cnf.neg', [status(esa)], [prove_this_7])).
% 1.01/0.98 thf(zip_derived_cl9, plain,
% 1.01/0.98 ((((multiply @ sk_c5 @ sk_c8) = (sk_c4)) | ((inverse @ sk_c1) = (sk_c8)))),
% 1.01/0.98 inference('cnf', [status(esa)], [zf_stmt_4])).
% 1.01/0.98 thf(zip_derived_cl8, plain,
% 1.01/0.98 ((((inverse @ sk_c4) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c8)))),
% 1.01/0.98 inference('cnf', [status(esa)], [zf_stmt_3])).
% 1.01/0.98 thf(zip_derived_cl41, plain,
% 1.01/0.98 ((((inverse @ (multiply @ sk_c5 @ sk_c8)) = (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8)))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl8])).
% 1.01/0.98 thf(zip_derived_cl43, plain,
% 1.01/0.98 ((((inverse @ sk_c1) = (sk_c8))
% 1.01/0.98 | ((inverse @ (multiply @ sk_c5 @ sk_c8)) = (sk_c8)))),
% 1.01/0.98 inference('simplify', [status(thm)], [zip_derived_cl41])).
% 1.01/0.98 thf(prove_this_3, conjecture,
% 1.01/0.98 (~( ( ( inverse @ sk_c3 ) = ( sk_c8 ) ) |
% 1.01/0.98 ( ( inverse @ sk_c1 ) = ( sk_c8 ) ) ))).
% 1.01/0.98 thf(zf_stmt_5, negated_conjecture,
% 1.01/0.98 (( ( inverse @ sk_c3 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c8 ) )),
% 1.01/0.98 inference('cnf.neg', [status(esa)], [prove_this_3])).
% 1.01/0.98 thf(zip_derived_cl5, plain,
% 1.01/0.98 ((((inverse @ sk_c3) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c8)))),
% 1.01/0.98 inference('cnf', [status(esa)], [zf_stmt_5])).
% 1.01/0.98 thf(zip_derived_cl463, plain,
% 1.01/0.98 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl116, zip_derived_cl113])).
% 1.01/0.98 thf(zip_derived_cl116, plain,
% 1.01/0.98 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl97])).
% 1.01/0.98 thf(zip_derived_cl509, plain,
% 1.01/0.98 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl463, zip_derived_cl116])).
% 1.01/0.98 thf(zip_derived_cl1, plain,
% 1.01/0.98 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.01/0.98 inference('cnf', [status(esa)], [left_inverse])).
% 1.01/0.98 thf(zip_derived_cl620, plain,
% 1.01/0.98 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl509, zip_derived_cl1])).
% 1.01/0.98 thf(zip_derived_cl646, plain,
% 1.01/0.98 ((((multiply @ sk_c3 @ sk_c8) = (identity))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8)))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl620])).
% 1.01/0.98 thf(zip_derived_cl5, plain,
% 1.01/0.98 ((((inverse @ sk_c3) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c8)))),
% 1.01/0.98 inference('cnf', [status(esa)], [zf_stmt_5])).
% 1.01/0.98 thf(zip_derived_cl497, plain,
% 1.01/0.98 ((((sk_c5) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c8)))),
% 1.01/0.98 inference('demod', [status(thm)], [zip_derived_cl346, zip_derived_cl463])).
% 1.01/0.98 thf(zip_derived_cl43, plain,
% 1.01/0.98 ((((inverse @ sk_c1) = (sk_c8))
% 1.01/0.98 | ((inverse @ (multiply @ sk_c5 @ sk_c8)) = (sk_c8)))),
% 1.01/0.98 inference('simplify', [status(thm)], [zip_derived_cl41])).
% 1.01/0.98 thf(zip_derived_cl509, plain,
% 1.01/0.98 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl463, zip_derived_cl116])).
% 1.01/0.98 thf(prove_this_26, conjecture,
% 1.01/0.98 (~( ( ( multiply @ X2 @ sk_c8 ) != ( X5 ) ) |
% 1.01/0.98 ( ( inverse @ X5 ) != ( sk_c8 ) ) | ( ( inverse @ X2 ) != ( X5 ) ) |
% 1.01/0.98 ( ( multiply @ X1 @ sk_c7 ) != ( sk_c8 ) ) |
% 1.01/0.98 ( ( inverse @ X1 ) != ( sk_c8 ) ) |
% 1.01/0.98 ( ( inverse @ sk_c8 ) != ( sk_c7 ) ) |
% 1.01/0.98 ( ( inverse @ X4 ) != ( sk_c8 ) ) |
% 1.01/0.98 ( ( multiply @ X4 @ sk_c8 ) != ( sk_c6 ) ) |
% 1.01/0.98 ( ( multiply @ X3 @ sk_c7 ) != ( sk_c8 ) ) |
% 1.01/0.98 ( ( inverse @ X3 ) != ( sk_c8 ) ) |
% 1.01/0.98 ( ( multiply @ sk_c8 @ sk_c7 ) != ( sk_c6 ) ) ))).
% 1.01/0.98 thf(zf_stmt_6, negated_conjecture,
% 1.01/0.98 (( ( multiply @ X2 @ sk_c8 ) != ( X5 ) ) |
% 1.01/0.98 ( ( inverse @ X5 ) != ( sk_c8 ) ) | ( ( inverse @ X2 ) != ( X5 ) ) |
% 1.01/0.98 ( ( multiply @ X1 @ sk_c7 ) != ( sk_c8 ) ) |
% 1.01/0.98 ( ( inverse @ X1 ) != ( sk_c8 ) ) |
% 1.01/0.98 ( ( inverse @ sk_c8 ) != ( sk_c7 ) ) |
% 1.01/0.98 ( ( inverse @ X4 ) != ( sk_c8 ) ) |
% 1.01/0.98 ( ( multiply @ X4 @ sk_c8 ) != ( sk_c6 ) ) |
% 1.01/0.98 ( ( multiply @ X3 @ sk_c7 ) != ( sk_c8 ) ) |
% 1.01/0.98 ( ( inverse @ X3 ) != ( sk_c8 ) ) |
% 1.01/0.98 ( ( multiply @ sk_c8 @ sk_c7 ) != ( sk_c6 ) )),
% 1.01/0.98 inference('cnf.neg', [status(esa)], [prove_this_26])).
% 1.01/0.98 thf(zip_derived_cl28, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.01/0.98 (((multiply @ X1 @ sk_c8) != (X0))
% 1.01/0.98 | ((inverse @ X0) != (sk_c8))
% 1.01/0.98 | ((inverse @ X1) != (X0))
% 1.01/0.98 | ((multiply @ X2 @ sk_c7) != (sk_c8))
% 1.01/0.98 | ((inverse @ X2) != (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c8) != (sk_c7))
% 1.01/0.98 | ((inverse @ X3) != (sk_c8))
% 1.01/0.98 | ((multiply @ X3 @ sk_c8) != (sk_c6))
% 1.01/0.98 | ((multiply @ X4 @ sk_c7) != (sk_c8))
% 1.01/0.98 | ((inverse @ X4) != (sk_c8))
% 1.01/0.98 | ((multiply @ sk_c8 @ sk_c7) != (sk_c6)))),
% 1.01/0.98 inference('cnf', [status(esa)], [zf_stmt_6])).
% 1.01/0.98 thf(zip_derived_cl29, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.01/0.98 (((multiply @ X1 @ sk_c8) != (X0))
% 1.01/0.98 | ((inverse @ X0) != (sk_c8))
% 1.01/0.98 | ((inverse @ X1) != (X0))
% 1.01/0.98 | ((multiply @ X2 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((inverse @ X2) != (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c8) != (sk_c7))
% 1.01/0.98 | ((inverse @ X3) != (sk_c8))
% 1.01/0.98 | ((multiply @ X3 @ sk_c8) != (multiply @ sk_c8 @ (inverse @ sk_c8)))
% 1.01/0.98 | ((multiply @ X4 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((inverse @ X4) != (sk_c8))
% 1.01/0.98 | ((multiply @ sk_c8 @ (inverse @ sk_c8)) != (sk_c6)))),
% 1.01/0.98 inference('local_rewriting', [status(thm)], [zip_derived_cl28])).
% 1.01/0.98 thf(prove_this_1, conjecture, (( multiply @ sk_c8 @ sk_c7 ) != ( sk_c6 ))).
% 1.01/0.98 thf(zf_stmt_7, negated_conjecture,
% 1.01/0.98 (( multiply @ sk_c8 @ sk_c7 ) = ( sk_c6 )),
% 1.01/0.98 inference('cnf.neg', [status(esa)], [prove_this_1])).
% 1.01/0.98 thf(zip_derived_cl3, plain, (((multiply @ sk_c8 @ sk_c7) = (sk_c6))),
% 1.01/0.98 inference('cnf', [status(esa)], [zf_stmt_7])).
% 1.01/0.98 thf(zip_derived_cl30, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.01/0.98 (((multiply @ X1 @ sk_c8) != (X0))
% 1.01/0.98 | ((inverse @ X0) != (sk_c8))
% 1.01/0.98 | ((inverse @ X1) != (X0))
% 1.01/0.98 | ((multiply @ X2 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((inverse @ X2) != (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c8) != (sk_c7))
% 1.01/0.98 | ((inverse @ X3) != (sk_c8))
% 1.01/0.98 | ((multiply @ X3 @ sk_c8) != (multiply @ sk_c8 @ (inverse @ sk_c8)))
% 1.01/0.98 | ((multiply @ X4 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((inverse @ X4) != (sk_c8))
% 1.01/0.98 | ((multiply @ sk_c8 @ (inverse @ sk_c8))
% 1.01/0.98 != (multiply @ sk_c8 @ sk_c7)))),
% 1.01/0.98 inference('demod', [status(thm)], [zip_derived_cl29, zip_derived_cl3])).
% 1.01/0.98 thf(zip_derived_cl31, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.01/0.98 (((multiply @ X1 @ sk_c8) != (X0))
% 1.01/0.98 | ((inverse @ X0) != (sk_c8))
% 1.01/0.98 | ((inverse @ X1) != (X0))
% 1.01/0.98 | ((multiply @ X2 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((inverse @ X2) != (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c8) != (sk_c7))
% 1.01/0.98 | ((inverse @ X3) != (sk_c8))
% 1.01/0.98 | ((multiply @ X3 @ sk_c8) != (multiply @ sk_c8 @ (inverse @ sk_c8)))
% 1.01/0.98 | ((multiply @ X4 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((inverse @ X4) != (sk_c8))
% 1.01/0.98 | ((multiply @ sk_c8 @ (inverse @ sk_c8))
% 1.01/0.98 != (multiply @ sk_c8 @ (inverse @ sk_c8))))),
% 1.01/0.98 inference('local_rewriting', [status(thm)], [zip_derived_cl30])).
% 1.01/0.98 thf(zip_derived_cl32, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.01/0.98 (((inverse @ X4) != (sk_c8))
% 1.01/0.98 | ((multiply @ X4 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((multiply @ X3 @ sk_c8) != (multiply @ sk_c8 @ (inverse @ sk_c8)))
% 1.01/0.98 | ((inverse @ X3) != (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c8) != (sk_c7))
% 1.01/0.98 | ((inverse @ X2) != (sk_c8))
% 1.01/0.98 | ((multiply @ X2 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((inverse @ X1) != (X0))
% 1.01/0.98 | ((inverse @ X0) != (sk_c8))
% 1.01/0.98 | ((multiply @ X1 @ sk_c8) != (X0)))),
% 1.01/0.98 inference('simplify', [status(thm)], [zip_derived_cl31])).
% 1.01/0.98 thf(prove_this_20, conjecture,
% 1.01/0.98 (~( ( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 1.01/0.98 ( ( inverse @ sk_c2 ) = ( sk_c8 ) ) ))).
% 1.01/0.98 thf(zf_stmt_8, negated_conjecture,
% 1.01/0.98 (( ( inverse @ sk_c8 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c8 ) )),
% 1.01/0.98 inference('cnf.neg', [status(esa)], [prove_this_20])).
% 1.01/0.98 thf(zip_derived_cl22, plain,
% 1.01/0.98 ((((inverse @ sk_c8) = (sk_c7)) | ((inverse @ sk_c2) = (sk_c8)))),
% 1.01/0.98 inference('cnf', [status(esa)], [zf_stmt_8])).
% 1.01/0.98 thf(zip_derived_cl1, plain,
% 1.01/0.98 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.01/0.98 inference('cnf', [status(esa)], [left_inverse])).
% 1.01/0.98 thf(zip_derived_cl34, plain,
% 1.01/0.98 ((((multiply @ sk_c8 @ sk_c2) = (identity))
% 1.01/0.98 | ((inverse @ sk_c8) = (sk_c7)))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl1])).
% 1.01/0.98 thf(zip_derived_cl97, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i]:
% 1.01/0.98 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.01/0.98 inference('demod', [status(thm)], [zip_derived_cl80, zip_derived_cl0])).
% 1.01/0.98 thf(zip_derived_cl121, plain,
% 1.01/0.98 ((((sk_c2) = (multiply @ (inverse @ sk_c8) @ identity))
% 1.01/0.98 | ((inverse @ sk_c8) = (sk_c7)))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl34, zip_derived_cl97])).
% 1.01/0.98 thf(prove_this_14, conjecture,
% 1.01/0.98 (~( ( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 1.01/0.98 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c6 ) ) ))).
% 1.01/0.98 thf(zf_stmt_9, negated_conjecture,
% 1.01/0.98 (( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 1.01/0.98 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c6 ) )),
% 1.01/0.98 inference('cnf.neg', [status(esa)], [prove_this_14])).
% 1.01/0.98 thf(zip_derived_cl16, plain,
% 1.01/0.98 ((((inverse @ sk_c8) = (sk_c7)) | ((multiply @ sk_c2 @ sk_c8) = (sk_c6)))),
% 1.01/0.98 inference('cnf', [status(esa)], [zf_stmt_9])).
% 1.01/0.98 thf(zip_derived_cl3, plain, (((multiply @ sk_c8 @ sk_c7) = (sk_c6))),
% 1.01/0.98 inference('cnf', [status(esa)], [zf_stmt_7])).
% 1.01/0.98 thf(zip_derived_cl54, plain,
% 1.01/0.98 ((((inverse @ sk_c8) = (sk_c7))
% 1.01/0.98 | ((multiply @ sk_c2 @ sk_c8) = (multiply @ sk_c8 @ sk_c7)))),
% 1.01/0.98 inference('demod', [status(thm)], [zip_derived_cl16, zip_derived_cl3])).
% 1.01/0.98 thf(zip_derived_cl216, plain,
% 1.01/0.98 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c8)
% 1.01/0.98 = (multiply @ sk_c8 @ sk_c7))
% 1.01/0.98 | ((inverse @ sk_c8) = (sk_c7))
% 1.01/0.98 | ((inverse @ sk_c8) = (sk_c7)))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl54])).
% 1.01/0.98 thf(zip_derived_cl2, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.01/0.98 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.01/0.98 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.01/0.98 inference('cnf', [status(esa)], [associativity])).
% 1.01/0.98 thf(zip_derived_cl0, plain,
% 1.01/0.98 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.01/0.98 inference('cnf', [status(esa)], [left_identity])).
% 1.01/0.98 thf(zip_derived_cl1, plain,
% 1.01/0.98 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.01/0.98 inference('cnf', [status(esa)], [left_inverse])).
% 1.01/0.98 thf(zip_derived_cl225, plain,
% 1.01/0.98 ((((identity) = (multiply @ sk_c8 @ sk_c7))
% 1.01/0.98 | ((inverse @ sk_c8) = (sk_c7))
% 1.01/0.98 | ((inverse @ sk_c8) = (sk_c7)))),
% 1.01/0.98 inference('demod', [status(thm)],
% 1.01/0.98 [zip_derived_cl216, zip_derived_cl2, zip_derived_cl0,
% 1.01/0.98 zip_derived_cl1])).
% 1.01/0.98 thf(zip_derived_cl226, plain,
% 1.01/0.98 ((((inverse @ sk_c8) = (sk_c7))
% 1.01/0.98 | ((identity) = (multiply @ sk_c8 @ sk_c7)))),
% 1.01/0.98 inference('simplify', [status(thm)], [zip_derived_cl225])).
% 1.01/0.98 thf(zip_derived_cl97, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i]:
% 1.01/0.98 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.01/0.98 inference('demod', [status(thm)], [zip_derived_cl80, zip_derived_cl0])).
% 1.01/0.98 thf(zip_derived_cl372, plain,
% 1.01/0.98 ((((sk_c7) = (multiply @ (inverse @ sk_c8) @ identity))
% 1.01/0.98 | ((inverse @ sk_c8) = (sk_c7)))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl226, zip_derived_cl97])).
% 1.01/0.98 thf(zip_derived_cl463, plain,
% 1.01/0.98 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl116, zip_derived_cl113])).
% 1.01/0.98 thf(zip_derived_cl499, plain,
% 1.01/0.98 ((((sk_c7) = (inverse @ sk_c8)) | ((inverse @ sk_c8) = (sk_c7)))),
% 1.01/0.98 inference('demod', [status(thm)], [zip_derived_cl372, zip_derived_cl463])).
% 1.01/0.98 thf(zip_derived_cl500, plain, (((sk_c7) = (inverse @ sk_c8))),
% 1.01/0.98 inference('simplify', [status(thm)], [zip_derived_cl499])).
% 1.01/0.98 thf(zip_derived_cl521, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.01/0.98 (((inverse @ X4) != (sk_c8))
% 1.01/0.98 | ((multiply @ X4 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((multiply @ X3 @ sk_c8) != (multiply @ sk_c8 @ (inverse @ sk_c8)))
% 1.01/0.98 | ((inverse @ X3) != (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c8) != (inverse @ sk_c8))
% 1.01/0.98 | ((inverse @ X2) != (sk_c8))
% 1.01/0.98 | ((multiply @ X2 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((inverse @ X1) != (X0))
% 1.01/0.98 | ((inverse @ X0) != (sk_c8))
% 1.01/0.98 | ((multiply @ X1 @ sk_c8) != (X0)))),
% 1.01/0.98 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl500])).
% 1.01/0.98 thf(zip_derived_cl522, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.01/0.98 (((multiply @ X1 @ sk_c8) != (X0))
% 1.01/0.98 | ((inverse @ X0) != (sk_c8))
% 1.01/0.98 | ((inverse @ X1) != (X0))
% 1.01/0.98 | ((multiply @ X2 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((inverse @ X2) != (sk_c8))
% 1.01/0.98 | ((inverse @ X3) != (sk_c8))
% 1.01/0.98 | ((multiply @ X3 @ sk_c8) != (multiply @ sk_c8 @ (inverse @ sk_c8)))
% 1.01/0.98 | ((multiply @ X4 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((inverse @ X4) != (sk_c8)))),
% 1.01/0.98 inference('simplify', [status(thm)], [zip_derived_cl521])).
% 1.01/0.98 thf(zip_derived_cl620, plain,
% 1.01/0.98 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl509, zip_derived_cl1])).
% 1.01/0.98 thf(zip_derived_cl637, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.01/0.98 (((multiply @ X1 @ sk_c8) != (X0))
% 1.01/0.98 | ((inverse @ X0) != (sk_c8))
% 1.01/0.98 | ((inverse @ X1) != (X0))
% 1.01/0.98 | ((multiply @ X2 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((inverse @ X2) != (sk_c8))
% 1.01/0.98 | ((inverse @ X3) != (sk_c8))
% 1.01/0.98 | ((multiply @ X3 @ sk_c8) != (identity))
% 1.01/0.98 | ((multiply @ X4 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((inverse @ X4) != (sk_c8)))),
% 1.01/0.98 inference('demod', [status(thm)], [zip_derived_cl522, zip_derived_cl620])).
% 1.01/0.98 thf(zip_derived_cl672, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.01/0.98 (((X0) != (sk_c8))
% 1.01/0.98 | ((inverse @ X1) != (sk_c8))
% 1.01/0.98 | ((multiply @ X1 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((multiply @ X2 @ sk_c8) != (identity))
% 1.01/0.98 | ((inverse @ X2) != (sk_c8))
% 1.01/0.98 | ((inverse @ X3) != (sk_c8))
% 1.01/0.98 | ((multiply @ X3 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((inverse @ X4) != (inverse @ X0))
% 1.01/0.98 | ((multiply @ X4 @ sk_c8) != (inverse @ X0)))),
% 1.01/0.98 inference('sup-', [status(thm)], [zip_derived_cl509, zip_derived_cl637])).
% 1.01/0.98 thf(zip_derived_cl689, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.01/0.98 (((multiply @ X0 @ sk_c8) != (inverse @ sk_c8))
% 1.01/0.98 | ((inverse @ X0) != (inverse @ sk_c8))
% 1.01/0.98 | ((multiply @ X1 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((inverse @ X1) != (sk_c8))
% 1.01/0.98 | ((inverse @ X2) != (sk_c8))
% 1.01/0.98 | ((multiply @ X2 @ sk_c8) != (identity))
% 1.01/0.98 | ((multiply @ X3 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((inverse @ X3) != (sk_c8)))),
% 1.01/0.98 inference('eq_res', [status(thm)], [zip_derived_cl672])).
% 1.01/0.98 thf(zip_derived_cl690, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.01/0.98 (((sk_c8) != (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8))
% 1.01/0.98 | ((inverse @ X0) != (sk_c8))
% 1.01/0.98 | ((multiply @ X0 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((multiply @ X1 @ sk_c8) != (identity))
% 1.01/0.98 | ((inverse @ X1) != (sk_c8))
% 1.01/0.98 | ((multiply @ (multiply @ sk_c5 @ sk_c8) @ (inverse @ sk_c8))
% 1.01/0.98 != (sk_c8))
% 1.01/0.98 | ((inverse @ X2) != (inverse @ sk_c8))
% 1.01/0.98 | ((multiply @ X2 @ sk_c8) != (inverse @ sk_c8)))),
% 1.01/0.98 inference('sup-', [status(thm)], [zip_derived_cl43, zip_derived_cl689])).
% 1.01/0.98 thf(zip_derived_cl2, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.01/0.98 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.01/0.98 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.01/0.98 inference('cnf', [status(esa)], [associativity])).
% 1.01/0.98 thf(zip_derived_cl620, plain,
% 1.01/0.98 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl509, zip_derived_cl1])).
% 1.01/0.98 thf(zip_derived_cl463, plain,
% 1.01/0.98 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl116, zip_derived_cl113])).
% 1.01/0.98 thf(zip_derived_cl700, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.01/0.98 (((sk_c8) != (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8))
% 1.01/0.98 | ((inverse @ X0) != (sk_c8))
% 1.01/0.98 | ((multiply @ X0 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((multiply @ X1 @ sk_c8) != (identity))
% 1.01/0.98 | ((inverse @ X1) != (sk_c8))
% 1.01/0.98 | ((sk_c5) != (sk_c8))
% 1.01/0.98 | ((inverse @ X2) != (inverse @ sk_c8))
% 1.01/0.98 | ((multiply @ X2 @ sk_c8) != (inverse @ sk_c8)))),
% 1.01/0.98 inference('demod', [status(thm)],
% 1.01/0.98 [zip_derived_cl690, zip_derived_cl2, zip_derived_cl620,
% 1.01/0.98 zip_derived_cl463])).
% 1.01/0.98 thf(zip_derived_cl701, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.01/0.98 (((multiply @ X2 @ sk_c8) != (inverse @ sk_c8))
% 1.01/0.98 | ((inverse @ X2) != (inverse @ sk_c8))
% 1.01/0.98 | ((sk_c5) != (sk_c8))
% 1.01/0.98 | ((inverse @ X1) != (sk_c8))
% 1.01/0.98 | ((multiply @ X1 @ sk_c8) != (identity))
% 1.01/0.98 | ((multiply @ X0 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((inverse @ X0) != (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8)))),
% 1.01/0.98 inference('simplify', [status(thm)], [zip_derived_cl700])).
% 1.01/0.98 thf(zip_derived_cl837, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.01/0.98 (((sk_c8) != (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8))
% 1.01/0.98 | ((inverse @ X0) != (sk_c8))
% 1.01/0.98 | ((multiply @ X0 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((multiply @ X1 @ sk_c8) != (identity))
% 1.01/0.98 | ((inverse @ X1) != (sk_c8))
% 1.01/0.98 | ((inverse @ X2) != (inverse @ sk_c8))
% 1.01/0.98 | ((multiply @ X2 @ sk_c8) != (inverse @ sk_c8)))),
% 1.01/0.98 inference('sup-', [status(thm)], [zip_derived_cl497, zip_derived_cl701])).
% 1.01/0.98 thf(zip_derived_cl839, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.01/0.98 (((multiply @ X2 @ sk_c8) != (inverse @ sk_c8))
% 1.01/0.98 | ((inverse @ X2) != (inverse @ sk_c8))
% 1.01/0.98 | ((inverse @ X1) != (sk_c8))
% 1.01/0.98 | ((multiply @ X1 @ sk_c8) != (identity))
% 1.01/0.98 | ((multiply @ X0 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((inverse @ X0) != (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8)))),
% 1.01/0.98 inference('simplify', [status(thm)], [zip_derived_cl837])).
% 1.01/0.98 thf(zip_derived_cl846, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i]:
% 1.01/0.98 (((sk_c8) != (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8))
% 1.01/0.98 | ((inverse @ X0) != (sk_c8))
% 1.01/0.98 | ((multiply @ X0 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((multiply @ sk_c3 @ sk_c8) != (identity))
% 1.01/0.98 | ((inverse @ X1) != (inverse @ sk_c8))
% 1.01/0.98 | ((multiply @ X1 @ sk_c8) != (inverse @ sk_c8)))),
% 1.01/0.98 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl839])).
% 1.01/0.98 thf(zip_derived_cl858, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i]:
% 1.01/0.98 (((multiply @ X1 @ sk_c8) != (inverse @ sk_c8))
% 1.01/0.98 | ((inverse @ X1) != (inverse @ sk_c8))
% 1.01/0.98 | ((multiply @ sk_c3 @ sk_c8) != (identity))
% 1.01/0.98 | ((multiply @ X0 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((inverse @ X0) != (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8)))),
% 1.01/0.98 inference('simplify', [status(thm)], [zip_derived_cl846])).
% 1.01/0.98 thf(zip_derived_cl865, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i]:
% 1.01/0.98 (((identity) != (identity))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8))
% 1.01/0.98 | ((inverse @ X0) != (sk_c8))
% 1.01/0.98 | ((multiply @ X0 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((inverse @ X1) != (inverse @ sk_c8))
% 1.01/0.98 | ((multiply @ X1 @ sk_c8) != (inverse @ sk_c8)))),
% 1.01/0.98 inference('sup-', [status(thm)], [zip_derived_cl646, zip_derived_cl858])).
% 1.01/0.98 thf(zip_derived_cl868, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i]:
% 1.01/0.98 (((multiply @ X1 @ sk_c8) != (inverse @ sk_c8))
% 1.01/0.98 | ((inverse @ X1) != (inverse @ sk_c8))
% 1.01/0.98 | ((multiply @ X0 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((inverse @ X0) != (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8)))),
% 1.01/0.98 inference('simplify', [status(thm)], [zip_derived_cl865])).
% 1.01/0.98 thf(zip_derived_cl873, plain,
% 1.01/0.98 (![X0 : $i]:
% 1.01/0.98 (((sk_c8) != (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8))
% 1.01/0.98 | ((multiply @ (multiply @ sk_c5 @ sk_c8) @ (inverse @ sk_c8))
% 1.01/0.98 != (sk_c8))
% 1.01/0.98 | ((inverse @ X0) != (inverse @ sk_c8))
% 1.01/0.98 | ((multiply @ X0 @ sk_c8) != (inverse @ sk_c8)))),
% 1.01/0.98 inference('sup-', [status(thm)], [zip_derived_cl43, zip_derived_cl868])).
% 1.01/0.98 thf(zip_derived_cl2, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.01/0.98 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.01/0.98 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.01/0.98 inference('cnf', [status(esa)], [associativity])).
% 1.01/0.98 thf(zip_derived_cl620, plain,
% 1.01/0.98 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl509, zip_derived_cl1])).
% 1.01/0.98 thf(zip_derived_cl463, plain,
% 1.01/0.98 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl116, zip_derived_cl113])).
% 1.01/0.98 thf(zip_derived_cl885, plain,
% 1.01/0.98 (![X0 : $i]:
% 1.01/0.98 (((sk_c8) != (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8))
% 1.01/0.98 | ((sk_c5) != (sk_c8))
% 1.01/0.98 | ((inverse @ X0) != (inverse @ sk_c8))
% 1.01/0.98 | ((multiply @ X0 @ sk_c8) != (inverse @ sk_c8)))),
% 1.01/0.98 inference('demod', [status(thm)],
% 1.01/0.98 [zip_derived_cl873, zip_derived_cl2, zip_derived_cl620,
% 1.01/0.98 zip_derived_cl463])).
% 1.01/0.98 thf(zip_derived_cl886, plain,
% 1.01/0.98 (![X0 : $i]:
% 1.01/0.98 (((multiply @ X0 @ sk_c8) != (inverse @ sk_c8))
% 1.01/0.98 | ((inverse @ X0) != (inverse @ sk_c8))
% 1.01/0.98 | ((sk_c5) != (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8)))),
% 1.01/0.98 inference('simplify', [status(thm)], [zip_derived_cl885])).
% 1.01/0.98 thf(zip_derived_cl897, plain,
% 1.01/0.98 (![X0 : $i]:
% 1.01/0.98 (((sk_c8) != (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8))
% 1.01/0.98 | ((inverse @ X0) != (inverse @ sk_c8))
% 1.01/0.98 | ((multiply @ X0 @ sk_c8) != (inverse @ sk_c8)))),
% 1.01/0.98 inference('sup-', [status(thm)], [zip_derived_cl497, zip_derived_cl886])).
% 1.01/0.98 thf(zip_derived_cl899, plain,
% 1.01/0.98 (![X0 : $i]:
% 1.01/0.98 (((multiply @ X0 @ sk_c8) != (inverse @ sk_c8))
% 1.01/0.98 | ((inverse @ X0) != (inverse @ sk_c8))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8)))),
% 1.01/0.98 inference('simplify', [status(thm)], [zip_derived_cl897])).
% 1.01/0.98 thf(zip_derived_cl913, plain,
% 1.01/0.98 ((((inverse @ sk_c1) = (sk_c8))
% 1.01/0.98 | ((multiply @ sk_c8 @ sk_c8) != (inverse @ sk_c8)))),
% 1.01/0.98 inference('eq_res', [status(thm)], [zip_derived_cl899])).
% 1.01/0.98 thf(zip_derived_cl497, plain,
% 1.01/0.98 ((((sk_c5) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c8)))),
% 1.01/0.98 inference('demod', [status(thm)], [zip_derived_cl346, zip_derived_cl463])).
% 1.01/0.98 thf(zip_derived_cl497, plain,
% 1.01/0.98 ((((sk_c5) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c8)))),
% 1.01/0.98 inference('demod', [status(thm)], [zip_derived_cl346, zip_derived_cl463])).
% 1.01/0.98 thf(zip_derived_cl9, plain,
% 1.01/0.98 ((((multiply @ sk_c5 @ sk_c8) = (sk_c4)) | ((inverse @ sk_c1) = (sk_c8)))),
% 1.01/0.98 inference('cnf', [status(esa)], [zf_stmt_4])).
% 1.01/0.98 thf(zip_derived_cl7, plain,
% 1.01/0.98 ((((inverse @ sk_c5) = (sk_c4)) | ((inverse @ sk_c1) = (sk_c8)))),
% 1.01/0.98 inference('cnf', [status(esa)], [zf_stmt_2])).
% 1.01/0.98 thf(zip_derived_cl40, plain,
% 1.01/0.98 ((((inverse @ sk_c5) = (multiply @ sk_c5 @ sk_c8))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8)))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl7])).
% 1.01/0.98 thf(zip_derived_cl42, plain,
% 1.01/0.98 ((((inverse @ sk_c1) = (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c5) = (multiply @ sk_c5 @ sk_c8)))),
% 1.01/0.98 inference('simplify', [status(thm)], [zip_derived_cl40])).
% 1.01/0.98 thf(zip_derived_cl537, plain,
% 1.01/0.98 ((((inverse @ sk_c8) = (multiply @ sk_c5 @ sk_c8))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8)))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl497, zip_derived_cl42])).
% 1.01/0.98 thf(zip_derived_cl540, plain,
% 1.01/0.98 ((((inverse @ sk_c1) = (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c8) = (multiply @ sk_c5 @ sk_c8)))),
% 1.01/0.98 inference('simplify', [status(thm)], [zip_derived_cl537])).
% 1.01/0.98 thf(zip_derived_cl729, plain,
% 1.01/0.98 ((((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c8))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c1) = (sk_c8)))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl497, zip_derived_cl540])).
% 1.01/0.98 thf(zip_derived_cl731, plain,
% 1.01/0.98 ((((inverse @ sk_c1) = (sk_c8))
% 1.01/0.98 | ((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c8)))),
% 1.01/0.98 inference('simplify', [status(thm)], [zip_derived_cl729])).
% 1.01/0.98 thf(zip_derived_cl930, plain, (((inverse @ sk_c1) = (sk_c8))),
% 1.01/0.98 inference('clc', [status(thm)], [zip_derived_cl913, zip_derived_cl731])).
% 1.01/0.98 thf(zip_derived_cl509, plain,
% 1.01/0.98 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl463, zip_derived_cl116])).
% 1.01/0.98 thf(zip_derived_cl932, plain, (((sk_c1) = (inverse @ sk_c8))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl930, zip_derived_cl509])).
% 1.01/0.98 thf(zip_derived_cl500, plain, (((sk_c7) = (inverse @ sk_c8))),
% 1.01/0.98 inference('simplify', [status(thm)], [zip_derived_cl499])).
% 1.01/0.98 thf(zip_derived_cl500, plain, (((sk_c7) = (inverse @ sk_c8))),
% 1.01/0.98 inference('simplify', [status(thm)], [zip_derived_cl499])).
% 1.01/0.98 thf(zip_derived_cl1488, plain,
% 1.01/0.98 ((((multiply @ (inverse @ sk_c8) @ (inverse @ sk_c8)) = (sk_c8))
% 1.01/0.98 | ((multiply @ (inverse @ sk_c8) @ (inverse @ sk_c8)) = (sk_c8)))),
% 1.01/0.98 inference('demod', [status(thm)],
% 1.01/0.98 [zip_derived_cl413, zip_derived_cl932, zip_derived_cl500,
% 1.01/0.98 zip_derived_cl500])).
% 1.01/0.98 thf(zip_derived_cl1489, plain,
% 1.01/0.98 (((multiply @ (inverse @ sk_c8) @ (inverse @ sk_c8)) = (sk_c8))),
% 1.01/0.98 inference('simplify', [status(thm)], [zip_derived_cl1488])).
% 1.01/0.98 thf(zip_derived_cl509, plain,
% 1.01/0.98 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl463, zip_derived_cl116])).
% 1.01/0.98 thf(zip_derived_cl97, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i]:
% 1.01/0.98 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.01/0.98 inference('demod', [status(thm)], [zip_derived_cl80, zip_derived_cl0])).
% 1.01/0.98 thf(zip_derived_cl623, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i]:
% 1.01/0.98 ((X1) = (multiply @ X0 @ (multiply @ (inverse @ X0) @ X1)))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl509, zip_derived_cl97])).
% 1.01/0.98 thf(zip_derived_cl1498, plain,
% 1.01/0.98 (((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c8))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl1489, zip_derived_cl623])).
% 1.01/0.98 thf(zip_derived_cl1498, plain,
% 1.01/0.98 (((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c8))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl1489, zip_derived_cl623])).
% 1.01/0.98 thf(zip_derived_cl509, plain,
% 1.01/0.98 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl463, zip_derived_cl116])).
% 1.01/0.98 thf(zip_derived_cl1538, plain,
% 1.01/0.98 (((sk_c8) = (inverse @ (multiply @ sk_c8 @ sk_c8)))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl1498, zip_derived_cl509])).
% 1.01/0.98 thf(zip_derived_cl509, plain,
% 1.01/0.98 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl463, zip_derived_cl116])).
% 1.01/0.98 thf(zip_derived_cl509, plain,
% 1.01/0.98 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl463, zip_derived_cl116])).
% 1.01/0.98 thf(zip_derived_cl689, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.01/0.98 (((multiply @ X0 @ sk_c8) != (inverse @ sk_c8))
% 1.01/0.98 | ((inverse @ X0) != (inverse @ sk_c8))
% 1.01/0.98 | ((multiply @ X1 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((inverse @ X1) != (sk_c8))
% 1.01/0.98 | ((inverse @ X2) != (sk_c8))
% 1.01/0.98 | ((multiply @ X2 @ sk_c8) != (identity))
% 1.01/0.98 | ((multiply @ X3 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((inverse @ X3) != (sk_c8)))),
% 1.01/0.98 inference('eq_res', [status(thm)], [zip_derived_cl672])).
% 1.01/0.98 thf(zip_derived_cl691, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.01/0.98 (((X0) != (sk_c8))
% 1.01/0.98 | ((inverse @ X1) != (sk_c8))
% 1.01/0.98 | ((multiply @ X1 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((multiply @ X2 @ sk_c8) != (identity))
% 1.01/0.98 | ((inverse @ X2) != (sk_c8))
% 1.01/0.98 | ((multiply @ (inverse @ X0) @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((inverse @ X3) != (inverse @ sk_c8))
% 1.01/0.98 | ((multiply @ X3 @ sk_c8) != (inverse @ sk_c8)))),
% 1.01/0.98 inference('sup-', [status(thm)], [zip_derived_cl509, zip_derived_cl689])).
% 1.01/0.98 thf(zip_derived_cl709, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.01/0.98 (((multiply @ X0 @ sk_c8) != (inverse @ sk_c8))
% 1.01/0.98 | ((inverse @ X0) != (inverse @ sk_c8))
% 1.01/0.98 | ((multiply @ (inverse @ sk_c8) @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((inverse @ X1) != (sk_c8))
% 1.01/0.98 | ((multiply @ X1 @ sk_c8) != (identity))
% 1.01/0.98 | ((multiply @ X2 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((inverse @ X2) != (sk_c8)))),
% 1.01/0.98 inference('eq_res', [status(thm)], [zip_derived_cl691])).
% 1.01/0.98 thf(zip_derived_cl1489, plain,
% 1.01/0.98 (((multiply @ (inverse @ sk_c8) @ (inverse @ sk_c8)) = (sk_c8))),
% 1.01/0.98 inference('simplify', [status(thm)], [zip_derived_cl1488])).
% 1.01/0.98 thf(zip_derived_cl1490, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.01/0.98 (((multiply @ X0 @ sk_c8) != (inverse @ sk_c8))
% 1.01/0.98 | ((inverse @ X0) != (inverse @ sk_c8))
% 1.01/0.98 | ((sk_c8) != (sk_c8))
% 1.01/0.98 | ((inverse @ X1) != (sk_c8))
% 1.01/0.98 | ((multiply @ X1 @ sk_c8) != (identity))
% 1.01/0.98 | ((multiply @ X2 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((inverse @ X2) != (sk_c8)))),
% 1.01/0.98 inference('demod', [status(thm)], [zip_derived_cl709, zip_derived_cl1489])).
% 1.01/0.98 thf(zip_derived_cl1491, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.01/0.98 (((inverse @ X2) != (sk_c8))
% 1.01/0.98 | ((multiply @ X2 @ (inverse @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((multiply @ X1 @ sk_c8) != (identity))
% 1.01/0.98 | ((inverse @ X1) != (sk_c8))
% 1.01/0.98 | ((inverse @ X0) != (inverse @ sk_c8))
% 1.01/0.98 | ((multiply @ X0 @ sk_c8) != (inverse @ sk_c8)))),
% 1.01/0.98 inference('simplify', [status(thm)], [zip_derived_cl1490])).
% 1.01/0.98 thf(zip_derived_cl1498, plain,
% 1.01/0.98 (((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c8))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl1489, zip_derived_cl623])).
% 1.01/0.98 thf(zip_derived_cl1498, plain,
% 1.01/0.98 (((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c8))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl1489, zip_derived_cl623])).
% 1.01/0.98 thf(zip_derived_cl1498, plain,
% 1.01/0.98 (((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c8))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl1489, zip_derived_cl623])).
% 1.01/0.98 thf(zip_derived_cl1599, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.01/0.98 (((inverse @ X2) != (sk_c8))
% 1.01/0.98 | ((multiply @ X2 @ (multiply @ sk_c8 @ sk_c8)) != (sk_c8))
% 1.01/0.98 | ((multiply @ X1 @ sk_c8) != (identity))
% 1.01/0.98 | ((inverse @ X1) != (sk_c8))
% 1.01/0.98 | ((inverse @ X0) != (multiply @ sk_c8 @ sk_c8))
% 1.01/0.98 | ((multiply @ X0 @ sk_c8) != (multiply @ sk_c8 @ sk_c8)))),
% 1.01/0.98 inference('demod', [status(thm)],
% 1.01/0.98 [zip_derived_cl1491, zip_derived_cl1498, zip_derived_cl1498,
% 1.01/0.98 zip_derived_cl1498])).
% 1.01/0.98 thf(zip_derived_cl1600, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.01/0.98 (((X0) != (sk_c8))
% 1.01/0.98 | ((multiply @ X1 @ sk_c8) != (multiply @ sk_c8 @ sk_c8))
% 1.01/0.98 | ((inverse @ X1) != (multiply @ sk_c8 @ sk_c8))
% 1.01/0.98 | ((inverse @ X2) != (sk_c8))
% 1.01/0.98 | ((multiply @ X2 @ sk_c8) != (identity))
% 1.01/0.98 | ((multiply @ (inverse @ X0) @ (multiply @ sk_c8 @ sk_c8))
% 1.01/0.98 != (sk_c8)))),
% 1.01/0.98 inference('sup-', [status(thm)], [zip_derived_cl509, zip_derived_cl1599])).
% 1.01/0.98 thf(zip_derived_cl1612, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i]:
% 1.01/0.98 (((multiply @ (inverse @ sk_c8) @ (multiply @ sk_c8 @ sk_c8))
% 1.01/0.98 != (sk_c8))
% 1.01/0.98 | ((multiply @ X0 @ sk_c8) != (identity))
% 1.01/0.98 | ((inverse @ X0) != (sk_c8))
% 1.01/0.98 | ((inverse @ X1) != (multiply @ sk_c8 @ sk_c8))
% 1.01/0.98 | ((multiply @ X1 @ sk_c8) != (multiply @ sk_c8 @ sk_c8)))),
% 1.01/0.98 inference('eq_res', [status(thm)], [zip_derived_cl1600])).
% 1.01/0.98 thf(zip_derived_cl1498, plain,
% 1.01/0.98 (((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c8))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl1489, zip_derived_cl623])).
% 1.01/0.98 thf(zip_derived_cl2, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.01/0.98 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.01/0.98 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.01/0.98 inference('cnf', [status(esa)], [associativity])).
% 1.01/0.98 thf(zip_derived_cl1613, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i]:
% 1.01/0.98 (((multiply @ sk_c8 @ (multiply @ sk_c8 @ (multiply @ sk_c8 @ sk_c8)))
% 1.01/0.98 != (sk_c8))
% 1.01/0.98 | ((multiply @ X0 @ sk_c8) != (identity))
% 1.01/0.98 | ((inverse @ X0) != (sk_c8))
% 1.01/0.98 | ((inverse @ X1) != (multiply @ sk_c8 @ sk_c8))
% 1.01/0.98 | ((multiply @ X1 @ sk_c8) != (multiply @ sk_c8 @ sk_c8)))),
% 1.01/0.98 inference('demod', [status(thm)],
% 1.01/0.98 [zip_derived_cl1612, zip_derived_cl1498, zip_derived_cl2])).
% 1.01/0.98 thf(zip_derived_cl1498, plain,
% 1.01/0.98 (((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c8))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl1489, zip_derived_cl623])).
% 1.01/0.98 thf(zip_derived_cl620, plain,
% 1.01/0.98 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl509, zip_derived_cl1])).
% 1.01/0.98 thf(zip_derived_cl1539, plain,
% 1.01/0.98 (((multiply @ sk_c8 @ (multiply @ sk_c8 @ sk_c8)) = (identity))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl1498, zip_derived_cl620])).
% 1.01/0.98 thf(zip_derived_cl463, plain,
% 1.01/0.98 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl116, zip_derived_cl113])).
% 1.01/0.98 thf(zip_derived_cl1738, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i]:
% 1.01/0.98 (((sk_c8) != (sk_c8))
% 1.01/0.98 | ((multiply @ X0 @ sk_c8) != (identity))
% 1.01/0.98 | ((inverse @ X0) != (sk_c8))
% 1.01/0.98 | ((inverse @ X1) != (multiply @ sk_c8 @ sk_c8))
% 1.01/0.98 | ((multiply @ X1 @ sk_c8) != (multiply @ sk_c8 @ sk_c8)))),
% 1.01/0.98 inference('demod', [status(thm)],
% 1.01/0.98 [zip_derived_cl1613, zip_derived_cl1539, zip_derived_cl463])).
% 1.01/0.98 thf(zip_derived_cl1739, plain,
% 1.01/0.98 (![X0 : $i, X1 : $i]:
% 1.01/0.98 (((multiply @ X1 @ sk_c8) != (multiply @ sk_c8 @ sk_c8))
% 1.01/0.98 | ((inverse @ X1) != (multiply @ sk_c8 @ sk_c8))
% 1.01/0.98 | ((inverse @ X0) != (sk_c8))
% 1.01/0.98 | ((multiply @ X0 @ sk_c8) != (identity)))),
% 1.01/0.98 inference('simplify', [status(thm)], [zip_derived_cl1738])).
% 1.01/0.98 thf(zip_derived_cl1748, plain,
% 1.01/0.98 (![X0 : $i]:
% 1.01/0.98 (((sk_c8) != (sk_c8))
% 1.01/0.98 | ((multiply @ (multiply @ sk_c8 @ sk_c8) @ sk_c8) != (identity))
% 1.01/0.98 | ((inverse @ X0) != (multiply @ sk_c8 @ sk_c8))
% 1.01/0.98 | ((multiply @ X0 @ sk_c8) != (multiply @ sk_c8 @ sk_c8)))),
% 1.01/0.98 inference('sup-', [status(thm)], [zip_derived_cl1538, zip_derived_cl1739])).
% 1.01/0.98 thf(zip_derived_cl1498, plain,
% 1.01/0.98 (((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c8))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl1489, zip_derived_cl623])).
% 1.01/0.98 thf(zip_derived_cl1, plain,
% 1.01/0.98 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.01/0.98 inference('cnf', [status(esa)], [left_inverse])).
% 1.01/0.98 thf(zip_derived_cl1537, plain,
% 1.01/0.98 (((multiply @ (multiply @ sk_c8 @ sk_c8) @ sk_c8) = (identity))),
% 1.01/0.98 inference('sup+', [status(thm)], [zip_derived_cl1498, zip_derived_cl1])).
% 1.01/0.98 thf(zip_derived_cl1755, plain,
% 1.01/0.98 (![X0 : $i]:
% 1.01/0.98 (((sk_c8) != (sk_c8))
% 1.01/0.98 | ((identity) != (identity))
% 1.01/0.98 | ((inverse @ X0) != (multiply @ sk_c8 @ sk_c8))
% 1.01/0.98 | ((multiply @ X0 @ sk_c8) != (multiply @ sk_c8 @ sk_c8)))),
% 1.01/0.98 inference('demod', [status(thm)],
% 1.01/0.98 [zip_derived_cl1748, zip_derived_cl1537])).
% 1.01/0.98 thf(zip_derived_cl1756, plain,
% 1.01/0.98 (![X0 : $i]:
% 1.01/0.98 (((multiply @ X0 @ sk_c8) != (multiply @ sk_c8 @ sk_c8))
% 1.01/0.98 | ((inverse @ X0) != (multiply @ sk_c8 @ sk_c8)))),
% 1.01/0.98 inference('simplify', [status(thm)], [zip_derived_cl1755])).
% 1.01/0.98 thf(zip_derived_cl1764, plain,
% 1.01/0.98 ((((multiply @ sk_c8 @ sk_c8) != (multiply @ sk_c8 @ sk_c8))
% 1.01/0.98 | ((multiply @ sk_c8 @ sk_c8) != (multiply @ sk_c8 @ sk_c8)))),
% 1.01/0.98 inference('sup-', [status(thm)], [zip_derived_cl1498, zip_derived_cl1756])).
% 1.01/0.98 thf(zip_derived_cl1770, plain, ($false),
% 1.01/0.98 inference('simplify', [status(thm)], [zip_derived_cl1764])).
% 1.01/0.98
% 1.01/0.98 % SZS output end Refutation
% 1.01/0.98
% 1.01/0.98
% 1.01/0.98 % Terminating...
% 1.18/1.12 % Runner terminated.
% 1.18/1.12 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------