TSTP Solution File: GRP265-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP265-1 : 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.s070rGMqRR true
% Computer : n008.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 01:50:58 EDT 2023
% Result : Unsatisfiable 1.37s 1.34s
% Output : Refutation 1.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP265-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.s070rGMqRR true
% 0.15/0.35 % Computer : n008.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon Aug 28 20:37:17 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % Running portfolio for 300 s
% 0.15/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.36 % Number of cores: 8
% 0.15/0.36 % Python version: Python 3.6.8
% 0.15/0.36 % 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
% 0.22/0.71 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.75 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 1.37/1.34 % Solved by fo/fo7.sh.
% 1.37/1.34 % done 1323 iterations in 0.553s
% 1.37/1.34 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.37/1.34 % SZS output start Refutation
% 1.37/1.34 thf(sk_c6_type, type, sk_c6: $i).
% 1.37/1.34 thf(sk_c8_type, type, sk_c8: $i).
% 1.37/1.34 thf(sk_c2_type, type, sk_c2: $i).
% 1.37/1.34 thf(sk_c7_type, type, sk_c7: $i).
% 1.37/1.34 thf(sk_c4_type, type, sk_c4: $i).
% 1.37/1.34 thf(identity_type, type, identity: $i).
% 1.37/1.34 thf(multiply_type, type, multiply: $i > $i > $i).
% 1.37/1.34 thf(sk_c9_type, type, sk_c9: $i).
% 1.37/1.34 thf(inverse_type, type, inverse: $i > $i).
% 1.37/1.34 thf(sk_c3_type, type, sk_c3: $i).
% 1.37/1.34 thf(sk_c5_type, type, sk_c5: $i).
% 1.37/1.34 thf(sk_c1_type, type, sk_c1: $i).
% 1.37/1.34 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 1.37/1.34 thf(zip_derived_cl1, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.37/1.34 inference('cnf', [status(esa)], [left_inverse])).
% 1.37/1.34 thf(zip_derived_cl1, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.37/1.34 inference('cnf', [status(esa)], [left_inverse])).
% 1.37/1.34 thf(associativity, axiom,
% 1.37/1.34 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 1.37/1.34 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 1.37/1.34 thf(zip_derived_cl2, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.37/1.34 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.37/1.34 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.37/1.34 inference('cnf', [status(esa)], [associativity])).
% 1.37/1.34 thf(zip_derived_cl90, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i]:
% 1.37/1.34 ((multiply @ identity @ X0)
% 1.37/1.34 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 1.37/1.34 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 1.37/1.34 thf(zip_derived_cl0, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.37/1.34 inference('cnf', [status(esa)], [left_identity])).
% 1.37/1.34 thf(zip_derived_cl110, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i]:
% 1.37/1.34 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.37/1.34 inference('demod', [status(thm)], [zip_derived_cl90, zip_derived_cl0])).
% 1.37/1.34 thf(zip_derived_cl123, plain,
% 1.37/1.34 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl110])).
% 1.37/1.34 thf(zip_derived_cl110, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i]:
% 1.37/1.34 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.37/1.34 inference('demod', [status(thm)], [zip_derived_cl90, zip_derived_cl0])).
% 1.37/1.34 thf(zip_derived_cl110, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i]:
% 1.37/1.34 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.37/1.34 inference('demod', [status(thm)], [zip_derived_cl90, zip_derived_cl0])).
% 1.37/1.34 thf(zip_derived_cl120, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i]:
% 1.37/1.34 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl110, zip_derived_cl110])).
% 1.37/1.34 thf(zip_derived_cl5618, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl123, zip_derived_cl120])).
% 1.37/1.34 thf(zip_derived_cl123, plain,
% 1.37/1.34 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl110])).
% 1.37/1.34 thf(zip_derived_cl5677, plain,
% 1.37/1.34 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl5618, zip_derived_cl123])).
% 1.37/1.34 thf(prove_this_29, conjecture,
% 1.37/1.34 (~( ( ( inverse @ X6 ) != ( sk_c7 ) ) |
% 1.37/1.34 ( ( multiply @ X6 @ sk_c7 ) != ( X5 ) ) |
% 1.37/1.34 ( ( multiply @ sk_c7 @ X5 ) != ( sk_c8 ) ) |
% 1.37/1.34 ( ( inverse @ X2 ) != ( sk_c7 ) ) |
% 1.37/1.34 ( ( multiply @ X2 @ sk_c7 ) != ( sk_c8 ) ) |
% 1.37/1.34 ( ( inverse @ X1 ) != ( sk_c9 ) ) |
% 1.37/1.34 ( ( multiply @ X1 @ sk_c9 ) != ( sk_c8 ) ) |
% 1.37/1.34 ( ( inverse @ X4 ) != ( sk_c8 ) ) |
% 1.37/1.34 ( ( multiply @ X4 @ sk_c8 ) != ( sk_c7 ) ) |
% 1.37/1.34 ( ( inverse @ X3 ) != ( sk_c9 ) ) |
% 1.37/1.34 ( ( multiply @ X3 @ sk_c9 ) != ( sk_c8 ) ) ))).
% 1.37/1.34 thf(zf_stmt_0, negated_conjecture,
% 1.37/1.34 (( ( inverse @ X6 ) != ( sk_c7 ) ) |
% 1.37/1.34 ( ( multiply @ X6 @ sk_c7 ) != ( X5 ) ) |
% 1.37/1.34 ( ( multiply @ sk_c7 @ X5 ) != ( sk_c8 ) ) |
% 1.37/1.34 ( ( inverse @ X2 ) != ( sk_c7 ) ) |
% 1.37/1.34 ( ( multiply @ X2 @ sk_c7 ) != ( sk_c8 ) ) |
% 1.37/1.34 ( ( inverse @ X1 ) != ( sk_c9 ) ) |
% 1.37/1.34 ( ( multiply @ X1 @ sk_c9 ) != ( sk_c8 ) ) |
% 1.37/1.34 ( ( inverse @ X4 ) != ( sk_c8 ) ) |
% 1.37/1.34 ( ( multiply @ X4 @ sk_c8 ) != ( sk_c7 ) ) |
% 1.37/1.34 ( ( inverse @ X3 ) != ( sk_c9 ) ) |
% 1.37/1.34 ( ( multiply @ X3 @ sk_c9 ) != ( sk_c8 ) )),
% 1.37/1.34 inference('cnf.neg', [status(esa)], [prove_this_29])).
% 1.37/1.34 thf(zip_derived_cl31, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 1.37/1.34 (((inverse @ X0) != (sk_c7))
% 1.37/1.34 | ((multiply @ X0 @ sk_c7) != (X1))
% 1.37/1.34 | ((multiply @ sk_c7 @ X1) != (sk_c8))
% 1.37/1.34 | ((inverse @ X2) != (sk_c7))
% 1.37/1.34 | ((multiply @ X2 @ sk_c7) != (sk_c8))
% 1.37/1.34 | ((inverse @ X3) != (sk_c9))
% 1.37/1.34 | ((multiply @ X3 @ sk_c9) != (sk_c8))
% 1.37/1.34 | ((inverse @ X4) != (sk_c8))
% 1.37/1.34 | ((multiply @ X4 @ sk_c8) != (sk_c7))
% 1.37/1.34 | ((inverse @ X5) != (sk_c9))
% 1.37/1.34 | ((multiply @ X5 @ sk_c9) != (sk_c8)))),
% 1.37/1.34 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.37/1.34 thf(zip_derived_cl5935, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 1.37/1.34 (((X0) != (sk_c7))
% 1.37/1.34 | ((multiply @ X1 @ sk_c9) != (sk_c8))
% 1.37/1.34 | ((inverse @ X1) != (sk_c9))
% 1.37/1.34 | ((multiply @ X2 @ sk_c8) != (sk_c7))
% 1.37/1.34 | ((inverse @ X2) != (sk_c8))
% 1.37/1.34 | ((multiply @ X3 @ sk_c9) != (sk_c8))
% 1.37/1.34 | ((inverse @ X3) != (sk_c9))
% 1.37/1.34 | ((multiply @ X4 @ sk_c7) != (sk_c8))
% 1.37/1.34 | ((inverse @ X4) != (sk_c7))
% 1.37/1.34 | ((multiply @ sk_c7 @ X5) != (sk_c8))
% 1.37/1.34 | ((multiply @ (inverse @ X0) @ sk_c7) != (X5)))),
% 1.37/1.34 inference('sup-', [status(thm)], [zip_derived_cl5677, zip_derived_cl31])).
% 1.37/1.34 thf(zip_derived_cl6256, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.37/1.34 (((multiply @ (inverse @ sk_c7) @ sk_c7) != (X0))
% 1.37/1.34 | ((multiply @ sk_c7 @ X0) != (sk_c8))
% 1.37/1.34 | ((inverse @ X1) != (sk_c7))
% 1.37/1.34 | ((multiply @ X1 @ sk_c7) != (sk_c8))
% 1.37/1.34 | ((inverse @ X2) != (sk_c9))
% 1.37/1.34 | ((multiply @ X2 @ sk_c9) != (sk_c8))
% 1.37/1.34 | ((inverse @ X3) != (sk_c8))
% 1.37/1.34 | ((multiply @ X3 @ sk_c8) != (sk_c7))
% 1.37/1.34 | ((inverse @ X4) != (sk_c9))
% 1.37/1.34 | ((multiply @ X4 @ sk_c9) != (sk_c8)))),
% 1.37/1.34 inference('eq_res', [status(thm)], [zip_derived_cl5935])).
% 1.37/1.34 thf(zip_derived_cl1, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.37/1.34 inference('cnf', [status(esa)], [left_inverse])).
% 1.37/1.34 thf(zip_derived_cl6257, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.37/1.34 (((identity) != (X0))
% 1.37/1.34 | ((multiply @ sk_c7 @ X0) != (sk_c8))
% 1.37/1.34 | ((inverse @ X1) != (sk_c7))
% 1.37/1.34 | ((multiply @ X1 @ sk_c7) != (sk_c8))
% 1.37/1.34 | ((inverse @ X2) != (sk_c9))
% 1.37/1.34 | ((multiply @ X2 @ sk_c9) != (sk_c8))
% 1.37/1.34 | ((inverse @ X3) != (sk_c8))
% 1.37/1.34 | ((multiply @ X3 @ sk_c8) != (sk_c7))
% 1.37/1.34 | ((inverse @ X4) != (sk_c9))
% 1.37/1.34 | ((multiply @ X4 @ sk_c9) != (sk_c8)))),
% 1.37/1.34 inference('demod', [status(thm)], [zip_derived_cl6256, zip_derived_cl1])).
% 1.37/1.34 thf(zip_derived_cl6258, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.37/1.34 (((multiply @ X0 @ sk_c9) != (sk_c8))
% 1.37/1.34 | ((inverse @ X0) != (sk_c9))
% 1.37/1.34 | ((multiply @ X1 @ sk_c8) != (sk_c7))
% 1.37/1.34 | ((inverse @ X1) != (sk_c8))
% 1.37/1.34 | ((multiply @ X2 @ sk_c9) != (sk_c8))
% 1.37/1.34 | ((inverse @ X2) != (sk_c9))
% 1.37/1.34 | ((multiply @ X3 @ sk_c7) != (sk_c8))
% 1.37/1.34 | ((inverse @ X3) != (sk_c7))
% 1.37/1.34 | ((multiply @ sk_c7 @ identity) != (sk_c8)))),
% 1.37/1.34 inference('eq_res', [status(thm)], [zip_derived_cl6257])).
% 1.37/1.34 thf(zip_derived_cl5618, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl123, zip_derived_cl120])).
% 1.37/1.34 thf(zip_derived_cl6259, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.37/1.34 (((multiply @ X0 @ sk_c9) != (sk_c8))
% 1.37/1.34 | ((inverse @ X0) != (sk_c9))
% 1.37/1.34 | ((multiply @ X1 @ sk_c8) != (sk_c7))
% 1.37/1.34 | ((inverse @ X1) != (sk_c8))
% 1.37/1.34 | ((multiply @ X2 @ sk_c9) != (sk_c8))
% 1.37/1.34 | ((inverse @ X2) != (sk_c9))
% 1.37/1.34 | ((multiply @ X3 @ sk_c7) != (sk_c8))
% 1.37/1.34 | ((inverse @ X3) != (sk_c7))
% 1.37/1.34 | ((sk_c7) != (sk_c8)))),
% 1.37/1.34 inference('demod', [status(thm)],
% 1.37/1.34 [zip_derived_cl6258, zip_derived_cl5618])).
% 1.37/1.34 thf(zip_derived_cl6260, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.37/1.34 (((multiply @ X0 @ sk_c9) != (sk_c8))
% 1.37/1.34 | ((inverse @ X0) != (sk_c9))
% 1.37/1.34 | ((multiply @ X1 @ sk_c8) != (sk_c8))
% 1.37/1.34 | ((inverse @ X1) != (sk_c8))
% 1.37/1.34 | ((multiply @ X2 @ sk_c9) != (sk_c8))
% 1.37/1.34 | ((inverse @ X2) != (sk_c9))
% 1.37/1.34 | ((multiply @ X3 @ sk_c8) != (sk_c8))
% 1.37/1.34 | ((inverse @ X3) != (sk_c8))
% 1.37/1.34 | ((sk_c7) != (sk_c8)))),
% 1.37/1.34 inference('local_rewriting', [status(thm)], [zip_derived_cl6259])).
% 1.37/1.34 thf(prove_this_26, conjecture,
% 1.37/1.34 (~( ( ( multiply @ sk_c7 @ sk_c6 ) = ( sk_c8 ) ) |
% 1.37/1.34 ( ( inverse @ sk_c2 ) = ( sk_c8 ) ) ))).
% 1.37/1.34 thf(zf_stmt_1, negated_conjecture,
% 1.37/1.34 (( ( multiply @ sk_c7 @ sk_c6 ) = ( sk_c8 ) ) |
% 1.37/1.34 ( ( inverse @ sk_c2 ) = ( sk_c8 ) )),
% 1.37/1.34 inference('cnf.neg', [status(esa)], [prove_this_26])).
% 1.37/1.34 thf(zip_derived_cl28, plain,
% 1.37/1.34 ((((multiply @ sk_c7 @ sk_c6) = (sk_c8)) | ((inverse @ sk_c2) = (sk_c8)))),
% 1.37/1.34 inference('cnf', [status(esa)], [zf_stmt_1])).
% 1.37/1.34 thf(zip_derived_cl5677, plain,
% 1.37/1.34 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl5618, zip_derived_cl123])).
% 1.37/1.34 thf(zip_derived_cl5953, plain,
% 1.37/1.34 ((((sk_c2) = (inverse @ sk_c8)) | ((multiply @ sk_c7 @ sk_c6) = (sk_c8)))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl28, zip_derived_cl5677])).
% 1.37/1.34 thf(prove_this_19, conjecture,
% 1.37/1.34 (~( ( ( multiply @ sk_c7 @ sk_c6 ) = ( sk_c8 ) ) |
% 1.37/1.34 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) ) ))).
% 1.37/1.34 thf(zf_stmt_2, negated_conjecture,
% 1.37/1.34 (( ( multiply @ sk_c7 @ sk_c6 ) = ( sk_c8 ) ) |
% 1.37/1.34 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) )),
% 1.37/1.34 inference('cnf.neg', [status(esa)], [prove_this_19])).
% 1.37/1.34 thf(zip_derived_cl21, plain,
% 1.37/1.34 ((((multiply @ sk_c7 @ sk_c6) = (sk_c8))
% 1.37/1.34 | ((multiply @ sk_c2 @ sk_c8) = (sk_c7)))),
% 1.37/1.34 inference('cnf', [status(esa)], [zf_stmt_2])).
% 1.37/1.34 thf(zip_derived_cl8229, plain,
% 1.37/1.34 ((((multiply @ (inverse @ sk_c8) @ sk_c8) = (sk_c7))
% 1.37/1.34 | ((multiply @ sk_c7 @ sk_c6) = (sk_c8))
% 1.37/1.34 | ((multiply @ sk_c7 @ sk_c6) = (sk_c8)))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl5953, zip_derived_cl21])).
% 1.37/1.34 thf(zip_derived_cl1, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.37/1.34 inference('cnf', [status(esa)], [left_inverse])).
% 1.37/1.34 thf(zip_derived_cl8247, plain,
% 1.37/1.34 ((((identity) = (sk_c7))
% 1.37/1.34 | ((multiply @ sk_c7 @ sk_c6) = (sk_c8))
% 1.37/1.34 | ((multiply @ sk_c7 @ sk_c6) = (sk_c8)))),
% 1.37/1.34 inference('demod', [status(thm)], [zip_derived_cl8229, zip_derived_cl1])).
% 1.37/1.34 thf(zip_derived_cl8248, plain,
% 1.37/1.34 ((((multiply @ sk_c7 @ sk_c6) = (sk_c8)) | ((identity) = (sk_c7)))),
% 1.37/1.34 inference('simplify', [status(thm)], [zip_derived_cl8247])).
% 1.37/1.34 thf(prove_this_28, conjecture,
% 1.37/1.34 (~( ( ( inverse @ sk_c5 ) = ( sk_c7 ) ) |
% 1.37/1.34 ( ( inverse @ sk_c2 ) = ( sk_c8 ) ) ))).
% 1.37/1.34 thf(zf_stmt_3, negated_conjecture,
% 1.37/1.34 (( ( inverse @ sk_c5 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c8 ) )),
% 1.37/1.34 inference('cnf.neg', [status(esa)], [prove_this_28])).
% 1.37/1.34 thf(zip_derived_cl30, plain,
% 1.37/1.34 ((((inverse @ sk_c5) = (sk_c7)) | ((inverse @ sk_c2) = (sk_c8)))),
% 1.37/1.34 inference('cnf', [status(esa)], [zf_stmt_3])).
% 1.37/1.34 thf(zip_derived_cl1, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.37/1.34 inference('cnf', [status(esa)], [left_inverse])).
% 1.37/1.34 thf(zip_derived_cl48, plain,
% 1.37/1.34 ((((multiply @ sk_c8 @ sk_c2) = (identity))
% 1.37/1.34 | ((inverse @ sk_c5) = (sk_c7)))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl1])).
% 1.37/1.34 thf(zip_derived_cl110, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i]:
% 1.37/1.34 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.37/1.34 inference('demod', [status(thm)], [zip_derived_cl90, zip_derived_cl0])).
% 1.37/1.34 thf(zip_derived_cl129, plain,
% 1.37/1.34 ((((sk_c2) = (multiply @ (inverse @ sk_c8) @ identity))
% 1.37/1.34 | ((inverse @ sk_c5) = (sk_c7)))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl48, zip_derived_cl110])).
% 1.37/1.34 thf(prove_this_21, conjecture,
% 1.37/1.34 (~( ( ( inverse @ sk_c5 ) = ( sk_c7 ) ) |
% 1.37/1.34 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) ) ))).
% 1.37/1.34 thf(zf_stmt_4, negated_conjecture,
% 1.37/1.34 (( ( inverse @ sk_c5 ) = ( sk_c7 ) ) |
% 1.37/1.34 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) )),
% 1.37/1.34 inference('cnf.neg', [status(esa)], [prove_this_21])).
% 1.37/1.34 thf(zip_derived_cl23, plain,
% 1.37/1.34 ((((inverse @ sk_c5) = (sk_c7)) | ((multiply @ sk_c2 @ sk_c8) = (sk_c7)))),
% 1.37/1.34 inference('cnf', [status(esa)], [zf_stmt_4])).
% 1.37/1.34 thf(zip_derived_cl258, plain,
% 1.37/1.34 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c8)
% 1.37/1.34 = (sk_c7))
% 1.37/1.34 | ((inverse @ sk_c5) = (sk_c7))
% 1.37/1.34 | ((inverse @ sk_c5) = (sk_c7)))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl129, zip_derived_cl23])).
% 1.37/1.34 thf(zip_derived_cl2, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.37/1.34 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.37/1.34 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.37/1.34 inference('cnf', [status(esa)], [associativity])).
% 1.37/1.34 thf(zip_derived_cl0, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.37/1.34 inference('cnf', [status(esa)], [left_identity])).
% 1.37/1.34 thf(zip_derived_cl1, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.37/1.34 inference('cnf', [status(esa)], [left_inverse])).
% 1.37/1.34 thf(zip_derived_cl275, plain,
% 1.37/1.34 ((((identity) = (sk_c7))
% 1.37/1.34 | ((inverse @ sk_c5) = (sk_c7))
% 1.37/1.34 | ((inverse @ sk_c5) = (sk_c7)))),
% 1.37/1.34 inference('demod', [status(thm)],
% 1.37/1.34 [zip_derived_cl258, zip_derived_cl2, zip_derived_cl0,
% 1.37/1.34 zip_derived_cl1])).
% 1.37/1.34 thf(zip_derived_cl276, plain,
% 1.37/1.34 ((((inverse @ sk_c5) = (sk_c7)) | ((identity) = (sk_c7)))),
% 1.37/1.34 inference('simplify', [status(thm)], [zip_derived_cl275])).
% 1.37/1.34 thf(prove_this_27, conjecture,
% 1.37/1.34 (~( ( ( multiply @ sk_c5 @ sk_c7 ) = ( sk_c6 ) ) |
% 1.37/1.34 ( ( inverse @ sk_c2 ) = ( sk_c8 ) ) ))).
% 1.37/1.34 thf(zf_stmt_5, negated_conjecture,
% 1.37/1.34 (( ( multiply @ sk_c5 @ sk_c7 ) = ( sk_c6 ) ) |
% 1.37/1.34 ( ( inverse @ sk_c2 ) = ( sk_c8 ) )),
% 1.37/1.34 inference('cnf.neg', [status(esa)], [prove_this_27])).
% 1.37/1.34 thf(zip_derived_cl29, plain,
% 1.37/1.34 ((((multiply @ sk_c5 @ sk_c7) = (sk_c6)) | ((inverse @ sk_c2) = (sk_c8)))),
% 1.37/1.34 inference('cnf', [status(esa)], [zf_stmt_5])).
% 1.37/1.34 thf(zip_derived_cl123, plain,
% 1.37/1.34 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl110])).
% 1.37/1.34 thf(zip_derived_cl477, plain,
% 1.37/1.34 ((((sk_c2) = (multiply @ (inverse @ sk_c8) @ identity))
% 1.37/1.34 | ((multiply @ sk_c5 @ sk_c7) = (sk_c6)))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl29, zip_derived_cl123])).
% 1.37/1.34 thf(prove_this_20, conjecture,
% 1.37/1.34 (~( ( ( multiply @ sk_c5 @ sk_c7 ) = ( sk_c6 ) ) |
% 1.37/1.34 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) ) ))).
% 1.37/1.34 thf(zf_stmt_6, negated_conjecture,
% 1.37/1.34 (( ( multiply @ sk_c5 @ sk_c7 ) = ( sk_c6 ) ) |
% 1.37/1.34 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) )),
% 1.37/1.34 inference('cnf.neg', [status(esa)], [prove_this_20])).
% 1.37/1.34 thf(zip_derived_cl22, plain,
% 1.37/1.34 ((((multiply @ sk_c5 @ sk_c7) = (sk_c6))
% 1.37/1.34 | ((multiply @ sk_c2 @ sk_c8) = (sk_c7)))),
% 1.37/1.34 inference('cnf', [status(esa)], [zf_stmt_6])).
% 1.37/1.34 thf(zip_derived_cl4044, plain,
% 1.37/1.34 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c8)
% 1.37/1.34 = (sk_c7))
% 1.37/1.34 | ((multiply @ sk_c5 @ sk_c7) = (sk_c6))
% 1.37/1.34 | ((multiply @ sk_c5 @ sk_c7) = (sk_c6)))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl477, zip_derived_cl22])).
% 1.37/1.34 thf(zip_derived_cl2, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.37/1.34 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.37/1.34 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.37/1.34 inference('cnf', [status(esa)], [associativity])).
% 1.37/1.34 thf(zip_derived_cl0, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.37/1.34 inference('cnf', [status(esa)], [left_identity])).
% 1.37/1.34 thf(zip_derived_cl1, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.37/1.34 inference('cnf', [status(esa)], [left_inverse])).
% 1.37/1.34 thf(zip_derived_cl4062, plain,
% 1.37/1.34 ((((identity) = (sk_c7))
% 1.37/1.34 | ((multiply @ sk_c5 @ sk_c7) = (sk_c6))
% 1.37/1.34 | ((multiply @ sk_c5 @ sk_c7) = (sk_c6)))),
% 1.37/1.34 inference('demod', [status(thm)],
% 1.37/1.34 [zip_derived_cl4044, zip_derived_cl2, zip_derived_cl0,
% 1.37/1.34 zip_derived_cl1])).
% 1.37/1.34 thf(zip_derived_cl4063, plain,
% 1.37/1.34 ((((multiply @ sk_c5 @ sk_c7) = (sk_c6)) | ((identity) = (sk_c7)))),
% 1.37/1.34 inference('simplify', [status(thm)], [zip_derived_cl4062])).
% 1.37/1.34 thf(zip_derived_cl110, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i]:
% 1.37/1.34 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.37/1.34 inference('demod', [status(thm)], [zip_derived_cl90, zip_derived_cl0])).
% 1.37/1.34 thf(zip_derived_cl4070, plain,
% 1.37/1.34 ((((sk_c7) = (multiply @ (inverse @ sk_c5) @ sk_c6))
% 1.37/1.34 | ((identity) = (sk_c7)))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl4063, zip_derived_cl110])).
% 1.37/1.34 thf(zip_derived_cl4245, plain,
% 1.37/1.34 ((((sk_c7) = (multiply @ sk_c7 @ sk_c6))
% 1.37/1.34 | ((identity) = (sk_c7))
% 1.37/1.34 | ((identity) = (sk_c7)))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl276, zip_derived_cl4070])).
% 1.37/1.34 thf(zip_derived_cl4256, plain,
% 1.37/1.34 ((((identity) = (sk_c7)) | ((sk_c7) = (multiply @ sk_c7 @ sk_c6)))),
% 1.37/1.34 inference('simplify', [status(thm)], [zip_derived_cl4245])).
% 1.37/1.34 thf(zip_derived_cl8543, plain,
% 1.37/1.34 ((((sk_c7) = (sk_c8)) | ((identity) = (sk_c7)) | ((identity) = (sk_c7)))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl8248, zip_derived_cl4256])).
% 1.37/1.34 thf(zip_derived_cl8600, plain,
% 1.37/1.34 ((((identity) = (sk_c7)) | ((sk_c7) = (sk_c8)))),
% 1.37/1.34 inference('simplify', [status(thm)], [zip_derived_cl8543])).
% 1.37/1.34 thf(zip_derived_cl8870, plain,
% 1.37/1.34 ((((sk_c8) != (identity)) | ((identity) = (sk_c7)))),
% 1.37/1.34 inference('eq_fact', [status(thm)], [zip_derived_cl8600])).
% 1.37/1.34 thf(prove_this_25, conjecture,
% 1.37/1.34 (~( ( ( inverse @ sk_c4 ) = ( sk_c7 ) ) |
% 1.37/1.34 ( ( inverse @ sk_c2 ) = ( sk_c8 ) ) ))).
% 1.37/1.34 thf(zf_stmt_7, negated_conjecture,
% 1.37/1.34 (( ( inverse @ sk_c4 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c8 ) )),
% 1.37/1.34 inference('cnf.neg', [status(esa)], [prove_this_25])).
% 1.37/1.34 thf(zip_derived_cl27, plain,
% 1.37/1.34 ((((inverse @ sk_c4) = (sk_c7)) | ((inverse @ sk_c2) = (sk_c8)))),
% 1.37/1.34 inference('cnf', [status(esa)], [zf_stmt_7])).
% 1.37/1.34 thf(zip_derived_cl1, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.37/1.34 inference('cnf', [status(esa)], [left_inverse])).
% 1.37/1.34 thf(zip_derived_cl38, plain,
% 1.37/1.34 ((((multiply @ sk_c8 @ sk_c2) = (identity))
% 1.37/1.34 | ((inverse @ sk_c4) = (sk_c7)))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl1])).
% 1.37/1.34 thf(zip_derived_cl110, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i]:
% 1.37/1.34 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.37/1.34 inference('demod', [status(thm)], [zip_derived_cl90, zip_derived_cl0])).
% 1.37/1.34 thf(zip_derived_cl127, plain,
% 1.37/1.34 ((((sk_c2) = (multiply @ (inverse @ sk_c8) @ identity))
% 1.37/1.34 | ((inverse @ sk_c4) = (sk_c7)))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl38, zip_derived_cl110])).
% 1.37/1.34 thf(prove_this_18, conjecture,
% 1.37/1.34 (~( ( ( inverse @ sk_c4 ) = ( sk_c7 ) ) |
% 1.37/1.34 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) ) ))).
% 1.37/1.34 thf(zf_stmt_8, negated_conjecture,
% 1.37/1.34 (( ( inverse @ sk_c4 ) = ( sk_c7 ) ) |
% 1.37/1.34 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) )),
% 1.37/1.34 inference('cnf.neg', [status(esa)], [prove_this_18])).
% 1.37/1.34 thf(zip_derived_cl20, plain,
% 1.37/1.34 ((((inverse @ sk_c4) = (sk_c7)) | ((multiply @ sk_c2 @ sk_c8) = (sk_c7)))),
% 1.37/1.34 inference('cnf', [status(esa)], [zf_stmt_8])).
% 1.37/1.34 thf(zip_derived_cl190, plain,
% 1.37/1.34 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c8)
% 1.37/1.34 = (sk_c7))
% 1.37/1.34 | ((inverse @ sk_c4) = (sk_c7))
% 1.37/1.34 | ((inverse @ sk_c4) = (sk_c7)))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl127, zip_derived_cl20])).
% 1.37/1.34 thf(zip_derived_cl2, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.37/1.34 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.37/1.34 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.37/1.34 inference('cnf', [status(esa)], [associativity])).
% 1.37/1.34 thf(zip_derived_cl0, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.37/1.34 inference('cnf', [status(esa)], [left_identity])).
% 1.37/1.34 thf(zip_derived_cl1, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.37/1.34 inference('cnf', [status(esa)], [left_inverse])).
% 1.37/1.34 thf(zip_derived_cl207, plain,
% 1.37/1.34 ((((identity) = (sk_c7))
% 1.37/1.34 | ((inverse @ sk_c4) = (sk_c7))
% 1.37/1.34 | ((inverse @ sk_c4) = (sk_c7)))),
% 1.37/1.34 inference('demod', [status(thm)],
% 1.37/1.34 [zip_derived_cl190, zip_derived_cl2, zip_derived_cl0,
% 1.37/1.34 zip_derived_cl1])).
% 1.37/1.34 thf(zip_derived_cl208, plain,
% 1.37/1.34 ((((inverse @ sk_c4) = (sk_c7)) | ((identity) = (sk_c7)))),
% 1.37/1.34 inference('simplify', [status(thm)], [zip_derived_cl207])).
% 1.37/1.34 thf(prove_this_24, conjecture,
% 1.37/1.34 (~( ( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 1.37/1.34 ( ( inverse @ sk_c2 ) = ( sk_c8 ) ) ))).
% 1.37/1.34 thf(zf_stmt_9, negated_conjecture,
% 1.37/1.34 (( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 1.37/1.34 ( ( inverse @ sk_c2 ) = ( sk_c8 ) )),
% 1.37/1.34 inference('cnf.neg', [status(esa)], [prove_this_24])).
% 1.37/1.34 thf(zip_derived_cl26, plain,
% 1.37/1.34 ((((multiply @ sk_c4 @ sk_c7) = (sk_c8)) | ((inverse @ sk_c2) = (sk_c8)))),
% 1.37/1.34 inference('cnf', [status(esa)], [zf_stmt_9])).
% 1.37/1.34 thf(zip_derived_cl5677, plain,
% 1.37/1.34 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl5618, zip_derived_cl123])).
% 1.37/1.34 thf(zip_derived_cl5951, plain,
% 1.37/1.34 ((((sk_c2) = (inverse @ sk_c8)) | ((multiply @ sk_c4 @ sk_c7) = (sk_c8)))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl5677])).
% 1.37/1.34 thf(prove_this_17, conjecture,
% 1.37/1.34 (~( ( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 1.37/1.34 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) ) ))).
% 1.37/1.34 thf(zf_stmt_10, negated_conjecture,
% 1.37/1.34 (( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 1.37/1.34 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) )),
% 1.37/1.34 inference('cnf.neg', [status(esa)], [prove_this_17])).
% 1.37/1.34 thf(zip_derived_cl19, plain,
% 1.37/1.34 ((((multiply @ sk_c4 @ sk_c7) = (sk_c8))
% 1.37/1.34 | ((multiply @ sk_c2 @ sk_c8) = (sk_c7)))),
% 1.37/1.34 inference('cnf', [status(esa)], [zf_stmt_10])).
% 1.37/1.34 thf(zip_derived_cl8189, plain,
% 1.37/1.34 ((((multiply @ (inverse @ sk_c8) @ sk_c8) = (sk_c7))
% 1.37/1.34 | ((multiply @ sk_c4 @ sk_c7) = (sk_c8))
% 1.37/1.34 | ((multiply @ sk_c4 @ sk_c7) = (sk_c8)))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl5951, zip_derived_cl19])).
% 1.37/1.34 thf(zip_derived_cl1, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.37/1.34 inference('cnf', [status(esa)], [left_inverse])).
% 1.37/1.34 thf(zip_derived_cl8207, plain,
% 1.37/1.34 ((((identity) = (sk_c7))
% 1.37/1.34 | ((multiply @ sk_c4 @ sk_c7) = (sk_c8))
% 1.37/1.34 | ((multiply @ sk_c4 @ sk_c7) = (sk_c8)))),
% 1.37/1.34 inference('demod', [status(thm)], [zip_derived_cl8189, zip_derived_cl1])).
% 1.37/1.34 thf(zip_derived_cl8208, plain,
% 1.37/1.34 ((((multiply @ sk_c4 @ sk_c7) = (sk_c8)) | ((identity) = (sk_c7)))),
% 1.37/1.34 inference('simplify', [status(thm)], [zip_derived_cl8207])).
% 1.37/1.34 thf(zip_derived_cl8276, plain,
% 1.37/1.34 ((((multiply @ sk_c4 @ (inverse @ sk_c4)) = (sk_c8))
% 1.37/1.34 | ((identity) = (sk_c7))
% 1.37/1.34 | ((identity) = (sk_c7)))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl208, zip_derived_cl8208])).
% 1.37/1.34 thf(zip_derived_cl5677, plain,
% 1.37/1.34 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl5618, zip_derived_cl123])).
% 1.37/1.34 thf(zip_derived_cl1, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.37/1.34 inference('cnf', [status(esa)], [left_inverse])).
% 1.37/1.34 thf(zip_derived_cl5934, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl5677, zip_derived_cl1])).
% 1.37/1.34 thf(zip_derived_cl8303, plain,
% 1.37/1.34 ((((identity) = (sk_c8))
% 1.37/1.34 | ((identity) = (sk_c7))
% 1.37/1.34 | ((identity) = (sk_c7)))),
% 1.37/1.34 inference('demod', [status(thm)],
% 1.37/1.34 [zip_derived_cl8276, zip_derived_cl5934])).
% 1.37/1.34 thf(zip_derived_cl8304, plain,
% 1.37/1.34 ((((identity) = (sk_c7)) | ((identity) = (sk_c8)))),
% 1.37/1.34 inference('simplify', [status(thm)], [zip_derived_cl8303])).
% 1.37/1.34 thf(zip_derived_cl8988, plain, (((identity) = (sk_c7))),
% 1.37/1.34 inference('clc', [status(thm)], [zip_derived_cl8870, zip_derived_cl8304])).
% 1.37/1.34 thf(zip_derived_cl9077, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.37/1.34 (((multiply @ X0 @ sk_c9) != (sk_c8))
% 1.37/1.34 | ((inverse @ X0) != (sk_c9))
% 1.37/1.34 | ((multiply @ X1 @ sk_c8) != (sk_c8))
% 1.37/1.34 | ((inverse @ X1) != (sk_c8))
% 1.37/1.34 | ((multiply @ X2 @ sk_c9) != (sk_c8))
% 1.37/1.34 | ((inverse @ X2) != (sk_c9))
% 1.37/1.34 | ((multiply @ X3 @ sk_c8) != (sk_c8))
% 1.37/1.34 | ((inverse @ X3) != (sk_c8))
% 1.37/1.34 | ((identity) != (sk_c8)))),
% 1.37/1.34 inference('demod', [status(thm)],
% 1.37/1.34 [zip_derived_cl6260, zip_derived_cl8988])).
% 1.37/1.34 thf(zip_derived_cl9078, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.37/1.34 (((multiply @ X0 @ sk_c9) != (identity))
% 1.37/1.34 | ((inverse @ X0) != (sk_c9))
% 1.37/1.34 | ((multiply @ X1 @ identity) != (identity))
% 1.37/1.34 | ((inverse @ X1) != (identity))
% 1.37/1.34 | ((multiply @ X2 @ sk_c9) != (identity))
% 1.37/1.34 | ((inverse @ X2) != (sk_c9))
% 1.37/1.34 | ((multiply @ X3 @ identity) != (identity))
% 1.37/1.34 | ((inverse @ X3) != (identity))
% 1.37/1.34 | ((identity) != (sk_c8)))),
% 1.37/1.34 inference('local_rewriting', [status(thm)], [zip_derived_cl9077])).
% 1.37/1.34 thf(zip_derived_cl5618, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl123, zip_derived_cl120])).
% 1.37/1.34 thf(zip_derived_cl5618, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl123, zip_derived_cl120])).
% 1.37/1.34 thf(zip_derived_cl9079, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.37/1.34 (((multiply @ X0 @ sk_c9) != (identity))
% 1.37/1.34 | ((inverse @ X0) != (sk_c9))
% 1.37/1.34 | ((X1) != (identity))
% 1.37/1.34 | ((inverse @ X1) != (identity))
% 1.37/1.34 | ((multiply @ X2 @ sk_c9) != (identity))
% 1.37/1.34 | ((inverse @ X2) != (sk_c9))
% 1.37/1.34 | ((X3) != (identity))
% 1.37/1.34 | ((inverse @ X3) != (identity))
% 1.37/1.34 | ((identity) != (sk_c8)))),
% 1.37/1.34 inference('demod', [status(thm)],
% 1.37/1.34 [zip_derived_cl9078, zip_derived_cl5618, zip_derived_cl5618])).
% 1.37/1.34 thf(prove_this_8, conjecture,
% 1.37/1.34 (~( ( ( multiply @ sk_c3 @ sk_c9 ) = ( sk_c8 ) ) |
% 1.37/1.34 ( ( inverse @ sk_c1 ) = ( sk_c9 ) ) ))).
% 1.37/1.34 thf(zf_stmt_11, negated_conjecture,
% 1.37/1.34 (( ( multiply @ sk_c3 @ sk_c9 ) = ( sk_c8 ) ) |
% 1.37/1.34 ( ( inverse @ sk_c1 ) = ( sk_c9 ) )),
% 1.37/1.34 inference('cnf.neg', [status(esa)], [prove_this_8])).
% 1.37/1.34 thf(zip_derived_cl10, plain,
% 1.37/1.34 ((((multiply @ sk_c3 @ sk_c9) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c9)))),
% 1.37/1.34 inference('cnf', [status(esa)], [zf_stmt_11])).
% 1.37/1.34 thf(prove_this_9, conjecture,
% 1.37/1.34 (~( ( ( inverse @ sk_c3 ) = ( sk_c9 ) ) |
% 1.37/1.34 ( ( inverse @ sk_c1 ) = ( sk_c9 ) ) ))).
% 1.37/1.34 thf(zf_stmt_12, negated_conjecture,
% 1.37/1.34 (( ( inverse @ sk_c3 ) = ( sk_c9 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c9 ) )),
% 1.37/1.34 inference('cnf.neg', [status(esa)], [prove_this_9])).
% 1.37/1.34 thf(zip_derived_cl11, plain,
% 1.37/1.34 ((((inverse @ sk_c3) = (sk_c9)) | ((inverse @ sk_c1) = (sk_c9)))),
% 1.37/1.34 inference('cnf', [status(esa)], [zf_stmt_12])).
% 1.37/1.34 thf(zip_derived_cl11, plain,
% 1.37/1.34 ((((inverse @ sk_c3) = (sk_c9)) | ((inverse @ sk_c1) = (sk_c9)))),
% 1.37/1.34 inference('cnf', [status(esa)], [zf_stmt_12])).
% 1.37/1.34 thf(zip_derived_cl1, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.37/1.34 inference('cnf', [status(esa)], [left_inverse])).
% 1.37/1.34 thf(zip_derived_cl34, plain,
% 1.37/1.34 ((((multiply @ sk_c9 @ sk_c3) = (identity))
% 1.37/1.34 | ((inverse @ sk_c1) = (sk_c9)))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl1])).
% 1.37/1.34 thf(zip_derived_cl110, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i]:
% 1.37/1.34 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.37/1.34 inference('demod', [status(thm)], [zip_derived_cl90, zip_derived_cl0])).
% 1.37/1.34 thf(zip_derived_cl125, plain,
% 1.37/1.34 ((((sk_c3) = (multiply @ (inverse @ sk_c9) @ identity))
% 1.37/1.34 | ((inverse @ sk_c1) = (sk_c9)))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl34, zip_derived_cl110])).
% 1.37/1.34 thf(zip_derived_cl5618, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl123, zip_derived_cl120])).
% 1.37/1.34 thf(zip_derived_cl5641, plain,
% 1.37/1.34 ((((sk_c3) = (inverse @ sk_c9)) | ((inverse @ sk_c1) = (sk_c9)))),
% 1.37/1.34 inference('demod', [status(thm)], [zip_derived_cl125, zip_derived_cl5618])).
% 1.37/1.34 thf(zip_derived_cl11, plain,
% 1.37/1.34 ((((inverse @ sk_c3) = (sk_c9)) | ((inverse @ sk_c1) = (sk_c9)))),
% 1.37/1.34 inference('cnf', [status(esa)], [zf_stmt_12])).
% 1.37/1.34 thf(zip_derived_cl125, plain,
% 1.37/1.34 ((((sk_c3) = (multiply @ (inverse @ sk_c9) @ identity))
% 1.37/1.34 | ((inverse @ sk_c1) = (sk_c9)))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl34, zip_derived_cl110])).
% 1.37/1.34 thf(zip_derived_cl10, plain,
% 1.37/1.34 ((((multiply @ sk_c3 @ sk_c9) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c9)))),
% 1.37/1.34 inference('cnf', [status(esa)], [zf_stmt_11])).
% 1.37/1.34 thf(zip_derived_cl160, plain,
% 1.37/1.34 ((((multiply @ (multiply @ (inverse @ sk_c9) @ identity) @ sk_c9)
% 1.37/1.34 = (sk_c8))
% 1.37/1.34 | ((inverse @ sk_c1) = (sk_c9))
% 1.37/1.34 | ((inverse @ sk_c1) = (sk_c9)))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl125, zip_derived_cl10])).
% 1.37/1.34 thf(zip_derived_cl2, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.37/1.34 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.37/1.34 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.37/1.34 inference('cnf', [status(esa)], [associativity])).
% 1.37/1.34 thf(zip_derived_cl0, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.37/1.34 inference('cnf', [status(esa)], [left_identity])).
% 1.37/1.34 thf(zip_derived_cl1, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.37/1.34 inference('cnf', [status(esa)], [left_inverse])).
% 1.37/1.34 thf(zip_derived_cl165, plain,
% 1.37/1.34 ((((identity) = (sk_c8))
% 1.37/1.34 | ((inverse @ sk_c1) = (sk_c9))
% 1.37/1.34 | ((inverse @ sk_c1) = (sk_c9)))),
% 1.37/1.34 inference('demod', [status(thm)],
% 1.37/1.34 [zip_derived_cl160, zip_derived_cl2, zip_derived_cl0,
% 1.37/1.34 zip_derived_cl1])).
% 1.37/1.34 thf(zip_derived_cl166, plain,
% 1.37/1.34 ((((inverse @ sk_c1) = (sk_c9)) | ((identity) = (sk_c8)))),
% 1.37/1.34 inference('simplify', [status(thm)], [zip_derived_cl165])).
% 1.37/1.34 thf(zip_derived_cl9079, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.37/1.34 (((multiply @ X0 @ sk_c9) != (identity))
% 1.37/1.34 | ((inverse @ X0) != (sk_c9))
% 1.37/1.34 | ((X1) != (identity))
% 1.37/1.34 | ((inverse @ X1) != (identity))
% 1.37/1.34 | ((multiply @ X2 @ sk_c9) != (identity))
% 1.37/1.34 | ((inverse @ X2) != (sk_c9))
% 1.37/1.34 | ((X3) != (identity))
% 1.37/1.34 | ((inverse @ X3) != (identity))
% 1.37/1.34 | ((identity) != (sk_c8)))),
% 1.37/1.34 inference('demod', [status(thm)],
% 1.37/1.34 [zip_derived_cl9078, zip_derived_cl5618, zip_derived_cl5618])).
% 1.37/1.34 thf(zip_derived_cl9202, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.37/1.34 (((identity) != (identity))
% 1.37/1.34 | ((inverse @ sk_c1) = (sk_c9))
% 1.37/1.34 | ((inverse @ X0) != (identity))
% 1.37/1.34 | ((X0) != (identity))
% 1.37/1.34 | ((inverse @ X1) != (sk_c9))
% 1.37/1.34 | ((multiply @ X1 @ sk_c9) != (identity))
% 1.37/1.34 | ((inverse @ X2) != (identity))
% 1.37/1.34 | ((X2) != (identity))
% 1.37/1.34 | ((inverse @ X3) != (sk_c9))
% 1.37/1.34 | ((multiply @ X3 @ sk_c9) != (identity)))),
% 1.37/1.34 inference('sup-', [status(thm)], [zip_derived_cl166, zip_derived_cl9079])).
% 1.37/1.34 thf(zip_derived_cl9204, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.37/1.34 (((multiply @ X3 @ sk_c9) != (identity))
% 1.37/1.34 | ((inverse @ X3) != (sk_c9))
% 1.37/1.34 | ((X2) != (identity))
% 1.37/1.34 | ((inverse @ X2) != (identity))
% 1.37/1.34 | ((multiply @ X1 @ sk_c9) != (identity))
% 1.37/1.34 | ((inverse @ X1) != (sk_c9))
% 1.37/1.34 | ((X0) != (identity))
% 1.37/1.34 | ((inverse @ X0) != (identity))
% 1.37/1.34 | ((inverse @ sk_c1) = (sk_c9)))),
% 1.37/1.34 inference('simplify', [status(thm)], [zip_derived_cl9202])).
% 1.37/1.34 thf(zip_derived_cl10517, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.37/1.34 (((inverse @ sk_c1) = (sk_c9))
% 1.37/1.34 | ((inverse @ X0) != (identity))
% 1.37/1.34 | ((X0) != (identity))
% 1.37/1.34 | ((inverse @ X1) != (sk_c9))
% 1.37/1.34 | ((multiply @ X1 @ sk_c9) != (identity))
% 1.37/1.34 | ((inverse @ identity) != (identity))
% 1.37/1.34 | ((inverse @ X2) != (sk_c9))
% 1.37/1.34 | ((multiply @ X2 @ sk_c9) != (identity)))),
% 1.37/1.34 inference('eq_res', [status(thm)], [zip_derived_cl9204])).
% 1.37/1.34 thf(zip_derived_cl0, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.37/1.34 inference('cnf', [status(esa)], [left_identity])).
% 1.37/1.34 thf(zip_derived_cl110, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i]:
% 1.37/1.34 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.37/1.34 inference('demod', [status(thm)], [zip_derived_cl90, zip_derived_cl0])).
% 1.37/1.34 thf(zip_derived_cl122, plain,
% 1.37/1.34 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl110])).
% 1.37/1.34 thf(zip_derived_cl110, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i]:
% 1.37/1.34 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.37/1.34 inference('demod', [status(thm)], [zip_derived_cl90, zip_derived_cl0])).
% 1.37/1.34 thf(zip_derived_cl156, plain,
% 1.37/1.34 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ identity)) @ X0))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl122, zip_derived_cl110])).
% 1.37/1.34 thf(zip_derived_cl1, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.37/1.34 inference('cnf', [status(esa)], [left_inverse])).
% 1.37/1.34 thf(zip_derived_cl610, plain, (((inverse @ identity) = (identity))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl156, zip_derived_cl1])).
% 1.37/1.34 thf(zip_derived_cl10518, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.37/1.34 (((inverse @ sk_c1) = (sk_c9))
% 1.37/1.34 | ((inverse @ X0) != (identity))
% 1.37/1.34 | ((X0) != (identity))
% 1.37/1.34 | ((inverse @ X1) != (sk_c9))
% 1.37/1.34 | ((multiply @ X1 @ sk_c9) != (identity))
% 1.37/1.34 | ((identity) != (identity))
% 1.37/1.34 | ((inverse @ X2) != (sk_c9))
% 1.37/1.34 | ((multiply @ X2 @ sk_c9) != (identity)))),
% 1.37/1.34 inference('demod', [status(thm)],
% 1.37/1.34 [zip_derived_cl10517, zip_derived_cl610])).
% 1.37/1.34 thf(zip_derived_cl10519, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.37/1.34 (((multiply @ X2 @ sk_c9) != (identity))
% 1.37/1.34 | ((inverse @ X2) != (sk_c9))
% 1.37/1.34 | ((multiply @ X1 @ sk_c9) != (identity))
% 1.37/1.34 | ((inverse @ X1) != (sk_c9))
% 1.37/1.34 | ((X0) != (identity))
% 1.37/1.34 | ((inverse @ X0) != (identity))
% 1.37/1.34 | ((inverse @ sk_c1) = (sk_c9)))),
% 1.37/1.34 inference('simplify', [status(thm)], [zip_derived_cl10518])).
% 1.37/1.34 thf(zip_derived_cl10520, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i]:
% 1.37/1.34 (((inverse @ sk_c1) = (sk_c9))
% 1.37/1.34 | ((inverse @ identity) != (identity))
% 1.37/1.34 | ((inverse @ X0) != (sk_c9))
% 1.37/1.34 | ((multiply @ X0 @ sk_c9) != (identity))
% 1.37/1.34 | ((inverse @ X1) != (sk_c9))
% 1.37/1.34 | ((multiply @ X1 @ sk_c9) != (identity)))),
% 1.37/1.34 inference('eq_res', [status(thm)], [zip_derived_cl10519])).
% 1.37/1.34 thf(zip_derived_cl610, plain, (((inverse @ identity) = (identity))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl156, zip_derived_cl1])).
% 1.37/1.34 thf(zip_derived_cl10521, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i]:
% 1.37/1.34 (((inverse @ sk_c1) = (sk_c9))
% 1.37/1.34 | ((identity) != (identity))
% 1.37/1.34 | ((inverse @ X0) != (sk_c9))
% 1.37/1.34 | ((multiply @ X0 @ sk_c9) != (identity))
% 1.37/1.34 | ((inverse @ X1) != (sk_c9))
% 1.37/1.34 | ((multiply @ X1 @ sk_c9) != (identity)))),
% 1.37/1.34 inference('demod', [status(thm)],
% 1.37/1.34 [zip_derived_cl10520, zip_derived_cl610])).
% 1.37/1.34 thf(zip_derived_cl10522, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i]:
% 1.37/1.34 (((multiply @ X1 @ sk_c9) != (identity))
% 1.37/1.34 | ((inverse @ X1) != (sk_c9))
% 1.37/1.34 | ((multiply @ X0 @ sk_c9) != (identity))
% 1.37/1.34 | ((inverse @ X0) != (sk_c9))
% 1.37/1.34 | ((inverse @ sk_c1) = (sk_c9)))),
% 1.37/1.34 inference('simplify', [status(thm)], [zip_derived_cl10521])).
% 1.37/1.34 thf(zip_derived_cl10533, plain,
% 1.37/1.34 (![X0 : $i]:
% 1.37/1.34 (((sk_c9) != (sk_c9))
% 1.37/1.34 | ((inverse @ sk_c1) = (sk_c9))
% 1.37/1.34 | ((inverse @ sk_c1) = (sk_c9))
% 1.37/1.34 | ((inverse @ X0) != (sk_c9))
% 1.37/1.34 | ((multiply @ X0 @ sk_c9) != (identity))
% 1.37/1.34 | ((multiply @ sk_c3 @ sk_c9) != (identity)))),
% 1.37/1.34 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl10522])).
% 1.37/1.34 thf(zip_derived_cl10573, plain,
% 1.37/1.34 (![X0 : $i]:
% 1.37/1.34 (((multiply @ sk_c3 @ sk_c9) != (identity))
% 1.37/1.34 | ((multiply @ X0 @ sk_c9) != (identity))
% 1.37/1.34 | ((inverse @ X0) != (sk_c9))
% 1.37/1.34 | ((inverse @ sk_c1) = (sk_c9)))),
% 1.37/1.34 inference('simplify', [status(thm)], [zip_derived_cl10533])).
% 1.37/1.34 thf(zip_derived_cl10600, plain,
% 1.37/1.34 (![X0 : $i]:
% 1.37/1.34 (((multiply @ (inverse @ sk_c9) @ sk_c9) != (identity))
% 1.37/1.34 | ((inverse @ sk_c1) = (sk_c9))
% 1.37/1.34 | ((inverse @ sk_c1) = (sk_c9))
% 1.37/1.34 | ((inverse @ X0) != (sk_c9))
% 1.37/1.34 | ((multiply @ X0 @ sk_c9) != (identity)))),
% 1.37/1.34 inference('sup-', [status(thm)],
% 1.37/1.34 [zip_derived_cl5641, zip_derived_cl10573])).
% 1.37/1.34 thf(zip_derived_cl1, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.37/1.34 inference('cnf', [status(esa)], [left_inverse])).
% 1.37/1.34 thf(zip_derived_cl10604, plain,
% 1.37/1.34 (![X0 : $i]:
% 1.37/1.34 (((identity) != (identity))
% 1.37/1.34 | ((inverse @ sk_c1) = (sk_c9))
% 1.37/1.34 | ((inverse @ sk_c1) = (sk_c9))
% 1.37/1.34 | ((inverse @ X0) != (sk_c9))
% 1.37/1.34 | ((multiply @ X0 @ sk_c9) != (identity)))),
% 1.37/1.34 inference('demod', [status(thm)], [zip_derived_cl10600, zip_derived_cl1])).
% 1.37/1.34 thf(zip_derived_cl10605, plain,
% 1.37/1.34 (![X0 : $i]:
% 1.37/1.34 (((multiply @ X0 @ sk_c9) != (identity))
% 1.37/1.34 | ((inverse @ X0) != (sk_c9))
% 1.37/1.34 | ((inverse @ sk_c1) = (sk_c9)))),
% 1.37/1.34 inference('simplify', [status(thm)], [zip_derived_cl10604])).
% 1.37/1.34 thf(zip_derived_cl10618, plain,
% 1.37/1.34 ((((sk_c9) != (sk_c9))
% 1.37/1.34 | ((inverse @ sk_c1) = (sk_c9))
% 1.37/1.34 | ((inverse @ sk_c1) = (sk_c9))
% 1.37/1.34 | ((multiply @ sk_c3 @ sk_c9) != (identity)))),
% 1.37/1.34 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl10605])).
% 1.37/1.34 thf(zip_derived_cl10658, plain,
% 1.37/1.34 ((((multiply @ sk_c3 @ sk_c9) != (identity))
% 1.37/1.34 | ((inverse @ sk_c1) = (sk_c9)))),
% 1.37/1.34 inference('simplify', [status(thm)], [zip_derived_cl10618])).
% 1.37/1.34 thf(zip_derived_cl10684, plain,
% 1.37/1.34 ((((sk_c8) != (identity))
% 1.37/1.34 | ((inverse @ sk_c1) = (sk_c9))
% 1.37/1.34 | ((inverse @ sk_c1) = (sk_c9)))),
% 1.37/1.34 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl10658])).
% 1.37/1.34 thf(zip_derived_cl10688, plain,
% 1.37/1.34 ((((inverse @ sk_c1) = (sk_c9)) | ((sk_c8) != (identity)))),
% 1.37/1.34 inference('simplify', [status(thm)], [zip_derived_cl10684])).
% 1.37/1.34 thf(zip_derived_cl166, plain,
% 1.37/1.34 ((((inverse @ sk_c1) = (sk_c9)) | ((identity) = (sk_c8)))),
% 1.37/1.34 inference('simplify', [status(thm)], [zip_derived_cl165])).
% 1.37/1.34 thf(zip_derived_cl10693, plain, (((inverse @ sk_c1) = (sk_c9))),
% 1.37/1.34 inference('clc', [status(thm)], [zip_derived_cl10688, zip_derived_cl166])).
% 1.37/1.34 thf(zip_derived_cl10693, plain, (((inverse @ sk_c1) = (sk_c9))),
% 1.37/1.34 inference('clc', [status(thm)], [zip_derived_cl10688, zip_derived_cl166])).
% 1.37/1.34 thf(zip_derived_cl10693, plain, (((inverse @ sk_c1) = (sk_c9))),
% 1.37/1.34 inference('clc', [status(thm)], [zip_derived_cl10688, zip_derived_cl166])).
% 1.37/1.34 thf(zip_derived_cl10693, plain, (((inverse @ sk_c1) = (sk_c9))),
% 1.37/1.34 inference('clc', [status(thm)], [zip_derived_cl10688, zip_derived_cl166])).
% 1.37/1.34 thf(zip_derived_cl10725, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.37/1.34 (((multiply @ X0 @ (inverse @ sk_c1)) != (identity))
% 1.37/1.34 | ((inverse @ X0) != (inverse @ sk_c1))
% 1.37/1.34 | ((X1) != (identity))
% 1.37/1.34 | ((inverse @ X1) != (identity))
% 1.37/1.34 | ((multiply @ X2 @ (inverse @ sk_c1)) != (identity))
% 1.37/1.34 | ((inverse @ X2) != (inverse @ sk_c1))
% 1.37/1.34 | ((X3) != (identity))
% 1.37/1.34 | ((inverse @ X3) != (identity))
% 1.37/1.34 | ((identity) != (sk_c8)))),
% 1.37/1.34 inference('demod', [status(thm)],
% 1.37/1.34 [zip_derived_cl9079, zip_derived_cl10693, zip_derived_cl10693,
% 1.37/1.34 zip_derived_cl10693, zip_derived_cl10693])).
% 1.37/1.34 thf(prove_this_2, conjecture,
% 1.37/1.34 (~( ( ( inverse @ sk_c3 ) = ( sk_c9 ) ) |
% 1.37/1.34 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 1.37/1.34 thf(zf_stmt_13, negated_conjecture,
% 1.37/1.34 (( ( inverse @ sk_c3 ) = ( sk_c9 ) ) |
% 1.37/1.34 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) )),
% 1.37/1.34 inference('cnf.neg', [status(esa)], [prove_this_2])).
% 1.37/1.34 thf(zip_derived_cl4, plain,
% 1.37/1.34 ((((inverse @ sk_c3) = (sk_c9)) | ((multiply @ sk_c1 @ sk_c9) = (sk_c8)))),
% 1.37/1.34 inference('cnf', [status(esa)], [zf_stmt_13])).
% 1.37/1.34 thf(zip_derived_cl1, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.37/1.34 inference('cnf', [status(esa)], [left_inverse])).
% 1.37/1.34 thf(zip_derived_cl41, plain,
% 1.37/1.34 ((((multiply @ sk_c9 @ sk_c3) = (identity))
% 1.37/1.34 | ((multiply @ sk_c1 @ sk_c9) = (sk_c8)))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl1])).
% 1.37/1.34 thf(zip_derived_cl110, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i]:
% 1.37/1.34 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.37/1.34 inference('demod', [status(thm)], [zip_derived_cl90, zip_derived_cl0])).
% 1.37/1.34 thf(zip_derived_cl126, plain,
% 1.37/1.34 ((((sk_c3) = (multiply @ (inverse @ sk_c9) @ identity))
% 1.37/1.34 | ((multiply @ sk_c1 @ sk_c9) = (sk_c8)))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl110])).
% 1.37/1.34 thf(prove_this_1, conjecture,
% 1.37/1.34 (~( ( ( multiply @ sk_c3 @ sk_c9 ) = ( sk_c8 ) ) |
% 1.37/1.34 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 1.37/1.34 thf(zf_stmt_14, negated_conjecture,
% 1.37/1.34 (( ( multiply @ sk_c3 @ sk_c9 ) = ( sk_c8 ) ) |
% 1.37/1.34 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) )),
% 1.37/1.34 inference('cnf.neg', [status(esa)], [prove_this_1])).
% 1.37/1.34 thf(zip_derived_cl3, plain,
% 1.37/1.34 ((((multiply @ sk_c3 @ sk_c9) = (sk_c8))
% 1.37/1.34 | ((multiply @ sk_c1 @ sk_c9) = (sk_c8)))),
% 1.37/1.34 inference('cnf', [status(esa)], [zf_stmt_14])).
% 1.37/1.34 thf(zip_derived_cl333, plain,
% 1.37/1.34 ((((multiply @ (multiply @ (inverse @ sk_c9) @ identity) @ sk_c9)
% 1.37/1.34 = (sk_c8))
% 1.37/1.34 | ((multiply @ sk_c1 @ sk_c9) = (sk_c8))
% 1.37/1.34 | ((multiply @ sk_c1 @ sk_c9) = (sk_c8)))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl126, zip_derived_cl3])).
% 1.37/1.34 thf(zip_derived_cl2, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.37/1.34 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.37/1.34 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.37/1.34 inference('cnf', [status(esa)], [associativity])).
% 1.37/1.34 thf(zip_derived_cl0, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.37/1.34 inference('cnf', [status(esa)], [left_identity])).
% 1.37/1.34 thf(zip_derived_cl1, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.37/1.34 inference('cnf', [status(esa)], [left_inverse])).
% 1.37/1.34 thf(zip_derived_cl339, plain,
% 1.37/1.34 ((((identity) = (sk_c8))
% 1.37/1.34 | ((multiply @ sk_c1 @ sk_c9) = (sk_c8))
% 1.37/1.34 | ((multiply @ sk_c1 @ sk_c9) = (sk_c8)))),
% 1.37/1.34 inference('demod', [status(thm)],
% 1.37/1.34 [zip_derived_cl333, zip_derived_cl2, zip_derived_cl0,
% 1.37/1.34 zip_derived_cl1])).
% 1.37/1.34 thf(zip_derived_cl340, plain,
% 1.37/1.34 ((((multiply @ sk_c1 @ sk_c9) = (sk_c8)) | ((identity) = (sk_c8)))),
% 1.37/1.34 inference('simplify', [status(thm)], [zip_derived_cl339])).
% 1.37/1.34 thf(zip_derived_cl10693, plain, (((inverse @ sk_c1) = (sk_c9))),
% 1.37/1.34 inference('clc', [status(thm)], [zip_derived_cl10688, zip_derived_cl166])).
% 1.37/1.34 thf(zip_derived_cl5934, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl5677, zip_derived_cl1])).
% 1.37/1.34 thf(zip_derived_cl10703, plain,
% 1.37/1.34 ((((identity) = (sk_c8)) | ((identity) = (sk_c8)))),
% 1.37/1.34 inference('demod', [status(thm)],
% 1.37/1.34 [zip_derived_cl340, zip_derived_cl10693, zip_derived_cl5934])).
% 1.37/1.34 thf(zip_derived_cl10704, plain, (((identity) = (sk_c8))),
% 1.37/1.34 inference('simplify', [status(thm)], [zip_derived_cl10703])).
% 1.37/1.34 thf(zip_derived_cl10762, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.37/1.34 (((multiply @ X0 @ (inverse @ sk_c1)) != (identity))
% 1.37/1.34 | ((inverse @ X0) != (inverse @ sk_c1))
% 1.37/1.34 | ((X1) != (identity))
% 1.37/1.34 | ((inverse @ X1) != (identity))
% 1.37/1.34 | ((multiply @ X2 @ (inverse @ sk_c1)) != (identity))
% 1.37/1.34 | ((inverse @ X2) != (inverse @ sk_c1))
% 1.37/1.34 | ((X3) != (identity))
% 1.37/1.34 | ((inverse @ X3) != (identity))
% 1.37/1.34 | ((identity) != (identity)))),
% 1.37/1.34 inference('demod', [status(thm)],
% 1.37/1.34 [zip_derived_cl10725, zip_derived_cl10704])).
% 1.37/1.34 thf(zip_derived_cl10763, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.37/1.34 (((inverse @ X3) != (identity))
% 1.37/1.34 | ((X3) != (identity))
% 1.37/1.34 | ((inverse @ X2) != (inverse @ sk_c1))
% 1.37/1.34 | ((multiply @ X2 @ (inverse @ sk_c1)) != (identity))
% 1.37/1.34 | ((inverse @ X1) != (identity))
% 1.37/1.34 | ((X1) != (identity))
% 1.37/1.34 | ((inverse @ X0) != (inverse @ sk_c1))
% 1.37/1.34 | ((multiply @ X0 @ (inverse @ sk_c1)) != (identity)))),
% 1.37/1.34 inference('simplify', [status(thm)], [zip_derived_cl10762])).
% 1.37/1.34 thf(zip_derived_cl10764, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.37/1.34 (((multiply @ X0 @ (inverse @ sk_c1)) != (identity))
% 1.37/1.34 | ((inverse @ X0) != (inverse @ sk_c1))
% 1.37/1.34 | ((X1) != (identity))
% 1.37/1.34 | ((inverse @ X1) != (identity))
% 1.37/1.34 | ((multiply @ X2 @ (inverse @ sk_c1)) != (identity))
% 1.37/1.34 | ((inverse @ X2) != (inverse @ sk_c1))
% 1.37/1.34 | ((inverse @ identity) != (identity)))),
% 1.37/1.34 inference('eq_res', [status(thm)], [zip_derived_cl10763])).
% 1.37/1.34 thf(zip_derived_cl610, plain, (((inverse @ identity) = (identity))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl156, zip_derived_cl1])).
% 1.37/1.34 thf(zip_derived_cl10765, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.37/1.34 (((multiply @ X0 @ (inverse @ sk_c1)) != (identity))
% 1.37/1.34 | ((inverse @ X0) != (inverse @ sk_c1))
% 1.37/1.34 | ((X1) != (identity))
% 1.37/1.34 | ((inverse @ X1) != (identity))
% 1.37/1.34 | ((multiply @ X2 @ (inverse @ sk_c1)) != (identity))
% 1.37/1.34 | ((inverse @ X2) != (inverse @ sk_c1))
% 1.37/1.34 | ((identity) != (identity)))),
% 1.37/1.34 inference('demod', [status(thm)],
% 1.37/1.34 [zip_derived_cl10764, zip_derived_cl610])).
% 1.37/1.34 thf(zip_derived_cl10766, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.37/1.34 (((inverse @ X2) != (inverse @ sk_c1))
% 1.37/1.34 | ((multiply @ X2 @ (inverse @ sk_c1)) != (identity))
% 1.37/1.34 | ((inverse @ X1) != (identity))
% 1.37/1.34 | ((X1) != (identity))
% 1.37/1.34 | ((inverse @ X0) != (inverse @ sk_c1))
% 1.37/1.34 | ((multiply @ X0 @ (inverse @ sk_c1)) != (identity)))),
% 1.37/1.34 inference('simplify', [status(thm)], [zip_derived_cl10765])).
% 1.37/1.34 thf(zip_derived_cl10767, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i]:
% 1.37/1.34 (((multiply @ X0 @ (inverse @ sk_c1)) != (identity))
% 1.37/1.34 | ((inverse @ X0) != (inverse @ sk_c1))
% 1.37/1.34 | ((inverse @ identity) != (identity))
% 1.37/1.34 | ((multiply @ X1 @ (inverse @ sk_c1)) != (identity))
% 1.37/1.34 | ((inverse @ X1) != (inverse @ sk_c1)))),
% 1.37/1.34 inference('eq_res', [status(thm)], [zip_derived_cl10766])).
% 1.37/1.34 thf(zip_derived_cl610, plain, (((inverse @ identity) = (identity))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl156, zip_derived_cl1])).
% 1.37/1.34 thf(zip_derived_cl10768, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i]:
% 1.37/1.34 (((multiply @ X0 @ (inverse @ sk_c1)) != (identity))
% 1.37/1.34 | ((inverse @ X0) != (inverse @ sk_c1))
% 1.37/1.34 | ((identity) != (identity))
% 1.37/1.34 | ((multiply @ X1 @ (inverse @ sk_c1)) != (identity))
% 1.37/1.34 | ((inverse @ X1) != (inverse @ sk_c1)))),
% 1.37/1.34 inference('demod', [status(thm)],
% 1.37/1.34 [zip_derived_cl10767, zip_derived_cl610])).
% 1.37/1.34 thf(zip_derived_cl10769, plain,
% 1.37/1.34 (![X0 : $i, X1 : $i]:
% 1.37/1.34 (((inverse @ X1) != (inverse @ sk_c1))
% 1.37/1.34 | ((multiply @ X1 @ (inverse @ sk_c1)) != (identity))
% 1.37/1.34 | ((inverse @ X0) != (inverse @ sk_c1))
% 1.37/1.34 | ((multiply @ X0 @ (inverse @ sk_c1)) != (identity)))),
% 1.37/1.34 inference('simplify', [status(thm)], [zip_derived_cl10768])).
% 1.37/1.34 thf(zip_derived_cl10771, plain,
% 1.37/1.34 (![X0 : $i]:
% 1.37/1.34 (((multiply @ X0 @ (inverse @ sk_c1)) != (identity))
% 1.37/1.34 | ((inverse @ X0) != (inverse @ sk_c1))
% 1.37/1.34 | ((multiply @ sk_c1 @ (inverse @ sk_c1)) != (identity)))),
% 1.37/1.34 inference('eq_res', [status(thm)], [zip_derived_cl10769])).
% 1.37/1.34 thf(zip_derived_cl5934, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl5677, zip_derived_cl1])).
% 1.37/1.34 thf(zip_derived_cl10772, plain,
% 1.37/1.34 (![X0 : $i]:
% 1.37/1.34 (((multiply @ X0 @ (inverse @ sk_c1)) != (identity))
% 1.37/1.34 | ((inverse @ X0) != (inverse @ sk_c1))
% 1.37/1.34 | ((identity) != (identity)))),
% 1.37/1.34 inference('demod', [status(thm)],
% 1.37/1.34 [zip_derived_cl10771, zip_derived_cl5934])).
% 1.37/1.34 thf(zip_derived_cl10773, plain,
% 1.37/1.34 (![X0 : $i]:
% 1.37/1.34 (((inverse @ X0) != (inverse @ sk_c1))
% 1.37/1.34 | ((multiply @ X0 @ (inverse @ sk_c1)) != (identity)))),
% 1.37/1.34 inference('simplify', [status(thm)], [zip_derived_cl10772])).
% 1.37/1.34 thf(zip_derived_cl10775, plain,
% 1.37/1.34 (((multiply @ sk_c1 @ (inverse @ sk_c1)) != (identity))),
% 1.37/1.34 inference('eq_res', [status(thm)], [zip_derived_cl10773])).
% 1.37/1.34 thf(zip_derived_cl5934, plain,
% 1.37/1.34 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 1.37/1.34 inference('sup+', [status(thm)], [zip_derived_cl5677, zip_derived_cl1])).
% 1.37/1.34 thf(zip_derived_cl10776, plain, (((identity) != (identity))),
% 1.37/1.34 inference('demod', [status(thm)],
% 1.37/1.34 [zip_derived_cl10775, zip_derived_cl5934])).
% 1.37/1.34 thf(zip_derived_cl10777, plain, ($false),
% 1.37/1.34 inference('simplify', [status(thm)], [zip_derived_cl10776])).
% 1.37/1.34
% 1.37/1.34 % SZS output end Refutation
% 1.37/1.34
% 1.37/1.34
% 1.37/1.34 % Terminating...
% 2.05/1.46 % Runner terminated.
% 2.05/1.47 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------