TSTP Solution File: GRP217-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP217-1 : 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.VWUvuDA0bi 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 01:50:45 EDT 2023
% Result : Unsatisfiable 0.55s 1.06s
% Output : Refutation 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP217-1 : TPTP v8.1.2. Released v2.5.0.
% 0.04/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.VWUvuDA0bi true
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 23:38:30 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.54/0.64 % Total configuration time : 435
% 0.54/0.64 % Estimated wc time : 1092
% 0.54/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.54/0.73 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.54/0.73 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.54/0.74 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.54/0.76 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.54/0.76 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.54/0.76 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.55/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.55/1.06 % Solved by fo/fo7.sh.
% 0.55/1.06 % done 771 iterations in 0.274s
% 0.55/1.06 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.55/1.06 % SZS output start Refutation
% 0.55/1.06 thf(sk_c8_type, type, sk_c8: $i).
% 0.55/1.06 thf(sk_c6_type, type, sk_c6: $i).
% 0.55/1.06 thf(sk_c3_type, type, sk_c3: $i).
% 0.55/1.06 thf(sk_c9_type, type, sk_c9: $i).
% 0.55/1.06 thf(sk_c10_type, type, sk_c10: $i).
% 0.55/1.06 thf(identity_type, type, identity: $i).
% 0.55/1.06 thf(multiply_type, type, multiply: $i > $i > $i).
% 0.55/1.06 thf(sk_c11_type, type, sk_c11: $i).
% 0.55/1.06 thf(sk_c4_type, type, sk_c4: $i).
% 0.55/1.06 thf(inverse_type, type, inverse: $i > $i).
% 0.55/1.06 thf(sk_c7_type, type, sk_c7: $i).
% 0.55/1.06 thf(sk_c5_type, type, sk_c5: $i).
% 0.55/1.06 thf(sk_c2_type, type, sk_c2: $i).
% 0.55/1.06 thf(sk_c1_type, type, sk_c1: $i).
% 0.55/1.06 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 0.55/1.06 thf(zip_derived_cl0, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.55/1.06 inference('cnf', [status(esa)], [left_identity])).
% 0.55/1.06 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 0.55/1.06 thf(zip_derived_cl1, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.55/1.06 inference('cnf', [status(esa)], [left_inverse])).
% 0.55/1.06 thf(associativity, axiom,
% 0.55/1.06 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 0.55/1.06 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 0.55/1.06 thf(zip_derived_cl2, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/1.06 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.55/1.06 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.55/1.06 inference('cnf', [status(esa)], [associativity])).
% 0.55/1.06 thf(zip_derived_cl111, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i]:
% 0.55/1.06 ((multiply @ identity @ X0)
% 0.55/1.06 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 0.55/1.06 thf(zip_derived_cl0, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.55/1.06 inference('cnf', [status(esa)], [left_identity])).
% 0.55/1.06 thf(zip_derived_cl129, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i]:
% 0.55/1.06 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.55/1.06 inference('demod', [status(thm)], [zip_derived_cl111, zip_derived_cl0])).
% 0.55/1.06 thf(zip_derived_cl137, plain,
% 0.55/1.06 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl129])).
% 0.55/1.06 thf(zip_derived_cl129, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i]:
% 0.55/1.06 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.55/1.06 inference('demod', [status(thm)], [zip_derived_cl111, zip_derived_cl0])).
% 0.55/1.06 thf(zip_derived_cl166, plain,
% 0.55/1.06 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ identity)) @ X0))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl137, zip_derived_cl129])).
% 0.55/1.06 thf(zip_derived_cl1, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.55/1.06 inference('cnf', [status(esa)], [left_inverse])).
% 0.55/1.06 thf(zip_derived_cl443, plain, (((inverse @ identity) = (identity))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl166, zip_derived_cl1])).
% 0.55/1.06 thf(zip_derived_cl1, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.55/1.06 inference('cnf', [status(esa)], [left_inverse])).
% 0.55/1.06 thf(zip_derived_cl129, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i]:
% 0.55/1.06 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.55/1.06 inference('demod', [status(thm)], [zip_derived_cl111, zip_derived_cl0])).
% 0.55/1.06 thf(zip_derived_cl138, plain,
% 0.55/1.06 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl129])).
% 0.55/1.06 thf(zip_derived_cl129, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i]:
% 0.55/1.06 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.55/1.06 inference('demod', [status(thm)], [zip_derived_cl111, zip_derived_cl0])).
% 0.55/1.06 thf(zip_derived_cl129, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i]:
% 0.55/1.06 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.55/1.06 inference('demod', [status(thm)], [zip_derived_cl111, zip_derived_cl0])).
% 0.55/1.06 thf(zip_derived_cl135, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i]:
% 0.55/1.06 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl129, zip_derived_cl129])).
% 0.55/1.06 thf(zip_derived_cl618, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl138, zip_derived_cl135])).
% 0.55/1.06 thf(zip_derived_cl138, plain,
% 0.55/1.06 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl129])).
% 0.55/1.06 thf(zip_derived_cl644, plain,
% 0.55/1.06 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl618, zip_derived_cl138])).
% 0.55/1.06 thf(prove_this_49, conjecture,
% 0.55/1.06 (~( ( ( inverse @ X4 ) != ( sk_c11 ) ) |
% 0.55/1.06 ( ( multiply @ X4 @ sk_c11 ) != ( X3 ) ) |
% 0.55/1.06 ( ( multiply @ sk_c11 @ X3 ) != ( sk_c10 ) ) |
% 0.55/1.06 ( ( multiply @ X1 @ sk_c10 ) != ( sk_c11 ) ) |
% 0.55/1.06 ( ( inverse @ X2 ) != ( X1 ) ) |
% 0.55/1.06 ( ( multiply @ X2 @ X1 ) != ( sk_c11 ) ) |
% 0.55/1.06 ( ( inverse @ X9 ) != ( sk_c11 ) ) |
% 0.55/1.06 ( ( multiply @ X9 @ sk_c11 ) != ( X8 ) ) |
% 0.55/1.06 ( ( multiply @ sk_c11 @ X8 ) != ( sk_c10 ) ) |
% 0.55/1.06 ( ( multiply @ X7 @ sk_c11 ) != ( sk_c10 ) ) |
% 0.55/1.06 ( ( inverse @ X6 ) != ( X7 ) ) |
% 0.55/1.06 ( ( multiply @ X6 @ X7 ) != ( sk_c10 ) ) |
% 0.55/1.06 ( ( multiply @ X5 @ sk_c10 ) != ( sk_c11 ) ) |
% 0.55/1.06 ( ( inverse @ X5 ) != ( sk_c11 ) ) ))).
% 0.55/1.06 thf(zf_stmt_0, negated_conjecture,
% 0.55/1.06 (( ( inverse @ X4 ) != ( sk_c11 ) ) |
% 0.55/1.06 ( ( multiply @ X4 @ sk_c11 ) != ( X3 ) ) |
% 0.55/1.06 ( ( multiply @ sk_c11 @ X3 ) != ( sk_c10 ) ) |
% 0.55/1.06 ( ( multiply @ X1 @ sk_c10 ) != ( sk_c11 ) ) |
% 0.55/1.06 ( ( inverse @ X2 ) != ( X1 ) ) |
% 0.55/1.06 ( ( multiply @ X2 @ X1 ) != ( sk_c11 ) ) |
% 0.55/1.06 ( ( inverse @ X9 ) != ( sk_c11 ) ) |
% 0.55/1.06 ( ( multiply @ X9 @ sk_c11 ) != ( X8 ) ) |
% 0.55/1.06 ( ( multiply @ sk_c11 @ X8 ) != ( sk_c10 ) ) |
% 0.55/1.06 ( ( multiply @ X7 @ sk_c11 ) != ( sk_c10 ) ) |
% 0.55/1.06 ( ( inverse @ X6 ) != ( X7 ) ) |
% 0.55/1.06 ( ( multiply @ X6 @ X7 ) != ( sk_c10 ) ) |
% 0.55/1.06 ( ( multiply @ X5 @ sk_c10 ) != ( sk_c11 ) ) |
% 0.55/1.06 ( ( inverse @ X5 ) != ( sk_c11 ) )),
% 0.55/1.06 inference('cnf.neg', [status(esa)], [prove_this_49])).
% 0.55/1.06 thf(zip_derived_cl51, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i,
% 0.55/1.06 X7 : $i, X8 : $i]:
% 0.55/1.06 (((inverse @ X0) != (sk_c11))
% 0.55/1.06 | ((multiply @ X0 @ sk_c11) != (X1))
% 0.55/1.06 | ((multiply @ sk_c11 @ X1) != (sk_c10))
% 0.55/1.06 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 0.55/1.06 | ((inverse @ X3) != (X2))
% 0.55/1.06 | ((multiply @ X3 @ X2) != (sk_c11))
% 0.55/1.06 | ((inverse @ X4) != (sk_c11))
% 0.55/1.06 | ((multiply @ X4 @ sk_c11) != (X5))
% 0.55/1.06 | ((multiply @ sk_c11 @ X5) != (sk_c10))
% 0.55/1.06 | ((multiply @ X6 @ sk_c11) != (sk_c10))
% 0.55/1.06 | ((inverse @ X7) != (X6))
% 0.55/1.06 | ((multiply @ X7 @ X6) != (sk_c10))
% 0.55/1.06 | ((multiply @ X8 @ sk_c10) != (sk_c11))
% 0.55/1.06 | ((inverse @ X8) != (sk_c11)))),
% 0.55/1.06 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.55/1.06 thf(zip_derived_cl664, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i,
% 0.55/1.06 X7 : $i, X8 : $i]:
% 0.55/1.06 (((X0) != (sk_c11))
% 0.55/1.06 | ((inverse @ X1) != (sk_c11))
% 0.55/1.06 | ((multiply @ X1 @ sk_c10) != (sk_c11))
% 0.55/1.06 | ((multiply @ X3 @ X2) != (sk_c10))
% 0.55/1.06 | ((inverse @ X3) != (X2))
% 0.55/1.06 | ((multiply @ X2 @ sk_c11) != (sk_c10))
% 0.55/1.06 | ((multiply @ sk_c11 @ X4) != (sk_c10))
% 0.55/1.06 | ((multiply @ X5 @ sk_c11) != (X4))
% 0.55/1.06 | ((inverse @ X5) != (sk_c11))
% 0.55/1.06 | ((multiply @ X7 @ X6) != (sk_c11))
% 0.55/1.06 | ((inverse @ X7) != (X6))
% 0.55/1.06 | ((multiply @ X6 @ sk_c10) != (sk_c11))
% 0.55/1.06 | ((multiply @ sk_c11 @ X8) != (sk_c10))
% 0.55/1.06 | ((multiply @ (inverse @ X0) @ sk_c11) != (X8)))),
% 0.55/1.06 inference('sup-', [status(thm)], [zip_derived_cl644, zip_derived_cl51])).
% 0.55/1.06 thf(zip_derived_cl719, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 0.55/1.06 (((multiply @ (inverse @ sk_c11) @ sk_c11) != (X0))
% 0.55/1.06 | ((multiply @ sk_c11 @ X0) != (sk_c10))
% 0.55/1.06 | ((multiply @ X1 @ sk_c10) != (sk_c11))
% 0.55/1.06 | ((inverse @ X2) != (X1))
% 0.55/1.06 | ((multiply @ X2 @ X1) != (sk_c11))
% 0.55/1.06 | ((inverse @ X3) != (sk_c11))
% 0.55/1.06 | ((multiply @ X3 @ sk_c11) != (X4))
% 0.55/1.06 | ((multiply @ sk_c11 @ X4) != (sk_c10))
% 0.55/1.06 | ((multiply @ X5 @ sk_c11) != (sk_c10))
% 0.55/1.06 | ((inverse @ X6) != (X5))
% 0.55/1.06 | ((multiply @ X6 @ X5) != (sk_c10))
% 0.55/1.06 | ((multiply @ X7 @ sk_c10) != (sk_c11))
% 0.55/1.06 | ((inverse @ X7) != (sk_c11)))),
% 0.55/1.06 inference('eq_res', [status(thm)], [zip_derived_cl664])).
% 0.55/1.06 thf(zip_derived_cl1, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.55/1.06 inference('cnf', [status(esa)], [left_inverse])).
% 0.55/1.06 thf(zip_derived_cl720, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 0.55/1.06 (((identity) != (X0))
% 0.55/1.06 | ((multiply @ sk_c11 @ X0) != (sk_c10))
% 0.55/1.06 | ((multiply @ X1 @ sk_c10) != (sk_c11))
% 0.55/1.06 | ((inverse @ X2) != (X1))
% 0.55/1.06 | ((multiply @ X2 @ X1) != (sk_c11))
% 0.55/1.06 | ((inverse @ X3) != (sk_c11))
% 0.55/1.06 | ((multiply @ X3 @ sk_c11) != (X4))
% 0.55/1.06 | ((multiply @ sk_c11 @ X4) != (sk_c10))
% 0.55/1.06 | ((multiply @ X5 @ sk_c11) != (sk_c10))
% 0.55/1.06 | ((inverse @ X6) != (X5))
% 0.55/1.06 | ((multiply @ X6 @ X5) != (sk_c10))
% 0.55/1.06 | ((multiply @ X7 @ sk_c10) != (sk_c11))
% 0.55/1.06 | ((inverse @ X7) != (sk_c11)))),
% 0.55/1.06 inference('demod', [status(thm)], [zip_derived_cl719, zip_derived_cl1])).
% 0.55/1.06 thf(zip_derived_cl721, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 0.55/1.06 (((inverse @ X0) != (sk_c11))
% 0.55/1.06 | ((multiply @ X0 @ sk_c10) != (sk_c11))
% 0.55/1.06 | ((multiply @ X2 @ X1) != (sk_c10))
% 0.55/1.06 | ((inverse @ X2) != (X1))
% 0.55/1.06 | ((multiply @ X1 @ sk_c11) != (sk_c10))
% 0.55/1.06 | ((multiply @ sk_c11 @ X3) != (sk_c10))
% 0.55/1.06 | ((multiply @ X4 @ sk_c11) != (X3))
% 0.55/1.06 | ((inverse @ X4) != (sk_c11))
% 0.55/1.06 | ((multiply @ X6 @ X5) != (sk_c11))
% 0.55/1.06 | ((inverse @ X6) != (X5))
% 0.55/1.06 | ((multiply @ X5 @ sk_c10) != (sk_c11))
% 0.55/1.06 | ((multiply @ sk_c11 @ identity) != (sk_c10)))),
% 0.55/1.06 inference('eq_res', [status(thm)], [zip_derived_cl720])).
% 0.55/1.06 thf(zip_derived_cl722, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 0.55/1.06 (((inverse @ X0) != (sk_c11))
% 0.55/1.06 | ((multiply @ X0 @ (multiply @ sk_c11 @ identity)) != (sk_c11))
% 0.55/1.06 | ((multiply @ X2 @ X1) != (multiply @ sk_c11 @ identity))
% 0.55/1.06 | ((inverse @ X2) != (X1))
% 0.55/1.06 | ((multiply @ X1 @ sk_c11) != (multiply @ sk_c11 @ identity))
% 0.55/1.06 | ((multiply @ sk_c11 @ X3) != (multiply @ sk_c11 @ identity))
% 0.55/1.06 | ((multiply @ X4 @ sk_c11) != (X3))
% 0.55/1.06 | ((inverse @ X4) != (sk_c11))
% 0.55/1.06 | ((multiply @ X6 @ X5) != (sk_c11))
% 0.55/1.06 | ((inverse @ X6) != (X5))
% 0.55/1.06 | ((multiply @ X5 @ (multiply @ sk_c11 @ identity)) != (sk_c11))
% 0.55/1.06 | ((multiply @ sk_c11 @ identity) != (sk_c10)))),
% 0.55/1.06 inference('local_rewriting', [status(thm)], [zip_derived_cl721])).
% 0.55/1.06 thf(zip_derived_cl618, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl138, zip_derived_cl135])).
% 0.55/1.06 thf(zip_derived_cl618, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl138, zip_derived_cl135])).
% 0.55/1.06 thf(zip_derived_cl618, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl138, zip_derived_cl135])).
% 0.55/1.06 thf(zip_derived_cl618, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl138, zip_derived_cl135])).
% 0.55/1.06 thf(zip_derived_cl618, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl138, zip_derived_cl135])).
% 0.55/1.06 thf(zip_derived_cl618, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl138, zip_derived_cl135])).
% 0.55/1.06 thf(zip_derived_cl723, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 0.55/1.06 (((inverse @ X0) != (sk_c11))
% 0.55/1.06 | ((multiply @ X0 @ sk_c11) != (sk_c11))
% 0.55/1.06 | ((multiply @ X2 @ X1) != (sk_c11))
% 0.55/1.06 | ((inverse @ X2) != (X1))
% 0.55/1.06 | ((multiply @ X1 @ sk_c11) != (sk_c11))
% 0.55/1.06 | ((multiply @ sk_c11 @ X3) != (sk_c11))
% 0.55/1.06 | ((multiply @ X4 @ sk_c11) != (X3))
% 0.55/1.06 | ((inverse @ X4) != (sk_c11))
% 0.55/1.06 | ((multiply @ X6 @ X5) != (sk_c11))
% 0.55/1.06 | ((inverse @ X6) != (X5))
% 0.55/1.06 | ((multiply @ X5 @ sk_c11) != (sk_c11))
% 0.55/1.06 | ((sk_c11) != (sk_c10)))),
% 0.55/1.06 inference('demod', [status(thm)],
% 0.55/1.06 [zip_derived_cl722, zip_derived_cl618, zip_derived_cl618,
% 0.55/1.06 zip_derived_cl618, zip_derived_cl618, zip_derived_cl618,
% 0.55/1.06 zip_derived_cl618])).
% 0.55/1.06 thf(prove_this_48, conjecture,
% 0.55/1.06 (~( ( ( inverse @ sk_c8 ) = ( sk_c11 ) ) |
% 0.55/1.06 ( ( inverse @ sk_c4 ) = ( sk_c11 ) ) ))).
% 0.55/1.06 thf(zf_stmt_1, negated_conjecture,
% 0.55/1.06 (( ( inverse @ sk_c8 ) = ( sk_c11 ) ) |
% 0.55/1.06 ( ( inverse @ sk_c4 ) = ( sk_c11 ) )),
% 0.55/1.06 inference('cnf.neg', [status(esa)], [prove_this_48])).
% 0.55/1.06 thf(zip_derived_cl50, plain,
% 0.55/1.06 ((((inverse @ sk_c8) = (sk_c11)) | ((inverse @ sk_c4) = (sk_c11)))),
% 0.55/1.06 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.55/1.06 thf(zip_derived_cl1, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.55/1.06 inference('cnf', [status(esa)], [left_inverse])).
% 0.55/1.06 thf(zip_derived_cl58, plain,
% 0.55/1.06 ((((multiply @ sk_c11 @ sk_c4) = (identity))
% 0.55/1.06 | ((inverse @ sk_c8) = (sk_c11)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl1])).
% 0.55/1.06 thf(zip_derived_cl129, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i]:
% 0.55/1.06 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.55/1.06 inference('demod', [status(thm)], [zip_derived_cl111, zip_derived_cl0])).
% 0.55/1.06 thf(zip_derived_cl146, plain,
% 0.55/1.06 ((((sk_c4) = (multiply @ (inverse @ sk_c11) @ identity))
% 0.55/1.06 | ((inverse @ sk_c8) = (sk_c11)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl58, zip_derived_cl129])).
% 0.55/1.06 thf(prove_this_42, conjecture,
% 0.55/1.06 (~( ( ( inverse @ sk_c8 ) = ( sk_c11 ) ) |
% 0.55/1.06 ( ( multiply @ sk_c4 @ sk_c11 ) = ( sk_c5 ) ) ))).
% 0.55/1.06 thf(zf_stmt_2, negated_conjecture,
% 0.55/1.06 (( ( inverse @ sk_c8 ) = ( sk_c11 ) ) |
% 0.55/1.06 ( ( multiply @ sk_c4 @ sk_c11 ) = ( sk_c5 ) )),
% 0.55/1.06 inference('cnf.neg', [status(esa)], [prove_this_42])).
% 0.55/1.06 thf(zip_derived_cl44, plain,
% 0.55/1.06 ((((inverse @ sk_c8) = (sk_c11))
% 0.55/1.06 | ((multiply @ sk_c4 @ sk_c11) = (sk_c5)))),
% 0.55/1.06 inference('cnf', [status(esa)], [zf_stmt_2])).
% 0.55/1.06 thf(zip_derived_cl281, plain,
% 0.55/1.06 ((((multiply @ (multiply @ (inverse @ sk_c11) @ identity) @ sk_c11)
% 0.55/1.06 = (sk_c5))
% 0.55/1.06 | ((inverse @ sk_c8) = (sk_c11))
% 0.55/1.06 | ((inverse @ sk_c8) = (sk_c11)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl146, zip_derived_cl44])).
% 0.55/1.06 thf(zip_derived_cl2, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/1.06 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.55/1.06 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.55/1.06 inference('cnf', [status(esa)], [associativity])).
% 0.55/1.06 thf(zip_derived_cl0, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.55/1.06 inference('cnf', [status(esa)], [left_identity])).
% 0.55/1.06 thf(zip_derived_cl1, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.55/1.06 inference('cnf', [status(esa)], [left_inverse])).
% 0.55/1.06 thf(zip_derived_cl291, plain,
% 0.55/1.06 ((((identity) = (sk_c5))
% 0.55/1.06 | ((inverse @ sk_c8) = (sk_c11))
% 0.55/1.06 | ((inverse @ sk_c8) = (sk_c11)))),
% 0.55/1.06 inference('demod', [status(thm)],
% 0.55/1.06 [zip_derived_cl281, zip_derived_cl2, zip_derived_cl0,
% 0.55/1.06 zip_derived_cl1])).
% 0.55/1.06 thf(zip_derived_cl292, plain,
% 0.55/1.06 ((((inverse @ sk_c8) = (sk_c11)) | ((identity) = (sk_c5)))),
% 0.55/1.06 inference('simplify', [status(thm)], [zip_derived_cl291])).
% 0.55/1.06 thf(prove_this_36, conjecture,
% 0.55/1.06 (~( ( ( inverse @ sk_c8 ) = ( sk_c11 ) ) |
% 0.55/1.06 ( ( multiply @ sk_c11 @ sk_c5 ) = ( sk_c10 ) ) ))).
% 0.55/1.06 thf(zf_stmt_3, negated_conjecture,
% 0.55/1.06 (( ( inverse @ sk_c8 ) = ( sk_c11 ) ) |
% 0.55/1.06 ( ( multiply @ sk_c11 @ sk_c5 ) = ( sk_c10 ) )),
% 0.55/1.06 inference('cnf.neg', [status(esa)], [prove_this_36])).
% 0.55/1.06 thf(zip_derived_cl38, plain,
% 0.55/1.06 ((((inverse @ sk_c8) = (sk_c11))
% 0.55/1.06 | ((multiply @ sk_c11 @ sk_c5) = (sk_c10)))),
% 0.55/1.06 inference('cnf', [status(esa)], [zf_stmt_3])).
% 0.55/1.06 thf(zip_derived_cl296, plain,
% 0.55/1.06 ((((multiply @ sk_c11 @ identity) = (sk_c10))
% 0.55/1.06 | ((inverse @ sk_c8) = (sk_c11))
% 0.55/1.06 | ((inverse @ sk_c8) = (sk_c11)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl292, zip_derived_cl38])).
% 0.55/1.06 thf(zip_derived_cl299, plain,
% 0.55/1.06 ((((inverse @ sk_c8) = (sk_c11))
% 0.55/1.06 | ((multiply @ sk_c11 @ identity) = (sk_c10)))),
% 0.55/1.06 inference('simplify', [status(thm)], [zip_derived_cl296])).
% 0.55/1.06 thf(zip_derived_cl138, plain,
% 0.55/1.06 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl129])).
% 0.55/1.06 thf(zip_derived_cl325, plain,
% 0.55/1.06 ((((sk_c8) = (multiply @ (inverse @ sk_c11) @ identity))
% 0.55/1.06 | ((multiply @ sk_c11 @ identity) = (sk_c10)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl299, zip_derived_cl138])).
% 0.55/1.06 thf(zip_derived_cl618, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl138, zip_derived_cl135])).
% 0.55/1.06 thf(zip_derived_cl618, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl138, zip_derived_cl135])).
% 0.55/1.06 thf(zip_derived_cl638, plain,
% 0.55/1.06 ((((sk_c8) = (inverse @ sk_c11)) | ((sk_c11) = (sk_c10)))),
% 0.55/1.06 inference('demod', [status(thm)],
% 0.55/1.06 [zip_derived_cl325, zip_derived_cl618, zip_derived_cl618])).
% 0.55/1.06 thf(prove_this_47, conjecture,
% 0.55/1.06 (~( ( ( multiply @ sk_c8 @ sk_c11 ) = ( sk_c9 ) ) |
% 0.55/1.06 ( ( inverse @ sk_c4 ) = ( sk_c11 ) ) ))).
% 0.55/1.06 thf(zf_stmt_4, negated_conjecture,
% 0.55/1.06 (( ( multiply @ sk_c8 @ sk_c11 ) = ( sk_c9 ) ) |
% 0.55/1.06 ( ( inverse @ sk_c4 ) = ( sk_c11 ) )),
% 0.55/1.06 inference('cnf.neg', [status(esa)], [prove_this_47])).
% 0.55/1.06 thf(zip_derived_cl49, plain,
% 0.55/1.06 ((((multiply @ sk_c8 @ sk_c11) = (sk_c9))
% 0.55/1.06 | ((inverse @ sk_c4) = (sk_c11)))),
% 0.55/1.06 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.55/1.06 thf(zip_derived_cl644, plain,
% 0.55/1.06 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl618, zip_derived_cl138])).
% 0.55/1.06 thf(zip_derived_cl675, plain,
% 0.55/1.06 ((((sk_c4) = (inverse @ sk_c11))
% 0.55/1.06 | ((multiply @ sk_c8 @ sk_c11) = (sk_c9)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl49, zip_derived_cl644])).
% 0.55/1.06 thf(prove_this_41, conjecture,
% 0.55/1.06 (~( ( ( multiply @ sk_c8 @ sk_c11 ) = ( sk_c9 ) ) |
% 0.55/1.06 ( ( multiply @ sk_c4 @ sk_c11 ) = ( sk_c5 ) ) ))).
% 0.55/1.06 thf(zf_stmt_5, negated_conjecture,
% 0.55/1.06 (( ( multiply @ sk_c8 @ sk_c11 ) = ( sk_c9 ) ) |
% 0.55/1.06 ( ( multiply @ sk_c4 @ sk_c11 ) = ( sk_c5 ) )),
% 0.55/1.06 inference('cnf.neg', [status(esa)], [prove_this_41])).
% 0.55/1.06 thf(zip_derived_cl43, plain,
% 0.55/1.06 ((((multiply @ sk_c8 @ sk_c11) = (sk_c9))
% 0.55/1.06 | ((multiply @ sk_c4 @ sk_c11) = (sk_c5)))),
% 0.55/1.06 inference('cnf', [status(esa)], [zf_stmt_5])).
% 0.55/1.06 thf(zip_derived_cl2170, plain,
% 0.55/1.06 ((((multiply @ (inverse @ sk_c11) @ sk_c11) = (sk_c5))
% 0.55/1.06 | ((multiply @ sk_c8 @ sk_c11) = (sk_c9))
% 0.55/1.06 | ((multiply @ sk_c8 @ sk_c11) = (sk_c9)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl675, zip_derived_cl43])).
% 0.55/1.06 thf(zip_derived_cl1, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.55/1.06 inference('cnf', [status(esa)], [left_inverse])).
% 0.55/1.06 thf(zip_derived_cl2176, plain,
% 0.55/1.06 ((((identity) = (sk_c5))
% 0.55/1.06 | ((multiply @ sk_c8 @ sk_c11) = (sk_c9))
% 0.55/1.06 | ((multiply @ sk_c8 @ sk_c11) = (sk_c9)))),
% 0.55/1.06 inference('demod', [status(thm)], [zip_derived_cl2170, zip_derived_cl1])).
% 0.55/1.06 thf(zip_derived_cl2177, plain,
% 0.55/1.06 ((((multiply @ sk_c8 @ sk_c11) = (sk_c9)) | ((identity) = (sk_c5)))),
% 0.55/1.06 inference('simplify', [status(thm)], [zip_derived_cl2176])).
% 0.55/1.06 thf(prove_this_35, conjecture,
% 0.55/1.06 (~( ( ( multiply @ sk_c8 @ sk_c11 ) = ( sk_c9 ) ) |
% 0.55/1.06 ( ( multiply @ sk_c11 @ sk_c5 ) = ( sk_c10 ) ) ))).
% 0.55/1.06 thf(zf_stmt_6, negated_conjecture,
% 0.55/1.06 (( ( multiply @ sk_c8 @ sk_c11 ) = ( sk_c9 ) ) |
% 0.55/1.06 ( ( multiply @ sk_c11 @ sk_c5 ) = ( sk_c10 ) )),
% 0.55/1.06 inference('cnf.neg', [status(esa)], [prove_this_35])).
% 0.55/1.06 thf(zip_derived_cl37, plain,
% 0.55/1.06 ((((multiply @ sk_c8 @ sk_c11) = (sk_c9))
% 0.55/1.06 | ((multiply @ sk_c11 @ sk_c5) = (sk_c10)))),
% 0.55/1.06 inference('cnf', [status(esa)], [zf_stmt_6])).
% 0.55/1.06 thf(zip_derived_cl2182, plain,
% 0.55/1.06 ((((multiply @ sk_c11 @ identity) = (sk_c10))
% 0.55/1.06 | ((multiply @ sk_c8 @ sk_c11) = (sk_c9))
% 0.55/1.06 | ((multiply @ sk_c8 @ sk_c11) = (sk_c9)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl2177, zip_derived_cl37])).
% 0.55/1.06 thf(zip_derived_cl618, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl138, zip_derived_cl135])).
% 0.55/1.06 thf(zip_derived_cl2196, plain,
% 0.55/1.06 ((((sk_c11) = (sk_c10))
% 0.55/1.06 | ((multiply @ sk_c8 @ sk_c11) = (sk_c9))
% 0.55/1.06 | ((multiply @ sk_c8 @ sk_c11) = (sk_c9)))),
% 0.55/1.06 inference('demod', [status(thm)], [zip_derived_cl2182, zip_derived_cl618])).
% 0.55/1.06 thf(zip_derived_cl2197, plain,
% 0.55/1.06 ((((multiply @ sk_c8 @ sk_c11) = (sk_c9)) | ((sk_c11) = (sk_c10)))),
% 0.55/1.06 inference('simplify', [status(thm)], [zip_derived_cl2196])).
% 0.55/1.06 thf(zip_derived_cl2207, plain,
% 0.55/1.06 ((((multiply @ (inverse @ sk_c11) @ sk_c11) = (sk_c9))
% 0.55/1.06 | ((sk_c11) = (sk_c10))
% 0.55/1.06 | ((sk_c11) = (sk_c10)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl638, zip_derived_cl2197])).
% 0.55/1.06 thf(zip_derived_cl1, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.55/1.06 inference('cnf', [status(esa)], [left_inverse])).
% 0.55/1.06 thf(zip_derived_cl2211, plain,
% 0.55/1.06 ((((identity) = (sk_c9)) | ((sk_c11) = (sk_c10)) | ((sk_c11) = (sk_c10)))),
% 0.55/1.06 inference('demod', [status(thm)], [zip_derived_cl2207, zip_derived_cl1])).
% 0.55/1.06 thf(zip_derived_cl2212, plain,
% 0.55/1.06 ((((sk_c11) = (sk_c10)) | ((identity) = (sk_c9)))),
% 0.55/1.06 inference('simplify', [status(thm)], [zip_derived_cl2211])).
% 0.55/1.06 thf(prove_this_46, conjecture,
% 0.55/1.06 (~( ( ( multiply @ sk_c11 @ sk_c9 ) = ( sk_c10 ) ) |
% 0.55/1.06 ( ( inverse @ sk_c4 ) = ( sk_c11 ) ) ))).
% 0.55/1.06 thf(zf_stmt_7, negated_conjecture,
% 0.55/1.06 (( ( multiply @ sk_c11 @ sk_c9 ) = ( sk_c10 ) ) |
% 0.55/1.06 ( ( inverse @ sk_c4 ) = ( sk_c11 ) )),
% 0.55/1.06 inference('cnf.neg', [status(esa)], [prove_this_46])).
% 0.55/1.06 thf(zip_derived_cl48, plain,
% 0.55/1.06 ((((multiply @ sk_c11 @ sk_c9) = (sk_c10))
% 0.55/1.06 | ((inverse @ sk_c4) = (sk_c11)))),
% 0.55/1.06 inference('cnf', [status(esa)], [zf_stmt_7])).
% 0.55/1.06 thf(zip_derived_cl644, plain,
% 0.55/1.06 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl618, zip_derived_cl138])).
% 0.55/1.06 thf(zip_derived_cl674, plain,
% 0.55/1.06 ((((sk_c4) = (inverse @ sk_c11))
% 0.55/1.06 | ((multiply @ sk_c11 @ sk_c9) = (sk_c10)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl48, zip_derived_cl644])).
% 0.55/1.06 thf(prove_this_40, conjecture,
% 0.55/1.06 (~( ( ( multiply @ sk_c11 @ sk_c9 ) = ( sk_c10 ) ) |
% 0.55/1.06 ( ( multiply @ sk_c4 @ sk_c11 ) = ( sk_c5 ) ) ))).
% 0.55/1.06 thf(zf_stmt_8, negated_conjecture,
% 0.55/1.06 (( ( multiply @ sk_c11 @ sk_c9 ) = ( sk_c10 ) ) |
% 0.55/1.06 ( ( multiply @ sk_c4 @ sk_c11 ) = ( sk_c5 ) )),
% 0.55/1.06 inference('cnf.neg', [status(esa)], [prove_this_40])).
% 0.55/1.06 thf(zip_derived_cl42, plain,
% 0.55/1.06 ((((multiply @ sk_c11 @ sk_c9) = (sk_c10))
% 0.55/1.06 | ((multiply @ sk_c4 @ sk_c11) = (sk_c5)))),
% 0.55/1.06 inference('cnf', [status(esa)], [zf_stmt_8])).
% 0.55/1.06 thf(zip_derived_cl1572, plain,
% 0.55/1.06 ((((multiply @ (inverse @ sk_c11) @ sk_c11) = (sk_c5))
% 0.55/1.06 | ((multiply @ sk_c11 @ sk_c9) = (sk_c10))
% 0.55/1.06 | ((multiply @ sk_c11 @ sk_c9) = (sk_c10)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl674, zip_derived_cl42])).
% 0.55/1.06 thf(zip_derived_cl1, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.55/1.06 inference('cnf', [status(esa)], [left_inverse])).
% 0.55/1.06 thf(zip_derived_cl1578, plain,
% 0.55/1.06 ((((identity) = (sk_c5))
% 0.55/1.06 | ((multiply @ sk_c11 @ sk_c9) = (sk_c10))
% 0.55/1.06 | ((multiply @ sk_c11 @ sk_c9) = (sk_c10)))),
% 0.55/1.06 inference('demod', [status(thm)], [zip_derived_cl1572, zip_derived_cl1])).
% 0.55/1.06 thf(zip_derived_cl1579, plain,
% 0.55/1.06 ((((multiply @ sk_c11 @ sk_c9) = (sk_c10)) | ((identity) = (sk_c5)))),
% 0.55/1.06 inference('simplify', [status(thm)], [zip_derived_cl1578])).
% 0.55/1.06 thf(prove_this_34, conjecture,
% 0.55/1.06 (~( ( ( multiply @ sk_c11 @ sk_c9 ) = ( sk_c10 ) ) |
% 0.55/1.06 ( ( multiply @ sk_c11 @ sk_c5 ) = ( sk_c10 ) ) ))).
% 0.55/1.06 thf(zf_stmt_9, negated_conjecture,
% 0.55/1.06 (( ( multiply @ sk_c11 @ sk_c9 ) = ( sk_c10 ) ) |
% 0.55/1.06 ( ( multiply @ sk_c11 @ sk_c5 ) = ( sk_c10 ) )),
% 0.55/1.06 inference('cnf.neg', [status(esa)], [prove_this_34])).
% 0.55/1.06 thf(zip_derived_cl36, plain,
% 0.55/1.06 ((((multiply @ sk_c11 @ sk_c9) = (sk_c10))
% 0.55/1.06 | ((multiply @ sk_c11 @ sk_c5) = (sk_c10)))),
% 0.55/1.06 inference('cnf', [status(esa)], [zf_stmt_9])).
% 0.55/1.06 thf(zip_derived_cl1584, plain,
% 0.55/1.06 ((((multiply @ sk_c11 @ identity) = (sk_c10))
% 0.55/1.06 | ((multiply @ sk_c11 @ sk_c9) = (sk_c10))
% 0.55/1.06 | ((multiply @ sk_c11 @ sk_c9) = (sk_c10)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl1579, zip_derived_cl36])).
% 0.55/1.06 thf(zip_derived_cl618, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl138, zip_derived_cl135])).
% 0.55/1.06 thf(zip_derived_cl1598, plain,
% 0.55/1.06 ((((sk_c11) = (sk_c10))
% 0.55/1.06 | ((multiply @ sk_c11 @ sk_c9) = (sk_c10))
% 0.55/1.06 | ((multiply @ sk_c11 @ sk_c9) = (sk_c10)))),
% 0.55/1.06 inference('demod', [status(thm)], [zip_derived_cl1584, zip_derived_cl618])).
% 0.55/1.06 thf(zip_derived_cl1599, plain,
% 0.55/1.06 ((((multiply @ sk_c11 @ sk_c9) = (sk_c10)) | ((sk_c11) = (sk_c10)))),
% 0.55/1.06 inference('simplify', [status(thm)], [zip_derived_cl1598])).
% 0.55/1.06 thf(zip_derived_cl2220, plain,
% 0.55/1.06 ((((multiply @ sk_c11 @ identity) = (sk_c10))
% 0.55/1.06 | ((sk_c11) = (sk_c10))
% 0.55/1.06 | ((sk_c11) = (sk_c10)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl2212, zip_derived_cl1599])).
% 0.55/1.06 thf(zip_derived_cl618, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl138, zip_derived_cl135])).
% 0.55/1.06 thf(zip_derived_cl2226, plain,
% 0.55/1.06 ((((sk_c11) = (sk_c10)) | ((sk_c11) = (sk_c10)) | ((sk_c11) = (sk_c10)))),
% 0.55/1.06 inference('demod', [status(thm)], [zip_derived_cl2220, zip_derived_cl618])).
% 0.55/1.06 thf(zip_derived_cl2227, plain, (((sk_c11) = (sk_c10))),
% 0.55/1.06 inference('simplify', [status(thm)], [zip_derived_cl2226])).
% 0.55/1.06 thf(zip_derived_cl2290, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 0.55/1.06 (((inverse @ X0) != (sk_c11))
% 0.55/1.06 | ((multiply @ X0 @ sk_c11) != (sk_c11))
% 0.55/1.06 | ((multiply @ X2 @ X1) != (sk_c11))
% 0.55/1.06 | ((inverse @ X2) != (X1))
% 0.55/1.06 | ((multiply @ X1 @ sk_c11) != (sk_c11))
% 0.55/1.06 | ((multiply @ sk_c11 @ X3) != (sk_c11))
% 0.55/1.06 | ((multiply @ X4 @ sk_c11) != (X3))
% 0.55/1.06 | ((inverse @ X4) != (sk_c11))
% 0.55/1.06 | ((multiply @ X6 @ X5) != (sk_c11))
% 0.55/1.06 | ((inverse @ X6) != (X5))
% 0.55/1.06 | ((multiply @ X5 @ sk_c11) != (sk_c11))
% 0.55/1.06 | ((sk_c11) != (sk_c11)))),
% 0.55/1.06 inference('demod', [status(thm)], [zip_derived_cl723, zip_derived_cl2227])).
% 0.55/1.06 thf(zip_derived_cl2291, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 0.55/1.06 (((multiply @ X5 @ sk_c11) != (sk_c11))
% 0.55/1.06 | ((inverse @ X6) != (X5))
% 0.55/1.06 | ((multiply @ X6 @ X5) != (sk_c11))
% 0.55/1.06 | ((inverse @ X4) != (sk_c11))
% 0.55/1.06 | ((multiply @ X4 @ sk_c11) != (X3))
% 0.55/1.06 | ((multiply @ sk_c11 @ X3) != (sk_c11))
% 0.55/1.06 | ((multiply @ X1 @ sk_c11) != (sk_c11))
% 0.55/1.06 | ((inverse @ X2) != (X1))
% 0.55/1.06 | ((multiply @ X2 @ X1) != (sk_c11))
% 0.55/1.06 | ((multiply @ X0 @ sk_c11) != (sk_c11))
% 0.55/1.06 | ((inverse @ X0) != (sk_c11)))),
% 0.55/1.06 inference('simplify', [status(thm)], [zip_derived_cl2290])).
% 0.55/1.06 thf(zip_derived_cl2314, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 0.55/1.06 (((identity) != (X0))
% 0.55/1.06 | ((inverse @ X1) != (sk_c11))
% 0.55/1.06 | ((multiply @ X1 @ sk_c11) != (sk_c11))
% 0.55/1.06 | ((multiply @ X3 @ X2) != (sk_c11))
% 0.55/1.06 | ((inverse @ X3) != (X2))
% 0.55/1.06 | ((multiply @ X2 @ sk_c11) != (sk_c11))
% 0.55/1.06 | ((multiply @ sk_c11 @ X4) != (sk_c11))
% 0.55/1.06 | ((multiply @ X5 @ sk_c11) != (X4))
% 0.55/1.06 | ((inverse @ X5) != (sk_c11))
% 0.55/1.06 | ((multiply @ identity @ X0) != (sk_c11))
% 0.55/1.06 | ((multiply @ X0 @ sk_c11) != (sk_c11)))),
% 0.55/1.06 inference('sup-', [status(thm)], [zip_derived_cl443, zip_derived_cl2291])).
% 0.55/1.06 thf(zip_derived_cl0, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.55/1.06 inference('cnf', [status(esa)], [left_identity])).
% 0.55/1.06 thf(zip_derived_cl2326, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 0.55/1.06 (((identity) != (X0))
% 0.55/1.06 | ((inverse @ X1) != (sk_c11))
% 0.55/1.06 | ((multiply @ X1 @ sk_c11) != (sk_c11))
% 0.55/1.06 | ((multiply @ X3 @ X2) != (sk_c11))
% 0.55/1.06 | ((inverse @ X3) != (X2))
% 0.55/1.06 | ((multiply @ X2 @ sk_c11) != (sk_c11))
% 0.55/1.06 | ((multiply @ sk_c11 @ X4) != (sk_c11))
% 0.55/1.06 | ((multiply @ X5 @ sk_c11) != (X4))
% 0.55/1.06 | ((inverse @ X5) != (sk_c11))
% 0.55/1.06 | ((X0) != (sk_c11))
% 0.55/1.06 | ((multiply @ X0 @ sk_c11) != (sk_c11)))),
% 0.55/1.06 inference('demod', [status(thm)], [zip_derived_cl2314, zip_derived_cl0])).
% 0.55/1.06 thf(zip_derived_cl2331, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.55/1.06 (((multiply @ identity @ sk_c11) != (sk_c11))
% 0.55/1.06 | ((identity) != (sk_c11))
% 0.55/1.06 | ((inverse @ X0) != (sk_c11))
% 0.55/1.06 | ((multiply @ X0 @ sk_c11) != (X1))
% 0.55/1.06 | ((multiply @ sk_c11 @ X1) != (sk_c11))
% 0.55/1.06 | ((multiply @ X2 @ sk_c11) != (sk_c11))
% 0.55/1.06 | ((inverse @ X3) != (X2))
% 0.55/1.06 | ((multiply @ X3 @ X2) != (sk_c11))
% 0.55/1.06 | ((multiply @ X4 @ sk_c11) != (sk_c11))
% 0.55/1.06 | ((inverse @ X4) != (sk_c11)))),
% 0.55/1.06 inference('eq_res', [status(thm)], [zip_derived_cl2326])).
% 0.55/1.06 thf(zip_derived_cl2332, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.55/1.06 (((multiply @ identity @ identity) != (identity))
% 0.55/1.06 | ((identity) != (sk_c11))
% 0.55/1.06 | ((inverse @ X0) != (identity))
% 0.55/1.06 | ((multiply @ X0 @ identity) != (X1))
% 0.55/1.06 | ((multiply @ identity @ X1) != (identity))
% 0.55/1.06 | ((multiply @ X2 @ identity) != (identity))
% 0.55/1.06 | ((inverse @ X3) != (X2))
% 0.55/1.06 | ((multiply @ X3 @ X2) != (identity))
% 0.55/1.06 | ((multiply @ X4 @ identity) != (identity))
% 0.55/1.06 | ((inverse @ X4) != (identity)))),
% 0.55/1.06 inference('local_rewriting', [status(thm)], [zip_derived_cl2331])).
% 0.55/1.06 thf(zip_derived_cl0, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.55/1.06 inference('cnf', [status(esa)], [left_identity])).
% 0.55/1.06 thf(zip_derived_cl618, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl138, zip_derived_cl135])).
% 0.55/1.06 thf(zip_derived_cl0, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.55/1.06 inference('cnf', [status(esa)], [left_identity])).
% 0.55/1.06 thf(zip_derived_cl618, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl138, zip_derived_cl135])).
% 0.55/1.06 thf(zip_derived_cl618, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl138, zip_derived_cl135])).
% 0.55/1.06 thf(zip_derived_cl2333, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.55/1.06 (((identity) != (identity))
% 0.55/1.06 | ((identity) != (sk_c11))
% 0.55/1.06 | ((inverse @ X0) != (identity))
% 0.55/1.06 | ((X0) != (X1))
% 0.55/1.06 | ((X1) != (identity))
% 0.55/1.06 | ((X2) != (identity))
% 0.55/1.06 | ((inverse @ X3) != (X2))
% 0.55/1.06 | ((multiply @ X3 @ X2) != (identity))
% 0.55/1.06 | ((X4) != (identity))
% 0.55/1.06 | ((inverse @ X4) != (identity)))),
% 0.55/1.06 inference('demod', [status(thm)],
% 0.55/1.06 [zip_derived_cl2332, zip_derived_cl0, zip_derived_cl618,
% 0.55/1.06 zip_derived_cl0, zip_derived_cl618, zip_derived_cl618])).
% 0.55/1.06 thf(zip_derived_cl2334, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.55/1.06 (((inverse @ X4) != (identity))
% 0.55/1.06 | ((X4) != (identity))
% 0.55/1.06 | ((multiply @ X3 @ X2) != (identity))
% 0.55/1.06 | ((inverse @ X3) != (X2))
% 0.55/1.06 | ((X2) != (identity))
% 0.55/1.06 | ((X1) != (identity))
% 0.55/1.06 | ((X0) != (X1))
% 0.55/1.06 | ((inverse @ X0) != (identity))
% 0.55/1.06 | ((identity) != (sk_c11)))),
% 0.55/1.06 inference('simplify', [status(thm)], [zip_derived_cl2333])).
% 0.55/1.06 thf(zip_derived_cl2336, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/1.06 (((identity) != (sk_c11))
% 0.55/1.06 | ((inverse @ X0) != (identity))
% 0.55/1.06 | ((X0) != (identity))
% 0.55/1.06 | ((X1) != (identity))
% 0.55/1.06 | ((inverse @ X2) != (X1))
% 0.55/1.06 | ((multiply @ X2 @ X1) != (identity))
% 0.55/1.06 | ((X3) != (identity))
% 0.55/1.06 | ((inverse @ X3) != (identity)))),
% 0.55/1.06 inference('eq_res', [status(thm)], [zip_derived_cl2334])).
% 0.55/1.06 thf(prove_this_20, conjecture,
% 0.55/1.06 (~( ( ( inverse @ sk_c6 ) = ( sk_c7 ) ) |
% 0.55/1.06 ( ( inverse @ sk_c2 ) = ( sk_c3 ) ) ))).
% 0.55/1.06 thf(zf_stmt_10, negated_conjecture,
% 0.55/1.06 (( ( inverse @ sk_c6 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c3 ) )),
% 0.55/1.06 inference('cnf.neg', [status(esa)], [prove_this_20])).
% 0.55/1.06 thf(zip_derived_cl22, plain,
% 0.55/1.06 ((((inverse @ sk_c6) = (sk_c7)) | ((inverse @ sk_c2) = (sk_c3)))),
% 0.55/1.06 inference('cnf', [status(esa)], [zf_stmt_10])).
% 0.55/1.06 thf(prove_this_14, conjecture,
% 0.55/1.06 (~( ( ( inverse @ sk_c6 ) = ( sk_c7 ) ) |
% 0.55/1.06 ( ( multiply @ sk_c2 @ sk_c3 ) = ( sk_c10 ) ) ))).
% 0.55/1.06 thf(zf_stmt_11, negated_conjecture,
% 0.55/1.06 (( ( inverse @ sk_c6 ) = ( sk_c7 ) ) |
% 0.55/1.06 ( ( multiply @ sk_c2 @ sk_c3 ) = ( sk_c10 ) )),
% 0.55/1.06 inference('cnf.neg', [status(esa)], [prove_this_14])).
% 0.55/1.06 thf(zip_derived_cl16, plain,
% 0.55/1.06 ((((inverse @ sk_c6) = (sk_c7)) | ((multiply @ sk_c2 @ sk_c3) = (sk_c10)))),
% 0.55/1.06 inference('cnf', [status(esa)], [zf_stmt_11])).
% 0.55/1.06 thf(zip_derived_cl72, plain,
% 0.55/1.06 ((((multiply @ sk_c2 @ (inverse @ sk_c2)) = (sk_c10))
% 0.55/1.06 | ((inverse @ sk_c6) = (sk_c7))
% 0.55/1.06 | ((inverse @ sk_c6) = (sk_c7)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl16])).
% 0.55/1.06 thf(zip_derived_cl77, plain,
% 0.55/1.06 ((((inverse @ sk_c6) = (sk_c7))
% 0.55/1.06 | ((multiply @ sk_c2 @ (inverse @ sk_c2)) = (sk_c10)))),
% 0.55/1.06 inference('simplify', [status(thm)], [zip_derived_cl72])).
% 0.55/1.06 thf(zip_derived_cl644, plain,
% 0.55/1.06 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl618, zip_derived_cl138])).
% 0.55/1.06 thf(zip_derived_cl1, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.55/1.06 inference('cnf', [status(esa)], [left_inverse])).
% 0.55/1.06 thf(zip_derived_cl663, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl644, zip_derived_cl1])).
% 0.55/1.06 thf(zip_derived_cl1622, plain,
% 0.55/1.06 ((((inverse @ sk_c6) = (sk_c7)) | ((identity) = (sk_c10)))),
% 0.55/1.06 inference('demod', [status(thm)], [zip_derived_cl77, zip_derived_cl663])).
% 0.55/1.06 thf(prove_this_44, conjecture,
% 0.55/1.06 (~( ( ( inverse @ sk_c6 ) = ( sk_c7 ) ) |
% 0.55/1.06 ( ( inverse @ sk_c4 ) = ( sk_c11 ) ) ))).
% 0.55/1.06 thf(zf_stmt_12, negated_conjecture,
% 0.55/1.06 (( ( inverse @ sk_c6 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c4 ) = ( sk_c11 ) )),
% 0.55/1.06 inference('cnf.neg', [status(esa)], [prove_this_44])).
% 0.55/1.06 thf(zip_derived_cl46, plain,
% 0.55/1.06 ((((inverse @ sk_c6) = (sk_c7)) | ((inverse @ sk_c4) = (sk_c11)))),
% 0.55/1.06 inference('cnf', [status(esa)], [zf_stmt_12])).
% 0.55/1.06 thf(prove_this_38, conjecture,
% 0.55/1.06 (~( ( ( inverse @ sk_c6 ) = ( sk_c7 ) ) |
% 0.55/1.06 ( ( multiply @ sk_c4 @ sk_c11 ) = ( sk_c5 ) ) ))).
% 0.55/1.06 thf(zf_stmt_13, negated_conjecture,
% 0.55/1.06 (( ( inverse @ sk_c6 ) = ( sk_c7 ) ) |
% 0.55/1.06 ( ( multiply @ sk_c4 @ sk_c11 ) = ( sk_c5 ) )),
% 0.55/1.06 inference('cnf.neg', [status(esa)], [prove_this_38])).
% 0.55/1.06 thf(zip_derived_cl40, plain,
% 0.55/1.06 ((((inverse @ sk_c6) = (sk_c7)) | ((multiply @ sk_c4 @ sk_c11) = (sk_c5)))),
% 0.55/1.06 inference('cnf', [status(esa)], [zf_stmt_13])).
% 0.55/1.06 thf(zip_derived_cl129, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i]:
% 0.55/1.06 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.55/1.06 inference('demod', [status(thm)], [zip_derived_cl111, zip_derived_cl0])).
% 0.55/1.06 thf(zip_derived_cl154, plain,
% 0.55/1.06 ((((sk_c11) = (multiply @ (inverse @ sk_c4) @ sk_c5))
% 0.55/1.06 | ((inverse @ sk_c6) = (sk_c7)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl129])).
% 0.55/1.06 thf(zip_derived_cl415, plain,
% 0.55/1.06 ((((sk_c11) = (multiply @ sk_c11 @ sk_c5))
% 0.55/1.06 | ((inverse @ sk_c6) = (sk_c7))
% 0.55/1.06 | ((inverse @ sk_c6) = (sk_c7)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl46, zip_derived_cl154])).
% 0.55/1.06 thf(zip_derived_cl424, plain,
% 0.55/1.06 ((((inverse @ sk_c6) = (sk_c7))
% 0.55/1.06 | ((sk_c11) = (multiply @ sk_c11 @ sk_c5)))),
% 0.55/1.06 inference('simplify', [status(thm)], [zip_derived_cl415])).
% 0.55/1.06 thf(prove_this_32, conjecture,
% 0.55/1.06 (~( ( ( inverse @ sk_c6 ) = ( sk_c7 ) ) |
% 0.55/1.06 ( ( multiply @ sk_c11 @ sk_c5 ) = ( sk_c10 ) ) ))).
% 0.55/1.06 thf(zf_stmt_14, negated_conjecture,
% 0.55/1.06 (( ( inverse @ sk_c6 ) = ( sk_c7 ) ) |
% 0.55/1.06 ( ( multiply @ sk_c11 @ sk_c5 ) = ( sk_c10 ) )),
% 0.55/1.06 inference('cnf.neg', [status(esa)], [prove_this_32])).
% 0.55/1.06 thf(zip_derived_cl34, plain,
% 0.55/1.06 ((((inverse @ sk_c6) = (sk_c7))
% 0.55/1.06 | ((multiply @ sk_c11 @ sk_c5) = (sk_c10)))),
% 0.55/1.06 inference('cnf', [status(esa)], [zf_stmt_14])).
% 0.55/1.06 thf(zip_derived_cl454, plain,
% 0.55/1.06 ((((sk_c11) = (sk_c10))
% 0.55/1.06 | ((inverse @ sk_c6) = (sk_c7))
% 0.55/1.06 | ((inverse @ sk_c6) = (sk_c7)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl424, zip_derived_cl34])).
% 0.55/1.06 thf(zip_derived_cl463, plain,
% 0.55/1.06 ((((inverse @ sk_c6) = (sk_c7)) | ((sk_c11) = (sk_c10)))),
% 0.55/1.06 inference('simplify', [status(thm)], [zip_derived_cl454])).
% 0.55/1.06 thf(zip_derived_cl1634, plain,
% 0.55/1.06 ((((sk_c11) = (identity))
% 0.55/1.06 | ((inverse @ sk_c6) = (sk_c7))
% 0.55/1.06 | ((inverse @ sk_c6) = (sk_c7)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl1622, zip_derived_cl463])).
% 0.55/1.06 thf(zip_derived_cl1656, plain,
% 0.55/1.06 ((((inverse @ sk_c6) = (sk_c7)) | ((sk_c11) = (identity)))),
% 0.55/1.06 inference('simplify', [status(thm)], [zip_derived_cl1634])).
% 0.55/1.06 thf(prove_this_1, conjecture,
% 0.55/1.06 (~( ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c11 ) ) |
% 0.55/1.06 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 0.55/1.06 thf(zf_stmt_15, negated_conjecture,
% 0.55/1.06 (( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c11 ) ) |
% 0.55/1.06 ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 0.55/1.06 inference('cnf.neg', [status(esa)], [prove_this_1])).
% 0.55/1.06 thf(zip_derived_cl3, plain,
% 0.55/1.06 ((((multiply @ sk_c6 @ sk_c7) = (sk_c11))
% 0.55/1.06 | ((inverse @ sk_c1) = (sk_c11)))),
% 0.55/1.06 inference('cnf', [status(esa)], [zf_stmt_15])).
% 0.55/1.06 thf(zip_derived_cl1672, plain,
% 0.55/1.06 ((((multiply @ sk_c6 @ (inverse @ sk_c6)) = (sk_c11))
% 0.55/1.06 | ((sk_c11) = (identity))
% 0.55/1.06 | ((inverse @ sk_c1) = (sk_c11)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl1656, zip_derived_cl3])).
% 0.55/1.06 thf(zip_derived_cl663, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl644, zip_derived_cl1])).
% 0.55/1.06 thf(zip_derived_cl1680, plain,
% 0.55/1.06 ((((identity) = (sk_c11))
% 0.55/1.06 | ((sk_c11) = (identity))
% 0.55/1.06 | ((inverse @ sk_c1) = (sk_c11)))),
% 0.55/1.06 inference('demod', [status(thm)], [zip_derived_cl1672, zip_derived_cl663])).
% 0.55/1.06 thf(zip_derived_cl1681, plain,
% 0.55/1.06 ((((inverse @ sk_c1) = (sk_c11)) | ((identity) = (sk_c11)))),
% 0.55/1.06 inference('simplify', [status(thm)], [zip_derived_cl1680])).
% 0.55/1.06 thf(zip_derived_cl463, plain,
% 0.55/1.06 ((((inverse @ sk_c6) = (sk_c7)) | ((sk_c11) = (sk_c10)))),
% 0.55/1.06 inference('simplify', [status(thm)], [zip_derived_cl454])).
% 0.55/1.06 thf(prove_this_8, conjecture,
% 0.55/1.06 (~( ( ( inverse @ sk_c6 ) = ( sk_c7 ) ) |
% 0.55/1.06 ( ( multiply @ sk_c1 @ sk_c10 ) = ( sk_c11 ) ) ))).
% 0.55/1.06 thf(zf_stmt_16, negated_conjecture,
% 0.55/1.06 (( ( inverse @ sk_c6 ) = ( sk_c7 ) ) |
% 0.55/1.06 ( ( multiply @ sk_c1 @ sk_c10 ) = ( sk_c11 ) )),
% 0.55/1.06 inference('cnf.neg', [status(esa)], [prove_this_8])).
% 0.55/1.06 thf(zip_derived_cl10, plain,
% 0.55/1.06 ((((inverse @ sk_c6) = (sk_c7))
% 0.55/1.06 | ((multiply @ sk_c1 @ sk_c10) = (sk_c11)))),
% 0.55/1.06 inference('cnf', [status(esa)], [zf_stmt_16])).
% 0.55/1.06 thf(zip_derived_cl466, plain,
% 0.55/1.06 ((((multiply @ sk_c1 @ sk_c11) = (sk_c11))
% 0.55/1.06 | ((inverse @ sk_c6) = (sk_c7))
% 0.55/1.06 | ((inverse @ sk_c6) = (sk_c7)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl463, zip_derived_cl10])).
% 0.55/1.06 thf(zip_derived_cl473, plain,
% 0.55/1.06 ((((inverse @ sk_c6) = (sk_c7))
% 0.55/1.06 | ((multiply @ sk_c1 @ sk_c11) = (sk_c11)))),
% 0.55/1.06 inference('simplify', [status(thm)], [zip_derived_cl466])).
% 0.55/1.06 thf(prove_this_43, conjecture,
% 0.55/1.06 (~( ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c11 ) ) |
% 0.55/1.06 ( ( inverse @ sk_c4 ) = ( sk_c11 ) ) ))).
% 0.55/1.06 thf(zf_stmt_17, negated_conjecture,
% 0.55/1.06 (( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c11 ) ) |
% 0.55/1.06 ( ( inverse @ sk_c4 ) = ( sk_c11 ) )),
% 0.55/1.06 inference('cnf.neg', [status(esa)], [prove_this_43])).
% 0.55/1.06 thf(zip_derived_cl45, plain,
% 0.55/1.06 ((((multiply @ sk_c6 @ sk_c7) = (sk_c11))
% 0.55/1.06 | ((inverse @ sk_c4) = (sk_c11)))),
% 0.55/1.06 inference('cnf', [status(esa)], [zf_stmt_17])).
% 0.55/1.06 thf(zip_derived_cl644, plain,
% 0.55/1.06 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl618, zip_derived_cl138])).
% 0.55/1.06 thf(zip_derived_cl671, plain,
% 0.55/1.06 ((((sk_c4) = (inverse @ sk_c11))
% 0.55/1.06 | ((multiply @ sk_c6 @ sk_c7) = (sk_c11)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl45, zip_derived_cl644])).
% 0.55/1.06 thf(prove_this_37, conjecture,
% 0.55/1.06 (~( ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c11 ) ) |
% 0.55/1.06 ( ( multiply @ sk_c4 @ sk_c11 ) = ( sk_c5 ) ) ))).
% 0.55/1.06 thf(zf_stmt_18, negated_conjecture,
% 0.55/1.06 (( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c11 ) ) |
% 0.55/1.06 ( ( multiply @ sk_c4 @ sk_c11 ) = ( sk_c5 ) )),
% 0.55/1.06 inference('cnf.neg', [status(esa)], [prove_this_37])).
% 0.55/1.06 thf(zip_derived_cl39, plain,
% 0.55/1.06 ((((multiply @ sk_c6 @ sk_c7) = (sk_c11))
% 0.55/1.06 | ((multiply @ sk_c4 @ sk_c11) = (sk_c5)))),
% 0.55/1.06 inference('cnf', [status(esa)], [zf_stmt_18])).
% 0.55/1.06 thf(zip_derived_cl1261, plain,
% 0.55/1.06 ((((multiply @ (inverse @ sk_c11) @ sk_c11) = (sk_c5))
% 0.55/1.06 | ((multiply @ sk_c6 @ sk_c7) = (sk_c11))
% 0.55/1.06 | ((multiply @ sk_c6 @ sk_c7) = (sk_c11)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl671, zip_derived_cl39])).
% 0.55/1.06 thf(zip_derived_cl1, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.55/1.06 inference('cnf', [status(esa)], [left_inverse])).
% 0.55/1.06 thf(zip_derived_cl1267, plain,
% 0.55/1.06 ((((identity) = (sk_c5))
% 0.55/1.06 | ((multiply @ sk_c6 @ sk_c7) = (sk_c11))
% 0.55/1.06 | ((multiply @ sk_c6 @ sk_c7) = (sk_c11)))),
% 0.55/1.06 inference('demod', [status(thm)], [zip_derived_cl1261, zip_derived_cl1])).
% 0.55/1.06 thf(zip_derived_cl1268, plain,
% 0.55/1.06 ((((multiply @ sk_c6 @ sk_c7) = (sk_c11)) | ((identity) = (sk_c5)))),
% 0.55/1.06 inference('simplify', [status(thm)], [zip_derived_cl1267])).
% 0.55/1.06 thf(prove_this_31, conjecture,
% 0.55/1.06 (~( ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c11 ) ) |
% 0.55/1.06 ( ( multiply @ sk_c11 @ sk_c5 ) = ( sk_c10 ) ) ))).
% 0.55/1.06 thf(zf_stmt_19, negated_conjecture,
% 0.55/1.06 (( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c11 ) ) |
% 0.55/1.06 ( ( multiply @ sk_c11 @ sk_c5 ) = ( sk_c10 ) )),
% 0.55/1.06 inference('cnf.neg', [status(esa)], [prove_this_31])).
% 0.55/1.06 thf(zip_derived_cl33, plain,
% 0.55/1.06 ((((multiply @ sk_c6 @ sk_c7) = (sk_c11))
% 0.55/1.06 | ((multiply @ sk_c11 @ sk_c5) = (sk_c10)))),
% 0.55/1.06 inference('cnf', [status(esa)], [zf_stmt_19])).
% 0.55/1.06 thf(zip_derived_cl1272, plain,
% 0.55/1.06 ((((multiply @ sk_c11 @ identity) = (sk_c10))
% 0.55/1.06 | ((multiply @ sk_c6 @ sk_c7) = (sk_c11))
% 0.55/1.06 | ((multiply @ sk_c6 @ sk_c7) = (sk_c11)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl1268, zip_derived_cl33])).
% 0.55/1.06 thf(zip_derived_cl618, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl138, zip_derived_cl135])).
% 0.55/1.06 thf(zip_derived_cl1282, plain,
% 0.55/1.06 ((((sk_c11) = (sk_c10))
% 0.55/1.06 | ((multiply @ sk_c6 @ sk_c7) = (sk_c11))
% 0.55/1.06 | ((multiply @ sk_c6 @ sk_c7) = (sk_c11)))),
% 0.55/1.06 inference('demod', [status(thm)], [zip_derived_cl1272, zip_derived_cl618])).
% 0.55/1.06 thf(zip_derived_cl1283, plain,
% 0.55/1.06 ((((multiply @ sk_c6 @ sk_c7) = (sk_c11)) | ((sk_c11) = (sk_c10)))),
% 0.55/1.06 inference('simplify', [status(thm)], [zip_derived_cl1282])).
% 0.55/1.06 thf(prove_this_7, conjecture,
% 0.55/1.06 (~( ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c11 ) ) |
% 0.55/1.06 ( ( multiply @ sk_c1 @ sk_c10 ) = ( sk_c11 ) ) ))).
% 0.55/1.06 thf(zf_stmt_20, negated_conjecture,
% 0.55/1.06 (( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c11 ) ) |
% 0.55/1.06 ( ( multiply @ sk_c1 @ sk_c10 ) = ( sk_c11 ) )),
% 0.55/1.06 inference('cnf.neg', [status(esa)], [prove_this_7])).
% 0.55/1.06 thf(zip_derived_cl9, plain,
% 0.55/1.06 ((((multiply @ sk_c6 @ sk_c7) = (sk_c11))
% 0.55/1.06 | ((multiply @ sk_c1 @ sk_c10) = (sk_c11)))),
% 0.55/1.06 inference('cnf', [status(esa)], [zf_stmt_20])).
% 0.55/1.06 thf(zip_derived_cl1293, plain,
% 0.55/1.06 ((((multiply @ sk_c1 @ sk_c11) = (sk_c11))
% 0.55/1.06 | ((multiply @ sk_c6 @ sk_c7) = (sk_c11))
% 0.55/1.06 | ((multiply @ sk_c6 @ sk_c7) = (sk_c11)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl1283, zip_derived_cl9])).
% 0.55/1.06 thf(zip_derived_cl1307, plain,
% 0.55/1.06 ((((multiply @ sk_c6 @ sk_c7) = (sk_c11))
% 0.55/1.06 | ((multiply @ sk_c1 @ sk_c11) = (sk_c11)))),
% 0.55/1.06 inference('simplify', [status(thm)], [zip_derived_cl1293])).
% 0.55/1.06 thf(zip_derived_cl3780, plain,
% 0.55/1.06 ((((multiply @ sk_c6 @ (inverse @ sk_c6)) = (sk_c11))
% 0.55/1.06 | ((multiply @ sk_c1 @ sk_c11) = (sk_c11))
% 0.55/1.06 | ((multiply @ sk_c1 @ sk_c11) = (sk_c11)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl473, zip_derived_cl1307])).
% 0.55/1.06 thf(zip_derived_cl663, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl644, zip_derived_cl1])).
% 0.55/1.06 thf(zip_derived_cl3791, plain,
% 0.55/1.06 ((((identity) = (sk_c11))
% 0.55/1.06 | ((multiply @ sk_c1 @ sk_c11) = (sk_c11))
% 0.55/1.06 | ((multiply @ sk_c1 @ sk_c11) = (sk_c11)))),
% 0.55/1.06 inference('demod', [status(thm)], [zip_derived_cl3780, zip_derived_cl663])).
% 0.55/1.06 thf(zip_derived_cl3792, plain,
% 0.55/1.06 ((((multiply @ sk_c1 @ sk_c11) = (sk_c11)) | ((identity) = (sk_c11)))),
% 0.55/1.06 inference('simplify', [status(thm)], [zip_derived_cl3791])).
% 0.55/1.06 thf(zip_derived_cl3806, plain,
% 0.55/1.06 ((((multiply @ sk_c1 @ (inverse @ sk_c1)) = (sk_c11))
% 0.55/1.06 | ((identity) = (sk_c11))
% 0.55/1.06 | ((identity) = (sk_c11)))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl1681, zip_derived_cl3792])).
% 0.55/1.06 thf(zip_derived_cl663, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl644, zip_derived_cl1])).
% 0.55/1.06 thf(zip_derived_cl3807, plain,
% 0.55/1.06 ((((identity) = (sk_c11))
% 0.55/1.06 | ((identity) = (sk_c11))
% 0.55/1.06 | ((identity) = (sk_c11)))),
% 0.55/1.06 inference('demod', [status(thm)], [zip_derived_cl3806, zip_derived_cl663])).
% 0.55/1.06 thf(zip_derived_cl3808, plain, (((identity) = (sk_c11))),
% 0.55/1.06 inference('simplify', [status(thm)], [zip_derived_cl3807])).
% 0.55/1.06 thf(zip_derived_cl3903, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/1.06 (((identity) != (identity))
% 0.55/1.06 | ((inverse @ X0) != (identity))
% 0.55/1.06 | ((X0) != (identity))
% 0.55/1.06 | ((X1) != (identity))
% 0.55/1.06 | ((inverse @ X2) != (X1))
% 0.55/1.06 | ((multiply @ X2 @ X1) != (identity))
% 0.55/1.06 | ((X3) != (identity))
% 0.55/1.06 | ((inverse @ X3) != (identity)))),
% 0.55/1.06 inference('demod', [status(thm)],
% 0.55/1.06 [zip_derived_cl2336, zip_derived_cl3808])).
% 0.55/1.06 thf(zip_derived_cl3904, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/1.06 (((inverse @ X3) != (identity))
% 0.55/1.06 | ((X3) != (identity))
% 0.55/1.06 | ((multiply @ X2 @ X1) != (identity))
% 0.55/1.06 | ((inverse @ X2) != (X1))
% 0.55/1.06 | ((X1) != (identity))
% 0.55/1.06 | ((X0) != (identity))
% 0.55/1.06 | ((inverse @ X0) != (identity)))),
% 0.55/1.06 inference('simplify', [status(thm)], [zip_derived_cl3903])).
% 0.55/1.06 thf(zip_derived_cl3933, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/1.06 (((inverse @ X0) != (identity))
% 0.55/1.06 | ((X0) != (identity))
% 0.55/1.06 | ((X1) != (identity))
% 0.55/1.06 | ((inverse @ X2) != (X1))
% 0.55/1.06 | ((multiply @ X2 @ X1) != (identity))
% 0.55/1.06 | ((inverse @ identity) != (identity)))),
% 0.55/1.06 inference('eq_res', [status(thm)], [zip_derived_cl3904])).
% 0.55/1.06 thf(zip_derived_cl443, plain, (((inverse @ identity) = (identity))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl166, zip_derived_cl1])).
% 0.55/1.06 thf(zip_derived_cl3934, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/1.06 (((inverse @ X0) != (identity))
% 0.55/1.06 | ((X0) != (identity))
% 0.55/1.06 | ((X1) != (identity))
% 0.55/1.06 | ((inverse @ X2) != (X1))
% 0.55/1.06 | ((multiply @ X2 @ X1) != (identity))
% 0.55/1.06 | ((identity) != (identity)))),
% 0.55/1.06 inference('demod', [status(thm)], [zip_derived_cl3933, zip_derived_cl443])).
% 0.55/1.06 thf(zip_derived_cl3935, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/1.06 (((multiply @ X2 @ X1) != (identity))
% 0.55/1.06 | ((inverse @ X2) != (X1))
% 0.55/1.06 | ((X1) != (identity))
% 0.55/1.06 | ((X0) != (identity))
% 0.55/1.06 | ((inverse @ X0) != (identity)))),
% 0.55/1.06 inference('simplify', [status(thm)], [zip_derived_cl3934])).
% 0.55/1.06 thf(zip_derived_cl3936, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i]:
% 0.55/1.06 (((inverse @ X0) != (identity))
% 0.55/1.06 | ((X0) != (identity))
% 0.55/1.06 | ((inverse @ X1) != (identity))
% 0.55/1.06 | ((multiply @ X1 @ identity) != (identity)))),
% 0.55/1.06 inference('eq_res', [status(thm)], [zip_derived_cl3935])).
% 0.55/1.06 thf(zip_derived_cl618, plain,
% 0.55/1.06 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl138, zip_derived_cl135])).
% 0.55/1.06 thf(zip_derived_cl3937, plain,
% 0.55/1.06 (![X0 : $i, X1 : $i]:
% 0.55/1.06 (((inverse @ X0) != (identity))
% 0.55/1.06 | ((X0) != (identity))
% 0.55/1.06 | ((inverse @ X1) != (identity))
% 0.55/1.06 | ((X1) != (identity)))),
% 0.55/1.06 inference('demod', [status(thm)], [zip_derived_cl3936, zip_derived_cl618])).
% 0.55/1.06 thf(zip_derived_cl3938, plain,
% 0.55/1.06 (![X0 : $i]:
% 0.55/1.06 (((X0) != (identity))
% 0.55/1.06 | ((inverse @ X0) != (identity))
% 0.55/1.06 | ((inverse @ identity) != (identity)))),
% 0.55/1.06 inference('eq_res', [status(thm)], [zip_derived_cl3937])).
% 0.55/1.06 thf(zip_derived_cl443, plain, (((inverse @ identity) = (identity))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl166, zip_derived_cl1])).
% 0.55/1.06 thf(zip_derived_cl3939, plain,
% 0.55/1.06 (![X0 : $i]:
% 0.55/1.06 (((X0) != (identity))
% 0.55/1.06 | ((inverse @ X0) != (identity))
% 0.55/1.06 | ((identity) != (identity)))),
% 0.55/1.06 inference('demod', [status(thm)], [zip_derived_cl3938, zip_derived_cl443])).
% 0.55/1.06 thf(zip_derived_cl3940, plain,
% 0.55/1.06 (![X0 : $i]: (((inverse @ X0) != (identity)) | ((X0) != (identity)))),
% 0.55/1.06 inference('simplify', [status(thm)], [zip_derived_cl3939])).
% 0.55/1.06 thf(zip_derived_cl3941, plain, (((inverse @ identity) != (identity))),
% 0.55/1.06 inference('eq_res', [status(thm)], [zip_derived_cl3940])).
% 0.55/1.06 thf(zip_derived_cl443, plain, (((inverse @ identity) = (identity))),
% 0.55/1.06 inference('sup+', [status(thm)], [zip_derived_cl166, zip_derived_cl1])).
% 0.55/1.06 thf(zip_derived_cl3942, plain, (((identity) != (identity))),
% 0.55/1.06 inference('demod', [status(thm)], [zip_derived_cl3941, zip_derived_cl443])).
% 0.55/1.06 thf(zip_derived_cl3943, plain, ($false),
% 0.55/1.06 inference('simplify', [status(thm)], [zip_derived_cl3942])).
% 0.55/1.06
% 0.55/1.06 % SZS output end Refutation
% 0.55/1.06
% 0.55/1.06
% 0.55/1.06 % Terminating...
% 3.53/1.15 % Runner terminated.
% 3.53/1.16 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------