TSTP Solution File: GRP242-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP242-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.dOopLvaKgr 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 01:50:52 EDT 2023
% Result : Unsatisfiable 43.11s 6.77s
% Output : Refutation 43.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP242-1 : TPTP v8.1.2. Released v2.5.0.
% 0.07/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.dOopLvaKgr 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 22:32:30 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/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
% 0.52/0.62 % Total configuration time : 435
% 0.52/0.62 % Estimated wc time : 1092
% 0.52/0.62 % Estimated cpu time (7 cpus) : 156.0
% 0.54/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.54/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.54/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.54/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.54/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.54/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.54/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 43.11/6.77 % Solved by fo/fo7.sh.
% 43.11/6.77 % done 8450 iterations in 5.981s
% 43.11/6.77 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 43.11/6.77 % SZS output start Refutation
% 43.11/6.77 thf(sk_c2_type, type, sk_c2: $i).
% 43.11/6.77 thf(sk_c10_type, type, sk_c10: $i).
% 43.11/6.77 thf(sk_c6_type, type, sk_c6: $i).
% 43.11/6.77 thf(sk_c8_type, type, sk_c8: $i).
% 43.11/6.77 thf(sk_c7_type, type, sk_c7: $i).
% 43.11/6.77 thf(identity_type, type, identity: $i).
% 43.11/6.77 thf(multiply_type, type, multiply: $i > $i > $i).
% 43.11/6.77 thf(sk_c11_type, type, sk_c11: $i).
% 43.11/6.77 thf(sk_c4_type, type, sk_c4: $i).
% 43.11/6.77 thf(inverse_type, type, inverse: $i > $i).
% 43.11/6.77 thf(sk_c9_type, type, sk_c9: $i).
% 43.11/6.77 thf(sk_c5_type, type, sk_c5: $i).
% 43.11/6.77 thf(sk_c3_type, type, sk_c3: $i).
% 43.11/6.77 thf(sk_c1_type, type, sk_c1: $i).
% 43.11/6.77 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 43.11/6.77 thf(zip_derived_cl0, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 43.11/6.77 inference('cnf', [status(esa)], [left_identity])).
% 43.11/6.77 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 43.11/6.77 thf(zip_derived_cl1, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 43.11/6.77 inference('cnf', [status(esa)], [left_inverse])).
% 43.11/6.77 thf(associativity, axiom,
% 43.11/6.77 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 43.11/6.77 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 43.11/6.77 thf(zip_derived_cl2, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 43.11/6.77 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 43.11/6.77 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 43.11/6.77 inference('cnf', [status(esa)], [associativity])).
% 43.11/6.77 thf(zip_derived_cl375, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i]:
% 43.11/6.77 ((multiply @ identity @ X0)
% 43.11/6.77 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 43.11/6.77 thf(zip_derived_cl0, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 43.11/6.77 inference('cnf', [status(esa)], [left_identity])).
% 43.11/6.77 thf(zip_derived_cl408, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i]:
% 43.11/6.77 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 43.11/6.77 inference('demod', [status(thm)], [zip_derived_cl375, zip_derived_cl0])).
% 43.11/6.77 thf(zip_derived_cl425, plain,
% 43.11/6.77 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl408])).
% 43.11/6.77 thf(zip_derived_cl408, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i]:
% 43.11/6.77 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 43.11/6.77 inference('demod', [status(thm)], [zip_derived_cl375, zip_derived_cl0])).
% 43.11/6.77 thf(zip_derived_cl483, plain,
% 43.11/6.77 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ identity)) @ X0))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl425, zip_derived_cl408])).
% 43.11/6.77 thf(zip_derived_cl1, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 43.11/6.77 inference('cnf', [status(esa)], [left_inverse])).
% 43.11/6.77 thf(zip_derived_cl1313, plain, (((inverse @ identity) = (identity))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl483, zip_derived_cl1])).
% 43.11/6.77 thf(prove_this_61, conjecture,
% 43.11/6.77 (~( ( ( inverse @ X2 ) != ( sk_c11 ) ) |
% 43.11/6.77 ( ( multiply @ X2 @ sk_c11 ) != ( sk_c9 ) ) |
% 43.11/6.77 ( ( inverse @ X1 ) != ( sk_c10 ) ) |
% 43.11/6.77 ( ( multiply @ X1 @ sk_c10 ) != ( sk_c11 ) ) |
% 43.11/6.77 ( ( inverse @ sk_c10 ) != ( sk_c9 ) ) |
% 43.11/6.77 ( ( multiply @ sk_c10 @ sk_c9 ) != ( sk_c11 ) ) |
% 43.11/6.77 ( ( multiply @ X7 @ X6 ) != ( X8 ) ) |
% 43.11/6.77 ( ( inverse @ X8 ) != ( X6 ) ) | ( ( inverse @ X7 ) != ( X8 ) ) |
% 43.11/6.77 ( ( multiply @ X6 @ sk_c10 ) != ( sk_c11 ) ) |
% 43.11/6.77 ( ( inverse @ X5 ) != ( X6 ) ) |
% 43.11/6.77 ( ( multiply @ X5 @ X6 ) != ( sk_c11 ) ) |
% 43.11/6.77 ( ( inverse @ X4 ) != ( sk_c10 ) ) |
% 43.11/6.77 ( ( multiply @ X4 @ sk_c10 ) != ( sk_c9 ) ) |
% 43.11/6.77 ( ( inverse @ X3 ) != ( sk_c11 ) ) |
% 43.11/6.77 ( ( multiply @ X3 @ sk_c11 ) != ( sk_c10 ) ) ))).
% 43.11/6.77 thf(zf_stmt_0, negated_conjecture,
% 43.11/6.77 (( ( inverse @ X2 ) != ( sk_c11 ) ) |
% 43.11/6.77 ( ( multiply @ X2 @ sk_c11 ) != ( sk_c9 ) ) |
% 43.11/6.77 ( ( inverse @ X1 ) != ( sk_c10 ) ) |
% 43.11/6.77 ( ( multiply @ X1 @ sk_c10 ) != ( sk_c11 ) ) |
% 43.11/6.77 ( ( inverse @ sk_c10 ) != ( sk_c9 ) ) |
% 43.11/6.77 ( ( multiply @ sk_c10 @ sk_c9 ) != ( sk_c11 ) ) |
% 43.11/6.77 ( ( multiply @ X7 @ X6 ) != ( X8 ) ) | ( ( inverse @ X8 ) != ( X6 ) ) |
% 43.11/6.77 ( ( inverse @ X7 ) != ( X8 ) ) |
% 43.11/6.77 ( ( multiply @ X6 @ sk_c10 ) != ( sk_c11 ) ) |
% 43.11/6.77 ( ( inverse @ X5 ) != ( X6 ) ) |
% 43.11/6.77 ( ( multiply @ X5 @ X6 ) != ( sk_c11 ) ) |
% 43.11/6.77 ( ( inverse @ X4 ) != ( sk_c10 ) ) |
% 43.11/6.77 ( ( multiply @ X4 @ sk_c10 ) != ( sk_c9 ) ) |
% 43.11/6.77 ( ( inverse @ X3 ) != ( sk_c11 ) ) |
% 43.11/6.77 ( ( multiply @ X3 @ sk_c11 ) != ( sk_c10 ) )),
% 43.11/6.77 inference('cnf.neg', [status(esa)], [prove_this_61])).
% 43.11/6.77 thf(zip_derived_cl63, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 43.11/6.77 (((inverse @ X0) != (sk_c11))
% 43.11/6.77 | ((multiply @ X0 @ sk_c11) != (sk_c9))
% 43.11/6.77 | ((inverse @ X1) != (sk_c10))
% 43.11/6.77 | ((multiply @ X1 @ sk_c10) != (sk_c11))
% 43.11/6.77 | ((inverse @ sk_c10) != (sk_c9))
% 43.11/6.77 | ((multiply @ sk_c10 @ sk_c9) != (sk_c11))
% 43.11/6.77 | ((multiply @ X3 @ X4) != (X2))
% 43.11/6.77 | ((inverse @ X2) != (X4))
% 43.11/6.77 | ((inverse @ X3) != (X2))
% 43.11/6.77 | ((multiply @ X4 @ sk_c10) != (sk_c11))
% 43.11/6.77 | ((inverse @ X5) != (X4))
% 43.11/6.77 | ((multiply @ X5 @ X4) != (sk_c11))
% 43.11/6.77 | ((inverse @ X6) != (sk_c10))
% 43.11/6.77 | ((multiply @ X6 @ sk_c10) != (sk_c9))
% 43.11/6.77 | ((inverse @ X7) != (sk_c11))
% 43.11/6.77 | ((multiply @ X7 @ sk_c11) != (sk_c10)))),
% 43.11/6.77 inference('cnf', [status(esa)], [zf_stmt_0])).
% 43.11/6.77 thf(zip_derived_cl64, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 43.11/6.77 (((inverse @ X0) != (sk_c11))
% 43.11/6.77 | ((multiply @ X0 @ sk_c11) != (inverse @ sk_c10))
% 43.11/6.77 | ((inverse @ X1) != (sk_c10))
% 43.11/6.77 | ((multiply @ X1 @ sk_c10) != (sk_c11))
% 43.11/6.77 | ((inverse @ sk_c10) != (sk_c9))
% 43.11/6.77 | ((multiply @ sk_c10 @ (inverse @ sk_c10)) != (sk_c11))
% 43.11/6.77 | ((multiply @ X3 @ X4) != (X2))
% 43.11/6.77 | ((inverse @ X2) != (X4))
% 43.11/6.77 | ((inverse @ X3) != (X2))
% 43.11/6.77 | ((multiply @ X4 @ sk_c10) != (sk_c11))
% 43.11/6.77 | ((inverse @ X5) != (X4))
% 43.11/6.77 | ((multiply @ X5 @ X4) != (sk_c11))
% 43.11/6.77 | ((inverse @ X6) != (sk_c10))
% 43.11/6.77 | ((multiply @ X6 @ sk_c10) != (inverse @ sk_c10))
% 43.11/6.77 | ((inverse @ X7) != (sk_c11))
% 43.11/6.77 | ((multiply @ X7 @ sk_c11) != (sk_c10)))),
% 43.11/6.77 inference('local_rewriting', [status(thm)], [zip_derived_cl63])).
% 43.11/6.77 thf(prove_this_24, conjecture,
% 43.11/6.77 (~( ( ( inverse @ sk_c8 ) = ( sk_c11 ) ) |
% 43.11/6.77 ( ( inverse @ sk_c2 ) = ( sk_c10 ) ) ))).
% 43.11/6.77 thf(zf_stmt_1, negated_conjecture,
% 43.11/6.77 (( ( inverse @ sk_c8 ) = ( sk_c11 ) ) |
% 43.11/6.77 ( ( inverse @ sk_c2 ) = ( sk_c10 ) )),
% 43.11/6.77 inference('cnf.neg', [status(esa)], [prove_this_24])).
% 43.11/6.77 thf(zip_derived_cl26, plain,
% 43.11/6.77 ((((inverse @ sk_c8) = (sk_c11)) | ((inverse @ sk_c2) = (sk_c10)))),
% 43.11/6.77 inference('cnf', [status(esa)], [zf_stmt_1])).
% 43.11/6.77 thf(zip_derived_cl1, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 43.11/6.77 inference('cnf', [status(esa)], [left_inverse])).
% 43.11/6.77 thf(zip_derived_cl78, plain,
% 43.11/6.77 ((((multiply @ sk_c10 @ sk_c2) = (identity))
% 43.11/6.77 | ((inverse @ sk_c8) = (sk_c11)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl1])).
% 43.11/6.77 thf(zip_derived_cl408, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i]:
% 43.11/6.77 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 43.11/6.77 inference('demod', [status(thm)], [zip_derived_cl375, zip_derived_cl0])).
% 43.11/6.77 thf(zip_derived_cl437, plain,
% 43.11/6.77 ((((sk_c2) = (multiply @ (inverse @ sk_c10) @ identity))
% 43.11/6.77 | ((inverse @ sk_c8) = (sk_c11)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl78, zip_derived_cl408])).
% 43.11/6.77 thf(prove_this_18, conjecture,
% 43.11/6.77 (~( ( ( inverse @ sk_c8 ) = ( sk_c11 ) ) |
% 43.11/6.77 ( ( multiply @ sk_c2 @ sk_c10 ) = ( sk_c9 ) ) ))).
% 43.11/6.77 thf(zf_stmt_2, negated_conjecture,
% 43.11/6.77 (( ( inverse @ sk_c8 ) = ( sk_c11 ) ) |
% 43.11/6.77 ( ( multiply @ sk_c2 @ sk_c10 ) = ( sk_c9 ) )),
% 43.11/6.77 inference('cnf.neg', [status(esa)], [prove_this_18])).
% 43.11/6.77 thf(zip_derived_cl20, plain,
% 43.11/6.77 ((((inverse @ sk_c8) = (sk_c11))
% 43.11/6.77 | ((multiply @ sk_c2 @ sk_c10) = (sk_c9)))),
% 43.11/6.77 inference('cnf', [status(esa)], [zf_stmt_2])).
% 43.11/6.77 thf(zip_derived_cl600, plain,
% 43.11/6.77 ((((multiply @ (multiply @ (inverse @ sk_c10) @ identity) @ sk_c10)
% 43.11/6.77 = (sk_c9))
% 43.11/6.77 | ((inverse @ sk_c8) = (sk_c11))
% 43.11/6.77 | ((inverse @ sk_c8) = (sk_c11)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl437, zip_derived_cl20])).
% 43.11/6.77 thf(zip_derived_cl2, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 43.11/6.77 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 43.11/6.77 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 43.11/6.77 inference('cnf', [status(esa)], [associativity])).
% 43.11/6.77 thf(zip_derived_cl0, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 43.11/6.77 inference('cnf', [status(esa)], [left_identity])).
% 43.11/6.77 thf(zip_derived_cl1, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 43.11/6.77 inference('cnf', [status(esa)], [left_inverse])).
% 43.11/6.77 thf(zip_derived_cl615, plain,
% 43.11/6.77 ((((identity) = (sk_c9))
% 43.11/6.77 | ((inverse @ sk_c8) = (sk_c11))
% 43.11/6.77 | ((inverse @ sk_c8) = (sk_c11)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl600, zip_derived_cl2, zip_derived_cl0,
% 43.11/6.77 zip_derived_cl1])).
% 43.11/6.77 thf(zip_derived_cl616, plain,
% 43.11/6.77 ((((inverse @ sk_c8) = (sk_c11)) | ((identity) = (sk_c9)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl615])).
% 43.11/6.77 thf(zip_derived_cl1, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 43.11/6.77 inference('cnf', [status(esa)], [left_inverse])).
% 43.11/6.77 thf(zip_derived_cl619, plain,
% 43.11/6.77 ((((multiply @ sk_c11 @ sk_c8) = (identity)) | ((identity) = (sk_c9)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl616, zip_derived_cl1])).
% 43.11/6.77 thf(zip_derived_cl408, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i]:
% 43.11/6.77 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 43.11/6.77 inference('demod', [status(thm)], [zip_derived_cl375, zip_derived_cl0])).
% 43.11/6.77 thf(zip_derived_cl732, plain,
% 43.11/6.77 ((((sk_c8) = (multiply @ (inverse @ sk_c11) @ identity))
% 43.11/6.77 | ((identity) = (sk_c9)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl619, zip_derived_cl408])).
% 43.11/6.77 thf(prove_this_23, conjecture,
% 43.11/6.77 (~( ( ( multiply @ sk_c8 @ sk_c11 ) = ( sk_c9 ) ) |
% 43.11/6.77 ( ( inverse @ sk_c2 ) = ( sk_c10 ) ) ))).
% 43.11/6.77 thf(zf_stmt_3, negated_conjecture,
% 43.11/6.77 (( ( multiply @ sk_c8 @ sk_c11 ) = ( sk_c9 ) ) |
% 43.11/6.77 ( ( inverse @ sk_c2 ) = ( sk_c10 ) )),
% 43.11/6.77 inference('cnf.neg', [status(esa)], [prove_this_23])).
% 43.11/6.77 thf(zip_derived_cl25, plain,
% 43.11/6.77 ((((multiply @ sk_c8 @ sk_c11) = (sk_c9))
% 43.11/6.77 | ((inverse @ sk_c2) = (sk_c10)))),
% 43.11/6.77 inference('cnf', [status(esa)], [zf_stmt_3])).
% 43.11/6.77 thf(zip_derived_cl1, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 43.11/6.77 inference('cnf', [status(esa)], [left_inverse])).
% 43.11/6.77 thf(zip_derived_cl408, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i]:
% 43.11/6.77 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 43.11/6.77 inference('demod', [status(thm)], [zip_derived_cl375, zip_derived_cl0])).
% 43.11/6.77 thf(zip_derived_cl426, plain,
% 43.11/6.77 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl408])).
% 43.11/6.77 thf(zip_derived_cl1091, plain,
% 43.11/6.77 ((((sk_c2) = (multiply @ (inverse @ sk_c10) @ identity))
% 43.11/6.77 | ((multiply @ sk_c8 @ sk_c11) = (sk_c9)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl25, zip_derived_cl426])).
% 43.11/6.77 thf(prove_this_17, conjecture,
% 43.11/6.77 (~( ( ( multiply @ sk_c8 @ sk_c11 ) = ( sk_c9 ) ) |
% 43.11/6.77 ( ( multiply @ sk_c2 @ sk_c10 ) = ( sk_c9 ) ) ))).
% 43.11/6.77 thf(zf_stmt_4, negated_conjecture,
% 43.11/6.77 (( ( multiply @ sk_c8 @ sk_c11 ) = ( sk_c9 ) ) |
% 43.11/6.77 ( ( multiply @ sk_c2 @ sk_c10 ) = ( sk_c9 ) )),
% 43.11/6.77 inference('cnf.neg', [status(esa)], [prove_this_17])).
% 43.11/6.77 thf(zip_derived_cl19, plain,
% 43.11/6.77 ((((multiply @ sk_c8 @ sk_c11) = (sk_c9))
% 43.11/6.77 | ((multiply @ sk_c2 @ sk_c10) = (sk_c9)))),
% 43.11/6.77 inference('cnf', [status(esa)], [zf_stmt_4])).
% 43.11/6.77 thf(zip_derived_cl1570, plain,
% 43.11/6.77 ((((multiply @ (multiply @ (inverse @ sk_c10) @ identity) @ sk_c10)
% 43.11/6.77 = (sk_c9))
% 43.11/6.77 | ((multiply @ sk_c8 @ sk_c11) = (sk_c9))
% 43.11/6.77 | ((multiply @ sk_c8 @ sk_c11) = (sk_c9)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl1091, zip_derived_cl19])).
% 43.11/6.77 thf(zip_derived_cl2, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 43.11/6.77 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 43.11/6.77 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 43.11/6.77 inference('cnf', [status(esa)], [associativity])).
% 43.11/6.77 thf(zip_derived_cl0, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 43.11/6.77 inference('cnf', [status(esa)], [left_identity])).
% 43.11/6.77 thf(zip_derived_cl1, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 43.11/6.77 inference('cnf', [status(esa)], [left_inverse])).
% 43.11/6.77 thf(zip_derived_cl1585, plain,
% 43.11/6.77 ((((identity) = (sk_c9))
% 43.11/6.77 | ((multiply @ sk_c8 @ sk_c11) = (sk_c9))
% 43.11/6.77 | ((multiply @ sk_c8 @ sk_c11) = (sk_c9)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl1570, zip_derived_cl2, zip_derived_cl0,
% 43.11/6.77 zip_derived_cl1])).
% 43.11/6.77 thf(zip_derived_cl1586, plain,
% 43.11/6.77 ((((multiply @ sk_c8 @ sk_c11) = (sk_c9)) | ((identity) = (sk_c9)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl1585])).
% 43.11/6.77 thf(zip_derived_cl1626, plain,
% 43.11/6.77 ((((multiply @ (multiply @ (inverse @ sk_c11) @ identity) @ sk_c11)
% 43.11/6.77 = (sk_c9))
% 43.11/6.77 | ((identity) = (sk_c9))
% 43.11/6.77 | ((identity) = (sk_c9)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl732, zip_derived_cl1586])).
% 43.11/6.77 thf(zip_derived_cl2, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 43.11/6.77 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 43.11/6.77 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 43.11/6.77 inference('cnf', [status(esa)], [associativity])).
% 43.11/6.77 thf(zip_derived_cl0, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 43.11/6.77 inference('cnf', [status(esa)], [left_identity])).
% 43.11/6.77 thf(zip_derived_cl1, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 43.11/6.77 inference('cnf', [status(esa)], [left_inverse])).
% 43.11/6.77 thf(zip_derived_cl1632, plain,
% 43.11/6.77 ((((identity) = (sk_c9))
% 43.11/6.77 | ((identity) = (sk_c9))
% 43.11/6.77 | ((identity) = (sk_c9)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl1626, zip_derived_cl2, zip_derived_cl0,
% 43.11/6.77 zip_derived_cl1])).
% 43.11/6.77 thf(zip_derived_cl1633, plain, (((identity) = (sk_c9))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl1632])).
% 43.11/6.77 thf(zip_derived_cl1665, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 43.11/6.77 (((inverse @ X0) != (sk_c11))
% 43.11/6.77 | ((multiply @ X0 @ sk_c11) != (inverse @ sk_c10))
% 43.11/6.77 | ((inverse @ X1) != (sk_c10))
% 43.11/6.77 | ((multiply @ X1 @ sk_c10) != (sk_c11))
% 43.11/6.77 | ((inverse @ sk_c10) != (identity))
% 43.11/6.77 | ((multiply @ sk_c10 @ (inverse @ sk_c10)) != (sk_c11))
% 43.11/6.77 | ((multiply @ X3 @ X4) != (X2))
% 43.11/6.77 | ((inverse @ X2) != (X4))
% 43.11/6.77 | ((inverse @ X3) != (X2))
% 43.11/6.77 | ((multiply @ X4 @ sk_c10) != (sk_c11))
% 43.11/6.77 | ((inverse @ X5) != (X4))
% 43.11/6.77 | ((multiply @ X5 @ X4) != (sk_c11))
% 43.11/6.77 | ((inverse @ X6) != (sk_c10))
% 43.11/6.77 | ((multiply @ X6 @ sk_c10) != (inverse @ sk_c10))
% 43.11/6.77 | ((inverse @ X7) != (sk_c11))
% 43.11/6.77 | ((multiply @ X7 @ sk_c11) != (sk_c10)))),
% 43.11/6.77 inference('demod', [status(thm)], [zip_derived_cl64, zip_derived_cl1633])).
% 43.11/6.77 thf(zip_derived_cl1666, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 43.11/6.77 (((inverse @ X0) != (sk_c11))
% 43.11/6.77 | ((multiply @ X0 @ sk_c11) != (identity))
% 43.11/6.77 | ((inverse @ X1) != (sk_c10))
% 43.11/6.77 | ((multiply @ X1 @ sk_c10) != (sk_c11))
% 43.11/6.77 | ((inverse @ sk_c10) != (identity))
% 43.11/6.77 | ((multiply @ sk_c10 @ identity) != (sk_c11))
% 43.11/6.77 | ((multiply @ X3 @ X4) != (X2))
% 43.11/6.77 | ((inverse @ X2) != (X4))
% 43.11/6.77 | ((inverse @ X3) != (X2))
% 43.11/6.77 | ((multiply @ X4 @ sk_c10) != (sk_c11))
% 43.11/6.77 | ((inverse @ X5) != (X4))
% 43.11/6.77 | ((multiply @ X5 @ X4) != (sk_c11))
% 43.11/6.77 | ((inverse @ X6) != (sk_c10))
% 43.11/6.77 | ((multiply @ X6 @ sk_c10) != (identity))
% 43.11/6.77 | ((inverse @ X7) != (sk_c11))
% 43.11/6.77 | ((multiply @ X7 @ sk_c11) != (sk_c10)))),
% 43.11/6.77 inference('local_rewriting', [status(thm)], [zip_derived_cl1665])).
% 43.11/6.77 thf(zip_derived_cl426, plain,
% 43.11/6.77 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl408])).
% 43.11/6.77 thf(zip_derived_cl408, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i]:
% 43.11/6.77 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 43.11/6.77 inference('demod', [status(thm)], [zip_derived_cl375, zip_derived_cl0])).
% 43.11/6.77 thf(zip_derived_cl408, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i]:
% 43.11/6.77 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 43.11/6.77 inference('demod', [status(thm)], [zip_derived_cl375, zip_derived_cl0])).
% 43.11/6.77 thf(zip_derived_cl423, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i]:
% 43.11/6.77 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl408, zip_derived_cl408])).
% 43.11/6.77 thf(zip_derived_cl2194, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl426, zip_derived_cl423])).
% 43.11/6.77 thf(zip_derived_cl2247, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 43.11/6.77 (((inverse @ X0) != (sk_c11))
% 43.11/6.77 | ((multiply @ X0 @ sk_c11) != (identity))
% 43.11/6.77 | ((inverse @ X1) != (sk_c10))
% 43.11/6.77 | ((multiply @ X1 @ sk_c10) != (sk_c11))
% 43.11/6.77 | ((inverse @ sk_c10) != (identity))
% 43.11/6.77 | ((sk_c10) != (sk_c11))
% 43.11/6.77 | ((multiply @ X3 @ X4) != (X2))
% 43.11/6.77 | ((inverse @ X2) != (X4))
% 43.11/6.77 | ((inverse @ X3) != (X2))
% 43.11/6.77 | ((multiply @ X4 @ sk_c10) != (sk_c11))
% 43.11/6.77 | ((inverse @ X5) != (X4))
% 43.11/6.77 | ((multiply @ X5 @ X4) != (sk_c11))
% 43.11/6.77 | ((inverse @ X6) != (sk_c10))
% 43.11/6.77 | ((multiply @ X6 @ sk_c10) != (identity))
% 43.11/6.77 | ((inverse @ X7) != (sk_c11))
% 43.11/6.77 | ((multiply @ X7 @ sk_c11) != (sk_c10)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl1666, zip_derived_cl2194])).
% 43.11/6.77 thf(zip_derived_cl2248, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 43.11/6.77 (((inverse @ X0) != (sk_c11))
% 43.11/6.77 | ((multiply @ X0 @ sk_c11) != (identity))
% 43.11/6.77 | ((inverse @ X1) != (sk_c11))
% 43.11/6.77 | ((multiply @ X1 @ sk_c11) != (sk_c11))
% 43.11/6.77 | ((inverse @ sk_c11) != (identity))
% 43.11/6.77 | ((sk_c10) != (sk_c11))
% 43.11/6.77 | ((multiply @ X3 @ X4) != (X2))
% 43.11/6.77 | ((inverse @ X2) != (X4))
% 43.11/6.77 | ((inverse @ X3) != (X2))
% 43.11/6.77 | ((multiply @ X4 @ sk_c11) != (sk_c11))
% 43.11/6.77 | ((inverse @ X5) != (X4))
% 43.11/6.77 | ((multiply @ X5 @ X4) != (sk_c11))
% 43.11/6.77 | ((inverse @ X6) != (sk_c11))
% 43.11/6.77 | ((multiply @ X6 @ sk_c11) != (identity))
% 43.11/6.77 | ((inverse @ X7) != (sk_c11))
% 43.11/6.77 | ((multiply @ X7 @ sk_c11) != (sk_c11)))),
% 43.11/6.77 inference('local_rewriting', [status(thm)], [zip_derived_cl2247])).
% 43.11/6.77 thf(prove_this_31, conjecture,
% 43.11/6.77 (~( ( ( multiply @ sk_c10 @ sk_c9 ) = ( sk_c11 ) ) |
% 43.11/6.77 ( ( inverse @ sk_c3 ) = ( sk_c6 ) ) ))).
% 43.11/6.77 thf(zf_stmt_5, negated_conjecture,
% 43.11/6.77 (( ( multiply @ sk_c10 @ sk_c9 ) = ( sk_c11 ) ) |
% 43.11/6.77 ( ( inverse @ sk_c3 ) = ( sk_c6 ) )),
% 43.11/6.77 inference('cnf.neg', [status(esa)], [prove_this_31])).
% 43.11/6.77 thf(zip_derived_cl33, plain,
% 43.11/6.77 ((((multiply @ sk_c10 @ sk_c9) = (sk_c11))
% 43.11/6.77 | ((inverse @ sk_c3) = (sk_c6)))),
% 43.11/6.77 inference('cnf', [status(esa)], [zf_stmt_5])).
% 43.11/6.77 thf(zip_derived_cl1633, plain, (((identity) = (sk_c9))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl1632])).
% 43.11/6.77 thf(zip_derived_cl1652, plain,
% 43.11/6.77 ((((multiply @ sk_c10 @ identity) = (sk_c11))
% 43.11/6.77 | ((inverse @ sk_c3) = (sk_c6)))),
% 43.11/6.77 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl1633])).
% 43.11/6.77 thf(zip_derived_cl2194, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl426, zip_derived_cl423])).
% 43.11/6.77 thf(zip_derived_cl2243, plain,
% 43.11/6.77 ((((sk_c10) = (sk_c11)) | ((inverse @ sk_c3) = (sk_c6)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl1652, zip_derived_cl2194])).
% 43.11/6.77 thf(prove_this_49, conjecture,
% 43.11/6.77 (~( ( ( multiply @ sk_c10 @ sk_c9 ) = ( sk_c11 ) ) |
% 43.11/6.77 ( ( inverse @ sk_c4 ) = ( sk_c6 ) ) ))).
% 43.11/6.77 thf(zf_stmt_6, negated_conjecture,
% 43.11/6.77 (( ( multiply @ sk_c10 @ sk_c9 ) = ( sk_c11 ) ) |
% 43.11/6.77 ( ( inverse @ sk_c4 ) = ( sk_c6 ) )),
% 43.11/6.77 inference('cnf.neg', [status(esa)], [prove_this_49])).
% 43.11/6.77 thf(zip_derived_cl51, plain,
% 43.11/6.77 ((((multiply @ sk_c10 @ sk_c9) = (sk_c11))
% 43.11/6.77 | ((inverse @ sk_c4) = (sk_c6)))),
% 43.11/6.77 inference('cnf', [status(esa)], [zf_stmt_6])).
% 43.11/6.77 thf(zip_derived_cl1633, plain, (((identity) = (sk_c9))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl1632])).
% 43.11/6.77 thf(zip_derived_cl1659, plain,
% 43.11/6.77 ((((multiply @ sk_c10 @ identity) = (sk_c11))
% 43.11/6.77 | ((inverse @ sk_c4) = (sk_c6)))),
% 43.11/6.77 inference('demod', [status(thm)], [zip_derived_cl51, zip_derived_cl1633])).
% 43.11/6.77 thf(zip_derived_cl2194, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl426, zip_derived_cl423])).
% 43.11/6.77 thf(zip_derived_cl2245, plain,
% 43.11/6.77 ((((sk_c10) = (sk_c11)) | ((inverse @ sk_c4) = (sk_c6)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl1659, zip_derived_cl2194])).
% 43.11/6.77 thf(zip_derived_cl1, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 43.11/6.77 inference('cnf', [status(esa)], [left_inverse])).
% 43.11/6.77 thf(zip_derived_cl2316, plain,
% 43.11/6.77 ((((multiply @ sk_c6 @ sk_c4) = (identity)) | ((sk_c10) = (sk_c11)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl2245, zip_derived_cl1])).
% 43.11/6.77 thf(zip_derived_cl2824, plain,
% 43.11/6.77 ((((multiply @ (inverse @ sk_c3) @ sk_c4) = (identity))
% 43.11/6.77 | ((sk_c10) = (sk_c11))
% 43.11/6.77 | ((sk_c10) = (sk_c11)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl2243, zip_derived_cl2316])).
% 43.11/6.77 thf(zip_derived_cl2828, plain,
% 43.11/6.77 ((((sk_c10) = (sk_c11))
% 43.11/6.77 | ((multiply @ (inverse @ sk_c3) @ sk_c4) = (identity)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl2824])).
% 43.11/6.77 thf(zip_derived_cl408, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i]:
% 43.11/6.77 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 43.11/6.77 inference('demod', [status(thm)], [zip_derived_cl375, zip_derived_cl0])).
% 43.11/6.77 thf(zip_derived_cl3053, plain,
% 43.11/6.77 ((((sk_c4) = (multiply @ (inverse @ (inverse @ sk_c3)) @ identity))
% 43.11/6.77 | ((sk_c10) = (sk_c11)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl2828, zip_derived_cl408])).
% 43.11/6.77 thf(zip_derived_cl2194, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl426, zip_derived_cl423])).
% 43.11/6.77 thf(zip_derived_cl426, plain,
% 43.11/6.77 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl408])).
% 43.11/6.77 thf(zip_derived_cl2261, plain,
% 43.11/6.77 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl2194, zip_derived_cl426])).
% 43.11/6.77 thf(zip_derived_cl2194, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl426, zip_derived_cl423])).
% 43.11/6.77 thf(zip_derived_cl3077, plain,
% 43.11/6.77 ((((sk_c4) = (sk_c3)) | ((sk_c10) = (sk_c11)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl3053, zip_derived_cl2261, zip_derived_cl2194])).
% 43.11/6.77 thf(zip_derived_cl2245, plain,
% 43.11/6.77 ((((sk_c10) = (sk_c11)) | ((inverse @ sk_c4) = (sk_c6)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl1659, zip_derived_cl2194])).
% 43.11/6.77 thf(zip_derived_cl426, plain,
% 43.11/6.77 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl408])).
% 43.11/6.77 thf(zip_derived_cl2317, plain,
% 43.11/6.77 ((((sk_c4) = (multiply @ (inverse @ sk_c6) @ identity))
% 43.11/6.77 | ((sk_c10) = (sk_c11)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl2245, zip_derived_cl426])).
% 43.11/6.77 thf(zip_derived_cl2194, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl426, zip_derived_cl423])).
% 43.11/6.77 thf(zip_derived_cl2333, plain,
% 43.11/6.77 ((((sk_c4) = (inverse @ sk_c6)) | ((sk_c10) = (sk_c11)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl2317, zip_derived_cl2194])).
% 43.11/6.77 thf(zip_derived_cl3103, plain,
% 43.11/6.77 ((((sk_c3) = (inverse @ sk_c6))
% 43.11/6.77 | ((sk_c10) = (sk_c11))
% 43.11/6.77 | ((sk_c10) = (sk_c11)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl3077, zip_derived_cl2333])).
% 43.11/6.77 thf(zip_derived_cl3110, plain,
% 43.11/6.77 ((((sk_c10) = (sk_c11)) | ((sk_c3) = (inverse @ sk_c6)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl3103])).
% 43.11/6.77 thf(zip_derived_cl1, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 43.11/6.77 inference('cnf', [status(esa)], [left_inverse])).
% 43.11/6.77 thf(zip_derived_cl3160, plain,
% 43.11/6.77 ((((multiply @ sk_c3 @ sk_c6) = (identity)) | ((sk_c10) = (sk_c11)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl3110, zip_derived_cl1])).
% 43.11/6.77 thf(prove_this_28, conjecture,
% 43.11/6.77 (~( ( ( inverse @ sk_c7 ) = ( sk_c10 ) ) |
% 43.11/6.77 ( ( multiply @ sk_c3 @ sk_c6 ) = ( sk_c11 ) ) ))).
% 43.11/6.77 thf(zf_stmt_7, negated_conjecture,
% 43.11/6.77 (( ( inverse @ sk_c7 ) = ( sk_c10 ) ) |
% 43.11/6.77 ( ( multiply @ sk_c3 @ sk_c6 ) = ( sk_c11 ) )),
% 43.11/6.77 inference('cnf.neg', [status(esa)], [prove_this_28])).
% 43.11/6.77 thf(zip_derived_cl30, plain,
% 43.11/6.77 ((((inverse @ sk_c7) = (sk_c10))
% 43.11/6.77 | ((multiply @ sk_c3 @ sk_c6) = (sk_c11)))),
% 43.11/6.77 inference('cnf', [status(esa)], [zf_stmt_7])).
% 43.11/6.77 thf(zip_derived_cl3594, plain,
% 43.11/6.77 ((((identity) = (sk_c11))
% 43.11/6.77 | ((sk_c10) = (sk_c11))
% 43.11/6.77 | ((inverse @ sk_c7) = (sk_c10)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl3160, zip_derived_cl30])).
% 43.11/6.77 thf(zip_derived_cl2261, plain,
% 43.11/6.77 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl2194, zip_derived_cl426])).
% 43.11/6.77 thf(zip_derived_cl3700, plain,
% 43.11/6.77 ((((sk_c7) = (inverse @ sk_c10))
% 43.11/6.77 | ((sk_c10) = (sk_c11))
% 43.11/6.77 | ((identity) = (sk_c11)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl3594, zip_derived_cl2261])).
% 43.11/6.77 thf(prove_this_33, conjecture,
% 43.11/6.77 (~( ( ( multiply @ sk_c7 @ sk_c10 ) = ( sk_c11 ) ) |
% 43.11/6.77 ( ( inverse @ sk_c3 ) = ( sk_c6 ) ) ))).
% 43.11/6.77 thf(zf_stmt_8, negated_conjecture,
% 43.11/6.77 (( ( multiply @ sk_c7 @ sk_c10 ) = ( sk_c11 ) ) |
% 43.11/6.77 ( ( inverse @ sk_c3 ) = ( sk_c6 ) )),
% 43.11/6.77 inference('cnf.neg', [status(esa)], [prove_this_33])).
% 43.11/6.77 thf(zip_derived_cl35, plain,
% 43.11/6.77 ((((multiply @ sk_c7 @ sk_c10) = (sk_c11))
% 43.11/6.77 | ((inverse @ sk_c3) = (sk_c6)))),
% 43.11/6.77 inference('cnf', [status(esa)], [zf_stmt_8])).
% 43.11/6.77 thf(prove_this_27, conjecture,
% 43.11/6.77 (~( ( ( multiply @ sk_c7 @ sk_c10 ) = ( sk_c11 ) ) |
% 43.11/6.77 ( ( multiply @ sk_c3 @ sk_c6 ) = ( sk_c11 ) ) ))).
% 43.11/6.77 thf(zf_stmt_9, negated_conjecture,
% 43.11/6.77 (( ( multiply @ sk_c7 @ sk_c10 ) = ( sk_c11 ) ) |
% 43.11/6.77 ( ( multiply @ sk_c3 @ sk_c6 ) = ( sk_c11 ) )),
% 43.11/6.77 inference('cnf.neg', [status(esa)], [prove_this_27])).
% 43.11/6.77 thf(zip_derived_cl29, plain,
% 43.11/6.77 ((((multiply @ sk_c7 @ sk_c10) = (sk_c11))
% 43.11/6.77 | ((multiply @ sk_c3 @ sk_c6) = (sk_c11)))),
% 43.11/6.77 inference('cnf', [status(esa)], [zf_stmt_9])).
% 43.11/6.77 thf(zip_derived_cl6738, plain,
% 43.11/6.77 ((((multiply @ sk_c3 @ (inverse @ sk_c3)) = (sk_c11))
% 43.11/6.77 | ((multiply @ sk_c7 @ sk_c10) = (sk_c11))
% 43.11/6.77 | ((multiply @ sk_c7 @ sk_c10) = (sk_c11)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl29])).
% 43.11/6.77 thf(zip_derived_cl2261, plain,
% 43.11/6.77 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl2194, zip_derived_cl426])).
% 43.11/6.77 thf(zip_derived_cl1, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 43.11/6.77 inference('cnf', [status(esa)], [left_inverse])).
% 43.11/6.77 thf(zip_derived_cl2394, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl2261, zip_derived_cl1])).
% 43.11/6.77 thf(zip_derived_cl6749, plain,
% 43.11/6.77 ((((identity) = (sk_c11))
% 43.11/6.77 | ((multiply @ sk_c7 @ sk_c10) = (sk_c11))
% 43.11/6.77 | ((multiply @ sk_c7 @ sk_c10) = (sk_c11)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl6738, zip_derived_cl2394])).
% 43.11/6.77 thf(zip_derived_cl6750, plain,
% 43.11/6.77 ((((multiply @ sk_c7 @ sk_c10) = (sk_c11)) | ((identity) = (sk_c11)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl6749])).
% 43.11/6.77 thf(zip_derived_cl6775, plain,
% 43.11/6.77 ((((multiply @ (inverse @ sk_c10) @ sk_c10) = (sk_c11))
% 43.11/6.77 | ((identity) = (sk_c11))
% 43.11/6.77 | ((sk_c10) = (sk_c11))
% 43.11/6.77 | ((identity) = (sk_c11)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl3700, zip_derived_cl6750])).
% 43.11/6.77 thf(zip_derived_cl1, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 43.11/6.77 inference('cnf', [status(esa)], [left_inverse])).
% 43.11/6.77 thf(zip_derived_cl6783, plain,
% 43.11/6.77 ((((identity) = (sk_c11))
% 43.11/6.77 | ((identity) = (sk_c11))
% 43.11/6.77 | ((sk_c10) = (sk_c11))
% 43.11/6.77 | ((identity) = (sk_c11)))),
% 43.11/6.77 inference('demod', [status(thm)], [zip_derived_cl6775, zip_derived_cl1])).
% 43.11/6.77 thf(zip_derived_cl6784, plain,
% 43.11/6.77 ((((sk_c10) = (sk_c11)) | ((identity) = (sk_c11)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl6783])).
% 43.11/6.77 thf(prove_this_12, conjecture,
% 43.11/6.77 (~( ( ( inverse @ sk_c8 ) = ( sk_c11 ) ) |
% 43.11/6.77 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 43.11/6.77 thf(zf_stmt_10, negated_conjecture,
% 43.11/6.77 (( ( inverse @ sk_c8 ) = ( sk_c11 ) ) |
% 43.11/6.77 ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 43.11/6.77 inference('cnf.neg', [status(esa)], [prove_this_12])).
% 43.11/6.77 thf(zip_derived_cl14, plain,
% 43.11/6.77 ((((inverse @ sk_c8) = (sk_c11)) | ((inverse @ sk_c1) = (sk_c11)))),
% 43.11/6.77 inference('cnf', [status(esa)], [zf_stmt_10])).
% 43.11/6.77 thf(zip_derived_cl1, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 43.11/6.77 inference('cnf', [status(esa)], [left_inverse])).
% 43.11/6.77 thf(zip_derived_cl70, plain,
% 43.11/6.77 ((((multiply @ sk_c11 @ sk_c8) = (identity))
% 43.11/6.77 | ((inverse @ sk_c1) = (sk_c11)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl1])).
% 43.11/6.77 thf(zip_derived_cl408, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i]:
% 43.11/6.77 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 43.11/6.77 inference('demod', [status(thm)], [zip_derived_cl375, zip_derived_cl0])).
% 43.11/6.77 thf(zip_derived_cl429, plain,
% 43.11/6.77 ((((sk_c8) = (multiply @ (inverse @ sk_c11) @ identity))
% 43.11/6.77 | ((inverse @ sk_c1) = (sk_c11)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl70, zip_derived_cl408])).
% 43.11/6.77 thf(prove_this_11, conjecture,
% 43.11/6.77 (~( ( ( multiply @ sk_c8 @ sk_c11 ) = ( sk_c9 ) ) |
% 43.11/6.77 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 43.11/6.77 thf(zf_stmt_11, negated_conjecture,
% 43.11/6.77 (( ( multiply @ sk_c8 @ sk_c11 ) = ( sk_c9 ) ) |
% 43.11/6.77 ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 43.11/6.77 inference('cnf.neg', [status(esa)], [prove_this_11])).
% 43.11/6.77 thf(zip_derived_cl13, plain,
% 43.11/6.77 ((((multiply @ sk_c8 @ sk_c11) = (sk_c9))
% 43.11/6.77 | ((inverse @ sk_c1) = (sk_c11)))),
% 43.11/6.77 inference('cnf', [status(esa)], [zf_stmt_11])).
% 43.11/6.77 thf(zip_derived_cl487, plain,
% 43.11/6.77 ((((multiply @ (multiply @ (inverse @ sk_c11) @ identity) @ sk_c11)
% 43.11/6.77 = (sk_c9))
% 43.11/6.77 | ((inverse @ sk_c1) = (sk_c11))
% 43.11/6.77 | ((inverse @ sk_c1) = (sk_c11)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl429, zip_derived_cl13])).
% 43.11/6.77 thf(zip_derived_cl2, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 43.11/6.77 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 43.11/6.77 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 43.11/6.77 inference('cnf', [status(esa)], [associativity])).
% 43.11/6.77 thf(zip_derived_cl0, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 43.11/6.77 inference('cnf', [status(esa)], [left_identity])).
% 43.11/6.77 thf(zip_derived_cl1, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 43.11/6.77 inference('cnf', [status(esa)], [left_inverse])).
% 43.11/6.77 thf(zip_derived_cl492, plain,
% 43.11/6.77 ((((identity) = (sk_c9))
% 43.11/6.77 | ((inverse @ sk_c1) = (sk_c11))
% 43.11/6.77 | ((inverse @ sk_c1) = (sk_c11)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl487, zip_derived_cl2, zip_derived_cl0,
% 43.11/6.77 zip_derived_cl1])).
% 43.11/6.77 thf(zip_derived_cl493, plain,
% 43.11/6.77 ((((inverse @ sk_c1) = (sk_c11)) | ((identity) = (sk_c9)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl492])).
% 43.11/6.77 thf(prove_this_8, conjecture,
% 43.11/6.77 (~( ( ( inverse @ sk_c10 ) = ( sk_c9 ) ) |
% 43.11/6.77 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 43.11/6.77 thf(zf_stmt_12, negated_conjecture,
% 43.11/6.77 (( ( inverse @ sk_c10 ) = ( sk_c9 ) ) |
% 43.11/6.77 ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 43.11/6.77 inference('cnf.neg', [status(esa)], [prove_this_8])).
% 43.11/6.77 thf(zip_derived_cl10, plain,
% 43.11/6.77 ((((inverse @ sk_c10) = (sk_c9)) | ((inverse @ sk_c1) = (sk_c11)))),
% 43.11/6.77 inference('cnf', [status(esa)], [zf_stmt_12])).
% 43.11/6.77 thf(zip_derived_cl499, plain,
% 43.11/6.77 ((((inverse @ sk_c10) = (identity))
% 43.11/6.77 | ((inverse @ sk_c1) = (sk_c11))
% 43.11/6.77 | ((inverse @ sk_c1) = (sk_c11)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl493, zip_derived_cl10])).
% 43.11/6.77 thf(zip_derived_cl502, plain,
% 43.11/6.77 ((((inverse @ sk_c1) = (sk_c11)) | ((inverse @ sk_c10) = (identity)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl499])).
% 43.11/6.77 thf(zip_derived_cl1, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 43.11/6.77 inference('cnf', [status(esa)], [left_inverse])).
% 43.11/6.77 thf(zip_derived_cl504, plain,
% 43.11/6.77 ((((multiply @ identity @ sk_c10) = (identity))
% 43.11/6.77 | ((inverse @ sk_c1) = (sk_c11)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl502, zip_derived_cl1])).
% 43.11/6.77 thf(zip_derived_cl0, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 43.11/6.77 inference('cnf', [status(esa)], [left_identity])).
% 43.11/6.77 thf(zip_derived_cl562, plain,
% 43.11/6.77 ((((identity) = (sk_c10)) | ((inverse @ sk_c1) = (sk_c11)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl504, zip_derived_cl0])).
% 43.11/6.77 thf(zip_derived_cl493, plain,
% 43.11/6.77 ((((inverse @ sk_c1) = (sk_c11)) | ((identity) = (sk_c9)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl492])).
% 43.11/6.77 thf(prove_this_7, conjecture,
% 43.11/6.77 (~( ( ( multiply @ sk_c10 @ sk_c9 ) = ( sk_c11 ) ) |
% 43.11/6.77 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 43.11/6.77 thf(zf_stmt_13, negated_conjecture,
% 43.11/6.77 (( ( multiply @ sk_c10 @ sk_c9 ) = ( sk_c11 ) ) |
% 43.11/6.77 ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 43.11/6.77 inference('cnf.neg', [status(esa)], [prove_this_7])).
% 43.11/6.77 thf(zip_derived_cl9, plain,
% 43.11/6.77 ((((multiply @ sk_c10 @ sk_c9) = (sk_c11))
% 43.11/6.77 | ((inverse @ sk_c1) = (sk_c11)))),
% 43.11/6.77 inference('cnf', [status(esa)], [zf_stmt_13])).
% 43.11/6.77 thf(zip_derived_cl498, plain,
% 43.11/6.77 ((((multiply @ sk_c10 @ identity) = (sk_c11))
% 43.11/6.77 | ((inverse @ sk_c1) = (sk_c11))
% 43.11/6.77 | ((inverse @ sk_c1) = (sk_c11)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl493, zip_derived_cl9])).
% 43.11/6.77 thf(zip_derived_cl501, plain,
% 43.11/6.77 ((((inverse @ sk_c1) = (sk_c11))
% 43.11/6.77 | ((multiply @ sk_c10 @ identity) = (sk_c11)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl498])).
% 43.11/6.77 thf(zip_derived_cl583, plain,
% 43.11/6.77 ((((multiply @ identity @ identity) = (sk_c11))
% 43.11/6.77 | ((inverse @ sk_c1) = (sk_c11))
% 43.11/6.77 | ((inverse @ sk_c1) = (sk_c11)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl562, zip_derived_cl501])).
% 43.11/6.77 thf(zip_derived_cl0, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 43.11/6.77 inference('cnf', [status(esa)], [left_identity])).
% 43.11/6.77 thf(zip_derived_cl590, plain,
% 43.11/6.77 ((((identity) = (sk_c11))
% 43.11/6.77 | ((inverse @ sk_c1) = (sk_c11))
% 43.11/6.77 | ((inverse @ sk_c1) = (sk_c11)))),
% 43.11/6.77 inference('demod', [status(thm)], [zip_derived_cl583, zip_derived_cl0])).
% 43.11/6.77 thf(zip_derived_cl591, plain,
% 43.11/6.77 ((((inverse @ sk_c1) = (sk_c11)) | ((identity) = (sk_c11)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl590])).
% 43.11/6.77 thf(prove_this_6, conjecture,
% 43.11/6.77 (~( ( ( inverse @ sk_c8 ) = ( sk_c11 ) ) |
% 43.11/6.77 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 43.11/6.77 thf(zf_stmt_14, negated_conjecture,
% 43.11/6.77 (( ( inverse @ sk_c8 ) = ( sk_c11 ) ) |
% 43.11/6.77 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) )),
% 43.11/6.77 inference('cnf.neg', [status(esa)], [prove_this_6])).
% 43.11/6.77 thf(zip_derived_cl8, plain,
% 43.11/6.77 ((((inverse @ sk_c8) = (sk_c11))
% 43.11/6.77 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 43.11/6.77 inference('cnf', [status(esa)], [zf_stmt_14])).
% 43.11/6.77 thf(zip_derived_cl1, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 43.11/6.77 inference('cnf', [status(esa)], [left_inverse])).
% 43.11/6.77 thf(zip_derived_cl114, plain,
% 43.11/6.77 ((((multiply @ sk_c11 @ sk_c8) = (identity))
% 43.11/6.77 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl1])).
% 43.11/6.77 thf(zip_derived_cl408, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i]:
% 43.11/6.77 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 43.11/6.77 inference('demod', [status(thm)], [zip_derived_cl375, zip_derived_cl0])).
% 43.11/6.77 thf(zip_derived_cl430, plain,
% 43.11/6.77 ((((sk_c8) = (multiply @ (inverse @ sk_c11) @ identity))
% 43.11/6.77 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl114, zip_derived_cl408])).
% 43.11/6.77 thf(prove_this_5, conjecture,
% 43.11/6.77 (~( ( ( multiply @ sk_c8 @ sk_c11 ) = ( sk_c9 ) ) |
% 43.11/6.77 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 43.11/6.77 thf(zf_stmt_15, negated_conjecture,
% 43.11/6.77 (( ( multiply @ sk_c8 @ sk_c11 ) = ( sk_c9 ) ) |
% 43.11/6.77 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) )),
% 43.11/6.77 inference('cnf.neg', [status(esa)], [prove_this_5])).
% 43.11/6.77 thf(zip_derived_cl7, plain,
% 43.11/6.77 ((((multiply @ sk_c8 @ sk_c11) = (sk_c9))
% 43.11/6.77 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 43.11/6.77 inference('cnf', [status(esa)], [zf_stmt_15])).
% 43.11/6.77 thf(zip_derived_cl683, plain,
% 43.11/6.77 ((((multiply @ (multiply @ (inverse @ sk_c11) @ identity) @ sk_c11)
% 43.11/6.77 = (sk_c9))
% 43.11/6.77 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10))
% 43.11/6.77 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl430, zip_derived_cl7])).
% 43.11/6.77 thf(zip_derived_cl2, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 43.11/6.77 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 43.11/6.77 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 43.11/6.77 inference('cnf', [status(esa)], [associativity])).
% 43.11/6.77 thf(zip_derived_cl0, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 43.11/6.77 inference('cnf', [status(esa)], [left_identity])).
% 43.11/6.77 thf(zip_derived_cl1, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 43.11/6.77 inference('cnf', [status(esa)], [left_inverse])).
% 43.11/6.77 thf(zip_derived_cl690, plain,
% 43.11/6.77 ((((identity) = (sk_c9))
% 43.11/6.77 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10))
% 43.11/6.77 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl683, zip_derived_cl2, zip_derived_cl0,
% 43.11/6.77 zip_derived_cl1])).
% 43.11/6.77 thf(zip_derived_cl691, plain,
% 43.11/6.77 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10)) | ((identity) = (sk_c9)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl690])).
% 43.11/6.77 thf(prove_this_2, conjecture,
% 43.11/6.77 (~( ( ( inverse @ sk_c10 ) = ( sk_c9 ) ) |
% 43.11/6.77 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 43.11/6.77 thf(zf_stmt_16, negated_conjecture,
% 43.11/6.77 (( ( inverse @ sk_c10 ) = ( sk_c9 ) ) |
% 43.11/6.77 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) )),
% 43.11/6.77 inference('cnf.neg', [status(esa)], [prove_this_2])).
% 43.11/6.77 thf(zip_derived_cl4, plain,
% 43.11/6.77 ((((inverse @ sk_c10) = (sk_c9))
% 43.11/6.77 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 43.11/6.77 inference('cnf', [status(esa)], [zf_stmt_16])).
% 43.11/6.77 thf(zip_derived_cl696, plain,
% 43.11/6.77 ((((inverse @ sk_c10) = (identity))
% 43.11/6.77 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10))
% 43.11/6.77 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl691, zip_derived_cl4])).
% 43.11/6.77 thf(zip_derived_cl703, plain,
% 43.11/6.77 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))
% 43.11/6.77 | ((inverse @ sk_c10) = (identity)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl696])).
% 43.11/6.77 thf(zip_derived_cl426, plain,
% 43.11/6.77 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl408])).
% 43.11/6.77 thf(zip_derived_cl1079, plain,
% 43.11/6.77 ((((sk_c10) = (multiply @ (inverse @ identity) @ identity))
% 43.11/6.77 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl703, zip_derived_cl426])).
% 43.11/6.77 thf(zip_derived_cl425, plain,
% 43.11/6.77 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl408])).
% 43.11/6.77 thf(zip_derived_cl1103, plain,
% 43.11/6.77 ((((sk_c10) = (identity)) | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 43.11/6.77 inference('demod', [status(thm)], [zip_derived_cl1079, zip_derived_cl425])).
% 43.11/6.77 thf(zip_derived_cl1132, plain,
% 43.11/6.77 ((((multiply @ sk_c1 @ sk_c11) != (identity)) | ((sk_c10) = (identity)))),
% 43.11/6.77 inference('eq_fact', [status(thm)], [zip_derived_cl1103])).
% 43.11/6.77 thf(zip_derived_cl1135, plain,
% 43.11/6.77 ((((multiply @ sk_c1 @ (inverse @ sk_c1)) != (identity))
% 43.11/6.77 | ((identity) = (sk_c11))
% 43.11/6.77 | ((sk_c10) = (identity)))),
% 43.11/6.77 inference('sup-', [status(thm)], [zip_derived_cl591, zip_derived_cl1132])).
% 43.11/6.77 thf(zip_derived_cl2394, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl2261, zip_derived_cl1])).
% 43.11/6.77 thf(zip_derived_cl2845, plain,
% 43.11/6.77 ((((identity) != (identity))
% 43.11/6.77 | ((identity) = (sk_c11))
% 43.11/6.77 | ((sk_c10) = (identity)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl1135, zip_derived_cl2394])).
% 43.11/6.77 thf(zip_derived_cl2846, plain,
% 43.11/6.77 ((((sk_c10) = (identity)) | ((identity) = (sk_c11)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl2845])).
% 43.11/6.77 thf(zip_derived_cl6822, plain,
% 43.11/6.77 ((((sk_c11) = (identity))
% 43.11/6.77 | ((identity) = (sk_c11))
% 43.11/6.77 | ((identity) = (sk_c11)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl6784, zip_derived_cl2846])).
% 43.11/6.77 thf(zip_derived_cl6841, plain, (((sk_c11) = (identity))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl6822])).
% 43.11/6.77 thf(zip_derived_cl6841, plain, (((sk_c11) = (identity))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl6822])).
% 43.11/6.77 thf(zip_derived_cl2194, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl426, zip_derived_cl423])).
% 43.11/6.77 thf(zip_derived_cl6841, plain, (((sk_c11) = (identity))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl6822])).
% 43.11/6.77 thf(zip_derived_cl6841, plain, (((sk_c11) = (identity))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl6822])).
% 43.11/6.77 thf(zip_derived_cl2194, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl426, zip_derived_cl423])).
% 43.11/6.77 thf(zip_derived_cl6841, plain, (((sk_c11) = (identity))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl6822])).
% 43.11/6.77 thf(zip_derived_cl6841, plain, (((sk_c11) = (identity))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl6822])).
% 43.11/6.77 thf(zip_derived_cl1313, plain, (((inverse @ identity) = (identity))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl483, zip_derived_cl1])).
% 43.11/6.77 thf(zip_derived_cl6841, plain, (((sk_c11) = (identity))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl6822])).
% 43.11/6.77 thf(zip_derived_cl6841, plain, (((sk_c11) = (identity))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl6822])).
% 43.11/6.77 thf(zip_derived_cl2194, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl426, zip_derived_cl423])).
% 43.11/6.77 thf(zip_derived_cl6841, plain, (((sk_c11) = (identity))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl6822])).
% 43.11/6.77 thf(zip_derived_cl6841, plain, (((sk_c11) = (identity))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl6822])).
% 43.11/6.77 thf(zip_derived_cl6841, plain, (((sk_c11) = (identity))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl6822])).
% 43.11/6.77 thf(zip_derived_cl6841, plain, (((sk_c11) = (identity))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl6822])).
% 43.11/6.77 thf(zip_derived_cl2194, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl426, zip_derived_cl423])).
% 43.11/6.77 thf(zip_derived_cl6841, plain, (((sk_c11) = (identity))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl6822])).
% 43.11/6.77 thf(zip_derived_cl6841, plain, (((sk_c11) = (identity))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl6822])).
% 43.11/6.77 thf(zip_derived_cl2194, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl426, zip_derived_cl423])).
% 43.11/6.77 thf(zip_derived_cl6841, plain, (((sk_c11) = (identity))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl6822])).
% 43.11/6.77 thf(zip_derived_cl6935, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 43.11/6.77 (((inverse @ X0) != (identity))
% 43.11/6.77 | ((X0) != (identity))
% 43.11/6.77 | ((inverse @ X1) != (identity))
% 43.11/6.77 | ((X1) != (identity))
% 43.11/6.77 | ((identity) != (identity))
% 43.11/6.77 | ((sk_c10) != (identity))
% 43.11/6.77 | ((multiply @ X3 @ X4) != (X2))
% 43.11/6.77 | ((inverse @ X2) != (X4))
% 43.11/6.77 | ((inverse @ X3) != (X2))
% 43.11/6.77 | ((X4) != (identity))
% 43.11/6.77 | ((inverse @ X5) != (X4))
% 43.11/6.77 | ((multiply @ X5 @ X4) != (identity))
% 43.11/6.77 | ((inverse @ X6) != (identity))
% 43.11/6.77 | ((X6) != (identity))
% 43.11/6.77 | ((inverse @ X7) != (identity))
% 43.11/6.77 | ((X7) != (identity)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl2248, zip_derived_cl6841, zip_derived_cl6841,
% 43.11/6.77 zip_derived_cl2194, zip_derived_cl6841, zip_derived_cl6841,
% 43.11/6.77 zip_derived_cl2194, zip_derived_cl6841, zip_derived_cl6841,
% 43.11/6.77 zip_derived_cl1313, zip_derived_cl6841, zip_derived_cl6841,
% 43.11/6.77 zip_derived_cl2194, zip_derived_cl6841, zip_derived_cl6841,
% 43.11/6.77 zip_derived_cl6841, zip_derived_cl6841, zip_derived_cl2194,
% 43.11/6.77 zip_derived_cl6841, zip_derived_cl6841, zip_derived_cl2194,
% 43.11/6.77 zip_derived_cl6841])).
% 43.11/6.77 thf(zip_derived_cl6936, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 43.11/6.77 (((X7) != (identity))
% 43.11/6.77 | ((inverse @ X7) != (identity))
% 43.11/6.77 | ((X6) != (identity))
% 43.11/6.77 | ((inverse @ X6) != (identity))
% 43.11/6.77 | ((multiply @ X5 @ X4) != (identity))
% 43.11/6.77 | ((inverse @ X5) != (X4))
% 43.11/6.77 | ((X4) != (identity))
% 43.11/6.77 | ((inverse @ X3) != (X2))
% 43.11/6.77 | ((inverse @ X2) != (X4))
% 43.11/6.77 | ((multiply @ X3 @ X4) != (X2))
% 43.11/6.77 | ((sk_c10) != (identity))
% 43.11/6.77 | ((X1) != (identity))
% 43.11/6.77 | ((inverse @ X1) != (identity))
% 43.11/6.77 | ((X0) != (identity))
% 43.11/6.77 | ((inverse @ X0) != (identity)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl6935])).
% 43.11/6.77 thf(zip_derived_cl2243, plain,
% 43.11/6.77 ((((sk_c10) = (sk_c11)) | ((inverse @ sk_c3) = (sk_c6)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl1652, zip_derived_cl2194])).
% 43.11/6.77 thf(zip_derived_cl6841, plain, (((sk_c11) = (identity))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl6822])).
% 43.11/6.77 thf(zip_derived_cl6931, plain,
% 43.11/6.77 ((((sk_c10) = (identity)) | ((inverse @ sk_c3) = (sk_c6)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl2243, zip_derived_cl6841])).
% 43.11/6.77 thf(prove_this_37, conjecture,
% 43.11/6.77 (~( ( ( multiply @ sk_c10 @ sk_c9 ) = ( sk_c11 ) ) |
% 43.11/6.77 ( ( multiply @ sk_c6 @ sk_c10 ) = ( sk_c11 ) ) ))).
% 43.11/6.77 thf(zf_stmt_17, negated_conjecture,
% 43.11/6.77 (( ( multiply @ sk_c10 @ sk_c9 ) = ( sk_c11 ) ) |
% 43.11/6.77 ( ( multiply @ sk_c6 @ sk_c10 ) = ( sk_c11 ) )),
% 43.11/6.77 inference('cnf.neg', [status(esa)], [prove_this_37])).
% 43.11/6.77 thf(zip_derived_cl39, plain,
% 43.11/6.77 ((((multiply @ sk_c10 @ sk_c9) = (sk_c11))
% 43.11/6.77 | ((multiply @ sk_c6 @ sk_c10) = (sk_c11)))),
% 43.11/6.77 inference('cnf', [status(esa)], [zf_stmt_17])).
% 43.11/6.77 thf(zip_derived_cl1633, plain, (((identity) = (sk_c9))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl1632])).
% 43.11/6.77 thf(zip_derived_cl2194, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl426, zip_derived_cl423])).
% 43.11/6.77 thf(zip_derived_cl6841, plain, (((sk_c11) = (identity))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl6822])).
% 43.11/6.77 thf(zip_derived_cl6841, plain, (((sk_c11) = (identity))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl6822])).
% 43.11/6.77 thf(zip_derived_cl10540, plain,
% 43.11/6.77 ((((sk_c10) = (identity)) | ((multiply @ sk_c6 @ sk_c10) = (identity)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl39, zip_derived_cl1633, zip_derived_cl2194,
% 43.11/6.77 zip_derived_cl6841, zip_derived_cl6841])).
% 43.11/6.77 thf(zip_derived_cl408, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i]:
% 43.11/6.77 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 43.11/6.77 inference('demod', [status(thm)], [zip_derived_cl375, zip_derived_cl0])).
% 43.11/6.77 thf(zip_derived_cl10542, plain,
% 43.11/6.77 ((((sk_c10) = (multiply @ (inverse @ sk_c6) @ identity))
% 43.11/6.77 | ((sk_c10) = (identity)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl10540, zip_derived_cl408])).
% 43.11/6.77 thf(zip_derived_cl23503, plain,
% 43.11/6.77 ((((sk_c10) = (multiply @ (inverse @ (inverse @ sk_c3)) @ identity))
% 43.11/6.77 | ((sk_c10) = (identity))
% 43.11/6.77 | ((sk_c10) = (identity)))),
% 43.11/6.77 inference('sup+', [status(thm)],
% 43.11/6.77 [zip_derived_cl6931, zip_derived_cl10542])).
% 43.11/6.77 thf(zip_derived_cl2261, plain,
% 43.11/6.77 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl2194, zip_derived_cl426])).
% 43.11/6.77 thf(zip_derived_cl2194, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl426, zip_derived_cl423])).
% 43.11/6.77 thf(zip_derived_cl23548, plain,
% 43.11/6.77 ((((sk_c10) = (sk_c3))
% 43.11/6.77 | ((sk_c10) = (identity))
% 43.11/6.77 | ((sk_c10) = (identity)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl23503, zip_derived_cl2261, zip_derived_cl2194])).
% 43.11/6.77 thf(zip_derived_cl23549, plain,
% 43.11/6.77 ((((sk_c10) = (identity)) | ((sk_c10) = (sk_c3)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl23548])).
% 43.11/6.77 thf(zip_derived_cl23549, plain,
% 43.11/6.77 ((((sk_c10) = (identity)) | ((sk_c10) = (sk_c3)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl23548])).
% 43.11/6.77 thf(zip_derived_cl6931, plain,
% 43.11/6.77 ((((sk_c10) = (identity)) | ((inverse @ sk_c3) = (sk_c6)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl2243, zip_derived_cl6841])).
% 43.11/6.77 thf(zip_derived_cl1103, plain,
% 43.11/6.77 ((((sk_c10) = (identity)) | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 43.11/6.77 inference('demod', [status(thm)], [zip_derived_cl1079, zip_derived_cl425])).
% 43.11/6.77 thf(zip_derived_cl6841, plain, (((sk_c11) = (identity))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl6822])).
% 43.11/6.77 thf(zip_derived_cl2194, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl426, zip_derived_cl423])).
% 43.11/6.77 thf(zip_derived_cl6896, plain,
% 43.11/6.77 ((((sk_c10) = (identity)) | ((sk_c1) = (sk_c10)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl1103, zip_derived_cl6841, zip_derived_cl2194])).
% 43.11/6.77 thf(zip_derived_cl10540, plain,
% 43.11/6.77 ((((sk_c10) = (identity)) | ((multiply @ sk_c6 @ sk_c10) = (identity)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl39, zip_derived_cl1633, zip_derived_cl2194,
% 43.11/6.77 zip_derived_cl6841, zip_derived_cl6841])).
% 43.11/6.77 thf(zip_derived_cl10544, plain,
% 43.11/6.77 ((((multiply @ sk_c6 @ sk_c1) = (identity))
% 43.11/6.77 | ((sk_c10) = (identity))
% 43.11/6.77 | ((sk_c10) = (identity)))),
% 43.11/6.77 inference('sup+', [status(thm)],
% 43.11/6.77 [zip_derived_cl6896, zip_derived_cl10540])).
% 43.11/6.77 thf(zip_derived_cl10554, plain,
% 43.11/6.77 ((((sk_c10) = (identity)) | ((multiply @ sk_c6 @ sk_c1) = (identity)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl10544])).
% 43.11/6.77 thf(zip_derived_cl408, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i]:
% 43.11/6.77 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 43.11/6.77 inference('demod', [status(thm)], [zip_derived_cl375, zip_derived_cl0])).
% 43.11/6.77 thf(zip_derived_cl10561, plain,
% 43.11/6.77 ((((sk_c1) = (multiply @ (inverse @ sk_c6) @ identity))
% 43.11/6.77 | ((sk_c10) = (identity)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl10554, zip_derived_cl408])).
% 43.11/6.77 thf(zip_derived_cl12356, plain,
% 43.11/6.77 ((((sk_c1) = (multiply @ (inverse @ (inverse @ sk_c3)) @ identity))
% 43.11/6.77 | ((sk_c10) = (identity))
% 43.11/6.77 | ((sk_c10) = (identity)))),
% 43.11/6.77 inference('sup+', [status(thm)],
% 43.11/6.77 [zip_derived_cl6931, zip_derived_cl10561])).
% 43.11/6.77 thf(zip_derived_cl2261, plain,
% 43.11/6.77 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl2194, zip_derived_cl426])).
% 43.11/6.77 thf(zip_derived_cl2194, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl426, zip_derived_cl423])).
% 43.11/6.77 thf(zip_derived_cl12372, plain,
% 43.11/6.77 ((((sk_c1) = (sk_c3)) | ((sk_c10) = (identity)) | ((sk_c10) = (identity)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl12356, zip_derived_cl2261, zip_derived_cl2194])).
% 43.11/6.77 thf(zip_derived_cl12373, plain,
% 43.11/6.77 ((((sk_c10) = (identity)) | ((sk_c1) = (sk_c3)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl12372])).
% 43.11/6.77 thf(zip_derived_cl3077, plain,
% 43.11/6.77 ((((sk_c4) = (sk_c3)) | ((sk_c10) = (sk_c11)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl3053, zip_derived_cl2261, zip_derived_cl2194])).
% 43.11/6.77 thf(prove_this_43, conjecture,
% 43.11/6.77 (~( ( ( multiply @ sk_c10 @ sk_c9 ) = ( sk_c11 ) ) |
% 43.11/6.77 ( ( inverse @ sk_c5 ) = ( sk_c4 ) ) ))).
% 43.11/6.77 thf(zf_stmt_18, negated_conjecture,
% 43.11/6.77 (( ( multiply @ sk_c10 @ sk_c9 ) = ( sk_c11 ) ) |
% 43.11/6.77 ( ( inverse @ sk_c5 ) = ( sk_c4 ) )),
% 43.11/6.77 inference('cnf.neg', [status(esa)], [prove_this_43])).
% 43.11/6.77 thf(zip_derived_cl45, plain,
% 43.11/6.77 ((((multiply @ sk_c10 @ sk_c9) = (sk_c11))
% 43.11/6.77 | ((inverse @ sk_c5) = (sk_c4)))),
% 43.11/6.77 inference('cnf', [status(esa)], [zf_stmt_18])).
% 43.11/6.77 thf(zip_derived_cl1633, plain, (((identity) = (sk_c9))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl1632])).
% 43.11/6.77 thf(zip_derived_cl1656, plain,
% 43.11/6.77 ((((multiply @ sk_c10 @ identity) = (sk_c11))
% 43.11/6.77 | ((inverse @ sk_c5) = (sk_c4)))),
% 43.11/6.77 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl1633])).
% 43.11/6.77 thf(zip_derived_cl2194, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl426, zip_derived_cl423])).
% 43.11/6.77 thf(zip_derived_cl2244, plain,
% 43.11/6.77 ((((sk_c10) = (sk_c11)) | ((inverse @ sk_c5) = (sk_c4)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl1656, zip_derived_cl2194])).
% 43.11/6.77 thf(zip_derived_cl3098, plain,
% 43.11/6.77 ((((inverse @ sk_c5) = (sk_c3))
% 43.11/6.77 | ((sk_c10) = (sk_c11))
% 43.11/6.77 | ((sk_c10) = (sk_c11)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl3077, zip_derived_cl2244])).
% 43.11/6.77 thf(zip_derived_cl3106, plain,
% 43.11/6.77 ((((sk_c10) = (sk_c11)) | ((inverse @ sk_c5) = (sk_c3)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl3098])).
% 43.11/6.77 thf(zip_derived_cl3077, plain,
% 43.11/6.77 ((((sk_c4) = (sk_c3)) | ((sk_c10) = (sk_c11)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl3053, zip_derived_cl2261, zip_derived_cl2194])).
% 43.11/6.77 thf(prove_this_55, conjecture,
% 43.11/6.77 (~( ( ( multiply @ sk_c10 @ sk_c9 ) = ( sk_c11 ) ) |
% 43.11/6.77 ( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c4 ) ) ))).
% 43.11/6.77 thf(zf_stmt_19, negated_conjecture,
% 43.11/6.77 (( ( multiply @ sk_c10 @ sk_c9 ) = ( sk_c11 ) ) |
% 43.11/6.77 ( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c4 ) )),
% 43.11/6.77 inference('cnf.neg', [status(esa)], [prove_this_55])).
% 43.11/6.77 thf(zip_derived_cl57, plain,
% 43.11/6.77 ((((multiply @ sk_c10 @ sk_c9) = (sk_c11))
% 43.11/6.77 | ((multiply @ sk_c5 @ sk_c6) = (sk_c4)))),
% 43.11/6.77 inference('cnf', [status(esa)], [zf_stmt_19])).
% 43.11/6.77 thf(zip_derived_cl1633, plain, (((identity) = (sk_c9))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl1632])).
% 43.11/6.77 thf(zip_derived_cl1662, plain,
% 43.11/6.77 ((((multiply @ sk_c10 @ identity) = (sk_c11))
% 43.11/6.77 | ((multiply @ sk_c5 @ sk_c6) = (sk_c4)))),
% 43.11/6.77 inference('demod', [status(thm)], [zip_derived_cl57, zip_derived_cl1633])).
% 43.11/6.77 thf(zip_derived_cl2194, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl426, zip_derived_cl423])).
% 43.11/6.77 thf(zip_derived_cl2246, plain,
% 43.11/6.77 ((((sk_c10) = (sk_c11)) | ((multiply @ sk_c5 @ sk_c6) = (sk_c4)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl1662, zip_derived_cl2194])).
% 43.11/6.77 thf(zip_derived_cl3100, plain,
% 43.11/6.77 ((((multiply @ sk_c5 @ sk_c6) = (sk_c3))
% 43.11/6.77 | ((sk_c10) = (sk_c11))
% 43.11/6.77 | ((sk_c10) = (sk_c11)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl3077, zip_derived_cl2246])).
% 43.11/6.77 thf(zip_derived_cl3108, plain,
% 43.11/6.77 ((((sk_c10) = (sk_c11)) | ((multiply @ sk_c5 @ sk_c6) = (sk_c3)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl3100])).
% 43.11/6.77 thf(zip_derived_cl408, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i]:
% 43.11/6.77 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 43.11/6.77 inference('demod', [status(thm)], [zip_derived_cl375, zip_derived_cl0])).
% 43.11/6.77 thf(zip_derived_cl3486, plain,
% 43.11/6.77 ((((sk_c6) = (multiply @ (inverse @ sk_c5) @ sk_c3))
% 43.11/6.77 | ((sk_c10) = (sk_c11)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl3108, zip_derived_cl408])).
% 43.11/6.77 thf(zip_derived_cl3801, plain,
% 43.11/6.77 ((((sk_c6) = (multiply @ sk_c3 @ sk_c3))
% 43.11/6.77 | ((sk_c10) = (sk_c11))
% 43.11/6.77 | ((sk_c10) = (sk_c11)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl3106, zip_derived_cl3486])).
% 43.11/6.77 thf(zip_derived_cl3809, plain,
% 43.11/6.77 ((((sk_c10) = (sk_c11)) | ((sk_c6) = (multiply @ sk_c3 @ sk_c3)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl3801])).
% 43.11/6.77 thf(zip_derived_cl2243, plain,
% 43.11/6.77 ((((sk_c10) = (sk_c11)) | ((inverse @ sk_c3) = (sk_c6)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl1652, zip_derived_cl2194])).
% 43.11/6.77 thf(zip_derived_cl3861, plain,
% 43.11/6.77 ((((inverse @ sk_c3) = (multiply @ sk_c3 @ sk_c3))
% 43.11/6.77 | ((sk_c10) = (sk_c11))
% 43.11/6.77 | ((sk_c10) = (sk_c11)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl3809, zip_derived_cl2243])).
% 43.11/6.77 thf(zip_derived_cl3878, plain,
% 43.11/6.77 ((((sk_c10) = (sk_c11))
% 43.11/6.77 | ((inverse @ sk_c3) = (multiply @ sk_c3 @ sk_c3)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl3861])).
% 43.11/6.77 thf(zip_derived_cl6841, plain, (((sk_c11) = (identity))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl6822])).
% 43.11/6.77 thf(zip_derived_cl6994, plain,
% 43.11/6.77 ((((sk_c10) = (identity))
% 43.11/6.77 | ((inverse @ sk_c3) = (multiply @ sk_c3 @ sk_c3)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl3878, zip_derived_cl6841])).
% 43.11/6.77 thf(zip_derived_cl12447, plain,
% 43.11/6.77 ((((inverse @ sk_c1) = (multiply @ sk_c3 @ sk_c3))
% 43.11/6.77 | ((sk_c10) = (identity))
% 43.11/6.77 | ((sk_c10) = (identity)))),
% 43.11/6.77 inference('sup+', [status(thm)],
% 43.11/6.77 [zip_derived_cl12373, zip_derived_cl6994])).
% 43.11/6.77 thf(zip_derived_cl12479, plain,
% 43.11/6.77 ((((sk_c10) = (identity))
% 43.11/6.77 | ((inverse @ sk_c1) = (multiply @ sk_c3 @ sk_c3)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl12447])).
% 43.11/6.77 thf(zip_derived_cl23626, plain,
% 43.11/6.77 ((((inverse @ sk_c1) = (multiply @ sk_c3 @ sk_c10))
% 43.11/6.77 | ((sk_c10) = (identity))
% 43.11/6.77 | ((sk_c10) = (identity)))),
% 43.11/6.77 inference('sup+', [status(thm)],
% 43.11/6.77 [zip_derived_cl23549, zip_derived_cl12479])).
% 43.11/6.77 thf(zip_derived_cl23691, plain,
% 43.11/6.77 ((((sk_c10) = (identity))
% 43.11/6.77 | ((inverse @ sk_c1) = (multiply @ sk_c3 @ sk_c10)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl23626])).
% 43.11/6.77 thf(zip_derived_cl25456, plain,
% 43.11/6.77 ((((inverse @ sk_c1) = (multiply @ sk_c10 @ sk_c10))
% 43.11/6.77 | ((sk_c10) = (identity))
% 43.11/6.77 | ((sk_c10) = (identity)))),
% 43.11/6.77 inference('sup+', [status(thm)],
% 43.11/6.77 [zip_derived_cl23549, zip_derived_cl23691])).
% 43.11/6.77 thf(zip_derived_cl25467, plain,
% 43.11/6.77 ((((sk_c10) = (identity))
% 43.11/6.77 | ((inverse @ sk_c1) = (multiply @ sk_c10 @ sk_c10)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl25456])).
% 43.11/6.77 thf(prove_this_32, conjecture,
% 43.11/6.77 (~( ( ( inverse @ sk_c10 ) = ( sk_c9 ) ) |
% 43.11/6.77 ( ( inverse @ sk_c3 ) = ( sk_c6 ) ) ))).
% 43.11/6.77 thf(zf_stmt_20, negated_conjecture,
% 43.11/6.77 (( ( inverse @ sk_c10 ) = ( sk_c9 ) ) | ( ( inverse @ sk_c3 ) = ( sk_c6 ) )),
% 43.11/6.77 inference('cnf.neg', [status(esa)], [prove_this_32])).
% 43.11/6.77 thf(zip_derived_cl34, plain,
% 43.11/6.77 ((((inverse @ sk_c10) = (sk_c9)) | ((inverse @ sk_c3) = (sk_c6)))),
% 43.11/6.77 inference('cnf', [status(esa)], [zf_stmt_20])).
% 43.11/6.77 thf(prove_this_38, conjecture,
% 43.11/6.77 (~( ( ( inverse @ sk_c10 ) = ( sk_c9 ) ) |
% 43.11/6.77 ( ( multiply @ sk_c6 @ sk_c10 ) = ( sk_c11 ) ) ))).
% 43.11/6.77 thf(zf_stmt_21, negated_conjecture,
% 43.11/6.77 (( ( inverse @ sk_c10 ) = ( sk_c9 ) ) |
% 43.11/6.77 ( ( multiply @ sk_c6 @ sk_c10 ) = ( sk_c11 ) )),
% 43.11/6.77 inference('cnf.neg', [status(esa)], [prove_this_38])).
% 43.11/6.77 thf(zip_derived_cl40, plain,
% 43.11/6.77 ((((inverse @ sk_c10) = (sk_c9))
% 43.11/6.77 | ((multiply @ sk_c6 @ sk_c10) = (sk_c11)))),
% 43.11/6.77 inference('cnf', [status(esa)], [zf_stmt_21])).
% 43.11/6.77 thf(zip_derived_cl229, plain,
% 43.11/6.77 ((((multiply @ (inverse @ sk_c3) @ sk_c10) = (sk_c11))
% 43.11/6.77 | ((inverse @ sk_c10) = (sk_c9))
% 43.11/6.77 | ((inverse @ sk_c10) = (sk_c9)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl34, zip_derived_cl40])).
% 43.11/6.77 thf(zip_derived_cl234, plain,
% 43.11/6.77 ((((inverse @ sk_c10) = (sk_c9))
% 43.11/6.77 | ((multiply @ (inverse @ sk_c3) @ sk_c10) = (sk_c11)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl229])).
% 43.11/6.77 thf(zip_derived_cl1633, plain, (((identity) = (sk_c9))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl1632])).
% 43.11/6.77 thf(zip_derived_cl6841, plain, (((sk_c11) = (identity))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl6822])).
% 43.11/6.77 thf(zip_derived_cl11970, plain,
% 43.11/6.77 ((((inverse @ sk_c10) = (identity))
% 43.11/6.77 | ((multiply @ (inverse @ sk_c3) @ sk_c10) = (identity)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl234, zip_derived_cl1633, zip_derived_cl6841])).
% 43.11/6.77 thf(zip_derived_cl408, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i]:
% 43.11/6.77 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 43.11/6.77 inference('demod', [status(thm)], [zip_derived_cl375, zip_derived_cl0])).
% 43.11/6.77 thf(zip_derived_cl11972, plain,
% 43.11/6.77 ((((sk_c10) = (multiply @ (inverse @ (inverse @ sk_c3)) @ identity))
% 43.11/6.77 | ((inverse @ sk_c10) = (identity)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl11970, zip_derived_cl408])).
% 43.11/6.77 thf(zip_derived_cl2261, plain,
% 43.11/6.77 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl2194, zip_derived_cl426])).
% 43.11/6.77 thf(zip_derived_cl2194, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl426, zip_derived_cl423])).
% 43.11/6.77 thf(zip_derived_cl11979, plain,
% 43.11/6.77 ((((sk_c10) = (sk_c3)) | ((inverse @ sk_c10) = (identity)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl11972, zip_derived_cl2261, zip_derived_cl2194])).
% 43.11/6.77 thf(zip_derived_cl11979, plain,
% 43.11/6.77 ((((sk_c10) = (sk_c3)) | ((inverse @ sk_c10) = (identity)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl11972, zip_derived_cl2261, zip_derived_cl2194])).
% 43.11/6.77 thf(zip_derived_cl34, plain,
% 43.11/6.77 ((((inverse @ sk_c10) = (sk_c9)) | ((inverse @ sk_c3) = (sk_c6)))),
% 43.11/6.77 inference('cnf', [status(esa)], [zf_stmt_20])).
% 43.11/6.77 thf(prove_this_50, conjecture,
% 43.11/6.77 (~( ( ( inverse @ sk_c10 ) = ( sk_c9 ) ) |
% 43.11/6.77 ( ( inverse @ sk_c4 ) = ( sk_c6 ) ) ))).
% 43.11/6.77 thf(zf_stmt_22, negated_conjecture,
% 43.11/6.77 (( ( inverse @ sk_c10 ) = ( sk_c9 ) ) | ( ( inverse @ sk_c4 ) = ( sk_c6 ) )),
% 43.11/6.77 inference('cnf.neg', [status(esa)], [prove_this_50])).
% 43.11/6.77 thf(zip_derived_cl52, plain,
% 43.11/6.77 ((((inverse @ sk_c10) = (sk_c9)) | ((inverse @ sk_c4) = (sk_c6)))),
% 43.11/6.77 inference('cnf', [status(esa)], [zf_stmt_22])).
% 43.11/6.77 thf(zip_derived_cl1, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 43.11/6.77 inference('cnf', [status(esa)], [left_inverse])).
% 43.11/6.77 thf(zip_derived_cl72, plain,
% 43.11/6.77 ((((multiply @ sk_c6 @ sk_c4) = (identity))
% 43.11/6.77 | ((inverse @ sk_c10) = (sk_c9)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl52, zip_derived_cl1])).
% 43.11/6.77 thf(zip_derived_cl248, plain,
% 43.11/6.77 ((((multiply @ (inverse @ sk_c3) @ sk_c4) = (identity))
% 43.11/6.77 | ((inverse @ sk_c10) = (sk_c9))
% 43.11/6.77 | ((inverse @ sk_c10) = (sk_c9)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl34, zip_derived_cl72])).
% 43.11/6.77 thf(zip_derived_cl255, plain,
% 43.11/6.77 ((((inverse @ sk_c10) = (sk_c9))
% 43.11/6.77 | ((multiply @ (inverse @ sk_c3) @ sk_c4) = (identity)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl248])).
% 43.11/6.77 thf(zip_derived_cl408, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i]:
% 43.11/6.77 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 43.11/6.77 inference('demod', [status(thm)], [zip_derived_cl375, zip_derived_cl0])).
% 43.11/6.77 thf(zip_derived_cl428, plain,
% 43.11/6.77 ((((sk_c4) = (multiply @ (inverse @ (inverse @ sk_c3)) @ identity))
% 43.11/6.77 | ((inverse @ sk_c10) = (sk_c9)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl255, zip_derived_cl408])).
% 43.11/6.77 thf(zip_derived_cl426, plain,
% 43.11/6.77 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl408])).
% 43.11/6.77 thf(zip_derived_cl1246, plain,
% 43.11/6.77 ((((sk_c4) = (sk_c3)) | ((inverse @ sk_c10) = (sk_c9)))),
% 43.11/6.77 inference('demod', [status(thm)], [zip_derived_cl428, zip_derived_cl426])).
% 43.11/6.77 thf(prove_this_44, conjecture,
% 43.11/6.77 (~( ( ( inverse @ sk_c10 ) = ( sk_c9 ) ) |
% 43.11/6.77 ( ( inverse @ sk_c5 ) = ( sk_c4 ) ) ))).
% 43.11/6.77 thf(zf_stmt_23, negated_conjecture,
% 43.11/6.77 (( ( inverse @ sk_c10 ) = ( sk_c9 ) ) | ( ( inverse @ sk_c5 ) = ( sk_c4 ) )),
% 43.11/6.77 inference('cnf.neg', [status(esa)], [prove_this_44])).
% 43.11/6.77 thf(zip_derived_cl46, plain,
% 43.11/6.77 ((((inverse @ sk_c10) = (sk_c9)) | ((inverse @ sk_c5) = (sk_c4)))),
% 43.11/6.77 inference('cnf', [status(esa)], [zf_stmt_23])).
% 43.11/6.77 thf(zip_derived_cl1248, plain,
% 43.11/6.77 ((((inverse @ sk_c5) = (sk_c3))
% 43.11/6.77 | ((inverse @ sk_c10) = (sk_c9))
% 43.11/6.77 | ((inverse @ sk_c10) = (sk_c9)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl1246, zip_derived_cl46])).
% 43.11/6.77 thf(zip_derived_cl1272, plain,
% 43.11/6.77 ((((inverse @ sk_c10) = (sk_c9)) | ((inverse @ sk_c5) = (sk_c3)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl1248])).
% 43.11/6.77 thf(zip_derived_cl1, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 43.11/6.77 inference('cnf', [status(esa)], [left_inverse])).
% 43.11/6.77 thf(zip_derived_cl1278, plain,
% 43.11/6.77 ((((multiply @ sk_c3 @ sk_c5) = (identity))
% 43.11/6.77 | ((inverse @ sk_c10) = (sk_c9)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl1272, zip_derived_cl1])).
% 43.11/6.77 thf(zip_derived_cl1633, plain, (((identity) = (sk_c9))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl1632])).
% 43.11/6.77 thf(zip_derived_cl1688, plain,
% 43.11/6.77 ((((multiply @ sk_c3 @ sk_c5) = (identity))
% 43.11/6.77 | ((inverse @ sk_c10) = (identity)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl1278, zip_derived_cl1633])).
% 43.11/6.77 thf(zip_derived_cl11981, plain,
% 43.11/6.77 ((((multiply @ sk_c10 @ sk_c5) = (identity))
% 43.11/6.77 | ((inverse @ sk_c10) = (identity))
% 43.11/6.77 | ((inverse @ sk_c10) = (identity)))),
% 43.11/6.77 inference('sup+', [status(thm)],
% 43.11/6.77 [zip_derived_cl11979, zip_derived_cl1688])).
% 43.11/6.77 thf(zip_derived_cl12017, plain,
% 43.11/6.77 ((((inverse @ sk_c10) = (identity))
% 43.11/6.77 | ((multiply @ sk_c10 @ sk_c5) = (identity)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl11981])).
% 43.11/6.77 thf(zip_derived_cl408, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i]:
% 43.11/6.77 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 43.11/6.77 inference('demod', [status(thm)], [zip_derived_cl375, zip_derived_cl0])).
% 43.11/6.77 thf(zip_derived_cl12029, plain,
% 43.11/6.77 ((((sk_c5) = (multiply @ (inverse @ sk_c10) @ identity))
% 43.11/6.77 | ((inverse @ sk_c10) = (identity)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl12017, zip_derived_cl408])).
% 43.11/6.77 thf(zip_derived_cl2194, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl426, zip_derived_cl423])).
% 43.11/6.77 thf(zip_derived_cl12050, plain,
% 43.11/6.77 ((((sk_c5) = (inverse @ sk_c10)) | ((inverse @ sk_c10) = (identity)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl12029, zip_derived_cl2194])).
% 43.11/6.77 thf(zip_derived_cl1246, plain,
% 43.11/6.77 ((((sk_c4) = (sk_c3)) | ((inverse @ sk_c10) = (sk_c9)))),
% 43.11/6.77 inference('demod', [status(thm)], [zip_derived_cl428, zip_derived_cl426])).
% 43.11/6.77 thf(prove_this_56, conjecture,
% 43.11/6.77 (~( ( ( inverse @ sk_c10 ) = ( sk_c9 ) ) |
% 43.11/6.77 ( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c4 ) ) ))).
% 43.11/6.77 thf(zf_stmt_24, negated_conjecture,
% 43.11/6.77 (( ( inverse @ sk_c10 ) = ( sk_c9 ) ) |
% 43.11/6.77 ( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c4 ) )),
% 43.11/6.77 inference('cnf.neg', [status(esa)], [prove_this_56])).
% 43.11/6.77 thf(zip_derived_cl58, plain,
% 43.11/6.77 ((((inverse @ sk_c10) = (sk_c9)) | ((multiply @ sk_c5 @ sk_c6) = (sk_c4)))),
% 43.11/6.77 inference('cnf', [status(esa)], [zf_stmt_24])).
% 43.11/6.77 thf(zip_derived_cl1260, plain,
% 43.11/6.77 ((((multiply @ sk_c5 @ sk_c6) = (sk_c3))
% 43.11/6.77 | ((inverse @ sk_c10) = (sk_c9))
% 43.11/6.77 | ((inverse @ sk_c10) = (sk_c9)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl1246, zip_derived_cl58])).
% 43.11/6.77 thf(zip_derived_cl1274, plain,
% 43.11/6.77 ((((inverse @ sk_c10) = (sk_c9)) | ((multiply @ sk_c5 @ sk_c6) = (sk_c3)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl1260])).
% 43.11/6.77 thf(zip_derived_cl1633, plain, (((identity) = (sk_c9))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl1632])).
% 43.11/6.77 thf(zip_derived_cl1686, plain,
% 43.11/6.77 ((((inverse @ sk_c10) = (identity))
% 43.11/6.77 | ((multiply @ sk_c5 @ sk_c6) = (sk_c3)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl1274, zip_derived_cl1633])).
% 43.11/6.77 thf(zip_derived_cl408, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i]:
% 43.11/6.77 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 43.11/6.77 inference('demod', [status(thm)], [zip_derived_cl375, zip_derived_cl0])).
% 43.11/6.77 thf(zip_derived_cl1991, plain,
% 43.11/6.77 ((((sk_c6) = (multiply @ (inverse @ sk_c5) @ sk_c3))
% 43.11/6.77 | ((inverse @ sk_c10) = (identity)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl1686, zip_derived_cl408])).
% 43.11/6.77 thf(zip_derived_cl83431, plain,
% 43.11/6.77 ((((sk_c6) = (multiply @ (inverse @ (inverse @ sk_c10)) @ sk_c3))
% 43.11/6.77 | ((inverse @ sk_c10) = (identity))
% 43.11/6.77 | ((inverse @ sk_c10) = (identity)))),
% 43.11/6.77 inference('sup+', [status(thm)],
% 43.11/6.77 [zip_derived_cl12050, zip_derived_cl1991])).
% 43.11/6.77 thf(zip_derived_cl2261, plain,
% 43.11/6.77 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl2194, zip_derived_cl426])).
% 43.11/6.77 thf(zip_derived_cl83463, plain,
% 43.11/6.77 ((((sk_c6) = (multiply @ sk_c10 @ sk_c3))
% 43.11/6.77 | ((inverse @ sk_c10) = (identity))
% 43.11/6.77 | ((inverse @ sk_c10) = (identity)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl83431, zip_derived_cl2261])).
% 43.11/6.77 thf(zip_derived_cl83464, plain,
% 43.11/6.77 ((((inverse @ sk_c10) = (identity))
% 43.11/6.77 | ((sk_c6) = (multiply @ sk_c10 @ sk_c3)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl83463])).
% 43.11/6.77 thf(zip_derived_cl12050, plain,
% 43.11/6.77 ((((sk_c5) = (inverse @ sk_c10)) | ((inverse @ sk_c10) = (identity)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl12029, zip_derived_cl2194])).
% 43.11/6.77 thf(zip_derived_cl46, plain,
% 43.11/6.77 ((((inverse @ sk_c10) = (sk_c9)) | ((inverse @ sk_c5) = (sk_c4)))),
% 43.11/6.77 inference('cnf', [status(esa)], [zf_stmt_23])).
% 43.11/6.77 thf(zip_derived_cl52, plain,
% 43.11/6.77 ((((inverse @ sk_c10) = (sk_c9)) | ((inverse @ sk_c4) = (sk_c6)))),
% 43.11/6.77 inference('cnf', [status(esa)], [zf_stmt_22])).
% 43.11/6.77 thf(zip_derived_cl73, plain,
% 43.11/6.77 ((((inverse @ (inverse @ sk_c5)) = (sk_c6))
% 43.11/6.77 | ((inverse @ sk_c10) = (sk_c9))
% 43.11/6.77 | ((inverse @ sk_c10) = (sk_c9)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl46, zip_derived_cl52])).
% 43.11/6.77 thf(zip_derived_cl76, plain,
% 43.11/6.77 ((((inverse @ sk_c10) = (sk_c9))
% 43.11/6.77 | ((inverse @ (inverse @ sk_c5)) = (sk_c6)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl73])).
% 43.11/6.77 thf(zip_derived_cl1633, plain, (((identity) = (sk_c9))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl1632])).
% 43.11/6.77 thf(zip_derived_cl1669, plain,
% 43.11/6.77 ((((inverse @ sk_c10) = (identity))
% 43.11/6.77 | ((inverse @ (inverse @ sk_c5)) = (sk_c6)))),
% 43.11/6.77 inference('demod', [status(thm)], [zip_derived_cl76, zip_derived_cl1633])).
% 43.11/6.77 thf(zip_derived_cl12053, plain,
% 43.11/6.77 ((((inverse @ (inverse @ (inverse @ sk_c10))) = (sk_c6))
% 43.11/6.77 | ((inverse @ sk_c10) = (identity))
% 43.11/6.77 | ((inverse @ sk_c10) = (identity)))),
% 43.11/6.77 inference('sup+', [status(thm)],
% 43.11/6.77 [zip_derived_cl12050, zip_derived_cl1669])).
% 43.11/6.77 thf(zip_derived_cl2261, plain,
% 43.11/6.77 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl2194, zip_derived_cl426])).
% 43.11/6.77 thf(zip_derived_cl12111, plain,
% 43.11/6.77 ((((inverse @ sk_c10) = (sk_c6))
% 43.11/6.77 | ((inverse @ sk_c10) = (identity))
% 43.11/6.77 | ((inverse @ sk_c10) = (identity)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl12053, zip_derived_cl2261])).
% 43.11/6.77 thf(zip_derived_cl12112, plain,
% 43.11/6.77 ((((inverse @ sk_c10) = (identity)) | ((inverse @ sk_c10) = (sk_c6)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl12111])).
% 43.11/6.77 thf(zip_derived_cl83961, plain,
% 43.11/6.77 ((((inverse @ sk_c10) = (multiply @ sk_c10 @ sk_c3))
% 43.11/6.77 | ((inverse @ sk_c10) = (identity))
% 43.11/6.77 | ((inverse @ sk_c10) = (identity)))),
% 43.11/6.77 inference('sup+', [status(thm)],
% 43.11/6.77 [zip_derived_cl83464, zip_derived_cl12112])).
% 43.11/6.77 thf(zip_derived_cl84197, plain,
% 43.11/6.77 ((((inverse @ sk_c10) = (identity))
% 43.11/6.77 | ((inverse @ sk_c10) = (multiply @ sk_c10 @ sk_c3)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl83961])).
% 43.11/6.77 thf(zip_derived_cl136995, plain,
% 43.11/6.77 ((((inverse @ sk_c10) = (multiply @ sk_c10 @ sk_c10))
% 43.11/6.77 | ((inverse @ sk_c10) = (identity))
% 43.11/6.77 | ((inverse @ sk_c10) = (identity)))),
% 43.11/6.77 inference('sup+', [status(thm)],
% 43.11/6.77 [zip_derived_cl11979, zip_derived_cl84197])).
% 43.11/6.77 thf(zip_derived_cl137060, plain,
% 43.11/6.77 ((((inverse @ sk_c10) = (identity))
% 43.11/6.77 | ((inverse @ sk_c10) = (multiply @ sk_c10 @ sk_c10)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl136995])).
% 43.11/6.77 thf(zip_derived_cl137801, plain,
% 43.11/6.77 ((((multiply @ sk_c10 @ sk_c10) != (identity))
% 43.11/6.77 | ((inverse @ sk_c10) = (identity)))),
% 43.11/6.77 inference('eq_fact', [status(thm)], [zip_derived_cl137060])).
% 43.11/6.77 thf(zip_derived_cl137826, plain,
% 43.11/6.77 ((((inverse @ sk_c1) != (identity))
% 43.11/6.77 | ((sk_c10) = (identity))
% 43.11/6.77 | ((inverse @ sk_c10) = (identity)))),
% 43.11/6.77 inference('sup-', [status(thm)],
% 43.11/6.77 [zip_derived_cl25467, zip_derived_cl137801])).
% 43.11/6.77 thf(zip_derived_cl562, plain,
% 43.11/6.77 ((((identity) = (sk_c10)) | ((inverse @ sk_c1) = (sk_c11)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl504, zip_derived_cl0])).
% 43.11/6.77 thf(zip_derived_cl6841, plain, (((sk_c11) = (identity))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl6822])).
% 43.11/6.77 thf(zip_derived_cl6886, plain,
% 43.11/6.77 ((((identity) = (sk_c10)) | ((inverse @ sk_c1) = (identity)))),
% 43.11/6.77 inference('demod', [status(thm)], [zip_derived_cl562, zip_derived_cl6841])).
% 43.11/6.77 thf(zip_derived_cl137920, plain,
% 43.11/6.77 ((((inverse @ sk_c10) = (identity)) | ((sk_c10) = (identity)))),
% 43.11/6.77 inference('clc', [status(thm)],
% 43.11/6.77 [zip_derived_cl137826, zip_derived_cl6886])).
% 43.11/6.77 thf(zip_derived_cl2261, plain,
% 43.11/6.77 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl2194, zip_derived_cl426])).
% 43.11/6.77 thf(zip_derived_cl137922, plain,
% 43.11/6.77 ((((sk_c10) = (inverse @ identity)) | ((sk_c10) = (identity)))),
% 43.11/6.77 inference('sup+', [status(thm)],
% 43.11/6.77 [zip_derived_cl137920, zip_derived_cl2261])).
% 43.11/6.77 thf(zip_derived_cl1313, plain, (((inverse @ identity) = (identity))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl483, zip_derived_cl1])).
% 43.11/6.77 thf(zip_derived_cl138029, plain,
% 43.11/6.77 ((((sk_c10) = (identity)) | ((sk_c10) = (identity)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl137922, zip_derived_cl1313])).
% 43.11/6.77 thf(zip_derived_cl138030, plain, (((sk_c10) = (identity))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl138029])).
% 43.11/6.77 thf(zip_derived_cl138167, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 43.11/6.77 (((X7) != (identity))
% 43.11/6.77 | ((inverse @ X7) != (identity))
% 43.11/6.77 | ((X6) != (identity))
% 43.11/6.77 | ((inverse @ X6) != (identity))
% 43.11/6.77 | ((multiply @ X5 @ X4) != (identity))
% 43.11/6.77 | ((inverse @ X5) != (X4))
% 43.11/6.77 | ((X4) != (identity))
% 43.11/6.77 | ((inverse @ X3) != (X2))
% 43.11/6.77 | ((inverse @ X2) != (X4))
% 43.11/6.77 | ((multiply @ X3 @ X4) != (X2))
% 43.11/6.77 | ((identity) != (identity))
% 43.11/6.77 | ((X1) != (identity))
% 43.11/6.77 | ((inverse @ X1) != (identity))
% 43.11/6.77 | ((X0) != (identity))
% 43.11/6.77 | ((inverse @ X0) != (identity)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl6936, zip_derived_cl138030])).
% 43.11/6.77 thf(zip_derived_cl138168, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 43.11/6.77 (((inverse @ X0) != (identity))
% 43.11/6.77 | ((X0) != (identity))
% 43.11/6.77 | ((inverse @ X1) != (identity))
% 43.11/6.77 | ((X1) != (identity))
% 43.11/6.77 | ((multiply @ X3 @ X4) != (X2))
% 43.11/6.77 | ((inverse @ X2) != (X4))
% 43.11/6.77 | ((inverse @ X3) != (X2))
% 43.11/6.77 | ((X4) != (identity))
% 43.11/6.77 | ((inverse @ X5) != (X4))
% 43.11/6.77 | ((multiply @ X5 @ X4) != (identity))
% 43.11/6.77 | ((inverse @ X6) != (identity))
% 43.11/6.77 | ((X6) != (identity))
% 43.11/6.77 | ((inverse @ X7) != (identity))
% 43.11/6.77 | ((X7) != (identity)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl138167])).
% 43.11/6.77 thf(zip_derived_cl138403, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 43.11/6.77 (((X0) != (identity))
% 43.11/6.77 | ((inverse @ X0) != (identity))
% 43.11/6.77 | ((X1) != (identity))
% 43.11/6.77 | ((inverse @ X1) != (identity))
% 43.11/6.77 | ((multiply @ X3 @ X2) != (identity))
% 43.11/6.77 | ((inverse @ X3) != (X2))
% 43.11/6.77 | ((X2) != (identity))
% 43.11/6.77 | ((inverse @ X4) != (X5))
% 43.11/6.77 | ((inverse @ X5) != (X2))
% 43.11/6.77 | ((multiply @ X4 @ X2) != (X5))
% 43.11/6.77 | ((X6) != (identity))
% 43.11/6.77 | ((inverse @ X6) != (identity))
% 43.11/6.77 | ((inverse @ identity) != (identity)))),
% 43.11/6.77 inference('eq_res', [status(thm)], [zip_derived_cl138168])).
% 43.11/6.77 thf(zip_derived_cl1313, plain, (((inverse @ identity) = (identity))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl483, zip_derived_cl1])).
% 43.11/6.77 thf(zip_derived_cl138404, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 43.11/6.77 (((X0) != (identity))
% 43.11/6.77 | ((inverse @ X0) != (identity))
% 43.11/6.77 | ((X1) != (identity))
% 43.11/6.77 | ((inverse @ X1) != (identity))
% 43.11/6.77 | ((multiply @ X3 @ X2) != (identity))
% 43.11/6.77 | ((inverse @ X3) != (X2))
% 43.11/6.77 | ((X2) != (identity))
% 43.11/6.77 | ((inverse @ X4) != (X5))
% 43.11/6.77 | ((inverse @ X5) != (X2))
% 43.11/6.77 | ((multiply @ X4 @ X2) != (X5))
% 43.11/6.77 | ((X6) != (identity))
% 43.11/6.77 | ((inverse @ X6) != (identity))
% 43.11/6.77 | ((identity) != (identity)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl138403, zip_derived_cl1313])).
% 43.11/6.77 thf(zip_derived_cl138405, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 43.11/6.77 (((inverse @ X6) != (identity))
% 43.11/6.77 | ((X6) != (identity))
% 43.11/6.77 | ((multiply @ X4 @ X2) != (X5))
% 43.11/6.77 | ((inverse @ X5) != (X2))
% 43.11/6.77 | ((inverse @ X4) != (X5))
% 43.11/6.77 | ((X2) != (identity))
% 43.11/6.77 | ((inverse @ X3) != (X2))
% 43.11/6.77 | ((multiply @ X3 @ X2) != (identity))
% 43.11/6.77 | ((inverse @ X1) != (identity))
% 43.11/6.77 | ((X1) != (identity))
% 43.11/6.77 | ((inverse @ X0) != (identity))
% 43.11/6.77 | ((X0) != (identity)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl138404])).
% 43.11/6.77 thf(zip_derived_cl138406, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 43.11/6.77 (((X0) != (identity))
% 43.11/6.77 | ((inverse @ X0) != (identity))
% 43.11/6.77 | ((X1) != (identity))
% 43.11/6.77 | ((inverse @ X1) != (identity))
% 43.11/6.77 | ((multiply @ X3 @ X2) != (identity))
% 43.11/6.77 | ((inverse @ X3) != (X2))
% 43.11/6.77 | ((X2) != (identity))
% 43.11/6.77 | ((inverse @ X4) != (X5))
% 43.11/6.77 | ((inverse @ X5) != (X2))
% 43.11/6.77 | ((multiply @ X4 @ X2) != (X5))
% 43.11/6.77 | ((inverse @ identity) != (identity)))),
% 43.11/6.77 inference('eq_res', [status(thm)], [zip_derived_cl138405])).
% 43.11/6.77 thf(zip_derived_cl1313, plain, (((inverse @ identity) = (identity))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl483, zip_derived_cl1])).
% 43.11/6.77 thf(zip_derived_cl138407, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 43.11/6.77 (((X0) != (identity))
% 43.11/6.77 | ((inverse @ X0) != (identity))
% 43.11/6.77 | ((X1) != (identity))
% 43.11/6.77 | ((inverse @ X1) != (identity))
% 43.11/6.77 | ((multiply @ X3 @ X2) != (identity))
% 43.11/6.77 | ((inverse @ X3) != (X2))
% 43.11/6.77 | ((X2) != (identity))
% 43.11/6.77 | ((inverse @ X4) != (X5))
% 43.11/6.77 | ((inverse @ X5) != (X2))
% 43.11/6.77 | ((multiply @ X4 @ X2) != (X5))
% 43.11/6.77 | ((identity) != (identity)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl138406, zip_derived_cl1313])).
% 43.11/6.77 thf(zip_derived_cl138408, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 43.11/6.77 (((multiply @ X4 @ X2) != (X5))
% 43.11/6.77 | ((inverse @ X5) != (X2))
% 43.11/6.77 | ((inverse @ X4) != (X5))
% 43.11/6.77 | ((X2) != (identity))
% 43.11/6.77 | ((inverse @ X3) != (X2))
% 43.11/6.77 | ((multiply @ X3 @ X2) != (identity))
% 43.11/6.77 | ((inverse @ X1) != (identity))
% 43.11/6.77 | ((X1) != (identity))
% 43.11/6.77 | ((inverse @ X0) != (identity))
% 43.11/6.77 | ((X0) != (identity)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl138407])).
% 43.11/6.77 thf(zip_derived_cl138409, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 43.11/6.77 (((X0) != (identity))
% 43.11/6.77 | ((inverse @ X0) != (identity))
% 43.11/6.77 | ((X1) != (identity))
% 43.11/6.77 | ((inverse @ X1) != (identity))
% 43.11/6.77 | ((multiply @ X2 @ identity) != (identity))
% 43.11/6.77 | ((inverse @ X2) != (identity))
% 43.11/6.77 | ((inverse @ X3) != (X4))
% 43.11/6.77 | ((inverse @ X4) != (identity))
% 43.11/6.77 | ((multiply @ X3 @ identity) != (X4)))),
% 43.11/6.77 inference('eq_res', [status(thm)], [zip_derived_cl138408])).
% 43.11/6.77 thf(zip_derived_cl2194, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl426, zip_derived_cl423])).
% 43.11/6.77 thf(zip_derived_cl2194, plain,
% 43.11/6.77 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl426, zip_derived_cl423])).
% 43.11/6.77 thf(zip_derived_cl138410, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 43.11/6.77 (((X0) != (identity))
% 43.11/6.77 | ((inverse @ X0) != (identity))
% 43.11/6.77 | ((X1) != (identity))
% 43.11/6.77 | ((inverse @ X1) != (identity))
% 43.11/6.77 | ((X2) != (identity))
% 43.11/6.77 | ((inverse @ X2) != (identity))
% 43.11/6.77 | ((inverse @ X3) != (X4))
% 43.11/6.77 | ((inverse @ X4) != (identity))
% 43.11/6.77 | ((X3) != (X4)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl138409, zip_derived_cl2194, zip_derived_cl2194])).
% 43.11/6.77 thf(zip_derived_cl138411, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 43.11/6.77 (((inverse @ X0) != (identity))
% 43.11/6.77 | ((inverse @ X0) != (X0))
% 43.11/6.77 | ((inverse @ X1) != (identity))
% 43.11/6.77 | ((X1) != (identity))
% 43.11/6.77 | ((inverse @ X2) != (identity))
% 43.11/6.77 | ((X2) != (identity))
% 43.11/6.77 | ((inverse @ X3) != (identity))
% 43.11/6.77 | ((X3) != (identity)))),
% 43.11/6.77 inference('eq_res', [status(thm)], [zip_derived_cl138410])).
% 43.11/6.77 thf(zip_derived_cl138412, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 43.11/6.77 (((X0) != (identity))
% 43.11/6.77 | ((inverse @ X0) != (identity))
% 43.11/6.77 | ((X1) != (identity))
% 43.11/6.77 | ((inverse @ X1) != (identity))
% 43.11/6.77 | ((inverse @ identity) != (identity))
% 43.11/6.77 | ((inverse @ X2) != (X2))
% 43.11/6.77 | ((inverse @ X2) != (identity)))),
% 43.11/6.77 inference('eq_res', [status(thm)], [zip_derived_cl138411])).
% 43.11/6.77 thf(zip_derived_cl1313, plain, (((inverse @ identity) = (identity))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl483, zip_derived_cl1])).
% 43.11/6.77 thf(zip_derived_cl138413, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 43.11/6.77 (((X0) != (identity))
% 43.11/6.77 | ((inverse @ X0) != (identity))
% 43.11/6.77 | ((X1) != (identity))
% 43.11/6.77 | ((inverse @ X1) != (identity))
% 43.11/6.77 | ((identity) != (identity))
% 43.11/6.77 | ((inverse @ X2) != (X2))
% 43.11/6.77 | ((inverse @ X2) != (identity)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl138412, zip_derived_cl1313])).
% 43.11/6.77 thf(zip_derived_cl138414, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 43.11/6.77 (((inverse @ X2) != (identity))
% 43.11/6.77 | ((inverse @ X2) != (X2))
% 43.11/6.77 | ((inverse @ X1) != (identity))
% 43.11/6.77 | ((X1) != (identity))
% 43.11/6.77 | ((inverse @ X0) != (identity))
% 43.11/6.77 | ((X0) != (identity)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl138413])).
% 43.11/6.77 thf(zip_derived_cl138557, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i]:
% 43.11/6.77 (((X0) != (identity))
% 43.11/6.77 | ((inverse @ X0) != (identity))
% 43.11/6.77 | ((inverse @ identity) != (identity))
% 43.11/6.77 | ((inverse @ X1) != (X1))
% 43.11/6.77 | ((inverse @ X1) != (identity)))),
% 43.11/6.77 inference('eq_res', [status(thm)], [zip_derived_cl138414])).
% 43.11/6.77 thf(zip_derived_cl1313, plain, (((inverse @ identity) = (identity))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl483, zip_derived_cl1])).
% 43.11/6.77 thf(zip_derived_cl138558, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i]:
% 43.11/6.77 (((X0) != (identity))
% 43.11/6.77 | ((inverse @ X0) != (identity))
% 43.11/6.77 | ((identity) != (identity))
% 43.11/6.77 | ((inverse @ X1) != (X1))
% 43.11/6.77 | ((inverse @ X1) != (identity)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl138557, zip_derived_cl1313])).
% 43.11/6.77 thf(zip_derived_cl138559, plain,
% 43.11/6.77 (![X0 : $i, X1 : $i]:
% 43.11/6.77 (((inverse @ X1) != (identity))
% 43.11/6.77 | ((inverse @ X1) != (X1))
% 43.11/6.77 | ((inverse @ X0) != (identity))
% 43.11/6.77 | ((X0) != (identity)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl138558])).
% 43.11/6.77 thf(zip_derived_cl138560, plain,
% 43.11/6.77 (![X0 : $i]:
% 43.11/6.77 (((inverse @ identity) != (identity))
% 43.11/6.77 | ((inverse @ X0) != (X0))
% 43.11/6.77 | ((inverse @ X0) != (identity)))),
% 43.11/6.77 inference('eq_res', [status(thm)], [zip_derived_cl138559])).
% 43.11/6.77 thf(zip_derived_cl1313, plain, (((inverse @ identity) = (identity))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl483, zip_derived_cl1])).
% 43.11/6.77 thf(zip_derived_cl138561, plain,
% 43.11/6.77 (![X0 : $i]:
% 43.11/6.77 (((identity) != (identity))
% 43.11/6.77 | ((inverse @ X0) != (X0))
% 43.11/6.77 | ((inverse @ X0) != (identity)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl138560, zip_derived_cl1313])).
% 43.11/6.77 thf(zip_derived_cl138562, plain,
% 43.11/6.77 (![X0 : $i]: (((inverse @ X0) != (identity)) | ((inverse @ X0) != (X0)))),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl138561])).
% 43.11/6.77 thf(zip_derived_cl138568, plain,
% 43.11/6.77 ((((identity) != (identity)) | ((inverse @ identity) != (identity)))),
% 43.11/6.77 inference('sup-', [status(thm)],
% 43.11/6.77 [zip_derived_cl1313, zip_derived_cl138562])).
% 43.11/6.77 thf(zip_derived_cl1313, plain, (((inverse @ identity) = (identity))),
% 43.11/6.77 inference('sup+', [status(thm)], [zip_derived_cl483, zip_derived_cl1])).
% 43.11/6.77 thf(zip_derived_cl138602, plain,
% 43.11/6.77 ((((identity) != (identity)) | ((identity) != (identity)))),
% 43.11/6.77 inference('demod', [status(thm)],
% 43.11/6.77 [zip_derived_cl138568, zip_derived_cl1313])).
% 43.11/6.77 thf(zip_derived_cl138603, plain, ($false),
% 43.11/6.77 inference('simplify', [status(thm)], [zip_derived_cl138602])).
% 43.11/6.77
% 43.11/6.77 % SZS output end Refutation
% 43.11/6.77
% 43.11/6.77
% 43.11/6.77 % Terminating...
% 43.71/6.86 % Runner terminated.
% 43.71/6.87 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------