TSTP Solution File: GRP362-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP362-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.zILsmZeVI1 true
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:51:21 EDT 2023
% Result : Unsatisfiable 67.88s 10.42s
% Output : Refutation 67.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP362-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.zILsmZeVI1 true
% 0.13/0.34 % Computer : n025.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 21:14:09 EDT 2023
% 0.20/0.34 % CPUTime :
% 0.20/0.34 % Running portfolio for 300 s
% 0.20/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.34 % Number of cores: 8
% 0.20/0.35 % Python version: Python 3.6.8
% 0.20/0.35 % Running in FO mode
% 0.21/0.62 % Total configuration time : 435
% 0.21/0.62 % Estimated wc time : 1092
% 0.21/0.62 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.79 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.21/0.79 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 67.88/10.42 % Solved by fo/fo1_av.sh.
% 67.88/10.42 % done 10604 iterations in 9.600s
% 67.88/10.42 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 67.88/10.42 % SZS output start Refutation
% 67.88/10.42 thf(sk_c6_type, type, sk_c6: $i).
% 67.88/10.42 thf(sk_c10_type, type, sk_c10: $i).
% 67.88/10.42 thf(sk_c2_type, type, sk_c2: $i).
% 67.88/10.42 thf(sk_c5_type, type, sk_c5: $i).
% 67.88/10.42 thf(sk_c3_type, type, sk_c3: $i).
% 67.88/10.42 thf(identity_type, type, identity: $i).
% 67.88/10.42 thf(multiply_type, type, multiply: $i > $i > $i).
% 67.88/10.42 thf(sk_c8_type, type, sk_c8: $i).
% 67.88/10.42 thf(inverse_type, type, inverse: $i > $i).
% 67.88/10.42 thf(sk_c4_type, type, sk_c4: $i).
% 67.88/10.42 thf(sk_c1_type, type, sk_c1: $i).
% 67.88/10.42 thf(sk_c7_type, type, sk_c7: $i).
% 67.88/10.42 thf(sk_c9_type, type, sk_c9: $i).
% 67.88/10.42 thf(prove_this_27, conjecture,
% 67.88/10.42 (~( ( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c10 ) ) |
% 67.88/10.42 ( ( multiply @ sk_c10 @ sk_c8 ) = ( sk_c9 ) ) ))).
% 67.88/10.42 thf(zf_stmt_0, negated_conjecture,
% 67.88/10.42 (( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c10 ) ) |
% 67.88/10.42 ( ( multiply @ sk_c10 @ sk_c8 ) = ( sk_c9 ) )),
% 67.88/10.42 inference('cnf.neg', [status(esa)], [prove_this_27])).
% 67.88/10.42 thf(zip_derived_cl29, plain,
% 67.88/10.42 ((((multiply @ sk_c7 @ sk_c8) = (sk_c10))
% 67.88/10.42 | ((multiply @ sk_c10 @ sk_c8) = (sk_c9)))),
% 67.88/10.42 inference('cnf', [status(esa)], [zf_stmt_0])).
% 67.88/10.42 thf('0', plain,
% 67.88/10.42 ((((multiply @ sk_c7 @ sk_c8) = (sk_c10))) |
% 67.88/10.42 (((multiply @ sk_c10 @ sk_c8) = (sk_c9)))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl29])).
% 67.88/10.42 thf(prove_this_26, conjecture,
% 67.88/10.42 (~( ( ( inverse @ sk_c7 ) = ( sk_c10 ) ) |
% 67.88/10.42 ( ( multiply @ sk_c10 @ sk_c8 ) = ( sk_c9 ) ) ))).
% 67.88/10.42 thf(zf_stmt_1, negated_conjecture,
% 67.88/10.42 (( ( inverse @ sk_c7 ) = ( sk_c10 ) ) |
% 67.88/10.42 ( ( multiply @ sk_c10 @ sk_c8 ) = ( sk_c9 ) )),
% 67.88/10.42 inference('cnf.neg', [status(esa)], [prove_this_26])).
% 67.88/10.42 thf(zip_derived_cl28, plain,
% 67.88/10.42 ((((inverse @ sk_c7) = (sk_c10))
% 67.88/10.42 | ((multiply @ sk_c10 @ sk_c8) = (sk_c9)))),
% 67.88/10.42 inference('cnf', [status(esa)], [zf_stmt_1])).
% 67.88/10.42 thf('1', plain,
% 67.88/10.42 ((((inverse @ sk_c7) = (sk_c10))) |
% 67.88/10.42 (((multiply @ sk_c10 @ sk_c8) = (sk_c9)))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl28])).
% 67.88/10.42 thf(prove_this_10, conjecture,
% 67.88/10.42 (~( ( ( inverse @ sk_c10 ) = ( sk_c9 ) ) |
% 67.88/10.42 ( ( inverse @ sk_c9 ) = ( sk_c10 ) ) ))).
% 67.88/10.42 thf(zf_stmt_2, negated_conjecture,
% 67.88/10.42 (( ( inverse @ sk_c10 ) = ( sk_c9 ) ) |
% 67.88/10.42 ( ( inverse @ sk_c9 ) = ( sk_c10 ) )),
% 67.88/10.42 inference('cnf.neg', [status(esa)], [prove_this_10])).
% 67.88/10.42 thf(zip_derived_cl12, plain,
% 67.88/10.42 ((((inverse @ sk_c10) = (sk_c9)) | ((inverse @ sk_c9) = (sk_c10)))),
% 67.88/10.42 inference('cnf', [status(esa)], [zf_stmt_2])).
% 67.88/10.42 thf('2', plain,
% 67.88/10.42 ((((inverse @ sk_c10) = (sk_c9))) | (((inverse @ sk_c9) = (sk_c10)))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl12])).
% 67.88/10.42 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 67.88/10.42 thf(zip_derived_cl1, plain,
% 67.88/10.42 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 67.88/10.42 inference('cnf', [status(esa)], [left_inverse])).
% 67.88/10.42 thf(associativity, axiom,
% 67.88/10.42 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 67.88/10.42 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 67.88/10.42 thf(zip_derived_cl2, plain,
% 67.88/10.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.88/10.42 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 67.88/10.42 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 67.88/10.42 inference('cnf', [status(esa)], [associativity])).
% 67.88/10.42 thf(zip_derived_cl198, plain,
% 67.88/10.42 (![X0 : $i, X1 : $i]:
% 67.88/10.42 ((multiply @ identity @ X0)
% 67.88/10.42 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 67.88/10.42 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 67.88/10.42 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 67.88/10.42 thf(zip_derived_cl0, plain,
% 67.88/10.42 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 67.88/10.42 inference('cnf', [status(esa)], [left_identity])).
% 67.88/10.42 thf(zip_derived_cl200, plain,
% 67.88/10.42 (![X0 : $i, X1 : $i]:
% 67.88/10.42 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 67.88/10.42 inference('demod', [status(thm)], [zip_derived_cl198, zip_derived_cl0])).
% 67.88/10.42 thf(zip_derived_cl200, plain,
% 67.88/10.42 (![X0 : $i, X1 : $i]:
% 67.88/10.42 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 67.88/10.42 inference('demod', [status(thm)], [zip_derived_cl198, zip_derived_cl0])).
% 67.88/10.42 thf(zip_derived_cl464, plain,
% 67.88/10.42 (![X0 : $i, X1 : $i]:
% 67.88/10.42 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 67.88/10.42 inference('s_sup+', [status(thm)], [zip_derived_cl200, zip_derived_cl200])).
% 67.88/10.42 thf(zip_derived_cl1, plain,
% 67.88/10.42 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 67.88/10.42 inference('cnf', [status(esa)], [left_inverse])).
% 67.88/10.42 thf(zip_derived_cl1551, plain,
% 67.88/10.42 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 67.88/10.42 inference('s_sup+', [status(thm)], [zip_derived_cl464, zip_derived_cl1])).
% 67.88/10.42 thf(prove_this_1, conjecture,
% 67.88/10.42 (~( ( ( inverse @ sk_c10 ) = ( sk_c9 ) ) |
% 67.88/10.42 ( ( multiply @ sk_c9 @ sk_c8 ) = ( sk_c10 ) ) ))).
% 67.88/10.42 thf(zf_stmt_3, negated_conjecture,
% 67.88/10.42 (( ( inverse @ sk_c10 ) = ( sk_c9 ) ) |
% 67.88/10.42 ( ( multiply @ sk_c9 @ sk_c8 ) = ( sk_c10 ) )),
% 67.88/10.42 inference('cnf.neg', [status(esa)], [prove_this_1])).
% 67.88/10.42 thf(zip_derived_cl3, plain,
% 67.88/10.42 ((((inverse @ sk_c10) = (sk_c9))
% 67.88/10.42 | ((multiply @ sk_c9 @ sk_c8) = (sk_c10)))),
% 67.88/10.42 inference('cnf', [status(esa)], [zf_stmt_3])).
% 67.88/10.42 thf(zip_derived_cl59, plain,
% 67.88/10.42 ((((inverse @ sk_c10) = (sk_c9))) <= ((((inverse @ sk_c10) = (sk_c9))))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl3])).
% 67.88/10.42 thf(zip_derived_cl1, plain,
% 67.88/10.42 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 67.88/10.42 inference('cnf', [status(esa)], [left_inverse])).
% 67.88/10.42 thf(zip_derived_cl189, plain,
% 67.88/10.42 ((((multiply @ sk_c9 @ sk_c10) = (identity)))
% 67.88/10.42 <= ((((inverse @ sk_c10) = (sk_c9))))),
% 67.88/10.42 inference('s_sup+', [status(thm)], [zip_derived_cl59, zip_derived_cl1])).
% 67.88/10.42 thf(zip_derived_cl200, plain,
% 67.88/10.42 (![X0 : $i, X1 : $i]:
% 67.88/10.42 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 67.88/10.42 inference('demod', [status(thm)], [zip_derived_cl198, zip_derived_cl0])).
% 67.88/10.42 thf(zip_derived_cl471, plain,
% 67.88/10.42 ((((sk_c10) = (multiply @ (inverse @ sk_c9) @ identity)))
% 67.88/10.42 <= ((((inverse @ sk_c10) = (sk_c9))))),
% 67.88/10.42 inference('s_sup+', [status(thm)], [zip_derived_cl189, zip_derived_cl200])).
% 67.88/10.42 thf(zip_derived_cl2, plain,
% 67.88/10.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.88/10.42 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 67.88/10.42 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 67.88/10.42 inference('cnf', [status(esa)], [associativity])).
% 67.88/10.42 thf(zip_derived_cl522, plain,
% 67.88/10.42 ((![X0 : $i]:
% 67.88/10.42 ((multiply @ sk_c10 @ X0)
% 67.88/10.42 = (multiply @ (inverse @ sk_c9) @ (multiply @ identity @ X0))))
% 67.88/10.42 <= ((((inverse @ sk_c10) = (sk_c9))))),
% 67.88/10.42 inference('s_sup+', [status(thm)], [zip_derived_cl471, zip_derived_cl2])).
% 67.88/10.42 thf(zip_derived_cl0, plain,
% 67.88/10.42 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 67.88/10.42 inference('cnf', [status(esa)], [left_identity])).
% 67.88/10.42 thf(zip_derived_cl526, plain,
% 67.88/10.42 ((![X0 : $i]:
% 67.88/10.42 ((multiply @ sk_c10 @ X0) = (multiply @ (inverse @ sk_c9) @ X0)))
% 67.88/10.42 <= ((((inverse @ sk_c10) = (sk_c9))))),
% 67.88/10.42 inference('demod', [status(thm)], [zip_derived_cl522, zip_derived_cl0])).
% 67.88/10.42 thf(zip_derived_cl200, plain,
% 67.88/10.42 (![X0 : $i, X1 : $i]:
% 67.88/10.42 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 67.88/10.42 inference('demod', [status(thm)], [zip_derived_cl198, zip_derived_cl0])).
% 67.88/10.42 thf(zip_derived_cl998, plain,
% 67.88/10.42 ((![X0 : $i]: ((X0) = (multiply @ sk_c10 @ (multiply @ sk_c9 @ X0))))
% 67.88/10.42 <= ((((inverse @ sk_c10) = (sk_c9))))),
% 67.88/10.42 inference('s_sup+', [status(thm)], [zip_derived_cl526, zip_derived_cl200])).
% 67.88/10.42 thf(zip_derived_cl42759, plain,
% 67.88/10.42 ((((inverse @ sk_c9) = (multiply @ sk_c10 @ identity)))
% 67.88/10.42 <= ((((inverse @ sk_c10) = (sk_c9))))),
% 67.88/10.42 inference('s_sup+', [status(thm)],
% 67.88/10.42 [zip_derived_cl1551, zip_derived_cl998])).
% 67.88/10.42 thf(zip_derived_cl526, plain,
% 67.88/10.42 ((![X0 : $i]:
% 67.88/10.42 ((multiply @ sk_c10 @ X0) = (multiply @ (inverse @ sk_c9) @ X0)))
% 67.88/10.42 <= ((((inverse @ sk_c10) = (sk_c9))))),
% 67.88/10.42 inference('demod', [status(thm)], [zip_derived_cl522, zip_derived_cl0])).
% 67.88/10.42 thf(zip_derived_cl471, plain,
% 67.88/10.42 ((((sk_c10) = (multiply @ (inverse @ sk_c9) @ identity)))
% 67.88/10.42 <= ((((inverse @ sk_c10) = (sk_c9))))),
% 67.88/10.42 inference('s_sup+', [status(thm)], [zip_derived_cl189, zip_derived_cl200])).
% 67.88/10.42 thf(zip_derived_cl999, plain,
% 67.88/10.42 ((((sk_c10) = (multiply @ sk_c10 @ identity)))
% 67.88/10.42 <= ((((inverse @ sk_c10) = (sk_c9))))),
% 67.88/10.42 inference('s_sup+', [status(thm)], [zip_derived_cl526, zip_derived_cl471])).
% 67.88/10.42 thf(zip_derived_cl42972, plain,
% 67.88/10.42 ((((inverse @ sk_c9) = (sk_c10))) <= ((((inverse @ sk_c10) = (sk_c9))))),
% 67.88/10.42 inference('demod', [status(thm)],
% 67.88/10.42 [zip_derived_cl42759, zip_derived_cl999])).
% 67.88/10.42 thf(prove_this_55, conjecture,
% 67.88/10.42 (~( ( ( multiply @ X7 @ sk_c8 ) != ( sk_c10 ) ) |
% 67.88/10.42 ( ( inverse @ X7 ) != ( sk_c10 ) ) |
% 67.88/10.42 ( ( multiply @ X6 @ sk_c9 ) != ( sk_c8 ) ) |
% 67.88/10.42 ( ( inverse @ X5 ) != ( X6 ) ) |
% 67.88/10.42 ( ( multiply @ X5 @ X6 ) != ( sk_c8 ) ) |
% 67.88/10.42 ( ( inverse @ X2 ) != ( sk_c10 ) ) |
% 67.88/10.42 ( ( multiply @ X2 @ sk_c10 ) != ( X1 ) ) |
% 67.88/10.42 ( ( multiply @ sk_c10 @ X1 ) != ( sk_c9 ) ) |
% 67.88/10.42 ( ( inverse @ sk_c10 ) != ( sk_c9 ) ) |
% 67.88/10.42 ( ( inverse @ X4 ) != ( sk_c10 ) ) |
% 67.88/10.42 ( ( multiply @ X4 @ sk_c10 ) != ( X3 ) ) |
% 67.88/10.42 ( ( multiply @ sk_c10 @ X3 ) != ( sk_c9 ) ) |
% 67.88/10.42 ( ( multiply @ sk_c10 @ sk_c8 ) != ( sk_c9 ) ) |
% 67.88/10.42 ( ( inverse @ sk_c9 ) != ( sk_c10 ) ) |
% 67.88/10.42 ( ( multiply @ sk_c9 @ sk_c8 ) != ( sk_c10 ) ) ))).
% 67.88/10.42 thf(zf_stmt_4, negated_conjecture,
% 67.88/10.42 (( ( multiply @ X7 @ sk_c8 ) != ( sk_c10 ) ) |
% 67.88/10.42 ( ( inverse @ X7 ) != ( sk_c10 ) ) |
% 67.88/10.42 ( ( multiply @ X6 @ sk_c9 ) != ( sk_c8 ) ) |
% 67.88/10.42 ( ( inverse @ X5 ) != ( X6 ) ) |
% 67.88/10.42 ( ( multiply @ X5 @ X6 ) != ( sk_c8 ) ) |
% 67.88/10.42 ( ( inverse @ X2 ) != ( sk_c10 ) ) |
% 67.88/10.42 ( ( multiply @ X2 @ sk_c10 ) != ( X1 ) ) |
% 67.88/10.42 ( ( multiply @ sk_c10 @ X1 ) != ( sk_c9 ) ) |
% 67.88/10.42 ( ( inverse @ sk_c10 ) != ( sk_c9 ) ) |
% 67.88/10.42 ( ( inverse @ X4 ) != ( sk_c10 ) ) |
% 67.88/10.42 ( ( multiply @ X4 @ sk_c10 ) != ( X3 ) ) |
% 67.88/10.42 ( ( multiply @ sk_c10 @ X3 ) != ( sk_c9 ) ) |
% 67.88/10.42 ( ( multiply @ sk_c10 @ sk_c8 ) != ( sk_c9 ) ) |
% 67.88/10.42 ( ( inverse @ sk_c9 ) != ( sk_c10 ) ) |
% 67.88/10.42 ( ( multiply @ sk_c9 @ sk_c8 ) != ( sk_c10 ) )),
% 67.88/10.42 inference('cnf.neg', [status(esa)], [prove_this_55])).
% 67.88/10.42 thf(zip_derived_cl57, plain,
% 67.88/10.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 67.88/10.42 (((multiply @ X0 @ sk_c8) != (sk_c10))
% 67.88/10.42 | ((inverse @ X0) != (sk_c10))
% 67.88/10.42 | ((multiply @ X1 @ sk_c9) != (sk_c8))
% 67.88/10.42 | ((inverse @ X2) != (X1))
% 67.88/10.42 | ((multiply @ X2 @ X1) != (sk_c8))
% 67.88/10.42 | ((inverse @ X3) != (sk_c10))
% 67.88/10.42 | ((multiply @ X3 @ sk_c10) != (X4))
% 67.88/10.42 | ((multiply @ sk_c10 @ X4) != (sk_c9))
% 67.88/10.42 | ((inverse @ sk_c10) != (sk_c9))
% 67.88/10.42 | ((inverse @ X5) != (sk_c10))
% 67.88/10.42 | ((multiply @ X5 @ sk_c10) != (X6))
% 67.88/10.42 | ((multiply @ sk_c10 @ X6) != (sk_c9))
% 67.88/10.42 | ((multiply @ sk_c10 @ sk_c8) != (sk_c9))
% 67.88/10.42 | ((inverse @ sk_c9) != (sk_c10))
% 67.88/10.42 | ((multiply @ sk_c9 @ sk_c8) != (sk_c10)))),
% 67.88/10.42 inference('cnf', [status(esa)], [zf_stmt_4])).
% 67.88/10.42 thf(zip_derived_cl171, plain,
% 67.88/10.42 ((((inverse @ sk_c9) != (sk_c10)))
% 67.88/10.42 <= (~ (((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl57])).
% 67.88/10.42 thf(zip_derived_cl59196, plain,
% 67.88/10.42 ((((sk_c10) != (sk_c10)))
% 67.88/10.42 <= (~ (((inverse @ sk_c9) = (sk_c10))) &
% 67.88/10.42 (((inverse @ sk_c10) = (sk_c9))))),
% 67.88/10.42 inference('s_sup-', [status(thm)],
% 67.88/10.42 [zip_derived_cl42972, zip_derived_cl171])).
% 67.88/10.42 thf('3', plain,
% 67.88/10.42 ((((inverse @ sk_c9) = (sk_c10))) | ~ (((inverse @ sk_c10) = (sk_c9)))),
% 67.88/10.42 inference('simplify', [status(thm)], [zip_derived_cl59196])).
% 67.88/10.42 thf('4', plain,
% 67.88/10.42 (~ (((multiply @ sk_c9 @ sk_c8) = (sk_c10))) |
% 67.88/10.42 ~ (((multiply @ sk_c10 @ sk_c8) = (sk_c9))) |
% 67.88/10.42 (![X5 : $i, X6 : $i]:
% 67.88/10.42 (((inverse @ X5) != (sk_c10))
% 67.88/10.42 | ((multiply @ X5 @ sk_c10) != (X6))
% 67.88/10.42 | ((multiply @ sk_c10 @ X6) != (sk_c9)))) |
% 67.88/10.42 (![X1 : $i, X2 : $i]:
% 67.88/10.42 (((multiply @ X1 @ sk_c9) != (sk_c8))
% 67.88/10.42 | ((inverse @ X2) != (X1))
% 67.88/10.42 | ((multiply @ X2 @ X1) != (sk_c8)))) |
% 67.88/10.42 (![X0 : $i]:
% 67.88/10.42 (((inverse @ X0) != (sk_c10)) | ((multiply @ X0 @ sk_c8) != (sk_c10)))) |
% 67.88/10.42 ~ (((inverse @ sk_c10) = (sk_c9))) | ~ (((inverse @ sk_c9) = (sk_c10)))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl57])).
% 67.88/10.42 thf(prove_this_3, conjecture,
% 67.88/10.42 (~( ( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c4 ) ) |
% 67.88/10.42 ( ( multiply @ sk_c9 @ sk_c8 ) = ( sk_c10 ) ) ))).
% 67.88/10.42 thf(zf_stmt_5, negated_conjecture,
% 67.88/10.42 (( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c4 ) ) |
% 67.88/10.42 ( ( multiply @ sk_c9 @ sk_c8 ) = ( sk_c10 ) )),
% 67.88/10.42 inference('cnf.neg', [status(esa)], [prove_this_3])).
% 67.88/10.42 thf(zip_derived_cl5, plain,
% 67.88/10.42 ((((multiply @ sk_c3 @ sk_c10) = (sk_c4))
% 67.88/10.42 | ((multiply @ sk_c9 @ sk_c8) = (sk_c10)))),
% 67.88/10.42 inference('cnf', [status(esa)], [zf_stmt_5])).
% 67.88/10.42 thf(zip_derived_cl62, plain,
% 67.88/10.42 ((((multiply @ sk_c3 @ sk_c10) = (sk_c4)))
% 67.88/10.42 <= ((((multiply @ sk_c3 @ sk_c10) = (sk_c4))))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl5])).
% 67.88/10.42 thf(zip_derived_cl166, plain,
% 67.88/10.42 ((![X5 : $i, X6 : $i]:
% 67.88/10.42 (((inverse @ X5) != (sk_c10))
% 67.88/10.42 | ((multiply @ X5 @ sk_c10) != (X6))
% 67.88/10.42 | ((multiply @ sk_c10 @ X6) != (sk_c9))))
% 67.88/10.42 <= ((![X5 : $i, X6 : $i]:
% 67.88/10.42 (((inverse @ X5) != (sk_c10))
% 67.88/10.42 | ((multiply @ X5 @ sk_c10) != (X6))
% 67.88/10.42 | ((multiply @ sk_c10 @ X6) != (sk_c9)))))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl57])).
% 67.88/10.42 thf(zip_derived_cl205, plain,
% 67.88/10.42 ((![X0 : $i]:
% 67.88/10.42 (((multiply @ sk_c10 @ (multiply @ X0 @ sk_c10)) != (sk_c9))
% 67.88/10.42 | ((inverse @ X0) != (sk_c10))))
% 67.88/10.42 <= ((![X5 : $i, X6 : $i]:
% 67.88/10.42 (((inverse @ X5) != (sk_c10))
% 67.88/10.42 | ((multiply @ X5 @ sk_c10) != (X6))
% 67.88/10.42 | ((multiply @ sk_c10 @ X6) != (sk_c9)))))),
% 67.88/10.42 inference('eq_res', [status(thm)], [zip_derived_cl166])).
% 67.88/10.42 thf(zip_derived_cl237, plain,
% 67.88/10.42 (((((multiply @ sk_c10 @ sk_c4) != (sk_c9))
% 67.88/10.42 | ((inverse @ sk_c3) != (sk_c10))))
% 67.88/10.42 <= ((((multiply @ sk_c3 @ sk_c10) = (sk_c4))) &
% 67.88/10.42 (![X5 : $i, X6 : $i]:
% 67.88/10.42 (((inverse @ X5) != (sk_c10))
% 67.88/10.42 | ((multiply @ X5 @ sk_c10) != (X6))
% 67.88/10.42 | ((multiply @ sk_c10 @ X6) != (sk_c9)))))),
% 67.88/10.42 inference('s_sup-', [status(thm)], [zip_derived_cl62, zip_derived_cl205])).
% 67.88/10.42 thf('5', plain,
% 67.88/10.42 (~
% 67.88/10.42 (![X5 : $i, X6 : $i]:
% 67.88/10.42 (((inverse @ X5) != (sk_c10))
% 67.88/10.42 | ((multiply @ X5 @ sk_c10) != (X6))
% 67.88/10.42 | ((multiply @ sk_c10 @ X6) != (sk_c9)))) |
% 67.88/10.42 ~ (((multiply @ sk_c3 @ sk_c10) = (sk_c4))) |
% 67.88/10.42 ~ (((inverse @ sk_c3) = (sk_c10))) |
% 67.88/10.42 ~ (((multiply @ sk_c10 @ sk_c4) = (sk_c9)))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl237])).
% 67.88/10.42 thf(prove_this_37, conjecture,
% 67.88/10.42 (~( ( ( inverse @ sk_c10 ) = ( sk_c9 ) ) |
% 67.88/10.42 ( ( multiply @ sk_c1 @ sk_c10 ) = ( sk_c2 ) ) ))).
% 67.88/10.42 thf(zf_stmt_6, negated_conjecture,
% 67.88/10.42 (( ( inverse @ sk_c10 ) = ( sk_c9 ) ) |
% 67.88/10.42 ( ( multiply @ sk_c1 @ sk_c10 ) = ( sk_c2 ) )),
% 67.88/10.42 inference('cnf.neg', [status(esa)], [prove_this_37])).
% 67.88/10.42 thf(zip_derived_cl39, plain,
% 67.88/10.42 ((((inverse @ sk_c10) = (sk_c9))
% 67.88/10.42 | ((multiply @ sk_c1 @ sk_c10) = (sk_c2)))),
% 67.88/10.42 inference('cnf', [status(esa)], [zf_stmt_6])).
% 67.88/10.42 thf(zip_derived_cl130, plain,
% 67.88/10.42 ((((multiply @ sk_c1 @ sk_c10) = (sk_c2)))
% 67.88/10.42 <= ((((multiply @ sk_c1 @ sk_c10) = (sk_c2))))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl39])).
% 67.88/10.42 thf(zip_derived_cl205, plain,
% 67.88/10.42 ((![X0 : $i]:
% 67.88/10.42 (((multiply @ sk_c10 @ (multiply @ X0 @ sk_c10)) != (sk_c9))
% 67.88/10.42 | ((inverse @ X0) != (sk_c10))))
% 67.88/10.42 <= ((![X5 : $i, X6 : $i]:
% 67.88/10.42 (((inverse @ X5) != (sk_c10))
% 67.88/10.42 | ((multiply @ X5 @ sk_c10) != (X6))
% 67.88/10.42 | ((multiply @ sk_c10 @ X6) != (sk_c9)))))),
% 67.88/10.42 inference('eq_res', [status(thm)], [zip_derived_cl166])).
% 67.88/10.42 thf(zip_derived_cl376, plain,
% 67.88/10.42 (((((multiply @ sk_c10 @ sk_c2) != (sk_c9))
% 67.88/10.42 | ((inverse @ sk_c1) != (sk_c10))))
% 67.88/10.42 <= ((((multiply @ sk_c1 @ sk_c10) = (sk_c2))) &
% 67.88/10.42 (![X5 : $i, X6 : $i]:
% 67.88/10.42 (((inverse @ X5) != (sk_c10))
% 67.88/10.42 | ((multiply @ X5 @ sk_c10) != (X6))
% 67.88/10.42 | ((multiply @ sk_c10 @ X6) != (sk_c9)))))),
% 67.88/10.42 inference('s_sup-', [status(thm)], [zip_derived_cl130, zip_derived_cl205])).
% 67.88/10.42 thf('6', plain,
% 67.88/10.42 (~
% 67.88/10.42 (![X5 : $i, X6 : $i]:
% 67.88/10.42 (((inverse @ X5) != (sk_c10))
% 67.88/10.42 | ((multiply @ X5 @ sk_c10) != (X6))
% 67.88/10.42 | ((multiply @ sk_c10 @ X6) != (sk_c9)))) |
% 67.88/10.42 ~ (((multiply @ sk_c10 @ sk_c2) = (sk_c9))) |
% 67.88/10.42 ~ (((inverse @ sk_c1) = (sk_c10))) |
% 67.88/10.42 ~ (((multiply @ sk_c1 @ sk_c10) = (sk_c2)))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl376])).
% 67.88/10.42 thf(prove_this_31, conjecture,
% 67.88/10.42 (~( ( ( inverse @ sk_c3 ) = ( sk_c10 ) ) |
% 67.88/10.42 ( ( multiply @ sk_c10 @ sk_c2 ) = ( sk_c9 ) ) ))).
% 67.88/10.42 thf(zf_stmt_7, negated_conjecture,
% 67.88/10.42 (( ( inverse @ sk_c3 ) = ( sk_c10 ) ) |
% 67.88/10.42 ( ( multiply @ sk_c10 @ sk_c2 ) = ( sk_c9 ) )),
% 67.88/10.42 inference('cnf.neg', [status(esa)], [prove_this_31])).
% 67.88/10.42 thf(zip_derived_cl33, plain,
% 67.88/10.42 ((((inverse @ sk_c3) = (sk_c10))
% 67.88/10.42 | ((multiply @ sk_c10 @ sk_c2) = (sk_c9)))),
% 67.88/10.42 inference('cnf', [status(esa)], [zf_stmt_7])).
% 67.88/10.42 thf('7', plain,
% 67.88/10.42 ((((multiply @ sk_c10 @ sk_c2) = (sk_c9))) |
% 67.88/10.42 (((inverse @ sk_c3) = (sk_c10)))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl33])).
% 67.88/10.42 thf(prove_this_40, conjecture,
% 67.88/10.42 (~( ( ( inverse @ sk_c3 ) = ( sk_c10 ) ) |
% 67.88/10.42 ( ( multiply @ sk_c1 @ sk_c10 ) = ( sk_c2 ) ) ))).
% 67.88/10.42 thf(zf_stmt_8, negated_conjecture,
% 67.88/10.42 (( ( inverse @ sk_c3 ) = ( sk_c10 ) ) |
% 67.88/10.42 ( ( multiply @ sk_c1 @ sk_c10 ) = ( sk_c2 ) )),
% 67.88/10.42 inference('cnf.neg', [status(esa)], [prove_this_40])).
% 67.88/10.42 thf(zip_derived_cl42, plain,
% 67.88/10.42 ((((inverse @ sk_c3) = (sk_c10))
% 67.88/10.42 | ((multiply @ sk_c1 @ sk_c10) = (sk_c2)))),
% 67.88/10.42 inference('cnf', [status(esa)], [zf_stmt_8])).
% 67.88/10.42 thf('8', plain,
% 67.88/10.42 ((((multiply @ sk_c1 @ sk_c10) = (sk_c2))) |
% 67.88/10.42 (((inverse @ sk_c3) = (sk_c10)))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl42])).
% 67.88/10.42 thf(prove_this_49, conjecture,
% 67.88/10.42 (~( ( ( inverse @ sk_c3 ) = ( sk_c10 ) ) |
% 67.88/10.42 ( ( inverse @ sk_c1 ) = ( sk_c10 ) ) ))).
% 67.88/10.42 thf(zf_stmt_9, negated_conjecture,
% 67.88/10.42 (( ( inverse @ sk_c3 ) = ( sk_c10 ) ) |
% 67.88/10.42 ( ( inverse @ sk_c1 ) = ( sk_c10 ) )),
% 67.88/10.42 inference('cnf.neg', [status(esa)], [prove_this_49])).
% 67.88/10.42 thf(zip_derived_cl51, plain,
% 67.88/10.42 ((((inverse @ sk_c3) = (sk_c10)) | ((inverse @ sk_c1) = (sk_c10)))),
% 67.88/10.42 inference('cnf', [status(esa)], [zf_stmt_9])).
% 67.88/10.42 thf('9', plain,
% 67.88/10.42 ((((inverse @ sk_c1) = (sk_c10))) | (((inverse @ sk_c3) = (sk_c10)))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl51])).
% 67.88/10.42 thf(zip_derived_cl59, plain,
% 67.88/10.42 ((((inverse @ sk_c10) = (sk_c9))) <= ((((inverse @ sk_c10) = (sk_c9))))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl3])).
% 67.88/10.42 thf(zip_derived_cl76, plain,
% 67.88/10.42 ((((inverse @ sk_c9) = (sk_c10))) <= ((((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl12])).
% 67.88/10.42 thf(zip_derived_cl1, plain,
% 67.88/10.42 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 67.88/10.42 inference('cnf', [status(esa)], [left_inverse])).
% 67.88/10.42 thf(zip_derived_cl1, plain,
% 67.88/10.42 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 67.88/10.42 inference('cnf', [status(esa)], [left_inverse])).
% 67.88/10.42 thf(zip_derived_cl168, plain,
% 67.88/10.42 ((![X1 : $i, X2 : $i]:
% 67.88/10.42 (((multiply @ X1 @ sk_c9) != (sk_c8))
% 67.88/10.42 | ((inverse @ X2) != (X1))
% 67.88/10.42 | ((multiply @ X2 @ X1) != (sk_c8))))
% 67.88/10.42 <= ((![X1 : $i, X2 : $i]:
% 67.88/10.42 (((multiply @ X1 @ sk_c9) != (sk_c8))
% 67.88/10.42 | ((inverse @ X2) != (X1))
% 67.88/10.42 | ((multiply @ X2 @ X1) != (sk_c8)))))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl57])).
% 67.88/10.42 thf(zip_derived_cl249, plain,
% 67.88/10.42 ((![X0 : $i]:
% 67.88/10.42 (((identity) != (sk_c8))
% 67.88/10.42 | ((inverse @ X0) != (inverse @ sk_c9))
% 67.88/10.42 | ((multiply @ X0 @ (inverse @ sk_c9)) != (sk_c8))))
% 67.88/10.42 <= ((![X1 : $i, X2 : $i]:
% 67.88/10.42 (((multiply @ X1 @ sk_c9) != (sk_c8))
% 67.88/10.42 | ((inverse @ X2) != (X1))
% 67.88/10.42 | ((multiply @ X2 @ X1) != (sk_c8)))))),
% 67.88/10.42 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl168])).
% 67.88/10.42 thf(zip_derived_cl305, plain,
% 67.88/10.42 ((![X0 : $i]:
% 67.88/10.42 (((inverse @ X0) != (inverse @ sk_c9))
% 67.88/10.42 | ((multiply @ X0 @ (inverse @ sk_c9)) != (sk_c8))))
% 67.88/10.42 <= ((![X0 : $i]:
% 67.88/10.42 (((inverse @ X0) != (inverse @ sk_c9))
% 67.88/10.42 | ((multiply @ X0 @ (inverse @ sk_c9)) != (sk_c8)))))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl249])).
% 67.88/10.42 thf(zip_derived_cl309, plain,
% 67.88/10.42 (((((inverse @ (inverse @ (inverse @ sk_c9))) != (inverse @ sk_c9))
% 67.88/10.42 | ((identity) != (sk_c8))))
% 67.88/10.42 <= ((![X0 : $i]:
% 67.88/10.42 (((inverse @ X0) != (inverse @ sk_c9))
% 67.88/10.42 | ((multiply @ X0 @ (inverse @ sk_c9)) != (sk_c8)))))),
% 67.88/10.42 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl305])).
% 67.88/10.42 thf(zip_derived_cl315, plain,
% 67.88/10.42 ((((inverse @ (inverse @ (inverse @ sk_c9))) != (inverse @ sk_c9)))
% 67.88/10.42 <= (~
% 67.88/10.42 (((inverse @ (inverse @ (inverse @ sk_c9))) = (inverse @ sk_c9))))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl309])).
% 67.88/10.42 thf(zip_derived_cl317, plain,
% 67.88/10.42 ((((inverse @ (inverse @ sk_c10)) != (sk_c10)))
% 67.88/10.42 <= (~
% 67.88/10.42 (((inverse @ (inverse @ (inverse @ sk_c9))) = (inverse @ sk_c9))) &
% 67.88/10.42 (((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.42 inference('s_sup-', [status(thm)], [zip_derived_cl76, zip_derived_cl315])).
% 67.88/10.42 thf(zip_derived_cl318, plain,
% 67.88/10.42 ((((inverse @ sk_c9) != (sk_c10)))
% 67.88/10.42 <= (~
% 67.88/10.42 (((inverse @ (inverse @ (inverse @ sk_c9))) = (inverse @ sk_c9))) &
% 67.88/10.42 (((inverse @ sk_c10) = (sk_c9))) &
% 67.88/10.42 (((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.42 inference('s_sup-', [status(thm)], [zip_derived_cl59, zip_derived_cl317])).
% 67.88/10.42 thf(zip_derived_cl76, plain,
% 67.88/10.42 ((((inverse @ sk_c9) = (sk_c10))) <= ((((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl12])).
% 67.88/10.42 thf(zip_derived_cl319, plain,
% 67.88/10.42 ((((sk_c10) != (sk_c10)))
% 67.88/10.42 <= (~
% 67.88/10.42 (((inverse @ (inverse @ (inverse @ sk_c9))) = (inverse @ sk_c9))) &
% 67.88/10.42 (((inverse @ sk_c10) = (sk_c9))) &
% 67.88/10.42 (((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.42 inference('demod', [status(thm)], [zip_derived_cl318, zip_derived_cl76])).
% 67.88/10.42 thf('10', plain,
% 67.88/10.42 ((((inverse @ (inverse @ (inverse @ sk_c9))) = (inverse @ sk_c9))) |
% 67.88/10.42 ~ (((inverse @ sk_c10) = (sk_c9))) | ~ (((inverse @ sk_c9) = (sk_c10)))),
% 67.88/10.42 inference('simplify', [status(thm)], [zip_derived_cl319])).
% 67.88/10.42 thf(prove_this_2, conjecture,
% 67.88/10.42 (~( ( ( multiply @ sk_c10 @ sk_c4 ) = ( sk_c9 ) ) |
% 67.88/10.42 ( ( multiply @ sk_c9 @ sk_c8 ) = ( sk_c10 ) ) ))).
% 67.88/10.42 thf(zf_stmt_10, negated_conjecture,
% 67.88/10.42 (( ( multiply @ sk_c10 @ sk_c4 ) = ( sk_c9 ) ) |
% 67.88/10.42 ( ( multiply @ sk_c9 @ sk_c8 ) = ( sk_c10 ) )),
% 67.88/10.42 inference('cnf.neg', [status(esa)], [prove_this_2])).
% 67.88/10.42 thf(zip_derived_cl4, plain,
% 67.88/10.42 ((((multiply @ sk_c10 @ sk_c4) = (sk_c9))
% 67.88/10.42 | ((multiply @ sk_c9 @ sk_c8) = (sk_c10)))),
% 67.88/10.42 inference('cnf', [status(esa)], [zf_stmt_10])).
% 67.88/10.42 thf(zip_derived_cl60, plain,
% 67.88/10.42 ((((multiply @ sk_c10 @ sk_c4) = (sk_c9)))
% 67.88/10.42 <= ((((multiply @ sk_c10 @ sk_c4) = (sk_c9))))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl4])).
% 67.88/10.42 thf(zip_derived_cl200, plain,
% 67.88/10.42 (![X0 : $i, X1 : $i]:
% 67.88/10.42 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 67.88/10.42 inference('demod', [status(thm)], [zip_derived_cl198, zip_derived_cl0])).
% 67.88/10.42 thf(zip_derived_cl474, plain,
% 67.88/10.42 ((((sk_c4) = (multiply @ (inverse @ sk_c10) @ sk_c9)))
% 67.88/10.42 <= ((((multiply @ sk_c10 @ sk_c4) = (sk_c9))))),
% 67.88/10.42 inference('s_sup+', [status(thm)], [zip_derived_cl60, zip_derived_cl200])).
% 67.88/10.42 thf(prove_this_19, conjecture,
% 67.88/10.42 (~( ( ( inverse @ sk_c10 ) = ( sk_c9 ) ) |
% 67.88/10.42 ( ( multiply @ sk_c10 @ sk_c8 ) = ( sk_c9 ) ) ))).
% 67.88/10.42 thf(zf_stmt_11, negated_conjecture,
% 67.88/10.42 (( ( inverse @ sk_c10 ) = ( sk_c9 ) ) |
% 67.88/10.42 ( ( multiply @ sk_c10 @ sk_c8 ) = ( sk_c9 ) )),
% 67.88/10.42 inference('cnf.neg', [status(esa)], [prove_this_19])).
% 67.88/10.42 thf(zip_derived_cl21, plain,
% 67.88/10.42 ((((inverse @ sk_c10) = (sk_c9))
% 67.88/10.42 | ((multiply @ sk_c10 @ sk_c8) = (sk_c9)))),
% 67.88/10.42 inference('cnf', [status(esa)], [zf_stmt_11])).
% 67.88/10.42 thf(zip_derived_cl94, plain,
% 67.88/10.42 ((((multiply @ sk_c10 @ sk_c8) = (sk_c9)))
% 67.88/10.42 <= ((((multiply @ sk_c10 @ sk_c8) = (sk_c9))))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl21])).
% 67.88/10.42 thf(zip_derived_cl200, plain,
% 67.88/10.42 (![X0 : $i, X1 : $i]:
% 67.88/10.42 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 67.88/10.42 inference('demod', [status(thm)], [zip_derived_cl198, zip_derived_cl0])).
% 67.88/10.42 thf(zip_derived_cl473, plain,
% 67.88/10.42 ((((sk_c8) = (multiply @ (inverse @ sk_c10) @ sk_c9)))
% 67.88/10.42 <= ((((multiply @ sk_c10 @ sk_c8) = (sk_c9))))),
% 67.88/10.42 inference('s_sup+', [status(thm)], [zip_derived_cl94, zip_derived_cl200])).
% 67.88/10.42 thf(zip_derived_cl567, plain,
% 67.88/10.42 ((((sk_c8) = (sk_c4)))
% 67.88/10.42 <= ((((multiply @ sk_c10 @ sk_c4) = (sk_c9))) &
% 67.88/10.42 (((multiply @ sk_c10 @ sk_c8) = (sk_c9))))),
% 67.88/10.42 inference('s_sup+', [status(thm)], [zip_derived_cl474, zip_derived_cl473])).
% 67.88/10.42 thf(zip_derived_cl62, plain,
% 67.88/10.42 ((((multiply @ sk_c3 @ sk_c10) = (sk_c4)))
% 67.88/10.42 <= ((((multiply @ sk_c3 @ sk_c10) = (sk_c4))))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl5])).
% 67.88/10.42 thf(prove_this_4, conjecture,
% 67.88/10.42 (~( ( ( inverse @ sk_c3 ) = ( sk_c10 ) ) |
% 67.88/10.42 ( ( multiply @ sk_c9 @ sk_c8 ) = ( sk_c10 ) ) ))).
% 67.88/10.42 thf(zf_stmt_12, negated_conjecture,
% 67.88/10.42 (( ( inverse @ sk_c3 ) = ( sk_c10 ) ) |
% 67.88/10.42 ( ( multiply @ sk_c9 @ sk_c8 ) = ( sk_c10 ) )),
% 67.88/10.42 inference('cnf.neg', [status(esa)], [prove_this_4])).
% 67.88/10.42 thf(zip_derived_cl6, plain,
% 67.88/10.42 ((((inverse @ sk_c3) = (sk_c10))
% 67.88/10.42 | ((multiply @ sk_c9 @ sk_c8) = (sk_c10)))),
% 67.88/10.42 inference('cnf', [status(esa)], [zf_stmt_12])).
% 67.88/10.42 thf(zip_derived_cl64, plain,
% 67.88/10.42 ((((inverse @ sk_c3) = (sk_c10))) <= ((((inverse @ sk_c3) = (sk_c10))))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl6])).
% 67.88/10.42 thf(zip_derived_cl76, plain,
% 67.88/10.42 ((((inverse @ sk_c9) = (sk_c10))) <= ((((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl12])).
% 67.88/10.42 thf(zip_derived_cl305, plain,
% 67.88/10.42 ((![X0 : $i]:
% 67.88/10.42 (((inverse @ X0) != (inverse @ sk_c9))
% 67.88/10.42 | ((multiply @ X0 @ (inverse @ sk_c9)) != (sk_c8))))
% 67.88/10.42 <= ((![X0 : $i]:
% 67.88/10.42 (((inverse @ X0) != (inverse @ sk_c9))
% 67.88/10.42 | ((multiply @ X0 @ (inverse @ sk_c9)) != (sk_c8)))))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl249])).
% 67.88/10.42 thf(zip_derived_cl310, plain,
% 67.88/10.42 ((![X0 : $i]:
% 67.88/10.42 (((inverse @ X0) != (sk_c10)) | ((multiply @ X0 @ sk_c10) != (sk_c8))))
% 67.88/10.42 <= ((((inverse @ sk_c9) = (sk_c10))) &
% 67.88/10.42 (![X0 : $i]:
% 67.88/10.42 (((inverse @ X0) != (inverse @ sk_c9))
% 67.88/10.42 | ((multiply @ X0 @ (inverse @ sk_c9)) != (sk_c8)))))),
% 67.88/10.42 inference('s_sup-', [status(thm)], [zip_derived_cl76, zip_derived_cl305])).
% 67.88/10.42 thf(zip_derived_cl323, plain,
% 67.88/10.42 (((((sk_c10) != (sk_c10)) | ((multiply @ sk_c3 @ sk_c10) != (sk_c8))))
% 67.88/10.42 <= ((((inverse @ sk_c3) = (sk_c10))) &
% 67.88/10.42 (((inverse @ sk_c9) = (sk_c10))) &
% 67.88/10.42 (![X0 : $i]:
% 67.88/10.42 (((inverse @ X0) != (inverse @ sk_c9))
% 67.88/10.42 | ((multiply @ X0 @ (inverse @ sk_c9)) != (sk_c8)))))),
% 67.88/10.42 inference('s_sup-', [status(thm)], [zip_derived_cl64, zip_derived_cl310])).
% 67.88/10.42 thf(zip_derived_cl328, plain,
% 67.88/10.42 ((((multiply @ sk_c3 @ sk_c10) != (sk_c8)))
% 67.88/10.42 <= ((((inverse @ sk_c3) = (sk_c10))) &
% 67.88/10.42 (((inverse @ sk_c9) = (sk_c10))) &
% 67.88/10.42 (![X0 : $i]:
% 67.88/10.42 (((inverse @ X0) != (inverse @ sk_c9))
% 67.88/10.42 | ((multiply @ X0 @ (inverse @ sk_c9)) != (sk_c8)))))),
% 67.88/10.42 inference('simplify', [status(thm)], [zip_derived_cl323])).
% 67.88/10.42 thf(zip_derived_cl331, plain,
% 67.88/10.42 ((((sk_c4) != (sk_c8)))
% 67.88/10.42 <= ((((multiply @ sk_c3 @ sk_c10) = (sk_c4))) &
% 67.88/10.42 (((inverse @ sk_c3) = (sk_c10))) &
% 67.88/10.42 (((inverse @ sk_c9) = (sk_c10))) &
% 67.88/10.42 (![X0 : $i]:
% 67.88/10.42 (((inverse @ X0) != (inverse @ sk_c9))
% 67.88/10.42 | ((multiply @ X0 @ (inverse @ sk_c9)) != (sk_c8)))))),
% 67.88/10.42 inference('s_sup-', [status(thm)], [zip_derived_cl62, zip_derived_cl328])).
% 67.88/10.42 thf(zip_derived_cl600, plain,
% 67.88/10.42 ((((sk_c8) != (sk_c8)))
% 67.88/10.42 <= ((((multiply @ sk_c10 @ sk_c4) = (sk_c9))) &
% 67.88/10.42 (((multiply @ sk_c3 @ sk_c10) = (sk_c4))) &
% 67.88/10.42 (((inverse @ sk_c3) = (sk_c10))) &
% 67.88/10.42 (((inverse @ sk_c9) = (sk_c10))) &
% 67.88/10.42 (((multiply @ sk_c10 @ sk_c8) = (sk_c9))) &
% 67.88/10.42 (![X0 : $i]:
% 67.88/10.42 (((inverse @ X0) != (inverse @ sk_c9))
% 67.88/10.42 | ((multiply @ X0 @ (inverse @ sk_c9)) != (sk_c8)))))),
% 67.88/10.42 inference('s_sup-', [status(thm)], [zip_derived_cl567, zip_derived_cl331])).
% 67.88/10.42 thf('11', plain,
% 67.88/10.42 (~
% 67.88/10.42 (![X0 : $i]:
% 67.88/10.42 (((inverse @ X0) != (inverse @ sk_c9))
% 67.88/10.42 | ((multiply @ X0 @ (inverse @ sk_c9)) != (sk_c8)))) |
% 67.88/10.42 ~ (((inverse @ sk_c3) = (sk_c10))) |
% 67.88/10.42 ~ (((multiply @ sk_c10 @ sk_c8) = (sk_c9))) |
% 67.88/10.42 ~ (((multiply @ sk_c3 @ sk_c10) = (sk_c4))) |
% 67.88/10.42 ~ (((inverse @ sk_c9) = (sk_c10))) |
% 67.88/10.42 ~ (((multiply @ sk_c10 @ sk_c4) = (sk_c9)))),
% 67.88/10.42 inference('simplify', [status(thm)], [zip_derived_cl600])).
% 67.88/10.42 thf('12', plain,
% 67.88/10.42 (~ (((identity) = (sk_c8))) |
% 67.88/10.42 ~
% 67.88/10.42 (![X0 : $i]:
% 67.88/10.42 (((inverse @ X0) != (inverse @ sk_c9))
% 67.88/10.42 | ((multiply @ X0 @ (inverse @ sk_c9)) != (sk_c8)))) |
% 67.88/10.42 ~ (((inverse @ (inverse @ (inverse @ sk_c9))) = (inverse @ sk_c9)))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl309])).
% 67.88/10.42 thf('13', plain,
% 67.88/10.42 (~ (((identity) = (sk_c8))) |
% 67.88/10.42 (![X0 : $i]:
% 67.88/10.42 (((inverse @ X0) != (inverse @ sk_c9))
% 67.88/10.42 | ((multiply @ X0 @ (inverse @ sk_c9)) != (sk_c8)))) |
% 67.88/10.42 ~
% 67.88/10.42 (![X1 : $i, X2 : $i]:
% 67.88/10.42 (((multiply @ X1 @ sk_c9) != (sk_c8))
% 67.88/10.42 | ((inverse @ X2) != (X1))
% 67.88/10.42 | ((multiply @ X2 @ X1) != (sk_c8))))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl249])).
% 67.88/10.42 thf('14', plain,
% 67.88/10.42 ((((inverse @ sk_c10) = (sk_c9))) |
% 67.88/10.42 (((multiply @ sk_c10 @ sk_c8) = (sk_c9)))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl21])).
% 67.88/10.42 thf(zip_derived_cl64, plain,
% 67.88/10.42 ((((inverse @ sk_c3) = (sk_c10))) <= ((((inverse @ sk_c3) = (sk_c10))))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl6])).
% 67.88/10.42 thf(zip_derived_cl1, plain,
% 67.88/10.42 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 67.88/10.42 inference('cnf', [status(esa)], [left_inverse])).
% 67.88/10.42 thf(zip_derived_cl190, plain,
% 67.88/10.42 ((((multiply @ sk_c10 @ sk_c3) = (identity)))
% 67.88/10.42 <= ((((inverse @ sk_c3) = (sk_c10))))),
% 67.88/10.42 inference('s_sup+', [status(thm)], [zip_derived_cl64, zip_derived_cl1])).
% 67.88/10.42 thf(zip_derived_cl200, plain,
% 67.88/10.42 (![X0 : $i, X1 : $i]:
% 67.88/10.42 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 67.88/10.42 inference('demod', [status(thm)], [zip_derived_cl198, zip_derived_cl0])).
% 67.88/10.42 thf(zip_derived_cl475, plain,
% 67.88/10.42 ((((sk_c3) = (multiply @ (inverse @ sk_c10) @ identity)))
% 67.88/10.42 <= ((((inverse @ sk_c3) = (sk_c10))))),
% 67.88/10.42 inference('s_sup+', [status(thm)], [zip_derived_cl190, zip_derived_cl200])).
% 67.88/10.42 thf(zip_derived_cl76, plain,
% 67.88/10.42 ((((inverse @ sk_c9) = (sk_c10))) <= ((((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl12])).
% 67.88/10.42 thf(zip_derived_cl1, plain,
% 67.88/10.42 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 67.88/10.42 inference('cnf', [status(esa)], [left_inverse])).
% 67.88/10.42 thf(zip_derived_cl188, plain,
% 67.88/10.42 ((((multiply @ sk_c10 @ sk_c9) = (identity)))
% 67.88/10.42 <= ((((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.42 inference('s_sup+', [status(thm)], [zip_derived_cl76, zip_derived_cl1])).
% 67.88/10.42 thf(zip_derived_cl200, plain,
% 67.88/10.42 (![X0 : $i, X1 : $i]:
% 67.88/10.42 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 67.88/10.42 inference('demod', [status(thm)], [zip_derived_cl198, zip_derived_cl0])).
% 67.88/10.42 thf(zip_derived_cl472, plain,
% 67.88/10.42 ((((sk_c9) = (multiply @ (inverse @ sk_c10) @ identity)))
% 67.88/10.42 <= ((((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.42 inference('s_sup+', [status(thm)], [zip_derived_cl188, zip_derived_cl200])).
% 67.88/10.42 thf(zip_derived_cl572, plain,
% 67.88/10.42 ((((sk_c9) = (sk_c3)))
% 67.88/10.42 <= ((((inverse @ sk_c3) = (sk_c10))) &
% 67.88/10.42 (((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.42 inference('s_sup+', [status(thm)], [zip_derived_cl475, zip_derived_cl472])).
% 67.88/10.42 thf(zip_derived_cl62, plain,
% 67.88/10.42 ((((multiply @ sk_c3 @ sk_c10) = (sk_c4)))
% 67.88/10.42 <= ((((multiply @ sk_c3 @ sk_c10) = (sk_c4))))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl5])).
% 67.88/10.42 thf(zip_derived_cl683, plain,
% 67.88/10.42 ((((multiply @ sk_c9 @ sk_c10) = (sk_c4)))
% 67.88/10.42 <= ((((multiply @ sk_c3 @ sk_c10) = (sk_c4))) &
% 67.88/10.42 (((inverse @ sk_c3) = (sk_c10))) &
% 67.88/10.42 (((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.42 inference('s_sup+', [status(thm)], [zip_derived_cl572, zip_derived_cl62])).
% 67.88/10.42 thf(zip_derived_cl472, plain,
% 67.88/10.42 ((((sk_c9) = (multiply @ (inverse @ sk_c10) @ identity)))
% 67.88/10.42 <= ((((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.42 inference('s_sup+', [status(thm)], [zip_derived_cl188, zip_derived_cl200])).
% 67.88/10.42 thf(zip_derived_cl2, plain,
% 67.88/10.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.88/10.42 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 67.88/10.42 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 67.88/10.42 inference('cnf', [status(esa)], [associativity])).
% 67.88/10.42 thf(zip_derived_cl528, plain,
% 67.88/10.42 ((![X0 : $i]:
% 67.88/10.42 ((multiply @ sk_c9 @ X0)
% 67.88/10.42 = (multiply @ (inverse @ sk_c10) @ (multiply @ identity @ X0))))
% 67.88/10.42 <= ((((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.42 inference('s_sup+', [status(thm)], [zip_derived_cl472, zip_derived_cl2])).
% 67.88/10.42 thf(zip_derived_cl0, plain,
% 67.88/10.42 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 67.88/10.42 inference('cnf', [status(esa)], [left_identity])).
% 67.88/10.42 thf(zip_derived_cl532, plain,
% 67.88/10.42 ((![X0 : $i]:
% 67.88/10.42 ((multiply @ sk_c9 @ X0) = (multiply @ (inverse @ sk_c10) @ X0)))
% 67.88/10.42 <= ((((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.42 inference('demod', [status(thm)], [zip_derived_cl528, zip_derived_cl0])).
% 67.88/10.42 thf(zip_derived_cl1, plain,
% 67.88/10.42 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 67.88/10.42 inference('cnf', [status(esa)], [left_inverse])).
% 67.88/10.42 thf(zip_derived_cl1111, plain,
% 67.88/10.42 ((((multiply @ sk_c9 @ sk_c10) = (identity)))
% 67.88/10.42 <= ((((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.42 inference('s_sup+', [status(thm)], [zip_derived_cl532, zip_derived_cl1])).
% 67.88/10.42 thf(zip_derived_cl2204, plain,
% 67.88/10.42 ((((identity) = (sk_c4)))
% 67.88/10.42 <= ((((multiply @ sk_c3 @ sk_c10) = (sk_c4))) &
% 67.88/10.42 (((inverse @ sk_c3) = (sk_c10))) &
% 67.88/10.42 (((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.42 inference('demod', [status(thm)], [zip_derived_cl683, zip_derived_cl1111])).
% 67.88/10.42 thf(zip_derived_cl567, plain,
% 67.88/10.42 ((((sk_c8) = (sk_c4)))
% 67.88/10.42 <= ((((multiply @ sk_c10 @ sk_c4) = (sk_c9))) &
% 67.88/10.42 (((multiply @ sk_c10 @ sk_c8) = (sk_c9))))),
% 67.88/10.42 inference('s_sup+', [status(thm)], [zip_derived_cl474, zip_derived_cl473])).
% 67.88/10.42 thf(zip_derived_cl2225, plain,
% 67.88/10.42 ((((sk_c8) = (identity)))
% 67.88/10.42 <= ((((multiply @ sk_c10 @ sk_c4) = (sk_c9))) &
% 67.88/10.42 (((multiply @ sk_c3 @ sk_c10) = (sk_c4))) &
% 67.88/10.42 (((inverse @ sk_c3) = (sk_c10))) &
% 67.88/10.42 (((inverse @ sk_c9) = (sk_c10))) &
% 67.88/10.42 (((multiply @ sk_c10 @ sk_c8) = (sk_c9))))),
% 67.88/10.42 inference('s_sup+', [status(thm)],
% 67.88/10.42 [zip_derived_cl2204, zip_derived_cl567])).
% 67.88/10.42 thf(zip_derived_cl306, plain,
% 67.88/10.42 ((((identity) != (sk_c8))) <= (~ (((identity) = (sk_c8))))),
% 67.88/10.42 inference('split', [status(esa)], [zip_derived_cl249])).
% 67.88/10.42 thf(zip_derived_cl2409, plain,
% 67.88/10.42 ((((identity) != (identity)))
% 67.88/10.43 <= (~ (((identity) = (sk_c8))) &
% 67.88/10.43 (((multiply @ sk_c10 @ sk_c4) = (sk_c9))) &
% 67.88/10.43 (((multiply @ sk_c3 @ sk_c10) = (sk_c4))) &
% 67.88/10.43 (((inverse @ sk_c3) = (sk_c10))) &
% 67.88/10.43 (((inverse @ sk_c9) = (sk_c10))) &
% 67.88/10.43 (((multiply @ sk_c10 @ sk_c8) = (sk_c9))))),
% 67.88/10.43 inference('s_sup-', [status(thm)],
% 67.88/10.43 [zip_derived_cl2225, zip_derived_cl306])).
% 67.88/10.43 thf('15', plain,
% 67.88/10.43 (~ (((inverse @ sk_c3) = (sk_c10))) | (((identity) = (sk_c8))) |
% 67.88/10.43 ~ (((multiply @ sk_c10 @ sk_c4) = (sk_c9))) |
% 67.88/10.43 ~ (((multiply @ sk_c10 @ sk_c8) = (sk_c9))) |
% 67.88/10.43 ~ (((multiply @ sk_c3 @ sk_c10) = (sk_c4))) |
% 67.88/10.43 ~ (((inverse @ sk_c9) = (sk_c10)))),
% 67.88/10.43 inference('simplify', [status(thm)], [zip_derived_cl2409])).
% 67.88/10.43 thf(prove_this_29, conjecture,
% 67.88/10.43 (~( ( ( multiply @ sk_c10 @ sk_c4 ) = ( sk_c9 ) ) |
% 67.88/10.43 ( ( multiply @ sk_c10 @ sk_c2 ) = ( sk_c9 ) ) ))).
% 67.88/10.43 thf(zf_stmt_13, negated_conjecture,
% 67.88/10.43 (( ( multiply @ sk_c10 @ sk_c4 ) = ( sk_c9 ) ) |
% 67.88/10.43 ( ( multiply @ sk_c10 @ sk_c2 ) = ( sk_c9 ) )),
% 67.88/10.43 inference('cnf.neg', [status(esa)], [prove_this_29])).
% 67.88/10.43 thf(zip_derived_cl31, plain,
% 67.88/10.43 ((((multiply @ sk_c10 @ sk_c4) = (sk_c9))
% 67.88/10.43 | ((multiply @ sk_c10 @ sk_c2) = (sk_c9)))),
% 67.88/10.43 inference('cnf', [status(esa)], [zf_stmt_13])).
% 67.88/10.43 thf('16', plain,
% 67.88/10.43 ((((multiply @ sk_c10 @ sk_c2) = (sk_c9))) |
% 67.88/10.43 (((multiply @ sk_c10 @ sk_c4) = (sk_c9)))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl31])).
% 67.88/10.43 thf(prove_this_38, conjecture,
% 67.88/10.43 (~( ( ( multiply @ sk_c10 @ sk_c4 ) = ( sk_c9 ) ) |
% 67.88/10.43 ( ( multiply @ sk_c1 @ sk_c10 ) = ( sk_c2 ) ) ))).
% 67.88/10.43 thf(zf_stmt_14, negated_conjecture,
% 67.88/10.43 (( ( multiply @ sk_c10 @ sk_c4 ) = ( sk_c9 ) ) |
% 67.88/10.43 ( ( multiply @ sk_c1 @ sk_c10 ) = ( sk_c2 ) )),
% 67.88/10.43 inference('cnf.neg', [status(esa)], [prove_this_38])).
% 67.88/10.43 thf(zip_derived_cl40, plain,
% 67.88/10.43 ((((multiply @ sk_c10 @ sk_c4) = (sk_c9))
% 67.88/10.43 | ((multiply @ sk_c1 @ sk_c10) = (sk_c2)))),
% 67.88/10.43 inference('cnf', [status(esa)], [zf_stmt_14])).
% 67.88/10.43 thf('17', plain,
% 67.88/10.43 ((((multiply @ sk_c1 @ sk_c10) = (sk_c2))) |
% 67.88/10.43 (((multiply @ sk_c10 @ sk_c4) = (sk_c9)))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl40])).
% 67.88/10.43 thf(prove_this_47, conjecture,
% 67.88/10.43 (~( ( ( multiply @ sk_c10 @ sk_c4 ) = ( sk_c9 ) ) |
% 67.88/10.43 ( ( inverse @ sk_c1 ) = ( sk_c10 ) ) ))).
% 67.88/10.43 thf(zf_stmt_15, negated_conjecture,
% 67.88/10.43 (( ( multiply @ sk_c10 @ sk_c4 ) = ( sk_c9 ) ) |
% 67.88/10.43 ( ( inverse @ sk_c1 ) = ( sk_c10 ) )),
% 67.88/10.43 inference('cnf.neg', [status(esa)], [prove_this_47])).
% 67.88/10.43 thf(zip_derived_cl49, plain,
% 67.88/10.43 ((((multiply @ sk_c10 @ sk_c4) = (sk_c9))
% 67.88/10.43 | ((inverse @ sk_c1) = (sk_c10)))),
% 67.88/10.43 inference('cnf', [status(esa)], [zf_stmt_15])).
% 67.88/10.43 thf('18', plain,
% 67.88/10.43 ((((inverse @ sk_c1) = (sk_c10))) |
% 67.88/10.43 (((multiply @ sk_c10 @ sk_c4) = (sk_c9)))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl49])).
% 67.88/10.43 thf(prove_this_30, conjecture,
% 67.88/10.43 (~( ( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c4 ) ) |
% 67.88/10.43 ( ( multiply @ sk_c10 @ sk_c2 ) = ( sk_c9 ) ) ))).
% 67.88/10.43 thf(zf_stmt_16, negated_conjecture,
% 67.88/10.43 (( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c4 ) ) |
% 67.88/10.43 ( ( multiply @ sk_c10 @ sk_c2 ) = ( sk_c9 ) )),
% 67.88/10.43 inference('cnf.neg', [status(esa)], [prove_this_30])).
% 67.88/10.43 thf(zip_derived_cl32, plain,
% 67.88/10.43 ((((multiply @ sk_c3 @ sk_c10) = (sk_c4))
% 67.88/10.43 | ((multiply @ sk_c10 @ sk_c2) = (sk_c9)))),
% 67.88/10.43 inference('cnf', [status(esa)], [zf_stmt_16])).
% 67.88/10.43 thf('19', plain,
% 67.88/10.43 ((((multiply @ sk_c10 @ sk_c2) = (sk_c9))) |
% 67.88/10.43 (((multiply @ sk_c3 @ sk_c10) = (sk_c4)))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl32])).
% 67.88/10.43 thf(prove_this_39, conjecture,
% 67.88/10.43 (~( ( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c4 ) ) |
% 67.88/10.43 ( ( multiply @ sk_c1 @ sk_c10 ) = ( sk_c2 ) ) ))).
% 67.88/10.43 thf(zf_stmt_17, negated_conjecture,
% 67.88/10.43 (( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c4 ) ) |
% 67.88/10.43 ( ( multiply @ sk_c1 @ sk_c10 ) = ( sk_c2 ) )),
% 67.88/10.43 inference('cnf.neg', [status(esa)], [prove_this_39])).
% 67.88/10.43 thf(zip_derived_cl41, plain,
% 67.88/10.43 ((((multiply @ sk_c3 @ sk_c10) = (sk_c4))
% 67.88/10.43 | ((multiply @ sk_c1 @ sk_c10) = (sk_c2)))),
% 67.88/10.43 inference('cnf', [status(esa)], [zf_stmt_17])).
% 67.88/10.43 thf('20', plain,
% 67.88/10.43 ((((multiply @ sk_c1 @ sk_c10) = (sk_c2))) |
% 67.88/10.43 (((multiply @ sk_c3 @ sk_c10) = (sk_c4)))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl41])).
% 67.88/10.43 thf(prove_this_48, conjecture,
% 67.88/10.43 (~( ( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c4 ) ) |
% 67.88/10.43 ( ( inverse @ sk_c1 ) = ( sk_c10 ) ) ))).
% 67.88/10.43 thf(zf_stmt_18, negated_conjecture,
% 67.88/10.43 (( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c4 ) ) |
% 67.88/10.43 ( ( inverse @ sk_c1 ) = ( sk_c10 ) )),
% 67.88/10.43 inference('cnf.neg', [status(esa)], [prove_this_48])).
% 67.88/10.43 thf(zip_derived_cl50, plain,
% 67.88/10.43 ((((multiply @ sk_c3 @ sk_c10) = (sk_c4))
% 67.88/10.43 | ((inverse @ sk_c1) = (sk_c10)))),
% 67.88/10.43 inference('cnf', [status(esa)], [zf_stmt_18])).
% 67.88/10.43 thf('21', plain,
% 67.88/10.43 ((((inverse @ sk_c1) = (sk_c10))) |
% 67.88/10.43 (((multiply @ sk_c3 @ sk_c10) = (sk_c4)))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl50])).
% 67.88/10.43 thf(zip_derived_cl532, plain,
% 67.88/10.43 ((![X0 : $i]:
% 67.88/10.43 ((multiply @ sk_c9 @ X0) = (multiply @ (inverse @ sk_c10) @ X0)))
% 67.88/10.43 <= ((((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.43 inference('demod', [status(thm)], [zip_derived_cl528, zip_derived_cl0])).
% 67.88/10.43 thf(zip_derived_cl168, plain,
% 67.88/10.43 ((![X1 : $i, X2 : $i]:
% 67.88/10.43 (((multiply @ X1 @ sk_c9) != (sk_c8))
% 67.88/10.43 | ((inverse @ X2) != (X1))
% 67.88/10.43 | ((multiply @ X2 @ X1) != (sk_c8))))
% 67.88/10.43 <= ((![X1 : $i, X2 : $i]:
% 67.88/10.43 (((multiply @ X1 @ sk_c9) != (sk_c8))
% 67.88/10.43 | ((inverse @ X2) != (X1))
% 67.88/10.43 | ((multiply @ X2 @ X1) != (sk_c8)))))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl57])).
% 67.88/10.43 thf(zip_derived_cl1109, plain,
% 67.88/10.43 ((![X0 : $i]:
% 67.88/10.43 (((multiply @ sk_c9 @ sk_c9) != (sk_c8))
% 67.88/10.43 | ((inverse @ X0) != (inverse @ sk_c10))
% 67.88/10.43 | ((multiply @ X0 @ (inverse @ sk_c10)) != (sk_c8))))
% 67.88/10.43 <= ((((inverse @ sk_c9) = (sk_c10))) &
% 67.88/10.43 (![X1 : $i, X2 : $i]:
% 67.88/10.43 (((multiply @ X1 @ sk_c9) != (sk_c8))
% 67.88/10.43 | ((inverse @ X2) != (X1))
% 67.88/10.43 | ((multiply @ X2 @ X1) != (sk_c8)))))),
% 67.88/10.43 inference('s_sup-', [status(thm)], [zip_derived_cl532, zip_derived_cl168])).
% 67.88/10.43 thf('22', plain,
% 67.88/10.43 ((![X0 : $i]:
% 67.88/10.43 (((inverse @ X0) != (inverse @ sk_c10))
% 67.88/10.43 | ((multiply @ X0 @ (inverse @ sk_c10)) != (sk_c8)))) |
% 67.88/10.43 ~
% 67.88/10.43 (![X1 : $i, X2 : $i]:
% 67.88/10.43 (((multiply @ X1 @ sk_c9) != (sk_c8))
% 67.88/10.43 | ((inverse @ X2) != (X1))
% 67.88/10.43 | ((multiply @ X2 @ X1) != (sk_c8)))) |
% 67.88/10.43 ~ (((inverse @ sk_c9) = (sk_c10))) |
% 67.88/10.43 ~ (((multiply @ sk_c9 @ sk_c9) = (sk_c8)))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl1109])).
% 67.88/10.43 thf(zip_derived_cl532, plain,
% 67.88/10.43 ((![X0 : $i]:
% 67.88/10.43 ((multiply @ sk_c9 @ X0) = (multiply @ (inverse @ sk_c10) @ X0)))
% 67.88/10.43 <= ((((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.43 inference('demod', [status(thm)], [zip_derived_cl528, zip_derived_cl0])).
% 67.88/10.43 thf(zip_derived_cl473, plain,
% 67.88/10.43 ((((sk_c8) = (multiply @ (inverse @ sk_c10) @ sk_c9)))
% 67.88/10.43 <= ((((multiply @ sk_c10 @ sk_c8) = (sk_c9))))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl94, zip_derived_cl200])).
% 67.88/10.43 thf(zip_derived_cl1117, plain,
% 67.88/10.43 ((((sk_c8) = (multiply @ sk_c9 @ sk_c9)))
% 67.88/10.43 <= ((((inverse @ sk_c9) = (sk_c10))) &
% 67.88/10.43 (((multiply @ sk_c10 @ sk_c8) = (sk_c9))))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl532, zip_derived_cl473])).
% 67.88/10.43 thf(zip_derived_cl26401, plain,
% 67.88/10.43 ((((multiply @ sk_c9 @ sk_c9) != (sk_c8)))
% 67.88/10.43 <= (~ (((multiply @ sk_c9 @ sk_c9) = (sk_c8))))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl1109])).
% 67.88/10.43 thf(zip_derived_cl26797, plain,
% 67.88/10.43 ((((sk_c8) != (sk_c8)))
% 67.88/10.43 <= (~ (((multiply @ sk_c9 @ sk_c9) = (sk_c8))) &
% 67.88/10.43 (((inverse @ sk_c9) = (sk_c10))) &
% 67.88/10.43 (((multiply @ sk_c10 @ sk_c8) = (sk_c9))))),
% 67.88/10.43 inference('s_sup-', [status(thm)],
% 67.88/10.43 [zip_derived_cl1117, zip_derived_cl26401])).
% 67.88/10.43 thf('23', plain,
% 67.88/10.43 ((((multiply @ sk_c9 @ sk_c9) = (sk_c8))) |
% 67.88/10.43 ~ (((multiply @ sk_c10 @ sk_c8) = (sk_c9))) |
% 67.88/10.43 ~ (((inverse @ sk_c9) = (sk_c10)))),
% 67.88/10.43 inference('simplify', [status(thm)], [zip_derived_cl26797])).
% 67.88/10.43 thf(prove_this_14, conjecture,
% 67.88/10.43 (~( ( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c8 ) ) |
% 67.88/10.43 ( ( inverse @ sk_c9 ) = ( sk_c10 ) ) ))).
% 67.88/10.43 thf(zf_stmt_19, negated_conjecture,
% 67.88/10.43 (( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c8 ) ) |
% 67.88/10.43 ( ( inverse @ sk_c9 ) = ( sk_c10 ) )),
% 67.88/10.43 inference('cnf.neg', [status(esa)], [prove_this_14])).
% 67.88/10.43 thf(zip_derived_cl16, plain,
% 67.88/10.43 ((((multiply @ sk_c5 @ sk_c6) = (sk_c8)) | ((inverse @ sk_c9) = (sk_c10)))),
% 67.88/10.43 inference('cnf', [status(esa)], [zf_stmt_19])).
% 67.88/10.43 thf('24', plain,
% 67.88/10.43 ((((multiply @ sk_c5 @ sk_c6) = (sk_c8))) |
% 67.88/10.43 (((inverse @ sk_c9) = (sk_c10)))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl16])).
% 67.88/10.43 thf(prove_this_15, conjecture,
% 67.88/10.43 (~( ( ( inverse @ sk_c5 ) = ( sk_c6 ) ) |
% 67.88/10.43 ( ( inverse @ sk_c9 ) = ( sk_c10 ) ) ))).
% 67.88/10.43 thf(zf_stmt_20, negated_conjecture,
% 67.88/10.43 (( ( inverse @ sk_c5 ) = ( sk_c6 ) ) | ( ( inverse @ sk_c9 ) = ( sk_c10 ) )),
% 67.88/10.43 inference('cnf.neg', [status(esa)], [prove_this_15])).
% 67.88/10.43 thf(zip_derived_cl17, plain,
% 67.88/10.43 ((((inverse @ sk_c5) = (sk_c6)) | ((inverse @ sk_c9) = (sk_c10)))),
% 67.88/10.43 inference('cnf', [status(esa)], [zf_stmt_20])).
% 67.88/10.43 thf('25', plain,
% 67.88/10.43 ((((inverse @ sk_c5) = (sk_c6))) | (((inverse @ sk_c9) = (sk_c10)))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl17])).
% 67.88/10.43 thf(prove_this_16, conjecture,
% 67.88/10.43 (~( ( ( multiply @ sk_c6 @ sk_c9 ) = ( sk_c8 ) ) |
% 67.88/10.43 ( ( inverse @ sk_c9 ) = ( sk_c10 ) ) ))).
% 67.88/10.43 thf(zf_stmt_21, negated_conjecture,
% 67.88/10.43 (( ( multiply @ sk_c6 @ sk_c9 ) = ( sk_c8 ) ) |
% 67.88/10.43 ( ( inverse @ sk_c9 ) = ( sk_c10 ) )),
% 67.88/10.43 inference('cnf.neg', [status(esa)], [prove_this_16])).
% 67.88/10.43 thf(zip_derived_cl18, plain,
% 67.88/10.43 ((((multiply @ sk_c6 @ sk_c9) = (sk_c8)) | ((inverse @ sk_c9) = (sk_c10)))),
% 67.88/10.43 inference('cnf', [status(esa)], [zf_stmt_21])).
% 67.88/10.43 thf('26', plain,
% 67.88/10.43 ((((multiply @ sk_c6 @ sk_c9) = (sk_c8))) |
% 67.88/10.43 (((inverse @ sk_c9) = (sk_c10)))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl18])).
% 67.88/10.43 thf(prove_this_24, conjecture,
% 67.88/10.43 (~( ( ( inverse @ sk_c5 ) = ( sk_c6 ) ) |
% 67.88/10.43 ( ( multiply @ sk_c10 @ sk_c8 ) = ( sk_c9 ) ) ))).
% 67.88/10.43 thf(zf_stmt_22, negated_conjecture,
% 67.88/10.43 (( ( inverse @ sk_c5 ) = ( sk_c6 ) ) |
% 67.88/10.43 ( ( multiply @ sk_c10 @ sk_c8 ) = ( sk_c9 ) )),
% 67.88/10.43 inference('cnf.neg', [status(esa)], [prove_this_24])).
% 67.88/10.43 thf(zip_derived_cl26, plain,
% 67.88/10.43 ((((inverse @ sk_c5) = (sk_c6)) | ((multiply @ sk_c10 @ sk_c8) = (sk_c9)))),
% 67.88/10.43 inference('cnf', [status(esa)], [zf_stmt_22])).
% 67.88/10.43 thf('27', plain,
% 67.88/10.43 ((((inverse @ sk_c5) = (sk_c6))) |
% 67.88/10.43 (((multiply @ sk_c10 @ sk_c8) = (sk_c9)))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl26])).
% 67.88/10.43 thf(prove_this_25, conjecture,
% 67.88/10.43 (~( ( ( multiply @ sk_c6 @ sk_c9 ) = ( sk_c8 ) ) |
% 67.88/10.43 ( ( multiply @ sk_c10 @ sk_c8 ) = ( sk_c9 ) ) ))).
% 67.88/10.43 thf(zf_stmt_23, negated_conjecture,
% 67.88/10.43 (( ( multiply @ sk_c6 @ sk_c9 ) = ( sk_c8 ) ) |
% 67.88/10.43 ( ( multiply @ sk_c10 @ sk_c8 ) = ( sk_c9 ) )),
% 67.88/10.43 inference('cnf.neg', [status(esa)], [prove_this_25])).
% 67.88/10.43 thf(zip_derived_cl27, plain,
% 67.88/10.43 ((((multiply @ sk_c6 @ sk_c9) = (sk_c8))
% 67.88/10.43 | ((multiply @ sk_c10 @ sk_c8) = (sk_c9)))),
% 67.88/10.43 inference('cnf', [status(esa)], [zf_stmt_23])).
% 67.88/10.43 thf('28', plain,
% 67.88/10.43 ((((multiply @ sk_c6 @ sk_c9) = (sk_c8))) |
% 67.88/10.43 (((multiply @ sk_c10 @ sk_c8) = (sk_c9)))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl27])).
% 67.88/10.43 thf(prove_this_5, conjecture,
% 67.88/10.43 (~( ( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c8 ) ) |
% 67.88/10.43 ( ( multiply @ sk_c9 @ sk_c8 ) = ( sk_c10 ) ) ))).
% 67.88/10.43 thf(zf_stmt_24, negated_conjecture,
% 67.88/10.43 (( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c8 ) ) |
% 67.88/10.43 ( ( multiply @ sk_c9 @ sk_c8 ) = ( sk_c10 ) )),
% 67.88/10.43 inference('cnf.neg', [status(esa)], [prove_this_5])).
% 67.88/10.43 thf(zip_derived_cl7, plain,
% 67.88/10.43 ((((multiply @ sk_c5 @ sk_c6) = (sk_c8))
% 67.88/10.43 | ((multiply @ sk_c9 @ sk_c8) = (sk_c10)))),
% 67.88/10.43 inference('cnf', [status(esa)], [zf_stmt_24])).
% 67.88/10.43 thf(zip_derived_cl66, plain,
% 67.88/10.43 ((((multiply @ sk_c5 @ sk_c6) = (sk_c8)))
% 67.88/10.43 <= ((((multiply @ sk_c5 @ sk_c6) = (sk_c8))))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl7])).
% 67.88/10.43 thf(prove_this_6, conjecture,
% 67.88/10.43 (~( ( ( inverse @ sk_c5 ) = ( sk_c6 ) ) |
% 67.88/10.43 ( ( multiply @ sk_c9 @ sk_c8 ) = ( sk_c10 ) ) ))).
% 67.88/10.43 thf(zf_stmt_25, negated_conjecture,
% 67.88/10.43 (( ( inverse @ sk_c5 ) = ( sk_c6 ) ) |
% 67.88/10.43 ( ( multiply @ sk_c9 @ sk_c8 ) = ( sk_c10 ) )),
% 67.88/10.43 inference('cnf.neg', [status(esa)], [prove_this_6])).
% 67.88/10.43 thf(zip_derived_cl8, plain,
% 67.88/10.43 ((((inverse @ sk_c5) = (sk_c6)) | ((multiply @ sk_c9 @ sk_c8) = (sk_c10)))),
% 67.88/10.43 inference('cnf', [status(esa)], [zf_stmt_25])).
% 67.88/10.43 thf(zip_derived_cl68, plain,
% 67.88/10.43 ((((inverse @ sk_c5) = (sk_c6))) <= ((((inverse @ sk_c5) = (sk_c6))))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl8])).
% 67.88/10.43 thf(prove_this_7, conjecture,
% 67.88/10.43 (~( ( ( multiply @ sk_c6 @ sk_c9 ) = ( sk_c8 ) ) |
% 67.88/10.43 ( ( multiply @ sk_c9 @ sk_c8 ) = ( sk_c10 ) ) ))).
% 67.88/10.43 thf(zf_stmt_26, negated_conjecture,
% 67.88/10.43 (( ( multiply @ sk_c6 @ sk_c9 ) = ( sk_c8 ) ) |
% 67.88/10.43 ( ( multiply @ sk_c9 @ sk_c8 ) = ( sk_c10 ) )),
% 67.88/10.43 inference('cnf.neg', [status(esa)], [prove_this_7])).
% 67.88/10.43 thf(zip_derived_cl9, plain,
% 67.88/10.43 ((((multiply @ sk_c6 @ sk_c9) = (sk_c8))
% 67.88/10.43 | ((multiply @ sk_c9 @ sk_c8) = (sk_c10)))),
% 67.88/10.43 inference('cnf', [status(esa)], [zf_stmt_26])).
% 67.88/10.43 thf(zip_derived_cl70, plain,
% 67.88/10.43 ((((multiply @ sk_c6 @ sk_c9) = (sk_c8)))
% 67.88/10.43 <= ((((multiply @ sk_c6 @ sk_c9) = (sk_c8))))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl9])).
% 67.88/10.43 thf(zip_derived_cl168, plain,
% 67.88/10.43 ((![X1 : $i, X2 : $i]:
% 67.88/10.43 (((multiply @ X1 @ sk_c9) != (sk_c8))
% 67.88/10.43 | ((inverse @ X2) != (X1))
% 67.88/10.43 | ((multiply @ X2 @ X1) != (sk_c8))))
% 67.88/10.43 <= ((![X1 : $i, X2 : $i]:
% 67.88/10.43 (((multiply @ X1 @ sk_c9) != (sk_c8))
% 67.88/10.43 | ((inverse @ X2) != (X1))
% 67.88/10.43 | ((multiply @ X2 @ X1) != (sk_c8)))))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl57])).
% 67.88/10.43 thf(zip_derived_cl259, plain,
% 67.88/10.43 ((![X0 : $i]:
% 67.88/10.43 (((sk_c8) != (sk_c8))
% 67.88/10.43 | ((inverse @ X0) != (sk_c6))
% 67.88/10.43 | ((multiply @ X0 @ sk_c6) != (sk_c8))))
% 67.88/10.43 <= ((((multiply @ sk_c6 @ sk_c9) = (sk_c8))) &
% 67.88/10.43 (![X1 : $i, X2 : $i]:
% 67.88/10.43 (((multiply @ X1 @ sk_c9) != (sk_c8))
% 67.88/10.43 | ((inverse @ X2) != (X1))
% 67.88/10.43 | ((multiply @ X2 @ X1) != (sk_c8)))))),
% 67.88/10.43 inference('s_sup-', [status(thm)], [zip_derived_cl70, zip_derived_cl168])).
% 67.88/10.43 thf(zip_derived_cl260, plain,
% 67.88/10.43 ((![X0 : $i]:
% 67.88/10.43 (((multiply @ X0 @ sk_c6) != (sk_c8)) | ((inverse @ X0) != (sk_c6))))
% 67.88/10.43 <= ((((multiply @ sk_c6 @ sk_c9) = (sk_c8))) &
% 67.88/10.43 (![X1 : $i, X2 : $i]:
% 67.88/10.43 (((multiply @ X1 @ sk_c9) != (sk_c8))
% 67.88/10.43 | ((inverse @ X2) != (X1))
% 67.88/10.43 | ((multiply @ X2 @ X1) != (sk_c8)))))),
% 67.88/10.43 inference('simplify', [status(thm)], [zip_derived_cl259])).
% 67.88/10.43 thf(zip_derived_cl279, plain,
% 67.88/10.43 (((((multiply @ sk_c5 @ sk_c6) != (sk_c8)) | ((sk_c6) != (sk_c6))))
% 67.88/10.43 <= ((((inverse @ sk_c5) = (sk_c6))) &
% 67.88/10.43 (((multiply @ sk_c6 @ sk_c9) = (sk_c8))) &
% 67.88/10.43 (![X1 : $i, X2 : $i]:
% 67.88/10.43 (((multiply @ X1 @ sk_c9) != (sk_c8))
% 67.88/10.43 | ((inverse @ X2) != (X1))
% 67.88/10.43 | ((multiply @ X2 @ X1) != (sk_c8)))))),
% 67.88/10.43 inference('s_sup-', [status(thm)], [zip_derived_cl68, zip_derived_cl260])).
% 67.88/10.43 thf(zip_derived_cl282, plain,
% 67.88/10.43 ((((multiply @ sk_c5 @ sk_c6) != (sk_c8)))
% 67.88/10.43 <= ((((inverse @ sk_c5) = (sk_c6))) &
% 67.88/10.43 (((multiply @ sk_c6 @ sk_c9) = (sk_c8))) &
% 67.88/10.43 (![X1 : $i, X2 : $i]:
% 67.88/10.43 (((multiply @ X1 @ sk_c9) != (sk_c8))
% 67.88/10.43 | ((inverse @ X2) != (X1))
% 67.88/10.43 | ((multiply @ X2 @ X1) != (sk_c8)))))),
% 67.88/10.43 inference('simplify', [status(thm)], [zip_derived_cl279])).
% 67.88/10.43 thf(zip_derived_cl283, plain,
% 67.88/10.43 ((((sk_c8) != (sk_c8)))
% 67.88/10.43 <= ((((multiply @ sk_c5 @ sk_c6) = (sk_c8))) &
% 67.88/10.43 (((inverse @ sk_c5) = (sk_c6))) &
% 67.88/10.43 (((multiply @ sk_c6 @ sk_c9) = (sk_c8))) &
% 67.88/10.43 (![X1 : $i, X2 : $i]:
% 67.88/10.43 (((multiply @ X1 @ sk_c9) != (sk_c8))
% 67.88/10.43 | ((inverse @ X2) != (X1))
% 67.88/10.43 | ((multiply @ X2 @ X1) != (sk_c8)))))),
% 67.88/10.43 inference('s_sup-', [status(thm)], [zip_derived_cl66, zip_derived_cl282])).
% 67.88/10.43 thf('29', plain,
% 67.88/10.43 (~ (((multiply @ sk_c5 @ sk_c6) = (sk_c8))) |
% 67.88/10.43 ~ (((multiply @ sk_c6 @ sk_c9) = (sk_c8))) |
% 67.88/10.43 ~
% 67.88/10.43 (![X1 : $i, X2 : $i]:
% 67.88/10.43 (((multiply @ X1 @ sk_c9) != (sk_c8))
% 67.88/10.43 | ((inverse @ X2) != (X1))
% 67.88/10.43 | ((multiply @ X2 @ X1) != (sk_c8)))) |
% 67.88/10.43 ~ (((inverse @ sk_c5) = (sk_c6)))),
% 67.88/10.43 inference('simplify', [status(thm)], [zip_derived_cl283])).
% 67.88/10.43 thf(prove_this_46, conjecture,
% 67.88/10.43 (~( ( ( inverse @ sk_c10 ) = ( sk_c9 ) ) |
% 67.88/10.43 ( ( inverse @ sk_c1 ) = ( sk_c10 ) ) ))).
% 67.88/10.43 thf(zf_stmt_27, negated_conjecture,
% 67.88/10.43 (( ( inverse @ sk_c10 ) = ( sk_c9 ) ) |
% 67.88/10.43 ( ( inverse @ sk_c1 ) = ( sk_c10 ) )),
% 67.88/10.43 inference('cnf.neg', [status(esa)], [prove_this_46])).
% 67.88/10.43 thf(zip_derived_cl48, plain,
% 67.88/10.43 ((((inverse @ sk_c10) = (sk_c9)) | ((inverse @ sk_c1) = (sk_c10)))),
% 67.88/10.43 inference('cnf', [status(esa)], [zf_stmt_27])).
% 67.88/10.43 thf(zip_derived_cl148, plain,
% 67.88/10.43 ((((inverse @ sk_c1) = (sk_c10))) <= ((((inverse @ sk_c1) = (sk_c10))))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl48])).
% 67.88/10.43 thf(zip_derived_cl130, plain,
% 67.88/10.43 ((((multiply @ sk_c1 @ sk_c10) = (sk_c2)))
% 67.88/10.43 <= ((((multiply @ sk_c1 @ sk_c10) = (sk_c2))))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl39])).
% 67.88/10.43 thf(zip_derived_cl200, plain,
% 67.88/10.43 (![X0 : $i, X1 : $i]:
% 67.88/10.43 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 67.88/10.43 inference('demod', [status(thm)], [zip_derived_cl198, zip_derived_cl0])).
% 67.88/10.43 thf(zip_derived_cl484, plain,
% 67.88/10.43 ((((sk_c10) = (multiply @ (inverse @ sk_c1) @ sk_c2)))
% 67.88/10.43 <= ((((multiply @ sk_c1 @ sk_c10) = (sk_c2))))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl130, zip_derived_cl200])).
% 67.88/10.43 thf(zip_derived_cl676, plain,
% 67.88/10.43 ((((sk_c10) = (multiply @ sk_c10 @ sk_c2)))
% 67.88/10.43 <= ((((multiply @ sk_c1 @ sk_c10) = (sk_c2))) &
% 67.88/10.43 (((inverse @ sk_c1) = (sk_c10))))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl148, zip_derived_cl484])).
% 67.88/10.43 thf(prove_this_28, conjecture,
% 67.88/10.43 (~( ( ( inverse @ sk_c10 ) = ( sk_c9 ) ) |
% 67.88/10.43 ( ( multiply @ sk_c10 @ sk_c2 ) = ( sk_c9 ) ) ))).
% 67.88/10.43 thf(zf_stmt_28, negated_conjecture,
% 67.88/10.43 (( ( inverse @ sk_c10 ) = ( sk_c9 ) ) |
% 67.88/10.43 ( ( multiply @ sk_c10 @ sk_c2 ) = ( sk_c9 ) )),
% 67.88/10.43 inference('cnf.neg', [status(esa)], [prove_this_28])).
% 67.88/10.43 thf(zip_derived_cl30, plain,
% 67.88/10.43 ((((inverse @ sk_c10) = (sk_c9))
% 67.88/10.43 | ((multiply @ sk_c10 @ sk_c2) = (sk_c9)))),
% 67.88/10.43 inference('cnf', [status(esa)], [zf_stmt_28])).
% 67.88/10.43 thf(zip_derived_cl112, plain,
% 67.88/10.43 ((((multiply @ sk_c10 @ sk_c2) = (sk_c9)))
% 67.88/10.43 <= ((((multiply @ sk_c10 @ sk_c2) = (sk_c9))))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl30])).
% 67.88/10.43 thf(zip_derived_cl7621, plain,
% 67.88/10.43 ((((sk_c10) = (sk_c9)))
% 67.88/10.43 <= ((((multiply @ sk_c10 @ sk_c2) = (sk_c9))) &
% 67.88/10.43 (((multiply @ sk_c1 @ sk_c10) = (sk_c2))) &
% 67.88/10.43 (((inverse @ sk_c1) = (sk_c10))))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl676, zip_derived_cl112])).
% 67.88/10.43 thf(zip_derived_cl189, plain,
% 67.88/10.43 ((((multiply @ sk_c9 @ sk_c10) = (identity)))
% 67.88/10.43 <= ((((inverse @ sk_c10) = (sk_c9))))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl59, zip_derived_cl1])).
% 67.88/10.43 thf(zip_derived_cl2, plain,
% 67.88/10.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.88/10.43 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 67.88/10.43 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 67.88/10.43 inference('cnf', [status(esa)], [associativity])).
% 67.88/10.43 thf(zip_derived_cl394, plain,
% 67.88/10.43 ((![X0 : $i]:
% 67.88/10.43 ((multiply @ identity @ X0)
% 67.88/10.43 = (multiply @ sk_c9 @ (multiply @ sk_c10 @ X0))))
% 67.88/10.43 <= ((((inverse @ sk_c10) = (sk_c9))))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl189, zip_derived_cl2])).
% 67.88/10.43 thf(zip_derived_cl0, plain,
% 67.88/10.43 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 67.88/10.43 inference('cnf', [status(esa)], [left_identity])).
% 67.88/10.43 thf(zip_derived_cl396, plain,
% 67.88/10.43 ((![X0 : $i]: ((X0) = (multiply @ sk_c9 @ (multiply @ sk_c10 @ X0))))
% 67.88/10.43 <= ((((inverse @ sk_c10) = (sk_c9))))),
% 67.88/10.43 inference('demod', [status(thm)], [zip_derived_cl394, zip_derived_cl0])).
% 67.88/10.43 thf(zip_derived_cl473, plain,
% 67.88/10.43 ((((sk_c8) = (multiply @ (inverse @ sk_c10) @ sk_c9)))
% 67.88/10.43 <= ((((multiply @ sk_c10 @ sk_c8) = (sk_c9))))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl94, zip_derived_cl200])).
% 67.88/10.43 thf(zip_derived_cl2, plain,
% 67.88/10.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.88/10.43 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 67.88/10.43 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 67.88/10.43 inference('cnf', [status(esa)], [associativity])).
% 67.88/10.43 thf(zip_derived_cl535, plain,
% 67.88/10.43 ((![X0 : $i]:
% 67.88/10.43 ((multiply @ sk_c8 @ X0)
% 67.88/10.43 = (multiply @ (inverse @ sk_c10) @ (multiply @ sk_c9 @ X0))))
% 67.88/10.43 <= ((((multiply @ sk_c10 @ sk_c8) = (sk_c9))))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl473, zip_derived_cl2])).
% 67.88/10.43 thf(zip_derived_cl2468, plain,
% 67.88/10.43 ((![X0 : $i]:
% 67.88/10.43 ((multiply @ sk_c8 @ (multiply @ sk_c10 @ X0))
% 67.88/10.43 = (multiply @ (inverse @ sk_c10) @ X0)))
% 67.88/10.43 <= ((((inverse @ sk_c10) = (sk_c9))) &
% 67.88/10.43 (((multiply @ sk_c10 @ sk_c8) = (sk_c9))))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl396, zip_derived_cl535])).
% 67.88/10.43 thf(zip_derived_cl59, plain,
% 67.88/10.43 ((((inverse @ sk_c10) = (sk_c9))) <= ((((inverse @ sk_c10) = (sk_c9))))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl3])).
% 67.88/10.43 thf(zip_derived_cl2476, plain,
% 67.88/10.43 ((![X0 : $i]:
% 67.88/10.43 ((multiply @ sk_c8 @ (multiply @ sk_c10 @ X0))
% 67.88/10.43 = (multiply @ sk_c9 @ X0)))
% 67.88/10.43 <= ((((inverse @ sk_c10) = (sk_c9))) &
% 67.88/10.43 (((multiply @ sk_c10 @ sk_c8) = (sk_c9))))),
% 67.88/10.43 inference('demod', [status(thm)], [zip_derived_cl2468, zip_derived_cl59])).
% 67.88/10.43 thf(zip_derived_cl2, plain,
% 67.88/10.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.88/10.43 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 67.88/10.43 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 67.88/10.43 inference('cnf', [status(esa)], [associativity])).
% 67.88/10.43 thf(zip_derived_cl0, plain,
% 67.88/10.43 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 67.88/10.43 inference('cnf', [status(esa)], [left_identity])).
% 67.88/10.43 thf(zip_derived_cl2, plain,
% 67.88/10.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.88/10.43 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 67.88/10.43 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 67.88/10.43 inference('cnf', [status(esa)], [associativity])).
% 67.88/10.43 thf(zip_derived_cl474, plain,
% 67.88/10.43 ((((sk_c4) = (multiply @ (inverse @ sk_c10) @ sk_c9)))
% 67.88/10.43 <= ((((multiply @ sk_c10 @ sk_c4) = (sk_c9))))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl60, zip_derived_cl200])).
% 67.88/10.43 thf(zip_derived_cl168, plain,
% 67.88/10.43 ((![X1 : $i, X2 : $i]:
% 67.88/10.43 (((multiply @ X1 @ sk_c9) != (sk_c8))
% 67.88/10.43 | ((inverse @ X2) != (X1))
% 67.88/10.43 | ((multiply @ X2 @ X1) != (sk_c8))))
% 67.88/10.43 <= ((![X1 : $i, X2 : $i]:
% 67.88/10.43 (((multiply @ X1 @ sk_c9) != (sk_c8))
% 67.88/10.43 | ((inverse @ X2) != (X1))
% 67.88/10.43 | ((multiply @ X2 @ X1) != (sk_c8)))))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl57])).
% 67.88/10.43 thf(zip_derived_cl566, plain,
% 67.88/10.43 ((![X0 : $i]:
% 67.88/10.43 (((sk_c4) != (sk_c8))
% 67.88/10.43 | ((inverse @ X0) != (inverse @ sk_c10))
% 67.88/10.43 | ((multiply @ X0 @ (inverse @ sk_c10)) != (sk_c8))))
% 67.88/10.43 <= ((((multiply @ sk_c10 @ sk_c4) = (sk_c9))) &
% 67.88/10.43 (![X1 : $i, X2 : $i]:
% 67.88/10.43 (((multiply @ X1 @ sk_c9) != (sk_c8))
% 67.88/10.43 | ((inverse @ X2) != (X1))
% 67.88/10.43 | ((multiply @ X2 @ X1) != (sk_c8)))))),
% 67.88/10.43 inference('s_sup-', [status(thm)], [zip_derived_cl474, zip_derived_cl168])).
% 67.88/10.43 thf(zip_derived_cl3529, plain,
% 67.88/10.43 ((![X0 : $i]:
% 67.88/10.43 (((inverse @ X0) != (inverse @ sk_c10))
% 67.88/10.43 | ((multiply @ X0 @ (inverse @ sk_c10)) != (sk_c8))))
% 67.88/10.43 <= ((![X0 : $i]:
% 67.88/10.43 (((inverse @ X0) != (inverse @ sk_c10))
% 67.88/10.43 | ((multiply @ X0 @ (inverse @ sk_c10)) != (sk_c8)))))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl566])).
% 67.88/10.43 thf(zip_derived_cl3531, plain,
% 67.88/10.43 ((![X0 : $i, X1 : $i]:
% 67.88/10.43 (((inverse @ (multiply @ X1 @ X0)) != (inverse @ sk_c10))
% 67.88/10.43 | ((multiply @ X1 @ (multiply @ X0 @ (inverse @ sk_c10))) != (sk_c8))))
% 67.88/10.43 <= ((![X0 : $i]:
% 67.88/10.43 (((inverse @ X0) != (inverse @ sk_c10))
% 67.88/10.43 | ((multiply @ X0 @ (inverse @ sk_c10)) != (sk_c8)))))),
% 67.88/10.43 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl3529])).
% 67.88/10.43 thf(zip_derived_cl3827, plain,
% 67.88/10.43 ((![X0 : $i]:
% 67.88/10.43 (((inverse @ (multiply @ X0 @ identity)) != (inverse @ sk_c10))
% 67.88/10.43 | ((multiply @ X0 @ (inverse @ sk_c10)) != (sk_c8))))
% 67.88/10.43 <= ((![X0 : $i]:
% 67.88/10.43 (((inverse @ X0) != (inverse @ sk_c10))
% 67.88/10.43 | ((multiply @ X0 @ (inverse @ sk_c10)) != (sk_c8)))))),
% 67.88/10.43 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl3531])).
% 67.88/10.43 thf(zip_derived_cl3929, plain,
% 67.88/10.43 ((![X0 : $i, X1 : $i]:
% 67.88/10.43 (((inverse @ (multiply @ X1 @ (multiply @ X0 @ identity)))
% 67.88/10.43 != (inverse @ sk_c10))
% 67.88/10.43 | ((multiply @ (multiply @ X1 @ X0) @ (inverse @ sk_c10)) != (sk_c8))))
% 67.88/10.43 <= ((![X0 : $i]:
% 67.88/10.43 (((inverse @ X0) != (inverse @ sk_c10))
% 67.88/10.43 | ((multiply @ X0 @ (inverse @ sk_c10)) != (sk_c8)))))),
% 67.88/10.43 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl3827])).
% 67.88/10.43 thf(zip_derived_cl2, plain,
% 67.88/10.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.88/10.43 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 67.88/10.43 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 67.88/10.43 inference('cnf', [status(esa)], [associativity])).
% 67.88/10.43 thf(zip_derived_cl3959, plain,
% 67.88/10.43 ((![X0 : $i, X1 : $i]:
% 67.88/10.43 (((inverse @ (multiply @ X1 @ (multiply @ X0 @ identity)))
% 67.88/10.43 != (inverse @ sk_c10))
% 67.88/10.43 | ((multiply @ X1 @ (multiply @ X0 @ (inverse @ sk_c10))) != (sk_c8))))
% 67.88/10.43 <= ((![X0 : $i]:
% 67.88/10.43 (((inverse @ X0) != (inverse @ sk_c10))
% 67.88/10.43 | ((multiply @ X0 @ (inverse @ sk_c10)) != (sk_c8)))))),
% 67.88/10.43 inference('demod', [status(thm)], [zip_derived_cl3929, zip_derived_cl2])).
% 67.88/10.43 thf(zip_derived_cl84952, plain,
% 67.88/10.43 (((((inverse @ (multiply @ sk_c9 @ identity)) != (inverse @ sk_c10))
% 67.88/10.43 | ((multiply @ sk_c8 @ (multiply @ sk_c10 @ (inverse @ sk_c10)))
% 67.88/10.43 != (sk_c8))))
% 67.88/10.43 <= ((((inverse @ sk_c10) = (sk_c9))) &
% 67.88/10.43 (((multiply @ sk_c10 @ sk_c8) = (sk_c9))) &
% 67.88/10.43 (![X0 : $i]:
% 67.88/10.43 (((inverse @ X0) != (inverse @ sk_c10))
% 67.88/10.43 | ((multiply @ X0 @ (inverse @ sk_c10)) != (sk_c8)))))),
% 67.88/10.43 inference('s_sup-', [status(thm)],
% 67.88/10.43 [zip_derived_cl2476, zip_derived_cl3959])).
% 67.88/10.43 thf(zip_derived_cl1, plain,
% 67.88/10.43 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 67.88/10.43 inference('cnf', [status(esa)], [left_inverse])).
% 67.88/10.43 thf(zip_derived_cl200, plain,
% 67.88/10.43 (![X0 : $i, X1 : $i]:
% 67.88/10.43 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 67.88/10.43 inference('demod', [status(thm)], [zip_derived_cl198, zip_derived_cl0])).
% 67.88/10.43 thf(zip_derived_cl468, plain,
% 67.88/10.43 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl200])).
% 67.88/10.43 thf(zip_derived_cl464, plain,
% 67.88/10.43 (![X0 : $i, X1 : $i]:
% 67.88/10.43 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl200, zip_derived_cl200])).
% 67.88/10.43 thf(zip_derived_cl1957, plain,
% 67.88/10.43 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl468, zip_derived_cl464])).
% 67.88/10.43 thf(zip_derived_cl42972, plain,
% 67.88/10.43 ((((inverse @ sk_c9) = (sk_c10))) <= ((((inverse @ sk_c10) = (sk_c9))))),
% 67.88/10.43 inference('demod', [status(thm)],
% 67.88/10.43 [zip_derived_cl42759, zip_derived_cl999])).
% 67.88/10.43 thf(zip_derived_cl59, plain,
% 67.88/10.43 ((((inverse @ sk_c10) = (sk_c9))) <= ((((inverse @ sk_c10) = (sk_c9))))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl3])).
% 67.88/10.43 thf(zip_derived_cl59, plain,
% 67.88/10.43 ((((inverse @ sk_c10) = (sk_c9))) <= ((((inverse @ sk_c10) = (sk_c9))))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl3])).
% 67.88/10.43 thf(zip_derived_cl526, plain,
% 67.88/10.43 ((![X0 : $i]:
% 67.88/10.43 ((multiply @ sk_c10 @ X0) = (multiply @ (inverse @ sk_c9) @ X0)))
% 67.88/10.43 <= ((((inverse @ sk_c10) = (sk_c9))))),
% 67.88/10.43 inference('demod', [status(thm)], [zip_derived_cl522, zip_derived_cl0])).
% 67.88/10.43 thf(zip_derived_cl1, plain,
% 67.88/10.43 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 67.88/10.43 inference('cnf', [status(esa)], [left_inverse])).
% 67.88/10.43 thf(zip_derived_cl997, plain,
% 67.88/10.43 ((((multiply @ sk_c10 @ sk_c9) = (identity)))
% 67.88/10.43 <= ((((inverse @ sk_c10) = (sk_c9))))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl526, zip_derived_cl1])).
% 67.88/10.43 thf(zip_derived_cl1957, plain,
% 67.88/10.43 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl468, zip_derived_cl464])).
% 67.88/10.43 thf(zip_derived_cl85157, plain,
% 67.88/10.43 (((((sk_c10) != (sk_c9)) | ((sk_c8) != (sk_c8))))
% 67.88/10.43 <= ((((inverse @ sk_c10) = (sk_c9))) &
% 67.88/10.43 (((multiply @ sk_c10 @ sk_c8) = (sk_c9))) &
% 67.88/10.43 (![X0 : $i]:
% 67.88/10.43 (((inverse @ X0) != (inverse @ sk_c10))
% 67.88/10.43 | ((multiply @ X0 @ (inverse @ sk_c10)) != (sk_c8)))))),
% 67.88/10.43 inference('demod', [status(thm)],
% 67.88/10.43 [zip_derived_cl84952, zip_derived_cl1957, zip_derived_cl42972,
% 67.88/10.43 zip_derived_cl59, zip_derived_cl59, zip_derived_cl997,
% 67.88/10.43 zip_derived_cl1957])).
% 67.88/10.43 thf(zip_derived_cl85158, plain,
% 67.88/10.43 ((((sk_c10) != (sk_c9)))
% 67.88/10.43 <= ((((inverse @ sk_c10) = (sk_c9))) &
% 67.88/10.43 (((multiply @ sk_c10 @ sk_c8) = (sk_c9))) &
% 67.88/10.43 (![X0 : $i]:
% 67.88/10.43 (((inverse @ X0) != (inverse @ sk_c10))
% 67.88/10.43 | ((multiply @ X0 @ (inverse @ sk_c10)) != (sk_c8)))))),
% 67.88/10.43 inference('simplify', [status(thm)], [zip_derived_cl85157])).
% 67.88/10.43 thf(zip_derived_cl99874, plain,
% 67.88/10.43 ((((sk_c9) != (sk_c9)))
% 67.88/10.43 <= ((((inverse @ sk_c10) = (sk_c9))) &
% 67.88/10.43 (((multiply @ sk_c10 @ sk_c8) = (sk_c9))) &
% 67.88/10.43 (((multiply @ sk_c10 @ sk_c2) = (sk_c9))) &
% 67.88/10.43 (((multiply @ sk_c1 @ sk_c10) = (sk_c2))) &
% 67.88/10.43 (((inverse @ sk_c1) = (sk_c10))) &
% 67.88/10.43 (![X0 : $i]:
% 67.88/10.43 (((inverse @ X0) != (inverse @ sk_c10))
% 67.88/10.43 | ((multiply @ X0 @ (inverse @ sk_c10)) != (sk_c8)))))),
% 67.88/10.43 inference('s_sup-', [status(thm)],
% 67.88/10.43 [zip_derived_cl7621, zip_derived_cl85158])).
% 67.88/10.43 thf('30', plain,
% 67.88/10.43 (~ (((inverse @ sk_c1) = (sk_c10))) |
% 67.88/10.43 ~
% 67.88/10.43 (![X0 : $i]:
% 67.88/10.43 (((inverse @ X0) != (inverse @ sk_c10))
% 67.88/10.43 | ((multiply @ X0 @ (inverse @ sk_c10)) != (sk_c8)))) |
% 67.88/10.43 ~ (((multiply @ sk_c1 @ sk_c10) = (sk_c2))) |
% 67.88/10.43 ~ (((multiply @ sk_c10 @ sk_c2) = (sk_c9))) |
% 67.88/10.43 ~ (((multiply @ sk_c10 @ sk_c8) = (sk_c9))) |
% 67.88/10.43 ~ (((inverse @ sk_c10) = (sk_c9)))),
% 67.88/10.43 inference('simplify', [status(thm)], [zip_derived_cl99874])).
% 67.88/10.43 thf(zip_derived_cl1551, plain,
% 67.88/10.43 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl464, zip_derived_cl1])).
% 67.88/10.43 thf(zip_derived_cl532, plain,
% 67.88/10.43 ((![X0 : $i]:
% 67.88/10.43 ((multiply @ sk_c9 @ X0) = (multiply @ (inverse @ sk_c10) @ X0)))
% 67.88/10.43 <= ((((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.43 inference('demod', [status(thm)], [zip_derived_cl528, zip_derived_cl0])).
% 67.88/10.43 thf(zip_derived_cl200, plain,
% 67.88/10.43 (![X0 : $i, X1 : $i]:
% 67.88/10.43 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 67.88/10.43 inference('demod', [status(thm)], [zip_derived_cl198, zip_derived_cl0])).
% 67.88/10.43 thf(zip_derived_cl1112, plain,
% 67.88/10.43 ((![X0 : $i]: ((X0) = (multiply @ sk_c9 @ (multiply @ sk_c10 @ X0))))
% 67.88/10.43 <= ((((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl532, zip_derived_cl200])).
% 67.88/10.43 thf(zip_derived_cl42800, plain,
% 67.88/10.43 ((((inverse @ sk_c10) = (multiply @ sk_c9 @ identity)))
% 67.88/10.43 <= ((((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.43 inference('s_sup+', [status(thm)],
% 67.88/10.43 [zip_derived_cl1551, zip_derived_cl1112])).
% 67.88/10.43 thf(zip_derived_cl532, plain,
% 67.88/10.43 ((![X0 : $i]:
% 67.88/10.43 ((multiply @ sk_c9 @ X0) = (multiply @ (inverse @ sk_c10) @ X0)))
% 67.88/10.43 <= ((((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.43 inference('demod', [status(thm)], [zip_derived_cl528, zip_derived_cl0])).
% 67.88/10.43 thf(zip_derived_cl472, plain,
% 67.88/10.43 ((((sk_c9) = (multiply @ (inverse @ sk_c10) @ identity)))
% 67.88/10.43 <= ((((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl188, zip_derived_cl200])).
% 67.88/10.43 thf(zip_derived_cl1113, plain,
% 67.88/10.43 ((((sk_c9) = (multiply @ sk_c9 @ identity)))
% 67.88/10.43 <= ((((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl532, zip_derived_cl472])).
% 67.88/10.43 thf(zip_derived_cl42988, plain,
% 67.88/10.43 ((((inverse @ sk_c10) = (sk_c9))) <= ((((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.43 inference('demod', [status(thm)],
% 67.88/10.43 [zip_derived_cl42800, zip_derived_cl1113])).
% 67.88/10.43 thf(zip_derived_cl173, plain,
% 67.88/10.43 ((((inverse @ sk_c10) != (sk_c9)))
% 67.88/10.43 <= (~ (((inverse @ sk_c10) = (sk_c9))))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl57])).
% 67.88/10.43 thf(zip_derived_cl60029, plain,
% 67.88/10.43 ((((sk_c9) != (sk_c9)))
% 67.88/10.43 <= (~ (((inverse @ sk_c10) = (sk_c9))) &
% 67.88/10.43 (((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.43 inference('s_sup-', [status(thm)],
% 67.88/10.43 [zip_derived_cl42988, zip_derived_cl173])).
% 67.88/10.43 thf('31', plain,
% 67.88/10.43 ((((inverse @ sk_c10) = (sk_c9))) | ~ (((inverse @ sk_c9) = (sk_c10)))),
% 67.88/10.43 inference('simplify', [status(thm)], [zip_derived_cl60029])).
% 67.88/10.43 thf(prove_this_8, conjecture,
% 67.88/10.43 (~( ( ( inverse @ sk_c7 ) = ( sk_c10 ) ) |
% 67.88/10.43 ( ( multiply @ sk_c9 @ sk_c8 ) = ( sk_c10 ) ) ))).
% 67.88/10.43 thf(zf_stmt_29, negated_conjecture,
% 67.88/10.43 (( ( inverse @ sk_c7 ) = ( sk_c10 ) ) |
% 67.88/10.43 ( ( multiply @ sk_c9 @ sk_c8 ) = ( sk_c10 ) )),
% 67.88/10.43 inference('cnf.neg', [status(esa)], [prove_this_8])).
% 67.88/10.43 thf(zip_derived_cl10, plain,
% 67.88/10.43 ((((inverse @ sk_c7) = (sk_c10))
% 67.88/10.43 | ((multiply @ sk_c9 @ sk_c8) = (sk_c10)))),
% 67.88/10.43 inference('cnf', [status(esa)], [zf_stmt_29])).
% 67.88/10.43 thf('32', plain,
% 67.88/10.43 ((((inverse @ sk_c7) = (sk_c10))) |
% 67.88/10.43 (((multiply @ sk_c9 @ sk_c8) = (sk_c10)))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl10])).
% 67.88/10.43 thf(prove_this_9, conjecture,
% 67.88/10.43 (~( ( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c10 ) ) |
% 67.88/10.43 ( ( multiply @ sk_c9 @ sk_c8 ) = ( sk_c10 ) ) ))).
% 67.88/10.43 thf(zf_stmt_30, negated_conjecture,
% 67.88/10.43 (( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c10 ) ) |
% 67.88/10.43 ( ( multiply @ sk_c9 @ sk_c8 ) = ( sk_c10 ) )),
% 67.88/10.43 inference('cnf.neg', [status(esa)], [prove_this_9])).
% 67.88/10.43 thf(zip_derived_cl11, plain,
% 67.88/10.43 ((((multiply @ sk_c7 @ sk_c8) = (sk_c10))
% 67.88/10.43 | ((multiply @ sk_c9 @ sk_c8) = (sk_c10)))),
% 67.88/10.43 inference('cnf', [status(esa)], [zf_stmt_30])).
% 67.88/10.43 thf('33', plain,
% 67.88/10.43 ((((multiply @ sk_c7 @ sk_c8) = (sk_c10))) |
% 67.88/10.43 (((multiply @ sk_c9 @ sk_c8) = (sk_c10)))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl11])).
% 67.88/10.43 thf(zip_derived_cl58, plain,
% 67.88/10.43 ((((multiply @ sk_c9 @ sk_c8) = (sk_c10)))
% 67.88/10.43 <= ((((multiply @ sk_c9 @ sk_c8) = (sk_c10))))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl3])).
% 67.88/10.43 thf(zip_derived_cl76, plain,
% 67.88/10.43 ((((inverse @ sk_c9) = (sk_c10))) <= ((((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl12])).
% 67.88/10.43 thf(zip_derived_cl169, plain,
% 67.88/10.43 ((![X0 : $i]:
% 67.88/10.43 (((inverse @ X0) != (sk_c10)) | ((multiply @ X0 @ sk_c8) != (sk_c10))))
% 67.88/10.43 <= ((![X0 : $i]:
% 67.88/10.43 (((inverse @ X0) != (sk_c10))
% 67.88/10.43 | ((multiply @ X0 @ sk_c8) != (sk_c10)))))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl57])).
% 67.88/10.43 thf(zip_derived_cl182, plain,
% 67.88/10.43 (((((sk_c10) != (sk_c10)) | ((multiply @ sk_c9 @ sk_c8) != (sk_c10))))
% 67.88/10.43 <= ((((inverse @ sk_c9) = (sk_c10))) &
% 67.88/10.43 (![X0 : $i]:
% 67.88/10.43 (((inverse @ X0) != (sk_c10))
% 67.88/10.43 | ((multiply @ X0 @ sk_c8) != (sk_c10)))))),
% 67.88/10.43 inference('s_sup-', [status(thm)], [zip_derived_cl76, zip_derived_cl169])).
% 67.88/10.43 thf(zip_derived_cl184, plain,
% 67.88/10.43 ((((multiply @ sk_c9 @ sk_c8) != (sk_c10)))
% 67.88/10.43 <= ((((inverse @ sk_c9) = (sk_c10))) &
% 67.88/10.43 (![X0 : $i]:
% 67.88/10.43 (((inverse @ X0) != (sk_c10))
% 67.88/10.43 | ((multiply @ X0 @ sk_c8) != (sk_c10)))))),
% 67.88/10.43 inference('simplify', [status(thm)], [zip_derived_cl182])).
% 67.88/10.43 thf(zip_derived_cl208, plain,
% 67.88/10.43 ((((sk_c10) != (sk_c10)))
% 67.88/10.43 <= ((((multiply @ sk_c9 @ sk_c8) = (sk_c10))) &
% 67.88/10.43 (((inverse @ sk_c9) = (sk_c10))) &
% 67.88/10.43 (![X0 : $i]:
% 67.88/10.43 (((inverse @ X0) != (sk_c10))
% 67.88/10.43 | ((multiply @ X0 @ sk_c8) != (sk_c10)))))),
% 67.88/10.43 inference('s_sup-', [status(thm)], [zip_derived_cl58, zip_derived_cl184])).
% 67.88/10.43 thf('34', plain,
% 67.88/10.43 (~
% 67.88/10.43 (![X0 : $i]:
% 67.88/10.43 (((inverse @ X0) != (sk_c10)) | ((multiply @ X0 @ sk_c8) != (sk_c10)))) |
% 67.88/10.43 ~ (((multiply @ sk_c9 @ sk_c8) = (sk_c10))) |
% 67.88/10.43 ~ (((inverse @ sk_c9) = (sk_c10)))),
% 67.88/10.43 inference('simplify', [status(thm)], [zip_derived_cl208])).
% 67.88/10.43 thf(zip_derived_cl74, plain,
% 67.88/10.43 ((((multiply @ sk_c7 @ sk_c8) = (sk_c10)))
% 67.88/10.43 <= ((((multiply @ sk_c7 @ sk_c8) = (sk_c10))))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl11])).
% 67.88/10.43 thf(zip_derived_cl72, plain,
% 67.88/10.43 ((((inverse @ sk_c7) = (sk_c10))) <= ((((inverse @ sk_c7) = (sk_c10))))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl10])).
% 67.88/10.43 thf(zip_derived_cl169, plain,
% 67.88/10.43 ((![X0 : $i]:
% 67.88/10.43 (((inverse @ X0) != (sk_c10)) | ((multiply @ X0 @ sk_c8) != (sk_c10))))
% 67.88/10.43 <= ((![X0 : $i]:
% 67.88/10.43 (((inverse @ X0) != (sk_c10))
% 67.88/10.43 | ((multiply @ X0 @ sk_c8) != (sk_c10)))))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl57])).
% 67.88/10.43 thf(zip_derived_cl180, plain,
% 67.88/10.43 (((((sk_c10) != (sk_c10)) | ((multiply @ sk_c7 @ sk_c8) != (sk_c10))))
% 67.88/10.43 <= ((((inverse @ sk_c7) = (sk_c10))) &
% 67.88/10.43 (![X0 : $i]:
% 67.88/10.43 (((inverse @ X0) != (sk_c10))
% 67.88/10.43 | ((multiply @ X0 @ sk_c8) != (sk_c10)))))),
% 67.88/10.43 inference('s_sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl169])).
% 67.88/10.43 thf(zip_derived_cl181, plain,
% 67.88/10.43 ((((multiply @ sk_c7 @ sk_c8) != (sk_c10)))
% 67.88/10.43 <= ((((inverse @ sk_c7) = (sk_c10))) &
% 67.88/10.43 (![X0 : $i]:
% 67.88/10.43 (((inverse @ X0) != (sk_c10))
% 67.88/10.43 | ((multiply @ X0 @ sk_c8) != (sk_c10)))))),
% 67.88/10.43 inference('simplify', [status(thm)], [zip_derived_cl180])).
% 67.88/10.43 thf(zip_derived_cl270, plain,
% 67.88/10.43 ((((sk_c10) != (sk_c10)))
% 67.88/10.43 <= ((((inverse @ sk_c7) = (sk_c10))) &
% 67.88/10.43 (((multiply @ sk_c7 @ sk_c8) = (sk_c10))) &
% 67.88/10.43 (![X0 : $i]:
% 67.88/10.43 (((inverse @ X0) != (sk_c10))
% 67.88/10.43 | ((multiply @ X0 @ sk_c8) != (sk_c10)))))),
% 67.88/10.43 inference('s_sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl181])).
% 67.88/10.43 thf('35', plain,
% 67.88/10.43 (~
% 67.88/10.43 (![X0 : $i]:
% 67.88/10.43 (((inverse @ X0) != (sk_c10)) | ((multiply @ X0 @ sk_c8) != (sk_c10)))) |
% 67.88/10.43 ~ (((inverse @ sk_c7) = (sk_c10))) |
% 67.88/10.43 ~ (((multiply @ sk_c7 @ sk_c8) = (sk_c10)))),
% 67.88/10.43 inference('simplify', [status(thm)], [zip_derived_cl270])).
% 67.88/10.43 thf(zip_derived_cl72, plain,
% 67.88/10.43 ((((inverse @ sk_c7) = (sk_c10))) <= ((((inverse @ sk_c7) = (sk_c10))))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl10])).
% 67.88/10.43 thf(zip_derived_cl1, plain,
% 67.88/10.43 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 67.88/10.43 inference('cnf', [status(esa)], [left_inverse])).
% 67.88/10.43 thf(zip_derived_cl192, plain,
% 67.88/10.43 ((((multiply @ sk_c10 @ sk_c7) = (identity)))
% 67.88/10.43 <= ((((inverse @ sk_c7) = (sk_c10))))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl72, zip_derived_cl1])).
% 67.88/10.43 thf(zip_derived_cl200, plain,
% 67.88/10.43 (![X0 : $i, X1 : $i]:
% 67.88/10.43 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 67.88/10.43 inference('demod', [status(thm)], [zip_derived_cl198, zip_derived_cl0])).
% 67.88/10.43 thf(zip_derived_cl476, plain,
% 67.88/10.43 ((((sk_c7) = (multiply @ (inverse @ sk_c10) @ identity)))
% 67.88/10.43 <= ((((inverse @ sk_c7) = (sk_c10))))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl192, zip_derived_cl200])).
% 67.88/10.43 thf(zip_derived_cl472, plain,
% 67.88/10.43 ((((sk_c9) = (multiply @ (inverse @ sk_c10) @ identity)))
% 67.88/10.43 <= ((((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl188, zip_derived_cl200])).
% 67.88/10.43 thf(zip_derived_cl579, plain,
% 67.88/10.43 ((((sk_c9) = (sk_c7)))
% 67.88/10.43 <= ((((inverse @ sk_c7) = (sk_c10))) &
% 67.88/10.43 (((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl476, zip_derived_cl472])).
% 67.88/10.43 thf(zip_derived_cl74, plain,
% 67.88/10.43 ((((multiply @ sk_c7 @ sk_c8) = (sk_c10)))
% 67.88/10.43 <= ((((multiply @ sk_c7 @ sk_c8) = (sk_c10))))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl11])).
% 67.88/10.43 thf(zip_derived_cl807, plain,
% 67.88/10.43 ((((multiply @ sk_c9 @ sk_c8) = (sk_c10)))
% 67.88/10.43 <= ((((inverse @ sk_c7) = (sk_c10))) &
% 67.88/10.43 (((multiply @ sk_c7 @ sk_c8) = (sk_c10))) &
% 67.88/10.43 (((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl579, zip_derived_cl74])).
% 67.88/10.43 thf(zip_derived_cl172, plain,
% 67.88/10.43 ((((multiply @ sk_c9 @ sk_c8) != (sk_c10)))
% 67.88/10.43 <= (~ (((multiply @ sk_c9 @ sk_c8) = (sk_c10))))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl57])).
% 67.88/10.43 thf(zip_derived_cl13348, plain,
% 67.88/10.43 ((((sk_c10) != (sk_c10)))
% 67.88/10.43 <= (~ (((multiply @ sk_c9 @ sk_c8) = (sk_c10))) &
% 67.88/10.43 (((inverse @ sk_c7) = (sk_c10))) &
% 67.88/10.43 (((multiply @ sk_c7 @ sk_c8) = (sk_c10))) &
% 67.88/10.43 (((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.43 inference('s_sup-', [status(thm)], [zip_derived_cl807, zip_derived_cl172])).
% 67.88/10.43 thf('36', plain,
% 67.88/10.43 ((((multiply @ sk_c9 @ sk_c8) = (sk_c10))) |
% 67.88/10.43 ~ (((inverse @ sk_c7) = (sk_c10))) |
% 67.88/10.43 ~ (((inverse @ sk_c9) = (sk_c10))) |
% 67.88/10.43 ~ (((multiply @ sk_c7 @ sk_c8) = (sk_c10)))),
% 67.88/10.43 inference('simplify', [status(thm)], [zip_derived_cl13348])).
% 67.88/10.43 thf(prove_this_23, conjecture,
% 67.88/10.43 (~( ( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c8 ) ) |
% 67.88/10.43 ( ( multiply @ sk_c10 @ sk_c8 ) = ( sk_c9 ) ) ))).
% 67.88/10.43 thf(zf_stmt_31, negated_conjecture,
% 67.88/10.43 (( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c8 ) ) |
% 67.88/10.43 ( ( multiply @ sk_c10 @ sk_c8 ) = ( sk_c9 ) )),
% 67.88/10.43 inference('cnf.neg', [status(esa)], [prove_this_23])).
% 67.88/10.43 thf(zip_derived_cl25, plain,
% 67.88/10.43 ((((multiply @ sk_c5 @ sk_c6) = (sk_c8))
% 67.88/10.43 | ((multiply @ sk_c10 @ sk_c8) = (sk_c9)))),
% 67.88/10.43 inference('cnf', [status(esa)], [zf_stmt_31])).
% 67.88/10.43 thf('37', plain,
% 67.88/10.43 ((((multiply @ sk_c5 @ sk_c6) = (sk_c8))) |
% 67.88/10.43 (((multiply @ sk_c10 @ sk_c8) = (sk_c9)))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl25])).
% 67.88/10.43 thf(zip_derived_cl68, plain,
% 67.88/10.43 ((((inverse @ sk_c5) = (sk_c6))) <= ((((inverse @ sk_c5) = (sk_c6))))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl8])).
% 67.88/10.43 thf(zip_derived_cl1, plain,
% 67.88/10.43 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 67.88/10.43 inference('cnf', [status(esa)], [left_inverse])).
% 67.88/10.43 thf(zip_derived_cl191, plain,
% 67.88/10.43 ((((multiply @ sk_c6 @ sk_c5) = (identity)))
% 67.88/10.43 <= ((((inverse @ sk_c5) = (sk_c6))))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl68, zip_derived_cl1])).
% 67.88/10.43 thf(zip_derived_cl200, plain,
% 67.88/10.43 (![X0 : $i, X1 : $i]:
% 67.88/10.43 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 67.88/10.43 inference('demod', [status(thm)], [zip_derived_cl198, zip_derived_cl0])).
% 67.88/10.43 thf(zip_derived_cl482, plain,
% 67.88/10.43 ((((sk_c5) = (multiply @ (inverse @ sk_c6) @ identity)))
% 67.88/10.43 <= ((((inverse @ sk_c5) = (sk_c6))))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl191, zip_derived_cl200])).
% 67.88/10.43 thf(zip_derived_cl2, plain,
% 67.88/10.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.88/10.43 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 67.88/10.43 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 67.88/10.43 inference('cnf', [status(esa)], [associativity])).
% 67.88/10.43 thf(zip_derived_cl666, plain,
% 67.88/10.43 ((![X0 : $i]:
% 67.88/10.43 ((multiply @ sk_c5 @ X0)
% 67.88/10.43 = (multiply @ (inverse @ sk_c6) @ (multiply @ identity @ X0))))
% 67.88/10.43 <= ((((inverse @ sk_c5) = (sk_c6))))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl482, zip_derived_cl2])).
% 67.88/10.43 thf(zip_derived_cl0, plain,
% 67.88/10.43 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 67.88/10.43 inference('cnf', [status(esa)], [left_identity])).
% 67.88/10.43 thf(zip_derived_cl669, plain,
% 67.88/10.43 ((![X0 : $i]:
% 67.88/10.43 ((multiply @ sk_c5 @ X0) = (multiply @ (inverse @ sk_c6) @ X0)))
% 67.88/10.43 <= ((((inverse @ sk_c5) = (sk_c6))))),
% 67.88/10.43 inference('demod', [status(thm)], [zip_derived_cl666, zip_derived_cl0])).
% 67.88/10.43 thf(zip_derived_cl1, plain,
% 67.88/10.43 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 67.88/10.43 inference('cnf', [status(esa)], [left_inverse])).
% 67.88/10.43 thf(zip_derived_cl3278, plain,
% 67.88/10.43 ((((multiply @ sk_c5 @ sk_c6) = (identity)))
% 67.88/10.43 <= ((((inverse @ sk_c5) = (sk_c6))))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl669, zip_derived_cl1])).
% 67.88/10.43 thf(zip_derived_cl66, plain,
% 67.88/10.43 ((((multiply @ sk_c5 @ sk_c6) = (sk_c8)))
% 67.88/10.43 <= ((((multiply @ sk_c5 @ sk_c6) = (sk_c8))))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl7])).
% 67.88/10.43 thf(zip_derived_cl3311, plain,
% 67.88/10.43 ((((identity) = (sk_c8)))
% 67.88/10.43 <= ((((multiply @ sk_c5 @ sk_c6) = (sk_c8))) &
% 67.88/10.43 (((inverse @ sk_c5) = (sk_c6))))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl3278, zip_derived_cl66])).
% 67.88/10.43 thf(zip_derived_cl807, plain,
% 67.88/10.43 ((((multiply @ sk_c9 @ sk_c8) = (sk_c10)))
% 67.88/10.43 <= ((((inverse @ sk_c7) = (sk_c10))) &
% 67.88/10.43 (((multiply @ sk_c7 @ sk_c8) = (sk_c10))) &
% 67.88/10.43 (((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl579, zip_derived_cl74])).
% 67.88/10.43 thf(zip_derived_cl20129, plain,
% 67.88/10.43 ((((multiply @ sk_c9 @ identity) = (sk_c10)))
% 67.88/10.43 <= ((((multiply @ sk_c5 @ sk_c6) = (sk_c8))) &
% 67.88/10.43 (((inverse @ sk_c5) = (sk_c6))) &
% 67.88/10.43 (((inverse @ sk_c7) = (sk_c10))) &
% 67.88/10.43 (((multiply @ sk_c7 @ sk_c8) = (sk_c10))) &
% 67.88/10.43 (((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.43 inference('s_sup+', [status(thm)],
% 67.88/10.43 [zip_derived_cl3311, zip_derived_cl807])).
% 67.88/10.43 thf(zip_derived_cl1113, plain,
% 67.88/10.43 ((((sk_c9) = (multiply @ sk_c9 @ identity)))
% 67.88/10.43 <= ((((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl532, zip_derived_cl472])).
% 67.88/10.43 thf(zip_derived_cl20214, plain,
% 67.88/10.43 ((((sk_c9) = (sk_c10)))
% 67.88/10.43 <= ((((multiply @ sk_c5 @ sk_c6) = (sk_c8))) &
% 67.88/10.43 (((inverse @ sk_c5) = (sk_c6))) &
% 67.88/10.43 (((inverse @ sk_c7) = (sk_c10))) &
% 67.88/10.43 (((multiply @ sk_c7 @ sk_c8) = (sk_c10))) &
% 67.88/10.43 (((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.43 inference('demod', [status(thm)],
% 67.88/10.43 [zip_derived_cl20129, zip_derived_cl1113])).
% 67.88/10.43 thf(zip_derived_cl170, plain,
% 67.88/10.43 ((((multiply @ sk_c10 @ sk_c8) != (sk_c9)))
% 67.88/10.43 <= (~ (((multiply @ sk_c10 @ sk_c8) = (sk_c9))))),
% 67.88/10.43 inference('split', [status(esa)], [zip_derived_cl57])).
% 67.88/10.43 thf(zip_derived_cl24336, plain,
% 67.88/10.43 ((((multiply @ sk_c9 @ sk_c8) != (sk_c9)))
% 67.88/10.43 <= (~ (((multiply @ sk_c10 @ sk_c8) = (sk_c9))) &
% 67.88/10.43 (((multiply @ sk_c5 @ sk_c6) = (sk_c8))) &
% 67.88/10.43 (((inverse @ sk_c5) = (sk_c6))) &
% 67.88/10.43 (((inverse @ sk_c7) = (sk_c10))) &
% 67.88/10.43 (((multiply @ sk_c7 @ sk_c8) = (sk_c10))) &
% 67.88/10.43 (((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.43 inference('s_sup-', [status(thm)],
% 67.88/10.43 [zip_derived_cl20214, zip_derived_cl170])).
% 67.88/10.43 thf(zip_derived_cl3311, plain,
% 67.88/10.43 ((((identity) = (sk_c8)))
% 67.88/10.43 <= ((((multiply @ sk_c5 @ sk_c6) = (sk_c8))) &
% 67.88/10.43 (((inverse @ sk_c5) = (sk_c6))))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl3278, zip_derived_cl66])).
% 67.88/10.43 thf(zip_derived_cl1113, plain,
% 67.88/10.43 ((((sk_c9) = (multiply @ sk_c9 @ identity)))
% 67.88/10.43 <= ((((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.43 inference('s_sup+', [status(thm)], [zip_derived_cl532, zip_derived_cl472])).
% 67.88/10.43 thf(zip_derived_cl24559, plain,
% 67.88/10.43 ((((sk_c9) != (sk_c9)))
% 67.88/10.43 <= (~ (((multiply @ sk_c10 @ sk_c8) = (sk_c9))) &
% 67.88/10.43 (((multiply @ sk_c5 @ sk_c6) = (sk_c8))) &
% 67.88/10.43 (((inverse @ sk_c5) = (sk_c6))) &
% 67.88/10.43 (((inverse @ sk_c7) = (sk_c10))) &
% 67.88/10.43 (((multiply @ sk_c7 @ sk_c8) = (sk_c10))) &
% 67.88/10.43 (((inverse @ sk_c9) = (sk_c10))))),
% 67.88/10.43 inference('demod', [status(thm)],
% 67.88/10.43 [zip_derived_cl24336, zip_derived_cl3311, zip_derived_cl1113])).
% 67.88/10.43 thf('38', plain,
% 67.88/10.43 (~ (((multiply @ sk_c5 @ sk_c6) = (sk_c8))) |
% 67.88/10.43 ~ (((inverse @ sk_c7) = (sk_c10))) |
% 67.88/10.43 ~ (((inverse @ sk_c9) = (sk_c10))) |
% 67.88/10.43 ~ (((inverse @ sk_c5) = (sk_c6))) |
% 67.88/10.43 ~ (((multiply @ sk_c7 @ sk_c8) = (sk_c10))) |
% 67.88/10.43 (((multiply @ sk_c10 @ sk_c8) = (sk_c9)))),
% 67.88/10.43 inference('simplify', [status(thm)], [zip_derived_cl24559])).
% 67.88/10.43 thf(zip_derived_cl99881, plain, ($false),
% 67.88/10.43 inference('sat_resolution*', [status(thm)],
% 67.88/10.43 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 67.88/10.43 '12', '13', '14', '15', '16', '17', '18', '19', '20', '21',
% 67.88/10.43 '22', '23', '24', '25', '26', '27', '28', '29', '30', '31',
% 67.88/10.43 '32', '33', '34', '35', '36', '37', '38'])).
% 67.88/10.43
% 67.88/10.43 % SZS output end Refutation
% 67.88/10.43
% 67.88/10.43
% 67.88/10.43 % Terminating...
% 68.00/10.50 % Runner terminated.
% 68.00/10.50 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------