TSTP Solution File: GRP239-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP239-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.pHh0y50i9l true
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:50:51 EDT 2023
% Result : Unsatisfiable 0.55s 1.05s
% Output : Refutation 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP239-1 : TPTP v8.1.2. Released v2.5.0.
% 0.06/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.pHh0y50i9l true
% 0.14/0.34 % Computer : n013.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 02:18:47 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in FO mode
% 0.22/0.65 % Total configuration time : 435
% 0.22/0.65 % Estimated wc time : 1092
% 0.22/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.53/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.53/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.53/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.53/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.53/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.53/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.53/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.55/1.05 % Solved by fo/fo7.sh.
% 0.55/1.05 % done 889 iterations in 0.273s
% 0.55/1.05 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.55/1.05 % SZS output start Refutation
% 0.55/1.05 thf(sk_c1_type, type, sk_c1: $i).
% 0.55/1.05 thf(sk_c4_type, type, sk_c4: $i).
% 0.55/1.05 thf(sk_c2_type, type, sk_c2: $i).
% 0.55/1.05 thf(sk_c7_type, type, sk_c7: $i).
% 0.55/1.05 thf(sk_c6_type, type, sk_c6: $i).
% 0.55/1.05 thf(identity_type, type, identity: $i).
% 0.55/1.05 thf(multiply_type, type, multiply: $i > $i > $i).
% 0.55/1.05 thf(sk_c8_type, type, sk_c8: $i).
% 0.55/1.05 thf(inverse_type, type, inverse: $i > $i).
% 0.55/1.05 thf(sk_c5_type, type, sk_c5: $i).
% 0.55/1.05 thf(sk_c3_type, type, sk_c3: $i).
% 0.55/1.05 thf(sk_c9_type, type, sk_c9: $i).
% 0.55/1.05 thf(prove_this_43, conjecture,
% 0.55/1.05 (~( ( ( multiply @ X3 @ sk_c9 ) != ( sk_c8 ) ) |
% 0.55/1.05 ( ( inverse @ X7 ) != ( X3 ) ) |
% 0.55/1.05 ( ( multiply @ X7 @ X3 ) != ( sk_c8 ) ) |
% 0.55/1.05 ( ( inverse @ X2 ) != ( sk_c8 ) ) |
% 0.55/1.05 ( ( multiply @ X2 @ sk_c8 ) != ( sk_c9 ) ) |
% 0.55/1.05 ( ( multiply @ X1 @ sk_c8 ) != ( sk_c9 ) ) |
% 0.55/1.05 ( ( inverse @ X1 ) != ( sk_c9 ) ) |
% 0.55/1.05 ( ( inverse @ X6 ) != ( sk_c9 ) ) |
% 0.55/1.05 ( ( multiply @ X6 @ sk_c9 ) != ( X5 ) ) |
% 0.55/1.05 ( ( multiply @ sk_c9 @ X5 ) != ( sk_c8 ) ) |
% 0.55/1.05 ( ( multiply @ X4 @ sk_c8 ) != ( sk_c9 ) ) |
% 0.55/1.05 ( ( inverse @ X4 ) != ( sk_c9 ) ) |
% 0.55/1.05 ( ( inverse @ sk_c9 ) != ( sk_c8 ) ) ))).
% 0.55/1.05 thf(zf_stmt_0, negated_conjecture,
% 0.55/1.05 (( ( multiply @ X3 @ sk_c9 ) != ( sk_c8 ) ) |
% 0.55/1.05 ( ( inverse @ X7 ) != ( X3 ) ) |
% 0.55/1.05 ( ( multiply @ X7 @ X3 ) != ( sk_c8 ) ) |
% 0.55/1.05 ( ( inverse @ X2 ) != ( sk_c8 ) ) |
% 0.55/1.05 ( ( multiply @ X2 @ sk_c8 ) != ( sk_c9 ) ) |
% 0.55/1.05 ( ( multiply @ X1 @ sk_c8 ) != ( sk_c9 ) ) |
% 0.55/1.05 ( ( inverse @ X1 ) != ( sk_c9 ) ) | ( ( inverse @ X6 ) != ( sk_c9 ) ) |
% 0.55/1.05 ( ( multiply @ X6 @ sk_c9 ) != ( X5 ) ) |
% 0.55/1.05 ( ( multiply @ sk_c9 @ X5 ) != ( sk_c8 ) ) |
% 0.55/1.05 ( ( multiply @ X4 @ sk_c8 ) != ( sk_c9 ) ) |
% 0.55/1.05 ( ( inverse @ X4 ) != ( sk_c9 ) ) | ( ( inverse @ sk_c9 ) != ( sk_c8 ) )),
% 0.55/1.05 inference('cnf.neg', [status(esa)], [prove_this_43])).
% 0.55/1.05 thf(zip_derived_cl45, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 0.55/1.05 (((multiply @ X0 @ sk_c9) != (sk_c8))
% 0.55/1.05 | ((inverse @ X1) != (X0))
% 0.55/1.05 | ((multiply @ X1 @ X0) != (sk_c8))
% 0.55/1.05 | ((inverse @ X2) != (sk_c8))
% 0.55/1.05 | ((multiply @ X2 @ sk_c8) != (sk_c9))
% 0.55/1.05 | ((multiply @ X3 @ sk_c8) != (sk_c9))
% 0.55/1.05 | ((inverse @ X3) != (sk_c9))
% 0.55/1.05 | ((inverse @ X4) != (sk_c9))
% 0.55/1.05 | ((multiply @ X4 @ sk_c9) != (X5))
% 0.55/1.05 | ((multiply @ sk_c9 @ X5) != (sk_c8))
% 0.55/1.05 | ((multiply @ X6 @ sk_c8) != (sk_c9))
% 0.55/1.05 | ((inverse @ X6) != (sk_c9))
% 0.55/1.05 | ((inverse @ sk_c9) != (sk_c8)))),
% 0.55/1.05 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.55/1.05 thf(zip_derived_cl46, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 0.55/1.05 (((multiply @ X0 @ sk_c9) != (inverse @ sk_c9))
% 0.55/1.05 | ((inverse @ X1) != (X0))
% 0.55/1.05 | ((multiply @ X1 @ X0) != (inverse @ sk_c9))
% 0.55/1.05 | ((inverse @ X2) != (inverse @ sk_c9))
% 0.55/1.05 | ((multiply @ X2 @ (inverse @ sk_c9)) != (sk_c9))
% 0.55/1.05 | ((multiply @ X3 @ (inverse @ sk_c9)) != (sk_c9))
% 0.55/1.05 | ((inverse @ X3) != (sk_c9))
% 0.55/1.05 | ((inverse @ X4) != (sk_c9))
% 0.55/1.05 | ((multiply @ X4 @ sk_c9) != (X5))
% 0.55/1.05 | ((multiply @ sk_c9 @ X5) != (inverse @ sk_c9))
% 0.55/1.05 | ((multiply @ X6 @ (inverse @ sk_c9)) != (sk_c9))
% 0.55/1.05 | ((inverse @ X6) != (sk_c9))
% 0.55/1.05 | ((inverse @ sk_c9) != (sk_c8)))),
% 0.55/1.05 inference('local_rewriting', [status(thm)], [zip_derived_cl45])).
% 0.55/1.05 thf(prove_this_41, conjecture,
% 0.55/1.05 (~( ( ( inverse @ sk_c6 ) = ( sk_c7 ) ) |
% 0.55/1.05 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 0.55/1.05 thf(zf_stmt_1, negated_conjecture,
% 0.55/1.05 (( ( inverse @ sk_c6 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 0.55/1.05 inference('cnf.neg', [status(esa)], [prove_this_41])).
% 0.55/1.05 thf(zip_derived_cl43, plain,
% 0.55/1.05 ((((inverse @ sk_c6) = (sk_c7)) | ((inverse @ sk_c2) = (sk_c9)))),
% 0.55/1.05 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.55/1.05 thf(prove_this_34, conjecture,
% 0.55/1.05 (~( ( ( inverse @ sk_c6 ) = ( sk_c7 ) ) |
% 0.55/1.05 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c3 ) ) ))).
% 0.55/1.05 thf(zf_stmt_2, negated_conjecture,
% 0.55/1.05 (( ( inverse @ sk_c6 ) = ( sk_c7 ) ) |
% 0.55/1.05 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c3 ) )),
% 0.55/1.05 inference('cnf.neg', [status(esa)], [prove_this_34])).
% 0.55/1.05 thf(zip_derived_cl36, plain,
% 0.55/1.05 ((((inverse @ sk_c6) = (sk_c7)) | ((multiply @ sk_c2 @ sk_c9) = (sk_c3)))),
% 0.55/1.05 inference('cnf', [status(esa)], [zf_stmt_2])).
% 0.55/1.05 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 0.55/1.05 thf(zip_derived_cl1, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.55/1.05 inference('cnf', [status(esa)], [left_inverse])).
% 0.55/1.05 thf(associativity, axiom,
% 0.55/1.05 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 0.55/1.05 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 0.55/1.05 thf(zip_derived_cl2, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/1.05 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.55/1.05 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.55/1.05 inference('cnf', [status(esa)], [associativity])).
% 0.55/1.05 thf(zip_derived_cl70, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i]:
% 0.55/1.05 ((multiply @ identity @ X0)
% 0.55/1.05 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 0.55/1.05 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 0.55/1.05 thf(zip_derived_cl0, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.55/1.05 inference('cnf', [status(esa)], [left_identity])).
% 0.55/1.05 thf(zip_derived_cl105, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i]:
% 0.55/1.05 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl70, zip_derived_cl0])).
% 0.55/1.05 thf(zip_derived_cl155, plain,
% 0.55/1.05 ((((sk_c9) = (multiply @ (inverse @ sk_c2) @ sk_c3))
% 0.55/1.05 | ((inverse @ sk_c6) = (sk_c7)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl36, zip_derived_cl105])).
% 0.55/1.05 thf(zip_derived_cl675, plain,
% 0.55/1.05 ((((sk_c9) = (multiply @ sk_c9 @ sk_c3))
% 0.55/1.05 | ((inverse @ sk_c6) = (sk_c7))
% 0.55/1.05 | ((inverse @ sk_c6) = (sk_c7)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl43, zip_derived_cl155])).
% 0.55/1.05 thf(zip_derived_cl683, plain,
% 0.55/1.05 ((((inverse @ sk_c6) = (sk_c7)) | ((sk_c9) = (multiply @ sk_c9 @ sk_c3)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl675])).
% 0.55/1.05 thf(prove_this_27, conjecture,
% 0.55/1.05 (~( ( ( inverse @ sk_c6 ) = ( sk_c7 ) ) |
% 0.55/1.05 ( ( multiply @ sk_c9 @ sk_c3 ) = ( sk_c8 ) ) ))).
% 0.55/1.05 thf(zf_stmt_3, negated_conjecture,
% 0.55/1.05 (( ( inverse @ sk_c6 ) = ( sk_c7 ) ) |
% 0.55/1.05 ( ( multiply @ sk_c9 @ sk_c3 ) = ( sk_c8 ) )),
% 0.55/1.05 inference('cnf.neg', [status(esa)], [prove_this_27])).
% 0.55/1.05 thf(zip_derived_cl29, plain,
% 0.55/1.05 ((((inverse @ sk_c6) = (sk_c7)) | ((multiply @ sk_c9 @ sk_c3) = (sk_c8)))),
% 0.55/1.05 inference('cnf', [status(esa)], [zf_stmt_3])).
% 0.55/1.05 thf(zip_derived_cl695, plain,
% 0.55/1.05 ((((sk_c9) = (sk_c8))
% 0.55/1.05 | ((inverse @ sk_c6) = (sk_c7))
% 0.55/1.05 | ((inverse @ sk_c6) = (sk_c7)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl683, zip_derived_cl29])).
% 0.55/1.05 thf(zip_derived_cl709, plain,
% 0.55/1.05 ((((inverse @ sk_c6) = (sk_c7)) | ((sk_c9) = (sk_c8)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl695])).
% 0.55/1.05 thf(prove_this_40, conjecture,
% 0.55/1.05 (~( ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c8 ) ) |
% 0.55/1.05 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 0.55/1.05 thf(zf_stmt_4, negated_conjecture,
% 0.55/1.05 (( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c8 ) ) |
% 0.55/1.05 ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 0.55/1.05 inference('cnf.neg', [status(esa)], [prove_this_40])).
% 0.55/1.05 thf(zip_derived_cl42, plain,
% 0.55/1.05 ((((multiply @ sk_c6 @ sk_c7) = (sk_c8)) | ((inverse @ sk_c2) = (sk_c9)))),
% 0.55/1.05 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.55/1.05 thf(zip_derived_cl1, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.55/1.05 inference('cnf', [status(esa)], [left_inverse])).
% 0.55/1.05 thf(zip_derived_cl65, plain,
% 0.55/1.05 ((((multiply @ sk_c9 @ sk_c2) = (identity))
% 0.55/1.05 | ((multiply @ sk_c6 @ sk_c7) = (sk_c8)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl42, zip_derived_cl1])).
% 0.55/1.05 thf(zip_derived_cl105, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i]:
% 0.55/1.05 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl70, zip_derived_cl0])).
% 0.55/1.05 thf(zip_derived_cl138, plain,
% 0.55/1.05 ((((sk_c2) = (multiply @ (inverse @ sk_c9) @ identity))
% 0.55/1.05 | ((multiply @ sk_c6 @ sk_c7) = (sk_c8)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl65, zip_derived_cl105])).
% 0.55/1.05 thf(prove_this_33, conjecture,
% 0.55/1.05 (~( ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c8 ) ) |
% 0.55/1.05 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c3 ) ) ))).
% 0.55/1.05 thf(zf_stmt_5, negated_conjecture,
% 0.55/1.05 (( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c8 ) ) |
% 0.55/1.05 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c3 ) )),
% 0.55/1.05 inference('cnf.neg', [status(esa)], [prove_this_33])).
% 0.55/1.05 thf(zip_derived_cl35, plain,
% 0.55/1.05 ((((multiply @ sk_c6 @ sk_c7) = (sk_c8))
% 0.55/1.05 | ((multiply @ sk_c2 @ sk_c9) = (sk_c3)))),
% 0.55/1.05 inference('cnf', [status(esa)], [zf_stmt_5])).
% 0.55/1.05 thf(zip_derived_cl512, plain,
% 0.55/1.05 ((((multiply @ (multiply @ (inverse @ sk_c9) @ identity) @ sk_c9)
% 0.55/1.05 = (sk_c3))
% 0.55/1.05 | ((multiply @ sk_c6 @ sk_c7) = (sk_c8))
% 0.55/1.05 | ((multiply @ sk_c6 @ sk_c7) = (sk_c8)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl138, zip_derived_cl35])).
% 0.55/1.05 thf(zip_derived_cl2, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/1.05 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.55/1.05 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.55/1.05 inference('cnf', [status(esa)], [associativity])).
% 0.55/1.05 thf(zip_derived_cl0, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.55/1.05 inference('cnf', [status(esa)], [left_identity])).
% 0.55/1.05 thf(zip_derived_cl1, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.55/1.05 inference('cnf', [status(esa)], [left_inverse])).
% 0.55/1.05 thf(zip_derived_cl531, plain,
% 0.55/1.05 ((((identity) = (sk_c3))
% 0.55/1.05 | ((multiply @ sk_c6 @ sk_c7) = (sk_c8))
% 0.55/1.05 | ((multiply @ sk_c6 @ sk_c7) = (sk_c8)))),
% 0.55/1.05 inference('demod', [status(thm)],
% 0.55/1.05 [zip_derived_cl512, zip_derived_cl2, zip_derived_cl0,
% 0.55/1.05 zip_derived_cl1])).
% 0.55/1.05 thf(zip_derived_cl532, plain,
% 0.55/1.05 ((((multiply @ sk_c6 @ sk_c7) = (sk_c8)) | ((identity) = (sk_c3)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl531])).
% 0.55/1.05 thf(prove_this_26, conjecture,
% 0.55/1.05 (~( ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c8 ) ) |
% 0.55/1.05 ( ( multiply @ sk_c9 @ sk_c3 ) = ( sk_c8 ) ) ))).
% 0.55/1.05 thf(zf_stmt_6, negated_conjecture,
% 0.55/1.05 (( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c8 ) ) |
% 0.55/1.05 ( ( multiply @ sk_c9 @ sk_c3 ) = ( sk_c8 ) )),
% 0.55/1.05 inference('cnf.neg', [status(esa)], [prove_this_26])).
% 0.55/1.05 thf(zip_derived_cl28, plain,
% 0.55/1.05 ((((multiply @ sk_c6 @ sk_c7) = (sk_c8))
% 0.55/1.05 | ((multiply @ sk_c9 @ sk_c3) = (sk_c8)))),
% 0.55/1.05 inference('cnf', [status(esa)], [zf_stmt_6])).
% 0.55/1.05 thf(zip_derived_cl541, plain,
% 0.55/1.05 ((((multiply @ sk_c9 @ identity) = (sk_c8))
% 0.55/1.05 | ((multiply @ sk_c6 @ sk_c7) = (sk_c8))
% 0.55/1.05 | ((multiply @ sk_c6 @ sk_c7) = (sk_c8)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl532, zip_derived_cl28])).
% 0.55/1.05 thf(zip_derived_cl547, plain,
% 0.55/1.05 ((((multiply @ sk_c6 @ sk_c7) = (sk_c8))
% 0.55/1.05 | ((multiply @ sk_c9 @ identity) = (sk_c8)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl541])).
% 0.55/1.05 thf(zip_derived_cl1, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.55/1.05 inference('cnf', [status(esa)], [left_inverse])).
% 0.55/1.05 thf(zip_derived_cl105, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i]:
% 0.55/1.05 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl70, zip_derived_cl0])).
% 0.55/1.05 thf(zip_derived_cl121, plain,
% 0.55/1.05 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl105])).
% 0.55/1.05 thf(zip_derived_cl105, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i]:
% 0.55/1.05 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl70, zip_derived_cl0])).
% 0.55/1.05 thf(zip_derived_cl105, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i]:
% 0.55/1.05 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl70, zip_derived_cl0])).
% 0.55/1.05 thf(zip_derived_cl118, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i]:
% 0.55/1.05 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl105, zip_derived_cl105])).
% 0.55/1.05 thf(zip_derived_cl733, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl118])).
% 0.55/1.05 thf(zip_derived_cl2146, plain,
% 0.55/1.05 ((((multiply @ sk_c6 @ sk_c7) = (sk_c8)) | ((sk_c9) = (sk_c8)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl547, zip_derived_cl733])).
% 0.55/1.05 thf(zip_derived_cl2154, plain,
% 0.55/1.05 ((((multiply @ sk_c6 @ (inverse @ sk_c6)) = (sk_c8))
% 0.55/1.05 | ((sk_c9) = (sk_c8))
% 0.55/1.05 | ((sk_c9) = (sk_c8)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl709, zip_derived_cl2146])).
% 0.55/1.05 thf(zip_derived_cl733, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl118])).
% 0.55/1.05 thf(zip_derived_cl121, plain,
% 0.55/1.05 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl105])).
% 0.55/1.05 thf(zip_derived_cl776, plain,
% 0.55/1.05 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl733, zip_derived_cl121])).
% 0.55/1.05 thf(zip_derived_cl1, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.55/1.05 inference('cnf', [status(esa)], [left_inverse])).
% 0.55/1.05 thf(zip_derived_cl935, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl776, zip_derived_cl1])).
% 0.55/1.05 thf(zip_derived_cl2159, plain,
% 0.55/1.05 ((((identity) = (sk_c8)) | ((sk_c9) = (sk_c8)) | ((sk_c9) = (sk_c8)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl2154, zip_derived_cl935])).
% 0.55/1.05 thf(zip_derived_cl2160, plain,
% 0.55/1.05 ((((sk_c9) = (sk_c8)) | ((identity) = (sk_c8)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl2159])).
% 0.55/1.05 thf(prove_this_6, conjecture,
% 0.55/1.05 (~( ( ( inverse @ sk_c6 ) = ( sk_c7 ) ) |
% 0.55/1.05 ( ( inverse @ sk_c9 ) = ( sk_c8 ) ) ))).
% 0.55/1.05 thf(zf_stmt_7, negated_conjecture,
% 0.55/1.05 (( ( inverse @ sk_c6 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c9 ) = ( sk_c8 ) )),
% 0.55/1.05 inference('cnf.neg', [status(esa)], [prove_this_6])).
% 0.55/1.05 thf(zip_derived_cl8, plain,
% 0.55/1.05 ((((inverse @ sk_c6) = (sk_c7)) | ((inverse @ sk_c9) = (sk_c8)))),
% 0.55/1.05 inference('cnf', [status(esa)], [zf_stmt_7])).
% 0.55/1.05 thf(prove_this_5, conjecture,
% 0.55/1.05 (~( ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c8 ) ) |
% 0.55/1.05 ( ( inverse @ sk_c9 ) = ( sk_c8 ) ) ))).
% 0.55/1.05 thf(zf_stmt_8, negated_conjecture,
% 0.55/1.05 (( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c8 ) ) |
% 0.55/1.05 ( ( inverse @ sk_c9 ) = ( sk_c8 ) )),
% 0.55/1.05 inference('cnf.neg', [status(esa)], [prove_this_5])).
% 0.55/1.05 thf(zip_derived_cl7, plain,
% 0.55/1.05 ((((multiply @ sk_c6 @ sk_c7) = (sk_c8)) | ((inverse @ sk_c9) = (sk_c8)))),
% 0.55/1.05 inference('cnf', [status(esa)], [zf_stmt_8])).
% 0.55/1.05 thf(zip_derived_cl58, plain,
% 0.55/1.05 ((((multiply @ sk_c6 @ (inverse @ sk_c6)) = (sk_c8))
% 0.55/1.05 | ((inverse @ sk_c9) = (sk_c8))
% 0.55/1.05 | ((inverse @ sk_c9) = (sk_c8)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl7])).
% 0.55/1.05 thf(zip_derived_cl59, plain,
% 0.55/1.05 ((((inverse @ sk_c9) = (sk_c8))
% 0.55/1.05 | ((multiply @ sk_c6 @ (inverse @ sk_c6)) = (sk_c8)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl58])).
% 0.55/1.05 thf(zip_derived_cl935, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl776, zip_derived_cl1])).
% 0.55/1.05 thf(zip_derived_cl1126, plain,
% 0.55/1.05 ((((inverse @ sk_c9) = (sk_c8)) | ((identity) = (sk_c8)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl59, zip_derived_cl935])).
% 0.55/1.05 thf(zip_derived_cl2175, plain,
% 0.55/1.05 ((((inverse @ sk_c9) = (sk_c9))
% 0.55/1.05 | ((identity) = (sk_c8))
% 0.55/1.05 | ((identity) = (sk_c8)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl2160, zip_derived_cl1126])).
% 0.55/1.05 thf(zip_derived_cl2183, plain,
% 0.55/1.05 ((((identity) = (sk_c8)) | ((inverse @ sk_c9) = (sk_c9)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl2175])).
% 0.55/1.05 thf(prove_this_36, conjecture,
% 0.55/1.05 (~( ( ( inverse @ sk_c4 ) = ( sk_c9 ) ) |
% 0.55/1.05 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 0.55/1.05 thf(zf_stmt_9, negated_conjecture,
% 0.55/1.05 (( ( inverse @ sk_c4 ) = ( sk_c9 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 0.55/1.05 inference('cnf.neg', [status(esa)], [prove_this_36])).
% 0.55/1.05 thf(zip_derived_cl38, plain,
% 0.55/1.05 ((((inverse @ sk_c4) = (sk_c9)) | ((inverse @ sk_c2) = (sk_c9)))),
% 0.55/1.05 inference('cnf', [status(esa)], [zf_stmt_9])).
% 0.55/1.05 thf(zip_derived_cl1, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.55/1.05 inference('cnf', [status(esa)], [left_inverse])).
% 0.55/1.05 thf(zip_derived_cl53, plain,
% 0.55/1.05 ((((multiply @ sk_c9 @ sk_c2) = (identity))
% 0.55/1.05 | ((inverse @ sk_c4) = (sk_c9)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl38, zip_derived_cl1])).
% 0.55/1.05 thf(zip_derived_cl105, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i]:
% 0.55/1.05 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl70, zip_derived_cl0])).
% 0.55/1.05 thf(zip_derived_cl136, plain,
% 0.55/1.05 ((((sk_c2) = (multiply @ (inverse @ sk_c9) @ identity))
% 0.55/1.05 | ((inverse @ sk_c4) = (sk_c9)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl53, zip_derived_cl105])).
% 0.55/1.05 thf(prove_this_29, conjecture,
% 0.55/1.05 (~( ( ( inverse @ sk_c4 ) = ( sk_c9 ) ) |
% 0.55/1.05 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c3 ) ) ))).
% 0.55/1.05 thf(zf_stmt_10, negated_conjecture,
% 0.55/1.05 (( ( inverse @ sk_c4 ) = ( sk_c9 ) ) |
% 0.55/1.05 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c3 ) )),
% 0.55/1.05 inference('cnf.neg', [status(esa)], [prove_this_29])).
% 0.55/1.05 thf(zip_derived_cl31, plain,
% 0.55/1.05 ((((inverse @ sk_c4) = (sk_c9)) | ((multiply @ sk_c2 @ sk_c9) = (sk_c3)))),
% 0.55/1.05 inference('cnf', [status(esa)], [zf_stmt_10])).
% 0.55/1.05 thf(zip_derived_cl402, plain,
% 0.55/1.05 ((((multiply @ (multiply @ (inverse @ sk_c9) @ identity) @ sk_c9)
% 0.55/1.05 = (sk_c3))
% 0.55/1.05 | ((inverse @ sk_c4) = (sk_c9))
% 0.55/1.05 | ((inverse @ sk_c4) = (sk_c9)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl136, zip_derived_cl31])).
% 0.55/1.05 thf(zip_derived_cl2, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/1.05 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.55/1.05 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.55/1.05 inference('cnf', [status(esa)], [associativity])).
% 0.55/1.05 thf(zip_derived_cl0, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.55/1.05 inference('cnf', [status(esa)], [left_identity])).
% 0.55/1.05 thf(zip_derived_cl1, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.55/1.05 inference('cnf', [status(esa)], [left_inverse])).
% 0.55/1.05 thf(zip_derived_cl420, plain,
% 0.55/1.05 ((((identity) = (sk_c3))
% 0.55/1.05 | ((inverse @ sk_c4) = (sk_c9))
% 0.55/1.05 | ((inverse @ sk_c4) = (sk_c9)))),
% 0.55/1.05 inference('demod', [status(thm)],
% 0.55/1.05 [zip_derived_cl402, zip_derived_cl2, zip_derived_cl0,
% 0.55/1.05 zip_derived_cl1])).
% 0.55/1.05 thf(zip_derived_cl421, plain,
% 0.55/1.05 ((((inverse @ sk_c4) = (sk_c9)) | ((identity) = (sk_c3)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl420])).
% 0.55/1.05 thf(prove_this_22, conjecture,
% 0.55/1.05 (~( ( ( inverse @ sk_c4 ) = ( sk_c9 ) ) |
% 0.55/1.05 ( ( multiply @ sk_c9 @ sk_c3 ) = ( sk_c8 ) ) ))).
% 0.55/1.05 thf(zf_stmt_11, negated_conjecture,
% 0.55/1.05 (( ( inverse @ sk_c4 ) = ( sk_c9 ) ) |
% 0.55/1.05 ( ( multiply @ sk_c9 @ sk_c3 ) = ( sk_c8 ) )),
% 0.55/1.05 inference('cnf.neg', [status(esa)], [prove_this_22])).
% 0.55/1.05 thf(zip_derived_cl24, plain,
% 0.55/1.05 ((((inverse @ sk_c4) = (sk_c9)) | ((multiply @ sk_c9 @ sk_c3) = (sk_c8)))),
% 0.55/1.05 inference('cnf', [status(esa)], [zf_stmt_11])).
% 0.55/1.05 thf(zip_derived_cl430, plain,
% 0.55/1.05 ((((multiply @ sk_c9 @ identity) = (sk_c8))
% 0.55/1.05 | ((inverse @ sk_c4) = (sk_c9))
% 0.55/1.05 | ((inverse @ sk_c4) = (sk_c9)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl421, zip_derived_cl24])).
% 0.55/1.05 thf(zip_derived_cl440, plain,
% 0.55/1.05 ((((inverse @ sk_c4) = (sk_c9))
% 0.55/1.05 | ((multiply @ sk_c9 @ identity) = (sk_c8)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl430])).
% 0.55/1.05 thf(zip_derived_cl121, plain,
% 0.55/1.05 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl105])).
% 0.55/1.05 thf(zip_derived_cl578, plain,
% 0.55/1.05 ((((sk_c4) = (multiply @ (inverse @ sk_c9) @ identity))
% 0.55/1.05 | ((multiply @ sk_c9 @ identity) = (sk_c8)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl440, zip_derived_cl121])).
% 0.55/1.05 thf(zip_derived_cl733, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl118])).
% 0.55/1.05 thf(zip_derived_cl733, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl118])).
% 0.55/1.05 thf(zip_derived_cl768, plain,
% 0.55/1.05 ((((sk_c4) = (inverse @ sk_c9)) | ((sk_c9) = (sk_c8)))),
% 0.55/1.05 inference('demod', [status(thm)],
% 0.55/1.05 [zip_derived_cl578, zip_derived_cl733, zip_derived_cl733])).
% 0.55/1.05 thf(prove_this_37, conjecture,
% 0.55/1.05 (~( ( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c9 ) ) |
% 0.55/1.05 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 0.55/1.05 thf(zf_stmt_12, negated_conjecture,
% 0.55/1.05 (( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c9 ) ) |
% 0.55/1.05 ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 0.55/1.05 inference('cnf.neg', [status(esa)], [prove_this_37])).
% 0.55/1.05 thf(zip_derived_cl39, plain,
% 0.55/1.05 ((((multiply @ sk_c4 @ sk_c8) = (sk_c9)) | ((inverse @ sk_c2) = (sk_c9)))),
% 0.55/1.05 inference('cnf', [status(esa)], [zf_stmt_12])).
% 0.55/1.05 thf(zip_derived_cl776, plain,
% 0.55/1.05 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl733, zip_derived_cl121])).
% 0.55/1.05 thf(zip_derived_cl952, plain,
% 0.55/1.05 ((((sk_c2) = (inverse @ sk_c9)) | ((multiply @ sk_c4 @ sk_c8) = (sk_c9)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl39, zip_derived_cl776])).
% 0.55/1.05 thf(prove_this_30, conjecture,
% 0.55/1.05 (~( ( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c9 ) ) |
% 0.55/1.05 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c3 ) ) ))).
% 0.55/1.05 thf(zf_stmt_13, negated_conjecture,
% 0.55/1.05 (( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c9 ) ) |
% 0.55/1.05 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c3 ) )),
% 0.55/1.05 inference('cnf.neg', [status(esa)], [prove_this_30])).
% 0.55/1.05 thf(zip_derived_cl32, plain,
% 0.55/1.05 ((((multiply @ sk_c4 @ sk_c8) = (sk_c9))
% 0.55/1.05 | ((multiply @ sk_c2 @ sk_c9) = (sk_c3)))),
% 0.55/1.05 inference('cnf', [status(esa)], [zf_stmt_13])).
% 0.55/1.05 thf(zip_derived_cl1333, plain,
% 0.55/1.05 ((((multiply @ (inverse @ sk_c9) @ sk_c9) = (sk_c3))
% 0.55/1.05 | ((multiply @ sk_c4 @ sk_c8) = (sk_c9))
% 0.55/1.05 | ((multiply @ sk_c4 @ sk_c8) = (sk_c9)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl952, zip_derived_cl32])).
% 0.55/1.05 thf(zip_derived_cl1, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.55/1.05 inference('cnf', [status(esa)], [left_inverse])).
% 0.55/1.05 thf(zip_derived_cl1355, plain,
% 0.55/1.05 ((((identity) = (sk_c3))
% 0.55/1.05 | ((multiply @ sk_c4 @ sk_c8) = (sk_c9))
% 0.55/1.05 | ((multiply @ sk_c4 @ sk_c8) = (sk_c9)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl1333, zip_derived_cl1])).
% 0.55/1.05 thf(zip_derived_cl1356, plain,
% 0.55/1.05 ((((multiply @ sk_c4 @ sk_c8) = (sk_c9)) | ((identity) = (sk_c3)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl1355])).
% 0.55/1.05 thf(prove_this_23, conjecture,
% 0.55/1.05 (~( ( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c9 ) ) |
% 0.55/1.05 ( ( multiply @ sk_c9 @ sk_c3 ) = ( sk_c8 ) ) ))).
% 0.55/1.05 thf(zf_stmt_14, negated_conjecture,
% 0.55/1.05 (( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c9 ) ) |
% 0.55/1.05 ( ( multiply @ sk_c9 @ sk_c3 ) = ( sk_c8 ) )),
% 0.55/1.05 inference('cnf.neg', [status(esa)], [prove_this_23])).
% 0.55/1.05 thf(zip_derived_cl25, plain,
% 0.55/1.05 ((((multiply @ sk_c4 @ sk_c8) = (sk_c9))
% 0.55/1.05 | ((multiply @ sk_c9 @ sk_c3) = (sk_c8)))),
% 0.55/1.05 inference('cnf', [status(esa)], [zf_stmt_14])).
% 0.55/1.05 thf(zip_derived_cl1380, plain,
% 0.55/1.05 ((((multiply @ sk_c9 @ identity) = (sk_c8))
% 0.55/1.05 | ((multiply @ sk_c4 @ sk_c8) = (sk_c9))
% 0.55/1.05 | ((multiply @ sk_c4 @ sk_c8) = (sk_c9)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl1356, zip_derived_cl25])).
% 0.55/1.05 thf(zip_derived_cl733, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl118])).
% 0.55/1.05 thf(zip_derived_cl1394, plain,
% 0.55/1.05 ((((sk_c9) = (sk_c8))
% 0.55/1.05 | ((multiply @ sk_c4 @ sk_c8) = (sk_c9))
% 0.55/1.05 | ((multiply @ sk_c4 @ sk_c8) = (sk_c9)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl1380, zip_derived_cl733])).
% 0.55/1.05 thf(zip_derived_cl1395, plain,
% 0.55/1.05 ((((multiply @ sk_c4 @ sk_c8) = (sk_c9)) | ((sk_c9) = (sk_c8)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl1394])).
% 0.55/1.05 thf(zip_derived_cl1569, plain,
% 0.55/1.05 ((((multiply @ (inverse @ sk_c9) @ sk_c8) = (sk_c9))
% 0.55/1.05 | ((sk_c9) = (sk_c8))
% 0.55/1.05 | ((sk_c9) = (sk_c8)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl768, zip_derived_cl1395])).
% 0.55/1.05 thf(zip_derived_cl1570, plain,
% 0.55/1.05 ((((sk_c9) = (sk_c8))
% 0.55/1.05 | ((multiply @ (inverse @ sk_c9) @ sk_c8) = (sk_c9)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl1569])).
% 0.55/1.05 thf(zip_derived_cl2419, plain,
% 0.55/1.05 ((((multiply @ (inverse @ sk_c9) @ identity) = (sk_c9))
% 0.55/1.05 | ((inverse @ sk_c9) = (sk_c9))
% 0.55/1.05 | ((sk_c9) = (sk_c8)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl2183, zip_derived_cl1570])).
% 0.55/1.05 thf(zip_derived_cl733, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl118])).
% 0.55/1.05 thf(zip_derived_cl2425, plain,
% 0.55/1.05 ((((inverse @ sk_c9) = (sk_c9))
% 0.55/1.05 | ((inverse @ sk_c9) = (sk_c9))
% 0.55/1.05 | ((sk_c9) = (sk_c8)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl2419, zip_derived_cl733])).
% 0.55/1.05 thf(zip_derived_cl2426, plain,
% 0.55/1.05 ((((sk_c9) = (sk_c8)) | ((inverse @ sk_c9) = (sk_c9)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl2425])).
% 0.55/1.05 thf(prove_this_1, conjecture,
% 0.55/1.05 (~( ( ( inverse @ sk_c4 ) = ( sk_c9 ) ) |
% 0.55/1.05 ( ( inverse @ sk_c9 ) = ( sk_c8 ) ) ))).
% 0.55/1.05 thf(zf_stmt_15, negated_conjecture,
% 0.55/1.05 (( ( inverse @ sk_c4 ) = ( sk_c9 ) ) | ( ( inverse @ sk_c9 ) = ( sk_c8 ) )),
% 0.55/1.05 inference('cnf.neg', [status(esa)], [prove_this_1])).
% 0.55/1.05 thf(zip_derived_cl3, plain,
% 0.55/1.05 ((((inverse @ sk_c4) = (sk_c9)) | ((inverse @ sk_c9) = (sk_c8)))),
% 0.55/1.05 inference('cnf', [status(esa)], [zf_stmt_15])).
% 0.55/1.05 thf(prove_this_2, conjecture,
% 0.55/1.05 (~( ( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c9 ) ) |
% 0.55/1.05 ( ( inverse @ sk_c9 ) = ( sk_c8 ) ) ))).
% 0.55/1.05 thf(zf_stmt_16, negated_conjecture,
% 0.55/1.05 (( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c9 ) ) |
% 0.55/1.05 ( ( inverse @ sk_c9 ) = ( sk_c8 ) )),
% 0.55/1.05 inference('cnf.neg', [status(esa)], [prove_this_2])).
% 0.55/1.05 thf(zip_derived_cl4, plain,
% 0.55/1.05 ((((multiply @ sk_c4 @ sk_c8) = (sk_c9)) | ((inverse @ sk_c9) = (sk_c8)))),
% 0.55/1.05 inference('cnf', [status(esa)], [zf_stmt_16])).
% 0.55/1.05 thf(zip_derived_cl105, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i]:
% 0.55/1.05 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl70, zip_derived_cl0])).
% 0.55/1.05 thf(zip_derived_cl140, plain,
% 0.55/1.05 ((((sk_c8) = (multiply @ (inverse @ sk_c4) @ sk_c9))
% 0.55/1.05 | ((inverse @ sk_c9) = (sk_c8)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl105])).
% 0.55/1.05 thf(zip_derived_cl622, plain,
% 0.55/1.05 ((((sk_c8) = (multiply @ sk_c9 @ sk_c9))
% 0.55/1.05 | ((inverse @ sk_c9) = (sk_c8))
% 0.55/1.05 | ((inverse @ sk_c9) = (sk_c8)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl140])).
% 0.55/1.05 thf(zip_derived_cl626, plain,
% 0.55/1.05 ((((inverse @ sk_c9) = (sk_c8)) | ((sk_c8) = (multiply @ sk_c9 @ sk_c9)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl622])).
% 0.55/1.05 thf(zip_derived_cl2442, plain,
% 0.55/1.05 ((((inverse @ sk_c9) = (sk_c9))
% 0.55/1.05 | ((inverse @ sk_c9) = (sk_c9))
% 0.55/1.05 | ((sk_c8) = (multiply @ sk_c9 @ sk_c9)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl2426, zip_derived_cl626])).
% 0.55/1.05 thf(zip_derived_cl2455, plain,
% 0.55/1.05 ((((sk_c8) = (multiply @ sk_c9 @ sk_c9)) | ((inverse @ sk_c9) = (sk_c9)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl2442])).
% 0.55/1.05 thf(zip_derived_cl2183, plain,
% 0.55/1.05 ((((identity) = (sk_c8)) | ((inverse @ sk_c9) = (sk_c9)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl2175])).
% 0.55/1.05 thf(zip_derived_cl2526, plain,
% 0.55/1.05 ((((identity) = (multiply @ sk_c9 @ sk_c9))
% 0.55/1.05 | ((inverse @ sk_c9) = (sk_c9))
% 0.55/1.05 | ((inverse @ sk_c9) = (sk_c9)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl2455, zip_derived_cl2183])).
% 0.55/1.05 thf(zip_derived_cl2530, plain,
% 0.55/1.05 ((((inverse @ sk_c9) = (sk_c9))
% 0.55/1.05 | ((identity) = (multiply @ sk_c9 @ sk_c9)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl2526])).
% 0.55/1.05 thf(zip_derived_cl1, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.55/1.05 inference('cnf', [status(esa)], [left_inverse])).
% 0.55/1.05 thf(zip_derived_cl2533, plain,
% 0.55/1.05 ((((multiply @ sk_c9 @ sk_c9) = (identity))
% 0.55/1.05 | ((identity) = (multiply @ sk_c9 @ sk_c9)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl2530, zip_derived_cl1])).
% 0.55/1.05 thf(zip_derived_cl2541, plain, (((multiply @ sk_c9 @ sk_c9) = (identity))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl2533])).
% 0.55/1.05 thf(zip_derived_cl105, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i]:
% 0.55/1.05 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl70, zip_derived_cl0])).
% 0.55/1.05 thf(zip_derived_cl2556, plain,
% 0.55/1.05 (((sk_c9) = (multiply @ (inverse @ sk_c9) @ identity))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl2541, zip_derived_cl105])).
% 0.55/1.05 thf(zip_derived_cl733, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl118])).
% 0.55/1.05 thf(zip_derived_cl2560, plain, (((sk_c9) = (inverse @ sk_c9))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl2556, zip_derived_cl733])).
% 0.55/1.05 thf(zip_derived_cl2560, plain, (((sk_c9) = (inverse @ sk_c9))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl2556, zip_derived_cl733])).
% 0.55/1.05 thf(zip_derived_cl2560, plain, (((sk_c9) = (inverse @ sk_c9))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl2556, zip_derived_cl733])).
% 0.55/1.05 thf(zip_derived_cl2560, plain, (((sk_c9) = (inverse @ sk_c9))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl2556, zip_derived_cl733])).
% 0.55/1.05 thf(zip_derived_cl2560, plain, (((sk_c9) = (inverse @ sk_c9))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl2556, zip_derived_cl733])).
% 0.55/1.05 thf(zip_derived_cl2560, plain, (((sk_c9) = (inverse @ sk_c9))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl2556, zip_derived_cl733])).
% 0.55/1.05 thf(zip_derived_cl2560, plain, (((sk_c9) = (inverse @ sk_c9))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl2556, zip_derived_cl733])).
% 0.55/1.05 thf(zip_derived_cl2560, plain, (((sk_c9) = (inverse @ sk_c9))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl2556, zip_derived_cl733])).
% 0.55/1.05 thf(zip_derived_cl2572, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 0.55/1.05 (((multiply @ X0 @ sk_c9) != (sk_c9))
% 0.55/1.05 | ((inverse @ X1) != (X0))
% 0.55/1.05 | ((multiply @ X1 @ X0) != (sk_c9))
% 0.55/1.05 | ((inverse @ X2) != (sk_c9))
% 0.55/1.05 | ((multiply @ X2 @ sk_c9) != (sk_c9))
% 0.55/1.05 | ((multiply @ X3 @ sk_c9) != (sk_c9))
% 0.55/1.05 | ((inverse @ X3) != (sk_c9))
% 0.55/1.05 | ((inverse @ X4) != (sk_c9))
% 0.55/1.05 | ((multiply @ X4 @ sk_c9) != (X5))
% 0.55/1.05 | ((multiply @ sk_c9 @ X5) != (sk_c9))
% 0.55/1.05 | ((multiply @ X6 @ sk_c9) != (sk_c9))
% 0.55/1.05 | ((inverse @ X6) != (sk_c9))
% 0.55/1.05 | ((sk_c9) != (sk_c8)))),
% 0.55/1.05 inference('demod', [status(thm)],
% 0.55/1.05 [zip_derived_cl46, zip_derived_cl2560, zip_derived_cl2560,
% 0.55/1.05 zip_derived_cl2560, zip_derived_cl2560, zip_derived_cl2560,
% 0.55/1.05 zip_derived_cl2560, zip_derived_cl2560, zip_derived_cl2560])).
% 0.55/1.05 thf(prove_this_13, conjecture,
% 0.55/1.05 (~( ( ( inverse @ sk_c6 ) = ( sk_c7 ) ) |
% 0.55/1.05 ( ( inverse @ sk_c1 ) = ( sk_c9 ) ) ))).
% 0.55/1.05 thf(zf_stmt_17, negated_conjecture,
% 0.55/1.05 (( ( inverse @ sk_c6 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c9 ) )),
% 0.55/1.05 inference('cnf.neg', [status(esa)], [prove_this_13])).
% 0.55/1.05 thf(zip_derived_cl15, plain,
% 0.55/1.05 ((((inverse @ sk_c6) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c9)))),
% 0.55/1.05 inference('cnf', [status(esa)], [zf_stmt_17])).
% 0.55/1.05 thf(zip_derived_cl1, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.55/1.05 inference('cnf', [status(esa)], [left_inverse])).
% 0.55/1.05 thf(zip_derived_cl49, plain,
% 0.55/1.05 ((((multiply @ sk_c9 @ sk_c1) = (identity))
% 0.55/1.05 | ((inverse @ sk_c6) = (sk_c7)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl15, zip_derived_cl1])).
% 0.55/1.05 thf(zip_derived_cl105, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i]:
% 0.55/1.05 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl70, zip_derived_cl0])).
% 0.55/1.05 thf(zip_derived_cl124, plain,
% 0.55/1.05 ((((sk_c1) = (multiply @ (inverse @ sk_c9) @ identity))
% 0.55/1.05 | ((inverse @ sk_c6) = (sk_c7)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl49, zip_derived_cl105])).
% 0.55/1.05 thf(zip_derived_cl733, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl118])).
% 0.55/1.05 thf(zip_derived_cl756, plain,
% 0.55/1.05 ((((sk_c1) = (inverse @ sk_c9)) | ((inverse @ sk_c6) = (sk_c7)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl124, zip_derived_cl733])).
% 0.55/1.05 thf(zip_derived_cl2160, plain,
% 0.55/1.05 ((((sk_c9) = (sk_c8)) | ((identity) = (sk_c8)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl2159])).
% 0.55/1.05 thf(prove_this_20, conjecture,
% 0.55/1.05 (~( ( ( inverse @ sk_c6 ) = ( sk_c7 ) ) |
% 0.55/1.05 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c9 ) ) ))).
% 0.55/1.05 thf(zf_stmt_18, negated_conjecture,
% 0.55/1.05 (( ( inverse @ sk_c6 ) = ( sk_c7 ) ) |
% 0.55/1.05 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c9 ) )),
% 0.55/1.05 inference('cnf.neg', [status(esa)], [prove_this_20])).
% 0.55/1.05 thf(zip_derived_cl22, plain,
% 0.55/1.05 ((((inverse @ sk_c6) = (sk_c7)) | ((multiply @ sk_c1 @ sk_c8) = (sk_c9)))),
% 0.55/1.05 inference('cnf', [status(esa)], [zf_stmt_18])).
% 0.55/1.05 thf(zip_derived_cl2168, plain,
% 0.55/1.05 ((((multiply @ sk_c1 @ sk_c9) = (sk_c9))
% 0.55/1.05 | ((identity) = (sk_c8))
% 0.55/1.05 | ((inverse @ sk_c6) = (sk_c7)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl2160, zip_derived_cl22])).
% 0.55/1.05 thf(zip_derived_cl2228, plain,
% 0.55/1.05 ((((multiply @ (inverse @ sk_c9) @ sk_c9) = (sk_c9))
% 0.55/1.05 | ((inverse @ sk_c6) = (sk_c7))
% 0.55/1.05 | ((inverse @ sk_c6) = (sk_c7))
% 0.55/1.05 | ((identity) = (sk_c8)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl756, zip_derived_cl2168])).
% 0.55/1.05 thf(zip_derived_cl1, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.55/1.05 inference('cnf', [status(esa)], [left_inverse])).
% 0.55/1.05 thf(zip_derived_cl2235, plain,
% 0.55/1.05 ((((identity) = (sk_c9))
% 0.55/1.05 | ((inverse @ sk_c6) = (sk_c7))
% 0.55/1.05 | ((inverse @ sk_c6) = (sk_c7))
% 0.55/1.05 | ((identity) = (sk_c8)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl2228, zip_derived_cl1])).
% 0.55/1.05 thf(zip_derived_cl2236, plain,
% 0.55/1.05 ((((identity) = (sk_c8))
% 0.55/1.05 | ((inverse @ sk_c6) = (sk_c7))
% 0.55/1.05 | ((identity) = (sk_c9)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl2235])).
% 0.55/1.05 thf(zip_derived_cl2160, plain,
% 0.55/1.05 ((((sk_c9) = (sk_c8)) | ((identity) = (sk_c8)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl2159])).
% 0.55/1.05 thf(zip_derived_cl2181, plain,
% 0.55/1.05 ((((sk_c9) != (identity)) | ((identity) = (sk_c8)))),
% 0.55/1.05 inference('eq_fact', [status(thm)], [zip_derived_cl2160])).
% 0.55/1.05 thf(zip_derived_cl2245, plain,
% 0.55/1.05 ((((inverse @ sk_c6) = (sk_c7)) | ((identity) = (sk_c8)))),
% 0.55/1.05 inference('clc', [status(thm)], [zip_derived_cl2236, zip_derived_cl2181])).
% 0.55/1.05 thf(prove_this_12, conjecture,
% 0.55/1.05 (~( ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c8 ) ) |
% 0.55/1.05 ( ( inverse @ sk_c1 ) = ( sk_c9 ) ) ))).
% 0.55/1.05 thf(zf_stmt_19, negated_conjecture,
% 0.55/1.05 (( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c8 ) ) |
% 0.55/1.05 ( ( inverse @ sk_c1 ) = ( sk_c9 ) )),
% 0.55/1.05 inference('cnf.neg', [status(esa)], [prove_this_12])).
% 0.55/1.05 thf(zip_derived_cl14, plain,
% 0.55/1.05 ((((multiply @ sk_c6 @ sk_c7) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c9)))),
% 0.55/1.05 inference('cnf', [status(esa)], [zf_stmt_19])).
% 0.55/1.05 thf(zip_derived_cl1, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.55/1.05 inference('cnf', [status(esa)], [left_inverse])).
% 0.55/1.05 thf(zip_derived_cl57, plain,
% 0.55/1.05 ((((multiply @ sk_c9 @ sk_c1) = (identity))
% 0.55/1.05 | ((multiply @ sk_c6 @ sk_c7) = (sk_c8)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl1])).
% 0.55/1.05 thf(zip_derived_cl105, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i]:
% 0.55/1.05 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl70, zip_derived_cl0])).
% 0.55/1.05 thf(zip_derived_cl127, plain,
% 0.55/1.05 ((((sk_c1) = (multiply @ (inverse @ sk_c9) @ identity))
% 0.55/1.05 | ((multiply @ sk_c6 @ sk_c7) = (sk_c8)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl57, zip_derived_cl105])).
% 0.55/1.05 thf(zip_derived_cl733, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl118])).
% 0.55/1.05 thf(zip_derived_cl759, plain,
% 0.55/1.05 ((((sk_c1) = (inverse @ sk_c9)) | ((multiply @ sk_c6 @ sk_c7) = (sk_c8)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl127, zip_derived_cl733])).
% 0.55/1.05 thf(zip_derived_cl2560, plain, (((sk_c9) = (inverse @ sk_c9))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl2556, zip_derived_cl733])).
% 0.55/1.05 thf(zip_derived_cl2595, plain,
% 0.55/1.05 ((((sk_c1) = (sk_c9)) | ((multiply @ sk_c6 @ sk_c7) = (sk_c8)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl759, zip_derived_cl2560])).
% 0.55/1.05 thf(prove_this_19, conjecture,
% 0.55/1.05 (~( ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c8 ) ) |
% 0.55/1.05 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c9 ) ) ))).
% 0.55/1.05 thf(zf_stmt_20, negated_conjecture,
% 0.55/1.05 (( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c8 ) ) |
% 0.55/1.05 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c9 ) )),
% 0.55/1.05 inference('cnf.neg', [status(esa)], [prove_this_19])).
% 0.55/1.05 thf(zip_derived_cl21, plain,
% 0.55/1.05 ((((multiply @ sk_c6 @ sk_c7) = (sk_c8))
% 0.55/1.05 | ((multiply @ sk_c1 @ sk_c8) = (sk_c9)))),
% 0.55/1.05 inference('cnf', [status(esa)], [zf_stmt_20])).
% 0.55/1.05 thf(zip_derived_cl3060, plain,
% 0.55/1.05 ((((multiply @ sk_c9 @ sk_c8) = (sk_c9))
% 0.55/1.05 | ((multiply @ sk_c6 @ sk_c7) = (sk_c8))
% 0.55/1.05 | ((multiply @ sk_c6 @ sk_c7) = (sk_c8)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl2595, zip_derived_cl21])).
% 0.55/1.05 thf(zip_derived_cl3083, plain,
% 0.55/1.05 ((((multiply @ sk_c6 @ sk_c7) = (sk_c8))
% 0.55/1.05 | ((multiply @ sk_c9 @ sk_c8) = (sk_c9)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl3060])).
% 0.55/1.05 thf(zip_derived_cl4807, plain,
% 0.55/1.05 ((((multiply @ sk_c6 @ (inverse @ sk_c6)) = (sk_c8))
% 0.55/1.05 | ((identity) = (sk_c8))
% 0.55/1.05 | ((multiply @ sk_c9 @ sk_c8) = (sk_c9)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl2245, zip_derived_cl3083])).
% 0.55/1.05 thf(zip_derived_cl935, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl776, zip_derived_cl1])).
% 0.55/1.05 thf(zip_derived_cl4812, plain,
% 0.55/1.05 ((((identity) = (sk_c8))
% 0.55/1.05 | ((identity) = (sk_c8))
% 0.55/1.05 | ((multiply @ sk_c9 @ sk_c8) = (sk_c9)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl4807, zip_derived_cl935])).
% 0.55/1.05 thf(zip_derived_cl4813, plain,
% 0.55/1.05 ((((multiply @ sk_c9 @ sk_c8) = (sk_c9)) | ((identity) = (sk_c8)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl4812])).
% 0.55/1.05 thf(zip_derived_cl105, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i]:
% 0.55/1.05 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl70, zip_derived_cl0])).
% 0.55/1.05 thf(zip_derived_cl4819, plain,
% 0.55/1.05 ((((sk_c8) = (multiply @ (inverse @ sk_c9) @ sk_c9))
% 0.55/1.05 | ((identity) = (sk_c8)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl4813, zip_derived_cl105])).
% 0.55/1.05 thf(zip_derived_cl2560, plain, (((sk_c9) = (inverse @ sk_c9))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl2556, zip_derived_cl733])).
% 0.55/1.05 thf(zip_derived_cl2541, plain, (((multiply @ sk_c9 @ sk_c9) = (identity))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl2533])).
% 0.55/1.05 thf(zip_derived_cl4828, plain,
% 0.55/1.05 ((((sk_c8) = (identity)) | ((identity) = (sk_c8)))),
% 0.55/1.05 inference('demod', [status(thm)],
% 0.55/1.05 [zip_derived_cl4819, zip_derived_cl2560, zip_derived_cl2541])).
% 0.55/1.05 thf(zip_derived_cl4829, plain, (((sk_c8) = (identity))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl4828])).
% 0.55/1.05 thf(zip_derived_cl4919, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 0.55/1.05 (((multiply @ X0 @ sk_c9) != (sk_c9))
% 0.55/1.05 | ((inverse @ X1) != (X0))
% 0.55/1.05 | ((multiply @ X1 @ X0) != (sk_c9))
% 0.55/1.05 | ((inverse @ X2) != (sk_c9))
% 0.55/1.05 | ((multiply @ X2 @ sk_c9) != (sk_c9))
% 0.55/1.05 | ((multiply @ X3 @ sk_c9) != (sk_c9))
% 0.55/1.05 | ((inverse @ X3) != (sk_c9))
% 0.55/1.05 | ((inverse @ X4) != (sk_c9))
% 0.55/1.05 | ((multiply @ X4 @ sk_c9) != (X5))
% 0.55/1.05 | ((multiply @ sk_c9 @ X5) != (sk_c9))
% 0.55/1.05 | ((multiply @ X6 @ sk_c9) != (sk_c9))
% 0.55/1.05 | ((inverse @ X6) != (sk_c9))
% 0.55/1.05 | ((sk_c9) != (identity)))),
% 0.55/1.05 inference('demod', [status(thm)],
% 0.55/1.05 [zip_derived_cl2572, zip_derived_cl4829])).
% 0.55/1.05 thf(zip_derived_cl4920, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 0.55/1.05 (((multiply @ X0 @ identity) != (identity))
% 0.55/1.05 | ((inverse @ X1) != (X0))
% 0.55/1.05 | ((multiply @ X1 @ X0) != (identity))
% 0.55/1.05 | ((inverse @ X2) != (identity))
% 0.55/1.05 | ((multiply @ X2 @ identity) != (identity))
% 0.55/1.05 | ((multiply @ X3 @ identity) != (identity))
% 0.55/1.05 | ((inverse @ X3) != (identity))
% 0.55/1.05 | ((inverse @ X4) != (identity))
% 0.55/1.05 | ((multiply @ X4 @ identity) != (X5))
% 0.55/1.05 | ((multiply @ identity @ X5) != (identity))
% 0.55/1.05 | ((multiply @ X6 @ identity) != (identity))
% 0.55/1.05 | ((inverse @ X6) != (identity))
% 0.55/1.05 | ((sk_c9) != (identity)))),
% 0.55/1.05 inference('local_rewriting', [status(thm)], [zip_derived_cl4919])).
% 0.55/1.05 thf(zip_derived_cl733, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl118])).
% 0.55/1.05 thf(zip_derived_cl733, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl118])).
% 0.55/1.05 thf(zip_derived_cl733, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl118])).
% 0.55/1.05 thf(zip_derived_cl733, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl118])).
% 0.55/1.05 thf(zip_derived_cl0, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.55/1.05 inference('cnf', [status(esa)], [left_identity])).
% 0.55/1.05 thf(zip_derived_cl733, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl118])).
% 0.55/1.05 thf(zip_derived_cl4921, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 0.55/1.05 (((X0) != (identity))
% 0.55/1.05 | ((inverse @ X1) != (X0))
% 0.55/1.05 | ((multiply @ X1 @ X0) != (identity))
% 0.55/1.05 | ((inverse @ X2) != (identity))
% 0.55/1.05 | ((X2) != (identity))
% 0.55/1.05 | ((X3) != (identity))
% 0.55/1.05 | ((inverse @ X3) != (identity))
% 0.55/1.05 | ((inverse @ X4) != (identity))
% 0.55/1.05 | ((X4) != (X5))
% 0.55/1.05 | ((X5) != (identity))
% 0.55/1.05 | ((X6) != (identity))
% 0.55/1.05 | ((inverse @ X6) != (identity))
% 0.55/1.05 | ((sk_c9) != (identity)))),
% 0.55/1.05 inference('demod', [status(thm)],
% 0.55/1.05 [zip_derived_cl4920, zip_derived_cl733, zip_derived_cl733,
% 0.55/1.05 zip_derived_cl733, zip_derived_cl733, zip_derived_cl0,
% 0.55/1.05 zip_derived_cl733])).
% 0.55/1.05 thf(prove_this_39, conjecture,
% 0.55/1.05 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 0.55/1.05 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 0.55/1.05 thf(zf_stmt_21, negated_conjecture,
% 0.55/1.05 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 0.55/1.05 inference('cnf.neg', [status(esa)], [prove_this_39])).
% 0.55/1.05 thf(zip_derived_cl41, plain,
% 0.55/1.05 ((((inverse @ sk_c5) = (sk_c8)) | ((inverse @ sk_c2) = (sk_c9)))),
% 0.55/1.05 inference('cnf', [status(esa)], [zf_stmt_21])).
% 0.55/1.05 thf(zip_derived_cl1, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.55/1.05 inference('cnf', [status(esa)], [left_inverse])).
% 0.55/1.05 thf(zip_derived_cl54, plain,
% 0.55/1.05 ((((multiply @ sk_c9 @ sk_c2) = (identity))
% 0.55/1.05 | ((inverse @ sk_c5) = (sk_c8)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl1])).
% 0.55/1.05 thf(zip_derived_cl105, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i]:
% 0.55/1.05 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl70, zip_derived_cl0])).
% 0.55/1.05 thf(zip_derived_cl137, plain,
% 0.55/1.05 ((((sk_c2) = (multiply @ (inverse @ sk_c9) @ identity))
% 0.55/1.05 | ((inverse @ sk_c5) = (sk_c8)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl54, zip_derived_cl105])).
% 0.55/1.05 thf(prove_this_32, conjecture,
% 0.55/1.05 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 0.55/1.05 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c3 ) ) ))).
% 0.55/1.05 thf(zf_stmt_22, negated_conjecture,
% 0.55/1.05 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 0.55/1.05 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c3 ) )),
% 0.55/1.05 inference('cnf.neg', [status(esa)], [prove_this_32])).
% 0.55/1.05 thf(zip_derived_cl34, plain,
% 0.55/1.05 ((((inverse @ sk_c5) = (sk_c8)) | ((multiply @ sk_c2 @ sk_c9) = (sk_c3)))),
% 0.55/1.05 inference('cnf', [status(esa)], [zf_stmt_22])).
% 0.55/1.05 thf(zip_derived_cl300, plain,
% 0.55/1.05 ((((multiply @ (multiply @ (inverse @ sk_c9) @ identity) @ sk_c9)
% 0.55/1.05 = (sk_c3))
% 0.55/1.05 | ((inverse @ sk_c5) = (sk_c8))
% 0.55/1.05 | ((inverse @ sk_c5) = (sk_c8)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl137, zip_derived_cl34])).
% 0.55/1.05 thf(zip_derived_cl2, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/1.05 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.55/1.05 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.55/1.05 inference('cnf', [status(esa)], [associativity])).
% 0.55/1.05 thf(zip_derived_cl0, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.55/1.05 inference('cnf', [status(esa)], [left_identity])).
% 0.55/1.05 thf(zip_derived_cl1, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.55/1.05 inference('cnf', [status(esa)], [left_inverse])).
% 0.55/1.05 thf(zip_derived_cl318, plain,
% 0.55/1.05 ((((identity) = (sk_c3))
% 0.55/1.05 | ((inverse @ sk_c5) = (sk_c8))
% 0.55/1.05 | ((inverse @ sk_c5) = (sk_c8)))),
% 0.55/1.05 inference('demod', [status(thm)],
% 0.55/1.05 [zip_derived_cl300, zip_derived_cl2, zip_derived_cl0,
% 0.55/1.05 zip_derived_cl1])).
% 0.55/1.05 thf(zip_derived_cl319, plain,
% 0.55/1.05 ((((inverse @ sk_c5) = (sk_c8)) | ((identity) = (sk_c3)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl318])).
% 0.55/1.05 thf(prove_this_25, conjecture,
% 0.55/1.05 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 0.55/1.05 ( ( multiply @ sk_c9 @ sk_c3 ) = ( sk_c8 ) ) ))).
% 0.55/1.05 thf(zf_stmt_23, negated_conjecture,
% 0.55/1.05 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 0.55/1.05 ( ( multiply @ sk_c9 @ sk_c3 ) = ( sk_c8 ) )),
% 0.55/1.05 inference('cnf.neg', [status(esa)], [prove_this_25])).
% 0.55/1.05 thf(zip_derived_cl27, plain,
% 0.55/1.05 ((((inverse @ sk_c5) = (sk_c8)) | ((multiply @ sk_c9 @ sk_c3) = (sk_c8)))),
% 0.55/1.05 inference('cnf', [status(esa)], [zf_stmt_23])).
% 0.55/1.05 thf(zip_derived_cl328, plain,
% 0.55/1.05 ((((multiply @ sk_c9 @ identity) = (sk_c8))
% 0.55/1.05 | ((inverse @ sk_c5) = (sk_c8))
% 0.55/1.05 | ((inverse @ sk_c5) = (sk_c8)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl319, zip_derived_cl27])).
% 0.55/1.05 thf(zip_derived_cl333, plain,
% 0.55/1.05 ((((inverse @ sk_c5) = (sk_c8))
% 0.55/1.05 | ((multiply @ sk_c9 @ identity) = (sk_c8)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl328])).
% 0.55/1.05 thf(zip_derived_cl121, plain,
% 0.55/1.05 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl105])).
% 0.55/1.05 thf(zip_derived_cl580, plain,
% 0.55/1.05 ((((sk_c5) = (multiply @ (inverse @ sk_c8) @ identity))
% 0.55/1.05 | ((multiply @ sk_c9 @ identity) = (sk_c8)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl333, zip_derived_cl121])).
% 0.55/1.05 thf(zip_derived_cl733, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl118])).
% 0.55/1.05 thf(zip_derived_cl733, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl118])).
% 0.55/1.05 thf(zip_derived_cl769, plain,
% 0.55/1.05 ((((sk_c5) = (inverse @ sk_c8)) | ((sk_c9) = (sk_c8)))),
% 0.55/1.05 inference('demod', [status(thm)],
% 0.55/1.05 [zip_derived_cl580, zip_derived_cl733, zip_derived_cl733])).
% 0.55/1.05 thf(prove_this_38, conjecture,
% 0.55/1.05 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c9 ) ) |
% 0.55/1.05 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 0.55/1.05 thf(zf_stmt_24, negated_conjecture,
% 0.55/1.05 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c9 ) ) |
% 0.55/1.05 ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 0.55/1.05 inference('cnf.neg', [status(esa)], [prove_this_38])).
% 0.55/1.05 thf(zip_derived_cl40, plain,
% 0.55/1.05 ((((multiply @ sk_c5 @ sk_c8) = (sk_c9)) | ((inverse @ sk_c2) = (sk_c9)))),
% 0.55/1.05 inference('cnf', [status(esa)], [zf_stmt_24])).
% 0.55/1.05 thf(zip_derived_cl776, plain,
% 0.55/1.05 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl733, zip_derived_cl121])).
% 0.55/1.05 thf(zip_derived_cl953, plain,
% 0.55/1.05 ((((sk_c2) = (inverse @ sk_c9)) | ((multiply @ sk_c5 @ sk_c8) = (sk_c9)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl776])).
% 0.55/1.05 thf(prove_this_31, conjecture,
% 0.55/1.05 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c9 ) ) |
% 0.55/1.05 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c3 ) ) ))).
% 0.55/1.05 thf(zf_stmt_25, negated_conjecture,
% 0.55/1.05 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c9 ) ) |
% 0.55/1.05 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c3 ) )),
% 0.55/1.05 inference('cnf.neg', [status(esa)], [prove_this_31])).
% 0.55/1.05 thf(zip_derived_cl33, plain,
% 0.55/1.05 ((((multiply @ sk_c5 @ sk_c8) = (sk_c9))
% 0.55/1.05 | ((multiply @ sk_c2 @ sk_c9) = (sk_c3)))),
% 0.55/1.05 inference('cnf', [status(esa)], [zf_stmt_25])).
% 0.55/1.05 thf(zip_derived_cl1405, plain,
% 0.55/1.05 ((((multiply @ (inverse @ sk_c9) @ sk_c9) = (sk_c3))
% 0.55/1.05 | ((multiply @ sk_c5 @ sk_c8) = (sk_c9))
% 0.55/1.05 | ((multiply @ sk_c5 @ sk_c8) = (sk_c9)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl953, zip_derived_cl33])).
% 0.55/1.05 thf(zip_derived_cl1, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.55/1.05 inference('cnf', [status(esa)], [left_inverse])).
% 0.55/1.05 thf(zip_derived_cl1427, plain,
% 0.55/1.05 ((((identity) = (sk_c3))
% 0.55/1.05 | ((multiply @ sk_c5 @ sk_c8) = (sk_c9))
% 0.55/1.05 | ((multiply @ sk_c5 @ sk_c8) = (sk_c9)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl1405, zip_derived_cl1])).
% 0.55/1.05 thf(zip_derived_cl1428, plain,
% 0.55/1.05 ((((multiply @ sk_c5 @ sk_c8) = (sk_c9)) | ((identity) = (sk_c3)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl1427])).
% 0.55/1.05 thf(prove_this_24, conjecture,
% 0.55/1.05 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c9 ) ) |
% 0.55/1.05 ( ( multiply @ sk_c9 @ sk_c3 ) = ( sk_c8 ) ) ))).
% 0.55/1.05 thf(zf_stmt_26, negated_conjecture,
% 0.55/1.05 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c9 ) ) |
% 0.55/1.05 ( ( multiply @ sk_c9 @ sk_c3 ) = ( sk_c8 ) )),
% 0.55/1.05 inference('cnf.neg', [status(esa)], [prove_this_24])).
% 0.55/1.05 thf(zip_derived_cl26, plain,
% 0.55/1.05 ((((multiply @ sk_c5 @ sk_c8) = (sk_c9))
% 0.55/1.05 | ((multiply @ sk_c9 @ sk_c3) = (sk_c8)))),
% 0.55/1.05 inference('cnf', [status(esa)], [zf_stmt_26])).
% 0.55/1.05 thf(zip_derived_cl1452, plain,
% 0.55/1.05 ((((multiply @ sk_c9 @ identity) = (sk_c8))
% 0.55/1.05 | ((multiply @ sk_c5 @ sk_c8) = (sk_c9))
% 0.55/1.05 | ((multiply @ sk_c5 @ sk_c8) = (sk_c9)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl1428, zip_derived_cl26])).
% 0.55/1.05 thf(zip_derived_cl733, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl118])).
% 0.55/1.05 thf(zip_derived_cl1466, plain,
% 0.55/1.05 ((((sk_c9) = (sk_c8))
% 0.55/1.05 | ((multiply @ sk_c5 @ sk_c8) = (sk_c9))
% 0.55/1.05 | ((multiply @ sk_c5 @ sk_c8) = (sk_c9)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl1452, zip_derived_cl733])).
% 0.55/1.05 thf(zip_derived_cl1467, plain,
% 0.55/1.05 ((((multiply @ sk_c5 @ sk_c8) = (sk_c9)) | ((sk_c9) = (sk_c8)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl1466])).
% 0.55/1.05 thf(zip_derived_cl1578, plain,
% 0.55/1.05 ((((multiply @ (inverse @ sk_c8) @ sk_c8) = (sk_c9))
% 0.55/1.05 | ((sk_c9) = (sk_c8))
% 0.55/1.05 | ((sk_c9) = (sk_c8)))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl769, zip_derived_cl1467])).
% 0.55/1.05 thf(zip_derived_cl1, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.55/1.05 inference('cnf', [status(esa)], [left_inverse])).
% 0.55/1.05 thf(zip_derived_cl1580, plain,
% 0.55/1.05 ((((identity) = (sk_c9)) | ((sk_c9) = (sk_c8)) | ((sk_c9) = (sk_c8)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl1578, zip_derived_cl1])).
% 0.55/1.05 thf(zip_derived_cl1581, plain,
% 0.55/1.05 ((((sk_c9) = (sk_c8)) | ((identity) = (sk_c9)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl1580])).
% 0.55/1.05 thf(zip_derived_cl4829, plain, (((sk_c8) = (identity))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl4828])).
% 0.55/1.05 thf(zip_derived_cl4908, plain,
% 0.55/1.05 ((((sk_c9) = (identity)) | ((identity) = (sk_c9)))),
% 0.55/1.05 inference('demod', [status(thm)],
% 0.55/1.05 [zip_derived_cl1581, zip_derived_cl4829])).
% 0.55/1.05 thf(zip_derived_cl4909, plain, (((sk_c9) = (identity))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl4908])).
% 0.55/1.05 thf(zip_derived_cl4994, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 0.55/1.05 (((X0) != (identity))
% 0.55/1.05 | ((inverse @ X1) != (X0))
% 0.55/1.05 | ((multiply @ X1 @ X0) != (identity))
% 0.55/1.05 | ((inverse @ X2) != (identity))
% 0.55/1.05 | ((X2) != (identity))
% 0.55/1.05 | ((X3) != (identity))
% 0.55/1.05 | ((inverse @ X3) != (identity))
% 0.55/1.05 | ((inverse @ X4) != (identity))
% 0.55/1.05 | ((X4) != (X5))
% 0.55/1.05 | ((X5) != (identity))
% 0.55/1.05 | ((X6) != (identity))
% 0.55/1.05 | ((inverse @ X6) != (identity))
% 0.55/1.05 | ((identity) != (identity)))),
% 0.55/1.05 inference('demod', [status(thm)],
% 0.55/1.05 [zip_derived_cl4921, zip_derived_cl4909])).
% 0.55/1.05 thf(zip_derived_cl4995, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 0.55/1.05 (((inverse @ X6) != (identity))
% 0.55/1.05 | ((X6) != (identity))
% 0.55/1.05 | ((X5) != (identity))
% 0.55/1.05 | ((X4) != (X5))
% 0.55/1.05 | ((inverse @ X4) != (identity))
% 0.55/1.05 | ((inverse @ X3) != (identity))
% 0.55/1.05 | ((X3) != (identity))
% 0.55/1.05 | ((X2) != (identity))
% 0.55/1.05 | ((inverse @ X2) != (identity))
% 0.55/1.05 | ((multiply @ X1 @ X0) != (identity))
% 0.55/1.05 | ((inverse @ X1) != (X0))
% 0.55/1.05 | ((X0) != (identity)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl4994])).
% 0.55/1.05 thf(zip_derived_cl4996, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 0.55/1.05 (((X0) != (identity))
% 0.55/1.05 | ((inverse @ X1) != (X0))
% 0.55/1.05 | ((multiply @ X1 @ X0) != (identity))
% 0.55/1.05 | ((inverse @ X2) != (identity))
% 0.55/1.05 | ((X2) != (identity))
% 0.55/1.05 | ((X3) != (identity))
% 0.55/1.05 | ((inverse @ X3) != (identity))
% 0.55/1.05 | ((inverse @ X4) != (identity))
% 0.55/1.05 | ((X4) != (identity))
% 0.55/1.05 | ((X5) != (identity))
% 0.55/1.05 | ((inverse @ X5) != (identity)))),
% 0.55/1.05 inference('eq_res', [status(thm)], [zip_derived_cl4995])).
% 0.55/1.05 thf(zip_derived_cl4997, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.55/1.05 (((inverse @ X0) != (identity))
% 0.55/1.05 | ((X0) != (identity))
% 0.55/1.05 | ((X1) != (identity))
% 0.55/1.05 | ((inverse @ X1) != (identity))
% 0.55/1.05 | ((inverse @ X2) != (identity))
% 0.55/1.05 | ((X2) != (identity))
% 0.55/1.05 | ((X3) != (identity))
% 0.55/1.05 | ((inverse @ X3) != (identity))
% 0.55/1.05 | ((multiply @ X4 @ identity) != (identity))
% 0.55/1.05 | ((inverse @ X4) != (identity)))),
% 0.55/1.05 inference('eq_res', [status(thm)], [zip_derived_cl4996])).
% 0.55/1.05 thf(zip_derived_cl733, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl118])).
% 0.55/1.05 thf(zip_derived_cl4998, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.55/1.05 (((inverse @ X0) != (identity))
% 0.55/1.05 | ((X0) != (identity))
% 0.55/1.05 | ((X1) != (identity))
% 0.55/1.05 | ((inverse @ X1) != (identity))
% 0.55/1.05 | ((inverse @ X2) != (identity))
% 0.55/1.05 | ((X2) != (identity))
% 0.55/1.05 | ((X3) != (identity))
% 0.55/1.05 | ((inverse @ X3) != (identity))
% 0.55/1.05 | ((X4) != (identity))
% 0.55/1.05 | ((inverse @ X4) != (identity)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl4997, zip_derived_cl733])).
% 0.55/1.05 thf(zip_derived_cl4999, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/1.05 (((inverse @ X0) != (identity))
% 0.55/1.05 | ((X0) != (identity))
% 0.55/1.05 | ((inverse @ X1) != (identity))
% 0.55/1.05 | ((X1) != (identity))
% 0.55/1.05 | ((X2) != (identity))
% 0.55/1.05 | ((inverse @ X2) != (identity))
% 0.55/1.05 | ((inverse @ X3) != (identity))
% 0.55/1.05 | ((X3) != (identity))
% 0.55/1.05 | ((inverse @ identity) != (identity)))),
% 0.55/1.05 inference('eq_res', [status(thm)], [zip_derived_cl4998])).
% 0.55/1.05 thf(zip_derived_cl0, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.55/1.05 inference('cnf', [status(esa)], [left_identity])).
% 0.55/1.05 thf(zip_derived_cl105, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i]:
% 0.55/1.05 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl70, zip_derived_cl0])).
% 0.55/1.05 thf(zip_derived_cl120, plain,
% 0.55/1.05 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl105])).
% 0.55/1.05 thf(zip_derived_cl105, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i]:
% 0.55/1.05 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl70, zip_derived_cl0])).
% 0.55/1.05 thf(zip_derived_cl174, plain,
% 0.55/1.05 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ identity)) @ X0))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl120, zip_derived_cl105])).
% 0.55/1.05 thf(zip_derived_cl1, plain,
% 0.55/1.05 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.55/1.05 inference('cnf', [status(esa)], [left_inverse])).
% 0.55/1.05 thf(zip_derived_cl720, plain, (((inverse @ identity) = (identity))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl174, zip_derived_cl1])).
% 0.55/1.05 thf(zip_derived_cl5000, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/1.05 (((inverse @ X0) != (identity))
% 0.55/1.05 | ((X0) != (identity))
% 0.55/1.05 | ((inverse @ X1) != (identity))
% 0.55/1.05 | ((X1) != (identity))
% 0.55/1.05 | ((X2) != (identity))
% 0.55/1.05 | ((inverse @ X2) != (identity))
% 0.55/1.05 | ((inverse @ X3) != (identity))
% 0.55/1.05 | ((X3) != (identity))
% 0.55/1.05 | ((identity) != (identity)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl4999, zip_derived_cl720])).
% 0.55/1.05 thf(zip_derived_cl5001, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/1.05 (((X3) != (identity))
% 0.55/1.05 | ((inverse @ X3) != (identity))
% 0.55/1.05 | ((inverse @ X2) != (identity))
% 0.55/1.05 | ((X2) != (identity))
% 0.55/1.05 | ((X1) != (identity))
% 0.55/1.05 | ((inverse @ X1) != (identity))
% 0.55/1.05 | ((X0) != (identity))
% 0.55/1.05 | ((inverse @ X0) != (identity)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl5000])).
% 0.55/1.05 thf(zip_derived_cl5002, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/1.05 (((inverse @ X0) != (identity))
% 0.55/1.05 | ((X0) != (identity))
% 0.55/1.05 | ((inverse @ X1) != (identity))
% 0.55/1.05 | ((X1) != (identity))
% 0.55/1.05 | ((X2) != (identity))
% 0.55/1.05 | ((inverse @ X2) != (identity))
% 0.55/1.05 | ((inverse @ identity) != (identity)))),
% 0.55/1.05 inference('eq_res', [status(thm)], [zip_derived_cl5001])).
% 0.55/1.05 thf(zip_derived_cl720, plain, (((inverse @ identity) = (identity))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl174, zip_derived_cl1])).
% 0.55/1.05 thf(zip_derived_cl5003, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/1.05 (((inverse @ X0) != (identity))
% 0.55/1.05 | ((X0) != (identity))
% 0.55/1.05 | ((inverse @ X1) != (identity))
% 0.55/1.05 | ((X1) != (identity))
% 0.55/1.05 | ((X2) != (identity))
% 0.55/1.05 | ((inverse @ X2) != (identity))
% 0.55/1.05 | ((identity) != (identity)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl5002, zip_derived_cl720])).
% 0.55/1.05 thf(zip_derived_cl5004, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/1.05 (((inverse @ X2) != (identity))
% 0.55/1.05 | ((X2) != (identity))
% 0.55/1.05 | ((X1) != (identity))
% 0.55/1.05 | ((inverse @ X1) != (identity))
% 0.55/1.05 | ((X0) != (identity))
% 0.55/1.05 | ((inverse @ X0) != (identity)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl5003])).
% 0.55/1.05 thf(zip_derived_cl5005, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i]:
% 0.55/1.05 (((inverse @ X0) != (identity))
% 0.55/1.05 | ((X0) != (identity))
% 0.55/1.05 | ((inverse @ X1) != (identity))
% 0.55/1.05 | ((X1) != (identity))
% 0.55/1.05 | ((inverse @ identity) != (identity)))),
% 0.55/1.05 inference('eq_res', [status(thm)], [zip_derived_cl5004])).
% 0.55/1.05 thf(zip_derived_cl720, plain, (((inverse @ identity) = (identity))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl174, zip_derived_cl1])).
% 0.55/1.05 thf(zip_derived_cl5006, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i]:
% 0.55/1.05 (((inverse @ X0) != (identity))
% 0.55/1.05 | ((X0) != (identity))
% 0.55/1.05 | ((inverse @ X1) != (identity))
% 0.55/1.05 | ((X1) != (identity))
% 0.55/1.05 | ((identity) != (identity)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl5005, zip_derived_cl720])).
% 0.55/1.05 thf(zip_derived_cl5007, plain,
% 0.55/1.05 (![X0 : $i, X1 : $i]:
% 0.55/1.05 (((X1) != (identity))
% 0.55/1.05 | ((inverse @ X1) != (identity))
% 0.55/1.05 | ((X0) != (identity))
% 0.55/1.05 | ((inverse @ X0) != (identity)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl5006])).
% 0.55/1.05 thf(zip_derived_cl5038, plain,
% 0.55/1.05 (![X0 : $i]:
% 0.55/1.05 (((inverse @ X0) != (identity))
% 0.55/1.05 | ((X0) != (identity))
% 0.55/1.05 | ((inverse @ identity) != (identity)))),
% 0.55/1.05 inference('eq_res', [status(thm)], [zip_derived_cl5007])).
% 0.55/1.05 thf(zip_derived_cl720, plain, (((inverse @ identity) = (identity))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl174, zip_derived_cl1])).
% 0.55/1.05 thf(zip_derived_cl5039, plain,
% 0.55/1.05 (![X0 : $i]:
% 0.55/1.05 (((inverse @ X0) != (identity))
% 0.55/1.05 | ((X0) != (identity))
% 0.55/1.05 | ((identity) != (identity)))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl5038, zip_derived_cl720])).
% 0.55/1.05 thf(zip_derived_cl5040, plain,
% 0.55/1.05 (![X0 : $i]: (((X0) != (identity)) | ((inverse @ X0) != (identity)))),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl5039])).
% 0.55/1.05 thf(zip_derived_cl5041, plain, (((inverse @ identity) != (identity))),
% 0.55/1.05 inference('eq_res', [status(thm)], [zip_derived_cl5040])).
% 0.55/1.05 thf(zip_derived_cl720, plain, (((inverse @ identity) = (identity))),
% 0.55/1.05 inference('sup+', [status(thm)], [zip_derived_cl174, zip_derived_cl1])).
% 0.55/1.05 thf(zip_derived_cl5042, plain, (((identity) != (identity))),
% 0.55/1.05 inference('demod', [status(thm)], [zip_derived_cl5041, zip_derived_cl720])).
% 0.55/1.05 thf(zip_derived_cl5043, plain, ($false),
% 0.55/1.05 inference('simplify', [status(thm)], [zip_derived_cl5042])).
% 0.55/1.05
% 0.55/1.05 % SZS output end Refutation
% 0.55/1.05
% 0.55/1.05
% 0.55/1.05 % Terminating...
% 1.74/1.15 % Runner terminated.
% 1.74/1.16 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------