TSTP Solution File: GRP334-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP334-1 : 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.KL2iofu7la true
% Computer : n010.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 01:51:14 EDT 2023
% Result : Unsatisfiable 7.70s 1.75s
% Output : Refutation 7.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP334-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.KL2iofu7la true
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Aug 28 22:12:49 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Running portfolio for 300 s
% 0.14/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in FO mode
% 0.22/0.68 % Total configuration time : 435
% 0.22/0.68 % Estimated wc time : 1092
% 0.22/0.68 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.74 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.75 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.75 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.77 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.97/0.82 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 7.70/1.75 % Solved by fo/fo3_bce.sh.
% 7.70/1.75 % BCE start: 25
% 7.70/1.75 % BCE eliminated: 0
% 7.70/1.75 % PE start: 25
% 7.70/1.75 logic: eq
% 7.70/1.75 % PE eliminated: 0
% 7.70/1.75 % done 2329 iterations in 0.975s
% 7.70/1.75 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 7.70/1.75 % SZS output start Refutation
% 7.70/1.75 thf(sk_c2_type, type, sk_c2: $i).
% 7.70/1.75 thf(sk_c5_type, type, sk_c5: $i).
% 7.70/1.75 thf(sk_c3_type, type, sk_c3: $i).
% 7.70/1.75 thf(sk_c4_type, type, sk_c4: $i).
% 7.70/1.75 thf(identity_type, type, identity: $i).
% 7.70/1.75 thf(multiply_type, type, multiply: $i > $i > $i).
% 7.70/1.75 thf(sk_c7_type, type, sk_c7: $i).
% 7.70/1.75 thf(inverse_type, type, inverse: $i > $i).
% 7.70/1.75 thf(sk_c1_type, type, sk_c1: $i).
% 7.70/1.75 thf(sk_c6_type, type, sk_c6: $i).
% 7.70/1.75 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 7.70/1.75 thf(zip_derived_cl0, plain,
% 7.70/1.75 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 7.70/1.75 inference('cnf', [status(esa)], [left_identity])).
% 7.70/1.75 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 7.70/1.75 thf(zip_derived_cl1, plain,
% 7.70/1.75 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 7.70/1.75 inference('cnf', [status(esa)], [left_inverse])).
% 7.70/1.75 thf(zip_derived_cl0, plain,
% 7.70/1.75 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 7.70/1.75 inference('cnf', [status(esa)], [left_identity])).
% 7.70/1.75 thf(prove_this_22, conjecture,
% 7.70/1.75 (~( ( ( inverse @ X2 ) != ( sk_c6 ) ) |
% 7.70/1.75 ( ( multiply @ X2 @ sk_c6 ) != ( X1 ) ) |
% 7.70/1.75 ( ( multiply @ sk_c6 @ X1 ) != ( sk_c5 ) ) |
% 7.70/1.75 ( ( inverse @ sk_c7 ) != ( sk_c5 ) ) |
% 7.70/1.75 ( ( inverse @ sk_c6 ) != ( sk_c5 ) ) |
% 7.70/1.75 ( ( multiply @ X4 @ sk_c5 ) != ( sk_c6 ) ) |
% 7.70/1.75 ( ( inverse @ X4 ) != ( sk_c6 ) ) |
% 7.70/1.75 ( ( inverse @ X3 ) != ( sk_c6 ) ) |
% 7.70/1.75 ( ( multiply @ X3 @ sk_c6 ) != ( sk_c7 ) ) |
% 7.70/1.75 ( ( multiply @ sk_c6 @ sk_c7 ) != ( sk_c5 ) ) ))).
% 7.70/1.75 thf(zf_stmt_0, negated_conjecture,
% 7.70/1.75 (( ( inverse @ X2 ) != ( sk_c6 ) ) |
% 7.70/1.75 ( ( multiply @ X2 @ sk_c6 ) != ( X1 ) ) |
% 7.70/1.75 ( ( multiply @ sk_c6 @ X1 ) != ( sk_c5 ) ) |
% 7.70/1.75 ( ( inverse @ sk_c7 ) != ( sk_c5 ) ) |
% 7.70/1.75 ( ( inverse @ sk_c6 ) != ( sk_c5 ) ) |
% 7.70/1.75 ( ( multiply @ X4 @ sk_c5 ) != ( sk_c6 ) ) |
% 7.70/1.75 ( ( inverse @ X4 ) != ( sk_c6 ) ) | ( ( inverse @ X3 ) != ( sk_c6 ) ) |
% 7.70/1.75 ( ( multiply @ X3 @ sk_c6 ) != ( sk_c7 ) ) |
% 7.70/1.75 ( ( multiply @ sk_c6 @ sk_c7 ) != ( sk_c5 ) )),
% 7.70/1.75 inference('cnf.neg', [status(esa)], [prove_this_22])).
% 7.70/1.75 thf(zip_derived_cl24, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.70/1.75 (((inverse @ X0) != (sk_c6))
% 7.70/1.75 | ((multiply @ X0 @ sk_c6) != (X1))
% 7.70/1.75 | ((multiply @ sk_c6 @ X1) != (sk_c5))
% 7.70/1.75 | ((inverse @ sk_c7) != (sk_c5))
% 7.70/1.75 | ((inverse @ sk_c6) != (sk_c5))
% 7.70/1.75 | ((multiply @ X2 @ sk_c5) != (sk_c6))
% 7.70/1.75 | ((inverse @ X2) != (sk_c6))
% 7.70/1.75 | ((inverse @ X3) != (sk_c6))
% 7.70/1.75 | ((multiply @ X3 @ sk_c6) != (sk_c7))
% 7.70/1.75 | ((multiply @ sk_c6 @ sk_c7) != (sk_c5)))),
% 7.70/1.75 inference('cnf', [status(esa)], [zf_stmt_0])).
% 7.70/1.75 thf(prove_this_1, conjecture, (( multiply @ sk_c6 @ sk_c7 ) != ( sk_c5 ))).
% 7.70/1.75 thf(zf_stmt_1, negated_conjecture,
% 7.70/1.75 (( multiply @ sk_c6 @ sk_c7 ) = ( sk_c5 )),
% 7.70/1.75 inference('cnf.neg', [status(esa)], [prove_this_1])).
% 7.70/1.75 thf(zip_derived_cl3, plain, (((multiply @ sk_c6 @ sk_c7) = (sk_c5))),
% 7.70/1.75 inference('cnf', [status(esa)], [zf_stmt_1])).
% 7.70/1.75 thf(zip_derived_cl63, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.70/1.75 (((inverse @ X0) != (sk_c6))
% 7.70/1.75 | ((multiply @ X0 @ sk_c6) != (X1))
% 7.70/1.75 | ((multiply @ sk_c6 @ X1) != (sk_c5))
% 7.70/1.75 | ((inverse @ sk_c7) != (sk_c5))
% 7.70/1.75 | ((inverse @ sk_c6) != (sk_c5))
% 7.70/1.75 | ((multiply @ X2 @ sk_c5) != (sk_c6))
% 7.70/1.75 | ((inverse @ X2) != (sk_c6))
% 7.70/1.75 | ((inverse @ X3) != (sk_c6))
% 7.70/1.75 | ((multiply @ X3 @ sk_c6) != (sk_c7))
% 7.70/1.75 | ((sk_c5) != (sk_c5)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl24, zip_derived_cl3])).
% 7.70/1.75 thf(zip_derived_cl64, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.70/1.75 (((multiply @ X3 @ sk_c6) != (sk_c7))
% 7.70/1.75 | ((inverse @ X3) != (sk_c6))
% 7.70/1.75 | ((inverse @ X2) != (sk_c6))
% 7.70/1.75 | ((multiply @ X2 @ sk_c5) != (sk_c6))
% 7.70/1.75 | ((inverse @ sk_c6) != (sk_c5))
% 7.70/1.75 | ((inverse @ sk_c7) != (sk_c5))
% 7.70/1.75 | ((multiply @ sk_c6 @ X1) != (sk_c5))
% 7.70/1.75 | ((multiply @ X0 @ sk_c6) != (X1))
% 7.70/1.75 | ((inverse @ X0) != (sk_c6)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl63])).
% 7.70/1.75 thf(zip_derived_cl66, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i, X2 : $i]:
% 7.70/1.75 (((sk_c6) != (sk_c7))
% 7.70/1.75 | ((inverse @ X0) != (sk_c6))
% 7.70/1.75 | ((multiply @ X0 @ sk_c6) != (X1))
% 7.70/1.75 | ((multiply @ sk_c6 @ X1) != (sk_c5))
% 7.70/1.75 | ((inverse @ sk_c7) != (sk_c5))
% 7.70/1.75 | ((inverse @ sk_c6) != (sk_c5))
% 7.70/1.75 | ((multiply @ X2 @ sk_c5) != (sk_c6))
% 7.70/1.75 | ((inverse @ X2) != (sk_c6))
% 7.70/1.75 | ((inverse @ identity) != (sk_c6)))),
% 7.70/1.75 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl64])).
% 7.70/1.75 thf(zip_derived_cl76, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i, X2 : $i]:
% 7.70/1.75 (((sk_c6) != (sk_c7))
% 7.70/1.75 | ((inverse @ X0) != (sk_c6))
% 7.70/1.75 | ((multiply @ X0 @ sk_c6) != (X1))
% 7.70/1.75 | ((multiply @ sk_c6 @ X1) != (sk_c5))
% 7.70/1.75 | ((sk_c5) != (sk_c5))
% 7.70/1.75 | ((inverse @ sk_c6) != (sk_c5))
% 7.70/1.75 | ((multiply @ X2 @ sk_c5) != (sk_c6))
% 7.70/1.75 | ((inverse @ X2) != (sk_c6))
% 7.70/1.75 | ((inverse @ identity) != (sk_c6)))),
% 7.70/1.75 inference('local_rewriting', [status(thm)], [zip_derived_cl66])).
% 7.70/1.75 thf(zip_derived_cl77, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i, X2 : $i]:
% 7.70/1.75 (((inverse @ identity) != (sk_c6))
% 7.70/1.75 | ((inverse @ X2) != (sk_c6))
% 7.70/1.75 | ((multiply @ X2 @ sk_c5) != (sk_c6))
% 7.70/1.75 | ((inverse @ sk_c6) != (sk_c5))
% 7.70/1.75 | ((multiply @ sk_c6 @ X1) != (sk_c5))
% 7.70/1.75 | ((multiply @ X0 @ sk_c6) != (X1))
% 7.70/1.75 | ((inverse @ X0) != (sk_c6))
% 7.70/1.75 | ((sk_c6) != (sk_c7)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl76])).
% 7.70/1.75 thf(zip_derived_cl2415, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i]:
% 7.70/1.75 (((identity) != (sk_c6))
% 7.70/1.75 | ((sk_c6) != (sk_c7))
% 7.70/1.75 | ((inverse @ X0) != (sk_c6))
% 7.70/1.75 | ((multiply @ X0 @ sk_c6) != (X1))
% 7.70/1.75 | ((multiply @ sk_c6 @ X1) != (sk_c5))
% 7.70/1.75 | ((inverse @ sk_c6) != (sk_c5))
% 7.70/1.75 | ((inverse @ (inverse @ sk_c5)) != (sk_c6))
% 7.70/1.75 | ((inverse @ identity) != (sk_c6)))),
% 7.70/1.75 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl77])).
% 7.70/1.75 thf(zip_derived_cl2452, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i]:
% 7.70/1.75 (((identity) != (sk_c6))
% 7.70/1.75 | ((identity) != (sk_c7))
% 7.70/1.75 | ((inverse @ X0) != (identity))
% 7.70/1.75 | ((multiply @ X0 @ identity) != (X1))
% 7.70/1.75 | ((multiply @ identity @ X1) != (sk_c5))
% 7.70/1.75 | ((identity) != (sk_c5))
% 7.70/1.75 | ((inverse @ (inverse @ sk_c5)) != (identity))
% 7.70/1.75 | ((inverse @ identity) != (identity)))),
% 7.70/1.75 inference('local_rewriting', [status(thm)], [zip_derived_cl2415])).
% 7.70/1.75 thf(zip_derived_cl2453, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i]:
% 7.70/1.75 (((identity) != (sk_c6))
% 7.70/1.75 | ((identity) != (sk_c7))
% 7.70/1.75 | ((inverse @ X0) != (identity))
% 7.70/1.75 | ((multiply @ X0 @ identity) != (X1))
% 7.70/1.75 | ((multiply @ identity @ X1) != (identity))
% 7.70/1.75 | ((identity) != (sk_c5))
% 7.70/1.75 | ((identity) != (identity))
% 7.70/1.75 | ((inverse @ identity) != (identity)))),
% 7.70/1.75 inference('local_rewriting', [status(thm)], [zip_derived_cl2452])).
% 7.70/1.75 thf(zip_derived_cl2454, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i]:
% 7.70/1.75 (((inverse @ identity) != (identity))
% 7.70/1.75 | ((identity) != (sk_c5))
% 7.70/1.75 | ((multiply @ identity @ X1) != (identity))
% 7.70/1.75 | ((multiply @ X0 @ identity) != (X1))
% 7.70/1.75 | ((inverse @ X0) != (identity))
% 7.70/1.75 | ((identity) != (sk_c7))
% 7.70/1.75 | ((identity) != (sk_c6)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl2453])).
% 7.70/1.75 thf(zip_derived_cl3, plain, (((multiply @ sk_c6 @ sk_c7) = (sk_c5))),
% 7.70/1.75 inference('cnf', [status(esa)], [zf_stmt_1])).
% 7.70/1.75 thf(prove_this_2, conjecture,
% 7.70/1.75 (~( ( ( inverse @ sk_c6 ) = ( sk_c5 ) ) |
% 7.70/1.75 ( ( multiply @ sk_c1 @ sk_c6 ) = ( sk_c7 ) ) ))).
% 7.70/1.75 thf(zf_stmt_2, negated_conjecture,
% 7.70/1.75 (( ( inverse @ sk_c6 ) = ( sk_c5 ) ) |
% 7.70/1.75 ( ( multiply @ sk_c1 @ sk_c6 ) = ( sk_c7 ) )),
% 7.70/1.75 inference('cnf.neg', [status(esa)], [prove_this_2])).
% 7.70/1.75 thf(zip_derived_cl4, plain,
% 7.70/1.75 ((((inverse @ sk_c6) = (sk_c5)) | ((multiply @ sk_c1 @ sk_c6) = (sk_c7)))),
% 7.70/1.75 inference('cnf', [status(esa)], [zf_stmt_2])).
% 7.70/1.75 thf(prove_this_7, conjecture,
% 7.70/1.75 (~( ( ( inverse @ sk_c6 ) = ( sk_c5 ) ) |
% 7.70/1.75 ( ( inverse @ sk_c1 ) = ( sk_c6 ) ) ))).
% 7.70/1.75 thf(zf_stmt_3, negated_conjecture,
% 7.70/1.75 (( ( inverse @ sk_c6 ) = ( sk_c5 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c6 ) )),
% 7.70/1.75 inference('cnf.neg', [status(esa)], [prove_this_7])).
% 7.70/1.75 thf(zip_derived_cl9, plain,
% 7.70/1.75 ((((inverse @ sk_c6) = (sk_c5)) | ((inverse @ sk_c1) = (sk_c6)))),
% 7.70/1.75 inference('cnf', [status(esa)], [zf_stmt_3])).
% 7.70/1.75 thf(zip_derived_cl1, plain,
% 7.70/1.75 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 7.70/1.75 inference('cnf', [status(esa)], [left_inverse])).
% 7.70/1.75 thf(zip_derived_cl25, plain,
% 7.70/1.75 ((((multiply @ sk_c6 @ sk_c1) = (identity))
% 7.70/1.75 | ((inverse @ sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl1])).
% 7.70/1.75 thf(associativity, axiom,
% 7.70/1.75 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 7.70/1.75 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 7.70/1.75 thf(zip_derived_cl2, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i, X2 : $i]:
% 7.70/1.75 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 7.70/1.75 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 7.70/1.75 inference('cnf', [status(esa)], [associativity])).
% 7.70/1.75 thf(zip_derived_cl53, plain,
% 7.70/1.75 (![X0 : $i]:
% 7.70/1.75 (((multiply @ identity @ X0)
% 7.70/1.75 = (multiply @ sk_c6 @ (multiply @ sk_c1 @ X0)))
% 7.70/1.75 | ((inverse @ sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl25, zip_derived_cl2])).
% 7.70/1.75 thf(zip_derived_cl0, plain,
% 7.70/1.75 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 7.70/1.75 inference('cnf', [status(esa)], [left_identity])).
% 7.70/1.75 thf(zip_derived_cl54, plain,
% 7.70/1.75 (![X0 : $i]:
% 7.70/1.75 (((X0) = (multiply @ sk_c6 @ (multiply @ sk_c1 @ X0)))
% 7.70/1.75 | ((inverse @ sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl53, zip_derived_cl0])).
% 7.70/1.75 thf(zip_derived_cl94, plain,
% 7.70/1.75 ((((sk_c6) = (multiply @ sk_c6 @ sk_c7))
% 7.70/1.75 | ((inverse @ sk_c6) = (sk_c5))
% 7.70/1.75 | ((inverse @ sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl54])).
% 7.70/1.75 thf(zip_derived_cl98, plain,
% 7.70/1.75 ((((inverse @ sk_c6) = (sk_c5)) | ((sk_c6) = (multiply @ sk_c6 @ sk_c7)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl94])).
% 7.70/1.75 thf(zip_derived_cl3, plain, (((multiply @ sk_c6 @ sk_c7) = (sk_c5))),
% 7.70/1.75 inference('cnf', [status(esa)], [zf_stmt_1])).
% 7.70/1.75 thf(zip_derived_cl102, plain,
% 7.70/1.75 ((((sk_c6) = (sk_c5)) | ((inverse @ sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl98, zip_derived_cl3])).
% 7.70/1.75 thf(zip_derived_cl1, plain,
% 7.70/1.75 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 7.70/1.75 inference('cnf', [status(esa)], [left_inverse])).
% 7.70/1.75 thf(zip_derived_cl103, plain,
% 7.70/1.75 ((((multiply @ sk_c5 @ sk_c6) = (identity)) | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl102, zip_derived_cl1])).
% 7.70/1.75 thf(zip_derived_cl2, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i, X2 : $i]:
% 7.70/1.75 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 7.70/1.75 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 7.70/1.75 inference('cnf', [status(esa)], [associativity])).
% 7.70/1.75 thf(zip_derived_cl107, plain,
% 7.70/1.75 (![X0 : $i]:
% 7.70/1.75 (((multiply @ identity @ X0)
% 7.70/1.75 = (multiply @ sk_c5 @ (multiply @ sk_c6 @ X0)))
% 7.70/1.75 | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl103, zip_derived_cl2])).
% 7.70/1.75 thf(zip_derived_cl0, plain,
% 7.70/1.75 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 7.70/1.75 inference('cnf', [status(esa)], [left_identity])).
% 7.70/1.75 thf(zip_derived_cl110, plain,
% 7.70/1.75 (![X0 : $i]:
% 7.70/1.75 (((X0) = (multiply @ sk_c5 @ (multiply @ sk_c6 @ X0)))
% 7.70/1.75 | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl107, zip_derived_cl0])).
% 7.70/1.75 thf(zip_derived_cl115, plain,
% 7.70/1.75 ((((sk_c7) = (multiply @ sk_c5 @ sk_c5)) | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl110])).
% 7.70/1.75 thf(zip_derived_cl3, plain, (((multiply @ sk_c6 @ sk_c7) = (sk_c5))),
% 7.70/1.75 inference('cnf', [status(esa)], [zf_stmt_1])).
% 7.70/1.75 thf(zip_derived_cl2, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i, X2 : $i]:
% 7.70/1.75 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 7.70/1.75 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 7.70/1.75 inference('cnf', [status(esa)], [associativity])).
% 7.70/1.75 thf(zip_derived_cl35, plain,
% 7.70/1.75 (![X0 : $i]:
% 7.70/1.75 ((multiply @ sk_c5 @ X0)
% 7.70/1.75 = (multiply @ sk_c6 @ (multiply @ sk_c7 @ X0)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl2])).
% 7.70/1.75 thf(zip_derived_cl128, plain,
% 7.70/1.75 ((((sk_c7) = (multiply @ sk_c6 @ (multiply @ sk_c7 @ sk_c5)))
% 7.70/1.75 | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl115, zip_derived_cl35])).
% 7.70/1.75 thf(zip_derived_cl110, plain,
% 7.70/1.75 (![X0 : $i]:
% 7.70/1.75 (((X0) = (multiply @ sk_c5 @ (multiply @ sk_c6 @ X0)))
% 7.70/1.75 | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl107, zip_derived_cl0])).
% 7.70/1.75 thf(zip_derived_cl149, plain,
% 7.70/1.75 ((((multiply @ sk_c7 @ sk_c5) = (multiply @ sk_c5 @ sk_c7))
% 7.70/1.75 | ((sk_c6) = (sk_c5))
% 7.70/1.75 | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl128, zip_derived_cl110])).
% 7.70/1.75 thf(zip_derived_cl35, plain,
% 7.70/1.75 (![X0 : $i]:
% 7.70/1.75 ((multiply @ sk_c5 @ X0)
% 7.70/1.75 = (multiply @ sk_c6 @ (multiply @ sk_c7 @ X0)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl2])).
% 7.70/1.75 thf(zip_derived_cl151, plain,
% 7.70/1.75 ((((multiply @ sk_c7 @ sk_c5)
% 7.70/1.75 = (multiply @ sk_c6 @ (multiply @ sk_c7 @ sk_c7)))
% 7.70/1.75 | ((sk_c6) = (sk_c5))
% 7.70/1.75 | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl149, zip_derived_cl35])).
% 7.70/1.75 thf(zip_derived_cl152, plain,
% 7.70/1.75 ((((sk_c6) = (sk_c5))
% 7.70/1.75 | ((multiply @ sk_c7 @ sk_c5)
% 7.70/1.75 = (multiply @ sk_c6 @ (multiply @ sk_c7 @ sk_c7))))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl151])).
% 7.70/1.75 thf(zip_derived_cl128, plain,
% 7.70/1.75 ((((sk_c7) = (multiply @ sk_c6 @ (multiply @ sk_c7 @ sk_c5)))
% 7.70/1.75 | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl115, zip_derived_cl35])).
% 7.70/1.75 thf(zip_derived_cl190, plain,
% 7.70/1.75 ((((sk_c7)
% 7.70/1.75 = (multiply @ sk_c6 @ (multiply @ sk_c6 @ (multiply @ sk_c7 @ sk_c7))))
% 7.70/1.75 | ((sk_c6) = (sk_c5))
% 7.70/1.75 | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl152, zip_derived_cl128])).
% 7.70/1.75 thf(zip_derived_cl192, plain,
% 7.70/1.75 ((((sk_c6) = (sk_c5))
% 7.70/1.75 | ((sk_c7)
% 7.70/1.75 = (multiply @ sk_c6 @
% 7.70/1.75 (multiply @ sk_c6 @ (multiply @ sk_c7 @ sk_c7)))))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl190])).
% 7.70/1.75 thf(prove_this_12, conjecture,
% 7.70/1.75 (~( ( ( inverse @ sk_c6 ) = ( sk_c5 ) ) |
% 7.70/1.75 ( ( inverse @ sk_c2 ) = ( sk_c6 ) ) ))).
% 7.70/1.75 thf(zf_stmt_4, negated_conjecture,
% 7.70/1.75 (( ( inverse @ sk_c6 ) = ( sk_c5 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c6 ) )),
% 7.70/1.75 inference('cnf.neg', [status(esa)], [prove_this_12])).
% 7.70/1.75 thf(zip_derived_cl14, plain,
% 7.70/1.75 ((((inverse @ sk_c6) = (sk_c5)) | ((inverse @ sk_c2) = (sk_c6)))),
% 7.70/1.75 inference('cnf', [status(esa)], [zf_stmt_4])).
% 7.70/1.75 thf(prove_this_17, conjecture,
% 7.70/1.75 (~( ( ( inverse @ sk_c6 ) = ( sk_c5 ) ) |
% 7.70/1.75 ( ( multiply @ sk_c2 @ sk_c5 ) = ( sk_c6 ) ) ))).
% 7.70/1.75 thf(zf_stmt_5, negated_conjecture,
% 7.70/1.75 (( ( inverse @ sk_c6 ) = ( sk_c5 ) ) |
% 7.70/1.75 ( ( multiply @ sk_c2 @ sk_c5 ) = ( sk_c6 ) )),
% 7.70/1.75 inference('cnf.neg', [status(esa)], [prove_this_17])).
% 7.70/1.75 thf(zip_derived_cl19, plain,
% 7.70/1.75 ((((inverse @ sk_c6) = (sk_c5)) | ((multiply @ sk_c2 @ sk_c5) = (sk_c6)))),
% 7.70/1.75 inference('cnf', [status(esa)], [zf_stmt_5])).
% 7.70/1.75 thf(zip_derived_cl1, plain,
% 7.70/1.75 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 7.70/1.75 inference('cnf', [status(esa)], [left_inverse])).
% 7.70/1.75 thf(zip_derived_cl2, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i, X2 : $i]:
% 7.70/1.75 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 7.70/1.75 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 7.70/1.75 inference('cnf', [status(esa)], [associativity])).
% 7.70/1.75 thf(zip_derived_cl34, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i]:
% 7.70/1.75 ((multiply @ identity @ X0)
% 7.70/1.75 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 7.70/1.75 thf(zip_derived_cl0, plain,
% 7.70/1.75 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 7.70/1.75 inference('cnf', [status(esa)], [left_identity])).
% 7.70/1.75 thf(zip_derived_cl44, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i]:
% 7.70/1.75 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl34, zip_derived_cl0])).
% 7.70/1.75 thf(zip_derived_cl869, plain,
% 7.70/1.75 ((((sk_c5) = (multiply @ (inverse @ sk_c2) @ sk_c6))
% 7.70/1.75 | ((inverse @ sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl44])).
% 7.70/1.75 thf(zip_derived_cl1724, plain,
% 7.70/1.75 ((((sk_c5) = (multiply @ sk_c6 @ sk_c6))
% 7.70/1.75 | ((inverse @ sk_c6) = (sk_c5))
% 7.70/1.75 | ((inverse @ sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl869])).
% 7.70/1.75 thf(zip_derived_cl1729, plain,
% 7.70/1.75 ((((inverse @ sk_c6) = (sk_c5)) | ((sk_c5) = (multiply @ sk_c6 @ sk_c6)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl1724])).
% 7.70/1.75 thf(zip_derived_cl44, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i]:
% 7.70/1.75 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl34, zip_derived_cl0])).
% 7.70/1.75 thf(zip_derived_cl1786, plain,
% 7.70/1.75 ((((sk_c6) = (multiply @ (inverse @ sk_c6) @ sk_c5))
% 7.70/1.75 | ((inverse @ sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl1729, zip_derived_cl44])).
% 7.70/1.75 thf(zip_derived_cl3, plain, (((multiply @ sk_c6 @ sk_c7) = (sk_c5))),
% 7.70/1.75 inference('cnf', [status(esa)], [zf_stmt_1])).
% 7.70/1.75 thf(zip_derived_cl44, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i]:
% 7.70/1.75 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl34, zip_derived_cl0])).
% 7.70/1.75 thf(zip_derived_cl807, plain,
% 7.70/1.75 (((sk_c7) = (multiply @ (inverse @ sk_c6) @ sk_c5))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl44])).
% 7.70/1.75 thf(zip_derived_cl2668, plain,
% 7.70/1.75 ((((sk_c7) = (sk_c6)) | ((inverse @ sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl1786, zip_derived_cl807])).
% 7.70/1.75 thf(prove_this_3, conjecture,
% 7.70/1.75 (~( ( ( inverse @ sk_c7 ) = ( sk_c5 ) ) |
% 7.70/1.75 ( ( multiply @ sk_c1 @ sk_c6 ) = ( sk_c7 ) ) ))).
% 7.70/1.75 thf(zf_stmt_6, negated_conjecture,
% 7.70/1.75 (( ( inverse @ sk_c7 ) = ( sk_c5 ) ) |
% 7.70/1.75 ( ( multiply @ sk_c1 @ sk_c6 ) = ( sk_c7 ) )),
% 7.70/1.75 inference('cnf.neg', [status(esa)], [prove_this_3])).
% 7.70/1.75 thf(zip_derived_cl5, plain,
% 7.70/1.75 ((((inverse @ sk_c7) = (sk_c5)) | ((multiply @ sk_c1 @ sk_c6) = (sk_c7)))),
% 7.70/1.75 inference('cnf', [status(esa)], [zf_stmt_6])).
% 7.70/1.75 thf(prove_this_8, conjecture,
% 7.70/1.75 (~( ( ( inverse @ sk_c7 ) = ( sk_c5 ) ) |
% 7.70/1.75 ( ( inverse @ sk_c1 ) = ( sk_c6 ) ) ))).
% 7.70/1.75 thf(zf_stmt_7, negated_conjecture,
% 7.70/1.75 (( ( inverse @ sk_c7 ) = ( sk_c5 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c6 ) )),
% 7.70/1.75 inference('cnf.neg', [status(esa)], [prove_this_8])).
% 7.70/1.75 thf(zip_derived_cl10, plain,
% 7.70/1.75 ((((inverse @ sk_c7) = (sk_c5)) | ((inverse @ sk_c1) = (sk_c6)))),
% 7.70/1.75 inference('cnf', [status(esa)], [zf_stmt_7])).
% 7.70/1.75 thf(zip_derived_cl1, plain,
% 7.70/1.75 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 7.70/1.75 inference('cnf', [status(esa)], [left_inverse])).
% 7.70/1.75 thf(zip_derived_cl26, plain,
% 7.70/1.75 ((((multiply @ sk_c6 @ sk_c1) = (identity))
% 7.70/1.75 | ((inverse @ sk_c7) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl1])).
% 7.70/1.75 thf(zip_derived_cl2, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i, X2 : $i]:
% 7.70/1.75 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 7.70/1.75 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 7.70/1.75 inference('cnf', [status(esa)], [associativity])).
% 7.70/1.75 thf(zip_derived_cl61, plain,
% 7.70/1.75 (![X0 : $i]:
% 7.70/1.75 (((multiply @ identity @ X0)
% 7.70/1.75 = (multiply @ sk_c6 @ (multiply @ sk_c1 @ X0)))
% 7.70/1.75 | ((inverse @ sk_c7) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl2])).
% 7.70/1.75 thf(zip_derived_cl0, plain,
% 7.70/1.75 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 7.70/1.75 inference('cnf', [status(esa)], [left_identity])).
% 7.70/1.75 thf(zip_derived_cl62, plain,
% 7.70/1.75 (![X0 : $i]:
% 7.70/1.75 (((X0) = (multiply @ sk_c6 @ (multiply @ sk_c1 @ X0)))
% 7.70/1.75 | ((inverse @ sk_c7) = (sk_c5)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl61, zip_derived_cl0])).
% 7.70/1.75 thf(zip_derived_cl498, plain,
% 7.70/1.75 ((((sk_c6) = (multiply @ sk_c6 @ sk_c7))
% 7.70/1.75 | ((inverse @ sk_c7) = (sk_c5))
% 7.70/1.75 | ((inverse @ sk_c7) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl62])).
% 7.70/1.75 thf(zip_derived_cl510, plain,
% 7.70/1.75 ((((inverse @ sk_c7) = (sk_c5)) | ((sk_c6) = (multiply @ sk_c6 @ sk_c7)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl498])).
% 7.70/1.75 thf(zip_derived_cl3, plain, (((multiply @ sk_c6 @ sk_c7) = (sk_c5))),
% 7.70/1.75 inference('cnf', [status(esa)], [zf_stmt_1])).
% 7.70/1.75 thf(zip_derived_cl524, plain,
% 7.70/1.75 ((((sk_c6) = (sk_c5)) | ((inverse @ sk_c7) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl510, zip_derived_cl3])).
% 7.70/1.75 thf(zip_derived_cl1, plain,
% 7.70/1.75 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 7.70/1.75 inference('cnf', [status(esa)], [left_inverse])).
% 7.70/1.75 thf(zip_derived_cl526, plain,
% 7.70/1.75 ((((multiply @ sk_c5 @ sk_c7) = (identity)) | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl524, zip_derived_cl1])).
% 7.70/1.75 thf(zip_derived_cl44, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i]:
% 7.70/1.75 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl34, zip_derived_cl0])).
% 7.70/1.75 thf(zip_derived_cl835, plain,
% 7.70/1.75 ((((sk_c7) = (multiply @ (inverse @ sk_c5) @ identity))
% 7.70/1.75 | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl526, zip_derived_cl44])).
% 7.70/1.75 thf(zip_derived_cl103, plain,
% 7.70/1.75 ((((multiply @ sk_c5 @ sk_c6) = (identity)) | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl102, zip_derived_cl1])).
% 7.70/1.75 thf(zip_derived_cl44, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i]:
% 7.70/1.75 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl34, zip_derived_cl0])).
% 7.70/1.75 thf(zip_derived_cl834, plain,
% 7.70/1.75 ((((sk_c6) = (multiply @ (inverse @ sk_c5) @ identity))
% 7.70/1.75 | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl103, zip_derived_cl44])).
% 7.70/1.75 thf(zip_derived_cl1149, plain,
% 7.70/1.75 ((((sk_c6) = (sk_c7)) | ((sk_c6) = (sk_c5)) | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl835, zip_derived_cl834])).
% 7.70/1.75 thf(zip_derived_cl1152, plain, ((((sk_c6) = (sk_c5)) | ((sk_c6) = (sk_c7)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl1149])).
% 7.70/1.75 thf(zip_derived_cl2668, plain,
% 7.70/1.75 ((((sk_c7) = (sk_c6)) | ((inverse @ sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl1786, zip_derived_cl807])).
% 7.70/1.75 thf(zip_derived_cl807, plain,
% 7.70/1.75 (((sk_c7) = (multiply @ (inverse @ sk_c6) @ sk_c5))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl44])).
% 7.70/1.75 thf(zip_derived_cl2778, plain,
% 7.70/1.75 ((((sk_c7) = (multiply @ sk_c5 @ sk_c5)) | ((sk_c7) = (sk_c6)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl2668, zip_derived_cl807])).
% 7.70/1.75 thf(zip_derived_cl2815, plain,
% 7.70/1.75 ((((sk_c7) = (multiply @ sk_c6 @ sk_c5))
% 7.70/1.75 | ((sk_c6) = (sk_c7))
% 7.70/1.75 | ((sk_c7) = (sk_c6)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl1152, zip_derived_cl2778])).
% 7.70/1.75 thf(zip_derived_cl2819, plain,
% 7.70/1.75 ((((sk_c6) = (sk_c7)) | ((sk_c7) = (multiply @ sk_c6 @ sk_c5)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl2815])).
% 7.70/1.75 thf(zip_derived_cl44, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i]:
% 7.70/1.75 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl34, zip_derived_cl0])).
% 7.70/1.75 thf(zip_derived_cl2857, plain,
% 7.70/1.75 ((((sk_c5) = (multiply @ (inverse @ sk_c6) @ sk_c7))
% 7.70/1.75 | ((sk_c6) = (sk_c7)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl2819, zip_derived_cl44])).
% 7.70/1.75 thf(zip_derived_cl3157, plain,
% 7.70/1.75 ((((sk_c5) = (multiply @ sk_c5 @ sk_c7))
% 7.70/1.75 | ((sk_c7) = (sk_c6))
% 7.70/1.75 | ((sk_c6) = (sk_c7)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl2668, zip_derived_cl2857])).
% 7.70/1.75 thf(zip_derived_cl3160, plain,
% 7.70/1.75 ((((sk_c7) = (sk_c6)) | ((sk_c5) = (multiply @ sk_c5 @ sk_c7)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl3157])).
% 7.70/1.75 thf(prove_this_13, conjecture,
% 7.70/1.75 (~( ( ( inverse @ sk_c7 ) = ( sk_c5 ) ) |
% 7.70/1.75 ( ( inverse @ sk_c2 ) = ( sk_c6 ) ) ))).
% 7.70/1.75 thf(zf_stmt_8, negated_conjecture,
% 7.70/1.75 (( ( inverse @ sk_c7 ) = ( sk_c5 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c6 ) )),
% 7.70/1.75 inference('cnf.neg', [status(esa)], [prove_this_13])).
% 7.70/1.75 thf(zip_derived_cl15, plain,
% 7.70/1.75 ((((inverse @ sk_c7) = (sk_c5)) | ((inverse @ sk_c2) = (sk_c6)))),
% 7.70/1.75 inference('cnf', [status(esa)], [zf_stmt_8])).
% 7.70/1.75 thf(zip_derived_cl510, plain,
% 7.70/1.75 ((((inverse @ sk_c7) = (sk_c5)) | ((sk_c6) = (multiply @ sk_c6 @ sk_c7)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl498])).
% 7.70/1.75 thf(zip_derived_cl5, plain,
% 7.70/1.75 ((((inverse @ sk_c7) = (sk_c5)) | ((multiply @ sk_c1 @ sk_c6) = (sk_c7)))),
% 7.70/1.75 inference('cnf', [status(esa)], [zf_stmt_6])).
% 7.70/1.75 thf(zip_derived_cl2, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i, X2 : $i]:
% 7.70/1.75 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 7.70/1.75 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 7.70/1.75 inference('cnf', [status(esa)], [associativity])).
% 7.70/1.75 thf(zip_derived_cl39, plain,
% 7.70/1.75 (![X0 : $i]:
% 7.70/1.75 (((multiply @ sk_c7 @ X0)
% 7.70/1.75 = (multiply @ sk_c1 @ (multiply @ sk_c6 @ X0)))
% 7.70/1.75 | ((inverse @ sk_c7) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl2])).
% 7.70/1.75 thf(zip_derived_cl519, plain,
% 7.70/1.75 ((((multiply @ sk_c7 @ sk_c7) = (multiply @ sk_c1 @ sk_c6))
% 7.70/1.75 | ((inverse @ sk_c7) = (sk_c5))
% 7.70/1.75 | ((inverse @ sk_c7) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl510, zip_derived_cl39])).
% 7.70/1.75 thf(zip_derived_cl525, plain,
% 7.70/1.75 ((((inverse @ sk_c7) = (sk_c5))
% 7.70/1.75 | ((multiply @ sk_c7 @ sk_c7) = (multiply @ sk_c1 @ sk_c6)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl519])).
% 7.70/1.75 thf(zip_derived_cl5, plain,
% 7.70/1.75 ((((inverse @ sk_c7) = (sk_c5)) | ((multiply @ sk_c1 @ sk_c6) = (sk_c7)))),
% 7.70/1.75 inference('cnf', [status(esa)], [zf_stmt_6])).
% 7.70/1.75 thf(zip_derived_cl534, plain,
% 7.70/1.75 ((((multiply @ sk_c7 @ sk_c7) = (sk_c7))
% 7.70/1.75 | ((inverse @ sk_c7) = (sk_c5))
% 7.70/1.75 | ((inverse @ sk_c7) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl525, zip_derived_cl5])).
% 7.70/1.75 thf(zip_derived_cl540, plain,
% 7.70/1.75 ((((inverse @ sk_c7) = (sk_c5)) | ((multiply @ sk_c7 @ sk_c7) = (sk_c7)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl534])).
% 7.70/1.75 thf(prove_this_18, conjecture,
% 7.70/1.75 (~( ( ( inverse @ sk_c7 ) = ( sk_c5 ) ) |
% 7.70/1.75 ( ( multiply @ sk_c2 @ sk_c5 ) = ( sk_c6 ) ) ))).
% 7.70/1.75 thf(zf_stmt_9, negated_conjecture,
% 7.70/1.75 (( ( inverse @ sk_c7 ) = ( sk_c5 ) ) |
% 7.70/1.75 ( ( multiply @ sk_c2 @ sk_c5 ) = ( sk_c6 ) )),
% 7.70/1.75 inference('cnf.neg', [status(esa)], [prove_this_18])).
% 7.70/1.75 thf(zip_derived_cl20, plain,
% 7.70/1.75 ((((inverse @ sk_c7) = (sk_c5)) | ((multiply @ sk_c2 @ sk_c5) = (sk_c6)))),
% 7.70/1.75 inference('cnf', [status(esa)], [zf_stmt_9])).
% 7.70/1.75 thf(zip_derived_cl2, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i, X2 : $i]:
% 7.70/1.75 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 7.70/1.75 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 7.70/1.75 inference('cnf', [status(esa)], [associativity])).
% 7.70/1.75 thf(zip_derived_cl49, plain,
% 7.70/1.75 (![X0 : $i]:
% 7.70/1.75 (((multiply @ sk_c6 @ X0)
% 7.70/1.75 = (multiply @ sk_c2 @ (multiply @ sk_c5 @ X0)))
% 7.70/1.75 | ((inverse @ sk_c7) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl20, zip_derived_cl2])).
% 7.70/1.75 thf(zip_derived_cl35, plain,
% 7.70/1.75 (![X0 : $i]:
% 7.70/1.75 ((multiply @ sk_c5 @ X0)
% 7.70/1.75 = (multiply @ sk_c6 @ (multiply @ sk_c7 @ X0)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl2])).
% 7.70/1.75 thf(zip_derived_cl50, plain,
% 7.70/1.75 (![X0 : $i]:
% 7.70/1.75 (((multiply @ sk_c6 @ X0)
% 7.70/1.75 = (multiply @ sk_c2 @ (multiply @ sk_c6 @ (multiply @ sk_c7 @ X0))))
% 7.70/1.75 | ((inverse @ sk_c7) = (sk_c5)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl49, zip_derived_cl35])).
% 7.70/1.75 thf(zip_derived_cl1119, plain,
% 7.70/1.75 ((((multiply @ sk_c6 @ sk_c7)
% 7.70/1.75 = (multiply @ sk_c2 @ (multiply @ sk_c6 @ sk_c7)))
% 7.70/1.75 | ((inverse @ sk_c7) = (sk_c5))
% 7.70/1.75 | ((inverse @ sk_c7) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl540, zip_derived_cl50])).
% 7.70/1.75 thf(zip_derived_cl3, plain, (((multiply @ sk_c6 @ sk_c7) = (sk_c5))),
% 7.70/1.75 inference('cnf', [status(esa)], [zf_stmt_1])).
% 7.70/1.75 thf(zip_derived_cl3, plain, (((multiply @ sk_c6 @ sk_c7) = (sk_c5))),
% 7.70/1.75 inference('cnf', [status(esa)], [zf_stmt_1])).
% 7.70/1.75 thf(zip_derived_cl1128, plain,
% 7.70/1.75 ((((sk_c5) = (multiply @ sk_c2 @ sk_c5))
% 7.70/1.75 | ((inverse @ sk_c7) = (sk_c5))
% 7.70/1.75 | ((inverse @ sk_c7) = (sk_c5)))),
% 7.70/1.75 inference('demod', [status(thm)],
% 7.70/1.75 [zip_derived_cl1119, zip_derived_cl3, zip_derived_cl3])).
% 7.70/1.75 thf(zip_derived_cl1129, plain,
% 7.70/1.75 ((((inverse @ sk_c7) = (sk_c5)) | ((sk_c5) = (multiply @ sk_c2 @ sk_c5)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl1128])).
% 7.70/1.75 thf(zip_derived_cl44, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i]:
% 7.70/1.75 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl34, zip_derived_cl0])).
% 7.70/1.75 thf(zip_derived_cl1136, plain,
% 7.70/1.75 ((((sk_c5) = (multiply @ (inverse @ sk_c2) @ sk_c5))
% 7.70/1.75 | ((inverse @ sk_c7) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl1129, zip_derived_cl44])).
% 7.70/1.75 thf(zip_derived_cl2540, plain,
% 7.70/1.75 ((((sk_c5) = (multiply @ sk_c6 @ sk_c5))
% 7.70/1.75 | ((inverse @ sk_c7) = (sk_c5))
% 7.70/1.75 | ((inverse @ sk_c7) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl15, zip_derived_cl1136])).
% 7.70/1.75 thf(zip_derived_cl2545, plain,
% 7.70/1.75 ((((inverse @ sk_c7) = (sk_c5)) | ((sk_c5) = (multiply @ sk_c6 @ sk_c5)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl2540])).
% 7.70/1.75 thf(zip_derived_cl44, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i]:
% 7.70/1.75 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl34, zip_derived_cl0])).
% 7.70/1.75 thf(zip_derived_cl2551, plain,
% 7.70/1.75 ((((sk_c5) = (multiply @ (inverse @ sk_c6) @ sk_c5))
% 7.70/1.75 | ((inverse @ sk_c7) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl2545, zip_derived_cl44])).
% 7.70/1.75 thf(zip_derived_cl807, plain,
% 7.70/1.75 (((sk_c7) = (multiply @ (inverse @ sk_c6) @ sk_c5))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl44])).
% 7.70/1.75 thf(zip_derived_cl2569, plain,
% 7.70/1.75 ((((sk_c5) = (sk_c7)) | ((inverse @ sk_c7) = (sk_c5)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl2551, zip_derived_cl807])).
% 7.70/1.75 thf(zip_derived_cl1, plain,
% 7.70/1.75 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 7.70/1.75 inference('cnf', [status(esa)], [left_inverse])).
% 7.70/1.75 thf(zip_derived_cl2574, plain,
% 7.70/1.75 ((((multiply @ sk_c5 @ sk_c7) = (identity)) | ((sk_c5) = (sk_c7)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl2569, zip_derived_cl1])).
% 7.70/1.75 thf(zip_derived_cl3208, plain,
% 7.70/1.75 ((((sk_c5) = (identity)) | ((sk_c7) = (sk_c6)) | ((sk_c5) = (sk_c7)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl3160, zip_derived_cl2574])).
% 7.70/1.75 thf(zip_derived_cl1152, plain, ((((sk_c6) = (sk_c5)) | ((sk_c6) = (sk_c7)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl1149])).
% 7.70/1.75 thf(zip_derived_cl3357, plain,
% 7.70/1.75 ((((sk_c6) = (sk_c7))
% 7.70/1.75 | ((sk_c7) = (sk_c6))
% 7.70/1.75 | ((sk_c5) = (identity))
% 7.70/1.75 | ((sk_c6) = (sk_c7)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl3208, zip_derived_cl1152])).
% 7.70/1.75 thf(zip_derived_cl3392, plain,
% 7.70/1.75 ((((sk_c5) = (identity)) | ((sk_c6) = (sk_c7)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl3357])).
% 7.70/1.75 thf(zip_derived_cl1152, plain, ((((sk_c6) = (sk_c5)) | ((sk_c6) = (sk_c7)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl1149])).
% 7.70/1.75 thf(zip_derived_cl2778, plain,
% 7.70/1.75 ((((sk_c7) = (multiply @ sk_c5 @ sk_c5)) | ((sk_c7) = (sk_c6)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl2668, zip_derived_cl807])).
% 7.70/1.75 thf(zip_derived_cl2813, plain,
% 7.70/1.75 ((((sk_c7) = (multiply @ sk_c5 @ sk_c6))
% 7.70/1.75 | ((sk_c6) = (sk_c7))
% 7.70/1.75 | ((sk_c7) = (sk_c6)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl1152, zip_derived_cl2778])).
% 7.70/1.75 thf(zip_derived_cl2817, plain,
% 7.70/1.75 ((((sk_c6) = (sk_c7)) | ((sk_c7) = (multiply @ sk_c5 @ sk_c6)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl2813])).
% 7.70/1.75 thf(zip_derived_cl3482, plain,
% 7.70/1.75 ((((sk_c7) = (multiply @ identity @ sk_c6))
% 7.70/1.75 | ((sk_c6) = (sk_c7))
% 7.70/1.75 | ((sk_c6) = (sk_c7)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl3392, zip_derived_cl2817])).
% 7.70/1.75 thf(zip_derived_cl0, plain,
% 7.70/1.75 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 7.70/1.75 inference('cnf', [status(esa)], [left_identity])).
% 7.70/1.75 thf(zip_derived_cl3506, plain,
% 7.70/1.75 ((((sk_c7) = (sk_c6)) | ((sk_c6) = (sk_c7)) | ((sk_c6) = (sk_c7)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl3482, zip_derived_cl0])).
% 7.70/1.75 thf(zip_derived_cl3507, plain, (((sk_c7) = (sk_c6))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl3506])).
% 7.70/1.75 thf(zip_derived_cl3507, plain, (((sk_c7) = (sk_c6))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl3506])).
% 7.70/1.75 thf(zip_derived_cl3507, plain, (((sk_c7) = (sk_c6))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl3506])).
% 7.70/1.75 thf(zip_derived_cl3, plain, (((multiply @ sk_c6 @ sk_c7) = (sk_c5))),
% 7.70/1.75 inference('cnf', [status(esa)], [zf_stmt_1])).
% 7.70/1.75 thf(zip_derived_cl3507, plain, (((sk_c7) = (sk_c6))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl3506])).
% 7.70/1.75 thf(zip_derived_cl3512, plain, (((multiply @ sk_c6 @ sk_c6) = (sk_c5))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl3, zip_derived_cl3507])).
% 7.70/1.75 thf(zip_derived_cl4350, plain,
% 7.70/1.75 ((((sk_c6) = (sk_c5))
% 7.70/1.75 | ((sk_c6) = (multiply @ sk_c6 @ (multiply @ sk_c6 @ sk_c5))))),
% 7.70/1.75 inference('demod', [status(thm)],
% 7.70/1.75 [zip_derived_cl192, zip_derived_cl3507, zip_derived_cl3507,
% 7.70/1.75 zip_derived_cl3507, zip_derived_cl3512])).
% 7.70/1.75 thf(zip_derived_cl110, plain,
% 7.70/1.75 (![X0 : $i]:
% 7.70/1.75 (((X0) = (multiply @ sk_c5 @ (multiply @ sk_c6 @ X0)))
% 7.70/1.75 | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl107, zip_derived_cl0])).
% 7.70/1.75 thf(zip_derived_cl4357, plain,
% 7.70/1.75 ((((multiply @ sk_c6 @ sk_c5) = (multiply @ sk_c5 @ sk_c6))
% 7.70/1.75 | ((sk_c6) = (sk_c5))
% 7.70/1.75 | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl4350, zip_derived_cl110])).
% 7.70/1.75 thf(zip_derived_cl4373, plain,
% 7.70/1.75 ((((sk_c6) = (sk_c5))
% 7.70/1.75 | ((multiply @ sk_c6 @ sk_c5) = (multiply @ sk_c5 @ sk_c6)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl4357])).
% 7.70/1.75 thf(zip_derived_cl4380, plain,
% 7.70/1.75 (((multiply @ sk_c6 @ sk_c5) = (multiply @ sk_c5 @ sk_c6))),
% 7.70/1.75 inference('condensation', [status(thm)], [zip_derived_cl4373])).
% 7.70/1.75 thf(zip_derived_cl44, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i]:
% 7.70/1.75 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl34, zip_derived_cl0])).
% 7.70/1.75 thf(zip_derived_cl4383, plain,
% 7.70/1.75 (((sk_c6) = (multiply @ (inverse @ sk_c5) @ (multiply @ sk_c6 @ sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl4380, zip_derived_cl44])).
% 7.70/1.75 thf(zip_derived_cl44, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i]:
% 7.70/1.75 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl34, zip_derived_cl0])).
% 7.70/1.75 thf(zip_derived_cl5247, plain,
% 7.70/1.75 (((multiply @ sk_c6 @ sk_c5)
% 7.70/1.75 = (multiply @ (inverse @ (inverse @ sk_c5)) @ sk_c6))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl4383, zip_derived_cl44])).
% 7.70/1.75 thf(zip_derived_cl35, plain,
% 7.70/1.75 (![X0 : $i]:
% 7.70/1.75 ((multiply @ sk_c5 @ X0)
% 7.70/1.75 = (multiply @ sk_c6 @ (multiply @ sk_c7 @ X0)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl2])).
% 7.70/1.75 thf(zip_derived_cl3507, plain, (((sk_c7) = (sk_c6))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl3506])).
% 7.70/1.75 thf(zip_derived_cl3523, plain,
% 7.70/1.75 (![X0 : $i]:
% 7.70/1.75 ((multiply @ sk_c5 @ X0)
% 7.70/1.75 = (multiply @ sk_c6 @ (multiply @ sk_c6 @ X0)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl35, zip_derived_cl3507])).
% 7.70/1.75 thf(zip_derived_cl103, plain,
% 7.70/1.75 ((((multiply @ sk_c5 @ sk_c6) = (identity)) | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl102, zip_derived_cl1])).
% 7.70/1.75 thf(zip_derived_cl4005, plain,
% 7.70/1.75 ((((multiply @ sk_c6 @ (multiply @ sk_c6 @ sk_c6)) = (identity))
% 7.70/1.75 | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl3523, zip_derived_cl103])).
% 7.70/1.75 thf(zip_derived_cl3512, plain, (((multiply @ sk_c6 @ sk_c6) = (sk_c5))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl3, zip_derived_cl3507])).
% 7.70/1.75 thf(zip_derived_cl4022, plain,
% 7.70/1.75 ((((multiply @ sk_c6 @ sk_c5) = (identity)) | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('demod', [status(thm)],
% 7.70/1.75 [zip_derived_cl4005, zip_derived_cl3512])).
% 7.70/1.75 thf(zip_derived_cl110, plain,
% 7.70/1.75 (![X0 : $i]:
% 7.70/1.75 (((X0) = (multiply @ sk_c5 @ (multiply @ sk_c6 @ X0)))
% 7.70/1.75 | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl107, zip_derived_cl0])).
% 7.70/1.75 thf(zip_derived_cl4050, plain,
% 7.70/1.75 ((((sk_c5) = (multiply @ sk_c5 @ identity))
% 7.70/1.75 | ((sk_c6) = (sk_c5))
% 7.70/1.75 | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl4022, zip_derived_cl110])).
% 7.70/1.75 thf(zip_derived_cl4058, plain,
% 7.70/1.75 ((((sk_c6) = (sk_c5)) | ((sk_c5) = (multiply @ sk_c5 @ identity)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl4050])).
% 7.70/1.75 thf(prove_this_11, conjecture,
% 7.70/1.75 (~( ( ( inverse @ sk_c3 ) = ( sk_c6 ) ) |
% 7.70/1.75 ( ( inverse @ sk_c1 ) = ( sk_c6 ) ) ))).
% 7.70/1.75 thf(zf_stmt_10, negated_conjecture,
% 7.70/1.75 (( ( inverse @ sk_c3 ) = ( sk_c6 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c6 ) )),
% 7.70/1.75 inference('cnf.neg', [status(esa)], [prove_this_11])).
% 7.70/1.75 thf(zip_derived_cl13, plain,
% 7.70/1.75 ((((inverse @ sk_c3) = (sk_c6)) | ((inverse @ sk_c1) = (sk_c6)))),
% 7.70/1.75 inference('cnf', [status(esa)], [zf_stmt_10])).
% 7.70/1.75 thf(prove_this_10, conjecture,
% 7.70/1.75 (~( ( ( multiply @ sk_c3 @ sk_c6 ) = ( sk_c4 ) ) |
% 7.70/1.75 ( ( inverse @ sk_c1 ) = ( sk_c6 ) ) ))).
% 7.70/1.75 thf(zf_stmt_11, negated_conjecture,
% 7.70/1.75 (( ( multiply @ sk_c3 @ sk_c6 ) = ( sk_c4 ) ) |
% 7.70/1.75 ( ( inverse @ sk_c1 ) = ( sk_c6 ) )),
% 7.70/1.75 inference('cnf.neg', [status(esa)], [prove_this_10])).
% 7.70/1.75 thf(zip_derived_cl12, plain,
% 7.70/1.75 ((((multiply @ sk_c3 @ sk_c6) = (sk_c4)) | ((inverse @ sk_c1) = (sk_c6)))),
% 7.70/1.75 inference('cnf', [status(esa)], [zf_stmt_11])).
% 7.70/1.75 thf(zip_derived_cl44, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i]:
% 7.70/1.75 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl34, zip_derived_cl0])).
% 7.70/1.75 thf(zip_derived_cl863, plain,
% 7.70/1.75 ((((sk_c6) = (multiply @ (inverse @ sk_c3) @ sk_c4))
% 7.70/1.75 | ((inverse @ sk_c1) = (sk_c6)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl44])).
% 7.70/1.75 thf(zip_derived_cl1608, plain,
% 7.70/1.75 ((((sk_c6) = (multiply @ sk_c6 @ sk_c4))
% 7.70/1.75 | ((inverse @ sk_c1) = (sk_c6))
% 7.70/1.75 | ((inverse @ sk_c1) = (sk_c6)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl863])).
% 7.70/1.75 thf(zip_derived_cl1609, plain,
% 7.70/1.75 ((((inverse @ sk_c1) = (sk_c6)) | ((sk_c6) = (multiply @ sk_c6 @ sk_c4)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl1608])).
% 7.70/1.75 thf(prove_this_9, conjecture,
% 7.70/1.75 (~( ( ( multiply @ sk_c6 @ sk_c4 ) = ( sk_c5 ) ) |
% 7.70/1.75 ( ( inverse @ sk_c1 ) = ( sk_c6 ) ) ))).
% 7.70/1.75 thf(zf_stmt_12, negated_conjecture,
% 7.70/1.75 (( ( multiply @ sk_c6 @ sk_c4 ) = ( sk_c5 ) ) |
% 7.70/1.75 ( ( inverse @ sk_c1 ) = ( sk_c6 ) )),
% 7.70/1.75 inference('cnf.neg', [status(esa)], [prove_this_9])).
% 7.70/1.75 thf(zip_derived_cl11, plain,
% 7.70/1.75 ((((multiply @ sk_c6 @ sk_c4) = (sk_c5)) | ((inverse @ sk_c1) = (sk_c6)))),
% 7.70/1.75 inference('cnf', [status(esa)], [zf_stmt_12])).
% 7.70/1.75 thf(zip_derived_cl1622, plain,
% 7.70/1.75 ((((sk_c6) = (sk_c5))
% 7.70/1.75 | ((inverse @ sk_c1) = (sk_c6))
% 7.70/1.75 | ((inverse @ sk_c1) = (sk_c6)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl1609, zip_derived_cl11])).
% 7.70/1.75 thf(zip_derived_cl1627, plain,
% 7.70/1.75 ((((inverse @ sk_c1) = (sk_c6)) | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl1622])).
% 7.70/1.75 thf(zip_derived_cl1, plain,
% 7.70/1.75 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 7.70/1.75 inference('cnf', [status(esa)], [left_inverse])).
% 7.70/1.75 thf(zip_derived_cl1628, plain,
% 7.70/1.75 ((((multiply @ sk_c6 @ sk_c1) = (identity)) | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl1627, zip_derived_cl1])).
% 7.70/1.75 thf(zip_derived_cl110, plain,
% 7.70/1.75 (![X0 : $i]:
% 7.70/1.75 (((X0) = (multiply @ sk_c5 @ (multiply @ sk_c6 @ X0)))
% 7.70/1.75 | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl107, zip_derived_cl0])).
% 7.70/1.75 thf(zip_derived_cl1678, plain,
% 7.70/1.75 ((((sk_c1) = (multiply @ sk_c5 @ identity))
% 7.70/1.75 | ((sk_c6) = (sk_c5))
% 7.70/1.75 | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl1628, zip_derived_cl110])).
% 7.70/1.75 thf(zip_derived_cl1681, plain,
% 7.70/1.75 ((((sk_c6) = (sk_c5)) | ((sk_c1) = (multiply @ sk_c5 @ identity)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl1678])).
% 7.70/1.75 thf(zip_derived_cl4109, plain,
% 7.70/1.75 ((((sk_c1) = (sk_c5)) | ((sk_c6) = (sk_c5)) | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl4058, zip_derived_cl1681])).
% 7.70/1.75 thf(zip_derived_cl4119, plain, ((((sk_c6) = (sk_c5)) | ((sk_c1) = (sk_c5)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl4109])).
% 7.70/1.75 thf(zip_derived_cl1627, plain,
% 7.70/1.75 ((((inverse @ sk_c1) = (sk_c6)) | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl1622])).
% 7.70/1.75 thf(prove_this_6, conjecture,
% 7.70/1.75 (~( ( ( inverse @ sk_c3 ) = ( sk_c6 ) ) |
% 7.70/1.75 ( ( multiply @ sk_c1 @ sk_c6 ) = ( sk_c7 ) ) ))).
% 7.70/1.75 thf(zf_stmt_13, negated_conjecture,
% 7.70/1.75 (( ( inverse @ sk_c3 ) = ( sk_c6 ) ) |
% 7.70/1.75 ( ( multiply @ sk_c1 @ sk_c6 ) = ( sk_c7 ) )),
% 7.70/1.75 inference('cnf.neg', [status(esa)], [prove_this_6])).
% 7.70/1.75 thf(zip_derived_cl8, plain,
% 7.70/1.75 ((((inverse @ sk_c3) = (sk_c6)) | ((multiply @ sk_c1 @ sk_c6) = (sk_c7)))),
% 7.70/1.75 inference('cnf', [status(esa)], [zf_stmt_13])).
% 7.70/1.75 thf(zip_derived_cl44, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i]:
% 7.70/1.75 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl34, zip_derived_cl0])).
% 7.70/1.75 thf(zip_derived_cl850, plain,
% 7.70/1.75 ((((sk_c6) = (multiply @ (inverse @ sk_c1) @ sk_c7))
% 7.70/1.75 | ((inverse @ sk_c3) = (sk_c6)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl44])).
% 7.70/1.75 thf(zip_derived_cl3507, plain, (((sk_c7) = (sk_c6))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl3506])).
% 7.70/1.75 thf(zip_derived_cl3593, plain,
% 7.70/1.75 ((((sk_c6) = (multiply @ (inverse @ sk_c1) @ sk_c6))
% 7.70/1.75 | ((inverse @ sk_c3) = (sk_c6)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl850, zip_derived_cl3507])).
% 7.70/1.75 thf(zip_derived_cl4293, plain,
% 7.70/1.75 ((((sk_c6) = (multiply @ sk_c6 @ sk_c6))
% 7.70/1.75 | ((sk_c6) = (sk_c5))
% 7.70/1.75 | ((inverse @ sk_c3) = (sk_c6)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl1627, zip_derived_cl3593])).
% 7.70/1.75 thf(zip_derived_cl3512, plain, (((multiply @ sk_c6 @ sk_c6) = (sk_c5))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl3, zip_derived_cl3507])).
% 7.70/1.75 thf(zip_derived_cl4463, plain,
% 7.70/1.75 ((((sk_c6) = (sk_c5))
% 7.70/1.75 | ((inverse @ sk_c3) = (sk_c6))
% 7.70/1.75 | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl4293, zip_derived_cl3512])).
% 7.70/1.75 thf(zip_derived_cl4470, plain,
% 7.70/1.75 ((((inverse @ sk_c3) = (sk_c6)) | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl4463])).
% 7.70/1.75 thf(zip_derived_cl1, plain,
% 7.70/1.75 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 7.70/1.75 inference('cnf', [status(esa)], [left_inverse])).
% 7.70/1.75 thf(zip_derived_cl4471, plain,
% 7.70/1.75 ((((multiply @ sk_c6 @ sk_c3) = (identity)) | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl4470, zip_derived_cl1])).
% 7.70/1.75 thf(zip_derived_cl110, plain,
% 7.70/1.75 (![X0 : $i]:
% 7.70/1.75 (((X0) = (multiply @ sk_c5 @ (multiply @ sk_c6 @ X0)))
% 7.70/1.75 | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl107, zip_derived_cl0])).
% 7.70/1.75 thf(zip_derived_cl4483, plain,
% 7.70/1.75 ((((sk_c3) = (multiply @ sk_c5 @ identity))
% 7.70/1.75 | ((sk_c6) = (sk_c5))
% 7.70/1.75 | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl4471, zip_derived_cl110])).
% 7.70/1.75 thf(zip_derived_cl4487, plain,
% 7.70/1.75 ((((sk_c6) = (sk_c5)) | ((sk_c3) = (multiply @ sk_c5 @ identity)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl4483])).
% 7.70/1.75 thf(zip_derived_cl1681, plain,
% 7.70/1.75 ((((sk_c6) = (sk_c5)) | ((sk_c1) = (multiply @ sk_c5 @ identity)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl1678])).
% 7.70/1.75 thf(zip_derived_cl4494, plain,
% 7.70/1.75 ((((sk_c1) = (sk_c3)) | ((sk_c6) = (sk_c5)) | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl4487, zip_derived_cl1681])).
% 7.70/1.75 thf(zip_derived_cl4502, plain, ((((sk_c6) = (sk_c5)) | ((sk_c1) = (sk_c3)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl4494])).
% 7.70/1.75 thf(prove_this_5, conjecture,
% 7.70/1.75 (~( ( ( multiply @ sk_c3 @ sk_c6 ) = ( sk_c4 ) ) |
% 7.70/1.75 ( ( multiply @ sk_c1 @ sk_c6 ) = ( sk_c7 ) ) ))).
% 7.70/1.75 thf(zf_stmt_14, negated_conjecture,
% 7.70/1.75 (( ( multiply @ sk_c3 @ sk_c6 ) = ( sk_c4 ) ) |
% 7.70/1.75 ( ( multiply @ sk_c1 @ sk_c6 ) = ( sk_c7 ) )),
% 7.70/1.75 inference('cnf.neg', [status(esa)], [prove_this_5])).
% 7.70/1.75 thf(zip_derived_cl7, plain,
% 7.70/1.75 ((((multiply @ sk_c3 @ sk_c6) = (sk_c4))
% 7.70/1.75 | ((multiply @ sk_c1 @ sk_c6) = (sk_c7)))),
% 7.70/1.75 inference('cnf', [status(esa)], [zf_stmt_14])).
% 7.70/1.75 thf(zip_derived_cl3507, plain, (((sk_c7) = (sk_c6))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl3506])).
% 7.70/1.75 thf(zip_derived_cl3516, plain,
% 7.70/1.75 ((((multiply @ sk_c3 @ sk_c6) = (sk_c4))
% 7.70/1.75 | ((multiply @ sk_c1 @ sk_c6) = (sk_c6)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl3507])).
% 7.70/1.75 thf(zip_derived_cl4516, plain,
% 7.70/1.75 ((((multiply @ sk_c1 @ sk_c6) = (sk_c4))
% 7.70/1.75 | ((sk_c6) = (sk_c5))
% 7.70/1.75 | ((multiply @ sk_c1 @ sk_c6) = (sk_c6)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl4502, zip_derived_cl3516])).
% 7.70/1.75 thf(zip_derived_cl6942, plain,
% 7.70/1.75 ((((sk_c4) != (sk_c6))
% 7.70/1.75 | ((multiply @ sk_c1 @ sk_c6) = (sk_c6))
% 7.70/1.75 | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('eq_fact', [status(thm)], [zip_derived_cl4516])).
% 7.70/1.75 thf(prove_this_4, conjecture,
% 7.70/1.75 (~( ( ( multiply @ sk_c6 @ sk_c4 ) = ( sk_c5 ) ) |
% 7.70/1.75 ( ( multiply @ sk_c1 @ sk_c6 ) = ( sk_c7 ) ) ))).
% 7.70/1.75 thf(zf_stmt_15, negated_conjecture,
% 7.70/1.75 (( ( multiply @ sk_c6 @ sk_c4 ) = ( sk_c5 ) ) |
% 7.70/1.75 ( ( multiply @ sk_c1 @ sk_c6 ) = ( sk_c7 ) )),
% 7.70/1.75 inference('cnf.neg', [status(esa)], [prove_this_4])).
% 7.70/1.75 thf(zip_derived_cl6, plain,
% 7.70/1.75 ((((multiply @ sk_c6 @ sk_c4) = (sk_c5))
% 7.70/1.75 | ((multiply @ sk_c1 @ sk_c6) = (sk_c7)))),
% 7.70/1.75 inference('cnf', [status(esa)], [zf_stmt_15])).
% 7.70/1.75 thf(zip_derived_cl3507, plain, (((sk_c7) = (sk_c6))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl3506])).
% 7.70/1.75 thf(zip_derived_cl3515, plain,
% 7.70/1.75 ((((multiply @ sk_c6 @ sk_c4) = (sk_c5))
% 7.70/1.75 | ((multiply @ sk_c1 @ sk_c6) = (sk_c6)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl6, zip_derived_cl3507])).
% 7.70/1.75 thf(zip_derived_cl11, plain,
% 7.70/1.75 ((((multiply @ sk_c6 @ sk_c4) = (sk_c5)) | ((inverse @ sk_c1) = (sk_c6)))),
% 7.70/1.75 inference('cnf', [status(esa)], [zf_stmt_12])).
% 7.70/1.75 thf(zip_derived_cl110, plain,
% 7.70/1.75 (![X0 : $i]:
% 7.70/1.75 (((X0) = (multiply @ sk_c5 @ (multiply @ sk_c6 @ X0)))
% 7.70/1.75 | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl107, zip_derived_cl0])).
% 7.70/1.75 thf(zip_derived_cl119, plain,
% 7.70/1.75 ((((sk_c4) = (multiply @ sk_c5 @ sk_c5))
% 7.70/1.75 | ((inverse @ sk_c1) = (sk_c6))
% 7.70/1.75 | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl110])).
% 7.70/1.75 thf(zip_derived_cl115, plain,
% 7.70/1.75 ((((sk_c7) = (multiply @ sk_c5 @ sk_c5)) | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl110])).
% 7.70/1.75 thf(zip_derived_cl138, plain,
% 7.70/1.75 ((((sk_c7) = (sk_c4))
% 7.70/1.75 | ((sk_c6) = (sk_c5))
% 7.70/1.75 | ((inverse @ sk_c1) = (sk_c6))
% 7.70/1.75 | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl119, zip_derived_cl115])).
% 7.70/1.75 thf(zip_derived_cl140, plain,
% 7.70/1.75 ((((inverse @ sk_c1) = (sk_c6))
% 7.70/1.75 | ((sk_c6) = (sk_c5))
% 7.70/1.75 | ((sk_c7) = (sk_c4)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl138])).
% 7.70/1.75 thf(zip_derived_cl1, plain,
% 7.70/1.75 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 7.70/1.75 inference('cnf', [status(esa)], [left_inverse])).
% 7.70/1.75 thf(zip_derived_cl141, plain,
% 7.70/1.75 ((((multiply @ sk_c6 @ sk_c1) = (identity))
% 7.70/1.75 | ((sk_c7) = (sk_c4))
% 7.70/1.75 | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl140, zip_derived_cl1])).
% 7.70/1.75 thf(zip_derived_cl2, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i, X2 : $i]:
% 7.70/1.75 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 7.70/1.75 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 7.70/1.75 inference('cnf', [status(esa)], [associativity])).
% 7.70/1.75 thf(zip_derived_cl158, plain,
% 7.70/1.75 (![X0 : $i]:
% 7.70/1.75 (((multiply @ identity @ X0)
% 7.70/1.75 = (multiply @ sk_c6 @ (multiply @ sk_c1 @ X0)))
% 7.70/1.75 | ((sk_c6) = (sk_c5))
% 7.70/1.75 | ((sk_c7) = (sk_c4)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl141, zip_derived_cl2])).
% 7.70/1.75 thf(zip_derived_cl0, plain,
% 7.70/1.75 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 7.70/1.75 inference('cnf', [status(esa)], [left_identity])).
% 7.70/1.75 thf(zip_derived_cl160, plain,
% 7.70/1.75 (![X0 : $i]:
% 7.70/1.75 (((X0) = (multiply @ sk_c6 @ (multiply @ sk_c1 @ X0)))
% 7.70/1.75 | ((sk_c6) = (sk_c5))
% 7.70/1.75 | ((sk_c7) = (sk_c4)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl158, zip_derived_cl0])).
% 7.70/1.75 thf(zip_derived_cl3507, plain, (((sk_c7) = (sk_c6))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl3506])).
% 7.70/1.75 thf(zip_derived_cl4190, plain,
% 7.70/1.75 (![X0 : $i]:
% 7.70/1.75 (((X0) = (multiply @ sk_c6 @ (multiply @ sk_c1 @ X0)))
% 7.70/1.75 | ((sk_c6) = (sk_c5))
% 7.70/1.75 | ((sk_c6) = (sk_c4)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl160, zip_derived_cl3507])).
% 7.70/1.75 thf(zip_derived_cl4222, plain,
% 7.70/1.75 ((((sk_c6) = (multiply @ sk_c6 @ sk_c6))
% 7.70/1.75 | ((multiply @ sk_c6 @ sk_c4) = (sk_c5))
% 7.70/1.75 | ((sk_c6) = (sk_c4))
% 7.70/1.75 | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl3515, zip_derived_cl4190])).
% 7.70/1.75 thf(zip_derived_cl3512, plain, (((multiply @ sk_c6 @ sk_c6) = (sk_c5))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl3, zip_derived_cl3507])).
% 7.70/1.75 thf(zip_derived_cl4226, plain,
% 7.70/1.75 ((((sk_c6) = (sk_c5))
% 7.70/1.75 | ((multiply @ sk_c6 @ sk_c4) = (sk_c5))
% 7.70/1.75 | ((sk_c6) = (sk_c4))
% 7.70/1.75 | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('demod', [status(thm)],
% 7.70/1.75 [zip_derived_cl4222, zip_derived_cl3512])).
% 7.70/1.75 thf(zip_derived_cl4227, plain,
% 7.70/1.75 ((((sk_c6) = (sk_c4))
% 7.70/1.75 | ((multiply @ sk_c6 @ sk_c4) = (sk_c5))
% 7.70/1.75 | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl4226])).
% 7.70/1.75 thf(zip_derived_cl44, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i]:
% 7.70/1.75 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl34, zip_derived_cl0])).
% 7.70/1.75 thf(zip_derived_cl4230, plain,
% 7.70/1.75 ((((sk_c4) = (multiply @ (inverse @ sk_c6) @ sk_c5))
% 7.70/1.75 | ((sk_c6) = (sk_c5))
% 7.70/1.75 | ((sk_c6) = (sk_c4)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl4227, zip_derived_cl44])).
% 7.70/1.75 thf(zip_derived_cl807, plain,
% 7.70/1.75 (((sk_c7) = (multiply @ (inverse @ sk_c6) @ sk_c5))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl44])).
% 7.70/1.75 thf(zip_derived_cl3507, plain, (((sk_c7) = (sk_c6))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl3506])).
% 7.70/1.75 thf(zip_derived_cl3588, plain,
% 7.70/1.75 (((sk_c6) = (multiply @ (inverse @ sk_c6) @ sk_c5))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl807, zip_derived_cl3507])).
% 7.70/1.75 thf(zip_derived_cl4238, plain,
% 7.70/1.75 ((((sk_c4) = (sk_c6)) | ((sk_c6) = (sk_c5)) | ((sk_c6) = (sk_c4)))),
% 7.70/1.75 inference('demod', [status(thm)],
% 7.70/1.75 [zip_derived_cl4230, zip_derived_cl3588])).
% 7.70/1.75 thf(zip_derived_cl4239, plain, ((((sk_c6) = (sk_c5)) | ((sk_c4) = (sk_c6)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl4238])).
% 7.70/1.75 thf(zip_derived_cl6946, plain,
% 7.70/1.75 ((((sk_c6) = (sk_c5)) | ((multiply @ sk_c1 @ sk_c6) = (sk_c6)))),
% 7.70/1.75 inference('clc', [status(thm)], [zip_derived_cl6942, zip_derived_cl4239])).
% 7.70/1.75 thf(zip_derived_cl6953, plain,
% 7.70/1.75 ((((multiply @ sk_c5 @ sk_c6) = (sk_c6))
% 7.70/1.75 | ((sk_c6) = (sk_c5))
% 7.70/1.75 | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl4119, zip_derived_cl6946])).
% 7.70/1.75 thf(zip_derived_cl6955, plain,
% 7.70/1.75 ((((sk_c6) = (sk_c5)) | ((multiply @ sk_c5 @ sk_c6) = (sk_c6)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl6953])).
% 7.70/1.75 thf(zip_derived_cl103, plain,
% 7.70/1.75 ((((multiply @ sk_c5 @ sk_c6) = (identity)) | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl102, zip_derived_cl1])).
% 7.70/1.75 thf(zip_derived_cl6962, plain,
% 7.70/1.75 ((((sk_c6) = (identity)) | ((sk_c6) = (sk_c5)) | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl6955, zip_derived_cl103])).
% 7.70/1.75 thf(zip_derived_cl6973, plain,
% 7.70/1.75 ((((sk_c6) = (sk_c5)) | ((sk_c6) = (identity)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl6962])).
% 7.70/1.75 thf(zip_derived_cl3588, plain,
% 7.70/1.75 (((sk_c6) = (multiply @ (inverse @ sk_c6) @ sk_c5))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl807, zip_derived_cl3507])).
% 7.70/1.75 thf(zip_derived_cl7001, plain,
% 7.70/1.75 ((((sk_c6) = (multiply @ (inverse @ sk_c6) @ sk_c6))
% 7.70/1.75 | ((sk_c6) = (identity)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl6973, zip_derived_cl3588])).
% 7.70/1.75 thf(zip_derived_cl1, plain,
% 7.70/1.75 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 7.70/1.75 inference('cnf', [status(esa)], [left_inverse])).
% 7.70/1.75 thf(zip_derived_cl7072, plain,
% 7.70/1.75 ((((sk_c6) = (identity)) | ((sk_c6) = (identity)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl7001, zip_derived_cl1])).
% 7.70/1.75 thf(zip_derived_cl7073, plain, (((sk_c6) = (identity))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl7072])).
% 7.70/1.75 thf(zip_derived_cl0, plain,
% 7.70/1.75 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 7.70/1.75 inference('cnf', [status(esa)], [left_identity])).
% 7.70/1.75 thf(zip_derived_cl7073, plain, (((sk_c6) = (identity))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl7072])).
% 7.70/1.75 thf(zip_derived_cl7258, plain,
% 7.70/1.75 (((sk_c5) = (multiply @ (inverse @ (inverse @ sk_c5)) @ identity))),
% 7.70/1.75 inference('demod', [status(thm)],
% 7.70/1.75 [zip_derived_cl5247, zip_derived_cl7073, zip_derived_cl0,
% 7.70/1.75 zip_derived_cl7073])).
% 7.70/1.75 thf(zip_derived_cl1152, plain, ((((sk_c6) = (sk_c5)) | ((sk_c6) = (sk_c7)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl1149])).
% 7.70/1.75 thf(zip_derived_cl807, plain,
% 7.70/1.75 (((sk_c7) = (multiply @ (inverse @ sk_c6) @ sk_c5))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl44])).
% 7.70/1.75 thf(zip_derived_cl1183, plain,
% 7.70/1.75 ((((sk_c7) = (multiply @ (inverse @ sk_c6) @ sk_c6))
% 7.70/1.75 | ((sk_c6) = (sk_c7)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl1152, zip_derived_cl807])).
% 7.70/1.75 thf(zip_derived_cl1, plain,
% 7.70/1.75 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 7.70/1.75 inference('cnf', [status(esa)], [left_inverse])).
% 7.70/1.75 thf(zip_derived_cl1198, plain,
% 7.70/1.75 ((((sk_c7) = (identity)) | ((sk_c6) = (sk_c7)))),
% 7.70/1.75 inference('demod', [status(thm)], [zip_derived_cl1183, zip_derived_cl1])).
% 7.70/1.75 thf(zip_derived_cl1232, plain,
% 7.70/1.75 ((((sk_c6) != (identity)) | ((sk_c7) = (identity)))),
% 7.70/1.75 inference('eq_fact', [status(thm)], [zip_derived_cl1198])).
% 7.70/1.75 thf(zip_derived_cl526, plain,
% 7.70/1.75 ((((multiply @ sk_c5 @ sk_c7) = (identity)) | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl524, zip_derived_cl1])).
% 7.70/1.75 thf(zip_derived_cl35, plain,
% 7.70/1.75 (![X0 : $i]:
% 7.70/1.75 ((multiply @ sk_c5 @ X0)
% 7.70/1.75 = (multiply @ sk_c6 @ (multiply @ sk_c7 @ X0)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl2])).
% 7.70/1.75 thf(zip_derived_cl738, plain,
% 7.70/1.75 ((((identity) = (multiply @ sk_c6 @ (multiply @ sk_c7 @ sk_c7)))
% 7.70/1.75 | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl526, zip_derived_cl35])).
% 7.70/1.75 thf(zip_derived_cl1259, plain,
% 7.70/1.75 ((((identity) = (multiply @ sk_c6 @ (multiply @ identity @ sk_c7)))
% 7.70/1.75 | ((sk_c6) != (identity))
% 7.70/1.75 | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl1232, zip_derived_cl738])).
% 7.70/1.75 thf(zip_derived_cl0, plain,
% 7.70/1.75 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 7.70/1.75 inference('cnf', [status(esa)], [left_identity])).
% 7.70/1.75 thf(zip_derived_cl3, plain, (((multiply @ sk_c6 @ sk_c7) = (sk_c5))),
% 7.70/1.75 inference('cnf', [status(esa)], [zf_stmt_1])).
% 7.70/1.75 thf(zip_derived_cl1298, plain,
% 7.70/1.75 ((((identity) = (sk_c5)) | ((sk_c6) != (identity)) | ((sk_c6) = (sk_c5)))),
% 7.70/1.75 inference('demod', [status(thm)],
% 7.70/1.75 [zip_derived_cl1259, zip_derived_cl0, zip_derived_cl3])).
% 7.70/1.75 thf(zip_derived_cl1299, plain,
% 7.70/1.75 ((((identity) = (sk_c5))
% 7.70/1.75 | ((sk_c6) != (identity))
% 7.70/1.75 | ((identity) = (sk_c5)))),
% 7.70/1.75 inference('local_rewriting', [status(thm)], [zip_derived_cl1298])).
% 7.70/1.75 thf(zip_derived_cl1300, plain,
% 7.70/1.75 ((((sk_c6) != (identity)) | ((identity) = (sk_c5)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl1299])).
% 7.70/1.75 thf(zip_derived_cl7073, plain, (((sk_c6) = (identity))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl7072])).
% 7.70/1.75 thf(zip_derived_cl7152, plain,
% 7.70/1.75 ((((identity) != (identity)) | ((identity) = (sk_c5)))),
% 7.70/1.75 inference('demod', [status(thm)],
% 7.70/1.75 [zip_derived_cl1300, zip_derived_cl7073])).
% 7.70/1.75 thf(zip_derived_cl7153, plain, (((identity) = (sk_c5))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl7152])).
% 7.70/1.75 thf(zip_derived_cl7153, plain, (((identity) = (sk_c5))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl7152])).
% 7.70/1.75 thf(zip_derived_cl9084, plain,
% 7.70/1.75 (((identity) = (multiply @ (inverse @ (inverse @ identity)) @ identity))),
% 7.70/1.75 inference('demod', [status(thm)],
% 7.70/1.75 [zip_derived_cl7258, zip_derived_cl7153, zip_derived_cl7153])).
% 7.70/1.75 thf(zip_derived_cl2, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i, X2 : $i]:
% 7.70/1.75 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 7.70/1.75 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 7.70/1.75 inference('cnf', [status(esa)], [associativity])).
% 7.70/1.75 thf(zip_derived_cl9085, plain,
% 7.70/1.75 (![X0 : $i]:
% 7.70/1.75 ((multiply @ identity @ X0)
% 7.70/1.75 = (multiply @ (inverse @ (inverse @ identity)) @
% 7.70/1.75 (multiply @ identity @ X0)))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl9084, zip_derived_cl2])).
% 7.70/1.75 thf(zip_derived_cl0, plain,
% 7.70/1.75 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 7.70/1.75 inference('cnf', [status(esa)], [left_identity])).
% 7.70/1.75 thf(zip_derived_cl0, plain,
% 7.70/1.75 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 7.70/1.75 inference('cnf', [status(esa)], [left_identity])).
% 7.70/1.75 thf(zip_derived_cl9098, plain,
% 7.70/1.75 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ identity)) @ X0))),
% 7.70/1.75 inference('demod', [status(thm)],
% 7.70/1.75 [zip_derived_cl9085, zip_derived_cl0, zip_derived_cl0])).
% 7.70/1.75 thf(zip_derived_cl1, plain,
% 7.70/1.75 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 7.70/1.75 inference('cnf', [status(esa)], [left_inverse])).
% 7.70/1.75 thf(zip_derived_cl9165, plain, (((inverse @ identity) = (identity))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl9098, zip_derived_cl1])).
% 7.70/1.75 thf(zip_derived_cl7153, plain, (((identity) = (sk_c5))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl7152])).
% 7.70/1.75 thf(zip_derived_cl0, plain,
% 7.70/1.75 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 7.70/1.75 inference('cnf', [status(esa)], [left_identity])).
% 7.70/1.75 thf(zip_derived_cl1232, plain,
% 7.70/1.75 ((((sk_c6) != (identity)) | ((sk_c7) = (identity)))),
% 7.70/1.75 inference('eq_fact', [status(thm)], [zip_derived_cl1198])).
% 7.70/1.75 thf(zip_derived_cl7073, plain, (((sk_c6) = (identity))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl7072])).
% 7.70/1.75 thf(zip_derived_cl7146, plain,
% 7.70/1.75 ((((identity) != (identity)) | ((sk_c7) = (identity)))),
% 7.70/1.75 inference('demod', [status(thm)],
% 7.70/1.75 [zip_derived_cl1232, zip_derived_cl7073])).
% 7.70/1.75 thf(zip_derived_cl7147, plain, (((sk_c7) = (identity))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl7146])).
% 7.70/1.75 thf(zip_derived_cl7073, plain, (((sk_c6) = (identity))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl7072])).
% 7.70/1.75 thf(zip_derived_cl13905, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i]:
% 7.70/1.75 (((identity) != (identity))
% 7.70/1.75 | ((identity) != (identity))
% 7.70/1.75 | ((X1) != (identity))
% 7.70/1.75 | ((multiply @ X0 @ identity) != (X1))
% 7.70/1.75 | ((inverse @ X0) != (identity))
% 7.70/1.75 | ((identity) != (identity))
% 7.70/1.75 | ((identity) != (identity)))),
% 7.70/1.75 inference('demod', [status(thm)],
% 7.70/1.75 [zip_derived_cl2454, zip_derived_cl9165, zip_derived_cl7153,
% 7.70/1.75 zip_derived_cl0, zip_derived_cl7147, zip_derived_cl7073])).
% 7.70/1.75 thf(zip_derived_cl13906, plain,
% 7.70/1.75 (![X0 : $i, X1 : $i]:
% 7.70/1.75 (((inverse @ X0) != (identity))
% 7.70/1.75 | ((multiply @ X0 @ identity) != (X1))
% 7.70/1.75 | ((X1) != (identity)))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl13905])).
% 7.70/1.75 thf(zip_derived_cl13911, plain,
% 7.70/1.75 (![X0 : $i]:
% 7.70/1.75 (((identity) != (X0))
% 7.70/1.75 | ((X0) != (identity))
% 7.70/1.75 | ((inverse @ identity) != (identity)))),
% 7.70/1.75 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl13906])).
% 7.70/1.75 thf(zip_derived_cl9165, plain, (((inverse @ identity) = (identity))),
% 7.70/1.75 inference('sup+', [status(thm)], [zip_derived_cl9098, zip_derived_cl1])).
% 7.70/1.75 thf(zip_derived_cl13955, plain,
% 7.70/1.75 (![X0 : $i]:
% 7.70/1.75 (((identity) != (X0))
% 7.70/1.75 | ((X0) != (identity))
% 7.70/1.75 | ((identity) != (identity)))),
% 7.70/1.75 inference('demod', [status(thm)],
% 7.70/1.75 [zip_derived_cl13911, zip_derived_cl9165])).
% 7.70/1.75 thf(zip_derived_cl13956, plain, (![X0 : $i]: ((identity) != (X0))),
% 7.70/1.75 inference('simplify', [status(thm)], [zip_derived_cl13955])).
% 7.70/1.75 thf(zip_derived_cl13985, plain, ($false),
% 7.70/1.75 inference('eq_res', [status(thm)], [zip_derived_cl13956])).
% 7.70/1.75
% 7.70/1.75 % SZS output end Refutation
% 7.70/1.75
% 7.70/1.75
% 7.70/1.75 % Terminating...
% 8.13/1.82 % Runner terminated.
% 8.13/1.82 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------