TSTP Solution File: GRP283-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP283-1 : 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.jFYDqxI1f4 true
% Computer : n014.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 01:51:02 EDT 2023
% Result : Unsatisfiable 2.09s 0.94s
% Output : Refutation 2.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP283-1 : 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.jFYDqxI1f4 true
% 0.17/0.35 % Computer : n014.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Mon Aug 28 20:02:45 EDT 2023
% 0.17/0.36 % CPUTime :
% 0.17/0.36 % Running portfolio for 300 s
% 0.17/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.36 % Number of cores: 8
% 0.17/0.36 % Python version: Python 3.6.8
% 0.17/0.36 % Running in FO mode
% 0.21/0.64 % Total configuration time : 435
% 0.21/0.64 % Estimated wc time : 1092
% 0.21/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.71 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.72 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 2.09/0.94 % Solved by fo/fo7.sh.
% 2.09/0.94 % done 315 iterations in 0.127s
% 2.09/0.94 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 2.09/0.94 % SZS output start Refutation
% 2.09/0.94 thf(sk_c3_type, type, sk_c3: $i).
% 2.09/0.94 thf(sk_c6_type, type, sk_c6: $i).
% 2.09/0.94 thf(sk_c1_type, type, sk_c1: $i).
% 2.09/0.94 thf(sk_c5_type, type, sk_c5: $i).
% 2.09/0.94 thf(identity_type, type, identity: $i).
% 2.09/0.94 thf(multiply_type, type, multiply: $i > $i > $i).
% 2.09/0.94 thf(sk_c7_type, type, sk_c7: $i).
% 2.09/0.94 thf(inverse_type, type, inverse: $i > $i).
% 2.09/0.94 thf(sk_c4_type, type, sk_c4: $i).
% 2.09/0.94 thf(sk_c2_type, type, sk_c2: $i).
% 2.09/0.94 thf(sk_c8_type, type, sk_c8: $i).
% 2.09/0.94 thf(prove_this_37, conjecture,
% 2.09/0.94 (~( ( ( inverse @ X2 ) != ( sk_c8 ) ) |
% 2.09/0.94 ( ( multiply @ X2 @ sk_c8 ) != ( sk_c6 ) ) |
% 2.09/0.94 ( ( inverse @ X1 ) != ( sk_c7 ) ) |
% 2.09/0.94 ( ( multiply @ X1 @ sk_c7 ) != ( sk_c8 ) ) |
% 2.09/0.94 ( ( inverse @ sk_c7 ) != ( sk_c6 ) ) |
% 2.09/0.94 ( ( multiply @ sk_c7 @ sk_c6 ) != ( sk_c8 ) ) |
% 2.09/0.94 ( ( inverse @ X5 ) != ( sk_c8 ) ) |
% 2.09/0.94 ( ( multiply @ X5 @ sk_c8 ) != ( X4 ) ) |
% 2.09/0.94 ( ( multiply @ sk_c8 @ X4 ) != ( sk_c7 ) ) |
% 2.09/0.94 ( ( inverse @ X3 ) != ( sk_c8 ) ) |
% 2.09/0.94 ( ( multiply @ X3 @ sk_c8 ) != ( sk_c7 ) ) |
% 2.09/0.94 ( ( multiply @ sk_c8 @ sk_c7 ) != ( sk_c6 ) ) ))).
% 2.09/0.94 thf(zf_stmt_0, negated_conjecture,
% 2.09/0.94 (( ( inverse @ X2 ) != ( sk_c8 ) ) |
% 2.09/0.94 ( ( multiply @ X2 @ sk_c8 ) != ( sk_c6 ) ) |
% 2.09/0.94 ( ( inverse @ X1 ) != ( sk_c7 ) ) |
% 2.09/0.94 ( ( multiply @ X1 @ sk_c7 ) != ( sk_c8 ) ) |
% 2.09/0.94 ( ( inverse @ sk_c7 ) != ( sk_c6 ) ) |
% 2.09/0.94 ( ( multiply @ sk_c7 @ sk_c6 ) != ( sk_c8 ) ) |
% 2.09/0.94 ( ( inverse @ X5 ) != ( sk_c8 ) ) |
% 2.09/0.94 ( ( multiply @ X5 @ sk_c8 ) != ( X4 ) ) |
% 2.09/0.94 ( ( multiply @ sk_c8 @ X4 ) != ( sk_c7 ) ) |
% 2.09/0.94 ( ( inverse @ X3 ) != ( sk_c8 ) ) |
% 2.09/0.94 ( ( multiply @ X3 @ sk_c8 ) != ( sk_c7 ) ) |
% 2.09/0.94 ( ( multiply @ sk_c8 @ sk_c7 ) != ( sk_c6 ) )),
% 2.09/0.94 inference('cnf.neg', [status(esa)], [prove_this_37])).
% 2.09/0.94 thf(zip_derived_cl39, plain,
% 2.09/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 2.09/0.94 (((inverse @ X0) != (sk_c8))
% 2.09/0.94 | ((multiply @ X0 @ sk_c8) != (sk_c6))
% 2.09/0.94 | ((inverse @ X1) != (sk_c7))
% 2.09/0.94 | ((multiply @ X1 @ sk_c7) != (sk_c8))
% 2.09/0.94 | ((inverse @ sk_c7) != (sk_c6))
% 2.09/0.94 | ((multiply @ sk_c7 @ sk_c6) != (sk_c8))
% 2.09/0.94 | ((inverse @ X2) != (sk_c8))
% 2.09/0.94 | ((multiply @ X2 @ sk_c8) != (X3))
% 2.09/0.94 | ((multiply @ sk_c8 @ X3) != (sk_c7))
% 2.09/0.94 | ((inverse @ X4) != (sk_c8))
% 2.09/0.94 | ((multiply @ X4 @ sk_c8) != (sk_c7))
% 2.09/0.94 | ((multiply @ sk_c8 @ sk_c7) != (sk_c6)))),
% 2.09/0.94 inference('cnf', [status(esa)], [zf_stmt_0])).
% 2.09/0.94 thf(zip_derived_cl40, plain,
% 2.09/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 2.09/0.94 (((inverse @ X0) != (sk_c8))
% 2.09/0.94 | ((multiply @ X0 @ sk_c8) != (multiply @ sk_c8 @ sk_c7))
% 2.09/0.94 | ((inverse @ X1) != (sk_c7))
% 2.09/0.94 | ((multiply @ X1 @ sk_c7) != (sk_c8))
% 2.09/0.94 | ((inverse @ sk_c7) != (sk_c6))
% 2.09/0.94 | ((multiply @ sk_c7 @ (multiply @ sk_c8 @ sk_c7)) != (sk_c8))
% 2.09/0.94 | ((inverse @ X2) != (sk_c8))
% 2.09/0.94 | ((multiply @ X2 @ sk_c8) != (X3))
% 2.09/0.94 | ((multiply @ sk_c8 @ X3) != (sk_c7))
% 2.09/0.94 | ((inverse @ X4) != (sk_c8))
% 2.09/0.94 | ((multiply @ X4 @ sk_c8) != (sk_c7))
% 2.09/0.94 | ((multiply @ sk_c8 @ sk_c7) != (sk_c6)))),
% 2.09/0.94 inference('local_rewriting', [status(thm)], [zip_derived_cl39])).
% 2.09/0.94 thf(prove_this_16, conjecture,
% 2.09/0.94 (~( ( ( inverse @ sk_c4 ) = ( sk_c7 ) ) |
% 2.09/0.94 ( ( inverse @ sk_c1 ) = ( sk_c8 ) ) ))).
% 2.09/0.94 thf(zf_stmt_1, negated_conjecture,
% 2.09/0.94 (( ( inverse @ sk_c4 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c8 ) )),
% 2.09/0.94 inference('cnf.neg', [status(esa)], [prove_this_16])).
% 2.09/0.94 thf(zip_derived_cl18, plain,
% 2.09/0.94 ((((inverse @ sk_c4) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c8)))),
% 2.09/0.94 inference('cnf', [status(esa)], [zf_stmt_1])).
% 2.09/0.94 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 2.09/0.94 thf(zip_derived_cl1, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.94 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.94 thf(zip_derived_cl49, plain,
% 2.09/0.94 ((((multiply @ sk_c8 @ sk_c1) = (identity))
% 2.09/0.94 | ((inverse @ sk_c4) = (sk_c7)))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl18, zip_derived_cl1])).
% 2.09/0.94 thf(zip_derived_cl1, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.94 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.94 thf(associativity, axiom,
% 2.09/0.94 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 2.09/0.94 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 2.09/0.94 thf(zip_derived_cl2, plain,
% 2.09/0.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.09/0.94 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 2.09/0.94 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 2.09/0.94 inference('cnf', [status(esa)], [associativity])).
% 2.09/0.94 thf(zip_derived_cl68, plain,
% 2.09/0.94 (![X0 : $i, X1 : $i]:
% 2.09/0.94 ((multiply @ identity @ X0)
% 2.09/0.94 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 2.09/0.94 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 2.09/0.94 thf(zip_derived_cl0, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 2.09/0.94 inference('cnf', [status(esa)], [left_identity])).
% 2.09/0.94 thf(zip_derived_cl103, plain,
% 2.09/0.94 (![X0 : $i, X1 : $i]:
% 2.09/0.94 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.09/0.94 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl0])).
% 2.09/0.94 thf(zip_derived_cl125, plain,
% 2.09/0.94 ((((sk_c1) = (multiply @ (inverse @ sk_c8) @ identity))
% 2.09/0.94 | ((inverse @ sk_c4) = (sk_c7)))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl49, zip_derived_cl103])).
% 2.09/0.94 thf(prove_this_10, conjecture,
% 2.09/0.94 (~( ( ( inverse @ sk_c4 ) = ( sk_c7 ) ) |
% 2.09/0.94 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c7 ) ) ))).
% 2.09/0.94 thf(zf_stmt_2, negated_conjecture,
% 2.09/0.94 (( ( inverse @ sk_c4 ) = ( sk_c7 ) ) |
% 2.09/0.94 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c7 ) )),
% 2.09/0.94 inference('cnf.neg', [status(esa)], [prove_this_10])).
% 2.09/0.94 thf(zip_derived_cl12, plain,
% 2.09/0.94 ((((inverse @ sk_c4) = (sk_c7)) | ((multiply @ sk_c1 @ sk_c8) = (sk_c7)))),
% 2.09/0.94 inference('cnf', [status(esa)], [zf_stmt_2])).
% 2.09/0.94 thf(zip_derived_cl261, plain,
% 2.09/0.94 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c8)
% 2.09/0.94 = (sk_c7))
% 2.09/0.94 | ((inverse @ sk_c4) = (sk_c7))
% 2.09/0.94 | ((inverse @ sk_c4) = (sk_c7)))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl125, zip_derived_cl12])).
% 2.09/0.94 thf(zip_derived_cl2, plain,
% 2.09/0.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.09/0.94 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 2.09/0.94 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 2.09/0.94 inference('cnf', [status(esa)], [associativity])).
% 2.09/0.94 thf(zip_derived_cl0, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 2.09/0.94 inference('cnf', [status(esa)], [left_identity])).
% 2.09/0.94 thf(zip_derived_cl1, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.94 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.94 thf(zip_derived_cl279, plain,
% 2.09/0.94 ((((identity) = (sk_c7))
% 2.09/0.94 | ((inverse @ sk_c4) = (sk_c7))
% 2.09/0.94 | ((inverse @ sk_c4) = (sk_c7)))),
% 2.09/0.94 inference('demod', [status(thm)],
% 2.09/0.94 [zip_derived_cl261, zip_derived_cl2, zip_derived_cl0,
% 2.09/0.94 zip_derived_cl1])).
% 2.09/0.94 thf(zip_derived_cl280, plain,
% 2.09/0.94 ((((inverse @ sk_c4) = (sk_c7)) | ((identity) = (sk_c7)))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl279])).
% 2.09/0.94 thf(zip_derived_cl1, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.94 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.94 thf(zip_derived_cl319, plain,
% 2.09/0.94 ((((multiply @ sk_c7 @ sk_c4) = (identity)) | ((identity) = (sk_c7)))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl280, zip_derived_cl1])).
% 2.09/0.94 thf(zip_derived_cl103, plain,
% 2.09/0.94 (![X0 : $i, X1 : $i]:
% 2.09/0.94 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.09/0.94 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl0])).
% 2.09/0.94 thf(zip_derived_cl440, plain,
% 2.09/0.94 ((((sk_c4) = (multiply @ (inverse @ sk_c7) @ identity))
% 2.09/0.94 | ((identity) = (sk_c7)))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl319, zip_derived_cl103])).
% 2.09/0.94 thf(zip_derived_cl1, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.94 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.94 thf(zip_derived_cl103, plain,
% 2.09/0.94 (![X0 : $i, X1 : $i]:
% 2.09/0.94 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.09/0.94 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl0])).
% 2.09/0.94 thf(zip_derived_cl121, plain,
% 2.09/0.94 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl103])).
% 2.09/0.94 thf(zip_derived_cl103, plain,
% 2.09/0.94 (![X0 : $i, X1 : $i]:
% 2.09/0.94 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.09/0.94 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl0])).
% 2.09/0.94 thf(zip_derived_cl103, plain,
% 2.09/0.94 (![X0 : $i, X1 : $i]:
% 2.09/0.94 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.09/0.94 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl0])).
% 2.09/0.94 thf(zip_derived_cl118, plain,
% 2.09/0.94 (![X0 : $i, X1 : $i]:
% 2.09/0.94 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl103, zip_derived_cl103])).
% 2.09/0.94 thf(zip_derived_cl778, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl118])).
% 2.09/0.94 thf(zip_derived_cl815, plain,
% 2.09/0.94 ((((sk_c4) = (inverse @ sk_c7)) | ((identity) = (sk_c7)))),
% 2.09/0.94 inference('demod', [status(thm)], [zip_derived_cl440, zip_derived_cl778])).
% 2.09/0.94 thf(prove_this_15, conjecture,
% 2.09/0.94 (~( ( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 2.09/0.94 ( ( inverse @ sk_c1 ) = ( sk_c8 ) ) ))).
% 2.09/0.94 thf(zf_stmt_3, negated_conjecture,
% 2.09/0.94 (( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 2.09/0.94 ( ( inverse @ sk_c1 ) = ( sk_c8 ) )),
% 2.09/0.94 inference('cnf.neg', [status(esa)], [prove_this_15])).
% 2.09/0.94 thf(zip_derived_cl17, plain,
% 2.09/0.94 ((((multiply @ sk_c4 @ sk_c7) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c8)))),
% 2.09/0.94 inference('cnf', [status(esa)], [zf_stmt_3])).
% 2.09/0.94 thf(zip_derived_cl1, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.94 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.94 thf(zip_derived_cl54, plain,
% 2.09/0.94 ((((multiply @ sk_c8 @ sk_c1) = (identity))
% 2.09/0.94 | ((multiply @ sk_c4 @ sk_c7) = (sk_c8)))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl17, zip_derived_cl1])).
% 2.09/0.94 thf(zip_derived_cl103, plain,
% 2.09/0.94 (![X0 : $i, X1 : $i]:
% 2.09/0.94 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.09/0.94 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl0])).
% 2.09/0.94 thf(zip_derived_cl128, plain,
% 2.09/0.94 ((((sk_c1) = (multiply @ (inverse @ sk_c8) @ identity))
% 2.09/0.94 | ((multiply @ sk_c4 @ sk_c7) = (sk_c8)))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl54, zip_derived_cl103])).
% 2.09/0.94 thf(prove_this_9, conjecture,
% 2.09/0.94 (~( ( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 2.09/0.94 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c7 ) ) ))).
% 2.09/0.94 thf(zf_stmt_4, negated_conjecture,
% 2.09/0.94 (( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 2.09/0.94 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c7 ) )),
% 2.09/0.94 inference('cnf.neg', [status(esa)], [prove_this_9])).
% 2.09/0.94 thf(zip_derived_cl11, plain,
% 2.09/0.94 ((((multiply @ sk_c4 @ sk_c7) = (sk_c8))
% 2.09/0.94 | ((multiply @ sk_c1 @ sk_c8) = (sk_c7)))),
% 2.09/0.94 inference('cnf', [status(esa)], [zf_stmt_4])).
% 2.09/0.94 thf(zip_derived_cl738, plain,
% 2.09/0.94 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c8)
% 2.09/0.94 = (sk_c7))
% 2.09/0.94 | ((multiply @ sk_c4 @ sk_c7) = (sk_c8))
% 2.09/0.94 | ((multiply @ sk_c4 @ sk_c7) = (sk_c8)))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl128, zip_derived_cl11])).
% 2.09/0.94 thf(zip_derived_cl2, plain,
% 2.09/0.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.09/0.94 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 2.09/0.94 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 2.09/0.94 inference('cnf', [status(esa)], [associativity])).
% 2.09/0.94 thf(zip_derived_cl0, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 2.09/0.94 inference('cnf', [status(esa)], [left_identity])).
% 2.09/0.94 thf(zip_derived_cl1, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.94 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.94 thf(zip_derived_cl756, plain,
% 2.09/0.94 ((((identity) = (sk_c7))
% 2.09/0.94 | ((multiply @ sk_c4 @ sk_c7) = (sk_c8))
% 2.09/0.94 | ((multiply @ sk_c4 @ sk_c7) = (sk_c8)))),
% 2.09/0.94 inference('demod', [status(thm)],
% 2.09/0.94 [zip_derived_cl738, zip_derived_cl2, zip_derived_cl0,
% 2.09/0.94 zip_derived_cl1])).
% 2.09/0.94 thf(zip_derived_cl757, plain,
% 2.09/0.94 ((((multiply @ sk_c4 @ sk_c7) = (sk_c8)) | ((identity) = (sk_c7)))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl756])).
% 2.09/0.94 thf(zip_derived_cl872, plain,
% 2.09/0.94 ((((multiply @ (inverse @ sk_c7) @ sk_c7) = (sk_c8))
% 2.09/0.94 | ((identity) = (sk_c7))
% 2.09/0.94 | ((identity) = (sk_c7)))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl815, zip_derived_cl757])).
% 2.09/0.94 thf(zip_derived_cl1, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.94 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.94 thf(zip_derived_cl878, plain,
% 2.09/0.94 ((((identity) = (sk_c8))
% 2.09/0.94 | ((identity) = (sk_c7))
% 2.09/0.94 | ((identity) = (sk_c7)))),
% 2.09/0.94 inference('demod', [status(thm)], [zip_derived_cl872, zip_derived_cl1])).
% 2.09/0.94 thf(zip_derived_cl879, plain,
% 2.09/0.94 ((((identity) = (sk_c7)) | ((identity) = (sk_c8)))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl878])).
% 2.09/0.94 thf(zip_derived_cl879, plain,
% 2.09/0.94 ((((identity) = (sk_c7)) | ((identity) = (sk_c8)))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl878])).
% 2.09/0.94 thf(zip_derived_cl879, plain,
% 2.09/0.94 ((((identity) = (sk_c7)) | ((identity) = (sk_c8)))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl878])).
% 2.09/0.94 thf(prove_this_1, conjecture,
% 2.09/0.94 (~( ( ( multiply @ sk_c7 @ sk_c6 ) = ( sk_c8 ) ) |
% 2.09/0.94 ( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c6 ) ) ))).
% 2.09/0.94 thf(zf_stmt_5, negated_conjecture,
% 2.09/0.94 (( ( multiply @ sk_c7 @ sk_c6 ) = ( sk_c8 ) ) |
% 2.09/0.94 ( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c6 ) )),
% 2.09/0.94 inference('cnf.neg', [status(esa)], [prove_this_1])).
% 2.09/0.94 thf(zip_derived_cl3, plain,
% 2.09/0.94 ((((multiply @ sk_c7 @ sk_c6) = (sk_c8))
% 2.09/0.94 | ((multiply @ sk_c8 @ sk_c7) = (sk_c6)))),
% 2.09/0.94 inference('cnf', [status(esa)], [zf_stmt_5])).
% 2.09/0.94 thf(zip_derived_cl103, plain,
% 2.09/0.94 (![X0 : $i, X1 : $i]:
% 2.09/0.94 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.09/0.94 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl0])).
% 2.09/0.94 thf(zip_derived_cl140, plain,
% 2.09/0.94 ((((sk_c6) = (multiply @ (inverse @ sk_c7) @ sk_c8))
% 2.09/0.94 | ((multiply @ sk_c8 @ sk_c7) = (sk_c6)))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl103])).
% 2.09/0.94 thf(zip_derived_cl435, plain,
% 2.09/0.94 ((((multiply @ (inverse @ sk_c7) @ sk_c8) != (multiply @ sk_c8 @ sk_c7))
% 2.09/0.94 | ((multiply @ sk_c8 @ sk_c7) = (sk_c6)))),
% 2.09/0.94 inference('eq_fact', [status(thm)], [zip_derived_cl140])).
% 2.09/0.94 thf(zip_derived_cl944, plain,
% 2.09/0.94 ((((multiply @ (inverse @ identity) @ sk_c8)
% 2.09/0.94 != (multiply @ sk_c8 @ sk_c7))
% 2.09/0.94 | ((identity) = (sk_c8))
% 2.09/0.94 | ((multiply @ sk_c8 @ sk_c7) = (sk_c6)))),
% 2.09/0.94 inference('sup-', [status(thm)], [zip_derived_cl879, zip_derived_cl435])).
% 2.09/0.94 thf(zip_derived_cl0, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 2.09/0.94 inference('cnf', [status(esa)], [left_identity])).
% 2.09/0.94 thf(zip_derived_cl103, plain,
% 2.09/0.94 (![X0 : $i, X1 : $i]:
% 2.09/0.94 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.09/0.94 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl0])).
% 2.09/0.94 thf(zip_derived_cl120, plain,
% 2.09/0.94 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl103])).
% 2.09/0.94 thf(zip_derived_cl103, plain,
% 2.09/0.94 (![X0 : $i, X1 : $i]:
% 2.09/0.94 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.09/0.94 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl0])).
% 2.09/0.94 thf(zip_derived_cl172, plain,
% 2.09/0.94 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ identity)) @ X0))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl120, zip_derived_cl103])).
% 2.09/0.94 thf(zip_derived_cl1, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.94 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.94 thf(zip_derived_cl639, plain, (((inverse @ identity) = (identity))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl172, zip_derived_cl1])).
% 2.09/0.94 thf(zip_derived_cl0, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 2.09/0.94 inference('cnf', [status(esa)], [left_identity])).
% 2.09/0.94 thf(zip_derived_cl952, plain,
% 2.09/0.94 ((((sk_c8) != (multiply @ sk_c8 @ sk_c7))
% 2.09/0.94 | ((identity) = (sk_c8))
% 2.09/0.94 | ((multiply @ sk_c8 @ sk_c7) = (sk_c6)))),
% 2.09/0.94 inference('demod', [status(thm)],
% 2.09/0.94 [zip_derived_cl944, zip_derived_cl639, zip_derived_cl0])).
% 2.09/0.94 thf(zip_derived_cl953, plain,
% 2.09/0.94 ((((sk_c8) != (multiply @ sk_c8 @ sk_c7))
% 2.09/0.94 | ((identity) = (sk_c8))
% 2.09/0.94 | ((sk_c8) = (sk_c6)))),
% 2.09/0.94 inference('local_rewriting', [status(thm)], [zip_derived_cl952])).
% 2.09/0.94 thf(zip_derived_cl1017, plain,
% 2.09/0.94 ((((sk_c8) != (multiply @ sk_c8 @ identity))
% 2.09/0.94 | ((identity) = (sk_c8))
% 2.09/0.94 | ((sk_c8) = (sk_c6))
% 2.09/0.94 | ((identity) = (sk_c8)))),
% 2.09/0.94 inference('sup-', [status(thm)], [zip_derived_cl879, zip_derived_cl953])).
% 2.09/0.94 thf(zip_derived_cl778, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl118])).
% 2.09/0.94 thf(zip_derived_cl1018, plain,
% 2.09/0.94 ((((sk_c8) != (sk_c8))
% 2.09/0.94 | ((identity) = (sk_c8))
% 2.09/0.94 | ((sk_c8) = (sk_c6))
% 2.09/0.94 | ((identity) = (sk_c8)))),
% 2.09/0.94 inference('demod', [status(thm)], [zip_derived_cl1017, zip_derived_cl778])).
% 2.09/0.94 thf(zip_derived_cl1019, plain,
% 2.09/0.94 ((((sk_c8) = (sk_c6)) | ((identity) = (sk_c8)))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl1018])).
% 2.09/0.94 thf(prove_this_32, conjecture,
% 2.09/0.94 (~( ( ( inverse @ sk_c7 ) = ( sk_c6 ) ) |
% 2.09/0.94 ( ( inverse @ sk_c2 ) = ( sk_c8 ) ) ))).
% 2.09/0.94 thf(zf_stmt_6, negated_conjecture,
% 2.09/0.94 (( ( inverse @ sk_c7 ) = ( sk_c6 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c8 ) )),
% 2.09/0.94 inference('cnf.neg', [status(esa)], [prove_this_32])).
% 2.09/0.94 thf(zip_derived_cl34, plain,
% 2.09/0.94 ((((inverse @ sk_c7) = (sk_c6)) | ((inverse @ sk_c2) = (sk_c8)))),
% 2.09/0.94 inference('cnf', [status(esa)], [zf_stmt_6])).
% 2.09/0.94 thf(prove_this_26, conjecture,
% 2.09/0.94 (~( ( ( inverse @ sk_c7 ) = ( sk_c6 ) ) |
% 2.09/0.94 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c3 ) ) ))).
% 2.09/0.94 thf(zf_stmt_7, negated_conjecture,
% 2.09/0.94 (( ( inverse @ sk_c7 ) = ( sk_c6 ) ) |
% 2.09/0.94 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c3 ) )),
% 2.09/0.94 inference('cnf.neg', [status(esa)], [prove_this_26])).
% 2.09/0.94 thf(zip_derived_cl28, plain,
% 2.09/0.94 ((((inverse @ sk_c7) = (sk_c6)) | ((multiply @ sk_c2 @ sk_c8) = (sk_c3)))),
% 2.09/0.94 inference('cnf', [status(esa)], [zf_stmt_7])).
% 2.09/0.94 thf(zip_derived_cl103, plain,
% 2.09/0.94 (![X0 : $i, X1 : $i]:
% 2.09/0.94 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.09/0.94 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl0])).
% 2.09/0.94 thf(zip_derived_cl151, plain,
% 2.09/0.94 ((((sk_c8) = (multiply @ (inverse @ sk_c2) @ sk_c3))
% 2.09/0.94 | ((inverse @ sk_c7) = (sk_c6)))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl28, zip_derived_cl103])).
% 2.09/0.94 thf(zip_derived_cl483, plain,
% 2.09/0.94 ((((sk_c8) = (multiply @ sk_c8 @ sk_c3))
% 2.09/0.94 | ((inverse @ sk_c7) = (sk_c6))
% 2.09/0.94 | ((inverse @ sk_c7) = (sk_c6)))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl34, zip_derived_cl151])).
% 2.09/0.94 thf(zip_derived_cl493, plain,
% 2.09/0.94 ((((inverse @ sk_c7) = (sk_c6)) | ((sk_c8) = (multiply @ sk_c8 @ sk_c3)))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl483])).
% 2.09/0.94 thf(prove_this_20, conjecture,
% 2.09/0.94 (~( ( ( inverse @ sk_c7 ) = ( sk_c6 ) ) |
% 2.09/0.94 ( ( multiply @ sk_c8 @ sk_c3 ) = ( sk_c7 ) ) ))).
% 2.09/0.94 thf(zf_stmt_8, negated_conjecture,
% 2.09/0.94 (( ( inverse @ sk_c7 ) = ( sk_c6 ) ) |
% 2.09/0.94 ( ( multiply @ sk_c8 @ sk_c3 ) = ( sk_c7 ) )),
% 2.09/0.94 inference('cnf.neg', [status(esa)], [prove_this_20])).
% 2.09/0.94 thf(zip_derived_cl22, plain,
% 2.09/0.94 ((((inverse @ sk_c7) = (sk_c6)) | ((multiply @ sk_c8 @ sk_c3) = (sk_c7)))),
% 2.09/0.94 inference('cnf', [status(esa)], [zf_stmt_8])).
% 2.09/0.94 thf(zip_derived_cl575, plain,
% 2.09/0.94 ((((sk_c8) = (sk_c7))
% 2.09/0.94 | ((inverse @ sk_c7) = (sk_c6))
% 2.09/0.94 | ((inverse @ sk_c7) = (sk_c6)))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl493, zip_derived_cl22])).
% 2.09/0.94 thf(zip_derived_cl589, plain,
% 2.09/0.94 ((((inverse @ sk_c7) = (sk_c6)) | ((sk_c8) = (sk_c7)))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl575])).
% 2.09/0.94 thf(zip_derived_cl1030, plain,
% 2.09/0.94 ((((inverse @ sk_c7) = (sk_c8))
% 2.09/0.94 | ((identity) = (sk_c8))
% 2.09/0.94 | ((sk_c8) = (sk_c7)))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl1019, zip_derived_cl589])).
% 2.09/0.94 thf(zip_derived_cl1599, plain,
% 2.09/0.94 ((((inverse @ identity) = (sk_c8))
% 2.09/0.94 | ((identity) = (sk_c8))
% 2.09/0.94 | ((sk_c8) = (sk_c7))
% 2.09/0.94 | ((identity) = (sk_c8)))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl879, zip_derived_cl1030])).
% 2.09/0.94 thf(zip_derived_cl639, plain, (((inverse @ identity) = (identity))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl172, zip_derived_cl1])).
% 2.09/0.94 thf(zip_derived_cl1600, plain,
% 2.09/0.94 ((((identity) = (sk_c8))
% 2.09/0.94 | ((identity) = (sk_c8))
% 2.09/0.94 | ((sk_c8) = (sk_c7))
% 2.09/0.94 | ((identity) = (sk_c8)))),
% 2.09/0.94 inference('demod', [status(thm)], [zip_derived_cl1599, zip_derived_cl639])).
% 2.09/0.94 thf(zip_derived_cl1601, plain,
% 2.09/0.94 ((((sk_c8) = (sk_c7)) | ((identity) = (sk_c8)))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl1600])).
% 2.09/0.94 thf(zip_derived_cl879, plain,
% 2.09/0.94 ((((identity) = (sk_c7)) | ((identity) = (sk_c8)))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl878])).
% 2.09/0.94 thf(zip_derived_cl1615, plain,
% 2.09/0.94 ((((identity) = (sk_c8))
% 2.09/0.94 | ((identity) = (sk_c8))
% 2.09/0.94 | ((identity) = (sk_c8)))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl1601, zip_derived_cl879])).
% 2.09/0.94 thf(zip_derived_cl1619, plain, (((identity) = (sk_c8))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl1615])).
% 2.09/0.94 thf(zip_derived_cl1619, plain, (((identity) = (sk_c8))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl1615])).
% 2.09/0.94 thf(zip_derived_cl778, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl118])).
% 2.09/0.94 thf(zip_derived_cl1619, plain, (((identity) = (sk_c8))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl1615])).
% 2.09/0.94 thf(zip_derived_cl0, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 2.09/0.94 inference('cnf', [status(esa)], [left_identity])).
% 2.09/0.94 thf(zip_derived_cl1619, plain, (((identity) = (sk_c8))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl1615])).
% 2.09/0.94 thf(zip_derived_cl1619, plain, (((identity) = (sk_c8))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl1615])).
% 2.09/0.94 thf(zip_derived_cl0, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 2.09/0.94 inference('cnf', [status(esa)], [left_identity])).
% 2.09/0.94 thf(zip_derived_cl1619, plain, (((identity) = (sk_c8))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl1615])).
% 2.09/0.94 thf(zip_derived_cl1619, plain, (((identity) = (sk_c8))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl1615])).
% 2.09/0.94 thf(zip_derived_cl1619, plain, (((identity) = (sk_c8))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl1615])).
% 2.09/0.94 thf(zip_derived_cl778, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl118])).
% 2.09/0.94 thf(zip_derived_cl1619, plain, (((identity) = (sk_c8))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl1615])).
% 2.09/0.94 thf(zip_derived_cl0, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 2.09/0.94 inference('cnf', [status(esa)], [left_identity])).
% 2.09/0.94 thf(zip_derived_cl1619, plain, (((identity) = (sk_c8))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl1615])).
% 2.09/0.94 thf(zip_derived_cl1619, plain, (((identity) = (sk_c8))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl1615])).
% 2.09/0.94 thf(zip_derived_cl778, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl118])).
% 2.09/0.94 thf(zip_derived_cl1619, plain, (((identity) = (sk_c8))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl1615])).
% 2.09/0.94 thf(zip_derived_cl0, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 2.09/0.94 inference('cnf', [status(esa)], [left_identity])).
% 2.09/0.94 thf(zip_derived_cl1656, plain,
% 2.09/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 2.09/0.94 (((inverse @ X0) != (identity))
% 2.09/0.94 | ((X0) != (sk_c7))
% 2.09/0.94 | ((inverse @ X1) != (sk_c7))
% 2.09/0.94 | ((multiply @ X1 @ sk_c7) != (identity))
% 2.09/0.94 | ((inverse @ sk_c7) != (sk_c6))
% 2.09/0.94 | ((multiply @ sk_c7 @ sk_c7) != (identity))
% 2.09/0.94 | ((inverse @ X2) != (identity))
% 2.09/0.94 | ((X2) != (X3))
% 2.09/0.94 | ((X3) != (sk_c7))
% 2.09/0.94 | ((inverse @ X4) != (identity))
% 2.09/0.94 | ((X4) != (sk_c7))
% 2.09/0.94 | ((sk_c7) != (sk_c6)))),
% 2.09/0.94 inference('demod', [status(thm)],
% 2.09/0.94 [zip_derived_cl40, zip_derived_cl1619, zip_derived_cl1619,
% 2.09/0.94 zip_derived_cl778, zip_derived_cl1619, zip_derived_cl0,
% 2.09/0.94 zip_derived_cl1619, zip_derived_cl1619, zip_derived_cl0,
% 2.09/0.94 zip_derived_cl1619, zip_derived_cl1619, zip_derived_cl1619,
% 2.09/0.94 zip_derived_cl778, zip_derived_cl1619, zip_derived_cl0,
% 2.09/0.94 zip_derived_cl1619, zip_derived_cl1619, zip_derived_cl778,
% 2.09/0.94 zip_derived_cl1619, zip_derived_cl0])).
% 2.09/0.94 thf(zip_derived_cl1723, plain,
% 2.09/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.09/0.94 (((sk_c7) != (sk_c6))
% 2.09/0.94 | ((X0) != (sk_c7))
% 2.09/0.94 | ((inverse @ X0) != (identity))
% 2.09/0.94 | ((X1) != (sk_c7))
% 2.09/0.94 | ((inverse @ X1) != (identity))
% 2.09/0.94 | ((multiply @ sk_c7 @ sk_c7) != (identity))
% 2.09/0.94 | ((inverse @ sk_c7) != (sk_c6))
% 2.09/0.94 | ((multiply @ X2 @ sk_c7) != (identity))
% 2.09/0.94 | ((inverse @ X2) != (sk_c7))
% 2.09/0.94 | ((X3) != (sk_c7))
% 2.09/0.94 | ((inverse @ X3) != (identity)))),
% 2.09/0.94 inference('eq_res', [status(thm)], [zip_derived_cl1656])).
% 2.09/0.94 thf(prove_this_17, conjecture,
% 2.09/0.94 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c6 ) ) |
% 2.09/0.94 ( ( inverse @ sk_c1 ) = ( sk_c8 ) ) ))).
% 2.09/0.94 thf(zf_stmt_9, negated_conjecture,
% 2.09/0.94 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c6 ) ) |
% 2.09/0.94 ( ( inverse @ sk_c1 ) = ( sk_c8 ) )),
% 2.09/0.94 inference('cnf.neg', [status(esa)], [prove_this_17])).
% 2.09/0.94 thf(zip_derived_cl19, plain,
% 2.09/0.94 ((((multiply @ sk_c5 @ sk_c8) = (sk_c6)) | ((inverse @ sk_c1) = (sk_c8)))),
% 2.09/0.94 inference('cnf', [status(esa)], [zf_stmt_9])).
% 2.09/0.94 thf(zip_derived_cl1, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.94 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.94 thf(zip_derived_cl55, plain,
% 2.09/0.94 ((((multiply @ sk_c8 @ sk_c1) = (identity))
% 2.09/0.94 | ((multiply @ sk_c5 @ sk_c8) = (sk_c6)))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl1])).
% 2.09/0.94 thf(zip_derived_cl1619, plain, (((identity) = (sk_c8))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl1615])).
% 2.09/0.94 thf(zip_derived_cl0, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 2.09/0.94 inference('cnf', [status(esa)], [left_identity])).
% 2.09/0.94 thf(zip_derived_cl1619, plain, (((identity) = (sk_c8))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl1615])).
% 2.09/0.94 thf(zip_derived_cl778, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl118])).
% 2.09/0.94 thf(zip_derived_cl1668, plain,
% 2.09/0.94 ((((sk_c1) = (identity)) | ((sk_c5) = (sk_c6)))),
% 2.09/0.94 inference('demod', [status(thm)],
% 2.09/0.94 [zip_derived_cl55, zip_derived_cl1619, zip_derived_cl0,
% 2.09/0.94 zip_derived_cl1619, zip_derived_cl778])).
% 2.09/0.94 thf(prove_this_11, conjecture,
% 2.09/0.94 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c6 ) ) |
% 2.09/0.94 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c7 ) ) ))).
% 2.09/0.94 thf(zf_stmt_10, negated_conjecture,
% 2.09/0.94 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c6 ) ) |
% 2.09/0.94 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c7 ) )),
% 2.09/0.94 inference('cnf.neg', [status(esa)], [prove_this_11])).
% 2.09/0.94 thf(zip_derived_cl13, plain,
% 2.09/0.94 ((((multiply @ sk_c5 @ sk_c8) = (sk_c6))
% 2.09/0.94 | ((multiply @ sk_c1 @ sk_c8) = (sk_c7)))),
% 2.09/0.94 inference('cnf', [status(esa)], [zf_stmt_10])).
% 2.09/0.94 thf(zip_derived_cl1619, plain, (((identity) = (sk_c8))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl1615])).
% 2.09/0.94 thf(zip_derived_cl778, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl118])).
% 2.09/0.94 thf(zip_derived_cl1619, plain, (((identity) = (sk_c8))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl1615])).
% 2.09/0.94 thf(zip_derived_cl778, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl118])).
% 2.09/0.94 thf(zip_derived_cl1630, plain, ((((sk_c5) = (sk_c6)) | ((sk_c1) = (sk_c7)))),
% 2.09/0.94 inference('demod', [status(thm)],
% 2.09/0.94 [zip_derived_cl13, zip_derived_cl1619, zip_derived_cl778,
% 2.09/0.94 zip_derived_cl1619, zip_derived_cl778])).
% 2.09/0.94 thf(zip_derived_cl1742, plain,
% 2.09/0.94 ((((identity) = (sk_c7)) | ((sk_c5) = (sk_c6)) | ((sk_c5) = (sk_c6)))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl1668, zip_derived_cl1630])).
% 2.09/0.94 thf(zip_derived_cl1744, plain,
% 2.09/0.94 ((((sk_c5) = (sk_c6)) | ((identity) = (sk_c7)))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl1742])).
% 2.09/0.94 thf(prove_this_18, conjecture,
% 2.09/0.94 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 2.09/0.94 ( ( inverse @ sk_c1 ) = ( sk_c8 ) ) ))).
% 2.09/0.94 thf(zf_stmt_11, negated_conjecture,
% 2.09/0.94 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c8 ) )),
% 2.09/0.94 inference('cnf.neg', [status(esa)], [prove_this_18])).
% 2.09/0.94 thf(zip_derived_cl20, plain,
% 2.09/0.94 ((((inverse @ sk_c5) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c8)))),
% 2.09/0.94 inference('cnf', [status(esa)], [zf_stmt_11])).
% 2.09/0.94 thf(zip_derived_cl1, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.94 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.94 thf(zip_derived_cl50, plain,
% 2.09/0.94 ((((multiply @ sk_c8 @ sk_c1) = (identity))
% 2.09/0.94 | ((inverse @ sk_c5) = (sk_c8)))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl20, zip_derived_cl1])).
% 2.09/0.94 thf(zip_derived_cl103, plain,
% 2.09/0.94 (![X0 : $i, X1 : $i]:
% 2.09/0.94 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.09/0.94 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl0])).
% 2.09/0.94 thf(zip_derived_cl126, plain,
% 2.09/0.94 ((((sk_c1) = (multiply @ (inverse @ sk_c8) @ identity))
% 2.09/0.94 | ((inverse @ sk_c5) = (sk_c8)))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl103])).
% 2.09/0.94 thf(prove_this_12, conjecture,
% 2.09/0.94 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 2.09/0.94 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c7 ) ) ))).
% 2.09/0.94 thf(zf_stmt_12, negated_conjecture,
% 2.09/0.94 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 2.09/0.94 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c7 ) )),
% 2.09/0.94 inference('cnf.neg', [status(esa)], [prove_this_12])).
% 2.09/0.94 thf(zip_derived_cl14, plain,
% 2.09/0.94 ((((inverse @ sk_c5) = (sk_c8)) | ((multiply @ sk_c1 @ sk_c8) = (sk_c7)))),
% 2.09/0.94 inference('cnf', [status(esa)], [zf_stmt_12])).
% 2.09/0.94 thf(zip_derived_cl343, plain,
% 2.09/0.94 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c8)
% 2.09/0.94 = (sk_c7))
% 2.09/0.94 | ((inverse @ sk_c5) = (sk_c8))
% 2.09/0.94 | ((inverse @ sk_c5) = (sk_c8)))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl126, zip_derived_cl14])).
% 2.09/0.94 thf(zip_derived_cl2, plain,
% 2.09/0.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.09/0.94 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 2.09/0.94 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 2.09/0.94 inference('cnf', [status(esa)], [associativity])).
% 2.09/0.94 thf(zip_derived_cl0, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 2.09/0.94 inference('cnf', [status(esa)], [left_identity])).
% 2.09/0.94 thf(zip_derived_cl1, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.94 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.94 thf(zip_derived_cl361, plain,
% 2.09/0.94 ((((identity) = (sk_c7))
% 2.09/0.94 | ((inverse @ sk_c5) = (sk_c8))
% 2.09/0.94 | ((inverse @ sk_c5) = (sk_c8)))),
% 2.09/0.94 inference('demod', [status(thm)],
% 2.09/0.94 [zip_derived_cl343, zip_derived_cl2, zip_derived_cl0,
% 2.09/0.94 zip_derived_cl1])).
% 2.09/0.94 thf(zip_derived_cl362, plain,
% 2.09/0.94 ((((inverse @ sk_c5) = (sk_c8)) | ((identity) = (sk_c7)))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl361])).
% 2.09/0.94 thf(zip_derived_cl1, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.94 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.94 thf(zip_derived_cl365, plain,
% 2.09/0.94 ((((multiply @ sk_c8 @ sk_c5) = (identity)) | ((identity) = (sk_c7)))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl362, zip_derived_cl1])).
% 2.09/0.94 thf(zip_derived_cl1619, plain, (((identity) = (sk_c8))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl1615])).
% 2.09/0.94 thf(zip_derived_cl0, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 2.09/0.94 inference('cnf', [status(esa)], [left_identity])).
% 2.09/0.94 thf(zip_derived_cl1681, plain,
% 2.09/0.94 ((((sk_c5) = (identity)) | ((identity) = (sk_c7)))),
% 2.09/0.94 inference('demod', [status(thm)],
% 2.09/0.94 [zip_derived_cl365, zip_derived_cl1619, zip_derived_cl0])).
% 2.09/0.94 thf(zip_derived_cl1790, plain,
% 2.09/0.94 ((((sk_c6) = (identity))
% 2.09/0.94 | ((identity) = (sk_c7))
% 2.09/0.94 | ((identity) = (sk_c7)))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl1744, zip_derived_cl1681])).
% 2.09/0.94 thf(zip_derived_cl1791, plain,
% 2.09/0.94 ((((identity) = (sk_c7)) | ((sk_c6) = (identity)))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl1790])).
% 2.09/0.94 thf(prove_this_6, conjecture,
% 2.09/0.94 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 2.09/0.94 ( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c6 ) ) ))).
% 2.09/0.94 thf(zf_stmt_13, negated_conjecture,
% 2.09/0.94 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 2.09/0.94 ( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c6 ) )),
% 2.09/0.94 inference('cnf.neg', [status(esa)], [prove_this_6])).
% 2.09/0.94 thf(zip_derived_cl8, plain,
% 2.09/0.94 ((((inverse @ sk_c5) = (sk_c8)) | ((multiply @ sk_c8 @ sk_c7) = (sk_c6)))),
% 2.09/0.94 inference('cnf', [status(esa)], [zf_stmt_13])).
% 2.09/0.94 thf(zip_derived_cl1, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.94 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.94 thf(zip_derived_cl48, plain,
% 2.09/0.94 ((((multiply @ sk_c8 @ sk_c5) = (identity))
% 2.09/0.94 | ((multiply @ sk_c8 @ sk_c7) = (sk_c6)))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl1])).
% 2.09/0.94 thf(zip_derived_cl103, plain,
% 2.09/0.94 (![X0 : $i, X1 : $i]:
% 2.09/0.94 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.09/0.94 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl0])).
% 2.09/0.94 thf(zip_derived_cl123, plain,
% 2.09/0.94 ((((sk_c5) = (multiply @ (inverse @ sk_c8) @ identity))
% 2.09/0.94 | ((multiply @ sk_c8 @ sk_c7) = (sk_c6)))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl48, zip_derived_cl103])).
% 2.09/0.94 thf(prove_this_5, conjecture,
% 2.09/0.94 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c6 ) ) |
% 2.09/0.94 ( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c6 ) ) ))).
% 2.09/0.94 thf(zf_stmt_14, negated_conjecture,
% 2.09/0.94 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c6 ) ) |
% 2.09/0.94 ( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c6 ) )),
% 2.09/0.94 inference('cnf.neg', [status(esa)], [prove_this_5])).
% 2.09/0.94 thf(zip_derived_cl7, plain,
% 2.09/0.94 ((((multiply @ sk_c5 @ sk_c8) = (sk_c6))
% 2.09/0.94 | ((multiply @ sk_c8 @ sk_c7) = (sk_c6)))),
% 2.09/0.94 inference('cnf', [status(esa)], [zf_stmt_14])).
% 2.09/0.94 thf(zip_derived_cl324, plain,
% 2.09/0.94 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c8)
% 2.09/0.94 = (sk_c6))
% 2.09/0.94 | ((multiply @ sk_c8 @ sk_c7) = (sk_c6))
% 2.09/0.94 | ((multiply @ sk_c8 @ sk_c7) = (sk_c6)))),
% 2.09/0.94 inference('sup+', [status(thm)], [zip_derived_cl123, zip_derived_cl7])).
% 2.09/0.94 thf(zip_derived_cl2, plain,
% 2.09/0.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.09/0.94 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 2.09/0.94 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 2.09/0.94 inference('cnf', [status(esa)], [associativity])).
% 2.09/0.94 thf(zip_derived_cl0, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 2.09/0.94 inference('cnf', [status(esa)], [left_identity])).
% 2.09/0.94 thf(zip_derived_cl1, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.09/0.94 inference('cnf', [status(esa)], [left_inverse])).
% 2.09/0.94 thf(zip_derived_cl327, plain,
% 2.09/0.94 ((((identity) = (sk_c6))
% 2.09/0.94 | ((multiply @ sk_c8 @ sk_c7) = (sk_c6))
% 2.09/0.94 | ((multiply @ sk_c8 @ sk_c7) = (sk_c6)))),
% 2.09/0.94 inference('demod', [status(thm)],
% 2.09/0.94 [zip_derived_cl324, zip_derived_cl2, zip_derived_cl0,
% 2.09/0.94 zip_derived_cl1])).
% 2.09/0.94 thf(zip_derived_cl328, plain,
% 2.09/0.94 ((((multiply @ sk_c8 @ sk_c7) = (sk_c6)) | ((identity) = (sk_c6)))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl327])).
% 2.09/0.94 thf(zip_derived_cl336, plain,
% 2.09/0.94 ((((multiply @ sk_c8 @ sk_c7) != (identity)) | ((identity) = (sk_c6)))),
% 2.09/0.94 inference('eq_fact', [status(thm)], [zip_derived_cl328])).
% 2.09/0.94 thf(zip_derived_cl1619, plain, (((identity) = (sk_c8))),
% 2.09/0.94 inference('simplify', [status(thm)], [zip_derived_cl1615])).
% 2.09/0.94 thf(zip_derived_cl0, plain,
% 2.09/0.94 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 2.09/0.94 inference('cnf', [status(esa)], [left_identity])).
% 2.09/0.94 thf(zip_derived_cl1679, plain,
% 2.09/0.94 ((((sk_c7) != (identity)) | ((identity) = (sk_c6)))),
% 2.09/0.94 inference('demod', [status(thm)],
% 2.09/0.94 [zip_derived_cl336, zip_derived_cl1619, zip_derived_cl0])).
% 2.09/0.94 thf(zip_derived_cl1792, plain, (((sk_c6) = (identity))),
% 2.09/0.94 inference('clc', [status(thm)], [zip_derived_cl1791, zip_derived_cl1679])).
% 2.09/0.94 thf(zip_derived_cl1792, plain, (((sk_c6) = (identity))),
% 2.09/0.94 inference('clc', [status(thm)], [zip_derived_cl1791, zip_derived_cl1679])).
% 2.09/0.94 thf(zip_derived_cl1815, plain,
% 2.09/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.09/0.94 (((sk_c7) != (identity))
% 2.09/0.94 | ((X0) != (sk_c7))
% 2.09/0.94 | ((inverse @ X0) != (identity))
% 2.09/0.95 | ((X1) != (sk_c7))
% 2.09/0.95 | ((inverse @ X1) != (identity))
% 2.09/0.95 | ((multiply @ sk_c7 @ sk_c7) != (identity))
% 2.09/0.95 | ((inverse @ sk_c7) != (identity))
% 2.09/0.95 | ((multiply @ X2 @ sk_c7) != (identity))
% 2.09/0.95 | ((inverse @ X2) != (sk_c7))
% 2.09/0.95 | ((X3) != (sk_c7))
% 2.09/0.95 | ((inverse @ X3) != (identity)))),
% 2.09/0.95 inference('demod', [status(thm)],
% 2.09/0.95 [zip_derived_cl1723, zip_derived_cl1792, zip_derived_cl1792])).
% 2.09/0.95 thf(zip_derived_cl1816, plain,
% 2.09/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.09/0.95 (((sk_c7) != (identity))
% 2.09/0.95 | ((X0) != (identity))
% 2.09/0.95 | ((inverse @ X0) != (identity))
% 2.09/0.95 | ((X1) != (identity))
% 2.09/0.95 | ((inverse @ X1) != (identity))
% 2.09/0.95 | ((multiply @ identity @ identity) != (identity))
% 2.09/0.95 | ((inverse @ identity) != (identity))
% 2.09/0.95 | ((multiply @ X2 @ identity) != (identity))
% 2.09/0.95 | ((inverse @ X2) != (identity))
% 2.09/0.95 | ((X3) != (identity))
% 2.09/0.95 | ((inverse @ X3) != (identity)))),
% 2.09/0.95 inference('local_rewriting', [status(thm)], [zip_derived_cl1815])).
% 2.09/0.95 thf(zip_derived_cl0, plain,
% 2.09/0.95 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 2.09/0.95 inference('cnf', [status(esa)], [left_identity])).
% 2.09/0.95 thf(zip_derived_cl639, plain, (((inverse @ identity) = (identity))),
% 2.09/0.95 inference('sup+', [status(thm)], [zip_derived_cl172, zip_derived_cl1])).
% 2.09/0.95 thf(zip_derived_cl778, plain,
% 2.09/0.95 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.09/0.95 inference('sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl118])).
% 2.09/0.95 thf(zip_derived_cl1817, plain,
% 2.09/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.09/0.95 (((sk_c7) != (identity))
% 2.09/0.95 | ((X0) != (identity))
% 2.09/0.95 | ((inverse @ X0) != (identity))
% 2.09/0.95 | ((X1) != (identity))
% 2.09/0.95 | ((inverse @ X1) != (identity))
% 2.09/0.95 | ((identity) != (identity))
% 2.09/0.95 | ((identity) != (identity))
% 2.09/0.95 | ((X2) != (identity))
% 2.09/0.95 | ((inverse @ X2) != (identity))
% 2.09/0.95 | ((X3) != (identity))
% 2.09/0.95 | ((inverse @ X3) != (identity)))),
% 2.09/0.95 inference('demod', [status(thm)],
% 2.09/0.95 [zip_derived_cl1816, zip_derived_cl0, zip_derived_cl639,
% 2.09/0.95 zip_derived_cl778])).
% 2.09/0.95 thf(zip_derived_cl1818, plain,
% 2.09/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.09/0.95 (((inverse @ X3) != (identity))
% 2.09/0.95 | ((X3) != (identity))
% 2.09/0.95 | ((inverse @ X2) != (identity))
% 2.09/0.95 | ((X2) != (identity))
% 2.09/0.95 | ((inverse @ X1) != (identity))
% 2.09/0.95 | ((X1) != (identity))
% 2.09/0.95 | ((inverse @ X0) != (identity))
% 2.09/0.95 | ((X0) != (identity))
% 2.09/0.95 | ((sk_c7) != (identity)))),
% 2.09/0.95 inference('simplify', [status(thm)], [zip_derived_cl1817])).
% 2.09/0.95 thf(prove_this_2, conjecture,
% 2.09/0.95 (~( ( ( inverse @ sk_c7 ) = ( sk_c6 ) ) |
% 2.09/0.95 ( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c6 ) ) ))).
% 2.09/0.95 thf(zf_stmt_15, negated_conjecture,
% 2.09/0.95 (( ( inverse @ sk_c7 ) = ( sk_c6 ) ) |
% 2.09/0.95 ( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c6 ) )),
% 2.09/0.95 inference('cnf.neg', [status(esa)], [prove_this_2])).
% 2.09/0.95 thf(zip_derived_cl4, plain,
% 2.09/0.95 ((((inverse @ sk_c7) = (sk_c6)) | ((multiply @ sk_c8 @ sk_c7) = (sk_c6)))),
% 2.09/0.95 inference('cnf', [status(esa)], [zf_stmt_15])).
% 2.09/0.95 thf(zip_derived_cl1619, plain, (((identity) = (sk_c8))),
% 2.09/0.95 inference('simplify', [status(thm)], [zip_derived_cl1615])).
% 2.09/0.95 thf(zip_derived_cl0, plain,
% 2.09/0.95 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 2.09/0.95 inference('cnf', [status(esa)], [left_identity])).
% 2.09/0.95 thf(zip_derived_cl1621, plain,
% 2.09/0.95 ((((inverse @ sk_c7) = (sk_c6)) | ((sk_c7) = (sk_c6)))),
% 2.09/0.95 inference('demod', [status(thm)],
% 2.09/0.95 [zip_derived_cl4, zip_derived_cl1619, zip_derived_cl0])).
% 2.09/0.95 thf(zip_derived_cl1792, plain, (((sk_c6) = (identity))),
% 2.09/0.95 inference('clc', [status(thm)], [zip_derived_cl1791, zip_derived_cl1679])).
% 2.09/0.95 thf(zip_derived_cl1792, plain, (((sk_c6) = (identity))),
% 2.09/0.95 inference('clc', [status(thm)], [zip_derived_cl1791, zip_derived_cl1679])).
% 2.09/0.95 thf(zip_derived_cl1865, plain,
% 2.09/0.95 ((((inverse @ sk_c7) = (identity)) | ((sk_c7) = (identity)))),
% 2.09/0.95 inference('demod', [status(thm)],
% 2.09/0.95 [zip_derived_cl1621, zip_derived_cl1792, zip_derived_cl1792])).
% 2.09/0.95 thf(zip_derived_cl778, plain,
% 2.09/0.95 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.09/0.95 inference('sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl118])).
% 2.09/0.95 thf(zip_derived_cl121, plain,
% 2.09/0.95 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 2.09/0.95 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl103])).
% 2.09/0.95 thf(zip_derived_cl831, plain,
% 2.09/0.95 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 2.09/0.95 inference('sup+', [status(thm)], [zip_derived_cl778, zip_derived_cl121])).
% 2.09/0.95 thf(zip_derived_cl1867, plain,
% 2.09/0.95 ((((sk_c7) = (inverse @ identity)) | ((sk_c7) = (identity)))),
% 2.09/0.95 inference('sup+', [status(thm)], [zip_derived_cl1865, zip_derived_cl831])).
% 2.09/0.95 thf(zip_derived_cl639, plain, (((inverse @ identity) = (identity))),
% 2.09/0.95 inference('sup+', [status(thm)], [zip_derived_cl172, zip_derived_cl1])).
% 2.09/0.95 thf(zip_derived_cl1871, plain,
% 2.09/0.95 ((((sk_c7) = (identity)) | ((sk_c7) = (identity)))),
% 2.09/0.95 inference('demod', [status(thm)], [zip_derived_cl1867, zip_derived_cl639])).
% 2.09/0.95 thf(zip_derived_cl1872, plain, (((sk_c7) = (identity))),
% 2.09/0.95 inference('simplify', [status(thm)], [zip_derived_cl1871])).
% 2.09/0.95 thf(zip_derived_cl1885, plain,
% 2.09/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.09/0.95 (((inverse @ X3) != (identity))
% 2.09/0.95 | ((X3) != (identity))
% 2.09/0.95 | ((inverse @ X2) != (identity))
% 2.09/0.95 | ((X2) != (identity))
% 2.09/0.95 | ((inverse @ X1) != (identity))
% 2.09/0.95 | ((X1) != (identity))
% 2.09/0.95 | ((inverse @ X0) != (identity))
% 2.09/0.95 | ((X0) != (identity))
% 2.09/0.95 | ((identity) != (identity)))),
% 2.09/0.95 inference('demod', [status(thm)],
% 2.09/0.95 [zip_derived_cl1818, zip_derived_cl1872])).
% 2.09/0.95 thf(zip_derived_cl1886, plain,
% 2.09/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.09/0.95 (((X0) != (identity))
% 2.09/0.95 | ((inverse @ X0) != (identity))
% 2.09/0.95 | ((X1) != (identity))
% 2.09/0.95 | ((inverse @ X1) != (identity))
% 2.09/0.95 | ((X2) != (identity))
% 2.09/0.95 | ((inverse @ X2) != (identity))
% 2.09/0.95 | ((X3) != (identity))
% 2.09/0.95 | ((inverse @ X3) != (identity)))),
% 2.09/0.95 inference('simplify', [status(thm)], [zip_derived_cl1885])).
% 2.09/0.95 thf(zip_derived_cl1899, plain,
% 2.09/0.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.09/0.95 (((inverse @ X0) != (identity))
% 2.09/0.95 | ((X0) != (identity))
% 2.09/0.95 | ((inverse @ X1) != (identity))
% 2.09/0.95 | ((X1) != (identity))
% 2.09/0.95 | ((inverse @ X2) != (identity))
% 2.09/0.95 | ((X2) != (identity))
% 2.09/0.95 | ((inverse @ identity) != (identity)))),
% 2.09/0.95 inference('eq_res', [status(thm)], [zip_derived_cl1886])).
% 2.09/0.95 thf(zip_derived_cl639, plain, (((inverse @ identity) = (identity))),
% 2.09/0.95 inference('sup+', [status(thm)], [zip_derived_cl172, zip_derived_cl1])).
% 2.09/0.95 thf(zip_derived_cl1900, plain,
% 2.09/0.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.09/0.95 (((inverse @ X0) != (identity))
% 2.09/0.95 | ((X0) != (identity))
% 2.09/0.95 | ((inverse @ X1) != (identity))
% 2.09/0.95 | ((X1) != (identity))
% 2.09/0.95 | ((inverse @ X2) != (identity))
% 2.09/0.95 | ((X2) != (identity))
% 2.09/0.95 | ((identity) != (identity)))),
% 2.09/0.95 inference('demod', [status(thm)], [zip_derived_cl1899, zip_derived_cl639])).
% 2.09/0.95 thf(zip_derived_cl1901, plain,
% 2.09/0.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.09/0.95 (((X2) != (identity))
% 2.09/0.95 | ((inverse @ X2) != (identity))
% 2.09/0.95 | ((X1) != (identity))
% 2.09/0.95 | ((inverse @ X1) != (identity))
% 2.09/0.95 | ((X0) != (identity))
% 2.09/0.95 | ((inverse @ X0) != (identity)))),
% 2.09/0.95 inference('simplify', [status(thm)], [zip_derived_cl1900])).
% 2.09/0.95 thf(zip_derived_cl1902, plain,
% 2.09/0.95 (![X0 : $i, X1 : $i]:
% 2.09/0.95 (((inverse @ X0) != (identity))
% 2.09/0.95 | ((X0) != (identity))
% 2.09/0.95 | ((inverse @ X1) != (identity))
% 2.09/0.95 | ((X1) != (identity))
% 2.09/0.95 | ((inverse @ identity) != (identity)))),
% 2.09/0.95 inference('eq_res', [status(thm)], [zip_derived_cl1901])).
% 2.09/0.95 thf(zip_derived_cl639, plain, (((inverse @ identity) = (identity))),
% 2.09/0.95 inference('sup+', [status(thm)], [zip_derived_cl172, zip_derived_cl1])).
% 2.09/0.95 thf(zip_derived_cl1903, plain,
% 2.09/0.95 (![X0 : $i, X1 : $i]:
% 2.09/0.95 (((inverse @ X0) != (identity))
% 2.09/0.95 | ((X0) != (identity))
% 2.09/0.95 | ((inverse @ X1) != (identity))
% 2.09/0.95 | ((X1) != (identity))
% 2.09/0.95 | ((identity) != (identity)))),
% 2.09/0.95 inference('demod', [status(thm)], [zip_derived_cl1902, zip_derived_cl639])).
% 2.09/0.95 thf(zip_derived_cl1904, plain,
% 2.09/0.95 (![X0 : $i, X1 : $i]:
% 2.09/0.95 (((X1) != (identity))
% 2.09/0.95 | ((inverse @ X1) != (identity))
% 2.09/0.95 | ((X0) != (identity))
% 2.09/0.95 | ((inverse @ X0) != (identity)))),
% 2.09/0.95 inference('simplify', [status(thm)], [zip_derived_cl1903])).
% 2.09/0.95 thf(zip_derived_cl1905, plain,
% 2.09/0.95 (![X0 : $i]:
% 2.09/0.95 (((inverse @ X0) != (identity))
% 2.09/0.95 | ((X0) != (identity))
% 2.09/0.95 | ((inverse @ identity) != (identity)))),
% 2.09/0.95 inference('eq_res', [status(thm)], [zip_derived_cl1904])).
% 2.09/0.95 thf(zip_derived_cl639, plain, (((inverse @ identity) = (identity))),
% 2.09/0.95 inference('sup+', [status(thm)], [zip_derived_cl172, zip_derived_cl1])).
% 2.09/0.95 thf(zip_derived_cl1906, plain,
% 2.09/0.95 (![X0 : $i]:
% 2.09/0.95 (((inverse @ X0) != (identity))
% 2.09/0.95 | ((X0) != (identity))
% 2.09/0.95 | ((identity) != (identity)))),
% 2.09/0.95 inference('demod', [status(thm)], [zip_derived_cl1905, zip_derived_cl639])).
% 2.09/0.95 thf(zip_derived_cl1907, plain,
% 2.09/0.95 (![X0 : $i]: (((X0) != (identity)) | ((inverse @ X0) != (identity)))),
% 2.09/0.95 inference('simplify', [status(thm)], [zip_derived_cl1906])).
% 2.09/0.95 thf(zip_derived_cl1908, plain, (((inverse @ identity) != (identity))),
% 2.09/0.95 inference('eq_res', [status(thm)], [zip_derived_cl1907])).
% 2.09/0.95 thf(zip_derived_cl639, plain, (((inverse @ identity) = (identity))),
% 2.09/0.95 inference('sup+', [status(thm)], [zip_derived_cl172, zip_derived_cl1])).
% 2.09/0.95 thf(zip_derived_cl1909, plain, (((identity) != (identity))),
% 2.09/0.95 inference('demod', [status(thm)], [zip_derived_cl1908, zip_derived_cl639])).
% 2.09/0.95 thf(zip_derived_cl1910, plain, ($false),
% 2.09/0.95 inference('simplify', [status(thm)], [zip_derived_cl1909])).
% 2.09/0.95
% 2.09/0.95 % SZS output end Refutation
% 2.09/0.95
% 2.09/0.95
% 2.09/0.95 % Terminating...
% 3.16/1.08 % Runner terminated.
% 3.16/1.09 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------