%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP504-1 : TPTP v9.2.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.HiHTYYc5BM true
% Computer : n008.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 Oct 2 04:36:34 PM UTC 2025
% Result : Unsatisfiable 104.19s 15.59s
% Output : Refutation 104.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP504-1 : TPTP v9.2.0. Released v2.6.0.
% 0.07/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.HiHTYYc5BM true
% 0.13/0.36 % Computer : n008.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Wed Oct 1 14:25:23 EDT 2025
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Running portfolio for 300 s
% 0.13/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.37 % Number of cores: 8
% 0.13/0.37 % Python version: Python 3.6.8
% 0.13/0.37 % Running in FO mode
% 0.50/0.62 % Total configuration time : 435
% 0.50/0.62 % Estimated wc time : 1092
% 0.50/0.62 % Estimated cpu time (7 cpus) : 156.0
% 0.52/0.71 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.52/0.74 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.52/0.74 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.52/0.74 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.52/0.74 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.52/0.75 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.52/0.75 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 104.19/15.59 % Solved by fo/fo4.sh.
% 104.19/15.59 % done 2761 iterations in 14.793s
% 104.19/15.59 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 104.19/15.59 % SZS output start Refutation
% 104.19/15.59 thf(inverse_type, type, inverse: $i > $i).
% 104.19/15.59 thf(a3_type, type, a3: $i).
% 104.19/15.59 thf(multiply_type, type, multiply: $i > $i > $i).
% 104.19/15.59 thf(c3_type, type, c3: $i).
% 104.19/15.59 thf(double_divide_type, type, double_divide: $i > $i > $i).
% 104.19/15.59 thf(b3_type, type, b3: $i).
% 104.19/15.59 thf(prove_these_axioms_3, conjecture,
% 104.19/15.59 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) =
% 104.19/15.59 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ))).
% 104.19/15.59 thf(zf_stmt_0, negated_conjecture,
% 104.19/15.59 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 104.19/15.59 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) )),
% 104.19/15.59 inference('cnf.neg', [status(esa)], [prove_these_axioms_3])).
% 104.19/15.59 thf(zip_derived_cl2, plain,
% 104.19/15.59 (((multiply @ (multiply @ a3 @ b3) @ c3)
% 104.19/15.59 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 104.19/15.59 inference('cnf', [status(esa)], [zf_stmt_0])).
% 104.19/15.59 thf(multiply, axiom,
% 104.19/15.59 (( multiply @ A @ B ) = ( inverse @ ( double_divide @ B @ A ) ))).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(single_axiom, axiom,
% 104.19/15.59 (( double_divide @
% 104.19/15.59 ( double_divide @ A @ ( inverse @ ( double_divide @ B @ C ) ) ) @
% 104.19/15.59 ( double_divide @
% 104.19/15.59 ( inverse @ B ) @
% 104.19/15.59 ( inverse @ ( double_divide @ D @ ( double_divide @ A @ D ) ) ) ) ) =
% 104.19/15.59 ( C ))).
% 104.19/15.59 thf(zip_derived_cl0, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((double_divide @
% 104.19/15.59 (double_divide @ X1 @ (inverse @ (double_divide @ X2 @ X0))) @
% 104.19/15.59 (double_divide @ (inverse @ X2) @
% 104.19/15.59 (inverse @ (double_divide @ X3 @ (double_divide @ X1 @ X3)))))
% 104.19/15.59 = (X0))),
% 104.19/15.59 inference('cnf', [status(esa)], [single_axiom])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl3, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((double_divide @ (double_divide @ X1 @ (multiply @ X0 @ X2)) @
% 104.19/15.59 (double_divide @ (inverse @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X1 @ X3) @ X3)))
% 104.19/15.59 = (X0))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl5, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @ (inverse @ X3) @
% 104.19/15.59 (multiply @ (double_divide @ X2 @ X1) @ X1)) @
% 104.19/15.59 (double_divide @ X2 @ (multiply @ X0 @ X3))) = (inverse @ X0))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl5, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @ (inverse @ X3) @
% 104.19/15.59 (multiply @ (double_divide @ X2 @ X1) @ X1)) @
% 104.19/15.59 (double_divide @ X2 @ (multiply @ X0 @ X3))) = (inverse @ X0))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl5, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @ (inverse @ X3) @
% 104.19/15.59 (multiply @ (double_divide @ X2 @ X1) @ X1)) @
% 104.19/15.59 (double_divide @ X2 @ (multiply @ X0 @ X3))) = (inverse @ X0))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl10, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @
% 104.19/15.59 (inverse @ (double_divide @ X2 @ (multiply @ X0 @ X3))) @
% 104.19/15.59 (multiply @ (double_divide @ X4 @ X5) @ X5)) @
% 104.19/15.59 (double_divide @ X4 @ (inverse @ X0)))
% 104.19/15.59 = (inverse @
% 104.19/15.59 (double_divide @ (inverse @ X3) @
% 104.19/15.59 (multiply @ (double_divide @ X2 @ X1) @ X1))))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl5])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl13, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @ (multiply @ (multiply @ X0 @ X3) @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X4 @ X5) @ X5)) @
% 104.19/15.59 (double_divide @ X4 @ (inverse @ X0)))
% 104.19/15.59 = (inverse @
% 104.19/15.59 (double_divide @ (inverse @ X3) @
% 104.19/15.59 (multiply @ (double_divide @ X2 @ X1) @ X1))))),
% 104.19/15.59 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl13, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @ (multiply @ (multiply @ X0 @ X3) @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X4 @ X5) @ X5)) @
% 104.19/15.59 (double_divide @ X4 @ (inverse @ X0)))
% 104.19/15.59 = (inverse @
% 104.19/15.59 (double_divide @ (inverse @ X3) @
% 104.19/15.59 (multiply @ (double_divide @ X2 @ X1) @ X1))))),
% 104.19/15.59 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl64, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((inverse @
% 104.19/15.59 (double_divide @ (inverse @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X1 @ X0) @ X0)))
% 104.19/15.59 = (inverse @
% 104.19/15.59 (double_divide @ (inverse @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X1 @ X3) @ X3))))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl13])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl100, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ (multiply @ (double_divide @ X1 @ X3) @ X3) @
% 104.19/15.59 (inverse @ X2))
% 104.19/15.59 = (inverse @
% 104.19/15.59 (double_divide @ (inverse @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X1 @ X0) @ X0))))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl64, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl3, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((double_divide @ (double_divide @ X1 @ (multiply @ X0 @ X2)) @
% 104.19/15.59 (double_divide @ (inverse @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X1 @ X3) @ X3)))
% 104.19/15.59 = (X0))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl165, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 104.19/15.59 ((double_divide @
% 104.19/15.59 (double_divide @ X5 @
% 104.19/15.59 (inverse @
% 104.19/15.59 (double_divide @ (inverse @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X1 @ X0) @ X0)))) @
% 104.19/15.59 (double_divide @ (inverse @ (inverse @ X2)) @
% 104.19/15.59 (multiply @ (double_divide @ X5 @ X4) @ X4)))
% 104.19/15.59 = (multiply @ (double_divide @ X1 @ X3) @ X3))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl100, zip_derived_cl3])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl3, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((double_divide @ (double_divide @ X1 @ (multiply @ X0 @ X2)) @
% 104.19/15.59 (double_divide @ (inverse @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X1 @ X3) @ X3)))
% 104.19/15.59 = (X0))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl202, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ (double_divide @ X1 @ X0) @ X0)
% 104.19/15.59 = (multiply @ (double_divide @ X1 @ X3) @ X3))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl165, zip_derived_cl1, zip_derived_cl3])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl3, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((double_divide @ (double_divide @ X1 @ (multiply @ X0 @ X2)) @
% 104.19/15.59 (double_divide @ (inverse @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X1 @ X3) @ X3)))
% 104.19/15.59 = (X0))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl7, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 104.19/15.59 ((double_divide @
% 104.19/15.59 (double_divide @ X4 @ (multiply @ X2 @ (double_divide @ X0 @ X1))) @
% 104.19/15.59 (double_divide @ (multiply @ X1 @ X0) @
% 104.19/15.59 (multiply @ (double_divide @ X4 @ X3) @ X3)))
% 104.19/15.59 = (X2))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl3])).
% 104.19/15.59 thf(zip_derived_cl267, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 104.19/15.59 ((double_divide @
% 104.19/15.59 (double_divide @ X5 @ (multiply @ (double_divide @ X1 @ X0) @ X0)) @
% 104.19/15.59 (double_divide @ (multiply @ X2 @ X3) @
% 104.19/15.59 (multiply @ (double_divide @ X5 @ X4) @ X4)))
% 104.19/15.59 = (double_divide @ X1 @ (double_divide @ X3 @ X2)))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl202, zip_derived_cl7])).
% 104.19/15.59 thf(zip_derived_cl202, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ (double_divide @ X1 @ X0) @ X0)
% 104.19/15.59 = (multiply @ (double_divide @ X1 @ X3) @ X3))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl165, zip_derived_cl1, zip_derived_cl3])).
% 104.19/15.59 thf(zip_derived_cl7, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 104.19/15.59 ((double_divide @
% 104.19/15.59 (double_divide @ X4 @ (multiply @ X2 @ (double_divide @ X0 @ X1))) @
% 104.19/15.59 (double_divide @ (multiply @ X1 @ X0) @
% 104.19/15.59 (multiply @ (double_divide @ X4 @ X3) @ X3)))
% 104.19/15.59 = (X2))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl3])).
% 104.19/15.59 thf(zip_derived_cl259, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 104.19/15.59 ((double_divide @
% 104.19/15.59 (double_divide @ X4 @
% 104.19/15.59 (multiply @ X2 @ (double_divide @ X5 @ (double_divide @ X1 @ X5)))) @
% 104.19/15.59 (double_divide @ (multiply @ (double_divide @ X1 @ X0) @ X0) @
% 104.19/15.59 (multiply @ (double_divide @ X4 @ X3) @ X3)))
% 104.19/15.59 = (X2))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl202, zip_derived_cl7])).
% 104.19/15.59 thf(zip_derived_cl3481, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((double_divide @ X2 @
% 104.19/15.59 (double_divide @ X0 @ (double_divide @ X1 @ X0)))
% 104.19/15.59 = (double_divide @ X2 @
% 104.19/15.59 (double_divide @ X3 @ (double_divide @ X1 @ X3))))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl267, zip_derived_cl259])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl3568, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ (double_divide @ X3 @ (double_divide @ X1 @ X3)) @ X2)
% 104.19/15.59 = (inverse @
% 104.19/15.59 (double_divide @ X2 @
% 104.19/15.59 (double_divide @ X0 @ (double_divide @ X1 @ X0)))))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl3481, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl3, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((double_divide @ (double_divide @ X1 @ (multiply @ X0 @ X2)) @
% 104.19/15.59 (double_divide @ (inverse @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X1 @ X3) @ X3)))
% 104.19/15.59 = (X0))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl4237, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 104.19/15.59 ((double_divide @
% 104.19/15.59 (double_divide @ X5 @
% 104.19/15.59 (inverse @
% 104.19/15.59 (double_divide @ X2 @
% 104.19/15.59 (double_divide @ X0 @ (double_divide @ X1 @ X0))))) @
% 104.19/15.59 (double_divide @ (inverse @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X5 @ X4) @ X4)))
% 104.19/15.59 = (double_divide @ X3 @ (double_divide @ X1 @ X3)))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl3568, zip_derived_cl3])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl3, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((double_divide @ (double_divide @ X1 @ (multiply @ X0 @ X2)) @
% 104.19/15.59 (double_divide @ (inverse @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X1 @ X3) @ X3)))
% 104.19/15.59 = (X0))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl4396, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X3 : $i]:
% 104.19/15.59 ((double_divide @ X0 @ (double_divide @ X1 @ X0))
% 104.19/15.59 = (double_divide @ X3 @ (double_divide @ X1 @ X3)))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl4237, zip_derived_cl1, zip_derived_cl3])).
% 104.19/15.59 thf(zip_derived_cl202, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ (double_divide @ X1 @ X0) @ X0)
% 104.19/15.59 = (multiply @ (double_divide @ X1 @ X3) @ X3))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl165, zip_derived_cl1, zip_derived_cl3])).
% 104.19/15.59 thf(zip_derived_cl4486, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ (double_divide @ X2 @ X3) @ X3)
% 104.19/15.59 = (multiply @ (double_divide @ X0 @ (double_divide @ X1 @ X0)) @
% 104.19/15.59 (double_divide @ X1 @ X2)))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl4396, zip_derived_cl202])).
% 104.19/15.59 thf(zip_derived_cl13, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @ (multiply @ (multiply @ X0 @ X3) @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X4 @ X5) @ X5)) @
% 104.19/15.59 (double_divide @ X4 @ (inverse @ X0)))
% 104.19/15.59 = (inverse @
% 104.19/15.59 (double_divide @ (inverse @ X3) @
% 104.19/15.59 (multiply @ (double_divide @ X2 @ X1) @ X1))))),
% 104.19/15.59 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl5338, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @
% 104.19/15.59 (multiply @ (multiply @ (double_divide @ X1 @ X0) @ X0) @ X3) @
% 104.19/15.59 (multiply @ (double_divide @ X6 @ X7) @ X7)) @
% 104.19/15.59 (double_divide @ X6 @
% 104.19/15.59 (inverse @ (double_divide @ X5 @ (double_divide @ X4 @ X5)))))
% 104.19/15.59 = (inverse @
% 104.19/15.59 (double_divide @ (inverse @ (double_divide @ X4 @ X1)) @
% 104.19/15.59 (multiply @ (double_divide @ X3 @ X2) @ X2))))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl4486, zip_derived_cl13])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl202, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ (double_divide @ X1 @ X0) @ X0)
% 104.19/15.59 = (multiply @ (double_divide @ X1 @ X3) @ X3))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl165, zip_derived_cl1, zip_derived_cl3])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl5, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @ (inverse @ X3) @
% 104.19/15.59 (multiply @ (double_divide @ X2 @ X1) @ X1)) @
% 104.19/15.59 (double_divide @ X2 @ (multiply @ X0 @ X3))) = (inverse @ X0))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl12, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @ (multiply @ X1 @ X0) @
% 104.19/15.59 (multiply @ (double_divide @ X3 @ X4) @ X4)) @
% 104.19/15.59 (double_divide @ X3 @ (multiply @ X2 @ (double_divide @ X0 @ X1))))
% 104.19/15.59 = (inverse @ X2))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl5])).
% 104.19/15.59 thf(zip_derived_cl268, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @ (multiply @ X2 @ X3) @
% 104.19/15.59 (multiply @ (double_divide @ X4 @ X5) @ X5)) @
% 104.19/15.59 (double_divide @ X4 @ (multiply @ (double_divide @ X1 @ X0) @ X0)))
% 104.19/15.59 = (inverse @ (double_divide @ X1 @ (double_divide @ X3 @ X2))))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl202, zip_derived_cl12])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl313, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @ (multiply @ X2 @ X3) @
% 104.19/15.59 (multiply @ (double_divide @ X4 @ X5) @ X5)) @
% 104.19/15.59 (double_divide @ X4 @ (multiply @ (double_divide @ X1 @ X0) @ X0)))
% 104.19/15.59 = (multiply @ (double_divide @ X3 @ X2) @ X1))),
% 104.19/15.59 inference('demod', [status(thm)], [zip_derived_cl268, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl64, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((inverse @
% 104.19/15.59 (double_divide @ (inverse @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X1 @ X0) @ X0)))
% 104.19/15.59 = (inverse @
% 104.19/15.59 (double_divide @ (inverse @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X1 @ X3) @ X3))))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl13])).
% 104.19/15.59 thf(zip_derived_cl118, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 104.19/15.59 ((inverse @
% 104.19/15.59 (double_divide @ (multiply @ X1 @ X0) @
% 104.19/15.59 (multiply @ (double_divide @ X3 @ X4) @ X4)))
% 104.19/15.59 = (inverse @
% 104.19/15.59 (double_divide @ (inverse @ (double_divide @ X0 @ X1)) @
% 104.19/15.59 (multiply @ (double_divide @ X3 @ X2) @ X2))))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl64])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl130, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 104.19/15.59 ((inverse @
% 104.19/15.59 (double_divide @ (multiply @ X1 @ X0) @
% 104.19/15.59 (multiply @ (double_divide @ X3 @ X4) @ X4)))
% 104.19/15.59 = (multiply @ (multiply @ (double_divide @ X3 @ X2) @ X2) @
% 104.19/15.59 (multiply @ X1 @ X0)))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl118, zip_derived_cl1, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl5623, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @ X3 @ (multiply @ (double_divide @ X1 @ X0) @ X0)) @
% 104.19/15.59 X4)
% 104.19/15.59 = (multiply @ (multiply @ (double_divide @ X3 @ X2) @ X2) @
% 104.19/15.59 (multiply @ X1 @ X4)))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl5338, zip_derived_cl1, zip_derived_cl313,
% 104.19/15.59 zip_derived_cl1, zip_derived_cl130])).
% 104.19/15.59 thf(zip_derived_cl202, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ (double_divide @ X1 @ X0) @ X0)
% 104.19/15.59 = (multiply @ (double_divide @ X1 @ X3) @ X3))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl165, zip_derived_cl1, zip_derived_cl3])).
% 104.19/15.59 thf(zip_derived_cl5, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @ (inverse @ X3) @
% 104.19/15.59 (multiply @ (double_divide @ X2 @ X1) @ X1)) @
% 104.19/15.59 (double_divide @ X2 @ (multiply @ X0 @ X3))) = (inverse @ X0))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl264, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @ (inverse @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X3 @ X4) @ X4)) @
% 104.19/15.59 (double_divide @ X3 @ (multiply @ (double_divide @ X1 @ X0) @ X0)))
% 104.19/15.59 = (inverse @ (double_divide @ X1 @ X2)))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl202, zip_derived_cl5])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl311, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @ (inverse @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X3 @ X4) @ X4)) @
% 104.19/15.59 (double_divide @ X3 @ (multiply @ (double_divide @ X1 @ X0) @ X0)))
% 104.19/15.59 = (multiply @ X2 @ X1))),
% 104.19/15.59 inference('demod', [status(thm)], [zip_derived_cl264, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl3, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((double_divide @ (double_divide @ X1 @ (multiply @ X0 @ X2)) @
% 104.19/15.59 (double_divide @ (inverse @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X1 @ X3) @ X3)))
% 104.19/15.59 = (X0))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl202, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ (double_divide @ X1 @ X0) @ X0)
% 104.19/15.59 = (multiply @ (double_divide @ X1 @ X3) @ X3))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl165, zip_derived_cl1, zip_derived_cl3])).
% 104.19/15.59 thf(zip_derived_cl303, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 104.19/15.59 ((multiply @ X0 @
% 104.19/15.59 (double_divide @ (inverse @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X3 @ X4) @ X4)))
% 104.19/15.59 = (multiply @
% 104.19/15.59 (double_divide @ (double_divide @ X3 @ (multiply @ X0 @ X2)) @ X1) @
% 104.19/15.59 X1))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl202])).
% 104.19/15.59 thf(zip_derived_cl532, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0)
% 104.19/15.59 = (multiply @
% 104.19/15.59 (double_divide @
% 104.19/15.59 (double_divide @ X0 @
% 104.19/15.59 (multiply @
% 104.19/15.59 (double_divide @ (inverse @ X1) @
% 104.19/15.59 (multiply @ (double_divide @ (inverse @ X3) @ X4) @ X4)) @
% 104.19/15.59 X3)) @
% 104.19/15.59 X2) @
% 104.19/15.59 X2))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl311, zip_derived_cl303])).
% 104.19/15.59 thf(zip_derived_cl7489, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 104.19/15.59 ((multiply @ X5 @ X6)
% 104.19/15.59 = (multiply @
% 104.19/15.59 (multiply @
% 104.19/15.59 (double_divide @
% 104.19/15.59 (double_divide @ X6 @
% 104.19/15.59 (multiply @
% 104.19/15.59 (double_divide @ (inverse @ X5) @
% 104.19/15.59 (multiply @ (double_divide @ (inverse @ X3) @ X4) @ X4)) @
% 104.19/15.59 X3)) @
% 104.19/15.59 X2) @
% 104.19/15.59 X2) @
% 104.19/15.59 (multiply @ X1 @ (multiply @ (double_divide @ X1 @ X0) @ X0))))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl5623, zip_derived_cl532])).
% 104.19/15.59 thf(zip_derived_cl532, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0)
% 104.19/15.59 = (multiply @
% 104.19/15.59 (double_divide @
% 104.19/15.59 (double_divide @ X0 @
% 104.19/15.59 (multiply @
% 104.19/15.59 (double_divide @ (inverse @ X1) @
% 104.19/15.59 (multiply @ (double_divide @ (inverse @ X3) @ X4) @ X4)) @
% 104.19/15.59 X3)) @
% 104.19/15.59 X2) @
% 104.19/15.59 X2))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl311, zip_derived_cl303])).
% 104.19/15.59 thf(zip_derived_cl7659, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X5 : $i, X6 : $i]:
% 104.19/15.59 ((multiply @ X5 @ X6)
% 104.19/15.59 = (multiply @ (multiply @ X5 @ X6) @
% 104.19/15.59 (multiply @ X1 @ (multiply @ (double_divide @ X1 @ X0) @ X0))))),
% 104.19/15.59 inference('demod', [status(thm)], [zip_derived_cl7489, zip_derived_cl532])).
% 104.19/15.59 thf(zip_derived_cl7765, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @ (inverse @ X3) @
% 104.19/15.59 (multiply @ (double_divide @ X4 @ X5) @ X5)) @
% 104.19/15.59 (double_divide @ X4 @ (multiply @ X0 @ X3)))
% 104.19/15.59 = (multiply @ (inverse @ X0) @
% 104.19/15.59 (multiply @ X2 @ (multiply @ (double_divide @ X2 @ X1) @ X1))))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl7659])).
% 104.19/15.59 thf(zip_derived_cl5, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @ (inverse @ X3) @
% 104.19/15.59 (multiply @ (double_divide @ X2 @ X1) @ X1)) @
% 104.19/15.59 (double_divide @ X2 @ (multiply @ X0 @ X3))) = (inverse @ X0))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl7813, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.19/15.59 ((inverse @ X0)
% 104.19/15.59 = (multiply @ (inverse @ X0) @
% 104.19/15.59 (multiply @ X2 @ (multiply @ (double_divide @ X2 @ X1) @ X1))))),
% 104.19/15.59 inference('demod', [status(thm)], [zip_derived_cl7765, zip_derived_cl5])).
% 104.19/15.59 thf(zip_derived_cl303, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 104.19/15.59 ((multiply @ X0 @
% 104.19/15.59 (double_divide @ (inverse @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X3 @ X4) @ X4)))
% 104.19/15.59 = (multiply @
% 104.19/15.59 (double_divide @ (double_divide @ X3 @ (multiply @ X0 @ X2)) @ X1) @
% 104.19/15.59 X1))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl202])).
% 104.19/15.59 thf(zip_derived_cl12, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @ (multiply @ X1 @ X0) @
% 104.19/15.59 (multiply @ (double_divide @ X3 @ X4) @ X4)) @
% 104.19/15.59 (double_divide @ X3 @ (multiply @ X2 @ (double_divide @ X0 @ X1))))
% 104.19/15.59 = (inverse @ X2))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl5])).
% 104.19/15.59 thf(zip_derived_cl528, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @
% 104.19/15.59 (double_divide @ X5 @
% 104.19/15.59 (multiply @
% 104.19/15.59 (double_divide @ (multiply @ X4 @ X3) @
% 104.19/15.59 (multiply @ (double_divide @ (inverse @ X1) @ X2) @ X2)) @
% 104.19/15.59 X1)) @
% 104.19/15.59 X0) @
% 104.19/15.59 X0) = (inverse @ (double_divide @ X5 @ (double_divide @ X3 @ X4))))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl303, zip_derived_cl12])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl581, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @
% 104.19/15.59 (double_divide @ X5 @
% 104.19/15.59 (multiply @
% 104.19/15.59 (double_divide @ (multiply @ X4 @ X3) @
% 104.19/15.59 (multiply @ (double_divide @ (inverse @ X1) @ X2) @ X2)) @
% 104.19/15.59 X1)) @
% 104.19/15.59 X0) @
% 104.19/15.59 X0) = (multiply @ (double_divide @ X3 @ X4) @ X5))),
% 104.19/15.59 inference('demod', [status(thm)], [zip_derived_cl528, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl7864, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @
% 104.19/15.59 (double_divide @ X1 @
% 104.19/15.59 (multiply @
% 104.19/15.59 (double_divide @ (inverse @ X0) @
% 104.19/15.59 (multiply @ (double_divide @ (inverse @ X5) @ X6) @ X6)) @
% 104.19/15.59 X5)) @
% 104.19/15.59 X4) @
% 104.19/15.59 X4)
% 104.19/15.59 = (multiply @
% 104.19/15.59 (double_divide @
% 104.19/15.59 (multiply @ X3 @ (multiply @ (double_divide @ X3 @ X2) @ X2)) @
% 104.19/15.59 (inverse @ X0)) @
% 104.19/15.59 X1))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl7813, zip_derived_cl581])).
% 104.19/15.59 thf(zip_derived_cl532, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0)
% 104.19/15.59 = (multiply @
% 104.19/15.59 (double_divide @
% 104.19/15.59 (double_divide @ X0 @
% 104.19/15.59 (multiply @
% 104.19/15.59 (double_divide @ (inverse @ X1) @
% 104.19/15.59 (multiply @ (double_divide @ (inverse @ X3) @ X4) @ X4)) @
% 104.19/15.59 X3)) @
% 104.19/15.59 X2) @
% 104.19/15.59 X2))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl311, zip_derived_cl303])).
% 104.19/15.59 thf(zip_derived_cl7965, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ X0 @ X1)
% 104.19/15.59 = (multiply @
% 104.19/15.59 (double_divide @
% 104.19/15.59 (multiply @ X3 @ (multiply @ (double_divide @ X3 @ X2) @ X2)) @
% 104.19/15.59 (inverse @ X0)) @
% 104.19/15.59 X1))),
% 104.19/15.59 inference('demod', [status(thm)], [zip_derived_cl7864, zip_derived_cl532])).
% 104.19/15.59 thf(zip_derived_cl3, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((double_divide @ (double_divide @ X1 @ (multiply @ X0 @ X2)) @
% 104.19/15.59 (double_divide @ (inverse @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X1 @ X3) @ X3)))
% 104.19/15.59 = (X0))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl8360, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 104.19/15.59 ((double_divide @ (double_divide @ X5 @ (multiply @ X1 @ X0)) @
% 104.19/15.59 (double_divide @ (inverse @ X0) @
% 104.19/15.59 (multiply @ (double_divide @ X5 @ X4) @ X4)))
% 104.19/15.59 = (double_divide @
% 104.19/15.59 (multiply @ X3 @ (multiply @ (double_divide @ X3 @ X2) @ X2)) @
% 104.19/15.59 (inverse @ X1)))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl7965, zip_derived_cl3])).
% 104.19/15.59 thf(zip_derived_cl3, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((double_divide @ (double_divide @ X1 @ (multiply @ X0 @ X2)) @
% 104.19/15.59 (double_divide @ (inverse @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X1 @ X3) @ X3)))
% 104.19/15.59 = (X0))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl8564, plain,
% 104.19/15.59 (![X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((X1)
% 104.19/15.59 = (double_divide @
% 104.19/15.59 (multiply @ X3 @ (multiply @ (double_divide @ X3 @ X2) @ X2)) @
% 104.19/15.59 (inverse @ X1)))),
% 104.19/15.59 inference('demod', [status(thm)], [zip_derived_cl8360, zip_derived_cl3])).
% 104.19/15.59 thf(zip_derived_cl202, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ (double_divide @ X1 @ X0) @ X0)
% 104.19/15.59 = (multiply @ (double_divide @ X1 @ X3) @ X3))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl165, zip_derived_cl1, zip_derived_cl3])).
% 104.19/15.59 thf(zip_derived_cl8611, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @
% 104.19/15.59 (multiply @ X2 @ (multiply @ (double_divide @ X2 @ X1) @ X1)) @ X3) @
% 104.19/15.59 X3) = (multiply @ X0 @ (inverse @ X0)))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl8564, zip_derived_cl202])).
% 104.19/15.59 thf(zip_derived_cl3, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((double_divide @ (double_divide @ X1 @ (multiply @ X0 @ X2)) @
% 104.19/15.59 (double_divide @ (inverse @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X1 @ X3) @ X3)))
% 104.19/15.59 = (X0))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl9809, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 104.19/15.59 ((double_divide @
% 104.19/15.59 (double_divide @
% 104.19/15.59 (multiply @ X4 @ (multiply @ (double_divide @ X4 @ X3) @ X3)) @
% 104.19/15.59 (multiply @ X1 @ X5)) @
% 104.19/15.59 (double_divide @ (inverse @ X5) @ (multiply @ X0 @ (inverse @ X0))))
% 104.19/15.59 = (X1))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl8611, zip_derived_cl3])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl8564, plain,
% 104.19/15.59 (![X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((X1)
% 104.19/15.59 = (double_divide @
% 104.19/15.59 (multiply @ X3 @ (multiply @ (double_divide @ X3 @ X2) @ X2)) @
% 104.19/15.59 (inverse @ X1)))),
% 104.19/15.59 inference('demod', [status(thm)], [zip_derived_cl8360, zip_derived_cl3])).
% 104.19/15.59 thf(zip_derived_cl8709, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((double_divide @ X0 @ X1)
% 104.19/15.59 = (double_divide @
% 104.19/15.59 (multiply @ X3 @ (multiply @ (double_divide @ X3 @ X2) @ X2)) @
% 104.19/15.59 (multiply @ X1 @ X0)))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl8564])).
% 104.19/15.59 thf(zip_derived_cl10027, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X5 : $i]:
% 104.19/15.59 ((double_divide @ (double_divide @ X5 @ X1) @
% 104.19/15.59 (double_divide @ (inverse @ X5) @ (multiply @ X0 @ (inverse @ X0))))
% 104.19/15.59 = (X1))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl9809, zip_derived_cl8709])).
% 104.19/15.59 thf(zip_derived_cl4396, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X3 : $i]:
% 104.19/15.59 ((double_divide @ X0 @ (double_divide @ X1 @ X0))
% 104.19/15.59 = (double_divide @ X3 @ (double_divide @ X1 @ X3)))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl4237, zip_derived_cl1, zip_derived_cl3])).
% 104.19/15.59 thf(zip_derived_cl4396, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X3 : $i]:
% 104.19/15.59 ((double_divide @ X0 @ (double_divide @ X1 @ X0))
% 104.19/15.59 = (double_divide @ X3 @ (double_divide @ X1 @ X3)))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl4237, zip_derived_cl1, zip_derived_cl3])).
% 104.19/15.59 thf(zip_derived_cl4488, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((double_divide @ X3 @ (double_divide @ X2 @ X3))
% 104.19/15.59 = (double_divide @ (double_divide @ X1 @ X2) @
% 104.19/15.59 (double_divide @ X0 @ (double_divide @ X1 @ X0))))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl4396, zip_derived_cl4396])).
% 104.19/15.59 thf(zip_derived_cl8611, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @
% 104.19/15.59 (multiply @ X2 @ (multiply @ (double_divide @ X2 @ X1) @ X1)) @ X3) @
% 104.19/15.59 X3) = (multiply @ X0 @ (inverse @ X0)))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl8564, zip_derived_cl202])).
% 104.19/15.59 thf(zip_derived_cl8709, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((double_divide @ X0 @ X1)
% 104.19/15.59 = (double_divide @
% 104.19/15.59 (multiply @ X3 @ (multiply @ (double_divide @ X3 @ X2) @ X2)) @
% 104.19/15.59 (multiply @ X1 @ X0)))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl8564])).
% 104.19/15.59 thf(zip_derived_cl9699, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 104.19/15.59 ((double_divide @ (inverse @ X3) @ X3)
% 104.19/15.59 = (double_divide @
% 104.19/15.59 (multiply @ X5 @ (multiply @ (double_divide @ X5 @ X4) @ X4)) @
% 104.19/15.59 (multiply @
% 104.19/15.59 (double_divide @
% 104.19/15.59 (multiply @ X2 @ (multiply @ (double_divide @ X2 @ X1) @ X1)) @
% 104.19/15.59 X0) @
% 104.19/15.59 X0)))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl8611, zip_derived_cl8709])).
% 104.19/15.59 thf(zip_derived_cl8611, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @
% 104.19/15.59 (multiply @ X2 @ (multiply @ (double_divide @ X2 @ X1) @ X1)) @ X3) @
% 104.19/15.59 X3) = (multiply @ X0 @ (inverse @ X0)))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl8564, zip_derived_cl202])).
% 104.19/15.59 thf(zip_derived_cl8709, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((double_divide @ X0 @ X1)
% 104.19/15.59 = (double_divide @
% 104.19/15.59 (multiply @ X3 @ (multiply @ (double_divide @ X3 @ X2) @ X2)) @
% 104.19/15.59 (multiply @ X1 @ X0)))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl8564])).
% 104.19/15.59 thf(zip_derived_cl9978, plain,
% 104.19/15.59 (![X0 : $i, X3 : $i]:
% 104.19/15.59 ((double_divide @ (inverse @ X3) @ X3)
% 104.19/15.59 = (double_divide @ (inverse @ X0) @ X0))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl9699, zip_derived_cl8611, zip_derived_cl8709])).
% 104.19/15.59 thf(zip_derived_cl10027, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X5 : $i]:
% 104.19/15.59 ((double_divide @ (double_divide @ X5 @ X1) @
% 104.19/15.59 (double_divide @ (inverse @ X5) @ (multiply @ X0 @ (inverse @ X0))))
% 104.19/15.59 = (X1))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl9809, zip_derived_cl8709])).
% 104.19/15.59 thf(zip_derived_cl13474, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.19/15.59 ((double_divide @
% 104.19/15.59 (double_divide @ (multiply @ X2 @ (inverse @ X2)) @ X1) @
% 104.19/15.59 (double_divide @ (inverse @ X0) @ X0)) = (X1))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl9978, zip_derived_cl10027])).
% 104.19/15.59 thf(zip_derived_cl3, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((double_divide @ (double_divide @ X1 @ (multiply @ X0 @ X2)) @
% 104.19/15.59 (double_divide @ (inverse @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X1 @ X3) @ X3)))
% 104.19/15.59 = (X0))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl13700, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.19/15.59 ((multiply @ X2 @
% 104.19/15.59 (multiply @
% 104.19/15.59 (double_divide @ (multiply @ X1 @ (inverse @ X1)) @ X0) @ X0))
% 104.19/15.59 = (X2))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl13474, zip_derived_cl3])).
% 104.19/15.59 thf(zip_derived_cl8564, plain,
% 104.19/15.59 (![X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((X1)
% 104.19/15.59 = (double_divide @
% 104.19/15.59 (multiply @ X3 @ (multiply @ (double_divide @ X3 @ X2) @ X2)) @
% 104.19/15.59 (inverse @ X1)))),
% 104.19/15.59 inference('demod', [status(thm)], [zip_derived_cl8360, zip_derived_cl3])).
% 104.19/15.59 thf(zip_derived_cl13833, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((X1)
% 104.19/15.59 = (double_divide @ (multiply @ X0 @ (inverse @ X0)) @ (inverse @ X1)))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl13700, zip_derived_cl8564])).
% 104.19/15.59 thf(zip_derived_cl4488, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((double_divide @ X3 @ (double_divide @ X2 @ X3))
% 104.19/15.59 = (double_divide @ (double_divide @ X1 @ X2) @
% 104.19/15.59 (double_divide @ X0 @ (double_divide @ X1 @ X0))))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl4396, zip_derived_cl4396])).
% 104.19/15.59 thf(zip_derived_cl14109, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((double_divide @ X3 @ (double_divide @ X2 @ X3))
% 104.19/15.59 = (double_divide @
% 104.19/15.59 (double_divide @ (multiply @ X1 @ (inverse @ X1)) @ X2) @
% 104.19/15.59 (double_divide @ (inverse @ X0) @ X0)))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl13833, zip_derived_cl4488])).
% 104.19/15.59 thf(zip_derived_cl13474, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.19/15.59 ((double_divide @
% 104.19/15.59 (double_divide @ (multiply @ X2 @ (inverse @ X2)) @ X1) @
% 104.19/15.59 (double_divide @ (inverse @ X0) @ X0)) = (X1))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl9978, zip_derived_cl10027])).
% 104.19/15.59 thf(zip_derived_cl14207, plain,
% 104.19/15.59 (![X2 : $i, X3 : $i]:
% 104.19/15.59 ((double_divide @ X3 @ (double_divide @ X2 @ X3)) = (X2))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl14109, zip_derived_cl13474])).
% 104.19/15.59 thf(zip_derived_cl14207, plain,
% 104.19/15.59 (![X2 : $i, X3 : $i]:
% 104.19/15.59 ((double_divide @ X3 @ (double_divide @ X2 @ X3)) = (X2))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl14109, zip_derived_cl13474])).
% 104.19/15.59 thf(zip_derived_cl14350, plain,
% 104.19/15.59 (![X1 : $i, X2 : $i]:
% 104.19/15.59 ((X2) = (double_divide @ (double_divide @ X1 @ X2) @ X1))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl4488, zip_derived_cl14207, zip_derived_cl14207])).
% 104.19/15.59 thf(zip_derived_cl14380, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.19/15.59 ((double_divide @ (inverse @ X1) @ (multiply @ X2 @ (inverse @ X2)))
% 104.19/15.59 = (double_divide @ X0 @ (double_divide @ X1 @ X0)))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl10027, zip_derived_cl14350])).
% 104.19/15.59 thf(zip_derived_cl14207, plain,
% 104.19/15.59 (![X2 : $i, X3 : $i]:
% 104.19/15.59 ((double_divide @ X3 @ (double_divide @ X2 @ X3)) = (X2))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl14109, zip_derived_cl13474])).
% 104.19/15.59 thf(zip_derived_cl14387, plain,
% 104.19/15.59 (![X1 : $i, X2 : $i]:
% 104.19/15.59 ((double_divide @ (inverse @ X1) @ (multiply @ X2 @ (inverse @ X2)))
% 104.19/15.59 = (X1))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl14380, zip_derived_cl14207])).
% 104.19/15.59 thf(zip_derived_cl13833, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((X1)
% 104.19/15.59 = (double_divide @ (multiply @ X0 @ (inverse @ X0)) @ (inverse @ X1)))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl13700, zip_derived_cl8564])).
% 104.19/15.59 thf(zip_derived_cl14350, plain,
% 104.19/15.59 (![X1 : $i, X2 : $i]:
% 104.19/15.59 ((X2) = (double_divide @ (double_divide @ X1 @ X2) @ X1))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl4488, zip_derived_cl14207, zip_derived_cl14207])).
% 104.19/15.59 thf(zip_derived_cl14386, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((inverse @ X0)
% 104.19/15.59 = (double_divide @ X0 @ (multiply @ X1 @ (inverse @ X1))))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl13833, zip_derived_cl14350])).
% 104.19/15.59 thf(zip_derived_cl14838, plain,
% 104.19/15.59 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl14387, zip_derived_cl14386])).
% 104.19/15.59 thf(zip_derived_cl14838, plain,
% 104.19/15.59 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl14387, zip_derived_cl14386])).
% 104.19/15.59 thf(zip_derived_cl13833, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((X1)
% 104.19/15.59 = (double_divide @ (multiply @ X0 @ (inverse @ X0)) @ (inverse @ X1)))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl13700, zip_derived_cl8564])).
% 104.19/15.59 thf(zip_derived_cl13474, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.19/15.59 ((double_divide @
% 104.19/15.59 (double_divide @ (multiply @ X2 @ (inverse @ X2)) @ X1) @
% 104.19/15.59 (double_divide @ (inverse @ X0) @ X0)) = (X1))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl9978, zip_derived_cl10027])).
% 104.19/15.59 thf(zip_derived_cl14141, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((double_divide @ X0 @ (double_divide @ (inverse @ X1) @ X1))
% 104.19/15.59 = (inverse @ X0))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl13833, zip_derived_cl13474])).
% 104.19/15.59 thf(zip_derived_cl14902, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((double_divide @ X1 @ (double_divide @ X0 @ (inverse @ X0)))
% 104.19/15.59 = (inverse @ X1))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl14838, zip_derived_cl14141])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl15477, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ (double_divide @ X1 @ (inverse @ X1)) @ X0)
% 104.19/15.59 = (inverse @ (inverse @ X0)))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl14902, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl14838, plain,
% 104.19/15.59 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl14387, zip_derived_cl14386])).
% 104.19/15.59 thf(zip_derived_cl15504, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ (double_divide @ X1 @ (inverse @ X1)) @ X0) = (X0))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl15477, zip_derived_cl14838])).
% 104.19/15.59 thf(zip_derived_cl13, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @ (multiply @ (multiply @ X0 @ X3) @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X4 @ X5) @ X5)) @
% 104.19/15.59 (double_divide @ X4 @ (inverse @ X0)))
% 104.19/15.59 = (inverse @
% 104.19/15.59 (double_divide @ (inverse @ X3) @
% 104.19/15.59 (multiply @ (double_divide @ X2 @ X1) @ X1))))),
% 104.19/15.59 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl13, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @ (multiply @ (multiply @ X0 @ X3) @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X4 @ X5) @ X5)) @
% 104.19/15.59 (double_divide @ X4 @ (inverse @ X0)))
% 104.19/15.59 = (inverse @
% 104.19/15.59 (double_divide @ (inverse @ X3) @
% 104.19/15.59 (multiply @ (double_divide @ X2 @ X1) @ X1))))),
% 104.19/15.59 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl67, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i,
% 104.19/15.59 X7 : $i, X8 : $i, X9 : $i, X10 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @
% 104.19/15.59 (multiply @
% 104.19/15.59 (multiply @
% 104.19/15.59 (double_divide @ (inverse @ X4) @
% 104.19/15.59 (multiply @ (double_divide @ X3 @ X8) @ X8)) @
% 104.19/15.59 X7) @
% 104.19/15.59 X6) @
% 104.19/15.59 (multiply @ (double_divide @ X9 @ X10) @ X10)) @
% 104.19/15.59 (double_divide @ X9 @
% 104.19/15.59 (multiply @
% 104.19/15.59 (double_divide @ (multiply @ (multiply @ X0 @ X4) @ X3) @
% 104.19/15.59 (multiply @ (double_divide @ X1 @ X2) @ X2)) @
% 104.19/15.59 (double_divide @ X1 @ (inverse @ X0)))))
% 104.19/15.59 = (inverse @
% 104.19/15.59 (double_divide @ (inverse @ X7) @
% 104.19/15.59 (multiply @ (double_divide @ X6 @ X5) @ X5))))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl13])).
% 104.19/15.59 thf(zip_derived_cl13, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @ (multiply @ (multiply @ X0 @ X3) @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X4 @ X5) @ X5)) @
% 104.19/15.59 (double_divide @ X4 @ (inverse @ X0)))
% 104.19/15.59 = (inverse @
% 104.19/15.59 (double_divide @ (inverse @ X3) @
% 104.19/15.59 (multiply @ (double_divide @ X2 @ X1) @ X1))))),
% 104.19/15.59 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl78, plain,
% 104.19/15.59 (![X1 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i, X8 : $i,
% 104.19/15.59 X9 : $i, X10 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @
% 104.19/15.59 (multiply @
% 104.19/15.59 (multiply @
% 104.19/15.59 (double_divide @ (inverse @ X4) @
% 104.19/15.59 (multiply @ (double_divide @ X3 @ X8) @ X8)) @
% 104.19/15.59 X7) @
% 104.19/15.59 X6) @
% 104.19/15.59 (multiply @ (double_divide @ X9 @ X10) @ X10)) @
% 104.19/15.59 (double_divide @ X9 @
% 104.19/15.59 (multiply @ (multiply @ (double_divide @ X3 @ X1) @ X1) @
% 104.19/15.59 (inverse @ X4))))
% 104.19/15.59 = (inverse @
% 104.19/15.59 (double_divide @ (inverse @ X7) @
% 104.19/15.59 (multiply @ (double_divide @ X6 @ X5) @ X5))))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl67, zip_derived_cl13, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl13833, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((X1)
% 104.19/15.59 = (double_divide @ (multiply @ X0 @ (inverse @ X0)) @ (inverse @ X1)))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl13700, zip_derived_cl8564])).
% 104.19/15.59 thf(zip_derived_cl3568, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ (double_divide @ X3 @ (double_divide @ X1 @ X3)) @ X2)
% 104.19/15.59 = (inverse @
% 104.19/15.59 (double_divide @ X2 @
% 104.19/15.59 (double_divide @ X0 @ (double_divide @ X1 @ X0)))))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl3481, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl202, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ (double_divide @ X1 @ X0) @ X0)
% 104.19/15.59 = (multiply @ (double_divide @ X1 @ X3) @ X3))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl165, zip_derived_cl1, zip_derived_cl3])).
% 104.19/15.59 thf(zip_derived_cl4279, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ (double_divide @ X2 @ X3) @ X3)
% 104.19/15.59 = (inverse @
% 104.19/15.59 (double_divide @ (double_divide @ X1 @ X2) @
% 104.19/15.59 (double_divide @ X0 @ (double_divide @ X1 @ X0)))))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl3568, zip_derived_cl202])).
% 104.19/15.59 thf(zip_derived_cl14105, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ (double_divide @ X2 @ X3) @ X3)
% 104.19/15.59 = (inverse @
% 104.19/15.59 (double_divide @
% 104.19/15.59 (double_divide @ (multiply @ X1 @ (inverse @ X1)) @ X2) @
% 104.19/15.59 (double_divide @ (inverse @ X0) @ X0))))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl13833, zip_derived_cl4279])).
% 104.19/15.59 thf(zip_derived_cl13474, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.19/15.59 ((double_divide @
% 104.19/15.59 (double_divide @ (multiply @ X2 @ (inverse @ X2)) @ X1) @
% 104.19/15.59 (double_divide @ (inverse @ X0) @ X0)) = (X1))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl9978, zip_derived_cl10027])).
% 104.19/15.59 thf(zip_derived_cl14206, plain,
% 104.19/15.59 (![X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ (double_divide @ X2 @ X3) @ X3) = (inverse @ X2))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl14105, zip_derived_cl13474])).
% 104.19/15.59 thf(zip_derived_cl14206, plain,
% 104.19/15.59 (![X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ (double_divide @ X2 @ X3) @ X3) = (inverse @ X2))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl14105, zip_derived_cl13474])).
% 104.19/15.59 thf(zip_derived_cl14206, plain,
% 104.19/15.59 (![X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ (double_divide @ X2 @ X3) @ X3) = (inverse @ X2))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl14105, zip_derived_cl13474])).
% 104.19/15.59 thf(zip_derived_cl14206, plain,
% 104.19/15.59 (![X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ (double_divide @ X2 @ X3) @ X3) = (inverse @ X2))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl14105, zip_derived_cl13474])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl14278, plain,
% 104.19/15.59 (![X3 : $i, X4 : $i, X6 : $i, X7 : $i, X9 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @
% 104.19/15.59 (multiply @
% 104.19/15.59 (multiply @ (double_divide @ (inverse @ X4) @ (inverse @ X3)) @ X7) @
% 104.19/15.59 X6) @
% 104.19/15.59 (inverse @ X9)) @
% 104.19/15.59 (double_divide @ X9 @ (multiply @ (inverse @ X3) @ (inverse @ X4))))
% 104.19/15.59 = (multiply @ (inverse @ X6) @ (inverse @ X7)))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl78, zip_derived_cl14206, zip_derived_cl14206,
% 104.19/15.59 zip_derived_cl14206, zip_derived_cl14206, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl15639, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @ (multiply @ X0 @ X1) @ (inverse @ X3)) @
% 104.19/15.59 (double_divide @ X3 @
% 104.19/15.59 (multiply @ (inverse @ (inverse @ X2)) @ (inverse @ X2))))
% 104.19/15.59 = (multiply @ (inverse @ X1) @ (inverse @ X0)))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl15504, zip_derived_cl14278])).
% 104.19/15.59 thf(zip_derived_cl14838, plain,
% 104.19/15.59 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl14387, zip_derived_cl14386])).
% 104.19/15.59 thf(zip_derived_cl14386, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((inverse @ X0)
% 104.19/15.59 = (double_divide @ X0 @ (multiply @ X1 @ (inverse @ X1))))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl13833, zip_derived_cl14350])).
% 104.19/15.59 thf(zip_derived_cl14206, plain,
% 104.19/15.59 (![X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ (double_divide @ X2 @ X3) @ X3) = (inverse @ X2))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl14105, zip_derived_cl13474])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl14838, plain,
% 104.19/15.59 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl14387, zip_derived_cl14386])).
% 104.19/15.59 thf(zip_derived_cl14913, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl14838])).
% 104.19/15.59 thf(zip_derived_cl15663, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((double_divide @ X1 @ X0)
% 104.19/15.59 = (multiply @ (inverse @ X1) @ (inverse @ X0)))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl15639, zip_derived_cl14838,
% 104.19/15.59 zip_derived_cl14386, zip_derived_cl14206, zip_derived_cl14913])).
% 104.19/15.59 thf(zip_derived_cl15976, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((double_divide @ X1 @ (inverse @ X0))
% 104.19/15.59 = (multiply @ (inverse @ X1) @ X0))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl14838, zip_derived_cl15663])).
% 104.19/15.59 thf(zip_derived_cl16011, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.19/15.59 ((double_divide @ (double_divide @ X0 @ X1) @ (inverse @ X2))
% 104.19/15.59 = (multiply @ (multiply @ X1 @ X0) @ X2))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl15976])).
% 104.19/15.59 thf(zip_derived_cl19254, plain,
% 104.19/15.59 (((double_divide @ (double_divide @ b3 @ a3) @ (inverse @ c3))
% 104.19/15.59 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 104.19/15.59 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl16011])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl14838, plain,
% 104.19/15.59 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl14387, zip_derived_cl14386])).
% 104.19/15.59 thf(zip_derived_cl15663, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((double_divide @ X1 @ X0)
% 104.19/15.59 = (multiply @ (inverse @ X1) @ (inverse @ X0)))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl15639, zip_derived_cl14838,
% 104.19/15.59 zip_derived_cl14386, zip_derived_cl14206, zip_derived_cl14913])).
% 104.19/15.59 thf(zip_derived_cl15980, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((double_divide @ (inverse @ X0) @ X1)
% 104.19/15.59 = (multiply @ X0 @ (inverse @ X1)))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl14838, zip_derived_cl15663])).
% 104.19/15.59 thf(zip_derived_cl16054, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.19/15.59 ((double_divide @ (inverse @ X2) @ (double_divide @ X0 @ X1))
% 104.19/15.59 = (multiply @ X2 @ (multiply @ X1 @ X0)))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl15980])).
% 104.19/15.59 thf(zip_derived_cl19524, plain,
% 104.19/15.59 (((double_divide @ (double_divide @ b3 @ a3) @ (inverse @ c3))
% 104.19/15.59 != (double_divide @ (inverse @ a3) @ (double_divide @ c3 @ b3)))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl19254, zip_derived_cl16054])).
% 104.19/15.59 thf(zip_derived_cl13, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @ (multiply @ (multiply @ X0 @ X3) @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X4 @ X5) @ X5)) @
% 104.19/15.59 (double_divide @ X4 @ (inverse @ X0)))
% 104.19/15.59 = (inverse @
% 104.19/15.59 (double_divide @ (inverse @ X3) @
% 104.19/15.59 (multiply @ (double_divide @ X2 @ X1) @ X1))))),
% 104.19/15.59 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl311, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @ (inverse @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X3 @ X4) @ X4)) @
% 104.19/15.59 (double_divide @ X3 @ (multiply @ (double_divide @ X1 @ X0) @ X0)))
% 104.19/15.59 = (multiply @ X2 @ X1))),
% 104.19/15.59 inference('demod', [status(thm)], [zip_derived_cl264, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl448, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i,
% 104.19/15.59 X7 : $i, X8 : $i, X9 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @
% 104.19/15.59 (multiply @
% 104.19/15.59 (double_divide @ (multiply @ (multiply @ X0 @ X4) @ X3) @
% 104.19/15.59 (multiply @ (double_divide @ X1 @ X2) @ X2)) @
% 104.19/15.59 (double_divide @ X1 @ (inverse @ X0))) @
% 104.19/15.59 (multiply @ (double_divide @ X8 @ X9) @ X9)) @
% 104.19/15.59 (double_divide @ X8 @ (multiply @ (double_divide @ X5 @ X7) @ X7)))
% 104.19/15.59 = (multiply @
% 104.19/15.59 (double_divide @ (inverse @ X4) @
% 104.19/15.59 (multiply @ (double_divide @ X3 @ X6) @ X6)) @
% 104.19/15.59 X5))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl311])).
% 104.19/15.59 thf(zip_derived_cl13, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @ (multiply @ (multiply @ X0 @ X3) @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X4 @ X5) @ X5)) @
% 104.19/15.59 (double_divide @ X4 @ (inverse @ X0)))
% 104.19/15.59 = (inverse @
% 104.19/15.59 (double_divide @ (inverse @ X3) @
% 104.19/15.59 (multiply @ (double_divide @ X2 @ X1) @ X1))))),
% 104.19/15.59 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl451, plain,
% 104.19/15.59 (![X1 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i, X8 : $i, X9 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @
% 104.19/15.59 (multiply @ (multiply @ (double_divide @ X3 @ X1) @ X1) @
% 104.19/15.59 (inverse @ X4)) @
% 104.19/15.59 (multiply @ (double_divide @ X8 @ X9) @ X9)) @
% 104.19/15.59 (double_divide @ X8 @ (multiply @ (double_divide @ X5 @ X7) @ X7)))
% 104.19/15.59 = (multiply @
% 104.19/15.59 (double_divide @ (inverse @ X4) @
% 104.19/15.59 (multiply @ (double_divide @ X3 @ X6) @ X6)) @
% 104.19/15.59 X5))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl448, zip_derived_cl13, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl14206, plain,
% 104.19/15.59 (![X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ (double_divide @ X2 @ X3) @ X3) = (inverse @ X2))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl14105, zip_derived_cl13474])).
% 104.19/15.59 thf(zip_derived_cl15663, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((double_divide @ X1 @ X0)
% 104.19/15.59 = (multiply @ (inverse @ X1) @ (inverse @ X0)))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl15639, zip_derived_cl14838,
% 104.19/15.59 zip_derived_cl14386, zip_derived_cl14206, zip_derived_cl14913])).
% 104.19/15.59 thf(zip_derived_cl14206, plain,
% 104.19/15.59 (![X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ (double_divide @ X2 @ X3) @ X3) = (inverse @ X2))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl14105, zip_derived_cl13474])).
% 104.19/15.59 thf(zip_derived_cl14206, plain,
% 104.19/15.59 (![X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ (double_divide @ X2 @ X3) @ X3) = (inverse @ X2))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl14105, zip_derived_cl13474])).
% 104.19/15.59 thf(zip_derived_cl14838, plain,
% 104.19/15.59 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl14387, zip_derived_cl14386])).
% 104.19/15.59 thf(zip_derived_cl8611, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @
% 104.19/15.59 (multiply @ X2 @ (multiply @ (double_divide @ X2 @ X1) @ X1)) @ X3) @
% 104.19/15.59 X3) = (multiply @ X0 @ (inverse @ X0)))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl8564, zip_derived_cl202])).
% 104.19/15.59 thf(zip_derived_cl8611, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @
% 104.19/15.59 (multiply @ X2 @ (multiply @ (double_divide @ X2 @ X1) @ X1)) @ X3) @
% 104.19/15.59 X3) = (multiply @ X0 @ (inverse @ X0)))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl8564, zip_derived_cl202])).
% 104.19/15.59 thf(zip_derived_cl9880, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X0 @ (inverse @ X0)) = (multiply @ X1 @ (inverse @ X1)))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl8611, zip_derived_cl8611])).
% 104.19/15.59 thf(zip_derived_cl13700, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.19/15.59 ((multiply @ X2 @
% 104.19/15.59 (multiply @
% 104.19/15.59 (double_divide @ (multiply @ X1 @ (inverse @ X1)) @ X0) @ X0))
% 104.19/15.59 = (X2))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl13474, zip_derived_cl3])).
% 104.19/15.59 thf(zip_derived_cl14206, plain,
% 104.19/15.59 (![X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ (double_divide @ X2 @ X3) @ X3) = (inverse @ X2))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl14105, zip_derived_cl13474])).
% 104.19/15.59 thf(zip_derived_cl14260, plain,
% 104.19/15.59 (![X1 : $i, X2 : $i]:
% 104.19/15.59 ((multiply @ X2 @ (inverse @ (multiply @ X1 @ (inverse @ X1)))) = (X2))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl13700, zip_derived_cl14206])).
% 104.19/15.59 thf(zip_derived_cl14521, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ (inverse @ (multiply @ X0 @ (inverse @ X0)))) = (X1))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl9880, zip_derived_cl14260])).
% 104.19/15.59 thf(zip_derived_cl13833, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((X1)
% 104.19/15.59 = (double_divide @ (multiply @ X0 @ (inverse @ X0)) @ (inverse @ X1)))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl13700, zip_derived_cl8564])).
% 104.19/15.59 thf(zip_derived_cl14207, plain,
% 104.19/15.59 (![X2 : $i, X3 : $i]:
% 104.19/15.59 ((double_divide @ X3 @ (double_divide @ X2 @ X3)) = (X2))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl14109, zip_derived_cl13474])).
% 104.19/15.59 thf(zip_derived_cl14367, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((double_divide @ (inverse @ X0) @ X0)
% 104.19/15.59 = (multiply @ X1 @ (inverse @ X1)))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl13833, zip_derived_cl14207])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl14367, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((double_divide @ (inverse @ X0) @ X0)
% 104.19/15.59 = (multiply @ X1 @ (inverse @ X1)))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl13833, zip_derived_cl14207])).
% 104.19/15.59 thf(zip_derived_cl14529, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ (double_divide @ (inverse @ X0) @ X0)) = (X1))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl14521, zip_derived_cl14367, zip_derived_cl1,
% 104.19/15.59 zip_derived_cl14367])).
% 104.19/15.59 thf(zip_derived_cl14895, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ (double_divide @ X0 @ (inverse @ X0))) = (X1))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl14838, zip_derived_cl14529])).
% 104.19/15.59 thf(zip_derived_cl14913, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl14838])).
% 104.19/15.59 thf(zip_derived_cl14986, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((inverse @ X0)
% 104.19/15.59 = (double_divide @ (double_divide @ X1 @ (inverse @ X1)) @ X0))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl14895, zip_derived_cl14913])).
% 104.19/15.59 thf(zip_derived_cl13, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @ (multiply @ (multiply @ X0 @ X3) @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X4 @ X5) @ X5)) @
% 104.19/15.59 (double_divide @ X4 @ (inverse @ X0)))
% 104.19/15.59 = (inverse @
% 104.19/15.59 (double_divide @ (inverse @ X3) @
% 104.19/15.59 (multiply @ (double_divide @ X2 @ X1) @ X1))))),
% 104.19/15.59 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl5, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @ (inverse @ X3) @
% 104.19/15.59 (multiply @ (double_divide @ X2 @ X1) @ X1)) @
% 104.19/15.59 (double_divide @ X2 @ (multiply @ X0 @ X3))) = (inverse @ X0))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl60, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @
% 104.19/15.59 (inverse @ (double_divide @ X4 @ (inverse @ X5))) @
% 104.19/15.59 (multiply @ (double_divide @ X6 @ X7) @ X7)) @
% 104.19/15.59 (double_divide @ X6 @
% 104.19/15.59 (inverse @
% 104.19/15.59 (double_divide @ (inverse @ X2) @
% 104.19/15.59 (multiply @ (double_divide @ X1 @ X0) @ X0)))))
% 104.19/15.59 = (inverse @
% 104.19/15.59 (double_divide @ (multiply @ (multiply @ X5 @ X2) @ X1) @
% 104.19/15.59 (multiply @ (double_divide @ X4 @ X3) @ X3))))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl5])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl90, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @ (multiply @ (inverse @ X5) @ X4) @
% 104.19/15.59 (multiply @ (double_divide @ X6 @ X7) @ X7)) @
% 104.19/15.59 (double_divide @ X6 @
% 104.19/15.59 (multiply @ (multiply @ (double_divide @ X1 @ X0) @ X0) @
% 104.19/15.59 (inverse @ X2))))
% 104.19/15.59 = (inverse @
% 104.19/15.59 (double_divide @ (multiply @ (multiply @ X5 @ X2) @ X1) @
% 104.19/15.59 (multiply @ (double_divide @ X4 @ X3) @ X3))))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl60, zip_derived_cl1, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl15976, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((double_divide @ X1 @ (inverse @ X0))
% 104.19/15.59 = (multiply @ (inverse @ X1) @ X0))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl14838, zip_derived_cl15663])).
% 104.19/15.59 thf(zip_derived_cl14206, plain,
% 104.19/15.59 (![X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ (double_divide @ X2 @ X3) @ X3) = (inverse @ X2))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl14105, zip_derived_cl13474])).
% 104.19/15.59 thf(zip_derived_cl14206, plain,
% 104.19/15.59 (![X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ (double_divide @ X2 @ X3) @ X3) = (inverse @ X2))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl14105, zip_derived_cl13474])).
% 104.19/15.59 thf(zip_derived_cl15663, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((double_divide @ X1 @ X0)
% 104.19/15.59 = (multiply @ (inverse @ X1) @ (inverse @ X0)))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl15639, zip_derived_cl14838,
% 104.19/15.59 zip_derived_cl14386, zip_derived_cl14206, zip_derived_cl14913])).
% 104.19/15.59 thf(zip_derived_cl14206, plain,
% 104.19/15.59 (![X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ (double_divide @ X2 @ X3) @ X3) = (inverse @ X2))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl14105, zip_derived_cl13474])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl15976, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((double_divide @ X1 @ (inverse @ X0))
% 104.19/15.59 = (multiply @ (inverse @ X1) @ X0))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl14838, zip_derived_cl15663])).
% 104.19/15.59 thf(zip_derived_cl14913, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl14838])).
% 104.19/15.59 thf(zip_derived_cl17697, plain,
% 104.19/15.59 (![X1 : $i, X2 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 104.19/15.59 ((multiply @
% 104.19/15.59 (double_divide @ (double_divide @ X5 @ (inverse @ X4)) @
% 104.19/15.59 (inverse @ X6)) @
% 104.19/15.59 (double_divide @ X6 @ (double_divide @ X1 @ X2)))
% 104.19/15.59 = (double_divide @ X4 @ (double_divide @ X1 @ (multiply @ X5 @ X2))))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl90, zip_derived_cl15976, zip_derived_cl14206,
% 104.19/15.59 zip_derived_cl14206, zip_derived_cl15663,
% 104.19/15.59 zip_derived_cl14206, zip_derived_cl1, zip_derived_cl15976,
% 104.19/15.59 zip_derived_cl14913])).
% 104.19/15.59 thf(zip_derived_cl17756, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ (inverse @ (inverse @ X0)) @
% 104.19/15.59 (double_divide @ X0 @ (double_divide @ X3 @ X1)))
% 104.19/15.59 = (double_divide @ X2 @ (double_divide @ X3 @ (multiply @ X2 @ X1))))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl14986, zip_derived_cl17697])).
% 104.19/15.59 thf(zip_derived_cl14838, plain,
% 104.19/15.59 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl14387, zip_derived_cl14386])).
% 104.19/15.59 thf(zip_derived_cl4396, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X3 : $i]:
% 104.19/15.59 ((double_divide @ X0 @ (double_divide @ X1 @ X0))
% 104.19/15.59 = (double_divide @ X3 @ (double_divide @ X1 @ X3)))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl4237, zip_derived_cl1, zip_derived_cl3])).
% 104.19/15.59 thf(zip_derived_cl3568, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ (double_divide @ X3 @ (double_divide @ X1 @ X3)) @ X2)
% 104.19/15.59 = (inverse @
% 104.19/15.59 (double_divide @ X2 @
% 104.19/15.59 (double_divide @ X0 @ (double_divide @ X1 @ X0)))))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl3481, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl4554, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ (double_divide @ X3 @ (double_divide @ X2 @ X3)) @
% 104.19/15.59 (double_divide @ X2 @ X1))
% 104.19/15.59 = (inverse @ (double_divide @ X0 @ (double_divide @ X1 @ X0))))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl4396, zip_derived_cl3568])).
% 104.19/15.59 thf(zip_derived_cl14207, plain,
% 104.19/15.59 (![X2 : $i, X3 : $i]:
% 104.19/15.59 ((double_divide @ X3 @ (double_divide @ X2 @ X3)) = (X2))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl14109, zip_derived_cl13474])).
% 104.19/15.59 thf(zip_derived_cl14207, plain,
% 104.19/15.59 (![X2 : $i, X3 : $i]:
% 104.19/15.59 ((double_divide @ X3 @ (double_divide @ X2 @ X3)) = (X2))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl14109, zip_derived_cl13474])).
% 104.19/15.59 thf(zip_derived_cl14351, plain,
% 104.19/15.59 (![X1 : $i, X2 : $i]:
% 104.19/15.59 ((multiply @ X2 @ (double_divide @ X2 @ X1)) = (inverse @ X1))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl4554, zip_derived_cl14207, zip_derived_cl14207])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl17819, plain,
% 104.19/15.59 (![X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X3)
% 104.19/15.59 = (double_divide @ X2 @ (double_divide @ X3 @ (multiply @ X2 @ X1))))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl17756, zip_derived_cl14838,
% 104.19/15.59 zip_derived_cl14351, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl14350, plain,
% 104.19/15.59 (![X1 : $i, X2 : $i]:
% 104.19/15.59 ((X2) = (double_divide @ (double_divide @ X1 @ X2) @ X1))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl4488, zip_derived_cl14207, zip_derived_cl14207])).
% 104.19/15.59 thf(zip_derived_cl20119, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.19/15.59 ((double_divide @ X0 @ (multiply @ X2 @ X1))
% 104.19/15.59 = (double_divide @ (multiply @ X1 @ X0) @ X2))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl17819, zip_derived_cl14350])).
% 104.19/15.59 thf(zip_derived_cl15976, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((double_divide @ X1 @ (inverse @ X0))
% 104.19/15.59 = (multiply @ (inverse @ X1) @ X0))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl14838, zip_derived_cl15663])).
% 104.19/15.59 thf(zip_derived_cl14913, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl14838])).
% 104.19/15.59 thf(zip_derived_cl15990, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((inverse @ (double_divide @ X1 @ (inverse @ X0)))
% 104.19/15.59 = (double_divide @ X0 @ (inverse @ X1)))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl15976, zip_derived_cl14913])).
% 104.19/15.59 thf(zip_derived_cl20237, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.19/15.59 ((inverse @ (double_divide @ X2 @ (multiply @ (inverse @ X1) @ X0)))
% 104.19/15.59 = (double_divide @ X1 @ (inverse @ (multiply @ X0 @ X2))))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl20119, zip_derived_cl15990])).
% 104.19/15.59 thf(zip_derived_cl15976, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((double_divide @ X1 @ (inverse @ X0))
% 104.19/15.59 = (multiply @ (inverse @ X1) @ X0))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl14838, zip_derived_cl15663])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl14913, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl14838])).
% 104.19/15.59 thf(zip_derived_cl20318, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.19/15.59 ((multiply @ (double_divide @ X1 @ (inverse @ X0)) @ X2)
% 104.19/15.59 = (double_divide @ X1 @ (double_divide @ X2 @ X0)))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl20237, zip_derived_cl15976, zip_derived_cl1,
% 104.19/15.59 zip_derived_cl14913])).
% 104.19/15.59 thf(zip_derived_cl14350, plain,
% 104.19/15.59 (![X1 : $i, X2 : $i]:
% 104.19/15.59 ((X2) = (double_divide @ (double_divide @ X1 @ X2) @ X1))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl4488, zip_derived_cl14207, zip_derived_cl14207])).
% 104.19/15.59 thf(zip_derived_cl14206, plain,
% 104.19/15.59 (![X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ (double_divide @ X2 @ X3) @ X3) = (inverse @ X2))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl14105, zip_derived_cl13474])).
% 104.19/15.59 thf(zip_derived_cl15663, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((double_divide @ X1 @ X0)
% 104.19/15.59 = (multiply @ (inverse @ X1) @ (inverse @ X0)))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl15639, zip_derived_cl14838,
% 104.19/15.59 zip_derived_cl14386, zip_derived_cl14206, zip_derived_cl14913])).
% 104.19/15.59 thf(zip_derived_cl14913, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 104.19/15.59 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl14838])).
% 104.19/15.59 thf(zip_derived_cl15954, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((inverse @ (double_divide @ X1 @ X0))
% 104.19/15.59 = (double_divide @ (inverse @ X0) @ (inverse @ X1)))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl15663, zip_derived_cl14913])).
% 104.19/15.59 thf(zip_derived_cl1, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 104.19/15.59 inference('cnf', [status(esa)], [multiply])).
% 104.19/15.59 thf(zip_derived_cl15984, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X0 @ X1)
% 104.19/15.59 = (double_divide @ (inverse @ X0) @ (inverse @ X1)))),
% 104.19/15.59 inference('demod', [status(thm)], [zip_derived_cl15954, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl15984, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ X0 @ X1)
% 104.19/15.59 = (double_divide @ (inverse @ X0) @ (inverse @ X1)))),
% 104.19/15.59 inference('demod', [status(thm)], [zip_derived_cl15954, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl14351, plain,
% 104.19/15.59 (![X1 : $i, X2 : $i]:
% 104.19/15.59 ((multiply @ X2 @ (double_divide @ X2 @ X1)) = (inverse @ X1))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl4554, zip_derived_cl14207, zip_derived_cl14207])).
% 104.19/15.59 thf(zip_derived_cl16285, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ (inverse @ X1) @ (multiply @ X1 @ X0))
% 104.19/15.59 = (inverse @ (inverse @ X0)))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl15984, zip_derived_cl14351])).
% 104.19/15.59 thf(zip_derived_cl14838, plain,
% 104.19/15.59 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl14387, zip_derived_cl14386])).
% 104.19/15.59 thf(zip_derived_cl16316, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i]:
% 104.19/15.59 ((multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)) = (X0))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl16285, zip_derived_cl14838])).
% 104.19/15.59 thf(zip_derived_cl17819, plain,
% 104.19/15.59 (![X1 : $i, X2 : $i, X3 : $i]:
% 104.19/15.59 ((multiply @ X1 @ X3)
% 104.19/15.59 = (double_divide @ X2 @ (double_divide @ X3 @ (multiply @ X2 @ X1))))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl17756, zip_derived_cl14838,
% 104.19/15.59 zip_derived_cl14351, zip_derived_cl1])).
% 104.19/15.59 thf(zip_derived_cl20169, plain,
% 104.19/15.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.19/15.59 ((multiply @ (multiply @ X1 @ X0) @ X2)
% 104.19/15.59 = (double_divide @ (inverse @ X1) @ (double_divide @ X2 @ X0)))),
% 104.19/15.59 inference('sup+', [status(thm)],
% 104.19/15.59 [zip_derived_cl16316, zip_derived_cl17819])).
% 104.19/15.59 thf(zip_derived_cl34535, plain,
% 104.19/15.59 (![X3 : $i, X4 : $i, X5 : $i]:
% 104.19/15.59 ((double_divide @ (double_divide @ X3 @ X4) @ (inverse @ X5))
% 104.19/15.59 = (double_divide @ (inverse @ X4) @ (double_divide @ X5 @ X3)))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl451, zip_derived_cl14206, zip_derived_cl15663,
% 104.19/15.59 zip_derived_cl14206, zip_derived_cl14206,
% 104.19/15.59 zip_derived_cl20318, zip_derived_cl14350,
% 104.19/15.59 zip_derived_cl14206, zip_derived_cl15984, zip_derived_cl20169])).
% 104.19/15.59 thf(zip_derived_cl34536, plain,
% 104.19/15.59 (((double_divide @ (inverse @ a3) @ (double_divide @ c3 @ b3))
% 104.19/15.59 != (double_divide @ (inverse @ a3) @ (double_divide @ c3 @ b3)))),
% 104.19/15.59 inference('demod', [status(thm)],
% 104.19/15.59 [zip_derived_cl19524, zip_derived_cl34535])).
% 104.19/15.59 thf(zip_derived_cl34537, plain, ($false),
% 104.19/15.59 inference('simplify', [status(thm)], [zip_derived_cl34536])).
% 104.19/15.59
% 104.19/15.59 % SZS output end Refutation
% 104.19/15.59
% 104.19/15.59
% 104.19/15.59 % Terminating...
% 104.62/15.68 % Runner terminated.
% 104.62/15.69 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------