TSTP Solution File: GRP579-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP579-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.VnXnckQUg0 true
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:52:11 EDT 2023
% Result : Unsatisfiable 13.71s 2.58s
% Output : Refutation 13.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP579-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.VnXnckQUg0 true
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 02:16:15 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in FO mode
% 0.22/0.65 % Total configuration time : 435
% 0.22/0.65 % Estimated wc time : 1092
% 0.22/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.22/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.22/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.22/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 13.71/2.58 % Solved by fo/fo5.sh.
% 13.71/2.58 % done 1509 iterations in 1.798s
% 13.71/2.58 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 13.71/2.58 % SZS output start Refutation
% 13.71/2.58 thf(c3_type, type, c3: $i).
% 13.71/2.58 thf(identity_type, type, identity: $i).
% 13.71/2.58 thf(multiply_type, type, multiply: $i > $i > $i).
% 13.71/2.58 thf(b3_type, type, b3: $i).
% 13.71/2.58 thf(a3_type, type, a3: $i).
% 13.71/2.58 thf(double_divide_type, type, double_divide: $i > $i > $i).
% 13.71/2.58 thf(inverse_type, type, inverse: $i > $i).
% 13.71/2.58 thf(prove_these_axioms_3, conjecture,
% 13.71/2.58 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) =
% 13.71/2.58 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ))).
% 13.71/2.58 thf(zf_stmt_0, negated_conjecture,
% 13.71/2.58 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 13.71/2.58 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) )),
% 13.71/2.58 inference('cnf.neg', [status(esa)], [prove_these_axioms_3])).
% 13.71/2.58 thf(zip_derived_cl4, plain,
% 13.71/2.58 (((multiply @ (multiply @ a3 @ b3) @ c3)
% 13.71/2.58 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 13.71/2.58 inference('cnf', [status(esa)], [zf_stmt_0])).
% 13.71/2.58 thf(identity, axiom,
% 13.71/2.58 (( identity ) = ( double_divide @ A @ ( inverse @ A ) ))).
% 13.71/2.58 thf(zip_derived_cl3, plain,
% 13.71/2.58 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 13.71/2.58 inference('cnf', [status(esa)], [identity])).
% 13.71/2.58 thf(single_axiom, axiom,
% 13.71/2.58 (( double_divide @
% 13.71/2.58 ( double_divide @
% 13.71/2.58 A @
% 13.71/2.58 ( double_divide @
% 13.71/2.58 ( double_divide @ ( double_divide @ B @ A ) @ C ) @
% 13.71/2.58 ( double_divide @ B @ identity ) ) ) @
% 13.71/2.58 ( double_divide @ identity @ identity ) ) =
% 13.71/2.58 ( C ))).
% 13.71/2.58 thf(zip_derived_cl0, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ X1 @
% 13.71/2.58 (double_divide @
% 13.71/2.58 (double_divide @ (double_divide @ X2 @ X1) @ X0) @
% 13.71/2.58 (double_divide @ X2 @ identity))) @
% 13.71/2.58 (double_divide @ identity @ identity)) = (X0))),
% 13.71/2.58 inference('cnf', [status(esa)], [single_axiom])).
% 13.71/2.58 thf(inverse, axiom, (( inverse @ A ) = ( double_divide @ A @ identity ))).
% 13.71/2.58 thf(zip_derived_cl2, plain,
% 13.71/2.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 13.71/2.58 inference('cnf', [status(esa)], [inverse])).
% 13.71/2.58 thf(zip_derived_cl2, plain,
% 13.71/2.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 13.71/2.58 inference('cnf', [status(esa)], [inverse])).
% 13.71/2.58 thf(zip_derived_cl13, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ X1 @
% 13.71/2.58 (double_divide @
% 13.71/2.58 (double_divide @ (double_divide @ X2 @ X1) @ X0) @ (inverse @ X2))) @
% 13.71/2.58 (inverse @ identity)) = (X0))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 13.71/2.58 thf(zip_derived_cl20, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ X0 @ (double_divide @ identity @ (inverse @ X1))) @
% 13.71/2.58 (inverse @ identity)) = (inverse @ (double_divide @ X1 @ X0)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl13])).
% 13.71/2.58 thf(zip_derived_cl2, plain,
% 13.71/2.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 13.71/2.58 inference('cnf', [status(esa)], [inverse])).
% 13.71/2.58 thf(multiply, axiom,
% 13.71/2.58 (( multiply @ A @ B ) =
% 13.71/2.58 ( double_divide @ ( double_divide @ B @ A ) @ identity ))).
% 13.71/2.58 thf(zip_derived_cl1, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X1 @ X0)
% 13.71/2.58 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 13.71/2.58 inference('cnf', [status(esa)], [multiply])).
% 13.71/2.58 thf(zip_derived_cl6, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 13.71/2.58 thf(zip_derived_cl642, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ X0 @ (double_divide @ identity @ (inverse @ X1))) @
% 13.71/2.58 (inverse @ identity)) = (multiply @ X0 @ X1))),
% 13.71/2.58 inference('demod', [status(thm)], [zip_derived_cl20, zip_derived_cl6])).
% 13.71/2.58 thf(zip_derived_cl3, plain,
% 13.71/2.58 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 13.71/2.58 inference('cnf', [status(esa)], [identity])).
% 13.71/2.58 thf(zip_derived_cl642, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ X0 @ (double_divide @ identity @ (inverse @ X1))) @
% 13.71/2.58 (inverse @ identity)) = (multiply @ X0 @ X1))),
% 13.71/2.58 inference('demod', [status(thm)], [zip_derived_cl20, zip_derived_cl6])).
% 13.71/2.58 thf(zip_derived_cl664, plain,
% 13.71/2.58 (![X0 : $i]:
% 13.71/2.58 ((double_divide @ (double_divide @ X0 @ identity) @
% 13.71/2.58 (inverse @ identity)) = (multiply @ X0 @ identity))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl642])).
% 13.71/2.58 thf(zip_derived_cl2, plain,
% 13.71/2.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 13.71/2.58 inference('cnf', [status(esa)], [inverse])).
% 13.71/2.58 thf(zip_derived_cl668, plain,
% 13.71/2.58 (![X0 : $i]:
% 13.71/2.58 ((double_divide @ (inverse @ X0) @ (inverse @ identity))
% 13.71/2.58 = (multiply @ X0 @ identity))),
% 13.71/2.58 inference('demod', [status(thm)], [zip_derived_cl664, zip_derived_cl2])).
% 13.71/2.58 thf(zip_derived_cl3, plain,
% 13.71/2.58 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 13.71/2.58 inference('cnf', [status(esa)], [identity])).
% 13.71/2.58 thf(zip_derived_cl1, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X1 @ X0)
% 13.71/2.58 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 13.71/2.58 inference('cnf', [status(esa)], [multiply])).
% 13.71/2.58 thf(zip_derived_cl8, plain,
% 13.71/2.58 (![X0 : $i]:
% 13.71/2.58 ((multiply @ (inverse @ X0) @ X0)
% 13.71/2.58 = (double_divide @ identity @ identity))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 13.71/2.58 thf(zip_derived_cl6, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 13.71/2.58 thf(zip_derived_cl51, plain,
% 13.71/2.58 (![X0 : $i]:
% 13.71/2.58 ((multiply @ identity @ identity)
% 13.71/2.58 = (inverse @ (multiply @ (inverse @ X0) @ X0)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl6])).
% 13.71/2.58 thf(zip_derived_cl3, plain,
% 13.71/2.58 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 13.71/2.58 inference('cnf', [status(esa)], [identity])).
% 13.71/2.58 thf(zip_derived_cl146, plain,
% 13.71/2.58 (![X0 : $i]:
% 13.71/2.58 ((identity)
% 13.71/2.58 = (double_divide @ (multiply @ (inverse @ X0) @ X0) @
% 13.71/2.58 (multiply @ identity @ identity)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl3])).
% 13.71/2.58 thf(zip_derived_cl2, plain,
% 13.71/2.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 13.71/2.58 inference('cnf', [status(esa)], [inverse])).
% 13.71/2.58 thf(zip_derived_cl1, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X1 @ X0)
% 13.71/2.58 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 13.71/2.58 inference('cnf', [status(esa)], [multiply])).
% 13.71/2.58 thf(zip_derived_cl7, plain,
% 13.71/2.58 (![X0 : $i]:
% 13.71/2.58 ((multiply @ identity @ X0)
% 13.71/2.58 = (double_divide @ (inverse @ X0) @ identity))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 13.71/2.58 thf(zip_derived_cl2, plain,
% 13.71/2.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 13.71/2.58 inference('cnf', [status(esa)], [inverse])).
% 13.71/2.58 thf(zip_derived_cl10, plain,
% 13.71/2.58 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 13.71/2.58 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 13.71/2.58 thf(zip_derived_cl170, plain,
% 13.71/2.58 (![X0 : $i]:
% 13.71/2.58 ((identity)
% 13.71/2.58 = (double_divide @ (multiply @ (inverse @ X0) @ X0) @
% 13.71/2.58 (inverse @ (inverse @ identity))))),
% 13.71/2.58 inference('demod', [status(thm)], [zip_derived_cl146, zip_derived_cl10])).
% 13.71/2.58 thf(zip_derived_cl2, plain,
% 13.71/2.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 13.71/2.58 inference('cnf', [status(esa)], [inverse])).
% 13.71/2.58 thf(zip_derived_cl13, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ X1 @
% 13.71/2.58 (double_divide @
% 13.71/2.58 (double_divide @ (double_divide @ X2 @ X1) @ X0) @ (inverse @ X2))) @
% 13.71/2.58 (inverse @ identity)) = (X0))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 13.71/2.58 thf(zip_derived_cl19, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ X0 @
% 13.71/2.58 (double_divide @ (inverse @ (double_divide @ X1 @ X0)) @
% 13.71/2.58 (inverse @ X1))) @
% 13.71/2.58 (inverse @ identity)) = (identity))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 13.71/2.58 thf(zip_derived_cl6, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 13.71/2.58 thf(zip_derived_cl557, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ X0 @
% 13.71/2.58 (double_divide @ (multiply @ X0 @ X1) @ (inverse @ X1))) @
% 13.71/2.58 (inverse @ identity)) = (identity))),
% 13.71/2.58 inference('demod', [status(thm)], [zip_derived_cl19, zip_derived_cl6])).
% 13.71/2.58 thf(zip_derived_cl621, plain,
% 13.71/2.58 (((double_divide @
% 13.71/2.58 (double_divide @ (inverse @ (inverse @ identity)) @ identity) @
% 13.71/2.58 (inverse @ identity)) = (identity))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl170, zip_derived_cl557])).
% 13.71/2.58 thf(zip_derived_cl2, plain,
% 13.71/2.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 13.71/2.58 inference('cnf', [status(esa)], [inverse])).
% 13.71/2.58 thf(zip_derived_cl641, plain,
% 13.71/2.58 (((double_divide @ (inverse @ (inverse @ (inverse @ identity))) @
% 13.71/2.58 (inverse @ identity)) = (identity))),
% 13.71/2.58 inference('demod', [status(thm)], [zip_derived_cl621, zip_derived_cl2])).
% 13.71/2.58 thf(zip_derived_cl724, plain,
% 13.71/2.58 (((multiply @ (inverse @ (inverse @ identity)) @ identity) = (identity))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl668, zip_derived_cl641])).
% 13.71/2.58 thf(zip_derived_cl6, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 13.71/2.58 thf(zip_derived_cl3, plain,
% 13.71/2.58 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 13.71/2.58 inference('cnf', [status(esa)], [identity])).
% 13.71/2.58 thf(zip_derived_cl6, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 13.71/2.58 thf(zip_derived_cl31, plain,
% 13.71/2.58 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 13.71/2.58 thf(zip_derived_cl39, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ (multiply @ X1 @ X0) @ (double_divide @ X0 @ X1))
% 13.71/2.58 = (inverse @ identity))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl31])).
% 13.71/2.58 thf(zip_derived_cl734, plain,
% 13.71/2.58 (((multiply @ identity @
% 13.71/2.58 (double_divide @ identity @ (inverse @ (inverse @ identity))))
% 13.71/2.58 = (inverse @ identity))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl724, zip_derived_cl39])).
% 13.71/2.58 thf(zip_derived_cl642, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ X0 @ (double_divide @ identity @ (inverse @ X1))) @
% 13.71/2.58 (inverse @ identity)) = (multiply @ X0 @ X1))),
% 13.71/2.58 inference('demod', [status(thm)], [zip_derived_cl20, zip_derived_cl6])).
% 13.71/2.58 thf(zip_derived_cl13, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ X1 @
% 13.71/2.58 (double_divide @
% 13.71/2.58 (double_divide @ (double_divide @ X2 @ X1) @ X0) @ (inverse @ X2))) @
% 13.71/2.58 (inverse @ identity)) = (X0))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 13.71/2.58 thf(zip_derived_cl13, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ X1 @
% 13.71/2.58 (double_divide @
% 13.71/2.58 (double_divide @ (double_divide @ X2 @ X1) @ X0) @ (inverse @ X2))) @
% 13.71/2.58 (inverse @ identity)) = (X0))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 13.71/2.58 thf(zip_derived_cl16, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @
% 13.71/2.58 (double_divide @
% 13.71/2.58 (double_divide @ (double_divide @ X2 @ X1) @ X0) @ (inverse @ X2)) @
% 13.71/2.58 (double_divide @ X0 @ (inverse @ X1))) @
% 13.71/2.58 (inverse @ identity)) = (inverse @ identity))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl13])).
% 13.71/2.58 thf(zip_derived_cl662, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @
% 13.71/2.58 (double_divide @
% 13.71/2.58 (double_divide @ (double_divide @ X1 @ X0) @ identity) @
% 13.71/2.58 (inverse @ X1)) @
% 13.71/2.58 X0) = (inverse @ identity))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl642, zip_derived_cl16])).
% 13.71/2.58 thf(zip_derived_cl1, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X1 @ X0)
% 13.71/2.58 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 13.71/2.58 inference('cnf', [status(esa)], [multiply])).
% 13.71/2.58 thf(zip_derived_cl679, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @
% 13.71/2.58 (double_divide @ (multiply @ X0 @ X1) @ (inverse @ X1)) @ X0)
% 13.71/2.58 = (inverse @ identity))),
% 13.71/2.58 inference('demod', [status(thm)], [zip_derived_cl662, zip_derived_cl1])).
% 13.71/2.58 thf(zip_derived_cl1074, plain,
% 13.71/2.58 (((multiply @
% 13.71/2.58 (double_divide @ (inverse @ identity) @
% 13.71/2.58 (inverse @
% 13.71/2.58 (double_divide @ identity @ (inverse @ (inverse @ identity))))) @
% 13.71/2.58 identity) = (inverse @ identity))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl734, zip_derived_cl679])).
% 13.71/2.58 thf(zip_derived_cl724, plain,
% 13.71/2.58 (((multiply @ (inverse @ (inverse @ identity)) @ identity) = (identity))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl668, zip_derived_cl641])).
% 13.71/2.58 thf(zip_derived_cl6, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 13.71/2.58 thf(zip_derived_cl3, plain,
% 13.71/2.58 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 13.71/2.58 inference('cnf', [status(esa)], [identity])).
% 13.71/2.58 thf(zip_derived_cl28, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((identity)
% 13.71/2.58 = (double_divide @ (double_divide @ X0 @ X1) @ (multiply @ X1 @ X0)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl3])).
% 13.71/2.58 thf(zip_derived_cl733, plain,
% 13.71/2.58 (((identity)
% 13.71/2.58 = (double_divide @
% 13.71/2.58 (double_divide @ identity @ (inverse @ (inverse @ identity))) @
% 13.71/2.58 identity))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl724, zip_derived_cl28])).
% 13.71/2.58 thf(zip_derived_cl2, plain,
% 13.71/2.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 13.71/2.58 inference('cnf', [status(esa)], [inverse])).
% 13.71/2.58 thf(zip_derived_cl771, plain,
% 13.71/2.58 (((inverse @
% 13.71/2.58 (double_divide @ identity @ (inverse @ (inverse @ identity))))
% 13.71/2.58 = (identity))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl733, zip_derived_cl2])).
% 13.71/2.58 thf(zip_derived_cl2, plain,
% 13.71/2.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 13.71/2.58 inference('cnf', [status(esa)], [inverse])).
% 13.71/2.58 thf(zip_derived_cl724, plain,
% 13.71/2.58 (((multiply @ (inverse @ (inverse @ identity)) @ identity) = (identity))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl668, zip_derived_cl641])).
% 13.71/2.58 thf(zip_derived_cl1098, plain, (((identity) = (inverse @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1074, zip_derived_cl771, zip_derived_cl2,
% 13.71/2.58 zip_derived_cl724])).
% 13.71/2.58 thf(zip_derived_cl1, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X1 @ X0)
% 13.71/2.58 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 13.71/2.58 inference('cnf', [status(esa)], [multiply])).
% 13.71/2.58 thf(zip_derived_cl1124, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ (double_divide @ identity @ (inverse @ X1)) @ X0)
% 13.71/2.58 = (multiply @ X0 @ X1))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl642, zip_derived_cl1098, zip_derived_cl1])).
% 13.71/2.58 thf(zip_derived_cl2, plain,
% 13.71/2.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 13.71/2.58 inference('cnf', [status(esa)], [inverse])).
% 13.71/2.58 thf(zip_derived_cl13, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ X1 @
% 13.71/2.58 (double_divide @
% 13.71/2.58 (double_divide @ (double_divide @ X2 @ X1) @ X0) @ (inverse @ X2))) @
% 13.71/2.58 (inverse @ identity)) = (X0))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 13.71/2.58 thf(zip_derived_cl13, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ X1 @
% 13.71/2.58 (double_divide @
% 13.71/2.58 (double_divide @ (double_divide @ X2 @ X1) @ X0) @ (inverse @ X2))) @
% 13.71/2.58 (inverse @ identity)) = (X0))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 13.71/2.58 thf(zip_derived_cl14, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ (inverse @ identity) @
% 13.71/2.58 (double_divide @ (double_divide @ X0 @ X1) @
% 13.71/2.58 (inverse @
% 13.71/2.58 (double_divide @ X3 @
% 13.71/2.58 (double_divide @
% 13.71/2.58 (double_divide @ (double_divide @ X2 @ X3) @ X0) @
% 13.71/2.58 (inverse @ X2)))))) @
% 13.71/2.58 (inverse @ identity)) = (X1))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl13])).
% 13.71/2.58 thf(zip_derived_cl6, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 13.71/2.58 thf(zip_derived_cl102, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ (inverse @ identity) @
% 13.71/2.58 (double_divide @ (double_divide @ X0 @ X1) @
% 13.71/2.58 (multiply @
% 13.71/2.58 (double_divide @
% 13.71/2.58 (double_divide @ (double_divide @ X2 @ X3) @ X0) @
% 13.71/2.58 (inverse @ X2)) @
% 13.71/2.58 X3))) @
% 13.71/2.58 (inverse @ identity)) = (X1))),
% 13.71/2.58 inference('demod', [status(thm)], [zip_derived_cl14, zip_derived_cl6])).
% 13.71/2.58 thf(zip_derived_cl115, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ (inverse @ identity) @
% 13.71/2.58 (double_divide @ (double_divide @ identity @ X2) @
% 13.71/2.58 (multiply @
% 13.71/2.58 (double_divide @ (inverse @ (double_divide @ X1 @ X0)) @
% 13.71/2.58 (inverse @ X1)) @
% 13.71/2.58 X0))) @
% 13.71/2.58 (inverse @ identity)) = (X2))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl102])).
% 13.71/2.58 thf(zip_derived_cl6, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 13.71/2.58 thf(zip_derived_cl135, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ (inverse @ identity) @
% 13.71/2.58 (double_divide @ (double_divide @ identity @ X2) @
% 13.71/2.58 (multiply @
% 13.71/2.58 (double_divide @ (multiply @ X0 @ X1) @ (inverse @ X1)) @ X0))) @
% 13.71/2.58 (inverse @ identity)) = (X2))),
% 13.71/2.58 inference('demod', [status(thm)], [zip_derived_cl115, zip_derived_cl6])).
% 13.71/2.58 thf(zip_derived_cl1098, plain, (((identity) = (inverse @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1074, zip_derived_cl771, zip_derived_cl2,
% 13.71/2.58 zip_derived_cl724])).
% 13.71/2.58 thf(zip_derived_cl1098, plain, (((identity) = (inverse @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1074, zip_derived_cl771, zip_derived_cl2,
% 13.71/2.58 zip_derived_cl724])).
% 13.71/2.58 thf(zip_derived_cl1, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X1 @ X0)
% 13.71/2.58 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 13.71/2.58 inference('cnf', [status(esa)], [multiply])).
% 13.71/2.58 thf(zip_derived_cl668, plain,
% 13.71/2.58 (![X0 : $i]:
% 13.71/2.58 ((double_divide @ (inverse @ X0) @ (inverse @ identity))
% 13.71/2.58 = (multiply @ X0 @ identity))),
% 13.71/2.58 inference('demod', [status(thm)], [zip_derived_cl664, zip_derived_cl2])).
% 13.71/2.58 thf(zip_derived_cl1098, plain, (((identity) = (inverse @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1074, zip_derived_cl771, zip_derived_cl2,
% 13.71/2.58 zip_derived_cl724])).
% 13.71/2.58 thf(zip_derived_cl2, plain,
% 13.71/2.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 13.71/2.58 inference('cnf', [status(esa)], [inverse])).
% 13.71/2.58 thf(zip_derived_cl1125, plain,
% 13.71/2.58 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (multiply @ X0 @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl668, zip_derived_cl1098, zip_derived_cl2])).
% 13.71/2.58 thf(zip_derived_cl6, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 13.71/2.58 thf(zip_derived_cl1452, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((inverse @
% 13.71/2.58 (multiply @
% 13.71/2.58 (multiply @
% 13.71/2.58 (double_divide @ (multiply @ X0 @ X1) @ (inverse @ X1)) @ X0) @
% 13.71/2.58 (double_divide @ identity @ X2)))
% 13.71/2.58 = (X2))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl135, zip_derived_cl1098, zip_derived_cl1098,
% 13.71/2.58 zip_derived_cl1, zip_derived_cl1125, zip_derived_cl6])).
% 13.71/2.58 thf(zip_derived_cl1098, plain, (((identity) = (inverse @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1074, zip_derived_cl771, zip_derived_cl2,
% 13.71/2.58 zip_derived_cl724])).
% 13.71/2.58 thf(zip_derived_cl3, plain,
% 13.71/2.58 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 13.71/2.58 inference('cnf', [status(esa)], [identity])).
% 13.71/2.58 thf(zip_derived_cl1137, plain,
% 13.71/2.58 (((identity) = (double_divide @ identity @ identity))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl1098, zip_derived_cl3])).
% 13.71/2.58 thf(zip_derived_cl13, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ X1 @
% 13.71/2.58 (double_divide @
% 13.71/2.58 (double_divide @ (double_divide @ X2 @ X1) @ X0) @ (inverse @ X2))) @
% 13.71/2.58 (inverse @ identity)) = (X0))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 13.71/2.58 thf(zip_derived_cl1, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X1 @ X0)
% 13.71/2.58 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 13.71/2.58 inference('cnf', [status(esa)], [multiply])).
% 13.71/2.58 thf(zip_derived_cl15, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((multiply @ (inverse @ identity) @
% 13.71/2.58 (double_divide @ X2 @
% 13.71/2.58 (double_divide @
% 13.71/2.58 (double_divide @ (double_divide @ X1 @ X2) @ X0) @ (inverse @ X1))))
% 13.71/2.58 = (double_divide @ X0 @ identity))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl1])).
% 13.71/2.58 thf(zip_derived_cl2, plain,
% 13.71/2.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 13.71/2.58 inference('cnf', [status(esa)], [inverse])).
% 13.71/2.58 thf(zip_derived_cl27, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((multiply @ (inverse @ identity) @
% 13.71/2.58 (double_divide @ X2 @
% 13.71/2.58 (double_divide @
% 13.71/2.58 (double_divide @ (double_divide @ X1 @ X2) @ X0) @ (inverse @ X1))))
% 13.71/2.58 = (inverse @ X0))),
% 13.71/2.58 inference('demod', [status(thm)], [zip_derived_cl15, zip_derived_cl2])).
% 13.71/2.58 thf(zip_derived_cl1098, plain, (((identity) = (inverse @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1074, zip_derived_cl771, zip_derived_cl2,
% 13.71/2.58 zip_derived_cl724])).
% 13.71/2.58 thf(zip_derived_cl1, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X1 @ X0)
% 13.71/2.58 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 13.71/2.58 inference('cnf', [status(esa)], [multiply])).
% 13.71/2.58 thf(zip_derived_cl1, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X1 @ X0)
% 13.71/2.58 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 13.71/2.58 inference('cnf', [status(esa)], [multiply])).
% 13.71/2.58 thf(zip_derived_cl9, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ identity @ (double_divide @ X0 @ X1))
% 13.71/2.58 = (double_divide @ (multiply @ X1 @ X0) @ identity))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl1])).
% 13.71/2.58 thf(zip_derived_cl2, plain,
% 13.71/2.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 13.71/2.58 inference('cnf', [status(esa)], [inverse])).
% 13.71/2.58 thf(zip_derived_cl11, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ identity @ (double_divide @ X0 @ X1))
% 13.71/2.58 = (inverse @ (multiply @ X1 @ X0)))),
% 13.71/2.58 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl2])).
% 13.71/2.58 thf(zip_derived_cl1154, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((inverse @
% 13.71/2.58 (multiply @
% 13.71/2.58 (double_divide @
% 13.71/2.58 (double_divide @ (double_divide @ X1 @ X2) @ X0) @ (inverse @ X1)) @
% 13.71/2.58 X2))
% 13.71/2.58 = (inverse @ X0))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl27, zip_derived_cl1098, zip_derived_cl11])).
% 13.71/2.58 thf(zip_derived_cl1211, plain,
% 13.71/2.58 (![X0 : $i]:
% 13.71/2.58 ((inverse @
% 13.71/2.58 (multiply @
% 13.71/2.58 (double_divide @ (double_divide @ identity @ X0) @
% 13.71/2.58 (inverse @ identity)) @
% 13.71/2.58 identity))
% 13.71/2.58 = (inverse @ X0))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl1137, zip_derived_cl1154])).
% 13.71/2.58 thf(zip_derived_cl1098, plain, (((identity) = (inverse @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1074, zip_derived_cl771, zip_derived_cl2,
% 13.71/2.58 zip_derived_cl724])).
% 13.71/2.58 thf(zip_derived_cl1, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X1 @ X0)
% 13.71/2.58 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 13.71/2.58 inference('cnf', [status(esa)], [multiply])).
% 13.71/2.58 thf(zip_derived_cl1218, plain,
% 13.71/2.58 (![X0 : $i]:
% 13.71/2.58 ((inverse @ (multiply @ (multiply @ X0 @ identity) @ identity))
% 13.71/2.58 = (inverse @ X0))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1211, zip_derived_cl1098, zip_derived_cl1])).
% 13.71/2.58 thf(zip_derived_cl1125, plain,
% 13.71/2.58 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (multiply @ X0 @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl668, zip_derived_cl1098, zip_derived_cl2])).
% 13.71/2.58 thf(zip_derived_cl1125, plain,
% 13.71/2.58 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (multiply @ X0 @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl668, zip_derived_cl1098, zip_derived_cl2])).
% 13.71/2.58 thf(zip_derived_cl1261, plain,
% 13.71/2.58 (![X0 : $i]:
% 13.71/2.58 ((inverse @ (inverse @ (inverse @ (inverse @ (inverse @ X0)))))
% 13.71/2.58 = (inverse @ X0))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1218, zip_derived_cl1125, zip_derived_cl1125])).
% 13.71/2.58 thf(zip_derived_cl1125, plain,
% 13.71/2.58 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (multiply @ X0 @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl668, zip_derived_cl1098, zip_derived_cl2])).
% 13.71/2.58 thf(zip_derived_cl642, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ X0 @ (double_divide @ identity @ (inverse @ X1))) @
% 13.71/2.58 (inverse @ identity)) = (multiply @ X0 @ X1))),
% 13.71/2.58 inference('demod', [status(thm)], [zip_derived_cl20, zip_derived_cl6])).
% 13.71/2.58 thf(zip_derived_cl13, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ X1 @
% 13.71/2.58 (double_divide @
% 13.71/2.58 (double_divide @ (double_divide @ X2 @ X1) @ X0) @ (inverse @ X2))) @
% 13.71/2.58 (inverse @ identity)) = (X0))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 13.71/2.58 thf(zip_derived_cl13, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ X1 @
% 13.71/2.58 (double_divide @
% 13.71/2.58 (double_divide @ (double_divide @ X2 @ X1) @ X0) @ (inverse @ X2))) @
% 13.71/2.58 (inverse @ identity)) = (X0))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 13.71/2.58 thf(zip_derived_cl17, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((double_divide @ (double_divide @ X2 @ X0) @ (inverse @ identity))
% 13.71/2.58 = (double_divide @
% 13.71/2.58 (double_divide @
% 13.71/2.58 (double_divide @ X1 @ (double_divide @ identity @ X2)) @ X0) @
% 13.71/2.58 (inverse @ X1)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl13])).
% 13.71/2.58 thf(zip_derived_cl661, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ X1 @ (double_divide @ identity @ (inverse @ X0))) @
% 13.71/2.58 (inverse @ identity))
% 13.71/2.58 = (multiply @
% 13.71/2.58 (double_divide @ identity @ (double_divide @ identity @ X1)) @ X0))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl642, zip_derived_cl17])).
% 13.71/2.58 thf(zip_derived_cl642, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ X0 @ (double_divide @ identity @ (inverse @ X1))) @
% 13.71/2.58 (inverse @ identity)) = (multiply @ X0 @ X1))),
% 13.71/2.58 inference('demod', [status(thm)], [zip_derived_cl20, zip_derived_cl6])).
% 13.71/2.58 thf(zip_derived_cl678, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X1 @ X0)
% 13.71/2.58 = (multiply @
% 13.71/2.58 (double_divide @ identity @ (double_divide @ identity @ X1)) @ X0))),
% 13.71/2.58 inference('demod', [status(thm)], [zip_derived_cl661, zip_derived_cl642])).
% 13.71/2.58 thf(zip_derived_cl1222, plain,
% 13.71/2.58 (![X0 : $i]:
% 13.71/2.58 ((multiply @ X0 @ identity)
% 13.71/2.58 = (inverse @
% 13.71/2.58 (inverse @
% 13.71/2.58 (double_divide @ identity @ (double_divide @ identity @ X0)))))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl1125, zip_derived_cl678])).
% 13.71/2.58 thf(zip_derived_cl1125, plain,
% 13.71/2.58 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (multiply @ X0 @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl668, zip_derived_cl1098, zip_derived_cl2])).
% 13.71/2.58 thf(zip_derived_cl6, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 13.71/2.58 thf(zip_derived_cl1125, plain,
% 13.71/2.58 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (multiply @ X0 @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl668, zip_derived_cl1098, zip_derived_cl2])).
% 13.71/2.58 thf(zip_derived_cl6, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 13.71/2.58 thf(zip_derived_cl1125, plain,
% 13.71/2.58 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (multiply @ X0 @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl668, zip_derived_cl1098, zip_derived_cl2])).
% 13.71/2.58 thf(zip_derived_cl1227, plain,
% 13.71/2.58 (![X0 : $i]:
% 13.71/2.58 ((inverse @ (inverse @ X0))
% 13.71/2.58 = (inverse @ (inverse @ (inverse @ (inverse @ X0)))))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1222, zip_derived_cl1125, zip_derived_cl6,
% 13.71/2.58 zip_derived_cl1125, zip_derived_cl6, zip_derived_cl1125])).
% 13.71/2.58 thf(zip_derived_cl1322, plain,
% 13.71/2.58 (![X0 : $i]: ((inverse @ (inverse @ (inverse @ X0))) = (inverse @ X0))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1261, zip_derived_cl1227])).
% 13.71/2.58 thf(zip_derived_cl3, plain,
% 13.71/2.58 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 13.71/2.58 inference('cnf', [status(esa)], [identity])).
% 13.71/2.58 thf(zip_derived_cl1346, plain,
% 13.71/2.58 (![X0 : $i]:
% 13.71/2.58 ((identity)
% 13.71/2.58 = (double_divide @ (inverse @ (inverse @ X0)) @ (inverse @ X0)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl1322, zip_derived_cl3])).
% 13.71/2.58 thf(zip_derived_cl1458, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((identity)
% 13.71/2.58 = (double_divide @
% 13.71/2.58 (inverse @
% 13.71/2.58 (inverse @
% 13.71/2.58 (multiply @
% 13.71/2.58 (multiply @
% 13.71/2.58 (double_divide @ (multiply @ X1 @ X2) @ (inverse @ X2)) @ X1) @
% 13.71/2.58 (double_divide @ identity @ X0)))) @
% 13.71/2.58 X0))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl1452, zip_derived_cl1346])).
% 13.71/2.58 thf(zip_derived_cl1452, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((inverse @
% 13.71/2.58 (multiply @
% 13.71/2.58 (multiply @
% 13.71/2.58 (double_divide @ (multiply @ X0 @ X1) @ (inverse @ X1)) @ X0) @
% 13.71/2.58 (double_divide @ identity @ X2)))
% 13.71/2.58 = (X2))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl135, zip_derived_cl1098, zip_derived_cl1098,
% 13.71/2.58 zip_derived_cl1, zip_derived_cl1125, zip_derived_cl6])).
% 13.71/2.58 thf(zip_derived_cl1499, plain,
% 13.71/2.58 (![X0 : $i]: ((identity) = (double_divide @ (inverse @ X0) @ X0))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1458, zip_derived_cl1452])).
% 13.71/2.58 thf(zip_derived_cl3, plain,
% 13.71/2.58 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 13.71/2.58 inference('cnf', [status(esa)], [identity])).
% 13.71/2.58 thf(zip_derived_cl3, plain,
% 13.71/2.58 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 13.71/2.58 inference('cnf', [status(esa)], [identity])).
% 13.71/2.58 thf(zip_derived_cl102, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ (inverse @ identity) @
% 13.71/2.58 (double_divide @ (double_divide @ X0 @ X1) @
% 13.71/2.58 (multiply @
% 13.71/2.58 (double_divide @
% 13.71/2.58 (double_divide @ (double_divide @ X2 @ X3) @ X0) @
% 13.71/2.58 (inverse @ X2)) @
% 13.71/2.58 X3))) @
% 13.71/2.58 (inverse @ identity)) = (X1))),
% 13.71/2.58 inference('demod', [status(thm)], [zip_derived_cl14, zip_derived_cl6])).
% 13.71/2.58 thf(zip_derived_cl116, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ (inverse @ identity) @
% 13.71/2.58 (double_divide @
% 13.71/2.58 (double_divide @ (inverse @ (double_divide @ X2 @ X1)) @ X0) @
% 13.71/2.58 (multiply @ (double_divide @ identity @ (inverse @ X2)) @ X1))) @
% 13.71/2.58 (inverse @ identity)) = (X0))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl102])).
% 13.71/2.58 thf(zip_derived_cl6, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 13.71/2.58 thf(zip_derived_cl136, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ (inverse @ identity) @
% 13.71/2.58 (double_divide @ (double_divide @ (multiply @ X1 @ X2) @ X0) @
% 13.71/2.58 (multiply @ (double_divide @ identity @ (inverse @ X2)) @ X1))) @
% 13.71/2.58 (inverse @ identity)) = (X0))),
% 13.71/2.58 inference('demod', [status(thm)], [zip_derived_cl116, zip_derived_cl6])).
% 13.71/2.58 thf(zip_derived_cl1098, plain, (((identity) = (inverse @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1074, zip_derived_cl771, zip_derived_cl2,
% 13.71/2.58 zip_derived_cl724])).
% 13.71/2.58 thf(zip_derived_cl1098, plain, (((identity) = (inverse @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1074, zip_derived_cl771, zip_derived_cl2,
% 13.71/2.58 zip_derived_cl724])).
% 13.71/2.58 thf(zip_derived_cl1, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X1 @ X0)
% 13.71/2.58 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 13.71/2.58 inference('cnf', [status(esa)], [multiply])).
% 13.71/2.58 thf(zip_derived_cl1125, plain,
% 13.71/2.58 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (multiply @ X0 @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl668, zip_derived_cl1098, zip_derived_cl2])).
% 13.71/2.58 thf(zip_derived_cl1125, plain,
% 13.71/2.58 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (multiply @ X0 @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl668, zip_derived_cl1098, zip_derived_cl2])).
% 13.71/2.58 thf(zip_derived_cl1452, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((inverse @
% 13.71/2.58 (multiply @
% 13.71/2.58 (multiply @
% 13.71/2.58 (double_divide @ (multiply @ X0 @ X1) @ (inverse @ X1)) @ X0) @
% 13.71/2.58 (double_divide @ identity @ X2)))
% 13.71/2.58 = (X2))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl135, zip_derived_cl1098, zip_derived_cl1098,
% 13.71/2.58 zip_derived_cl1, zip_derived_cl1125, zip_derived_cl6])).
% 13.71/2.58 thf(zip_derived_cl1469, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((inverse @
% 13.71/2.58 (multiply @
% 13.71/2.58 (inverse @
% 13.71/2.58 (inverse @
% 13.71/2.58 (double_divide @ (multiply @ identity @ X0) @ (inverse @ X0)))) @
% 13.71/2.58 (double_divide @ identity @ X1)))
% 13.71/2.58 = (X1))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl1125, zip_derived_cl1452])).
% 13.71/2.58 thf(zip_derived_cl10, plain,
% 13.71/2.58 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 13.71/2.58 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 13.71/2.58 thf(zip_derived_cl1346, plain,
% 13.71/2.58 (![X0 : $i]:
% 13.71/2.58 ((identity)
% 13.71/2.58 = (double_divide @ (inverse @ (inverse @ X0)) @ (inverse @ X0)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl1322, zip_derived_cl3])).
% 13.71/2.58 thf(zip_derived_cl1098, plain, (((identity) = (inverse @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1074, zip_derived_cl771, zip_derived_cl2,
% 13.71/2.58 zip_derived_cl724])).
% 13.71/2.58 thf(zip_derived_cl1098, plain, (((identity) = (inverse @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1074, zip_derived_cl771, zip_derived_cl2,
% 13.71/2.58 zip_derived_cl724])).
% 13.71/2.58 thf(zip_derived_cl11, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ identity @ (double_divide @ X0 @ X1))
% 13.71/2.58 = (inverse @ (multiply @ X1 @ X0)))),
% 13.71/2.58 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl2])).
% 13.71/2.58 thf(zip_derived_cl1125, plain,
% 13.71/2.58 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (multiply @ X0 @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl668, zip_derived_cl1098, zip_derived_cl2])).
% 13.71/2.58 thf(zip_derived_cl1322, plain,
% 13.71/2.58 (![X0 : $i]: ((inverse @ (inverse @ (inverse @ X0))) = (inverse @ X0))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1261, zip_derived_cl1227])).
% 13.71/2.58 thf(zip_derived_cl1489, plain,
% 13.71/2.58 (![X1 : $i]: ((inverse @ (inverse @ X1)) = (X1))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1469, zip_derived_cl10, zip_derived_cl1346,
% 13.71/2.58 zip_derived_cl1098, zip_derived_cl1098, zip_derived_cl11,
% 13.71/2.58 zip_derived_cl1125, zip_derived_cl1322])).
% 13.71/2.58 thf(zip_derived_cl1504, plain,
% 13.71/2.58 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1125, zip_derived_cl1489])).
% 13.71/2.58 thf(zip_derived_cl1567, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((double_divide @ (double_divide @ (multiply @ X1 @ X2) @ X0) @
% 13.71/2.58 (multiply @ (double_divide @ identity @ (inverse @ X2)) @ X1))
% 13.71/2.58 = (X0))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl136, zip_derived_cl1098, zip_derived_cl1098,
% 13.71/2.58 zip_derived_cl1, zip_derived_cl1504])).
% 13.71/2.58 thf(zip_derived_cl1576, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((double_divide @ (double_divide @ (multiply @ X1 @ identity) @ X0) @
% 13.71/2.58 (multiply @ identity @ X1)) = (X0))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1567])).
% 13.71/2.58 thf(zip_derived_cl1504, plain,
% 13.71/2.58 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1125, zip_derived_cl1489])).
% 13.71/2.58 thf(zip_derived_cl10, plain,
% 13.71/2.58 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 13.71/2.58 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 13.71/2.58 thf(zip_derived_cl1489, plain,
% 13.71/2.58 (![X1 : $i]: ((inverse @ (inverse @ X1)) = (X1))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1469, zip_derived_cl10, zip_derived_cl1346,
% 13.71/2.58 zip_derived_cl1098, zip_derived_cl1098, zip_derived_cl11,
% 13.71/2.58 zip_derived_cl1125, zip_derived_cl1322])).
% 13.71/2.58 thf(zip_derived_cl1503, plain,
% 13.71/2.58 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 13.71/2.58 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl1489])).
% 13.71/2.58 thf(zip_derived_cl1592, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((double_divide @ (double_divide @ X1 @ X0) @ X1) = (X0))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1576, zip_derived_cl1504, zip_derived_cl1503])).
% 13.71/2.58 thf(zip_derived_cl1708, plain,
% 13.71/2.58 (![X0 : $i]: ((double_divide @ identity @ (inverse @ X0)) = (X0))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl1499, zip_derived_cl1592])).
% 13.71/2.58 thf(zip_derived_cl3336, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1124, zip_derived_cl1708])).
% 13.71/2.58 thf(zip_derived_cl3336, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1124, zip_derived_cl1708])).
% 13.71/2.58 thf(zip_derived_cl3337, plain,
% 13.71/2.58 (((multiply @ c3 @ (multiply @ a3 @ b3))
% 13.71/2.58 != (multiply @ a3 @ (multiply @ c3 @ b3)))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl4, zip_derived_cl3336, zip_derived_cl3336])).
% 13.71/2.58 thf(zip_derived_cl3336, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1124, zip_derived_cl1708])).
% 13.71/2.58 thf(zip_derived_cl1489, plain,
% 13.71/2.58 (![X1 : $i]: ((inverse @ (inverse @ X1)) = (X1))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1469, zip_derived_cl10, zip_derived_cl1346,
% 13.71/2.58 zip_derived_cl1098, zip_derived_cl1098, zip_derived_cl11,
% 13.71/2.58 zip_derived_cl1125, zip_derived_cl1322])).
% 13.71/2.58 thf(zip_derived_cl8, plain,
% 13.71/2.58 (![X0 : $i]:
% 13.71/2.58 ((multiply @ (inverse @ X0) @ X0)
% 13.71/2.58 = (double_divide @ identity @ identity))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 13.71/2.58 thf(zip_derived_cl102, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ (inverse @ identity) @
% 13.71/2.58 (double_divide @ (double_divide @ X0 @ X1) @
% 13.71/2.58 (multiply @
% 13.71/2.58 (double_divide @
% 13.71/2.58 (double_divide @ (double_divide @ X2 @ X3) @ X0) @
% 13.71/2.58 (inverse @ X2)) @
% 13.71/2.58 X3))) @
% 13.71/2.58 (inverse @ identity)) = (X1))),
% 13.71/2.58 inference('demod', [status(thm)], [zip_derived_cl14, zip_derived_cl6])).
% 13.71/2.58 thf(zip_derived_cl132, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ (inverse @ identity) @
% 13.71/2.58 (double_divide @ (multiply @ (inverse @ X0) @ X0) @
% 13.71/2.58 (multiply @
% 13.71/2.58 (double_divide @
% 13.71/2.58 (double_divide @ (double_divide @ X2 @ X1) @ identity) @
% 13.71/2.58 (inverse @ X2)) @
% 13.71/2.58 X1))) @
% 13.71/2.58 (inverse @ identity)) = (identity))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl102])).
% 13.71/2.58 thf(zip_derived_cl1, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X1 @ X0)
% 13.71/2.58 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 13.71/2.58 inference('cnf', [status(esa)], [multiply])).
% 13.71/2.58 thf(zip_derived_cl140, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ (inverse @ identity) @
% 13.71/2.58 (double_divide @ (multiply @ (inverse @ X0) @ X0) @
% 13.71/2.58 (multiply @
% 13.71/2.58 (double_divide @ (multiply @ X1 @ X2) @ (inverse @ X2)) @ X1))) @
% 13.71/2.58 (inverse @ identity)) = (identity))),
% 13.71/2.58 inference('demod', [status(thm)], [zip_derived_cl132, zip_derived_cl1])).
% 13.71/2.58 thf(zip_derived_cl1098, plain, (((identity) = (inverse @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1074, zip_derived_cl771, zip_derived_cl2,
% 13.71/2.58 zip_derived_cl724])).
% 13.71/2.58 thf(zip_derived_cl31, plain,
% 13.71/2.58 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 13.71/2.58 thf(zip_derived_cl1098, plain, (((identity) = (inverse @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1074, zip_derived_cl771, zip_derived_cl2,
% 13.71/2.58 zip_derived_cl724])).
% 13.71/2.58 thf(zip_derived_cl1114, plain,
% 13.71/2.58 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 13.71/2.58 inference('demod', [status(thm)], [zip_derived_cl31, zip_derived_cl1098])).
% 13.71/2.58 thf(zip_derived_cl3, plain,
% 13.71/2.58 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 13.71/2.58 inference('cnf', [status(esa)], [identity])).
% 13.71/2.58 thf(zip_derived_cl1592, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((double_divide @ (double_divide @ X1 @ X0) @ X1) = (X0))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1576, zip_derived_cl1504, zip_derived_cl1503])).
% 13.71/2.58 thf(zip_derived_cl1701, plain,
% 13.71/2.58 (![X0 : $i]: ((double_divide @ identity @ X0) = (inverse @ X0))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1592])).
% 13.71/2.58 thf(zip_derived_cl6, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 13.71/2.58 thf(zip_derived_cl1489, plain,
% 13.71/2.58 (![X1 : $i]: ((inverse @ (inverse @ X1)) = (X1))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1469, zip_derived_cl10, zip_derived_cl1346,
% 13.71/2.58 zip_derived_cl1098, zip_derived_cl1098, zip_derived_cl11,
% 13.71/2.58 zip_derived_cl1125, zip_derived_cl1322])).
% 13.71/2.58 thf(zip_derived_cl1514, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1489])).
% 13.71/2.58 thf(zip_derived_cl1701, plain,
% 13.71/2.58 (![X0 : $i]: ((double_divide @ identity @ X0) = (inverse @ X0))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1592])).
% 13.71/2.58 thf(zip_derived_cl6, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 13.71/2.58 thf(zip_derived_cl1098, plain, (((identity) = (inverse @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1074, zip_derived_cl771, zip_derived_cl2,
% 13.71/2.58 zip_derived_cl724])).
% 13.71/2.58 thf(zip_derived_cl2, plain,
% 13.71/2.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 13.71/2.58 inference('cnf', [status(esa)], [inverse])).
% 13.71/2.58 thf(zip_derived_cl1514, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1489])).
% 13.71/2.58 thf(zip_derived_cl2038, plain,
% 13.71/2.58 (![X1 : $i, X2 : $i]:
% 13.71/2.58 ((double_divide @ X1 @
% 13.71/2.58 (double_divide @ (multiply @ X1 @ X2) @ (inverse @ X2)))
% 13.71/2.58 = (identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl140, zip_derived_cl1098, zip_derived_cl1114,
% 13.71/2.58 zip_derived_cl1701, zip_derived_cl1514, zip_derived_cl1701,
% 13.71/2.58 zip_derived_cl6, zip_derived_cl1098, zip_derived_cl2,
% 13.71/2.58 zip_derived_cl1514])).
% 13.71/2.58 thf(zip_derived_cl1592, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((double_divide @ (double_divide @ X1 @ X0) @ X1) = (X0))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1576, zip_derived_cl1504, zip_derived_cl1503])).
% 13.71/2.58 thf(zip_derived_cl2043, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((double_divide @ identity @ X1)
% 13.71/2.58 = (double_divide @ (multiply @ X1 @ X0) @ (inverse @ X0)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl2038, zip_derived_cl1592])).
% 13.71/2.58 thf(zip_derived_cl1701, plain,
% 13.71/2.58 (![X0 : $i]: ((double_divide @ identity @ X0) = (inverse @ X0))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1592])).
% 13.71/2.58 thf(zip_derived_cl2077, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((inverse @ X1)
% 13.71/2.58 = (double_divide @ (multiply @ X1 @ X0) @ (inverse @ X0)))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl2043, zip_derived_cl1701])).
% 13.71/2.58 thf(zip_derived_cl1592, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((double_divide @ (double_divide @ X1 @ X0) @ X1) = (X0))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1576, zip_derived_cl1504, zip_derived_cl1503])).
% 13.71/2.58 thf(zip_derived_cl6, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 13.71/2.58 thf(zip_derived_cl1694, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X1 @ (double_divide @ X1 @ X0)) = (inverse @ X0))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl1592, zip_derived_cl6])).
% 13.71/2.58 thf(zip_derived_cl2581, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ (multiply @ X0 @ X1) @ (inverse @ X0))
% 13.71/2.58 = (inverse @ (inverse @ X1)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl2077, zip_derived_cl1694])).
% 13.71/2.58 thf(zip_derived_cl1489, plain,
% 13.71/2.58 (![X1 : $i]: ((inverse @ (inverse @ X1)) = (X1))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1469, zip_derived_cl10, zip_derived_cl1346,
% 13.71/2.58 zip_derived_cl1098, zip_derived_cl1098, zip_derived_cl11,
% 13.71/2.58 zip_derived_cl1125, zip_derived_cl1322])).
% 13.71/2.58 thf(zip_derived_cl2622, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ (multiply @ X0 @ X1) @ (inverse @ X0)) = (X1))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl2581, zip_derived_cl1489])).
% 13.71/2.58 thf(zip_derived_cl2684, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ (multiply @ (inverse @ X0) @ X1) @ X0) = (X1))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl1489, zip_derived_cl2622])).
% 13.71/2.58 thf(zip_derived_cl3360, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ (multiply @ X1 @ (inverse @ X0)) @ X0) = (X1))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl3336, zip_derived_cl2684])).
% 13.71/2.58 thf(zip_derived_cl102, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ (inverse @ identity) @
% 13.71/2.58 (double_divide @ (double_divide @ X0 @ X1) @
% 13.71/2.58 (multiply @
% 13.71/2.58 (double_divide @
% 13.71/2.58 (double_divide @ (double_divide @ X2 @ X3) @ X0) @
% 13.71/2.58 (inverse @ X2)) @
% 13.71/2.58 X3))) @
% 13.71/2.58 (inverse @ identity)) = (X1))),
% 13.71/2.58 inference('demod', [status(thm)], [zip_derived_cl14, zip_derived_cl6])).
% 13.71/2.58 thf(zip_derived_cl102, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ (inverse @ identity) @
% 13.71/2.58 (double_divide @ (double_divide @ X0 @ X1) @
% 13.71/2.58 (multiply @
% 13.71/2.58 (double_divide @
% 13.71/2.58 (double_divide @ (double_divide @ X2 @ X3) @ X0) @
% 13.71/2.58 (inverse @ X2)) @
% 13.71/2.58 X3))) @
% 13.71/2.58 (inverse @ identity)) = (X1))),
% 13.71/2.58 inference('demod', [status(thm)], [zip_derived_cl14, zip_derived_cl6])).
% 13.71/2.58 thf(zip_derived_cl108, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ (inverse @ identity) @
% 13.71/2.58 (double_divide @ (double_divide @ X5 @ X1) @
% 13.71/2.58 (multiply @
% 13.71/2.58 (double_divide @ (double_divide @ X0 @ X5) @
% 13.71/2.58 (inverse @
% 13.71/2.58 (double_divide @ (inverse @ identity) @
% 13.71/2.58 (double_divide @ (double_divide @ X4 @ X0) @
% 13.71/2.58 (multiply @
% 13.71/2.58 (double_divide @
% 13.71/2.58 (double_divide @ (double_divide @ X3 @ X2) @ X4) @
% 13.71/2.58 (inverse @ X3)) @
% 13.71/2.58 X2))))) @
% 13.71/2.58 (inverse @ identity)))) @
% 13.71/2.58 (inverse @ identity)) = (X1))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl102, zip_derived_cl102])).
% 13.71/2.58 thf(zip_derived_cl6, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 13.71/2.58 thf(zip_derived_cl145, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 13.71/2.58 ((double_divide @
% 13.71/2.58 (double_divide @ (inverse @ identity) @
% 13.71/2.58 (double_divide @ (double_divide @ X5 @ X1) @
% 13.71/2.58 (multiply @
% 13.71/2.58 (double_divide @ (double_divide @ X0 @ X5) @
% 13.71/2.58 (multiply @
% 13.71/2.58 (double_divide @ (double_divide @ X4 @ X0) @
% 13.71/2.58 (multiply @
% 13.71/2.58 (double_divide @
% 13.71/2.58 (double_divide @ (double_divide @ X3 @ X2) @ X4) @
% 13.71/2.58 (inverse @ X3)) @
% 13.71/2.58 X2)) @
% 13.71/2.58 (inverse @ identity))) @
% 13.71/2.58 (inverse @ identity)))) @
% 13.71/2.58 (inverse @ identity)) = (X1))),
% 13.71/2.58 inference('demod', [status(thm)], [zip_derived_cl108, zip_derived_cl6])).
% 13.71/2.58 thf(zip_derived_cl1098, plain, (((identity) = (inverse @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1074, zip_derived_cl771, zip_derived_cl2,
% 13.71/2.58 zip_derived_cl724])).
% 13.71/2.58 thf(zip_derived_cl1592, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((double_divide @ (double_divide @ X1 @ X0) @ X1) = (X0))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1576, zip_derived_cl1504, zip_derived_cl1503])).
% 13.71/2.58 thf(zip_derived_cl1592, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((double_divide @ (double_divide @ X1 @ X0) @ X1) = (X0))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1576, zip_derived_cl1504, zip_derived_cl1503])).
% 13.71/2.58 thf(zip_derived_cl1695, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((double_divide @ X0 @ (double_divide @ X1 @ X0)) = (X1))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl1592, zip_derived_cl1592])).
% 13.71/2.58 thf(zip_derived_cl6, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 13.71/2.58 thf(zip_derived_cl2006, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ (double_divide @ X0 @ X1) @ X1) = (inverse @ X0))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl1695, zip_derived_cl6])).
% 13.71/2.58 thf(zip_derived_cl1489, plain,
% 13.71/2.58 (![X1 : $i]: ((inverse @ (inverse @ X1)) = (X1))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1469, zip_derived_cl10, zip_derived_cl1346,
% 13.71/2.58 zip_derived_cl1098, zip_derived_cl1098, zip_derived_cl11,
% 13.71/2.58 zip_derived_cl1125, zip_derived_cl1322])).
% 13.71/2.58 thf(zip_derived_cl2077, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((inverse @ X1)
% 13.71/2.58 = (double_divide @ (multiply @ X1 @ X0) @ (inverse @ X0)))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl2043, zip_derived_cl1701])).
% 13.71/2.58 thf(zip_derived_cl1, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X1 @ X0)
% 13.71/2.58 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 13.71/2.58 inference('cnf', [status(esa)], [multiply])).
% 13.71/2.58 thf(zip_derived_cl2572, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ (inverse @ X1) @ (multiply @ X0 @ X1))
% 13.71/2.58 = (double_divide @ (inverse @ X0) @ identity))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl2077, zip_derived_cl1])).
% 13.71/2.58 thf(zip_derived_cl1701, plain,
% 13.71/2.58 (![X0 : $i]: ((double_divide @ identity @ X0) = (inverse @ X0))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1592])).
% 13.71/2.58 thf(zip_derived_cl1592, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((double_divide @ (double_divide @ X1 @ X0) @ X1) = (X0))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1576, zip_derived_cl1504, zip_derived_cl1503])).
% 13.71/2.58 thf(zip_derived_cl1735, plain,
% 13.71/2.58 (![X0 : $i]: ((double_divide @ (inverse @ X0) @ identity) = (X0))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl1701, zip_derived_cl1592])).
% 13.71/2.58 thf(zip_derived_cl2618, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ (inverse @ X1) @ (multiply @ X0 @ X1)) = (X0))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl2572, zip_derived_cl1735])).
% 13.71/2.58 thf(zip_derived_cl2651, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X0 @ (multiply @ X1 @ (inverse @ X0))) = (X1))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl1489, zip_derived_cl2618])).
% 13.71/2.58 thf(zip_derived_cl2722, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X1 @ (inverse @ X0))
% 13.71/2.58 = (double_divide @ X0 @ (inverse @ X1)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl2006, zip_derived_cl2651])).
% 13.71/2.58 thf(zip_derived_cl6, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 13.71/2.58 thf(zip_derived_cl1098, plain, (((identity) = (inverse @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1074, zip_derived_cl771, zip_derived_cl2,
% 13.71/2.58 zip_derived_cl724])).
% 13.71/2.58 thf(zip_derived_cl1504, plain,
% 13.71/2.58 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1125, zip_derived_cl1489])).
% 13.71/2.58 thf(zip_derived_cl1098, plain, (((identity) = (inverse @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1074, zip_derived_cl771, zip_derived_cl2,
% 13.71/2.58 zip_derived_cl724])).
% 13.71/2.58 thf(zip_derived_cl1504, plain,
% 13.71/2.58 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1125, zip_derived_cl1489])).
% 13.71/2.58 thf(zip_derived_cl28, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((identity)
% 13.71/2.58 = (double_divide @ (double_divide @ X0 @ X1) @ (multiply @ X1 @ X0)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl3])).
% 13.71/2.58 thf(zip_derived_cl1592, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((double_divide @ (double_divide @ X1 @ X0) @ X1) = (X0))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1576, zip_derived_cl1504, zip_derived_cl1503])).
% 13.71/2.58 thf(zip_derived_cl1705, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((double_divide @ identity @ (double_divide @ X0 @ X1))
% 13.71/2.58 = (multiply @ X1 @ X0))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl28, zip_derived_cl1592])).
% 13.71/2.58 thf(zip_derived_cl1098, plain, (((identity) = (inverse @ identity))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1074, zip_derived_cl771, zip_derived_cl2,
% 13.71/2.58 zip_derived_cl724])).
% 13.71/2.58 thf(zip_derived_cl6, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 13.71/2.58 thf(zip_derived_cl1735, plain,
% 13.71/2.58 (![X0 : $i]: ((double_divide @ (inverse @ X0) @ identity) = (X0))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl1701, zip_derived_cl1592])).
% 13.71/2.58 thf(zip_derived_cl1850, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((double_divide @ (multiply @ X1 @ X0) @ identity)
% 13.71/2.58 = (double_divide @ X0 @ X1))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1735])).
% 13.71/2.58 thf(zip_derived_cl2831, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 13.71/2.58 ((double_divide @ (double_divide @ X5 @ X1) @
% 13.71/2.58 (double_divide @ (double_divide @ X0 @ X5) @
% 13.71/2.58 (double_divide @ (double_divide @ X4 @ X0) @
% 13.71/2.58 (multiply @
% 13.71/2.58 (multiply @ X3 @ (multiply @ X4 @ (double_divide @ X3 @ X2))) @
% 13.71/2.58 X2))))
% 13.71/2.58 = (X1))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl145, zip_derived_cl1098, zip_derived_cl2722,
% 13.71/2.58 zip_derived_cl6, zip_derived_cl1098, zip_derived_cl1504,
% 13.71/2.58 zip_derived_cl1098, zip_derived_cl1504, zip_derived_cl1705,
% 13.71/2.58 zip_derived_cl1098, zip_derived_cl1850])).
% 13.71/2.58 thf(zip_derived_cl1695, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((double_divide @ X0 @ (double_divide @ X1 @ X0)) = (X1))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl1592, zip_derived_cl1592])).
% 13.71/2.58 thf(zip_derived_cl2847, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.71/2.58 ((multiply @
% 13.71/2.58 (multiply @ X1 @ (multiply @ X2 @ (double_divide @ X1 @ X0))) @ X0)
% 13.71/2.58 = (double_divide @ X3 @ (double_divide @ X2 @ X3)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl2831, zip_derived_cl1695])).
% 13.71/2.58 thf(zip_derived_cl1695, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((double_divide @ X0 @ (double_divide @ X1 @ X0)) = (X1))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl1592, zip_derived_cl1592])).
% 13.71/2.58 thf(zip_derived_cl3001, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((multiply @
% 13.71/2.58 (multiply @ X1 @ (multiply @ X2 @ (double_divide @ X1 @ X0))) @ X0)
% 13.71/2.58 = (X2))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl2847, zip_derived_cl1695])).
% 13.71/2.58 thf(zip_derived_cl10162, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((multiply @ (multiply @ X2 @ X0) @ X1)
% 13.71/2.58 = (multiply @ X0 @ (inverse @ (double_divide @ X2 @ X1))))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl3360, zip_derived_cl3001])).
% 13.71/2.58 thf(zip_derived_cl3336, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1124, zip_derived_cl1708])).
% 13.71/2.58 thf(zip_derived_cl1514, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1489])).
% 13.71/2.58 thf(zip_derived_cl3341, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X1 @ X0))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl3336, zip_derived_cl1514])).
% 13.71/2.58 thf(zip_derived_cl1489, plain,
% 13.71/2.58 (![X1 : $i]: ((inverse @ (inverse @ X1)) = (X1))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1469, zip_derived_cl10, zip_derived_cl1346,
% 13.71/2.58 zip_derived_cl1098, zip_derived_cl1098, zip_derived_cl11,
% 13.71/2.58 zip_derived_cl1125, zip_derived_cl1322])).
% 13.71/2.58 thf(zip_derived_cl3531, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((inverse @ (double_divide @ X1 @ X0)) = (multiply @ X1 @ X0))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl3341, zip_derived_cl1489])).
% 13.71/2.58 thf(zip_derived_cl10226, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((multiply @ (multiply @ X2 @ X0) @ X1)
% 13.71/2.58 = (multiply @ X0 @ (multiply @ X2 @ X1)))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl10162, zip_derived_cl3531])).
% 13.71/2.58 thf(zip_derived_cl3360, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ (multiply @ X1 @ (inverse @ X0)) @ X0) = (X1))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl3336, zip_derived_cl2684])).
% 13.71/2.58 thf(zip_derived_cl6, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 13.71/2.58 thf(zip_derived_cl2618, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((multiply @ (inverse @ X1) @ (multiply @ X0 @ X1)) = (X0))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl2572, zip_derived_cl1735])).
% 13.71/2.58 thf(zip_derived_cl2646, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((multiply @ (multiply @ X1 @ X0) @
% 13.71/2.58 (multiply @ X2 @ (double_divide @ X0 @ X1))) = (X2))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl2618])).
% 13.71/2.58 thf(zip_derived_cl7820, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((multiply @ (multiply @ X1 @ X2) @ X0)
% 13.71/2.58 = (multiply @ X0 @ (inverse @ (double_divide @ X2 @ X1))))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl3360, zip_derived_cl2646])).
% 13.71/2.58 thf(zip_derived_cl3531, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]:
% 13.71/2.58 ((inverse @ (double_divide @ X1 @ X0)) = (multiply @ X1 @ X0))),
% 13.71/2.58 inference('sup+', [status(thm)], [zip_derived_cl3341, zip_derived_cl1489])).
% 13.71/2.58 thf(zip_derived_cl7904, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((multiply @ (multiply @ X1 @ X2) @ X0)
% 13.71/2.58 = (multiply @ X0 @ (multiply @ X2 @ X1)))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl7820, zip_derived_cl3531])).
% 13.71/2.58 thf(zip_derived_cl10909, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.71/2.58 ((multiply @ X2 @ (multiply @ X1 @ X0))
% 13.71/2.58 = (multiply @ X0 @ (multiply @ X2 @ X1)))),
% 13.71/2.58 inference('sup+', [status(thm)],
% 13.71/2.58 [zip_derived_cl10226, zip_derived_cl7904])).
% 13.71/2.58 thf(zip_derived_cl3336, plain,
% 13.71/2.58 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl1124, zip_derived_cl1708])).
% 13.71/2.58 thf(zip_derived_cl12811, plain,
% 13.71/2.58 (((multiply @ a3 @ (multiply @ c3 @ b3))
% 13.71/2.58 != (multiply @ a3 @ (multiply @ c3 @ b3)))),
% 13.71/2.58 inference('demod', [status(thm)],
% 13.71/2.58 [zip_derived_cl3337, zip_derived_cl10909, zip_derived_cl3336])).
% 13.71/2.58 thf(zip_derived_cl12812, plain, ($false),
% 13.71/2.58 inference('simplify', [status(thm)], [zip_derived_cl12811])).
% 13.71/2.58
% 13.71/2.58 % SZS output end Refutation
% 13.71/2.58
% 13.71/2.58
% 13.71/2.58 % Terminating...
% 13.71/2.66 % Runner terminated.
% 13.71/2.67 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------