TSTP Solution File: GRP080-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP080-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.UJ3FxZq7aw true
% Computer : n003.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 01:49:50 EDT 2023
% Result : Unsatisfiable 0.55s 0.99s
% Output : Refutation 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP080-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% 0.03/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.UJ3FxZq7aw true
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 21:14:55 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Running portfolio for 300 s
% 0.12/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34 % Number of cores: 8
% 0.12/0.34 % Python version: Python 3.6.8
% 0.12/0.35 % Running in FO mode
% 0.52/0.64 % Total configuration time : 435
% 0.52/0.64 % Estimated wc time : 1092
% 0.52/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.54/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.54/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.54/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.54/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.55/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.55/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.55/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.55/0.99 % Solved by fo/fo5.sh.
% 0.55/0.99 % done 422 iterations in 0.212s
% 0.55/0.99 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.55/0.99 % SZS output start Refutation
% 0.55/0.99 thf(a3_type, type, a3: $i).
% 0.55/0.99 thf(multiply_type, type, multiply: $i > $i > $i).
% 0.55/0.99 thf(c3_type, type, c3: $i).
% 0.55/0.99 thf(a2_type, type, a2: $i).
% 0.55/0.99 thf(a1_type, type, a1: $i).
% 0.55/0.99 thf(identity_type, type, identity: $i).
% 0.55/0.99 thf(double_divide_type, type, double_divide: $i > $i > $i).
% 0.55/0.99 thf(inverse_type, type, inverse: $i > $i).
% 0.55/0.99 thf(b3_type, type, b3: $i).
% 0.55/0.99 thf(prove_these_axioms, conjecture,
% 0.55/0.99 (~( ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 0.55/0.99 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) |
% 0.55/0.99 ( ( multiply @ identity @ a2 ) != ( a2 ) ) |
% 0.55/0.99 ( ( multiply @ ( inverse @ a1 ) @ a1 ) != ( identity ) ) ))).
% 0.55/0.99 thf(zf_stmt_0, negated_conjecture,
% 0.55/0.99 (( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 0.55/0.99 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) |
% 0.55/0.99 ( ( multiply @ identity @ a2 ) != ( a2 ) ) |
% 0.55/0.99 ( ( multiply @ ( inverse @ a1 ) @ a1 ) != ( identity ) )),
% 0.55/0.99 inference('cnf.neg', [status(esa)], [prove_these_axioms])).
% 0.55/0.99 thf(zip_derived_cl4, plain,
% 0.55/0.99 ((((multiply @ (multiply @ a3 @ b3) @ c3)
% 0.55/0.99 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 0.55/0.99 | ((multiply @ identity @ a2) != (a2))
% 0.55/0.99 | ((multiply @ (inverse @ a1) @ a1) != (identity)))),
% 0.55/0.99 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.55/0.99 thf(inverse, axiom, (( inverse @ X ) = ( double_divide @ X @ identity ))).
% 0.55/0.99 thf(zip_derived_cl2, plain,
% 0.55/0.99 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.55/0.99 inference('cnf', [status(esa)], [inverse])).
% 0.55/0.99 thf(multiply, axiom,
% 0.55/0.99 (( multiply @ X @ Y ) =
% 0.55/0.99 ( double_divide @ ( double_divide @ Y @ X ) @ identity ))).
% 0.55/0.99 thf(zip_derived_cl1, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((multiply @ X1 @ X0)
% 0.55/0.99 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 0.55/0.99 inference('cnf', [status(esa)], [multiply])).
% 0.55/0.99 thf(zip_derived_cl7, plain,
% 0.55/0.99 (![X0 : $i]:
% 0.55/0.99 ((multiply @ identity @ X0)
% 0.55/0.99 = (double_divide @ (inverse @ X0) @ identity))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.55/0.99 thf(zip_derived_cl2, plain,
% 0.55/0.99 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.55/0.99 inference('cnf', [status(esa)], [inverse])).
% 0.55/0.99 thf(zip_derived_cl10, plain,
% 0.55/0.99 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 0.55/0.99 thf(zip_derived_cl23, plain,
% 0.55/0.99 ((((multiply @ (multiply @ a3 @ b3) @ c3)
% 0.55/0.99 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 0.55/0.99 | ((inverse @ (inverse @ a2)) != (a2))
% 0.55/0.99 | ((multiply @ (inverse @ a1) @ a1) != (identity)))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl4, zip_derived_cl10])).
% 0.55/0.99 thf(identity, axiom,
% 0.55/0.99 (( identity ) = ( double_divide @ X @ ( inverse @ X ) ))).
% 0.55/0.99 thf(zip_derived_cl3, plain,
% 0.55/0.99 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 0.55/0.99 inference('cnf', [status(esa)], [identity])).
% 0.55/0.99 thf(zip_derived_cl2, plain,
% 0.55/0.99 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.55/0.99 inference('cnf', [status(esa)], [inverse])).
% 0.55/0.99 thf(zip_derived_cl1, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((multiply @ X1 @ X0)
% 0.55/0.99 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 0.55/0.99 inference('cnf', [status(esa)], [multiply])).
% 0.55/0.99 thf(zip_derived_cl6, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.55/0.99 thf(zip_derived_cl27, plain,
% 0.55/0.99 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 0.55/0.99 thf(zip_derived_cl65, plain,
% 0.55/0.99 ((((multiply @ (multiply @ a3 @ b3) @ c3)
% 0.55/0.99 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 0.55/0.99 | ((inverse @ (inverse @ a2)) != (a2))
% 0.55/0.99 | ((inverse @ identity) != (identity)))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl23, zip_derived_cl27])).
% 0.55/0.99 thf(zip_derived_cl6, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.55/0.99 thf(zip_derived_cl3, plain,
% 0.55/0.99 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 0.55/0.99 inference('cnf', [status(esa)], [identity])).
% 0.55/0.99 thf(zip_derived_cl24, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((identity)
% 0.55/0.99 = (double_divide @ (double_divide @ X0 @ X1) @ (multiply @ X1 @ X0)))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl3])).
% 0.55/0.99 thf(single_axiom, axiom,
% 0.55/0.99 (( double_divide @
% 0.55/0.99 ( double_divide @
% 0.55/0.99 identity @ ( double_divide @ X @ ( double_divide @ Y @ identity ) ) ) @
% 0.55/0.99 ( double_divide @
% 0.55/0.99 ( double_divide @ Y @ ( double_divide @ Z @ X ) ) @ identity ) ) =
% 0.55/0.99 ( Z ))).
% 0.55/0.99 thf(zip_derived_cl0, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/0.99 ((double_divide @
% 0.55/0.99 (double_divide @ identity @
% 0.55/0.99 (double_divide @ X1 @ (double_divide @ X2 @ identity))) @
% 0.55/0.99 (double_divide @ (double_divide @ X2 @ (double_divide @ X0 @ X1)) @
% 0.55/0.99 identity))
% 0.55/0.99 = (X0))),
% 0.55/0.99 inference('cnf', [status(esa)], [single_axiom])).
% 0.55/0.99 thf(zip_derived_cl2, plain,
% 0.55/0.99 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.55/0.99 inference('cnf', [status(esa)], [inverse])).
% 0.55/0.99 thf(zip_derived_cl1, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((multiply @ X1 @ X0)
% 0.55/0.99 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 0.55/0.99 inference('cnf', [status(esa)], [multiply])).
% 0.55/0.99 thf(zip_derived_cl13, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/0.99 ((double_divide @
% 0.55/0.99 (double_divide @ identity @ (double_divide @ X1 @ (inverse @ X2))) @
% 0.55/0.99 (multiply @ (double_divide @ X0 @ X1) @ X2)) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl1])).
% 0.55/0.99 thf(zip_derived_cl110, plain, (((identity) = (inverse @ identity))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl24, zip_derived_cl13])).
% 0.55/0.99 thf(zip_derived_cl174, plain,
% 0.55/0.99 ((((multiply @ (multiply @ a3 @ b3) @ c3)
% 0.55/0.99 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 0.55/0.99 | ((inverse @ (inverse @ a2)) != (a2))
% 0.55/0.99 | ((identity) != (identity)))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl65, zip_derived_cl110])).
% 0.55/0.99 thf(zip_derived_cl175, plain,
% 0.55/0.99 ((((inverse @ (inverse @ a2)) != (a2))
% 0.55/0.99 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 0.55/0.99 != (multiply @ a3 @ (multiply @ b3 @ c3))))),
% 0.55/0.99 inference('simplify', [status(thm)], [zip_derived_cl174])).
% 0.55/0.99 thf(zip_derived_cl3, plain,
% 0.55/0.99 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 0.55/0.99 inference('cnf', [status(esa)], [identity])).
% 0.55/0.99 thf(zip_derived_cl3, plain,
% 0.55/0.99 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 0.55/0.99 inference('cnf', [status(esa)], [identity])).
% 0.55/0.99 thf(zip_derived_cl13, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/0.99 ((double_divide @
% 0.55/0.99 (double_divide @ identity @ (double_divide @ X1 @ (inverse @ X2))) @
% 0.55/0.99 (multiply @ (double_divide @ X0 @ X1) @ X2)) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl1])).
% 0.55/0.99 thf(zip_derived_cl20, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((double_divide @ (double_divide @ identity @ identity) @
% 0.55/0.99 (multiply @ (double_divide @ X0 @ X1) @ X1)) = (X0))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl13])).
% 0.55/0.99 thf(zip_derived_cl2, plain,
% 0.55/0.99 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.55/0.99 inference('cnf', [status(esa)], [inverse])).
% 0.55/0.99 thf(zip_derived_cl21, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((double_divide @ (inverse @ identity) @
% 0.55/0.99 (multiply @ (double_divide @ X0 @ X1) @ X1)) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl20, zip_derived_cl2])).
% 0.55/0.99 thf(zip_derived_cl110, plain, (((identity) = (inverse @ identity))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl24, zip_derived_cl13])).
% 0.55/0.99 thf(zip_derived_cl303, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((double_divide @ identity @
% 0.55/0.99 (multiply @ (double_divide @ X0 @ X1) @ X1)) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl21, zip_derived_cl110])).
% 0.55/0.99 thf(zip_derived_cl313, plain,
% 0.55/0.99 (![X0 : $i]:
% 0.55/0.99 ((double_divide @ identity @ (multiply @ identity @ (inverse @ X0)))
% 0.55/0.99 = (X0))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl303])).
% 0.55/0.99 thf(zip_derived_cl10, plain,
% 0.55/0.99 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 0.55/0.99 thf(zip_derived_cl322, plain,
% 0.55/0.99 (![X0 : $i]:
% 0.55/0.99 ((double_divide @ identity @ (inverse @ (inverse @ (inverse @ X0))))
% 0.55/0.99 = (X0))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl313, zip_derived_cl10])).
% 0.55/0.99 thf(zip_derived_cl27, plain,
% 0.55/0.99 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 0.55/0.99 thf(zip_derived_cl3, plain,
% 0.55/0.99 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 0.55/0.99 inference('cnf', [status(esa)], [identity])).
% 0.55/0.99 thf(zip_derived_cl30, plain,
% 0.55/0.99 (![X0 : $i]:
% 0.55/0.99 ((identity)
% 0.55/0.99 = (double_divide @ identity @ (multiply @ (inverse @ X0) @ X0)))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl3])).
% 0.55/0.99 thf(zip_derived_cl13, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/0.99 ((double_divide @
% 0.55/0.99 (double_divide @ identity @ (double_divide @ X1 @ (inverse @ X2))) @
% 0.55/0.99 (multiply @ (double_divide @ X0 @ X1) @ X2)) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl1])).
% 0.55/0.99 thf(zip_derived_cl38, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((double_divide @
% 0.55/0.99 (double_divide @ identity @
% 0.55/0.99 (double_divide @ (multiply @ (inverse @ X1) @ X1) @ (inverse @ X0))) @
% 0.55/0.99 (multiply @ identity @ X0)) = (identity))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl13])).
% 0.55/0.99 thf(zip_derived_cl10, plain,
% 0.55/0.99 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 0.55/0.99 thf(zip_derived_cl44, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((double_divide @
% 0.55/0.99 (double_divide @ identity @
% 0.55/0.99 (double_divide @ (multiply @ (inverse @ X1) @ X1) @ (inverse @ X0))) @
% 0.55/0.99 (inverse @ (inverse @ X0))) = (identity))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl38, zip_derived_cl10])).
% 0.55/0.99 thf(zip_derived_cl27, plain,
% 0.55/0.99 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 0.55/0.99 thf(zip_derived_cl110, plain, (((identity) = (inverse @ identity))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl24, zip_derived_cl13])).
% 0.55/0.99 thf(zip_derived_cl172, plain,
% 0.55/0.99 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl27, zip_derived_cl110])).
% 0.55/0.99 thf(zip_derived_cl110, plain, (((identity) = (inverse @ identity))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl24, zip_derived_cl13])).
% 0.55/0.99 thf(zip_derived_cl3, plain,
% 0.55/0.99 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 0.55/0.99 inference('cnf', [status(esa)], [identity])).
% 0.55/0.99 thf(zip_derived_cl13, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/0.99 ((double_divide @
% 0.55/0.99 (double_divide @ identity @ (double_divide @ X1 @ (inverse @ X2))) @
% 0.55/0.99 (multiply @ (double_divide @ X0 @ X1) @ X2)) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl1])).
% 0.55/0.99 thf(zip_derived_cl17, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((double_divide @
% 0.55/0.99 (double_divide @ identity @
% 0.55/0.99 (double_divide @ (inverse @ X0) @ (inverse @ X1))) @
% 0.55/0.99 (multiply @ identity @ X1)) = (X0))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl13])).
% 0.55/0.99 thf(zip_derived_cl10, plain,
% 0.55/0.99 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 0.55/0.99 thf(zip_derived_cl328, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((double_divide @
% 0.55/0.99 (double_divide @ identity @
% 0.55/0.99 (double_divide @ (inverse @ X0) @ (inverse @ X1))) @
% 0.55/0.99 (inverse @ (inverse @ X1))) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl17, zip_derived_cl10])).
% 0.55/0.99 thf(zip_derived_cl339, plain,
% 0.55/0.99 (![X0 : $i]:
% 0.55/0.99 ((double_divide @
% 0.55/0.99 (double_divide @ identity @
% 0.55/0.99 (double_divide @ (inverse @ X0) @ (inverse @ identity))) @
% 0.55/0.99 (inverse @ identity)) = (X0))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl110, zip_derived_cl328])).
% 0.55/0.99 thf(zip_derived_cl110, plain, (((identity) = (inverse @ identity))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl24, zip_derived_cl13])).
% 0.55/0.99 thf(zip_derived_cl2, plain,
% 0.55/0.99 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.55/0.99 inference('cnf', [status(esa)], [inverse])).
% 0.55/0.99 thf(zip_derived_cl110, plain, (((identity) = (inverse @ identity))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl24, zip_derived_cl13])).
% 0.55/0.99 thf(zip_derived_cl1, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((multiply @ X1 @ X0)
% 0.55/0.99 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 0.55/0.99 inference('cnf', [status(esa)], [multiply])).
% 0.55/0.99 thf(zip_derived_cl346, plain,
% 0.55/0.99 (![X0 : $i]: ((multiply @ (inverse @ (inverse @ X0)) @ identity) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl339, zip_derived_cl110, zip_derived_cl2,
% 0.55/0.99 zip_derived_cl110, zip_derived_cl1])).
% 0.55/0.99 thf(zip_derived_cl2, plain,
% 0.55/0.99 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.55/0.99 inference('cnf', [status(esa)], [inverse])).
% 0.55/0.99 thf(zip_derived_cl13, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/0.99 ((double_divide @
% 0.55/0.99 (double_divide @ identity @ (double_divide @ X1 @ (inverse @ X2))) @
% 0.55/0.99 (multiply @ (double_divide @ X0 @ X1) @ X2)) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl1])).
% 0.55/0.99 thf(zip_derived_cl16, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((double_divide @
% 0.55/0.99 (double_divide @ identity @
% 0.55/0.99 (double_divide @ identity @ (inverse @ X1))) @
% 0.55/0.99 (multiply @ (inverse @ X0) @ X1)) = (X0))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 0.55/0.99 thf(zip_derived_cl355, plain,
% 0.55/0.99 (![X0 : $i]:
% 0.55/0.99 ((double_divide @
% 0.55/0.99 (double_divide @ identity @
% 0.55/0.99 (double_divide @ identity @ (inverse @ identity))) @
% 0.55/0.99 X0) = (inverse @ X0))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl346, zip_derived_cl16])).
% 0.55/0.99 thf(zip_derived_cl110, plain, (((identity) = (inverse @ identity))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl24, zip_derived_cl13])).
% 0.55/0.99 thf(zip_derived_cl110, plain, (((identity) = (inverse @ identity))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl24, zip_derived_cl13])).
% 0.55/0.99 thf(zip_derived_cl3, plain,
% 0.55/0.99 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 0.55/0.99 inference('cnf', [status(esa)], [identity])).
% 0.55/0.99 thf(zip_derived_cl176, plain,
% 0.55/0.99 (((identity) = (double_divide @ identity @ identity))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl110, zip_derived_cl3])).
% 0.55/0.99 thf(zip_derived_cl176, plain,
% 0.55/0.99 (((identity) = (double_divide @ identity @ identity))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl110, zip_derived_cl3])).
% 0.55/0.99 thf(zip_derived_cl362, plain,
% 0.55/0.99 (![X0 : $i]: ((double_divide @ identity @ X0) = (inverse @ X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl355, zip_derived_cl110, zip_derived_cl176,
% 0.55/0.99 zip_derived_cl176])).
% 0.55/0.99 thf(zip_derived_cl362, plain,
% 0.55/0.99 (![X0 : $i]: ((double_divide @ identity @ X0) = (inverse @ X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl355, zip_derived_cl110, zip_derived_cl176,
% 0.55/0.99 zip_derived_cl176])).
% 0.55/0.99 thf(zip_derived_cl570, plain,
% 0.55/0.99 (![X0 : $i]:
% 0.55/0.99 ((double_divide @ (inverse @ (inverse @ (inverse @ X0))) @
% 0.55/0.99 (inverse @ (inverse @ X0))) = (identity))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl44, zip_derived_cl172, zip_derived_cl362,
% 0.55/0.99 zip_derived_cl362])).
% 0.55/0.99 thf(zip_derived_cl303, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((double_divide @ identity @
% 0.55/0.99 (multiply @ (double_divide @ X0 @ X1) @ X1)) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl21, zip_derived_cl110])).
% 0.55/0.99 thf(zip_derived_cl575, plain,
% 0.55/0.99 (![X0 : $i]:
% 0.55/0.99 ((double_divide @ identity @
% 0.55/0.99 (multiply @ identity @ (inverse @ (inverse @ X0))))
% 0.55/0.99 = (inverse @ (inverse @ (inverse @ X0))))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl570, zip_derived_cl303])).
% 0.55/0.99 thf(zip_derived_cl10, plain,
% 0.55/0.99 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 0.55/0.99 thf(zip_derived_cl346, plain,
% 0.55/0.99 (![X0 : $i]: ((multiply @ (inverse @ (inverse @ X0)) @ identity) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl339, zip_derived_cl110, zip_derived_cl2,
% 0.55/0.99 zip_derived_cl110, zip_derived_cl1])).
% 0.55/0.99 thf(zip_derived_cl3, plain,
% 0.55/0.99 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 0.55/0.99 inference('cnf', [status(esa)], [identity])).
% 0.55/0.99 thf(zip_derived_cl16, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((double_divide @
% 0.55/0.99 (double_divide @ identity @
% 0.55/0.99 (double_divide @ identity @ (inverse @ X1))) @
% 0.55/0.99 (multiply @ (inverse @ X0) @ X1)) = (X0))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 0.55/0.99 thf(zip_derived_cl259, plain,
% 0.55/0.99 (![X0 : $i]:
% 0.55/0.99 ((double_divide @ (double_divide @ identity @ identity) @
% 0.55/0.99 (multiply @ (inverse @ X0) @ identity)) = (X0))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl16])).
% 0.55/0.99 thf(zip_derived_cl176, plain,
% 0.55/0.99 (((identity) = (double_divide @ identity @ identity))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl110, zip_derived_cl3])).
% 0.55/0.99 thf(zip_derived_cl263, plain,
% 0.55/0.99 (![X0 : $i]:
% 0.55/0.99 ((double_divide @ identity @ (multiply @ (inverse @ X0) @ identity))
% 0.55/0.99 = (X0))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl259, zip_derived_cl176])).
% 0.55/0.99 thf(zip_derived_cl6, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.55/0.99 thf(zip_derived_cl272, plain,
% 0.55/0.99 (![X0 : $i]:
% 0.55/0.99 ((multiply @ (multiply @ (inverse @ X0) @ identity) @ identity)
% 0.55/0.99 = (inverse @ X0))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl263, zip_derived_cl6])).
% 0.55/0.99 thf(zip_derived_cl357, plain,
% 0.55/0.99 (![X0 : $i]: ((multiply @ X0 @ identity) = (inverse @ (inverse @ X0)))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl346, zip_derived_cl272])).
% 0.55/0.99 thf(zip_derived_cl346, plain,
% 0.55/0.99 (![X0 : $i]: ((multiply @ (inverse @ (inverse @ X0)) @ identity) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl339, zip_derived_cl110, zip_derived_cl2,
% 0.55/0.99 zip_derived_cl110, zip_derived_cl1])).
% 0.55/0.99 thf(zip_derived_cl374, plain,
% 0.55/0.99 (![X0 : $i]: ((inverse @ (inverse @ (inverse @ (inverse @ X0)))) = (X0))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl357, zip_derived_cl346])).
% 0.55/0.99 thf(zip_derived_cl362, plain,
% 0.55/0.99 (![X0 : $i]: ((double_divide @ identity @ X0) = (inverse @ X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl355, zip_derived_cl110, zip_derived_cl176,
% 0.55/0.99 zip_derived_cl176])).
% 0.55/0.99 thf(zip_derived_cl604, plain,
% 0.55/0.99 (![X0 : $i]: ((inverse @ X0) = (inverse @ (inverse @ (inverse @ X0))))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl575, zip_derived_cl10, zip_derived_cl374,
% 0.55/0.99 zip_derived_cl362])).
% 0.55/0.99 thf(zip_derived_cl362, plain,
% 0.55/0.99 (![X0 : $i]: ((double_divide @ identity @ X0) = (inverse @ X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl355, zip_derived_cl110, zip_derived_cl176,
% 0.55/0.99 zip_derived_cl176])).
% 0.55/0.99 thf(zip_derived_cl630, plain,
% 0.55/0.99 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl322, zip_derived_cl604, zip_derived_cl362])).
% 0.55/0.99 thf(zip_derived_cl655, plain,
% 0.55/0.99 ((((a2) != (a2))
% 0.55/0.99 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 0.55/0.99 != (multiply @ a3 @ (multiply @ b3 @ c3))))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl175, zip_derived_cl630])).
% 0.55/0.99 thf(zip_derived_cl656, plain,
% 0.55/0.99 (((multiply @ (multiply @ a3 @ b3) @ c3)
% 0.55/0.99 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 0.55/0.99 inference('simplify', [status(thm)], [zip_derived_cl655])).
% 0.55/0.99 thf(zip_derived_cl24, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((identity)
% 0.55/0.99 = (double_divide @ (double_divide @ X0 @ X1) @ (multiply @ X1 @ X0)))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl3])).
% 0.55/0.99 thf(zip_derived_cl13, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/0.99 ((double_divide @
% 0.55/0.99 (double_divide @ identity @ (double_divide @ X1 @ (inverse @ X2))) @
% 0.55/0.99 (multiply @ (double_divide @ X0 @ X1) @ X2)) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl1])).
% 0.55/0.99 thf(zip_derived_cl13, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/0.99 ((double_divide @
% 0.55/0.99 (double_divide @ identity @ (double_divide @ X1 @ (inverse @ X2))) @
% 0.55/0.99 (multiply @ (double_divide @ X0 @ X1) @ X2)) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl1])).
% 0.55/0.99 thf(zip_derived_cl15, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/0.99 ((double_divide @
% 0.55/0.99 (double_divide @ identity @
% 0.55/0.99 (double_divide @ (multiply @ (double_divide @ X0 @ X2) @ X1) @
% 0.55/0.99 (inverse @ X3))) @
% 0.55/0.99 (multiply @ X0 @ X3))
% 0.55/0.99 = (double_divide @ identity @ (double_divide @ X2 @ (inverse @ X1))))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl13])).
% 0.55/0.99 thf(zip_derived_cl156, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/0.99 ((double_divide @
% 0.55/0.99 (double_divide @ identity @
% 0.55/0.99 (double_divide @ (multiply @ identity @ X0) @ (inverse @ X3))) @
% 0.55/0.99 (multiply @ (double_divide @ X1 @ X2) @ X3))
% 0.55/0.99 = (double_divide @ identity @
% 0.55/0.99 (double_divide @ (multiply @ X2 @ X1) @ (inverse @ X0))))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl24, zip_derived_cl15])).
% 0.55/0.99 thf(zip_derived_cl10, plain,
% 0.55/0.99 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 0.55/0.99 thf(zip_derived_cl166, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/0.99 ((double_divide @
% 0.55/0.99 (double_divide @ identity @
% 0.55/0.99 (double_divide @ (inverse @ (inverse @ X0)) @ (inverse @ X3))) @
% 0.55/0.99 (multiply @ (double_divide @ X1 @ X2) @ X3))
% 0.55/0.99 = (double_divide @ identity @
% 0.55/0.99 (double_divide @ (multiply @ X2 @ X1) @ (inverse @ X0))))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl156, zip_derived_cl10])).
% 0.55/0.99 thf(zip_derived_cl630, plain,
% 0.55/0.99 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl322, zip_derived_cl604, zip_derived_cl362])).
% 0.55/0.99 thf(zip_derived_cl362, plain,
% 0.55/0.99 (![X0 : $i]: ((double_divide @ identity @ X0) = (inverse @ X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl355, zip_derived_cl110, zip_derived_cl176,
% 0.55/0.99 zip_derived_cl176])).
% 0.55/0.99 thf(zip_derived_cl303, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((double_divide @ identity @
% 0.55/0.99 (multiply @ (double_divide @ X0 @ X1) @ X1)) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl21, zip_derived_cl110])).
% 0.55/0.99 thf(zip_derived_cl417, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((inverse @ (multiply @ (double_divide @ X1 @ X0) @ X0)) = (X1))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl362, zip_derived_cl303])).
% 0.55/0.99 thf(zip_derived_cl630, plain,
% 0.55/0.99 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl322, zip_derived_cl604, zip_derived_cl362])).
% 0.55/0.99 thf(zip_derived_cl667, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((inverse @ X0) = (multiply @ (double_divide @ X0 @ X1) @ X1))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl417, zip_derived_cl630])).
% 0.55/0.99 thf(zip_derived_cl417, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((inverse @ (multiply @ (double_divide @ X1 @ X0) @ X0)) = (X1))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl362, zip_derived_cl303])).
% 0.55/0.99 thf(zip_derived_cl346, plain,
% 0.55/0.99 (![X0 : $i]: ((multiply @ (inverse @ (inverse @ X0)) @ identity) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl339, zip_derived_cl110, zip_derived_cl2,
% 0.55/0.99 zip_derived_cl110, zip_derived_cl1])).
% 0.55/0.99 thf(zip_derived_cl13, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/0.99 ((double_divide @
% 0.55/0.99 (double_divide @ identity @ (double_divide @ X1 @ (inverse @ X2))) @
% 0.55/0.99 (multiply @ (double_divide @ X0 @ X1) @ X2)) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl1])).
% 0.55/0.99 thf(zip_derived_cl1, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((multiply @ X1 @ X0)
% 0.55/0.99 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 0.55/0.99 inference('cnf', [status(esa)], [multiply])).
% 0.55/0.99 thf(zip_derived_cl14, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/0.99 ((multiply @ (multiply @ (double_divide @ X0 @ X2) @ X1) @
% 0.55/0.99 (double_divide @ identity @ (double_divide @ X2 @ (inverse @ X1))))
% 0.55/0.99 = (double_divide @ X0 @ identity))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl1])).
% 0.55/0.99 thf(zip_derived_cl2, plain,
% 0.55/0.99 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.55/0.99 inference('cnf', [status(esa)], [inverse])).
% 0.55/0.99 thf(zip_derived_cl22, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/0.99 ((multiply @ (multiply @ (double_divide @ X0 @ X2) @ X1) @
% 0.55/0.99 (double_divide @ identity @ (double_divide @ X2 @ (inverse @ X1))))
% 0.55/0.99 = (inverse @ X0))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl14, zip_derived_cl2])).
% 0.55/0.99 thf(zip_derived_cl362, plain,
% 0.55/0.99 (![X0 : $i]: ((double_divide @ identity @ X0) = (inverse @ X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl355, zip_derived_cl110, zip_derived_cl176,
% 0.55/0.99 zip_derived_cl176])).
% 0.55/0.99 thf(zip_derived_cl6, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.55/0.99 thf(zip_derived_cl452, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/0.99 ((multiply @ (multiply @ (double_divide @ X0 @ X2) @ X1) @
% 0.55/0.99 (multiply @ (inverse @ X1) @ X2)) = (inverse @ X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl22, zip_derived_cl362, zip_derived_cl6])).
% 0.55/0.99 thf(zip_derived_cl458, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((multiply @
% 0.55/0.99 (multiply @ (double_divide @ X1 @ identity) @ (inverse @ X0)) @ X0)
% 0.55/0.99 = (inverse @ X1))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl346, zip_derived_cl452])).
% 0.55/0.99 thf(zip_derived_cl2, plain,
% 0.55/0.99 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.55/0.99 inference('cnf', [status(esa)], [inverse])).
% 0.55/0.99 thf(zip_derived_cl474, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((multiply @ (multiply @ (inverse @ X1) @ (inverse @ X0)) @ X0)
% 0.55/0.99 = (inverse @ X1))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl458, zip_derived_cl2])).
% 0.55/0.99 thf(zip_derived_cl732, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/0.99 ((multiply @ (multiply @ X0 @ (inverse @ X2)) @ X2)
% 0.55/0.99 = (inverse @ (multiply @ (double_divide @ X0 @ X1) @ X1)))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl417, zip_derived_cl474])).
% 0.55/0.99 thf(zip_derived_cl417, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((inverse @ (multiply @ (double_divide @ X1 @ X0) @ X0)) = (X1))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl362, zip_derived_cl303])).
% 0.55/0.99 thf(zip_derived_cl740, plain,
% 0.55/0.99 (![X0 : $i, X2 : $i]:
% 0.55/0.99 ((multiply @ (multiply @ X0 @ (inverse @ X2)) @ X2) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl732, zip_derived_cl417])).
% 0.55/0.99 thf(zip_derived_cl794, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((multiply @ (inverse @ X0) @ X1)
% 0.55/0.99 = (double_divide @ X0 @ (inverse @ X1)))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl667, zip_derived_cl740])).
% 0.55/0.99 thf(zip_derived_cl1, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((multiply @ X1 @ X0)
% 0.55/0.99 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 0.55/0.99 inference('cnf', [status(esa)], [multiply])).
% 0.55/0.99 thf(zip_derived_cl667, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((inverse @ X0) = (multiply @ (double_divide @ X0 @ X1) @ X1))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl417, zip_derived_cl630])).
% 0.55/0.99 thf(zip_derived_cl6, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.55/0.99 thf(zip_derived_cl630, plain,
% 0.55/0.99 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl322, zip_derived_cl604, zip_derived_cl362])).
% 0.55/0.99 thf(zip_derived_cl665, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl630])).
% 0.55/0.99 thf(zip_derived_cl791, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((inverse @ (inverse @ X0))
% 0.55/0.99 = (double_divide @ X1 @ (double_divide @ X0 @ X1)))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl667, zip_derived_cl665])).
% 0.55/0.99 thf(zip_derived_cl630, plain,
% 0.55/0.99 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl322, zip_derived_cl604, zip_derived_cl362])).
% 0.55/0.99 thf(zip_derived_cl808, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((X0) = (double_divide @ X1 @ (double_divide @ X0 @ X1)))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl791, zip_derived_cl630])).
% 0.55/0.99 thf(zip_derived_cl880, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((double_divide @ X0 @ X1)
% 0.55/0.99 = (double_divide @ identity @ (multiply @ X1 @ X0)))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl808])).
% 0.55/0.99 thf(zip_derived_cl794, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((multiply @ (inverse @ X0) @ X1)
% 0.55/0.99 = (double_divide @ X0 @ (inverse @ X1)))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl667, zip_derived_cl740])).
% 0.55/0.99 thf(zip_derived_cl3, plain,
% 0.55/0.99 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 0.55/0.99 inference('cnf', [status(esa)], [identity])).
% 0.55/0.99 thf(zip_derived_cl15, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/0.99 ((double_divide @
% 0.55/0.99 (double_divide @ identity @
% 0.55/0.99 (double_divide @ (multiply @ (double_divide @ X0 @ X2) @ X1) @
% 0.55/0.99 (inverse @ X3))) @
% 0.55/0.99 (multiply @ X0 @ X3))
% 0.55/0.99 = (double_divide @ identity @ (double_divide @ X2 @ (inverse @ X1))))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl13])).
% 0.55/0.99 thf(zip_derived_cl154, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/0.99 ((double_divide @
% 0.55/0.99 (double_divide @ identity @
% 0.55/0.99 (double_divide @ (multiply @ identity @ X0) @ (inverse @ X2))) @
% 0.55/0.99 (multiply @ X1 @ X2))
% 0.55/0.99 = (double_divide @ identity @
% 0.55/0.99 (double_divide @ (inverse @ X1) @ (inverse @ X0))))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl15])).
% 0.55/0.99 thf(zip_derived_cl10, plain,
% 0.55/0.99 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 0.55/0.99 thf(zip_derived_cl165, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/0.99 ((double_divide @
% 0.55/0.99 (double_divide @ identity @
% 0.55/0.99 (double_divide @ (inverse @ (inverse @ X0)) @ (inverse @ X2))) @
% 0.55/0.99 (multiply @ X1 @ X2))
% 0.55/0.99 = (double_divide @ identity @
% 0.55/0.99 (double_divide @ (inverse @ X1) @ (inverse @ X0))))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl154, zip_derived_cl10])).
% 0.55/0.99 thf(zip_derived_cl630, plain,
% 0.55/0.99 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl322, zip_derived_cl604, zip_derived_cl362])).
% 0.55/0.99 thf(zip_derived_cl794, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((multiply @ (inverse @ X0) @ X1)
% 0.55/0.99 = (double_divide @ X0 @ (inverse @ X1)))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl667, zip_derived_cl740])).
% 0.55/0.99 thf(zip_derived_cl880, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((double_divide @ X0 @ X1)
% 0.55/0.99 = (double_divide @ identity @ (multiply @ X1 @ X0)))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl808])).
% 0.55/0.99 thf(zip_derived_cl794, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((multiply @ (inverse @ X0) @ X1)
% 0.55/0.99 = (double_divide @ X0 @ (inverse @ X1)))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl667, zip_derived_cl740])).
% 0.55/0.99 thf(zip_derived_cl630, plain,
% 0.55/0.99 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl322, zip_derived_cl604, zip_derived_cl362])).
% 0.55/0.99 thf(zip_derived_cl740, plain,
% 0.55/0.99 (![X0 : $i, X2 : $i]:
% 0.55/0.99 ((multiply @ (multiply @ X0 @ (inverse @ X2)) @ X2) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl732, zip_derived_cl417])).
% 0.55/0.99 thf(zip_derived_cl756, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl630, zip_derived_cl740])).
% 0.55/0.99 thf(zip_derived_cl665, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl630])).
% 0.55/0.99 thf(zip_derived_cl764, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((inverse @ X0)
% 0.55/0.99 = (double_divide @ (inverse @ X1) @ (multiply @ X0 @ X1)))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl756, zip_derived_cl665])).
% 0.55/0.99 thf(zip_derived_cl808, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((X0) = (double_divide @ X1 @ (double_divide @ X0 @ X1)))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl791, zip_derived_cl630])).
% 0.55/0.99 thf(zip_derived_cl808, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((X0) = (double_divide @ X1 @ (double_divide @ X0 @ X1)))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl791, zip_derived_cl630])).
% 0.55/0.99 thf(zip_derived_cl873, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((X1) = (double_divide @ (double_divide @ X0 @ X1) @ X0))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl808, zip_derived_cl808])).
% 0.55/0.99 thf(zip_derived_cl1307, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((multiply @ X0 @ X1)
% 0.55/0.99 = (double_divide @ (inverse @ X0) @ (inverse @ X1)))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl764, zip_derived_cl873])).
% 0.55/0.99 thf(zip_derived_cl880, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((double_divide @ X0 @ X1)
% 0.55/0.99 = (double_divide @ identity @ (multiply @ X1 @ X0)))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl808])).
% 0.55/0.99 thf(zip_derived_cl2384, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/0.99 ((double_divide @ (multiply @ (inverse @ X2) @ X0) @
% 0.55/0.99 (multiply @ X1 @ X2)) = (double_divide @ X0 @ X1))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl165, zip_derived_cl630, zip_derived_cl794,
% 0.55/0.99 zip_derived_cl880, zip_derived_cl794, zip_derived_cl1307,
% 0.55/0.99 zip_derived_cl880])).
% 0.55/0.99 thf(zip_derived_cl630, plain,
% 0.55/0.99 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl322, zip_derived_cl604, zip_derived_cl362])).
% 0.55/0.99 thf(zip_derived_cl374, plain,
% 0.55/0.99 (![X0 : $i]: ((inverse @ (inverse @ (inverse @ (inverse @ X0)))) = (X0))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl357, zip_derived_cl346])).
% 0.55/0.99 thf(zip_derived_cl3, plain,
% 0.55/0.99 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 0.55/0.99 inference('cnf', [status(esa)], [identity])).
% 0.55/0.99 thf(zip_derived_cl382, plain,
% 0.55/0.99 (![X0 : $i]:
% 0.55/0.99 ((identity)
% 0.55/0.99 = (double_divide @ (inverse @ (inverse @ (inverse @ X0))) @ X0))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl374, zip_derived_cl3])).
% 0.55/0.99 thf(zip_derived_cl452, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/0.99 ((multiply @ (multiply @ (double_divide @ X0 @ X2) @ X1) @
% 0.55/0.99 (multiply @ (inverse @ X1) @ X2)) = (inverse @ X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl22, zip_derived_cl362, zip_derived_cl6])).
% 0.55/0.99 thf(zip_derived_cl492, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((multiply @ (multiply @ identity @ X1) @
% 0.55/0.99 (multiply @ (inverse @ X1) @ X0))
% 0.55/0.99 = (inverse @ (inverse @ (inverse @ (inverse @ X0)))))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl382, zip_derived_cl452])).
% 0.55/0.99 thf(zip_derived_cl10, plain,
% 0.55/0.99 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 0.55/0.99 thf(zip_derived_cl374, plain,
% 0.55/0.99 (![X0 : $i]: ((inverse @ (inverse @ (inverse @ (inverse @ X0)))) = (X0))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl357, zip_derived_cl346])).
% 0.55/0.99 thf(zip_derived_cl506, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((multiply @ (inverse @ (inverse @ X1)) @
% 0.55/0.99 (multiply @ (inverse @ X1) @ X0)) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl492, zip_derived_cl10, zip_derived_cl374])).
% 0.55/0.99 thf(zip_derived_cl630, plain,
% 0.55/0.99 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl322, zip_derived_cl604, zip_derived_cl362])).
% 0.55/0.99 thf(zip_derived_cl811, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl506, zip_derived_cl630])).
% 0.55/0.99 thf(zip_derived_cl827, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)) = (X1))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl630, zip_derived_cl811])).
% 0.55/0.99 thf(zip_derived_cl2384, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/0.99 ((double_divide @ (multiply @ (inverse @ X2) @ X0) @
% 0.55/0.99 (multiply @ X1 @ X2)) = (double_divide @ X0 @ X1))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl165, zip_derived_cl630, zip_derived_cl794,
% 0.55/0.99 zip_derived_cl880, zip_derived_cl794, zip_derived_cl1307,
% 0.55/0.99 zip_derived_cl880])).
% 0.55/0.99 thf(zip_derived_cl2422, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/0.99 ((double_divide @ X0 @ (multiply @ X1 @ X2))
% 0.55/0.99 = (double_divide @ (multiply @ X2 @ X0) @ X1))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl827, zip_derived_cl2384])).
% 0.55/0.99 thf(zip_derived_cl665, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl630])).
% 0.55/0.99 thf(zip_derived_cl2, plain,
% 0.55/0.99 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.55/0.99 inference('cnf', [status(esa)], [inverse])).
% 0.55/0.99 thf(zip_derived_cl808, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((X0) = (double_divide @ X1 @ (double_divide @ X0 @ X1)))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl791, zip_derived_cl630])).
% 0.55/0.99 thf(zip_derived_cl878, plain,
% 0.55/0.99 (![X0 : $i]: ((X0) = (double_divide @ identity @ (inverse @ X0)))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl808])).
% 0.55/0.99 thf(zip_derived_cl899, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((multiply @ X0 @ X1)
% 0.55/0.99 = (double_divide @ identity @ (double_divide @ X1 @ X0)))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl665, zip_derived_cl878])).
% 0.55/0.99 thf(zip_derived_cl2588, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/0.99 ((double_divide @ X0 @ (double_divide @ X1 @ X2))
% 0.55/0.99 = (multiply @ (multiply @ (inverse @ X0) @ X2) @ X1))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl166, zip_derived_cl630, zip_derived_cl794,
% 0.55/0.99 zip_derived_cl880, zip_derived_cl794, zip_derived_cl2384,
% 0.55/0.99 zip_derived_cl2422, zip_derived_cl899])).
% 0.55/0.99 thf(zip_derived_cl827, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)) = (X1))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl630, zip_derived_cl811])).
% 0.55/0.99 thf(zip_derived_cl756, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl630, zip_derived_cl740])).
% 0.55/0.99 thf(zip_derived_cl839, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl827, zip_derived_cl756])).
% 0.55/0.99 thf(zip_derived_cl665, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl630])).
% 0.55/0.99 thf(zip_derived_cl867, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((multiply @ X0 @ (double_divide @ X0 @ X1)) = (inverse @ X1))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl839, zip_derived_cl665])).
% 0.55/0.99 thf(zip_derived_cl811, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl506, zip_derived_cl630])).
% 0.55/0.99 thf(zip_derived_cl980, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((multiply @ X1 @ (inverse @ X0))
% 0.55/0.99 = (double_divide @ (inverse @ X1) @ X0))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl867, zip_derived_cl811])).
% 0.55/0.99 thf(zip_derived_cl2613, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/0.99 ((multiply @ X2 @ (inverse @ (double_divide @ X0 @ X1)))
% 0.55/0.99 = (multiply @ (multiply @ (inverse @ (inverse @ X2)) @ X1) @ X0))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl2588, zip_derived_cl980])).
% 0.55/0.99 thf(zip_derived_cl6, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i]:
% 0.55/0.99 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.55/0.99 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.55/0.99 thf(zip_derived_cl630, plain,
% 0.55/0.99 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl322, zip_derived_cl604, zip_derived_cl362])).
% 0.55/0.99 thf(zip_derived_cl2676, plain,
% 0.55/0.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/0.99 ((multiply @ X2 @ (multiply @ X1 @ X0))
% 0.55/0.99 = (multiply @ (multiply @ X2 @ X1) @ X0))),
% 0.55/0.99 inference('demod', [status(thm)],
% 0.55/0.99 [zip_derived_cl2613, zip_derived_cl6, zip_derived_cl630])).
% 0.55/0.99 thf(zip_derived_cl2905, plain,
% 0.55/0.99 (((multiply @ a3 @ (multiply @ b3 @ c3))
% 0.55/0.99 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 0.55/0.99 inference('demod', [status(thm)], [zip_derived_cl656, zip_derived_cl2676])).
% 0.55/0.99 thf(zip_derived_cl2906, plain, ($false),
% 0.55/0.99 inference('simplify', [status(thm)], [zip_derived_cl2905])).
% 0.55/0.99
% 0.55/0.99 % SZS output end Refutation
% 0.55/0.99
% 0.55/0.99
% 0.55/0.99 % Terminating...
% 1.62/1.05 % Runner terminated.
% 1.62/1.06 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------