%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP052-1 : TPTP v9.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.nLTpJNLXJq true
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:35:32 PM UTC 2025
% Result : Unsatisfiable 67.10s 14.94s
% Output : Refutation 67.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : GRP052-1 : TPTP v9.2.0. Released v1.0.0.
% 0.06/0.11 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.nLTpJNLXJq true
% 0.11/0.32 % Computer : n021.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Oct 1 14:04:08 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % Running portfolio for 300 s
% 0.11/0.32 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.32 % Number of cores: 8
% 0.11/0.32 % Python version: Python 3.6.8
% 0.11/0.32 % Running in FO mode
% 0.43/0.61 % Total configuration time : 435
% 0.43/0.61 % Estimated wc time : 1092
% 0.43/0.61 % Estimated cpu time (7 cpus) : 156.0
% 0.48/0.77 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.48/0.77 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.48/0.78 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.49/0.89 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.49/0.90 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.49/0.91 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.49/0.92 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 67.10/14.94 % Solved by fo/fo7.sh.
% 67.10/14.94 % done 1477 iterations in 13.894s
% 67.10/14.94 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 67.10/14.94 % SZS output start Refutation
% 67.10/14.94 thf(inverse_type, type, inverse: $i > $i).
% 67.10/14.94 thf(b1_type, type, b1: $i).
% 67.10/14.94 thf(b3_type, type, b3: $i).
% 67.10/14.94 thf(b2_type, type, b2: $i).
% 67.10/14.94 thf(multiply_type, type, multiply: $i > $i > $i).
% 67.10/14.94 thf(a3_type, type, a3: $i).
% 67.10/14.94 thf(c3_type, type, c3: $i).
% 67.10/14.94 thf(a2_type, type, a2: $i).
% 67.10/14.94 thf(a1_type, type, a1: $i).
% 67.10/14.94 thf(single_axiom, axiom,
% 67.10/14.94 (( multiply @
% 67.10/14.94 Z @
% 67.10/14.94 ( inverse @
% 67.10/14.94 ( multiply @
% 67.10/14.94 ( multiply @
% 67.10/14.94 ( multiply @ ( inverse @ Y ) @ Y ) @
% 67.10/14.94 ( inverse @
% 67.10/14.94 ( multiply @
% 67.10/14.94 ( inverse @ ( multiply @ Z @ ( inverse @ Y ) ) ) @ X ) ) ) @
% 67.10/14.94 Y ) ) ) =
% 67.10/14.94 ( X ))).
% 67.10/14.94 thf(zip_derived_cl0, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.94 ((multiply @ X1 @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 67.10/14.94 X2)))
% 67.10/14.94 = (X0))),
% 67.10/14.94 inference('cnf', [status(esa)], [single_axiom])).
% 67.10/14.94 thf(zip_derived_cl0, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.94 ((multiply @ X1 @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 67.10/14.94 X2)))
% 67.10/14.94 = (X0))),
% 67.10/14.94 inference('cnf', [status(esa)], [single_axiom])).
% 67.10/14.94 thf(zip_derived_cl0, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.94 ((multiply @ X1 @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 67.10/14.94 X2)))
% 67.10/14.94 = (X0))),
% 67.10/14.94 inference('cnf', [status(esa)], [single_axiom])).
% 67.10/14.94 thf(zip_derived_cl3, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 67.10/14.94 ((multiply @ X3 @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X0)) @
% 67.10/14.94 X2)))
% 67.10/14.94 = (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 67.10/14.94 (inverse @ X1))) @
% 67.10/14.94 X0))) @
% 67.10/14.94 X1)))),
% 67.10/14.94 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 67.10/14.94 thf(zip_derived_cl0, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.94 ((multiply @ X1 @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 67.10/14.94 X2)))
% 67.10/14.94 = (X0))),
% 67.10/14.94 inference('cnf', [status(esa)], [single_axiom])).
% 67.10/14.94 thf(zip_derived_cl13, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.94 ((multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 67.10/14.94 (multiply @ X2 @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X0) @ X0) @ (inverse @ X1)) @
% 67.10/14.94 X0))))
% 67.10/14.94 = (X1))),
% 67.10/14.94 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 67.10/14.94 thf(zip_derived_cl35, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 67.10/14.94 ((multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 67.10/14.94 (multiply @ X3 @ (inverse @ (multiply @ X0 @ X2))))
% 67.10/14.94 = (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1))) @
% 67.10/14.94 X0))) @
% 67.10/14.94 X1))),
% 67.10/14.94 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl13])).
% 67.10/14.94 thf(zip_derived_cl0, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.94 ((multiply @ X1 @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 67.10/14.94 X2)))
% 67.10/14.94 = (X0))),
% 67.10/14.94 inference('cnf', [status(esa)], [single_axiom])).
% 67.10/14.94 thf(zip_derived_cl0, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.94 ((multiply @ X1 @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 67.10/14.94 X2)))
% 67.10/14.94 = (X0))),
% 67.10/14.94 inference('cnf', [status(esa)], [single_axiom])).
% 67.10/14.94 thf(zip_derived_cl0, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.94 ((multiply @ X1 @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 67.10/14.94 X2)))
% 67.10/14.94 = (X0))),
% 67.10/14.94 inference('cnf', [status(esa)], [single_axiom])).
% 67.10/14.94 thf(zip_derived_cl3, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 67.10/14.94 ((multiply @ X3 @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X0)) @
% 67.10/14.94 X2)))
% 67.10/14.94 = (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 67.10/14.94 (inverse @ X1))) @
% 67.10/14.94 X0))) @
% 67.10/14.94 X1)))),
% 67.10/14.94 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 67.10/14.94 thf(zip_derived_cl0, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.94 ((multiply @ X1 @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 67.10/14.94 X2)))
% 67.10/14.94 = (X0))),
% 67.10/14.94 inference('cnf', [status(esa)], [single_axiom])).
% 67.10/14.94 thf(zip_derived_cl35, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 67.10/14.94 ((multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 67.10/14.94 (multiply @ X3 @ (inverse @ (multiply @ X0 @ X2))))
% 67.10/14.94 = (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1))) @
% 67.10/14.94 X0))) @
% 67.10/14.94 X1))),
% 67.10/14.94 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl13])).
% 67.10/14.94 thf(zip_derived_cl13, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.94 ((multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 67.10/14.94 (multiply @ X2 @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X0) @ X0) @ (inverse @ X1)) @
% 67.10/14.94 X0))))
% 67.10/14.94 = (X1))),
% 67.10/14.94 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 67.10/14.94 thf(zip_derived_cl57, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.94 ((multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X0) @ X0) @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X0))) @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1))))) @
% 67.10/14.94 X0) = (X1))),
% 67.10/14.94 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl13])).
% 67.10/14.94 thf(zip_derived_cl35, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 67.10/14.94 ((multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 67.10/14.94 (multiply @ X3 @ (inverse @ (multiply @ X0 @ X2))))
% 67.10/14.94 = (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1))) @
% 67.10/14.94 X0))) @
% 67.10/14.94 X1))),
% 67.10/14.94 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl13])).
% 67.10/14.94 thf(zip_derived_cl35, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 67.10/14.94 ((multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 67.10/14.94 (multiply @ X3 @ (inverse @ (multiply @ X0 @ X2))))
% 67.10/14.94 = (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1))) @
% 67.10/14.94 X0))) @
% 67.10/14.94 X1))),
% 67.10/14.94 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl13])).
% 67.10/14.94 thf(zip_derived_cl52, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 67.10/14.94 ((multiply @ (inverse @ (multiply @ X3 @ (inverse @ X0))) @
% 67.10/14.94 (multiply @ X3 @ (inverse @ (multiply @ X1 @ X0))))
% 67.10/14.94 = (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 67.10/14.94 (multiply @ X2 @ (inverse @ (multiply @ X1 @ X0)))))),
% 67.10/14.94 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl35])).
% 67.10/14.94 thf(zip_derived_cl196, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 67.10/14.94 ((multiply @ (inverse @ (multiply @ X4 @ (inverse @ X1))) @
% 67.10/14.94 (multiply @ X4 @ (inverse @ X0)))
% 67.10/14.94 = (multiply @ (inverse @ (multiply @ X3 @ (inverse @ X1))) @
% 67.10/14.94 (multiply @ X3 @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 67.10/14.94 (inverse @ X1))) @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 67.10/14.94 (inverse @ X0))))) @
% 67.10/14.94 X1)))))),
% 67.10/14.94 inference('sup+', [status(thm)], [zip_derived_cl57, zip_derived_cl52])).
% 67.10/14.94 thf(zip_derived_cl57, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.94 ((multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X0) @ X0) @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X0))) @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1))))) @
% 67.10/14.94 X0) = (X1))),
% 67.10/14.94 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl13])).
% 67.10/14.94 thf(zip_derived_cl234, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X3 : $i, X4 : $i]:
% 67.10/14.94 ((multiply @ (inverse @ (multiply @ X4 @ (inverse @ X1))) @
% 67.10/14.94 (multiply @ X4 @ (inverse @ X0)))
% 67.10/14.94 = (multiply @ (inverse @ (multiply @ X3 @ (inverse @ X1))) @
% 67.10/14.94 (multiply @ X3 @ (inverse @ X0))))),
% 67.10/14.94 inference('demod', [status(thm)], [zip_derived_cl196, zip_derived_cl57])).
% 67.10/14.94 thf(zip_derived_cl284, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 67.10/14.94 ((multiply @ (inverse @ X0) @ (multiply @ X4 @ (inverse @ X1)))
% 67.10/14.94 = (multiply @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ X2 @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ (inverse @ (multiply @ X4 @ (inverse @ X3))) @
% 67.10/14.94 X0))) @
% 67.10/14.94 X3)))) @
% 67.10/14.94 (multiply @ X2 @ (inverse @ X1))))),
% 67.10/14.94 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl234])).
% 67.10/14.94 thf(zip_derived_cl457, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 67.10/14.94 ((multiply @ (inverse @ X1) @
% 67.10/14.94 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 67.10/14.94 (inverse @ X3)))
% 67.10/14.94 = (multiply @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ X4 @
% 67.10/14.94 (multiply @ X2 @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X0) @ X0) @
% 67.10/14.94 (inverse @ X1)) @
% 67.10/14.94 X0))))) @
% 67.10/14.94 (multiply @ X4 @ (inverse @ X3))))),
% 67.10/14.94 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl284])).
% 67.10/14.94 thf(zip_derived_cl657, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 67.10/14.94 ((multiply @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ (inverse @ (multiply @ X4 @ (inverse @ X3))) @ X0)) @
% 67.10/14.94 (multiply @ (inverse @ (multiply @ X4 @ (inverse @ X3))) @
% 67.10/14.94 (inverse @ X1)))
% 67.10/14.94 = (multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 67.10/14.94 (multiply @ X2 @ (inverse @ X1))))),
% 67.10/14.94 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl457])).
% 67.10/14.94 thf(zip_derived_cl752, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 67.10/14.94 ((multiply @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @ X5)) @
% 67.10/14.94 X0)
% 67.10/14.94 = (multiply @ (inverse @ (multiply @ X4 @ X5)) @
% 67.10/14.94 (multiply @ X4 @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 67.10/14.94 (inverse @ X1))) @
% 67.10/14.94 X0))) @
% 67.10/14.94 X1)))))),
% 67.10/14.94 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl657])).
% 67.10/14.94 thf(zip_derived_cl3, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 67.10/14.94 ((multiply @ X3 @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X0)) @
% 67.10/14.94 X2)))
% 67.10/14.94 = (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 67.10/14.94 (inverse @ X1))) @
% 67.10/14.94 X0))) @
% 67.10/14.94 X1)))),
% 67.10/14.94 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 67.10/14.94 thf(zip_derived_cl804, plain,
% 67.10/14.94 (![X0 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 67.10/14.94 ((multiply @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @ X5)) @
% 67.10/14.94 X0)
% 67.10/14.94 = (multiply @ (inverse @ (multiply @ X4 @ X5)) @
% 67.10/14.94 (multiply @ X4 @
% 67.10/14.94 (multiply @ X3 @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X0)) @
% 67.10/14.94 X2))))))),
% 67.10/14.94 inference('demod', [status(thm)], [zip_derived_cl752, zip_derived_cl3])).
% 67.10/14.94 thf(zip_derived_cl1086, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 67.10/14.94 ((multiply @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X1))) @ X4)) @
% 67.10/14.94 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X1))) @ X0))
% 67.10/14.94 = (multiply @ (inverse @ (multiply @ X3 @ X4)) @
% 67.10/14.94 (multiply @ X3 @ X0)))),
% 67.10/14.94 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl804])).
% 67.10/14.94 thf(zip_derived_cl3, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 67.10/14.94 ((multiply @ X3 @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X0)) @
% 67.10/14.94 X2)))
% 67.10/14.94 = (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 67.10/14.94 (inverse @ X1))) @
% 67.10/14.94 X0))) @
% 67.10/14.94 X1)))),
% 67.10/14.94 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 67.10/14.94 thf(zip_derived_cl1222, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 67.10/14.94 ((multiply @ X4 @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ (inverse @ (multiply @ X4 @ (inverse @ X3))) @ X0))) @
% 67.10/14.94 X3)))
% 67.10/14.94 = (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @
% 67.10/14.94 (multiply @ X1 @ X0)))) @
% 67.10/14.94 X2)))),
% 67.10/14.94 inference('sup+', [status(thm)], [zip_derived_cl1086, zip_derived_cl3])).
% 67.10/14.94 thf(zip_derived_cl0, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.94 ((multiply @ X1 @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 67.10/14.94 X2)))
% 67.10/14.94 = (X0))),
% 67.10/14.94 inference('cnf', [status(esa)], [single_axiom])).
% 67.10/14.94 thf(zip_derived_cl1344, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.94 ((X0)
% 67.10/14.94 = (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @
% 67.10/14.94 (multiply @ X1 @ X0)))) @
% 67.10/14.94 X2)))),
% 67.10/14.94 inference('demod', [status(thm)], [zip_derived_cl1222, zip_derived_cl0])).
% 67.10/14.94 thf(zip_derived_cl1561, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.94 ((X1)
% 67.10/14.94 = (inverse @
% 67.10/14.94 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 67.10/14.94 (multiply @ X2 @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X0) @ X0) @ X1) @ X0))))))),
% 67.10/14.94 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl1344])).
% 67.10/14.94 thf(zip_derived_cl284, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 67.10/14.94 ((multiply @ (inverse @ X0) @ (multiply @ X4 @ (inverse @ X1)))
% 67.10/14.94 = (multiply @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ X2 @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @
% 67.10/14.94 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 67.10/14.94 (inverse @
% 67.10/14.94 (multiply @ (inverse @ (multiply @ X4 @ (inverse @ X3))) @
% 67.10/14.94 X0))) @
% 67.10/14.94 X3)))) @
% 67.10/14.94 (multiply @ X2 @ (inverse @ X1))))),
% 67.10/14.94 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl234])).
% 67.10/14.94 thf(zip_derived_cl234, plain,
% 67.10/14.94 (![X0 : $i, X1 : $i, X3 : $i, X4 : $i]:
% 67.10/14.94 ((multiply @ (inverse @ (multiply @ X4 @ (inverse @ X1))) @
% 67.10/14.94 (multiply @ X4 @ (inverse @ X0)))
% 67.10/14.95 = (multiply @ (inverse @ (multiply @ X3 @ (inverse @ X1))) @
% 67.10/14.95 (multiply @ X3 @ (inverse @ X0))))),
% 67.10/14.95 inference('demod', [status(thm)], [zip_derived_cl196, zip_derived_cl57])).
% 67.10/14.95 thf(zip_derived_cl57, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X0) @ X0) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X0))) @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1))))) @
% 67.10/14.95 X0) = (X1))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl13])).
% 67.10/14.95 thf(zip_derived_cl252, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @
% 67.10/14.95 (multiply @ X1 @ (inverse @ X0))))) @
% 67.10/14.95 X2) = (X0))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl234, zip_derived_cl57])).
% 67.10/14.95 thf(zip_derived_cl1086, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 67.10/14.95 ((multiply @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X1))) @ X4)) @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X1))) @ X0))
% 67.10/14.95 = (multiply @ (inverse @ (multiply @ X3 @ X4)) @
% 67.10/14.95 (multiply @ X3 @ X0)))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl804])).
% 67.10/14.95 thf(zip_derived_cl1086, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 67.10/14.95 ((multiply @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X1))) @ X4)) @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X1))) @ X0))
% 67.10/14.95 = (multiply @ (inverse @ (multiply @ X3 @ X4)) @
% 67.10/14.95 (multiply @ X3 @ X0)))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl804])).
% 67.10/14.95 thf(zip_derived_cl1241, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ (multiply @ X1 @ X2)) @ (multiply @ X1 @ X0))
% 67.10/14.95 = (multiply @ (inverse @ (multiply @ X3 @ X2)) @
% 67.10/14.95 (multiply @ X3 @ X0)))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl1086, zip_derived_cl1086])).
% 67.10/14.95 thf(zip_derived_cl0, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ X1 @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 67.10/14.95 X2)))
% 67.10/14.95 = (X0))),
% 67.10/14.95 inference('cnf', [status(esa)], [single_axiom])).
% 67.10/14.95 thf(zip_derived_cl1357, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 67.10/14.95 ((multiply @ X4 @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X1 @ X0)) @
% 67.10/14.95 (multiply @ X1 @ X0)) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (inverse @ (multiply @ X4 @ (inverse @ (multiply @ X3 @ X0)))) @
% 67.10/14.95 X2))) @
% 67.10/14.95 (multiply @ X3 @ X0))))
% 67.10/14.95 = (X2))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl1241, zip_derived_cl0])).
% 67.10/14.95 thf(zip_derived_cl3469, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 67.10/14.95 ((multiply @ X4 @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X5 @ X2)) @
% 67.10/14.95 (multiply @ X5 @ X2)) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ X4 @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 67.10/14.95 (multiply @ X3 @ (inverse @ X0))))) @
% 67.10/14.95 X2)))) @
% 67.10/14.95 X1))) @
% 67.10/14.95 X0)))
% 67.10/14.95 = (X1))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl252, zip_derived_cl1357])).
% 67.10/14.95 thf(zip_derived_cl252, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @
% 67.10/14.95 (multiply @ X1 @ (inverse @ X0))))) @
% 67.10/14.95 X2) = (X0))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl234, zip_derived_cl57])).
% 67.10/14.95 thf(zip_derived_cl3596, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X5 : $i]:
% 67.10/14.95 ((multiply @ X4 @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X5 @ X2)) @
% 67.10/14.95 (multiply @ X5 @ X2)) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X4 @ (inverse @ X0))) @ X1))) @
% 67.10/14.95 X0)))
% 67.10/14.95 = (X1))),
% 67.10/14.95 inference('demod', [status(thm)], [zip_derived_cl3469, zip_derived_cl252])).
% 67.10/14.95 thf(zip_derived_cl3755, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 67.10/14.95 ((multiply @ X5 @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (inverse @ X1) @
% 67.10/14.95 (multiply @ X2 @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X0) @ X0) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 67.10/14.95 X1))) @
% 67.10/14.95 X0)))) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X5 @ (inverse @ X4))) @ X3))) @
% 67.10/14.95 X4)))
% 67.10/14.95 = (X3))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl284, zip_derived_cl3596])).
% 67.10/14.95 thf(zip_derived_cl0, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ X1 @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 67.10/14.95 X2)))
% 67.10/14.95 = (X0))),
% 67.10/14.95 inference('cnf', [status(esa)], [single_axiom])).
% 67.10/14.95 thf(zip_derived_cl3815, plain,
% 67.10/14.95 (![X1 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 67.10/14.95 ((multiply @ X5 @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X5 @ (inverse @ X4))) @ X3))) @
% 67.10/14.95 X4)))
% 67.10/14.95 = (X3))),
% 67.10/14.95 inference('demod', [status(thm)], [zip_derived_cl3755, zip_derived_cl0])).
% 67.10/14.95 thf(zip_derived_cl3923, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @ X2 @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (multiply @ (multiply @ (inverse @ X3) @ X3) @ X0) @ X1)))
% 67.10/14.95 = (multiply @ X2 @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X1) @ X1) @ X0) @ X1))))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl1561, zip_derived_cl3815])).
% 67.10/14.95 thf(zip_derived_cl35, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 67.10/14.95 (multiply @ X3 @ (inverse @ (multiply @ X0 @ X2))))
% 67.10/14.95 = (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1))) @
% 67.10/14.95 X0))) @
% 67.10/14.95 X1))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl13])).
% 67.10/14.95 thf(zip_derived_cl0, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ X1 @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 67.10/14.95 X2)))
% 67.10/14.95 = (X0))),
% 67.10/14.95 inference('cnf', [status(esa)], [single_axiom])).
% 67.10/14.95 thf(zip_derived_cl50, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X0) @ X0) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 67.10/14.95 (multiply @ X2 @ (inverse @ (multiply @ X1 @ X0))))))
% 67.10/14.95 = (X1))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl0])).
% 67.10/14.95 thf(zip_derived_cl4120, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X0) @ X0) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 67.10/14.95 (multiply @ X2 @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X0) @ X0) @ X1) @ X0))))))
% 67.10/14.95 = (multiply @ (multiply @ (inverse @ X3) @ X3) @ X1))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl3923, zip_derived_cl50])).
% 67.10/14.95 thf(zip_derived_cl1561, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((X1)
% 67.10/14.95 = (inverse @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 67.10/14.95 (multiply @ X2 @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X0) @ X0) @ X1) @ X0))))))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl1344])).
% 67.10/14.95 thf(zip_derived_cl4275, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X0) @ X0) @ X1)
% 67.10/14.95 = (multiply @ (multiply @ (inverse @ X3) @ X3) @ X1))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl4120, zip_derived_cl1561])).
% 67.10/14.95 thf(zip_derived_cl4275, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X0) @ X0) @ X1)
% 67.10/14.95 = (multiply @ (multiply @ (inverse @ X3) @ X3) @ X1))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl4120, zip_derived_cl1561])).
% 67.10/14.95 thf(zip_derived_cl4275, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X0) @ X0) @ X1)
% 67.10/14.95 = (multiply @ (multiply @ (inverse @ X3) @ X3) @ X1))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl4120, zip_derived_cl1561])).
% 67.10/14.95 thf(zip_derived_cl50, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X0) @ X0) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 67.10/14.95 (multiply @ X2 @ (inverse @ (multiply @ X1 @ X0))))))
% 67.10/14.95 = (X1))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl0])).
% 67.10/14.95 thf(zip_derived_cl4350, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X3) @ X3) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 67.10/14.95 (multiply @ X2 @ (inverse @ (multiply @ X1 @ X0))))))
% 67.10/14.95 = (X1))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl4275, zip_derived_cl50])).
% 67.10/14.95 thf(zip_derived_cl4826, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X4) @ X4) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X3) @ X3) @ (inverse @ X0))) @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 67.10/14.95 (inverse @ (multiply @ X1 @ X0))))))
% 67.10/14.95 = (X1))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl4275, zip_derived_cl4350])).
% 67.10/14.95 thf(zip_derived_cl8372, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X5) @ X5) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X4) @ X4) @ (inverse @ X0))) @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 67.10/14.95 (inverse @ (multiply @ (multiply @ (inverse @ X1) @ X1) @ X0))))))
% 67.10/14.95 = (multiply @ (inverse @ X2) @ X2))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl4275, zip_derived_cl4826])).
% 67.10/14.95 thf(zip_derived_cl3923, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @ X2 @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (multiply @ (multiply @ (inverse @ X3) @ X3) @ X0) @ X1)))
% 67.10/14.95 = (multiply @ X2 @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X1) @ X1) @ X0) @ X1))))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl1561, zip_derived_cl3815])).
% 67.10/14.95 thf(zip_derived_cl50, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X0) @ X0) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 67.10/14.95 (multiply @ X2 @ (inverse @ (multiply @ X1 @ X0))))))
% 67.10/14.95 = (X1))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl0])).
% 67.10/14.95 thf(zip_derived_cl1241, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ (multiply @ X1 @ X2)) @ (multiply @ X1 @ X0))
% 67.10/14.95 = (multiply @ (inverse @ (multiply @ X3 @ X2)) @
% 67.10/14.95 (multiply @ X3 @ X0)))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl1086, zip_derived_cl1086])).
% 67.10/14.95 thf(zip_derived_cl1452, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ X0) @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X3) @ X3) @ X1))
% 67.10/14.95 = (multiply @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ X2 @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X4 @ (inverse @ X3))) @
% 67.10/14.95 (multiply @ X4 @ (inverse @ (multiply @ X0 @ X3))))))) @
% 67.10/14.95 (multiply @ X2 @ X1)))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl1241])).
% 67.10/14.95 thf(zip_derived_cl4122, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 67.10/14.95 ((multiply @
% 67.10/14.95 (inverse @ (multiply @ (multiply @ (inverse @ X5) @ X5) @ X1)) @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X0) @ X0) @ X3))
% 67.10/14.95 = (multiply @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ X4 @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 67.10/14.95 (multiply @ X2 @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X0) @ X0) @ X1) @ X0))))))) @
% 67.10/14.95 (multiply @ X4 @ X3)))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl3923, zip_derived_cl1452])).
% 67.10/14.95 thf(zip_derived_cl1561, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((X1)
% 67.10/14.95 = (inverse @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 67.10/14.95 (multiply @ X2 @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X0) @ X0) @ X1) @ X0))))))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl1344])).
% 67.10/14.95 thf(zip_derived_cl4277, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 67.10/14.95 ((multiply @
% 67.10/14.95 (inverse @ (multiply @ (multiply @ (inverse @ X5) @ X5) @ X1)) @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X0) @ X0) @ X3))
% 67.10/14.95 = (multiply @ (inverse @ (multiply @ X4 @ X1)) @
% 67.10/14.95 (multiply @ X4 @ X3)))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl4122, zip_derived_cl1561])).
% 67.10/14.95 thf(zip_derived_cl4350, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X3) @ X3) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 67.10/14.95 (multiply @ X2 @ (inverse @ (multiply @ X1 @ X0))))))
% 67.10/14.95 = (X1))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl4275, zip_derived_cl50])).
% 67.10/14.95 thf(zip_derived_cl8483, plain,
% 67.10/14.95 (![X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ X1) @ X1) = (multiply @ (inverse @ X2) @ X2))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl8372, zip_derived_cl4277, zip_derived_cl4350])).
% 67.10/14.95 thf(zip_derived_cl4275, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X0) @ X0) @ X1)
% 67.10/14.95 = (multiply @ (multiply @ (inverse @ X3) @ X3) @ X1))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl4120, zip_derived_cl1561])).
% 67.10/14.95 thf(prove_these_axioms, conjecture,
% 67.10/14.95 (~( ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 67.10/14.95 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) |
% 67.10/14.95 ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 ) != ( a2 ) ) |
% 67.10/14.95 ( ( multiply @ ( inverse @ a1 ) @ a1 ) !=
% 67.10/14.95 ( multiply @ ( inverse @ b1 ) @ b1 ) ) ))).
% 67.10/14.95 thf(zf_stmt_0, negated_conjecture,
% 67.10/14.95 (( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 67.10/14.95 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) |
% 67.10/14.95 ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 ) != ( a2 ) ) |
% 67.10/14.95 ( ( multiply @ ( inverse @ a1 ) @ a1 ) !=
% 67.10/14.95 ( multiply @ ( inverse @ b1 ) @ b1 ) )),
% 67.10/14.95 inference('cnf.neg', [status(esa)], [prove_these_axioms])).
% 67.10/14.95 thf(zip_derived_cl1, plain,
% 67.10/14.95 ((((multiply @ (multiply @ a3 @ b3) @ c3)
% 67.10/14.95 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 67.10/14.95 | ((multiply @ (multiply @ (inverse @ b2) @ b2) @ a2) != (a2))
% 67.10/14.95 | ((multiply @ (inverse @ a1) @ a1) != (multiply @ (inverse @ b1) @ b1)))),
% 67.10/14.95 inference('cnf', [status(esa)], [zf_stmt_0])).
% 67.10/14.95 thf(zip_derived_cl4355, plain,
% 67.10/14.95 (![X0 : $i]:
% 67.10/14.95 (((multiply @ (multiply @ (inverse @ X0) @ X0) @ a2) != (a2))
% 67.10/14.95 | ((multiply @ (inverse @ a1) @ a1)
% 67.10/14.95 != (multiply @ (inverse @ b1) @ b1))
% 67.10/14.95 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 67.10/14.95 != (multiply @ a3 @ (multiply @ b3 @ c3))))),
% 67.10/14.95 inference('sup-', [status(thm)], [zip_derived_cl4275, zip_derived_cl1])).
% 67.10/14.95 thf(zip_derived_cl8703, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i]:
% 67.10/14.95 (((multiply @ (inverse @ a1) @ a1) != (multiply @ (inverse @ X0) @ X0))
% 67.10/14.95 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 67.10/14.95 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 67.10/14.95 | ((multiply @ (multiply @ (inverse @ X1) @ X1) @ a2) != (a2)))),
% 67.10/14.95 inference('sup-', [status(thm)], [zip_derived_cl8483, zip_derived_cl4355])).
% 67.10/14.95 thf(zip_derived_cl8483, plain,
% 67.10/14.95 (![X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ X1) @ X1) = (multiply @ (inverse @ X2) @ X2))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl8372, zip_derived_cl4277, zip_derived_cl4350])).
% 67.10/14.95 thf(zip_derived_cl8880, plain,
% 67.10/14.95 (![X1 : $i]:
% 67.10/14.95 (((multiply @ (multiply @ (inverse @ X1) @ X1) @ a2) != (a2))
% 67.10/14.95 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 67.10/14.95 != (multiply @ a3 @ (multiply @ b3 @ c3))))),
% 67.10/14.95 inference('simplify_reflect+', [status(thm)],
% 67.10/14.95 [zip_derived_cl8703, zip_derived_cl8483])).
% 67.10/14.95 thf(zip_derived_cl8483, plain,
% 67.10/14.95 (![X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ X1) @ X1) = (multiply @ (inverse @ X2) @ X2))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl8372, zip_derived_cl4277, zip_derived_cl4350])).
% 67.10/14.95 thf(zip_derived_cl4275, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X0) @ X0) @ X1)
% 67.10/14.95 = (multiply @ (multiply @ (inverse @ X3) @ X3) @ X1))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl4120, zip_derived_cl1561])).
% 67.10/14.95 thf(zip_derived_cl252, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @
% 67.10/14.95 (multiply @ X1 @ (inverse @ X0))))) @
% 67.10/14.95 X2) = (X0))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl234, zip_derived_cl57])).
% 67.10/14.95 thf(zip_derived_cl4352, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @
% 67.10/14.95 (multiply @ X1 @ (inverse @ X0))))) @
% 67.10/14.95 X2) = (X0))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl4275, zip_derived_cl252])).
% 67.10/14.95 thf(zip_derived_cl8680, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 67.10/14.95 (inverse @ (multiply @ (inverse @ X0) @ X0))) @
% 67.10/14.95 X1) = (X1))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl8483, zip_derived_cl4352])).
% 67.10/14.95 thf(zip_derived_cl4275, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X0) @ X0) @ X1)
% 67.10/14.95 = (multiply @ (multiply @ (inverse @ X3) @ X3) @ X1))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl4120, zip_derived_cl1561])).
% 67.10/14.95 thf(zip_derived_cl1561, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((X1)
% 67.10/14.95 = (inverse @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 67.10/14.95 (multiply @ X2 @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X0) @ X0) @ X1) @ X0))))))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl1344])).
% 67.10/14.95 thf(zip_derived_cl4341, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 67.10/14.95 ((X0)
% 67.10/14.95 = (inverse @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 67.10/14.95 (multiply @ X3 @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X1) @ X1) @ X0) @ X2))))))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl4275, zip_derived_cl1561])).
% 67.10/14.95 thf(zip_derived_cl8939, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 67.10/14.95 ((X1)
% 67.10/14.95 = (inverse @
% 67.10/14.95 (multiply @ (inverse @ (inverse @ X0)) @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X4) @ X4) @
% 67.10/14.95 (inverse @ (multiply @ (inverse @ X3) @ X3))) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X2) @ X2) @ X1) @ X0))))))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl8680, zip_derived_cl4341])).
% 67.10/14.95 thf(zip_derived_cl8680, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 67.10/14.95 (inverse @ (multiply @ (inverse @ X0) @ X0))) @
% 67.10/14.95 X1) = (X1))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl8483, zip_derived_cl4352])).
% 67.10/14.95 thf(zip_derived_cl9089, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((X1)
% 67.10/14.95 = (inverse @
% 67.10/14.95 (multiply @ (inverse @ (inverse @ X0)) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X2) @ X2) @ X1) @ X0)))))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl8939, zip_derived_cl8680])).
% 67.10/14.95 thf(zip_derived_cl35, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 67.10/14.95 (multiply @ X3 @ (inverse @ (multiply @ X0 @ X2))))
% 67.10/14.95 = (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1))) @
% 67.10/14.95 X0))) @
% 67.10/14.95 X1))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl13])).
% 67.10/14.95 thf(zip_derived_cl4341, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 67.10/14.95 ((X0)
% 67.10/14.95 = (inverse @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 67.10/14.95 (multiply @ X3 @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X1) @ X1) @ X0) @ X2))))))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl4275, zip_derived_cl1561])).
% 67.10/14.95 thf(zip_derived_cl4535, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 67.10/14.95 ((X1)
% 67.10/14.95 = (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X0) @ X0) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 67.10/14.95 (inverse @ X0))) @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X2) @ X2) @ X1)))) @
% 67.10/14.95 X0)))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl4341])).
% 67.10/14.95 thf(zip_derived_cl8483, plain,
% 67.10/14.95 (![X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ X1) @ X1) = (multiply @ (inverse @ X2) @ X2))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl8372, zip_derived_cl4277, zip_derived_cl4350])).
% 67.10/14.95 thf(zip_derived_cl8680, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 67.10/14.95 (inverse @ (multiply @ (inverse @ X0) @ X0))) @
% 67.10/14.95 X1) = (X1))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl8483, zip_derived_cl4352])).
% 67.10/14.95 thf(zip_derived_cl4350, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X3) @ X3) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 67.10/14.95 (multiply @ X2 @ (inverse @ (multiply @ X1 @ X0))))))
% 67.10/14.95 = (X1))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl4275, zip_derived_cl50])).
% 67.10/14.95 thf(zip_derived_cl8942, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X4) @ X4) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (inverse @ (inverse @ X0)) @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 67.10/14.95 (inverse @ (multiply @ (inverse @ X2) @ X2))) @
% 67.10/14.95 (inverse @ (multiply @ X1 @ X0))))))
% 67.10/14.95 = (X1))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl8680, zip_derived_cl4350])).
% 67.10/14.95 thf(zip_derived_cl8680, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 67.10/14.95 (inverse @ (multiply @ (inverse @ X0) @ X0))) @
% 67.10/14.95 X1) = (X1))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl8483, zip_derived_cl4352])).
% 67.10/14.95 thf(zip_derived_cl9092, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X4 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X4) @ X4) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (inverse @ (inverse @ X0)) @
% 67.10/14.95 (inverse @ (multiply @ X1 @ X0)))))
% 67.10/14.95 = (X1))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl8942, zip_derived_cl8680])).
% 67.10/14.95 thf(zip_derived_cl8680, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 67.10/14.95 (inverse @ (multiply @ (inverse @ X0) @ X0))) @
% 67.10/14.95 X1) = (X1))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl8483, zip_derived_cl4352])).
% 67.10/14.95 thf(zip_derived_cl4275, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X0) @ X0) @ X1)
% 67.10/14.95 = (multiply @ (multiply @ (inverse @ X3) @ X3) @ X1))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl4120, zip_derived_cl1561])).
% 67.10/14.95 thf(zip_derived_cl13, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 67.10/14.95 (multiply @ X2 @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X0) @ X0) @ (inverse @ X1)) @
% 67.10/14.95 X0))))
% 67.10/14.95 = (X1))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 67.10/14.95 thf(zip_derived_cl4345, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 67.10/14.95 (multiply @ X3 @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X1) @ X1) @ (inverse @ X0)) @
% 67.10/14.95 X2))))
% 67.10/14.95 = (X0))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl4275, zip_derived_cl13])).
% 67.10/14.95 thf(zip_derived_cl8940, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ (inverse @ X0)) @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X4) @ X4) @
% 67.10/14.95 (inverse @ (multiply @ (inverse @ X3) @ X3))) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1)) @
% 67.10/14.95 X0))))
% 67.10/14.95 = (X1))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl8680, zip_derived_cl4345])).
% 67.10/14.95 thf(zip_derived_cl8680, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 67.10/14.95 (inverse @ (multiply @ (inverse @ X0) @ X0))) @
% 67.10/14.95 X1) = (X1))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl8483, zip_derived_cl4352])).
% 67.10/14.95 thf(zip_derived_cl9090, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ (inverse @ X0)) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1)) @
% 67.10/14.95 X0)))
% 67.10/14.95 = (X1))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl8940, zip_derived_cl8680])).
% 67.10/14.95 thf(zip_derived_cl11613, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ (inverse @ X2)) @
% 67.10/14.95 (inverse @ (multiply @ X0 @ X2)))
% 67.10/14.95 = (multiply @ (inverse @ (inverse @ X1)) @
% 67.10/14.95 (inverse @ (multiply @ X0 @ X1))))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl9092, zip_derived_cl9090])).
% 67.10/14.95 thf(zip_derived_cl11998, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ (inverse @ X2)) @
% 67.10/14.95 (inverse @ (multiply @ (inverse @ X0) @ X0)))
% 67.10/14.95 = (multiply @ (inverse @ (inverse @ X1)) @
% 67.10/14.95 (inverse @ (multiply @ (inverse @ X2) @ X1))))),
% 67.10/14.95 inference('sup+', [status(thm)],
% 67.10/14.95 [zip_derived_cl8483, zip_derived_cl11613])).
% 67.10/14.95 thf(zip_derived_cl12237, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ X0) @
% 67.10/14.95 (inverse @ (multiply @ (inverse @ X5) @ X5)))
% 67.10/14.95 = (multiply @ (inverse @ (inverse @ X1)) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X4) @ X4) @
% 67.10/14.95 (inverse @ X2))) @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X3) @ X3) @ X0)))) @
% 67.10/14.95 X2)) @
% 67.10/14.95 X1))))),
% 67.10/14.95 inference('sup+', [status(thm)],
% 67.10/14.95 [zip_derived_cl4535, zip_derived_cl11998])).
% 67.10/14.95 thf(zip_derived_cl4535, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 67.10/14.95 ((X1)
% 67.10/14.95 = (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X0) @ X0) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 67.10/14.95 (inverse @ X0))) @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X2) @ X2) @ X1)))) @
% 67.10/14.95 X0)))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl4341])).
% 67.10/14.95 thf(zip_derived_cl12290, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X5 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ X0) @
% 67.10/14.95 (inverse @ (multiply @ (inverse @ X5) @ X5)))
% 67.10/14.95 = (multiply @ (inverse @ (inverse @ X1)) @
% 67.10/14.95 (inverse @ (multiply @ X0 @ X1))))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl12237, zip_derived_cl4535])).
% 67.10/14.95 thf(zip_derived_cl35, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 67.10/14.95 (multiply @ X3 @ (inverse @ (multiply @ X0 @ X2))))
% 67.10/14.95 = (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1))) @
% 67.10/14.95 X0))) @
% 67.10/14.95 X1))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl13])).
% 67.10/14.95 thf(zip_derived_cl12407, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ (multiply @ X4 @ (inverse @ X2))) @
% 67.10/14.95 (multiply @ X4 @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ (inverse @ X3) @ X3)) @ X2))))
% 67.10/14.95 = (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (inverse @ (inverse @ X0)) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 67.10/14.95 (inverse @ X1)) @
% 67.10/14.95 X0))))) @
% 67.10/14.95 X1))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl12290, zip_derived_cl35])).
% 67.10/14.95 thf(zip_derived_cl3815, plain,
% 67.10/14.95 (![X1 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 67.10/14.95 ((multiply @ X5 @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X5 @ (inverse @ X4))) @ X3))) @
% 67.10/14.95 X4)))
% 67.10/14.95 = (X3))),
% 67.10/14.95 inference('demod', [status(thm)], [zip_derived_cl3755, zip_derived_cl0])).
% 67.10/14.95 thf(zip_derived_cl8483, plain,
% 67.10/14.95 (![X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ X1) @ X1) = (multiply @ (inverse @ X2) @ X2))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl8372, zip_derived_cl4277, zip_derived_cl4350])).
% 67.10/14.95 thf(zip_derived_cl8680, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 67.10/14.95 (inverse @ (multiply @ (inverse @ X0) @ X0))) @
% 67.10/14.95 X1) = (X1))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl8483, zip_derived_cl4352])).
% 67.10/14.95 thf(zip_derived_cl1241, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ (multiply @ X1 @ X2)) @ (multiply @ X1 @ X0))
% 67.10/14.95 = (multiply @ (inverse @ (multiply @ X3 @ X2)) @
% 67.10/14.95 (multiply @ X3 @ X0)))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl1086, zip_derived_cl1086])).
% 67.10/14.95 thf(zip_derived_cl8896, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 67.10/14.95 ((multiply @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X4) @ X4) @
% 67.10/14.95 (inverse @ (multiply @ (inverse @ X3) @ X3))) @
% 67.10/14.95 X2)) @
% 67.10/14.95 X0)
% 67.10/14.95 = (multiply @ (inverse @ (multiply @ X1 @ X2)) @
% 67.10/14.95 (multiply @ X1 @ X0)))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl8680, zip_derived_cl1241])).
% 67.10/14.95 thf(zip_derived_cl8680, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 67.10/14.95 (inverse @ (multiply @ (inverse @ X0) @ X0))) @
% 67.10/14.95 X1) = (X1))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl8483, zip_derived_cl4352])).
% 67.10/14.95 thf(zip_derived_cl9048, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ X2) @ X0)
% 67.10/14.95 = (multiply @ (inverse @ (multiply @ X1 @ X2)) @
% 67.10/14.95 (multiply @ X1 @ X0)))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl8896, zip_derived_cl8680])).
% 67.10/14.95 thf(zip_derived_cl9251, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ X2) @ X1)
% 67.10/14.95 = (multiply @ (inverse @ (multiply @ (inverse @ X0) @ X0)) @
% 67.10/14.95 (multiply @ (inverse @ X2) @ X1)))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl8483, zip_derived_cl9048])).
% 67.10/14.95 thf(zip_derived_cl9510, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ X2) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (inverse @ (multiply @ (inverse @ X2) @ (inverse @ X1))) @ X0))) @
% 67.10/14.95 X1)))
% 67.10/14.95 = (multiply @ (inverse @ (multiply @ (inverse @ X4) @ X4)) @ X0))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl3815, zip_derived_cl9251])).
% 67.10/14.95 thf(zip_derived_cl3815, plain,
% 67.10/14.95 (![X1 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 67.10/14.95 ((multiply @ X5 @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X5 @ (inverse @ X4))) @ X3))) @
% 67.10/14.95 X4)))
% 67.10/14.95 = (X3))),
% 67.10/14.95 inference('demod', [status(thm)], [zip_derived_cl3755, zip_derived_cl0])).
% 67.10/14.95 thf(zip_derived_cl9547, plain,
% 67.10/14.95 (![X0 : $i, X4 : $i]:
% 67.10/14.95 ((X0) = (multiply @ (inverse @ (multiply @ (inverse @ X4) @ X4)) @ X0))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl9510, zip_derived_cl3815])).
% 67.10/14.95 thf(zip_derived_cl9048, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ X2) @ X0)
% 67.10/14.95 = (multiply @ (inverse @ (multiply @ X1 @ X2)) @
% 67.10/14.95 (multiply @ X1 @ X0)))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl8896, zip_derived_cl8680])).
% 67.10/14.95 thf(zip_derived_cl8483, plain,
% 67.10/14.95 (![X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ X1) @ X1) = (multiply @ (inverse @ X2) @ X2))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl8372, zip_derived_cl4277, zip_derived_cl4350])).
% 67.10/14.95 thf(zip_derived_cl9090, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ (inverse @ X0)) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1)) @
% 67.10/14.95 X0)))
% 67.10/14.95 = (X1))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl8940, zip_derived_cl8680])).
% 67.10/14.95 thf(zip_derived_cl12538, plain,
% 67.10/14.95 (![X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ X2) @ X2)
% 67.10/14.95 = (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X1) @ X1) @ (inverse @ X1)) @
% 67.10/14.95 X1))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl12407, zip_derived_cl9547, zip_derived_cl9048,
% 67.10/14.95 zip_derived_cl8483, zip_derived_cl9090])).
% 67.10/14.95 thf(zip_derived_cl9090, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ (inverse @ X0)) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1)) @
% 67.10/14.95 X0)))
% 67.10/14.95 = (X1))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl8940, zip_derived_cl8680])).
% 67.10/14.95 thf(zip_derived_cl12589, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ (inverse @ X1)) @
% 67.10/14.95 (inverse @ (multiply @ (inverse @ X0) @ X0))) = (X1))),
% 67.10/14.95 inference('sup+', [status(thm)],
% 67.10/14.95 [zip_derived_cl12538, zip_derived_cl9090])).
% 67.10/14.95 thf(zip_derived_cl9092, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X4 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X4) @ X4) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (inverse @ (inverse @ X0)) @
% 67.10/14.95 (inverse @ (multiply @ X1 @ X0)))))
% 67.10/14.95 = (X1))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl8942, zip_derived_cl8680])).
% 67.10/14.95 thf(zip_derived_cl12908, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X1) @ X1) @ (inverse @ X0))
% 67.10/14.95 = (inverse @ X0))),
% 67.10/14.95 inference('sup+', [status(thm)],
% 67.10/14.95 [zip_derived_cl12589, zip_derived_cl9092])).
% 67.10/14.95 thf(zip_derived_cl13000, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X3) @ X3) @ X0)
% 67.10/14.95 = (inverse @
% 67.10/14.95 (multiply @ (inverse @ (inverse @ X1)) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X2) @ X2) @ X0) @ X1)))))),
% 67.10/14.95 inference('sup+', [status(thm)],
% 67.10/14.95 [zip_derived_cl9089, zip_derived_cl12908])).
% 67.10/14.95 thf(zip_derived_cl9089, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((X1)
% 67.10/14.95 = (inverse @
% 67.10/14.95 (multiply @ (inverse @ (inverse @ X0)) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X2) @ X2) @ X1) @ X0)))))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl8939, zip_derived_cl8680])).
% 67.10/14.95 thf(zip_derived_cl13016, plain,
% 67.10/14.95 (![X0 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X3) @ X3) @ X0) = (X0))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl13000, zip_derived_cl9089])).
% 67.10/14.95 thf(zip_derived_cl13036, plain,
% 67.10/14.95 ((((a2) != (a2))
% 67.10/14.95 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 67.10/14.95 != (multiply @ a3 @ (multiply @ b3 @ c3))))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl8880, zip_derived_cl13016])).
% 67.10/14.95 thf(zip_derived_cl13037, plain,
% 67.10/14.95 (((multiply @ (multiply @ a3 @ b3) @ c3)
% 67.10/14.95 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 67.10/14.95 inference('simplify', [status(thm)], [zip_derived_cl13036])).
% 67.10/14.95 thf(zip_derived_cl8483, plain,
% 67.10/14.95 (![X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ X1) @ X1) = (multiply @ (inverse @ X2) @ X2))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl8372, zip_derived_cl4277, zip_derived_cl4350])).
% 67.10/14.95 thf(zip_derived_cl9048, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ X2) @ X0)
% 67.10/14.95 = (multiply @ (inverse @ (multiply @ X1 @ X2)) @
% 67.10/14.95 (multiply @ X1 @ X0)))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl8896, zip_derived_cl8680])).
% 67.10/14.95 thf(zip_derived_cl9221, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ X2) @ X1)
% 67.10/14.95 = (multiply @ (inverse @ (multiply @ (inverse @ X1) @ X2)) @
% 67.10/14.95 (multiply @ (inverse @ X0) @ X0)))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl8483, zip_derived_cl9048])).
% 67.10/14.95 thf(zip_derived_cl4275, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X0) @ X0) @ X1)
% 67.10/14.95 = (multiply @ (multiply @ (inverse @ X3) @ X3) @ X1))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl4120, zip_derived_cl1561])).
% 67.10/14.95 thf(zip_derived_cl3815, plain,
% 67.10/14.95 (![X1 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 67.10/14.95 ((multiply @ X5 @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X5 @ (inverse @ X4))) @ X3))) @
% 67.10/14.95 X4)))
% 67.10/14.95 = (X3))),
% 67.10/14.95 inference('demod', [status(thm)], [zip_derived_cl3755, zip_derived_cl0])).
% 67.10/14.95 thf(zip_derived_cl4329, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X3) @ X3) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X4) @ X4) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X1) @ X1) @ (inverse @ X0))) @
% 67.10/14.95 X2))) @
% 67.10/14.95 X0)))
% 67.10/14.95 = (X2))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl4275, zip_derived_cl3815])).
% 67.10/14.95 thf(zip_derived_cl12908, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X1) @ X1) @ (inverse @ X0))
% 67.10/14.95 = (inverse @ X0))),
% 67.10/14.95 inference('sup+', [status(thm)],
% 67.10/14.95 [zip_derived_cl12589, zip_derived_cl9092])).
% 67.10/14.95 thf(zip_derived_cl12908, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X1) @ X1) @ (inverse @ X0))
% 67.10/14.95 = (inverse @ X0))),
% 67.10/14.95 inference('sup+', [status(thm)],
% 67.10/14.95 [zip_derived_cl12589, zip_derived_cl9092])).
% 67.10/14.95 thf(zip_derived_cl12908, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X1) @ X1) @ (inverse @ X0))
% 67.10/14.95 = (inverse @ X0))),
% 67.10/14.95 inference('sup+', [status(thm)],
% 67.10/14.95 [zip_derived_cl12589, zip_derived_cl9092])).
% 67.10/14.95 thf(zip_derived_cl12959, plain,
% 67.10/14.95 (![X0 : $i, X2 : $i]:
% 67.10/14.95 ((inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (inverse @ (multiply @ (inverse @ (inverse @ X0)) @ X2)) @ X0))
% 67.10/14.95 = (X2))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl4329, zip_derived_cl12908, zip_derived_cl12908,
% 67.10/14.95 zip_derived_cl12908])).
% 67.10/14.95 thf(zip_derived_cl13182, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i]:
% 67.10/14.95 ((inverse @
% 67.10/14.95 (multiply @ (inverse @ X1) @
% 67.10/14.95 (inverse @ (multiply @ (inverse @ X0) @ X0))))
% 67.10/14.95 = (X1))),
% 67.10/14.95 inference('sup+', [status(thm)],
% 67.10/14.95 [zip_derived_cl9221, zip_derived_cl12959])).
% 67.10/14.95 thf(zip_derived_cl9221, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ X2) @ X1)
% 67.10/14.95 = (multiply @ (inverse @ (multiply @ (inverse @ X1) @ X2)) @
% 67.10/14.95 (multiply @ (inverse @ X0) @ X0)))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl8483, zip_derived_cl9048])).
% 67.10/14.95 thf(zip_derived_cl13531, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @
% 67.10/14.95 (inverse @ (inverse @ (multiply @ (inverse @ X2) @ X2))) @ X0)
% 67.10/14.95 = (multiply @ X0 @ (multiply @ (inverse @ X1) @ X1)))),
% 67.10/14.95 inference('sup+', [status(thm)],
% 67.10/14.95 [zip_derived_cl13182, zip_derived_cl9221])).
% 67.10/14.95 thf(zip_derived_cl4826, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X4) @ X4) @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @
% 67.10/14.95 (inverse @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X3) @ X3) @ (inverse @ X0))) @
% 67.10/14.95 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 67.10/14.95 (inverse @ (multiply @ X1 @ X0))))))
% 67.10/14.95 = (X1))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl4275, zip_derived_cl4350])).
% 67.10/14.95 thf(zip_derived_cl12908, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X1) @ X1) @ (inverse @ X0))
% 67.10/14.95 = (inverse @ X0))),
% 67.10/14.95 inference('sup+', [status(thm)],
% 67.10/14.95 [zip_derived_cl12589, zip_derived_cl9092])).
% 67.10/14.95 thf(zip_derived_cl12908, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X1) @ X1) @ (inverse @ X0))
% 67.10/14.95 = (inverse @ X0))),
% 67.10/14.95 inference('sup+', [status(thm)],
% 67.10/14.95 [zip_derived_cl12589, zip_derived_cl9092])).
% 67.10/14.95 thf(zip_derived_cl12908, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X1) @ X1) @ (inverse @ X0))
% 67.10/14.95 = (inverse @ X0))),
% 67.10/14.95 inference('sup+', [status(thm)],
% 67.10/14.95 [zip_derived_cl12589, zip_derived_cl9092])).
% 67.10/14.95 thf(zip_derived_cl12966, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i]:
% 67.10/14.95 ((inverse @
% 67.10/14.95 (multiply @ (inverse @ (inverse @ X0)) @
% 67.10/14.95 (inverse @ (multiply @ X1 @ X0))))
% 67.10/14.95 = (X1))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl4826, zip_derived_cl12908, zip_derived_cl12908,
% 67.10/14.95 zip_derived_cl12908])).
% 67.10/14.95 thf(zip_derived_cl12589, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ (inverse @ X1)) @
% 67.10/14.95 (inverse @ (multiply @ (inverse @ X0) @ X0))) = (X1))),
% 67.10/14.95 inference('sup+', [status(thm)],
% 67.10/14.95 [zip_derived_cl12538, zip_derived_cl9090])).
% 67.10/14.95 thf(zip_derived_cl12290, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X5 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ X0) @
% 67.10/14.95 (inverse @ (multiply @ (inverse @ X5) @ X5)))
% 67.10/14.95 = (multiply @ (inverse @ (inverse @ X1)) @
% 67.10/14.95 (inverse @ (multiply @ X0 @ X1))))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl12237, zip_derived_cl4535])).
% 67.10/14.95 thf(zip_derived_cl12906, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i]:
% 67.10/14.95 ((X0)
% 67.10/14.95 = (multiply @ (inverse @ (inverse @ X1)) @
% 67.10/14.95 (inverse @ (multiply @ (inverse @ X0) @ X1))))),
% 67.10/14.95 inference('sup+', [status(thm)],
% 67.10/14.95 [zip_derived_cl12589, zip_derived_cl12290])).
% 67.10/14.95 thf(zip_derived_cl13285, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i]:
% 67.10/14.95 ((inverse @ X1)
% 67.10/14.95 = (multiply @
% 67.10/14.95 (inverse @ (inverse @ (inverse @ (multiply @ X0 @ X1)))) @ X0))),
% 67.10/14.95 inference('sup+', [status(thm)],
% 67.10/14.95 [zip_derived_cl12966, zip_derived_cl12906])).
% 67.10/14.95 thf(zip_derived_cl12906, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i]:
% 67.10/14.95 ((X0)
% 67.10/14.95 = (multiply @ (inverse @ (inverse @ X1)) @
% 67.10/14.95 (inverse @ (multiply @ (inverse @ X0) @ X1))))),
% 67.10/14.95 inference('sup+', [status(thm)],
% 67.10/14.95 [zip_derived_cl12589, zip_derived_cl12290])).
% 67.10/14.95 thf(zip_derived_cl13353, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i]:
% 67.10/14.95 ((inverse @ (inverse @ (multiply @ X1 @ X0)))
% 67.10/14.95 = (multiply @ (inverse @ (inverse @ X1)) @
% 67.10/14.95 (inverse @ (inverse @ X0))))),
% 67.10/14.95 inference('sup+', [status(thm)],
% 67.10/14.95 [zip_derived_cl13285, zip_derived_cl12906])).
% 67.10/14.95 thf(zip_derived_cl8483, plain,
% 67.10/14.95 (![X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ X1) @ X1) = (multiply @ (inverse @ X2) @ X2))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl8372, zip_derived_cl4277, zip_derived_cl4350])).
% 67.10/14.95 thf(zip_derived_cl13016, plain,
% 67.10/14.95 (![X0 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X3) @ X3) @ X0) = (X0))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl13000, zip_derived_cl9089])).
% 67.10/14.95 thf(zip_derived_cl13586, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i]:
% 67.10/14.95 ((X0) = (multiply @ X0 @ (multiply @ (inverse @ X1) @ X1)))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl13531, zip_derived_cl13353, zip_derived_cl8483,
% 67.10/14.95 zip_derived_cl13016])).
% 67.10/14.95 thf(zip_derived_cl9048, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ X2) @ X0)
% 67.10/14.95 = (multiply @ (inverse @ (multiply @ X1 @ X2)) @
% 67.10/14.95 (multiply @ X1 @ X0)))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl8896, zip_derived_cl8680])).
% 67.10/14.95 thf(zip_derived_cl13659, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ (multiply @ (inverse @ X2) @ X2)) @ X1)
% 67.10/14.95 = (multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)))),
% 67.10/14.95 inference('sup+', [status(thm)],
% 67.10/14.95 [zip_derived_cl13586, zip_derived_cl9048])).
% 67.10/14.95 thf(zip_derived_cl9547, plain,
% 67.10/14.95 (![X0 : $i, X4 : $i]:
% 67.10/14.95 ((X0) = (multiply @ (inverse @ (multiply @ (inverse @ X4) @ X4)) @ X0))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl9510, zip_derived_cl3815])).
% 67.10/14.95 thf(zip_derived_cl13728, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i]:
% 67.10/14.95 ((X1) = (multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl13659, zip_derived_cl9547])).
% 67.10/14.95 thf(zip_derived_cl13182, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i]:
% 67.10/14.95 ((inverse @
% 67.10/14.95 (multiply @ (inverse @ X1) @
% 67.10/14.95 (inverse @ (multiply @ (inverse @ X0) @ X0))))
% 67.10/14.95 = (X1))),
% 67.10/14.95 inference('sup+', [status(thm)],
% 67.10/14.95 [zip_derived_cl9221, zip_derived_cl12959])).
% 67.10/14.95 thf(zip_derived_cl1241, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ (multiply @ X1 @ X2)) @ (multiply @ X1 @ X0))
% 67.10/14.95 = (multiply @ (inverse @ (multiply @ X3 @ X2)) @
% 67.10/14.95 (multiply @ X3 @ X0)))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl1086, zip_derived_cl1086])).
% 67.10/14.95 thf(zip_derived_cl1241, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ (multiply @ X1 @ X2)) @ (multiply @ X1 @ X0))
% 67.10/14.95 = (multiply @ (inverse @ (multiply @ X3 @ X2)) @
% 67.10/14.95 (multiply @ X3 @ X0)))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl1086, zip_derived_cl1086])).
% 67.10/14.95 thf(zip_derived_cl1349, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 67.10/14.95 ((multiply @
% 67.10/14.95 (inverse @ (multiply @ (inverse @ (multiply @ X3 @ X2)) @ X5)) @
% 67.10/14.95 (multiply @ (inverse @ (multiply @ X1 @ X2)) @ (multiply @ X1 @ X0)))
% 67.10/14.95 = (multiply @ (inverse @ (multiply @ X4 @ X5)) @
% 67.10/14.95 (multiply @ X4 @ (multiply @ X3 @ X0))))),
% 67.10/14.95 inference('sup+', [status(thm)], [zip_derived_cl1241, zip_derived_cl1241])).
% 67.10/14.95 thf(zip_derived_cl9048, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ X2) @ X0)
% 67.10/14.95 = (multiply @ (inverse @ (multiply @ X1 @ X2)) @
% 67.10/14.95 (multiply @ X1 @ X0)))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl8896, zip_derived_cl8680])).
% 67.10/14.95 thf(zip_derived_cl9048, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ (inverse @ X2) @ X0)
% 67.10/14.95 = (multiply @ (inverse @ (multiply @ X1 @ X2)) @
% 67.10/14.95 (multiply @ X1 @ X0)))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl8896, zip_derived_cl8680])).
% 67.10/14.95 thf(zip_derived_cl9115, plain,
% 67.10/14.95 (![X0 : $i, X2 : $i, X3 : $i, X5 : $i]:
% 67.10/14.95 ((multiply @
% 67.10/14.95 (inverse @ (multiply @ (inverse @ (multiply @ X3 @ X2)) @ X5)) @
% 67.10/14.95 (multiply @ (inverse @ X2) @ X0))
% 67.10/14.95 = (multiply @ (inverse @ X5) @ (multiply @ X3 @ X0)))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl1349, zip_derived_cl9048, zip_derived_cl9048])).
% 67.10/14.95 thf(zip_derived_cl13523, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ X1 @ X0) @ (multiply @ (inverse @ X0) @ X2))
% 67.10/14.95 = (multiply @
% 67.10/14.95 (inverse @ (inverse @ (multiply @ (inverse @ X3) @ X3))) @
% 67.10/14.95 (multiply @ X1 @ X2)))),
% 67.10/14.95 inference('sup+', [status(thm)],
% 67.10/14.95 [zip_derived_cl13182, zip_derived_cl9115])).
% 67.10/14.95 thf(zip_derived_cl13353, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i]:
% 67.10/14.95 ((inverse @ (inverse @ (multiply @ X1 @ X0)))
% 67.10/14.95 = (multiply @ (inverse @ (inverse @ X1)) @
% 67.10/14.95 (inverse @ (inverse @ X0))))),
% 67.10/14.95 inference('sup+', [status(thm)],
% 67.10/14.95 [zip_derived_cl13285, zip_derived_cl12906])).
% 67.10/14.95 thf(zip_derived_cl13016, plain,
% 67.10/14.95 (![X0 : $i, X3 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ (inverse @ X3) @ X3) @ X0) = (X0))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl13000, zip_derived_cl9089])).
% 67.10/14.95 thf(zip_derived_cl13585, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ X1 @ X0) @ (multiply @ (inverse @ X0) @ X2))
% 67.10/14.95 = (multiply @ X1 @ X2))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl13523, zip_derived_cl13353, zip_derived_cl13016])).
% 67.10/14.95 thf(zip_derived_cl14585, plain,
% 67.10/14.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.10/14.95 ((multiply @ (multiply @ X2 @ X1) @ X0)
% 67.10/14.95 = (multiply @ X2 @ (multiply @ X1 @ X0)))),
% 67.10/14.95 inference('sup+', [status(thm)],
% 67.10/14.95 [zip_derived_cl13728, zip_derived_cl13585])).
% 67.10/14.95 thf(zip_derived_cl14643, plain,
% 67.10/14.95 (((multiply @ a3 @ (multiply @ b3 @ c3))
% 67.10/14.95 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 67.10/14.95 inference('demod', [status(thm)],
% 67.10/14.95 [zip_derived_cl13037, zip_derived_cl14585])).
% 67.10/14.95 thf(zip_derived_cl14644, plain, ($false),
% 67.10/14.95 inference('simplify', [status(thm)], [zip_derived_cl14643])).
% 67.10/14.95
% 67.10/14.95 % SZS output end Refutation
% 67.10/14.95
% 67.10/14.95
% 67.10/14.95 % Terminating...
% 67.47/15.12 % Runner terminated.
% 67.50/15.13 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------