%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP427-1 : TPTP v9.2.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.7LxdDLg3Kg true
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:36:25 PM UTC 2025
% Result : Unsatisfiable 101.35s 22.16s
% Output : Refutation 101.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP427-1 : TPTP v9.2.0. Released v2.6.0.
% 0.12/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.7LxdDLg3Kg true
% 0.13/0.36 % Computer : n001.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Wed Oct 1 14:17:38 EDT 2025
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Running portfolio for 300 s
% 0.13/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.36 % Number of cores: 8
% 0.13/0.36 % Python version: Python 3.6.8
% 0.13/0.37 % Running in FO mode
% 0.50/0.70 % Total configuration time : 435
% 0.50/0.70 % Estimated wc time : 1092
% 0.50/0.70 % Estimated cpu time (7 cpus) : 156.0
% 0.54/0.84 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.54/0.84 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.54/0.84 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.54/0.84 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.54/0.84 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.54/0.84 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.54/0.84 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 101.35/22.16 % Solved by fo/fo7.sh.
% 101.35/22.16 % done 746 iterations in 21.217s
% 101.35/22.16 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 101.35/22.16 % SZS output start Refutation
% 101.35/22.16 thf(inverse_type, type, inverse: $i > $i).
% 101.35/22.16 thf(a1_type, type, a1: $i).
% 101.35/22.16 thf(b1_type, type, b1: $i).
% 101.35/22.16 thf(multiply_type, type, multiply: $i > $i > $i).
% 101.35/22.16 thf(prove_these_axioms_1, conjecture,
% 101.35/22.16 (( multiply @ ( inverse @ a1 ) @ a1 ) =
% 101.35/22.16 ( multiply @ ( inverse @ b1 ) @ b1 ))).
% 101.35/22.16 thf(zf_stmt_0, negated_conjecture,
% 101.35/22.16 (( multiply @ ( inverse @ a1 ) @ a1 ) !=
% 101.35/22.16 ( multiply @ ( inverse @ b1 ) @ b1 )),
% 101.35/22.16 inference('cnf.neg', [status(esa)], [prove_these_axioms_1])).
% 101.35/22.16 thf(zip_derived_cl1, plain,
% 101.35/22.16 (((multiply @ (inverse @ a1) @ a1) != (multiply @ (inverse @ b1) @ b1))),
% 101.35/22.16 inference('cnf', [status(esa)], [zf_stmt_0])).
% 101.35/22.16 thf(single_axiom, axiom,
% 101.35/22.16 (( multiply @
% 101.35/22.16 A @
% 101.35/22.16 ( inverse @
% 101.35/22.16 ( multiply @
% 101.35/22.16 ( multiply @
% 101.35/22.16 ( inverse @
% 101.35/22.16 ( multiply @
% 101.35/22.16 ( inverse @ B ) @ ( multiply @ ( inverse @ A ) @ C ) ) ) @
% 101.35/22.16 D ) @
% 101.35/22.16 ( inverse @ ( multiply @ B @ D ) ) ) ) ) =
% 101.35/22.16 ( C ))).
% 101.35/22.16 thf(zip_derived_cl0, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.16 ((multiply @ X1 @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X1) @ X0))) @
% 101.35/22.16 X3) @
% 101.35/22.16 (inverse @ (multiply @ X2 @ X3)))))
% 101.35/22.16 = (X0))),
% 101.35/22.16 inference('cnf', [status(esa)], [single_axiom])).
% 101.35/22.16 thf(zip_derived_cl0, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.16 ((multiply @ X1 @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X1) @ X0))) @
% 101.35/22.16 X3) @
% 101.35/22.16 (inverse @ (multiply @ X2 @ X3)))))
% 101.35/22.16 = (X0))),
% 101.35/22.16 inference('cnf', [status(esa)], [single_axiom])).
% 101.35/22.16 thf(zip_derived_cl3, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 101.35/22.16 ((multiply @ X3 @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @ (inverse @ (multiply @ (inverse @ X5) @ X0)) @ X4) @
% 101.35/22.16 (inverse @ (multiply @ X5 @ X4)))))
% 101.35/22.16 = (inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @ (inverse @ X2) @
% 101.35/22.16 (multiply @ (inverse @ (inverse @ X3)) @ X0))) @
% 101.35/22.16 X1) @
% 101.35/22.16 (inverse @ (multiply @ X2 @ X1)))))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 101.35/22.16 thf(zip_derived_cl0, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.16 ((multiply @ X1 @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X1) @ X0))) @
% 101.35/22.16 X3) @
% 101.35/22.16 (inverse @ (multiply @ X2 @ X3)))))
% 101.35/22.16 = (X0))),
% 101.35/22.16 inference('cnf', [status(esa)], [single_axiom])).
% 101.35/22.16 thf(zip_derived_cl74, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.16 ((inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @ (inverse @ X1) @
% 101.35/22.16 (multiply @ (inverse @ (inverse @ X3)) @
% 101.35/22.16 (multiply @ (inverse @ X3) @ X2)))) @
% 101.35/22.16 X0) @
% 101.35/22.16 (inverse @ (multiply @ X1 @ X0))))
% 101.35/22.16 = (X2))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 101.35/22.16 thf(zip_derived_cl74, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.16 ((inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @ (inverse @ X1) @
% 101.35/22.16 (multiply @ (inverse @ (inverse @ X3)) @
% 101.35/22.16 (multiply @ (inverse @ X3) @ X2)))) @
% 101.35/22.16 X0) @
% 101.35/22.16 (inverse @ (multiply @ X1 @ X0))))
% 101.35/22.16 = (X2))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 101.35/22.16 thf(zip_derived_cl235, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 101.35/22.16 ((inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @ (inverse @ X3) @
% 101.35/22.16 (multiply @
% 101.35/22.16 (inverse @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @ (inverse @ X5) @
% 101.35/22.16 (multiply @ (inverse @ (inverse @ X6)) @
% 101.35/22.16 (multiply @ (inverse @ X6) @ X0)))) @
% 101.35/22.16 X4) @
% 101.35/22.16 (inverse @ (multiply @ X5 @ X4))))) @
% 101.35/22.16 (multiply @ X0 @ X1)))) @
% 101.35/22.16 X2) @
% 101.35/22.16 (inverse @ (multiply @ X3 @ X2))))
% 101.35/22.16 = (X1))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl74, zip_derived_cl74])).
% 101.35/22.16 thf(zip_derived_cl3, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 101.35/22.16 ((multiply @ X3 @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @ (inverse @ (multiply @ (inverse @ X5) @ X0)) @ X4) @
% 101.35/22.16 (inverse @ (multiply @ X5 @ X4)))))
% 101.35/22.16 = (inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @ (inverse @ X2) @
% 101.35/22.16 (multiply @ (inverse @ (inverse @ X3)) @ X0))) @
% 101.35/22.16 X1) @
% 101.35/22.16 (inverse @ (multiply @ X2 @ X1)))))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 101.35/22.16 thf(zip_derived_cl0, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.16 ((multiply @ X1 @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X1) @ X0))) @
% 101.35/22.16 X3) @
% 101.35/22.16 (inverse @ (multiply @ X2 @ X3)))))
% 101.35/22.16 = (X0))),
% 101.35/22.16 inference('cnf', [status(esa)], [single_axiom])).
% 101.35/22.16 thf(zip_derived_cl246, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.16 ((inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @ (inverse @ X3) @
% 101.35/22.16 (multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)))) @
% 101.35/22.16 X2) @
% 101.35/22.16 (inverse @ (multiply @ X3 @ X2))))
% 101.35/22.16 = (X1))),
% 101.35/22.16 inference('demod', [status(thm)],
% 101.35/22.16 [zip_derived_cl235, zip_derived_cl3, zip_derived_cl0])).
% 101.35/22.16 thf(zip_derived_cl246, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.16 ((inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @ (inverse @ X3) @
% 101.35/22.16 (multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)))) @
% 101.35/22.16 X2) @
% 101.35/22.16 (inverse @ (multiply @ X3 @ X2))))
% 101.35/22.16 = (X1))),
% 101.35/22.16 inference('demod', [status(thm)],
% 101.35/22.16 [zip_derived_cl235, zip_derived_cl3, zip_derived_cl0])).
% 101.35/22.16 thf(zip_derived_cl3, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 101.35/22.16 ((multiply @ X3 @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @ (inverse @ (multiply @ (inverse @ X5) @ X0)) @ X4) @
% 101.35/22.16 (inverse @ (multiply @ X5 @ X4)))))
% 101.35/22.16 = (inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @ (inverse @ X2) @
% 101.35/22.16 (multiply @ (inverse @ (inverse @ X3)) @ X0))) @
% 101.35/22.16 X1) @
% 101.35/22.16 (inverse @ (multiply @ X2 @ X1)))))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 101.35/22.16 thf(zip_derived_cl0, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.16 ((multiply @ X1 @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X1) @ X0))) @
% 101.35/22.16 X3) @
% 101.35/22.16 (inverse @ (multiply @ X2 @ X3)))))
% 101.35/22.16 = (X0))),
% 101.35/22.16 inference('cnf', [status(esa)], [single_axiom])).
% 101.35/22.16 thf(zip_derived_cl64, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.16 ((multiply @ (inverse @ X3) @
% 101.35/22.16 (multiply @ X3 @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @ (inverse @ (multiply @ (inverse @ X1) @ X2)) @ X0) @
% 101.35/22.16 (inverse @ (multiply @ X1 @ X0))))))
% 101.35/22.16 = (X2))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 101.35/22.16 thf(zip_derived_cl74, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.16 ((inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @ (inverse @ X1) @
% 101.35/22.16 (multiply @ (inverse @ (inverse @ X3)) @
% 101.35/22.16 (multiply @ (inverse @ X3) @ X2)))) @
% 101.35/22.16 X0) @
% 101.35/22.16 (inverse @ (multiply @ X1 @ X0))))
% 101.35/22.16 = (X2))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 101.35/22.16 thf(zip_derived_cl64, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.16 ((multiply @ (inverse @ X3) @
% 101.35/22.16 (multiply @ X3 @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @ (inverse @ (multiply @ (inverse @ X1) @ X2)) @ X0) @
% 101.35/22.16 (inverse @ (multiply @ X1 @ X0))))))
% 101.35/22.16 = (X2))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 101.35/22.16 thf(zip_derived_cl215, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X4 : $i]:
% 101.35/22.16 ((multiply @ (inverse @ X4) @ (multiply @ X4 @ X0))
% 101.35/22.16 = (multiply @ (inverse @ (inverse @ X1)) @
% 101.35/22.16 (multiply @ (inverse @ X1) @ X0)))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl74, zip_derived_cl64])).
% 101.35/22.16 thf(zip_derived_cl215, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X4 : $i]:
% 101.35/22.16 ((multiply @ (inverse @ X4) @ (multiply @ X4 @ X0))
% 101.35/22.16 = (multiply @ (inverse @ (inverse @ X1)) @
% 101.35/22.16 (multiply @ (inverse @ X1) @ X0)))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl74, zip_derived_cl64])).
% 101.35/22.16 thf(zip_derived_cl281, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i]:
% 101.35/22.16 ((multiply @ (inverse @ X2) @ (multiply @ X2 @ X0))
% 101.35/22.16 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl215, zip_derived_cl215])).
% 101.35/22.16 thf(zip_derived_cl281, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i]:
% 101.35/22.16 ((multiply @ (inverse @ X2) @ (multiply @ X2 @ X0))
% 101.35/22.16 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl215, zip_derived_cl215])).
% 101.35/22.16 thf(zip_derived_cl0, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.16 ((multiply @ X1 @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X1) @ X0))) @
% 101.35/22.16 X3) @
% 101.35/22.16 (inverse @ (multiply @ X2 @ X3)))))
% 101.35/22.16 = (X0))),
% 101.35/22.16 inference('cnf', [status(esa)], [single_axiom])).
% 101.35/22.16 thf(zip_derived_cl380, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.16 ((multiply @ X3 @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @
% 101.35/22.16 (inverse @ (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0))) @
% 101.35/22.16 X2) @
% 101.35/22.16 (inverse @ (multiply @ (inverse @ X3) @ X2)))))
% 101.35/22.16 = (X0))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl281, zip_derived_cl0])).
% 101.35/22.16 thf(zip_derived_cl711, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 101.35/22.16 ((multiply @ X3 @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @
% 101.35/22.16 (inverse @ (multiply @ (inverse @ X4) @ (multiply @ X4 @ X2))) @
% 101.35/22.16 (multiply @ X3 @ X0)) @
% 101.35/22.16 (inverse @ (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0))))))
% 101.35/22.16 = (X2))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl281, zip_derived_cl380])).
% 101.35/22.16 thf(zip_derived_cl5478, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 101.35/22.16 ((multiply @ (multiply @ (inverse @ X5) @ (multiply @ X5 @ X1)) @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @ X0 @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @ (inverse @ X4) @
% 101.35/22.16 (multiply @ X4 @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @ (inverse @ (multiply @ (inverse @ X3) @ X0)) @ X2) @
% 101.35/22.16 (inverse @ (multiply @ X3 @ X2))))))))))
% 101.35/22.16 = (X1))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl64, zip_derived_cl711])).
% 101.35/22.16 thf(zip_derived_cl64, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.16 ((multiply @ (inverse @ X3) @
% 101.35/22.16 (multiply @ X3 @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @ (inverse @ (multiply @ (inverse @ X1) @ X2)) @ X0) @
% 101.35/22.16 (inverse @ (multiply @ X1 @ X0))))))
% 101.35/22.16 = (X2))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 101.35/22.16 thf(zip_derived_cl5571, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X5 : $i]:
% 101.35/22.16 ((multiply @ (multiply @ (inverse @ X5) @ (multiply @ X5 @ X1)) @
% 101.35/22.16 (inverse @ (multiply @ X0 @ (inverse @ X0)))) = (X1))),
% 101.35/22.16 inference('demod', [status(thm)], [zip_derived_cl5478, zip_derived_cl64])).
% 101.35/22.16 thf(zip_derived_cl281, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i]:
% 101.35/22.16 ((multiply @ (inverse @ X2) @ (multiply @ X2 @ X0))
% 101.35/22.16 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl215, zip_derived_cl215])).
% 101.35/22.16 thf(zip_derived_cl281, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i]:
% 101.35/22.16 ((multiply @ (inverse @ X2) @ (multiply @ X2 @ X0))
% 101.35/22.16 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl215, zip_derived_cl215])).
% 101.35/22.16 thf(zip_derived_cl362, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.16 ((multiply @ (inverse @ X3) @ (multiply @ X3 @ (multiply @ X2 @ X0)))
% 101.35/22.16 = (multiply @ (inverse @ (inverse @ X2)) @
% 101.35/22.16 (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0))))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl281, zip_derived_cl281])).
% 101.35/22.16 thf(zip_derived_cl5571, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X5 : $i]:
% 101.35/22.16 ((multiply @ (multiply @ (inverse @ X5) @ (multiply @ X5 @ X1)) @
% 101.35/22.16 (inverse @ (multiply @ X0 @ (inverse @ X0)))) = (X1))),
% 101.35/22.16 inference('demod', [status(thm)], [zip_derived_cl5478, zip_derived_cl64])).
% 101.35/22.16 thf(zip_derived_cl5657, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.16 ((multiply @
% 101.35/22.16 (multiply @ (inverse @ (inverse @ X2)) @
% 101.35/22.16 (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0))) @
% 101.35/22.16 (inverse @ (multiply @ X3 @ (inverse @ X3)))) = (multiply @ X2 @ X0))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl362, zip_derived_cl5571])).
% 101.35/22.16 thf(zip_derived_cl6411, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 101.35/22.16 ((multiply @
% 101.35/22.16 (multiply @ (inverse @ (inverse @ X2)) @
% 101.35/22.16 (multiply @
% 101.35/22.16 (inverse @ (multiply @ (inverse @ X4) @ (multiply @ X4 @ X0))) @
% 101.35/22.16 X0)) @
% 101.35/22.16 (inverse @ (multiply @ X3 @ (inverse @ X3))))
% 101.35/22.16 = (multiply @ X2 @ (inverse @ (multiply @ X1 @ (inverse @ X1)))))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl5571, zip_derived_cl5657])).
% 101.35/22.16 thf(zip_derived_cl5571, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X5 : $i]:
% 101.35/22.16 ((multiply @ (multiply @ (inverse @ X5) @ (multiply @ X5 @ X1)) @
% 101.35/22.16 (inverse @ (multiply @ X0 @ (inverse @ X0)))) = (X1))),
% 101.35/22.16 inference('demod', [status(thm)], [zip_derived_cl5478, zip_derived_cl64])).
% 101.35/22.16 thf(zip_derived_cl246, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.16 ((inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @ (inverse @ X3) @
% 101.35/22.16 (multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)))) @
% 101.35/22.16 X2) @
% 101.35/22.16 (inverse @ (multiply @ X3 @ X2))))
% 101.35/22.16 = (X1))),
% 101.35/22.16 inference('demod', [status(thm)],
% 101.35/22.16 [zip_derived_cl235, zip_derived_cl3, zip_derived_cl0])).
% 101.35/22.16 thf(zip_derived_cl64, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.16 ((multiply @ (inverse @ X3) @
% 101.35/22.16 (multiply @ X3 @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @ (inverse @ (multiply @ (inverse @ X1) @ X2)) @ X0) @
% 101.35/22.16 (inverse @ (multiply @ X1 @ X0))))))
% 101.35/22.16 = (X2))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 101.35/22.16 thf(zip_derived_cl0, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.16 ((multiply @ X1 @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X1) @ X0))) @
% 101.35/22.16 X3) @
% 101.35/22.16 (inverse @ (multiply @ X2 @ X3)))))
% 101.35/22.16 = (X0))),
% 101.35/22.16 inference('cnf', [status(esa)], [single_axiom])).
% 101.35/22.16 thf(zip_derived_cl153, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 101.35/22.16 ((multiply @ X4 @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @ (multiply @ (inverse @ X0) @ X3) @
% 101.35/22.16 (inverse @ (multiply @ (inverse @ X4) @ X3)))))
% 101.35/22.16 = (inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @ (inverse @ (multiply @ (inverse @ X2) @ X0)) @ X1) @
% 101.35/22.16 (inverse @ (multiply @ X2 @ X1)))))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl64, zip_derived_cl0])).
% 101.35/22.16 thf(zip_derived_cl362, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.16 ((multiply @ (inverse @ X3) @ (multiply @ X3 @ (multiply @ X2 @ X0)))
% 101.35/22.16 = (multiply @ (inverse @ (inverse @ X2)) @
% 101.35/22.16 (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0))))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl281, zip_derived_cl281])).
% 101.35/22.16 thf(zip_derived_cl902, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 101.35/22.16 ((multiply @ (inverse @ X6) @
% 101.35/22.16 (multiply @ X6 @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @ (inverse @ (multiply @ (inverse @ X1) @ X2)) @ X0) @
% 101.35/22.16 (inverse @ (multiply @ X1 @ X0))))))
% 101.35/22.16 = (multiply @ (inverse @ (inverse @ X4)) @
% 101.35/22.16 (multiply @ (inverse @ X5) @
% 101.35/22.16 (multiply @ X5 @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @ (multiply @ (inverse @ X2) @ X3) @
% 101.35/22.16 (inverse @ (multiply @ (inverse @ X4) @ X3))))))))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl153, zip_derived_cl362])).
% 101.35/22.16 thf(zip_derived_cl64, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.16 ((multiply @ (inverse @ X3) @
% 101.35/22.16 (multiply @ X3 @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @ (inverse @ (multiply @ (inverse @ X1) @ X2)) @ X0) @
% 101.35/22.16 (inverse @ (multiply @ X1 @ X0))))))
% 101.35/22.16 = (X2))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 101.35/22.16 thf(zip_derived_cl1023, plain,
% 101.35/22.16 (![X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 101.35/22.16 ((X2)
% 101.35/22.16 = (multiply @ (inverse @ (inverse @ X4)) @
% 101.35/22.16 (multiply @ (inverse @ X5) @
% 101.35/22.16 (multiply @ X5 @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @ (multiply @ (inverse @ X2) @ X3) @
% 101.35/22.16 (inverse @ (multiply @ (inverse @ X4) @ X3))))))))),
% 101.35/22.16 inference('demod', [status(thm)], [zip_derived_cl902, zip_derived_cl64])).
% 101.35/22.16 thf(zip_derived_cl2937, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 101.35/22.16 ((X5)
% 101.35/22.16 = (multiply @
% 101.35/22.16 (inverse @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @ (inverse @ X3) @
% 101.35/22.16 (multiply @ (inverse @ X4) @ (multiply @ X4 @ X0)))) @
% 101.35/22.16 X2) @
% 101.35/22.16 (inverse @ (multiply @ X3 @ X2))))) @
% 101.35/22.16 (multiply @ (inverse @ X6) @
% 101.35/22.16 (multiply @ X6 @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @ (multiply @ (inverse @ X5) @ X1) @
% 101.35/22.16 (inverse @ (multiply @ X0 @ X1))))))))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl246, zip_derived_cl1023])).
% 101.35/22.16 thf(zip_derived_cl246, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.16 ((inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @ (inverse @ X3) @
% 101.35/22.16 (multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)))) @
% 101.35/22.16 X2) @
% 101.35/22.16 (inverse @ (multiply @ X3 @ X2))))
% 101.35/22.16 = (X1))),
% 101.35/22.16 inference('demod', [status(thm)],
% 101.35/22.16 [zip_derived_cl235, zip_derived_cl3, zip_derived_cl0])).
% 101.35/22.16 thf(zip_derived_cl2988, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X5 : $i, X6 : $i]:
% 101.35/22.16 ((X5)
% 101.35/22.16 = (multiply @ (inverse @ X0) @
% 101.35/22.16 (multiply @ (inverse @ X6) @
% 101.35/22.16 (multiply @ X6 @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @ (multiply @ (inverse @ X5) @ X1) @
% 101.35/22.16 (inverse @ (multiply @ X0 @ X1))))))))),
% 101.35/22.16 inference('demod', [status(thm)], [zip_derived_cl2937, zip_derived_cl246])).
% 101.35/22.16 thf(zip_derived_cl5636, plain,
% 101.35/22.16 (![X0 : $i, X2 : $i, X3 : $i]:
% 101.35/22.16 ((X2)
% 101.35/22.16 = (multiply @ (inverse @ (inverse @ X2)) @
% 101.35/22.16 (multiply @
% 101.35/22.16 (inverse @ (multiply @ (inverse @ X3) @ (multiply @ X3 @ X0))) @
% 101.35/22.16 X0)))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl5571, zip_derived_cl2988])).
% 101.35/22.16 thf(zip_derived_cl6456, plain,
% 101.35/22.16 (![X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.16 ((multiply @ X2 @ (inverse @ (multiply @ X3 @ (inverse @ X3))))
% 101.35/22.16 = (multiply @ X2 @ (inverse @ (multiply @ X1 @ (inverse @ X1)))))),
% 101.35/22.16 inference('demod', [status(thm)],
% 101.35/22.16 [zip_derived_cl6411, zip_derived_cl5636])).
% 101.35/22.16 thf(zip_derived_cl153, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 101.35/22.16 ((multiply @ X4 @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @ (multiply @ (inverse @ X0) @ X3) @
% 101.35/22.16 (inverse @ (multiply @ (inverse @ X4) @ X3)))))
% 101.35/22.16 = (inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @ (inverse @ (multiply @ (inverse @ X2) @ X0)) @ X1) @
% 101.35/22.16 (inverse @ (multiply @ X2 @ X1)))))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl64, zip_derived_cl0])).
% 101.35/22.16 thf(zip_derived_cl64, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.16 ((multiply @ (inverse @ X3) @
% 101.35/22.16 (multiply @ X3 @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @ (inverse @ (multiply @ (inverse @ X1) @ X2)) @ X0) @
% 101.35/22.16 (inverse @ (multiply @ X1 @ X0))))))
% 101.35/22.16 = (X2))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 101.35/22.16 thf(zip_derived_cl884, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X5 : $i]:
% 101.35/22.16 ((multiply @ (inverse @ X5) @
% 101.35/22.16 (multiply @ X5 @
% 101.35/22.16 (multiply @ X1 @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @ (multiply @ (inverse @ X2) @ X0) @
% 101.35/22.16 (inverse @ (multiply @ (inverse @ X1) @ X0)))))))
% 101.35/22.16 = (X2))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl153, zip_derived_cl64])).
% 101.35/22.16 thf(zip_derived_cl6513, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X3 : $i]:
% 101.35/22.16 ((multiply @ (inverse @ X3) @
% 101.35/22.16 (multiply @ X3 @
% 101.35/22.16 (multiply @ X1 @ (inverse @ (multiply @ X0 @ (inverse @ X0))))))
% 101.35/22.16 = (X1))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl6456, zip_derived_cl884])).
% 101.35/22.16 thf(zip_derived_cl246, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.16 ((inverse @
% 101.35/22.16 (multiply @
% 101.35/22.16 (multiply @
% 101.35/22.16 (inverse @
% 101.35/22.16 (multiply @ (inverse @ X3) @
% 101.35/22.16 (multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)))) @
% 101.35/22.16 X2) @
% 101.35/22.16 (inverse @ (multiply @ X3 @ X2))))
% 101.35/22.16 = (X1))),
% 101.35/22.16 inference('demod', [status(thm)],
% 101.35/22.16 [zip_derived_cl235, zip_derived_cl3, zip_derived_cl0])).
% 101.35/22.16 thf(zip_derived_cl6865, plain,
% 101.35/22.16 (![X0 : $i, X1 : $i, X2 : $i]:
% 101.35/22.16 ((inverse @
% 101.35/22.16 (multiply @ (multiply @ (inverse @ X0) @ X2) @
% 101.35/22.16 (inverse @ (multiply @ (inverse @ X0) @ X2))))
% 101.35/22.16 = (inverse @ (multiply @ X1 @ (inverse @ X1))))),
% 101.35/22.16 inference('sup+', [status(thm)], [zip_derived_cl6513, zip_derived_cl246])).
% 101.35/22.16 thf(zip_derived_cl884, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i, X5 : $i]:
% 101.35/22.17 ((multiply @ (inverse @ X5) @
% 101.35/22.17 (multiply @ X5 @
% 101.35/22.17 (multiply @ X1 @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @ (multiply @ (inverse @ X2) @ X0) @
% 101.35/22.17 (inverse @ (multiply @ (inverse @ X1) @ X0)))))))
% 101.35/22.17 = (X2))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl153, zip_derived_cl64])).
% 101.35/22.17 thf(zip_derived_cl7577, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 101.35/22.17 ((multiply @ (inverse @ X5) @
% 101.35/22.17 (multiply @ X5 @
% 101.35/22.17 (multiply @ X4 @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @
% 101.35/22.17 (multiply @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @ (multiply @ (inverse @ X1) @ X0) @
% 101.35/22.17 (inverse @ (multiply @ (inverse @ X1) @ X0)))) @
% 101.35/22.17 X3) @
% 101.35/22.17 (inverse @ (multiply @ (inverse @ X4) @ X3)))))))
% 101.35/22.17 = (multiply @ X2 @ (inverse @ X2)))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl6865, zip_derived_cl884])).
% 101.35/22.17 thf(zip_derived_cl6865, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i]:
% 101.35/22.17 ((inverse @
% 101.35/22.17 (multiply @ (multiply @ (inverse @ X0) @ X2) @
% 101.35/22.17 (inverse @ (multiply @ (inverse @ X0) @ X2))))
% 101.35/22.17 = (inverse @ (multiply @ X1 @ (inverse @ X1))))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl6513, zip_derived_cl246])).
% 101.35/22.17 thf(zip_derived_cl884, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i, X5 : $i]:
% 101.35/22.17 ((multiply @ (inverse @ X5) @
% 101.35/22.17 (multiply @ X5 @
% 101.35/22.17 (multiply @ X1 @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @ (multiply @ (inverse @ X2) @ X0) @
% 101.35/22.17 (inverse @ (multiply @ (inverse @ X1) @ X0)))))))
% 101.35/22.17 = (X2))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl153, zip_derived_cl64])).
% 101.35/22.17 thf(zip_derived_cl8002, plain,
% 101.35/22.17 (![X1 : $i, X2 : $i]:
% 101.35/22.17 ((multiply @ X1 @ (inverse @ X1)) = (multiply @ X2 @ (inverse @ X2)))),
% 101.35/22.17 inference('demod', [status(thm)],
% 101.35/22.17 [zip_derived_cl7577, zip_derived_cl6865, zip_derived_cl884])).
% 101.35/22.17 thf(zip_derived_cl281, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i]:
% 101.35/22.17 ((multiply @ (inverse @ X2) @ (multiply @ X2 @ X0))
% 101.35/22.17 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl215, zip_derived_cl215])).
% 101.35/22.17 thf(zip_derived_cl8145, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i]:
% 101.35/22.17 ((multiply @ (inverse @ X2) @ (multiply @ X2 @ (inverse @ X1)))
% 101.35/22.17 = (multiply @ (inverse @ X1) @ (multiply @ X0 @ (inverse @ X0))))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl8002, zip_derived_cl281])).
% 101.35/22.17 thf(zip_derived_cl9024, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 101.35/22.17 ((multiply @ (inverse @ X5) @ (multiply @ X5 @ X0))
% 101.35/22.17 = (multiply @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @
% 101.35/22.17 (multiply @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @ (inverse @ X3) @
% 101.35/22.17 (multiply @ (inverse @ X4) @ (multiply @ X4 @ X0)))) @
% 101.35/22.17 X2) @
% 101.35/22.17 (inverse @ (multiply @ X3 @ X2)))) @
% 101.35/22.17 (multiply @ X1 @ (inverse @ X1))))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl246, zip_derived_cl8145])).
% 101.35/22.17 thf(zip_derived_cl246, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.17 ((inverse @
% 101.35/22.17 (multiply @
% 101.35/22.17 (multiply @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @ (inverse @ X3) @
% 101.35/22.17 (multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)))) @
% 101.35/22.17 X2) @
% 101.35/22.17 (inverse @ (multiply @ X3 @ X2))))
% 101.35/22.17 = (X1))),
% 101.35/22.17 inference('demod', [status(thm)],
% 101.35/22.17 [zip_derived_cl235, zip_derived_cl3, zip_derived_cl0])).
% 101.35/22.17 thf(zip_derived_cl9075, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X5 : $i]:
% 101.35/22.17 ((multiply @ (inverse @ X5) @ (multiply @ X5 @ X0))
% 101.35/22.17 = (multiply @ X0 @ (multiply @ X1 @ (inverse @ X1))))),
% 101.35/22.17 inference('demod', [status(thm)], [zip_derived_cl9024, zip_derived_cl246])).
% 101.35/22.17 thf(zip_derived_cl6456, plain,
% 101.35/22.17 (![X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.17 ((multiply @ X2 @ (inverse @ (multiply @ X3 @ (inverse @ X3))))
% 101.35/22.17 = (multiply @ X2 @ (inverse @ (multiply @ X1 @ (inverse @ X1)))))),
% 101.35/22.17 inference('demod', [status(thm)],
% 101.35/22.17 [zip_derived_cl6411, zip_derived_cl5636])).
% 101.35/22.17 thf(zip_derived_cl153, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 101.35/22.17 ((multiply @ X4 @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @ (multiply @ (inverse @ X0) @ X3) @
% 101.35/22.17 (inverse @ (multiply @ (inverse @ X4) @ X3)))))
% 101.35/22.17 = (inverse @
% 101.35/22.17 (multiply @
% 101.35/22.17 (multiply @ (inverse @ (multiply @ (inverse @ X2) @ X0)) @ X1) @
% 101.35/22.17 (inverse @ (multiply @ X2 @ X1)))))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl64, zip_derived_cl0])).
% 101.35/22.17 thf(zip_derived_cl0, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.17 ((multiply @ X1 @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @
% 101.35/22.17 (multiply @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X1) @ X0))) @
% 101.35/22.17 X3) @
% 101.35/22.17 (inverse @ (multiply @ X2 @ X3)))))
% 101.35/22.17 = (X0))),
% 101.35/22.17 inference('cnf', [status(esa)], [single_axiom])).
% 101.35/22.17 thf(zip_derived_cl879, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.17 ((multiply @ X3 @
% 101.35/22.17 (multiply @ X1 @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @
% 101.35/22.17 (multiply @ (inverse @ (multiply @ (inverse @ X3) @ X2)) @ X0) @
% 101.35/22.17 (inverse @ (multiply @ (inverse @ X1) @ X0))))))
% 101.35/22.17 = (X2))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl153, zip_derived_cl0])).
% 101.35/22.17 thf(zip_derived_cl6514, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i]:
% 101.35/22.17 ((multiply @ X2 @
% 101.35/22.17 (multiply @ (multiply @ (inverse @ X2) @ X1) @
% 101.35/22.17 (inverse @ (multiply @ X0 @ (inverse @ X0)))))
% 101.35/22.17 = (X1))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl6456, zip_derived_cl879])).
% 101.35/22.17 thf(zip_derived_cl9557, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i]:
% 101.35/22.17 ((multiply @ (inverse @ X1) @ (multiply @ X1 @ X0))
% 101.35/22.17 = (inverse @ (inverse @ X0)))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl9075, zip_derived_cl6514])).
% 101.35/22.17 thf(zip_derived_cl9557, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i]:
% 101.35/22.17 ((multiply @ (inverse @ X1) @ (multiply @ X1 @ X0))
% 101.35/22.17 = (inverse @ (inverse @ X0)))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl9075, zip_derived_cl6514])).
% 101.35/22.17 thf(zip_derived_cl9981, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i]:
% 101.35/22.17 ((multiply @ (inverse @ X2) @ (multiply @ X2 @ (inverse @ X0)))
% 101.35/22.17 = (inverse @ (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0))))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl9557, zip_derived_cl9557])).
% 101.35/22.17 thf(zip_derived_cl6513, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X3 : $i]:
% 101.35/22.17 ((multiply @ (inverse @ X3) @
% 101.35/22.17 (multiply @ X3 @
% 101.35/22.17 (multiply @ X1 @ (inverse @ (multiply @ X0 @ (inverse @ X0))))))
% 101.35/22.17 = (X1))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl6456, zip_derived_cl884])).
% 101.35/22.17 thf(zip_derived_cl14516, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i]:
% 101.35/22.17 ((multiply @ (inverse @ (inverse @ X2)) @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @ (inverse @ X1) @
% 101.35/22.17 (multiply @ X1 @ (multiply @ X0 @ (inverse @ X0))))))
% 101.35/22.17 = (X2))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl9981, zip_derived_cl6513])).
% 101.35/22.17 thf(zip_derived_cl8002, plain,
% 101.35/22.17 (![X1 : $i, X2 : $i]:
% 101.35/22.17 ((multiply @ X1 @ (inverse @ X1)) = (multiply @ X2 @ (inverse @ X2)))),
% 101.35/22.17 inference('demod', [status(thm)],
% 101.35/22.17 [zip_derived_cl7577, zip_derived_cl6865, zip_derived_cl884])).
% 101.35/22.17 thf(zip_derived_cl6513, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X3 : $i]:
% 101.35/22.17 ((multiply @ (inverse @ X3) @
% 101.35/22.17 (multiply @ X3 @
% 101.35/22.17 (multiply @ X1 @ (inverse @ (multiply @ X0 @ (inverse @ X0))))))
% 101.35/22.17 = (X1))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl6456, zip_derived_cl884])).
% 101.35/22.17 thf(zip_derived_cl8188, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i]:
% 101.35/22.17 ((multiply @ (inverse @ X2) @
% 101.35/22.17 (multiply @ X2 @ (multiply @ X0 @ (inverse @ X0))))
% 101.35/22.17 = (multiply @ X1 @ (inverse @ X1)))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl8002, zip_derived_cl6513])).
% 101.35/22.17 thf(zip_derived_cl14863, plain,
% 101.35/22.17 (![X1 : $i, X2 : $i]:
% 101.35/22.17 ((multiply @ (inverse @ (inverse @ X2)) @
% 101.35/22.17 (inverse @ (multiply @ X1 @ (inverse @ X1)))) = (X2))),
% 101.35/22.17 inference('demod', [status(thm)],
% 101.35/22.17 [zip_derived_cl14516, zip_derived_cl8188])).
% 101.35/22.17 thf(zip_derived_cl362, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.17 ((multiply @ (inverse @ X3) @ (multiply @ X3 @ (multiply @ X2 @ X0)))
% 101.35/22.17 = (multiply @ (inverse @ (inverse @ X2)) @
% 101.35/22.17 (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0))))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl281, zip_derived_cl281])).
% 101.35/22.17 thf(zip_derived_cl3, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 101.35/22.17 ((multiply @ X3 @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @
% 101.35/22.17 (multiply @ (inverse @ (multiply @ (inverse @ X5) @ X0)) @ X4) @
% 101.35/22.17 (inverse @ (multiply @ X5 @ X4)))))
% 101.35/22.17 = (inverse @
% 101.35/22.17 (multiply @
% 101.35/22.17 (multiply @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @ (inverse @ X2) @
% 101.35/22.17 (multiply @ (inverse @ (inverse @ X3)) @ X0))) @
% 101.35/22.17 X1) @
% 101.35/22.17 (inverse @ (multiply @ X2 @ X1)))))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 101.35/22.17 thf(zip_derived_cl479, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 101.35/22.17 ((multiply @ X4 @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @
% 101.35/22.17 (multiply @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @ (inverse @ X6) @ (multiply @ (inverse @ X4) @ X0))) @
% 101.35/22.17 X5) @
% 101.35/22.17 (inverse @ (multiply @ X6 @ X5)))))
% 101.35/22.17 = (inverse @
% 101.35/22.17 (multiply @
% 101.35/22.17 (multiply @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @ (inverse @ X2) @
% 101.35/22.17 (multiply @ X2 @ (multiply @ X1 @ X0)))) @
% 101.35/22.17 X3) @
% 101.35/22.17 (inverse @ (multiply @ (inverse @ X1) @ X3)))))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl362, zip_derived_cl3])).
% 101.35/22.17 thf(zip_derived_cl0, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.17 ((multiply @ X1 @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @
% 101.35/22.17 (multiply @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X1) @ X0))) @
% 101.35/22.17 X3) @
% 101.35/22.17 (inverse @ (multiply @ X2 @ X3)))))
% 101.35/22.17 = (X0))),
% 101.35/22.17 inference('cnf', [status(esa)], [single_axiom])).
% 101.35/22.17 thf(zip_derived_cl577, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.17 ((X0)
% 101.35/22.17 = (inverse @
% 101.35/22.17 (multiply @
% 101.35/22.17 (multiply @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @ (inverse @ X2) @
% 101.35/22.17 (multiply @ X2 @ (multiply @ X1 @ X0)))) @
% 101.35/22.17 X3) @
% 101.35/22.17 (inverse @ (multiply @ (inverse @ X1) @ X3)))))),
% 101.35/22.17 inference('demod', [status(thm)], [zip_derived_cl479, zip_derived_cl0])).
% 101.35/22.17 thf(zip_derived_cl14985, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.17 ((X2)
% 101.35/22.17 = (inverse @
% 101.35/22.17 (multiply @
% 101.35/22.17 (multiply @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @ (inverse @ X3) @
% 101.35/22.17 (multiply @ X3 @ (multiply @ (inverse @ X0) @ X2)))) @
% 101.35/22.17 (inverse @ (multiply @ X1 @ (inverse @ X1)))) @
% 101.35/22.17 (inverse @ X0))))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl14863, zip_derived_cl577])).
% 101.35/22.17 thf(zip_derived_cl9981, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i]:
% 101.35/22.17 ((multiply @ (inverse @ X2) @ (multiply @ X2 @ (inverse @ X0)))
% 101.35/22.17 = (inverse @ (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0))))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl9557, zip_derived_cl9557])).
% 101.35/22.17 thf(zip_derived_cl5571, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X5 : $i]:
% 101.35/22.17 ((multiply @ (multiply @ (inverse @ X5) @ (multiply @ X5 @ X1)) @
% 101.35/22.17 (inverse @ (multiply @ X0 @ (inverse @ X0)))) = (X1))),
% 101.35/22.17 inference('demod', [status(thm)], [zip_derived_cl5478, zip_derived_cl64])).
% 101.35/22.17 thf(zip_derived_cl15134, plain,
% 101.35/22.17 (![X0 : $i, X2 : $i]:
% 101.35/22.17 ((X2)
% 101.35/22.17 = (inverse @
% 101.35/22.17 (multiply @ (inverse @ (multiply @ (inverse @ X0) @ X2)) @
% 101.35/22.17 (inverse @ X0))))),
% 101.35/22.17 inference('demod', [status(thm)],
% 101.35/22.17 [zip_derived_cl14985, zip_derived_cl9981, zip_derived_cl5571])).
% 101.35/22.17 thf(zip_derived_cl15298, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 101.35/22.17 ((X4)
% 101.35/22.17 = (inverse @
% 101.35/22.17 (multiply @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @
% 101.35/22.17 (multiply @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @ (inverse @ X2) @
% 101.35/22.17 (multiply @ (inverse @ X3) @ (multiply @ X3 @ X0)))) @
% 101.35/22.17 X1) @
% 101.35/22.17 (inverse @ (multiply @ X2 @ X1)))) @
% 101.35/22.17 X4)) @
% 101.35/22.17 X0)))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl246, zip_derived_cl15134])).
% 101.35/22.17 thf(zip_derived_cl246, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.17 ((inverse @
% 101.35/22.17 (multiply @
% 101.35/22.17 (multiply @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @ (inverse @ X3) @
% 101.35/22.17 (multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)))) @
% 101.35/22.17 X2) @
% 101.35/22.17 (inverse @ (multiply @ X3 @ X2))))
% 101.35/22.17 = (X1))),
% 101.35/22.17 inference('demod', [status(thm)],
% 101.35/22.17 [zip_derived_cl235, zip_derived_cl3, zip_derived_cl0])).
% 101.35/22.17 thf(zip_derived_cl15390, plain,
% 101.35/22.17 (![X0 : $i, X4 : $i]:
% 101.35/22.17 ((X4) = (inverse @ (multiply @ (inverse @ (multiply @ X0 @ X4)) @ X0)))),
% 101.35/22.17 inference('demod', [status(thm)],
% 101.35/22.17 [zip_derived_cl15298, zip_derived_cl246])).
% 101.35/22.17 thf(zip_derived_cl9557, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i]:
% 101.35/22.17 ((multiply @ (inverse @ X1) @ (multiply @ X1 @ X0))
% 101.35/22.17 = (inverse @ (inverse @ X0)))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl9075, zip_derived_cl6514])).
% 101.35/22.17 thf(zip_derived_cl6513, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X3 : $i]:
% 101.35/22.17 ((multiply @ (inverse @ X3) @
% 101.35/22.17 (multiply @ X3 @
% 101.35/22.17 (multiply @ X1 @ (inverse @ (multiply @ X0 @ (inverse @ X0))))))
% 101.35/22.17 = (X1))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl6456, zip_derived_cl884])).
% 101.35/22.17 thf(zip_derived_cl10139, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i]:
% 101.35/22.17 ((inverse @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @ X1 @ (inverse @ (multiply @ X0 @ (inverse @ X0))))))
% 101.35/22.17 = (X1))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl9557, zip_derived_cl6513])).
% 101.35/22.17 thf(zip_derived_cl15626, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i]:
% 101.35/22.17 ((inverse @ X0)
% 101.35/22.17 = (inverse @
% 101.35/22.17 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X1))) @ X0)))),
% 101.35/22.17 inference('sup+', [status(thm)],
% 101.35/22.17 [zip_derived_cl15390, zip_derived_cl10139])).
% 101.35/22.17 thf(zip_derived_cl884, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i, X5 : $i]:
% 101.35/22.17 ((multiply @ (inverse @ X5) @
% 101.35/22.17 (multiply @ X5 @
% 101.35/22.17 (multiply @ X1 @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @ (multiply @ (inverse @ X2) @ X0) @
% 101.35/22.17 (inverse @ (multiply @ (inverse @ X1) @ X0)))))))
% 101.35/22.17 = (X2))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl153, zip_derived_cl64])).
% 101.35/22.17 thf(zip_derived_cl16626, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 101.35/22.17 ((multiply @ (inverse @ X4) @
% 101.35/22.17 (multiply @ X4 @
% 101.35/22.17 (multiply @ X3 @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @ (multiply @ (inverse @ X0) @ X2) @
% 101.35/22.17 (inverse @ (multiply @ (inverse @ X3) @ X2)))))))
% 101.35/22.17 = (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X1))) @ X0))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl15626, zip_derived_cl884])).
% 101.35/22.17 thf(zip_derived_cl884, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i, X5 : $i]:
% 101.35/22.17 ((multiply @ (inverse @ X5) @
% 101.35/22.17 (multiply @ X5 @
% 101.35/22.17 (multiply @ X1 @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @ (multiply @ (inverse @ X2) @ X0) @
% 101.35/22.17 (inverse @ (multiply @ (inverse @ X1) @ X0)))))))
% 101.35/22.17 = (X2))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl153, zip_derived_cl64])).
% 101.35/22.17 thf(zip_derived_cl16899, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i]:
% 101.35/22.17 ((X0) = (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X1))) @ X0))),
% 101.35/22.17 inference('demod', [status(thm)],
% 101.35/22.17 [zip_derived_cl16626, zip_derived_cl884])).
% 101.35/22.17 thf(zip_derived_cl15390, plain,
% 101.35/22.17 (![X0 : $i, X4 : $i]:
% 101.35/22.17 ((X4) = (inverse @ (multiply @ (inverse @ (multiply @ X0 @ X4)) @ X0)))),
% 101.35/22.17 inference('demod', [status(thm)],
% 101.35/22.17 [zip_derived_cl15298, zip_derived_cl246])).
% 101.35/22.17 thf(zip_derived_cl15390, plain,
% 101.35/22.17 (![X0 : $i, X4 : $i]:
% 101.35/22.17 ((X4) = (inverse @ (multiply @ (inverse @ (multiply @ X0 @ X4)) @ X0)))),
% 101.35/22.17 inference('demod', [status(thm)],
% 101.35/22.17 [zip_derived_cl15298, zip_derived_cl246])).
% 101.35/22.17 thf(zip_derived_cl15623, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i]:
% 101.35/22.17 ((X1) = (inverse @ (multiply @ X0 @ (inverse @ (multiply @ X1 @ X0)))))),
% 101.35/22.17 inference('sup+', [status(thm)],
% 101.35/22.17 [zip_derived_cl15390, zip_derived_cl15390])).
% 101.35/22.17 thf(zip_derived_cl15626, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i]:
% 101.35/22.17 ((inverse @ X0)
% 101.35/22.17 = (inverse @
% 101.35/22.17 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X1))) @ X0)))),
% 101.35/22.17 inference('sup+', [status(thm)],
% 101.35/22.17 [zip_derived_cl15390, zip_derived_cl10139])).
% 101.35/22.17 thf(zip_derived_cl0, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.17 ((multiply @ X1 @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @
% 101.35/22.17 (multiply @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X1) @ X0))) @
% 101.35/22.17 X3) @
% 101.35/22.17 (inverse @ (multiply @ X2 @ X3)))))
% 101.35/22.17 = (X0))),
% 101.35/22.17 inference('cnf', [status(esa)], [single_axiom])).
% 101.35/22.17 thf(zip_derived_cl0, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.17 ((multiply @ X1 @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @
% 101.35/22.17 (multiply @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X1) @ X0))) @
% 101.35/22.17 X3) @
% 101.35/22.17 (inverse @ (multiply @ X2 @ X3)))))
% 101.35/22.17 = (X0))),
% 101.35/22.17 inference('cnf', [status(esa)], [single_axiom])).
% 101.35/22.17 thf(zip_derived_cl4, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 101.35/22.17 ((multiply @ X4 @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @ X0 @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @ X5 @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @
% 101.35/22.17 (multiply @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @ (inverse @ X3) @
% 101.35/22.17 (multiply @
% 101.35/22.17 (inverse @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @ (inverse @ X5) @
% 101.35/22.17 (multiply @ (inverse @ X4) @ X1)))) @
% 101.35/22.17 X0))) @
% 101.35/22.17 X2) @
% 101.35/22.17 (inverse @ (multiply @ X3 @ X2)))))))))
% 101.35/22.17 = (X1))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 101.35/22.17 thf(zip_derived_cl16762, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 101.35/22.17 ((multiply @ X4 @
% 101.35/22.17 (inverse @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @ X5 @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @
% 101.35/22.17 (multiply @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @ (inverse @ X1) @
% 101.35/22.17 (multiply @
% 101.35/22.17 (inverse @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @ (inverse @ X5) @
% 101.35/22.17 (multiply @ (inverse @ X4) @ X3)))) @
% 101.35/22.17 (inverse @ (multiply @ X2 @ (inverse @ X2)))))) @
% 101.35/22.17 X0) @
% 101.35/22.17 (inverse @ (multiply @ X1 @ X0))))))))
% 101.35/22.17 = (X3))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl15626, zip_derived_cl4])).
% 101.35/22.17 thf(zip_derived_cl14863, plain,
% 101.35/22.17 (![X1 : $i, X2 : $i]:
% 101.35/22.17 ((multiply @ (inverse @ (inverse @ X2)) @
% 101.35/22.17 (inverse @ (multiply @ X1 @ (inverse @ X1)))) = (X2))),
% 101.35/22.17 inference('demod', [status(thm)],
% 101.35/22.17 [zip_derived_cl14516, zip_derived_cl8188])).
% 101.35/22.17 thf(zip_derived_cl153, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 101.35/22.17 ((multiply @ X4 @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @ (multiply @ (inverse @ X0) @ X3) @
% 101.35/22.17 (inverse @ (multiply @ (inverse @ X4) @ X3)))))
% 101.35/22.17 = (inverse @
% 101.35/22.17 (multiply @
% 101.35/22.17 (multiply @ (inverse @ (multiply @ (inverse @ X2) @ X0)) @ X1) @
% 101.35/22.17 (inverse @ (multiply @ X2 @ X1)))))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl64, zip_derived_cl0])).
% 101.35/22.17 thf(zip_derived_cl879, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 101.35/22.17 ((multiply @ X3 @
% 101.35/22.17 (multiply @ X1 @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @
% 101.35/22.17 (multiply @ (inverse @ (multiply @ (inverse @ X3) @ X2)) @ X0) @
% 101.35/22.17 (inverse @ (multiply @ (inverse @ X1) @ X0))))))
% 101.35/22.17 = (X2))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl153, zip_derived_cl0])).
% 101.35/22.17 thf(zip_derived_cl16933, plain,
% 101.35/22.17 (![X3 : $i, X4 : $i]:
% 101.35/22.17 ((multiply @ X4 @
% 101.35/22.17 (inverse @ (inverse @ (multiply @ (inverse @ X4) @ X3)))) = (
% 101.35/22.17 X3))),
% 101.35/22.17 inference('demod', [status(thm)],
% 101.35/22.17 [zip_derived_cl16762, zip_derived_cl14863, zip_derived_cl153,
% 101.35/22.17 zip_derived_cl879])).
% 101.35/22.17 thf(zip_derived_cl17419, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i]:
% 101.35/22.17 ((multiply @ X1 @ (inverse @ X0))
% 101.35/22.17 = (inverse @ (multiply @ X0 @ (inverse @ X1))))),
% 101.35/22.17 inference('sup+', [status(thm)],
% 101.35/22.17 [zip_derived_cl15623, zip_derived_cl16933])).
% 101.35/22.17 thf(zip_derived_cl17902, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i]:
% 101.35/22.17 ((X0) = (multiply @ (multiply @ X1 @ (inverse @ X1)) @ X0))),
% 101.35/22.17 inference('demod', [status(thm)],
% 101.35/22.17 [zip_derived_cl16899, zip_derived_cl17419])).
% 101.35/22.17 thf(zip_derived_cl16933, plain,
% 101.35/22.17 (![X3 : $i, X4 : $i]:
% 101.35/22.17 ((multiply @ X4 @
% 101.35/22.17 (inverse @ (inverse @ (multiply @ (inverse @ X4) @ X3)))) = (
% 101.35/22.17 X3))),
% 101.35/22.17 inference('demod', [status(thm)],
% 101.35/22.17 [zip_derived_cl16762, zip_derived_cl14863, zip_derived_cl153,
% 101.35/22.17 zip_derived_cl879])).
% 101.35/22.17 thf(zip_derived_cl18080, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i]:
% 101.35/22.17 ((inverse @
% 101.35/22.17 (inverse @
% 101.35/22.17 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X1))) @ X0)))
% 101.35/22.17 = (X0))),
% 101.35/22.17 inference('sup+', [status(thm)],
% 101.35/22.17 [zip_derived_cl17902, zip_derived_cl16933])).
% 101.35/22.17 thf(zip_derived_cl17419, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i]:
% 101.35/22.17 ((multiply @ X1 @ (inverse @ X0))
% 101.35/22.17 = (inverse @ (multiply @ X0 @ (inverse @ X1))))),
% 101.35/22.17 inference('sup+', [status(thm)],
% 101.35/22.17 [zip_derived_cl15623, zip_derived_cl16933])).
% 101.35/22.17 thf(zip_derived_cl17902, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i]:
% 101.35/22.17 ((X0) = (multiply @ (multiply @ X1 @ (inverse @ X1)) @ X0))),
% 101.35/22.17 inference('demod', [status(thm)],
% 101.35/22.17 [zip_derived_cl16899, zip_derived_cl17419])).
% 101.35/22.17 thf(zip_derived_cl8002, plain,
% 101.35/22.17 (![X1 : $i, X2 : $i]:
% 101.35/22.17 ((multiply @ X1 @ (inverse @ X1)) = (multiply @ X2 @ (inverse @ X2)))),
% 101.35/22.17 inference('demod', [status(thm)],
% 101.35/22.17 [zip_derived_cl7577, zip_derived_cl6865, zip_derived_cl884])).
% 101.35/22.17 thf(zip_derived_cl6514, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i]:
% 101.35/22.17 ((multiply @ X2 @
% 101.35/22.17 (multiply @ (multiply @ (inverse @ X2) @ X1) @
% 101.35/22.17 (inverse @ (multiply @ X0 @ (inverse @ X0)))))
% 101.35/22.17 = (X1))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl6456, zip_derived_cl879])).
% 101.35/22.17 thf(zip_derived_cl8203, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i]:
% 101.35/22.17 ((multiply @ X1 @ (multiply @ X0 @ (inverse @ X0)))
% 101.35/22.17 = (inverse @ (inverse @ X1)))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl8002, zip_derived_cl6514])).
% 101.35/22.17 thf(zip_derived_cl18164, plain,
% 101.35/22.17 (![X0 : $i]: ((multiply @ X0 @ (multiply @ X0 @ (inverse @ X0))) = (X0))),
% 101.35/22.17 inference('demod', [status(thm)],
% 101.35/22.17 [zip_derived_cl18080, zip_derived_cl17419,
% 101.35/22.17 zip_derived_cl17902, zip_derived_cl8203])).
% 101.35/22.17 thf(zip_derived_cl17902, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i]:
% 101.35/22.17 ((X0) = (multiply @ (multiply @ X1 @ (inverse @ X1)) @ X0))),
% 101.35/22.17 inference('demod', [status(thm)],
% 101.35/22.17 [zip_derived_cl16899, zip_derived_cl17419])).
% 101.35/22.17 thf(zip_derived_cl281, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i]:
% 101.35/22.17 ((multiply @ (inverse @ X2) @ (multiply @ X2 @ X0))
% 101.35/22.17 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl215, zip_derived_cl215])).
% 101.35/22.17 thf(zip_derived_cl18031, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i, X2 : $i]:
% 101.35/22.17 ((multiply @ (inverse @ X2) @ (multiply @ X2 @ X0))
% 101.35/22.17 = (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X1))) @ X0))),
% 101.35/22.17 inference('sup+', [status(thm)], [zip_derived_cl17902, zip_derived_cl281])).
% 101.35/22.17 thf(zip_derived_cl17419, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i]:
% 101.35/22.17 ((multiply @ X1 @ (inverse @ X0))
% 101.35/22.17 = (inverse @ (multiply @ X0 @ (inverse @ X1))))),
% 101.35/22.17 inference('sup+', [status(thm)],
% 101.35/22.17 [zip_derived_cl15623, zip_derived_cl16933])).
% 101.35/22.17 thf(zip_derived_cl17902, plain,
% 101.35/22.17 (![X0 : $i, X1 : $i]:
% 101.35/22.17 ((X0) = (multiply @ (multiply @ X1 @ (inverse @ X1)) @ X0))),
% 101.35/22.17 inference('demod', [status(thm)],
% 101.35/22.17 [zip_derived_cl16899, zip_derived_cl17419])).
% 101.35/22.17 thf(zip_derived_cl18122, plain,
% 101.35/22.17 (![X0 : $i, X2 : $i]:
% 101.35/22.17 ((multiply @ (inverse @ X2) @ (multiply @ X2 @ X0)) = (X0))),
% 101.35/22.17 inference('demod', [status(thm)],
% 101.35/22.17 [zip_derived_cl18031, zip_derived_cl17419, zip_derived_cl17902])).
% 101.35/22.17 thf(zip_derived_cl18340, plain,
% 101.35/22.17 (![X0 : $i]:
% 101.35/22.17 ((multiply @ (inverse @ X0) @ X0) = (multiply @ X0 @ (inverse @ X0)))),
% 101.35/22.17 inference('sup+', [status(thm)],
% 101.35/22.17 [zip_derived_cl18164, zip_derived_cl18122])).
% 101.35/22.17 thf(zip_derived_cl18340, plain,
% 101.35/22.17 (![X0 : $i]:
% 101.35/22.17 ((multiply @ (inverse @ X0) @ X0) = (multiply @ X0 @ (inverse @ X0)))),
% 101.35/22.17 inference('sup+', [status(thm)],
% 101.35/22.17 [zip_derived_cl18164, zip_derived_cl18122])).
% 101.35/22.17 thf(zip_derived_cl18373, plain,
% 101.35/22.17 (((multiply @ a1 @ (inverse @ a1)) != (multiply @ b1 @ (inverse @ b1)))),
% 101.35/22.17 inference('demod', [status(thm)],
% 101.35/22.17 [zip_derived_cl1, zip_derived_cl18340, zip_derived_cl18340])).
% 101.35/22.17 thf(zip_derived_cl8002, plain,
% 101.35/22.17 (![X1 : $i, X2 : $i]:
% 101.35/22.17 ((multiply @ X1 @ (inverse @ X1)) = (multiply @ X2 @ (inverse @ X2)))),
% 101.35/22.17 inference('demod', [status(thm)],
% 101.35/22.17 [zip_derived_cl7577, zip_derived_cl6865, zip_derived_cl884])).
% 101.35/22.17 thf(zip_derived_cl18374, plain, ($false),
% 101.35/22.17 inference('simplify_reflect+', [status(thm)],
% 101.35/22.17 [zip_derived_cl18373, zip_derived_cl8002])).
% 101.35/22.17
% 101.35/22.17 % SZS output end Refutation
% 101.35/22.17
% 101.35/22.17
% 101.35/22.17 % Terminating...
% 102.24/22.32 % Runner terminated.
% 102.24/22.35 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------