TSTP Solution File: GRP414-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP414-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.K2tEIrhEDy true
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:51:33 EDT 2023
% Result : Unsatisfiable 38.24s 6.07s
% Output : Refutation 38.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP414-1 : TPTP v8.1.2. Released v2.6.0.
% 0.07/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.K2tEIrhEDy true
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 02:29:21 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.52/0.64 % Total configuration time : 435
% 0.52/0.64 % Estimated wc time : 1092
% 0.52/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.52/0.70 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.52/0.71 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.52/0.72 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.52/0.72 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 38.24/6.07 % Solved by fo/fo7.sh.
% 38.24/6.07 % done 1356 iterations in 5.322s
% 38.24/6.07 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 38.24/6.07 % SZS output start Refutation
% 38.24/6.07 thf(inverse_type, type, inverse: $i > $i).
% 38.24/6.07 thf(b3_type, type, b3: $i).
% 38.24/6.07 thf(c3_type, type, c3: $i).
% 38.24/6.07 thf(multiply_type, type, multiply: $i > $i > $i).
% 38.24/6.07 thf(a3_type, type, a3: $i).
% 38.24/6.07 thf(prove_these_axioms_3, conjecture,
% 38.24/6.07 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) =
% 38.24/6.07 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ))).
% 38.24/6.07 thf(zf_stmt_0, negated_conjecture,
% 38.24/6.07 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 38.24/6.07 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) )),
% 38.24/6.07 inference('cnf.neg', [status(esa)], [prove_these_axioms_3])).
% 38.24/6.07 thf(zip_derived_cl1, plain,
% 38.24/6.07 (((multiply @ (multiply @ a3 @ b3) @ c3)
% 38.24/6.07 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 38.24/6.07 inference('cnf', [status(esa)], [zf_stmt_0])).
% 38.24/6.07 thf(single_axiom, axiom,
% 38.24/6.07 (( multiply @
% 38.24/6.07 A @
% 38.24/6.07 ( inverse @
% 38.24/6.07 ( multiply @
% 38.24/6.07 ( multiply @
% 38.24/6.07 ( multiply @ ( inverse @ B ) @ B ) @
% 38.24/6.07 ( inverse @
% 38.24/6.07 ( multiply @
% 38.24/6.07 ( inverse @ ( multiply @ A @ ( inverse @ B ) ) ) @ C ) ) ) @
% 38.24/6.07 B ) ) ) =
% 38.24/6.07 ( C ))).
% 38.24/6.07 thf(zip_derived_cl0, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((multiply @ X1 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 38.24/6.07 X2)))
% 38.24/6.07 = (X0))),
% 38.24/6.07 inference('cnf', [status(esa)], [single_axiom])).
% 38.24/6.07 thf(zip_derived_cl0, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((multiply @ X1 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 38.24/6.07 X2)))
% 38.24/6.07 = (X0))),
% 38.24/6.07 inference('cnf', [status(esa)], [single_axiom])).
% 38.24/6.07 thf(zip_derived_cl0, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((multiply @ X1 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 38.24/6.07 X2)))
% 38.24/6.07 = (X0))),
% 38.24/6.07 inference('cnf', [status(esa)], [single_axiom])).
% 38.24/6.07 thf(zip_derived_cl3, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @ X3 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X0)) @
% 38.24/6.07 X2)))
% 38.24/6.07 = (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 38.24/6.07 (inverse @ X1))) @
% 38.24/6.07 X0))) @
% 38.24/6.07 X1)))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 38.24/6.07 thf(zip_derived_cl0, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((multiply @ X1 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 38.24/6.07 X2)))
% 38.24/6.07 = (X0))),
% 38.24/6.07 inference('cnf', [status(esa)], [single_axiom])).
% 38.24/6.07 thf(zip_derived_cl13, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 38.24/6.07 (multiply @ X2 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X0) @ X0) @ (inverse @ X1)) @
% 38.24/6.07 X0))))
% 38.24/6.07 = (X1))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 38.24/6.07 thf(zip_derived_cl35, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 38.24/6.07 (multiply @ X3 @ (inverse @ (multiply @ X0 @ X2))))
% 38.24/6.07 = (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1))) @
% 38.24/6.07 X0))) @
% 38.24/6.07 X1))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl13])).
% 38.24/6.07 thf(zip_derived_cl0, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((multiply @ X1 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 38.24/6.07 X2)))
% 38.24/6.07 = (X0))),
% 38.24/6.07 inference('cnf', [status(esa)], [single_axiom])).
% 38.24/6.07 thf(zip_derived_cl0, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((multiply @ X1 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 38.24/6.07 X2)))
% 38.24/6.07 = (X0))),
% 38.24/6.07 inference('cnf', [status(esa)], [single_axiom])).
% 38.24/6.07 thf(zip_derived_cl0, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((multiply @ X1 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 38.24/6.07 X2)))
% 38.24/6.07 = (X0))),
% 38.24/6.07 inference('cnf', [status(esa)], [single_axiom])).
% 38.24/6.07 thf(zip_derived_cl3, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @ X3 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X0)) @
% 38.24/6.07 X2)))
% 38.24/6.07 = (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 38.24/6.07 (inverse @ X1))) @
% 38.24/6.07 X0))) @
% 38.24/6.07 X1)))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 38.24/6.07 thf(zip_derived_cl0, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((multiply @ X1 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 38.24/6.07 X2)))
% 38.24/6.07 = (X0))),
% 38.24/6.07 inference('cnf', [status(esa)], [single_axiom])).
% 38.24/6.07 thf(zip_derived_cl35, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 38.24/6.07 (multiply @ X3 @ (inverse @ (multiply @ X0 @ X2))))
% 38.24/6.07 = (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1))) @
% 38.24/6.07 X0))) @
% 38.24/6.07 X1))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl13])).
% 38.24/6.07 thf(zip_derived_cl13, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 38.24/6.07 (multiply @ X2 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X0) @ X0) @ (inverse @ X1)) @
% 38.24/6.07 X0))))
% 38.24/6.07 = (X1))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 38.24/6.07 thf(zip_derived_cl57, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X0) @ X0) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X0))) @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1))))) @
% 38.24/6.07 X0) = (X1))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl13])).
% 38.24/6.07 thf(zip_derived_cl35, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 38.24/6.07 (multiply @ X3 @ (inverse @ (multiply @ X0 @ X2))))
% 38.24/6.07 = (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1))) @
% 38.24/6.07 X0))) @
% 38.24/6.07 X1))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl13])).
% 38.24/6.07 thf(zip_derived_cl35, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 38.24/6.07 (multiply @ X3 @ (inverse @ (multiply @ X0 @ X2))))
% 38.24/6.07 = (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1))) @
% 38.24/6.07 X0))) @
% 38.24/6.07 X1))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl13])).
% 38.24/6.07 thf(zip_derived_cl52, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @ (inverse @ (multiply @ X3 @ (inverse @ X0))) @
% 38.24/6.07 (multiply @ X3 @ (inverse @ (multiply @ X1 @ X0))))
% 38.24/6.07 = (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 38.24/6.07 (multiply @ X2 @ (inverse @ (multiply @ X1 @ X0)))))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl35])).
% 38.24/6.07 thf(zip_derived_cl197, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 38.24/6.07 ((multiply @ (inverse @ (multiply @ X4 @ (inverse @ X1))) @
% 38.24/6.07 (multiply @ X4 @ (inverse @ X0)))
% 38.24/6.07 = (multiply @ (inverse @ (multiply @ X3 @ (inverse @ X1))) @
% 38.24/6.07 (multiply @ X3 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 38.24/6.07 (inverse @ X1))) @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 38.24/6.07 (inverse @ X0))))) @
% 38.24/6.07 X1)))))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl57, zip_derived_cl52])).
% 38.24/6.07 thf(zip_derived_cl57, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X0) @ X0) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X0))) @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1))))) @
% 38.24/6.07 X0) = (X1))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl13])).
% 38.24/6.07 thf(zip_derived_cl236, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X3 : $i, X4 : $i]:
% 38.24/6.07 ((multiply @ (inverse @ (multiply @ X4 @ (inverse @ X1))) @
% 38.24/6.07 (multiply @ X4 @ (inverse @ X0)))
% 38.24/6.07 = (multiply @ (inverse @ (multiply @ X3 @ (inverse @ X1))) @
% 38.24/6.07 (multiply @ X3 @ (inverse @ X0))))),
% 38.24/6.07 inference('demod', [status(thm)], [zip_derived_cl197, zip_derived_cl57])).
% 38.24/6.07 thf(zip_derived_cl288, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 38.24/6.07 ((multiply @ (inverse @ X0) @ (multiply @ X4 @ (inverse @ X1)))
% 38.24/6.07 = (multiply @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ X2 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X4 @ (inverse @ X3))) @
% 38.24/6.07 X0))) @
% 38.24/6.07 X3)))) @
% 38.24/6.07 (multiply @ X2 @ (inverse @ X1))))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl236])).
% 38.24/6.07 thf(zip_derived_cl463, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 38.24/6.07 ((multiply @ (inverse @ X1) @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 38.24/6.07 (inverse @ X3)))
% 38.24/6.07 = (multiply @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ X4 @
% 38.24/6.07 (multiply @ X2 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X0) @ X0) @
% 38.24/6.07 (inverse @ X1)) @
% 38.24/6.07 X0))))) @
% 38.24/6.07 (multiply @ X4 @ (inverse @ X3))))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl288])).
% 38.24/6.07 thf(zip_derived_cl664, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 38.24/6.07 ((multiply @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X4 @ (inverse @ X3))) @ X0)) @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X4 @ (inverse @ X3))) @
% 38.24/6.07 (inverse @ X1)))
% 38.24/6.07 = (multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 38.24/6.07 (multiply @ X2 @ (inverse @ X1))))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl463])).
% 38.24/6.07 thf(zip_derived_cl760, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 38.24/6.07 ((multiply @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @ X5)) @
% 38.24/6.07 X0)
% 38.24/6.07 = (multiply @ (inverse @ (multiply @ X4 @ X5)) @
% 38.24/6.07 (multiply @ X4 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 38.24/6.07 (inverse @ X1))) @
% 38.24/6.07 X0))) @
% 38.24/6.07 X1)))))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl664])).
% 38.24/6.07 thf(zip_derived_cl3, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @ X3 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X0)) @
% 38.24/6.07 X2)))
% 38.24/6.07 = (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 38.24/6.07 (inverse @ X1))) @
% 38.24/6.07 X0))) @
% 38.24/6.07 X1)))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 38.24/6.07 thf(zip_derived_cl812, plain,
% 38.24/6.07 (![X0 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 38.24/6.07 ((multiply @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @ X5)) @
% 38.24/6.07 X0)
% 38.24/6.07 = (multiply @ (inverse @ (multiply @ X4 @ X5)) @
% 38.24/6.07 (multiply @ X4 @
% 38.24/6.07 (multiply @ X3 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X0)) @
% 38.24/6.07 X2))))))),
% 38.24/6.07 inference('demod', [status(thm)], [zip_derived_cl760, zip_derived_cl3])).
% 38.24/6.07 thf(zip_derived_cl1094, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 38.24/6.07 ((multiply @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X1))) @ X4)) @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X1))) @ X0))
% 38.24/6.07 = (multiply @ (inverse @ (multiply @ X3 @ X4)) @
% 38.24/6.07 (multiply @ X3 @ X0)))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl812])).
% 38.24/6.07 thf(zip_derived_cl3, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @ X3 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X0)) @
% 38.24/6.07 X2)))
% 38.24/6.07 = (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 38.24/6.07 (inverse @ X1))) @
% 38.24/6.07 X0))) @
% 38.24/6.07 X1)))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 38.24/6.07 thf(zip_derived_cl1230, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 38.24/6.07 ((multiply @ X4 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X4 @ (inverse @ X3))) @ X0))) @
% 38.24/6.07 X3)))
% 38.24/6.07 = (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @
% 38.24/6.07 (multiply @ X1 @ X0)))) @
% 38.24/6.07 X2)))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl1094, zip_derived_cl3])).
% 38.24/6.07 thf(zip_derived_cl0, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((multiply @ X1 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 38.24/6.07 X2)))
% 38.24/6.07 = (X0))),
% 38.24/6.07 inference('cnf', [status(esa)], [single_axiom])).
% 38.24/6.07 thf(zip_derived_cl1352, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((X0)
% 38.24/6.07 = (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @
% 38.24/6.07 (multiply @ X1 @ X0)))) @
% 38.24/6.07 X2)))),
% 38.24/6.07 inference('demod', [status(thm)], [zip_derived_cl1230, zip_derived_cl0])).
% 38.24/6.07 thf(zip_derived_cl1569, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((X1)
% 38.24/6.07 = (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 38.24/6.07 (multiply @ X2 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X0) @ X0) @ X1) @ X0))))))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl1352])).
% 38.24/6.07 thf(zip_derived_cl288, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 38.24/6.07 ((multiply @ (inverse @ X0) @ (multiply @ X4 @ (inverse @ X1)))
% 38.24/6.07 = (multiply @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ X2 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X4 @ (inverse @ X3))) @
% 38.24/6.07 X0))) @
% 38.24/6.07 X3)))) @
% 38.24/6.07 (multiply @ X2 @ (inverse @ X1))))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl236])).
% 38.24/6.07 thf(zip_derived_cl236, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X3 : $i, X4 : $i]:
% 38.24/6.07 ((multiply @ (inverse @ (multiply @ X4 @ (inverse @ X1))) @
% 38.24/6.07 (multiply @ X4 @ (inverse @ X0)))
% 38.24/6.07 = (multiply @ (inverse @ (multiply @ X3 @ (inverse @ X1))) @
% 38.24/6.07 (multiply @ X3 @ (inverse @ X0))))),
% 38.24/6.07 inference('demod', [status(thm)], [zip_derived_cl197, zip_derived_cl57])).
% 38.24/6.07 thf(zip_derived_cl57, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X0) @ X0) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X0))) @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1))))) @
% 38.24/6.07 X0) = (X1))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl13])).
% 38.24/6.07 thf(zip_derived_cl257, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @
% 38.24/6.07 (multiply @ X1 @ (inverse @ X0))))) @
% 38.24/6.07 X2) = (X0))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl236, zip_derived_cl57])).
% 38.24/6.07 thf(zip_derived_cl1094, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 38.24/6.07 ((multiply @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X1))) @ X4)) @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X1))) @ X0))
% 38.24/6.07 = (multiply @ (inverse @ (multiply @ X3 @ X4)) @
% 38.24/6.07 (multiply @ X3 @ X0)))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl812])).
% 38.24/6.07 thf(zip_derived_cl1094, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 38.24/6.07 ((multiply @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X1))) @ X4)) @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X1))) @ X0))
% 38.24/6.07 = (multiply @ (inverse @ (multiply @ X3 @ X4)) @
% 38.24/6.07 (multiply @ X3 @ X0)))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl812])).
% 38.24/6.07 thf(zip_derived_cl1249, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @ (inverse @ (multiply @ X1 @ X2)) @ (multiply @ X1 @ X0))
% 38.24/6.07 = (multiply @ (inverse @ (multiply @ X3 @ X2)) @
% 38.24/6.07 (multiply @ X3 @ X0)))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl1094, zip_derived_cl1094])).
% 38.24/6.07 thf(zip_derived_cl0, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((multiply @ X1 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 38.24/6.07 X2)))
% 38.24/6.07 = (X0))),
% 38.24/6.07 inference('cnf', [status(esa)], [single_axiom])).
% 38.24/6.07 thf(zip_derived_cl1365, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 38.24/6.07 ((multiply @ X4 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X1 @ X0)) @
% 38.24/6.07 (multiply @ X1 @ X0)) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (inverse @ (multiply @ X4 @ (inverse @ (multiply @ X3 @ X0)))) @
% 38.24/6.07 X2))) @
% 38.24/6.07 (multiply @ X3 @ X0))))
% 38.24/6.07 = (X2))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl1249, zip_derived_cl0])).
% 38.24/6.07 thf(zip_derived_cl3478, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 38.24/6.07 ((multiply @ X4 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X5 @ X2)) @
% 38.24/6.07 (multiply @ X5 @ X2)) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ X4 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 38.24/6.07 (multiply @ X3 @ (inverse @ X0))))) @
% 38.24/6.07 X2)))) @
% 38.24/6.07 X1))) @
% 38.24/6.07 X0)))
% 38.24/6.07 = (X1))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl257, zip_derived_cl1365])).
% 38.24/6.07 thf(zip_derived_cl257, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @
% 38.24/6.07 (multiply @ X1 @ (inverse @ X0))))) @
% 38.24/6.07 X2) = (X0))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl236, zip_derived_cl57])).
% 38.24/6.07 thf(zip_derived_cl3605, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X5 : $i]:
% 38.24/6.07 ((multiply @ X4 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X5 @ X2)) @
% 38.24/6.07 (multiply @ X5 @ X2)) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X4 @ (inverse @ X0))) @ X1))) @
% 38.24/6.07 X0)))
% 38.24/6.07 = (X1))),
% 38.24/6.07 inference('demod', [status(thm)], [zip_derived_cl3478, zip_derived_cl257])).
% 38.24/6.07 thf(zip_derived_cl3763, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 38.24/6.07 ((multiply @ X5 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (inverse @ X1) @
% 38.24/6.07 (multiply @ X2 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X0) @ X0) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 38.24/6.07 X1))) @
% 38.24/6.07 X0)))) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X5 @ (inverse @ X4))) @ X3))) @
% 38.24/6.07 X4)))
% 38.24/6.07 = (X3))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl288, zip_derived_cl3605])).
% 38.24/6.07 thf(zip_derived_cl0, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((multiply @ X1 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 38.24/6.07 X2)))
% 38.24/6.07 = (X0))),
% 38.24/6.07 inference('cnf', [status(esa)], [single_axiom])).
% 38.24/6.07 thf(zip_derived_cl3823, plain,
% 38.24/6.07 (![X1 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 38.24/6.07 ((multiply @ X5 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X5 @ (inverse @ X4))) @ X3))) @
% 38.24/6.07 X4)))
% 38.24/6.07 = (X3))),
% 38.24/6.07 inference('demod', [status(thm)], [zip_derived_cl3763, zip_derived_cl0])).
% 38.24/6.07 thf(zip_derived_cl3929, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @ X2 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (multiply @ (multiply @ (inverse @ X3) @ X3) @ X0) @ X1)))
% 38.24/6.07 = (multiply @ X2 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X1) @ X1) @ X0) @ X1))))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl1569, zip_derived_cl3823])).
% 38.24/6.07 thf(zip_derived_cl35, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 38.24/6.07 (multiply @ X3 @ (inverse @ (multiply @ X0 @ X2))))
% 38.24/6.07 = (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1))) @
% 38.24/6.07 X0))) @
% 38.24/6.07 X1))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl13])).
% 38.24/6.07 thf(zip_derived_cl0, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((multiply @ X1 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 38.24/6.07 X2)))
% 38.24/6.07 = (X0))),
% 38.24/6.07 inference('cnf', [status(esa)], [single_axiom])).
% 38.24/6.07 thf(zip_derived_cl50, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((multiply @ (multiply @ (inverse @ X0) @ X0) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 38.24/6.07 (multiply @ X2 @ (inverse @ (multiply @ X1 @ X0))))))
% 38.24/6.07 = (X1))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl0])).
% 38.24/6.07 thf(zip_derived_cl4125, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @ (multiply @ (inverse @ X0) @ X0) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 38.24/6.07 (multiply @ X2 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X0) @ X0) @ X1) @ X0))))))
% 38.24/6.07 = (multiply @ (multiply @ (inverse @ X3) @ X3) @ X1))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl3929, zip_derived_cl50])).
% 38.24/6.07 thf(zip_derived_cl1569, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((X1)
% 38.24/6.07 = (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 38.24/6.07 (multiply @ X2 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X0) @ X0) @ X1) @ X0))))))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl1352])).
% 38.24/6.07 thf(zip_derived_cl4281, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @ (multiply @ (inverse @ X0) @ X0) @ X1)
% 38.24/6.07 = (multiply @ (multiply @ (inverse @ X3) @ X3) @ X1))),
% 38.24/6.07 inference('demod', [status(thm)],
% 38.24/6.07 [zip_derived_cl4125, zip_derived_cl1569])).
% 38.24/6.07 thf(zip_derived_cl4281, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @ (multiply @ (inverse @ X0) @ X0) @ X1)
% 38.24/6.07 = (multiply @ (multiply @ (inverse @ X3) @ X3) @ X1))),
% 38.24/6.07 inference('demod', [status(thm)],
% 38.24/6.07 [zip_derived_cl4125, zip_derived_cl1569])).
% 38.24/6.07 thf(zip_derived_cl4281, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @ (multiply @ (inverse @ X0) @ X0) @ X1)
% 38.24/6.07 = (multiply @ (multiply @ (inverse @ X3) @ X3) @ X1))),
% 38.24/6.07 inference('demod', [status(thm)],
% 38.24/6.07 [zip_derived_cl4125, zip_derived_cl1569])).
% 38.24/6.07 thf(zip_derived_cl50, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((multiply @ (multiply @ (inverse @ X0) @ X0) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 38.24/6.07 (multiply @ X2 @ (inverse @ (multiply @ X1 @ X0))))))
% 38.24/6.07 = (X1))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl0])).
% 38.24/6.07 thf(zip_derived_cl4356, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @ (multiply @ (inverse @ X3) @ X3) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 38.24/6.07 (multiply @ X2 @ (inverse @ (multiply @ X1 @ X0))))))
% 38.24/6.07 = (X1))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl4281, zip_derived_cl50])).
% 38.24/6.07 thf(zip_derived_cl4833, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 38.24/6.07 ((multiply @ (multiply @ (inverse @ X4) @ X4) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X3) @ X3) @ (inverse @ X0))) @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 38.24/6.07 (inverse @ (multiply @ X1 @ X0))))))
% 38.24/6.07 = (X1))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl4281, zip_derived_cl4356])).
% 38.24/6.07 thf(zip_derived_cl8310, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 38.24/6.07 ((multiply @ (multiply @ (inverse @ X5) @ X5) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X4) @ X4) @ (inverse @ X0))) @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 38.24/6.07 (inverse @ (multiply @ (multiply @ (inverse @ X1) @ X1) @ X0))))))
% 38.24/6.07 = (multiply @ (inverse @ X2) @ X2))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl4281, zip_derived_cl4833])).
% 38.24/6.07 thf(zip_derived_cl3929, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @ X2 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (multiply @ (multiply @ (inverse @ X3) @ X3) @ X0) @ X1)))
% 38.24/6.07 = (multiply @ X2 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X1) @ X1) @ X0) @ X1))))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl1569, zip_derived_cl3823])).
% 38.24/6.07 thf(zip_derived_cl50, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((multiply @ (multiply @ (inverse @ X0) @ X0) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 38.24/6.07 (multiply @ X2 @ (inverse @ (multiply @ X1 @ X0))))))
% 38.24/6.07 = (X1))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl0])).
% 38.24/6.07 thf(zip_derived_cl1249, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @ (inverse @ (multiply @ X1 @ X2)) @ (multiply @ X1 @ X0))
% 38.24/6.07 = (multiply @ (inverse @ (multiply @ X3 @ X2)) @
% 38.24/6.07 (multiply @ X3 @ X0)))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl1094, zip_derived_cl1094])).
% 38.24/6.07 thf(zip_derived_cl1460, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 38.24/6.07 ((multiply @ (inverse @ X0) @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X3) @ X3) @ X1))
% 38.24/6.07 = (multiply @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ X2 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X4 @ (inverse @ X3))) @
% 38.24/6.07 (multiply @ X4 @ (inverse @ (multiply @ X0 @ X3))))))) @
% 38.24/6.07 (multiply @ X2 @ X1)))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl1249])).
% 38.24/6.07 thf(zip_derived_cl4127, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 38.24/6.07 ((multiply @
% 38.24/6.07 (inverse @ (multiply @ (multiply @ (inverse @ X5) @ X5) @ X1)) @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X0) @ X0) @ X3))
% 38.24/6.07 = (multiply @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ X4 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 38.24/6.07 (multiply @ X2 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X0) @ X0) @ X1) @ X0))))))) @
% 38.24/6.07 (multiply @ X4 @ X3)))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl3929, zip_derived_cl1460])).
% 38.24/6.07 thf(zip_derived_cl1569, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((X1)
% 38.24/6.07 = (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 38.24/6.07 (multiply @ X2 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X0) @ X0) @ X1) @ X0))))))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl1352])).
% 38.24/6.07 thf(zip_derived_cl4283, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 38.24/6.07 ((multiply @
% 38.24/6.07 (inverse @ (multiply @ (multiply @ (inverse @ X5) @ X5) @ X1)) @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X0) @ X0) @ X3))
% 38.24/6.07 = (multiply @ (inverse @ (multiply @ X4 @ X1)) @
% 38.24/6.07 (multiply @ X4 @ X3)))),
% 38.24/6.07 inference('demod', [status(thm)],
% 38.24/6.07 [zip_derived_cl4127, zip_derived_cl1569])).
% 38.24/6.07 thf(zip_derived_cl4356, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @ (multiply @ (inverse @ X3) @ X3) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 38.24/6.07 (multiply @ X2 @ (inverse @ (multiply @ X1 @ X0))))))
% 38.24/6.07 = (X1))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl4281, zip_derived_cl50])).
% 38.24/6.07 thf(zip_derived_cl8417, plain,
% 38.24/6.07 (![X1 : $i, X2 : $i]:
% 38.24/6.07 ((multiply @ (inverse @ X1) @ X1) = (multiply @ (inverse @ X2) @ X2))),
% 38.24/6.07 inference('demod', [status(thm)],
% 38.24/6.07 [zip_derived_cl8310, zip_derived_cl4283, zip_derived_cl4356])).
% 38.24/6.07 thf(zip_derived_cl4281, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @ (multiply @ (inverse @ X0) @ X0) @ X1)
% 38.24/6.07 = (multiply @ (multiply @ (inverse @ X3) @ X3) @ X1))),
% 38.24/6.07 inference('demod', [status(thm)],
% 38.24/6.07 [zip_derived_cl4125, zip_derived_cl1569])).
% 38.24/6.07 thf(zip_derived_cl257, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @
% 38.24/6.07 (multiply @ X1 @ (inverse @ X0))))) @
% 38.24/6.07 X2) = (X0))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl236, zip_derived_cl57])).
% 38.24/6.07 thf(zip_derived_cl4358, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @
% 38.24/6.07 (multiply @ X1 @ (inverse @ X0))))) @
% 38.24/6.07 X2) = (X0))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl4281, zip_derived_cl257])).
% 38.24/6.07 thf(zip_derived_cl8606, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 38.24/6.07 (inverse @ (multiply @ (inverse @ X0) @ X0))) @
% 38.24/6.07 X1) = (X1))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl8417, zip_derived_cl4358])).
% 38.24/6.07 thf(zip_derived_cl4356, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @ (multiply @ (inverse @ X3) @ X3) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 38.24/6.07 (multiply @ X2 @ (inverse @ (multiply @ X1 @ X0))))))
% 38.24/6.07 = (X1))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl4281, zip_derived_cl50])).
% 38.24/6.07 thf(zip_derived_cl8853, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 38.24/6.07 ((multiply @ (multiply @ (inverse @ X4) @ X4) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (inverse @ X0)) @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 38.24/6.07 (inverse @ (multiply @ (inverse @ X2) @ X2))) @
% 38.24/6.07 (inverse @ (multiply @ X1 @ X0))))))
% 38.24/6.07 = (X1))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl8606, zip_derived_cl4356])).
% 38.24/6.07 thf(zip_derived_cl8606, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 38.24/6.07 (inverse @ (multiply @ (inverse @ X0) @ X0))) @
% 38.24/6.07 X1) = (X1))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl8417, zip_derived_cl4358])).
% 38.24/6.07 thf(zip_derived_cl8999, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X4 : $i]:
% 38.24/6.07 ((multiply @ (multiply @ (inverse @ X4) @ X4) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (inverse @ X0)) @
% 38.24/6.07 (inverse @ (multiply @ X1 @ X0)))))
% 38.24/6.07 = (X1))),
% 38.24/6.07 inference('demod', [status(thm)],
% 38.24/6.07 [zip_derived_cl8853, zip_derived_cl8606])).
% 38.24/6.07 thf(zip_derived_cl8606, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 38.24/6.07 (inverse @ (multiply @ (inverse @ X0) @ X0))) @
% 38.24/6.07 X1) = (X1))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl8417, zip_derived_cl4358])).
% 38.24/6.07 thf(zip_derived_cl4281, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @ (multiply @ (inverse @ X0) @ X0) @ X1)
% 38.24/6.07 = (multiply @ (multiply @ (inverse @ X3) @ X3) @ X1))),
% 38.24/6.07 inference('demod', [status(thm)],
% 38.24/6.07 [zip_derived_cl4125, zip_derived_cl1569])).
% 38.24/6.07 thf(zip_derived_cl13, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 38.24/6.07 (multiply @ X2 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X0) @ X0) @ (inverse @ X1)) @
% 38.24/6.07 X0))))
% 38.24/6.07 = (X1))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 38.24/6.07 thf(zip_derived_cl4351, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 38.24/6.07 (multiply @ X3 @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X1) @ X1) @ (inverse @ X0)) @
% 38.24/6.07 X2))))
% 38.24/6.07 = (X0))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl4281, zip_derived_cl13])).
% 38.24/6.07 thf(zip_derived_cl8851, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 38.24/6.07 ((multiply @ (inverse @ (inverse @ X0)) @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X4) @ X4) @
% 38.24/6.07 (inverse @ (multiply @ (inverse @ X3) @ X3))) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1)) @
% 38.24/6.07 X0))))
% 38.24/6.07 = (X1))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl8606, zip_derived_cl4351])).
% 38.24/6.07 thf(zip_derived_cl8606, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 38.24/6.07 (inverse @ (multiply @ (inverse @ X0) @ X0))) @
% 38.24/6.07 X1) = (X1))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl8417, zip_derived_cl4358])).
% 38.24/6.07 thf(zip_derived_cl8997, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((multiply @ (inverse @ (inverse @ X0)) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1)) @
% 38.24/6.07 X0)))
% 38.24/6.07 = (X1))),
% 38.24/6.07 inference('demod', [status(thm)],
% 38.24/6.07 [zip_derived_cl8851, zip_derived_cl8606])).
% 38.24/6.07 thf(zip_derived_cl11288, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((multiply @ (inverse @ (inverse @ X2)) @
% 38.24/6.07 (inverse @ (multiply @ X0 @ X2)))
% 38.24/6.07 = (multiply @ (inverse @ (inverse @ X1)) @
% 38.24/6.07 (inverse @ (multiply @ X0 @ X1))))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl8999, zip_derived_cl8997])).
% 38.24/6.07 thf(zip_derived_cl8606, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 38.24/6.07 (inverse @ (multiply @ (inverse @ X0) @ X0))) @
% 38.24/6.07 X1) = (X1))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl8417, zip_derived_cl4358])).
% 38.24/6.07 thf(zip_derived_cl4281, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @ (multiply @ (inverse @ X0) @ X0) @ X1)
% 38.24/6.07 = (multiply @ (multiply @ (inverse @ X3) @ X3) @ X1))),
% 38.24/6.07 inference('demod', [status(thm)],
% 38.24/6.07 [zip_derived_cl4125, zip_derived_cl1569])).
% 38.24/6.07 thf(zip_derived_cl1352, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((X0)
% 38.24/6.07 = (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @
% 38.24/6.07 (multiply @ X1 @ X0)))) @
% 38.24/6.07 X2)))),
% 38.24/6.07 inference('demod', [status(thm)], [zip_derived_cl1230, zip_derived_cl0])).
% 38.24/6.07 thf(zip_derived_cl4359, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 38.24/6.07 ((X0)
% 38.24/6.07 = (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @
% 38.24/6.07 (multiply @ X1 @ X0)))) @
% 38.24/6.07 X2)))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl4281, zip_derived_cl1352])).
% 38.24/6.07 thf(zip_derived_cl8812, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 38.24/6.07 ((X0)
% 38.24/6.07 = (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X4) @ X4) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 38.24/6.07 (inverse @ (multiply @ (inverse @ X2) @ X2))) @
% 38.24/6.07 (inverse @ X1))) @
% 38.24/6.07 X0))) @
% 38.24/6.07 X1)))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl8606, zip_derived_cl4359])).
% 38.24/6.07 thf(zip_derived_cl8606, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X3 : $i]:
% 38.24/6.07 ((multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 38.24/6.07 (inverse @ (multiply @ (inverse @ X0) @ X0))) @
% 38.24/6.07 X1) = (X1))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl8417, zip_derived_cl4358])).
% 38.24/6.07 thf(zip_derived_cl8959, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X4 : $i]:
% 38.24/6.07 ((X0)
% 38.24/6.07 = (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X4) @ X4) @
% 38.24/6.07 (inverse @ (multiply @ (inverse @ (inverse @ X1)) @ X0))) @
% 38.24/6.07 X1)))),
% 38.24/6.07 inference('demod', [status(thm)],
% 38.24/6.07 [zip_derived_cl8812, zip_derived_cl8606])).
% 38.24/6.07 thf(zip_derived_cl8417, plain,
% 38.24/6.07 (![X1 : $i, X2 : $i]:
% 38.24/6.07 ((multiply @ (inverse @ X1) @ X1) = (multiply @ (inverse @ X2) @ X2))),
% 38.24/6.07 inference('demod', [status(thm)],
% 38.24/6.07 [zip_derived_cl8310, zip_derived_cl4283, zip_derived_cl4356])).
% 38.24/6.07 thf(zip_derived_cl11288, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((multiply @ (inverse @ (inverse @ X2)) @
% 38.24/6.07 (inverse @ (multiply @ X0 @ X2)))
% 38.24/6.07 = (multiply @ (inverse @ (inverse @ X1)) @
% 38.24/6.07 (inverse @ (multiply @ X0 @ X1))))),
% 38.24/6.07 inference('sup+', [status(thm)], [zip_derived_cl8999, zip_derived_cl8997])).
% 38.24/6.07 thf(zip_derived_cl11481, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.07 ((multiply @ (inverse @ (inverse @ X2)) @
% 38.24/6.07 (inverse @ (multiply @ (inverse @ X0) @ X0)))
% 38.24/6.07 = (multiply @ (inverse @ (inverse @ X1)) @
% 38.24/6.07 (inverse @ (multiply @ (inverse @ X2) @ X1))))),
% 38.24/6.07 inference('sup+', [status(thm)],
% 38.24/6.07 [zip_derived_cl8417, zip_derived_cl11288])).
% 38.24/6.07 thf(zip_derived_cl11916, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 38.24/6.07 ((multiply @ (inverse @ X0) @
% 38.24/6.07 (inverse @ (multiply @ (inverse @ X4) @ X4)))
% 38.24/6.07 = (multiply @ (inverse @ (inverse @ X1)) @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.07 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 38.24/6.07 (inverse @ (multiply @ (inverse @ (inverse @ X2)) @ X0))) @
% 38.24/6.07 X2)) @
% 38.24/6.07 X1))))),
% 38.24/6.07 inference('sup+', [status(thm)],
% 38.24/6.07 [zip_derived_cl8959, zip_derived_cl11481])).
% 38.24/6.07 thf(zip_derived_cl8959, plain,
% 38.24/6.07 (![X0 : $i, X1 : $i, X4 : $i]:
% 38.24/6.07 ((X0)
% 38.24/6.07 = (inverse @
% 38.24/6.07 (multiply @
% 38.24/6.08 (multiply @ (multiply @ (inverse @ X4) @ X4) @
% 38.24/6.08 (inverse @ (multiply @ (inverse @ (inverse @ X1)) @ X0))) @
% 38.24/6.08 X1)))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl8812, zip_derived_cl8606])).
% 38.24/6.08 thf(zip_derived_cl11966, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i, X4 : $i]:
% 38.24/6.08 ((multiply @ (inverse @ X0) @
% 38.24/6.08 (inverse @ (multiply @ (inverse @ X4) @ X4)))
% 38.24/6.08 = (multiply @ (inverse @ (inverse @ X1)) @
% 38.24/6.08 (inverse @ (multiply @ X0 @ X1))))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl11916, zip_derived_cl8959])).
% 38.24/6.08 thf(zip_derived_cl4356, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 38.24/6.08 ((multiply @ (multiply @ (inverse @ X3) @ X3) @
% 38.24/6.08 (inverse @
% 38.24/6.08 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 38.24/6.08 (multiply @ X2 @ (inverse @ (multiply @ X1 @ X0))))))
% 38.24/6.08 = (X1))),
% 38.24/6.08 inference('sup+', [status(thm)], [zip_derived_cl4281, zip_derived_cl50])).
% 38.24/6.08 thf(zip_derived_cl4356, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 38.24/6.08 ((multiply @ (multiply @ (inverse @ X3) @ X3) @
% 38.24/6.08 (inverse @
% 38.24/6.08 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 38.24/6.08 (multiply @ X2 @ (inverse @ (multiply @ X1 @ X0))))))
% 38.24/6.08 = (X1))),
% 38.24/6.08 inference('sup+', [status(thm)], [zip_derived_cl4281, zip_derived_cl50])).
% 38.24/6.08 thf(zip_derived_cl4801, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 38.24/6.08 ((multiply @ (multiply @ (inverse @ X4) @ X4) @
% 38.24/6.08 (inverse @
% 38.24/6.08 (multiply @
% 38.24/6.08 (inverse @
% 38.24/6.08 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 38.24/6.08 (inverse @ (multiply @ X2 @ (inverse @ (multiply @ X0 @ X1)))))) @
% 38.24/6.08 X0)))
% 38.24/6.08 = (inverse @ (multiply @ X2 @ (inverse @ X1))))),
% 38.24/6.08 inference('sup+', [status(thm)], [zip_derived_cl4356, zip_derived_cl4356])).
% 38.24/6.08 thf(zip_derived_cl12180, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 38.24/6.08 ((multiply @ (multiply @ (inverse @ X5) @ X5) @
% 38.24/6.08 (inverse @
% 38.24/6.08 (multiply @ (inverse @ (inverse @ X0)) @
% 38.24/6.08 (inverse @
% 38.24/6.08 (multiply @
% 38.24/6.08 (multiply @ (multiply @ (inverse @ X4) @ X4) @
% 38.24/6.08 (inverse @
% 38.24/6.08 (multiply @ X3 @
% 38.24/6.08 (inverse @
% 38.24/6.08 (multiply @ (inverse @ (multiply @ (inverse @ X2) @ X2)) @
% 38.24/6.08 X1))))) @
% 38.24/6.08 X0)))))
% 38.24/6.08 = (inverse @ (multiply @ X3 @ (inverse @ X1))))),
% 38.24/6.08 inference('sup+', [status(thm)],
% 38.24/6.08 [zip_derived_cl11966, zip_derived_cl4801])).
% 38.24/6.08 thf(zip_derived_cl3823, plain,
% 38.24/6.08 (![X1 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 38.24/6.08 ((multiply @ X5 @
% 38.24/6.08 (inverse @
% 38.24/6.08 (multiply @
% 38.24/6.08 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 38.24/6.08 (inverse @
% 38.24/6.08 (multiply @ (inverse @ (multiply @ X5 @ (inverse @ X4))) @ X3))) @
% 38.24/6.08 X4)))
% 38.24/6.08 = (X3))),
% 38.24/6.08 inference('demod', [status(thm)], [zip_derived_cl3763, zip_derived_cl0])).
% 38.24/6.08 thf(zip_derived_cl8417, plain,
% 38.24/6.08 (![X1 : $i, X2 : $i]:
% 38.24/6.08 ((multiply @ (inverse @ X1) @ X1) = (multiply @ (inverse @ X2) @ X2))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl8310, zip_derived_cl4283, zip_derived_cl4356])).
% 38.24/6.08 thf(zip_derived_cl8606, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i, X3 : $i]:
% 38.24/6.08 ((multiply @
% 38.24/6.08 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 38.24/6.08 (inverse @ (multiply @ (inverse @ X0) @ X0))) @
% 38.24/6.08 X1) = (X1))),
% 38.24/6.08 inference('sup+', [status(thm)], [zip_derived_cl8417, zip_derived_cl4358])).
% 38.24/6.08 thf(zip_derived_cl1249, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 38.24/6.08 ((multiply @ (inverse @ (multiply @ X1 @ X2)) @ (multiply @ X1 @ X0))
% 38.24/6.08 = (multiply @ (inverse @ (multiply @ X3 @ X2)) @
% 38.24/6.08 (multiply @ X3 @ X0)))),
% 38.24/6.08 inference('sup+', [status(thm)], [zip_derived_cl1094, zip_derived_cl1094])).
% 38.24/6.08 thf(zip_derived_cl8807, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 38.24/6.08 ((multiply @
% 38.24/6.08 (inverse @
% 38.24/6.08 (multiply @
% 38.24/6.08 (multiply @ (multiply @ (inverse @ X4) @ X4) @
% 38.24/6.08 (inverse @ (multiply @ (inverse @ X3) @ X3))) @
% 38.24/6.08 X2)) @
% 38.24/6.08 X0)
% 38.24/6.08 = (multiply @ (inverse @ (multiply @ X1 @ X2)) @
% 38.24/6.08 (multiply @ X1 @ X0)))),
% 38.24/6.08 inference('sup+', [status(thm)], [zip_derived_cl8606, zip_derived_cl1249])).
% 38.24/6.08 thf(zip_derived_cl8606, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i, X3 : $i]:
% 38.24/6.08 ((multiply @
% 38.24/6.08 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 38.24/6.08 (inverse @ (multiply @ (inverse @ X0) @ X0))) @
% 38.24/6.08 X1) = (X1))),
% 38.24/6.08 inference('sup+', [status(thm)], [zip_derived_cl8417, zip_derived_cl4358])).
% 38.24/6.08 thf(zip_derived_cl8955, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.08 ((multiply @ (inverse @ X2) @ X0)
% 38.24/6.08 = (multiply @ (inverse @ (multiply @ X1 @ X2)) @
% 38.24/6.08 (multiply @ X1 @ X0)))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl8807, zip_derived_cl8606])).
% 38.24/6.08 thf(zip_derived_cl9146, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.08 ((multiply @ (inverse @ X2) @ X1)
% 38.24/6.08 = (multiply @ (inverse @ (multiply @ (inverse @ X0) @ X0)) @
% 38.24/6.08 (multiply @ (inverse @ X2) @ X1)))),
% 38.24/6.08 inference('sup+', [status(thm)], [zip_derived_cl8417, zip_derived_cl8955])).
% 38.24/6.08 thf(zip_derived_cl9383, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 38.24/6.08 ((multiply @ (inverse @ X2) @
% 38.24/6.08 (inverse @
% 38.24/6.08 (multiply @
% 38.24/6.08 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 38.24/6.08 (inverse @
% 38.24/6.08 (multiply @
% 38.24/6.08 (inverse @ (multiply @ (inverse @ X2) @ (inverse @ X1))) @ X0))) @
% 38.24/6.08 X1)))
% 38.24/6.08 = (multiply @ (inverse @ (multiply @ (inverse @ X4) @ X4)) @ X0))),
% 38.24/6.08 inference('sup+', [status(thm)], [zip_derived_cl3823, zip_derived_cl9146])).
% 38.24/6.08 thf(zip_derived_cl3823, plain,
% 38.24/6.08 (![X1 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 38.24/6.08 ((multiply @ X5 @
% 38.24/6.08 (inverse @
% 38.24/6.08 (multiply @
% 38.24/6.08 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 38.24/6.08 (inverse @
% 38.24/6.08 (multiply @ (inverse @ (multiply @ X5 @ (inverse @ X4))) @ X3))) @
% 38.24/6.08 X4)))
% 38.24/6.08 = (X3))),
% 38.24/6.08 inference('demod', [status(thm)], [zip_derived_cl3763, zip_derived_cl0])).
% 38.24/6.08 thf(zip_derived_cl9417, plain,
% 38.24/6.08 (![X0 : $i, X4 : $i]:
% 38.24/6.08 ((X0) = (multiply @ (inverse @ (multiply @ (inverse @ X4) @ X4)) @ X0))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl9383, zip_derived_cl3823])).
% 38.24/6.08 thf(zip_derived_cl8997, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.08 ((multiply @ (inverse @ (inverse @ X0)) @
% 38.24/6.08 (inverse @
% 38.24/6.08 (multiply @
% 38.24/6.08 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1)) @
% 38.24/6.08 X0)))
% 38.24/6.08 = (X1))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl8851, zip_derived_cl8606])).
% 38.24/6.08 thf(zip_derived_cl12348, plain,
% 38.24/6.08 (![X1 : $i, X3 : $i, X5 : $i]:
% 38.24/6.08 ((multiply @ (multiply @ (inverse @ X5) @ X5) @
% 38.24/6.08 (inverse @ (multiply @ X3 @ (inverse @ X1))))
% 38.24/6.08 = (inverse @ (multiply @ X3 @ (inverse @ X1))))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl12180, zip_derived_cl9417, zip_derived_cl8997])).
% 38.24/6.08 thf(zip_derived_cl12441, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 38.24/6.08 ((multiply @ (multiply @ (inverse @ X3) @ X3) @
% 38.24/6.08 (inverse @
% 38.24/6.08 (multiply @ (inverse @ (inverse @ X0)) @
% 38.24/6.08 (inverse @ (multiply @ X1 @ X0)))))
% 38.24/6.08 = (inverse @
% 38.24/6.08 (multiply @ (inverse @ (inverse @ X2)) @
% 38.24/6.08 (inverse @ (multiply @ X1 @ X2)))))),
% 38.24/6.08 inference('sup+', [status(thm)],
% 38.24/6.08 [zip_derived_cl11288, zip_derived_cl12348])).
% 38.24/6.08 thf(zip_derived_cl8999, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i, X4 : $i]:
% 38.24/6.08 ((multiply @ (multiply @ (inverse @ X4) @ X4) @
% 38.24/6.08 (inverse @
% 38.24/6.08 (multiply @ (inverse @ (inverse @ X0)) @
% 38.24/6.08 (inverse @ (multiply @ X1 @ X0)))))
% 38.24/6.08 = (X1))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl8853, zip_derived_cl8606])).
% 38.24/6.08 thf(zip_derived_cl12488, plain,
% 38.24/6.08 (![X1 : $i, X2 : $i]:
% 38.24/6.08 ((X1)
% 38.24/6.08 = (inverse @
% 38.24/6.08 (multiply @ (inverse @ (inverse @ X2)) @
% 38.24/6.08 (inverse @ (multiply @ X1 @ X2)))))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl12441, zip_derived_cl8999])).
% 38.24/6.08 thf(zip_derived_cl4351, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 38.24/6.08 ((multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 38.24/6.08 (multiply @ X3 @
% 38.24/6.08 (inverse @
% 38.24/6.08 (multiply @
% 38.24/6.08 (multiply @ (multiply @ (inverse @ X1) @ X1) @ (inverse @ X0)) @
% 38.24/6.08 X2))))
% 38.24/6.08 = (X0))),
% 38.24/6.08 inference('sup+', [status(thm)], [zip_derived_cl4281, zip_derived_cl13])).
% 38.24/6.08 thf(zip_derived_cl8959, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i, X4 : $i]:
% 38.24/6.08 ((X0)
% 38.24/6.08 = (inverse @
% 38.24/6.08 (multiply @
% 38.24/6.08 (multiply @ (multiply @ (inverse @ X4) @ X4) @
% 38.24/6.08 (inverse @ (multiply @ (inverse @ (inverse @ X1)) @ X0))) @
% 38.24/6.08 X1)))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl8812, zip_derived_cl8606])).
% 38.24/6.08 thf(zip_derived_cl12348, plain,
% 38.24/6.08 (![X1 : $i, X3 : $i, X5 : $i]:
% 38.24/6.08 ((multiply @ (multiply @ (inverse @ X5) @ X5) @
% 38.24/6.08 (inverse @ (multiply @ X3 @ (inverse @ X1))))
% 38.24/6.08 = (inverse @ (multiply @ X3 @ (inverse @ X1))))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl12180, zip_derived_cl9417, zip_derived_cl8997])).
% 38.24/6.08 thf(zip_derived_cl12421, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 38.24/6.08 ((multiply @ (multiply @ (inverse @ X3) @ X3) @ X0)
% 38.24/6.08 = (inverse @
% 38.24/6.08 (multiply @
% 38.24/6.08 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 38.24/6.08 (inverse @
% 38.24/6.08 (multiply @ (inverse @ (inverse @ (inverse @ X1))) @ X0))) @
% 38.24/6.08 (inverse @ X1))))),
% 38.24/6.08 inference('sup+', [status(thm)],
% 38.24/6.08 [zip_derived_cl8959, zip_derived_cl12348])).
% 38.24/6.08 thf(zip_derived_cl8959, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i, X4 : $i]:
% 38.24/6.08 ((X0)
% 38.24/6.08 = (inverse @
% 38.24/6.08 (multiply @
% 38.24/6.08 (multiply @ (multiply @ (inverse @ X4) @ X4) @
% 38.24/6.08 (inverse @ (multiply @ (inverse @ (inverse @ X1)) @ X0))) @
% 38.24/6.08 X1)))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl8812, zip_derived_cl8606])).
% 38.24/6.08 thf(zip_derived_cl12469, plain,
% 38.24/6.08 (![X0 : $i, X3 : $i]:
% 38.24/6.08 ((multiply @ (multiply @ (inverse @ X3) @ X3) @ X0) = (X0))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl12421, zip_derived_cl8959])).
% 38.24/6.08 thf(zip_derived_cl8955, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.08 ((multiply @ (inverse @ X2) @ X0)
% 38.24/6.08 = (multiply @ (inverse @ (multiply @ X1 @ X2)) @
% 38.24/6.08 (multiply @ X1 @ X0)))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl8807, zip_derived_cl8606])).
% 38.24/6.08 thf(zip_derived_cl12528, plain,
% 38.24/6.08 (![X0 : $i, X2 : $i]:
% 38.24/6.08 ((multiply @ (inverse @ (inverse @ X2)) @
% 38.24/6.08 (inverse @ (multiply @ (inverse @ X0) @ X2))) = (X0))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl4351, zip_derived_cl12469, zip_derived_cl8955])).
% 38.24/6.08 thf(zip_derived_cl12873, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i]:
% 38.24/6.08 ((multiply @
% 38.24/6.08 (inverse @ (inverse @ (inverse @ (multiply @ X0 @ X1)))) @ X0)
% 38.24/6.08 = (inverse @ X1))),
% 38.24/6.08 inference('sup+', [status(thm)],
% 38.24/6.08 [zip_derived_cl12488, zip_derived_cl12528])).
% 38.24/6.08 thf(zip_derived_cl4281, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i, X3 : $i]:
% 38.24/6.08 ((multiply @ (multiply @ (inverse @ X0) @ X0) @ X1)
% 38.24/6.08 = (multiply @ (multiply @ (inverse @ X3) @ X3) @ X1))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl4125, zip_derived_cl1569])).
% 38.24/6.08 thf(zip_derived_cl3823, plain,
% 38.24/6.08 (![X1 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 38.24/6.08 ((multiply @ X5 @
% 38.24/6.08 (inverse @
% 38.24/6.08 (multiply @
% 38.24/6.08 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 38.24/6.08 (inverse @
% 38.24/6.08 (multiply @ (inverse @ (multiply @ X5 @ (inverse @ X4))) @ X3))) @
% 38.24/6.08 X4)))
% 38.24/6.08 = (X3))),
% 38.24/6.08 inference('demod', [status(thm)], [zip_derived_cl3763, zip_derived_cl0])).
% 38.24/6.08 thf(zip_derived_cl4335, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 38.24/6.08 ((multiply @ (multiply @ (inverse @ X3) @ X3) @
% 38.24/6.08 (inverse @
% 38.24/6.08 (multiply @
% 38.24/6.08 (multiply @ (multiply @ (inverse @ X4) @ X4) @
% 38.24/6.08 (inverse @
% 38.24/6.08 (multiply @
% 38.24/6.08 (inverse @
% 38.24/6.08 (multiply @ (multiply @ (inverse @ X1) @ X1) @ (inverse @ X0))) @
% 38.24/6.08 X2))) @
% 38.24/6.08 X0)))
% 38.24/6.08 = (X2))),
% 38.24/6.08 inference('sup+', [status(thm)], [zip_derived_cl4281, zip_derived_cl3823])).
% 38.24/6.08 thf(zip_derived_cl12469, plain,
% 38.24/6.08 (![X0 : $i, X3 : $i]:
% 38.24/6.08 ((multiply @ (multiply @ (inverse @ X3) @ X3) @ X0) = (X0))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl12421, zip_derived_cl8959])).
% 38.24/6.08 thf(zip_derived_cl12469, plain,
% 38.24/6.08 (![X0 : $i, X3 : $i]:
% 38.24/6.08 ((multiply @ (multiply @ (inverse @ X3) @ X3) @ X0) = (X0))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl12421, zip_derived_cl8959])).
% 38.24/6.08 thf(zip_derived_cl12469, plain,
% 38.24/6.08 (![X0 : $i, X3 : $i]:
% 38.24/6.08 ((multiply @ (multiply @ (inverse @ X3) @ X3) @ X0) = (X0))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl12421, zip_derived_cl8959])).
% 38.24/6.08 thf(zip_derived_cl12526, plain,
% 38.24/6.08 (![X0 : $i, X2 : $i]:
% 38.24/6.08 ((inverse @
% 38.24/6.08 (multiply @
% 38.24/6.08 (inverse @ (multiply @ (inverse @ (inverse @ X0)) @ X2)) @ X0))
% 38.24/6.08 = (X2))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl4335, zip_derived_cl12469, zip_derived_cl12469,
% 38.24/6.08 zip_derived_cl12469])).
% 38.24/6.08 thf(zip_derived_cl11966, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i, X4 : $i]:
% 38.24/6.08 ((multiply @ (inverse @ X0) @
% 38.24/6.08 (inverse @ (multiply @ (inverse @ X4) @ X4)))
% 38.24/6.08 = (multiply @ (inverse @ (inverse @ X1)) @
% 38.24/6.08 (inverse @ (multiply @ X0 @ X1))))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl11916, zip_derived_cl8959])).
% 38.24/6.08 thf(zip_derived_cl12348, plain,
% 38.24/6.08 (![X1 : $i, X3 : $i, X5 : $i]:
% 38.24/6.08 ((multiply @ (multiply @ (inverse @ X5) @ X5) @
% 38.24/6.08 (inverse @ (multiply @ X3 @ (inverse @ X1))))
% 38.24/6.08 = (inverse @ (multiply @ X3 @ (inverse @ X1))))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl12180, zip_derived_cl9417, zip_derived_cl8997])).
% 38.24/6.08 thf(zip_derived_cl12439, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 38.24/6.08 ((multiply @ (multiply @ (inverse @ X3) @ X3) @
% 38.24/6.08 (inverse @
% 38.24/6.08 (multiply @ (inverse @ (inverse @ X0)) @
% 38.24/6.08 (inverse @ (multiply @ X1 @ X0)))))
% 38.24/6.08 = (inverse @
% 38.24/6.08 (multiply @ (inverse @ X1) @
% 38.24/6.08 (inverse @ (multiply @ (inverse @ X2) @ X2)))))),
% 38.24/6.08 inference('sup+', [status(thm)],
% 38.24/6.08 [zip_derived_cl11966, zip_derived_cl12348])).
% 38.24/6.08 thf(zip_derived_cl8999, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i, X4 : $i]:
% 38.24/6.08 ((multiply @ (multiply @ (inverse @ X4) @ X4) @
% 38.24/6.08 (inverse @
% 38.24/6.08 (multiply @ (inverse @ (inverse @ X0)) @
% 38.24/6.08 (inverse @ (multiply @ X1 @ X0)))))
% 38.24/6.08 = (X1))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl8853, zip_derived_cl8606])).
% 38.24/6.08 thf(zip_derived_cl12486, plain,
% 38.24/6.08 (![X1 : $i, X2 : $i]:
% 38.24/6.08 ((X1)
% 38.24/6.08 = (inverse @
% 38.24/6.08 (multiply @ (inverse @ X1) @
% 38.24/6.08 (inverse @ (multiply @ (inverse @ X2) @ X2)))))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl12439, zip_derived_cl8999])).
% 38.24/6.08 thf(zip_derived_cl12814, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i]:
% 38.24/6.08 ((multiply @
% 38.24/6.08 (inverse @ (inverse @ (inverse @ (multiply @ (inverse @ X1) @ X1)))) @
% 38.24/6.08 X0) = (X0))),
% 38.24/6.08 inference('sup+', [status(thm)],
% 38.24/6.08 [zip_derived_cl12526, zip_derived_cl12486])).
% 38.24/6.08 thf(zip_derived_cl12469, plain,
% 38.24/6.08 (![X0 : $i, X3 : $i]:
% 38.24/6.08 ((multiply @ (multiply @ (inverse @ X3) @ X3) @ X0) = (X0))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl12421, zip_derived_cl8959])).
% 38.24/6.08 thf(zip_derived_cl13083, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i]:
% 38.24/6.08 ((multiply @
% 38.24/6.08 (inverse @ (inverse @ (multiply @ (inverse @ X0) @ X0))) @ X1)
% 38.24/6.08 = (X1))),
% 38.24/6.08 inference('sup+', [status(thm)],
% 38.24/6.08 [zip_derived_cl12814, zip_derived_cl12469])).
% 38.24/6.08 thf(zip_derived_cl12526, plain,
% 38.24/6.08 (![X0 : $i, X2 : $i]:
% 38.24/6.08 ((inverse @
% 38.24/6.08 (multiply @
% 38.24/6.08 (inverse @ (multiply @ (inverse @ (inverse @ X0)) @ X2)) @ X0))
% 38.24/6.08 = (X2))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl4335, zip_derived_cl12469, zip_derived_cl12469,
% 38.24/6.08 zip_derived_cl12469])).
% 38.24/6.08 thf(zip_derived_cl13171, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i]:
% 38.24/6.08 ((inverse @
% 38.24/6.08 (multiply @ (inverse @ X0) @ (multiply @ (inverse @ X1) @ X1)))
% 38.24/6.08 = (X0))),
% 38.24/6.08 inference('sup+', [status(thm)],
% 38.24/6.08 [zip_derived_cl13083, zip_derived_cl12526])).
% 38.24/6.08 thf(zip_derived_cl8955, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.08 ((multiply @ (inverse @ X2) @ X0)
% 38.24/6.08 = (multiply @ (inverse @ (multiply @ X1 @ X2)) @
% 38.24/6.08 (multiply @ X1 @ X0)))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl8807, zip_derived_cl8606])).
% 38.24/6.08 thf(zip_derived_cl13255, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.08 ((multiply @ (inverse @ (multiply @ (inverse @ X2) @ X2)) @ X1)
% 38.24/6.08 = (multiply @ X0 @ (multiply @ (inverse @ X0) @ X1)))),
% 38.24/6.08 inference('sup+', [status(thm)],
% 38.24/6.08 [zip_derived_cl13171, zip_derived_cl8955])).
% 38.24/6.08 thf(zip_derived_cl9417, plain,
% 38.24/6.08 (![X0 : $i, X4 : $i]:
% 38.24/6.08 ((X0) = (multiply @ (inverse @ (multiply @ (inverse @ X4) @ X4)) @ X0))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl9383, zip_derived_cl3823])).
% 38.24/6.08 thf(zip_derived_cl13329, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i]:
% 38.24/6.08 ((X1) = (multiply @ X0 @ (multiply @ (inverse @ X0) @ X1)))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl13255, zip_derived_cl9417])).
% 38.24/6.08 thf(zip_derived_cl13171, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i]:
% 38.24/6.08 ((inverse @
% 38.24/6.08 (multiply @ (inverse @ X0) @ (multiply @ (inverse @ X1) @ X1)))
% 38.24/6.08 = (X0))),
% 38.24/6.08 inference('sup+', [status(thm)],
% 38.24/6.08 [zip_derived_cl13083, zip_derived_cl12526])).
% 38.24/6.08 thf(zip_derived_cl13360, plain,
% 38.24/6.08 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 38.24/6.08 inference('sup+', [status(thm)],
% 38.24/6.08 [zip_derived_cl13329, zip_derived_cl13171])).
% 38.24/6.08 thf(zip_derived_cl13409, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i]:
% 38.24/6.08 ((multiply @ (inverse @ (multiply @ X0 @ X1)) @ X0) = (inverse @ X1))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl12873, zip_derived_cl13360])).
% 38.24/6.08 thf(zip_derived_cl13409, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i]:
% 38.24/6.08 ((multiply @ (inverse @ (multiply @ X0 @ X1)) @ X0) = (inverse @ X1))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl12873, zip_derived_cl13360])).
% 38.24/6.08 thf(zip_derived_cl13832, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i]:
% 38.24/6.08 ((multiply @ (inverse @ (inverse @ X0)) @
% 38.24/6.08 (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 38.24/6.08 inference('sup+', [status(thm)],
% 38.24/6.08 [zip_derived_cl13409, zip_derived_cl13409])).
% 38.24/6.08 thf(zip_derived_cl13360, plain,
% 38.24/6.08 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 38.24/6.08 inference('sup+', [status(thm)],
% 38.24/6.08 [zip_derived_cl13329, zip_derived_cl13171])).
% 38.24/6.08 thf(zip_derived_cl13845, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i]:
% 38.24/6.08 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl13832, zip_derived_cl13360])).
% 38.24/6.08 thf(zip_derived_cl8955, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.08 ((multiply @ (inverse @ X2) @ X0)
% 38.24/6.08 = (multiply @ (inverse @ (multiply @ X1 @ X2)) @
% 38.24/6.08 (multiply @ X1 @ X0)))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl8807, zip_derived_cl8606])).
% 38.24/6.08 thf(zip_derived_cl14019, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.08 ((multiply @ (inverse @ (inverse @ (multiply @ X0 @ X2))) @ X1)
% 38.24/6.08 = (multiply @ (inverse @ (inverse @ X0)) @ (multiply @ X2 @ X1)))),
% 38.24/6.08 inference('sup+', [status(thm)],
% 38.24/6.08 [zip_derived_cl13845, zip_derived_cl8955])).
% 38.24/6.08 thf(zip_derived_cl13360, plain,
% 38.24/6.08 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 38.24/6.08 inference('sup+', [status(thm)],
% 38.24/6.08 [zip_derived_cl13329, zip_derived_cl13171])).
% 38.24/6.08 thf(zip_derived_cl13360, plain,
% 38.24/6.08 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 38.24/6.08 inference('sup+', [status(thm)],
% 38.24/6.08 [zip_derived_cl13329, zip_derived_cl13171])).
% 38.24/6.08 thf(zip_derived_cl14078, plain,
% 38.24/6.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 38.24/6.08 ((multiply @ (multiply @ X0 @ X2) @ X1)
% 38.24/6.08 = (multiply @ X0 @ (multiply @ X2 @ X1)))),
% 38.24/6.08 inference('demod', [status(thm)],
% 38.24/6.08 [zip_derived_cl14019, zip_derived_cl13360, zip_derived_cl13360])).
% 38.24/6.08 thf(zip_derived_cl14091, plain,
% 38.24/6.08 (((multiply @ a3 @ (multiply @ b3 @ c3))
% 38.24/6.08 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 38.24/6.08 inference('demod', [status(thm)], [zip_derived_cl1, zip_derived_cl14078])).
% 38.24/6.08 thf(zip_derived_cl14092, plain, ($false),
% 38.24/6.08 inference('simplify', [status(thm)], [zip_derived_cl14091])).
% 38.24/6.08
% 38.24/6.08 % SZS output end Refutation
% 38.24/6.08
% 38.24/6.08
% 38.24/6.08 % Terminating...
% 38.57/6.15 % Runner terminated.
% 38.57/6.16 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------