TSTP Solution File: GRP501-1 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP501-1 : 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.t2ZPPH0ZAy true
% Computer : n008.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 01:51:54 EDT 2023
% Result : Unsatisfiable 27.19s 4.49s
% Output : Refutation 27.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP501-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.15 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.t2ZPPH0ZAy true
% 0.19/0.36 % Computer : n008.cluster.edu
% 0.19/0.36 % Model : x86_64 x86_64
% 0.19/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.36 % Memory : 8042.1875MB
% 0.19/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.36 % CPULimit : 300
% 0.19/0.36 % WCLimit : 300
% 0.19/0.36 % DateTime : Mon Aug 28 23:45:17 EDT 2023
% 0.19/0.36 % CPUTime :
% 0.19/0.36 % Running portfolio for 300 s
% 0.19/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.36 % Number of cores: 8
% 0.19/0.37 % Python version: Python 3.6.8
% 0.19/0.37 % Running in FO mode
% 0.22/0.67 % Total configuration time : 435
% 0.22/0.67 % Estimated wc time : 1092
% 0.22/0.67 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.73 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.73 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.77 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.22/0.77 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 1.32/0.78 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 1.32/0.78 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 27.19/4.49 % Solved by fo/fo4.sh.
% 27.19/4.49 % done 844 iterations in 3.676s
% 27.19/4.49 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 27.19/4.49 % SZS output start Refutation
% 27.19/4.49 thf(a3_type, type, a3: $i).
% 27.19/4.49 thf(multiply_type, type, multiply: $i > $i > $i).
% 27.19/4.49 thf(inverse_type, type, inverse: $i > $i).
% 27.19/4.49 thf(c3_type, type, c3: $i).
% 27.19/4.49 thf(double_divide_type, type, double_divide: $i > $i > $i).
% 27.19/4.49 thf(b3_type, type, b3: $i).
% 27.19/4.49 thf(prove_these_axioms_3, conjecture,
% 27.19/4.49 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) =
% 27.19/4.49 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ))).
% 27.19/4.49 thf(zf_stmt_0, negated_conjecture,
% 27.19/4.49 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 27.19/4.49 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) )),
% 27.19/4.49 inference('cnf.neg', [status(esa)], [prove_these_axioms_3])).
% 27.19/4.49 thf(zip_derived_cl2, plain,
% 27.19/4.49 (((multiply @ (multiply @ a3 @ b3) @ c3)
% 27.19/4.49 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 27.19/4.49 inference('cnf', [status(esa)], [zf_stmt_0])).
% 27.19/4.49 thf(single_axiom, axiom,
% 27.19/4.49 (( double_divide @
% 27.19/4.49 ( inverse @ A ) @
% 27.19/4.49 ( inverse @
% 27.19/4.49 ( double_divide @
% 27.19/4.49 ( inverse @ ( double_divide @ A @ ( double_divide @ B @ C ) ) ) @
% 27.19/4.49 ( double_divide @ D @ ( double_divide @ B @ D ) ) ) ) ) =
% 27.19/4.49 ( C ))).
% 27.19/4.49 thf(zip_derived_cl0, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X1) @
% 27.19/4.49 (inverse @
% 27.19/4.49 (double_divide @
% 27.19/4.49 (inverse @ (double_divide @ X1 @ (double_divide @ X2 @ X0))) @
% 27.19/4.49 (double_divide @ X3 @ (double_divide @ X2 @ X3)))))
% 27.19/4.49 = (X0))),
% 27.19/4.49 inference('cnf', [status(esa)], [single_axiom])).
% 27.19/4.49 thf(multiply, axiom,
% 27.19/4.49 (( multiply @ A @ B ) = ( inverse @ ( double_divide @ B @ A ) ))).
% 27.19/4.49 thf(zip_derived_cl1, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 27.19/4.49 inference('cnf', [status(esa)], [multiply])).
% 27.19/4.49 thf(zip_derived_cl1, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 27.19/4.49 inference('cnf', [status(esa)], [multiply])).
% 27.19/4.49 thf(zip_derived_cl3, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X1) @
% 27.19/4.49 (multiply @ (double_divide @ X3 @ (double_divide @ X2 @ X3)) @
% 27.19/4.49 (multiply @ (double_divide @ X2 @ X0) @ X1)))
% 27.19/4.49 = (X0))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1])).
% 27.19/4.49 thf(zip_derived_cl3, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X1) @
% 27.19/4.49 (multiply @ (double_divide @ X3 @ (double_divide @ X2 @ X3)) @
% 27.19/4.49 (multiply @ (double_divide @ X2 @ X0) @ X1)))
% 27.19/4.49 = (X0))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1])).
% 27.19/4.49 thf(zip_derived_cl4, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X4) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X5 @ (double_divide @ (inverse @ X1) @ X5)) @
% 27.19/4.49 (multiply @ X0 @ X4)))
% 27.19/4.49 = (multiply @ (double_divide @ X3 @ (double_divide @ X2 @ X3)) @
% 27.19/4.49 (multiply @ (double_divide @ X2 @ X0) @ X1)))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl3])).
% 27.19/4.49 thf(zip_derived_cl3, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X1) @
% 27.19/4.49 (multiply @ (double_divide @ X3 @ (double_divide @ X2 @ X3)) @
% 27.19/4.49 (multiply @ (double_divide @ X2 @ X0) @ X1)))
% 27.19/4.49 = (X0))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1])).
% 27.19/4.49 thf(zip_derived_cl72, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((multiply @ (double_divide @ X3 @ (double_divide @ X2 @ X3)) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X2 @ (double_divide @ (inverse @ X0) @ X1)) @ X0))
% 27.19/4.49 = (X1))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl3])).
% 27.19/4.49 thf(zip_derived_cl1, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 27.19/4.49 inference('cnf', [status(esa)], [multiply])).
% 27.19/4.49 thf(zip_derived_cl72, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((multiply @ (double_divide @ X3 @ (double_divide @ X2 @ X3)) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X2 @ (double_divide @ (inverse @ X0) @ X1)) @ X0))
% 27.19/4.49 = (X1))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl3])).
% 27.19/4.49 thf(zip_derived_cl4, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X4) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X5 @ (double_divide @ (inverse @ X1) @ X5)) @
% 27.19/4.49 (multiply @ X0 @ X4)))
% 27.19/4.49 = (multiply @ (double_divide @ X3 @ (double_divide @ X2 @ X3)) @
% 27.19/4.49 (multiply @ (double_divide @ X2 @ X0) @ X1)))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl3])).
% 27.19/4.49 thf(zip_derived_cl3, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X1) @
% 27.19/4.49 (multiply @ (double_divide @ X3 @ (double_divide @ X2 @ X3)) @
% 27.19/4.49 (multiply @ (double_divide @ X2 @ X0) @ X1)))
% 27.19/4.49 = (X0))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1])).
% 27.19/4.49 thf(zip_derived_cl52, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X3) @
% 27.19/4.49 (double_divide @ (inverse @ X0) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X2 @ (double_divide @ (inverse @ X3) @ X2)) @
% 27.19/4.49 (multiply @ X1 @ X0))))
% 27.19/4.49 = (X1))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl3])).
% 27.19/4.49 thf(zip_derived_cl72, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((multiply @ (double_divide @ X3 @ (double_divide @ X2 @ X3)) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X2 @ (double_divide @ (inverse @ X0) @ X1)) @ X0))
% 27.19/4.49 = (X1))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl3])).
% 27.19/4.49 thf(zip_derived_cl246, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 27.19/4.49 ((multiply @
% 27.19/4.49 (double_divide @ X4 @ (double_divide @ (inverse @ X3) @ X4)) @
% 27.19/4.49 (multiply @ X0 @ X1))
% 27.19/4.49 = (multiply @
% 27.19/4.49 (double_divide @ X2 @ (double_divide @ (inverse @ X3) @ X2)) @
% 27.19/4.49 (multiply @ X0 @ X1)))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl52, zip_derived_cl72])).
% 27.19/4.49 thf(zip_derived_cl443, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 27.19/4.49 ((multiply @
% 27.19/4.49 (double_divide @ X6 @ (double_divide @ (inverse @ X5) @ X6)) @ X0)
% 27.19/4.49 = (multiply @
% 27.19/4.49 (double_divide @ X4 @ (double_divide @ (inverse @ X5) @ X4)) @
% 27.19/4.49 (multiply @ (double_divide @ X3 @ (double_divide @ X2 @ X3)) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X2 @ (double_divide @ (inverse @ X1) @ X0)) @
% 27.19/4.49 X1))))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl72, zip_derived_cl246])).
% 27.19/4.49 thf(zip_derived_cl72, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((multiply @ (double_divide @ X3 @ (double_divide @ X2 @ X3)) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X2 @ (double_divide @ (inverse @ X0) @ X1)) @ X0))
% 27.19/4.49 = (X1))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl3])).
% 27.19/4.49 thf(zip_derived_cl473, plain,
% 27.19/4.49 (![X0 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 27.19/4.49 ((multiply @
% 27.19/4.49 (double_divide @ X6 @ (double_divide @ (inverse @ X5) @ X6)) @ X0)
% 27.19/4.49 = (multiply @
% 27.19/4.49 (double_divide @ X4 @ (double_divide @ (inverse @ X5) @ X4)) @ X0))),
% 27.19/4.49 inference('demod', [status(thm)], [zip_derived_cl443, zip_derived_cl72])).
% 27.19/4.49 thf(zip_derived_cl72, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((multiply @ (double_divide @ X3 @ (double_divide @ X2 @ X3)) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X2 @ (double_divide @ (inverse @ X0) @ X1)) @ X0))
% 27.19/4.49 = (X1))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl3])).
% 27.19/4.49 thf(zip_derived_cl504, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((multiply @ (double_divide @ X3 @ (double_divide @ X2 @ X3)) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X1 @ (double_divide @ (inverse @ X0) @ X1)) @ X0))
% 27.19/4.49 = (X2))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl473, zip_derived_cl72])).
% 27.19/4.49 thf(zip_derived_cl52, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X3) @
% 27.19/4.49 (double_divide @ (inverse @ X0) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X2 @ (double_divide @ (inverse @ X3) @ X2)) @
% 27.19/4.49 (multiply @ X1 @ X0))))
% 27.19/4.49 = (X1))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl3])).
% 27.19/4.49 thf(zip_derived_cl605, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X0) @
% 27.19/4.49 (double_divide @ (inverse @ X2) @ (inverse @ X0)))
% 27.19/4.49 = (double_divide @ X1 @ (double_divide @ (inverse @ X2) @ X1)))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl504, zip_derived_cl52])).
% 27.19/4.49 thf(zip_derived_cl605, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X0) @
% 27.19/4.49 (double_divide @ (inverse @ X2) @ (inverse @ X0)))
% 27.19/4.49 = (double_divide @ X1 @ (double_divide @ (inverse @ X2) @ X1)))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl504, zip_derived_cl52])).
% 27.19/4.49 thf(zip_derived_cl730, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.19/4.49 ((double_divide @ X0 @ (double_divide @ (inverse @ X1) @ X0))
% 27.19/4.49 = (double_divide @ X2 @ (double_divide @ (inverse @ X1) @ X2)))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl605, zip_derived_cl605])).
% 27.19/4.49 thf(zip_derived_cl1, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 27.19/4.49 inference('cnf', [status(esa)], [multiply])).
% 27.19/4.49 thf(zip_derived_cl762, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.19/4.49 ((multiply @ (double_divide @ (inverse @ X1) @ X2) @ X2)
% 27.19/4.49 = (inverse @
% 27.19/4.49 (double_divide @ X0 @ (double_divide @ (inverse @ X1) @ X0))))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl730, zip_derived_cl1])).
% 27.19/4.49 thf(zip_derived_cl920, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((multiply @ (double_divide @ (multiply @ X1 @ X0) @ X3) @ X3)
% 27.19/4.49 = (inverse @
% 27.19/4.49 (double_divide @ X2 @
% 27.19/4.49 (double_divide @ (inverse @ (double_divide @ X0 @ X1)) @ X2))))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl762])).
% 27.19/4.49 thf(zip_derived_cl1, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 27.19/4.49 inference('cnf', [status(esa)], [multiply])).
% 27.19/4.49 thf(zip_derived_cl1, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 27.19/4.49 inference('cnf', [status(esa)], [multiply])).
% 27.19/4.49 thf(zip_derived_cl933, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((multiply @ (double_divide @ (multiply @ X1 @ X0) @ X3) @ X3)
% 27.19/4.49 = (multiply @ (double_divide @ (multiply @ X1 @ X0) @ X2) @ X2))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl920, zip_derived_cl1, zip_derived_cl1])).
% 27.19/4.49 thf(zip_derived_cl1075, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 27.19/4.49 ((multiply @ (double_divide @ X0 @ X5) @ X5)
% 27.19/4.49 = (multiply @
% 27.19/4.49 (double_divide @
% 27.19/4.49 (multiply @ (double_divide @ X4 @ (double_divide @ X3 @ X4)) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X3 @ (double_divide @ (inverse @ X2) @ X0)) @
% 27.19/4.49 X2)) @
% 27.19/4.49 X1) @
% 27.19/4.49 X1))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl72, zip_derived_cl933])).
% 27.19/4.49 thf(zip_derived_cl72, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((multiply @ (double_divide @ X3 @ (double_divide @ X2 @ X3)) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X2 @ (double_divide @ (inverse @ X0) @ X1)) @ X0))
% 27.19/4.49 = (X1))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl3])).
% 27.19/4.49 thf(zip_derived_cl1102, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X5 : $i]:
% 27.19/4.49 ((multiply @ (double_divide @ X0 @ X5) @ X5)
% 27.19/4.49 = (multiply @ (double_divide @ X0 @ X1) @ X1))),
% 27.19/4.49 inference('demod', [status(thm)], [zip_derived_cl1075, zip_derived_cl72])).
% 27.19/4.49 thf(zip_derived_cl4, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X4) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X5 @ (double_divide @ (inverse @ X1) @ X5)) @
% 27.19/4.49 (multiply @ X0 @ X4)))
% 27.19/4.49 = (multiply @ (double_divide @ X3 @ (double_divide @ X2 @ X3)) @
% 27.19/4.49 (multiply @ (double_divide @ X2 @ X0) @ X1)))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl3])).
% 27.19/4.49 thf(zip_derived_cl72, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((multiply @ (double_divide @ X3 @ (double_divide @ X2 @ X3)) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X2 @ (double_divide @ (inverse @ X0) @ X1)) @ X0))
% 27.19/4.49 = (X1))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl3])).
% 27.19/4.49 thf(zip_derived_cl1102, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X5 : $i]:
% 27.19/4.49 ((multiply @ (double_divide @ X0 @ X5) @ X5)
% 27.19/4.49 = (multiply @ (double_divide @ X0 @ X1) @ X1))),
% 27.19/4.49 inference('demod', [status(thm)], [zip_derived_cl1075, zip_derived_cl72])).
% 27.19/4.49 thf(zip_derived_cl1, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 27.19/4.49 inference('cnf', [status(esa)], [multiply])).
% 27.19/4.49 thf(zip_derived_cl3, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X1) @
% 27.19/4.49 (multiply @ (double_divide @ X3 @ (double_divide @ X2 @ X3)) @
% 27.19/4.49 (multiply @ (double_divide @ X2 @ X0) @ X1)))
% 27.19/4.49 = (X0))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1])).
% 27.19/4.49 thf(zip_derived_cl1, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 27.19/4.49 inference('cnf', [status(esa)], [multiply])).
% 27.19/4.49 thf(zip_derived_cl6, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((multiply @
% 27.19/4.49 (multiply @ (double_divide @ X3 @ (double_divide @ X2 @ X3)) @
% 27.19/4.49 (multiply @ (double_divide @ X2 @ X0) @ X1)) @
% 27.19/4.49 (inverse @ X1)) = (inverse @ X0))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 27.19/4.49 thf(zip_derived_cl10, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 27.19/4.49 ((multiply @
% 27.19/4.49 (multiply @ (double_divide @ X4 @ (double_divide @ X3 @ X4)) @
% 27.19/4.49 (multiply @ (double_divide @ X3 @ X2) @ (double_divide @ X0 @ X1))) @
% 27.19/4.49 (multiply @ X1 @ X0)) = (inverse @ X2))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl6])).
% 27.19/4.49 thf(zip_derived_cl1135, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 27.19/4.49 ((multiply @
% 27.19/4.49 (multiply @ (double_divide @ X4 @ (double_divide @ X1 @ X4)) @
% 27.19/4.49 (multiply @ (double_divide @ X1 @ X0) @ X0)) @
% 27.19/4.49 (multiply @ X2 @ X3)) = (inverse @ (double_divide @ X3 @ X2)))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl1102, zip_derived_cl10])).
% 27.19/4.49 thf(zip_derived_cl1, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 27.19/4.49 inference('cnf', [status(esa)], [multiply])).
% 27.19/4.49 thf(zip_derived_cl1175, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 27.19/4.49 ((multiply @
% 27.19/4.49 (multiply @ (double_divide @ X4 @ (double_divide @ X1 @ X4)) @
% 27.19/4.49 (multiply @ (double_divide @ X1 @ X0) @ X0)) @
% 27.19/4.49 (multiply @ X2 @ X3)) = (multiply @ X2 @ X3))),
% 27.19/4.49 inference('demod', [status(thm)], [zip_derived_cl1135, zip_derived_cl1])).
% 27.19/4.49 thf(zip_derived_cl3840, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 27.19/4.49 ((multiply @
% 27.19/4.49 (multiply @ (double_divide @ X6 @ (double_divide @ X5 @ X6)) @
% 27.19/4.49 (multiply @ (double_divide @ X5 @ X4) @ X4)) @
% 27.19/4.49 X0)
% 27.19/4.49 = (multiply @ (double_divide @ X3 @ (double_divide @ X2 @ X3)) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X2 @ (double_divide @ (inverse @ X1) @ X0)) @
% 27.19/4.49 X1)))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl72, zip_derived_cl1175])).
% 27.19/4.49 thf(zip_derived_cl72, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((multiply @ (double_divide @ X3 @ (double_divide @ X2 @ X3)) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X2 @ (double_divide @ (inverse @ X0) @ X1)) @ X0))
% 27.19/4.49 = (X1))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl3])).
% 27.19/4.49 thf(zip_derived_cl3903, plain,
% 27.19/4.49 (![X0 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 27.19/4.49 ((multiply @
% 27.19/4.49 (multiply @ (double_divide @ X6 @ (double_divide @ X5 @ X6)) @
% 27.19/4.49 (multiply @ (double_divide @ X5 @ X4) @ X4)) @
% 27.19/4.49 X0) = (X0))),
% 27.19/4.49 inference('demod', [status(thm)], [zip_derived_cl3840, zip_derived_cl72])).
% 27.19/4.49 thf(zip_derived_cl3938, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((multiply @
% 27.19/4.49 (double_divide @ (inverse @ X0) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X2 @ (double_divide @ (inverse @ X1) @ X2)) @
% 27.19/4.49 (multiply @ X1 @ X0))) @
% 27.19/4.49 X3) = (X3))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl3903])).
% 27.19/4.49 thf(zip_derived_cl1, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 27.19/4.49 inference('cnf', [status(esa)], [multiply])).
% 27.19/4.49 thf(zip_derived_cl504, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((multiply @ (double_divide @ X3 @ (double_divide @ X2 @ X3)) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X1 @ (double_divide @ (inverse @ X0) @ X1)) @ X0))
% 27.19/4.49 = (X2))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl473, zip_derived_cl72])).
% 27.19/4.49 thf(zip_derived_cl3938, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((multiply @
% 27.19/4.49 (double_divide @ (inverse @ X0) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X2 @ (double_divide @ (inverse @ X1) @ X2)) @
% 27.19/4.49 (multiply @ X1 @ X0))) @
% 27.19/4.49 X3) = (X3))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl3903])).
% 27.19/4.49 thf(zip_derived_cl4655, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.19/4.49 ((multiply @
% 27.19/4.49 (double_divide @ (inverse @ X1) @
% 27.19/4.49 (inverse @
% 27.19/4.49 (double_divide @ X0 @ (double_divide @ (inverse @ X1) @ X0)))) @
% 27.19/4.49 X2) = (X2))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl504, zip_derived_cl3938])).
% 27.19/4.49 thf(zip_derived_cl1, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 27.19/4.49 inference('cnf', [status(esa)], [multiply])).
% 27.19/4.49 thf(zip_derived_cl4710, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.19/4.49 ((multiply @
% 27.19/4.49 (double_divide @ (inverse @ X1) @
% 27.19/4.49 (multiply @ (double_divide @ (inverse @ X1) @ X0) @ X0)) @
% 27.19/4.49 X2) = (X2))),
% 27.19/4.49 inference('demod', [status(thm)], [zip_derived_cl4655, zip_derived_cl1])).
% 27.19/4.49 thf(zip_derived_cl4802, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((multiply @
% 27.19/4.49 (double_divide @ (inverse @ (double_divide @ X0 @ X1)) @
% 27.19/4.49 (multiply @ (double_divide @ (multiply @ X1 @ X0) @ X3) @ X3)) @
% 27.19/4.49 X2) = (X2))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl4710])).
% 27.19/4.49 thf(zip_derived_cl1, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 27.19/4.49 inference('cnf', [status(esa)], [multiply])).
% 27.19/4.49 thf(zip_derived_cl4821, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((multiply @
% 27.19/4.49 (double_divide @ (multiply @ X1 @ X0) @
% 27.19/4.49 (multiply @ (double_divide @ (multiply @ X1 @ X0) @ X3) @ X3)) @
% 27.19/4.49 X2) = (X2))),
% 27.19/4.49 inference('demod', [status(thm)], [zip_derived_cl4802, zip_derived_cl1])).
% 27.19/4.49 thf(zip_derived_cl4901, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 27.19/4.49 ((multiply @
% 27.19/4.49 (double_divide @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ (inverse @ X3) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X5 @ (double_divide @ (inverse @ X4) @ X5)) @
% 27.19/4.49 (multiply @ X4 @ X3))) @
% 27.19/4.49 X0) @
% 27.19/4.49 (multiply @ (double_divide @ X0 @ X2) @ X2)) @
% 27.19/4.49 X1) = (X1))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl3938, zip_derived_cl4821])).
% 27.19/4.49 thf(zip_derived_cl3938, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((multiply @
% 27.19/4.49 (double_divide @ (inverse @ X0) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X2 @ (double_divide @ (inverse @ X1) @ X2)) @
% 27.19/4.49 (multiply @ X1 @ X0))) @
% 27.19/4.49 X3) = (X3))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl3903])).
% 27.19/4.49 thf(zip_derived_cl4961, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.19/4.49 ((multiply @
% 27.19/4.49 (double_divide @ X0 @ (multiply @ (double_divide @ X0 @ X2) @ X2)) @
% 27.19/4.49 X1) = (X1))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl4901, zip_derived_cl3938])).
% 27.19/4.49 thf(zip_derived_cl3, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X1) @
% 27.19/4.49 (multiply @ (double_divide @ X3 @ (double_divide @ X2 @ X3)) @
% 27.19/4.49 (multiply @ (double_divide @ X2 @ X0) @ X1)))
% 27.19/4.49 = (X0))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1])).
% 27.19/4.49 thf(zip_derived_cl5017, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X0) @
% 27.19/4.49 (multiply @ (double_divide @ X3 @ (double_divide @ X2 @ X3)) @ X0))
% 27.19/4.49 = (multiply @ (double_divide @ X2 @ X1) @ X1))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl4961, zip_derived_cl3])).
% 27.19/4.49 thf(zip_derived_cl5745, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ (double_divide @ X3 @ X1)) @
% 27.19/4.49 (multiply @ (double_divide @ X1 @ X0) @ X0))
% 27.19/4.49 = (multiply @ (double_divide @ X3 @ X2) @ X2))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl1102, zip_derived_cl5017])).
% 27.19/4.49 thf(zip_derived_cl1, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 27.19/4.49 inference('cnf', [status(esa)], [multiply])).
% 27.19/4.49 thf(zip_derived_cl5814, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((double_divide @ (multiply @ X1 @ X3) @
% 27.19/4.49 (multiply @ (double_divide @ X1 @ X0) @ X0))
% 27.19/4.49 = (multiply @ (double_divide @ X3 @ X2) @ X2))),
% 27.19/4.49 inference('demod', [status(thm)], [zip_derived_cl5745, zip_derived_cl1])).
% 27.19/4.49 thf(zip_derived_cl4961, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.19/4.49 ((multiply @
% 27.19/4.49 (double_divide @ X0 @ (multiply @ (double_divide @ X0 @ X2) @ X2)) @
% 27.19/4.49 X1) = (X1))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl4901, zip_derived_cl3938])).
% 27.19/4.49 thf(zip_derived_cl5920, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((multiply @
% 27.19/4.49 (double_divide @ X2 @
% 27.19/4.49 (double_divide @ (multiply @ X1 @ X2) @
% 27.19/4.49 (multiply @ (double_divide @ X1 @ X0) @ X0))) @
% 27.19/4.49 X3) = (X3))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl5814, zip_derived_cl4961])).
% 27.19/4.49 thf(zip_derived_cl52, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X3) @
% 27.19/4.49 (double_divide @ (inverse @ X0) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X2 @ (double_divide @ (inverse @ X3) @ X2)) @
% 27.19/4.49 (multiply @ X1 @ X0))))
% 27.19/4.49 = (X1))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl3])).
% 27.19/4.49 thf(zip_derived_cl5920, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((multiply @
% 27.19/4.49 (double_divide @ X2 @
% 27.19/4.49 (double_divide @ (multiply @ X1 @ X2) @
% 27.19/4.49 (multiply @ (double_divide @ X1 @ X0) @ X0))) @
% 27.19/4.49 X3) = (X3))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl5814, zip_derived_cl4961])).
% 27.19/4.49 thf(zip_derived_cl504, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((multiply @ (double_divide @ X3 @ (double_divide @ X2 @ X3)) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X1 @ (double_divide @ (inverse @ X0) @ X1)) @ X0))
% 27.19/4.49 = (X2))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl473, zip_derived_cl72])).
% 27.19/4.49 thf(zip_derived_cl6241, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((multiply @
% 27.19/4.49 (double_divide @ X1 @ (double_divide @ (inverse @ X0) @ X1)) @ X0)
% 27.19/4.49 = (multiply @ X3 @ (multiply @ (double_divide @ X3 @ X2) @ X2)))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl5920, zip_derived_cl504])).
% 27.19/4.49 thf(zip_derived_cl52, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X3) @
% 27.19/4.49 (double_divide @ (inverse @ X0) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X2 @ (double_divide @ (inverse @ X3) @ X2)) @
% 27.19/4.49 (multiply @ X1 @ X0))))
% 27.19/4.49 = (X1))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl3])).
% 27.19/4.49 thf(zip_derived_cl6357, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X5) @
% 27.19/4.49 (double_divide @
% 27.19/4.49 (inverse @ (multiply @ (double_divide @ X2 @ X3) @ X3)) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X4 @ (double_divide @ (inverse @ X5) @ X4)) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X1 @ (double_divide @ (inverse @ X0) @ X1)) @ X0))))
% 27.19/4.49 = (X2))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl6241, zip_derived_cl52])).
% 27.19/4.49 thf(zip_derived_cl504, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((multiply @ (double_divide @ X3 @ (double_divide @ X2 @ X3)) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X1 @ (double_divide @ (inverse @ X0) @ X1)) @ X0))
% 27.19/4.49 = (X2))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl473, zip_derived_cl72])).
% 27.19/4.49 thf(zip_derived_cl72, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((multiply @ (double_divide @ X3 @ (double_divide @ X2 @ X3)) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X2 @ (double_divide @ (inverse @ X0) @ X1)) @ X0))
% 27.19/4.49 = (X1))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl3])).
% 27.19/4.49 thf(zip_derived_cl1, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 27.19/4.49 inference('cnf', [status(esa)], [multiply])).
% 27.19/4.49 thf(zip_derived_cl730, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.19/4.49 ((double_divide @ X0 @ (double_divide @ (inverse @ X1) @ X0))
% 27.19/4.49 = (double_divide @ X2 @ (double_divide @ (inverse @ X1) @ X2)))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl605, zip_derived_cl605])).
% 27.19/4.49 thf(zip_derived_cl861, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((double_divide @ X3 @ (double_divide @ (multiply @ X1 @ X0) @ X3))
% 27.19/4.49 = (double_divide @ X2 @
% 27.19/4.49 (double_divide @ (inverse @ (double_divide @ X0 @ X1)) @ X2)))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl730])).
% 27.19/4.49 thf(zip_derived_cl1, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 27.19/4.49 inference('cnf', [status(esa)], [multiply])).
% 27.19/4.49 thf(zip_derived_cl871, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((double_divide @ X3 @ (double_divide @ (multiply @ X1 @ X0) @ X3))
% 27.19/4.49 = (double_divide @ X2 @ (double_divide @ (multiply @ X1 @ X0) @ X2)))),
% 27.19/4.49 inference('demod', [status(thm)], [zip_derived_cl861, zip_derived_cl1])).
% 27.19/4.49 thf(zip_derived_cl1411, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 27.19/4.49 ((double_divide @ X5 @ (double_divide @ X0 @ X5))
% 27.19/4.49 = (double_divide @ X1 @
% 27.19/4.49 (double_divide @
% 27.19/4.49 (multiply @ (double_divide @ X4 @ (double_divide @ X3 @ X4)) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X3 @ (double_divide @ (inverse @ X2) @ X0)) @
% 27.19/4.49 X2)) @
% 27.19/4.49 X1)))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl72, zip_derived_cl871])).
% 27.19/4.49 thf(zip_derived_cl72, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((multiply @ (double_divide @ X3 @ (double_divide @ X2 @ X3)) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X2 @ (double_divide @ (inverse @ X0) @ X1)) @ X0))
% 27.19/4.49 = (X1))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl3])).
% 27.19/4.49 thf(zip_derived_cl1440, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X5 : $i]:
% 27.19/4.49 ((double_divide @ X5 @ (double_divide @ X0 @ X5))
% 27.19/4.49 = (double_divide @ X1 @ (double_divide @ X0 @ X1)))),
% 27.19/4.49 inference('demod', [status(thm)], [zip_derived_cl1411, zip_derived_cl72])).
% 27.19/4.49 thf(zip_derived_cl6527, plain,
% 27.19/4.49 (![X2 : $i, X3 : $i, X5 : $i]:
% 27.19/4.49 ((double_divide @ X5 @
% 27.19/4.49 (double_divide @
% 27.19/4.49 (inverse @ (multiply @ (double_divide @ X2 @ X3) @ X3)) @ X5))
% 27.19/4.49 = (X2))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl6357, zip_derived_cl504, zip_derived_cl1440])).
% 27.19/4.49 thf(zip_derived_cl7253, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 27.19/4.49 ((double_divide @
% 27.19/4.49 (double_divide @ (inverse @ X2) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X3 @
% 27.19/4.49 (double_divide @
% 27.19/4.49 (inverse @ (multiply @ (double_divide @ X1 @ X4) @ X4)) @ X3)) @
% 27.19/4.49 (multiply @ X0 @ X2))) @
% 27.19/4.49 X0) = (X1))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl52, zip_derived_cl6527])).
% 27.19/4.49 thf(zip_derived_cl6527, plain,
% 27.19/4.49 (![X2 : $i, X3 : $i, X5 : $i]:
% 27.19/4.49 ((double_divide @ X5 @
% 27.19/4.49 (double_divide @
% 27.19/4.49 (inverse @ (multiply @ (double_divide @ X2 @ X3) @ X3)) @ X5))
% 27.19/4.49 = (X2))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl6357, zip_derived_cl504, zip_derived_cl1440])).
% 27.19/4.49 thf(zip_derived_cl7297, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.19/4.49 ((double_divide @
% 27.19/4.49 (double_divide @ (inverse @ X2) @
% 27.19/4.49 (multiply @ X1 @ (multiply @ X0 @ X2))) @
% 27.19/4.49 X0) = (X1))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl7253, zip_derived_cl6527])).
% 27.19/4.49 thf(zip_derived_cl1, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 27.19/4.49 inference('cnf', [status(esa)], [multiply])).
% 27.19/4.49 thf(zip_derived_cl7328, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.19/4.49 ((multiply @ X1 @
% 27.19/4.49 (double_divide @ (inverse @ X2) @
% 27.19/4.49 (multiply @ X0 @ (multiply @ X1 @ X2))))
% 27.19/4.49 = (inverse @ X0))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl7297, zip_derived_cl1])).
% 27.19/4.49 thf(zip_derived_cl7617, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 27.19/4.49 ((multiply @
% 27.19/4.49 (double_divide @ X4 @
% 27.19/4.49 (double_divide @ (multiply @ X3 @ X4) @
% 27.19/4.49 (multiply @ (double_divide @ X3 @ X2) @ X2))) @
% 27.19/4.49 (double_divide @ (inverse @ X0) @ (multiply @ X1 @ X0)))
% 27.19/4.49 = (inverse @ X1))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl5920, zip_derived_cl7328])).
% 27.19/4.49 thf(zip_derived_cl5814, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((double_divide @ (multiply @ X1 @ X3) @
% 27.19/4.49 (multiply @ (double_divide @ X1 @ X0) @ X0))
% 27.19/4.49 = (multiply @ (double_divide @ X3 @ X2) @ X2))),
% 27.19/4.49 inference('demod', [status(thm)], [zip_derived_cl5745, zip_derived_cl1])).
% 27.19/4.49 thf(zip_derived_cl4961, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.19/4.49 ((multiply @
% 27.19/4.49 (double_divide @ X0 @ (multiply @ (double_divide @ X0 @ X2) @ X2)) @
% 27.19/4.49 X1) = (X1))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl4901, zip_derived_cl3938])).
% 27.19/4.49 thf(zip_derived_cl7668, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X0) @ (multiply @ X1 @ X0))
% 27.19/4.49 = (inverse @ X1))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl7617, zip_derived_cl5814, zip_derived_cl4961])).
% 27.19/4.49 thf(zip_derived_cl4961, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.19/4.49 ((multiply @
% 27.19/4.49 (double_divide @ X0 @ (multiply @ (double_divide @ X0 @ X2) @ X2)) @
% 27.19/4.49 X1) = (X1))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl4901, zip_derived_cl3938])).
% 27.19/4.49 thf(zip_derived_cl7815, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ (inverse @ (double_divide @ (inverse @ X0) @ X0)) @ X1)
% 27.19/4.49 = (X1))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl7668, zip_derived_cl4961])).
% 27.19/4.49 thf(zip_derived_cl1, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 27.19/4.49 inference('cnf', [status(esa)], [multiply])).
% 27.19/4.49 thf(zip_derived_cl7892, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ (multiply @ X0 @ (inverse @ X0)) @ X1) = (X1))),
% 27.19/4.49 inference('demod', [status(thm)], [zip_derived_cl7815, zip_derived_cl1])).
% 27.19/4.49 thf(zip_derived_cl7297, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.19/4.49 ((double_divide @
% 27.19/4.49 (double_divide @ (inverse @ X2) @
% 27.19/4.49 (multiply @ X1 @ (multiply @ X0 @ X2))) @
% 27.19/4.49 X0) = (X1))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl7253, zip_derived_cl6527])).
% 27.19/4.49 thf(zip_derived_cl7926, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.19/4.49 ((double_divide @
% 27.19/4.49 (double_divide @ (inverse @ X0) @ (multiply @ X1 @ X0)) @ X1)
% 27.19/4.49 = (multiply @ X2 @ (inverse @ X2)))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl7892, zip_derived_cl7297])).
% 27.19/4.49 thf(zip_derived_cl7668, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X0) @ (multiply @ X1 @ X0))
% 27.19/4.49 = (inverse @ X1))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl7617, zip_derived_cl5814, zip_derived_cl4961])).
% 27.19/4.49 thf(zip_derived_cl7952, plain,
% 27.19/4.49 (![X1 : $i, X2 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X1) @ X1)
% 27.19/4.49 = (multiply @ X2 @ (inverse @ X2)))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl7926, zip_derived_cl7668])).
% 27.19/4.49 thf(zip_derived_cl7892, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ (multiply @ X0 @ (inverse @ X0)) @ X1) = (X1))),
% 27.19/4.49 inference('demod', [status(thm)], [zip_derived_cl7815, zip_derived_cl1])).
% 27.19/4.49 thf(zip_derived_cl8311, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ (double_divide @ (inverse @ X0) @ X0) @ X1) = (X1))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl7952, zip_derived_cl7892])).
% 27.19/4.49 thf(zip_derived_cl7297, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.19/4.49 ((double_divide @
% 27.19/4.49 (double_divide @ (inverse @ X2) @
% 27.19/4.49 (multiply @ X1 @ (multiply @ X0 @ X2))) @
% 27.19/4.49 X0) = (X1))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl7253, zip_derived_cl6527])).
% 27.19/4.49 thf(zip_derived_cl8985, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.19/4.49 ((double_divide @
% 27.19/4.49 (double_divide @ (inverse @ X0) @ (multiply @ X1 @ X0)) @
% 27.19/4.49 (double_divide @ (inverse @ X2) @ X2)) = (X1))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl8311, zip_derived_cl7297])).
% 27.19/4.49 thf(zip_derived_cl7668, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X0) @ (multiply @ X1 @ X0))
% 27.19/4.49 = (inverse @ X1))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl7617, zip_derived_cl5814, zip_derived_cl4961])).
% 27.19/4.49 thf(zip_derived_cl9058, plain,
% 27.19/4.49 (![X1 : $i, X2 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X1) @
% 27.19/4.49 (double_divide @ (inverse @ X2) @ X2)) = (X1))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl8985, zip_derived_cl7668])).
% 27.19/4.49 thf(zip_derived_cl72, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((multiply @ (double_divide @ X3 @ (double_divide @ X2 @ X3)) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X2 @ (double_divide @ (inverse @ X0) @ X1)) @ X0))
% 27.19/4.49 = (X1))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl3])).
% 27.19/4.49 thf(zip_derived_cl6, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((multiply @
% 27.19/4.49 (multiply @ (double_divide @ X3 @ (double_divide @ X2 @ X3)) @
% 27.19/4.49 (multiply @ (double_divide @ X2 @ X0) @ X1)) @
% 27.19/4.49 (inverse @ X1)) = (inverse @ X0))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 27.19/4.49 thf(zip_derived_cl200, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 27.19/4.49 ((multiply @
% 27.19/4.49 (multiply @ (double_divide @ X4 @ (double_divide @ X1 @ X4)) @ X0) @
% 27.19/4.49 (inverse @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X2 @ (double_divide @ (inverse @ X3) @ X0)) @ X3)))
% 27.19/4.49 = (inverse @ (double_divide @ X2 @ X1)))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl72, zip_derived_cl6])).
% 27.19/4.49 thf(zip_derived_cl1, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 27.19/4.49 inference('cnf', [status(esa)], [multiply])).
% 27.19/4.49 thf(zip_derived_cl222, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 27.19/4.49 ((multiply @
% 27.19/4.49 (multiply @ (double_divide @ X4 @ (double_divide @ X1 @ X4)) @ X0) @
% 27.19/4.49 (inverse @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X2 @ (double_divide @ (inverse @ X3) @ X0)) @ X3)))
% 27.19/4.49 = (multiply @ X1 @ X2))),
% 27.19/4.49 inference('demod', [status(thm)], [zip_derived_cl200, zip_derived_cl1])).
% 27.19/4.49 thf(zip_derived_cl7892, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ (multiply @ X0 @ (inverse @ X0)) @ X1) = (X1))),
% 27.19/4.49 inference('demod', [status(thm)], [zip_derived_cl7815, zip_derived_cl1])).
% 27.19/4.49 thf(zip_derived_cl7297, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.19/4.49 ((double_divide @
% 27.19/4.49 (double_divide @ (inverse @ X2) @
% 27.19/4.49 (multiply @ X1 @ (multiply @ X0 @ X2))) @
% 27.19/4.49 X0) = (X1))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl7253, zip_derived_cl6527])).
% 27.19/4.49 thf(zip_derived_cl7916, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.19/4.49 ((double_divide @
% 27.19/4.49 (double_divide @ (inverse @ X0) @ (multiply @ X1 @ X0)) @
% 27.19/4.49 (multiply @ X2 @ (inverse @ X2))) = (X1))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl7892, zip_derived_cl7297])).
% 27.19/4.49 thf(zip_derived_cl7668, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X0) @ (multiply @ X1 @ X0))
% 27.19/4.49 = (inverse @ X1))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl7617, zip_derived_cl5814, zip_derived_cl4961])).
% 27.19/4.49 thf(zip_derived_cl7949, plain,
% 27.19/4.49 (![X1 : $i, X2 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X1) @ (multiply @ X2 @ (inverse @ X2)))
% 27.19/4.49 = (X1))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl7916, zip_derived_cl7668])).
% 27.19/4.49 thf(zip_derived_cl7952, plain,
% 27.19/4.49 (![X1 : $i, X2 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X1) @ X1)
% 27.19/4.49 = (multiply @ X2 @ (inverse @ X2)))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl7926, zip_derived_cl7668])).
% 27.19/4.49 thf(zip_derived_cl3, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X1) @
% 27.19/4.49 (multiply @ (double_divide @ X3 @ (double_divide @ X2 @ X3)) @
% 27.19/4.49 (multiply @ (double_divide @ X2 @ X0) @ X1)))
% 27.19/4.49 = (X0))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1])).
% 27.19/4.49 thf(zip_derived_cl8337, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X2) @
% 27.19/4.49 (multiply @
% 27.19/4.49 (double_divide @ X3 @ (double_divide @ (inverse @ X1) @ X3)) @
% 27.19/4.49 (multiply @ (multiply @ X0 @ (inverse @ X0)) @ X2)))
% 27.19/4.49 = (X1))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl7952, zip_derived_cl3])).
% 27.19/4.49 thf(zip_derived_cl7892, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ (multiply @ X0 @ (inverse @ X0)) @ X1) = (X1))),
% 27.19/4.49 inference('demod', [status(thm)], [zip_derived_cl7815, zip_derived_cl1])).
% 27.19/4.49 thf(zip_derived_cl7668, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X0) @ (multiply @ X1 @ X0))
% 27.19/4.49 = (inverse @ X1))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl7617, zip_derived_cl5814, zip_derived_cl4961])).
% 27.19/4.49 thf(zip_derived_cl1, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 27.19/4.49 inference('cnf', [status(esa)], [multiply])).
% 27.19/4.49 thf(zip_derived_cl8488, plain,
% 27.19/4.49 (![X1 : $i, X3 : $i]:
% 27.19/4.49 ((multiply @ (double_divide @ (inverse @ X1) @ X3) @ X3) = (X1))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl8337, zip_derived_cl7892, zip_derived_cl7668,
% 27.19/4.49 zip_derived_cl1])).
% 27.19/4.49 thf(zip_derived_cl9160, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ X0 @ (multiply @ X1 @ (inverse @ X1))) = (X0))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl7949, zip_derived_cl8488])).
% 27.19/4.49 thf(zip_derived_cl7952, plain,
% 27.19/4.49 (![X1 : $i, X2 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X1) @ X1)
% 27.19/4.49 = (multiply @ X2 @ (inverse @ X2)))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl7926, zip_derived_cl7668])).
% 27.19/4.49 thf(zip_derived_cl9168, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ X0 @ (double_divide @ (inverse @ X1) @ X1)) = (X0))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl9160, zip_derived_cl7952])).
% 27.19/4.49 thf(zip_derived_cl6527, plain,
% 27.19/4.49 (![X2 : $i, X3 : $i, X5 : $i]:
% 27.19/4.49 ((double_divide @ X5 @
% 27.19/4.49 (double_divide @
% 27.19/4.49 (inverse @ (multiply @ (double_divide @ X2 @ X3) @ X3)) @ X5))
% 27.19/4.49 = (X2))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl6357, zip_derived_cl504, zip_derived_cl1440])).
% 27.19/4.49 thf(zip_derived_cl9829, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.19/4.49 ((double_divide @ X2 @
% 27.19/4.49 (double_divide @
% 27.19/4.49 (inverse @
% 27.19/4.49 (double_divide @ X1 @ (double_divide @ (inverse @ X0) @ X0))) @
% 27.19/4.49 X2))
% 27.19/4.49 = (X1))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl9168, zip_derived_cl6527])).
% 27.19/4.49 thf(zip_derived_cl1, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 27.19/4.49 inference('cnf', [status(esa)], [multiply])).
% 27.19/4.49 thf(zip_derived_cl8311, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ (double_divide @ (inverse @ X0) @ X0) @ X1) = (X1))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl7952, zip_derived_cl7892])).
% 27.19/4.49 thf(zip_derived_cl9910, plain,
% 27.19/4.49 (![X1 : $i, X2 : $i]:
% 27.19/4.49 ((double_divide @ X2 @ (double_divide @ X1 @ X2)) = (X1))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl9829, zip_derived_cl1, zip_derived_cl8311])).
% 27.19/4.49 thf(zip_derived_cl1, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 27.19/4.49 inference('cnf', [status(esa)], [multiply])).
% 27.19/4.49 thf(zip_derived_cl9168, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ X0 @ (double_divide @ (inverse @ X1) @ X1)) = (X0))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl9160, zip_derived_cl7952])).
% 27.19/4.49 thf(zip_derived_cl7668, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X0) @ (multiply @ X1 @ X0))
% 27.19/4.49 = (inverse @ X1))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl7617, zip_derived_cl5814, zip_derived_cl4961])).
% 27.19/4.49 thf(zip_derived_cl1, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 27.19/4.49 inference('cnf', [status(esa)], [multiply])).
% 27.19/4.49 thf(zip_derived_cl7738, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ (multiply @ X0 @ X1) @ (inverse @ X1))
% 27.19/4.49 = (inverse @ (inverse @ X0)))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl7668, zip_derived_cl1])).
% 27.19/4.49 thf(zip_derived_cl9804, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ X0 @ (inverse @ (double_divide @ (inverse @ X1) @ X1)))
% 27.19/4.49 = (inverse @ (inverse @ X0)))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl9168, zip_derived_cl7738])).
% 27.19/4.49 thf(zip_derived_cl1, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 27.19/4.49 inference('cnf', [status(esa)], [multiply])).
% 27.19/4.49 thf(zip_derived_cl7952, plain,
% 27.19/4.49 (![X1 : $i, X2 : $i]:
% 27.19/4.49 ((double_divide @ (inverse @ X1) @ X1)
% 27.19/4.49 = (multiply @ X2 @ (inverse @ X2)))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl7926, zip_derived_cl7668])).
% 27.19/4.49 thf(zip_derived_cl9168, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ X0 @ (double_divide @ (inverse @ X1) @ X1)) = (X0))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl9160, zip_derived_cl7952])).
% 27.19/4.49 thf(zip_derived_cl9896, plain,
% 27.19/4.49 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl9804, zip_derived_cl1, zip_derived_cl7952,
% 27.19/4.49 zip_derived_cl9168])).
% 27.19/4.49 thf(zip_derived_cl9976, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((double_divide @ X0 @ X1) = (inverse @ (multiply @ X1 @ X0)))),
% 27.19/4.49 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl9896])).
% 27.19/4.49 thf(zip_derived_cl11741, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.19/4.49 ((multiply @ (multiply @ X1 @ X0) @
% 27.19/4.49 (double_divide @ X3 @
% 27.19/4.49 (double_divide @ X2 @ (double_divide @ (inverse @ X3) @ X0))))
% 27.19/4.49 = (multiply @ X1 @ X2))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl222, zip_derived_cl9910, zip_derived_cl9976])).
% 27.19/4.49 thf(zip_derived_cl13182, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.19/4.49 ((multiply @ (multiply @ X2 @ X1) @ X0)
% 27.19/4.49 = (multiply @ X2 @
% 27.19/4.49 (inverse @ (double_divide @ (inverse @ (inverse @ X0)) @ X1))))),
% 27.19/4.49 inference('sup+', [status(thm)],
% 27.19/4.49 [zip_derived_cl9058, zip_derived_cl11741])).
% 27.19/4.49 thf(zip_derived_cl9896, plain,
% 27.19/4.49 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl9804, zip_derived_cl1, zip_derived_cl7952,
% 27.19/4.49 zip_derived_cl9168])).
% 27.19/4.49 thf(zip_derived_cl1, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i]:
% 27.19/4.49 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 27.19/4.49 inference('cnf', [status(esa)], [multiply])).
% 27.19/4.49 thf(zip_derived_cl13232, plain,
% 27.19/4.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.19/4.49 ((multiply @ (multiply @ X2 @ X1) @ X0)
% 27.19/4.49 = (multiply @ X2 @ (multiply @ X1 @ X0)))),
% 27.19/4.49 inference('demod', [status(thm)],
% 27.19/4.49 [zip_derived_cl13182, zip_derived_cl9896, zip_derived_cl1])).
% 27.19/4.49 thf(zip_derived_cl13240, plain,
% 27.19/4.49 (((multiply @ a3 @ (multiply @ b3 @ c3))
% 27.19/4.49 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 27.19/4.49 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl13232])).
% 27.19/4.49 thf(zip_derived_cl13241, plain, ($false),
% 27.19/4.49 inference('simplify', [status(thm)], [zip_derived_cl13240])).
% 27.19/4.49
% 27.19/4.49 % SZS output end Refutation
% 27.19/4.49
% 27.19/4.49
% 27.19/4.49 % Terminating...
% 27.62/4.60 % Runner terminated.
% 27.62/4.60 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------