TSTP Solution File: GRP489-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP489-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.BFWw7h6tiP true
% Computer : n029.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 01:51:51 EDT 2023
% Result : Unsatisfiable 0.51s 1.16s
% Output : Refutation 0.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP489-1 : TPTP v8.1.2. Released v2.6.0.
% 0.10/0.12 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.BFWw7h6tiP true
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 02:14:11 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % Running portfolio for 300 s
% 0.12/0.33 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Number of cores: 8
% 0.12/0.33 % Python version: Python 3.6.8
% 0.12/0.33 % Running in FO mode
% 0.50/0.59 % Total configuration time : 435
% 0.50/0.59 % Estimated wc time : 1092
% 0.50/0.59 % Estimated cpu time (7 cpus) : 156.0
% 0.50/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.50/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.50/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.50/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.50/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.50/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.50/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.51/1.16 % Solved by fo/fo5.sh.
% 0.51/1.16 % done 426 iterations in 0.428s
% 0.51/1.16 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.51/1.16 % SZS output start Refutation
% 0.51/1.16 thf(c3_type, type, c3: $i).
% 0.51/1.16 thf(multiply_type, type, multiply: $i > $i > $i).
% 0.51/1.16 thf(identity_type, type, identity: $i).
% 0.51/1.16 thf(b3_type, type, b3: $i).
% 0.51/1.16 thf(a3_type, type, a3: $i).
% 0.51/1.16 thf(double_divide_type, type, double_divide: $i > $i > $i).
% 0.51/1.16 thf(inverse_type, type, inverse: $i > $i).
% 0.51/1.16 thf(prove_these_axioms_3, conjecture,
% 0.51/1.16 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) =
% 0.51/1.16 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ))).
% 0.51/1.16 thf(zf_stmt_0, negated_conjecture,
% 0.51/1.16 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 0.51/1.16 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) )),
% 0.51/1.16 inference('cnf.neg', [status(esa)], [prove_these_axioms_3])).
% 0.51/1.16 thf(zip_derived_cl4, plain,
% 0.51/1.16 (((multiply @ (multiply @ a3 @ b3) @ c3)
% 0.51/1.16 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 0.51/1.16 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.51/1.16 thf(identity, axiom,
% 0.51/1.16 (( identity ) = ( double_divide @ A @ ( inverse @ A ) ))).
% 0.51/1.16 thf(zip_derived_cl3, plain,
% 0.51/1.16 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 0.51/1.16 inference('cnf', [status(esa)], [identity])).
% 0.51/1.16 thf(single_axiom, axiom,
% 0.51/1.16 (( double_divide @
% 0.51/1.16 A @
% 0.51/1.16 ( double_divide @
% 0.51/1.16 ( double_divide @
% 0.51/1.16 ( double_divide @
% 0.51/1.16 identity @
% 0.51/1.16 ( double_divide @
% 0.51/1.16 ( double_divide @ A @ identity ) @ ( double_divide @ B @ C ) ) ) @
% 0.51/1.16 B ) @
% 0.51/1.16 identity ) ) =
% 0.51/1.16 ( C ))).
% 0.51/1.16 thf(zip_derived_cl0, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.51/1.16 ((double_divide @ X1 @
% 0.51/1.16 (double_divide @
% 0.51/1.16 (double_divide @
% 0.51/1.16 (double_divide @ identity @
% 0.51/1.16 (double_divide @ (double_divide @ X1 @ identity) @
% 0.51/1.16 (double_divide @ X2 @ X0))) @
% 0.51/1.16 X2) @
% 0.51/1.16 identity))
% 0.51/1.16 = (X0))),
% 0.51/1.16 inference('cnf', [status(esa)], [single_axiom])).
% 0.51/1.16 thf(inverse, axiom, (( inverse @ A ) = ( double_divide @ A @ identity ))).
% 0.51/1.16 thf(zip_derived_cl2, plain,
% 0.51/1.16 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.51/1.16 inference('cnf', [status(esa)], [inverse])).
% 0.51/1.16 thf(multiply, axiom,
% 0.51/1.16 (( multiply @ A @ B ) =
% 0.51/1.16 ( double_divide @ ( double_divide @ B @ A ) @ identity ))).
% 0.51/1.16 thf(zip_derived_cl1, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X1 @ X0)
% 0.51/1.16 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 0.51/1.16 inference('cnf', [status(esa)], [multiply])).
% 0.51/1.16 thf(zip_derived_cl13, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.51/1.16 ((double_divide @ X1 @
% 0.51/1.16 (multiply @ X2 @
% 0.51/1.16 (double_divide @ identity @
% 0.51/1.16 (double_divide @ (inverse @ X1) @ (double_divide @ X2 @ X0)))))
% 0.51/1.16 = (X0))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl13, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.51/1.16 ((double_divide @ X1 @
% 0.51/1.16 (multiply @ X2 @
% 0.51/1.16 (double_divide @ identity @
% 0.51/1.16 (double_divide @ (inverse @ X1) @ (double_divide @ X2 @ X0)))))
% 0.51/1.16 = (X0))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl14, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.51/1.16 ((double_divide @ X3 @
% 0.51/1.16 (multiply @ X2 @
% 0.51/1.16 (double_divide @ identity @ (double_divide @ (inverse @ X3) @ X0))))
% 0.51/1.16 = (multiply @ X1 @
% 0.51/1.16 (double_divide @ identity @
% 0.51/1.16 (double_divide @ (inverse @ X2) @ (double_divide @ X1 @ X0)))))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl13])).
% 0.51/1.16 thf(zip_derived_cl124, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.51/1.16 ((double_divide @ X0 @
% 0.51/1.16 (multiply @ X2 @ (double_divide @ identity @ identity)))
% 0.51/1.16 = (multiply @ X1 @
% 0.51/1.16 (double_divide @ identity @
% 0.51/1.16 (double_divide @ (inverse @ X2) @
% 0.51/1.16 (double_divide @ X1 @ (inverse @ (inverse @ X0)))))))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl14])).
% 0.51/1.16 thf(zip_derived_cl2, plain,
% 0.51/1.16 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.51/1.16 inference('cnf', [status(esa)], [inverse])).
% 0.51/1.16 thf(zip_derived_cl144, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.51/1.16 ((double_divide @ X0 @ (multiply @ X2 @ (inverse @ identity)))
% 0.51/1.16 = (multiply @ X1 @
% 0.51/1.16 (double_divide @ identity @
% 0.51/1.16 (double_divide @ (inverse @ X2) @
% 0.51/1.16 (double_divide @ X1 @ (inverse @ (inverse @ X0)))))))),
% 0.51/1.16 inference('demod', [status(thm)], [zip_derived_cl124, zip_derived_cl2])).
% 0.51/1.16 thf(zip_derived_cl3, plain,
% 0.51/1.16 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 0.51/1.16 inference('cnf', [status(esa)], [identity])).
% 0.51/1.16 thf(zip_derived_cl2, plain,
% 0.51/1.16 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.51/1.16 inference('cnf', [status(esa)], [inverse])).
% 0.51/1.16 thf(zip_derived_cl1, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X1 @ X0)
% 0.51/1.16 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 0.51/1.16 inference('cnf', [status(esa)], [multiply])).
% 0.51/1.16 thf(zip_derived_cl6, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl27, plain,
% 0.51/1.16 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 0.51/1.16 thf(zip_derived_cl3, plain,
% 0.51/1.16 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 0.51/1.16 inference('cnf', [status(esa)], [identity])).
% 0.51/1.16 thf(zip_derived_cl29, plain,
% 0.51/1.16 (![X0 : $i]:
% 0.51/1.16 ((identity)
% 0.51/1.16 = (double_divide @ identity @ (multiply @ (inverse @ X0) @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl3])).
% 0.51/1.16 thf(zip_derived_cl3, plain,
% 0.51/1.16 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 0.51/1.16 inference('cnf', [status(esa)], [identity])).
% 0.51/1.16 thf(zip_derived_cl13, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.51/1.16 ((double_divide @ X1 @
% 0.51/1.16 (multiply @ X2 @
% 0.51/1.16 (double_divide @ identity @
% 0.51/1.16 (double_divide @ (inverse @ X1) @ (double_divide @ X2 @ X0)))))
% 0.51/1.16 = (X0))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl18, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((double_divide @ X1 @
% 0.51/1.16 (multiply @ X0 @
% 0.51/1.16 (double_divide @ identity @
% 0.51/1.16 (double_divide @ (inverse @ X1) @ identity))))
% 0.51/1.16 = (inverse @ X0))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl13])).
% 0.51/1.16 thf(zip_derived_cl2, plain,
% 0.51/1.16 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.51/1.16 inference('cnf', [status(esa)], [inverse])).
% 0.51/1.16 thf(zip_derived_cl20, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((double_divide @ X1 @
% 0.51/1.16 (multiply @ X0 @
% 0.51/1.16 (double_divide @ identity @ (inverse @ (inverse @ X1)))))
% 0.51/1.16 = (inverse @ X0))),
% 0.51/1.16 inference('demod', [status(thm)], [zip_derived_cl18, zip_derived_cl2])).
% 0.51/1.16 thf(zip_derived_cl609, plain,
% 0.51/1.16 (((identity)
% 0.51/1.16 = (inverse @
% 0.51/1.16 (inverse @
% 0.51/1.16 (double_divide @ identity @ (inverse @ (inverse @ identity))))))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl29, zip_derived_cl20])).
% 0.51/1.16 thf(zip_derived_cl6, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl623, plain,
% 0.51/1.16 (((identity)
% 0.51/1.16 = (inverse @ (multiply @ (inverse @ (inverse @ identity)) @ identity)))),
% 0.51/1.16 inference('demod', [status(thm)], [zip_derived_cl609, zip_derived_cl6])).
% 0.51/1.16 thf(zip_derived_cl27, plain,
% 0.51/1.16 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 0.51/1.16 thf(zip_derived_cl27, plain,
% 0.51/1.16 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 0.51/1.16 thf(zip_derived_cl32, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ (inverse @ X1) @ X1) = (multiply @ (inverse @ X0) @ X0))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl27])).
% 0.51/1.16 thf(zip_derived_cl3, plain,
% 0.51/1.16 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 0.51/1.16 inference('cnf', [status(esa)], [identity])).
% 0.51/1.16 thf(zip_derived_cl2, plain,
% 0.51/1.16 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.51/1.16 inference('cnf', [status(esa)], [inverse])).
% 0.51/1.16 thf(zip_derived_cl13, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.51/1.16 ((double_divide @ X1 @
% 0.51/1.16 (multiply @ X2 @
% 0.51/1.16 (double_divide @ identity @
% 0.51/1.16 (double_divide @ (inverse @ X1) @ (double_divide @ X2 @ X0)))))
% 0.51/1.16 = (X0))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl16, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((double_divide @ X1 @
% 0.51/1.16 (multiply @ X0 @
% 0.51/1.16 (double_divide @ identity @
% 0.51/1.16 (double_divide @ (inverse @ X1) @ (inverse @ X0)))))
% 0.51/1.16 = (identity))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 0.51/1.16 thf(zip_derived_cl258, plain,
% 0.51/1.16 (![X0 : $i]:
% 0.51/1.16 ((double_divide @ X0 @
% 0.51/1.16 (multiply @ (inverse @ X0) @ (double_divide @ identity @ identity)))
% 0.51/1.16 = (identity))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl16])).
% 0.51/1.16 thf(zip_derived_cl2, plain,
% 0.51/1.16 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.51/1.16 inference('cnf', [status(esa)], [inverse])).
% 0.51/1.16 thf(zip_derived_cl266, plain,
% 0.51/1.16 (![X0 : $i]:
% 0.51/1.16 ((double_divide @ X0 @
% 0.51/1.16 (multiply @ (inverse @ X0) @ (inverse @ identity))) = (identity))),
% 0.51/1.16 inference('demod', [status(thm)], [zip_derived_cl258, zip_derived_cl2])).
% 0.51/1.16 thf(zip_derived_cl284, plain,
% 0.51/1.16 (![X0 : $i]:
% 0.51/1.16 ((double_divide @ (inverse @ identity) @
% 0.51/1.16 (multiply @ (inverse @ X0) @ X0)) = (identity))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl32, zip_derived_cl266])).
% 0.51/1.16 thf(zip_derived_cl20, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((double_divide @ X1 @
% 0.51/1.16 (multiply @ X0 @
% 0.51/1.16 (double_divide @ identity @ (inverse @ (inverse @ X1)))))
% 0.51/1.16 = (inverse @ X0))),
% 0.51/1.16 inference('demod', [status(thm)], [zip_derived_cl18, zip_derived_cl2])).
% 0.51/1.16 thf(zip_derived_cl610, plain,
% 0.51/1.16 (((identity)
% 0.51/1.16 = (inverse @
% 0.51/1.16 (inverse @
% 0.51/1.16 (double_divide @ identity @
% 0.51/1.16 (inverse @ (inverse @ (inverse @ identity)))))))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl284, zip_derived_cl20])).
% 0.51/1.16 thf(zip_derived_cl27, plain,
% 0.51/1.16 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 0.51/1.16 thf(zip_derived_cl266, plain,
% 0.51/1.16 (![X0 : $i]:
% 0.51/1.16 ((double_divide @ X0 @
% 0.51/1.16 (multiply @ (inverse @ X0) @ (inverse @ identity))) = (identity))),
% 0.51/1.16 inference('demod', [status(thm)], [zip_derived_cl258, zip_derived_cl2])).
% 0.51/1.16 thf(zip_derived_cl283, plain,
% 0.51/1.16 (((double_divide @ (inverse @ identity) @ (inverse @ identity))
% 0.51/1.16 = (identity))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl266])).
% 0.51/1.16 thf(zip_derived_cl16, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((double_divide @ X1 @
% 0.51/1.16 (multiply @ X0 @
% 0.51/1.16 (double_divide @ identity @
% 0.51/1.16 (double_divide @ (inverse @ X1) @ (inverse @ X0)))))
% 0.51/1.16 = (identity))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 0.51/1.16 thf(zip_derived_cl304, plain,
% 0.51/1.16 (((double_divide @ identity @
% 0.51/1.16 (multiply @ identity @ (double_divide @ identity @ identity)))
% 0.51/1.16 = (identity))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl283, zip_derived_cl16])).
% 0.51/1.16 thf(zip_derived_cl2, plain,
% 0.51/1.16 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.51/1.16 inference('cnf', [status(esa)], [inverse])).
% 0.51/1.16 thf(zip_derived_cl2, plain,
% 0.51/1.16 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.51/1.16 inference('cnf', [status(esa)], [inverse])).
% 0.51/1.16 thf(zip_derived_cl1, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X1 @ X0)
% 0.51/1.16 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 0.51/1.16 inference('cnf', [status(esa)], [multiply])).
% 0.51/1.16 thf(zip_derived_cl7, plain,
% 0.51/1.16 (![X0 : $i]:
% 0.51/1.16 ((multiply @ identity @ X0)
% 0.51/1.16 = (double_divide @ (inverse @ X0) @ identity))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl2, plain,
% 0.51/1.16 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.51/1.16 inference('cnf', [status(esa)], [inverse])).
% 0.51/1.16 thf(zip_derived_cl10, plain,
% 0.51/1.16 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 0.51/1.16 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 0.51/1.16 thf(zip_derived_cl312, plain,
% 0.51/1.16 (((double_divide @ identity @
% 0.51/1.16 (inverse @ (inverse @ (inverse @ identity)))) = (identity))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl304, zip_derived_cl2, zip_derived_cl10])).
% 0.51/1.16 thf(zip_derived_cl624, plain,
% 0.51/1.16 (((identity) = (inverse @ (inverse @ identity)))),
% 0.51/1.16 inference('demod', [status(thm)], [zip_derived_cl610, zip_derived_cl312])).
% 0.51/1.16 thf(zip_derived_cl3, plain,
% 0.51/1.16 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 0.51/1.16 inference('cnf', [status(esa)], [identity])).
% 0.51/1.16 thf(zip_derived_cl1, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X1 @ X0)
% 0.51/1.16 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 0.51/1.16 inference('cnf', [status(esa)], [multiply])).
% 0.51/1.16 thf(zip_derived_cl8, plain,
% 0.51/1.16 (![X0 : $i]:
% 0.51/1.16 ((multiply @ (inverse @ X0) @ X0)
% 0.51/1.16 = (double_divide @ identity @ identity))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl6, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl46, plain,
% 0.51/1.16 (![X0 : $i]:
% 0.51/1.16 ((multiply @ identity @ identity)
% 0.51/1.16 = (inverse @ (multiply @ (inverse @ X0) @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl6])).
% 0.51/1.16 thf(zip_derived_cl27, plain,
% 0.51/1.16 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 0.51/1.16 thf(zip_derived_cl624, plain,
% 0.51/1.16 (((identity) = (inverse @ (inverse @ identity)))),
% 0.51/1.16 inference('demod', [status(thm)], [zip_derived_cl610, zip_derived_cl312])).
% 0.51/1.16 thf(zip_derived_cl659, plain,
% 0.51/1.16 (![X0 : $i]: ((identity) = (inverse @ (multiply @ (inverse @ X0) @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl624])).
% 0.51/1.16 thf(zip_derived_cl672, plain,
% 0.51/1.16 (((multiply @ identity @ identity) = (identity))),
% 0.51/1.16 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl659])).
% 0.51/1.16 thf(zip_derived_cl754, plain, (((identity) = (inverse @ identity))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl623, zip_derived_cl624, zip_derived_cl672])).
% 0.51/1.16 thf(zip_derived_cl754, plain, (((identity) = (inverse @ identity))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl623, zip_derived_cl624, zip_derived_cl672])).
% 0.51/1.16 thf(zip_derived_cl20, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((double_divide @ X1 @
% 0.51/1.16 (multiply @ X0 @
% 0.51/1.16 (double_divide @ identity @ (inverse @ (inverse @ X1)))))
% 0.51/1.16 = (inverse @ X0))),
% 0.51/1.16 inference('demod', [status(thm)], [zip_derived_cl18, zip_derived_cl2])).
% 0.51/1.16 thf(zip_derived_cl775, plain,
% 0.51/1.16 (![X0 : $i]:
% 0.51/1.16 ((double_divide @ identity @
% 0.51/1.16 (multiply @ X0 @ (double_divide @ identity @ (inverse @ identity))))
% 0.51/1.16 = (inverse @ X0))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl754, zip_derived_cl20])).
% 0.51/1.16 thf(zip_derived_cl754, plain, (((identity) = (inverse @ identity))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl623, zip_derived_cl624, zip_derived_cl672])).
% 0.51/1.16 thf(zip_derived_cl2, plain,
% 0.51/1.16 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.51/1.16 inference('cnf', [status(esa)], [inverse])).
% 0.51/1.16 thf(zip_derived_cl754, plain, (((identity) = (inverse @ identity))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl623, zip_derived_cl624, zip_derived_cl672])).
% 0.51/1.16 thf(zip_derived_cl787, plain,
% 0.51/1.16 (![X0 : $i]:
% 0.51/1.16 ((double_divide @ identity @ (multiply @ X0 @ identity))
% 0.51/1.16 = (inverse @ X0))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl775, zip_derived_cl754, zip_derived_cl2,
% 0.51/1.16 zip_derived_cl754])).
% 0.51/1.16 thf(zip_derived_cl6, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl978, plain,
% 0.51/1.16 (![X0 : $i]:
% 0.51/1.16 ((multiply @ (multiply @ X0 @ identity) @ identity)
% 0.51/1.16 = (inverse @ (inverse @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl787, zip_derived_cl6])).
% 0.51/1.16 thf(zip_derived_cl6, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl266, plain,
% 0.51/1.16 (![X0 : $i]:
% 0.51/1.16 ((double_divide @ X0 @
% 0.51/1.16 (multiply @ (inverse @ X0) @ (inverse @ identity))) = (identity))),
% 0.51/1.16 inference('demod', [status(thm)], [zip_derived_cl258, zip_derived_cl2])).
% 0.51/1.16 thf(zip_derived_cl754, plain, (((identity) = (inverse @ identity))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl623, zip_derived_cl624, zip_derived_cl672])).
% 0.51/1.16 thf(zip_derived_cl758, plain,
% 0.51/1.16 (![X0 : $i]:
% 0.51/1.16 ((double_divide @ X0 @ (multiply @ (inverse @ X0) @ identity))
% 0.51/1.16 = (identity))),
% 0.51/1.16 inference('demod', [status(thm)], [zip_derived_cl266, zip_derived_cl754])).
% 0.51/1.16 thf(zip_derived_cl13, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.51/1.16 ((double_divide @ X1 @
% 0.51/1.16 (multiply @ X2 @
% 0.51/1.16 (double_divide @ identity @
% 0.51/1.16 (double_divide @ (inverse @ X1) @ (double_divide @ X2 @ X0)))))
% 0.51/1.16 = (X0))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl935, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((double_divide @ X1 @
% 0.51/1.16 (multiply @ X0 @
% 0.51/1.16 (double_divide @ identity @
% 0.51/1.16 (double_divide @ (inverse @ X1) @ identity))))
% 0.51/1.16 = (multiply @ (inverse @ X0) @ identity))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl758, zip_derived_cl13])).
% 0.51/1.16 thf(zip_derived_cl2, plain,
% 0.51/1.16 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.51/1.16 inference('cnf', [status(esa)], [inverse])).
% 0.51/1.16 thf(zip_derived_cl20, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((double_divide @ X1 @
% 0.51/1.16 (multiply @ X0 @
% 0.51/1.16 (double_divide @ identity @ (inverse @ (inverse @ X1)))))
% 0.51/1.16 = (inverse @ X0))),
% 0.51/1.16 inference('demod', [status(thm)], [zip_derived_cl18, zip_derived_cl2])).
% 0.51/1.16 thf(zip_derived_cl951, plain,
% 0.51/1.16 (![X0 : $i]: ((inverse @ X0) = (multiply @ (inverse @ X0) @ identity))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl935, zip_derived_cl2, zip_derived_cl20])).
% 0.51/1.16 thf(zip_derived_cl966, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((inverse @ (double_divide @ X0 @ X1))
% 0.51/1.16 = (multiply @ (multiply @ X1 @ X0) @ identity))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl951])).
% 0.51/1.16 thf(zip_derived_cl6, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl968, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X1 @ X0) = (multiply @ (multiply @ X1 @ X0) @ identity))),
% 0.51/1.16 inference('demod', [status(thm)], [zip_derived_cl966, zip_derived_cl6])).
% 0.51/1.16 thf(zip_derived_cl1278, plain,
% 0.51/1.16 (![X0 : $i]: ((multiply @ X0 @ identity) = (inverse @ (inverse @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl978, zip_derived_cl968])).
% 0.51/1.16 thf(zip_derived_cl754, plain, (((identity) = (inverse @ identity))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl623, zip_derived_cl624, zip_derived_cl672])).
% 0.51/1.16 thf(zip_derived_cl1, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X1 @ X0)
% 0.51/1.16 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 0.51/1.16 inference('cnf', [status(esa)], [multiply])).
% 0.51/1.16 thf(zip_derived_cl1, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X1 @ X0)
% 0.51/1.16 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 0.51/1.16 inference('cnf', [status(esa)], [multiply])).
% 0.51/1.16 thf(zip_derived_cl9, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ identity @ (double_divide @ X0 @ X1))
% 0.51/1.16 = (double_divide @ (multiply @ X1 @ X0) @ identity))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl2, plain,
% 0.51/1.16 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.51/1.16 inference('cnf', [status(esa)], [inverse])).
% 0.51/1.16 thf(zip_derived_cl11, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ identity @ (double_divide @ X0 @ X1))
% 0.51/1.16 = (inverse @ (multiply @ X1 @ X0)))),
% 0.51/1.16 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl2])).
% 0.51/1.16 thf(zip_derived_cl13, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.51/1.16 ((double_divide @ X1 @
% 0.51/1.16 (multiply @ X2 @
% 0.51/1.16 (double_divide @ identity @
% 0.51/1.16 (double_divide @ (inverse @ X1) @ (double_divide @ X2 @ X0)))))
% 0.51/1.16 = (X0))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl85, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((double_divide @ X1 @
% 0.51/1.16 (inverse @
% 0.51/1.16 (multiply @
% 0.51/1.16 (double_divide @ (inverse @ X1) @ (double_divide @ identity @ X0)) @
% 0.51/1.16 identity)))
% 0.51/1.16 = (X0))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl13])).
% 0.51/1.16 thf(zip_derived_cl1278, plain,
% 0.51/1.16 (![X0 : $i]: ((multiply @ X0 @ identity) = (inverse @ (inverse @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl978, zip_derived_cl968])).
% 0.51/1.16 thf(zip_derived_cl6, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl6, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl951, plain,
% 0.51/1.16 (![X0 : $i]: ((inverse @ X0) = (multiply @ (inverse @ X0) @ identity))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl935, zip_derived_cl2, zip_derived_cl20])).
% 0.51/1.16 thf(zip_derived_cl787, plain,
% 0.51/1.16 (![X0 : $i]:
% 0.51/1.16 ((double_divide @ identity @ (multiply @ X0 @ identity))
% 0.51/1.16 = (inverse @ X0))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl775, zip_derived_cl754, zip_derived_cl2,
% 0.51/1.16 zip_derived_cl754])).
% 0.51/1.16 thf(zip_derived_cl986, plain,
% 0.51/1.16 (![X0 : $i]:
% 0.51/1.16 ((double_divide @ identity @ (inverse @ X0))
% 0.51/1.16 = (inverse @ (inverse @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl951, zip_derived_cl787])).
% 0.51/1.16 thf(zip_derived_cl1, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X1 @ X0)
% 0.51/1.16 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 0.51/1.16 inference('cnf', [status(esa)], [multiply])).
% 0.51/1.16 thf(zip_derived_cl998, plain,
% 0.51/1.16 (![X0 : $i]:
% 0.51/1.16 ((multiply @ (inverse @ X0) @ identity)
% 0.51/1.16 = (double_divide @ (inverse @ (inverse @ X0)) @ identity))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl986, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl951, plain,
% 0.51/1.16 (![X0 : $i]: ((inverse @ X0) = (multiply @ (inverse @ X0) @ identity))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl935, zip_derived_cl2, zip_derived_cl20])).
% 0.51/1.16 thf(zip_derived_cl2, plain,
% 0.51/1.16 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.51/1.16 inference('cnf', [status(esa)], [inverse])).
% 0.51/1.16 thf(zip_derived_cl1014, plain,
% 0.51/1.16 (![X0 : $i]: ((inverse @ X0) = (inverse @ (inverse @ (inverse @ X0))))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl998, zip_derived_cl951, zip_derived_cl2])).
% 0.51/1.16 thf(zip_derived_cl1039, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((inverse @ (double_divide @ X0 @ X1))
% 0.51/1.16 = (inverse @ (inverse @ (multiply @ X1 @ X0))))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1014])).
% 0.51/1.16 thf(zip_derived_cl6, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl1042, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X1 @ X0) = (inverse @ (inverse @ (multiply @ X1 @ X0))))),
% 0.51/1.16 inference('demod', [status(thm)], [zip_derived_cl1039, zip_derived_cl6])).
% 0.51/1.16 thf(zip_derived_cl1876, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((double_divide @ X1 @
% 0.51/1.16 (multiply @ (double_divide @ identity @ X0) @ (inverse @ X1)))
% 0.51/1.16 = (X0))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl85, zip_derived_cl1278, zip_derived_cl6,
% 0.51/1.16 zip_derived_cl1042])).
% 0.51/1.16 thf(zip_derived_cl1901, plain,
% 0.51/1.16 (![X0 : $i]:
% 0.51/1.16 ((double_divide @ identity @
% 0.51/1.16 (multiply @ (double_divide @ identity @ X0) @ identity)) = (
% 0.51/1.16 X0))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl754, zip_derived_cl1876])).
% 0.51/1.16 thf(zip_derived_cl1278, plain,
% 0.51/1.16 (![X0 : $i]: ((multiply @ X0 @ identity) = (inverse @ (inverse @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl978, zip_derived_cl968])).
% 0.51/1.16 thf(zip_derived_cl6, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl1278, plain,
% 0.51/1.16 (![X0 : $i]: ((multiply @ X0 @ identity) = (inverse @ (inverse @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl978, zip_derived_cl968])).
% 0.51/1.16 thf(zip_derived_cl1014, plain,
% 0.51/1.16 (![X0 : $i]: ((inverse @ X0) = (inverse @ (inverse @ (inverse @ X0))))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl998, zip_derived_cl951, zip_derived_cl2])).
% 0.51/1.16 thf(zip_derived_cl986, plain,
% 0.51/1.16 (![X0 : $i]:
% 0.51/1.16 ((double_divide @ identity @ (inverse @ X0))
% 0.51/1.16 = (inverse @ (inverse @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl951, zip_derived_cl787])).
% 0.51/1.16 thf(zip_derived_cl1916, plain,
% 0.51/1.16 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl1901, zip_derived_cl1278, zip_derived_cl6,
% 0.51/1.16 zip_derived_cl1278, zip_derived_cl1014, zip_derived_cl986])).
% 0.51/1.16 thf(zip_derived_cl1935, plain,
% 0.51/1.16 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl1278, zip_derived_cl1916])).
% 0.51/1.16 thf(zip_derived_cl1916, plain,
% 0.51/1.16 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl1901, zip_derived_cl1278, zip_derived_cl6,
% 0.51/1.16 zip_derived_cl1278, zip_derived_cl1014, zip_derived_cl986])).
% 0.51/1.16 thf(zip_derived_cl1935, plain,
% 0.51/1.16 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl1278, zip_derived_cl1916])).
% 0.51/1.16 thf(zip_derived_cl13, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.51/1.16 ((double_divide @ X1 @
% 0.51/1.16 (multiply @ X2 @
% 0.51/1.16 (double_divide @ identity @
% 0.51/1.16 (double_divide @ (inverse @ X1) @ (double_divide @ X2 @ X0)))))
% 0.51/1.16 = (X0))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl11, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ identity @ (double_divide @ X0 @ X1))
% 0.51/1.16 = (inverse @ (multiply @ X1 @ X0)))),
% 0.51/1.16 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl2])).
% 0.51/1.16 thf(zip_derived_cl88, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.51/1.16 ((multiply @ identity @ X0)
% 0.51/1.16 = (inverse @
% 0.51/1.16 (multiply @
% 0.51/1.16 (multiply @ X2 @
% 0.51/1.16 (double_divide @ identity @
% 0.51/1.16 (double_divide @ (inverse @ X1) @ (double_divide @ X2 @ X0)))) @
% 0.51/1.16 X1)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl11])).
% 0.51/1.16 thf(zip_derived_cl10, plain,
% 0.51/1.16 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 0.51/1.16 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 0.51/1.16 thf(zip_derived_cl94, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.51/1.16 ((inverse @ (inverse @ X0))
% 0.51/1.16 = (inverse @
% 0.51/1.16 (multiply @
% 0.51/1.16 (multiply @ X2 @
% 0.51/1.16 (double_divide @ identity @
% 0.51/1.16 (double_divide @ (inverse @ X1) @ (double_divide @ X2 @ X0)))) @
% 0.51/1.16 X1)))),
% 0.51/1.16 inference('demod', [status(thm)], [zip_derived_cl88, zip_derived_cl10])).
% 0.51/1.16 thf(zip_derived_cl1916, plain,
% 0.51/1.16 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl1901, zip_derived_cl1278, zip_derived_cl6,
% 0.51/1.16 zip_derived_cl1278, zip_derived_cl1014, zip_derived_cl986])).
% 0.51/1.16 thf(zip_derived_cl10, plain,
% 0.51/1.16 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 0.51/1.16 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 0.51/1.16 thf(zip_derived_cl1916, plain,
% 0.51/1.16 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl1901, zip_derived_cl1278, zip_derived_cl6,
% 0.51/1.16 zip_derived_cl1278, zip_derived_cl1014, zip_derived_cl986])).
% 0.51/1.16 thf(zip_derived_cl1932, plain,
% 0.51/1.16 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.51/1.16 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl1916])).
% 0.51/1.16 thf(zip_derived_cl6, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl986, plain,
% 0.51/1.16 (![X0 : $i]:
% 0.51/1.16 ((double_divide @ identity @ (inverse @ X0))
% 0.51/1.16 = (inverse @ (inverse @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl951, zip_derived_cl787])).
% 0.51/1.16 thf(zip_derived_cl1009, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((double_divide @ identity @ (multiply @ X1 @ X0))
% 0.51/1.16 = (inverse @ (inverse @ (double_divide @ X0 @ X1))))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl986])).
% 0.51/1.16 thf(zip_derived_cl6, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl1011, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((double_divide @ identity @ (multiply @ X1 @ X0))
% 0.51/1.16 = (inverse @ (multiply @ X1 @ X0)))),
% 0.51/1.16 inference('demod', [status(thm)], [zip_derived_cl1009, zip_derived_cl6])).
% 0.51/1.16 thf(zip_derived_cl1976, plain,
% 0.51/1.16 (![X0 : $i]:
% 0.51/1.16 ((double_divide @ identity @ X0)
% 0.51/1.16 = (inverse @ (multiply @ identity @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl1932, zip_derived_cl1011])).
% 0.51/1.16 thf(zip_derived_cl1932, plain,
% 0.51/1.16 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.51/1.16 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl1916])).
% 0.51/1.16 thf(zip_derived_cl1991, plain,
% 0.51/1.16 (![X0 : $i]: ((double_divide @ identity @ X0) = (inverse @ X0))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl1976, zip_derived_cl1932])).
% 0.51/1.16 thf(zip_derived_cl6, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl2057, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.51/1.16 ((X0)
% 0.51/1.16 = (inverse @
% 0.51/1.16 (multiply @
% 0.51/1.16 (multiply @ X2 @
% 0.51/1.16 (multiply @ (double_divide @ X2 @ X0) @ (inverse @ X1))) @
% 0.51/1.16 X1)))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl94, zip_derived_cl1916, zip_derived_cl1991,
% 0.51/1.16 zip_derived_cl6])).
% 0.51/1.16 thf(zip_derived_cl2068, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((X0)
% 0.51/1.16 = (inverse @
% 0.51/1.16 (multiply @ X1 @
% 0.51/1.16 (multiply @ (double_divide @ X1 @ X0) @ (inverse @ identity)))))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl1935, zip_derived_cl2057])).
% 0.51/1.16 thf(zip_derived_cl754, plain, (((identity) = (inverse @ identity))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl623, zip_derived_cl624, zip_derived_cl672])).
% 0.51/1.16 thf(zip_derived_cl1935, plain,
% 0.51/1.16 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl1278, zip_derived_cl1916])).
% 0.51/1.16 thf(zip_derived_cl2084, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((X0) = (inverse @ (multiply @ X1 @ (double_divide @ X1 @ X0))))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl2068, zip_derived_cl754, zip_derived_cl1935])).
% 0.51/1.16 thf(zip_derived_cl1916, plain,
% 0.51/1.16 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl1901, zip_derived_cl1278, zip_derived_cl6,
% 0.51/1.16 zip_derived_cl1278, zip_derived_cl1014, zip_derived_cl986])).
% 0.51/1.16 thf(zip_derived_cl2174, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((inverse @ X0) = (multiply @ X1 @ (double_divide @ X1 @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2084, zip_derived_cl1916])).
% 0.51/1.16 thf(zip_derived_cl1916, plain,
% 0.51/1.16 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl1901, zip_derived_cl1278, zip_derived_cl6,
% 0.51/1.16 zip_derived_cl1278, zip_derived_cl1014, zip_derived_cl986])).
% 0.51/1.16 thf(zip_derived_cl2174, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((inverse @ X0) = (multiply @ X1 @ (double_divide @ X1 @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2084, zip_derived_cl1916])).
% 0.51/1.16 thf(zip_derived_cl1916, plain,
% 0.51/1.16 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl1901, zip_derived_cl1278, zip_derived_cl6,
% 0.51/1.16 zip_derived_cl1278, zip_derived_cl1014, zip_derived_cl986])).
% 0.51/1.16 thf(zip_derived_cl10, plain,
% 0.51/1.16 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 0.51/1.16 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 0.51/1.16 thf(zip_derived_cl14, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.51/1.16 ((double_divide @ X3 @
% 0.51/1.16 (multiply @ X2 @
% 0.51/1.16 (double_divide @ identity @ (double_divide @ (inverse @ X3) @ X0))))
% 0.51/1.16 = (multiply @ X1 @
% 0.51/1.16 (double_divide @ identity @
% 0.51/1.16 (double_divide @ (inverse @ X2) @ (double_divide @ X1 @ X0)))))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl13])).
% 0.51/1.16 thf(zip_derived_cl115, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.51/1.16 ((double_divide @ X1 @
% 0.51/1.16 (inverse @
% 0.51/1.16 (inverse @
% 0.51/1.16 (double_divide @ identity @ (double_divide @ (inverse @ X1) @ X0)))))
% 0.51/1.16 = (multiply @ X2 @
% 0.51/1.16 (double_divide @ identity @
% 0.51/1.16 (double_divide @ (inverse @ identity) @
% 0.51/1.16 (double_divide @ X2 @ X0)))))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl14])).
% 0.51/1.16 thf(zip_derived_cl6, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl138, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.51/1.16 ((double_divide @ X1 @
% 0.51/1.16 (inverse @
% 0.51/1.16 (multiply @ (double_divide @ (inverse @ X1) @ X0) @ identity)))
% 0.51/1.16 = (multiply @ X2 @
% 0.51/1.16 (double_divide @ identity @
% 0.51/1.16 (double_divide @ (inverse @ identity) @
% 0.51/1.16 (double_divide @ X2 @ X0)))))),
% 0.51/1.16 inference('demod', [status(thm)], [zip_derived_cl115, zip_derived_cl6])).
% 0.51/1.16 thf(zip_derived_cl1935, plain,
% 0.51/1.16 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl1278, zip_derived_cl1916])).
% 0.51/1.16 thf(zip_derived_cl6, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl754, plain, (((identity) = (inverse @ identity))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl623, zip_derived_cl624, zip_derived_cl672])).
% 0.51/1.16 thf(zip_derived_cl1991, plain,
% 0.51/1.16 (![X0 : $i]: ((double_divide @ identity @ X0) = (inverse @ X0))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl1976, zip_derived_cl1932])).
% 0.51/1.16 thf(zip_derived_cl6, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl1991, plain,
% 0.51/1.16 (![X0 : $i]: ((double_divide @ identity @ X0) = (inverse @ X0))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl1976, zip_derived_cl1932])).
% 0.51/1.16 thf(zip_derived_cl6, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl1916, plain,
% 0.51/1.16 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl1901, zip_derived_cl1278, zip_derived_cl6,
% 0.51/1.16 zip_derived_cl1278, zip_derived_cl1014, zip_derived_cl986])).
% 0.51/1.16 thf(zip_derived_cl1957, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1916])).
% 0.51/1.16 thf(zip_derived_cl2244, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.51/1.16 ((double_divide @ X1 @ (multiply @ X0 @ (inverse @ X1)))
% 0.51/1.16 = (multiply @ X2 @ (double_divide @ X2 @ X0)))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl138, zip_derived_cl1935, zip_derived_cl6,
% 0.51/1.16 zip_derived_cl754, zip_derived_cl1991, zip_derived_cl6,
% 0.51/1.16 zip_derived_cl1991, zip_derived_cl1957])).
% 0.51/1.16 thf(zip_derived_cl6, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl2258, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.51/1.16 ((multiply @ (multiply @ X0 @ (inverse @ X2)) @ X2)
% 0.51/1.16 = (inverse @ (multiply @ X1 @ (double_divide @ X1 @ X0))))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2244, zip_derived_cl6])).
% 0.51/1.16 thf(zip_derived_cl2084, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((X0) = (inverse @ (multiply @ X1 @ (double_divide @ X1 @ X0))))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl2068, zip_derived_cl754, zip_derived_cl1935])).
% 0.51/1.16 thf(zip_derived_cl2304, plain,
% 0.51/1.16 (![X0 : $i, X2 : $i]:
% 0.51/1.16 ((multiply @ (multiply @ X0 @ (inverse @ X2)) @ X2) = (X0))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl2258, zip_derived_cl2084])).
% 0.51/1.16 thf(zip_derived_cl2322, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl1916, zip_derived_cl2304])).
% 0.51/1.16 thf(zip_derived_cl2444, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ (inverse @ X0) @ (inverse @ (double_divide @ X1 @ X0)))
% 0.51/1.16 = (X1))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2174, zip_derived_cl2322])).
% 0.51/1.16 thf(zip_derived_cl6, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl2468, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)) = (X1))),
% 0.51/1.16 inference('demod', [status(thm)], [zip_derived_cl2444, zip_derived_cl6])).
% 0.51/1.16 thf(zip_derived_cl2492, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X0 @ (multiply @ (inverse @ X0) @ X1)) = (X1))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl1916, zip_derived_cl2468])).
% 0.51/1.16 thf(zip_derived_cl2512, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X1 @ (inverse @ X0))
% 0.51/1.16 = (double_divide @ (inverse @ X1) @ X0))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2174, zip_derived_cl2492])).
% 0.51/1.16 thf(zip_derived_cl6, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl6, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl986, plain,
% 0.51/1.16 (![X0 : $i]:
% 0.51/1.16 ((double_divide @ identity @ (inverse @ X0))
% 0.51/1.16 = (inverse @ (inverse @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl951, zip_derived_cl787])).
% 0.51/1.16 thf(zip_derived_cl1916, plain,
% 0.51/1.16 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl1901, zip_derived_cl1278, zip_derived_cl6,
% 0.51/1.16 zip_derived_cl1278, zip_derived_cl1014, zip_derived_cl986])).
% 0.51/1.16 thf(zip_derived_cl1933, plain,
% 0.51/1.16 (![X0 : $i]: ((double_divide @ identity @ (inverse @ X0)) = (X0))),
% 0.51/1.16 inference('demod', [status(thm)], [zip_derived_cl986, zip_derived_cl1916])).
% 0.51/1.16 thf(zip_derived_cl2018, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((double_divide @ identity @ (multiply @ X1 @ X0))
% 0.51/1.16 = (double_divide @ X0 @ X1))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1933])).
% 0.51/1.16 thf(zip_derived_cl2972, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.51/1.16 ((double_divide @ X0 @ X2)
% 0.51/1.16 = (multiply @ X1 @ (double_divide @ (multiply @ X0 @ X1) @ X2)))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl144, zip_derived_cl754, zip_derived_cl1935,
% 0.51/1.16 zip_derived_cl1916, zip_derived_cl2512, zip_derived_cl6,
% 0.51/1.16 zip_derived_cl2018])).
% 0.51/1.16 thf(zip_derived_cl2468, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)) = (X1))),
% 0.51/1.16 inference('demod', [status(thm)], [zip_derived_cl2444, zip_derived_cl6])).
% 0.51/1.16 thf(zip_derived_cl1957, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1916])).
% 0.51/1.16 thf(zip_derived_cl2473, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((inverse @ X0)
% 0.51/1.16 = (double_divide @ (multiply @ X1 @ X0) @ (inverse @ X1)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2468, zip_derived_cl1957])).
% 0.51/1.16 thf(zip_derived_cl3156, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.51/1.16 ((inverse @ (double_divide @ (multiply @ X1 @ X2) @ X0))
% 0.51/1.16 = (double_divide @ (double_divide @ X1 @ X0) @ (inverse @ X2)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2972, zip_derived_cl2473])).
% 0.51/1.16 thf(zip_derived_cl6, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl2084, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((X0) = (inverse @ (multiply @ X1 @ (double_divide @ X1 @ X0))))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl2068, zip_derived_cl754, zip_derived_cl1935])).
% 0.51/1.16 thf(zip_derived_cl1957, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1916])).
% 0.51/1.16 thf(zip_derived_cl2178, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((X0) = (double_divide @ (double_divide @ X1 @ X0) @ X1))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2084, zip_derived_cl1957])).
% 0.51/1.16 thf(zip_derived_cl2178, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((X0) = (double_divide @ (double_divide @ X1 @ X0) @ X1))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2084, zip_derived_cl1957])).
% 0.51/1.16 thf(zip_derived_cl2206, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((X1) = (double_divide @ X0 @ (double_divide @ X1 @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2178, zip_derived_cl2178])).
% 0.51/1.16 thf(zip_derived_cl6, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl2335, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ (double_divide @ X0 @ X1) @ X1) = (inverse @ X0))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2206, zip_derived_cl6])).
% 0.51/1.16 thf(zip_derived_cl2304, plain,
% 0.51/1.16 (![X0 : $i, X2 : $i]:
% 0.51/1.16 ((multiply @ (multiply @ X0 @ (inverse @ X2)) @ X2) = (X0))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl2258, zip_derived_cl2084])).
% 0.51/1.16 thf(zip_derived_cl2540, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ (inverse @ X0) @ X1)
% 0.51/1.16 = (double_divide @ X0 @ (inverse @ X1)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2335, zip_derived_cl2304])).
% 0.51/1.16 thf(zip_derived_cl6, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i]:
% 0.51/1.16 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.51/1.16 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.51/1.16 thf(zip_derived_cl3173, plain,
% 0.51/1.16 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.51/1.16 ((multiply @ X0 @ (multiply @ X1 @ X2))
% 0.51/1.16 = (multiply @ (multiply @ X0 @ X1) @ X2))),
% 0.51/1.16 inference('demod', [status(thm)],
% 0.51/1.16 [zip_derived_cl3156, zip_derived_cl6, zip_derived_cl2540,
% 0.51/1.16 zip_derived_cl6])).
% 0.51/1.16 thf(zip_derived_cl3379, plain,
% 0.51/1.16 (((multiply @ a3 @ (multiply @ b3 @ c3))
% 0.51/1.16 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 0.51/1.16 inference('demod', [status(thm)], [zip_derived_cl4, zip_derived_cl3173])).
% 0.51/1.16 thf(zip_derived_cl3380, plain, ($false),
% 0.51/1.16 inference('simplify', [status(thm)], [zip_derived_cl3379])).
% 0.51/1.16
% 0.51/1.16 % SZS output end Refutation
% 0.51/1.16
% 0.51/1.16
% 0.51/1.16 % Terminating...
% 4.51/1.23 % Runner terminated.
% 4.56/1.24 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------