TSTP Solution File: GRP583-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP583-1 : 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.nEpbvPXs7D true
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:52:12 EDT 2023
% Result : Unsatisfiable 11.51s 2.29s
% Output : Refutation 11.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP583-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.nEpbvPXs7D true
% 0.17/0.34 % Computer : n001.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Mon Aug 28 23:39:21 EDT 2023
% 0.17/0.34 % CPUTime :
% 0.17/0.34 % Running portfolio for 300 s
% 0.17/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.34 % Number of cores: 8
% 0.17/0.34 % Python version: Python 3.6.8
% 0.17/0.35 % Running in FO mode
% 0.20/0.63 % Total configuration time : 435
% 0.20/0.63 % Estimated wc time : 1092
% 0.20/0.63 % Estimated cpu time (7 cpus) : 156.0
% 0.20/0.69 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.20/0.70 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.20/0.73 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.20/0.73 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.20/0.73 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.20/0.75 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.20/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 11.51/2.29 % Solved by fo/fo5.sh.
% 11.51/2.29 % done 1743 iterations in 1.525s
% 11.51/2.29 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 11.51/2.29 % SZS output start Refutation
% 11.51/2.29 thf(c3_type, type, c3: $i).
% 11.51/2.29 thf(multiply_type, type, multiply: $i > $i > $i).
% 11.51/2.29 thf(identity_type, type, identity: $i).
% 11.51/2.29 thf(b3_type, type, b3: $i).
% 11.51/2.29 thf(a3_type, type, a3: $i).
% 11.51/2.29 thf(double_divide_type, type, double_divide: $i > $i > $i).
% 11.51/2.29 thf(inverse_type, type, inverse: $i > $i).
% 11.51/2.29 thf(prove_these_axioms_3, conjecture,
% 11.51/2.29 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) =
% 11.51/2.29 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ))).
% 11.51/2.29 thf(zf_stmt_0, negated_conjecture,
% 11.51/2.29 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 11.51/2.29 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) )),
% 11.51/2.29 inference('cnf.neg', [status(esa)], [prove_these_axioms_3])).
% 11.51/2.29 thf(zip_derived_cl4, plain,
% 11.51/2.29 (((multiply @ (multiply @ a3 @ b3) @ c3)
% 11.51/2.29 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 11.51/2.29 inference('cnf', [status(esa)], [zf_stmt_0])).
% 11.51/2.29 thf(identity, axiom,
% 11.51/2.29 (( identity ) = ( double_divide @ A @ ( inverse @ A ) ))).
% 11.51/2.29 thf(zip_derived_cl3, plain,
% 11.51/2.29 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 11.51/2.29 inference('cnf', [status(esa)], [identity])).
% 11.51/2.29 thf(inverse, axiom, (( inverse @ A ) = ( double_divide @ A @ identity ))).
% 11.51/2.29 thf(zip_derived_cl2, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [inverse])).
% 11.51/2.29 thf(multiply, axiom,
% 11.51/2.29 (( multiply @ A @ B ) =
% 11.51/2.29 ( double_divide @ ( double_divide @ B @ A ) @ identity ))).
% 11.51/2.29 thf(zip_derived_cl1, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ X1 @ X0)
% 11.51/2.29 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [multiply])).
% 11.51/2.29 thf(zip_derived_cl6, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 11.51/2.29 thf(zip_derived_cl26, plain,
% 11.51/2.29 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 11.51/2.29 thf(zip_derived_cl3, plain,
% 11.51/2.29 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 11.51/2.29 inference('cnf', [status(esa)], [identity])).
% 11.51/2.29 thf(zip_derived_cl1, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ X1 @ X0)
% 11.51/2.29 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [multiply])).
% 11.51/2.29 thf(zip_derived_cl8, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((multiply @ (inverse @ X0) @ X0)
% 11.51/2.29 = (double_divide @ identity @ identity))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 11.51/2.29 thf(zip_derived_cl6, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 11.51/2.29 thf(zip_derived_cl47, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((multiply @ identity @ identity)
% 11.51/2.29 = (inverse @ (multiply @ (inverse @ X0) @ X0)))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl6])).
% 11.51/2.29 thf(zip_derived_cl3, plain,
% 11.51/2.29 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 11.51/2.29 inference('cnf', [status(esa)], [identity])).
% 11.51/2.29 thf(zip_derived_cl133, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((identity)
% 11.51/2.29 = (double_divide @ (multiply @ (inverse @ X0) @ X0) @
% 11.51/2.29 (multiply @ identity @ identity)))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl47, zip_derived_cl3])).
% 11.51/2.29 thf(zip_derived_cl2, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [inverse])).
% 11.51/2.29 thf(zip_derived_cl1, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ X1 @ X0)
% 11.51/2.29 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [multiply])).
% 11.51/2.29 thf(zip_derived_cl7, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((multiply @ identity @ X0)
% 11.51/2.29 = (double_divide @ (inverse @ X0) @ identity))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 11.51/2.29 thf(zip_derived_cl2, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [inverse])).
% 11.51/2.29 thf(zip_derived_cl10, plain,
% 11.51/2.29 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 11.51/2.29 thf(zip_derived_cl155, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((identity)
% 11.51/2.29 = (double_divide @ (multiply @ (inverse @ X0) @ X0) @
% 11.51/2.29 (inverse @ (inverse @ identity))))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl133, zip_derived_cl10])).
% 11.51/2.29 thf(zip_derived_cl2, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [inverse])).
% 11.51/2.29 thf(single_axiom, axiom,
% 11.51/2.29 (( double_divide @
% 11.51/2.29 ( double_divide @
% 11.51/2.29 A @
% 11.51/2.29 ( double_divide @
% 11.51/2.29 ( double_divide @ identity @ B ) @
% 11.51/2.29 ( double_divide @ C @ ( double_divide @ B @ A ) ) ) ) @
% 11.51/2.29 ( double_divide @ identity @ identity ) ) =
% 11.51/2.29 ( C ))).
% 11.51/2.29 thf(zip_derived_cl0, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((double_divide @
% 11.51/2.29 (double_divide @ X1 @
% 11.51/2.29 (double_divide @ (double_divide @ identity @ X2) @
% 11.51/2.29 (double_divide @ X0 @ (double_divide @ X2 @ X1)))) @
% 11.51/2.29 (double_divide @ identity @ identity)) = (X0))),
% 11.51/2.29 inference('cnf', [status(esa)], [single_axiom])).
% 11.51/2.29 thf(zip_derived_cl2, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [inverse])).
% 11.51/2.29 thf(zip_derived_cl13, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((double_divide @
% 11.51/2.29 (double_divide @ X1 @
% 11.51/2.29 (double_divide @ (double_divide @ identity @ X2) @
% 11.51/2.29 (double_divide @ X0 @ (double_divide @ X2 @ X1)))) @
% 11.51/2.29 (inverse @ identity)) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 11.51/2.29 thf(zip_derived_cl16, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((double_divide @
% 11.51/2.29 (double_divide @ identity @
% 11.51/2.29 (double_divide @ (double_divide @ identity @ X0) @
% 11.51/2.29 (double_divide @ X1 @ (inverse @ X0)))) @
% 11.51/2.29 (inverse @ identity)) = (X1))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 11.51/2.29 thf(zip_derived_cl546, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((double_divide @
% 11.51/2.29 (double_divide @ identity @
% 11.51/2.29 (double_divide @
% 11.51/2.29 (double_divide @ identity @ (inverse @ identity)) @ identity)) @
% 11.51/2.29 (inverse @ identity)) = (multiply @ (inverse @ X0) @ X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl155, zip_derived_cl16])).
% 11.51/2.29 thf(zip_derived_cl3, plain,
% 11.51/2.29 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 11.51/2.29 inference('cnf', [status(esa)], [identity])).
% 11.51/2.29 thf(zip_derived_cl2, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [inverse])).
% 11.51/2.29 thf(zip_derived_cl3, plain,
% 11.51/2.29 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 11.51/2.29 inference('cnf', [status(esa)], [identity])).
% 11.51/2.29 thf(zip_derived_cl3, plain,
% 11.51/2.29 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 11.51/2.29 inference('cnf', [status(esa)], [identity])).
% 11.51/2.29 thf(zip_derived_cl569, plain,
% 11.51/2.29 (![X0 : $i]: ((identity) = (multiply @ (inverse @ X0) @ X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl546, zip_derived_cl3, zip_derived_cl2,
% 11.51/2.29 zip_derived_cl3, zip_derived_cl3])).
% 11.51/2.29 thf(zip_derived_cl590, plain, (((identity) = (inverse @ identity))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl26, zip_derived_cl569])).
% 11.51/2.29 thf(zip_derived_cl3, plain,
% 11.51/2.29 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 11.51/2.29 inference('cnf', [status(esa)], [identity])).
% 11.51/2.29 thf(zip_derived_cl13, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((double_divide @
% 11.51/2.29 (double_divide @ X1 @
% 11.51/2.29 (double_divide @ (double_divide @ identity @ X2) @
% 11.51/2.29 (double_divide @ X0 @ (double_divide @ X2 @ X1)))) @
% 11.51/2.29 (inverse @ identity)) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 11.51/2.29 thf(zip_derived_cl17, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((double_divide @
% 11.51/2.29 (double_divide @ (inverse @ X1) @
% 11.51/2.29 (double_divide @ (double_divide @ identity @ X1) @
% 11.51/2.29 (double_divide @ X0 @ identity))) @
% 11.51/2.29 (inverse @ identity)) = (X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl13])).
% 11.51/2.29 thf(zip_derived_cl2, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [inverse])).
% 11.51/2.29 thf(zip_derived_cl22, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((double_divide @
% 11.51/2.29 (double_divide @ (inverse @ X1) @
% 11.51/2.29 (double_divide @ (double_divide @ identity @ X1) @ (inverse @ X0))) @
% 11.51/2.29 (inverse @ identity)) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl17, zip_derived_cl2])).
% 11.51/2.29 thf(zip_derived_cl590, plain, (((identity) = (inverse @ identity))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl26, zip_derived_cl569])).
% 11.51/2.29 thf(zip_derived_cl1, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ X1 @ X0)
% 11.51/2.29 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [multiply])).
% 11.51/2.29 thf(zip_derived_cl660, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @
% 11.51/2.29 (double_divide @ (double_divide @ identity @ X1) @ (inverse @ X0)) @
% 11.51/2.29 (inverse @ X1)) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl22, zip_derived_cl590, zip_derived_cl1])).
% 11.51/2.29 thf(zip_derived_cl664, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((multiply @
% 11.51/2.29 (double_divide @ (double_divide @ identity @ identity) @
% 11.51/2.29 (inverse @ X0)) @
% 11.51/2.29 identity) = (X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl590, zip_derived_cl660])).
% 11.51/2.29 thf(zip_derived_cl8, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((multiply @ (inverse @ X0) @ X0)
% 11.51/2.29 = (double_divide @ identity @ identity))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 11.51/2.29 thf(zip_derived_cl569, plain,
% 11.51/2.29 (![X0 : $i]: ((identity) = (multiply @ (inverse @ X0) @ X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl546, zip_derived_cl3, zip_derived_cl2,
% 11.51/2.29 zip_derived_cl3, zip_derived_cl3])).
% 11.51/2.29 thf(zip_derived_cl589, plain,
% 11.51/2.29 (((identity) = (double_divide @ identity @ identity))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl8, zip_derived_cl569])).
% 11.51/2.29 thf(zip_derived_cl671, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((multiply @ (double_divide @ identity @ (inverse @ X0)) @ identity)
% 11.51/2.29 = (X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl664, zip_derived_cl589])).
% 11.51/2.29 thf(zip_derived_cl590, plain, (((identity) = (inverse @ identity))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl26, zip_derived_cl569])).
% 11.51/2.29 thf(zip_derived_cl660, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @
% 11.51/2.29 (double_divide @ (double_divide @ identity @ X1) @ (inverse @ X0)) @
% 11.51/2.29 (inverse @ X1)) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl22, zip_derived_cl590, zip_derived_cl1])).
% 11.51/2.29 thf(zip_derived_cl667, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((multiply @
% 11.51/2.29 (double_divide @ (double_divide @ identity @ X0) @ identity) @
% 11.51/2.29 (inverse @ X0)) = (identity))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl590, zip_derived_cl660])).
% 11.51/2.29 thf(zip_derived_cl1, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ X1 @ X0)
% 11.51/2.29 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [multiply])).
% 11.51/2.29 thf(zip_derived_cl673, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((multiply @ (multiply @ X0 @ identity) @ (inverse @ X0)) = (identity))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl667, zip_derived_cl1])).
% 11.51/2.29 thf(zip_derived_cl690, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((multiply @ X0 @
% 11.51/2.29 (inverse @ (double_divide @ identity @ (inverse @ X0))))
% 11.51/2.29 = (identity))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl671, zip_derived_cl673])).
% 11.51/2.29 thf(zip_derived_cl6, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 11.51/2.29 thf(zip_derived_cl695, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((multiply @ X0 @ (multiply @ (inverse @ X0) @ identity)) = (identity))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl690, zip_derived_cl6])).
% 11.51/2.29 thf(zip_derived_cl6, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 11.51/2.29 thf(zip_derived_cl695, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((multiply @ X0 @ (multiply @ (inverse @ X0) @ identity)) = (identity))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl690, zip_derived_cl6])).
% 11.51/2.29 thf(zip_derived_cl700, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ (double_divide @ X0 @ X1) @
% 11.51/2.29 (multiply @ (multiply @ X1 @ X0) @ identity)) = (identity))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl695])).
% 11.51/2.29 thf(zip_derived_cl882, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((multiply @
% 11.51/2.29 (double_divide @ (multiply @ (inverse @ X0) @ identity) @ X0) @
% 11.51/2.29 (multiply @ identity @ identity)) = (identity))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl695, zip_derived_cl700])).
% 11.51/2.29 thf(zip_derived_cl590, plain, (((identity) = (inverse @ identity))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl26, zip_derived_cl569])).
% 11.51/2.29 thf(zip_derived_cl569, plain,
% 11.51/2.29 (![X0 : $i]: ((identity) = (multiply @ (inverse @ X0) @ X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl546, zip_derived_cl3, zip_derived_cl2,
% 11.51/2.29 zip_derived_cl3, zip_derived_cl3])).
% 11.51/2.29 thf(zip_derived_cl615, plain,
% 11.51/2.29 (((identity) = (multiply @ identity @ identity))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl590, zip_derived_cl569])).
% 11.51/2.29 thf(zip_derived_cl901, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((multiply @
% 11.51/2.29 (double_divide @ (multiply @ (inverse @ X0) @ identity) @ X0) @
% 11.51/2.29 identity) = (identity))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl882, zip_derived_cl615])).
% 11.51/2.29 thf(zip_derived_cl671, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((multiply @ (double_divide @ identity @ (inverse @ X0)) @ identity)
% 11.51/2.29 = (X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl664, zip_derived_cl589])).
% 11.51/2.29 thf(zip_derived_cl3, plain,
% 11.51/2.29 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 11.51/2.29 inference('cnf', [status(esa)], [identity])).
% 11.51/2.29 thf(zip_derived_cl660, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @
% 11.51/2.29 (double_divide @ (double_divide @ identity @ X1) @ (inverse @ X0)) @
% 11.51/2.29 (inverse @ X1)) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl22, zip_derived_cl590, zip_derived_cl1])).
% 11.51/2.29 thf(zip_derived_cl665, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((multiply @ identity @ (inverse @ X0))
% 11.51/2.29 = (double_divide @ identity @ X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl660])).
% 11.51/2.29 thf(zip_derived_cl10, plain,
% 11.51/2.29 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 11.51/2.29 thf(zip_derived_cl672, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((inverse @ (inverse @ (inverse @ X0)))
% 11.51/2.29 = (double_divide @ identity @ X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl665, zip_derived_cl10])).
% 11.51/2.29 thf(zip_derived_cl705, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((multiply @ (inverse @ (inverse @ (inverse @ (inverse @ X0)))) @
% 11.51/2.29 identity) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl671, zip_derived_cl672])).
% 11.51/2.29 thf(zip_derived_cl672, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((inverse @ (inverse @ (inverse @ X0)))
% 11.51/2.29 = (double_divide @ identity @ X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl665, zip_derived_cl10])).
% 11.51/2.29 thf(zip_derived_cl6, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 11.51/2.29 thf(zip_derived_cl710, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((multiply @ X0 @ identity)
% 11.51/2.29 = (inverse @ (inverse @ (inverse @ (inverse @ X0)))))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl672, zip_derived_cl6])).
% 11.51/2.29 thf(zip_derived_cl735, plain,
% 11.51/2.29 (![X0 : $i]: ((multiply @ (multiply @ X0 @ identity) @ identity) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl705, zip_derived_cl710])).
% 11.51/2.29 thf(zip_derived_cl1128, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((multiply @ identity @ identity)
% 11.51/2.29 = (double_divide @ (multiply @ (inverse @ X0) @ identity) @ X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl901, zip_derived_cl735])).
% 11.51/2.29 thf(zip_derived_cl615, plain,
% 11.51/2.29 (((identity) = (multiply @ identity @ identity))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl590, zip_derived_cl569])).
% 11.51/2.29 thf(zip_derived_cl1157, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((identity)
% 11.51/2.29 = (double_divide @ (multiply @ (inverse @ X0) @ identity) @ X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl1128, zip_derived_cl615])).
% 11.51/2.29 thf(zip_derived_cl672, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((inverse @ (inverse @ (inverse @ X0)))
% 11.51/2.29 = (double_divide @ identity @ X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl665, zip_derived_cl10])).
% 11.51/2.29 thf(zip_derived_cl1, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ X1 @ X0)
% 11.51/2.29 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [multiply])).
% 11.51/2.29 thf(zip_derived_cl706, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((multiply @ X0 @ identity)
% 11.51/2.29 = (double_divide @ (inverse @ (inverse @ (inverse @ X0))) @ identity))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl672, zip_derived_cl1])).
% 11.51/2.29 thf(zip_derived_cl3, plain,
% 11.51/2.29 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 11.51/2.29 inference('cnf', [status(esa)], [identity])).
% 11.51/2.29 thf(zip_derived_cl1157, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((identity)
% 11.51/2.29 = (double_divide @ (multiply @ (inverse @ X0) @ identity) @ X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl1128, zip_derived_cl615])).
% 11.51/2.29 thf(zip_derived_cl13, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((double_divide @
% 11.51/2.29 (double_divide @ X1 @
% 11.51/2.29 (double_divide @ (double_divide @ identity @ X2) @
% 11.51/2.29 (double_divide @ X0 @ (double_divide @ X2 @ X1)))) @
% 11.51/2.29 (inverse @ identity)) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 11.51/2.29 thf(zip_derived_cl1, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ X1 @ X0)
% 11.51/2.29 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [multiply])).
% 11.51/2.29 thf(zip_derived_cl15, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((multiply @ (inverse @ identity) @
% 11.51/2.29 (double_divide @ X1 @
% 11.51/2.29 (double_divide @ (double_divide @ identity @ X2) @
% 11.51/2.29 (double_divide @ X0 @ (double_divide @ X2 @ X1)))))
% 11.51/2.29 = (double_divide @ X0 @ identity))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl1])).
% 11.51/2.29 thf(zip_derived_cl2, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [inverse])).
% 11.51/2.29 thf(zip_derived_cl23, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((multiply @ (inverse @ identity) @
% 11.51/2.29 (double_divide @ X1 @
% 11.51/2.29 (double_divide @ (double_divide @ identity @ X2) @
% 11.51/2.29 (double_divide @ X0 @ (double_divide @ X2 @ X1)))))
% 11.51/2.29 = (inverse @ X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl15, zip_derived_cl2])).
% 11.51/2.29 thf(zip_derived_cl590, plain, (((identity) = (inverse @ identity))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl26, zip_derived_cl569])).
% 11.51/2.29 thf(zip_derived_cl672, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((inverse @ (inverse @ (inverse @ X0)))
% 11.51/2.29 = (double_divide @ identity @ X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl665, zip_derived_cl10])).
% 11.51/2.29 thf(zip_derived_cl1, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ X1 @ X0)
% 11.51/2.29 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [multiply])).
% 11.51/2.29 thf(zip_derived_cl1, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ X1 @ X0)
% 11.51/2.29 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [multiply])).
% 11.51/2.29 thf(zip_derived_cl9, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ identity @ (double_divide @ X0 @ X1))
% 11.51/2.29 = (double_divide @ (multiply @ X1 @ X0) @ identity))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl1])).
% 11.51/2.29 thf(zip_derived_cl2, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [inverse])).
% 11.51/2.29 thf(zip_derived_cl11, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ identity @ (double_divide @ X0 @ X1))
% 11.51/2.29 = (inverse @ (multiply @ X1 @ X0)))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl2])).
% 11.51/2.29 thf(zip_derived_cl786, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((inverse @
% 11.51/2.29 (multiply @
% 11.51/2.29 (double_divide @ (inverse @ (inverse @ (inverse @ X2))) @
% 11.51/2.29 (double_divide @ X0 @ (double_divide @ X2 @ X1))) @
% 11.51/2.29 X1))
% 11.51/2.29 = (inverse @ X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl23, zip_derived_cl590, zip_derived_cl672,
% 11.51/2.29 zip_derived_cl11])).
% 11.51/2.29 thf(zip_derived_cl1165, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((inverse @
% 11.51/2.29 (multiply @
% 11.51/2.29 (double_divide @
% 11.51/2.29 (inverse @
% 11.51/2.29 (inverse @ (inverse @ (multiply @ (inverse @ X1) @ identity)))) @
% 11.51/2.29 (double_divide @ X0 @ identity)) @
% 11.51/2.29 X1))
% 11.51/2.29 = (inverse @ X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1157, zip_derived_cl786])).
% 11.51/2.29 thf(zip_derived_cl710, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((multiply @ X0 @ identity)
% 11.51/2.29 = (inverse @ (inverse @ (inverse @ (inverse @ X0)))))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl672, zip_derived_cl6])).
% 11.51/2.29 thf(zip_derived_cl710, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((multiply @ X0 @ identity)
% 11.51/2.29 = (inverse @ (inverse @ (inverse @ (inverse @ X0)))))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl672, zip_derived_cl6])).
% 11.51/2.29 thf(zip_derived_cl744, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((multiply @ (inverse @ X0) @ identity)
% 11.51/2.29 = (inverse @ (multiply @ X0 @ identity)))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl710, zip_derived_cl710])).
% 11.51/2.29 thf(zip_derived_cl744, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((multiply @ (inverse @ X0) @ identity)
% 11.51/2.29 = (inverse @ (multiply @ X0 @ identity)))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl710, zip_derived_cl710])).
% 11.51/2.29 thf(zip_derived_cl744, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((multiply @ (inverse @ X0) @ identity)
% 11.51/2.29 = (inverse @ (multiply @ X0 @ identity)))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl710, zip_derived_cl710])).
% 11.51/2.29 thf(zip_derived_cl710, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((multiply @ X0 @ identity)
% 11.51/2.29 = (inverse @ (inverse @ (inverse @ (inverse @ X0)))))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl672, zip_derived_cl6])).
% 11.51/2.29 thf(zip_derived_cl735, plain,
% 11.51/2.29 (![X0 : $i]: ((multiply @ (multiply @ X0 @ identity) @ identity) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl705, zip_derived_cl710])).
% 11.51/2.29 thf(zip_derived_cl2, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [inverse])).
% 11.51/2.29 thf(zip_derived_cl1187, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((inverse @ (multiply @ (double_divide @ X1 @ (inverse @ X0)) @ X1))
% 11.51/2.29 = (inverse @ X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl1165, zip_derived_cl744, zip_derived_cl744,
% 11.51/2.29 zip_derived_cl744, zip_derived_cl710, zip_derived_cl735,
% 11.51/2.29 zip_derived_cl2])).
% 11.51/2.29 thf(zip_derived_cl1332, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ (multiply @ identity @ X0)) = (inverse @ X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1187])).
% 11.51/2.29 thf(zip_derived_cl10, plain,
% 11.51/2.29 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 11.51/2.29 thf(zip_derived_cl1342, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ (inverse @ (inverse @ X0))) = (inverse @ X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl1332, zip_derived_cl10])).
% 11.51/2.29 thf(zip_derived_cl2, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [inverse])).
% 11.51/2.29 thf(zip_derived_cl1358, plain,
% 11.51/2.29 (![X0 : $i]: ((multiply @ X0 @ identity) = (inverse @ (inverse @ X0)))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl706, zip_derived_cl1342, zip_derived_cl2])).
% 11.51/2.29 thf(zip_derived_cl1342, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ (inverse @ (inverse @ X0))) = (inverse @ X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl1332, zip_derived_cl10])).
% 11.51/2.29 thf(zip_derived_cl1414, plain,
% 11.51/2.29 (![X0 : $i]: ((identity) = (double_divide @ (inverse @ X0) @ X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl1157, zip_derived_cl1358, zip_derived_cl1342])).
% 11.51/2.29 thf(zip_derived_cl3, plain,
% 11.51/2.29 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 11.51/2.29 inference('cnf', [status(esa)], [identity])).
% 11.51/2.29 thf(zip_derived_cl13, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((double_divide @
% 11.51/2.29 (double_divide @ X1 @
% 11.51/2.29 (double_divide @ (double_divide @ identity @ X2) @
% 11.51/2.29 (double_divide @ X0 @ (double_divide @ X2 @ X1)))) @
% 11.51/2.29 (inverse @ identity)) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 11.51/2.29 thf(zip_derived_cl13, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((double_divide @
% 11.51/2.29 (double_divide @ X1 @
% 11.51/2.29 (double_divide @ (double_divide @ identity @ X2) @
% 11.51/2.29 (double_divide @ X0 @ (double_divide @ X2 @ X1)))) @
% 11.51/2.29 (inverse @ identity)) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 11.51/2.29 thf(zip_derived_cl14, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 11.51/2.29 ((double_divide @
% 11.51/2.29 (double_divide @ (inverse @ identity) @
% 11.51/2.29 (double_divide @
% 11.51/2.29 (double_divide @ identity @
% 11.51/2.29 (double_divide @ X2 @
% 11.51/2.29 (double_divide @ (double_divide @ identity @ X3) @
% 11.51/2.29 (double_divide @ X0 @ (double_divide @ X3 @ X2))))) @
% 11.51/2.29 (double_divide @ X1 @ X0))) @
% 11.51/2.29 (inverse @ identity)) = (X1))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl13])).
% 11.51/2.29 thf(zip_derived_cl108, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((double_divide @
% 11.51/2.29 (double_divide @ (inverse @ identity) @
% 11.51/2.29 (double_divide @
% 11.51/2.29 (double_divide @ identity @
% 11.51/2.29 (double_divide @ X1 @
% 11.51/2.29 (double_divide @ (double_divide @ identity @ X2) @
% 11.51/2.29 (double_divide @ (inverse @ X0) @ (double_divide @ X2 @ X1))))) @
% 11.51/2.29 identity)) @
% 11.51/2.29 (inverse @ identity)) = (X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl14])).
% 11.51/2.29 thf(zip_derived_cl1, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ X1 @ X0)
% 11.51/2.29 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [multiply])).
% 11.51/2.29 thf(zip_derived_cl126, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((double_divide @
% 11.51/2.29 (double_divide @ (inverse @ identity) @
% 11.51/2.29 (multiply @
% 11.51/2.29 (double_divide @ X1 @
% 11.51/2.29 (double_divide @ (double_divide @ identity @ X2) @
% 11.51/2.29 (double_divide @ (inverse @ X0) @ (double_divide @ X2 @ X1)))) @
% 11.51/2.29 identity)) @
% 11.51/2.29 (inverse @ identity)) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl108, zip_derived_cl1])).
% 11.51/2.29 thf(zip_derived_cl590, plain, (((identity) = (inverse @ identity))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl26, zip_derived_cl569])).
% 11.51/2.29 thf(zip_derived_cl672, plain,
% 11.51/2.29 (![X0 : $i]:
% 11.51/2.29 ((inverse @ (inverse @ (inverse @ X0)))
% 11.51/2.29 = (double_divide @ identity @ X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl665, zip_derived_cl10])).
% 11.51/2.29 thf(zip_derived_cl1342, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ (inverse @ (inverse @ X0))) = (inverse @ X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl1332, zip_derived_cl10])).
% 11.51/2.29 thf(zip_derived_cl1357, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ X0) = (double_divide @ identity @ X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl672, zip_derived_cl1342])).
% 11.51/2.29 thf(zip_derived_cl1358, plain,
% 11.51/2.29 (![X0 : $i]: ((multiply @ X0 @ identity) = (inverse @ (inverse @ X0)))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl706, zip_derived_cl1342, zip_derived_cl2])).
% 11.51/2.29 thf(zip_derived_cl735, plain,
% 11.51/2.29 (![X0 : $i]: ((multiply @ (multiply @ X0 @ identity) @ identity) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl705, zip_derived_cl710])).
% 11.51/2.29 thf(zip_derived_cl1358, plain,
% 11.51/2.29 (![X0 : $i]: ((multiply @ X0 @ identity) = (inverse @ (inverse @ X0)))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl706, zip_derived_cl1342, zip_derived_cl2])).
% 11.51/2.29 thf(zip_derived_cl1358, plain,
% 11.51/2.29 (![X0 : $i]: ((multiply @ X0 @ identity) = (inverse @ (inverse @ X0)))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl706, zip_derived_cl1342, zip_derived_cl2])).
% 11.51/2.29 thf(zip_derived_cl1342, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ (inverse @ (inverse @ X0))) = (inverse @ X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl1332, zip_derived_cl10])).
% 11.51/2.29 thf(zip_derived_cl1408, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl735, zip_derived_cl1358, zip_derived_cl1358,
% 11.51/2.29 zip_derived_cl1342])).
% 11.51/2.29 thf(zip_derived_cl1459, plain,
% 11.51/2.29 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl1358, zip_derived_cl1408])).
% 11.51/2.29 thf(zip_derived_cl1357, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ X0) = (double_divide @ identity @ X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl672, zip_derived_cl1342])).
% 11.51/2.29 thf(zip_derived_cl6, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 11.51/2.29 thf(zip_derived_cl590, plain, (((identity) = (inverse @ identity))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl26, zip_derived_cl569])).
% 11.51/2.29 thf(zip_derived_cl2, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [inverse])).
% 11.51/2.29 thf(zip_derived_cl1494, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((inverse @
% 11.51/2.29 (multiply @
% 11.51/2.29 (double_divide @ (inverse @ X2) @
% 11.51/2.29 (double_divide @ (inverse @ X0) @ (double_divide @ X2 @ X1))) @
% 11.51/2.29 X1))
% 11.51/2.29 = (X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl126, zip_derived_cl590, zip_derived_cl1357,
% 11.51/2.29 zip_derived_cl1459, zip_derived_cl1357, zip_derived_cl6,
% 11.51/2.29 zip_derived_cl590, zip_derived_cl2])).
% 11.51/2.29 thf(zip_derived_cl1537, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((inverse @
% 11.51/2.29 (multiply @ (double_divide @ (inverse @ X1) @ identity) @ X0))
% 11.51/2.29 = (double_divide @ X1 @ X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1414, zip_derived_cl1494])).
% 11.51/2.29 thf(zip_derived_cl2, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [inverse])).
% 11.51/2.29 thf(zip_derived_cl1408, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl735, zip_derived_cl1358, zip_derived_cl1358,
% 11.51/2.29 zip_derived_cl1342])).
% 11.51/2.29 thf(zip_derived_cl1550, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X1 @ X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl1537, zip_derived_cl2, zip_derived_cl1408])).
% 11.51/2.29 thf(zip_derived_cl1408, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl735, zip_derived_cl1358, zip_derived_cl1358,
% 11.51/2.29 zip_derived_cl1342])).
% 11.51/2.29 thf(zip_derived_cl1579, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((inverse @ (double_divide @ X1 @ X0)) = (multiply @ X1 @ X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1550, zip_derived_cl1408])).
% 11.51/2.29 thf(zip_derived_cl6, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 11.51/2.29 thf(zip_derived_cl1848, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1579, zip_derived_cl6])).
% 11.51/2.29 thf(zip_derived_cl1848, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1579, zip_derived_cl6])).
% 11.51/2.29 thf(zip_derived_cl1962, plain,
% 11.51/2.29 (((multiply @ c3 @ (multiply @ a3 @ b3))
% 11.51/2.29 != (multiply @ a3 @ (multiply @ c3 @ b3)))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl4, zip_derived_cl1848, zip_derived_cl1848])).
% 11.51/2.29 thf(zip_derived_cl1848, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1579, zip_derived_cl6])).
% 11.51/2.29 thf(zip_derived_cl1187, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((inverse @ (multiply @ (double_divide @ X1 @ (inverse @ X0)) @ X1))
% 11.51/2.29 = (inverse @ X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl1165, zip_derived_cl744, zip_derived_cl744,
% 11.51/2.29 zip_derived_cl744, zip_derived_cl710, zip_derived_cl735,
% 11.51/2.29 zip_derived_cl2])).
% 11.51/2.29 thf(zip_derived_cl1408, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl735, zip_derived_cl1358, zip_derived_cl1358,
% 11.51/2.29 zip_derived_cl1342])).
% 11.51/2.29 thf(zip_derived_cl1467, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((inverse @ (inverse @ X0))
% 11.51/2.29 = (multiply @ (double_divide @ X1 @ (inverse @ X0)) @ X1))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1187, zip_derived_cl1408])).
% 11.51/2.29 thf(zip_derived_cl1408, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl735, zip_derived_cl1358, zip_derived_cl1358,
% 11.51/2.29 zip_derived_cl1342])).
% 11.51/2.29 thf(zip_derived_cl1469, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((X0) = (multiply @ (double_divide @ X1 @ (inverse @ X0)) @ X1))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl1467, zip_derived_cl1408])).
% 11.51/2.29 thf(zip_derived_cl1459, plain,
% 11.51/2.29 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl1358, zip_derived_cl1408])).
% 11.51/2.29 thf(zip_derived_cl1661, plain,
% 11.51/2.29 (![X0 : $i]: ((X0) = (double_divide @ identity @ (inverse @ X0)))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1469, zip_derived_cl1459])).
% 11.51/2.29 thf(zip_derived_cl1494, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((inverse @
% 11.51/2.29 (multiply @
% 11.51/2.29 (double_divide @ (inverse @ X2) @
% 11.51/2.29 (double_divide @ (inverse @ X0) @ (double_divide @ X2 @ X1))) @
% 11.51/2.29 X1))
% 11.51/2.29 = (X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl126, zip_derived_cl590, zip_derived_cl1357,
% 11.51/2.29 zip_derived_cl1459, zip_derived_cl1357, zip_derived_cl6,
% 11.51/2.29 zip_derived_cl590, zip_derived_cl2])).
% 11.51/2.29 thf(zip_derived_cl1677, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((inverse @
% 11.51/2.29 (multiply @
% 11.51/2.29 (double_divide @ (inverse @ identity) @
% 11.51/2.29 (double_divide @ (inverse @ X1) @ X0)) @
% 11.51/2.29 (inverse @ X0)))
% 11.51/2.29 = (X1))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1661, zip_derived_cl1494])).
% 11.51/2.29 thf(zip_derived_cl590, plain, (((identity) = (inverse @ identity))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl26, zip_derived_cl569])).
% 11.51/2.29 thf(zip_derived_cl1357, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ X0) = (double_divide @ identity @ X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl672, zip_derived_cl1342])).
% 11.51/2.29 thf(zip_derived_cl6, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 11.51/2.29 thf(zip_derived_cl1550, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X1 @ X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl1537, zip_derived_cl2, zip_derived_cl1408])).
% 11.51/2.29 thf(zip_derived_cl1550, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X1 @ X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl1537, zip_derived_cl2, zip_derived_cl1408])).
% 11.51/2.29 thf(zip_derived_cl6, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 11.51/2.29 thf(zip_derived_cl1408, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl735, zip_derived_cl1358, zip_derived_cl1358,
% 11.51/2.29 zip_derived_cl1342])).
% 11.51/2.29 thf(zip_derived_cl1465, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1408])).
% 11.51/2.29 thf(zip_derived_cl1583, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((double_divide @ X1 @ X0) = (double_divide @ X0 @ X1))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1550, zip_derived_cl1465])).
% 11.51/2.29 thf(zip_derived_cl1693, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((double_divide @ (inverse @ X0) @ (multiply @ X0 @ (inverse @ X1)))
% 11.51/2.29 = (X1))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl1677, zip_derived_cl590, zip_derived_cl1357,
% 11.51/2.29 zip_derived_cl6, zip_derived_cl1550, zip_derived_cl1583])).
% 11.51/2.29 thf(zip_derived_cl3, plain,
% 11.51/2.29 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 11.51/2.29 inference('cnf', [status(esa)], [identity])).
% 11.51/2.29 thf(zip_derived_cl14, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 11.51/2.29 ((double_divide @
% 11.51/2.29 (double_divide @ (inverse @ identity) @
% 11.51/2.29 (double_divide @
% 11.51/2.29 (double_divide @ identity @
% 11.51/2.29 (double_divide @ X2 @
% 11.51/2.29 (double_divide @ (double_divide @ identity @ X3) @
% 11.51/2.29 (double_divide @ X0 @ (double_divide @ X3 @ X2))))) @
% 11.51/2.29 (double_divide @ X1 @ X0))) @
% 11.51/2.29 (inverse @ identity)) = (X1))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl13])).
% 11.51/2.29 thf(zip_derived_cl115, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((double_divide @
% 11.51/2.29 (double_divide @ (inverse @ identity) @
% 11.51/2.29 (double_divide @
% 11.51/2.29 (double_divide @ identity @
% 11.51/2.29 (double_divide @ (inverse @ X2) @
% 11.51/2.29 (double_divide @ (double_divide @ identity @ X2) @
% 11.51/2.29 (double_divide @ X1 @ identity)))) @
% 11.51/2.29 (double_divide @ X0 @ X1))) @
% 11.51/2.29 (inverse @ identity)) = (X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl14])).
% 11.51/2.29 thf(zip_derived_cl2, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [inverse])).
% 11.51/2.29 thf(zip_derived_cl128, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((double_divide @
% 11.51/2.29 (double_divide @ (inverse @ identity) @
% 11.51/2.29 (double_divide @
% 11.51/2.29 (double_divide @ identity @
% 11.51/2.29 (double_divide @ (inverse @ X2) @
% 11.51/2.29 (double_divide @ (double_divide @ identity @ X2) @
% 11.51/2.29 (inverse @ X1)))) @
% 11.51/2.29 (double_divide @ X0 @ X1))) @
% 11.51/2.29 (inverse @ identity)) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl115, zip_derived_cl2])).
% 11.51/2.29 thf(zip_derived_cl590, plain, (((identity) = (inverse @ identity))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl26, zip_derived_cl569])).
% 11.51/2.29 thf(zip_derived_cl1357, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ X0) = (double_divide @ identity @ X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl672, zip_derived_cl1342])).
% 11.51/2.29 thf(zip_derived_cl1357, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ X0) = (double_divide @ identity @ X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl672, zip_derived_cl1342])).
% 11.51/2.29 thf(zip_derived_cl6, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 11.51/2.29 thf(zip_derived_cl1469, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((X0) = (multiply @ (double_divide @ X1 @ (inverse @ X0)) @ X1))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl1467, zip_derived_cl1408])).
% 11.51/2.29 thf(zip_derived_cl1357, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ X0) = (double_divide @ identity @ X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl672, zip_derived_cl1342])).
% 11.51/2.29 thf(zip_derived_cl6, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 11.51/2.29 thf(zip_derived_cl590, plain, (((identity) = (inverse @ identity))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl26, zip_derived_cl569])).
% 11.51/2.29 thf(zip_derived_cl2, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [inverse])).
% 11.51/2.29 thf(zip_derived_cl1550, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X1 @ X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl1537, zip_derived_cl2, zip_derived_cl1408])).
% 11.51/2.29 thf(zip_derived_cl1583, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((double_divide @ X1 @ X0) = (double_divide @ X0 @ X1))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1550, zip_derived_cl1465])).
% 11.51/2.29 thf(zip_derived_cl1697, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((double_divide @ X1 @ (double_divide @ X0 @ X1)) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl128, zip_derived_cl590, zip_derived_cl1357,
% 11.51/2.29 zip_derived_cl1357, zip_derived_cl6, zip_derived_cl1469,
% 11.51/2.29 zip_derived_cl1357, zip_derived_cl6, zip_derived_cl590,
% 11.51/2.29 zip_derived_cl2, zip_derived_cl1550, zip_derived_cl1583])).
% 11.51/2.29 thf(zip_derived_cl1697, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((double_divide @ X1 @ (double_divide @ X0 @ X1)) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl128, zip_derived_cl590, zip_derived_cl1357,
% 11.51/2.29 zip_derived_cl1357, zip_derived_cl6, zip_derived_cl1469,
% 11.51/2.29 zip_derived_cl1357, zip_derived_cl6, zip_derived_cl590,
% 11.51/2.29 zip_derived_cl2, zip_derived_cl1550, zip_derived_cl1583])).
% 11.51/2.29 thf(zip_derived_cl1702, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((double_divide @ (double_divide @ X0 @ X1) @ X0) = (X1))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1697, zip_derived_cl1697])).
% 11.51/2.29 thf(zip_derived_cl1469, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((X0) = (multiply @ (double_divide @ X1 @ (inverse @ X0)) @ X1))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl1467, zip_derived_cl1408])).
% 11.51/2.29 thf(zip_derived_cl1753, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((X1) = (multiply @ X0 @ (double_divide @ (inverse @ X1) @ X0)))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1702, zip_derived_cl1469])).
% 11.51/2.29 thf(zip_derived_cl3594, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((X1) = (multiply @ (multiply @ X1 @ (inverse @ X0)) @ X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1693, zip_derived_cl1753])).
% 11.51/2.29 thf(zip_derived_cl3921, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((X0) = (multiply @ (multiply @ (inverse @ X1) @ X0) @ X1))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1848, zip_derived_cl3594])).
% 11.51/2.29 thf(zip_derived_cl13, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((double_divide @
% 11.51/2.29 (double_divide @ X1 @
% 11.51/2.29 (double_divide @ (double_divide @ identity @ X2) @
% 11.51/2.29 (double_divide @ X0 @ (double_divide @ X2 @ X1)))) @
% 11.51/2.29 (inverse @ identity)) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 11.51/2.29 thf(zip_derived_cl16, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((double_divide @
% 11.51/2.29 (double_divide @ identity @
% 11.51/2.29 (double_divide @ (double_divide @ identity @ X0) @
% 11.51/2.29 (double_divide @ X1 @ (inverse @ X0)))) @
% 11.51/2.29 (inverse @ identity)) = (X1))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 11.51/2.29 thf(zip_derived_cl236, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((double_divide @
% 11.51/2.29 (double_divide @ identity @
% 11.51/2.29 (double_divide @ (double_divide @ identity @ identity) @ X0)) @
% 11.51/2.29 (inverse @ identity))
% 11.51/2.29 = (double_divide @ X1 @
% 11.51/2.29 (double_divide @ (double_divide @ identity @ X2) @
% 11.51/2.29 (double_divide @ X0 @ (double_divide @ X2 @ X1)))))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl16])).
% 11.51/2.29 thf(zip_derived_cl2, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [inverse])).
% 11.51/2.29 thf(zip_derived_cl247, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((double_divide @
% 11.51/2.29 (double_divide @ identity @
% 11.51/2.29 (double_divide @ (inverse @ identity) @ X0)) @
% 11.51/2.29 (inverse @ identity))
% 11.51/2.29 = (double_divide @ X1 @
% 11.51/2.29 (double_divide @ (double_divide @ identity @ X2) @
% 11.51/2.29 (double_divide @ X0 @ (double_divide @ X2 @ X1)))))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl236, zip_derived_cl2])).
% 11.51/2.29 thf(zip_derived_cl590, plain, (((identity) = (inverse @ identity))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl26, zip_derived_cl569])).
% 11.51/2.29 thf(zip_derived_cl1357, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ X0) = (double_divide @ identity @ X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl672, zip_derived_cl1342])).
% 11.51/2.29 thf(zip_derived_cl1661, plain,
% 11.51/2.29 (![X0 : $i]: ((X0) = (double_divide @ identity @ (inverse @ X0)))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1469, zip_derived_cl1459])).
% 11.51/2.29 thf(zip_derived_cl590, plain, (((identity) = (inverse @ identity))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl26, zip_derived_cl569])).
% 11.51/2.29 thf(zip_derived_cl2, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [inverse])).
% 11.51/2.29 thf(zip_derived_cl1357, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ X0) = (double_divide @ identity @ X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl672, zip_derived_cl1342])).
% 11.51/2.29 thf(zip_derived_cl1408, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl735, zip_derived_cl1358, zip_derived_cl1358,
% 11.51/2.29 zip_derived_cl1342])).
% 11.51/2.29 thf(zip_derived_cl1469, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((X0) = (multiply @ (double_divide @ X1 @ (inverse @ X0)) @ X1))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl1467, zip_derived_cl1408])).
% 11.51/2.29 thf(zip_derived_cl1673, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((inverse @ X0) = (multiply @ (double_divide @ X1 @ X0) @ X1))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1408, zip_derived_cl1469])).
% 11.51/2.29 thf(zip_derived_cl3594, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((X1) = (multiply @ (multiply @ X1 @ (inverse @ X0)) @ X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1693, zip_derived_cl1753])).
% 11.51/2.29 thf(zip_derived_cl3924, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((double_divide @ (inverse @ X1) @ X0)
% 11.51/2.29 = (multiply @ (inverse @ X0) @ X1))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1673, zip_derived_cl3594])).
% 11.51/2.29 thf(zip_derived_cl1579, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((inverse @ (double_divide @ X1 @ X0)) = (multiply @ X1 @ X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1550, zip_derived_cl1408])).
% 11.51/2.29 thf(zip_derived_cl1848, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1579, zip_derived_cl6])).
% 11.51/2.29 thf(zip_derived_cl4830, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((inverse @ X0)
% 11.51/2.29 = (double_divide @ X1 @
% 11.51/2.29 (multiply @ X2 @ (multiply @ X0 @ (double_divide @ X2 @ X1)))))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl247, zip_derived_cl590, zip_derived_cl1357,
% 11.51/2.29 zip_derived_cl1661, zip_derived_cl590, zip_derived_cl2,
% 11.51/2.29 zip_derived_cl1357, zip_derived_cl3924, zip_derived_cl1579,
% 11.51/2.29 zip_derived_cl1848])).
% 11.51/2.29 thf(zip_derived_cl4873, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((inverse @ (multiply @ (inverse @ (double_divide @ X2 @ X1)) @ X0))
% 11.51/2.29 = (double_divide @ X1 @ (multiply @ X2 @ X0)))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl3921, zip_derived_cl4830])).
% 11.51/2.29 thf(zip_derived_cl1579, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((inverse @ (double_divide @ X1 @ X0)) = (multiply @ X1 @ X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1550, zip_derived_cl1408])).
% 11.51/2.29 thf(zip_derived_cl1550, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X1 @ X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl1537, zip_derived_cl2, zip_derived_cl1408])).
% 11.51/2.29 thf(zip_derived_cl4918, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((double_divide @ (multiply @ X2 @ X1) @ X0)
% 11.51/2.29 = (double_divide @ X1 @ (multiply @ X2 @ X0)))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl4873, zip_derived_cl1579, zip_derived_cl1550])).
% 11.51/2.29 thf(zip_derived_cl1579, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((inverse @ (double_divide @ X1 @ X0)) = (multiply @ X1 @ X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1550, zip_derived_cl1408])).
% 11.51/2.29 thf(zip_derived_cl11253, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((inverse @ (double_divide @ X2 @ (multiply @ X1 @ X0)))
% 11.51/2.29 = (multiply @ (multiply @ X1 @ X2) @ X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl4918, zip_derived_cl1579])).
% 11.51/2.29 thf(zip_derived_cl1579, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((inverse @ (double_divide @ X1 @ X0)) = (multiply @ X1 @ X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1550, zip_derived_cl1408])).
% 11.51/2.29 thf(zip_derived_cl11358, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((multiply @ X2 @ (multiply @ X1 @ X0))
% 11.51/2.29 = (multiply @ (multiply @ X1 @ X2) @ X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl11253, zip_derived_cl1579])).
% 11.51/2.29 thf(zip_derived_cl1, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ X1 @ X0)
% 11.51/2.29 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [multiply])).
% 11.51/2.29 thf(zip_derived_cl13, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((double_divide @
% 11.51/2.29 (double_divide @ X1 @
% 11.51/2.29 (double_divide @ (double_divide @ identity @ X2) @
% 11.51/2.29 (double_divide @ X0 @ (double_divide @ X2 @ X1)))) @
% 11.51/2.29 (inverse @ identity)) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 11.51/2.29 thf(zip_derived_cl18, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((double_divide @
% 11.51/2.29 (double_divide @ identity @
% 11.51/2.29 (double_divide @
% 11.51/2.29 (double_divide @ identity @ (double_divide @ X0 @ X1)) @
% 11.51/2.29 (double_divide @ X2 @ (multiply @ X1 @ X0)))) @
% 11.51/2.29 (inverse @ identity)) = (X2))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl13])).
% 11.51/2.29 thf(zip_derived_cl1, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ X1 @ X0)
% 11.51/2.29 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [multiply])).
% 11.51/2.29 thf(zip_derived_cl295, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((multiply @ (inverse @ identity) @
% 11.51/2.29 (double_divide @ identity @
% 11.51/2.29 (double_divide @
% 11.51/2.29 (double_divide @ identity @ (double_divide @ X1 @ X2)) @
% 11.51/2.29 (double_divide @ X0 @ (multiply @ X2 @ X1)))))
% 11.51/2.29 = (double_divide @ X0 @ identity))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl18, zip_derived_cl1])).
% 11.51/2.29 thf(zip_derived_cl2, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [inverse])).
% 11.51/2.29 thf(zip_derived_cl345, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((multiply @ (inverse @ identity) @
% 11.51/2.29 (double_divide @ identity @
% 11.51/2.29 (double_divide @
% 11.51/2.29 (double_divide @ identity @ (double_divide @ X1 @ X2)) @
% 11.51/2.29 (double_divide @ X0 @ (multiply @ X2 @ X1)))))
% 11.51/2.29 = (inverse @ X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl295, zip_derived_cl2])).
% 11.51/2.29 thf(zip_derived_cl590, plain, (((identity) = (inverse @ identity))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl26, zip_derived_cl569])).
% 11.51/2.29 thf(zip_derived_cl1550, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X1 @ X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl1537, zip_derived_cl2, zip_derived_cl1408])).
% 11.51/2.29 thf(zip_derived_cl1661, plain,
% 11.51/2.29 (![X0 : $i]: ((X0) = (double_divide @ identity @ (inverse @ X0)))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1469, zip_derived_cl1459])).
% 11.51/2.29 thf(zip_derived_cl1689, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ X1 @ X0)
% 11.51/2.29 = (double_divide @ identity @ (double_divide @ X1 @ X0)))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1550, zip_derived_cl1661])).
% 11.51/2.29 thf(zip_derived_cl1689, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ X1 @ X0)
% 11.51/2.29 = (double_divide @ identity @ (double_divide @ X1 @ X0)))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1550, zip_derived_cl1661])).
% 11.51/2.29 thf(zip_derived_cl3, plain,
% 11.51/2.29 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 11.51/2.29 inference('cnf', [status(esa)], [identity])).
% 11.51/2.29 thf(zip_derived_cl6, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 11.51/2.29 thf(zip_derived_cl3, plain,
% 11.51/2.29 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 11.51/2.29 inference('cnf', [status(esa)], [identity])).
% 11.51/2.29 thf(zip_derived_cl24, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((identity)
% 11.51/2.29 = (double_divide @ (double_divide @ X0 @ X1) @ (multiply @ X1 @ X0)))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl3])).
% 11.51/2.29 thf(zip_derived_cl13, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((double_divide @
% 11.51/2.29 (double_divide @ X1 @
% 11.51/2.29 (double_divide @ (double_divide @ identity @ X2) @
% 11.51/2.29 (double_divide @ X0 @ (double_divide @ X2 @ X1)))) @
% 11.51/2.29 (inverse @ identity)) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 11.51/2.29 thf(zip_derived_cl163, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((double_divide @
% 11.51/2.29 (double_divide @ (multiply @ X2 @ X1) @
% 11.51/2.29 (double_divide @
% 11.51/2.29 (double_divide @ identity @ (double_divide @ X1 @ X2)) @
% 11.51/2.29 (double_divide @ X0 @ identity))) @
% 11.51/2.29 (inverse @ identity)) = (X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl24, zip_derived_cl13])).
% 11.51/2.29 thf(zip_derived_cl2, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [inverse])).
% 11.51/2.29 thf(zip_derived_cl198, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((double_divide @
% 11.51/2.29 (double_divide @ (multiply @ X2 @ X1) @
% 11.51/2.29 (double_divide @
% 11.51/2.29 (double_divide @ identity @ (double_divide @ X1 @ X2)) @
% 11.51/2.29 (inverse @ X0))) @
% 11.51/2.29 (inverse @ identity)) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl163, zip_derived_cl2])).
% 11.51/2.29 thf(zip_derived_cl1689, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ X1 @ X0)
% 11.51/2.29 = (double_divide @ identity @ (double_divide @ X1 @ X0)))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1550, zip_derived_cl1661])).
% 11.51/2.29 thf(zip_derived_cl590, plain, (((identity) = (inverse @ identity))),
% 11.51/2.29 inference('demod', [status(thm)], [zip_derived_cl26, zip_derived_cl569])).
% 11.51/2.29 thf(zip_derived_cl1, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ X1 @ X0)
% 11.51/2.29 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 11.51/2.29 inference('cnf', [status(esa)], [multiply])).
% 11.51/2.29 thf(zip_derived_cl1848, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1579, zip_derived_cl6])).
% 11.51/2.29 thf(zip_derived_cl3296, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((multiply @ (multiply @ X2 @ X1) @
% 11.51/2.29 (double_divide @ (multiply @ X1 @ X2) @ (inverse @ X0))) = (
% 11.51/2.29 X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl198, zip_derived_cl1689, zip_derived_cl590,
% 11.51/2.29 zip_derived_cl1, zip_derived_cl1848])).
% 11.51/2.29 thf(zip_derived_cl3317, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ (multiply @ X0 @ X1) @ identity) = (multiply @ X1 @ X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl3296])).
% 11.51/2.29 thf(zip_derived_cl1848, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1579, zip_derived_cl6])).
% 11.51/2.29 thf(zip_derived_cl3422, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ identity @ (multiply @ X0 @ X1)) = (multiply @ X1 @ X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl3317, zip_derived_cl1848])).
% 11.51/2.29 thf(zip_derived_cl1848, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1579, zip_derived_cl6])).
% 11.51/2.29 thf(zip_derived_cl6411, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((multiply @ (multiply @ X1 @ X2) @
% 11.51/2.29 (double_divide @ X0 @ (multiply @ X2 @ X1))) = (inverse @ X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl345, zip_derived_cl590, zip_derived_cl1689,
% 11.51/2.29 zip_derived_cl1689, zip_derived_cl3422, zip_derived_cl1848])).
% 11.51/2.29 thf(zip_derived_cl1408, plain,
% 11.51/2.29 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl735, zip_derived_cl1358, zip_derived_cl1358,
% 11.51/2.29 zip_derived_cl1342])).
% 11.51/2.29 thf(zip_derived_cl1693, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((double_divide @ (inverse @ X0) @ (multiply @ X0 @ (inverse @ X1)))
% 11.51/2.29 = (X1))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl1677, zip_derived_cl590, zip_derived_cl1357,
% 11.51/2.29 zip_derived_cl6, zip_derived_cl1550, zip_derived_cl1583])).
% 11.51/2.29 thf(zip_derived_cl3610, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((double_divide @ (inverse @ X1) @ (multiply @ X1 @ X0))
% 11.51/2.29 = (inverse @ X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1408, zip_derived_cl1693])).
% 11.51/2.29 thf(zip_derived_cl6426, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((double_divide @ (inverse @ (multiply @ X1 @ X2)) @ (inverse @ X0))
% 11.51/2.29 = (inverse @ (double_divide @ X0 @ (multiply @ X2 @ X1))))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl6411, zip_derived_cl3610])).
% 11.51/2.29 thf(zip_derived_cl1550, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X1 @ X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl1537, zip_derived_cl2, zip_derived_cl1408])).
% 11.51/2.29 thf(zip_derived_cl1697, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((double_divide @ X1 @ (double_divide @ X0 @ X1)) = (X0))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl128, zip_derived_cl590, zip_derived_cl1357,
% 11.51/2.29 zip_derived_cl1357, zip_derived_cl6, zip_derived_cl1469,
% 11.51/2.29 zip_derived_cl1357, zip_derived_cl6, zip_derived_cl590,
% 11.51/2.29 zip_derived_cl2, zip_derived_cl1550, zip_derived_cl1583])).
% 11.51/2.29 thf(zip_derived_cl6, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 11.51/2.29 thf(zip_derived_cl1703, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((multiply @ (double_divide @ X0 @ X1) @ X1) = (inverse @ X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1697, zip_derived_cl6])).
% 11.51/2.29 thf(zip_derived_cl3594, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((X1) = (multiply @ (multiply @ X1 @ (inverse @ X0)) @ X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1693, zip_derived_cl1753])).
% 11.51/2.29 thf(zip_derived_cl3925, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((double_divide @ X0 @ (inverse @ X1))
% 11.51/2.29 = (multiply @ (inverse @ X0) @ X1))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1703, zip_derived_cl3594])).
% 11.51/2.29 thf(zip_derived_cl1579, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((inverse @ (double_divide @ X1 @ X0)) = (multiply @ X1 @ X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1550, zip_derived_cl1408])).
% 11.51/2.29 thf(zip_derived_cl1579, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]:
% 11.51/2.29 ((inverse @ (double_divide @ X1 @ X0)) = (multiply @ X1 @ X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1550, zip_derived_cl1408])).
% 11.51/2.29 thf(zip_derived_cl6594, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((multiply @ (multiply @ X1 @ X2) @ X0)
% 11.51/2.29 = (multiply @ X0 @ (multiply @ X2 @ X1)))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl6426, zip_derived_cl1550, zip_derived_cl3925,
% 11.51/2.29 zip_derived_cl1579, zip_derived_cl1579])).
% 11.51/2.29 thf(zip_derived_cl11450, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.51/2.29 ((multiply @ X2 @ (multiply @ X1 @ X0))
% 11.51/2.29 = (multiply @ X0 @ (multiply @ X2 @ X1)))),
% 11.51/2.29 inference('sup+', [status(thm)],
% 11.51/2.29 [zip_derived_cl11358, zip_derived_cl6594])).
% 11.51/2.29 thf(zip_derived_cl1848, plain,
% 11.51/2.29 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 11.51/2.29 inference('sup+', [status(thm)], [zip_derived_cl1579, zip_derived_cl6])).
% 11.51/2.29 thf(zip_derived_cl12145, plain,
% 11.51/2.29 (((multiply @ a3 @ (multiply @ c3 @ b3))
% 11.51/2.29 != (multiply @ a3 @ (multiply @ c3 @ b3)))),
% 11.51/2.29 inference('demod', [status(thm)],
% 11.51/2.29 [zip_derived_cl1962, zip_derived_cl11450, zip_derived_cl1848])).
% 11.51/2.29 thf(zip_derived_cl12146, plain, ($false),
% 11.51/2.29 inference('simplify', [status(thm)], [zip_derived_cl12145])).
% 11.51/2.29
% 11.51/2.29 % SZS output end Refutation
% 11.51/2.29
% 11.51/2.29
% 11.51/2.29 % Terminating...
% 11.99/2.36 % Runner terminated.
% 11.99/2.37 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------