TSTP Solution File: GRP002-4 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP002-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ZSCEWK7fa3 true
% Computer : n004.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 01:49:26 EDT 2023
% Result : Unsatisfiable 10.89s 2.23s
% Output : Refutation 10.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP002-4 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ZSCEWK7fa3 true
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 21:58:22 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.21/0.68 % Total configuration time : 435
% 0.21/0.68 % Estimated wc time : 1092
% 0.21/0.68 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 10.89/2.23 % Solved by fo/fo4.sh.
% 10.89/2.23 % done 495 iterations in 1.450s
% 10.89/2.23 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 10.89/2.23 % SZS output start Refutation
% 10.89/2.23 thf(b_type, type, b: $i).
% 10.89/2.23 thf(identity_type, type, identity: $i).
% 10.89/2.23 thf(multiply_type, type, multiply: $i > $i > $i).
% 10.89/2.23 thf(inverse_type, type, inverse: $i > $i).
% 10.89/2.23 thf(commutator_type, type, commutator: $i > $i > $i).
% 10.89/2.23 thf(a_type, type, a: $i).
% 10.89/2.23 thf(prove_commutator, conjecture,
% 10.89/2.23 (( commutator @ ( commutator @ a @ b ) @ b ) = ( identity ))).
% 10.89/2.23 thf(zf_stmt_0, negated_conjecture,
% 10.89/2.23 (( commutator @ ( commutator @ a @ b ) @ b ) != ( identity )),
% 10.89/2.23 inference('cnf.neg', [status(esa)], [prove_commutator])).
% 10.89/2.23 thf(zip_derived_cl7, plain,
% 10.89/2.23 (((commutator @ (commutator @ a @ b) @ b) != (identity))),
% 10.89/2.23 inference('cnf', [status(esa)], [zf_stmt_0])).
% 10.89/2.23 thf(commutator, axiom,
% 10.89/2.23 (( commutator @ X @ Y ) =
% 10.89/2.23 ( multiply @
% 10.89/2.23 X @ ( multiply @ Y @ ( multiply @ ( inverse @ X ) @ ( inverse @ Y ) ) ) ))).
% 10.89/2.23 thf(zip_derived_cl5, plain,
% 10.89/2.23 (![X0 : $i, X1 : $i]:
% 10.89/2.23 ((commutator @ X0 @ X1)
% 10.89/2.24 = (multiply @ X0 @
% 10.89/2.24 (multiply @ X1 @ (multiply @ (inverse @ X0) @ (inverse @ X1)))))),
% 10.89/2.24 inference('cnf', [status(esa)], [commutator])).
% 10.89/2.24 thf(right_inverse, axiom,
% 10.89/2.24 (( multiply @ X @ ( inverse @ X ) ) = ( identity ))).
% 10.89/2.24 thf(zip_derived_cl4, plain,
% 10.89/2.24 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 10.89/2.24 inference('cnf', [status(esa)], [right_inverse])).
% 10.89/2.24 thf(associativity, axiom,
% 10.89/2.24 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 10.89/2.24 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 10.89/2.24 thf(zip_derived_cl2, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.89/2.24 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 10.89/2.24 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 10.89/2.24 inference('cnf', [status(esa)], [associativity])).
% 10.89/2.24 thf(zip_derived_cl17, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((identity)
% 10.89/2.24 = (multiply @ X1 @
% 10.89/2.24 (multiply @ X0 @ (inverse @ (multiply @ X1 @ X0)))))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl2])).
% 10.89/2.24 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 10.89/2.24 thf(zip_derived_cl1, plain,
% 10.89/2.24 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 10.89/2.24 inference('cnf', [status(esa)], [left_inverse])).
% 10.89/2.24 thf(zip_derived_cl2, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.89/2.24 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 10.89/2.24 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 10.89/2.24 inference('cnf', [status(esa)], [associativity])).
% 10.89/2.24 thf(zip_derived_cl23, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ identity @ X0)
% 10.89/2.24 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 10.89/2.24 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 10.89/2.24 thf(zip_derived_cl0, plain,
% 10.89/2.24 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 10.89/2.24 inference('cnf', [status(esa)], [left_identity])).
% 10.89/2.24 thf(zip_derived_cl30, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 10.89/2.24 thf(zip_derived_cl257, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0)))
% 10.89/2.24 = (multiply @ (inverse @ X1) @ identity))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl17, zip_derived_cl30])).
% 10.89/2.24 thf(right_identity, axiom, (( multiply @ X @ identity ) = ( X ))).
% 10.89/2.24 thf(zip_derived_cl3, plain,
% 10.89/2.24 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 10.89/2.24 inference('cnf', [status(esa)], [right_identity])).
% 10.89/2.24 thf(zip_derived_cl300, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl257, zip_derived_cl3])).
% 10.89/2.24 thf(zip_derived_cl30, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 10.89/2.24 thf(zip_derived_cl309, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((inverse @ (multiply @ X0 @ X1))
% 10.89/2.24 = (multiply @ (inverse @ X1) @ (inverse @ X0)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl300, zip_derived_cl30])).
% 10.89/2.24 thf(zip_derived_cl341, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ X0 @ X1)
% 10.89/2.24 = (multiply @ X0 @
% 10.89/2.24 (multiply @ X1 @ (inverse @ (multiply @ X1 @ X0)))))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl309])).
% 10.89/2.24 thf(zip_derived_cl4, plain,
% 10.89/2.24 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 10.89/2.24 inference('cnf', [status(esa)], [right_inverse])).
% 10.89/2.24 thf(zip_derived_cl2, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.89/2.24 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 10.89/2.24 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 10.89/2.24 inference('cnf', [status(esa)], [associativity])).
% 10.89/2.24 thf(zip_derived_cl20, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ identity @ X0)
% 10.89/2.24 = (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl2])).
% 10.89/2.24 thf(zip_derived_cl0, plain,
% 10.89/2.24 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 10.89/2.24 inference('cnf', [status(esa)], [left_identity])).
% 10.89/2.24 thf(zip_derived_cl28, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((X0) = (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl20, zip_derived_cl0])).
% 10.89/2.24 thf(zip_derived_cl3878, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ X0 @ (inverse @ (multiply @ X0 @ (inverse @ X1))))
% 10.89/2.24 = (multiply @ X1 @ (commutator @ (inverse @ X1) @ X0)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl341, zip_derived_cl28])).
% 10.89/2.24 thf(zip_derived_cl300, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl257, zip_derived_cl3])).
% 10.89/2.24 thf(zip_derived_cl28, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((X0) = (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl20, zip_derived_cl0])).
% 10.89/2.24 thf(zip_derived_cl313, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((inverse @ (multiply @ X0 @ (inverse @ X1)))
% 10.89/2.24 = (multiply @ X1 @ (inverse @ X0)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl300, zip_derived_cl28])).
% 10.89/2.24 thf(zip_derived_cl3997, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ X0 @ (multiply @ X1 @ (inverse @ X0)))
% 10.89/2.24 = (multiply @ X1 @ (commutator @ (inverse @ X1) @ X0)))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl3878, zip_derived_cl313])).
% 10.89/2.24 thf(zip_derived_cl5, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ X0 @ X1)
% 10.89/2.24 = (multiply @ X0 @
% 10.89/2.24 (multiply @ X1 @ (multiply @ (inverse @ X0) @ (inverse @ X1)))))),
% 10.89/2.24 inference('cnf', [status(esa)], [commutator])).
% 10.89/2.24 thf(zip_derived_cl2, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.89/2.24 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 10.89/2.24 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 10.89/2.24 inference('cnf', [status(esa)], [associativity])).
% 10.89/2.24 thf(zip_derived_cl34, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.89/2.24 ((multiply @ (commutator @ X1 @ X0) @ X2)
% 10.89/2.24 = (multiply @ X1 @
% 10.89/2.24 (multiply @
% 10.89/2.24 (multiply @ X0 @ (multiply @ (inverse @ X1) @ (inverse @ X0))) @
% 10.89/2.24 X2)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl2])).
% 10.89/2.24 thf(zip_derived_cl2, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.89/2.24 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 10.89/2.24 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 10.89/2.24 inference('cnf', [status(esa)], [associativity])).
% 10.89/2.24 thf(zip_derived_cl2, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.89/2.24 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 10.89/2.24 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 10.89/2.24 inference('cnf', [status(esa)], [associativity])).
% 10.89/2.24 thf(zip_derived_cl48, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.89/2.24 ((multiply @ (commutator @ X1 @ X0) @ X2)
% 10.89/2.24 = (multiply @ X1 @
% 10.89/2.24 (multiply @ X0 @
% 10.89/2.24 (multiply @ (inverse @ X1) @ (multiply @ (inverse @ X0) @ X2)))))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl34, zip_derived_cl2, zip_derived_cl2])).
% 10.89/2.24 thf(zip_derived_cl9296, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (commutator @ X0 @ X1) @ (inverse @ (inverse @ X0)))
% 10.89/2.24 = (multiply @ X0 @
% 10.89/2.24 (multiply @ X1 @
% 10.89/2.24 (multiply @ (inverse @ X1) @
% 10.89/2.24 (commutator @ (inverse @ (inverse @ X1)) @ (inverse @ X0))))))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl3997, zip_derived_cl48])).
% 10.89/2.24 thf(zip_derived_cl4, plain,
% 10.89/2.24 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 10.89/2.24 inference('cnf', [status(esa)], [right_inverse])).
% 10.89/2.24 thf(zip_derived_cl28, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((X0) = (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl20, zip_derived_cl0])).
% 10.89/2.24 thf(zip_derived_cl62, plain,
% 10.89/2.24 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (multiply @ X0 @ identity))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl28])).
% 10.89/2.24 thf(zip_derived_cl3, plain,
% 10.89/2.24 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 10.89/2.24 inference('cnf', [status(esa)], [right_identity])).
% 10.89/2.24 thf(zip_derived_cl66, plain,
% 10.89/2.24 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl62, zip_derived_cl3])).
% 10.89/2.24 thf(zip_derived_cl66, plain,
% 10.89/2.24 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl62, zip_derived_cl3])).
% 10.89/2.24 thf(zip_derived_cl28, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((X0) = (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl20, zip_derived_cl0])).
% 10.89/2.24 thf(zip_derived_cl9433, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (commutator @ X0 @ X1) @ X0)
% 10.89/2.24 = (multiply @ X0 @ (commutator @ X1 @ (inverse @ X0))))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl9296, zip_derived_cl66, zip_derived_cl66,
% 10.89/2.24 zip_derived_cl28])).
% 10.89/2.24 thf(zip_derived_cl4, plain,
% 10.89/2.24 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 10.89/2.24 inference('cnf', [status(esa)], [right_inverse])).
% 10.89/2.24 thf(zip_derived_cl48, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.89/2.24 ((multiply @ (commutator @ X1 @ X0) @ X2)
% 10.89/2.24 = (multiply @ X1 @
% 10.89/2.24 (multiply @ X0 @
% 10.89/2.24 (multiply @ (inverse @ X1) @ (multiply @ (inverse @ X0) @ X2)))))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl34, zip_derived_cl2, zip_derived_cl2])).
% 10.89/2.24 thf(zip_derived_cl774, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (commutator @ X1 @ X0) @ (inverse @ (inverse @ X0)))
% 10.89/2.24 = (multiply @ X1 @
% 10.89/2.24 (multiply @ X0 @ (multiply @ (inverse @ X1) @ identity))))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl48])).
% 10.89/2.24 thf(zip_derived_cl66, plain,
% 10.89/2.24 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl62, zip_derived_cl3])).
% 10.89/2.24 thf(zip_derived_cl3, plain,
% 10.89/2.24 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 10.89/2.24 inference('cnf', [status(esa)], [right_identity])).
% 10.89/2.24 thf(zip_derived_cl808, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (commutator @ X1 @ X0) @ X0)
% 10.89/2.24 = (multiply @ X1 @ (multiply @ X0 @ (inverse @ X1))))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl774, zip_derived_cl66, zip_derived_cl3])).
% 10.89/2.24 thf(zip_derived_cl300, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl257, zip_derived_cl3])).
% 10.89/2.24 thf(x_cubed_is_identity, axiom,
% 10.89/2.24 (( multiply @ X @ ( multiply @ X @ X ) ) = ( identity ))).
% 10.89/2.24 thf(zip_derived_cl6, plain,
% 10.89/2.24 (![X0 : $i]: ((multiply @ X0 @ (multiply @ X0 @ X0)) = (identity))),
% 10.89/2.24 inference('cnf', [status(esa)], [x_cubed_is_identity])).
% 10.89/2.24 thf(zip_derived_cl28, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((X0) = (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl20, zip_derived_cl0])).
% 10.89/2.24 thf(zip_derived_cl59, plain,
% 10.89/2.24 (![X0 : $i]:
% 10.89/2.24 ((multiply @ (inverse @ X0) @ (inverse @ X0))
% 10.89/2.24 = (multiply @ X0 @ identity))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl28])).
% 10.89/2.24 thf(zip_derived_cl3, plain,
% 10.89/2.24 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 10.89/2.24 inference('cnf', [status(esa)], [right_identity])).
% 10.89/2.24 thf(zip_derived_cl65, plain,
% 10.89/2.24 (![X0 : $i]: ((multiply @ (inverse @ X0) @ (inverse @ X0)) = (X0))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl59, zip_derived_cl3])).
% 10.89/2.24 thf(zip_derived_cl28, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((X0) = (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl20, zip_derived_cl0])).
% 10.89/2.24 thf(zip_derived_cl144, plain,
% 10.89/2.24 (![X0 : $i]: ((inverse @ X0) = (multiply @ X0 @ X0))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl65, zip_derived_cl28])).
% 10.89/2.24 thf(zip_derived_cl2, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.89/2.24 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 10.89/2.24 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 10.89/2.24 inference('cnf', [status(esa)], [associativity])).
% 10.89/2.24 thf(zip_derived_cl158, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (inverse @ X0) @ X1)
% 10.89/2.24 = (multiply @ X0 @ (multiply @ X0 @ X1)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl144, zip_derived_cl2])).
% 10.89/2.24 thf(zip_derived_cl306, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (inverse @ X1) @ (inverse @ (multiply @ X0 @ X1)))
% 10.89/2.24 = (multiply @ X1 @ (inverse @ X0)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl300, zip_derived_cl158])).
% 10.89/2.24 thf(zip_derived_cl11441, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (inverse @ (multiply @ X0 @ (inverse @ X1))) @
% 10.89/2.24 (inverse @ (multiply @ (commutator @ X1 @ X0) @ X0)))
% 10.89/2.24 = (multiply @ (multiply @ X0 @ (inverse @ X1)) @ (inverse @ X1)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl808, zip_derived_cl306])).
% 10.89/2.24 thf(zip_derived_cl313, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((inverse @ (multiply @ X0 @ (inverse @ X1)))
% 10.89/2.24 = (multiply @ X1 @ (inverse @ X0)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl300, zip_derived_cl28])).
% 10.89/2.24 thf(zip_derived_cl808, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (commutator @ X1 @ X0) @ X0)
% 10.89/2.24 = (multiply @ X1 @ (multiply @ X0 @ (inverse @ X1))))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl774, zip_derived_cl66, zip_derived_cl3])).
% 10.89/2.24 thf(zip_derived_cl30, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 10.89/2.24 thf(zip_derived_cl66, plain,
% 10.89/2.24 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl62, zip_derived_cl3])).
% 10.89/2.24 thf(zip_derived_cl66, plain,
% 10.89/2.24 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl62, zip_derived_cl3])).
% 10.89/2.24 thf(zip_derived_cl30, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 10.89/2.24 thf(zip_derived_cl300, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl257, zip_derived_cl3])).
% 10.89/2.24 thf(zip_derived_cl326, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0))
% 10.89/2.24 = (inverse @ (inverse @ X1)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl300])).
% 10.89/2.24 thf(zip_derived_cl66, plain,
% 10.89/2.24 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl62, zip_derived_cl3])).
% 10.89/2.24 thf(zip_derived_cl334, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl326, zip_derived_cl66])).
% 10.89/2.24 thf(zip_derived_cl560, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (multiply @ X1 @ (inverse @ X0)) @ X0) = (X1))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl66, zip_derived_cl334])).
% 10.89/2.24 thf(zip_derived_cl158, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (inverse @ X0) @ X1)
% 10.89/2.24 = (multiply @ X0 @ (multiply @ X0 @ X1)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl144, zip_derived_cl2])).
% 10.89/2.24 thf(zip_derived_cl590, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (inverse @ (multiply @ X0 @ (inverse @ X1))) @ X1)
% 10.89/2.24 = (multiply @ (multiply @ X0 @ (inverse @ X1)) @ X0))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl560, zip_derived_cl158])).
% 10.89/2.24 thf(zip_derived_cl313, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((inverse @ (multiply @ X0 @ (inverse @ X1)))
% 10.89/2.24 = (multiply @ X1 @ (inverse @ X0)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl300, zip_derived_cl28])).
% 10.89/2.24 thf(zip_derived_cl2, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.89/2.24 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 10.89/2.24 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 10.89/2.24 inference('cnf', [status(esa)], [associativity])).
% 10.89/2.24 thf(zip_derived_cl619, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ X1 @ (multiply @ (inverse @ X0) @ X1))
% 10.89/2.24 = (multiply @ (multiply @ X0 @ (inverse @ X1)) @ X0))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl590, zip_derived_cl313, zip_derived_cl2])).
% 10.89/2.24 thf(zip_derived_cl925, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ X1 @ (multiply @ X0 @ X1))
% 10.89/2.24 = (multiply @ (multiply @ (inverse @ X0) @ (inverse @ X1)) @
% 10.89/2.24 (inverse @ X0)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl66, zip_derived_cl619])).
% 10.89/2.24 thf(zip_derived_cl309, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((inverse @ (multiply @ X0 @ X1))
% 10.89/2.24 = (multiply @ (inverse @ X1) @ (inverse @ X0)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl300, zip_derived_cl30])).
% 10.89/2.24 thf(zip_derived_cl309, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((inverse @ (multiply @ X0 @ X1))
% 10.89/2.24 = (multiply @ (inverse @ X1) @ (inverse @ X0)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl300, zip_derived_cl30])).
% 10.89/2.24 thf(zip_derived_cl955, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ X1 @ (multiply @ X0 @ X1))
% 10.89/2.24 = (inverse @ (multiply @ X0 @ (multiply @ X1 @ X0))))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl925, zip_derived_cl309, zip_derived_cl309])).
% 10.89/2.24 thf(zip_derived_cl341, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ X0 @ X1)
% 10.89/2.24 = (multiply @ X0 @
% 10.89/2.24 (multiply @ X1 @ (inverse @ (multiply @ X1 @ X0)))))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl309])).
% 10.89/2.24 thf(zip_derived_cl3900, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ (multiply @ X0 @ X1) @ X1)
% 10.89/2.24 = (multiply @ (multiply @ X0 @ X1) @
% 10.89/2.24 (multiply @ X1 @ (multiply @ X0 @ (multiply @ X1 @ X0)))))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl955, zip_derived_cl341])).
% 10.89/2.24 thf(zip_derived_cl144, plain,
% 10.89/2.24 (![X0 : $i]: ((inverse @ X0) = (multiply @ X0 @ X0))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl65, zip_derived_cl28])).
% 10.89/2.24 thf(zip_derived_cl2, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.89/2.24 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 10.89/2.24 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 10.89/2.24 inference('cnf', [status(esa)], [associativity])).
% 10.89/2.24 thf(zip_derived_cl162, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((inverse @ (multiply @ X1 @ X0))
% 10.89/2.24 = (multiply @ X1 @ (multiply @ X0 @ (multiply @ X1 @ X0))))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl144, zip_derived_cl2])).
% 10.89/2.24 thf(zip_derived_cl2, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.89/2.24 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 10.89/2.24 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 10.89/2.24 inference('cnf', [status(esa)], [associativity])).
% 10.89/2.24 thf(zip_derived_cl341, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ X0 @ X1)
% 10.89/2.24 = (multiply @ X0 @
% 10.89/2.24 (multiply @ X1 @ (inverse @ (multiply @ X1 @ X0)))))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl309])).
% 10.89/2.24 thf(zip_derived_cl3946, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ (multiply @ X0 @ X1) @ X1) = (commutator @ X0 @ X1))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl3900, zip_derived_cl162, zip_derived_cl2,
% 10.89/2.24 zip_derived_cl341])).
% 10.89/2.24 thf(zip_derived_cl4050, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ X0 @ (multiply @ X1 @ X0))
% 10.89/2.24 = (commutator @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl3946])).
% 10.89/2.24 thf(zip_derived_cl334, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl326, zip_derived_cl66])).
% 10.89/2.24 thf(zip_derived_cl300, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl257, zip_derived_cl3])).
% 10.89/2.24 thf(zip_derived_cl5, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ X0 @ X1)
% 10.89/2.24 = (multiply @ X0 @
% 10.89/2.24 (multiply @ X1 @ (multiply @ (inverse @ X0) @ (inverse @ X1)))))),
% 10.89/2.24 inference('cnf', [status(esa)], [commutator])).
% 10.89/2.24 thf(zip_derived_cl314, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ X1 @ (multiply @ X0 @ (inverse @ X1)))
% 10.89/2.24 = (multiply @ X1 @
% 10.89/2.24 (multiply @ (multiply @ X0 @ (inverse @ X1)) @ (inverse @ X0))))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl300, zip_derived_cl5])).
% 10.89/2.24 thf(zip_derived_cl2, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.89/2.24 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 10.89/2.24 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 10.89/2.24 inference('cnf', [status(esa)], [associativity])).
% 10.89/2.24 thf(zip_derived_cl5, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ X0 @ X1)
% 10.89/2.24 = (multiply @ X0 @
% 10.89/2.24 (multiply @ X1 @ (multiply @ (inverse @ X0) @ (inverse @ X1)))))),
% 10.89/2.24 inference('cnf', [status(esa)], [commutator])).
% 10.89/2.24 thf(zip_derived_cl340, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ X1 @ (multiply @ X0 @ (inverse @ X1)))
% 10.89/2.24 = (commutator @ X1 @ X0))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl314, zip_derived_cl2, zip_derived_cl5])).
% 10.89/2.24 thf(zip_derived_cl634, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ X1 @ X0) = (commutator @ X1 @ (multiply @ X0 @ X1)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl334, zip_derived_cl340])).
% 10.89/2.24 thf(zip_derived_cl4077, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ X0 @ X1)
% 10.89/2.24 = (commutator @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl4050, zip_derived_cl634])).
% 10.89/2.24 thf(zip_derived_cl4272, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ (multiply @ X0 @ (inverse @ X1)) @ X1)
% 10.89/2.24 = (commutator @ (inverse @ X1) @
% 10.89/2.24 (multiply @ (commutator @ X1 @ X0) @ X0)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl808, zip_derived_cl4077])).
% 10.89/2.24 thf(zip_derived_cl560, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (multiply @ X1 @ (inverse @ X0)) @ X0) = (X1))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl66, zip_derived_cl334])).
% 10.89/2.24 thf(zip_derived_cl3946, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ (multiply @ X0 @ X1) @ X1) = (commutator @ X0 @ X1))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl3900, zip_derived_cl162, zip_derived_cl2,
% 10.89/2.24 zip_derived_cl341])).
% 10.89/2.24 thf(zip_derived_cl4038, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ X0 @ X1)
% 10.89/2.24 = (commutator @ (multiply @ X0 @ (inverse @ X1)) @ X1))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl560, zip_derived_cl3946])).
% 10.89/2.24 thf(zip_derived_cl4312, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ X0 @ X1)
% 10.89/2.24 = (commutator @ (inverse @ X1) @
% 10.89/2.24 (multiply @ (commutator @ X1 @ X0) @ X0)))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl4272, zip_derived_cl4038])).
% 10.89/2.24 thf(zip_derived_cl808, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (commutator @ X1 @ X0) @ X0)
% 10.89/2.24 = (multiply @ X1 @ (multiply @ X0 @ (inverse @ X1))))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl774, zip_derived_cl66, zip_derived_cl3])).
% 10.89/2.24 thf(zip_derived_cl4838, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (commutator @ X1 @ X0) @
% 10.89/2.24 (multiply @ (commutator @ X0 @ X1) @ X1))
% 10.89/2.24 = (multiply @ (inverse @ X0) @
% 10.89/2.24 (multiply @ (multiply @ (commutator @ X0 @ X1) @ X1) @
% 10.89/2.24 (inverse @ (inverse @ X0)))))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl4312, zip_derived_cl808])).
% 10.89/2.24 thf(zip_derived_cl66, plain,
% 10.89/2.24 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl62, zip_derived_cl3])).
% 10.89/2.24 thf(zip_derived_cl2, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.89/2.24 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 10.89/2.24 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 10.89/2.24 inference('cnf', [status(esa)], [associativity])).
% 10.89/2.24 thf(zip_derived_cl634, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ X1 @ X0) = (commutator @ X1 @ (multiply @ X0 @ X1)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl334, zip_derived_cl340])).
% 10.89/2.24 thf(zip_derived_cl808, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (commutator @ X1 @ X0) @ X0)
% 10.89/2.24 = (multiply @ X1 @ (multiply @ X0 @ (inverse @ X1))))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl774, zip_derived_cl66, zip_derived_cl3])).
% 10.89/2.24 thf(zip_derived_cl1690, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (commutator @ X1 @ X0) @ (multiply @ X0 @ X1))
% 10.89/2.24 = (multiply @ X1 @
% 10.89/2.24 (multiply @ (multiply @ X0 @ X1) @ (inverse @ X1))))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl634, zip_derived_cl808])).
% 10.89/2.24 thf(zip_derived_cl2, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.89/2.24 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 10.89/2.24 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 10.89/2.24 inference('cnf', [status(esa)], [associativity])).
% 10.89/2.24 thf(zip_derived_cl4, plain,
% 10.89/2.24 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 10.89/2.24 inference('cnf', [status(esa)], [right_inverse])).
% 10.89/2.24 thf(zip_derived_cl3, plain,
% 10.89/2.24 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 10.89/2.24 inference('cnf', [status(esa)], [right_identity])).
% 10.89/2.24 thf(zip_derived_cl1706, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (commutator @ X1 @ X0) @ (multiply @ X0 @ X1))
% 10.89/2.24 = (multiply @ X1 @ X0))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl1690, zip_derived_cl2, zip_derived_cl4,
% 10.89/2.24 zip_derived_cl3])).
% 10.89/2.24 thf(zip_derived_cl30, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 10.89/2.24 thf(zip_derived_cl4901, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (commutator @ X1 @ X0) @
% 10.89/2.24 (multiply @ (commutator @ X0 @ X1) @ X1)) = (X1))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl4838, zip_derived_cl66, zip_derived_cl2,
% 10.89/2.24 zip_derived_cl1706, zip_derived_cl30])).
% 10.89/2.24 thf(zip_derived_cl300, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl257, zip_derived_cl3])).
% 10.89/2.24 thf(zip_derived_cl4922, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (multiply @ (commutator @ X1 @ X0) @ X0) @ (inverse @ X0))
% 10.89/2.24 = (inverse @ (commutator @ X0 @ X1)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl4901, zip_derived_cl300])).
% 10.89/2.24 thf(zip_derived_cl334, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl326, zip_derived_cl66])).
% 10.89/2.24 thf(zip_derived_cl5035, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ X1 @ X0) = (inverse @ (commutator @ X0 @ X1)))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl4922, zip_derived_cl334])).
% 10.89/2.24 thf(zip_derived_cl309, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((inverse @ (multiply @ X0 @ X1))
% 10.89/2.24 = (multiply @ (inverse @ X1) @ (inverse @ X0)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl300, zip_derived_cl30])).
% 10.89/2.24 thf(zip_derived_cl5051, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.89/2.24 ((inverse @ (multiply @ (commutator @ X0 @ X1) @ X2))
% 10.89/2.24 = (multiply @ (inverse @ X2) @ (commutator @ X1 @ X0)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl5035, zip_derived_cl309])).
% 10.89/2.24 thf(zip_derived_cl2, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.89/2.24 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 10.89/2.24 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 10.89/2.24 inference('cnf', [status(esa)], [associativity])).
% 10.89/2.24 thf(zip_derived_cl65, plain,
% 10.89/2.24 (![X0 : $i]: ((multiply @ (inverse @ X0) @ (inverse @ X0)) = (X0))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl59, zip_derived_cl3])).
% 10.89/2.24 thf(zip_derived_cl2, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.89/2.24 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 10.89/2.24 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 10.89/2.24 inference('cnf', [status(esa)], [associativity])).
% 10.89/2.24 thf(zip_derived_cl140, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ X0 @ X1)
% 10.89/2.24 = (multiply @ (inverse @ X0) @ (multiply @ (inverse @ X0) @ X1)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl65, zip_derived_cl2])).
% 10.89/2.24 thf(zip_derived_cl2, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.89/2.24 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 10.89/2.24 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 10.89/2.24 inference('cnf', [status(esa)], [associativity])).
% 10.89/2.24 thf(zip_derived_cl65, plain,
% 10.89/2.24 (![X0 : $i]: ((multiply @ (inverse @ X0) @ (inverse @ X0)) = (X0))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl59, zip_derived_cl3])).
% 10.89/2.24 thf(zip_derived_cl11517, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ X1 @ (multiply @ X0 @ (commutator @ X0 @ X1)))
% 10.89/2.24 = (multiply @ X0 @ X1))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl11441, zip_derived_cl313, zip_derived_cl5051,
% 10.89/2.24 zip_derived_cl2, zip_derived_cl140, zip_derived_cl2,
% 10.89/2.24 zip_derived_cl65])).
% 10.89/2.24 thf(zip_derived_cl48, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.89/2.24 ((multiply @ (commutator @ X1 @ X0) @ X2)
% 10.89/2.24 = (multiply @ X1 @
% 10.89/2.24 (multiply @ X0 @
% 10.89/2.24 (multiply @ (inverse @ X1) @ (multiply @ (inverse @ X0) @ X2)))))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl34, zip_derived_cl2, zip_derived_cl2])).
% 10.89/2.24 thf(zip_derived_cl12337, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (commutator @ X0 @ X1) @
% 10.89/2.24 (commutator @ (inverse @ X1) @ (inverse @ X0)))
% 10.89/2.24 = (multiply @ X0 @
% 10.89/2.24 (multiply @ X1 @ (multiply @ (inverse @ X1) @ (inverse @ X0)))))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl11517, zip_derived_cl48])).
% 10.89/2.24 thf(zip_derived_cl309, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((inverse @ (multiply @ X0 @ X1))
% 10.89/2.24 = (multiply @ (inverse @ X1) @ (inverse @ X0)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl300, zip_derived_cl30])).
% 10.89/2.24 thf(zip_derived_cl300, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl257, zip_derived_cl3])).
% 10.89/2.24 thf(zip_derived_cl4, plain,
% 10.89/2.24 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 10.89/2.24 inference('cnf', [status(esa)], [right_inverse])).
% 10.89/2.24 thf(zip_derived_cl12457, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (commutator @ X0 @ X1) @
% 10.89/2.24 (commutator @ (inverse @ X1) @ (inverse @ X0))) = (identity))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl12337, zip_derived_cl309, zip_derived_cl300,
% 10.89/2.24 zip_derived_cl4])).
% 10.89/2.24 thf(zip_derived_cl300, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl257, zip_derived_cl3])).
% 10.89/2.24 thf(zip_derived_cl300, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl257, zip_derived_cl3])).
% 10.89/2.24 thf(zip_derived_cl321, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (inverse @ (multiply @ X0 @ X1)) @
% 10.89/2.24 (inverse @ (inverse @ X0))) = (inverse @ X1))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl300, zip_derived_cl300])).
% 10.89/2.24 thf(zip_derived_cl66, plain,
% 10.89/2.24 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl62, zip_derived_cl3])).
% 10.89/2.24 thf(zip_derived_cl330, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (inverse @ (multiply @ X0 @ X1)) @ X0) = (inverse @ X1))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl321, zip_derived_cl66])).
% 10.89/2.24 thf(zip_derived_cl12464, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (inverse @ identity) @ (commutator @ X0 @ X1))
% 10.89/2.24 = (inverse @ (commutator @ (inverse @ X1) @ (inverse @ X0))))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl12457, zip_derived_cl330])).
% 10.89/2.24 thf(zip_derived_cl3, plain,
% 10.89/2.24 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 10.89/2.24 inference('cnf', [status(esa)], [right_identity])).
% 10.89/2.24 thf(zip_derived_cl1, plain,
% 10.89/2.24 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 10.89/2.24 inference('cnf', [status(esa)], [left_inverse])).
% 10.89/2.24 thf(zip_derived_cl8, plain, (((inverse @ identity) = (identity))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 10.89/2.24 thf(zip_derived_cl0, plain,
% 10.89/2.24 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 10.89/2.24 inference('cnf', [status(esa)], [left_identity])).
% 10.89/2.24 thf(zip_derived_cl5035, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ X1 @ X0) = (inverse @ (commutator @ X0 @ X1)))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl4922, zip_derived_cl334])).
% 10.89/2.24 thf(zip_derived_cl12615, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ X0 @ X1)
% 10.89/2.24 = (commutator @ (inverse @ X0) @ (inverse @ X1)))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl12464, zip_derived_cl8, zip_derived_cl0,
% 10.89/2.24 zip_derived_cl5035])).
% 10.89/2.24 thf(zip_derived_cl309, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((inverse @ (multiply @ X0 @ X1))
% 10.89/2.24 = (multiply @ (inverse @ X1) @ (inverse @ X0)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl300, zip_derived_cl30])).
% 10.89/2.24 thf(zip_derived_cl340, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ X1 @ (multiply @ X0 @ (inverse @ X1)))
% 10.89/2.24 = (commutator @ X1 @ X0))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl314, zip_derived_cl2, zip_derived_cl5])).
% 10.89/2.24 thf(zip_derived_cl637, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ X1 @ (inverse @ (multiply @ X1 @ X0)))
% 10.89/2.24 = (commutator @ X1 @ (inverse @ X0)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl309, zip_derived_cl340])).
% 10.89/2.24 thf(zip_derived_cl12693, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ X1 @ (multiply @ (inverse @ X1) @ X0))
% 10.89/2.24 = (commutator @ (inverse @ X1) @ (inverse @ X0)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl12615, zip_derived_cl637])).
% 10.89/2.24 thf(zip_derived_cl28, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((X0) = (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl20, zip_derived_cl0])).
% 10.89/2.24 thf(zip_derived_cl3946, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ (multiply @ X0 @ X1) @ X1) = (commutator @ X0 @ X1))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl3900, zip_derived_cl162, zip_derived_cl2,
% 10.89/2.24 zip_derived_cl341])).
% 10.89/2.24 thf(zip_derived_cl4021, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ X0 @ (multiply @ (inverse @ X1) @ X0))
% 10.89/2.24 = (commutator @ X1 @ (multiply @ (inverse @ X1) @ X0)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl28, zip_derived_cl3946])).
% 10.89/2.24 thf(zip_derived_cl634, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ X1 @ X0) = (commutator @ X1 @ (multiply @ X0 @ X1)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl334, zip_derived_cl340])).
% 10.89/2.24 thf(zip_derived_cl4059, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ X0 @ (inverse @ X1))
% 10.89/2.24 = (commutator @ X1 @ (multiply @ (inverse @ X1) @ X0)))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl4021, zip_derived_cl634])).
% 10.89/2.24 thf(zip_derived_cl12615, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ X0 @ X1)
% 10.89/2.24 = (commutator @ (inverse @ X0) @ (inverse @ X1)))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl12464, zip_derived_cl8, zip_derived_cl0,
% 10.89/2.24 zip_derived_cl5035])).
% 10.89/2.24 thf(zip_derived_cl12754, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ X0 @ (inverse @ X1)) = (commutator @ X1 @ X0))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl12693, zip_derived_cl4059, zip_derived_cl12615])).
% 10.89/2.24 thf(zip_derived_cl12763, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (commutator @ X0 @ X1) @ X0)
% 10.89/2.24 = (multiply @ X0 @ (commutator @ X0 @ X1)))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl9433, zip_derived_cl12754])).
% 10.89/2.24 thf(zip_derived_cl1706, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (commutator @ X1 @ X0) @ (multiply @ X0 @ X1))
% 10.89/2.24 = (multiply @ X1 @ X0))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl1690, zip_derived_cl2, zip_derived_cl4,
% 10.89/2.24 zip_derived_cl3])).
% 10.89/2.24 thf(zip_derived_cl334, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl326, zip_derived_cl66])).
% 10.89/2.24 thf(zip_derived_cl2518, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ (multiply @ X0 @ X1)))
% 10.89/2.24 = (commutator @ X1 @ X0))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl1706, zip_derived_cl334])).
% 10.89/2.24 thf(zip_derived_cl13229, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (multiply @ X1 @ (commutator @ X1 @ X0)) @
% 10.89/2.24 (inverse @ (multiply @ X1 @ (commutator @ X1 @ X0))))
% 10.89/2.24 = (commutator @ X1 @ (commutator @ X1 @ X0)))),
% 10.89/2.24 inference('sup+', [status(thm)],
% 10.89/2.24 [zip_derived_cl12763, zip_derived_cl2518])).
% 10.89/2.24 thf(zip_derived_cl5035, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ X1 @ X0) = (inverse @ (commutator @ X0 @ X1)))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl4922, zip_derived_cl334])).
% 10.89/2.24 thf(zip_derived_cl309, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((inverse @ (multiply @ X0 @ X1))
% 10.89/2.24 = (multiply @ (inverse @ X1) @ (inverse @ X0)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl300, zip_derived_cl30])).
% 10.89/2.24 thf(zip_derived_cl5071, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.89/2.24 ((inverse @ (multiply @ X2 @ (commutator @ X0 @ X1)))
% 10.89/2.24 = (multiply @ (commutator @ X1 @ X0) @ (inverse @ X2)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl5035, zip_derived_cl309])).
% 10.89/2.24 thf(zip_derived_cl2, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.89/2.24 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 10.89/2.24 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 10.89/2.24 inference('cnf', [status(esa)], [associativity])).
% 10.89/2.24 thf(zip_derived_cl4901, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (commutator @ X1 @ X0) @
% 10.89/2.24 (multiply @ (commutator @ X0 @ X1) @ X1)) = (X1))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl4838, zip_derived_cl66, zip_derived_cl2,
% 10.89/2.24 zip_derived_cl1706, zip_derived_cl30])).
% 10.89/2.24 thf(zip_derived_cl28, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((X0) = (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl20, zip_derived_cl0])).
% 10.89/2.24 thf(zip_derived_cl2, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.89/2.24 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 10.89/2.24 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 10.89/2.24 inference('cnf', [status(esa)], [associativity])).
% 10.89/2.24 thf(zip_derived_cl55, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.89/2.24 ((X0)
% 10.89/2.24 = (multiply @ X2 @
% 10.89/2.24 (multiply @ X1 @
% 10.89/2.24 (multiply @ (inverse @ (multiply @ X2 @ X1)) @ X0))))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl28, zip_derived_cl2])).
% 10.89/2.24 thf(zip_derived_cl4918, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.89/2.24 ((X1)
% 10.89/2.24 = (multiply @ (commutator @ X0 @ X2) @
% 10.89/2.24 (multiply @ (multiply @ (commutator @ X2 @ X0) @ X0) @
% 10.89/2.24 (multiply @ (inverse @ X0) @ X1))))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl4901, zip_derived_cl55])).
% 10.89/2.24 thf(zip_derived_cl2, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.89/2.24 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 10.89/2.24 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 10.89/2.24 inference('cnf', [status(esa)], [associativity])).
% 10.89/2.24 thf(zip_derived_cl28, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((X0) = (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl20, zip_derived_cl0])).
% 10.89/2.24 thf(zip_derived_cl5032, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.89/2.24 ((X1)
% 10.89/2.24 = (multiply @ (commutator @ X0 @ X2) @
% 10.89/2.24 (multiply @ (commutator @ X2 @ X0) @ X1)))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl4918, zip_derived_cl2, zip_derived_cl28])).
% 10.89/2.24 thf(zip_derived_cl4, plain,
% 10.89/2.24 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 10.89/2.24 inference('cnf', [status(esa)], [right_inverse])).
% 10.89/2.24 thf(zip_derived_cl13341, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((identity) = (commutator @ X1 @ (commutator @ X1 @ X0)))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl13229, zip_derived_cl5071, zip_derived_cl2,
% 10.89/2.24 zip_derived_cl5032, zip_derived_cl4])).
% 10.89/2.24 thf(zip_derived_cl12615, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ X0 @ X1)
% 10.89/2.24 = (commutator @ (inverse @ X0) @ (inverse @ X1)))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl12464, zip_derived_cl8, zip_derived_cl0,
% 10.89/2.24 zip_derived_cl5035])).
% 10.89/2.24 thf(zip_derived_cl330, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((multiply @ (inverse @ (multiply @ X0 @ X1)) @ X0) = (inverse @ X1))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl321, zip_derived_cl66])).
% 10.89/2.24 thf(zip_derived_cl3946, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ (multiply @ X0 @ X1) @ X1) = (commutator @ X0 @ X1))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl3900, zip_derived_cl162, zip_derived_cl2,
% 10.89/2.24 zip_derived_cl341])).
% 10.89/2.24 thf(zip_derived_cl4049, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ (inverse @ X0) @ X1)
% 10.89/2.24 = (commutator @ (inverse @ (multiply @ X1 @ X0)) @ X1))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl330, zip_derived_cl3946])).
% 10.89/2.24 thf(zip_derived_cl12703, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ (inverse @ X1) @ (inverse @ X0))
% 10.89/2.24 = (commutator @ (multiply @ (inverse @ X0) @ X1) @ X0))),
% 10.89/2.24 inference('sup+', [status(thm)],
% 10.89/2.24 [zip_derived_cl12615, zip_derived_cl4049])).
% 10.89/2.24 thf(zip_derived_cl12615, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ X0 @ X1)
% 10.89/2.24 = (commutator @ (inverse @ X0) @ (inverse @ X1)))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl12464, zip_derived_cl8, zip_derived_cl0,
% 10.89/2.24 zip_derived_cl5035])).
% 10.89/2.24 thf(zip_derived_cl28, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((X0) = (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl20, zip_derived_cl0])).
% 10.89/2.24 thf(zip_derived_cl66, plain,
% 10.89/2.24 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl62, zip_derived_cl3])).
% 10.89/2.24 thf(zip_derived_cl340, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ X1 @ (multiply @ X0 @ (inverse @ X1)))
% 10.89/2.24 = (commutator @ X1 @ X0))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl314, zip_derived_cl2, zip_derived_cl5])).
% 10.89/2.24 thf(zip_derived_cl642, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ (inverse @ X0) @ (multiply @ X1 @ X0))
% 10.89/2.24 = (commutator @ (inverse @ X0) @ X1))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl66, zip_derived_cl340])).
% 10.89/2.24 thf(zip_derived_cl1064, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ (inverse @ (multiply @ (inverse @ X1) @ X0)) @ X0)
% 10.89/2.24 = (commutator @ (inverse @ (multiply @ (inverse @ X1) @ X0)) @ X1))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl28, zip_derived_cl642])).
% 10.89/2.24 thf(zip_derived_cl66, plain,
% 10.89/2.24 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl62, zip_derived_cl3])).
% 10.89/2.24 thf(zip_derived_cl309, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((inverse @ (multiply @ X0 @ X1))
% 10.89/2.24 = (multiply @ (inverse @ X1) @ (inverse @ X0)))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl300, zip_derived_cl30])).
% 10.89/2.24 thf(zip_derived_cl355, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((inverse @ (multiply @ (inverse @ X0) @ X1))
% 10.89/2.24 = (multiply @ (inverse @ X1) @ X0))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl66, zip_derived_cl309])).
% 10.89/2.24 thf(zip_derived_cl355, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((inverse @ (multiply @ (inverse @ X0) @ X1))
% 10.89/2.24 = (multiply @ (inverse @ X1) @ X0))),
% 10.89/2.24 inference('sup+', [status(thm)], [zip_derived_cl66, zip_derived_cl309])).
% 10.89/2.24 thf(zip_derived_cl1088, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ (multiply @ (inverse @ X0) @ X1) @ X0)
% 10.89/2.24 = (commutator @ (multiply @ (inverse @ X0) @ X1) @ X1))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl1064, zip_derived_cl355, zip_derived_cl355])).
% 10.89/2.24 thf(zip_derived_cl3946, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ (multiply @ X0 @ X1) @ X1) = (commutator @ X0 @ X1))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl3900, zip_derived_cl162, zip_derived_cl2,
% 10.89/2.24 zip_derived_cl341])).
% 10.89/2.24 thf(zip_derived_cl4200, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ (multiply @ (inverse @ X0) @ X1) @ X0)
% 10.89/2.24 = (commutator @ (inverse @ X0) @ X1))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl1088, zip_derived_cl3946])).
% 10.89/2.24 thf(zip_derived_cl12758, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ X1 @ X0) = (commutator @ (inverse @ X0) @ X1))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl12703, zip_derived_cl12615, zip_derived_cl4200])).
% 10.89/2.24 thf(zip_derived_cl13409, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ (commutator @ (inverse @ X0) @ X1) @ X0) = (identity))),
% 10.89/2.24 inference('sup+', [status(thm)],
% 10.89/2.24 [zip_derived_cl13341, zip_derived_cl12758])).
% 10.89/2.24 thf(zip_derived_cl12758, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ X1 @ X0) = (commutator @ (inverse @ X0) @ X1))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl12703, zip_derived_cl12615, zip_derived_cl4200])).
% 10.89/2.24 thf(zip_derived_cl13452, plain,
% 10.89/2.24 (![X0 : $i, X1 : $i]:
% 10.89/2.24 ((commutator @ (commutator @ X1 @ X0) @ X0) = (identity))),
% 10.89/2.24 inference('demod', [status(thm)],
% 10.89/2.24 [zip_derived_cl13409, zip_derived_cl12758])).
% 10.89/2.24 thf(zip_derived_cl13595, plain, (((identity) != (identity))),
% 10.89/2.24 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl13452])).
% 10.89/2.24 thf(zip_derived_cl13596, plain, ($false),
% 10.89/2.24 inference('simplify', [status(thm)], [zip_derived_cl13595])).
% 10.89/2.24
% 10.89/2.24 % SZS output end Refutation
% 10.89/2.24
% 10.89/2.24
% 10.89/2.24 % Terminating...
% 11.58/2.29 % Runner terminated.
% 11.58/2.30 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------