%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP002-3 : TPTP v9.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.NFjDWBtpls true
% Computer : n025.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 Oct 2 04:35:23 PM UTC 2025
% Result : Unsatisfiable 21.05s 3.66s
% Output : Refutation 21.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : GRP002-3 : TPTP v9.2.0. Released v1.0.0.
% 0.09/0.12 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.NFjDWBtpls true
% 0.11/0.32 % Computer : n025.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Oct 1 14:26:23 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % Running portfolio for 300 s
% 0.11/0.33 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.33 % Number of cores: 8
% 0.11/0.33 % Python version: Python 3.6.8
% 0.11/0.33 % Running in FO mode
% 0.18/0.60 % Total configuration time : 435
% 0.18/0.60 % Estimated wc time : 1092
% 0.18/0.60 % Estimated cpu time (7 cpus) : 156.0
% 0.73/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.73/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.73/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.73/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.73/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.73/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.73/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 21.05/3.66 % Solved by fo/fo4.sh.
% 21.05/3.66 % done 516 iterations in 2.854s
% 21.05/3.66 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 21.05/3.66 % SZS output start Refutation
% 21.05/3.66 thf(b_type, type, b: $i).
% 21.05/3.66 thf(a_type, type, a: $i).
% 21.05/3.66 thf(identity_type, type, identity: $i).
% 21.05/3.66 thf(multiply_type, type, multiply: $i > $i > $i).
% 21.05/3.66 thf(commutator_type, type, commutator: $i > $i > $i).
% 21.05/3.66 thf(inverse_type, type, inverse: $i > $i).
% 21.05/3.66 thf(prove_commutator, conjecture,
% 21.05/3.66 (( commutator @ ( commutator @ a @ b ) @ b ) = ( identity ))).
% 21.05/3.66 thf(zf_stmt_0, negated_conjecture,
% 21.05/3.66 (( commutator @ ( commutator @ a @ b ) @ b ) != ( identity )),
% 21.05/3.66 inference('cnf.neg', [status(esa)], [prove_commutator])).
% 21.05/3.66 thf(zip_derived_cl5, plain,
% 21.05/3.66 (((commutator @ (commutator @ a @ b) @ b) != (identity))),
% 21.05/3.66 inference('cnf', [status(esa)], [zf_stmt_0])).
% 21.05/3.66 thf(commutator, axiom,
% 21.05/3.66 (( commutator @ X @ Y ) =
% 21.05/3.66 ( multiply @
% 21.05/3.66 X @ ( multiply @ Y @ ( multiply @ ( inverse @ X ) @ ( inverse @ Y ) ) ) ))).
% 21.05/3.66 thf(zip_derived_cl3, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X0 @ X1)
% 21.05/3.66 = (multiply @ X0 @
% 21.05/3.66 (multiply @ X1 @ (multiply @ (inverse @ X0) @ (inverse @ X1)))))),
% 21.05/3.66 inference('cnf', [status(esa)], [commutator])).
% 21.05/3.66 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 21.05/3.66 thf(zip_derived_cl1, plain,
% 21.05/3.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 21.05/3.66 inference('cnf', [status(esa)], [left_inverse])).
% 21.05/3.66 thf(zip_derived_cl1, plain,
% 21.05/3.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 21.05/3.66 inference('cnf', [status(esa)], [left_inverse])).
% 21.05/3.66 thf(associativity, axiom,
% 21.05/3.66 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 21.05/3.66 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 21.05/3.66 thf(zip_derived_cl2, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.05/3.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 21.05/3.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 21.05/3.66 inference('cnf', [status(esa)], [associativity])).
% 21.05/3.66 thf(zip_derived_cl14, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ identity @ X0)
% 21.05/3.66 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 21.05/3.66 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 21.05/3.66 thf(zip_derived_cl0, plain,
% 21.05/3.66 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 21.05/3.66 inference('cnf', [status(esa)], [left_identity])).
% 21.05/3.66 thf(zip_derived_cl18, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 21.05/3.66 inference('demod', [status(thm)], [zip_derived_cl14, zip_derived_cl0])).
% 21.05/3.66 thf(zip_derived_cl188, plain,
% 21.05/3.66 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl18])).
% 21.05/3.66 thf(zip_derived_cl18, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 21.05/3.66 inference('demod', [status(thm)], [zip_derived_cl14, zip_derived_cl0])).
% 21.05/3.66 thf(zip_derived_cl18, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 21.05/3.66 inference('demod', [status(thm)], [zip_derived_cl14, zip_derived_cl0])).
% 21.05/3.66 thf(zip_derived_cl175, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl18, zip_derived_cl18])).
% 21.05/3.66 thf(zip_derived_cl228, plain,
% 21.05/3.66 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl188, zip_derived_cl175])).
% 21.05/3.66 thf(zip_derived_cl188, plain,
% 21.05/3.66 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl18])).
% 21.05/3.66 thf(zip_derived_cl252, plain,
% 21.05/3.66 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl228, zip_derived_cl188])).
% 21.05/3.66 thf(zip_derived_cl18, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 21.05/3.66 inference('demod', [status(thm)], [zip_derived_cl14, zip_derived_cl0])).
% 21.05/3.66 thf(zip_derived_cl265, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((X1) = (multiply @ X0 @ (multiply @ (inverse @ X0) @ X1)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl252, zip_derived_cl18])).
% 21.05/3.66 thf(zip_derived_cl363, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ X0 @
% 21.05/3.66 (multiply @ (inverse @ (inverse @ X1)) @ (inverse @ X0)))
% 21.05/3.66 = (multiply @ X1 @ (commutator @ (inverse @ X1) @ X0)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl265])).
% 21.05/3.66 thf(zip_derived_cl252, plain,
% 21.05/3.66 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl228, zip_derived_cl188])).
% 21.05/3.66 thf(zip_derived_cl373, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ X0 @ (multiply @ X1 @ (inverse @ X0)))
% 21.05/3.66 = (multiply @ X1 @ (commutator @ (inverse @ X1) @ X0)))),
% 21.05/3.66 inference('demod', [status(thm)], [zip_derived_cl363, zip_derived_cl252])).
% 21.05/3.66 thf(zip_derived_cl3, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X0 @ X1)
% 21.05/3.66 = (multiply @ X0 @
% 21.05/3.66 (multiply @ X1 @ (multiply @ (inverse @ X0) @ (inverse @ X1)))))),
% 21.05/3.66 inference('cnf', [status(esa)], [commutator])).
% 21.05/3.66 thf(zip_derived_cl2, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.05/3.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 21.05/3.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 21.05/3.66 inference('cnf', [status(esa)], [associativity])).
% 21.05/3.66 thf(zip_derived_cl20, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.05/3.66 ((multiply @ (commutator @ X1 @ X0) @ X2)
% 21.05/3.66 = (multiply @ X1 @
% 21.05/3.66 (multiply @
% 21.05/3.66 (multiply @ X0 @ (multiply @ (inverse @ X1) @ (inverse @ X0))) @
% 21.05/3.66 X2)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl2])).
% 21.05/3.66 thf(zip_derived_cl2, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.05/3.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 21.05/3.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 21.05/3.66 inference('cnf', [status(esa)], [associativity])).
% 21.05/3.66 thf(zip_derived_cl2, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.05/3.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 21.05/3.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 21.05/3.66 inference('cnf', [status(esa)], [associativity])).
% 21.05/3.66 thf(zip_derived_cl26, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.05/3.66 ((multiply @ (commutator @ X1 @ X0) @ X2)
% 21.05/3.66 = (multiply @ X1 @
% 21.05/3.66 (multiply @ X0 @
% 21.05/3.66 (multiply @ (inverse @ X1) @ (multiply @ (inverse @ X0) @ X2)))))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl20, zip_derived_cl2, zip_derived_cl2])).
% 21.05/3.66 thf(zip_derived_cl1333, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ (commutator @ X0 @ X1) @ (inverse @ (inverse @ X0)))
% 21.05/3.66 = (multiply @ X0 @
% 21.05/3.66 (multiply @ X1 @
% 21.05/3.66 (multiply @ (inverse @ X1) @
% 21.05/3.66 (commutator @ (inverse @ (inverse @ X1)) @ (inverse @ X0))))))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl373, zip_derived_cl26])).
% 21.05/3.66 thf(zip_derived_cl252, plain,
% 21.05/3.66 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl228, zip_derived_cl188])).
% 21.05/3.66 thf(zip_derived_cl252, plain,
% 21.05/3.66 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl228, zip_derived_cl188])).
% 21.05/3.66 thf(zip_derived_cl265, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((X1) = (multiply @ X0 @ (multiply @ (inverse @ X0) @ X1)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl252, zip_derived_cl18])).
% 21.05/3.66 thf(zip_derived_cl1376, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ (commutator @ X0 @ X1) @ X0)
% 21.05/3.66 = (multiply @ X0 @ (commutator @ X1 @ (inverse @ X0))))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl1333, zip_derived_cl252, zip_derived_cl252,
% 21.05/3.66 zip_derived_cl265])).
% 21.05/3.66 thf(zip_derived_cl373, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ X0 @ (multiply @ X1 @ (inverse @ X0)))
% 21.05/3.66 = (multiply @ X1 @ (commutator @ (inverse @ X1) @ X0)))),
% 21.05/3.66 inference('demod', [status(thm)], [zip_derived_cl363, zip_derived_cl252])).
% 21.05/3.66 thf(zip_derived_cl252, plain,
% 21.05/3.66 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl228, zip_derived_cl188])).
% 21.05/3.66 thf(zip_derived_cl1, plain,
% 21.05/3.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 21.05/3.66 inference('cnf', [status(esa)], [left_inverse])).
% 21.05/3.66 thf(zip_derived_cl259, plain,
% 21.05/3.66 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl252, zip_derived_cl1])).
% 21.05/3.66 thf(zip_derived_cl2, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.05/3.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 21.05/3.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 21.05/3.66 inference('cnf', [status(esa)], [associativity])).
% 21.05/3.66 thf(zip_derived_cl337, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((identity)
% 21.05/3.66 = (multiply @ X1 @
% 21.05/3.66 (multiply @ X0 @ (inverse @ (multiply @ X1 @ X0)))))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl259, zip_derived_cl2])).
% 21.05/3.66 thf(zip_derived_cl18, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 21.05/3.66 inference('demod', [status(thm)], [zip_derived_cl14, zip_derived_cl0])).
% 21.05/3.66 thf(zip_derived_cl641, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0)))
% 21.05/3.66 = (multiply @ (inverse @ X1) @ identity))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl337, zip_derived_cl18])).
% 21.05/3.66 thf(zip_derived_cl228, plain,
% 21.05/3.66 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl188, zip_derived_cl175])).
% 21.05/3.66 thf(zip_derived_cl688, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 21.05/3.66 inference('demod', [status(thm)], [zip_derived_cl641, zip_derived_cl228])).
% 21.05/3.66 thf(x_cubed_is_identity, axiom,
% 21.05/3.66 (( multiply @ X @ ( multiply @ X @ X ) ) = ( identity ))).
% 21.05/3.66 thf(zip_derived_cl4, plain,
% 21.05/3.66 (![X0 : $i]: ((multiply @ X0 @ (multiply @ X0 @ X0)) = (identity))),
% 21.05/3.66 inference('cnf', [status(esa)], [x_cubed_is_identity])).
% 21.05/3.66 thf(zip_derived_cl18, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 21.05/3.66 inference('demod', [status(thm)], [zip_derived_cl14, zip_derived_cl0])).
% 21.05/3.66 thf(zip_derived_cl181, plain,
% 21.05/3.66 (![X0 : $i]:
% 21.05/3.66 ((multiply @ X0 @ X0) = (multiply @ (inverse @ X0) @ identity))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl18])).
% 21.05/3.66 thf(zip_derived_cl228, plain,
% 21.05/3.66 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl188, zip_derived_cl175])).
% 21.05/3.66 thf(zip_derived_cl393, plain,
% 21.05/3.66 (![X0 : $i]: ((multiply @ X0 @ X0) = (inverse @ X0))),
% 21.05/3.66 inference('demod', [status(thm)], [zip_derived_cl181, zip_derived_cl228])).
% 21.05/3.66 thf(zip_derived_cl2, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.05/3.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 21.05/3.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 21.05/3.66 inference('cnf', [status(esa)], [associativity])).
% 21.05/3.66 thf(zip_derived_cl395, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ (inverse @ X0) @ X1)
% 21.05/3.66 = (multiply @ X0 @ (multiply @ X0 @ X1)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl393, zip_derived_cl2])).
% 21.05/3.66 thf(zip_derived_cl697, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ (inverse @ X1) @ (inverse @ (multiply @ X0 @ X1)))
% 21.05/3.66 = (multiply @ X1 @ (inverse @ X0)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl688, zip_derived_cl395])).
% 21.05/3.66 thf(zip_derived_cl10770, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ (inverse @ (multiply @ X1 @ (inverse @ X0))) @
% 21.05/3.66 (inverse @ (multiply @ X1 @ (commutator @ (inverse @ X1) @ X0))))
% 21.05/3.66 = (multiply @ (multiply @ X1 @ (inverse @ X0)) @ (inverse @ X0)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl373, zip_derived_cl697])).
% 21.05/3.66 thf(zip_derived_cl688, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 21.05/3.66 inference('demod', [status(thm)], [zip_derived_cl641, zip_derived_cl228])).
% 21.05/3.66 thf(zip_derived_cl265, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((X1) = (multiply @ X0 @ (multiply @ (inverse @ X0) @ X1)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl252, zip_derived_cl18])).
% 21.05/3.66 thf(zip_derived_cl706, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((inverse @ (multiply @ X0 @ (inverse @ X1)))
% 21.05/3.66 = (multiply @ X1 @ (inverse @ X0)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl688, zip_derived_cl265])).
% 21.05/3.66 thf(zip_derived_cl259, plain,
% 21.05/3.66 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl252, zip_derived_cl1])).
% 21.05/3.66 thf(zip_derived_cl26, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.05/3.66 ((multiply @ (commutator @ X1 @ X0) @ X2)
% 21.05/3.66 = (multiply @ X1 @
% 21.05/3.66 (multiply @ X0 @
% 21.05/3.66 (multiply @ (inverse @ X1) @ (multiply @ (inverse @ X0) @ X2)))))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl20, zip_derived_cl2, zip_derived_cl2])).
% 21.05/3.66 thf(zip_derived_cl990, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ (commutator @ X1 @ X0) @ (inverse @ (inverse @ X0)))
% 21.05/3.66 = (multiply @ X1 @
% 21.05/3.66 (multiply @ X0 @ (multiply @ (inverse @ X1) @ identity))))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl259, zip_derived_cl26])).
% 21.05/3.66 thf(zip_derived_cl252, plain,
% 21.05/3.66 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl228, zip_derived_cl188])).
% 21.05/3.66 thf(zip_derived_cl228, plain,
% 21.05/3.66 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl188, zip_derived_cl175])).
% 21.05/3.66 thf(zip_derived_cl1023, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ (commutator @ X1 @ X0) @ X0)
% 21.05/3.66 = (multiply @ X1 @ (multiply @ X0 @ (inverse @ X1))))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl990, zip_derived_cl252, zip_derived_cl228])).
% 21.05/3.66 thf(zip_derived_cl373, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ X0 @ (multiply @ X1 @ (inverse @ X0)))
% 21.05/3.66 = (multiply @ X1 @ (commutator @ (inverse @ X1) @ X0)))),
% 21.05/3.66 inference('demod', [status(thm)], [zip_derived_cl363, zip_derived_cl252])).
% 21.05/3.66 thf(zip_derived_cl1389, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ (commutator @ X1 @ X0) @ X0)
% 21.05/3.66 = (multiply @ X0 @ (commutator @ (inverse @ X0) @ X1)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl1023, zip_derived_cl373])).
% 21.05/3.66 thf(zip_derived_cl688, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 21.05/3.66 inference('demod', [status(thm)], [zip_derived_cl641, zip_derived_cl228])).
% 21.05/3.66 thf(zip_derived_cl18, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 21.05/3.66 inference('demod', [status(thm)], [zip_derived_cl14, zip_derived_cl0])).
% 21.05/3.66 thf(zip_derived_cl702, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((inverse @ (multiply @ X0 @ X1))
% 21.05/3.66 = (multiply @ (inverse @ X1) @ (inverse @ X0)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl688, zip_derived_cl18])).
% 21.05/3.66 thf(zip_derived_cl373, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ X0 @ (multiply @ X1 @ (inverse @ X0)))
% 21.05/3.66 = (multiply @ X1 @ (commutator @ (inverse @ X1) @ X0)))),
% 21.05/3.66 inference('demod', [status(thm)], [zip_derived_cl363, zip_derived_cl252])).
% 21.05/3.66 thf(zip_derived_cl1337, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ X1 @ (inverse @ (multiply @ X1 @ X0)))
% 21.05/3.66 = (multiply @ (inverse @ X0) @
% 21.05/3.66 (commutator @ (inverse @ (inverse @ X0)) @ X1)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl702, zip_derived_cl373])).
% 21.05/3.66 thf(zip_derived_cl252, plain,
% 21.05/3.66 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl228, zip_derived_cl188])).
% 21.05/3.66 thf(zip_derived_cl1350, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ X1 @ (inverse @ (multiply @ X1 @ X0)))
% 21.05/3.66 = (multiply @ (inverse @ X0) @ (commutator @ X0 @ X1)))),
% 21.05/3.66 inference('demod', [status(thm)], [zip_derived_cl1337, zip_derived_cl252])).
% 21.05/3.66 thf(zip_derived_cl706, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((inverse @ (multiply @ X0 @ (inverse @ X1)))
% 21.05/3.66 = (multiply @ X1 @ (inverse @ X0)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl688, zip_derived_cl265])).
% 21.05/3.66 thf(zip_derived_cl1, plain,
% 21.05/3.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 21.05/3.66 inference('cnf', [status(esa)], [left_inverse])).
% 21.05/3.66 thf(zip_derived_cl904, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ (multiply @ X1 @ (inverse @ X0)) @
% 21.05/3.66 (multiply @ X0 @ (inverse @ X1))) = (identity))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl706, zip_derived_cl1])).
% 21.05/3.66 thf(zip_derived_cl2894, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ (multiply @ (multiply @ X0 @ X1) @ (inverse @ X0)) @
% 21.05/3.66 (multiply @ (inverse @ X1) @ (commutator @ X1 @ X0))) = (identity))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl1350, zip_derived_cl904])).
% 21.05/3.66 thf(zip_derived_cl2, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.05/3.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 21.05/3.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 21.05/3.66 inference('cnf', [status(esa)], [associativity])).
% 21.05/3.66 thf(zip_derived_cl2, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.05/3.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 21.05/3.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 21.05/3.66 inference('cnf', [status(esa)], [associativity])).
% 21.05/3.66 thf(zip_derived_cl2, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.05/3.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 21.05/3.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 21.05/3.66 inference('cnf', [status(esa)], [associativity])).
% 21.05/3.66 thf(zip_derived_cl26, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.05/3.66 ((multiply @ (commutator @ X1 @ X0) @ X2)
% 21.05/3.66 = (multiply @ X1 @
% 21.05/3.66 (multiply @ X0 @
% 21.05/3.66 (multiply @ (inverse @ X1) @ (multiply @ (inverse @ X0) @ X2)))))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl20, zip_derived_cl2, zip_derived_cl2])).
% 21.05/3.66 thf(zip_derived_cl2930, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ (commutator @ X0 @ X1) @ (commutator @ X1 @ X0))
% 21.05/3.66 = (identity))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl2894, zip_derived_cl2, zip_derived_cl2,
% 21.05/3.66 zip_derived_cl2, zip_derived_cl26])).
% 21.05/3.66 thf(zip_derived_cl688, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 21.05/3.66 inference('demod', [status(thm)], [zip_derived_cl641, zip_derived_cl228])).
% 21.05/3.66 thf(zip_derived_cl688, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 21.05/3.66 inference('demod', [status(thm)], [zip_derived_cl641, zip_derived_cl228])).
% 21.05/3.66 thf(zip_derived_cl717, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ (inverse @ (multiply @ X0 @ X1)) @
% 21.05/3.66 (inverse @ (inverse @ X0))) = (inverse @ X1))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl688, zip_derived_cl688])).
% 21.05/3.66 thf(zip_derived_cl252, plain,
% 21.05/3.66 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl228, zip_derived_cl188])).
% 21.05/3.66 thf(zip_derived_cl727, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ (inverse @ (multiply @ X0 @ X1)) @ X0) = (inverse @ X1))),
% 21.05/3.66 inference('demod', [status(thm)], [zip_derived_cl717, zip_derived_cl252])).
% 21.05/3.66 thf(zip_derived_cl2983, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ (inverse @ identity) @ (commutator @ X0 @ X1))
% 21.05/3.66 = (inverse @ (commutator @ X1 @ X0)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl2930, zip_derived_cl727])).
% 21.05/3.66 thf(zip_derived_cl1, plain,
% 21.05/3.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 21.05/3.66 inference('cnf', [status(esa)], [left_inverse])).
% 21.05/3.66 thf(zip_derived_cl1, plain,
% 21.05/3.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 21.05/3.66 inference('cnf', [status(esa)], [left_inverse])).
% 21.05/3.66 thf(zip_derived_cl3, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X0 @ X1)
% 21.05/3.66 = (multiply @ X0 @
% 21.05/3.66 (multiply @ X1 @ (multiply @ (inverse @ X0) @ (inverse @ X1)))))),
% 21.05/3.66 inference('cnf', [status(esa)], [commutator])).
% 21.05/3.66 thf(zip_derived_cl25, plain,
% 21.05/3.66 (![X0 : $i]:
% 21.05/3.66 ((commutator @ (inverse @ X0) @ X0)
% 21.05/3.66 = (multiply @ (inverse @ X0) @ (multiply @ X0 @ identity)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl3])).
% 21.05/3.66 thf(zip_derived_cl30, plain,
% 21.05/3.66 (((commutator @ (inverse @ (inverse @ identity)) @ (inverse @ identity))
% 21.05/3.66 = (multiply @ (inverse @ (inverse @ identity)) @ identity))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl25])).
% 21.05/3.66 thf(zip_derived_cl1, plain,
% 21.05/3.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 21.05/3.66 inference('cnf', [status(esa)], [left_inverse])).
% 21.05/3.66 thf(zip_derived_cl2, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.05/3.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 21.05/3.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 21.05/3.66 inference('cnf', [status(esa)], [associativity])).
% 21.05/3.66 thf(zip_derived_cl4, plain,
% 21.05/3.66 (![X0 : $i]: ((multiply @ X0 @ (multiply @ X0 @ X0)) = (identity))),
% 21.05/3.66 inference('cnf', [status(esa)], [x_cubed_is_identity])).
% 21.05/3.66 thf(zip_derived_cl9, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ (multiply @ X1 @ X0) @
% 21.05/3.66 (multiply @ X1 @ (multiply @ X0 @ (multiply @ X1 @ X0))))
% 21.05/3.66 = (identity))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 21.05/3.66 thf(zip_derived_cl47, plain,
% 21.05/3.66 (![X0 : $i]:
% 21.05/3.66 ((multiply @ (multiply @ (inverse @ X0) @ X0) @
% 21.05/3.66 (multiply @ (inverse @ X0) @ (multiply @ X0 @ identity)))
% 21.05/3.66 = (identity))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl9])).
% 21.05/3.66 thf(zip_derived_cl1, plain,
% 21.05/3.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 21.05/3.66 inference('cnf', [status(esa)], [left_inverse])).
% 21.05/3.66 thf(zip_derived_cl25, plain,
% 21.05/3.66 (![X0 : $i]:
% 21.05/3.66 ((commutator @ (inverse @ X0) @ X0)
% 21.05/3.66 = (multiply @ (inverse @ X0) @ (multiply @ X0 @ identity)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl3])).
% 21.05/3.66 thf(zip_derived_cl0, plain,
% 21.05/3.66 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 21.05/3.66 inference('cnf', [status(esa)], [left_identity])).
% 21.05/3.66 thf(zip_derived_cl63, plain,
% 21.05/3.66 (![X0 : $i]: ((commutator @ (inverse @ X0) @ X0) = (identity))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl47, zip_derived_cl1, zip_derived_cl25,
% 21.05/3.66 zip_derived_cl0])).
% 21.05/3.66 thf(zip_derived_cl76, plain,
% 21.05/3.66 (((identity) = (multiply @ (inverse @ (inverse @ identity)) @ identity))),
% 21.05/3.66 inference('demod', [status(thm)], [zip_derived_cl30, zip_derived_cl63])).
% 21.05/3.66 thf(zip_derived_cl2, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.05/3.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 21.05/3.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 21.05/3.66 inference('cnf', [status(esa)], [associativity])).
% 21.05/3.66 thf(zip_derived_cl77, plain,
% 21.05/3.66 (![X0 : $i]:
% 21.05/3.66 ((multiply @ identity @ X0)
% 21.05/3.66 = (multiply @ (inverse @ (inverse @ identity)) @
% 21.05/3.66 (multiply @ identity @ X0)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl76, zip_derived_cl2])).
% 21.05/3.66 thf(zip_derived_cl0, plain,
% 21.05/3.66 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 21.05/3.66 inference('cnf', [status(esa)], [left_identity])).
% 21.05/3.66 thf(zip_derived_cl0, plain,
% 21.05/3.66 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 21.05/3.66 inference('cnf', [status(esa)], [left_identity])).
% 21.05/3.66 thf(zip_derived_cl80, plain,
% 21.05/3.66 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ identity)) @ X0))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl77, zip_derived_cl0, zip_derived_cl0])).
% 21.05/3.66 thf(zip_derived_cl1, plain,
% 21.05/3.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 21.05/3.66 inference('cnf', [status(esa)], [left_inverse])).
% 21.05/3.66 thf(zip_derived_cl92, plain, (((inverse @ identity) = (identity))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl80, zip_derived_cl1])).
% 21.05/3.66 thf(zip_derived_cl0, plain,
% 21.05/3.66 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 21.05/3.66 inference('cnf', [status(esa)], [left_identity])).
% 21.05/3.66 thf(zip_derived_cl3047, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X0 @ X1) = (inverse @ (commutator @ X1 @ X0)))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl2983, zip_derived_cl92, zip_derived_cl0])).
% 21.05/3.66 thf(zip_derived_cl702, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((inverse @ (multiply @ X0 @ X1))
% 21.05/3.66 = (multiply @ (inverse @ X1) @ (inverse @ X0)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl688, zip_derived_cl18])).
% 21.05/3.66 thf(zip_derived_cl3071, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.05/3.66 ((inverse @ (multiply @ (commutator @ X0 @ X1) @ X2))
% 21.05/3.66 = (multiply @ (inverse @ X2) @ (commutator @ X1 @ X0)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl3047, zip_derived_cl702])).
% 21.05/3.66 thf(zip_derived_cl2, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.05/3.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 21.05/3.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 21.05/3.66 inference('cnf', [status(esa)], [associativity])).
% 21.05/3.66 thf(zip_derived_cl4, plain,
% 21.05/3.66 (![X0 : $i]: ((multiply @ X0 @ (multiply @ X0 @ X0)) = (identity))),
% 21.05/3.66 inference('cnf', [status(esa)], [x_cubed_is_identity])).
% 21.05/3.66 thf(zip_derived_cl265, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((X1) = (multiply @ X0 @ (multiply @ (inverse @ X0) @ X1)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl252, zip_derived_cl18])).
% 21.05/3.66 thf(zip_derived_cl364, plain,
% 21.05/3.66 (![X0 : $i]:
% 21.05/3.66 ((multiply @ (inverse @ X0) @ (inverse @ X0))
% 21.05/3.66 = (multiply @ X0 @ identity))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl265])).
% 21.05/3.66 thf(zip_derived_cl228, plain,
% 21.05/3.66 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl188, zip_derived_cl175])).
% 21.05/3.66 thf(zip_derived_cl374, plain,
% 21.05/3.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ (inverse @ X0)) = (X0))),
% 21.05/3.66 inference('demod', [status(thm)], [zip_derived_cl364, zip_derived_cl228])).
% 21.05/3.66 thf(zip_derived_cl2, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.05/3.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 21.05/3.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 21.05/3.66 inference('cnf', [status(esa)], [associativity])).
% 21.05/3.66 thf(zip_derived_cl463, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ X0 @ X1)
% 21.05/3.66 = (multiply @ (inverse @ X0) @ (multiply @ (inverse @ X0) @ X1)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl374, zip_derived_cl2])).
% 21.05/3.66 thf(zip_derived_cl2, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.05/3.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 21.05/3.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 21.05/3.66 inference('cnf', [status(esa)], [associativity])).
% 21.05/3.66 thf(zip_derived_cl374, plain,
% 21.05/3.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ (inverse @ X0)) = (X0))),
% 21.05/3.66 inference('demod', [status(thm)], [zip_derived_cl364, zip_derived_cl228])).
% 21.05/3.66 thf(zip_derived_cl10848, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ X0 @ (multiply @ X1 @ (commutator @ X1 @ X0)))
% 21.05/3.66 = (multiply @ X1 @ X0))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl10770, zip_derived_cl706, zip_derived_cl1389,
% 21.05/3.66 zip_derived_cl3071, zip_derived_cl2, zip_derived_cl463,
% 21.05/3.66 zip_derived_cl2, zip_derived_cl374])).
% 21.05/3.66 thf(zip_derived_cl26, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.05/3.66 ((multiply @ (commutator @ X1 @ X0) @ X2)
% 21.05/3.66 = (multiply @ X1 @
% 21.05/3.66 (multiply @ X0 @
% 21.05/3.66 (multiply @ (inverse @ X1) @ (multiply @ (inverse @ X0) @ X2)))))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl20, zip_derived_cl2, zip_derived_cl2])).
% 21.05/3.66 thf(zip_derived_cl11030, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ (commutator @ X0 @ X1) @
% 21.05/3.66 (commutator @ (inverse @ X1) @ (inverse @ X0)))
% 21.05/3.66 = (multiply @ X0 @
% 21.05/3.66 (multiply @ X1 @ (multiply @ (inverse @ X1) @ (inverse @ X0)))))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl10848, zip_derived_cl26])).
% 21.05/3.66 thf(zip_derived_cl702, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((inverse @ (multiply @ X0 @ X1))
% 21.05/3.66 = (multiply @ (inverse @ X1) @ (inverse @ X0)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl688, zip_derived_cl18])).
% 21.05/3.66 thf(zip_derived_cl688, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 21.05/3.66 inference('demod', [status(thm)], [zip_derived_cl641, zip_derived_cl228])).
% 21.05/3.66 thf(zip_derived_cl259, plain,
% 21.05/3.66 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl252, zip_derived_cl1])).
% 21.05/3.66 thf(zip_derived_cl11142, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ (commutator @ X0 @ X1) @
% 21.05/3.66 (commutator @ (inverse @ X1) @ (inverse @ X0))) = (identity))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl11030, zip_derived_cl702, zip_derived_cl688,
% 21.05/3.66 zip_derived_cl259])).
% 21.05/3.66 thf(zip_derived_cl727, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ (inverse @ (multiply @ X0 @ X1)) @ X0) = (inverse @ X1))),
% 21.05/3.66 inference('demod', [status(thm)], [zip_derived_cl717, zip_derived_cl252])).
% 21.05/3.66 thf(zip_derived_cl11149, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ (inverse @ identity) @ (commutator @ X0 @ X1))
% 21.05/3.66 = (inverse @ (commutator @ (inverse @ X1) @ (inverse @ X0))))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl11142, zip_derived_cl727])).
% 21.05/3.66 thf(zip_derived_cl92, plain, (((inverse @ identity) = (identity))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl80, zip_derived_cl1])).
% 21.05/3.66 thf(zip_derived_cl0, plain,
% 21.05/3.66 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 21.05/3.66 inference('cnf', [status(esa)], [left_identity])).
% 21.05/3.66 thf(zip_derived_cl3047, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X0 @ X1) = (inverse @ (commutator @ X1 @ X0)))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl2983, zip_derived_cl92, zip_derived_cl0])).
% 21.05/3.66 thf(zip_derived_cl11288, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X0 @ X1)
% 21.05/3.66 = (commutator @ (inverse @ X0) @ (inverse @ X1)))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl11149, zip_derived_cl92, zip_derived_cl0,
% 21.05/3.66 zip_derived_cl3047])).
% 21.05/3.66 thf(zip_derived_cl702, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((inverse @ (multiply @ X0 @ X1))
% 21.05/3.66 = (multiply @ (inverse @ X1) @ (inverse @ X0)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl688, zip_derived_cl18])).
% 21.05/3.66 thf(zip_derived_cl688, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 21.05/3.66 inference('demod', [status(thm)], [zip_derived_cl641, zip_derived_cl228])).
% 21.05/3.66 thf(zip_derived_cl3, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X0 @ X1)
% 21.05/3.66 = (multiply @ X0 @
% 21.05/3.66 (multiply @ X1 @ (multiply @ (inverse @ X0) @ (inverse @ X1)))))),
% 21.05/3.66 inference('cnf', [status(esa)], [commutator])).
% 21.05/3.66 thf(zip_derived_cl707, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X1 @ (multiply @ X0 @ (inverse @ X1)))
% 21.05/3.66 = (multiply @ X1 @
% 21.05/3.66 (multiply @ (multiply @ X0 @ (inverse @ X1)) @ (inverse @ X0))))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl688, zip_derived_cl3])).
% 21.05/3.66 thf(zip_derived_cl2, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.05/3.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 21.05/3.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 21.05/3.66 inference('cnf', [status(esa)], [associativity])).
% 21.05/3.66 thf(zip_derived_cl3, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X0 @ X1)
% 21.05/3.66 = (multiply @ X0 @
% 21.05/3.66 (multiply @ X1 @ (multiply @ (inverse @ X0) @ (inverse @ X1)))))),
% 21.05/3.66 inference('cnf', [status(esa)], [commutator])).
% 21.05/3.66 thf(zip_derived_cl738, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X1 @ (multiply @ X0 @ (inverse @ X1)))
% 21.05/3.66 = (commutator @ X1 @ X0))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl707, zip_derived_cl2, zip_derived_cl3])).
% 21.05/3.66 thf(zip_derived_cl1112, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X1 @ (inverse @ (multiply @ X1 @ X0)))
% 21.05/3.66 = (commutator @ X1 @ (inverse @ X0)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl702, zip_derived_cl738])).
% 21.05/3.66 thf(zip_derived_cl11359, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X1 @ (multiply @ (inverse @ X1) @ X0))
% 21.05/3.66 = (commutator @ (inverse @ X1) @ (inverse @ X0)))),
% 21.05/3.66 inference('sup+', [status(thm)],
% 21.05/3.66 [zip_derived_cl11288, zip_derived_cl1112])).
% 21.05/3.66 thf(zip_derived_cl265, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((X1) = (multiply @ X0 @ (multiply @ (inverse @ X0) @ X1)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl252, zip_derived_cl18])).
% 21.05/3.66 thf(zip_derived_cl18, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 21.05/3.66 inference('demod', [status(thm)], [zip_derived_cl14, zip_derived_cl0])).
% 21.05/3.66 thf(zip_derived_cl688, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 21.05/3.66 inference('demod', [status(thm)], [zip_derived_cl641, zip_derived_cl228])).
% 21.05/3.66 thf(zip_derived_cl722, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0))
% 21.05/3.66 = (inverse @ (inverse @ X1)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl18, zip_derived_cl688])).
% 21.05/3.66 thf(zip_derived_cl252, plain,
% 21.05/3.66 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl228, zip_derived_cl188])).
% 21.05/3.66 thf(zip_derived_cl731, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 21.05/3.66 inference('demod', [status(thm)], [zip_derived_cl722, zip_derived_cl252])).
% 21.05/3.66 thf(zip_derived_cl738, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X1 @ (multiply @ X0 @ (inverse @ X1)))
% 21.05/3.66 = (commutator @ X1 @ X0))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl707, zip_derived_cl2, zip_derived_cl3])).
% 21.05/3.66 thf(zip_derived_cl1108, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X1 @ X0) = (commutator @ X1 @ (multiply @ X0 @ X1)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl731, zip_derived_cl738])).
% 21.05/3.66 thf(zip_derived_cl3047, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X0 @ X1) = (inverse @ (commutator @ X1 @ X0)))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl2983, zip_derived_cl92, zip_derived_cl0])).
% 21.05/3.66 thf(zip_derived_cl3099, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ (multiply @ X0 @ X1) @ X1)
% 21.05/3.66 = (inverse @ (commutator @ X1 @ X0)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl1108, zip_derived_cl3047])).
% 21.05/3.66 thf(zip_derived_cl3047, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X0 @ X1) = (inverse @ (commutator @ X1 @ X0)))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl2983, zip_derived_cl92, zip_derived_cl0])).
% 21.05/3.66 thf(zip_derived_cl3114, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ (multiply @ X0 @ X1) @ X1) = (commutator @ X0 @ X1))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl3099, zip_derived_cl3047])).
% 21.05/3.66 thf(zip_derived_cl3215, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X0 @ (multiply @ (inverse @ X1) @ X0))
% 21.05/3.66 = (commutator @ X1 @ (multiply @ (inverse @ X1) @ X0)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl265, zip_derived_cl3114])).
% 21.05/3.66 thf(zip_derived_cl1108, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X1 @ X0) = (commutator @ X1 @ (multiply @ X0 @ X1)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl731, zip_derived_cl738])).
% 21.05/3.66 thf(zip_derived_cl3247, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X0 @ (inverse @ X1))
% 21.05/3.66 = (commutator @ X1 @ (multiply @ (inverse @ X1) @ X0)))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl3215, zip_derived_cl1108])).
% 21.05/3.66 thf(zip_derived_cl11288, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X0 @ X1)
% 21.05/3.66 = (commutator @ (inverse @ X0) @ (inverse @ X1)))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl11149, zip_derived_cl92, zip_derived_cl0,
% 21.05/3.66 zip_derived_cl3047])).
% 21.05/3.66 thf(zip_derived_cl11417, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X0 @ (inverse @ X1)) = (commutator @ X1 @ X0))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl11359, zip_derived_cl3247, zip_derived_cl11288])).
% 21.05/3.66 thf(zip_derived_cl11424, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ (commutator @ X0 @ X1) @ X0)
% 21.05/3.66 = (multiply @ X0 @ (commutator @ X0 @ X1)))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl1376, zip_derived_cl11417])).
% 21.05/3.66 thf(zip_derived_cl3, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X0 @ X1)
% 21.05/3.66 = (multiply @ X0 @
% 21.05/3.66 (multiply @ X1 @ (multiply @ (inverse @ X0) @ (inverse @ X1)))))),
% 21.05/3.66 inference('cnf', [status(esa)], [commutator])).
% 21.05/3.66 thf(zip_derived_cl702, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((inverse @ (multiply @ X0 @ X1))
% 21.05/3.66 = (multiply @ (inverse @ X1) @ (inverse @ X0)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl688, zip_derived_cl18])).
% 21.05/3.66 thf(zip_derived_cl865, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X0 @ X1)
% 21.05/3.66 = (multiply @ X0 @
% 21.05/3.66 (multiply @ X1 @ (inverse @ (multiply @ X1 @ X0)))))),
% 21.05/3.66 inference('demod', [status(thm)], [zip_derived_cl3, zip_derived_cl702])).
% 21.05/3.66 thf(zip_derived_cl11884, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X1 @ (commutator @ X1 @ X0))
% 21.05/3.66 = (multiply @ X1 @
% 21.05/3.66 (multiply @ (commutator @ X1 @ X0) @
% 21.05/3.66 (inverse @ (multiply @ X1 @ (commutator @ X1 @ X0))))))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl11424, zip_derived_cl865])).
% 21.05/3.66 thf(zip_derived_cl3047, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X0 @ X1) = (inverse @ (commutator @ X1 @ X0)))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl2983, zip_derived_cl92, zip_derived_cl0])).
% 21.05/3.66 thf(zip_derived_cl702, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((inverse @ (multiply @ X0 @ X1))
% 21.05/3.66 = (multiply @ (inverse @ X1) @ (inverse @ X0)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl688, zip_derived_cl18])).
% 21.05/3.66 thf(zip_derived_cl3086, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.05/3.66 ((inverse @ (multiply @ X2 @ (commutator @ X0 @ X1)))
% 21.05/3.66 = (multiply @ (commutator @ X1 @ X0) @ (inverse @ X2)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl3047, zip_derived_cl702])).
% 21.05/3.66 thf(zip_derived_cl2930, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((multiply @ (commutator @ X0 @ X1) @ (commutator @ X1 @ X0))
% 21.05/3.66 = (identity))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl2894, zip_derived_cl2, zip_derived_cl2,
% 21.05/3.66 zip_derived_cl2, zip_derived_cl26])).
% 21.05/3.66 thf(zip_derived_cl2, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.05/3.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 21.05/3.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 21.05/3.66 inference('cnf', [status(esa)], [associativity])).
% 21.05/3.66 thf(zip_derived_cl2981, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.05/3.66 ((multiply @ identity @ X0)
% 21.05/3.66 = (multiply @ (commutator @ X1 @ X2) @
% 21.05/3.66 (multiply @ (commutator @ X2 @ X1) @ X0)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl2930, zip_derived_cl2])).
% 21.05/3.66 thf(zip_derived_cl0, plain,
% 21.05/3.66 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 21.05/3.66 inference('cnf', [status(esa)], [left_identity])).
% 21.05/3.66 thf(zip_derived_cl3045, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.05/3.66 ((X0)
% 21.05/3.66 = (multiply @ (commutator @ X1 @ X2) @
% 21.05/3.66 (multiply @ (commutator @ X2 @ X1) @ X0)))),
% 21.05/3.66 inference('demod', [status(thm)], [zip_derived_cl2981, zip_derived_cl0])).
% 21.05/3.66 thf(zip_derived_cl259, plain,
% 21.05/3.66 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl252, zip_derived_cl1])).
% 21.05/3.66 thf(zip_derived_cl11981, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X1 @ (commutator @ X1 @ X0)) = (identity))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl11884, zip_derived_cl3086, zip_derived_cl3045,
% 21.05/3.66 zip_derived_cl259])).
% 21.05/3.66 thf(zip_derived_cl11288, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X0 @ X1)
% 21.05/3.66 = (commutator @ (inverse @ X0) @ (inverse @ X1)))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl11149, zip_derived_cl92, zip_derived_cl0,
% 21.05/3.66 zip_derived_cl3047])).
% 21.05/3.66 thf(zip_derived_cl1112, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X1 @ (inverse @ (multiply @ X1 @ X0)))
% 21.05/3.66 = (commutator @ X1 @ (inverse @ X0)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl702, zip_derived_cl738])).
% 21.05/3.66 thf(zip_derived_cl3047, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X0 @ X1) = (inverse @ (commutator @ X1 @ X0)))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl2983, zip_derived_cl92, zip_derived_cl0])).
% 21.05/3.66 thf(zip_derived_cl3102, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ (inverse @ (multiply @ X1 @ X0)) @ X1)
% 21.05/3.66 = (inverse @ (commutator @ X1 @ (inverse @ X0))))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl1112, zip_derived_cl3047])).
% 21.05/3.66 thf(zip_derived_cl3047, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X0 @ X1) = (inverse @ (commutator @ X1 @ X0)))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl2983, zip_derived_cl92, zip_derived_cl0])).
% 21.05/3.66 thf(zip_derived_cl3117, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ (inverse @ (multiply @ X1 @ X0)) @ X1)
% 21.05/3.66 = (commutator @ (inverse @ X0) @ X1))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl3102, zip_derived_cl3047])).
% 21.05/3.66 thf(zip_derived_cl11369, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ (multiply @ (inverse @ X0) @ X1) @ X0)
% 21.05/3.66 = (commutator @ (inverse @ X1) @ (inverse @ X0)))),
% 21.05/3.66 inference('sup+', [status(thm)],
% 21.05/3.66 [zip_derived_cl11288, zip_derived_cl3117])).
% 21.05/3.66 thf(zip_derived_cl265, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((X1) = (multiply @ X0 @ (multiply @ (inverse @ X0) @ X1)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl252, zip_derived_cl18])).
% 21.05/3.66 thf(zip_derived_cl1108, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X1 @ X0) = (commutator @ X1 @ (multiply @ X0 @ X1)))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl731, zip_derived_cl738])).
% 21.05/3.66 thf(zip_derived_cl1128, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ (multiply @ (inverse @ X1) @ X0) @ X1)
% 21.05/3.66 = (commutator @ (multiply @ (inverse @ X1) @ X0) @ X0))),
% 21.05/3.66 inference('sup+', [status(thm)], [zip_derived_cl265, zip_derived_cl1108])).
% 21.05/3.66 thf(zip_derived_cl3114, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ (multiply @ X0 @ X1) @ X1) = (commutator @ X0 @ X1))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl3099, zip_derived_cl3047])).
% 21.05/3.66 thf(zip_derived_cl3201, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ (multiply @ (inverse @ X1) @ X0) @ X1)
% 21.05/3.66 = (commutator @ (inverse @ X1) @ X0))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl1128, zip_derived_cl3114])).
% 21.05/3.66 thf(zip_derived_cl11288, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ X0 @ X1)
% 21.05/3.66 = (commutator @ (inverse @ X0) @ (inverse @ X1)))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl11149, zip_derived_cl92, zip_derived_cl0,
% 21.05/3.66 zip_derived_cl3047])).
% 21.05/3.66 thf(zip_derived_cl11422, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ (inverse @ X0) @ X1) = (commutator @ X1 @ X0))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl11369, zip_derived_cl3201, zip_derived_cl11288])).
% 21.05/3.66 thf(zip_derived_cl12034, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((identity) = (commutator @ (commutator @ (inverse @ X0) @ X1) @ X0))),
% 21.05/3.66 inference('sup+', [status(thm)],
% 21.05/3.66 [zip_derived_cl11981, zip_derived_cl11422])).
% 21.05/3.66 thf(zip_derived_cl11422, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((commutator @ (inverse @ X0) @ X1) = (commutator @ X1 @ X0))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl11369, zip_derived_cl3201, zip_derived_cl11288])).
% 21.05/3.66 thf(zip_derived_cl12074, plain,
% 21.05/3.66 (![X0 : $i, X1 : $i]:
% 21.05/3.66 ((identity) = (commutator @ (commutator @ X1 @ X0) @ X0))),
% 21.05/3.66 inference('demod', [status(thm)],
% 21.05/3.66 [zip_derived_cl12034, zip_derived_cl11422])).
% 21.05/3.66 thf(zip_derived_cl12209, plain, (((identity) != (identity))),
% 21.05/3.66 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl12074])).
% 21.05/3.66 thf(zip_derived_cl12210, plain, ($false),
% 21.05/3.66 inference('simplify', [status(thm)], [zip_derived_cl12209])).
% 21.05/3.66
% 21.05/3.66 % SZS output end Refutation
% 21.05/3.66
% 21.05/3.66
% 21.05/3.66 % Terminating...
% 21.84/3.75 % Runner terminated.
% 21.84/3.78 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------