TSTP Solution File: GRP113-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP113-1 : TPTP v8.1.2. Released v1.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.sMyh98rPkD true
% Computer : n017.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 01:49:58 EDT 2023
% Result : Unsatisfiable 284.90s 41.33s
% Output : Refutation 284.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GRP113-1 : TPTP v8.1.2. Released v1.1.0.
% 0.08/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.sMyh98rPkD true
% 0.16/0.37 % Computer : n017.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon Aug 28 19:16:13 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.16/0.37 % Running portfolio for 300 s
% 0.16/0.37 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.37 % Number of cores: 8
% 0.16/0.37 % Python version: Python 3.6.8
% 0.16/0.37 % Running in FO mode
% 0.23/0.67 % Total configuration time : 435
% 0.23/0.67 % Estimated wc time : 1092
% 0.23/0.67 % Estimated cpu time (7 cpus) : 156.0
% 0.23/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 1.30/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 1.30/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 1.30/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 1.30/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 1.30/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 1.30/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 284.90/41.33 % Solved by fo/fo4.sh.
% 284.90/41.33 % done 5327 iterations in 40.474s
% 284.90/41.33 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 284.90/41.33 % SZS output start Refutation
% 284.90/41.33 thf(c_type, type, c: $i).
% 284.90/41.33 thf(b_type, type, b: $i).
% 284.90/41.33 thf(identity_type, type, identity: $i).
% 284.90/41.33 thf(multiply_type, type, multiply: $i > $i > $i).
% 284.90/41.33 thf(inverse_type, type, inverse: $i > $i).
% 284.90/41.33 thf(a_type, type, a: $i).
% 284.90/41.33 thf(all_of_group1, axiom,
% 284.90/41.33 (( ( X ) = ( a ) ) | ( ( X ) = ( b ) ) | ( ( X ) = ( c ) ) |
% 284.90/41.33 ( ( X ) = ( identity ) ))).
% 284.90/41.33 thf(zip_derived_cl5, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((X0) = (a)) | ((X0) = (b)) | ((X0) = (c)) | ((X0) = (identity)))),
% 284.90/41.33 inference('cnf', [status(esa)], [all_of_group1])).
% 284.90/41.33 thf(right_identity, axiom, (( multiply @ X @ identity ) = ( X ))).
% 284.90/41.33 thf(zip_derived_cl3, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 284.90/41.33 inference('cnf', [status(esa)], [right_identity])).
% 284.90/41.33 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 284.90/41.33 thf(zip_derived_cl1, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 284.90/41.33 inference('cnf', [status(esa)], [left_inverse])).
% 284.90/41.33 thf(zip_derived_cl16, plain, (((inverse @ identity) = (identity))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 284.90/41.33 thf(zip_derived_cl83, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((inverse @ X0) = (identity))
% 284.90/41.33 | ((X0) = (c))
% 284.90/41.33 | ((X0) = (b))
% 284.90/41.33 | ((X0) = (a)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl16])).
% 284.90/41.33 thf(zip_derived_cl1, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 284.90/41.33 inference('cnf', [status(esa)], [left_inverse])).
% 284.90/41.33 thf(zip_derived_cl506, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((multiply @ identity @ X0) = (identity))
% 284.90/41.33 | ((X0) = (a))
% 284.90/41.33 | ((X0) = (b))
% 284.90/41.33 | ((X0) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl83, zip_derived_cl1])).
% 284.90/41.33 thf(associativity, axiom,
% 284.90/41.33 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 284.90/41.33 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 284.90/41.33 thf(zip_derived_cl2, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 284.90/41.33 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 284.90/41.33 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 284.90/41.33 inference('cnf', [status(esa)], [associativity])).
% 284.90/41.33 thf(zip_derived_cl1, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 284.90/41.33 inference('cnf', [status(esa)], [left_inverse])).
% 284.90/41.33 thf(zip_derived_cl2, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 284.90/41.33 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 284.90/41.33 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 284.90/41.33 inference('cnf', [status(esa)], [associativity])).
% 284.90/41.33 thf(zip_derived_cl23, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((multiply @ identity @ X0)
% 284.90/41.33 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 284.90/41.33 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 284.90/41.33 thf(zip_derived_cl0, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 284.90/41.33 inference('cnf', [status(esa)], [left_identity])).
% 284.90/41.33 thf(zip_derived_cl27, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 284.90/41.33 thf(zip_derived_cl38, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 284.90/41.33 ((X0)
% 284.90/41.33 = (multiply @ (inverse @ (multiply @ X2 @ X1)) @
% 284.90/41.33 (multiply @ X2 @ (multiply @ X1 @ X0))))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl27])).
% 284.90/41.33 thf(zip_derived_cl732, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 (((X0)
% 284.90/41.33 = (multiply @ (inverse @ (multiply @ identity @ X1)) @ identity))
% 284.90/41.33 | ((multiply @ X1 @ X0) = (c))
% 284.90/41.33 | ((multiply @ X1 @ X0) = (b))
% 284.90/41.33 | ((multiply @ X1 @ X0) = (a)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl506, zip_derived_cl38])).
% 284.90/41.33 thf(zip_derived_cl0, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 284.90/41.33 inference('cnf', [status(esa)], [left_identity])).
% 284.90/41.33 thf(zip_derived_cl3, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 284.90/41.33 inference('cnf', [status(esa)], [right_identity])).
% 284.90/41.33 thf(zip_derived_cl745, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 (((X0) = (inverse @ X1))
% 284.90/41.33 | ((multiply @ X1 @ X0) = (c))
% 284.90/41.33 | ((multiply @ X1 @ X0) = (b))
% 284.90/41.33 | ((multiply @ X1 @ X0) = (a)))),
% 284.90/41.33 inference('demod', [status(thm)],
% 284.90/41.33 [zip_derived_cl732, zip_derived_cl0, zip_derived_cl3])).
% 284.90/41.33 thf(zip_derived_cl0, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 284.90/41.33 inference('cnf', [status(esa)], [left_identity])).
% 284.90/41.33 thf(zip_derived_cl129131, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((a) = (X0))
% 284.90/41.33 | ((multiply @ identity @ X0) = (b))
% 284.90/41.33 | ((multiply @ identity @ X0) = (c))
% 284.90/41.33 | ((X0) = (inverse @ identity)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl745, zip_derived_cl0])).
% 284.90/41.33 thf(zip_derived_cl16, plain, (((inverse @ identity) = (identity))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 284.90/41.33 thf(zip_derived_cl130461, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((a) = (X0))
% 284.90/41.33 | ((multiply @ identity @ X0) = (b))
% 284.90/41.33 | ((multiply @ identity @ X0) = (c))
% 284.90/41.33 | ((X0) = (identity)))),
% 284.90/41.33 inference('demod', [status(thm)],
% 284.90/41.33 [zip_derived_cl129131, zip_derived_cl16])).
% 284.90/41.33 thf(zip_derived_cl0, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 284.90/41.33 inference('cnf', [status(esa)], [left_identity])).
% 284.90/41.33 thf(zip_derived_cl130705, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((b) = (X0))
% 284.90/41.33 | ((X0) = (identity))
% 284.90/41.33 | ((multiply @ identity @ X0) = (c))
% 284.90/41.33 | ((a) = (X0)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl130461, zip_derived_cl0])).
% 284.90/41.33 thf(right_inverse, axiom,
% 284.90/41.33 (( multiply @ X @ ( inverse @ X ) ) = ( identity ))).
% 284.90/41.33 thf(zip_derived_cl4, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 284.90/41.33 inference('cnf', [status(esa)], [right_inverse])).
% 284.90/41.33 thf(zip_derived_cl2, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 284.90/41.33 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 284.90/41.33 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 284.90/41.33 inference('cnf', [status(esa)], [associativity])).
% 284.90/41.33 thf(zip_derived_cl30, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((identity)
% 284.90/41.33 = (multiply @ X1 @
% 284.90/41.33 (multiply @ X0 @ (inverse @ (multiply @ X1 @ X0)))))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl2])).
% 284.90/41.33 thf(zip_derived_cl27, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 284.90/41.33 thf(zip_derived_cl167, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0)))
% 284.90/41.33 = (multiply @ (inverse @ X1) @ identity))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl27])).
% 284.90/41.33 thf(zip_derived_cl3, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 284.90/41.33 inference('cnf', [status(esa)], [right_identity])).
% 284.90/41.33 thf(zip_derived_cl195, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl167, zip_derived_cl3])).
% 284.90/41.33 thf(zip_derived_cl131004, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((multiply @ X0 @ (inverse @ c)) = (inverse @ identity))
% 284.90/41.33 | ((a) = (X0))
% 284.90/41.33 | ((X0) = (identity))
% 284.90/41.33 | ((b) = (X0)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl130705, zip_derived_cl195])).
% 284.90/41.33 thf(zip_derived_cl16, plain, (((inverse @ identity) = (identity))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 284.90/41.33 thf(zip_derived_cl131227, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((multiply @ X0 @ (inverse @ c)) = (identity))
% 284.90/41.33 | ((a) = (X0))
% 284.90/41.33 | ((X0) = (identity))
% 284.90/41.33 | ((b) = (X0)))),
% 284.90/41.33 inference('demod', [status(thm)],
% 284.90/41.33 [zip_derived_cl131004, zip_derived_cl16])).
% 284.90/41.33 thf(zip_derived_cl27, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 284.90/41.33 thf(zip_derived_cl195, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl167, zip_derived_cl3])).
% 284.90/41.33 thf(zip_derived_cl5765, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0))
% 284.90/41.33 = (inverse @ (inverse @ X1)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl195])).
% 284.90/41.33 thf(zip_derived_cl1, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 284.90/41.33 inference('cnf', [status(esa)], [left_inverse])).
% 284.90/41.33 thf(zip_derived_cl27, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 284.90/41.33 thf(zip_derived_cl40, plain,
% 284.90/41.33 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl27])).
% 284.90/41.33 thf(zip_derived_cl3, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 284.90/41.33 inference('cnf', [status(esa)], [right_identity])).
% 284.90/41.33 thf(zip_derived_cl48, plain,
% 284.90/41.33 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl3])).
% 284.90/41.33 thf(zip_derived_cl5794, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl5765, zip_derived_cl48])).
% 284.90/41.33 thf(zip_derived_cl152873, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((identity) = (X0))
% 284.90/41.33 | ((b) = (multiply @ X0 @ c))
% 284.90/41.33 | ((multiply @ X0 @ c) = (identity))
% 284.90/41.33 | ((a) = (multiply @ X0 @ c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl131227, zip_derived_cl5794])).
% 284.90/41.33 thf(zip_derived_cl38, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 284.90/41.33 ((X0)
% 284.90/41.33 = (multiply @ (inverse @ (multiply @ X2 @ X1)) @
% 284.90/41.33 (multiply @ X2 @ (multiply @ X1 @ X0))))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl27])).
% 284.90/41.33 thf(zip_derived_cl153636, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 (((c)
% 284.90/41.33 = (multiply @ (inverse @ (multiply @ X1 @ X0)) @
% 284.90/41.33 (multiply @ X1 @ identity)))
% 284.90/41.33 | ((a) = (multiply @ X0 @ c))
% 284.90/41.33 | ((b) = (multiply @ X0 @ c))
% 284.90/41.33 | ((identity) = (X0)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl152873, zip_derived_cl38])).
% 284.90/41.33 thf(zip_derived_cl3, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 284.90/41.33 inference('cnf', [status(esa)], [right_identity])).
% 284.90/41.33 thf(zip_derived_cl30, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((identity)
% 284.90/41.33 = (multiply @ X1 @
% 284.90/41.33 (multiply @ X0 @ (inverse @ (multiply @ X1 @ X0)))))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl2])).
% 284.90/41.33 thf(zip_derived_cl38, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 284.90/41.33 ((X0)
% 284.90/41.33 = (multiply @ (inverse @ (multiply @ X2 @ X1)) @
% 284.90/41.33 (multiply @ X2 @ (multiply @ X1 @ X0))))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl27])).
% 284.90/41.33 thf(zip_derived_cl411, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 284.90/41.33 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0)))
% 284.90/41.33 = (multiply @ (inverse @ (multiply @ X2 @ X1)) @
% 284.90/41.33 (multiply @ X2 @ identity)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl38])).
% 284.90/41.33 thf(zip_derived_cl3, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 284.90/41.33 inference('cnf', [status(esa)], [right_identity])).
% 284.90/41.33 thf(zip_derived_cl439, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 284.90/41.33 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0)))
% 284.90/41.33 = (multiply @ (inverse @ (multiply @ X2 @ X1)) @ X2))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl411, zip_derived_cl3])).
% 284.90/41.33 thf(zip_derived_cl195, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl167, zip_derived_cl3])).
% 284.90/41.33 thf(zip_derived_cl19001, plain,
% 284.90/41.33 (![X1 : $i, X2 : $i]:
% 284.90/41.33 ((inverse @ X1) = (multiply @ (inverse @ (multiply @ X2 @ X1)) @ X2))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl439, zip_derived_cl195])).
% 284.90/41.33 thf(zip_derived_cl153860, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((c) = (inverse @ X0))
% 284.90/41.33 | ((a) = (multiply @ X0 @ c))
% 284.90/41.33 | ((b) = (multiply @ X0 @ c))
% 284.90/41.33 | ((identity) = (X0)))),
% 284.90/41.33 inference('demod', [status(thm)],
% 284.90/41.33 [zip_derived_cl153636, zip_derived_cl3, zip_derived_cl19001])).
% 284.90/41.33 thf(zip_derived_cl48, plain,
% 284.90/41.33 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl3])).
% 284.90/41.33 thf(zip_derived_cl83, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((inverse @ X0) = (identity))
% 284.90/41.33 | ((X0) = (c))
% 284.90/41.33 | ((X0) = (b))
% 284.90/41.33 | ((X0) = (a)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl16])).
% 284.90/41.33 thf(b_not_identity, axiom, (( b ) != ( identity ))).
% 284.90/41.33 thf(zip_derived_cl10, plain, (((b) != (identity))),
% 284.90/41.33 inference('cnf', [status(esa)], [b_not_identity])).
% 284.90/41.33 thf(zip_derived_cl502, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((b) != (inverse @ X0)) | ((X0) = (a)) | ((X0) = (b)) | ((X0) = (c)))),
% 284.90/41.33 inference('sup-', [status(thm)], [zip_derived_cl83, zip_derived_cl10])).
% 284.90/41.33 thf(zip_derived_cl538, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((b) != (X0))
% 284.90/41.33 | ((inverse @ X0) = (c))
% 284.90/41.33 | ((inverse @ X0) = (b))
% 284.90/41.33 | ((inverse @ X0) = (a)))),
% 284.90/41.33 inference('sup-', [status(thm)], [zip_derived_cl48, zip_derived_cl502])).
% 284.90/41.33 thf(zip_derived_cl12574, plain,
% 284.90/41.33 ((((inverse @ b) = (a)) | ((inverse @ b) = (b)) | ((inverse @ b) = (c)))),
% 284.90/41.33 inference('eq_res', [status(thm)], [zip_derived_cl538])).
% 284.90/41.33 thf(zip_derived_cl27, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 284.90/41.33 thf(zip_derived_cl12592, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((X0) = (multiply @ a @ (multiply @ b @ X0)))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((inverse @ b) = (b)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl12574, zip_derived_cl27])).
% 284.90/41.33 thf(zip_derived_cl364465, plain,
% 284.90/41.33 ((((c) = (multiply @ a @ a))
% 284.90/41.33 | ((identity) = (b))
% 284.90/41.33 | ((b) = (multiply @ b @ c))
% 284.90/41.33 | ((c) = (inverse @ b))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((inverse @ b) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl153860, zip_derived_cl12592])).
% 284.90/41.33 thf(zip_derived_cl364772, plain,
% 284.90/41.33 ((((inverse @ b) = (b))
% 284.90/41.33 | ((c) = (inverse @ b))
% 284.90/41.33 | ((b) = (multiply @ b @ c))
% 284.90/41.33 | ((identity) = (b))
% 284.90/41.33 | ((c) = (multiply @ a @ a)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl364465])).
% 284.90/41.33 thf(zip_derived_cl10, plain, (((b) != (identity))),
% 284.90/41.33 inference('cnf', [status(esa)], [b_not_identity])).
% 284.90/41.33 thf(zip_derived_cl364773, plain,
% 284.90/41.33 ((((inverse @ b) = (b))
% 284.90/41.33 | ((c) = (inverse @ b))
% 284.90/41.33 | ((b) = (multiply @ b @ c))
% 284.90/41.33 | ((c) = (multiply @ a @ a)))),
% 284.90/41.33 inference('simplify_reflect-', [status(thm)],
% 284.90/41.33 [zip_derived_cl364772, zip_derived_cl10])).
% 284.90/41.33 thf(zip_derived_cl12574, plain,
% 284.90/41.33 ((((inverse @ b) = (a)) | ((inverse @ b) = (b)) | ((inverse @ b) = (c)))),
% 284.90/41.33 inference('eq_res', [status(thm)], [zip_derived_cl538])).
% 284.90/41.33 thf(zip_derived_cl48, plain,
% 284.90/41.33 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl3])).
% 284.90/41.33 thf(zip_derived_cl12585, plain,
% 284.90/41.33 ((((b) = (inverse @ a)) | ((inverse @ b) = (c)) | ((inverse @ b) = (b)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl12574, zip_derived_cl48])).
% 284.90/41.33 thf(zip_derived_cl5794, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl5765, zip_derived_cl48])).
% 284.90/41.33 thf(zip_derived_cl14372, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((multiply @ (multiply @ X0 @ a) @ b) = (X0))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((inverse @ b) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl12585, zip_derived_cl5794])).
% 284.90/41.33 thf(zip_derived_cl367828, plain,
% 284.90/41.33 ((((multiply @ c @ b) = (a))
% 284.90/41.33 | ((b) = (multiply @ b @ c))
% 284.90/41.33 | ((c) = (inverse @ b))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((inverse @ b) = (b)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl364773, zip_derived_cl14372])).
% 284.90/41.33 thf(zip_derived_cl368185, plain,
% 284.90/41.33 ((((inverse @ b) = (b))
% 284.90/41.33 | ((c) = (inverse @ b))
% 284.90/41.33 | ((b) = (multiply @ b @ c))
% 284.90/41.33 | ((multiply @ c @ b) = (a)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl367828])).
% 284.90/41.33 thf(zip_derived_cl12592, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((X0) = (multiply @ a @ (multiply @ b @ X0)))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((inverse @ b) = (b)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl12574, zip_derived_cl27])).
% 284.90/41.33 thf(zip_derived_cl368299, plain,
% 284.90/41.33 ((((c) = (multiply @ a @ b))
% 284.90/41.33 | ((multiply @ c @ b) = (a))
% 284.90/41.33 | ((c) = (inverse @ b))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((inverse @ b) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl368185, zip_derived_cl12592])).
% 284.90/41.33 thf(zip_derived_cl368548, plain,
% 284.90/41.33 ((((inverse @ b) = (b))
% 284.90/41.33 | ((c) = (inverse @ b))
% 284.90/41.33 | ((multiply @ c @ b) = (a))
% 284.90/41.33 | ((c) = (multiply @ a @ b)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl368299])).
% 284.90/41.33 thf(zip_derived_cl12574, plain,
% 284.90/41.33 ((((inverse @ b) = (a)) | ((inverse @ b) = (b)) | ((inverse @ b) = (c)))),
% 284.90/41.33 inference('eq_res', [status(thm)], [zip_derived_cl538])).
% 284.90/41.33 thf(zip_derived_cl1, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 284.90/41.33 inference('cnf', [status(esa)], [left_inverse])).
% 284.90/41.33 thf(zip_derived_cl12583, plain,
% 284.90/41.33 ((((multiply @ a @ b) = (identity))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((inverse @ b) = (b)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl12574, zip_derived_cl1])).
% 284.90/41.33 thf(zip_derived_cl378568, plain,
% 284.90/41.33 ((((c) = (identity))
% 284.90/41.33 | ((multiply @ c @ b) = (a))
% 284.90/41.33 | ((c) = (inverse @ b))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((inverse @ b) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl368548, zip_derived_cl12583])).
% 284.90/41.33 thf(zip_derived_cl378836, plain,
% 284.90/41.33 ((((inverse @ b) = (b))
% 284.90/41.33 | ((c) = (inverse @ b))
% 284.90/41.33 | ((multiply @ c @ b) = (a))
% 284.90/41.33 | ((c) = (identity)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl378568])).
% 284.90/41.33 thf(c_not_identity, axiom, (( c ) != ( identity ))).
% 284.90/41.33 thf(zip_derived_cl11, plain, (((c) != (identity))),
% 284.90/41.33 inference('cnf', [status(esa)], [c_not_identity])).
% 284.90/41.33 thf(zip_derived_cl378837, plain,
% 284.90/41.33 ((((inverse @ b) = (b))
% 284.90/41.33 | ((c) = (inverse @ b))
% 284.90/41.33 | ((multiply @ c @ b) = (a)))),
% 284.90/41.33 inference('simplify_reflect-', [status(thm)],
% 284.90/41.33 [zip_derived_cl378836, zip_derived_cl11])).
% 284.90/41.33 thf(zip_derived_cl12574, plain,
% 284.90/41.33 ((((inverse @ b) = (a)) | ((inverse @ b) = (b)) | ((inverse @ b) = (c)))),
% 284.90/41.33 inference('eq_res', [status(thm)], [zip_derived_cl538])).
% 284.90/41.33 thf(zip_derived_cl5794, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl5765, zip_derived_cl48])).
% 284.90/41.33 thf(zip_derived_cl14374, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((multiply @ (multiply @ X0 @ b) @ a) = (X0))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((inverse @ b) = (b)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl12574, zip_derived_cl5794])).
% 284.90/41.33 thf(zip_derived_cl378926, plain,
% 284.90/41.33 ((((multiply @ a @ a) = (c))
% 284.90/41.33 | ((c) = (inverse @ b))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((inverse @ b) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl378837, zip_derived_cl14374])).
% 284.90/41.33 thf(zip_derived_cl379124, plain,
% 284.90/41.33 ((((inverse @ b) = (b))
% 284.90/41.33 | ((c) = (inverse @ b))
% 284.90/41.33 | ((multiply @ a @ a) = (c)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl378926])).
% 284.90/41.33 thf(zip_derived_cl12574, plain,
% 284.90/41.33 ((((inverse @ b) = (a)) | ((inverse @ b) = (b)) | ((inverse @ b) = (c)))),
% 284.90/41.33 inference('eq_res', [status(thm)], [zip_derived_cl538])).
% 284.90/41.33 thf(zip_derived_cl4, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 284.90/41.33 inference('cnf', [status(esa)], [right_inverse])).
% 284.90/41.33 thf(zip_derived_cl2, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 284.90/41.33 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 284.90/41.33 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 284.90/41.33 inference('cnf', [status(esa)], [associativity])).
% 284.90/41.33 thf(zip_derived_cl29, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((multiply @ identity @ X0)
% 284.90/41.33 = (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl2])).
% 284.90/41.33 thf(zip_derived_cl0, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 284.90/41.33 inference('cnf', [status(esa)], [left_identity])).
% 284.90/41.33 thf(zip_derived_cl33, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((X0) = (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl29, zip_derived_cl0])).
% 284.90/41.33 thf(zip_derived_cl12593, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((X0) = (multiply @ b @ (multiply @ a @ X0)))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((inverse @ b) = (b)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl12574, zip_derived_cl33])).
% 284.90/41.33 thf(zip_derived_cl380007, plain,
% 284.90/41.33 ((((a) = (multiply @ b @ c))
% 284.90/41.33 | ((c) = (inverse @ b))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((inverse @ b) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl379124, zip_derived_cl12593])).
% 284.90/41.33 thf(zip_derived_cl380318, plain,
% 284.90/41.33 ((((inverse @ b) = (b))
% 284.90/41.33 | ((c) = (inverse @ b))
% 284.90/41.33 | ((a) = (multiply @ b @ c)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl380007])).
% 284.90/41.33 thf(zip_derived_cl379124, plain,
% 284.90/41.33 ((((inverse @ b) = (b))
% 284.90/41.33 | ((c) = (inverse @ b))
% 284.90/41.33 | ((multiply @ a @ a) = (c)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl378926])).
% 284.90/41.33 thf(zip_derived_cl130461, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((a) = (X0))
% 284.90/41.33 | ((multiply @ identity @ X0) = (b))
% 284.90/41.33 | ((multiply @ identity @ X0) = (c))
% 284.90/41.33 | ((X0) = (identity)))),
% 284.90/41.33 inference('demod', [status(thm)],
% 284.90/41.33 [zip_derived_cl129131, zip_derived_cl16])).
% 284.90/41.33 thf(zip_derived_cl195, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl167, zip_derived_cl3])).
% 284.90/41.33 thf(zip_derived_cl130576, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((multiply @ X0 @ (inverse @ b)) = (inverse @ identity))
% 284.90/41.33 | ((X0) = (identity))
% 284.90/41.33 | ((multiply @ identity @ X0) = (c))
% 284.90/41.33 | ((a) = (X0)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl130461, zip_derived_cl195])).
% 284.90/41.33 thf(zip_derived_cl16, plain, (((inverse @ identity) = (identity))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 284.90/41.33 thf(zip_derived_cl0, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 284.90/41.33 inference('cnf', [status(esa)], [left_identity])).
% 284.90/41.33 thf(zip_derived_cl130801, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((multiply @ X0 @ (inverse @ b)) = (identity))
% 284.90/41.33 | ((X0) = (identity))
% 284.90/41.33 | ((X0) = (c))
% 284.90/41.33 | ((a) = (X0)))),
% 284.90/41.33 inference('demod', [status(thm)],
% 284.90/41.33 [zip_derived_cl130576, zip_derived_cl16, zip_derived_cl0])).
% 284.90/41.33 thf(zip_derived_cl5794, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl5765, zip_derived_cl48])).
% 284.90/41.33 thf(zip_derived_cl132844, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((identity) = (X0))
% 284.90/41.33 | ((a) = (multiply @ X0 @ b))
% 284.90/41.33 | ((multiply @ X0 @ b) = (c))
% 284.90/41.33 | ((multiply @ X0 @ b) = (identity)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl130801, zip_derived_cl5794])).
% 284.90/41.33 thf(zip_derived_cl12583, plain,
% 284.90/41.33 ((((multiply @ a @ b) = (identity))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((inverse @ b) = (b)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl12574, zip_derived_cl1])).
% 284.90/41.33 thf(zip_derived_cl5794, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl5765, zip_derived_cl48])).
% 284.90/41.33 thf(zip_derived_cl14422, plain,
% 284.90/41.33 ((((multiply @ identity @ (inverse @ b)) = (a))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((inverse @ b) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl12583, zip_derived_cl5794])).
% 284.90/41.33 thf(zip_derived_cl195, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl167, zip_derived_cl3])).
% 284.90/41.33 thf(zip_derived_cl16521, plain,
% 284.90/41.33 ((((multiply @ (inverse @ b) @ (inverse @ a)) = (inverse @ identity))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((inverse @ b) = (b)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl14422, zip_derived_cl195])).
% 284.90/41.33 thf(zip_derived_cl16, plain, (((inverse @ identity) = (identity))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 284.90/41.33 thf(zip_derived_cl16644, plain,
% 284.90/41.33 ((((multiply @ (inverse @ b) @ (inverse @ a)) = (identity))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((inverse @ b) = (b)))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl16521, zip_derived_cl16])).
% 284.90/41.33 thf(zip_derived_cl195, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl167, zip_derived_cl3])).
% 284.90/41.33 thf(zip_derived_cl27, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 284.90/41.33 thf(zip_derived_cl5722, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((inverse @ (multiply @ X0 @ X1))
% 284.90/41.33 = (multiply @ (inverse @ X1) @ (inverse @ X0)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl195, zip_derived_cl27])).
% 284.90/41.33 thf(zip_derived_cl21656, plain,
% 284.90/41.33 ((((inverse @ (multiply @ a @ b)) = (identity))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((inverse @ b) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl16644, zip_derived_cl5722])).
% 284.90/41.33 thf(zip_derived_cl12574, plain,
% 284.90/41.33 ((((inverse @ b) = (a)) | ((inverse @ b) = (b)) | ((inverse @ b) = (c)))),
% 284.90/41.33 inference('eq_res', [status(thm)], [zip_derived_cl538])).
% 284.90/41.33 thf(zip_derived_cl5722, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((inverse @ (multiply @ X0 @ X1))
% 284.90/41.33 = (multiply @ (inverse @ X1) @ (inverse @ X0)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl195, zip_derived_cl27])).
% 284.90/41.33 thf(zip_derived_cl12594, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((inverse @ (multiply @ X0 @ b)) = (multiply @ a @ (inverse @ X0)))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((inverse @ b) = (b)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl12574, zip_derived_cl5722])).
% 284.90/41.33 thf(zip_derived_cl32562, plain,
% 284.90/41.33 ((((inverse @ (multiply @ (multiply @ a @ b) @ b))
% 284.90/41.33 = (multiply @ a @ identity))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((inverse @ b) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl21656, zip_derived_cl12594])).
% 284.90/41.33 thf(zip_derived_cl2, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 284.90/41.33 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 284.90/41.33 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 284.90/41.33 inference('cnf', [status(esa)], [associativity])).
% 284.90/41.33 thf(zip_derived_cl3, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 284.90/41.33 inference('cnf', [status(esa)], [right_identity])).
% 284.90/41.33 thf(zip_derived_cl32620, plain,
% 284.90/41.33 ((((inverse @ (multiply @ a @ (multiply @ b @ b))) = (a))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((inverse @ b) = (c)))),
% 284.90/41.33 inference('demod', [status(thm)],
% 284.90/41.33 [zip_derived_cl32562, zip_derived_cl2, zip_derived_cl3])).
% 284.90/41.33 thf(zip_derived_cl32621, plain,
% 284.90/41.33 ((((inverse @ b) = (b))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((inverse @ (multiply @ a @ (multiply @ b @ b))) = (a)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl32620])).
% 284.90/41.33 thf(zip_derived_cl12574, plain,
% 284.90/41.33 ((((inverse @ b) = (a)) | ((inverse @ b) = (b)) | ((inverse @ b) = (c)))),
% 284.90/41.33 inference('eq_res', [status(thm)], [zip_derived_cl538])).
% 284.90/41.33 thf(zip_derived_cl48, plain,
% 284.90/41.33 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl3])).
% 284.90/41.33 thf(zip_derived_cl5722, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((inverse @ (multiply @ X0 @ X1))
% 284.90/41.33 = (multiply @ (inverse @ X1) @ (inverse @ X0)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl195, zip_derived_cl27])).
% 284.90/41.33 thf(zip_derived_cl8307, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((inverse @ (multiply @ (inverse @ X0) @ X1))
% 284.90/41.33 = (multiply @ (inverse @ X1) @ X0))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl48, zip_derived_cl5722])).
% 284.90/41.33 thf(zip_derived_cl12591, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((inverse @ (multiply @ a @ X0)) = (multiply @ (inverse @ X0) @ b))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((inverse @ b) = (b)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl12574, zip_derived_cl8307])).
% 284.90/41.33 thf(zip_derived_cl42305, plain,
% 284.90/41.33 ((((a) = (multiply @ (inverse @ (multiply @ b @ b)) @ b))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((inverse @ b) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl32621, zip_derived_cl12591])).
% 284.90/41.33 thf(zip_derived_cl42478, plain,
% 284.90/41.33 ((((inverse @ b) = (b))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((a) = (multiply @ (inverse @ (multiply @ b @ b)) @ b)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl42305])).
% 284.90/41.33 thf(zip_derived_cl134696, plain,
% 284.90/41.33 ((((a) = (multiply @ (inverse @ identity) @ b))
% 284.90/41.33 | ((multiply @ b @ b) = (c))
% 284.90/41.33 | ((a) = (multiply @ b @ b))
% 284.90/41.33 | ((identity) = (b))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((inverse @ b) = (b)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl132844, zip_derived_cl42478])).
% 284.90/41.33 thf(zip_derived_cl16, plain, (((inverse @ identity) = (identity))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 284.90/41.33 thf(zip_derived_cl0, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 284.90/41.33 inference('cnf', [status(esa)], [left_identity])).
% 284.90/41.33 thf(zip_derived_cl135199, plain,
% 284.90/41.33 ((((a) = (b))
% 284.90/41.33 | ((multiply @ b @ b) = (c))
% 284.90/41.33 | ((a) = (multiply @ b @ b))
% 284.90/41.33 | ((identity) = (b))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((inverse @ b) = (b)))),
% 284.90/41.33 inference('demod', [status(thm)],
% 284.90/41.33 [zip_derived_cl134696, zip_derived_cl16, zip_derived_cl0])).
% 284.90/41.33 thf(zip_derived_cl10, plain, (((b) != (identity))),
% 284.90/41.33 inference('cnf', [status(esa)], [b_not_identity])).
% 284.90/41.33 thf(a_not_b, axiom, (( a ) != ( b ))).
% 284.90/41.33 thf(zip_derived_cl6, plain, (((a) != (b))),
% 284.90/41.33 inference('cnf', [status(esa)], [a_not_b])).
% 284.90/41.33 thf(zip_derived_cl135200, plain,
% 284.90/41.33 ((((multiply @ b @ b) = (c))
% 284.90/41.33 | ((a) = (multiply @ b @ b))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((inverse @ b) = (b)))),
% 284.90/41.33 inference('simplify_reflect-', [status(thm)],
% 284.90/41.33 [zip_derived_cl135199, zip_derived_cl10, zip_derived_cl6])).
% 284.90/41.33 thf(zip_derived_cl14374, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((multiply @ (multiply @ X0 @ b) @ a) = (X0))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((inverse @ b) = (b)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl12574, zip_derived_cl5794])).
% 284.90/41.33 thf(zip_derived_cl135533, plain,
% 284.90/41.33 ((((multiply @ a @ a) = (b))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((multiply @ b @ b) = (c))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((inverse @ b) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl135200, zip_derived_cl14374])).
% 284.90/41.33 thf(zip_derived_cl135788, plain,
% 284.90/41.33 ((((multiply @ b @ b) = (c))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((multiply @ a @ a) = (b)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl135533])).
% 284.90/41.33 thf(zip_derived_cl380137, plain,
% 284.90/41.33 ((((c) = (b))
% 284.90/41.33 | ((c) = (inverse @ b))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((multiply @ b @ b) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl379124, zip_derived_cl135788])).
% 284.90/41.33 thf(zip_derived_cl380345, plain,
% 284.90/41.33 ((((multiply @ b @ b) = (c))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((c) = (inverse @ b))
% 284.90/41.33 | ((c) = (b)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl380137])).
% 284.90/41.33 thf(b_not_c, axiom, (( b ) != ( c ))).
% 284.90/41.33 thf(zip_derived_cl9, plain, (((b) != (c))),
% 284.90/41.33 inference('cnf', [status(esa)], [b_not_c])).
% 284.90/41.33 thf(zip_derived_cl380346, plain,
% 284.90/41.33 ((((multiply @ b @ b) = (c))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((c) = (inverse @ b)))),
% 284.90/41.33 inference('simplify_reflect-', [status(thm)],
% 284.90/41.33 [zip_derived_cl380345, zip_derived_cl9])).
% 284.90/41.33 thf(zip_derived_cl380318, plain,
% 284.90/41.33 ((((inverse @ b) = (b))
% 284.90/41.33 | ((c) = (inverse @ b))
% 284.90/41.33 | ((a) = (multiply @ b @ c)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl380007])).
% 284.90/41.33 thf(zip_derived_cl380346, plain,
% 284.90/41.33 ((((multiply @ b @ b) = (c))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((c) = (inverse @ b)))),
% 284.90/41.33 inference('simplify_reflect-', [status(thm)],
% 284.90/41.33 [zip_derived_cl380345, zip_derived_cl9])).
% 284.90/41.33 thf(zip_derived_cl380346, plain,
% 284.90/41.33 ((((multiply @ b @ b) = (c))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((c) = (inverse @ b)))),
% 284.90/41.33 inference('simplify_reflect-', [status(thm)],
% 284.90/41.33 [zip_derived_cl380345, zip_derived_cl9])).
% 284.90/41.33 thf(condition_b, conjecture,
% 284.90/41.33 (~( ( ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ b ) ) ) !=
% 284.90/41.33 ( identity ) ) |
% 284.90/41.33 ( ( multiply @ b @ ( multiply @ b @ b ) ) != ( a ) ) |
% 284.90/41.33 ( ( multiply @ b @ b ) != ( c ) ) ))).
% 284.90/41.33 thf(zf_stmt_0, negated_conjecture,
% 284.90/41.33 (( ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ b ) ) ) !=
% 284.90/41.33 ( identity ) ) |
% 284.90/41.33 ( ( multiply @ b @ ( multiply @ b @ b ) ) != ( a ) ) |
% 284.90/41.33 ( ( multiply @ b @ b ) != ( c ) )),
% 284.90/41.33 inference('cnf.neg', [status(esa)], [condition_b])).
% 284.90/41.33 thf(zip_derived_cl14, plain,
% 284.90/41.33 ((((multiply @ b @ (multiply @ b @ (multiply @ b @ b))) != (identity))
% 284.90/41.33 | ((multiply @ b @ (multiply @ b @ b)) != (a))
% 284.90/41.33 | ((multiply @ b @ b) != (c)))),
% 284.90/41.33 inference('cnf', [status(esa)], [zf_stmt_0])).
% 284.90/41.33 thf(zip_derived_cl380702, plain,
% 284.90/41.33 ((((c) != (c))
% 284.90/41.33 | ((c) = (inverse @ b))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((multiply @ b @ (multiply @ b @ b)) != (a))
% 284.90/41.33 | ((multiply @ b @ (multiply @ b @ (multiply @ b @ b))) != (identity)))),
% 284.90/41.33 inference('sup-', [status(thm)], [zip_derived_cl380346, zip_derived_cl14])).
% 284.90/41.33 thf(zip_derived_cl381048, plain,
% 284.90/41.33 ((((multiply @ b @ (multiply @ b @ (multiply @ b @ b))) != (identity))
% 284.90/41.33 | ((multiply @ b @ (multiply @ b @ b)) != (a))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((c) = (inverse @ b)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl380702])).
% 284.90/41.33 thf(zip_derived_cl384844, plain,
% 284.90/41.33 ((((multiply @ b @ c) != (a))
% 284.90/41.33 | ((c) = (inverse @ b))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((c) = (inverse @ b))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((multiply @ b @ (multiply @ b @ (multiply @ b @ b))) != (identity)))),
% 284.90/41.33 inference('sup-', [status(thm)],
% 284.90/41.33 [zip_derived_cl380346, zip_derived_cl381048])).
% 284.90/41.33 thf(zip_derived_cl385046, plain,
% 284.90/41.33 ((((multiply @ b @ (multiply @ b @ (multiply @ b @ b))) != (identity))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((c) = (inverse @ b))
% 284.90/41.33 | ((multiply @ b @ c) != (a)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl384844])).
% 284.90/41.33 thf(zip_derived_cl386724, plain,
% 284.90/41.33 ((((a) != (a))
% 284.90/41.33 | ((c) = (inverse @ b))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((c) = (inverse @ b))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((multiply @ b @ (multiply @ b @ (multiply @ b @ b))) != (identity)))),
% 284.90/41.33 inference('sup-', [status(thm)],
% 284.90/41.33 [zip_derived_cl380318, zip_derived_cl385046])).
% 284.90/41.33 thf(zip_derived_cl386842, plain,
% 284.90/41.33 ((((multiply @ b @ (multiply @ b @ (multiply @ b @ b))) != (identity))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((c) = (inverse @ b)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl386724])).
% 284.90/41.33 thf(zip_derived_cl387095, plain,
% 284.90/41.33 ((((multiply @ b @ (multiply @ b @ c)) != (identity))
% 284.90/41.33 | ((c) = (inverse @ b))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((c) = (inverse @ b))
% 284.90/41.33 | ((inverse @ b) = (b)))),
% 284.90/41.33 inference('sup-', [status(thm)],
% 284.90/41.33 [zip_derived_cl380346, zip_derived_cl386842])).
% 284.90/41.33 thf(zip_derived_cl387390, plain,
% 284.90/41.33 ((((inverse @ b) = (b))
% 284.90/41.33 | ((c) = (inverse @ b))
% 284.90/41.33 | ((multiply @ b @ (multiply @ b @ c)) != (identity)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl387095])).
% 284.90/41.33 thf(zip_derived_cl387672, plain,
% 284.90/41.33 ((((multiply @ b @ a) != (identity))
% 284.90/41.33 | ((c) = (inverse @ b))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((c) = (inverse @ b))
% 284.90/41.33 | ((inverse @ b) = (b)))),
% 284.90/41.33 inference('sup-', [status(thm)],
% 284.90/41.33 [zip_derived_cl380318, zip_derived_cl387390])).
% 284.90/41.33 thf(zip_derived_cl387886, plain,
% 284.90/41.33 ((((inverse @ b) = (b))
% 284.90/41.33 | ((c) = (inverse @ b))
% 284.90/41.33 | ((multiply @ b @ a) != (identity)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl387672])).
% 284.90/41.33 thf(zip_derived_cl12574, plain,
% 284.90/41.33 ((((inverse @ b) = (a)) | ((inverse @ b) = (b)) | ((inverse @ b) = (c)))),
% 284.90/41.33 inference('eq_res', [status(thm)], [zip_derived_cl538])).
% 284.90/41.33 thf(zip_derived_cl4, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 284.90/41.33 inference('cnf', [status(esa)], [right_inverse])).
% 284.90/41.33 thf(zip_derived_cl12584, plain,
% 284.90/41.33 ((((multiply @ b @ a) = (identity))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((inverse @ b) = (b)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl12574, zip_derived_cl4])).
% 284.90/41.33 thf(zip_derived_cl388013, plain,
% 284.90/41.33 ((((c) = (inverse @ b)) | ((inverse @ b) = (b)))),
% 284.90/41.33 inference('clc', [status(thm)],
% 284.90/41.33 [zip_derived_cl387886, zip_derived_cl12584])).
% 284.90/41.33 thf(zip_derived_cl1, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 284.90/41.33 inference('cnf', [status(esa)], [left_inverse])).
% 284.90/41.33 thf(zip_derived_cl388014, plain,
% 284.90/41.33 ((((multiply @ b @ b) = (identity)) | ((c) = (inverse @ b)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl388013, zip_derived_cl1])).
% 284.90/41.33 thf(zip_derived_cl48, plain,
% 284.90/41.33 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl3])).
% 284.90/41.33 thf(zip_derived_cl83, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((inverse @ X0) = (identity))
% 284.90/41.33 | ((X0) = (c))
% 284.90/41.33 | ((X0) = (b))
% 284.90/41.33 | ((X0) = (a)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl16])).
% 284.90/41.33 thf(a_not_identity, axiom, (( a ) != ( identity ))).
% 284.90/41.33 thf(zip_derived_cl8, plain, (((a) != (identity))),
% 284.90/41.33 inference('cnf', [status(esa)], [a_not_identity])).
% 284.90/41.33 thf(zip_derived_cl501, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((a) != (inverse @ X0)) | ((X0) = (a)) | ((X0) = (b)) | ((X0) = (c)))),
% 284.90/41.33 inference('sup-', [status(thm)], [zip_derived_cl83, zip_derived_cl8])).
% 284.90/41.33 thf(zip_derived_cl530, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((a) != (X0))
% 284.90/41.33 | ((inverse @ X0) = (c))
% 284.90/41.33 | ((inverse @ X0) = (b))
% 284.90/41.33 | ((inverse @ X0) = (a)))),
% 284.90/41.33 inference('sup-', [status(thm)], [zip_derived_cl48, zip_derived_cl501])).
% 284.90/41.33 thf(zip_derived_cl11885, plain,
% 284.90/41.33 ((((inverse @ a) = (a)) | ((inverse @ a) = (b)) | ((inverse @ a) = (c)))),
% 284.90/41.33 inference('eq_res', [status(thm)], [zip_derived_cl530])).
% 284.90/41.33 thf(zip_derived_cl1, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 284.90/41.33 inference('cnf', [status(esa)], [left_inverse])).
% 284.90/41.33 thf(zip_derived_cl11898, plain,
% 284.90/41.33 ((((multiply @ a @ a) = (identity))
% 284.90/41.33 | ((inverse @ a) = (c))
% 284.90/41.33 | ((inverse @ a) = (b)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl11885, zip_derived_cl1])).
% 284.90/41.33 thf(square_identity, conjecture,
% 284.90/41.33 (~( ( ( multiply @ c @ c ) != ( identity ) ) |
% 284.90/41.33 ( ( multiply @ b @ b ) != ( identity ) ) |
% 284.90/41.33 ( ( multiply @ a @ a ) != ( identity ) ) ))).
% 284.90/41.33 thf(zf_stmt_1, negated_conjecture,
% 284.90/41.33 (( ( multiply @ c @ c ) != ( identity ) ) |
% 284.90/41.33 ( ( multiply @ b @ b ) != ( identity ) ) |
% 284.90/41.33 ( ( multiply @ a @ a ) != ( identity ) )),
% 284.90/41.33 inference('cnf.neg', [status(esa)], [square_identity])).
% 284.90/41.33 thf(zip_derived_cl12, plain,
% 284.90/41.33 ((((multiply @ c @ c) != (identity))
% 284.90/41.33 | ((multiply @ b @ b) != (identity))
% 284.90/41.33 | ((multiply @ a @ a) != (identity)))),
% 284.90/41.33 inference('cnf', [status(esa)], [zf_stmt_1])).
% 284.90/41.33 thf(zip_derived_cl132844, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((identity) = (X0))
% 284.90/41.33 | ((a) = (multiply @ X0 @ b))
% 284.90/41.33 | ((multiply @ X0 @ b) = (c))
% 284.90/41.33 | ((multiply @ X0 @ b) = (identity)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl130801, zip_derived_cl5794])).
% 284.90/41.33 thf(zip_derived_cl132844, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((identity) = (X0))
% 284.90/41.33 | ((a) = (multiply @ X0 @ b))
% 284.90/41.33 | ((multiply @ X0 @ b) = (c))
% 284.90/41.33 | ((multiply @ X0 @ b) = (identity)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl130801, zip_derived_cl5794])).
% 284.90/41.33 thf(zip_derived_cl48, plain,
% 284.90/41.33 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl3])).
% 284.90/41.33 thf(zip_derived_cl83, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((inverse @ X0) = (identity))
% 284.90/41.33 | ((X0) = (c))
% 284.90/41.33 | ((X0) = (b))
% 284.90/41.33 | ((X0) = (a)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl16])).
% 284.90/41.33 thf(zip_derived_cl11, plain, (((c) != (identity))),
% 284.90/41.33 inference('cnf', [status(esa)], [c_not_identity])).
% 284.90/41.33 thf(zip_derived_cl503, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((c) != (inverse @ X0)) | ((X0) = (a)) | ((X0) = (b)) | ((X0) = (c)))),
% 284.90/41.33 inference('sup-', [status(thm)], [zip_derived_cl83, zip_derived_cl11])).
% 284.90/41.33 thf(zip_derived_cl615, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((c) != (X0))
% 284.90/41.33 | ((inverse @ X0) = (c))
% 284.90/41.33 | ((inverse @ X0) = (b))
% 284.90/41.33 | ((inverse @ X0) = (a)))),
% 284.90/41.33 inference('sup-', [status(thm)], [zip_derived_cl48, zip_derived_cl503])).
% 284.90/41.33 thf(zip_derived_cl13524, plain,
% 284.90/41.33 ((((inverse @ c) = (a)) | ((inverse @ c) = (b)) | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('eq_res', [status(thm)], [zip_derived_cl615])).
% 284.90/41.33 thf(zip_derived_cl33, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((X0) = (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl29, zip_derived_cl0])).
% 284.90/41.33 thf(zip_derived_cl14097, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((X0) = (multiply @ c @ (multiply @ a @ X0)))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl13524, zip_derived_cl33])).
% 284.90/41.33 thf(zip_derived_cl134525, plain,
% 284.90/41.33 ((((b) = (multiply @ c @ identity))
% 284.90/41.33 | ((multiply @ a @ b) = (c))
% 284.90/41.33 | ((a) = (multiply @ a @ b))
% 284.90/41.33 | ((identity) = (a))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl132844, zip_derived_cl14097])).
% 284.90/41.33 thf(zip_derived_cl3, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 284.90/41.33 inference('cnf', [status(esa)], [right_identity])).
% 284.90/41.33 thf(zip_derived_cl134860, plain,
% 284.90/41.33 ((((b) = (c))
% 284.90/41.33 | ((multiply @ a @ b) = (c))
% 284.90/41.33 | ((a) = (multiply @ a @ b))
% 284.90/41.33 | ((identity) = (a))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl134525, zip_derived_cl3])).
% 284.90/41.33 thf(zip_derived_cl8, plain, (((a) != (identity))),
% 284.90/41.33 inference('cnf', [status(esa)], [a_not_identity])).
% 284.90/41.33 thf(zip_derived_cl9, plain, (((b) != (c))),
% 284.90/41.33 inference('cnf', [status(esa)], [b_not_c])).
% 284.90/41.33 thf(zip_derived_cl134861, plain,
% 284.90/41.33 ((((multiply @ a @ b) = (c))
% 284.90/41.33 | ((a) = (multiply @ a @ b))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('simplify_reflect-', [status(thm)],
% 284.90/41.33 [zip_derived_cl134860, zip_derived_cl8, zip_derived_cl9])).
% 284.90/41.33 thf(zip_derived_cl14097, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((X0) = (multiply @ c @ (multiply @ a @ X0)))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl13524, zip_derived_cl33])).
% 284.90/41.33 thf(zip_derived_cl135336, plain,
% 284.90/41.33 ((((b) = (multiply @ c @ a))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((multiply @ a @ b) = (c))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl134861, zip_derived_cl14097])).
% 284.90/41.33 thf(zip_derived_cl135479, plain,
% 284.90/41.33 ((((multiply @ a @ b) = (c))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((b) = (multiply @ c @ a)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl135336])).
% 284.90/41.33 thf(zip_derived_cl14097, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((X0) = (multiply @ c @ (multiply @ a @ X0)))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl13524, zip_derived_cl33])).
% 284.90/41.33 thf(zip_derived_cl137409, plain,
% 284.90/41.33 ((((b) = (multiply @ c @ c))
% 284.90/41.33 | ((b) = (multiply @ c @ a))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl135479, zip_derived_cl14097])).
% 284.90/41.33 thf(zip_derived_cl137553, plain,
% 284.90/41.33 ((((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((b) = (multiply @ c @ a))
% 284.90/41.33 | ((b) = (multiply @ c @ c)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl137409])).
% 284.90/41.33 thf(zip_derived_cl13524, plain,
% 284.90/41.33 ((((inverse @ c) = (a)) | ((inverse @ c) = (b)) | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('eq_res', [status(thm)], [zip_derived_cl615])).
% 284.90/41.33 thf(zip_derived_cl4, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 284.90/41.33 inference('cnf', [status(esa)], [right_inverse])).
% 284.90/41.33 thf(zip_derived_cl14088, plain,
% 284.90/41.33 ((((multiply @ c @ a) = (identity))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl13524, zip_derived_cl4])).
% 284.90/41.33 thf(zip_derived_cl137957, plain,
% 284.90/41.33 ((((b) = (identity))
% 284.90/41.33 | ((b) = (multiply @ c @ c))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl137553, zip_derived_cl14088])).
% 284.90/41.33 thf(zip_derived_cl138091, plain,
% 284.90/41.33 ((((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((b) = (multiply @ c @ c))
% 284.90/41.33 | ((b) = (identity)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl137957])).
% 284.90/41.33 thf(zip_derived_cl10, plain, (((b) != (identity))),
% 284.90/41.33 inference('cnf', [status(esa)], [b_not_identity])).
% 284.90/41.33 thf(zip_derived_cl138092, plain,
% 284.90/41.33 ((((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((b) = (multiply @ c @ c)))),
% 284.90/41.33 inference('simplify_reflect-', [status(thm)],
% 284.90/41.33 [zip_derived_cl138091, zip_derived_cl10])).
% 284.90/41.33 thf(zip_derived_cl13524, plain,
% 284.90/41.33 ((((inverse @ c) = (a)) | ((inverse @ c) = (b)) | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('eq_res', [status(thm)], [zip_derived_cl615])).
% 284.90/41.33 thf(zip_derived_cl13524, plain,
% 284.90/41.33 ((((inverse @ c) = (a)) | ((inverse @ c) = (b)) | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('eq_res', [status(thm)], [zip_derived_cl615])).
% 284.90/41.33 thf(zip_derived_cl5722, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((inverse @ (multiply @ X0 @ X1))
% 284.90/41.33 = (multiply @ (inverse @ X1) @ (inverse @ X0)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl195, zip_derived_cl27])).
% 284.90/41.33 thf(zip_derived_cl14094, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((inverse @ (multiply @ c @ X0)) = (multiply @ (inverse @ X0) @ a))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl13524, zip_derived_cl5722])).
% 284.90/41.33 thf(zip_derived_cl47691, plain,
% 284.90/41.33 ((((inverse @ (multiply @ c @ c)) = (multiply @ a @ a))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl13524, zip_derived_cl14094])).
% 284.90/41.33 thf(zip_derived_cl47739, plain,
% 284.90/41.33 ((((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ (multiply @ c @ c)) = (multiply @ a @ a)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl47691])).
% 284.90/41.33 thf(zip_derived_cl48, plain,
% 284.90/41.33 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl3])).
% 284.90/41.33 thf(zip_derived_cl48507, plain,
% 284.90/41.33 ((((multiply @ c @ c) = (inverse @ (multiply @ a @ a)))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl47739, zip_derived_cl48])).
% 284.90/41.33 thf(zip_derived_cl195, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl167, zip_derived_cl3])).
% 284.90/41.33 thf(zip_derived_cl52961, plain,
% 284.90/41.33 ((((multiply @ a @ (multiply @ c @ c)) = (inverse @ a))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl48507, zip_derived_cl195])).
% 284.90/41.33 thf(zip_derived_cl138244, plain,
% 284.90/41.33 ((((multiply @ a @ b) = (inverse @ a))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl138092, zip_derived_cl52961])).
% 284.90/41.33 thf(zip_derived_cl138360, plain,
% 284.90/41.33 ((((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((multiply @ a @ b) = (inverse @ a)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl138244])).
% 284.90/41.33 thf(zip_derived_cl13524, plain,
% 284.90/41.33 ((((inverse @ c) = (a)) | ((inverse @ c) = (b)) | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('eq_res', [status(thm)], [zip_derived_cl615])).
% 284.90/41.33 thf(zip_derived_cl48, plain,
% 284.90/41.33 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl3])).
% 284.90/41.33 thf(zip_derived_cl14089, plain,
% 284.90/41.33 ((((c) = (inverse @ a)) | ((inverse @ c) = (c)) | ((inverse @ c) = (b)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl13524, zip_derived_cl48])).
% 284.90/41.33 thf(zip_derived_cl12585, plain,
% 284.90/41.33 ((((b) = (inverse @ a)) | ((inverse @ b) = (c)) | ((inverse @ b) = (b)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl12574, zip_derived_cl48])).
% 284.90/41.33 thf(zip_derived_cl14153, plain,
% 284.90/41.33 ((((b) = (c))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((inverse @ b) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl14089, zip_derived_cl12585])).
% 284.90/41.33 thf(zip_derived_cl9, plain, (((b) != (c))),
% 284.90/41.33 inference('cnf', [status(esa)], [b_not_c])).
% 284.90/41.33 thf(zip_derived_cl14192, plain,
% 284.90/41.33 ((((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((inverse @ b) = (c)))),
% 284.90/41.33 inference('simplify_reflect-', [status(thm)],
% 284.90/41.33 [zip_derived_cl14153, zip_derived_cl9])).
% 284.90/41.33 thf(zip_derived_cl138092, plain,
% 284.90/41.33 ((((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((b) = (multiply @ c @ c)))),
% 284.90/41.33 inference('simplify_reflect-', [status(thm)],
% 284.90/41.33 [zip_derived_cl138091, zip_derived_cl10])).
% 284.90/41.33 thf(zip_derived_cl47739, plain,
% 284.90/41.33 ((((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ (multiply @ c @ c)) = (multiply @ a @ a)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl47691])).
% 284.90/41.33 thf(zip_derived_cl138241, plain,
% 284.90/41.33 ((((inverse @ b) = (multiply @ a @ a))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl138092, zip_derived_cl47739])).
% 284.90/41.33 thf(zip_derived_cl138357, plain,
% 284.90/41.33 ((((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ b) = (multiply @ a @ a)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl138241])).
% 284.90/41.33 thf(zip_derived_cl138092, plain,
% 284.90/41.33 ((((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((b) = (multiply @ c @ c)))),
% 284.90/41.33 inference('simplify_reflect-', [status(thm)],
% 284.90/41.33 [zip_derived_cl138091, zip_derived_cl10])).
% 284.90/41.33 thf(zip_derived_cl13524, plain,
% 284.90/41.33 ((((inverse @ c) = (a)) | ((inverse @ c) = (b)) | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('eq_res', [status(thm)], [zip_derived_cl615])).
% 284.90/41.33 thf(zip_derived_cl27, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 284.90/41.33 thf(zip_derived_cl14096, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((X0) = (multiply @ a @ (multiply @ c @ X0)))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl13524, zip_derived_cl27])).
% 284.90/41.33 thf(zip_derived_cl138170, plain,
% 284.90/41.33 ((((c) = (multiply @ a @ b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl138092, zip_derived_cl14096])).
% 284.90/41.33 thf(zip_derived_cl138348, plain,
% 284.90/41.33 ((((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((c) = (multiply @ a @ b)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl138170])).
% 284.90/41.33 thf(zip_derived_cl14192, plain,
% 284.90/41.33 ((((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((inverse @ b) = (c)))),
% 284.90/41.33 inference('simplify_reflect-', [status(thm)],
% 284.90/41.33 [zip_derived_cl14153, zip_derived_cl9])).
% 284.90/41.33 thf(zip_derived_cl138357, plain,
% 284.90/41.33 ((((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ b) = (multiply @ a @ a)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl138241])).
% 284.90/41.33 thf(zip_derived_cl14192, plain,
% 284.90/41.33 ((((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ b) = (b))
% 284.90/41.33 | ((inverse @ b) = (c)))),
% 284.90/41.33 inference('simplify_reflect-', [status(thm)],
% 284.90/41.33 [zip_derived_cl14153, zip_derived_cl9])).
% 284.90/41.33 thf(zip_derived_cl138357, plain,
% 284.90/41.33 ((((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ b) = (multiply @ a @ a)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl138241])).
% 284.90/41.33 thf(condition_a, conjecture,
% 284.90/41.33 (~( ( ( multiply @ a @ ( multiply @ a @ ( multiply @ a @ a ) ) ) !=
% 284.90/41.33 ( identity ) ) |
% 284.90/41.33 ( ( multiply @ a @ ( multiply @ a @ a ) ) != ( c ) ) |
% 284.90/41.33 ( ( multiply @ a @ a ) != ( b ) ) ))).
% 284.90/41.33 thf(zf_stmt_2, negated_conjecture,
% 284.90/41.33 (( ( multiply @ a @ ( multiply @ a @ ( multiply @ a @ a ) ) ) !=
% 284.90/41.33 ( identity ) ) |
% 284.90/41.33 ( ( multiply @ a @ ( multiply @ a @ a ) ) != ( c ) ) |
% 284.90/41.33 ( ( multiply @ a @ a ) != ( b ) )),
% 284.90/41.33 inference('cnf.neg', [status(esa)], [condition_a])).
% 284.90/41.33 thf(zip_derived_cl13, plain,
% 284.90/41.33 ((((multiply @ a @ (multiply @ a @ (multiply @ a @ a))) != (identity))
% 284.90/41.33 | ((multiply @ a @ (multiply @ a @ a)) != (c))
% 284.90/41.33 | ((multiply @ a @ a) != (b)))),
% 284.90/41.33 inference('cnf', [status(esa)], [zf_stmt_2])).
% 284.90/41.33 thf(zip_derived_cl139223, plain,
% 284.90/41.33 ((((inverse @ b) != (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((multiply @ a @ (multiply @ a @ a)) != (c))
% 284.90/41.33 | ((multiply @ a @ (multiply @ a @ (multiply @ a @ a))) != (identity)))),
% 284.90/41.33 inference('sup-', [status(thm)], [zip_derived_cl138357, zip_derived_cl13])).
% 284.90/41.33 thf(zip_derived_cl140480, plain,
% 284.90/41.33 ((((b) != (b))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((multiply @ a @ (multiply @ a @ (multiply @ a @ a))) != (identity))
% 284.90/41.33 | ((multiply @ a @ (multiply @ a @ a)) != (c))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('sup-', [status(thm)],
% 284.90/41.33 [zip_derived_cl14192, zip_derived_cl139223])).
% 284.90/41.33 thf(zip_derived_cl140501, plain,
% 284.90/41.33 ((((multiply @ a @ (multiply @ a @ a)) != (c))
% 284.90/41.33 | ((multiply @ a @ (multiply @ a @ (multiply @ a @ a))) != (identity))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ b) = (c)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl140480])).
% 284.90/41.33 thf(zip_derived_cl140570, plain,
% 284.90/41.33 ((((multiply @ a @ (inverse @ b)) != (c))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((multiply @ a @ (multiply @ a @ (multiply @ a @ a))) != (identity)))),
% 284.90/41.33 inference('sup-', [status(thm)],
% 284.90/41.33 [zip_derived_cl138357, zip_derived_cl140501])).
% 284.90/41.33 thf(zip_derived_cl140645, plain,
% 284.90/41.33 ((((multiply @ a @ (multiply @ a @ (multiply @ a @ a))) != (identity))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((multiply @ a @ (inverse @ b)) != (c)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl140570])).
% 284.90/41.33 thf(zip_derived_cl140738, plain,
% 284.90/41.33 ((((multiply @ a @ b) != (c))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((multiply @ a @ (multiply @ a @ (multiply @ a @ a))) != (identity)))),
% 284.90/41.33 inference('sup-', [status(thm)],
% 284.90/41.33 [zip_derived_cl14192, zip_derived_cl140645])).
% 284.90/41.33 thf(zip_derived_cl140812, plain,
% 284.90/41.33 ((((multiply @ a @ (multiply @ a @ (multiply @ a @ a))) != (identity))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((multiply @ a @ b) != (c)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl140738])).
% 284.90/41.33 thf(zip_derived_cl140863, plain,
% 284.90/41.33 ((((c) != (c))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((multiply @ a @ (multiply @ a @ (multiply @ a @ a))) != (identity)))),
% 284.90/41.33 inference('sup-', [status(thm)],
% 284.90/41.33 [zip_derived_cl138348, zip_derived_cl140812])).
% 284.90/41.33 thf(zip_derived_cl140907, plain,
% 284.90/41.33 ((((multiply @ a @ (multiply @ a @ (multiply @ a @ a))) != (identity))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl140863])).
% 284.90/41.33 thf(zip_derived_cl141019, plain,
% 284.90/41.33 ((((multiply @ a @ (multiply @ a @ (inverse @ b))) != (identity))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ b) = (c)))),
% 284.90/41.33 inference('sup-', [status(thm)],
% 284.90/41.33 [zip_derived_cl138357, zip_derived_cl140907])).
% 284.90/41.33 thf(zip_derived_cl141133, plain,
% 284.90/41.33 ((((inverse @ b) = (c))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((multiply @ a @ (multiply @ a @ (inverse @ b))) != (identity)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl141019])).
% 284.90/41.33 thf(zip_derived_cl141270, plain,
% 284.90/41.33 ((((multiply @ a @ (multiply @ a @ b)) != (identity))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ b) = (c)))),
% 284.90/41.33 inference('sup-', [status(thm)],
% 284.90/41.33 [zip_derived_cl14192, zip_derived_cl141133])).
% 284.90/41.33 thf(zip_derived_cl141386, plain,
% 284.90/41.33 ((((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((multiply @ a @ (multiply @ a @ b)) != (identity)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl141270])).
% 284.90/41.33 thf(zip_derived_cl141709, plain,
% 284.90/41.33 ((((multiply @ a @ (inverse @ a)) != (identity))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b)))),
% 284.90/41.33 inference('sup-', [status(thm)],
% 284.90/41.33 [zip_derived_cl138360, zip_derived_cl141386])).
% 284.90/41.33 thf(zip_derived_cl4, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 284.90/41.33 inference('cnf', [status(esa)], [right_inverse])).
% 284.90/41.33 thf(zip_derived_cl141859, plain,
% 284.90/41.33 ((((identity) != (identity))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b))
% 284.90/41.33 | ((inverse @ b) = (c))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (b)))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl141709, zip_derived_cl4])).
% 284.90/41.33 thf(zip_derived_cl141860, plain,
% 284.90/41.33 ((((inverse @ b) = (c)) | ((inverse @ c) = (b)) | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl141859])).
% 284.90/41.33 thf(zip_derived_cl48, plain,
% 284.90/41.33 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl3])).
% 284.90/41.33 thf(zip_derived_cl141863, plain,
% 284.90/41.33 ((((b) = (inverse @ c)) | ((inverse @ c) = (c)) | ((inverse @ c) = (b)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl141860, zip_derived_cl48])).
% 284.90/41.33 thf(zip_derived_cl141932, plain,
% 284.90/41.33 ((((inverse @ c) = (c)) | ((b) = (inverse @ c)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl141863])).
% 284.90/41.33 thf(zip_derived_cl33, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((X0) = (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl29, zip_derived_cl0])).
% 284.90/41.33 thf(zip_derived_cl141969, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((X0) = (multiply @ c @ (multiply @ b @ X0))) | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl141932, zip_derived_cl33])).
% 284.90/41.33 thf(zip_derived_cl154412, plain,
% 284.90/41.33 ((((b) = (multiply @ c @ identity))
% 284.90/41.33 | ((multiply @ b @ b) = (c))
% 284.90/41.33 | ((a) = (multiply @ b @ b))
% 284.90/41.33 | ((identity) = (b))
% 284.90/41.33 | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl132844, zip_derived_cl141969])).
% 284.90/41.33 thf(zip_derived_cl3, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 284.90/41.33 inference('cnf', [status(esa)], [right_identity])).
% 284.90/41.33 thf(zip_derived_cl154481, plain,
% 284.90/41.33 ((((b) = (c))
% 284.90/41.33 | ((multiply @ b @ b) = (c))
% 284.90/41.33 | ((a) = (multiply @ b @ b))
% 284.90/41.33 | ((identity) = (b))
% 284.90/41.33 | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl154412, zip_derived_cl3])).
% 284.90/41.33 thf(zip_derived_cl10, plain, (((b) != (identity))),
% 284.90/41.33 inference('cnf', [status(esa)], [b_not_identity])).
% 284.90/41.33 thf(zip_derived_cl9, plain, (((b) != (c))),
% 284.90/41.33 inference('cnf', [status(esa)], [b_not_c])).
% 284.90/41.33 thf(zip_derived_cl154482, plain,
% 284.90/41.33 ((((multiply @ b @ b) = (c))
% 284.90/41.33 | ((a) = (multiply @ b @ b))
% 284.90/41.33 | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('simplify_reflect-', [status(thm)],
% 284.90/41.33 [zip_derived_cl154481, zip_derived_cl10, zip_derived_cl9])).
% 284.90/41.33 thf(zip_derived_cl141969, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((X0) = (multiply @ c @ (multiply @ b @ X0))) | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl141932, zip_derived_cl33])).
% 284.90/41.33 thf(zip_derived_cl158098, plain,
% 284.90/41.33 ((((b) = (multiply @ c @ a))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((multiply @ b @ b) = (c))
% 284.90/41.33 | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl154482, zip_derived_cl141969])).
% 284.90/41.33 thf(zip_derived_cl158358, plain,
% 284.90/41.33 ((((multiply @ b @ b) = (c))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((b) = (multiply @ c @ a)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl158098])).
% 284.90/41.33 thf(zip_derived_cl141932, plain,
% 284.90/41.33 ((((inverse @ c) = (c)) | ((b) = (inverse @ c)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl141863])).
% 284.90/41.33 thf(zip_derived_cl48, plain,
% 284.90/41.33 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl3])).
% 284.90/41.33 thf(zip_derived_cl5794, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl5765, zip_derived_cl48])).
% 284.90/41.33 thf(zip_derived_cl14370, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((multiply @ (multiply @ X1 @ (inverse @ X0)) @ X0) = (X1))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl48, zip_derived_cl5794])).
% 284.90/41.33 thf(zip_derived_cl141967, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((multiply @ (multiply @ X0 @ b) @ c) = (X0)) | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl141932, zip_derived_cl14370])).
% 284.90/41.33 thf(zip_derived_cl158576, plain,
% 284.90/41.33 ((((multiply @ c @ c) = (b))
% 284.90/41.33 | ((b) = (multiply @ c @ a))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl158358, zip_derived_cl141967])).
% 284.90/41.33 thf(zip_derived_cl158836, plain,
% 284.90/41.33 ((((inverse @ c) = (c))
% 284.90/41.33 | ((b) = (multiply @ c @ a))
% 284.90/41.33 | ((multiply @ c @ c) = (b)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl158576])).
% 284.90/41.33 thf(zip_derived_cl152873, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((identity) = (X0))
% 284.90/41.33 | ((b) = (multiply @ X0 @ c))
% 284.90/41.33 | ((multiply @ X0 @ c) = (identity))
% 284.90/41.33 | ((a) = (multiply @ X0 @ c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl131227, zip_derived_cl5794])).
% 284.90/41.33 thf(zip_derived_cl19001, plain,
% 284.90/41.33 (![X1 : $i, X2 : $i]:
% 284.90/41.33 ((inverse @ X1) = (multiply @ (inverse @ (multiply @ X2 @ X1)) @ X2))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl439, zip_derived_cl195])).
% 284.90/41.33 thf(zip_derived_cl153634, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((inverse @ c) = (multiply @ (inverse @ identity) @ X0))
% 284.90/41.33 | ((a) = (multiply @ X0 @ c))
% 284.90/41.33 | ((b) = (multiply @ X0 @ c))
% 284.90/41.33 | ((identity) = (X0)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl152873, zip_derived_cl19001])).
% 284.90/41.33 thf(zip_derived_cl16, plain, (((inverse @ identity) = (identity))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 284.90/41.33 thf(zip_derived_cl0, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 284.90/41.33 inference('cnf', [status(esa)], [left_identity])).
% 284.90/41.33 thf(zip_derived_cl153859, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((inverse @ c) = (X0))
% 284.90/41.33 | ((a) = (multiply @ X0 @ c))
% 284.90/41.33 | ((b) = (multiply @ X0 @ c))
% 284.90/41.33 | ((identity) = (X0)))),
% 284.90/41.33 inference('demod', [status(thm)],
% 284.90/41.33 [zip_derived_cl153634, zip_derived_cl16, zip_derived_cl0])).
% 284.90/41.33 thf(zip_derived_cl158836, plain,
% 284.90/41.33 ((((inverse @ c) = (c))
% 284.90/41.33 | ((b) = (multiply @ c @ a))
% 284.90/41.33 | ((multiply @ c @ c) = (b)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl158576])).
% 284.90/41.33 thf(zip_derived_cl153859, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((inverse @ c) = (X0))
% 284.90/41.33 | ((a) = (multiply @ X0 @ c))
% 284.90/41.33 | ((b) = (multiply @ X0 @ c))
% 284.90/41.33 | ((identity) = (X0)))),
% 284.90/41.33 inference('demod', [status(thm)],
% 284.90/41.33 [zip_derived_cl153634, zip_derived_cl16, zip_derived_cl0])).
% 284.90/41.33 thf(zip_derived_cl153859, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((inverse @ c) = (X0))
% 284.90/41.33 | ((a) = (multiply @ X0 @ c))
% 284.90/41.33 | ((b) = (multiply @ X0 @ c))
% 284.90/41.33 | ((identity) = (X0)))),
% 284.90/41.33 inference('demod', [status(thm)],
% 284.90/41.33 [zip_derived_cl153634, zip_derived_cl16, zip_derived_cl0])).
% 284.90/41.33 thf(condition_c, conjecture,
% 284.90/41.33 (~( ( ( multiply @ c @ ( multiply @ c @ ( multiply @ c @ c ) ) ) !=
% 284.90/41.33 ( identity ) ) |
% 284.90/41.33 ( ( multiply @ c @ ( multiply @ c @ c ) ) != ( b ) ) |
% 284.90/41.33 ( ( multiply @ c @ c ) != ( a ) ) ))).
% 284.90/41.33 thf(zf_stmt_3, negated_conjecture,
% 284.90/41.33 (( ( multiply @ c @ ( multiply @ c @ ( multiply @ c @ c ) ) ) !=
% 284.90/41.33 ( identity ) ) |
% 284.90/41.33 ( ( multiply @ c @ ( multiply @ c @ c ) ) != ( b ) ) |
% 284.90/41.33 ( ( multiply @ c @ c ) != ( a ) )),
% 284.90/41.33 inference('cnf.neg', [status(esa)], [condition_c])).
% 284.90/41.33 thf(zip_derived_cl15, plain,
% 284.90/41.33 ((((multiply @ c @ (multiply @ c @ (multiply @ c @ c))) != (identity))
% 284.90/41.33 | ((multiply @ c @ (multiply @ c @ c)) != (b))
% 284.90/41.33 | ((multiply @ c @ c) != (a)))),
% 284.90/41.33 inference('cnf', [status(esa)], [zf_stmt_3])).
% 284.90/41.33 thf(zip_derived_cl363952, plain,
% 284.90/41.33 ((((a) != (a))
% 284.90/41.33 | ((identity) = (c))
% 284.90/41.33 | ((b) = (multiply @ c @ c))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((multiply @ c @ (multiply @ c @ c)) != (b))
% 284.90/41.33 | ((multiply @ c @ (multiply @ c @ (multiply @ c @ c))) != (identity)))),
% 284.90/41.33 inference('sup-', [status(thm)], [zip_derived_cl153859, zip_derived_cl15])).
% 284.90/41.33 thf(zip_derived_cl364258, plain,
% 284.90/41.33 ((((multiply @ c @ (multiply @ c @ (multiply @ c @ c))) != (identity))
% 284.90/41.33 | ((multiply @ c @ (multiply @ c @ c)) != (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((b) = (multiply @ c @ c))
% 284.90/41.33 | ((identity) = (c)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl363952])).
% 284.90/41.33 thf(zip_derived_cl11, plain, (((c) != (identity))),
% 284.90/41.33 inference('cnf', [status(esa)], [c_not_identity])).
% 284.90/41.33 thf(zip_derived_cl364259, plain,
% 284.90/41.33 ((((multiply @ c @ (multiply @ c @ (multiply @ c @ c))) != (identity))
% 284.90/41.33 | ((multiply @ c @ (multiply @ c @ c)) != (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((b) = (multiply @ c @ c)))),
% 284.90/41.33 inference('simplify_reflect-', [status(thm)],
% 284.90/41.33 [zip_derived_cl364258, zip_derived_cl11])).
% 284.90/41.33 thf(zip_derived_cl365037, plain,
% 284.90/41.33 ((((multiply @ c @ a) != (b))
% 284.90/41.33 | ((identity) = (c))
% 284.90/41.33 | ((b) = (multiply @ c @ c))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((b) = (multiply @ c @ c))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((multiply @ c @ (multiply @ c @ (multiply @ c @ c))) != (identity)))),
% 284.90/41.33 inference('sup-', [status(thm)],
% 284.90/41.33 [zip_derived_cl153859, zip_derived_cl364259])).
% 284.90/41.33 thf(zip_derived_cl365258, plain,
% 284.90/41.33 ((((multiply @ c @ (multiply @ c @ (multiply @ c @ c))) != (identity))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((b) = (multiply @ c @ c))
% 284.90/41.33 | ((identity) = (c))
% 284.90/41.33 | ((multiply @ c @ a) != (b)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl365037])).
% 284.90/41.33 thf(zip_derived_cl11, plain, (((c) != (identity))),
% 284.90/41.33 inference('cnf', [status(esa)], [c_not_identity])).
% 284.90/41.33 thf(zip_derived_cl365259, plain,
% 284.90/41.33 ((((multiply @ c @ (multiply @ c @ (multiply @ c @ c))) != (identity))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((b) = (multiply @ c @ c))
% 284.90/41.33 | ((multiply @ c @ a) != (b)))),
% 284.90/41.33 inference('simplify_reflect-', [status(thm)],
% 284.90/41.33 [zip_derived_cl365258, zip_derived_cl11])).
% 284.90/41.33 thf(zip_derived_cl365437, plain,
% 284.90/41.33 ((((b) != (b))
% 284.90/41.33 | ((multiply @ c @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((b) = (multiply @ c @ c))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((multiply @ c @ (multiply @ c @ (multiply @ c @ c))) != (identity)))),
% 284.90/41.33 inference('sup-', [status(thm)],
% 284.90/41.33 [zip_derived_cl158836, zip_derived_cl365259])).
% 284.90/41.33 thf(zip_derived_cl365547, plain,
% 284.90/41.33 ((((multiply @ c @ (multiply @ c @ (multiply @ c @ c))) != (identity))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((multiply @ c @ c) = (b)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl365437])).
% 284.90/41.33 thf(zip_derived_cl365795, plain,
% 284.90/41.33 ((((multiply @ c @ (multiply @ c @ a)) != (identity))
% 284.90/41.33 | ((identity) = (c))
% 284.90/41.33 | ((b) = (multiply @ c @ c))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((multiply @ c @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('sup-', [status(thm)],
% 284.90/41.33 [zip_derived_cl153859, zip_derived_cl365547])).
% 284.90/41.33 thf(zip_derived_cl366114, plain,
% 284.90/41.33 ((((inverse @ c) = (c))
% 284.90/41.33 | ((b) = (multiply @ c @ c))
% 284.90/41.33 | ((identity) = (c))
% 284.90/41.33 | ((multiply @ c @ (multiply @ c @ a)) != (identity)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl365795])).
% 284.90/41.33 thf(zip_derived_cl11, plain, (((c) != (identity))),
% 284.90/41.33 inference('cnf', [status(esa)], [c_not_identity])).
% 284.90/41.33 thf(zip_derived_cl366115, plain,
% 284.90/41.33 ((((inverse @ c) = (c))
% 284.90/41.33 | ((b) = (multiply @ c @ c))
% 284.90/41.33 | ((multiply @ c @ (multiply @ c @ a)) != (identity)))),
% 284.90/41.33 inference('simplify_reflect-', [status(thm)],
% 284.90/41.33 [zip_derived_cl366114, zip_derived_cl11])).
% 284.90/41.33 thf(zip_derived_cl366389, plain,
% 284.90/41.33 ((((multiply @ c @ b) != (identity))
% 284.90/41.33 | ((multiply @ c @ c) = (b))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((b) = (multiply @ c @ c))
% 284.90/41.33 | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('sup-', [status(thm)],
% 284.90/41.33 [zip_derived_cl158836, zip_derived_cl366115])).
% 284.90/41.33 thf(zip_derived_cl366598, plain,
% 284.90/41.33 ((((inverse @ c) = (c))
% 284.90/41.33 | ((multiply @ c @ c) = (b))
% 284.90/41.33 | ((multiply @ c @ b) != (identity)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl366389])).
% 284.90/41.33 thf(zip_derived_cl141932, plain,
% 284.90/41.33 ((((inverse @ c) = (c)) | ((b) = (inverse @ c)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl141863])).
% 284.90/41.33 thf(zip_derived_cl4, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 284.90/41.33 inference('cnf', [status(esa)], [right_inverse])).
% 284.90/41.33 thf(zip_derived_cl141951, plain,
% 284.90/41.33 ((((multiply @ c @ b) = (identity)) | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl141932, zip_derived_cl4])).
% 284.90/41.33 thf(zip_derived_cl366731, plain,
% 284.90/41.33 ((((multiply @ c @ c) = (b)) | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('clc', [status(thm)],
% 284.90/41.33 [zip_derived_cl366598, zip_derived_cl141951])).
% 284.90/41.33 thf(zip_derived_cl5794, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl5765, zip_derived_cl48])).
% 284.90/41.33 thf(zip_derived_cl366764, plain,
% 284.90/41.33 ((((multiply @ b @ (inverse @ c)) = (c)) | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl366731, zip_derived_cl5794])).
% 284.90/41.33 thf(zip_derived_cl132844, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((identity) = (X0))
% 284.90/41.33 | ((a) = (multiply @ X0 @ b))
% 284.90/41.33 | ((multiply @ X0 @ b) = (c))
% 284.90/41.33 | ((multiply @ X0 @ b) = (identity)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl130801, zip_derived_cl5794])).
% 284.90/41.33 thf(zip_derived_cl38, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 284.90/41.33 ((X0)
% 284.90/41.33 = (multiply @ (inverse @ (multiply @ X2 @ X1)) @
% 284.90/41.33 (multiply @ X2 @ (multiply @ X1 @ X0))))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl27])).
% 284.90/41.33 thf(zip_derived_cl134452, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 (((b)
% 284.90/41.33 = (multiply @ (inverse @ (multiply @ X1 @ X0)) @
% 284.90/41.33 (multiply @ X1 @ identity)))
% 284.90/41.33 | ((multiply @ X0 @ b) = (c))
% 284.90/41.33 | ((a) = (multiply @ X0 @ b))
% 284.90/41.33 | ((identity) = (X0)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl132844, zip_derived_cl38])).
% 284.90/41.33 thf(zip_derived_cl3, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 284.90/41.33 inference('cnf', [status(esa)], [right_identity])).
% 284.90/41.33 thf(zip_derived_cl19001, plain,
% 284.90/41.33 (![X1 : $i, X2 : $i]:
% 284.90/41.33 ((inverse @ X1) = (multiply @ (inverse @ (multiply @ X2 @ X1)) @ X2))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl439, zip_derived_cl195])).
% 284.90/41.33 thf(zip_derived_cl134773, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((b) = (inverse @ X0))
% 284.90/41.33 | ((multiply @ X0 @ b) = (c))
% 284.90/41.33 | ((a) = (multiply @ X0 @ b))
% 284.90/41.33 | ((identity) = (X0)))),
% 284.90/41.33 inference('demod', [status(thm)],
% 284.90/41.33 [zip_derived_cl134452, zip_derived_cl3, zip_derived_cl19001])).
% 284.90/41.33 thf(zip_derived_cl11885, plain,
% 284.90/41.33 ((((inverse @ a) = (a)) | ((inverse @ a) = (b)) | ((inverse @ a) = (c)))),
% 284.90/41.33 inference('eq_res', [status(thm)], [zip_derived_cl530])).
% 284.90/41.33 thf(zip_derived_cl27, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 284.90/41.33 thf(zip_derived_cl11907, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((X0) = (multiply @ a @ (multiply @ a @ X0)))
% 284.90/41.33 | ((inverse @ a) = (c))
% 284.90/41.33 | ((inverse @ a) = (b)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl11885, zip_derived_cl27])).
% 284.90/41.33 thf(zip_derived_cl266208, plain,
% 284.90/41.33 ((((b) = (multiply @ a @ a))
% 284.90/41.33 | ((identity) = (a))
% 284.90/41.33 | ((multiply @ a @ b) = (c))
% 284.90/41.33 | ((b) = (inverse @ a))
% 284.90/41.33 | ((inverse @ a) = (b))
% 284.90/41.33 | ((inverse @ a) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl134773, zip_derived_cl11907])).
% 284.90/41.33 thf(zip_derived_cl266595, plain,
% 284.90/41.33 ((((inverse @ a) = (c))
% 284.90/41.33 | ((b) = (inverse @ a))
% 284.90/41.33 | ((multiply @ a @ b) = (c))
% 284.90/41.33 | ((identity) = (a))
% 284.90/41.33 | ((b) = (multiply @ a @ a)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl266208])).
% 284.90/41.33 thf(zip_derived_cl8, plain, (((a) != (identity))),
% 284.90/41.33 inference('cnf', [status(esa)], [a_not_identity])).
% 284.90/41.33 thf(zip_derived_cl266596, plain,
% 284.90/41.33 ((((inverse @ a) = (c))
% 284.90/41.33 | ((b) = (inverse @ a))
% 284.90/41.33 | ((multiply @ a @ b) = (c))
% 284.90/41.33 | ((b) = (multiply @ a @ a)))),
% 284.90/41.33 inference('simplify_reflect-', [status(thm)],
% 284.90/41.33 [zip_derived_cl266595, zip_derived_cl8])).
% 284.90/41.33 thf(zip_derived_cl11898, plain,
% 284.90/41.33 ((((multiply @ a @ a) = (identity))
% 284.90/41.33 | ((inverse @ a) = (c))
% 284.90/41.33 | ((inverse @ a) = (b)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl11885, zip_derived_cl1])).
% 284.90/41.33 thf(zip_derived_cl295608, plain,
% 284.90/41.33 ((((b) = (identity))
% 284.90/41.33 | ((multiply @ a @ b) = (c))
% 284.90/41.33 | ((b) = (inverse @ a))
% 284.90/41.33 | ((inverse @ a) = (c))
% 284.90/41.33 | ((inverse @ a) = (b))
% 284.90/41.33 | ((inverse @ a) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl266596, zip_derived_cl11898])).
% 284.90/41.33 thf(zip_derived_cl295861, plain,
% 284.90/41.33 ((((inverse @ a) = (c))
% 284.90/41.33 | ((b) = (inverse @ a))
% 284.90/41.33 | ((multiply @ a @ b) = (c))
% 284.90/41.33 | ((b) = (identity)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl295608])).
% 284.90/41.33 thf(zip_derived_cl10, plain, (((b) != (identity))),
% 284.90/41.33 inference('cnf', [status(esa)], [b_not_identity])).
% 284.90/41.33 thf(zip_derived_cl295862, plain,
% 284.90/41.33 ((((inverse @ a) = (c))
% 284.90/41.33 | ((b) = (inverse @ a))
% 284.90/41.33 | ((multiply @ a @ b) = (c)))),
% 284.90/41.33 inference('simplify_reflect-', [status(thm)],
% 284.90/41.33 [zip_derived_cl295861, zip_derived_cl10])).
% 284.90/41.33 thf(zip_derived_cl11907, plain,
% 284.90/41.33 (![X0 : $i]:
% 284.90/41.33 (((X0) = (multiply @ a @ (multiply @ a @ X0)))
% 284.90/41.33 | ((inverse @ a) = (c))
% 284.90/41.33 | ((inverse @ a) = (b)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl11885, zip_derived_cl27])).
% 284.90/41.33 thf(zip_derived_cl295947, plain,
% 284.90/41.33 ((((b) = (multiply @ a @ c))
% 284.90/41.33 | ((b) = (inverse @ a))
% 284.90/41.33 | ((inverse @ a) = (c))
% 284.90/41.33 | ((inverse @ a) = (b))
% 284.90/41.33 | ((inverse @ a) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl295862, zip_derived_cl11907])).
% 284.90/41.33 thf(zip_derived_cl296142, plain,
% 284.90/41.33 ((((inverse @ a) = (c))
% 284.90/41.33 | ((b) = (inverse @ a))
% 284.90/41.33 | ((b) = (multiply @ a @ c)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl295947])).
% 284.90/41.33 thf(zip_derived_cl5794, plain,
% 284.90/41.33 (![X0 : $i, X1 : $i]:
% 284.90/41.33 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 284.90/41.33 inference('demod', [status(thm)], [zip_derived_cl5765, zip_derived_cl48])).
% 284.90/41.33 thf(zip_derived_cl296189, plain,
% 284.90/41.33 ((((multiply @ b @ (inverse @ c)) = (a))
% 284.90/41.33 | ((b) = (inverse @ a))
% 284.90/41.33 | ((inverse @ a) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl296142, zip_derived_cl5794])).
% 284.90/41.33 thf(zip_derived_cl383157, plain,
% 284.90/41.33 ((((c) = (a))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((inverse @ a) = (c))
% 284.90/41.33 | ((b) = (inverse @ a)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl366764, zip_derived_cl296189])).
% 284.90/41.33 thf(a_not_c, axiom, (( a ) != ( c ))).
% 284.90/41.33 thf(zip_derived_cl7, plain, (((a) != (c))),
% 284.90/41.33 inference('cnf', [status(esa)], [a_not_c])).
% 284.90/41.33 thf(zip_derived_cl383455, plain,
% 284.90/41.33 ((((inverse @ c) = (c)) | ((inverse @ a) = (c)) | ((b) = (inverse @ a)))),
% 284.90/41.33 inference('simplify_reflect-', [status(thm)],
% 284.90/41.33 [zip_derived_cl383157, zip_derived_cl7])).
% 284.90/41.33 thf(zip_derived_cl48, plain,
% 284.90/41.33 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl3])).
% 284.90/41.33 thf(zip_derived_cl396123, plain,
% 284.90/41.33 ((((a) = (inverse @ b)) | ((inverse @ a) = (c)) | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl383455, zip_derived_cl48])).
% 284.90/41.33 thf(zip_derived_cl48, plain,
% 284.90/41.33 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl3])).
% 284.90/41.33 thf(zip_derived_cl397633, plain,
% 284.90/41.33 ((((a) = (inverse @ c)) | ((inverse @ c) = (c)) | ((a) = (inverse @ b)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl396123, zip_derived_cl48])).
% 284.90/41.33 thf(zip_derived_cl141932, plain,
% 284.90/41.33 ((((inverse @ c) = (c)) | ((b) = (inverse @ c)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl141863])).
% 284.90/41.33 thf(zip_derived_cl48, plain,
% 284.90/41.33 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl3])).
% 284.90/41.33 thf(zip_derived_cl141952, plain,
% 284.90/41.33 ((((c) = (inverse @ b)) | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl141932, zip_derived_cl48])).
% 284.90/41.33 thf(zip_derived_cl397792, plain,
% 284.90/41.33 ((((c) = (a))
% 284.90/41.33 | ((inverse @ c) = (c))
% 284.90/41.33 | ((a) = (inverse @ c))
% 284.90/41.33 | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl397633, zip_derived_cl141952])).
% 284.90/41.33 thf(zip_derived_cl397879, plain,
% 284.90/41.33 ((((a) = (inverse @ c)) | ((inverse @ c) = (c)) | ((c) = (a)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl397792])).
% 284.90/41.33 thf(zip_derived_cl7, plain, (((a) != (c))),
% 284.90/41.33 inference('cnf', [status(esa)], [a_not_c])).
% 284.90/41.33 thf(zip_derived_cl397880, plain,
% 284.90/41.33 ((((a) = (inverse @ c)) | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('simplify_reflect-', [status(thm)],
% 284.90/41.33 [zip_derived_cl397879, zip_derived_cl7])).
% 284.90/41.33 thf(zip_derived_cl141932, plain,
% 284.90/41.33 ((((inverse @ c) = (c)) | ((b) = (inverse @ c)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl141863])).
% 284.90/41.33 thf(zip_derived_cl397919, plain,
% 284.90/41.33 ((((b) = (a)) | ((inverse @ c) = (c)) | ((inverse @ c) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl397880, zip_derived_cl141932])).
% 284.90/41.33 thf(zip_derived_cl398008, plain, ((((inverse @ c) = (c)) | ((b) = (a)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl397919])).
% 284.90/41.33 thf(zip_derived_cl6, plain, (((a) != (b))),
% 284.90/41.33 inference('cnf', [status(esa)], [a_not_b])).
% 284.90/41.33 thf(zip_derived_cl398009, plain, (((inverse @ c) = (c))),
% 284.90/41.33 inference('simplify_reflect-', [status(thm)],
% 284.90/41.33 [zip_derived_cl398008, zip_derived_cl6])).
% 284.90/41.33 thf(zip_derived_cl1, plain,
% 284.90/41.33 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 284.90/41.33 inference('cnf', [status(esa)], [left_inverse])).
% 284.90/41.33 thf(zip_derived_cl398027, plain, (((multiply @ c @ c) = (identity))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl398009, zip_derived_cl1])).
% 284.90/41.33 thf(zip_derived_cl398126, plain,
% 284.90/41.33 ((((identity) != (identity))
% 284.90/41.33 | ((multiply @ b @ b) != (identity))
% 284.90/41.33 | ((multiply @ a @ a) != (identity)))),
% 284.90/41.33 inference('demod', [status(thm)],
% 284.90/41.33 [zip_derived_cl12, zip_derived_cl398027])).
% 284.90/41.33 thf(zip_derived_cl398127, plain,
% 284.90/41.33 ((((multiply @ a @ a) != (identity)) | ((multiply @ b @ b) != (identity)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl398126])).
% 284.90/41.33 thf(zip_derived_cl399079, plain,
% 284.90/41.33 ((((identity) != (identity))
% 284.90/41.33 | ((inverse @ a) = (b))
% 284.90/41.33 | ((inverse @ a) = (c))
% 284.90/41.33 | ((multiply @ b @ b) != (identity)))),
% 284.90/41.33 inference('sup-', [status(thm)],
% 284.90/41.33 [zip_derived_cl11898, zip_derived_cl398127])).
% 284.90/41.33 thf(zip_derived_cl399214, plain,
% 284.90/41.33 ((((multiply @ b @ b) != (identity))
% 284.90/41.33 | ((inverse @ a) = (c))
% 284.90/41.33 | ((inverse @ a) = (b)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl399079])).
% 284.90/41.33 thf(zip_derived_cl399370, plain,
% 284.90/41.33 ((((identity) != (identity))
% 284.90/41.33 | ((c) = (inverse @ b))
% 284.90/41.33 | ((inverse @ a) = (b))
% 284.90/41.33 | ((inverse @ a) = (c)))),
% 284.90/41.33 inference('sup-', [status(thm)],
% 284.90/41.33 [zip_derived_cl388014, zip_derived_cl399214])).
% 284.90/41.33 thf(zip_derived_cl399501, plain,
% 284.90/41.33 ((((inverse @ a) = (c)) | ((inverse @ a) = (b)) | ((c) = (inverse @ b)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl399370])).
% 284.90/41.33 thf(zip_derived_cl48, plain,
% 284.90/41.33 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl3])).
% 284.90/41.33 thf(zip_derived_cl404730, plain,
% 284.90/41.33 ((((a) = (inverse @ b)) | ((c) = (inverse @ b)) | ((inverse @ a) = (c)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl399501, zip_derived_cl48])).
% 284.90/41.33 thf(zip_derived_cl48, plain,
% 284.90/41.33 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl3])).
% 284.90/41.33 thf(zip_derived_cl404895, plain,
% 284.90/41.33 ((((a) = (inverse @ c)) | ((c) = (inverse @ b)) | ((a) = (inverse @ b)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl404730, zip_derived_cl48])).
% 284.90/41.33 thf(zip_derived_cl398009, plain, (((inverse @ c) = (c))),
% 284.90/41.33 inference('simplify_reflect-', [status(thm)],
% 284.90/41.33 [zip_derived_cl398008, zip_derived_cl6])).
% 284.90/41.33 thf(zip_derived_cl404995, plain,
% 284.90/41.33 ((((a) = (c)) | ((c) = (inverse @ b)) | ((a) = (inverse @ b)))),
% 284.90/41.33 inference('demod', [status(thm)],
% 284.90/41.33 [zip_derived_cl404895, zip_derived_cl398009])).
% 284.90/41.33 thf(zip_derived_cl7, plain, (((a) != (c))),
% 284.90/41.33 inference('cnf', [status(esa)], [a_not_c])).
% 284.90/41.33 thf(zip_derived_cl404996, plain,
% 284.90/41.33 ((((c) = (inverse @ b)) | ((a) = (inverse @ b)))),
% 284.90/41.33 inference('simplify_reflect-', [status(thm)],
% 284.90/41.33 [zip_derived_cl404995, zip_derived_cl7])).
% 284.90/41.33 thf(zip_derived_cl388013, plain,
% 284.90/41.33 ((((c) = (inverse @ b)) | ((inverse @ b) = (b)))),
% 284.90/41.33 inference('clc', [status(thm)],
% 284.90/41.33 [zip_derived_cl387886, zip_derived_cl12584])).
% 284.90/41.33 thf(zip_derived_cl405047, plain,
% 284.90/41.33 ((((a) = (b)) | ((c) = (inverse @ b)) | ((c) = (inverse @ b)))),
% 284.90/41.33 inference('sup+', [status(thm)],
% 284.90/41.33 [zip_derived_cl404996, zip_derived_cl388013])).
% 284.90/41.33 thf(zip_derived_cl405122, plain, ((((c) = (inverse @ b)) | ((a) = (b)))),
% 284.90/41.33 inference('simplify', [status(thm)], [zip_derived_cl405047])).
% 284.90/41.33 thf(zip_derived_cl6, plain, (((a) != (b))),
% 284.90/41.33 inference('cnf', [status(esa)], [a_not_b])).
% 284.90/41.33 thf(zip_derived_cl405123, plain, (((c) = (inverse @ b))),
% 284.90/41.33 inference('simplify_reflect-', [status(thm)],
% 284.90/41.33 [zip_derived_cl405122, zip_derived_cl6])).
% 284.90/41.33 thf(zip_derived_cl48, plain,
% 284.90/41.33 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl3])).
% 284.90/41.33 thf(zip_derived_cl405139, plain, (((b) = (inverse @ c))),
% 284.90/41.33 inference('sup+', [status(thm)], [zip_derived_cl405123, zip_derived_cl48])).
% 284.90/41.33 thf(zip_derived_cl398009, plain, (((inverse @ c) = (c))),
% 284.90/41.33 inference('simplify_reflect-', [status(thm)],
% 284.90/41.33 [zip_derived_cl398008, zip_derived_cl6])).
% 284.90/41.33 thf(zip_derived_cl405221, plain, (((b) = (c))),
% 284.90/41.33 inference('demod', [status(thm)],
% 284.90/41.33 [zip_derived_cl405139, zip_derived_cl398009])).
% 284.90/41.33 thf(zip_derived_cl9, plain, (((b) != (c))),
% 284.90/41.33 inference('cnf', [status(esa)], [b_not_c])).
% 284.90/41.33 thf(zip_derived_cl405222, plain, ($false),
% 284.90/41.33 inference('simplify_reflect-', [status(thm)],
% 284.90/41.33 [zip_derived_cl405221, zip_derived_cl9])).
% 284.90/41.33
% 284.90/41.33 % SZS output end Refutation
% 284.90/41.33
% 284.90/41.33
% 284.90/41.34 % Terminating...
% 285.27/41.39 % Runner terminated.
% 285.27/41.40 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------