TSTP Solution File: GRP103-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP103-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.UsvNJlcxZZ true
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:49:56 EDT 2023
% Result : Unsatisfiable 6.17s 1.49s
% Output : Refutation 6.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP103-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.07/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.UsvNJlcxZZ true
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 02:34:26 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.56/0.65 % Total configuration time : 435
% 0.56/0.65 % Estimated wc time : 1092
% 0.56/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.56/0.69 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.56/0.71 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.56/0.72 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.56/0.74 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.56/0.74 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.56/0.74 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.56/0.74 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 6.17/1.49 % Solved by fo/fo5.sh.
% 6.17/1.49 % done 859 iterations in 0.730s
% 6.17/1.49 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 6.17/1.49 % SZS output start Refutation
% 6.17/1.49 thf(a3_type, type, a3: $i).
% 6.17/1.49 thf(multiply_type, type, multiply: $i > $i > $i).
% 6.17/1.49 thf(identity_type, type, identity: $i).
% 6.17/1.49 thf(c3_type, type, c3: $i).
% 6.17/1.49 thf(a2_type, type, a2: $i).
% 6.17/1.49 thf(a1_type, type, a1: $i).
% 6.17/1.49 thf(double_divide_type, type, double_divide: $i > $i > $i).
% 6.17/1.49 thf(inverse_type, type, inverse: $i > $i).
% 6.17/1.49 thf(b4_type, type, b4: $i).
% 6.17/1.49 thf(a4_type, type, a4: $i).
% 6.17/1.49 thf(b3_type, type, b3: $i).
% 6.17/1.49 thf(prove_these_axioms, conjecture,
% 6.17/1.49 (~( ( ( multiply @ a4 @ b4 ) != ( multiply @ b4 @ a4 ) ) |
% 6.17/1.49 ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 6.17/1.49 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) |
% 6.17/1.49 ( ( multiply @ identity @ a2 ) != ( a2 ) ) |
% 6.17/1.49 ( ( multiply @ ( inverse @ a1 ) @ a1 ) != ( identity ) ) ))).
% 6.17/1.49 thf(zf_stmt_0, negated_conjecture,
% 6.17/1.49 (( ( multiply @ a4 @ b4 ) != ( multiply @ b4 @ a4 ) ) |
% 6.17/1.49 ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 6.17/1.49 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) |
% 6.17/1.49 ( ( multiply @ identity @ a2 ) != ( a2 ) ) |
% 6.17/1.49 ( ( multiply @ ( inverse @ a1 ) @ a1 ) != ( identity ) )),
% 6.17/1.49 inference('cnf.neg', [status(esa)], [prove_these_axioms])).
% 6.17/1.49 thf(zip_derived_cl4, plain,
% 6.17/1.49 ((((multiply @ a4 @ b4) != (multiply @ b4 @ a4))
% 6.17/1.49 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 6.17/1.49 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 6.17/1.49 | ((multiply @ identity @ a2) != (a2))
% 6.17/1.49 | ((multiply @ (inverse @ a1) @ a1) != (identity)))),
% 6.17/1.49 inference('cnf', [status(esa)], [zf_stmt_0])).
% 6.17/1.49 thf(inverse, axiom, (( inverse @ X ) = ( double_divide @ X @ identity ))).
% 6.17/1.49 thf(zip_derived_cl2, plain,
% 6.17/1.49 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 6.17/1.49 inference('cnf', [status(esa)], [inverse])).
% 6.17/1.49 thf(multiply, axiom,
% 6.17/1.49 (( multiply @ X @ Y ) =
% 6.17/1.49 ( double_divide @ ( double_divide @ Y @ X ) @ identity ))).
% 6.17/1.49 thf(zip_derived_cl1, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i]:
% 6.17/1.49 ((multiply @ X1 @ X0)
% 6.17/1.49 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 6.17/1.49 inference('cnf', [status(esa)], [multiply])).
% 6.17/1.49 thf(zip_derived_cl7, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((multiply @ identity @ X0)
% 6.17/1.49 = (double_divide @ (inverse @ X0) @ identity))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 6.17/1.49 thf(zip_derived_cl2, plain,
% 6.17/1.49 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 6.17/1.49 inference('cnf', [status(esa)], [inverse])).
% 6.17/1.49 thf(zip_derived_cl10, plain,
% 6.17/1.49 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 6.17/1.49 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 6.17/1.49 thf(zip_derived_cl24, plain,
% 6.17/1.49 ((((multiply @ a4 @ b4) != (multiply @ b4 @ a4))
% 6.17/1.49 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 6.17/1.49 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 6.17/1.49 | ((inverse @ (inverse @ a2)) != (a2))
% 6.17/1.49 | ((multiply @ (inverse @ a1) @ a1) != (identity)))),
% 6.17/1.49 inference('demod', [status(thm)], [zip_derived_cl4, zip_derived_cl10])).
% 6.17/1.49 thf(identity, axiom,
% 6.17/1.49 (( identity ) = ( double_divide @ X @ ( inverse @ X ) ))).
% 6.17/1.49 thf(zip_derived_cl3, plain,
% 6.17/1.49 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 6.17/1.49 inference('cnf', [status(esa)], [identity])).
% 6.17/1.49 thf(zip_derived_cl2, plain,
% 6.17/1.49 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 6.17/1.49 inference('cnf', [status(esa)], [inverse])).
% 6.17/1.49 thf(zip_derived_cl1, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i]:
% 6.17/1.49 ((multiply @ X1 @ X0)
% 6.17/1.49 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 6.17/1.49 inference('cnf', [status(esa)], [multiply])).
% 6.17/1.49 thf(zip_derived_cl6, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i]:
% 6.17/1.49 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 6.17/1.49 thf(zip_derived_cl27, plain,
% 6.17/1.49 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 6.17/1.49 thf(zip_derived_cl66, plain,
% 6.17/1.49 ((((multiply @ a4 @ b4) != (multiply @ b4 @ a4))
% 6.17/1.49 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 6.17/1.49 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 6.17/1.49 | ((inverse @ (inverse @ a2)) != (a2))
% 6.17/1.49 | ((inverse @ identity) != (identity)))),
% 6.17/1.49 inference('demod', [status(thm)], [zip_derived_cl24, zip_derived_cl27])).
% 6.17/1.49 thf(zip_derived_cl3, plain,
% 6.17/1.49 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 6.17/1.49 inference('cnf', [status(esa)], [identity])).
% 6.17/1.49 thf(zip_derived_cl1, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i]:
% 6.17/1.49 ((multiply @ X1 @ X0)
% 6.17/1.49 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 6.17/1.49 inference('cnf', [status(esa)], [multiply])).
% 6.17/1.49 thf(zip_derived_cl8, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((multiply @ (inverse @ X0) @ X0)
% 6.17/1.49 = (double_divide @ identity @ identity))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 6.17/1.49 thf(zip_derived_cl6, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i]:
% 6.17/1.49 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 6.17/1.49 thf(zip_derived_cl48, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((multiply @ identity @ identity)
% 6.17/1.49 = (inverse @ (multiply @ (inverse @ X0) @ X0)))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl6])).
% 6.17/1.49 thf(zip_derived_cl6, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i]:
% 6.17/1.49 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 6.17/1.49 thf(zip_derived_cl3, plain,
% 6.17/1.49 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 6.17/1.49 inference('cnf', [status(esa)], [identity])).
% 6.17/1.49 thf(zip_derived_cl25, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i]:
% 6.17/1.49 ((identity)
% 6.17/1.49 = (double_divide @ (double_divide @ X0 @ X1) @ (multiply @ X1 @ X0)))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl3])).
% 6.17/1.49 thf(zip_derived_cl112, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((identity)
% 6.17/1.49 = (double_divide @ (double_divide @ identity @ identity) @
% 6.17/1.49 (inverse @ (multiply @ (inverse @ X0) @ X0))))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl48, zip_derived_cl25])).
% 6.17/1.49 thf(zip_derived_cl2, plain,
% 6.17/1.49 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 6.17/1.49 inference('cnf', [status(esa)], [inverse])).
% 6.17/1.49 thf(zip_derived_cl125, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((identity)
% 6.17/1.49 = (double_divide @ (inverse @ identity) @
% 6.17/1.49 (inverse @ (multiply @ (inverse @ X0) @ X0))))),
% 6.17/1.49 inference('demod', [status(thm)], [zip_derived_cl112, zip_derived_cl2])).
% 6.17/1.49 thf(zip_derived_cl2, plain,
% 6.17/1.49 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 6.17/1.49 inference('cnf', [status(esa)], [inverse])).
% 6.17/1.49 thf(single_axiom, axiom,
% 6.17/1.49 (( double_divide @
% 6.17/1.49 ( double_divide @
% 6.17/1.49 X @
% 6.17/1.49 ( double_divide @
% 6.17/1.49 ( double_divide @ identity @ Y ) @
% 6.17/1.49 ( double_divide @ Z @ ( double_divide @ Y @ X ) ) ) ) @
% 6.17/1.49 ( double_divide @ identity @ identity ) ) =
% 6.17/1.49 ( Z ))).
% 6.17/1.49 thf(zip_derived_cl0, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.17/1.49 ((double_divide @
% 6.17/1.49 (double_divide @ X1 @
% 6.17/1.49 (double_divide @ (double_divide @ identity @ X2) @
% 6.17/1.49 (double_divide @ X0 @ (double_divide @ X2 @ X1)))) @
% 6.17/1.49 (double_divide @ identity @ identity)) = (X0))),
% 6.17/1.49 inference('cnf', [status(esa)], [single_axiom])).
% 6.17/1.49 thf(zip_derived_cl2, plain,
% 6.17/1.49 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 6.17/1.49 inference('cnf', [status(esa)], [inverse])).
% 6.17/1.49 thf(zip_derived_cl13, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.17/1.49 ((double_divide @
% 6.17/1.49 (double_divide @ X1 @
% 6.17/1.49 (double_divide @ (double_divide @ identity @ X2) @
% 6.17/1.49 (double_divide @ X0 @ (double_divide @ X2 @ X1)))) @
% 6.17/1.49 (inverse @ identity)) = (X0))),
% 6.17/1.49 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 6.17/1.49 thf(zip_derived_cl16, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i]:
% 6.17/1.49 ((double_divide @
% 6.17/1.49 (double_divide @ identity @
% 6.17/1.49 (double_divide @ (double_divide @ identity @ X0) @
% 6.17/1.49 (double_divide @ X1 @ (inverse @ X0)))) @
% 6.17/1.49 (inverse @ identity)) = (X1))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 6.17/1.49 thf(zip_derived_cl315, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((double_divide @
% 6.17/1.49 (double_divide @ identity @
% 6.17/1.49 (double_divide @
% 6.17/1.49 (double_divide @ identity @ (multiply @ (inverse @ X0) @ X0)) @
% 6.17/1.49 identity)) @
% 6.17/1.49 (inverse @ identity)) = (inverse @ identity))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl125, zip_derived_cl16])).
% 6.17/1.49 thf(zip_derived_cl27, plain,
% 6.17/1.49 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 6.17/1.49 thf(zip_derived_cl3, plain,
% 6.17/1.49 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 6.17/1.49 inference('cnf', [status(esa)], [identity])).
% 6.17/1.49 thf(zip_derived_cl30, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((identity)
% 6.17/1.49 = (double_divide @ identity @ (multiply @ (inverse @ X0) @ X0)))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl3])).
% 6.17/1.49 thf(zip_derived_cl2, plain,
% 6.17/1.49 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 6.17/1.49 inference('cnf', [status(esa)], [inverse])).
% 6.17/1.49 thf(zip_derived_cl3, plain,
% 6.17/1.49 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 6.17/1.49 inference('cnf', [status(esa)], [identity])).
% 6.17/1.49 thf(zip_derived_cl3, plain,
% 6.17/1.49 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 6.17/1.49 inference('cnf', [status(esa)], [identity])).
% 6.17/1.49 thf(zip_derived_cl328, plain, (((identity) = (inverse @ identity))),
% 6.17/1.49 inference('demod', [status(thm)],
% 6.17/1.49 [zip_derived_cl315, zip_derived_cl30, zip_derived_cl2,
% 6.17/1.49 zip_derived_cl3, zip_derived_cl3])).
% 6.17/1.49 thf(zip_derived_cl340, plain,
% 6.17/1.49 ((((multiply @ a4 @ b4) != (multiply @ b4 @ a4))
% 6.17/1.49 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 6.17/1.49 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 6.17/1.49 | ((inverse @ (inverse @ a2)) != (a2))
% 6.17/1.49 | ((identity) != (identity)))),
% 6.17/1.49 inference('demod', [status(thm)], [zip_derived_cl66, zip_derived_cl328])).
% 6.17/1.49 thf(zip_derived_cl341, plain,
% 6.17/1.49 ((((inverse @ (inverse @ a2)) != (a2))
% 6.17/1.49 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 6.17/1.49 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 6.17/1.49 | ((multiply @ a4 @ b4) != (multiply @ b4 @ a4)))),
% 6.17/1.49 inference('simplify', [status(thm)], [zip_derived_cl340])).
% 6.17/1.49 thf(zip_derived_cl2, plain,
% 6.17/1.49 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 6.17/1.49 inference('cnf', [status(esa)], [inverse])).
% 6.17/1.49 thf(zip_derived_cl3, plain,
% 6.17/1.49 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 6.17/1.49 inference('cnf', [status(esa)], [identity])).
% 6.17/1.49 thf(zip_derived_cl13, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.17/1.49 ((double_divide @
% 6.17/1.49 (double_divide @ X1 @
% 6.17/1.49 (double_divide @ (double_divide @ identity @ X2) @
% 6.17/1.49 (double_divide @ X0 @ (double_divide @ X2 @ X1)))) @
% 6.17/1.49 (inverse @ identity)) = (X0))),
% 6.17/1.49 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 6.17/1.49 thf(zip_derived_cl17, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i]:
% 6.17/1.49 ((double_divide @
% 6.17/1.49 (double_divide @ (inverse @ X1) @
% 6.17/1.49 (double_divide @ (double_divide @ identity @ X1) @
% 6.17/1.49 (double_divide @ X0 @ identity))) @
% 6.17/1.49 (inverse @ identity)) = (X0))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl13])).
% 6.17/1.49 thf(zip_derived_cl2, plain,
% 6.17/1.49 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 6.17/1.49 inference('cnf', [status(esa)], [inverse])).
% 6.17/1.49 thf(zip_derived_cl22, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i]:
% 6.17/1.49 ((double_divide @
% 6.17/1.49 (double_divide @ (inverse @ X1) @
% 6.17/1.49 (double_divide @ (double_divide @ identity @ X1) @ (inverse @ X0))) @
% 6.17/1.49 (inverse @ identity)) = (X0))),
% 6.17/1.49 inference('demod', [status(thm)], [zip_derived_cl17, zip_derived_cl2])).
% 6.17/1.49 thf(zip_derived_cl328, plain, (((identity) = (inverse @ identity))),
% 6.17/1.49 inference('demod', [status(thm)],
% 6.17/1.49 [zip_derived_cl315, zip_derived_cl30, zip_derived_cl2,
% 6.17/1.49 zip_derived_cl3, zip_derived_cl3])).
% 6.17/1.49 thf(zip_derived_cl1, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i]:
% 6.17/1.49 ((multiply @ X1 @ X0)
% 6.17/1.49 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 6.17/1.49 inference('cnf', [status(esa)], [multiply])).
% 6.17/1.49 thf(zip_derived_cl378, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i]:
% 6.17/1.49 ((multiply @
% 6.17/1.49 (double_divide @ (double_divide @ identity @ X1) @ (inverse @ X0)) @
% 6.17/1.49 (inverse @ X1)) = (X0))),
% 6.17/1.49 inference('demod', [status(thm)],
% 6.17/1.49 [zip_derived_cl22, zip_derived_cl328, zip_derived_cl1])).
% 6.17/1.49 thf(zip_derived_cl385, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((multiply @
% 6.17/1.49 (double_divide @ (inverse @ identity) @ (inverse @ X0)) @
% 6.17/1.49 (inverse @ identity)) = (X0))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl378])).
% 6.17/1.49 thf(zip_derived_cl328, plain, (((identity) = (inverse @ identity))),
% 6.17/1.49 inference('demod', [status(thm)],
% 6.17/1.49 [zip_derived_cl315, zip_derived_cl30, zip_derived_cl2,
% 6.17/1.49 zip_derived_cl3, zip_derived_cl3])).
% 6.17/1.49 thf(zip_derived_cl328, plain, (((identity) = (inverse @ identity))),
% 6.17/1.49 inference('demod', [status(thm)],
% 6.17/1.49 [zip_derived_cl315, zip_derived_cl30, zip_derived_cl2,
% 6.17/1.49 zip_derived_cl3, zip_derived_cl3])).
% 6.17/1.49 thf(zip_derived_cl391, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((multiply @ (double_divide @ identity @ (inverse @ X0)) @ identity)
% 6.17/1.49 = (X0))),
% 6.17/1.49 inference('demod', [status(thm)],
% 6.17/1.49 [zip_derived_cl385, zip_derived_cl328, zip_derived_cl328])).
% 6.17/1.49 thf(zip_derived_cl3, plain,
% 6.17/1.49 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 6.17/1.49 inference('cnf', [status(esa)], [identity])).
% 6.17/1.49 thf(zip_derived_cl378, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i]:
% 6.17/1.49 ((multiply @
% 6.17/1.49 (double_divide @ (double_divide @ identity @ X1) @ (inverse @ X0)) @
% 6.17/1.49 (inverse @ X1)) = (X0))),
% 6.17/1.49 inference('demod', [status(thm)],
% 6.17/1.49 [zip_derived_cl22, zip_derived_cl328, zip_derived_cl1])).
% 6.17/1.49 thf(zip_derived_cl382, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((multiply @ identity @ (inverse @ X0))
% 6.17/1.49 = (double_divide @ identity @ X0))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl378])).
% 6.17/1.49 thf(zip_derived_cl10, plain,
% 6.17/1.49 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 6.17/1.49 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 6.17/1.49 thf(zip_derived_cl389, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((inverse @ (inverse @ (inverse @ X0)))
% 6.17/1.49 = (double_divide @ identity @ X0))),
% 6.17/1.49 inference('demod', [status(thm)], [zip_derived_cl382, zip_derived_cl10])).
% 6.17/1.49 thf(zip_derived_cl432, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((multiply @ (inverse @ (inverse @ (inverse @ (inverse @ X0)))) @
% 6.17/1.49 identity) = (X0))),
% 6.17/1.49 inference('demod', [status(thm)], [zip_derived_cl391, zip_derived_cl389])).
% 6.17/1.49 thf(zip_derived_cl389, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((inverse @ (inverse @ (inverse @ X0)))
% 6.17/1.49 = (double_divide @ identity @ X0))),
% 6.17/1.49 inference('demod', [status(thm)], [zip_derived_cl382, zip_derived_cl10])).
% 6.17/1.49 thf(zip_derived_cl6, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i]:
% 6.17/1.49 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 6.17/1.49 thf(zip_derived_cl425, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((multiply @ X0 @ identity)
% 6.17/1.49 = (inverse @ (inverse @ (inverse @ (inverse @ X0)))))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl389, zip_derived_cl6])).
% 6.17/1.49 thf(zip_derived_cl450, plain,
% 6.17/1.49 (![X0 : $i]: ((multiply @ (multiply @ X0 @ identity) @ identity) = (X0))),
% 6.17/1.49 inference('demod', [status(thm)], [zip_derived_cl432, zip_derived_cl425])).
% 6.17/1.49 thf(zip_derived_cl389, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((inverse @ (inverse @ (inverse @ X0)))
% 6.17/1.49 = (double_divide @ identity @ X0))),
% 6.17/1.49 inference('demod', [status(thm)], [zip_derived_cl382, zip_derived_cl10])).
% 6.17/1.49 thf(zip_derived_cl1, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i]:
% 6.17/1.49 ((multiply @ X1 @ X0)
% 6.17/1.49 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 6.17/1.49 inference('cnf', [status(esa)], [multiply])).
% 6.17/1.49 thf(zip_derived_cl422, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((multiply @ X0 @ identity)
% 6.17/1.49 = (double_divide @ (inverse @ (inverse @ (inverse @ X0))) @ identity))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl389, zip_derived_cl1])).
% 6.17/1.49 thf(zip_derived_cl3, plain,
% 6.17/1.49 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 6.17/1.49 inference('cnf', [status(esa)], [identity])).
% 6.17/1.49 thf(zip_derived_cl450, plain,
% 6.17/1.49 (![X0 : $i]: ((multiply @ (multiply @ X0 @ identity) @ identity) = (X0))),
% 6.17/1.49 inference('demod', [status(thm)], [zip_derived_cl432, zip_derived_cl425])).
% 6.17/1.49 thf(zip_derived_cl328, plain, (((identity) = (inverse @ identity))),
% 6.17/1.49 inference('demod', [status(thm)],
% 6.17/1.49 [zip_derived_cl315, zip_derived_cl30, zip_derived_cl2,
% 6.17/1.49 zip_derived_cl3, zip_derived_cl3])).
% 6.17/1.49 thf(zip_derived_cl378, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i]:
% 6.17/1.49 ((multiply @
% 6.17/1.49 (double_divide @ (double_divide @ identity @ X1) @ (inverse @ X0)) @
% 6.17/1.49 (inverse @ X1)) = (X0))),
% 6.17/1.49 inference('demod', [status(thm)],
% 6.17/1.49 [zip_derived_cl22, zip_derived_cl328, zip_derived_cl1])).
% 6.17/1.49 thf(zip_derived_cl384, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((multiply @
% 6.17/1.49 (double_divide @ (double_divide @ identity @ X0) @ identity) @
% 6.17/1.49 (inverse @ X0)) = (identity))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl328, zip_derived_cl378])).
% 6.17/1.49 thf(zip_derived_cl1, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i]:
% 6.17/1.49 ((multiply @ X1 @ X0)
% 6.17/1.49 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 6.17/1.49 inference('cnf', [status(esa)], [multiply])).
% 6.17/1.49 thf(zip_derived_cl390, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((multiply @ (multiply @ X0 @ identity) @ (inverse @ X0)) = (identity))),
% 6.17/1.49 inference('demod', [status(thm)], [zip_derived_cl384, zip_derived_cl1])).
% 6.17/1.49 thf(zip_derived_cl25, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i]:
% 6.17/1.49 ((identity)
% 6.17/1.49 = (double_divide @ (double_divide @ X0 @ X1) @ (multiply @ X1 @ X0)))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl3])).
% 6.17/1.49 thf(zip_derived_cl395, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((identity)
% 6.17/1.49 = (double_divide @
% 6.17/1.49 (double_divide @ (inverse @ X0) @ (multiply @ X0 @ identity)) @
% 6.17/1.49 identity))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl390, zip_derived_cl25])).
% 6.17/1.49 thf(zip_derived_cl2, plain,
% 6.17/1.49 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 6.17/1.49 inference('cnf', [status(esa)], [inverse])).
% 6.17/1.49 thf(zip_derived_cl984, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((inverse @
% 6.17/1.49 (double_divide @ (inverse @ X0) @ (multiply @ X0 @ identity)))
% 6.17/1.49 = (identity))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl395, zip_derived_cl2])).
% 6.17/1.49 thf(zip_derived_cl422, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((multiply @ X0 @ identity)
% 6.17/1.49 = (double_divide @ (inverse @ (inverse @ (inverse @ X0))) @ identity))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl389, zip_derived_cl1])).
% 6.17/1.49 thf(zip_derived_cl1018, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((multiply @
% 6.17/1.49 (double_divide @ (inverse @ X0) @ (multiply @ X0 @ identity)) @
% 6.17/1.49 identity)
% 6.17/1.49 = (double_divide @ (inverse @ (inverse @ identity)) @ identity))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl984, zip_derived_cl422])).
% 6.17/1.49 thf(zip_derived_cl328, plain, (((identity) = (inverse @ identity))),
% 6.17/1.49 inference('demod', [status(thm)],
% 6.17/1.49 [zip_derived_cl315, zip_derived_cl30, zip_derived_cl2,
% 6.17/1.49 zip_derived_cl3, zip_derived_cl3])).
% 6.17/1.49 thf(zip_derived_cl328, plain, (((identity) = (inverse @ identity))),
% 6.17/1.49 inference('demod', [status(thm)],
% 6.17/1.49 [zip_derived_cl315, zip_derived_cl30, zip_derived_cl2,
% 6.17/1.49 zip_derived_cl3, zip_derived_cl3])).
% 6.17/1.49 thf(zip_derived_cl328, plain, (((identity) = (inverse @ identity))),
% 6.17/1.49 inference('demod', [status(thm)],
% 6.17/1.49 [zip_derived_cl315, zip_derived_cl30, zip_derived_cl2,
% 6.17/1.49 zip_derived_cl3, zip_derived_cl3])).
% 6.17/1.49 thf(zip_derived_cl3, plain,
% 6.17/1.49 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 6.17/1.49 inference('cnf', [status(esa)], [identity])).
% 6.17/1.49 thf(zip_derived_cl346, plain,
% 6.17/1.49 (((identity) = (double_divide @ identity @ identity))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl328, zip_derived_cl3])).
% 6.17/1.49 thf(zip_derived_cl1060, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((multiply @
% 6.17/1.49 (double_divide @ (inverse @ X0) @ (multiply @ X0 @ identity)) @
% 6.17/1.49 identity) = (identity))),
% 6.17/1.49 inference('demod', [status(thm)],
% 6.17/1.49 [zip_derived_cl1018, zip_derived_cl328, zip_derived_cl328,
% 6.17/1.49 zip_derived_cl346])).
% 6.17/1.49 thf(zip_derived_cl450, plain,
% 6.17/1.49 (![X0 : $i]: ((multiply @ (multiply @ X0 @ identity) @ identity) = (X0))),
% 6.17/1.49 inference('demod', [status(thm)], [zip_derived_cl432, zip_derived_cl425])).
% 6.17/1.49 thf(zip_derived_cl1081, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((multiply @ identity @ identity)
% 6.17/1.49 = (double_divide @ (inverse @ X0) @ (multiply @ X0 @ identity)))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl1060, zip_derived_cl450])).
% 6.17/1.49 thf(zip_derived_cl346, plain,
% 6.17/1.49 (((identity) = (double_divide @ identity @ identity))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl328, zip_derived_cl3])).
% 6.17/1.49 thf(zip_derived_cl6, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i]:
% 6.17/1.49 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 6.17/1.49 thf(zip_derived_cl357, plain,
% 6.17/1.49 (((multiply @ identity @ identity) = (inverse @ identity))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl346, zip_derived_cl6])).
% 6.17/1.49 thf(zip_derived_cl328, plain, (((identity) = (inverse @ identity))),
% 6.17/1.49 inference('demod', [status(thm)],
% 6.17/1.49 [zip_derived_cl315, zip_derived_cl30, zip_derived_cl2,
% 6.17/1.49 zip_derived_cl3, zip_derived_cl3])).
% 6.17/1.49 thf(zip_derived_cl362, plain,
% 6.17/1.49 (((multiply @ identity @ identity) = (identity))),
% 6.17/1.49 inference('demod', [status(thm)], [zip_derived_cl357, zip_derived_cl328])).
% 6.17/1.49 thf(zip_derived_cl1122, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((identity)
% 6.17/1.49 = (double_divide @ (inverse @ X0) @ (multiply @ X0 @ identity)))),
% 6.17/1.49 inference('demod', [status(thm)], [zip_derived_cl1081, zip_derived_cl362])).
% 6.17/1.49 thf(zip_derived_cl1148, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((identity)
% 6.17/1.49 = (double_divide @ (inverse @ (multiply @ X0 @ identity)) @ X0))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl450, zip_derived_cl1122])).
% 6.17/1.49 thf(zip_derived_cl425, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((multiply @ X0 @ identity)
% 6.17/1.49 = (inverse @ (inverse @ (inverse @ (inverse @ X0)))))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl389, zip_derived_cl6])).
% 6.17/1.49 thf(zip_derived_cl425, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((multiply @ X0 @ identity)
% 6.17/1.49 = (inverse @ (inverse @ (inverse @ (inverse @ X0)))))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl389, zip_derived_cl6])).
% 6.17/1.49 thf(zip_derived_cl459, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((multiply @ (inverse @ X0) @ identity)
% 6.17/1.49 = (inverse @ (multiply @ X0 @ identity)))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl425, zip_derived_cl425])).
% 6.17/1.49 thf(zip_derived_cl1159, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((identity)
% 6.17/1.49 = (double_divide @ (multiply @ (inverse @ X0) @ identity) @ X0))),
% 6.17/1.49 inference('demod', [status(thm)], [zip_derived_cl1148, zip_derived_cl459])).
% 6.17/1.49 thf(zip_derived_cl13, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.17/1.49 ((double_divide @
% 6.17/1.49 (double_divide @ X1 @
% 6.17/1.49 (double_divide @ (double_divide @ identity @ X2) @
% 6.17/1.49 (double_divide @ X0 @ (double_divide @ X2 @ X1)))) @
% 6.17/1.49 (inverse @ identity)) = (X0))),
% 6.17/1.49 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 6.17/1.49 thf(zip_derived_cl1, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i]:
% 6.17/1.49 ((multiply @ X1 @ X0)
% 6.17/1.49 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 6.17/1.49 inference('cnf', [status(esa)], [multiply])).
% 6.17/1.49 thf(zip_derived_cl15, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.17/1.49 ((multiply @ (inverse @ identity) @
% 6.17/1.49 (double_divide @ X1 @
% 6.17/1.49 (double_divide @ (double_divide @ identity @ X2) @
% 6.17/1.49 (double_divide @ X0 @ (double_divide @ X2 @ X1)))))
% 6.17/1.49 = (double_divide @ X0 @ identity))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl1])).
% 6.17/1.49 thf(zip_derived_cl2, plain,
% 6.17/1.49 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 6.17/1.49 inference('cnf', [status(esa)], [inverse])).
% 6.17/1.49 thf(zip_derived_cl23, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.17/1.49 ((multiply @ (inverse @ identity) @
% 6.17/1.49 (double_divide @ X1 @
% 6.17/1.49 (double_divide @ (double_divide @ identity @ X2) @
% 6.17/1.49 (double_divide @ X0 @ (double_divide @ X2 @ X1)))))
% 6.17/1.49 = (inverse @ X0))),
% 6.17/1.49 inference('demod', [status(thm)], [zip_derived_cl15, zip_derived_cl2])).
% 6.17/1.49 thf(zip_derived_cl328, plain, (((identity) = (inverse @ identity))),
% 6.17/1.49 inference('demod', [status(thm)],
% 6.17/1.49 [zip_derived_cl315, zip_derived_cl30, zip_derived_cl2,
% 6.17/1.49 zip_derived_cl3, zip_derived_cl3])).
% 6.17/1.49 thf(zip_derived_cl389, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((inverse @ (inverse @ (inverse @ X0)))
% 6.17/1.49 = (double_divide @ identity @ X0))),
% 6.17/1.49 inference('demod', [status(thm)], [zip_derived_cl382, zip_derived_cl10])).
% 6.17/1.49 thf(zip_derived_cl1, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i]:
% 6.17/1.49 ((multiply @ X1 @ X0)
% 6.17/1.49 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 6.17/1.49 inference('cnf', [status(esa)], [multiply])).
% 6.17/1.49 thf(zip_derived_cl1, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i]:
% 6.17/1.49 ((multiply @ X1 @ X0)
% 6.17/1.49 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 6.17/1.49 inference('cnf', [status(esa)], [multiply])).
% 6.17/1.49 thf(zip_derived_cl9, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i]:
% 6.17/1.49 ((multiply @ identity @ (double_divide @ X0 @ X1))
% 6.17/1.49 = (double_divide @ (multiply @ X1 @ X0) @ identity))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl1])).
% 6.17/1.49 thf(zip_derived_cl2, plain,
% 6.17/1.49 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 6.17/1.49 inference('cnf', [status(esa)], [inverse])).
% 6.17/1.49 thf(zip_derived_cl11, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i]:
% 6.17/1.49 ((multiply @ identity @ (double_divide @ X0 @ X1))
% 6.17/1.49 = (inverse @ (multiply @ X1 @ X0)))),
% 6.17/1.49 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl2])).
% 6.17/1.49 thf(zip_derived_cl499, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.17/1.49 ((inverse @
% 6.17/1.49 (multiply @
% 6.17/1.49 (double_divide @ (inverse @ (inverse @ (inverse @ X2))) @
% 6.17/1.49 (double_divide @ X0 @ (double_divide @ X2 @ X1))) @
% 6.17/1.49 X1))
% 6.17/1.49 = (inverse @ X0))),
% 6.17/1.49 inference('demod', [status(thm)],
% 6.17/1.49 [zip_derived_cl23, zip_derived_cl328, zip_derived_cl389,
% 6.17/1.49 zip_derived_cl11])).
% 6.17/1.49 thf(zip_derived_cl1173, plain,
% 6.17/1.49 (![X0 : $i, X1 : $i]:
% 6.17/1.49 ((inverse @
% 6.17/1.49 (multiply @
% 6.17/1.49 (double_divide @
% 6.17/1.49 (inverse @
% 6.17/1.49 (inverse @ (inverse @ (multiply @ (inverse @ X1) @ identity)))) @
% 6.17/1.49 (double_divide @ X0 @ identity)) @
% 6.17/1.49 X1))
% 6.17/1.49 = (inverse @ X0))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl1159, zip_derived_cl499])).
% 6.17/1.49 thf(zip_derived_cl459, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((multiply @ (inverse @ X0) @ identity)
% 6.17/1.49 = (inverse @ (multiply @ X0 @ identity)))),
% 6.17/1.49 inference('sup+', [status(thm)], [zip_derived_cl425, zip_derived_cl425])).
% 6.17/1.49 thf(zip_derived_cl459, plain,
% 6.17/1.49 (![X0 : $i]:
% 6.17/1.49 ((multiply @ (inverse @ X0) @ identity)
% 6.17/1.49 = (inverse @ (multiply @ X0 @ identity)))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl425, zip_derived_cl425])).
% 6.17/1.50 thf(zip_derived_cl459, plain,
% 6.17/1.50 (![X0 : $i]:
% 6.17/1.50 ((multiply @ (inverse @ X0) @ identity)
% 6.17/1.50 = (inverse @ (multiply @ X0 @ identity)))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl425, zip_derived_cl425])).
% 6.17/1.50 thf(zip_derived_cl425, plain,
% 6.17/1.50 (![X0 : $i]:
% 6.17/1.50 ((multiply @ X0 @ identity)
% 6.17/1.50 = (inverse @ (inverse @ (inverse @ (inverse @ X0)))))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl389, zip_derived_cl6])).
% 6.17/1.50 thf(zip_derived_cl450, plain,
% 6.17/1.50 (![X0 : $i]: ((multiply @ (multiply @ X0 @ identity) @ identity) = (X0))),
% 6.17/1.50 inference('demod', [status(thm)], [zip_derived_cl432, zip_derived_cl425])).
% 6.17/1.50 thf(zip_derived_cl2, plain,
% 6.17/1.50 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 6.17/1.50 inference('cnf', [status(esa)], [inverse])).
% 6.17/1.50 thf(zip_derived_cl1194, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((inverse @ (multiply @ (double_divide @ X1 @ (inverse @ X0)) @ X1))
% 6.17/1.50 = (inverse @ X0))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl1173, zip_derived_cl459, zip_derived_cl459,
% 6.17/1.50 zip_derived_cl459, zip_derived_cl425, zip_derived_cl450,
% 6.17/1.50 zip_derived_cl2])).
% 6.17/1.50 thf(zip_derived_cl1267, plain,
% 6.17/1.50 (![X0 : $i]: ((inverse @ (multiply @ identity @ X0)) = (inverse @ X0))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1194])).
% 6.17/1.50 thf(zip_derived_cl10, plain,
% 6.17/1.50 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 6.17/1.50 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 6.17/1.50 thf(zip_derived_cl1279, plain,
% 6.17/1.50 (![X0 : $i]: ((inverse @ (inverse @ (inverse @ X0))) = (inverse @ X0))),
% 6.17/1.50 inference('demod', [status(thm)], [zip_derived_cl1267, zip_derived_cl10])).
% 6.17/1.50 thf(zip_derived_cl2, plain,
% 6.17/1.50 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 6.17/1.50 inference('cnf', [status(esa)], [inverse])).
% 6.17/1.50 thf(zip_derived_cl1296, plain,
% 6.17/1.50 (![X0 : $i]: ((multiply @ X0 @ identity) = (inverse @ (inverse @ X0)))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl422, zip_derived_cl1279, zip_derived_cl2])).
% 6.17/1.50 thf(zip_derived_cl1296, plain,
% 6.17/1.50 (![X0 : $i]: ((multiply @ X0 @ identity) = (inverse @ (inverse @ X0)))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl422, zip_derived_cl1279, zip_derived_cl2])).
% 6.17/1.50 thf(zip_derived_cl1279, plain,
% 6.17/1.50 (![X0 : $i]: ((inverse @ (inverse @ (inverse @ X0))) = (inverse @ X0))),
% 6.17/1.50 inference('demod', [status(thm)], [zip_derived_cl1267, zip_derived_cl10])).
% 6.17/1.50 thf(zip_derived_cl1376, plain,
% 6.17/1.50 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl450, zip_derived_cl1296, zip_derived_cl1296,
% 6.17/1.50 zip_derived_cl1279])).
% 6.17/1.50 thf(zip_derived_cl1395, plain,
% 6.17/1.50 ((((a2) != (a2))
% 6.17/1.50 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 6.17/1.50 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 6.17/1.50 | ((multiply @ a4 @ b4) != (multiply @ b4 @ a4)))),
% 6.17/1.50 inference('demod', [status(thm)], [zip_derived_cl341, zip_derived_cl1376])).
% 6.17/1.50 thf(zip_derived_cl1396, plain,
% 6.17/1.50 ((((multiply @ a4 @ b4) != (multiply @ b4 @ a4))
% 6.17/1.50 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 6.17/1.50 != (multiply @ a3 @ (multiply @ b3 @ c3))))),
% 6.17/1.50 inference('simplify', [status(thm)], [zip_derived_cl1395])).
% 6.17/1.50 thf(zip_derived_cl1159, plain,
% 6.17/1.50 (![X0 : $i]:
% 6.17/1.50 ((identity)
% 6.17/1.50 = (double_divide @ (multiply @ (inverse @ X0) @ identity) @ X0))),
% 6.17/1.50 inference('demod', [status(thm)], [zip_derived_cl1148, zip_derived_cl459])).
% 6.17/1.50 thf(zip_derived_cl499, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.17/1.50 ((inverse @
% 6.17/1.50 (multiply @
% 6.17/1.50 (double_divide @ (inverse @ (inverse @ (inverse @ X2))) @
% 6.17/1.50 (double_divide @ X0 @ (double_divide @ X2 @ X1))) @
% 6.17/1.50 X1))
% 6.17/1.50 = (inverse @ X0))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl23, zip_derived_cl328, zip_derived_cl389,
% 6.17/1.50 zip_derived_cl11])).
% 6.17/1.50 thf(zip_derived_cl1180, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((inverse @
% 6.17/1.50 (multiply @
% 6.17/1.50 (double_divide @ (inverse @ (inverse @ (inverse @ X1))) @ identity) @
% 6.17/1.50 X0))
% 6.17/1.50 = (inverse @
% 6.17/1.50 (multiply @ (inverse @ (double_divide @ X1 @ X0)) @ identity)))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl1159, zip_derived_cl499])).
% 6.17/1.50 thf(zip_derived_cl422, plain,
% 6.17/1.50 (![X0 : $i]:
% 6.17/1.50 ((multiply @ X0 @ identity)
% 6.17/1.50 = (double_divide @ (inverse @ (inverse @ (inverse @ X0))) @ identity))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl389, zip_derived_cl1])).
% 6.17/1.50 thf(zip_derived_cl6, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 6.17/1.50 thf(zip_derived_cl459, plain,
% 6.17/1.50 (![X0 : $i]:
% 6.17/1.50 ((multiply @ (inverse @ X0) @ identity)
% 6.17/1.50 = (inverse @ (multiply @ X0 @ identity)))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl425, zip_derived_cl425])).
% 6.17/1.50 thf(zip_derived_cl1201, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((inverse @ (multiply @ (multiply @ X1 @ identity) @ X0))
% 6.17/1.50 = (multiply @ (inverse @ (multiply @ X0 @ X1)) @ identity))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl1180, zip_derived_cl422, zip_derived_cl6,
% 6.17/1.50 zip_derived_cl459])).
% 6.17/1.50 thf(zip_derived_cl1296, plain,
% 6.17/1.50 (![X0 : $i]: ((multiply @ X0 @ identity) = (inverse @ (inverse @ X0)))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl422, zip_derived_cl1279, zip_derived_cl2])).
% 6.17/1.50 thf(zip_derived_cl1376, plain,
% 6.17/1.50 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl450, zip_derived_cl1296, zip_derived_cl1296,
% 6.17/1.50 zip_derived_cl1279])).
% 6.17/1.50 thf(zip_derived_cl1397, plain,
% 6.17/1.50 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl1296, zip_derived_cl1376])).
% 6.17/1.50 thf(zip_derived_cl1397, plain,
% 6.17/1.50 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl1296, zip_derived_cl1376])).
% 6.17/1.50 thf(zip_derived_cl1549, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((inverse @ (multiply @ X1 @ X0)) = (inverse @ (multiply @ X0 @ X1)))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl1201, zip_derived_cl1397, zip_derived_cl1397])).
% 6.17/1.50 thf(zip_derived_cl1376, plain,
% 6.17/1.50 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl450, zip_derived_cl1296, zip_derived_cl1296,
% 6.17/1.50 zip_derived_cl1279])).
% 6.17/1.50 thf(zip_derived_cl1553, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((inverse @ (inverse @ (multiply @ X1 @ X0))) = (multiply @ X0 @ X1))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl1549, zip_derived_cl1376])).
% 6.17/1.50 thf(zip_derived_cl1376, plain,
% 6.17/1.50 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl450, zip_derived_cl1296, zip_derived_cl1296,
% 6.17/1.50 zip_derived_cl1279])).
% 6.17/1.50 thf(zip_derived_cl1590, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl1553, zip_derived_cl1376])).
% 6.17/1.50 thf(zip_derived_cl1590, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl1553, zip_derived_cl1376])).
% 6.17/1.50 thf(zip_derived_cl1590, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl1553, zip_derived_cl1376])).
% 6.17/1.50 thf(zip_derived_cl1605, plain,
% 6.17/1.50 ((((multiply @ a4 @ b4) != (multiply @ a4 @ b4))
% 6.17/1.50 | ((multiply @ c3 @ (multiply @ a3 @ b3))
% 6.17/1.50 != (multiply @ a3 @ (multiply @ c3 @ b3))))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl1396, zip_derived_cl1590, zip_derived_cl1590,
% 6.17/1.50 zip_derived_cl1590])).
% 6.17/1.50 thf(zip_derived_cl1606, plain,
% 6.17/1.50 (((multiply @ c3 @ (multiply @ a3 @ b3))
% 6.17/1.50 != (multiply @ a3 @ (multiply @ c3 @ b3)))),
% 6.17/1.50 inference('simplify', [status(thm)], [zip_derived_cl1605])).
% 6.17/1.50 thf(zip_derived_cl30, plain,
% 6.17/1.50 (![X0 : $i]:
% 6.17/1.50 ((identity)
% 6.17/1.50 = (double_divide @ identity @ (multiply @ (inverse @ X0) @ X0)))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl3])).
% 6.17/1.50 thf(zip_derived_cl13, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.17/1.50 ((double_divide @
% 6.17/1.50 (double_divide @ X1 @
% 6.17/1.50 (double_divide @ (double_divide @ identity @ X2) @
% 6.17/1.50 (double_divide @ X0 @ (double_divide @ X2 @ X1)))) @
% 6.17/1.50 (inverse @ identity)) = (X0))),
% 6.17/1.50 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 6.17/1.50 thf(zip_derived_cl13, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.17/1.50 ((double_divide @
% 6.17/1.50 (double_divide @ X1 @
% 6.17/1.50 (double_divide @ (double_divide @ identity @ X2) @
% 6.17/1.50 (double_divide @ X0 @ (double_divide @ X2 @ X1)))) @
% 6.17/1.50 (inverse @ identity)) = (X0))),
% 6.17/1.50 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 6.17/1.50 thf(zip_derived_cl14, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.17/1.50 ((double_divide @
% 6.17/1.50 (double_divide @ (inverse @ identity) @
% 6.17/1.50 (double_divide @
% 6.17/1.50 (double_divide @ identity @
% 6.17/1.50 (double_divide @ X2 @
% 6.17/1.50 (double_divide @ (double_divide @ identity @ X3) @
% 6.17/1.50 (double_divide @ X0 @ (double_divide @ X3 @ X2))))) @
% 6.17/1.50 (double_divide @ X1 @ X0))) @
% 6.17/1.50 (inverse @ identity)) = (X1))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl13])).
% 6.17/1.50 thf(zip_derived_cl151, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.17/1.50 ((double_divide @
% 6.17/1.50 (double_divide @ (inverse @ identity) @
% 6.17/1.50 (double_divide @
% 6.17/1.50 (double_divide @ identity @
% 6.17/1.50 (double_divide @ X1 @
% 6.17/1.50 (double_divide @ (double_divide @ identity @ X2) @
% 6.17/1.50 (double_divide @ (multiply @ (inverse @ X0) @ X0) @
% 6.17/1.50 (double_divide @ X2 @ X1))))) @
% 6.17/1.50 identity)) @
% 6.17/1.50 (inverse @ identity)) = (identity))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl14])).
% 6.17/1.50 thf(zip_derived_cl1, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((multiply @ X1 @ X0)
% 6.17/1.50 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 6.17/1.50 inference('cnf', [status(esa)], [multiply])).
% 6.17/1.50 thf(zip_derived_cl167, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.17/1.50 ((double_divide @
% 6.17/1.50 (double_divide @ (inverse @ identity) @
% 6.17/1.50 (multiply @
% 6.17/1.50 (double_divide @ X1 @
% 6.17/1.50 (double_divide @ (double_divide @ identity @ X2) @
% 6.17/1.50 (double_divide @ (multiply @ (inverse @ X0) @ X0) @
% 6.17/1.50 (double_divide @ X2 @ X1)))) @
% 6.17/1.50 identity)) @
% 6.17/1.50 (inverse @ identity)) = (identity))),
% 6.17/1.50 inference('demod', [status(thm)], [zip_derived_cl151, zip_derived_cl1])).
% 6.17/1.50 thf(zip_derived_cl328, plain, (((identity) = (inverse @ identity))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl315, zip_derived_cl30, zip_derived_cl2,
% 6.17/1.50 zip_derived_cl3, zip_derived_cl3])).
% 6.17/1.50 thf(zip_derived_cl389, plain,
% 6.17/1.50 (![X0 : $i]:
% 6.17/1.50 ((inverse @ (inverse @ (inverse @ X0)))
% 6.17/1.50 = (double_divide @ identity @ X0))),
% 6.17/1.50 inference('demod', [status(thm)], [zip_derived_cl382, zip_derived_cl10])).
% 6.17/1.50 thf(zip_derived_cl1279, plain,
% 6.17/1.50 (![X0 : $i]: ((inverse @ (inverse @ (inverse @ X0))) = (inverse @ X0))),
% 6.17/1.50 inference('demod', [status(thm)], [zip_derived_cl1267, zip_derived_cl10])).
% 6.17/1.50 thf(zip_derived_cl1295, plain,
% 6.17/1.50 (![X0 : $i]: ((inverse @ X0) = (double_divide @ identity @ X0))),
% 6.17/1.50 inference('demod', [status(thm)], [zip_derived_cl389, zip_derived_cl1279])).
% 6.17/1.50 thf(zip_derived_cl48, plain,
% 6.17/1.50 (![X0 : $i]:
% 6.17/1.50 ((multiply @ identity @ identity)
% 6.17/1.50 = (inverse @ (multiply @ (inverse @ X0) @ X0)))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl6])).
% 6.17/1.50 thf(zip_derived_cl3, plain,
% 6.17/1.50 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 6.17/1.50 inference('cnf', [status(esa)], [identity])).
% 6.17/1.50 thf(zip_derived_cl67, plain,
% 6.17/1.50 (![X0 : $i]:
% 6.17/1.50 ((identity)
% 6.17/1.50 = (double_divide @ (multiply @ (inverse @ X0) @ X0) @
% 6.17/1.50 (multiply @ identity @ identity)))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl48, zip_derived_cl3])).
% 6.17/1.50 thf(zip_derived_cl10, plain,
% 6.17/1.50 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 6.17/1.50 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 6.17/1.50 thf(zip_derived_cl85, plain,
% 6.17/1.50 (![X0 : $i]:
% 6.17/1.50 ((identity)
% 6.17/1.50 = (double_divide @ (multiply @ (inverse @ X0) @ X0) @
% 6.17/1.50 (inverse @ (inverse @ identity))))),
% 6.17/1.50 inference('demod', [status(thm)], [zip_derived_cl67, zip_derived_cl10])).
% 6.17/1.50 thf(zip_derived_cl16, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((double_divide @
% 6.17/1.50 (double_divide @ identity @
% 6.17/1.50 (double_divide @ (double_divide @ identity @ X0) @
% 6.17/1.50 (double_divide @ X1 @ (inverse @ X0)))) @
% 6.17/1.50 (inverse @ identity)) = (X1))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 6.17/1.50 thf(zip_derived_cl314, plain,
% 6.17/1.50 (![X0 : $i]:
% 6.17/1.50 ((double_divide @
% 6.17/1.50 (double_divide @ identity @
% 6.17/1.50 (double_divide @
% 6.17/1.50 (double_divide @ identity @ (inverse @ identity)) @ identity)) @
% 6.17/1.50 (inverse @ identity)) = (multiply @ (inverse @ X0) @ X0))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl85, zip_derived_cl16])).
% 6.17/1.50 thf(zip_derived_cl3, plain,
% 6.17/1.50 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 6.17/1.50 inference('cnf', [status(esa)], [identity])).
% 6.17/1.50 thf(zip_derived_cl2, plain,
% 6.17/1.50 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 6.17/1.50 inference('cnf', [status(esa)], [inverse])).
% 6.17/1.50 thf(zip_derived_cl3, plain,
% 6.17/1.50 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 6.17/1.50 inference('cnf', [status(esa)], [identity])).
% 6.17/1.50 thf(zip_derived_cl3, plain,
% 6.17/1.50 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 6.17/1.50 inference('cnf', [status(esa)], [identity])).
% 6.17/1.50 thf(zip_derived_cl327, plain,
% 6.17/1.50 (![X0 : $i]: ((identity) = (multiply @ (inverse @ X0) @ X0))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl314, zip_derived_cl3, zip_derived_cl2,
% 6.17/1.50 zip_derived_cl3, zip_derived_cl3])).
% 6.17/1.50 thf(zip_derived_cl6, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 6.17/1.50 thf(zip_derived_cl1376, plain,
% 6.17/1.50 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl450, zip_derived_cl1296, zip_derived_cl1296,
% 6.17/1.50 zip_derived_cl1279])).
% 6.17/1.50 thf(zip_derived_cl1403, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1376])).
% 6.17/1.50 thf(zip_derived_cl1295, plain,
% 6.17/1.50 (![X0 : $i]: ((inverse @ X0) = (double_divide @ identity @ X0))),
% 6.17/1.50 inference('demod', [status(thm)], [zip_derived_cl389, zip_derived_cl1279])).
% 6.17/1.50 thf(zip_derived_cl1553, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((inverse @ (inverse @ (multiply @ X1 @ X0))) = (multiply @ X0 @ X1))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl1549, zip_derived_cl1376])).
% 6.17/1.50 thf(zip_derived_cl1403, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1376])).
% 6.17/1.50 thf(zip_derived_cl1590, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl1553, zip_derived_cl1376])).
% 6.17/1.50 thf(zip_derived_cl1403, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1376])).
% 6.17/1.50 thf(zip_derived_cl1590, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl1553, zip_derived_cl1376])).
% 6.17/1.50 thf(zip_derived_cl1397, plain,
% 6.17/1.50 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl1296, zip_derived_cl1376])).
% 6.17/1.50 thf(zip_derived_cl1295, plain,
% 6.17/1.50 (![X0 : $i]: ((inverse @ X0) = (double_divide @ identity @ X0))),
% 6.17/1.50 inference('demod', [status(thm)], [zip_derived_cl389, zip_derived_cl1279])).
% 6.17/1.50 thf(zip_derived_cl1553, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((inverse @ (inverse @ (multiply @ X1 @ X0))) = (multiply @ X0 @ X1))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl1549, zip_derived_cl1376])).
% 6.17/1.50 thf(zip_derived_cl1590, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl1553, zip_derived_cl1376])).
% 6.17/1.50 thf(zip_derived_cl328, plain, (((identity) = (inverse @ identity))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl315, zip_derived_cl30, zip_derived_cl2,
% 6.17/1.50 zip_derived_cl3, zip_derived_cl3])).
% 6.17/1.50 thf(zip_derived_cl2, plain,
% 6.17/1.50 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 6.17/1.50 inference('cnf', [status(esa)], [inverse])).
% 6.17/1.50 thf(zip_derived_cl2014, plain,
% 6.17/1.50 (![X1 : $i, X2 : $i]:
% 6.17/1.50 ((inverse @
% 6.17/1.50 (multiply @ X1 @
% 6.17/1.50 (inverse @ (multiply @ (inverse @ X2) @ (multiply @ X2 @ X1)))))
% 6.17/1.50 = (identity))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl167, zip_derived_cl328, zip_derived_cl1295,
% 6.17/1.50 zip_derived_cl327, zip_derived_cl1403, zip_derived_cl1295,
% 6.17/1.50 zip_derived_cl1553, zip_derived_cl1403, zip_derived_cl1590,
% 6.17/1.50 zip_derived_cl1403, zip_derived_cl1590, zip_derived_cl1397,
% 6.17/1.50 zip_derived_cl1295, zip_derived_cl1553, zip_derived_cl1590,
% 6.17/1.50 zip_derived_cl328, zip_derived_cl2])).
% 6.17/1.50 thf(zip_derived_cl1590, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl1553, zip_derived_cl1376])).
% 6.17/1.50 thf(zip_derived_cl1194, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((inverse @ (multiply @ (double_divide @ X1 @ (inverse @ X0)) @ X1))
% 6.17/1.50 = (inverse @ X0))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl1173, zip_derived_cl459, zip_derived_cl459,
% 6.17/1.50 zip_derived_cl459, zip_derived_cl425, zip_derived_cl450,
% 6.17/1.50 zip_derived_cl2])).
% 6.17/1.50 thf(zip_derived_cl1376, plain,
% 6.17/1.50 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl450, zip_derived_cl1296, zip_derived_cl1296,
% 6.17/1.50 zip_derived_cl1279])).
% 6.17/1.50 thf(zip_derived_cl1405, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((inverse @ (inverse @ X0))
% 6.17/1.50 = (multiply @ (double_divide @ X1 @ (inverse @ X0)) @ X1))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl1194, zip_derived_cl1376])).
% 6.17/1.50 thf(zip_derived_cl1376, plain,
% 6.17/1.50 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl450, zip_derived_cl1296, zip_derived_cl1296,
% 6.17/1.50 zip_derived_cl1279])).
% 6.17/1.50 thf(zip_derived_cl1407, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((X0) = (multiply @ (double_divide @ X1 @ (inverse @ X0)) @ X1))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl1405, zip_derived_cl1376])).
% 6.17/1.50 thf(zip_derived_cl1403, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1376])).
% 6.17/1.50 thf(zip_derived_cl1485, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((X0) = (multiply @ (inverse @ (multiply @ (inverse @ X0) @ X1)) @ X1))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl1407, zip_derived_cl1403])).
% 6.17/1.50 thf(zip_derived_cl1612, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((X0) = (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X0))) @ X1))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl1590, zip_derived_cl1485])).
% 6.17/1.50 thf(zip_derived_cl2034, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((multiply @ (inverse @ X1) @ (multiply @ X1 @ X0))
% 6.17/1.50 = (multiply @ identity @ X0))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl2014, zip_derived_cl1612])).
% 6.17/1.50 thf(zip_derived_cl10, plain,
% 6.17/1.50 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 6.17/1.50 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 6.17/1.50 thf(zip_derived_cl1376, plain,
% 6.17/1.50 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl450, zip_derived_cl1296, zip_derived_cl1296,
% 6.17/1.50 zip_derived_cl1279])).
% 6.17/1.50 thf(zip_derived_cl1394, plain,
% 6.17/1.50 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 6.17/1.50 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl1376])).
% 6.17/1.50 thf(zip_derived_cl2085, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)) = (X0))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl2034, zip_derived_cl1394])).
% 6.17/1.50 thf(zip_derived_cl1485, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((X0) = (multiply @ (inverse @ (multiply @ (inverse @ X0) @ X1)) @ X1))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl1407, zip_derived_cl1403])).
% 6.17/1.50 thf(zip_derived_cl2098, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((X1) = (multiply @ (inverse @ X0) @ (multiply @ X1 @ X0)))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl2085, zip_derived_cl1485])).
% 6.17/1.50 thf(zip_derived_cl13, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.17/1.50 ((double_divide @
% 6.17/1.50 (double_divide @ X1 @
% 6.17/1.50 (double_divide @ (double_divide @ identity @ X2) @
% 6.17/1.50 (double_divide @ X0 @ (double_divide @ X2 @ X1)))) @
% 6.17/1.50 (inverse @ identity)) = (X0))),
% 6.17/1.50 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 6.17/1.50 thf(zip_derived_cl328, plain, (((identity) = (inverse @ identity))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl315, zip_derived_cl30, zip_derived_cl2,
% 6.17/1.50 zip_derived_cl3, zip_derived_cl3])).
% 6.17/1.50 thf(zip_derived_cl1, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((multiply @ X1 @ X0)
% 6.17/1.50 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 6.17/1.50 inference('cnf', [status(esa)], [multiply])).
% 6.17/1.50 thf(zip_derived_cl334, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.17/1.50 ((multiply @
% 6.17/1.50 (double_divide @ (double_divide @ identity @ X2) @
% 6.17/1.50 (double_divide @ X0 @ (double_divide @ X2 @ X1))) @
% 6.17/1.50 X1) = (X0))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl13, zip_derived_cl328, zip_derived_cl1])).
% 6.17/1.50 thf(zip_derived_cl1295, plain,
% 6.17/1.50 (![X0 : $i]: ((inverse @ X0) = (double_divide @ identity @ X0))),
% 6.17/1.50 inference('demod', [status(thm)], [zip_derived_cl389, zip_derived_cl1279])).
% 6.17/1.50 thf(zip_derived_cl1403, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1376])).
% 6.17/1.50 thf(zip_derived_cl1403, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1376])).
% 6.17/1.50 thf(zip_derived_cl1485, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((X0) = (multiply @ (inverse @ (multiply @ (inverse @ X0) @ X1)) @ X1))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl1407, zip_derived_cl1403])).
% 6.17/1.50 thf(zip_derived_cl1553, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((inverse @ (inverse @ (multiply @ X1 @ X0))) = (multiply @ X0 @ X1))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl1549, zip_derived_cl1376])).
% 6.17/1.50 thf(zip_derived_cl1597, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((inverse @ (inverse @ X0))
% 6.17/1.50 = (multiply @ X1 @ (inverse @ (multiply @ (inverse @ X0) @ X1))))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl1485, zip_derived_cl1553])).
% 6.17/1.50 thf(zip_derived_cl1376, plain,
% 6.17/1.50 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl450, zip_derived_cl1296, zip_derived_cl1296,
% 6.17/1.50 zip_derived_cl1279])).
% 6.17/1.50 thf(zip_derived_cl1603, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((X0) = (multiply @ X1 @ (inverse @ (multiply @ (inverse @ X0) @ X1))))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl1597, zip_derived_cl1376])).
% 6.17/1.50 thf(zip_derived_cl2085, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)) = (X0))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl2034, zip_derived_cl1394])).
% 6.17/1.50 thf(zip_derived_cl2105, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((multiply @ (inverse @ X1) @ X0)
% 6.17/1.50 = (inverse @ (multiply @ (inverse @ X0) @ X1)))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl1603, zip_derived_cl2085])).
% 6.17/1.50 thf(zip_derived_cl1403, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1376])).
% 6.17/1.50 thf(zip_derived_cl1590, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl1553, zip_derived_cl1376])).
% 6.17/1.50 thf(zip_derived_cl2105, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((multiply @ (inverse @ X1) @ X0)
% 6.17/1.50 = (inverse @ (multiply @ (inverse @ X0) @ X1)))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl1603, zip_derived_cl2085])).
% 6.17/1.50 thf(zip_derived_cl2105, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]:
% 6.17/1.50 ((multiply @ (inverse @ X1) @ X0)
% 6.17/1.50 = (inverse @ (multiply @ (inverse @ X0) @ X1)))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl1603, zip_derived_cl2085])).
% 6.17/1.50 thf(zip_derived_cl1590, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl1553, zip_derived_cl1376])).
% 6.17/1.50 thf(zip_derived_cl1590, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl1553, zip_derived_cl1376])).
% 6.17/1.50 thf(zip_derived_cl4476, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.17/1.50 ((multiply @ X1 @
% 6.17/1.50 (multiply @ X2 @ (multiply @ (inverse @ (multiply @ X1 @ X2)) @ X0)))
% 6.17/1.50 = (X0))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl334, zip_derived_cl1295, zip_derived_cl1403,
% 6.17/1.50 zip_derived_cl1403, zip_derived_cl2105, zip_derived_cl1403,
% 6.17/1.50 zip_derived_cl1590, zip_derived_cl2105, zip_derived_cl2105,
% 6.17/1.50 zip_derived_cl1590, zip_derived_cl1590])).
% 6.17/1.50 thf(zip_derived_cl4530, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.17/1.50 ((multiply @ X2 @ (multiply @ X1 @ X0))
% 6.17/1.50 = (multiply @ X0 @ (multiply @ X2 @ X1)))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl2098, zip_derived_cl4476])).
% 6.17/1.50 thf(zip_derived_cl1590, plain,
% 6.17/1.50 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 6.17/1.50 inference('sup+', [status(thm)], [zip_derived_cl1553, zip_derived_cl1376])).
% 6.17/1.50 thf(zip_derived_cl6131, plain,
% 6.17/1.50 (((multiply @ a3 @ (multiply @ c3 @ b3))
% 6.17/1.50 != (multiply @ a3 @ (multiply @ c3 @ b3)))),
% 6.17/1.50 inference('demod', [status(thm)],
% 6.17/1.50 [zip_derived_cl1606, zip_derived_cl4530, zip_derived_cl1590])).
% 6.17/1.50 thf(zip_derived_cl6132, plain, ($false),
% 6.17/1.50 inference('simplify', [status(thm)], [zip_derived_cl6131])).
% 6.17/1.50
% 6.17/1.50 % SZS output end Refutation
% 6.17/1.50
% 6.17/1.50
% 6.17/1.50 % Terminating...
% 6.74/1.55 % Runner terminated.
% 6.74/1.57 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------