TSTP Solution File: GRP701-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP701-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.iOkiqjTKMW true
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:52:59 EDT 2023
% Result : Timeout 299.82s 43.81s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP701-1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.iOkiqjTKMW true
% 0.13/0.35 % Computer : n014.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 22:36:45 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
% 0.13/0.36 % Python version: Python 3.6.8
% 0.13/0.36 % Running in FO mode
% 0.21/0.68 % Total configuration time : 435
% 0.21/0.68 % Estimated wc time : 1092
% 0.21/0.68 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 1.11/0.77 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 1.11/0.79 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 1.11/0.79 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 1.11/0.79 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 1.11/0.80 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 1.11/0.80 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 299.82/43.81 % Solved by fo/fo4.sh.
% 299.82/43.81 % done 2169 iterations in 42.968s
% 299.82/43.81 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 299.82/43.81 % SZS output start Refutation
% 299.82/43.81 thf(a_type, type, a: $i).
% 299.82/43.81 thf(b_type, type, b: $i).
% 299.82/43.81 thf(ld_type, type, ld: $i > $i > $i).
% 299.82/43.81 thf(rd_type, type, rd: $i > $i > $i).
% 299.82/43.81 thf(i_type, type, i: $i > $i).
% 299.82/43.81 thf(mult_type, type, mult: $i > $i > $i).
% 299.82/43.81 thf(unit_type, type, unit: $i).
% 299.82/43.81 thf(goals, conjecture, (( mult @ a @ ( i @ ( mult @ b @ a ) ) ) = ( i @ b ))).
% 299.82/43.81 thf(zf_stmt_0, negated_conjecture,
% 299.82/43.81 (( mult @ a @ ( i @ ( mult @ b @ a ) ) ) != ( i @ b )),
% 299.82/43.81 inference('cnf.neg', [status(esa)], [goals])).
% 299.82/43.81 thf(zip_derived_cl10, plain,
% 299.82/43.81 (((mult @ a @ (i @ (mult @ b @ a))) != (i @ b))),
% 299.82/43.81 inference('cnf', [status(esa)], [zf_stmt_0])).
% 299.82/43.81 thf(c10, axiom, (( mult @ ( i @ A ) @ A ) = ( unit ))).
% 299.82/43.81 thf(zip_derived_cl9, plain, (![X0 : $i]: ((mult @ (i @ X0) @ X0) = (unit))),
% 299.82/43.81 inference('cnf', [status(esa)], [c10])).
% 299.82/43.81 thf(c02, axiom, (( ld @ A @ ( mult @ A @ B ) ) = ( B ))).
% 299.82/43.81 thf(zip_derived_cl1, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.81 inference('cnf', [status(esa)], [c02])).
% 299.82/43.81 thf(zip_derived_cl19, plain, (![X0 : $i]: ((ld @ (i @ X0) @ unit) = (X0))),
% 299.82/43.81 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl1])).
% 299.82/43.81 thf(c09, axiom, (( mult @ A @ ( i @ A ) ) = ( unit ))).
% 299.82/43.81 thf(zip_derived_cl8, plain, (![X0 : $i]: ((mult @ X0 @ (i @ X0)) = (unit))),
% 299.82/43.81 inference('cnf', [status(esa)], [c09])).
% 299.82/43.81 thf(zip_derived_cl1, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.81 inference('cnf', [status(esa)], [c02])).
% 299.82/43.81 thf(zip_derived_cl17, plain, (![X0 : $i]: ((ld @ X0 @ unit) = (i @ X0))),
% 299.82/43.81 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl1])).
% 299.82/43.81 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.81 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.81 thf(c05, axiom, (( mult @ A @ unit ) = ( A ))).
% 299.82/43.81 thf(zip_derived_cl4, plain, (![X0 : $i]: ((mult @ X0 @ unit) = (X0))),
% 299.82/43.81 inference('cnf', [status(esa)], [c05])).
% 299.82/43.81 thf(c07, axiom,
% 299.82/43.81 (( mult @ ( mult @ ( mult @ A @ B ) @ A ) @ ( mult @ A @ C ) ) =
% 299.82/43.81 ( mult @ A @ ( mult @ ( mult @ ( mult @ B @ A ) @ A ) @ C ) ))).
% 299.82/43.81 thf(zip_derived_cl6, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 299.82/43.81 ((mult @ (mult @ (mult @ X0 @ X1) @ X0) @ (mult @ X0 @ X2))
% 299.82/43.81 = (mult @ X0 @ (mult @ (mult @ (mult @ X1 @ X0) @ X0) @ X2)))),
% 299.82/43.81 inference('cnf', [status(esa)], [c07])).
% 299.82/43.81 thf(zip_derived_cl48, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i]:
% 299.82/43.81 ((mult @ (mult @ (mult @ X0 @ X1) @ X0) @ X0)
% 299.82/43.81 = (mult @ X0 @ (mult @ (mult @ (mult @ X1 @ X0) @ X0) @ unit)))),
% 299.82/43.81 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl6])).
% 299.82/43.81 thf(zip_derived_cl4, plain, (![X0 : $i]: ((mult @ X0 @ unit) = (X0))),
% 299.82/43.81 inference('cnf', [status(esa)], [c05])).
% 299.82/43.81 thf(zip_derived_cl63, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i]:
% 299.82/43.81 ((mult @ (mult @ (mult @ X0 @ X1) @ X0) @ X0)
% 299.82/43.81 = (mult @ X0 @ (mult @ (mult @ X1 @ X0) @ X0)))),
% 299.82/43.81 inference('demod', [status(thm)], [zip_derived_cl48, zip_derived_cl4])).
% 299.82/43.81 thf(c04, axiom, (( rd @ ( mult @ A @ B ) @ B ) = ( A ))).
% 299.82/43.81 thf(zip_derived_cl3, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.81 inference('cnf', [status(esa)], [c04])).
% 299.82/43.81 thf(zip_derived_cl178, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i]:
% 299.82/43.81 ((rd @ (mult @ X0 @ (mult @ (mult @ X1 @ X0) @ X0)) @ X0)
% 299.82/43.81 = (mult @ (mult @ X0 @ X1) @ X0))),
% 299.82/43.81 inference('sup+', [status(thm)], [zip_derived_cl63, zip_derived_cl3])).
% 299.82/43.81 thf(zip_derived_cl8, plain, (![X0 : $i]: ((mult @ X0 @ (i @ X0)) = (unit))),
% 299.82/43.81 inference('cnf', [status(esa)], [c09])).
% 299.82/43.81 thf(c01, axiom, (( mult @ A @ ( ld @ A @ B ) ) = ( B ))).
% 299.82/43.81 thf(zip_derived_cl0, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 299.82/43.81 inference('cnf', [status(esa)], [c01])).
% 299.82/43.81 thf(c08, axiom,
% 299.82/43.81 (( mult @ ( mult @ A @ B ) @ ( mult @ B @ ( mult @ C @ B ) ) ) =
% 299.82/43.81 ( mult @ ( mult @ A @ ( mult @ B @ ( mult @ B @ C ) ) ) @ B ))).
% 299.82/43.81 thf(zip_derived_cl7, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 299.82/43.81 ((mult @ (mult @ X0 @ X1) @ (mult @ X1 @ (mult @ X2 @ X1)))
% 299.82/43.81 = (mult @ (mult @ X0 @ (mult @ X1 @ (mult @ X1 @ X2))) @ X1))),
% 299.82/43.81 inference('cnf', [status(esa)], [c08])).
% 299.82/43.81 thf(zip_derived_cl86, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 299.82/43.81 ((mult @ (mult @ X2 @ X1) @ (mult @ X1 @ (mult @ (ld @ X1 @ X0) @ X1)))
% 299.82/43.81 = (mult @ (mult @ X2 @ (mult @ X1 @ X0)) @ X1))),
% 299.82/43.81 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl7])).
% 299.82/43.81 thf(zip_derived_cl0, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 299.82/43.81 inference('cnf', [status(esa)], [c01])).
% 299.82/43.81 thf(c06, axiom, (( mult @ unit @ A ) = ( A ))).
% 299.82/43.81 thf(zip_derived_cl5, plain, (![X0 : $i]: ((mult @ unit @ X0) = (X0))),
% 299.82/43.81 inference('cnf', [status(esa)], [c06])).
% 299.82/43.81 thf(zip_derived_cl7, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 299.82/43.81 ((mult @ (mult @ X0 @ X1) @ (mult @ X1 @ (mult @ X2 @ X1)))
% 299.82/43.81 = (mult @ (mult @ X0 @ (mult @ X1 @ (mult @ X1 @ X2))) @ X1))),
% 299.82/43.81 inference('cnf', [status(esa)], [c08])).
% 299.82/43.81 thf(zip_derived_cl83, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i]:
% 299.82/43.81 ((mult @ (mult @ unit @ X1) @ (mult @ X1 @ (mult @ X0 @ X1)))
% 299.82/43.81 = (mult @ (mult @ X1 @ (mult @ X1 @ X0)) @ X1))),
% 299.82/43.81 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl7])).
% 299.82/43.81 thf(zip_derived_cl5, plain, (![X0 : $i]: ((mult @ unit @ X0) = (X0))),
% 299.82/43.81 inference('cnf', [status(esa)], [c06])).
% 299.82/43.81 thf(zip_derived_cl94, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i]:
% 299.82/43.81 ((mult @ X1 @ (mult @ X1 @ (mult @ X0 @ X1)))
% 299.82/43.81 = (mult @ (mult @ X1 @ (mult @ X1 @ X0)) @ X1))),
% 299.82/43.81 inference('demod', [status(thm)], [zip_derived_cl83, zip_derived_cl5])).
% 299.82/43.81 thf(zip_derived_cl9, plain, (![X0 : $i]: ((mult @ (i @ X0) @ X0) = (unit))),
% 299.82/43.81 inference('cnf', [status(esa)], [c10])).
% 299.82/43.81 thf(zip_derived_cl6, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 299.82/43.81 ((mult @ (mult @ (mult @ X0 @ X1) @ X0) @ (mult @ X0 @ X2))
% 299.82/43.81 = (mult @ X0 @ (mult @ (mult @ (mult @ X1 @ X0) @ X0) @ X2)))),
% 299.82/43.81 inference('cnf', [status(esa)], [c07])).
% 299.82/43.81 thf(zip_derived_cl53, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i]:
% 299.82/43.81 ((mult @ (mult @ (mult @ (i @ X0) @ X1) @ (i @ X0)) @ unit)
% 299.82/43.81 = (mult @ (i @ X0) @
% 299.82/43.81 (mult @ (mult @ (mult @ X1 @ (i @ X0)) @ (i @ X0)) @ X0)))),
% 299.82/43.81 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl6])).
% 299.82/43.81 thf(zip_derived_cl4, plain, (![X0 : $i]: ((mult @ X0 @ unit) = (X0))),
% 299.82/43.81 inference('cnf', [status(esa)], [c05])).
% 299.82/43.81 thf(zip_derived_cl66, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i]:
% 299.82/43.81 ((mult @ (mult @ (i @ X0) @ X1) @ (i @ X0))
% 299.82/43.81 = (mult @ (i @ X0) @
% 299.82/43.81 (mult @ (mult @ (mult @ X1 @ (i @ X0)) @ (i @ X0)) @ X0)))),
% 299.82/43.81 inference('demod', [status(thm)], [zip_derived_cl53, zip_derived_cl4])).
% 299.82/43.81 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.81 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.81 thf(zip_derived_cl8, plain, (![X0 : $i]: ((mult @ X0 @ (i @ X0)) = (unit))),
% 299.82/43.81 inference('cnf', [status(esa)], [c09])).
% 299.82/43.81 thf(zip_derived_cl4, plain, (![X0 : $i]: ((mult @ X0 @ unit) = (X0))),
% 299.82/43.81 inference('cnf', [status(esa)], [c05])).
% 299.82/43.81 thf(zip_derived_cl6, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 299.82/43.81 ((mult @ (mult @ (mult @ X0 @ X1) @ X0) @ (mult @ X0 @ X2))
% 299.82/43.81 = (mult @ X0 @ (mult @ (mult @ (mult @ X1 @ X0) @ X0) @ X2)))),
% 299.82/43.81 inference('cnf', [status(esa)], [c07])).
% 299.82/43.81 thf(zip_derived_cl57, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i]:
% 299.82/43.81 ((mult @ (mult @ X0 @ X0) @ (mult @ X0 @ X1))
% 299.82/43.81 = (mult @ X0 @ (mult @ (mult @ (mult @ unit @ X0) @ X0) @ X1)))),
% 299.82/43.81 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl6])).
% 299.82/43.81 thf(zip_derived_cl5, plain, (![X0 : $i]: ((mult @ unit @ X0) = (X0))),
% 299.82/43.81 inference('cnf', [status(esa)], [c06])).
% 299.82/43.81 thf(zip_derived_cl68, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i]:
% 299.82/43.81 ((mult @ (mult @ X0 @ X0) @ (mult @ X0 @ X1))
% 299.82/43.81 = (mult @ X0 @ (mult @ (mult @ X0 @ X0) @ X1)))),
% 299.82/43.81 inference('demod', [status(thm)], [zip_derived_cl57, zip_derived_cl5])).
% 299.82/43.81 thf(zip_derived_cl299, plain,
% 299.82/43.81 (![X0 : $i]:
% 299.82/43.81 ((mult @ (mult @ X0 @ X0) @ unit)
% 299.82/43.81 = (mult @ X0 @ (mult @ (mult @ X0 @ X0) @ (i @ X0))))),
% 299.82/43.81 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl68])).
% 299.82/43.81 thf(zip_derived_cl4, plain, (![X0 : $i]: ((mult @ X0 @ unit) = (X0))),
% 299.82/43.81 inference('cnf', [status(esa)], [c05])).
% 299.82/43.81 thf(zip_derived_cl313, plain,
% 299.82/43.81 (![X0 : $i]:
% 299.82/43.81 ((mult @ X0 @ X0) = (mult @ X0 @ (mult @ (mult @ X0 @ X0) @ (i @ X0))))),
% 299.82/43.81 inference('demod', [status(thm)], [zip_derived_cl299, zip_derived_cl4])).
% 299.82/43.81 thf(zip_derived_cl1, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.81 inference('cnf', [status(esa)], [c02])).
% 299.82/43.81 thf(zip_derived_cl331, plain,
% 299.82/43.81 (![X0 : $i]:
% 299.82/43.81 ((ld @ X0 @ (mult @ X0 @ X0)) = (mult @ (mult @ X0 @ X0) @ (i @ X0)))),
% 299.82/43.81 inference('sup+', [status(thm)], [zip_derived_cl313, zip_derived_cl1])).
% 299.82/43.81 thf(zip_derived_cl1, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.81 inference('cnf', [status(esa)], [c02])).
% 299.82/43.81 thf(zip_derived_cl351, plain,
% 299.82/43.81 (![X0 : $i]: ((X0) = (mult @ (mult @ X0 @ X0) @ (i @ X0)))),
% 299.82/43.81 inference('demod', [status(thm)], [zip_derived_cl331, zip_derived_cl1])).
% 299.82/43.81 thf(zip_derived_cl3, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.81 inference('cnf', [status(esa)], [c04])).
% 299.82/43.81 thf(zip_derived_cl361, plain,
% 299.82/43.81 (![X0 : $i]: ((rd @ X0 @ (i @ X0)) = (mult @ X0 @ X0))),
% 299.82/43.81 inference('sup+', [status(thm)], [zip_derived_cl351, zip_derived_cl3])).
% 299.82/43.81 thf(zip_derived_cl386, plain,
% 299.82/43.81 (![X0 : $i]: ((rd @ (i @ X0) @ X0) = (mult @ (i @ X0) @ (i @ X0)))),
% 299.82/43.81 inference('sup+', [status(thm)], [zip_derived_cl32, zip_derived_cl361])).
% 299.82/43.81 thf(zip_derived_cl351, plain,
% 299.82/43.81 (![X0 : $i]: ((X0) = (mult @ (mult @ X0 @ X0) @ (i @ X0)))),
% 299.82/43.81 inference('demod', [status(thm)], [zip_derived_cl331, zip_derived_cl1])).
% 299.82/43.81 thf(zip_derived_cl6, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 299.82/43.81 ((mult @ (mult @ (mult @ X0 @ X1) @ X0) @ (mult @ X0 @ X2))
% 299.82/43.81 = (mult @ X0 @ (mult @ (mult @ (mult @ X1 @ X0) @ X0) @ X2)))),
% 299.82/43.81 inference('cnf', [status(esa)], [c07])).
% 299.82/43.81 thf(zip_derived_cl3, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.81 inference('cnf', [status(esa)], [c04])).
% 299.82/43.81 thf(zip_derived_cl43, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 299.82/43.81 ((rd @ (mult @ X1 @ (mult @ (mult @ (mult @ X2 @ X1) @ X1) @ X0)) @
% 299.82/43.81 (mult @ X1 @ X0)) = (mult @ (mult @ X1 @ X2) @ X1))),
% 299.82/43.81 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl3])).
% 299.82/43.81 thf(zip_derived_cl486, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i]:
% 299.82/43.81 ((rd @ (mult @ (i @ X0) @ (mult @ (mult @ X0 @ (i @ X0)) @ X1)) @
% 299.82/43.81 (mult @ (i @ X0) @ X1))
% 299.82/43.81 = (mult @ (mult @ (i @ X0) @ (mult @ X0 @ X0)) @ (i @ X0)))),
% 299.82/43.81 inference('sup+', [status(thm)], [zip_derived_cl351, zip_derived_cl43])).
% 299.82/43.81 thf(zip_derived_cl8, plain, (![X0 : $i]: ((mult @ X0 @ (i @ X0)) = (unit))),
% 299.82/43.81 inference('cnf', [status(esa)], [c09])).
% 299.82/43.81 thf(zip_derived_cl5, plain, (![X0 : $i]: ((mult @ unit @ X0) = (X0))),
% 299.82/43.81 inference('cnf', [status(esa)], [c06])).
% 299.82/43.81 thf(zip_derived_cl5, plain, (![X0 : $i]: ((mult @ unit @ X0) = (X0))),
% 299.82/43.81 inference('cnf', [status(esa)], [c06])).
% 299.82/43.81 thf(zip_derived_cl3, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.81 inference('cnf', [status(esa)], [c04])).
% 299.82/43.81 thf(zip_derived_cl40, plain, (![X0 : $i]: ((rd @ X0 @ X0) = (unit))),
% 299.82/43.81 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl3])).
% 299.82/43.81 thf(zip_derived_cl506, plain,
% 299.82/43.81 (![X0 : $i]:
% 299.82/43.81 ((unit) = (mult @ (mult @ (i @ X0) @ (mult @ X0 @ X0)) @ (i @ X0)))),
% 299.82/43.81 inference('demod', [status(thm)],
% 299.82/43.81 [zip_derived_cl486, zip_derived_cl8, zip_derived_cl5,
% 299.82/43.81 zip_derived_cl40])).
% 299.82/43.81 thf(zip_derived_cl3, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.81 inference('cnf', [status(esa)], [c04])).
% 299.82/43.81 thf(zip_derived_cl524, plain,
% 299.82/43.81 (![X0 : $i]:
% 299.82/43.81 ((rd @ unit @ (i @ X0)) = (mult @ (i @ X0) @ (mult @ X0 @ X0)))),
% 299.82/43.81 inference('sup+', [status(thm)], [zip_derived_cl506, zip_derived_cl3])).
% 299.82/43.81 thf(zip_derived_cl8, plain, (![X0 : $i]: ((mult @ X0 @ (i @ X0)) = (unit))),
% 299.82/43.81 inference('cnf', [status(esa)], [c09])).
% 299.82/43.81 thf(zip_derived_cl3, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.81 inference('cnf', [status(esa)], [c04])).
% 299.82/43.81 thf(zip_derived_cl38, plain, (![X0 : $i]: ((rd @ unit @ (i @ X0)) = (X0))),
% 299.82/43.81 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl3])).
% 299.82/43.81 thf(zip_derived_cl552, plain,
% 299.82/43.81 (![X0 : $i]: ((X0) = (mult @ (i @ X0) @ (mult @ X0 @ X0)))),
% 299.82/43.81 inference('demod', [status(thm)], [zip_derived_cl524, zip_derived_cl38])).
% 299.82/43.81 thf(zip_derived_cl579, plain,
% 299.82/43.81 (![X0 : $i]: ((i @ X0) = (mult @ (i @ (i @ X0)) @ (rd @ (i @ X0) @ X0)))),
% 299.82/43.81 inference('sup+', [status(thm)], [zip_derived_cl386, zip_derived_cl552])).
% 299.82/43.81 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.81 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.81 thf(zip_derived_cl585, plain,
% 299.82/43.81 (![X0 : $i]: ((i @ X0) = (mult @ X0 @ (rd @ (i @ X0) @ X0)))),
% 299.82/43.81 inference('demod', [status(thm)], [zip_derived_cl579, zip_derived_cl32])).
% 299.82/43.81 thf(zip_derived_cl68, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i]:
% 299.82/43.81 ((mult @ (mult @ X0 @ X0) @ (mult @ X0 @ X1))
% 299.82/43.81 = (mult @ X0 @ (mult @ (mult @ X0 @ X0) @ X1)))),
% 299.82/43.81 inference('demod', [status(thm)], [zip_derived_cl57, zip_derived_cl5])).
% 299.82/43.81 thf(zip_derived_cl629, plain,
% 299.82/43.81 (![X0 : $i]:
% 299.82/43.81 ((mult @ (mult @ X0 @ X0) @ (i @ X0))
% 299.82/43.81 = (mult @ X0 @ (mult @ (mult @ X0 @ X0) @ (rd @ (i @ X0) @ X0))))),
% 299.82/43.81 inference('sup+', [status(thm)], [zip_derived_cl585, zip_derived_cl68])).
% 299.82/43.81 thf(zip_derived_cl351, plain,
% 299.82/43.81 (![X0 : $i]: ((X0) = (mult @ (mult @ X0 @ X0) @ (i @ X0)))),
% 299.82/43.81 inference('demod', [status(thm)], [zip_derived_cl331, zip_derived_cl1])).
% 299.82/43.81 thf(zip_derived_cl646, plain,
% 299.82/43.81 (![X0 : $i]:
% 299.82/43.81 ((X0) = (mult @ X0 @ (mult @ (mult @ X0 @ X0) @ (rd @ (i @ X0) @ X0))))),
% 299.82/43.81 inference('demod', [status(thm)], [zip_derived_cl629, zip_derived_cl351])).
% 299.82/43.81 thf(zip_derived_cl1, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.81 inference('cnf', [status(esa)], [c02])).
% 299.82/43.81 thf(zip_derived_cl856, plain,
% 299.82/43.81 (![X0 : $i]:
% 299.82/43.81 ((ld @ X0 @ X0) = (mult @ (mult @ X0 @ X0) @ (rd @ (i @ X0) @ X0)))),
% 299.82/43.81 inference('sup+', [status(thm)], [zip_derived_cl646, zip_derived_cl1])).
% 299.82/43.81 thf(zip_derived_cl4, plain, (![X0 : $i]: ((mult @ X0 @ unit) = (X0))),
% 299.82/43.81 inference('cnf', [status(esa)], [c05])).
% 299.82/43.81 thf(zip_derived_cl1, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.81 inference('cnf', [status(esa)], [c02])).
% 299.82/43.81 thf(zip_derived_cl16, plain, (![X0 : $i]: ((ld @ X0 @ X0) = (unit))),
% 299.82/43.81 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl1])).
% 299.82/43.81 thf(zip_derived_cl889, plain,
% 299.82/43.81 (![X0 : $i]: ((unit) = (mult @ (mult @ X0 @ X0) @ (rd @ (i @ X0) @ X0)))),
% 299.82/43.81 inference('demod', [status(thm)], [zip_derived_cl856, zip_derived_cl16])).
% 299.82/43.81 thf(zip_derived_cl1, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.81 inference('cnf', [status(esa)], [c02])).
% 299.82/43.81 thf(zip_derived_cl901, plain,
% 299.82/43.81 (![X0 : $i]: ((ld @ (mult @ X0 @ X0) @ unit) = (rd @ (i @ X0) @ X0))),
% 299.82/43.81 inference('sup+', [status(thm)], [zip_derived_cl889, zip_derived_cl1])).
% 299.82/43.81 thf(zip_derived_cl17, plain, (![X0 : $i]: ((ld @ X0 @ unit) = (i @ X0))),
% 299.82/43.81 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl1])).
% 299.82/43.81 thf(zip_derived_cl929, plain,
% 299.82/43.81 (![X0 : $i]: ((i @ (mult @ X0 @ X0)) = (rd @ (i @ X0) @ X0))),
% 299.82/43.81 inference('demod', [status(thm)], [zip_derived_cl901, zip_derived_cl17])).
% 299.82/43.81 thf(c03, axiom, (( mult @ ( rd @ A @ B ) @ B ) = ( A ))).
% 299.82/43.81 thf(zip_derived_cl2, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.81 inference('cnf', [status(esa)], [c03])).
% 299.82/43.81 thf(zip_derived_cl949, plain,
% 299.82/43.81 (![X0 : $i]: ((mult @ (i @ (mult @ X0 @ X0)) @ X0) = (i @ X0))),
% 299.82/43.81 inference('sup+', [status(thm)], [zip_derived_cl929, zip_derived_cl2])).
% 299.82/43.81 thf(zip_derived_cl2, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.81 inference('cnf', [status(esa)], [c03])).
% 299.82/43.81 thf(zip_derived_cl178, plain,
% 299.82/43.81 (![X0 : $i, X1 : $i]:
% 299.82/43.81 ((rd @ (mult @ X0 @ (mult @ (mult @ X1 @ X0) @ X0)) @ X0)
% 299.82/43.81 = (mult @ (mult @ X0 @ X1) @ X0))),
% 299.82/43.81 inference('sup+', [status(thm)], [zip_derived_cl63, zip_derived_cl3])).
% 299.82/43.81 thf(zip_derived_cl1622, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (mult @ X1 @ (mult @ X0 @ X1)) @ X1)
% 299.82/43.82 = (mult @ (mult @ X1 @ (rd @ X0 @ X1)) @ X1))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl178])).
% 299.82/43.82 thf(zip_derived_cl1711, plain,
% 299.82/43.82 (![X0 : $i]:
% 299.82/43.82 ((rd @ (mult @ X0 @ (i @ X0)) @ X0)
% 299.82/43.82 = (mult @ (mult @ X0 @ (rd @ (i @ (mult @ X0 @ X0)) @ X0)) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl949, zip_derived_cl1622])).
% 299.82/43.82 thf(zip_derived_cl8, plain, (![X0 : $i]: ((mult @ X0 @ (i @ X0)) = (unit))),
% 299.82/43.82 inference('cnf', [status(esa)], [c09])).
% 299.82/43.82 thf(zip_derived_cl9, plain, (![X0 : $i]: ((mult @ (i @ X0) @ X0) = (unit))),
% 299.82/43.82 inference('cnf', [status(esa)], [c10])).
% 299.82/43.82 thf(zip_derived_cl3, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c04])).
% 299.82/43.82 thf(zip_derived_cl41, plain, (![X0 : $i]: ((rd @ unit @ X0) = (i @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl1726, plain,
% 299.82/43.82 (![X0 : $i]:
% 299.82/43.82 ((i @ X0)
% 299.82/43.82 = (mult @ (mult @ X0 @ (rd @ (i @ (mult @ X0 @ X0)) @ X0)) @ X0))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl1711, zip_derived_cl8, zip_derived_cl41])).
% 299.82/43.82 thf(zip_derived_cl3, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c04])).
% 299.82/43.82 thf(zip_derived_cl1974, plain,
% 299.82/43.82 (![X0 : $i]:
% 299.82/43.82 ((rd @ (i @ X0) @ X0)
% 299.82/43.82 = (mult @ X0 @ (rd @ (i @ (mult @ X0 @ X0)) @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl1726, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl929, plain,
% 299.82/43.82 (![X0 : $i]: ((i @ (mult @ X0 @ X0)) = (rd @ (i @ X0) @ X0))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl901, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl2019, plain,
% 299.82/43.82 (![X0 : $i]:
% 299.82/43.82 ((i @ (mult @ X0 @ X0))
% 299.82/43.82 = (mult @ X0 @ (rd @ (i @ (mult @ X0 @ X0)) @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl1974, zip_derived_cl929])).
% 299.82/43.82 thf(zip_derived_cl7, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 299.82/43.82 ((mult @ (mult @ X0 @ X1) @ (mult @ X1 @ (mult @ X2 @ X1)))
% 299.82/43.82 = (mult @ (mult @ X0 @ (mult @ X1 @ (mult @ X1 @ X2))) @ X1))),
% 299.82/43.82 inference('cnf', [status(esa)], [c08])).
% 299.82/43.82 thf(zip_derived_cl2354, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X1 @ X0) @
% 299.82/43.82 (mult @ X0 @ (mult @ (rd @ (i @ (mult @ X0 @ X0)) @ X0) @ X0)))
% 299.82/43.82 = (mult @ (mult @ X1 @ (mult @ X0 @ (i @ (mult @ X0 @ X0)))) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl2019, zip_derived_cl7])).
% 299.82/43.82 thf(zip_derived_cl2, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c03])).
% 299.82/43.82 thf(zip_derived_cl585, plain,
% 299.82/43.82 (![X0 : $i]: ((i @ X0) = (mult @ X0 @ (rd @ (i @ X0) @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl579, zip_derived_cl32])).
% 299.82/43.82 thf(zip_derived_cl929, plain,
% 299.82/43.82 (![X0 : $i]: ((i @ (mult @ X0 @ X0)) = (rd @ (i @ X0) @ X0))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl901, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl945, plain,
% 299.82/43.82 (![X0 : $i]: ((i @ X0) = (mult @ X0 @ (i @ (mult @ X0 @ X0))))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl585, zip_derived_cl929])).
% 299.82/43.82 thf(zip_derived_cl945, plain,
% 299.82/43.82 (![X0 : $i]: ((i @ X0) = (mult @ X0 @ (i @ (mult @ X0 @ X0))))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl585, zip_derived_cl929])).
% 299.82/43.82 thf(zip_derived_cl2392, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X1 @ X0) @ (i @ X0))
% 299.82/43.82 = (mult @ (mult @ X1 @ (i @ X0)) @ X0))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl2354, zip_derived_cl2, zip_derived_cl945,
% 299.82/43.82 zip_derived_cl945])).
% 299.82/43.82 thf(zip_derived_cl2392, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X1 @ X0) @ (i @ X0))
% 299.82/43.82 = (mult @ (mult @ X1 @ (i @ X0)) @ X0))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl2354, zip_derived_cl2, zip_derived_cl945,
% 299.82/43.82 zip_derived_cl945])).
% 299.82/43.82 thf(zip_derived_cl7288, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ (i @ X0) @ X1) @ (i @ X0))
% 299.82/43.82 = (mult @ (i @ X0) @
% 299.82/43.82 (mult @ (mult @ (mult @ X1 @ X0) @ (i @ X0)) @ (i @ X0))))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl66, zip_derived_cl2392, zip_derived_cl2392])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl7288, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ (i @ X0) @ X1) @ (i @ X0))
% 299.82/43.82 = (mult @ (i @ X0) @
% 299.82/43.82 (mult @ (mult @ (mult @ X1 @ X0) @ (i @ X0)) @ (i @ X0))))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl66, zip_derived_cl2392, zip_derived_cl2392])).
% 299.82/43.82 thf(zip_derived_cl178, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (mult @ X0 @ (mult @ (mult @ X1 @ X0) @ X0)) @ X0)
% 299.82/43.82 = (mult @ (mult @ X0 @ X1) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl63, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl7324, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (mult @ (mult @ (i @ X0) @ X1) @ (i @ X0)) @ (i @ X0))
% 299.82/43.82 = (mult @ (mult @ (i @ X0) @ (mult @ X1 @ X0)) @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl7288, zip_derived_cl178])).
% 299.82/43.82 thf(zip_derived_cl3, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c04])).
% 299.82/43.82 thf(zip_derived_cl7443, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X0) @ X1)
% 299.82/43.82 = (mult @ (mult @ (i @ X0) @ (mult @ X1 @ X0)) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl7324, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl7494, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ (i @ X0)) @ X1)
% 299.82/43.82 = (mult @ (mult @ (i @ (i @ X0)) @ (mult @ X1 @ (i @ X0))) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl32, zip_derived_cl7443])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl7555, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @ X1) = (mult @ (mult @ X0 @ (mult @ X1 @ (i @ X0))) @ X0))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl7494, zip_derived_cl32, zip_derived_cl32])).
% 299.82/43.82 thf(zip_derived_cl3, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c04])).
% 299.82/43.82 thf(zip_derived_cl7633, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (mult @ X1 @ X0) @ X1) = (mult @ X1 @ (mult @ X0 @ (i @ X1))))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl7555, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl7927, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X0 @ (rd @ (mult @ X0 @ X1) @ X0)) = (mult @ X1 @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl7633, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl8198, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (i @ X0) @
% 299.82/43.82 (rd @ (mult @ (mult @ (i @ X0) @ X1) @ (i @ X0)) @ (i @ X0)))
% 299.82/43.82 = (mult @
% 299.82/43.82 (mult @ (mult @ (mult @ X1 @ X0) @ (i @ X0)) @ (i @ X0)) @
% 299.82/43.82 (i @ (i @ X0))))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl7288, zip_derived_cl7927])).
% 299.82/43.82 thf(zip_derived_cl3, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c04])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl2392, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X1 @ X0) @ (i @ X0))
% 299.82/43.82 = (mult @ (mult @ X1 @ (i @ X0)) @ X0))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl2354, zip_derived_cl2, zip_derived_cl945,
% 299.82/43.82 zip_derived_cl945])).
% 299.82/43.82 thf(zip_derived_cl2392, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X1 @ X0) @ (i @ X0))
% 299.82/43.82 = (mult @ (mult @ X1 @ (i @ X0)) @ X0))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl2354, zip_derived_cl2, zip_derived_cl945,
% 299.82/43.82 zip_derived_cl945])).
% 299.82/43.82 thf(zip_derived_cl8, plain, (![X0 : $i]: ((mult @ X0 @ (i @ X0)) = (unit))),
% 299.82/43.82 inference('cnf', [status(esa)], [c09])).
% 299.82/43.82 thf(zip_derived_cl6, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 299.82/43.82 ((mult @ (mult @ (mult @ X0 @ X1) @ X0) @ (mult @ X0 @ X2))
% 299.82/43.82 = (mult @ X0 @ (mult @ (mult @ (mult @ X1 @ X0) @ X0) @ X2)))),
% 299.82/43.82 inference('cnf', [status(esa)], [c07])).
% 299.82/43.82 thf(zip_derived_cl49, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ (mult @ X0 @ X1) @ X0) @ unit)
% 299.82/43.82 = (mult @ X0 @ (mult @ (mult @ (mult @ X1 @ X0) @ X0) @ (i @ X0))))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl6])).
% 299.82/43.82 thf(zip_derived_cl4, plain, (![X0 : $i]: ((mult @ X0 @ unit) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c05])).
% 299.82/43.82 thf(zip_derived_cl64, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X0 @ X1) @ X0)
% 299.82/43.82 = (mult @ X0 @ (mult @ (mult @ (mult @ X1 @ X0) @ X0) @ (i @ X0))))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl49, zip_derived_cl4])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl6314, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X0 @ (mult @ (mult @ X0 @ X1) @ X0))
% 299.82/43.82 = (mult @ (mult @ (mult @ X1 @ X0) @ X0) @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl64, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl8231, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((X1) = (mult @ (ld @ X0 @ (mult @ (mult @ X0 @ X1) @ X0)) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl8198, zip_derived_cl3, zip_derived_cl1,
% 299.82/43.82 zip_derived_cl32, zip_derived_cl2392, zip_derived_cl2392,
% 299.82/43.82 zip_derived_cl6314])).
% 299.82/43.82 thf(zip_derived_cl9183, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @ X1)
% 299.82/43.82 = (mult @
% 299.82/43.82 (ld @ X0 @ (mult @ X0 @ (mult @ X0 @ (mult @ X1 @ X0)))) @
% 299.82/43.82 (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl94, zip_derived_cl8231])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl9253, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @ X1) = (mult @ (mult @ X0 @ (mult @ X1 @ X0)) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl9183, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl3, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c04])).
% 299.82/43.82 thf(zip_derived_cl9324, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (mult @ X1 @ X0) @ (i @ X1)) = (mult @ X1 @ (mult @ X0 @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl9253, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl9719, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ X0 @ (i @ X1)) = (mult @ X1 @ (mult @ (ld @ X1 @ X0) @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl9324])).
% 299.82/43.82 thf(zip_derived_cl25816, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 299.82/43.82 ((mult @ (mult @ X2 @ X1) @ (rd @ X0 @ (i @ X1)))
% 299.82/43.82 = (mult @ (mult @ X2 @ (mult @ X1 @ X0)) @ X1))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl86, zip_derived_cl9719])).
% 299.82/43.82 thf(zip_derived_cl25976, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ unit @ (rd @ X1 @ (i @ (i @ X0))))
% 299.82/43.82 = (mult @ (mult @ X0 @ (mult @ (i @ X0) @ X1)) @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl25816])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl5, plain, (![X0 : $i]: ((mult @ unit @ X0) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c06])).
% 299.82/43.82 thf(zip_derived_cl26075, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ X1 @ X0)
% 299.82/43.82 = (mult @ (mult @ X0 @ (mult @ (i @ X0) @ X1)) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl25976, zip_derived_cl32, zip_derived_cl5])).
% 299.82/43.82 thf(zip_derived_cl178, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (mult @ X0 @ (mult @ (mult @ X1 @ X0) @ X0)) @ X0)
% 299.82/43.82 = (mult @ (mult @ X0 @ X1) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl63, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl0, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c01])).
% 299.82/43.82 thf(zip_derived_cl7927, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X0 @ (rd @ (mult @ X0 @ X1) @ X0)) = (mult @ X1 @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl7633, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl8160, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X1 @ (rd @ X0 @ X1)) = (mult @ (ld @ X1 @ X0) @ (i @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl7927])).
% 299.82/43.82 thf(zip_derived_cl8287, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (i @ X0) @ (rd @ X1 @ (i @ X0)))
% 299.82/43.82 = (mult @ (ld @ (i @ X0) @ X1) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl32, zip_derived_cl8160])).
% 299.82/43.82 thf(zip_derived_cl10760, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (i @ X0) @ (mult @ (mult @ (i @ X0) @ X1) @ (i @ X0)))
% 299.82/43.82 = (mult @
% 299.82/43.82 (ld @ (i @ X0) @
% 299.82/43.82 (mult @ (i @ X0) @ (mult @ (mult @ X1 @ (i @ X0)) @ (i @ X0)))) @
% 299.82/43.82 X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl178, zip_derived_cl8287])).
% 299.82/43.82 thf(zip_derived_cl2, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c03])).
% 299.82/43.82 thf(zip_derived_cl7443, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X0) @ X1)
% 299.82/43.82 = (mult @ (mult @ (i @ X0) @ (mult @ X1 @ X0)) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl7324, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl7531, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X1) @ (rd @ X0 @ X1))
% 299.82/43.82 = (mult @ (mult @ (i @ X1) @ X0) @ (i @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl7443])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl2392, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X1 @ X0) @ (i @ X0))
% 299.82/43.82 = (mult @ (mult @ X1 @ (i @ X0)) @ X0))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl2354, zip_derived_cl2, zip_derived_cl945,
% 299.82/43.82 zip_derived_cl945])).
% 299.82/43.82 thf(zip_derived_cl2392, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X1 @ X0) @ (i @ X0))
% 299.82/43.82 = (mult @ (mult @ X1 @ (i @ X0)) @ X0))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl2354, zip_derived_cl2, zip_derived_cl945,
% 299.82/43.82 zip_derived_cl945])).
% 299.82/43.82 thf(zip_derived_cl10788, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ X1 @ X0)
% 299.82/43.82 = (mult @ (mult @ (mult @ X1 @ X0) @ (i @ X0)) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl10760, zip_derived_cl7531, zip_derived_cl1,
% 299.82/43.82 zip_derived_cl1, zip_derived_cl2392, zip_derived_cl2392])).
% 299.82/43.82 thf(zip_derived_cl26411, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (mult @ X0 @ (mult @ (i @ X0) @ X1)) @ (i @ X0))
% 299.82/43.82 = (mult @ (mult @ (rd @ X1 @ X0) @ (i @ (i @ X0))) @ (i @ (i @ X0))))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl26075, zip_derived_cl10788])).
% 299.82/43.82 thf(zip_derived_cl9324, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (mult @ X1 @ X0) @ (i @ X1)) = (mult @ X1 @ (mult @ X0 @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl9253, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl2, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c03])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl26603, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @ (mult @ (mult @ (i @ X0) @ X1) @ X0)) = (mult @ X1 @ X0))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl26411, zip_derived_cl9324, zip_derived_cl32,
% 299.82/43.82 zip_derived_cl2, zip_derived_cl32])).
% 299.82/43.82 thf(zip_derived_cl0, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c01])).
% 299.82/43.82 thf(zip_derived_cl1726, plain,
% 299.82/43.82 (![X0 : $i]:
% 299.82/43.82 ((i @ X0)
% 299.82/43.82 = (mult @ (mult @ X0 @ (rd @ (i @ (mult @ X0 @ X0)) @ X0)) @ X0))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl1711, zip_derived_cl8, zip_derived_cl41])).
% 299.82/43.82 thf(zip_derived_cl6, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 299.82/43.82 ((mult @ (mult @ (mult @ X0 @ X1) @ X0) @ (mult @ X0 @ X2))
% 299.82/43.82 = (mult @ X0 @ (mult @ (mult @ (mult @ X1 @ X0) @ X0) @ X2)))),
% 299.82/43.82 inference('cnf', [status(esa)], [c07])).
% 299.82/43.82 thf(zip_derived_cl1994, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X0) @ (mult @ X0 @ X1))
% 299.82/43.82 = (mult @ X0 @
% 299.82/43.82 (mult @
% 299.82/43.82 (mult @ (mult @ (rd @ (i @ (mult @ X0 @ X0)) @ X0) @ X0) @ X0) @
% 299.82/43.82 X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl1726, zip_derived_cl6])).
% 299.82/43.82 thf(zip_derived_cl2, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c03])).
% 299.82/43.82 thf(zip_derived_cl949, plain,
% 299.82/43.82 (![X0 : $i]: ((mult @ (i @ (mult @ X0 @ X0)) @ X0) = (i @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl929, zip_derived_cl2])).
% 299.82/43.82 thf(zip_derived_cl2032, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X0) @ (mult @ X0 @ X1))
% 299.82/43.82 = (mult @ X0 @ (mult @ (i @ X0) @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl1994, zip_derived_cl2, zip_derived_cl949])).
% 299.82/43.82 thf(zip_derived_cl2069, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X1) @ X0)
% 299.82/43.82 = (mult @ X1 @ (mult @ (i @ X1) @ (ld @ X1 @ X0))))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl2032])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl3548, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X1 @ (mult @ (i @ X1) @ X0))
% 299.82/43.82 = (mult @ (i @ X1) @ (ld @ X1 @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl2069, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl26773, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X0 @ (mult @ X1 @ (i @ X0)))
% 299.82/43.82 = (mult @ (i @ X0) @
% 299.82/43.82 (ld @ X0 @ (mult @ (mult @ (i @ (i @ X0)) @ X1) @ (i @ X0)))))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl26603, zip_derived_cl3548])).
% 299.82/43.82 thf(zip_derived_cl0, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c01])).
% 299.82/43.82 thf(zip_derived_cl2, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c03])).
% 299.82/43.82 thf(zip_derived_cl9253, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @ X1) = (mult @ (mult @ X0 @ (mult @ X1 @ X0)) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl9183, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl9401, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (rd @ X0 @ X1)) = (mult @ (mult @ X1 @ X0) @ (i @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl9253])).
% 299.82/43.82 thf(zip_derived_cl9900, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (rd @ (ld @ X1 @ X0) @ X1)) = (mult @ X0 @ (i @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl9401])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl12100, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X0 @ (mult @ X1 @ (i @ X0))) = (rd @ (ld @ X0 @ X1) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl9900, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl9401, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (rd @ X0 @ X1)) = (mult @ (mult @ X1 @ X0) @ (i @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl9253])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl26904, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (ld @ X0 @ X1) @ X0) = (mult @ (i @ X0) @ (rd @ X1 @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl26773, zip_derived_cl12100, zip_derived_cl32,
% 299.82/43.82 zip_derived_cl9401, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl28284, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (ld @ X0 @ (mult @ X0 @ (mult @ (mult @ X1 @ X0) @ X0))) @ X0)
% 299.82/43.82 = (mult @ (i @ X0) @ (mult @ (mult @ X0 @ X1) @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl178, zip_derived_cl26904])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl3, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c04])).
% 299.82/43.82 thf(zip_derived_cl28333, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ X0) = (mult @ (i @ X0) @ (mult @ (mult @ X0 @ X1) @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl28284, zip_derived_cl1, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl6314, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X0 @ (mult @ (mult @ X0 @ X1) @ X0))
% 299.82/43.82 = (mult @ (mult @ (mult @ X1 @ X0) @ X0) @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl64, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl2, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c03])).
% 299.82/43.82 thf(zip_derived_cl7633, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (mult @ X1 @ X0) @ X1) = (mult @ X1 @ (mult @ X0 @ (i @ X1))))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl7555, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl8016, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (mult @ X1 @ (rd @ X0 @ (i @ X1))) @ X1) = (mult @ X1 @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl7633])).
% 299.82/43.82 thf(zip_derived_cl2, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c03])).
% 299.82/43.82 thf(zip_derived_cl8371, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X1 @ X0) @ X1) = (mult @ X1 @ (rd @ X0 @ (i @ X1))))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl8016, zip_derived_cl2])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl8447, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X0 @ (mult @ (mult @ X0 @ X1) @ X0)) = (rd @ X1 @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl8371, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl10295, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ X1 @ (i @ X0))
% 299.82/43.82 = (mult @ (mult @ (mult @ X1 @ X0) @ X0) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl6314, zip_derived_cl8447])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl9401, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (rd @ X0 @ X1)) = (mult @ (mult @ X1 @ X0) @ (i @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl9253])).
% 299.82/43.82 thf(zip_derived_cl9893, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X0) @ (rd @ X1 @ (i @ X0)))
% 299.82/43.82 = (mult @ (mult @ (i @ X0) @ X1) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl32, zip_derived_cl9401])).
% 299.82/43.82 thf(zip_derived_cl26075, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ X1 @ X0)
% 299.82/43.82 = (mult @ (mult @ X0 @ (mult @ (i @ X0) @ X1)) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl25976, zip_derived_cl32, zip_derived_cl5])).
% 299.82/43.82 thf(zip_derived_cl26525, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (rd @ X1 @ (i @ X0)) @ X0)
% 299.82/43.82 = (mult @ (mult @ X0 @ (mult @ (mult @ (i @ X0) @ X1) @ X0)) @
% 299.82/43.82 (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl9893, zip_derived_cl26075])).
% 299.82/43.82 thf(zip_derived_cl2, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c03])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl2, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c03])).
% 299.82/43.82 thf(zip_derived_cl2392, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X1 @ X0) @ (i @ X0))
% 299.82/43.82 = (mult @ (mult @ X1 @ (i @ X0)) @ X0))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl2354, zip_derived_cl2, zip_derived_cl945,
% 299.82/43.82 zip_derived_cl945])).
% 299.82/43.82 thf(zip_derived_cl3, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c04])).
% 299.82/43.82 thf(zip_derived_cl2424, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (mult @ (mult @ X1 @ X0) @ (i @ X0)) @ X0)
% 299.82/43.82 = (mult @ X1 @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl2392, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl4273, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (mult @ X0 @ (i @ X1)) @ X1)
% 299.82/43.82 = (mult @ (rd @ X0 @ X1) @ (i @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl2424])).
% 299.82/43.82 thf(zip_derived_cl4343, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (mult @ X1 @ X0) @ (i @ X0))
% 299.82/43.82 = (mult @ (rd @ X1 @ (i @ X0)) @ (i @ (i @ X0))))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl32, zip_derived_cl4273])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl4362, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (mult @ X1 @ X0) @ (i @ X0))
% 299.82/43.82 = (mult @ (rd @ X1 @ (i @ X0)) @ X0))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl4343, zip_derived_cl32])).
% 299.82/43.82 thf(zip_derived_cl4401, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ X0 @ (i @ X1)) = (mult @ (rd @ (rd @ X0 @ X1) @ (i @ X1)) @ X1))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl4362])).
% 299.82/43.82 thf(zip_derived_cl3, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c04])).
% 299.82/43.82 thf(zip_derived_cl5299, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (rd @ X1 @ (i @ X0)) @ X0) = (rd @ (rd @ X1 @ X0) @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl4401, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl1622, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (mult @ X1 @ (mult @ X0 @ X1)) @ X1)
% 299.82/43.82 = (mult @ (mult @ X1 @ (rd @ X0 @ X1)) @ X1))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl178])).
% 299.82/43.82 thf(zip_derived_cl8287, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (i @ X0) @ (rd @ X1 @ (i @ X0)))
% 299.82/43.82 = (mult @ (ld @ (i @ X0) @ X1) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl32, zip_derived_cl8160])).
% 299.82/43.82 thf(zip_derived_cl10762, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (i @ X0) @
% 299.82/43.82 (mult @ (mult @ (i @ X0) @ (rd @ X1 @ (i @ X0))) @ (i @ X0)))
% 299.82/43.82 = (mult @
% 299.82/43.82 (ld @ (i @ X0) @ (mult @ (i @ X0) @ (mult @ X1 @ (i @ X0)))) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl1622, zip_derived_cl8287])).
% 299.82/43.82 thf(zip_derived_cl7531, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X1) @ (rd @ X0 @ X1))
% 299.82/43.82 = (mult @ (mult @ (i @ X1) @ X0) @ (i @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl7443])).
% 299.82/43.82 thf(zip_derived_cl5299, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (rd @ X1 @ (i @ X0)) @ X0) = (rd @ (rd @ X1 @ X0) @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl4401, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl2392, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X1 @ X0) @ (i @ X0))
% 299.82/43.82 = (mult @ (mult @ X1 @ (i @ X0)) @ X0))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl2354, zip_derived_cl2, zip_derived_cl945,
% 299.82/43.82 zip_derived_cl945])).
% 299.82/43.82 thf(zip_derived_cl10790, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (rd @ X1 @ X0) @ (i @ X0))
% 299.82/43.82 = (mult @ (mult @ X1 @ X0) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl10762, zip_derived_cl7531, zip_derived_cl5299,
% 299.82/43.82 zip_derived_cl1, zip_derived_cl1, zip_derived_cl2392])).
% 299.82/43.82 thf(zip_derived_cl10824, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (rd @ X1 @ (i @ X0)) @ X0)
% 299.82/43.82 = (mult @ (mult @ X1 @ X0) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl5299, zip_derived_cl10790])).
% 299.82/43.82 thf(zip_derived_cl9253, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @ X1) = (mult @ (mult @ X0 @ (mult @ X1 @ X0)) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl9183, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl26569, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X1 @ X0) @ (i @ X0))
% 299.82/43.82 = (mult @ X0 @ (mult @ (i @ X0) @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl26525, zip_derived_cl10824, zip_derived_cl9253])).
% 299.82/43.82 thf(zip_derived_cl12100, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X0 @ (mult @ X1 @ (i @ X0))) = (rd @ (ld @ X0 @ X1) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl9900, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl27006, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X1 @ (mult @ X1 @ (mult @ (i @ X1) @ X0)))
% 299.82/43.82 = (rd @ (ld @ X1 @ (mult @ X0 @ X1)) @ X1))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl26569, zip_derived_cl12100])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl27230, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X1) @ X0) = (rd @ (ld @ X1 @ (mult @ X0 @ X1)) @ X1))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl27006, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl2, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c03])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl22, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ (rd @ X0 @ X1) @ X0) = (X1))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl0, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c01])).
% 299.82/43.82 thf(zip_derived_cl8447, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X0 @ (mult @ (mult @ X0 @ X1) @ X0)) = (rd @ X1 @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl8371, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl10326, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X1 @ (mult @ X0 @ X1)) = (rd @ (ld @ X1 @ X0) @ (i @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl8447])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl10788, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ X1 @ X0)
% 299.82/43.82 = (mult @ (mult @ (mult @ X1 @ X0) @ (i @ X0)) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl10760, zip_derived_cl7531, zip_derived_cl1,
% 299.82/43.82 zip_derived_cl1, zip_derived_cl2392, zip_derived_cl2392])).
% 299.82/43.82 thf(zip_derived_cl8, plain, (![X0 : $i]: ((mult @ X0 @ (i @ X0)) = (unit))),
% 299.82/43.82 inference('cnf', [status(esa)], [c09])).
% 299.82/43.82 thf(zip_derived_cl6, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 299.82/43.82 ((mult @ (mult @ (mult @ X0 @ X1) @ X0) @ (mult @ X0 @ X2))
% 299.82/43.82 = (mult @ X0 @ (mult @ (mult @ (mult @ X1 @ X0) @ X0) @ X2)))),
% 299.82/43.82 inference('cnf', [status(esa)], [c07])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl42, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 299.82/43.82 ((ld @ (mult @ (mult @ X1 @ X2) @ X1) @
% 299.82/43.82 (mult @ X1 @ (mult @ (mult @ (mult @ X2 @ X1) @ X1) @ X0)))
% 299.82/43.82 = (mult @ X1 @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl140, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (mult @ (mult @ X0 @ X1) @ X0) @ (mult @ X0 @ unit))
% 299.82/43.82 = (mult @ X0 @ (i @ (mult @ (mult @ X1 @ X0) @ X0))))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl42])).
% 299.82/43.82 thf(zip_derived_cl4, plain, (![X0 : $i]: ((mult @ X0 @ unit) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c05])).
% 299.82/43.82 thf(zip_derived_cl165, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (mult @ (mult @ X0 @ X1) @ X0) @ X0)
% 299.82/43.82 = (mult @ X0 @ (i @ (mult @ (mult @ X1 @ X0) @ X0))))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl140, zip_derived_cl4])).
% 299.82/43.82 thf(zip_derived_cl11934, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (mult @ (mult @ (i @ X0) @ (mult @ X1 @ X0)) @ (i @ X0)) @
% 299.82/43.82 (i @ X0)) = (mult @ (i @ X0) @ (i @ (rd @ X1 @ X0))))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl10788, zip_derived_cl165])).
% 299.82/43.82 thf(zip_derived_cl7443, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X0) @ X1)
% 299.82/43.82 = (mult @ (mult @ (i @ X0) @ (mult @ X1 @ X0)) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl7324, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl12089, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (mult @ (i @ X0) @ X1) @ (i @ X0))
% 299.82/43.82 = (mult @ (i @ X0) @ (i @ (rd @ X1 @ X0))))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl11934, zip_derived_cl7443])).
% 299.82/43.82 thf(zip_derived_cl18272, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (mult @ (i @ (i @ X0)) @ X1) @ X0)
% 299.82/43.82 = (mult @ (i @ (i @ X0)) @ (i @ (rd @ X1 @ (i @ X0)))))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl32, zip_derived_cl12089])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl18308, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (mult @ X0 @ X1) @ X0)
% 299.82/43.82 = (mult @ X0 @ (i @ (rd @ X1 @ (i @ X0)))))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl18272, zip_derived_cl32, zip_derived_cl32])).
% 299.82/43.82 thf(zip_derived_cl19251, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (mult @ X0 @ (ld @ X0 @ X1)) @ X0)
% 299.82/43.82 = (mult @ X0 @ (i @ (ld @ X0 @ (mult @ X1 @ X0)))))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl10326, zip_derived_cl18308])).
% 299.82/43.82 thf(zip_derived_cl0, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c01])).
% 299.82/43.82 thf(zip_derived_cl19280, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X1 @ X0) = (mult @ X0 @ (i @ (ld @ X0 @ (mult @ X1 @ X0)))))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl19251, zip_derived_cl0])).
% 299.82/43.82 thf(zip_derived_cl3, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c04])).
% 299.82/43.82 thf(zip_derived_cl18308, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (mult @ X0 @ X1) @ X0)
% 299.82/43.82 = (mult @ X0 @ (i @ (rd @ X1 @ (i @ X0)))))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl18272, zip_derived_cl32, zip_derived_cl32])).
% 299.82/43.82 thf(zip_derived_cl19239, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (mult @ X1 @ (mult @ X0 @ (i @ X1))) @ X1)
% 299.82/43.82 = (mult @ X1 @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl18308])).
% 299.82/43.82 thf(zip_derived_cl7633, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (mult @ X1 @ X0) @ X1) = (mult @ X1 @ (mult @ X0 @ (i @ X1))))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl7555, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl19273, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (rd @ (mult @ X1 @ X0) @ X1) @ X1) = (mult @ X1 @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl19239, zip_derived_cl7633])).
% 299.82/43.82 thf(zip_derived_cl0, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c01])).
% 299.82/43.82 thf(zip_derived_cl19760, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (rd @ (mult @ X1 @ X0) @ X1) @ (mult @ X1 @ (i @ X0))) = (X1))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19273, zip_derived_cl0])).
% 299.82/43.82 thf(zip_derived_cl20573, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (rd @ (ld @ X1 @ X0) @ X0) @
% 299.82/43.82 (mult @ X0 @ (i @ (i @ (ld @ X0 @ (mult @ X1 @ X0)))))) = (X0))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl19280, zip_derived_cl19760])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl0, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c01])).
% 299.82/43.82 thf(zip_derived_cl20804, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (rd @ (ld @ X1 @ X0) @ X0) @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl20573, zip_derived_cl32, zip_derived_cl0])).
% 299.82/43.82 thf(zip_derived_cl21036, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (rd @ X0 @ X1) @ (mult @ (rd @ X1 @ X0) @ X1)) = (X1))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl20804])).
% 299.82/43.82 thf(zip_derived_cl42196, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ (i @ X1) @ X0) @
% 299.82/43.82 (mult @ (rd @ X1 @ (ld @ X1 @ (mult @ X0 @ X1))) @ X1)) = (X1))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl27230, zip_derived_cl21036])).
% 299.82/43.82 thf(zip_derived_cl2, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c03])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl26075, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ X1 @ X0)
% 299.82/43.82 = (mult @ (mult @ X0 @ (mult @ (i @ X0) @ X1)) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl25976, zip_derived_cl32, zip_derived_cl5])).
% 299.82/43.82 thf(zip_derived_cl26569, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X1 @ X0) @ (i @ X0))
% 299.82/43.82 = (mult @ X0 @ (mult @ (i @ X0) @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl26525, zip_derived_cl10824, zip_derived_cl9253])).
% 299.82/43.82 thf(zip_derived_cl27092, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (rd @ X1 @ X0) @ (i @ (i @ X0)))
% 299.82/43.82 = (mult @ (i @ X0) @
% 299.82/43.82 (mult @ (i @ (i @ X0)) @ (mult @ X0 @ (mult @ (i @ X0) @ X1)))))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl26075, zip_derived_cl26569])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl2, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c03])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl2032, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X0) @ (mult @ X0 @ X1))
% 299.82/43.82 = (mult @ X0 @ (mult @ (i @ X0) @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl1994, zip_derived_cl2, zip_derived_cl949])).
% 299.82/43.82 thf(zip_derived_cl2032, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X0) @ (mult @ X0 @ X1))
% 299.82/43.82 = (mult @ X0 @ (mult @ (i @ X0) @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl1994, zip_derived_cl2, zip_derived_cl949])).
% 299.82/43.82 thf(zip_derived_cl27150, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((X1)
% 299.82/43.82 = (mult @ X0 @
% 299.82/43.82 (mult @ X0 @ (mult @ (i @ X0) @ (mult @ (i @ X0) @ X1)))))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl27092, zip_derived_cl32, zip_derived_cl2,
% 299.82/43.82 zip_derived_cl32, zip_derived_cl2032, zip_derived_cl2032])).
% 299.82/43.82 thf(zip_derived_cl9, plain, (![X0 : $i]: ((mult @ (i @ X0) @ X0) = (unit))),
% 299.82/43.82 inference('cnf', [status(esa)], [c10])).
% 299.82/43.82 thf(zip_derived_cl7, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 299.82/43.82 ((mult @ (mult @ X0 @ X1) @ (mult @ X1 @ (mult @ X2 @ X1)))
% 299.82/43.82 = (mult @ (mult @ X0 @ (mult @ X1 @ (mult @ X1 @ X2))) @ X1))),
% 299.82/43.82 inference('cnf', [status(esa)], [c08])).
% 299.82/43.82 thf(zip_derived_cl84, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ (i @ (mult @ X0 @ (mult @ X0 @ X1))) @ X0) @
% 299.82/43.82 (mult @ X0 @ (mult @ X1 @ X0))) = (mult @ unit @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl7])).
% 299.82/43.82 thf(zip_derived_cl5, plain, (![X0 : $i]: ((mult @ unit @ X0) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c06])).
% 299.82/43.82 thf(zip_derived_cl95, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ (i @ (mult @ X0 @ (mult @ X0 @ X1))) @ X0) @
% 299.82/43.82 (mult @ X0 @ (mult @ X1 @ X0))) = (X0))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl84, zip_derived_cl5])).
% 299.82/43.82 thf(zip_derived_cl32079, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ (i @ X0) @ X1) @
% 299.82/43.82 (mult @ X1 @
% 299.82/43.82 (mult @ (mult @ (i @ X1) @ (mult @ (i @ X1) @ X0)) @ X1)))
% 299.82/43.82 = (X1))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl27150, zip_derived_cl95])).
% 299.82/43.82 thf(zip_derived_cl26603, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @ (mult @ (mult @ (i @ X0) @ X1) @ X0)) = (mult @ X1 @ X0))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl26411, zip_derived_cl9324, zip_derived_cl32,
% 299.82/43.82 zip_derived_cl2, zip_derived_cl32])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl26654, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X0 @ (mult @ X1 @ X0)) = (mult @ (mult @ (i @ X0) @ X1) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl26603, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl26654, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X0 @ (mult @ X1 @ X0)) = (mult @ (mult @ (i @ X0) @ X1) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl26603, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl0, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c01])).
% 299.82/43.82 thf(zip_derived_cl32216, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ (i @ X0) @ X1) @ (ld @ X1 @ (mult @ X0 @ X1))) = (X1))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl32079, zip_derived_cl26654,
% 299.82/43.82 zip_derived_cl26654, zip_derived_cl0])).
% 299.82/43.82 thf(zip_derived_cl32839, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X0 @ X1) @ (ld @ X1 @ (mult @ (i @ X0) @ X1))) = (X1))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl32, zip_derived_cl32216])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl33624, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (mult @ X1 @ X0) @ X0) = (ld @ X0 @ (mult @ (i @ X1) @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl32839, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl0, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c01])).
% 299.82/43.82 thf(zip_derived_cl34860, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @ (ld @ (mult @ X1 @ X0) @ X0)) = (mult @ (i @ X1) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl33624, zip_derived_cl0])).
% 299.82/43.82 thf(zip_derived_cl36248, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (ld @ X0 @ X1)) = (mult @ (i @ (rd @ X0 @ X1)) @ X1))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl34860])).
% 299.82/43.82 thf(zip_derived_cl32216, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ (i @ X0) @ X1) @ (ld @ X1 @ (mult @ X0 @ X1))) = (X1))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl32079, zip_derived_cl26654,
% 299.82/43.82 zip_derived_cl26654, zip_derived_cl0])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl32609, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (mult @ (i @ X1) @ X0) @ X0) = (ld @ X0 @ (mult @ X1 @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl32216, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl36835, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (mult @ X0 @ (ld @ X1 @ X0)) @ X0)
% 299.82/43.82 = (ld @ X0 @ (mult @ (rd @ X1 @ X0) @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl36248, zip_derived_cl32609])).
% 299.82/43.82 thf(zip_derived_cl2, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c03])).
% 299.82/43.82 thf(zip_derived_cl36987, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (mult @ X0 @ (ld @ X1 @ X0)) @ X0) = (ld @ X0 @ X1))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl36835, zip_derived_cl2])).
% 299.82/43.82 thf(zip_derived_cl0, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c01])).
% 299.82/43.82 thf(zip_derived_cl3, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c04])).
% 299.82/43.82 thf(zip_derived_cl36, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((rd @ X0 @ (ld @ X1 @ X0)) = (X1))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl36990, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ X1 @ (ld @ X1 @ X0)) = (mult @ X1 @ (ld @ X0 @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl36987, zip_derived_cl36])).
% 299.82/43.82 thf(zip_derived_cl34860, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @ (ld @ (mult @ X1 @ X0) @ X0)) = (mult @ (i @ X1) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl33624, zip_derived_cl0])).
% 299.82/43.82 thf(zip_derived_cl42402, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ (i @ X1) @ X0) @ (mult @ (mult @ (i @ X0) @ X1) @ X1))
% 299.82/43.82 = (X1))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl42196, zip_derived_cl36990, zip_derived_cl34860])).
% 299.82/43.82 thf(zip_derived_cl43507, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ (i @ X1) @ (i @ X0)) @ (mult @ (mult @ X0 @ X1) @ X1))
% 299.82/43.82 = (X1))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl32, zip_derived_cl42402])).
% 299.82/43.82 thf(zip_derived_cl43879, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @
% 299.82/43.82 (mult @ (i @ (i @ X0)) @ (i @ (mult @ (mult @ X1 @ X0) @ X0))) @
% 299.82/43.82 (mult @ (rd @ X1 @ (i @ X0)) @ (i @ X0))) = (i @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl10295, zip_derived_cl43507])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl165, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (mult @ (mult @ X0 @ X1) @ X0) @ X0)
% 299.82/43.82 = (mult @ X0 @ (i @ (mult @ (mult @ X1 @ X0) @ X0))))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl140, zip_derived_cl4])).
% 299.82/43.82 thf(zip_derived_cl2, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c03])).
% 299.82/43.82 thf(zip_derived_cl43974, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (ld @ (mult @ (mult @ X0 @ X1) @ X0) @ X0) @ X1) = (i @ X0))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl43879, zip_derived_cl32, zip_derived_cl165,
% 299.82/43.82 zip_derived_cl2])).
% 299.82/43.82 thf(zip_derived_cl3, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c04])).
% 299.82/43.82 thf(zip_derived_cl44103, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (i @ X0) @ X1) = (ld @ (mult @ (mult @ X0 @ X1) @ X0) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl43974, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl34860, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @ (ld @ (mult @ X1 @ X0) @ X0)) = (mult @ (i @ X1) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl33624, zip_derived_cl0])).
% 299.82/43.82 thf(zip_derived_cl56480, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (rd @ (i @ X1) @ X0))
% 299.82/43.82 = (mult @ (i @ (mult @ X1 @ X0)) @ X1))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl44103, zip_derived_cl34860])).
% 299.82/43.82 thf(zip_derived_cl1726, plain,
% 299.82/43.82 (![X0 : $i]:
% 299.82/43.82 ((i @ X0)
% 299.82/43.82 = (mult @ (mult @ X0 @ (rd @ (i @ (mult @ X0 @ X0)) @ X0)) @ X0))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl1711, zip_derived_cl8, zip_derived_cl41])).
% 299.82/43.82 thf(zip_derived_cl42, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 299.82/43.82 ((ld @ (mult @ (mult @ X1 @ X2) @ X1) @
% 299.82/43.82 (mult @ X1 @ (mult @ (mult @ (mult @ X2 @ X1) @ X1) @ X0)))
% 299.82/43.82 = (mult @ X1 @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl1996, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (i @ X0) @
% 299.82/43.82 (mult @ X0 @
% 299.82/43.82 (mult @
% 299.82/43.82 (mult @ (mult @ (rd @ (i @ (mult @ X0 @ X0)) @ X0) @ X0) @ X0) @
% 299.82/43.82 X1)))
% 299.82/43.82 = (mult @ X0 @ X1))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl1726, zip_derived_cl42])).
% 299.82/43.82 thf(zip_derived_cl2, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c03])).
% 299.82/43.82 thf(zip_derived_cl949, plain,
% 299.82/43.82 (![X0 : $i]: ((mult @ (i @ (mult @ X0 @ X0)) @ X0) = (i @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl929, zip_derived_cl2])).
% 299.82/43.82 thf(zip_derived_cl2034, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (i @ X0) @ (mult @ X0 @ (mult @ (i @ X0) @ X1)))
% 299.82/43.82 = (mult @ X0 @ X1))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl1996, zip_derived_cl2, zip_derived_cl949])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl2069, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X1) @ X0)
% 299.82/43.82 = (mult @ X1 @ (mult @ (i @ X1) @ (ld @ X1 @ X0))))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl2032])).
% 299.82/43.82 thf(zip_derived_cl3602, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ (i @ X0)) @ X1)
% 299.82/43.82 = (mult @ (i @ X0) @ (mult @ X0 @ (ld @ (i @ X0) @ X1))))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl32, zip_derived_cl2069])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl3618, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @ X1)
% 299.82/43.82 = (mult @ (i @ X0) @ (mult @ X0 @ (ld @ (i @ X0) @ X1))))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl3602, zip_derived_cl32])).
% 299.82/43.82 thf(zip_derived_cl5604, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (mult @ X1 @ (mult @ (i @ X1) @ X0)))
% 299.82/43.82 = (mult @ (i @ X1) @ (mult @ X1 @ (mult @ X1 @ X0))))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl2034, zip_derived_cl3618])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl7927, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X0 @ (rd @ (mult @ X0 @ X1) @ X0)) = (mult @ X1 @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl7633, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl36248, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (ld @ X0 @ X1)) = (mult @ (i @ (rd @ X0 @ X1)) @ X1))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl34860])).
% 299.82/43.82 thf(zip_derived_cl32216, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ (i @ X0) @ X1) @ (ld @ X1 @ (mult @ X0 @ X1))) = (X1))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl32079, zip_derived_cl26654,
% 299.82/43.82 zip_derived_cl26654, zip_derived_cl0])).
% 299.82/43.82 thf(zip_derived_cl36830, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X0 @ (ld @ X1 @ X0)) @
% 299.82/43.82 (ld @ X0 @ (mult @ (rd @ X1 @ X0) @ X0))) = (X0))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl36248, zip_derived_cl32216])).
% 299.82/43.82 thf(zip_derived_cl2, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c03])).
% 299.82/43.82 thf(zip_derived_cl36983, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X0 @ (ld @ X1 @ X0)) @ (ld @ X0 @ X1)) = (X0))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl36830, zip_derived_cl2])).
% 299.82/43.82 thf(zip_derived_cl37962, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X0 @ (ld @ (rd @ (mult @ X0 @ X1) @ X0) @ X0)) @
% 299.82/43.82 (mult @ X1 @ (i @ X0))) = (X0))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl7927, zip_derived_cl36983])).
% 299.82/43.82 thf(zip_derived_cl19273, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (rd @ (mult @ X1 @ X0) @ X1) @ X1) = (mult @ X1 @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl19239, zip_derived_cl7633])).
% 299.82/43.82 thf(zip_derived_cl38078, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X0 @ (mult @ X0 @ (i @ X1))) @ (mult @ X1 @ (i @ X0)))
% 299.82/43.82 = (X0))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl37962, zip_derived_cl19273])).
% 299.82/43.82 thf(zip_derived_cl38395, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X1 @ (mult @ X1 @ X0)) @ (mult @ (i @ X0) @ (i @ X1)))
% 299.82/43.82 = (X1))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl32, zip_derived_cl38078])).
% 299.82/43.82 thf(zip_derived_cl38741, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @
% 299.82/43.82 (mult @ (i @ X1) @
% 299.82/43.82 (mult @ X1 @ (mult @ X1 @ (mult @ (i @ X1) @ X0)))) @
% 299.82/43.82 (mult @ (i @ (mult @ X1 @ (mult @ X1 @ X0))) @ (i @ (i @ X1))))
% 299.82/43.82 = (i @ X1))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl5604, zip_derived_cl38395])).
% 299.82/43.82 thf(zip_derived_cl2032, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X0) @ (mult @ X0 @ X1))
% 299.82/43.82 = (mult @ X0 @ (mult @ (i @ X0) @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl1994, zip_derived_cl2, zip_derived_cl949])).
% 299.82/43.82 thf(zip_derived_cl2032, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X0) @ (mult @ X0 @ X1))
% 299.82/43.82 = (mult @ X0 @ (mult @ (i @ X0) @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl1994, zip_derived_cl2, zip_derived_cl949])).
% 299.82/43.82 thf(zip_derived_cl27150, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((X1)
% 299.82/43.82 = (mult @ X0 @
% 299.82/43.82 (mult @ X0 @ (mult @ (i @ X0) @ (mult @ (i @ X0) @ X1)))))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl27092, zip_derived_cl32, zip_derived_cl2,
% 299.82/43.82 zip_derived_cl32, zip_derived_cl2032, zip_derived_cl2032])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl38820, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @ (mult @ (i @ (mult @ X1 @ (mult @ X1 @ X0))) @ X1))
% 299.82/43.82 = (i @ X1))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl38741, zip_derived_cl2032, zip_derived_cl2032,
% 299.82/43.82 zip_derived_cl27150, zip_derived_cl32])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl38895, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X1 @ (i @ X0))
% 299.82/43.82 = (mult @ (i @ (mult @ X0 @ (mult @ X0 @ X1))) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl38820, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl82205, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (rd @ (i @ X0) @ X1) @ (i @ X0))
% 299.82/43.82 = (mult @
% 299.82/43.82 (i @ (mult @ X0 @ (mult @ (i @ (mult @ X0 @ X1)) @ X0))) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl56480, zip_derived_cl38895])).
% 299.82/43.82 thf(zip_derived_cl22, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ (rd @ X0 @ X1) @ X0) = (X1))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl82327, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((X1)
% 299.82/43.82 = (mult @
% 299.82/43.82 (i @ (mult @ X0 @ (mult @ (i @ (mult @ X0 @ X1)) @ X0))) @ X0))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl82205, zip_derived_cl22])).
% 299.82/43.82 thf(zip_derived_cl0, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c01])).
% 299.82/43.82 thf(zip_derived_cl3548, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X1 @ (mult @ (i @ X1) @ X0))
% 299.82/43.82 = (mult @ (i @ X1) @ (ld @ X1 @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl2069, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl3633, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X1 @ X0) = (mult @ (i @ X1) @ (ld @ X1 @ (ld @ (i @ X1) @ X0))))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl3548])).
% 299.82/43.82 thf(zip_derived_cl26075, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ X1 @ X0)
% 299.82/43.82 = (mult @ (mult @ X0 @ (mult @ (i @ X0) @ X1)) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl25976, zip_derived_cl32, zip_derived_cl5])).
% 299.82/43.82 thf(zip_derived_cl2392, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X1 @ X0) @ (i @ X0))
% 299.82/43.82 = (mult @ (mult @ X1 @ (i @ X0)) @ X0))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl2354, zip_derived_cl2, zip_derived_cl945,
% 299.82/43.82 zip_derived_cl945])).
% 299.82/43.82 thf(zip_derived_cl26466, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ (mult @ X0 @ (mult @ (i @ X0) @ X1)) @ X0) @ (i @ X0))
% 299.82/43.82 = (mult @ (rd @ X1 @ X0) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl26075, zip_derived_cl2392])).
% 299.82/43.82 thf(zip_derived_cl2, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c03])).
% 299.82/43.82 thf(zip_derived_cl26644, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ (mult @ X0 @ (mult @ (i @ X0) @ X1)) @ X0) @ (i @ X0))
% 299.82/43.82 = (X1))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl26466, zip_derived_cl2])).
% 299.82/43.82 thf(zip_derived_cl27401, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ (mult @ X1 @ (ld @ X1 @ X0)) @ X1) @ (i @ X1))
% 299.82/43.82 = (ld @ X1 @ (ld @ (i @ X1) @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl3633, zip_derived_cl26644])).
% 299.82/43.82 thf(zip_derived_cl0, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c01])).
% 299.82/43.82 thf(zip_derived_cl26569, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X1 @ X0) @ (i @ X0))
% 299.82/43.82 = (mult @ X0 @ (mult @ (i @ X0) @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl26525, zip_derived_cl10824, zip_derived_cl9253])).
% 299.82/43.82 thf(zip_derived_cl27448, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (mult @ (i @ X1) @ X0))
% 299.82/43.82 = (ld @ X1 @ (ld @ (i @ X1) @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl27401, zip_derived_cl0, zip_derived_cl26569])).
% 299.82/43.82 thf(zip_derived_cl36987, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (mult @ X0 @ (ld @ X1 @ X0)) @ X0) = (ld @ X0 @ X1))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl36835, zip_derived_cl2])).
% 299.82/43.82 thf(zip_derived_cl19280, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X1 @ X0) = (mult @ X0 @ (i @ (ld @ X0 @ (mult @ X1 @ X0)))))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl19251, zip_derived_cl0])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl20536, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X0 @ (ld @ X1 @ X0)) = (i @ (ld @ X0 @ (mult @ X1 @ X0))))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19280, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl24143, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X0 @ (mult @ X1 @ X0)) = (i @ (ld @ X0 @ (ld @ X1 @ X0))))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl20536, zip_derived_cl32])).
% 299.82/43.82 thf(zip_derived_cl37003, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X1 @ (mult @ (mult @ X1 @ (ld @ X0 @ X1)) @ X1))
% 299.82/43.82 = (i @ (ld @ X1 @ (ld @ X1 @ X0))))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl36987, zip_derived_cl24143])).
% 299.82/43.82 thf(zip_derived_cl8447, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X0 @ (mult @ (mult @ X0 @ X1) @ X0)) = (rd @ X1 @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl8371, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl37107, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (ld @ X0 @ X1) @ (i @ X1)) = (i @ (ld @ X1 @ (ld @ X1 @ X0))))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl37003, zip_derived_cl8447])).
% 299.82/43.82 thf(zip_derived_cl39773, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (ld @ (ld @ (i @ X1) @ X0) @ X1) @ (i @ X1))
% 299.82/43.82 = (i @ (ld @ X1 @ (mult @ X1 @ (mult @ (i @ X1) @ X0)))))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl27448, zip_derived_cl37107])).
% 299.82/43.82 thf(zip_derived_cl26603, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @ (mult @ (mult @ (i @ X0) @ X1) @ X0)) = (mult @ X1 @ X0))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl26411, zip_derived_cl9324, zip_derived_cl32,
% 299.82/43.82 zip_derived_cl2, zip_derived_cl32])).
% 299.82/43.82 thf(zip_derived_cl7443, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X0) @ X1)
% 299.82/43.82 = (mult @ (mult @ (i @ X0) @ (mult @ X1 @ X0)) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl7324, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl3, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c04])).
% 299.82/43.82 thf(zip_derived_cl7461, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (mult @ (i @ X1) @ X0) @ (i @ X1))
% 299.82/43.82 = (mult @ (i @ X1) @ (mult @ X0 @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl7443, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl26775, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (mult @ X1 @ (i @ X0)) @ (i @ X0))
% 299.82/43.82 = (mult @ (i @ X0) @
% 299.82/43.82 (mult @ (mult @ (mult @ (i @ (i @ X0)) @ X1) @ (i @ X0)) @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl26603, zip_derived_cl7461])).
% 299.82/43.82 thf(zip_derived_cl3, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c04])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl9401, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (rd @ X0 @ X1)) = (mult @ (mult @ X1 @ X0) @ (i @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl9253])).
% 299.82/43.82 thf(zip_derived_cl26906, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((X1) = (mult @ (i @ X0) @ (mult @ (mult @ X0 @ (rd @ X1 @ X0)) @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl26775, zip_derived_cl3, zip_derived_cl32,
% 299.82/43.82 zip_derived_cl9401])).
% 299.82/43.82 thf(zip_derived_cl7927, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X0 @ (rd @ (mult @ X0 @ X1) @ X0)) = (mult @ X1 @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl7633, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl29248, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (i @ X1) @ (rd @ X0 @ (i @ X1)))
% 299.82/43.82 = (mult @ (mult @ (mult @ X1 @ (rd @ X0 @ X1)) @ X1) @
% 299.82/43.82 (i @ (i @ X1))))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl26906, zip_derived_cl7927])).
% 299.82/43.82 thf(zip_derived_cl8287, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (i @ X0) @ (rd @ X1 @ (i @ X0)))
% 299.82/43.82 = (mult @ (ld @ (i @ X0) @ X1) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl32, zip_derived_cl8160])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl63, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ (mult @ X0 @ X1) @ X0) @ X0)
% 299.82/43.82 = (mult @ X0 @ (mult @ (mult @ X1 @ X0) @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl48, zip_derived_cl4])).
% 299.82/43.82 thf(zip_derived_cl2, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c03])).
% 299.82/43.82 thf(zip_derived_cl29434, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (ld @ (i @ X1) @ X0) @ X1) = (mult @ X1 @ (mult @ X0 @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl29248, zip_derived_cl8287, zip_derived_cl32,
% 299.82/43.82 zip_derived_cl63, zip_derived_cl2])).
% 299.82/43.82 thf(zip_derived_cl3, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c04])).
% 299.82/43.82 thf(zip_derived_cl21036, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (rd @ X0 @ X1) @ (mult @ (rd @ X1 @ X0) @ X1)) = (X1))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl20804])).
% 299.82/43.82 thf(zip_derived_cl21901, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @ (mult @ (rd @ X1 @ (mult @ X0 @ X1)) @ X1)) = (X1))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl21036])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl22020, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X1 @ X0) = (mult @ (rd @ X0 @ (mult @ X1 @ X0)) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl21901, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl31413, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (ld @ (i @ X0) @ X1) @ X0)
% 299.82/43.82 = (mult @ (rd @ X0 @ (mult @ X0 @ (mult @ X1 @ X0))) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl29434, zip_derived_cl22020])).
% 299.82/43.82 thf(zip_derived_cl21036, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (rd @ X0 @ X1) @ (mult @ (rd @ X1 @ X0) @ X1)) = (X1))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl20804])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl21751, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (rd @ X1 @ X0) @ X0) = (mult @ (rd @ X0 @ X1) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl21036, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl19273, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (rd @ (mult @ X1 @ X0) @ X1) @ X1) = (mult @ X1 @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl19239, zip_derived_cl7633])).
% 299.82/43.82 thf(zip_derived_cl22424, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (rd @ X0 @ (mult @ X0 @ X1)) @ X0) = (mult @ X0 @ (i @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl21751, zip_derived_cl19273])).
% 299.82/43.82 thf(zip_derived_cl31566, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (ld @ (i @ X0) @ X1) @ X0)
% 299.82/43.82 = (mult @ X0 @ (i @ (mult @ X1 @ X0))))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl31413, zip_derived_cl22424])).
% 299.82/43.82 thf(zip_derived_cl9324, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (mult @ X1 @ X0) @ (i @ X1)) = (mult @ X1 @ (mult @ X0 @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl9253, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl39831, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (mult @ (i @ (mult @ X0 @ X1)) @ X1))
% 299.82/43.82 = (i @ (mult @ (i @ X1) @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl39773, zip_derived_cl31566, zip_derived_cl9324,
% 299.82/43.82 zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl9253, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @ X1) = (mult @ (mult @ X0 @ (mult @ X1 @ X0)) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl9183, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl40498, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (i @ (mult @ X0 @ X1)))
% 299.82/43.82 = (mult @ (i @ (mult @ (i @ X1) @ X0)) @ (i @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl39831, zip_derived_cl9253])).
% 299.82/43.82 thf(zip_derived_cl85006, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @
% 299.82/43.82 (i @ (mult @ (mult @ (i @ (mult @ (i @ X1) @ X0)) @ (i @ X1)) @ X1)))
% 299.82/43.82 = (X0))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl82327, zip_derived_cl40498])).
% 299.82/43.82 thf(zip_derived_cl40498, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (i @ (mult @ X0 @ X1)))
% 299.82/43.82 = (mult @ (i @ (mult @ (i @ X1) @ X0)) @ (i @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl39831, zip_derived_cl9253])).
% 299.82/43.82 thf(zip_derived_cl85081, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (i @ (mult @ (mult @ X1 @ (i @ (mult @ X0 @ X1))) @ X1)))
% 299.82/43.82 = (X0))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl85006, zip_derived_cl40498])).
% 299.82/43.82 thf(zip_derived_cl38395, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X1 @ (mult @ X1 @ X0)) @ (mult @ (i @ X0) @ (i @ X1)))
% 299.82/43.82 = (X1))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl32, zip_derived_cl38078])).
% 299.82/43.82 thf(zip_derived_cl85406, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X1 @ X0) @
% 299.82/43.82 (mult @
% 299.82/43.82 (i @ (i @ (mult @ (mult @ X1 @ (i @ (mult @ X0 @ X1))) @ X1))) @
% 299.82/43.82 (i @ X1)))
% 299.82/43.82 = (X1))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl85081, zip_derived_cl38395])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl26569, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X1 @ X0) @ (i @ X0))
% 299.82/43.82 = (mult @ X0 @ (mult @ (i @ X0) @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl26525, zip_derived_cl10824, zip_derived_cl9253])).
% 299.82/43.82 thf(zip_derived_cl2032, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X0) @ (mult @ X0 @ X1))
% 299.82/43.82 = (mult @ X0 @ (mult @ (i @ X0) @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl1994, zip_derived_cl2, zip_derived_cl949])).
% 299.82/43.82 thf(zip_derived_cl0, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c01])).
% 299.82/43.82 thf(zip_derived_cl26075, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ X1 @ X0)
% 299.82/43.82 = (mult @ (mult @ X0 @ (mult @ (i @ X0) @ X1)) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl25976, zip_derived_cl32, zip_derived_cl5])).
% 299.82/43.82 thf(zip_derived_cl26502, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (ld @ (i @ X1) @ X0) @ X1)
% 299.82/43.82 = (mult @ (mult @ X1 @ X0) @ (i @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl26075])).
% 299.82/43.82 thf(zip_derived_cl9401, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (rd @ X0 @ X1)) = (mult @ (mult @ X1 @ X0) @ (i @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl9253])).
% 299.82/43.82 thf(zip_derived_cl26548, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (ld @ (i @ X1) @ X0) @ X1) = (mult @ X1 @ (rd @ X0 @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl26502, zip_derived_cl9401])).
% 299.82/43.82 thf(zip_derived_cl26906, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((X1) = (mult @ (i @ X0) @ (mult @ (mult @ X0 @ (rd @ X1 @ X0)) @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl26775, zip_derived_cl3, zip_derived_cl32,
% 299.82/43.82 zip_derived_cl9401])).
% 299.82/43.82 thf(zip_derived_cl29329, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (i @ X0) @ X1)
% 299.82/43.82 = (mult @ (i @ X0) @
% 299.82/43.82 (mult @ (mult @ X0 @ (mult @ X0 @ (rd @ X1 @ X0))) @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl26548, zip_derived_cl26906])).
% 299.82/43.82 thf(zip_derived_cl94, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (mult @ X1 @ (mult @ X0 @ X1)))
% 299.82/43.82 = (mult @ (mult @ X1 @ (mult @ X1 @ X0)) @ X1))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl83, zip_derived_cl5])).
% 299.82/43.82 thf(zip_derived_cl2, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c03])).
% 299.82/43.82 thf(zip_derived_cl2032, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X0) @ (mult @ X0 @ X1))
% 299.82/43.82 = (mult @ X0 @ (mult @ (i @ X0) @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl1994, zip_derived_cl2, zip_derived_cl949])).
% 299.82/43.82 thf(zip_derived_cl2032, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X0) @ (mult @ X0 @ X1))
% 299.82/43.82 = (mult @ X0 @ (mult @ (i @ X0) @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl1994, zip_derived_cl2, zip_derived_cl949])).
% 299.82/43.82 thf(zip_derived_cl29376, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (i @ X0) @ X1)
% 299.82/43.82 = (mult @ X0 @ (mult @ X0 @ (mult @ (i @ X0) @ X1))))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl29329, zip_derived_cl94, zip_derived_cl2,
% 299.82/43.82 zip_derived_cl2032, zip_derived_cl2032])).
% 299.82/43.82 thf(zip_derived_cl85864, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X1 @ X0) @ (ld @ (i @ X1) @ (i @ (mult @ X0 @ X1))))
% 299.82/43.82 = (X1))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl85406, zip_derived_cl32, zip_derived_cl26569,
% 299.82/43.82 zip_derived_cl2032, zip_derived_cl29376])).
% 299.82/43.82 thf(zip_derived_cl39831, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (mult @ (i @ (mult @ X0 @ X1)) @ X1))
% 299.82/43.82 = (i @ (mult @ (i @ X1) @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl39773, zip_derived_cl31566, zip_derived_cl9324,
% 299.82/43.82 zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl3, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c04])).
% 299.82/43.82 thf(zip_derived_cl26075, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ X1 @ X0)
% 299.82/43.82 = (mult @ (mult @ X0 @ (mult @ (i @ X0) @ X1)) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl25976, zip_derived_cl32, zip_derived_cl5])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl10326, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X1 @ (mult @ X0 @ X1)) = (rd @ (ld @ X1 @ X0) @ (i @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl8447])).
% 299.82/43.82 thf(zip_derived_cl10436, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (i @ X0) @ (mult @ X1 @ (i @ X0)))
% 299.82/43.82 = (rd @ (ld @ (i @ X0) @ X1) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl32, zip_derived_cl10326])).
% 299.82/43.82 thf(zip_derived_cl26472, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (i @ X0) @ (rd @ X1 @ X0))
% 299.82/43.82 = (rd @ (ld @ (i @ X0) @ (mult @ X0 @ (mult @ (i @ X0) @ X1))) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl26075, zip_derived_cl10436])).
% 299.82/43.82 thf(zip_derived_cl2034, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (i @ X0) @ (mult @ X0 @ (mult @ (i @ X0) @ X1)))
% 299.82/43.82 = (mult @ X0 @ X1))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl1996, zip_derived_cl2, zip_derived_cl949])).
% 299.82/43.82 thf(zip_derived_cl26647, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (i @ X0) @ (rd @ X1 @ X0)) = (rd @ (mult @ X0 @ X1) @ X0))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl26472, zip_derived_cl2034])).
% 299.82/43.82 thf(zip_derived_cl27665, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (i @ X1) @ X0) = (rd @ (mult @ X1 @ (mult @ X0 @ X1)) @ X1))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl26647])).
% 299.82/43.82 thf(zip_derived_cl45786, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (i @ X1) @ (i @ (mult @ X0 @ X1)))
% 299.82/43.82 = (rd @ (i @ (mult @ (i @ X1) @ X0)) @ X1))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl39831, zip_derived_cl27665])).
% 299.82/43.82 thf(zip_derived_cl149549, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X1 @ X0) @ (rd @ (i @ (mult @ (i @ X1) @ X0)) @ X1))
% 299.82/43.82 = (X1))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl85864, zip_derived_cl45786])).
% 299.82/43.82 thf(zip_derived_cl150052, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X1 @ X0) @
% 299.82/43.82 (rd @
% 299.82/43.82 (i @ (mult @ (i @ (i @ X0)) @ (mult @ (mult @ X0 @ X1) @ X0))) @
% 299.82/43.82 (i @ X0)))
% 299.82/43.82 = (i @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl28333, zip_derived_cl149549])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl25816, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 299.82/43.82 ((mult @ (mult @ X2 @ X1) @ (rd @ X0 @ (i @ X1)))
% 299.82/43.82 = (mult @ (mult @ X2 @ (mult @ X1 @ X0)) @ X1))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl86, zip_derived_cl9719])).
% 299.82/43.82 thf(zip_derived_cl29434, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (ld @ (i @ X1) @ X0) @ X1) = (mult @ X1 @ (mult @ X0 @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl29248, zip_derived_cl8287, zip_derived_cl32,
% 299.82/43.82 zip_derived_cl63, zip_derived_cl2])).
% 299.82/43.82 thf(zip_derived_cl39831, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (mult @ (i @ (mult @ X0 @ X1)) @ X1))
% 299.82/43.82 = (i @ (mult @ (i @ X1) @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl39773, zip_derived_cl31566, zip_derived_cl9324,
% 299.82/43.82 zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl40602, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @ (mult @ (i @ (mult @ X0 @ (mult @ X1 @ X0))) @ X0))
% 299.82/43.82 = (i @ (mult @ (i @ X0) @ (ld @ (i @ X0) @ X1))))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl29434, zip_derived_cl39831])).
% 299.82/43.82 thf(zip_derived_cl0, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c01])).
% 299.82/43.82 thf(zip_derived_cl40667, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @ (mult @ (i @ (mult @ X0 @ (mult @ X1 @ X0))) @ X0))
% 299.82/43.82 = (i @ X1))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl40602, zip_derived_cl0])).
% 299.82/43.82 thf(zip_derived_cl9253, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @ X1) = (mult @ (mult @ X0 @ (mult @ X1 @ X0)) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl9183, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl40856, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (i @ (mult @ X1 @ (mult @ X0 @ X1))))
% 299.82/43.82 = (mult @ (i @ X0) @ (i @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl40667, zip_derived_cl9253])).
% 299.82/43.82 thf(zip_derived_cl150199, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X1 @ (mult @ (i @ (mult @ X0 @ X1)) @ (i @ X0))) @ X0)
% 299.82/43.82 = (i @ X0))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl150052, zip_derived_cl32, zip_derived_cl25816,
% 299.82/43.82 zip_derived_cl40856])).
% 299.82/43.82 thf(zip_derived_cl150725, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X1 @ (mult @ (i @ (mult @ (i @ X0) @ X1)) @ X0)) @
% 299.82/43.82 (i @ X0)) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl32, zip_derived_cl150199])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl150930, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X1 @ (mult @ (i @ (mult @ (i @ X0) @ X1)) @ X0)) @
% 299.82/43.82 (i @ X0)) = (X0))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl150725, zip_derived_cl32])).
% 299.82/43.82 thf(zip_derived_cl3, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c04])).
% 299.82/43.82 thf(zip_derived_cl151398, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ X0 @ (i @ X0))
% 299.82/43.82 = (mult @ X1 @ (mult @ (i @ (mult @ (i @ X0) @ X1)) @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl150930, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl361, plain,
% 299.82/43.82 (![X0 : $i]: ((rd @ X0 @ (i @ X0)) = (mult @ X0 @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl351, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl151892, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @ X0)
% 299.82/43.82 = (mult @ X1 @ (mult @ (i @ (mult @ (i @ X0) @ X1)) @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl151398, zip_derived_cl361])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl152031, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X1 @ (mult @ X0 @ X0))
% 299.82/43.82 = (mult @ (i @ (mult @ (i @ X0) @ X1)) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl151892, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl3, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c04])).
% 299.82/43.82 thf(zip_derived_cl173278, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (ld @ X1 @ (mult @ X0 @ X0)) @ X0)
% 299.82/43.82 = (i @ (mult @ (i @ X0) @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl152031, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl8160, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X1 @ (rd @ X0 @ X1)) = (mult @ (ld @ X1 @ X0) @ (i @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl7927])).
% 299.82/43.82 thf(zip_derived_cl9900, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (rd @ (ld @ X1 @ X0) @ X1)) = (mult @ X0 @ (i @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl9401])).
% 299.82/43.82 thf(zip_derived_cl26904, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (ld @ X0 @ X1) @ X0) = (mult @ (i @ X0) @ (rd @ X1 @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl26773, zip_derived_cl12100, zip_derived_cl32,
% 299.82/43.82 zip_derived_cl9401, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl18308, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (mult @ X0 @ X1) @ X0)
% 299.82/43.82 = (mult @ X0 @ (i @ (rd @ X1 @ (i @ X0)))))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl18272, zip_derived_cl32, zip_derived_cl32])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl19131, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X0 @ (ld @ (mult @ X0 @ X1) @ X0)) = (i @ (rd @ X1 @ (i @ X0))))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl18308, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl69965, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (i @ X0) @ (ld @ (rd @ (ld @ X0 @ X1) @ X0) @ (i @ X0)))
% 299.82/43.82 = (i @ (rd @ (rd @ X1 @ X0) @ (i @ (i @ X0)))))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl26904, zip_derived_cl19131])).
% 299.82/43.82 thf(zip_derived_cl2032, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X0) @ (mult @ X0 @ X1))
% 299.82/43.82 = (mult @ X0 @ (mult @ (i @ X0) @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl1994, zip_derived_cl2, zip_derived_cl949])).
% 299.82/43.82 thf(zip_derived_cl44103, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (i @ X0) @ X1) = (ld @ (mult @ (mult @ X0 @ X1) @ X0) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl43974, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl56596, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (i @ (i @ X1)) @ (mult @ X1 @ X0))
% 299.82/43.82 = (ld @ (mult @ (mult @ X1 @ (mult @ (i @ X1) @ X0)) @ (i @ X1)) @
% 299.82/43.82 (i @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl2032, zip_derived_cl44103])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl26075, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ X1 @ X0)
% 299.82/43.82 = (mult @ (mult @ X0 @ (mult @ (i @ X0) @ X1)) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl25976, zip_derived_cl32, zip_derived_cl5])).
% 299.82/43.82 thf(zip_derived_cl56653, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ X1 @ (mult @ X1 @ X0)) = (ld @ (rd @ X0 @ X1) @ (i @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl56596, zip_derived_cl32, zip_derived_cl26075])).
% 299.82/43.82 thf(zip_derived_cl0, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c01])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl70035, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (i @ X0) @ (rd @ X0 @ X1)) = (i @ (rd @ (rd @ X1 @ X0) @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl69965, zip_derived_cl56653, zip_derived_cl0,
% 299.82/43.82 zip_derived_cl32])).
% 299.82/43.82 thf(zip_derived_cl10326, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X1 @ (mult @ X0 @ X1)) = (rd @ (ld @ X1 @ X0) @ (i @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl8447])).
% 299.82/43.82 thf(zip_derived_cl2, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c03])).
% 299.82/43.82 thf(zip_derived_cl10422, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (ld @ X0 @ (mult @ X1 @ X0)) @ (i @ X0)) = (ld @ X0 @ X1))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl10326, zip_derived_cl2])).
% 299.82/43.82 thf(zip_derived_cl26569, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X1 @ X0) @ (i @ X0))
% 299.82/43.82 = (mult @ X0 @ (mult @ (i @ X0) @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl26525, zip_derived_cl10824, zip_derived_cl9253])).
% 299.82/43.82 thf(zip_derived_cl27099, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (ld @ X1 @ X0) @ (i @ (i @ X1)))
% 299.82/43.82 = (mult @ (i @ X1) @
% 299.82/43.82 (mult @ (i @ (i @ X1)) @ (ld @ X1 @ (mult @ X0 @ X1)))))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl10422, zip_derived_cl26569])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl0, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c01])).
% 299.82/43.82 thf(zip_derived_cl27157, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (ld @ X1 @ X0) @ X1) = (mult @ (i @ X1) @ (mult @ X0 @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl27099, zip_derived_cl32, zip_derived_cl32,
% 299.82/43.82 zip_derived_cl0])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl29763, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (i @ X0) @ (mult @ (ld @ X0 @ X1) @ X0)) = (mult @ X1 @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl27157, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl70266, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (i @ (i @ X0)) @
% 299.82/43.82 (mult @ (i @ (rd @ (rd @ X1 @ X0) @ X0)) @ (i @ X0)))
% 299.82/43.82 = (mult @ (rd @ X0 @ X1) @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl70035, zip_derived_cl29763])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl12100, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X0 @ (mult @ X1 @ (i @ X0))) = (rd @ (ld @ X0 @ X1) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl9900, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl36248, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (ld @ X0 @ X1)) = (mult @ (i @ (rd @ X0 @ X1)) @ X1))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl34860])).
% 299.82/43.82 thf(zip_derived_cl10422, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (ld @ X0 @ (mult @ X1 @ X0)) @ (i @ X0)) = (ld @ X0 @ X1))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl10326, zip_derived_cl2])).
% 299.82/43.82 thf(zip_derived_cl36725, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (ld @ X0 @ (mult @ X0 @ (ld @ X1 @ X0))) @ (i @ X0))
% 299.82/43.82 = (ld @ X0 @ (i @ (rd @ X1 @ X0))))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl36248, zip_derived_cl10422])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl36930, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (ld @ X1 @ X0) @ (i @ X0)) = (ld @ X0 @ (i @ (rd @ X1 @ X0))))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl36725, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl36990, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ X1 @ (ld @ X1 @ X0)) = (mult @ X1 @ (ld @ X0 @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl36987, zip_derived_cl36])).
% 299.82/43.82 thf(zip_derived_cl37140, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ X1 @ X0) = (mult @ X1 @ (ld @ (mult @ X1 @ X0) @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl36990])).
% 299.82/43.82 thf(zip_derived_cl26654, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X0 @ (mult @ X1 @ X0)) = (mult @ (mult @ (i @ X0) @ X1) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl26603, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl37500, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X1 @ (mult @ (ld @ (mult @ (i @ X1) @ X0) @ (i @ X1)) @ X1))
% 299.82/43.82 = (mult @ (rd @ (i @ X1) @ X0) @ X1))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl37140, zip_derived_cl26654])).
% 299.82/43.82 thf(zip_derived_cl12089, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (mult @ (i @ X0) @ X1) @ (i @ X0))
% 299.82/43.82 = (mult @ (i @ X0) @ (i @ (rd @ X1 @ X0))))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl11934, zip_derived_cl7443])).
% 299.82/43.82 thf(zip_derived_cl26654, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X0 @ (mult @ X1 @ X0)) = (mult @ (mult @ (i @ X0) @ X1) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl26603, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl36248, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (ld @ X0 @ X1)) = (mult @ (i @ (rd @ X0 @ X1)) @ X1))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl34860])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl37697, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X1 @ (ld @ X0 @ X1)) = (mult @ (rd @ (i @ X1) @ X0) @ X1))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl37500, zip_derived_cl12089,
% 299.82/43.82 zip_derived_cl26654, zip_derived_cl36248, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl9253, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @ X1) = (mult @ (mult @ X0 @ (mult @ X1 @ X0)) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl9183, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl39287, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @ (rd @ (i @ X0) @ X1))
% 299.82/43.82 = (mult @ (mult @ X0 @ (ld @ X0 @ (ld @ X1 @ X0))) @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl37697, zip_derived_cl9253])).
% 299.82/43.82 thf(zip_derived_cl0, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c01])).
% 299.82/43.82 thf(zip_derived_cl39455, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @ (rd @ (i @ X0) @ X1))
% 299.82/43.82 = (mult @ (ld @ X1 @ X0) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl39287, zip_derived_cl0])).
% 299.82/43.82 thf(zip_derived_cl46003, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @ (rd @ (i @ X0) @ X1)) = (ld @ X0 @ (i @ (rd @ X1 @ X0))))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl36930, zip_derived_cl39455])).
% 299.82/43.82 thf(zip_derived_cl56480, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (rd @ (i @ X1) @ X0))
% 299.82/43.82 = (mult @ (i @ (mult @ X1 @ X0)) @ X1))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl44103, zip_derived_cl34860])).
% 299.82/43.82 thf(zip_derived_cl60892, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ (mult @ X0 @ X1)) @ X0)
% 299.82/43.82 = (ld @ X0 @ (i @ (rd @ X1 @ X0))))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl46003, zip_derived_cl56480])).
% 299.82/43.82 thf(zip_derived_cl3, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c04])).
% 299.82/43.82 thf(zip_derived_cl70443, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((i @ (mult @ X0 @ (rd @ X1 @ X0)))
% 299.82/43.82 = (mult @ (rd @ X0 @ X1) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl70266, zip_derived_cl32, zip_derived_cl12100,
% 299.82/43.82 zip_derived_cl60892, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl70625, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((i @ (mult @ X1 @ (i @ X0)))
% 299.82/43.82 = (mult @ (rd @ X0 @ (ld @ X0 @ X1)) @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl9900, zip_derived_cl70443])).
% 299.82/43.82 thf(zip_derived_cl36990, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ X1 @ (ld @ X1 @ X0)) = (mult @ X1 @ (ld @ X0 @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl36987, zip_derived_cl36])).
% 299.82/43.82 thf(zip_derived_cl9401, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (rd @ X0 @ X1)) = (mult @ (mult @ X1 @ X0) @ (i @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl9253])).
% 299.82/43.82 thf(zip_derived_cl20804, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (rd @ (ld @ X1 @ X0) @ X0) @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl20573, zip_derived_cl32, zip_derived_cl0])).
% 299.82/43.82 thf(zip_derived_cl3, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c04])).
% 299.82/43.82 thf(zip_derived_cl20881, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ X0 @ (mult @ X1 @ X0)) = (rd @ (ld @ X1 @ X0) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl20804, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl70698, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((i @ (mult @ X1 @ (i @ X0)))
% 299.82/43.82 = (mult @ X0 @ (rd @ X0 @ (mult @ X1 @ X0))))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl70625, zip_derived_cl36990, zip_derived_cl9401,
% 299.82/43.82 zip_derived_cl20881])).
% 299.82/43.82 thf(zip_derived_cl106497, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((i @ (mult @ (ld @ X0 @ X1) @ (i @ (i @ X0))))
% 299.82/43.82 = (mult @ (i @ X0) @ (rd @ (i @ X0) @ (ld @ X0 @ (rd @ X1 @ X0)))))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl8160, zip_derived_cl70698])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl36, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((rd @ X0 @ (ld @ X1 @ X0)) = (X1))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl39455, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @ (rd @ (i @ X0) @ X1))
% 299.82/43.82 = (mult @ (ld @ X1 @ X0) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl39287, zip_derived_cl0])).
% 299.82/43.82 thf(zip_derived_cl46141, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X0) @ (rd @ (i @ (i @ X0)) @ X1))
% 299.82/43.82 = (mult @ (ld @ X1 @ (i @ X0)) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl32, zip_derived_cl39455])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl46206, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X0) @ (rd @ X0 @ X1))
% 299.82/43.82 = (mult @ (ld @ X1 @ (i @ X0)) @ X0))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl46141, zip_derived_cl32])).
% 299.82/43.82 thf(zip_derived_cl9253, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @ X1) = (mult @ (mult @ X0 @ (mult @ X1 @ X0)) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl9183, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl51074, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (ld @ X0 @ (i @ X1)))
% 299.82/43.82 = (mult @ (mult @ X1 @ (mult @ (i @ X1) @ (rd @ X1 @ X0))) @
% 299.82/43.82 (i @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl46206, zip_derived_cl9253])).
% 299.82/43.82 thf(zip_derived_cl26075, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ X1 @ X0)
% 299.82/43.82 = (mult @ (mult @ X0 @ (mult @ (i @ X0) @ X1)) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl25976, zip_derived_cl32, zip_derived_cl5])).
% 299.82/43.82 thf(zip_derived_cl51283, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (ld @ X0 @ (i @ X1))) = (rd @ (rd @ X1 @ X0) @ X1))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl51074, zip_derived_cl26075])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl55181, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X0 @ (rd @ (rd @ X0 @ X1) @ X0)) = (ld @ X1 @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl51283, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl60565, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X1 @ (rd @ X0 @ X1)) = (ld @ (ld @ X0 @ X1) @ (i @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl36, zip_derived_cl55181])).
% 299.82/43.82 thf(zip_derived_cl36, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((rd @ X0 @ (ld @ X1 @ X0)) = (X1))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl60700, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (i @ X0) @ (ld @ X0 @ (rd @ X1 @ X0))) = (ld @ X1 @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl60565, zip_derived_cl36])).
% 299.82/43.82 thf(zip_derived_cl106607, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((i @ (mult @ (ld @ X0 @ X1) @ X0))
% 299.82/43.82 = (mult @ (i @ X0) @ (ld @ X1 @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl106497, zip_derived_cl32, zip_derived_cl60700])).
% 299.82/43.82 thf(zip_derived_cl0, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c01])).
% 299.82/43.82 thf(zip_derived_cl40856, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (i @ (mult @ X1 @ (mult @ X0 @ X1))))
% 299.82/43.82 = (mult @ (i @ X0) @ (i @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl40667, zip_derived_cl9253])).
% 299.82/43.82 thf(zip_derived_cl39831, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (mult @ (i @ (mult @ X0 @ X1)) @ X1))
% 299.82/43.82 = (i @ (mult @ (i @ X1) @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl39773, zip_derived_cl31566, zip_derived_cl9324,
% 299.82/43.82 zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl9, plain, (![X0 : $i]: ((mult @ (i @ X0) @ X0) = (unit))),
% 299.82/43.82 inference('cnf', [status(esa)], [c10])).
% 299.82/43.82 thf(zip_derived_cl25816, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 299.82/43.82 ((mult @ (mult @ X2 @ X1) @ (rd @ X0 @ (i @ X1)))
% 299.82/43.82 = (mult @ (mult @ X2 @ (mult @ X1 @ X0)) @ X1))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl86, zip_derived_cl9719])).
% 299.82/43.82 thf(zip_derived_cl26028, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ unit @ (rd @ X1 @ (i @ X0)))
% 299.82/43.82 = (mult @ (mult @ (i @ X0) @ (mult @ X0 @ X1)) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl25816])).
% 299.82/43.82 thf(zip_derived_cl5, plain, (![X0 : $i]: ((mult @ unit @ X0) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c06])).
% 299.82/43.82 thf(zip_derived_cl2032, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X0) @ (mult @ X0 @ X1))
% 299.82/43.82 = (mult @ X0 @ (mult @ (i @ X0) @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl1994, zip_derived_cl2, zip_derived_cl949])).
% 299.82/43.82 thf(zip_derived_cl26099, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ X1 @ (i @ X0))
% 299.82/43.82 = (mult @ (mult @ X0 @ (mult @ (i @ X0) @ X1)) @ X0))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl26028, zip_derived_cl5, zip_derived_cl2032])).
% 299.82/43.82 thf(zip_derived_cl40520, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (mult @ (i @ (mult @ X0 @ (i @ X1))) @ (i @ X1)) @ (i @ X1))
% 299.82/43.82 = (mult @ (mult @ X1 @ (i @ (mult @ (i @ (i @ X1)) @ X0))) @ X1))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl39831, zip_derived_cl26099])).
% 299.82/43.82 thf(zip_derived_cl3, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c04])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl40734, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((i @ (mult @ X0 @ (i @ X1)))
% 299.82/43.82 = (mult @ (mult @ X1 @ (i @ (mult @ X1 @ X0))) @ X1))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl40520, zip_derived_cl3, zip_derived_cl32])).
% 299.82/43.82 thf(zip_derived_cl44535, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((i @ (mult @ (mult @ X1 @ X0) @ (i @ X0)))
% 299.82/43.82 = (mult @ (mult @ (i @ X1) @ (i @ X0)) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl40856, zip_derived_cl40734])).
% 299.82/43.82 thf(zip_derived_cl26569, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X1 @ X0) @ (i @ X0))
% 299.82/43.82 = (mult @ X0 @ (mult @ (i @ X0) @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl26525, zip_derived_cl10824, zip_derived_cl9253])).
% 299.82/43.82 thf(zip_derived_cl2392, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X1 @ X0) @ (i @ X0))
% 299.82/43.82 = (mult @ (mult @ X1 @ (i @ X0)) @ X0))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl2354, zip_derived_cl2, zip_derived_cl945,
% 299.82/43.82 zip_derived_cl945])).
% 299.82/43.82 thf(zip_derived_cl26569, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X1 @ X0) @ (i @ X0))
% 299.82/43.82 = (mult @ X0 @ (mult @ (i @ X0) @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl26525, zip_derived_cl10824, zip_derived_cl9253])).
% 299.82/43.82 thf(zip_derived_cl26910, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @ (mult @ (i @ X0) @ X1))
% 299.82/43.82 = (mult @ (mult @ X1 @ (i @ X0)) @ X0))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl2392, zip_derived_cl26569])).
% 299.82/43.82 thf(zip_derived_cl44832, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((i @ (mult @ X0 @ (mult @ (i @ X0) @ X1)))
% 299.82/43.82 = (mult @ X0 @ (mult @ (i @ X0) @ (i @ X1))))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl44535, zip_derived_cl26569, zip_derived_cl26910])).
% 299.82/43.82 thf(zip_derived_cl152031, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X1 @ (mult @ X0 @ X0))
% 299.82/43.82 = (mult @ (i @ (mult @ (i @ X0) @ X1)) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl151892, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl173507, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (mult @ (i @ (i @ X1)) @ X0) @ (mult @ X1 @ X1))
% 299.82/43.82 = (mult @ (mult @ (i @ X1) @ (mult @ (i @ (i @ X1)) @ (i @ X0))) @
% 299.82/43.82 X1))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl44832, zip_derived_cl152031])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl2032, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X0) @ (mult @ X0 @ X1))
% 299.82/43.82 = (mult @ X0 @ (mult @ (i @ X0) @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl1994, zip_derived_cl2, zip_derived_cl949])).
% 299.82/43.82 thf(zip_derived_cl26099, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ X1 @ (i @ X0))
% 299.82/43.82 = (mult @ (mult @ X0 @ (mult @ (i @ X0) @ X1)) @ X0))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl26028, zip_derived_cl5, zip_derived_cl2032])).
% 299.82/43.82 thf(zip_derived_cl173609, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (mult @ X1 @ X0) @ (mult @ X1 @ X1))
% 299.82/43.82 = (rd @ (i @ X0) @ (i @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl173507, zip_derived_cl32, zip_derived_cl32,
% 299.82/43.82 zip_derived_cl2032, zip_derived_cl26099])).
% 299.82/43.82 thf(zip_derived_cl36987, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (mult @ X0 @ (ld @ X1 @ X0)) @ X0) = (ld @ X0 @ X1))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl36835, zip_derived_cl2])).
% 299.82/43.82 thf(zip_derived_cl174981, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (mult @ (mult @ X0 @ X0) @ (rd @ (i @ X1) @ (i @ X0))) @
% 299.82/43.82 (mult @ X0 @ X0)) = (ld @ (mult @ X0 @ X0) @ (mult @ X0 @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl173609, zip_derived_cl36987])).
% 299.82/43.82 thf(zip_derived_cl25816, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 299.82/43.82 ((mult @ (mult @ X2 @ X1) @ (rd @ X0 @ (i @ X1)))
% 299.82/43.82 = (mult @ (mult @ X2 @ (mult @ X1 @ X0)) @ X1))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl86, zip_derived_cl9719])).
% 299.82/43.82 thf(zip_derived_cl94, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (mult @ X1 @ (mult @ X0 @ X1)))
% 299.82/43.82 = (mult @ (mult @ X1 @ (mult @ X1 @ X0)) @ X1))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl83, zip_derived_cl5])).
% 299.82/43.82 thf(zip_derived_cl173609, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (mult @ X1 @ X0) @ (mult @ X1 @ X1))
% 299.82/43.82 = (rd @ (i @ X0) @ (i @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl173507, zip_derived_cl32, zip_derived_cl32,
% 299.82/43.82 zip_derived_cl2032, zip_derived_cl26099])).
% 299.82/43.82 thf(zip_derived_cl7927, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X0 @ (rd @ (mult @ X0 @ X1) @ X0)) = (mult @ X1 @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl7633, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl37107, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (ld @ X0 @ X1) @ (i @ X1)) = (i @ (ld @ X1 @ (ld @ X1 @ X0))))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl37003, zip_derived_cl8447])).
% 299.82/43.82 thf(zip_derived_cl39775, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (ld @ (rd @ (mult @ X0 @ X1) @ X0) @ X0) @ (i @ X0))
% 299.82/43.82 = (i @ (ld @ X0 @ (mult @ X1 @ (i @ X0)))))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl7927, zip_derived_cl37107])).
% 299.82/43.82 thf(zip_derived_cl19273, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (rd @ (mult @ X1 @ X0) @ X1) @ X1) = (mult @ X1 @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl19239, zip_derived_cl7633])).
% 299.82/43.82 thf(zip_derived_cl9324, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (mult @ X1 @ X0) @ (i @ X1)) = (mult @ X1 @ (mult @ X0 @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl9253, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl12100, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X0 @ (mult @ X1 @ (i @ X0))) = (rd @ (ld @ X0 @ X1) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl9900, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl39832, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @ (mult @ (i @ X1) @ X0))
% 299.82/43.82 = (i @ (rd @ (ld @ X0 @ X1) @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl39775, zip_derived_cl19273, zip_derived_cl9324,
% 299.82/43.82 zip_derived_cl12100])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl46312, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (ld @ X0 @ X1) @ X0)
% 299.82/43.82 = (i @ (mult @ X0 @ (mult @ (i @ X1) @ X0))))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl39832, zip_derived_cl32])).
% 299.82/43.82 thf(zip_derived_cl26075, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ X1 @ X0)
% 299.82/43.82 = (mult @ (mult @ X0 @ (mult @ (i @ X0) @ X1)) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl25976, zip_derived_cl32, zip_derived_cl5])).
% 299.82/43.82 thf(zip_derived_cl3, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c04])).
% 299.82/43.82 thf(zip_derived_cl26422, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (rd @ X1 @ X0) @ (i @ X0))
% 299.82/43.82 = (mult @ X0 @ (mult @ (i @ X0) @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl26075, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl2069, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X1) @ X0)
% 299.82/43.82 = (mult @ X1 @ (mult @ (i @ X1) @ (ld @ X1 @ X0))))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl2032])).
% 299.82/43.82 thf(zip_derived_cl175327, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X0) @ X1) = (ld @ (mult @ X0 @ X0) @ (mult @ X0 @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl174981, zip_derived_cl25816, zip_derived_cl94,
% 299.82/43.82 zip_derived_cl173609, zip_derived_cl46312,
% 299.82/43.82 zip_derived_cl26422, zip_derived_cl2069])).
% 299.82/43.82 thf(zip_derived_cl175440, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X1) @ (ld @ X1 @ X0)) = (ld @ (mult @ X1 @ X1) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl175327])).
% 299.82/43.82 thf(zip_derived_cl175327, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X0) @ X1) = (ld @ (mult @ X0 @ X0) @ (mult @ X0 @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl174981, zip_derived_cl25816, zip_derived_cl94,
% 299.82/43.82 zip_derived_cl173609, zip_derived_cl46312,
% 299.82/43.82 zip_derived_cl26422, zip_derived_cl2069])).
% 299.82/43.82 thf(zip_derived_cl175959, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ (i @ X1)) @ (ld @ X1 @ X0))
% 299.82/43.82 = (ld @ (mult @ (i @ X1) @ (i @ X1)) @ (ld @ (mult @ X1 @ X1) @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl175440, zip_derived_cl175327])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl0, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c01])).
% 299.82/43.82 thf(zip_derived_cl386, plain,
% 299.82/43.82 (![X0 : $i]: ((rd @ (i @ X0) @ X0) = (mult @ (i @ X0) @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl32, zip_derived_cl361])).
% 299.82/43.82 thf(zip_derived_cl929, plain,
% 299.82/43.82 (![X0 : $i]: ((i @ (mult @ X0 @ X0)) = (rd @ (i @ X0) @ X0))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl901, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl941, plain,
% 299.82/43.82 (![X0 : $i]: ((i @ (mult @ X0 @ X0)) = (mult @ (i @ X0) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl386, zip_derived_cl929])).
% 299.82/43.82 thf(zip_derived_cl0, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c01])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl3548, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X1 @ (mult @ (i @ X1) @ X0))
% 299.82/43.82 = (mult @ (i @ X1) @ (ld @ X1 @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl2069, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl3649, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (i @ X0) @ (mult @ X0 @ X1))
% 299.82/43.82 = (mult @ (i @ (i @ X0)) @ (ld @ (i @ X0) @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl32, zip_derived_cl3548])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl3666, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (i @ X0) @ (mult @ X0 @ X1))
% 299.82/43.82 = (mult @ X0 @ (ld @ (i @ X0) @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl3649, zip_derived_cl32])).
% 299.82/43.82 thf(zip_derived_cl3676, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (i @ X1) @ X0) = (mult @ X1 @ (ld @ (i @ X1) @ (ld @ X1 @ X0))))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl3666])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl4744, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X1 @ (ld @ (i @ X1) @ X0)) = (ld @ (i @ X1) @ (ld @ X1 @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl3676, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl27448, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (mult @ (i @ X1) @ X0))
% 299.82/43.82 = (ld @ X1 @ (ld @ (i @ X1) @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl27401, zip_derived_cl0, zip_derived_cl26569])).
% 299.82/43.82 thf(zip_derived_cl30462, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (mult @ (i @ X1) @ X0))
% 299.82/43.82 = (ld @ (i @ X1) @ (ld @ X1 @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl4744, zip_derived_cl27448])).
% 299.82/43.82 thf(zip_derived_cl176449, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((X0)
% 299.82/43.82 = (mult @ (mult @ X1 @ X1) @ (mult @ (i @ (mult @ X1 @ X1)) @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl175959, zip_derived_cl32, zip_derived_cl0,
% 299.82/43.82 zip_derived_cl941, zip_derived_cl30462])).
% 299.82/43.82 thf(zip_derived_cl1, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c02])).
% 299.82/43.82 thf(zip_derived_cl179183, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (mult @ X1 @ X1) @ X0) = (mult @ (i @ (mult @ X1 @ X1)) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl176449, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl70698, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((i @ (mult @ X1 @ (i @ X0)))
% 299.82/43.82 = (mult @ X0 @ (rd @ X0 @ (mult @ X1 @ X0))))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl70625, zip_derived_cl36990, zip_derived_cl9401,
% 299.82/43.82 zip_derived_cl20881])).
% 299.82/43.82 thf(zip_derived_cl182126, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((i @ (mult @ (i @ (mult @ X1 @ X1)) @ (i @ X0)))
% 299.82/43.82 = (mult @ X0 @ (rd @ X0 @ (ld @ (mult @ X1 @ X1) @ X0))))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl179183, zip_derived_cl70698])).
% 299.82/43.82 thf(zip_derived_cl179183, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (mult @ X1 @ X1) @ X0) = (mult @ (i @ (mult @ X1 @ X1)) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl176449, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl2069, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X1) @ X0)
% 299.82/43.82 = (mult @ X1 @ (mult @ (i @ X1) @ (ld @ X1 @ X0))))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl2032])).
% 299.82/43.82 thf(zip_derived_cl8371, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X1 @ X0) @ X1) = (mult @ X1 @ (rd @ X0 @ (i @ X1))))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl8016, zip_derived_cl2])).
% 299.82/43.82 thf(zip_derived_cl40734, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((i @ (mult @ X0 @ (i @ X1)))
% 299.82/43.82 = (mult @ (mult @ X1 @ (i @ (mult @ X1 @ X0))) @ X1))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl40520, zip_derived_cl3, zip_derived_cl32])).
% 299.82/43.82 thf(zip_derived_cl41632, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((i @ (mult @ (rd @ X1 @ (i @ X0)) @ (i @ X0)))
% 299.82/43.82 = (mult @ (mult @ X0 @ (i @ (mult @ (mult @ X0 @ X1) @ X0))) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl8371, zip_derived_cl40734])).
% 299.82/43.82 thf(zip_derived_cl2, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c03])).
% 299.82/43.82 thf(zip_derived_cl41729, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((i @ X1)
% 299.82/43.82 = (mult @ (mult @ X0 @ (i @ (mult @ (mult @ X0 @ X1) @ X0))) @ X0))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl41632, zip_derived_cl2])).
% 299.82/43.82 thf(zip_derived_cl43095, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((i @ (mult @ (i @ X1) @ (ld @ X1 @ X0)))
% 299.82/43.82 = (mult @
% 299.82/43.82 (mult @ X1 @ (i @ (mult @ (mult @ (i @ X1) @ X0) @ X1))) @ X1))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl2069, zip_derived_cl41729])).
% 299.82/43.82 thf(zip_derived_cl26654, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X0 @ (mult @ X1 @ X0)) = (mult @ (mult @ (i @ X0) @ X1) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl26603, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl20536, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X0 @ (ld @ X1 @ X0)) = (i @ (ld @ X0 @ (mult @ X1 @ X0))))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19280, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl0, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c01])).
% 299.82/43.82 thf(zip_derived_cl43207, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((i @ (mult @ (i @ X1) @ (ld @ X1 @ X0)))
% 299.82/43.82 = (mult @ (ld @ X0 @ X1) @ X1))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl43095, zip_derived_cl26654,
% 299.82/43.82 zip_derived_cl20536, zip_derived_cl0])).
% 299.82/43.82 thf(zip_derived_cl175440, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X1) @ (ld @ X1 @ X0)) = (ld @ (mult @ X1 @ X1) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl175327])).
% 299.82/43.82 thf(zip_derived_cl175762, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((i @ (ld @ (mult @ X1 @ X1) @ X0)) = (mult @ (ld @ X0 @ X1) @ X1))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl43207, zip_derived_cl175440])).
% 299.82/43.82 thf(zip_derived_cl36, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((rd @ X0 @ (ld @ X1 @ X0)) = (X1))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl182804, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (ld @ (i @ X0) @ X1) @ X1) = (mult @ X0 @ (mult @ X1 @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl182126, zip_derived_cl179183,
% 299.82/43.82 zip_derived_cl175762, zip_derived_cl36])).
% 299.82/43.82 thf(zip_derived_cl70698, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((i @ (mult @ X1 @ (i @ X0)))
% 299.82/43.82 = (mult @ X0 @ (rd @ X0 @ (mult @ X1 @ X0))))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl70625, zip_derived_cl36990, zip_derived_cl9401,
% 299.82/43.82 zip_derived_cl20881])).
% 299.82/43.82 thf(zip_derived_cl175327, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X0) @ X1) = (ld @ (mult @ X0 @ X0) @ (mult @ X0 @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl174981, zip_derived_cl25816, zip_derived_cl94,
% 299.82/43.82 zip_derived_cl173609, zip_derived_cl46312,
% 299.82/43.82 zip_derived_cl26422, zip_derived_cl2069])).
% 299.82/43.82 thf(zip_derived_cl0, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c01])).
% 299.82/43.82 thf(zip_derived_cl175349, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X1 @ X1) @ (mult @ (i @ X1) @ X0)) = (mult @ X1 @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl175327, zip_derived_cl0])).
% 299.82/43.82 thf(zip_derived_cl178218, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X0 @ X0) @ (i @ (mult @ X1 @ (i @ (i @ X0)))))
% 299.82/43.82 = (mult @ X0 @ (rd @ (i @ X0) @ (mult @ X1 @ (i @ X0)))))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl70698, zip_derived_cl175349])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl36930, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (ld @ X1 @ X0) @ (i @ X0)) = (ld @ X0 @ (i @ (rd @ X1 @ X0))))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl36725, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl3618, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @ X1)
% 299.82/43.82 = (mult @ (i @ X0) @ (mult @ X0 @ (ld @ (i @ X0) @ X1))))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl3602, zip_derived_cl32])).
% 299.82/43.82 thf(zip_derived_cl37735, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @ (i @ (rd @ X1 @ (i @ X0))))
% 299.82/43.82 = (mult @ (i @ X0) @
% 299.82/43.82 (mult @ X0 @ (mult @ (ld @ X1 @ (i @ X0)) @ (i @ (i @ X0))))))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl36930, zip_derived_cl3618])).
% 299.82/43.82 thf(zip_derived_cl18308, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (mult @ X0 @ X1) @ X0)
% 299.82/43.82 = (mult @ X0 @ (i @ (rd @ X1 @ (i @ X0)))))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl18272, zip_derived_cl32, zip_derived_cl32])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl2032, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ X0) @ (mult @ X0 @ X1))
% 299.82/43.82 = (mult @ X0 @ (mult @ (i @ X0) @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl1994, zip_derived_cl2, zip_derived_cl949])).
% 299.82/43.82 thf(zip_derived_cl27157, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (ld @ X1 @ X0) @ X1) = (mult @ (i @ X1) @ (mult @ X0 @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl27099, zip_derived_cl32, zip_derived_cl32,
% 299.82/43.82 zip_derived_cl0])).
% 299.82/43.82 thf(zip_derived_cl9719, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ X0 @ (i @ X1)) = (mult @ X1 @ (mult @ (ld @ X1 @ X0) @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl9324])).
% 299.82/43.82 thf(zip_derived_cl20881, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ X0 @ (mult @ X1 @ X0)) = (rd @ (ld @ X1 @ X0) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl20804, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl37836, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (mult @ X0 @ X1) @ X0)
% 299.82/43.82 = (rd @ (i @ X0) @ (mult @ X1 @ (i @ X0))))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl37735, zip_derived_cl18308, zip_derived_cl32,
% 299.82/43.82 zip_derived_cl2032, zip_derived_cl27157, zip_derived_cl9719,
% 299.82/43.82 zip_derived_cl20881])).
% 299.82/43.82 thf(zip_derived_cl37140, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ X1 @ X0) = (mult @ X1 @ (ld @ (mult @ X1 @ X0) @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl36990])).
% 299.82/43.82 thf(zip_derived_cl178318, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X0 @ X0) @ (i @ (mult @ X1 @ X0))) = (rd @ X0 @ X1))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl178218, zip_derived_cl32, zip_derived_cl37836,
% 299.82/43.82 zip_derived_cl37140])).
% 299.82/43.82 thf(zip_derived_cl193954, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X0 @ X0) @ (i @ (mult @ X1 @ (mult @ X0 @ X0))))
% 299.82/43.82 = (rd @ X0 @ (ld @ (i @ X1) @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl182804, zip_derived_cl178318])).
% 299.82/43.82 thf(zip_derived_cl36, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((rd @ X0 @ (ld @ X1 @ X0)) = (X1))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl194330, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X0 @ X0) @ (i @ (mult @ X1 @ (mult @ X0 @ X0))))
% 299.82/43.82 = (i @ X1))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl193954, zip_derived_cl36])).
% 299.82/43.82 thf(zip_derived_cl195712, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ X0 @ X0) @
% 299.82/43.82 (mult @ (i @ (mult @ X0 @ X0)) @ (ld @ X1 @ (mult @ X0 @ X0))))
% 299.82/43.82 = (i @ (ld @ (mult @ X0 @ X0) @ X1)))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl106607, zip_derived_cl194330])).
% 299.82/43.82 thf(zip_derived_cl179183, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ (mult @ X1 @ X1) @ X0) = (mult @ (i @ (mult @ X1 @ X1)) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl176449, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl0, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c01])).
% 299.82/43.82 thf(zip_derived_cl175762, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((i @ (ld @ (mult @ X1 @ X1) @ X0)) = (mult @ (ld @ X0 @ X1) @ X1))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl43207, zip_derived_cl175440])).
% 299.82/43.82 thf(zip_derived_cl195816, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X1 @ (mult @ X0 @ X0)) = (mult @ (ld @ X1 @ X0) @ X0))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl195712, zip_derived_cl179183, zip_derived_cl0,
% 299.82/43.82 zip_derived_cl175762])).
% 299.82/43.82 thf(zip_derived_cl3, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c04])).
% 299.82/43.82 thf(zip_derived_cl196908, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((ld @ X1 @ X0) = (i @ (mult @ (i @ X0) @ X1)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl173278, zip_derived_cl195816, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl82327, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((X1)
% 299.82/43.82 = (mult @
% 299.82/43.82 (i @ (mult @ X0 @ (mult @ (i @ (mult @ X0 @ X1)) @ X0))) @ X0))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl82205, zip_derived_cl22])).
% 299.82/43.82 thf(zip_derived_cl32216, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (mult @ (i @ X0) @ X1) @ (ld @ X1 @ (mult @ X0 @ X1))) = (X1))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl32079, zip_derived_cl26654,
% 299.82/43.82 zip_derived_cl26654, zip_derived_cl0])).
% 299.82/43.82 thf(zip_derived_cl83691, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @
% 299.82/43.82 (ld @ X1 @
% 299.82/43.82 (mult @ (mult @ X1 @ (mult @ (i @ (mult @ X1 @ X0)) @ X1)) @ X1)))
% 299.82/43.82 = (X1))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl82327, zip_derived_cl32216])).
% 299.82/43.82 thf(zip_derived_cl8447, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((ld @ X0 @ (mult @ (mult @ X0 @ X1) @ X0)) = (rd @ X1 @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl8371, zip_derived_cl1])).
% 299.82/43.82 thf(zip_derived_cl4362, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (mult @ X1 @ X0) @ (i @ X0))
% 299.82/43.82 = (mult @ (rd @ X1 @ (i @ X0)) @ X0))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl4343, zip_derived_cl32])).
% 299.82/43.82 thf(zip_derived_cl84094, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @ (mult @ (rd @ (i @ (mult @ X1 @ X0)) @ (i @ X1)) @ X1))
% 299.82/43.82 = (X1))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl83691, zip_derived_cl8447, zip_derived_cl4362])).
% 299.82/43.82 thf(zip_derived_cl197461, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @
% 299.82/43.82 (mult @ (rd @ (ld @ X1 @ X0) @ (i @ (i @ X0))) @ (i @ X0)))
% 299.82/43.82 = (i @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl196908, zip_derived_cl84094])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl20881, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ X0 @ (mult @ X1 @ X0)) = (rd @ (ld @ X1 @ X0) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl20804, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl39455, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X0 @ (rd @ (i @ X0) @ X1))
% 299.82/43.82 = (mult @ (ld @ X1 @ X0) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl39287, zip_derived_cl0])).
% 299.82/43.82 thf(zip_derived_cl56480, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ X1 @ (rd @ (i @ X1) @ X0))
% 299.82/43.82 = (mult @ (i @ (mult @ X1 @ X0)) @ X1))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl44103, zip_derived_cl34860])).
% 299.82/43.82 thf(zip_derived_cl60891, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((mult @ (i @ (mult @ X0 @ X1)) @ X0)
% 299.82/43.82 = (mult @ (ld @ X1 @ X0) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl39455, zip_derived_cl56480])).
% 299.82/43.82 thf(zip_derived_cl4362, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (mult @ X1 @ X0) @ (i @ X0))
% 299.82/43.82 = (mult @ (rd @ X1 @ (i @ X0)) @ X0))),
% 299.82/43.82 inference('demod', [status(thm)], [zip_derived_cl4343, zip_derived_cl32])).
% 299.82/43.82 thf(zip_derived_cl65740, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ (mult @ (i @ (mult @ X0 @ X1)) @ X0) @ (i @ (i @ X0)))
% 299.82/43.82 = (mult @ (rd @ (ld @ X1 @ X0) @ (i @ (i @ X0))) @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)],
% 299.82/43.82 [zip_derived_cl60891, zip_derived_cl4362])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl3, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 299.82/43.82 inference('cnf', [status(esa)], [c04])).
% 299.82/43.82 thf(zip_derived_cl32, plain, (![X0 : $i]: ((X0) = (i @ (i @ X0)))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 299.82/43.82 thf(zip_derived_cl20881, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((rd @ X0 @ (mult @ X1 @ X0)) = (rd @ (ld @ X1 @ X0) @ X0))),
% 299.82/43.82 inference('sup+', [status(thm)], [zip_derived_cl20804, zip_derived_cl3])).
% 299.82/43.82 thf(zip_derived_cl66041, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]:
% 299.82/43.82 ((i @ (mult @ X0 @ X1))
% 299.82/43.82 = (mult @ (rd @ X0 @ (mult @ X1 @ X0)) @ (i @ X0)))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl65740, zip_derived_cl32, zip_derived_cl3,
% 299.82/43.82 zip_derived_cl32, zip_derived_cl20881])).
% 299.82/43.82 thf(zip_derived_cl197801, plain,
% 299.82/43.82 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (i @ (mult @ X0 @ X1))) = (i @ X0))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl197461, zip_derived_cl32, zip_derived_cl20881,
% 299.82/43.82 zip_derived_cl66041])).
% 299.82/43.82 thf(zip_derived_cl202341, plain, (((i @ b) != (i @ b))),
% 299.82/43.82 inference('demod', [status(thm)],
% 299.82/43.82 [zip_derived_cl10, zip_derived_cl197801])).
% 299.82/43.82 thf(zip_derived_cl202342, plain, ($false),
% 299.82/43.82 inference('simplify', [status(thm)], [zip_derived_cl202341])).
% 299.82/43.82
% 299.82/43.82 % SZS output end Refutation
% 299.82/43.82
% 299.82/43.82
% 299.82/43.83 % Terminating...
% 300.29/43.93 % Runner terminated.
% 300.29/43.94 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------