TSTP Solution File: GRP705-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP705-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.DUoTy5lmVh true
% Computer : n022.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 01:53:02 EDT 2023
% Result : Unsatisfiable 109.69s 16.25s
% Output : Refutation 109.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP705-1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.DUoTy5lmVh true
% 0.14/0.34 % Computer : n022.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 01:56:24 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.14/0.34 % Running portfolio for 300 s
% 0.14/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.34 % Number of cores: 8
% 0.14/0.34 % Python version: Python 3.6.8
% 0.14/0.35 % Running in FO mode
% 0.20/0.64 % Total configuration time : 435
% 0.20/0.64 % Estimated wc time : 1092
% 0.20/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.52/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.52/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.52/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.52/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.52/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.52/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.52/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 109.69/16.25 % Solved by fo/fo13.sh.
% 109.69/16.25 % done 1761 iterations in 15.452s
% 109.69/16.25 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 109.69/16.25 % SZS output start Refutation
% 109.69/16.25 thf(op_a_type, type, op_a: $i).
% 109.69/16.25 thf(ld_type, type, ld: $i > $i > $i).
% 109.69/16.25 thf(rd_type, type, rd: $i > $i > $i).
% 109.69/16.25 thf(a_type, type, a: $i).
% 109.69/16.25 thf(mult_type, type, mult: $i > $i > $i).
% 109.69/16.25 thf(op_b_type, type, op_b: $i).
% 109.69/16.25 thf(unit_type, type, unit: $i).
% 109.69/16.25 thf(goals, conjecture,
% 109.69/16.25 (( mult @ op_a @ ( mult @ op_b @ a ) ) =
% 109.69/16.25 ( mult @ ( mult @ op_a @ op_b ) @ a ))).
% 109.69/16.25 thf(zf_stmt_0, negated_conjecture,
% 109.69/16.25 (( mult @ op_a @ ( mult @ op_b @ a ) ) !=
% 109.69/16.25 ( mult @ ( mult @ op_a @ op_b ) @ a )),
% 109.69/16.25 inference('cnf.neg', [status(esa)], [goals])).
% 109.69/16.25 thf(zip_derived_cl9, plain,
% 109.69/16.25 (((mult @ op_a @ (mult @ op_b @ a)) != (mult @ (mult @ op_a @ op_b) @ a))),
% 109.69/16.25 inference('cnf', [status(esa)], [zf_stmt_0])).
% 109.69/16.25 thf(c01, axiom, (( mult @ A @ ( ld @ A @ B ) ) = ( B ))).
% 109.69/16.25 thf(zip_derived_cl0, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c01])).
% 109.69/16.25 thf(c08, axiom,
% 109.69/16.25 (( mult @ op_a @ ( mult @ op_a @ ( mult @ op_a @ op_a ) ) ) = ( unit ))).
% 109.69/16.25 thf(zip_derived_cl7, plain,
% 109.69/16.25 (((mult @ op_a @ (mult @ op_a @ (mult @ op_a @ op_a))) = (unit))),
% 109.69/16.25 inference('cnf', [status(esa)], [c08])).
% 109.69/16.25 thf(c07, axiom,
% 109.69/16.25 (( mult @ A @ ( mult @ B @ ( mult @ B @ C ) ) ) =
% 109.69/16.25 ( mult @ ( mult @ ( mult @ A @ B ) @ B ) @ C ))).
% 109.69/16.25 thf(zip_derived_cl6, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X1 @ (mult @ X1 @ X2)))
% 109.69/16.25 = (mult @ (mult @ (mult @ X0 @ X1) @ X1) @ X2))),
% 109.69/16.25 inference('cnf', [status(esa)], [c07])).
% 109.69/16.25 thf(zip_derived_cl41, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ op_a @
% 109.69/16.25 (mult @ (mult @ op_a @ (mult @ op_a @ op_a)) @
% 109.69/16.25 (mult @ (mult @ op_a @ (mult @ op_a @ op_a)) @ X0)))
% 109.69/16.25 = (mult @ (mult @ unit @ (mult @ op_a @ (mult @ op_a @ op_a))) @ X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl6])).
% 109.69/16.25 thf(c06, axiom, (( mult @ unit @ A ) = ( A ))).
% 109.69/16.25 thf(zip_derived_cl5, plain, (![X0 : $i]: ((mult @ unit @ X0) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c06])).
% 109.69/16.25 thf(zip_derived_cl47, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ op_a @
% 109.69/16.25 (mult @ (mult @ op_a @ (mult @ op_a @ op_a)) @
% 109.69/16.25 (mult @ (mult @ op_a @ (mult @ op_a @ op_a)) @ X0)))
% 109.69/16.25 = (mult @ (mult @ op_a @ (mult @ op_a @ op_a)) @ X0))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl41, zip_derived_cl5])).
% 109.69/16.25 thf(zip_derived_cl76, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ op_a @ (mult @ (mult @ op_a @ (mult @ op_a @ op_a)) @ X0))
% 109.69/16.25 = (X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl47])).
% 109.69/16.25 thf(zip_derived_cl7, plain,
% 109.69/16.25 (((mult @ op_a @ (mult @ op_a @ (mult @ op_a @ op_a))) = (unit))),
% 109.69/16.25 inference('cnf', [status(esa)], [c08])).
% 109.69/16.25 thf(zip_derived_cl6, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X1 @ (mult @ X1 @ X2)))
% 109.69/16.25 = (mult @ (mult @ (mult @ X0 @ X1) @ X1) @ X2))),
% 109.69/16.25 inference('cnf', [status(esa)], [c07])).
% 109.69/16.25 thf(c02, axiom, (( ld @ A @ ( mult @ A @ B ) ) = ( B ))).
% 109.69/16.25 thf(zip_derived_cl1, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c02])).
% 109.69/16.25 thf(zip_derived_cl28, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((ld @ (mult @ (mult @ X2 @ X1) @ X1) @
% 109.69/16.25 (mult @ X2 @ (mult @ X1 @ (mult @ X1 @ X0)))) = (X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1])).
% 109.69/16.25 thf(zip_derived_cl92, plain,
% 109.69/16.25 (((ld @ (mult @ (mult @ op_a @ op_a) @ op_a) @ unit) = (op_a))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl28])).
% 109.69/16.25 thf(zip_derived_cl0, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c01])).
% 109.69/16.25 thf(zip_derived_cl134, plain,
% 109.69/16.25 (((mult @ (mult @ (mult @ op_a @ op_a) @ op_a) @ op_a) = (unit))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl92, zip_derived_cl0])).
% 109.69/16.25 thf(zip_derived_cl28, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((ld @ (mult @ (mult @ X2 @ X1) @ X1) @
% 109.69/16.25 (mult @ X2 @ (mult @ X1 @ (mult @ X1 @ X0)))) = (X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1])).
% 109.69/16.25 thf(zip_derived_cl140, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((ld @ (mult @ unit @ op_a) @
% 109.69/16.25 (mult @ (mult @ (mult @ op_a @ op_a) @ op_a) @
% 109.69/16.25 (mult @ op_a @ (mult @ op_a @ X0))))
% 109.69/16.25 = (X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl134, zip_derived_cl28])).
% 109.69/16.25 thf(zip_derived_cl5, plain, (![X0 : $i]: ((mult @ unit @ X0) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c06])).
% 109.69/16.25 thf(zip_derived_cl6, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X1 @ (mult @ X1 @ X2)))
% 109.69/16.25 = (mult @ (mult @ (mult @ X0 @ X1) @ X1) @ X2))),
% 109.69/16.25 inference('cnf', [status(esa)], [c07])).
% 109.69/16.25 thf(zip_derived_cl1, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c02])).
% 109.69/16.25 thf(zip_derived_cl146, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ op_a @ (mult @ op_a @ (mult @ op_a @ (mult @ op_a @ X0))))
% 109.69/16.25 = (X0))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl140, zip_derived_cl5, zip_derived_cl6,
% 109.69/16.25 zip_derived_cl1])).
% 109.69/16.25 thf(zip_derived_cl800, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ op_a @ (mult @ op_a @ (mult @ op_a @ X0)))
% 109.69/16.25 = (mult @ (mult @ op_a @ (mult @ op_a @ op_a)) @ X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl76, zip_derived_cl146])).
% 109.69/16.25 thf(zip_derived_cl0, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c01])).
% 109.69/16.25 thf(c09, axiom,
% 109.69/16.25 (( mult @
% 109.69/16.25 op_b @
% 109.69/16.25 ( mult @
% 109.69/16.25 op_b @
% 109.69/16.25 ( mult @
% 109.69/16.25 op_b @
% 109.69/16.25 ( mult @
% 109.69/16.25 op_b @
% 109.69/16.25 ( mult @
% 109.69/16.25 op_b @
% 109.69/16.25 ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ op_b ) ) ) ) ) ) ) ) =
% 109.69/16.25 ( unit ))).
% 109.69/16.25 thf(zip_derived_cl8, plain,
% 109.69/16.25 (((mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @ (mult @ op_b @ (mult @ op_b @ (mult @ op_b @ op_b))))))))
% 109.69/16.25 = (unit))),
% 109.69/16.25 inference('cnf', [status(esa)], [c09])).
% 109.69/16.25 thf(zip_derived_cl6, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X1 @ (mult @ X1 @ X2)))
% 109.69/16.25 = (mult @ (mult @ (mult @ X0 @ X1) @ X1) @ X2))),
% 109.69/16.25 inference('cnf', [status(esa)], [c07])).
% 109.69/16.25 thf(zip_derived_cl42, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ op_b @
% 109.69/16.25 (mult @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @ (mult @ op_b @ (mult @ op_b @ op_b))))))) @
% 109.69/16.25 (mult @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @ (mult @ op_b @ (mult @ op_b @ op_b))))))) @
% 109.69/16.25 X0)))
% 109.69/16.25 = (mult @
% 109.69/16.25 (mult @ unit @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @ (mult @ op_b @ (mult @ op_b @ op_b)))))))) @
% 109.69/16.25 X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl6])).
% 109.69/16.25 thf(zip_derived_cl5, plain, (![X0 : $i]: ((mult @ unit @ X0) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c06])).
% 109.69/16.25 thf(zip_derived_cl48, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ op_b @
% 109.69/16.25 (mult @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @ (mult @ op_b @ (mult @ op_b @ op_b))))))) @
% 109.69/16.25 (mult @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @ (mult @ op_b @ (mult @ op_b @ op_b))))))) @
% 109.69/16.25 X0)))
% 109.69/16.25 = (mult @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @ (mult @ op_b @ (mult @ op_b @ op_b))))))) @
% 109.69/16.25 X0))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl42, zip_derived_cl5])).
% 109.69/16.25 thf(zip_derived_cl8, plain,
% 109.69/16.25 (((mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @ (mult @ op_b @ (mult @ op_b @ (mult @ op_b @ op_b))))))))
% 109.69/16.25 = (unit))),
% 109.69/16.25 inference('cnf', [status(esa)], [c09])).
% 109.69/16.25 thf(zip_derived_cl1, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c02])).
% 109.69/16.25 thf(zip_derived_cl16, plain,
% 109.69/16.25 (((ld @ op_b @ unit)
% 109.69/16.25 = (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @ (mult @ op_b @ (mult @ op_b @ op_b))))))))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl1])).
% 109.69/16.25 thf(zip_derived_cl16, plain,
% 109.69/16.25 (((ld @ op_b @ unit)
% 109.69/16.25 = (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @ (mult @ op_b @ (mult @ op_b @ op_b))))))))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl1])).
% 109.69/16.25 thf(zip_derived_cl16, plain,
% 109.69/16.25 (((ld @ op_b @ unit)
% 109.69/16.25 = (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @ (mult @ op_b @ (mult @ op_b @ op_b))))))))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl1])).
% 109.69/16.25 thf(zip_derived_cl487, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ op_b @
% 109.69/16.25 (mult @ (ld @ op_b @ unit) @ (mult @ (ld @ op_b @ unit) @ X0)))
% 109.69/16.25 = (mult @ (ld @ op_b @ unit) @ X0))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl48, zip_derived_cl16, zip_derived_cl16,
% 109.69/16.25 zip_derived_cl16])).
% 109.69/16.25 thf(zip_derived_cl494, plain,
% 109.69/16.25 (![X0 : $i]: ((mult @ op_b @ (mult @ (ld @ op_b @ unit) @ X0)) = (X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl487])).
% 109.69/16.25 thf(zip_derived_cl1, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c02])).
% 109.69/16.25 thf(zip_derived_cl2295, plain,
% 109.69/16.25 (![X0 : $i]: ((ld @ op_b @ X0) = (mult @ (ld @ op_b @ unit) @ X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl494, zip_derived_cl1])).
% 109.69/16.25 thf(zip_derived_cl6, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X1 @ (mult @ X1 @ X2)))
% 109.69/16.25 = (mult @ (mult @ (mult @ X0 @ X1) @ X1) @ X2))),
% 109.69/16.25 inference('cnf', [status(esa)], [c07])).
% 109.69/16.25 thf(c05, axiom, (( mult @ A @ unit ) = ( A ))).
% 109.69/16.25 thf(zip_derived_cl4, plain, (![X0 : $i]: ((mult @ X0 @ unit) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c05])).
% 109.69/16.25 thf(zip_derived_cl32, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X1 @ (mult @ X0 @ (mult @ X0 @ unit)))
% 109.69/16.25 = (mult @ (mult @ X1 @ X0) @ X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl4])).
% 109.69/16.25 thf(zip_derived_cl4, plain, (![X0 : $i]: ((mult @ X0 @ unit) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c05])).
% 109.69/16.25 thf(zip_derived_cl50, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X1 @ (mult @ X0 @ X0)) = (mult @ (mult @ X1 @ X0) @ X0))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl4])).
% 109.69/16.25 thf(c04, axiom, (( rd @ ( mult @ A @ B ) @ B ) = ( A ))).
% 109.69/16.25 thf(zip_derived_cl3, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c04])).
% 109.69/16.25 thf(zip_derived_cl340, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((rd @ (mult @ X1 @ (mult @ X0 @ X0)) @ X0) = (mult @ X1 @ X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl3])).
% 109.69/16.25 thf(zip_derived_cl2470, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((rd @ (ld @ op_b @ (mult @ X0 @ X0)) @ X0)
% 109.69/16.25 = (mult @ (ld @ op_b @ unit) @ X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl2295, zip_derived_cl340])).
% 109.69/16.25 thf(zip_derived_cl2295, plain,
% 109.69/16.25 (![X0 : $i]: ((ld @ op_b @ X0) = (mult @ (ld @ op_b @ unit) @ X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl494, zip_derived_cl1])).
% 109.69/16.25 thf(zip_derived_cl2523, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((rd @ (ld @ op_b @ (mult @ X0 @ X0)) @ X0) = (ld @ op_b @ X0))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl2470, zip_derived_cl2295])).
% 109.69/16.25 thf(zip_derived_cl5788, plain,
% 109.69/16.25 (((rd @
% 109.69/16.25 (ld @ op_b @
% 109.69/16.25 (mult @ op_a @
% 109.69/16.25 (mult @ op_a @ (mult @ op_a @ (mult @ op_a @ (mult @ op_a @ op_a)))))) @
% 109.69/16.25 (mult @ op_a @ (mult @ op_a @ op_a)))
% 109.69/16.25 = (ld @ op_b @ (mult @ op_a @ (mult @ op_a @ op_a))))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl800, zip_derived_cl2523])).
% 109.69/16.25 thf(zip_derived_cl7, plain,
% 109.69/16.25 (((mult @ op_a @ (mult @ op_a @ (mult @ op_a @ op_a))) = (unit))),
% 109.69/16.25 inference('cnf', [status(esa)], [c08])).
% 109.69/16.25 thf(zip_derived_cl4, plain, (![X0 : $i]: ((mult @ X0 @ unit) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c05])).
% 109.69/16.25 thf(zip_derived_cl2295, plain,
% 109.69/16.25 (![X0 : $i]: ((ld @ op_b @ X0) = (mult @ (ld @ op_b @ unit) @ X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl494, zip_derived_cl1])).
% 109.69/16.25 thf(zip_derived_cl7, plain,
% 109.69/16.25 (((mult @ op_a @ (mult @ op_a @ (mult @ op_a @ op_a))) = (unit))),
% 109.69/16.25 inference('cnf', [status(esa)], [c08])).
% 109.69/16.25 thf(zip_derived_cl28, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((ld @ (mult @ (mult @ X2 @ X1) @ X1) @
% 109.69/16.25 (mult @ X2 @ (mult @ X1 @ (mult @ X1 @ X0)))) = (X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1])).
% 109.69/16.25 thf(zip_derived_cl105, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((ld @ (mult @ (mult @ X0 @ op_a) @ op_a) @
% 109.69/16.25 (mult @ X0 @ (mult @ op_a @ unit)))
% 109.69/16.25 = (mult @ op_a @ (mult @ op_a @ op_a)))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl28])).
% 109.69/16.25 thf(zip_derived_cl4, plain, (![X0 : $i]: ((mult @ X0 @ unit) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c05])).
% 109.69/16.25 thf(zip_derived_cl127, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((ld @ (mult @ (mult @ X0 @ op_a) @ op_a) @ (mult @ X0 @ op_a))
% 109.69/16.25 = (mult @ op_a @ (mult @ op_a @ op_a)))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl105, zip_derived_cl4])).
% 109.69/16.25 thf(zip_derived_cl50, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X1 @ (mult @ X0 @ X0)) = (mult @ (mult @ X1 @ X0) @ X0))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl4])).
% 109.69/16.25 thf(zip_derived_cl1574, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((ld @ (mult @ X0 @ (mult @ op_a @ op_a)) @ (mult @ X0 @ op_a))
% 109.69/16.25 = (mult @ op_a @ (mult @ op_a @ op_a)))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl127, zip_derived_cl50])).
% 109.69/16.25 thf(zip_derived_cl0, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c01])).
% 109.69/16.25 thf(zip_derived_cl1575, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ (mult @ X0 @ (mult @ op_a @ op_a)) @
% 109.69/16.25 (mult @ op_a @ (mult @ op_a @ op_a))) = (mult @ X0 @ op_a))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl1574, zip_derived_cl0])).
% 109.69/16.25 thf(zip_derived_cl3134, plain,
% 109.69/16.25 (((mult @ (ld @ op_b @ (mult @ op_a @ op_a)) @
% 109.69/16.25 (mult @ op_a @ (mult @ op_a @ op_a)))
% 109.69/16.25 = (mult @ (ld @ op_b @ unit) @ op_a))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl2295, zip_derived_cl1575])).
% 109.69/16.25 thf(zip_derived_cl2295, plain,
% 109.69/16.25 (![X0 : $i]: ((ld @ op_b @ X0) = (mult @ (ld @ op_b @ unit) @ X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl494, zip_derived_cl1])).
% 109.69/16.25 thf(zip_derived_cl3147, plain,
% 109.69/16.25 (((mult @ (ld @ op_b @ (mult @ op_a @ op_a)) @
% 109.69/16.25 (mult @ op_a @ (mult @ op_a @ op_a))) = (ld @ op_b @ op_a))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl3134, zip_derived_cl2295])).
% 109.69/16.25 thf(zip_derived_cl134, plain,
% 109.69/16.25 (((mult @ (mult @ (mult @ op_a @ op_a) @ op_a) @ op_a) = (unit))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl92, zip_derived_cl0])).
% 109.69/16.25 thf(zip_derived_cl28, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((ld @ (mult @ (mult @ X2 @ X1) @ X1) @
% 109.69/16.25 (mult @ X2 @ (mult @ X1 @ (mult @ X1 @ X0)))) = (X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1])).
% 109.69/16.25 thf(zip_derived_cl137, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((ld @
% 109.69/16.25 (mult @ (mult @ X0 @ (mult @ (mult @ op_a @ op_a) @ op_a)) @
% 109.69/16.25 (mult @ (mult @ op_a @ op_a) @ op_a)) @
% 109.69/16.25 (mult @ X0 @ (mult @ (mult @ (mult @ op_a @ op_a) @ op_a) @ unit)))
% 109.69/16.25 = (op_a))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl134, zip_derived_cl28])).
% 109.69/16.25 thf(zip_derived_cl6, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X1 @ (mult @ X1 @ X2)))
% 109.69/16.25 = (mult @ (mult @ (mult @ X0 @ X1) @ X1) @ X2))),
% 109.69/16.25 inference('cnf', [status(esa)], [c07])).
% 109.69/16.25 thf(zip_derived_cl4, plain, (![X0 : $i]: ((mult @ X0 @ unit) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c05])).
% 109.69/16.25 thf(zip_derived_cl144, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((ld @
% 109.69/16.25 (mult @ (mult @ X0 @ (mult @ (mult @ op_a @ op_a) @ op_a)) @
% 109.69/16.25 (mult @ (mult @ op_a @ op_a) @ op_a)) @
% 109.69/16.25 (mult @ X0 @ (mult @ op_a @ (mult @ op_a @ op_a)))) = (op_a))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl137, zip_derived_cl6, zip_derived_cl4])).
% 109.69/16.25 thf(zip_derived_cl5, plain, (![X0 : $i]: ((mult @ unit @ X0) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c06])).
% 109.69/16.25 thf(zip_derived_cl6, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X1 @ (mult @ X1 @ X2)))
% 109.69/16.25 = (mult @ (mult @ (mult @ X0 @ X1) @ X1) @ X2))),
% 109.69/16.25 inference('cnf', [status(esa)], [c07])).
% 109.69/16.25 thf(zip_derived_cl40, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ unit @ (mult @ X0 @ (mult @ X0 @ X1)))
% 109.69/16.25 = (mult @ (mult @ X0 @ X0) @ X1))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl6])).
% 109.69/16.25 thf(zip_derived_cl5, plain, (![X0 : $i]: ((mult @ unit @ X0) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c06])).
% 109.69/16.25 thf(zip_derived_cl46, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X0 @ X1)) = (mult @ (mult @ X0 @ X0) @ X1))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl40, zip_derived_cl5])).
% 109.69/16.25 thf(zip_derived_cl46, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X0 @ X1)) = (mult @ (mult @ X0 @ X0) @ X1))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl40, zip_derived_cl5])).
% 109.69/16.25 thf(zip_derived_cl50, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X1 @ (mult @ X0 @ X0)) = (mult @ (mult @ X1 @ X0) @ X0))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl4])).
% 109.69/16.25 thf(zip_derived_cl4, plain, (![X0 : $i]: ((mult @ X0 @ unit) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c05])).
% 109.69/16.25 thf(zip_derived_cl47, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ op_a @
% 109.69/16.25 (mult @ (mult @ op_a @ (mult @ op_a @ op_a)) @
% 109.69/16.25 (mult @ (mult @ op_a @ (mult @ op_a @ op_a)) @ X0)))
% 109.69/16.25 = (mult @ (mult @ op_a @ (mult @ op_a @ op_a)) @ X0))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl41, zip_derived_cl5])).
% 109.69/16.25 thf(zip_derived_cl77, plain,
% 109.69/16.25 (((mult @ op_a @
% 109.69/16.25 (mult @ (mult @ op_a @ (mult @ op_a @ op_a)) @
% 109.69/16.25 (mult @ op_a @ (mult @ op_a @ op_a))))
% 109.69/16.25 = (mult @ op_a @ (mult @ op_a @ op_a)))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl47])).
% 109.69/16.25 thf(zip_derived_cl1, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c02])).
% 109.69/16.25 thf(zip_derived_cl78, plain,
% 109.69/16.25 (((ld @ op_a @ (mult @ op_a @ (mult @ op_a @ op_a)))
% 109.69/16.25 = (mult @ (mult @ op_a @ (mult @ op_a @ op_a)) @
% 109.69/16.25 (mult @ op_a @ (mult @ op_a @ op_a))))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl77, zip_derived_cl1])).
% 109.69/16.25 thf(zip_derived_cl1, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c02])).
% 109.69/16.25 thf(zip_derived_cl81, plain,
% 109.69/16.25 (((mult @ op_a @ op_a)
% 109.69/16.25 = (mult @ (mult @ op_a @ (mult @ op_a @ op_a)) @
% 109.69/16.25 (mult @ op_a @ (mult @ op_a @ op_a))))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl78, zip_derived_cl1])).
% 109.69/16.25 thf(zip_derived_cl47, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ op_a @
% 109.69/16.25 (mult @ (mult @ op_a @ (mult @ op_a @ op_a)) @
% 109.69/16.25 (mult @ (mult @ op_a @ (mult @ op_a @ op_a)) @ X0)))
% 109.69/16.25 = (mult @ (mult @ op_a @ (mult @ op_a @ op_a)) @ X0))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl41, zip_derived_cl5])).
% 109.69/16.25 thf(zip_derived_cl85, plain,
% 109.69/16.25 (((mult @ op_a @
% 109.69/16.25 (mult @ (mult @ op_a @ (mult @ op_a @ op_a)) @ (mult @ op_a @ op_a)))
% 109.69/16.25 = (mult @ op_a @ op_a))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl81, zip_derived_cl47])).
% 109.69/16.25 thf(zip_derived_cl1, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c02])).
% 109.69/16.25 thf(zip_derived_cl148, plain,
% 109.69/16.25 (((ld @ op_a @ (mult @ op_a @ op_a))
% 109.69/16.25 = (mult @ (mult @ op_a @ (mult @ op_a @ op_a)) @ (mult @ op_a @ op_a)))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl85, zip_derived_cl1])).
% 109.69/16.25 thf(zip_derived_cl1, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c02])).
% 109.69/16.25 thf(zip_derived_cl153, plain,
% 109.69/16.25 (((op_a)
% 109.69/16.25 = (mult @ (mult @ op_a @ (mult @ op_a @ op_a)) @ (mult @ op_a @ op_a)))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl148, zip_derived_cl1])).
% 109.69/16.25 thf(zip_derived_cl47, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ op_a @
% 109.69/16.25 (mult @ (mult @ op_a @ (mult @ op_a @ op_a)) @
% 109.69/16.25 (mult @ (mult @ op_a @ (mult @ op_a @ op_a)) @ X0)))
% 109.69/16.25 = (mult @ (mult @ op_a @ (mult @ op_a @ op_a)) @ X0))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl41, zip_derived_cl5])).
% 109.69/16.25 thf(zip_derived_cl164, plain,
% 109.69/16.25 (((mult @ op_a @ (mult @ (mult @ op_a @ (mult @ op_a @ op_a)) @ op_a))
% 109.69/16.25 = (op_a))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl153, zip_derived_cl47])).
% 109.69/16.25 thf(zip_derived_cl1, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c02])).
% 109.69/16.25 thf(zip_derived_cl165, plain,
% 109.69/16.25 (((ld @ op_a @ op_a)
% 109.69/16.25 = (mult @ (mult @ op_a @ (mult @ op_a @ op_a)) @ op_a))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl164, zip_derived_cl1])).
% 109.69/16.25 thf(zip_derived_cl4, plain, (![X0 : $i]: ((mult @ X0 @ unit) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c05])).
% 109.69/16.25 thf(zip_derived_cl1, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c02])).
% 109.69/16.25 thf(zip_derived_cl13, plain, (![X0 : $i]: ((ld @ X0 @ X0) = (unit))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl1])).
% 109.69/16.25 thf(zip_derived_cl170, plain,
% 109.69/16.25 (((unit) = (mult @ (mult @ op_a @ (mult @ op_a @ op_a)) @ op_a))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl165, zip_derived_cl13])).
% 109.69/16.25 thf(zip_derived_cl6, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X1 @ (mult @ X1 @ X2)))
% 109.69/16.25 = (mult @ (mult @ (mult @ X0 @ X1) @ X1) @ X2))),
% 109.69/16.25 inference('cnf', [status(esa)], [c07])).
% 109.69/16.25 thf(zip_derived_cl0, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c01])).
% 109.69/16.25 thf(zip_derived_cl31, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((mult @ X2 @
% 109.69/16.25 (mult @ X1 @
% 109.69/16.25 (mult @ X1 @ (ld @ (mult @ (mult @ X2 @ X1) @ X1) @ X0))))
% 109.69/16.25 = (X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl0])).
% 109.69/16.25 thf(zip_derived_cl307, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ (mult @ op_a @ (mult @ op_a @ op_a)) @
% 109.69/16.25 (mult @ op_a @ (mult @ op_a @ (ld @ (mult @ unit @ op_a) @ X0))))
% 109.69/16.25 = (X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl170, zip_derived_cl31])).
% 109.69/16.25 thf(zip_derived_cl5, plain, (![X0 : $i]: ((mult @ unit @ X0) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c06])).
% 109.69/16.25 thf(zip_derived_cl0, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c01])).
% 109.69/16.25 thf(zip_derived_cl327, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ (mult @ op_a @ (mult @ op_a @ op_a)) @ (mult @ op_a @ X0))
% 109.69/16.25 = (X0))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl307, zip_derived_cl5, zip_derived_cl0])).
% 109.69/16.25 thf(zip_derived_cl2135, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((ld @ (mult @ X0 @ (mult @ op_a @ op_a)) @
% 109.69/16.25 (mult @ X0 @ (mult @ op_a @ (mult @ op_a @ op_a)))) = (op_a))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl144, zip_derived_cl46, zip_derived_cl46,
% 109.69/16.25 zip_derived_cl50, zip_derived_cl327])).
% 109.69/16.25 thf(zip_derived_cl0, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c01])).
% 109.69/16.25 thf(zip_derived_cl2136, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ (mult @ X0 @ (mult @ op_a @ op_a)) @ op_a)
% 109.69/16.25 = (mult @ X0 @ (mult @ op_a @ (mult @ op_a @ op_a))))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl2135, zip_derived_cl0])).
% 109.69/16.25 thf(zip_derived_cl50, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X1 @ (mult @ X0 @ X0)) = (mult @ (mult @ X1 @ X0) @ X0))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl4])).
% 109.69/16.25 thf(zip_derived_cl2249, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ (mult @ X0 @ (mult @ op_a @ op_a)) @ (mult @ op_a @ op_a))
% 109.69/16.25 = (mult @ (mult @ X0 @ (mult @ op_a @ (mult @ op_a @ op_a))) @ op_a))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl2136, zip_derived_cl50])).
% 109.69/16.25 thf(zip_derived_cl7, plain,
% 109.69/16.25 (((mult @ op_a @ (mult @ op_a @ (mult @ op_a @ op_a))) = (unit))),
% 109.69/16.25 inference('cnf', [status(esa)], [c08])).
% 109.69/16.25 thf(zip_derived_cl6, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X1 @ (mult @ X1 @ X2)))
% 109.69/16.25 = (mult @ (mult @ (mult @ X0 @ X1) @ X1) @ X2))),
% 109.69/16.25 inference('cnf', [status(esa)], [c07])).
% 109.69/16.25 thf(zip_derived_cl3, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c04])).
% 109.69/16.25 thf(zip_derived_cl29, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((rd @ (mult @ X2 @ (mult @ X1 @ (mult @ X1 @ X0))) @ X0)
% 109.69/16.25 = (mult @ (mult @ X2 @ X1) @ X1))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl3])).
% 109.69/16.25 thf(zip_derived_cl185, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((rd @ (mult @ X0 @ unit) @ (mult @ op_a @ op_a))
% 109.69/16.25 = (mult @ (mult @ X0 @ op_a) @ op_a))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl29])).
% 109.69/16.25 thf(zip_derived_cl4, plain, (![X0 : $i]: ((mult @ X0 @ unit) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c05])).
% 109.69/16.25 thf(zip_derived_cl205, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((rd @ X0 @ (mult @ op_a @ op_a)) = (mult @ (mult @ X0 @ op_a) @ op_a))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl185, zip_derived_cl4])).
% 109.69/16.25 thf(zip_derived_cl50, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X1 @ (mult @ X0 @ X0)) = (mult @ (mult @ X1 @ X0) @ X0))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl4])).
% 109.69/16.25 thf(zip_derived_cl626, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((rd @ X0 @ (mult @ op_a @ op_a)) = (mult @ X0 @ (mult @ op_a @ op_a)))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl205, zip_derived_cl50])).
% 109.69/16.25 thf(c03, axiom, (( mult @ ( rd @ A @ B ) @ B ) = ( A ))).
% 109.69/16.25 thf(zip_derived_cl2, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c03])).
% 109.69/16.25 thf(zip_derived_cl627, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ (mult @ X0 @ (mult @ op_a @ op_a)) @ (mult @ op_a @ op_a))
% 109.69/16.25 = (X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl626, zip_derived_cl2])).
% 109.69/16.25 thf(zip_derived_cl2288, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((X0)
% 109.69/16.25 = (mult @ (mult @ X0 @ (mult @ op_a @ (mult @ op_a @ op_a))) @ op_a))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl2249, zip_derived_cl627])).
% 109.69/16.25 thf(zip_derived_cl3571, plain,
% 109.69/16.25 (((ld @ op_b @ (mult @ op_a @ op_a)) = (mult @ (ld @ op_b @ op_a) @ op_a))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl3147, zip_derived_cl2288])).
% 109.69/16.25 thf(zip_derived_cl81, plain,
% 109.69/16.25 (((mult @ op_a @ op_a)
% 109.69/16.25 = (mult @ (mult @ op_a @ (mult @ op_a @ op_a)) @
% 109.69/16.25 (mult @ op_a @ (mult @ op_a @ op_a))))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl78, zip_derived_cl1])).
% 109.69/16.25 thf(zip_derived_cl29, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((rd @ (mult @ X2 @ (mult @ X1 @ (mult @ X1 @ X0))) @ X0)
% 109.69/16.25 = (mult @ (mult @ X2 @ X1) @ X1))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl3])).
% 109.69/16.25 thf(zip_derived_cl190, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((rd @
% 109.69/16.25 (mult @ X0 @
% 109.69/16.25 (mult @ (mult @ op_a @ (mult @ op_a @ op_a)) @ (mult @ op_a @ op_a))) @
% 109.69/16.25 (mult @ op_a @ (mult @ op_a @ op_a)))
% 109.69/16.25 = (mult @ (mult @ X0 @ (mult @ op_a @ (mult @ op_a @ op_a))) @
% 109.69/16.25 (mult @ op_a @ (mult @ op_a @ op_a))))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl81, zip_derived_cl29])).
% 109.69/16.25 thf(zip_derived_cl153, plain,
% 109.69/16.25 (((op_a)
% 109.69/16.25 = (mult @ (mult @ op_a @ (mult @ op_a @ op_a)) @ (mult @ op_a @ op_a)))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl148, zip_derived_cl1])).
% 109.69/16.25 thf(zip_derived_cl208, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((rd @ (mult @ X0 @ op_a) @ (mult @ op_a @ (mult @ op_a @ op_a)))
% 109.69/16.25 = (mult @ (mult @ X0 @ (mult @ op_a @ (mult @ op_a @ op_a))) @
% 109.69/16.25 (mult @ op_a @ (mult @ op_a @ op_a))))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl190, zip_derived_cl153])).
% 109.69/16.25 thf(zip_derived_cl50, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X1 @ (mult @ X0 @ X0)) = (mult @ (mult @ X1 @ X0) @ X0))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl4])).
% 109.69/16.25 thf(zip_derived_cl327, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ (mult @ op_a @ (mult @ op_a @ op_a)) @ (mult @ op_a @ X0))
% 109.69/16.25 = (X0))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl307, zip_derived_cl5, zip_derived_cl0])).
% 109.69/16.25 thf(zip_derived_cl3206, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((rd @ (mult @ X0 @ op_a) @ (mult @ op_a @ (mult @ op_a @ op_a)))
% 109.69/16.25 = (mult @ X0 @ (mult @ op_a @ op_a)))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl208, zip_derived_cl50, zip_derived_cl327])).
% 109.69/16.25 thf(zip_derived_cl5799, plain,
% 109.69/16.25 (((mult @ (ld @ op_b @ op_a) @ (mult @ op_a @ op_a))
% 109.69/16.25 = (ld @ op_b @ (mult @ op_a @ (mult @ op_a @ op_a))))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl5788, zip_derived_cl7, zip_derived_cl4,
% 109.69/16.25 zip_derived_cl3571, zip_derived_cl3206])).
% 109.69/16.25 thf(zip_derived_cl3, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c04])).
% 109.69/16.25 thf(zip_derived_cl1, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c02])).
% 109.69/16.25 thf(zip_derived_cl2295, plain,
% 109.69/16.25 (![X0 : $i]: ((ld @ op_b @ X0) = (mult @ (ld @ op_b @ unit) @ X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl494, zip_derived_cl1])).
% 109.69/16.25 thf(zip_derived_cl3, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c04])).
% 109.69/16.25 thf(zip_derived_cl2444, plain,
% 109.69/16.25 (![X0 : $i]: ((rd @ (ld @ op_b @ X0) @ X0) = (ld @ op_b @ unit))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl2295, zip_derived_cl3])).
% 109.69/16.25 thf(zip_derived_cl2548, plain,
% 109.69/16.25 (![X0 : $i]: ((rd @ X0 @ (mult @ op_b @ X0)) = (ld @ op_b @ unit))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2444])).
% 109.69/16.25 thf(zip_derived_cl2, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c03])).
% 109.69/16.25 thf(zip_derived_cl2710, plain,
% 109.69/16.25 (![X0 : $i]: ((mult @ (ld @ op_b @ unit) @ (mult @ op_b @ X0)) = (X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl2548, zip_derived_cl2])).
% 109.69/16.25 thf(zip_derived_cl6, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X1 @ (mult @ X1 @ X2)))
% 109.69/16.25 = (mult @ (mult @ (mult @ X0 @ X1) @ X1) @ X2))),
% 109.69/16.25 inference('cnf', [status(esa)], [c07])).
% 109.69/16.25 thf(zip_derived_cl29, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((rd @ (mult @ X2 @ (mult @ X1 @ (mult @ X1 @ X0))) @ X0)
% 109.69/16.25 = (mult @ (mult @ X2 @ X1) @ X1))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl3])).
% 109.69/16.25 thf(zip_derived_cl176, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 109.69/16.25 ((rd @
% 109.69/16.25 (mult @ X3 @
% 109.69/16.25 (mult @ X2 @ (mult @ X2 @ (mult @ X1 @ (mult @ X1 @ X0))))) @
% 109.69/16.25 X0) = (mult @ (mult @ (mult @ (mult @ X3 @ X2) @ X2) @ X1) @ X1))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl29])).
% 109.69/16.25 thf(zip_derived_cl6, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X1 @ (mult @ X1 @ X2)))
% 109.69/16.25 = (mult @ (mult @ (mult @ X0 @ X1) @ X1) @ X2))),
% 109.69/16.25 inference('cnf', [status(esa)], [c07])).
% 109.69/16.25 thf(zip_derived_cl199, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 109.69/16.25 ((rd @
% 109.69/16.25 (mult @ X3 @
% 109.69/16.25 (mult @ X2 @ (mult @ X2 @ (mult @ X1 @ (mult @ X1 @ X0))))) @
% 109.69/16.25 X0) = (mult @ (mult @ X3 @ (mult @ X2 @ (mult @ X2 @ X1))) @ X1))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl176, zip_derived_cl6])).
% 109.69/16.25 thf(zip_derived_cl3315, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((rd @
% 109.69/16.25 (mult @ X1 @ (mult @ (ld @ op_b @ unit) @ (mult @ op_b @ X0))) @ X0)
% 109.69/16.25 = (mult @
% 109.69/16.25 (mult @ X1 @
% 109.69/16.25 (mult @ (ld @ op_b @ unit) @ (mult @ (ld @ op_b @ unit) @ op_b))) @
% 109.69/16.25 op_b))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl2710, zip_derived_cl199])).
% 109.69/16.25 thf(zip_derived_cl2710, plain,
% 109.69/16.25 (![X0 : $i]: ((mult @ (ld @ op_b @ unit) @ (mult @ op_b @ X0)) = (X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl2548, zip_derived_cl2])).
% 109.69/16.25 thf(zip_derived_cl3, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c04])).
% 109.69/16.25 thf(zip_derived_cl13, plain, (![X0 : $i]: ((ld @ X0 @ X0) = (unit))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl1])).
% 109.69/16.25 thf(zip_derived_cl2444, plain,
% 109.69/16.25 (![X0 : $i]: ((rd @ (ld @ op_b @ X0) @ X0) = (ld @ op_b @ unit))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl2295, zip_derived_cl3])).
% 109.69/16.25 thf(zip_derived_cl2547, plain, (((rd @ unit @ op_b) = (ld @ op_b @ unit))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl2444])).
% 109.69/16.25 thf(zip_derived_cl2, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c03])).
% 109.69/16.25 thf(zip_derived_cl2632, plain,
% 109.69/16.25 (((mult @ (ld @ op_b @ unit) @ op_b) = (unit))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl2547, zip_derived_cl2])).
% 109.69/16.25 thf(zip_derived_cl2295, plain,
% 109.69/16.25 (![X0 : $i]: ((ld @ op_b @ X0) = (mult @ (ld @ op_b @ unit) @ X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl494, zip_derived_cl1])).
% 109.69/16.25 thf(zip_derived_cl3348, plain,
% 109.69/16.25 (![X1 : $i]: ((X1) = (mult @ (mult @ X1 @ (ld @ op_b @ unit)) @ op_b))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl3315, zip_derived_cl2710, zip_derived_cl3,
% 109.69/16.25 zip_derived_cl2632, zip_derived_cl2295])).
% 109.69/16.25 thf(zip_derived_cl3, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c04])).
% 109.69/16.25 thf(zip_derived_cl3876, plain,
% 109.69/16.25 (![X0 : $i]: ((rd @ X0 @ op_b) = (mult @ X0 @ (ld @ op_b @ unit)))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl3348, zip_derived_cl3])).
% 109.69/16.25 thf(zip_derived_cl1, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c02])).
% 109.69/16.25 thf(zip_derived_cl3900, plain,
% 109.69/16.25 (![X0 : $i]: ((ld @ X0 @ (rd @ X0 @ op_b)) = (ld @ op_b @ unit))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl3876, zip_derived_cl1])).
% 109.69/16.25 thf(zip_derived_cl4278, plain,
% 109.69/16.25 (![X0 : $i]: ((ld @ (mult @ X0 @ op_b) @ X0) = (ld @ op_b @ unit))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl3900])).
% 109.69/16.25 thf(zip_derived_cl0, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c01])).
% 109.69/16.25 thf(zip_derived_cl5, plain, (![X0 : $i]: ((mult @ unit @ X0) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c06])).
% 109.69/16.25 thf(zip_derived_cl3, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c04])).
% 109.69/16.25 thf(zip_derived_cl25, plain, (![X0 : $i]: ((rd @ X0 @ X0) = (unit))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl3])).
% 109.69/16.25 thf(zip_derived_cl2, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c03])).
% 109.69/16.25 thf(zip_derived_cl340, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((rd @ (mult @ X1 @ (mult @ X0 @ X0)) @ X0) = (mult @ X1 @ X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl3])).
% 109.69/16.25 thf(zip_derived_cl520, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((rd @ X0 @ X1) = (mult @ (rd @ X0 @ (mult @ X1 @ X1)) @ X1))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl340])).
% 109.69/16.25 thf(zip_derived_cl3, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c04])).
% 109.69/16.25 thf(zip_derived_cl1001, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((rd @ (rd @ X1 @ X0) @ X0) = (rd @ X1 @ (mult @ X0 @ X0)))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl520, zip_derived_cl3])).
% 109.69/16.25 thf(zip_derived_cl1133, plain,
% 109.69/16.25 (![X0 : $i]: ((rd @ unit @ X0) = (rd @ X0 @ (mult @ X0 @ X0)))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl25, zip_derived_cl1001])).
% 109.69/16.25 thf(zip_derived_cl2, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c03])).
% 109.69/16.25 thf(zip_derived_cl1162, plain,
% 109.69/16.25 (![X0 : $i]: ((mult @ (rd @ unit @ X0) @ (mult @ X0 @ X0)) = (X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl1133, zip_derived_cl2])).
% 109.69/16.25 thf(zip_derived_cl31, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((mult @ X2 @
% 109.69/16.25 (mult @ X1 @
% 109.69/16.25 (mult @ X1 @ (ld @ (mult @ (mult @ X2 @ X1) @ X1) @ X0))))
% 109.69/16.25 = (X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl0])).
% 109.69/16.25 thf(zip_derived_cl50, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X1 @ (mult @ X0 @ X0)) = (mult @ (mult @ X1 @ X0) @ X0))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl4])).
% 109.69/16.25 thf(zip_derived_cl337, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((mult @ X2 @
% 109.69/16.25 (mult @ X1 @
% 109.69/16.25 (mult @ X1 @ (ld @ (mult @ X2 @ (mult @ X1 @ X1)) @ X0))))
% 109.69/16.25 = (X0))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl31, zip_derived_cl50])).
% 109.69/16.25 thf(zip_derived_cl11983, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ (rd @ unit @ X0) @ (mult @ X0 @ (mult @ X0 @ (ld @ X0 @ X1))))
% 109.69/16.25 = (X1))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl1162, zip_derived_cl337])).
% 109.69/16.25 thf(zip_derived_cl0, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c01])).
% 109.69/16.25 thf(zip_derived_cl12036, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ (rd @ unit @ X0) @ (mult @ X0 @ X1)) = (X1))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl11983, zip_derived_cl0])).
% 109.69/16.25 thf(zip_derived_cl3, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c04])).
% 109.69/16.25 thf(zip_derived_cl12082, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((rd @ X0 @ (mult @ X1 @ X0)) = (rd @ unit @ X1))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl12036, zip_derived_cl3])).
% 109.69/16.25 thf(zip_derived_cl12036, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ (rd @ unit @ X0) @ (mult @ X0 @ X1)) = (X1))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl11983, zip_derived_cl0])).
% 109.69/16.25 thf(zip_derived_cl12082, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((rd @ X0 @ (mult @ X1 @ X0)) = (rd @ unit @ X1))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl12036, zip_derived_cl3])).
% 109.69/16.25 thf(zip_derived_cl12352, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((rd @ (mult @ X1 @ X0) @ X0) = (rd @ unit @ (rd @ unit @ X1)))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl12036, zip_derived_cl12082])).
% 109.69/16.25 thf(zip_derived_cl3, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c04])).
% 109.69/16.25 thf(zip_derived_cl12376, plain,
% 109.69/16.25 (![X1 : $i]: ((X1) = (rd @ unit @ (rd @ unit @ X1)))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl12352, zip_derived_cl3])).
% 109.69/16.25 thf(zip_derived_cl2, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c03])).
% 109.69/16.25 thf(zip_derived_cl1, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c02])).
% 109.69/16.25 thf(zip_derived_cl19, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((ld @ (rd @ X0 @ X1) @ X0) = (X1))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 109.69/16.25 thf(zip_derived_cl12585, plain,
% 109.69/16.25 (![X0 : $i]: ((ld @ X0 @ unit) = (rd @ unit @ X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl12376, zip_derived_cl19])).
% 109.69/16.25 thf(zip_derived_cl12626, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((rd @ X0 @ (mult @ X1 @ X0)) = (ld @ X1 @ unit))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl12082, zip_derived_cl12585])).
% 109.69/16.25 thf(zip_derived_cl13529, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((rd @ (ld @ X1 @ X0) @ X0) = (ld @ X1 @ unit))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl12626])).
% 109.69/16.25 thf(zip_derived_cl2, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c03])).
% 109.69/16.25 thf(zip_derived_cl13932, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ (ld @ X0 @ unit) @ X1) = (ld @ X0 @ X1))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl13529, zip_derived_cl2])).
% 109.69/16.25 thf(zip_derived_cl3206, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((rd @ (mult @ X0 @ op_a) @ (mult @ op_a @ (mult @ op_a @ op_a)))
% 109.69/16.25 = (mult @ X0 @ (mult @ op_a @ op_a)))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl208, zip_derived_cl50, zip_derived_cl327])).
% 109.69/16.25 thf(zip_derived_cl16570, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((rd @ (ld @ X0 @ op_a) @ (mult @ op_a @ (mult @ op_a @ op_a)))
% 109.69/16.25 = (mult @ (ld @ X0 @ unit) @ (mult @ op_a @ op_a)))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl13932, zip_derived_cl3206])).
% 109.69/16.25 thf(zip_derived_cl2136, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ (mult @ X0 @ (mult @ op_a @ op_a)) @ op_a)
% 109.69/16.25 = (mult @ X0 @ (mult @ op_a @ (mult @ op_a @ op_a))))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl2135, zip_derived_cl0])).
% 109.69/16.25 thf(zip_derived_cl2, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c03])).
% 109.69/16.25 thf(zip_derived_cl50, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X1 @ (mult @ X0 @ X0)) = (mult @ (mult @ X1 @ X0) @ X0))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl4])).
% 109.69/16.25 thf(zip_derived_cl351, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ (rd @ X0 @ X1) @ (mult @ X1 @ X1)) = (mult @ X0 @ X1))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl50])).
% 109.69/16.25 thf(zip_derived_cl627, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ (mult @ X0 @ (mult @ op_a @ op_a)) @ (mult @ op_a @ op_a))
% 109.69/16.25 = (X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl626, zip_derived_cl2])).
% 109.69/16.25 thf(zip_derived_cl1452, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ (mult @ X0 @ op_a) @ (mult @ op_a @ op_a)) = (rd @ X0 @ op_a))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl351, zip_derived_cl627])).
% 109.69/16.25 thf(zip_derived_cl2, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c03])).
% 109.69/16.25 thf(zip_derived_cl1488, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ (mult @ (mult @ X0 @ op_a) @ (mult @ op_a @ op_a)) @ op_a)
% 109.69/16.25 = (X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl1452, zip_derived_cl2])).
% 109.69/16.25 thf(zip_derived_cl2264, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ (mult @ X0 @ op_a) @ (mult @ op_a @ (mult @ op_a @ op_a)))
% 109.69/16.25 = (X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl2136, zip_derived_cl1488])).
% 109.69/16.25 thf(zip_derived_cl3, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c04])).
% 109.69/16.25 thf(zip_derived_cl2341, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((rd @ X0 @ (mult @ op_a @ (mult @ op_a @ op_a))) = (mult @ X0 @ op_a))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl2264, zip_derived_cl3])).
% 109.69/16.25 thf(zip_derived_cl13932, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ (ld @ X0 @ unit) @ X1) = (ld @ X0 @ X1))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl13529, zip_derived_cl2])).
% 109.69/16.25 thf(zip_derived_cl16754, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ (ld @ X0 @ op_a) @ op_a) = (ld @ X0 @ (mult @ op_a @ op_a)))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl16570, zip_derived_cl2341, zip_derived_cl13932])).
% 109.69/16.25 thf(zip_derived_cl0, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c01])).
% 109.69/16.25 thf(zip_derived_cl17932, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ (ld @ X0 @ op_a) @ op_a)) = (mult @ op_a @ op_a))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl16754, zip_derived_cl0])).
% 109.69/16.25 thf(zip_derived_cl18780, plain,
% 109.69/16.25 (((mult @ (mult @ op_a @ op_b) @ (mult @ (ld @ op_b @ unit) @ op_a))
% 109.69/16.25 = (mult @ op_a @ op_a))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl4278, zip_derived_cl17932])).
% 109.69/16.25 thf(zip_derived_cl13932, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ (ld @ X0 @ unit) @ X1) = (ld @ X0 @ X1))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl13529, zip_derived_cl2])).
% 109.69/16.25 thf(zip_derived_cl18791, plain,
% 109.69/16.25 (((mult @ (mult @ op_a @ op_b) @ (ld @ op_b @ op_a))
% 109.69/16.25 = (mult @ op_a @ op_a))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl18780, zip_derived_cl13932])).
% 109.69/16.25 thf(zip_derived_cl3, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c04])).
% 109.69/16.25 thf(zip_derived_cl18835, plain,
% 109.69/16.25 (((rd @ (mult @ op_a @ op_a) @ (ld @ op_b @ op_a)) = (mult @ op_a @ op_b))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl18791, zip_derived_cl3])).
% 109.69/16.25 thf(zip_derived_cl2, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c03])).
% 109.69/16.25 thf(zip_derived_cl12626, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((rd @ X0 @ (mult @ X1 @ X0)) = (ld @ X1 @ unit))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl12082, zip_derived_cl12585])).
% 109.69/16.25 thf(zip_derived_cl13586, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((rd @ X1 @ X0) = (ld @ (rd @ X0 @ X1) @ unit))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl12626])).
% 109.69/16.25 thf(zip_derived_cl0, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c01])).
% 109.69/16.25 thf(zip_derived_cl15686, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ (rd @ X1 @ X0)) = (unit))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl13586, zip_derived_cl0])).
% 109.69/16.25 thf(zip_derived_cl20843, plain,
% 109.69/16.25 (((mult @ (rd @ (ld @ op_b @ op_a) @ (mult @ op_a @ op_a)) @
% 109.69/16.25 (mult @ op_a @ op_b)) = (unit))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl18835, zip_derived_cl15686])).
% 109.69/16.25 thf(zip_derived_cl2295, plain,
% 109.69/16.25 (![X0 : $i]: ((ld @ op_b @ X0) = (mult @ (ld @ op_b @ unit) @ X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl494, zip_derived_cl1])).
% 109.69/16.25 thf(zip_derived_cl351, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ (rd @ X0 @ X1) @ (mult @ X1 @ X1)) = (mult @ X0 @ X1))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl50])).
% 109.69/16.25 thf(zip_derived_cl3, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c04])).
% 109.69/16.25 thf(zip_derived_cl546, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((rd @ (mult @ X1 @ X0) @ (mult @ X0 @ X0)) = (rd @ X1 @ X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl351, zip_derived_cl3])).
% 109.69/16.25 thf(zip_derived_cl2442, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((rd @ (ld @ op_b @ X0) @ (mult @ X0 @ X0))
% 109.69/16.25 = (rd @ (ld @ op_b @ unit) @ X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl2295, zip_derived_cl546])).
% 109.69/16.25 thf(zip_derived_cl2, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c03])).
% 109.69/16.25 thf(zip_derived_cl2264, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ (mult @ X0 @ op_a) @ (mult @ op_a @ (mult @ op_a @ op_a)))
% 109.69/16.25 = (X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl2136, zip_derived_cl1488])).
% 109.69/16.25 thf(zip_derived_cl2358, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ op_a @ (mult @ op_a @ op_a))) = (rd @ X0 @ op_a))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl2264])).
% 109.69/16.25 thf(zip_derived_cl13932, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ (ld @ X0 @ unit) @ X1) = (ld @ X0 @ X1))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl13529, zip_derived_cl2])).
% 109.69/16.25 thf(zip_derived_cl5799, plain,
% 109.69/16.25 (((mult @ (ld @ op_b @ op_a) @ (mult @ op_a @ op_a))
% 109.69/16.25 = (ld @ op_b @ (mult @ op_a @ (mult @ op_a @ op_a))))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl5788, zip_derived_cl7, zip_derived_cl4,
% 109.69/16.25 zip_derived_cl3571, zip_derived_cl3206])).
% 109.69/16.25 thf(zip_derived_cl6, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X1 @ (mult @ X1 @ X2)))
% 109.69/16.25 = (mult @ (mult @ (mult @ X0 @ X1) @ X1) @ X2))),
% 109.69/16.25 inference('cnf', [status(esa)], [c07])).
% 109.69/16.25 thf(zip_derived_cl50, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X1 @ (mult @ X0 @ X0)) = (mult @ (mult @ X1 @ X0) @ X0))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl4])).
% 109.69/16.25 thf(zip_derived_cl334, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X1 @ (mult @ X1 @ X2)))
% 109.69/16.25 = (mult @ (mult @ X0 @ (mult @ X1 @ X1)) @ X2))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl6, zip_derived_cl50])).
% 109.69/16.25 thf(zip_derived_cl20913, plain,
% 109.69/16.25 (((mult @ (ld @ op_b @ op_a) @
% 109.69/16.25 (mult @ op_a @ (mult @ op_a @ (mult @ op_a @ op_b)))) = (unit))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl20843, zip_derived_cl2442, zip_derived_cl2358,
% 109.69/16.25 zip_derived_cl13932, zip_derived_cl5799, zip_derived_cl334])).
% 109.69/16.25 thf(zip_derived_cl29, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((rd @ (mult @ X2 @ (mult @ X1 @ (mult @ X1 @ X0))) @ X0)
% 109.69/16.25 = (mult @ (mult @ X2 @ X1) @ X1))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl3])).
% 109.69/16.25 thf(zip_derived_cl50, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X1 @ (mult @ X0 @ X0)) = (mult @ (mult @ X1 @ X0) @ X0))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl4])).
% 109.69/16.25 thf(zip_derived_cl336, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((rd @ (mult @ X2 @ (mult @ X1 @ (mult @ X1 @ X0))) @ X0)
% 109.69/16.25 = (mult @ X2 @ (mult @ X1 @ X1)))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl29, zip_derived_cl50])).
% 109.69/16.25 thf(zip_derived_cl21117, plain,
% 109.69/16.25 (((rd @ unit @ (mult @ op_a @ op_b))
% 109.69/16.25 = (mult @ (ld @ op_b @ op_a) @ (mult @ op_a @ op_a)))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl20913, zip_derived_cl336])).
% 109.69/16.25 thf(zip_derived_cl12585, plain,
% 109.69/16.25 (![X0 : $i]: ((ld @ X0 @ unit) = (rd @ unit @ X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl12376, zip_derived_cl19])).
% 109.69/16.25 thf(zip_derived_cl21153, plain,
% 109.69/16.25 (((ld @ (mult @ op_a @ op_b) @ unit)
% 109.69/16.25 = (mult @ (ld @ op_b @ op_a) @ (mult @ op_a @ op_a)))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl21117, zip_derived_cl12585])).
% 109.69/16.25 thf(zip_derived_cl36764, plain,
% 109.69/16.25 (((ld @ (mult @ op_a @ op_b) @ unit)
% 109.69/16.25 = (ld @ op_b @ (mult @ op_a @ (mult @ op_a @ op_a))))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl5799, zip_derived_cl21153])).
% 109.69/16.25 thf(zip_derived_cl0, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c01])).
% 109.69/16.25 thf(zip_derived_cl45901, plain,
% 109.69/16.25 (((mult @ op_b @ (ld @ (mult @ op_a @ op_b) @ unit))
% 109.69/16.25 = (mult @ op_a @ (mult @ op_a @ op_a)))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl36764, zip_derived_cl0])).
% 109.69/16.25 thf(zip_derived_cl3571, plain,
% 109.69/16.25 (((ld @ op_b @ (mult @ op_a @ op_a)) = (mult @ (ld @ op_b @ op_a) @ op_a))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl3147, zip_derived_cl2288])).
% 109.69/16.25 thf(zip_derived_cl0, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c01])).
% 109.69/16.25 thf(zip_derived_cl3583, plain,
% 109.69/16.25 (((mult @ op_b @ (mult @ (ld @ op_b @ op_a) @ op_a))
% 109.69/16.25 = (mult @ op_a @ op_a))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl3571, zip_derived_cl0])).
% 109.69/16.25 thf(zip_derived_cl5, plain, (![X0 : $i]: ((mult @ unit @ X0) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c06])).
% 109.69/16.25 thf(zip_derived_cl28, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((ld @ (mult @ (mult @ X2 @ X1) @ X1) @
% 109.69/16.25 (mult @ X2 @ (mult @ X1 @ (mult @ X1 @ X0)))) = (X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1])).
% 109.69/16.25 thf(zip_derived_cl91, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((ld @ (mult @ (mult @ unit @ X1) @ X1) @
% 109.69/16.25 (mult @ X1 @ (mult @ X1 @ X0))) = (X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl28])).
% 109.69/16.25 thf(zip_derived_cl5, plain, (![X0 : $i]: ((mult @ unit @ X0) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c06])).
% 109.69/16.25 thf(zip_derived_cl120, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((ld @ (mult @ X1 @ X1) @ (mult @ X1 @ (mult @ X1 @ X0))) = (X0))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl91, zip_derived_cl5])).
% 109.69/16.25 thf(zip_derived_cl3606, plain,
% 109.69/16.25 (((ld @ (mult @ op_b @ op_b) @ (mult @ op_b @ (mult @ op_a @ op_a)))
% 109.69/16.25 = (mult @ (ld @ op_b @ op_a) @ op_a))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl3583, zip_derived_cl120])).
% 109.69/16.25 thf(zip_derived_cl0, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c01])).
% 109.69/16.25 thf(zip_derived_cl5, plain, (![X0 : $i]: ((mult @ unit @ X0) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c06])).
% 109.69/16.25 thf(zip_derived_cl29, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((rd @ (mult @ X2 @ (mult @ X1 @ (mult @ X1 @ X0))) @ X0)
% 109.69/16.25 = (mult @ (mult @ X2 @ X1) @ X1))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl3])).
% 109.69/16.25 thf(zip_derived_cl179, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((rd @ (mult @ X1 @ (mult @ X1 @ X0)) @ X0)
% 109.69/16.25 = (mult @ (mult @ unit @ X1) @ X1))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl29])).
% 109.69/16.25 thf(zip_derived_cl5, plain, (![X0 : $i]: ((mult @ unit @ X0) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c06])).
% 109.69/16.25 thf(zip_derived_cl201, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((rd @ (mult @ X1 @ (mult @ X1 @ X0)) @ X0) = (mult @ X1 @ X1))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl179, zip_derived_cl5])).
% 109.69/16.25 thf(zip_derived_cl446, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((rd @ (mult @ X1 @ X0) @ (ld @ X1 @ X0)) = (mult @ X1 @ X1))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl201])).
% 109.69/16.25 thf(zip_derived_cl2, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c03])).
% 109.69/16.25 thf(zip_derived_cl577, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ (mult @ X0 @ X0) @ (ld @ X0 @ X1)) = (mult @ X0 @ X1))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl446, zip_derived_cl2])).
% 109.69/16.25 thf(zip_derived_cl3651, plain,
% 109.69/16.25 (((mult @ (mult @ (mult @ op_b @ op_b) @ (mult @ op_b @ op_b)) @
% 109.69/16.25 (mult @ (ld @ op_b @ op_a) @ op_a))
% 109.69/16.25 = (mult @ (mult @ op_b @ op_b) @ (mult @ op_b @ (mult @ op_a @ op_a))))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl3606, zip_derived_cl577])).
% 109.69/16.25 thf(zip_derived_cl46, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X0 @ X1)) = (mult @ (mult @ X0 @ X0) @ X1))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl40, zip_derived_cl5])).
% 109.69/16.25 thf(zip_derived_cl46, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X0 @ X1)) = (mult @ (mult @ X0 @ X0) @ X1))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl40, zip_derived_cl5])).
% 109.69/16.25 thf(zip_derived_cl3656, plain,
% 109.69/16.25 (((mult @ (mult @ op_b @ (mult @ op_b @ (mult @ op_b @ op_b))) @
% 109.69/16.25 (mult @ (ld @ op_b @ op_a) @ op_a))
% 109.69/16.25 = (mult @ op_b @ (mult @ op_b @ (mult @ op_b @ (mult @ op_a @ op_a)))))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl3651, zip_derived_cl46, zip_derived_cl46])).
% 109.69/16.25 thf(zip_derived_cl120, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((ld @ (mult @ X1 @ X1) @ (mult @ X1 @ (mult @ X1 @ X0))) = (X0))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl91, zip_derived_cl5])).
% 109.69/16.25 thf(zip_derived_cl6337, plain,
% 109.69/16.25 (((ld @
% 109.69/16.25 (mult @ (mult @ op_b @ (mult @ op_b @ (mult @ op_b @ op_b))) @
% 109.69/16.25 (mult @ op_b @ (mult @ op_b @ (mult @ op_b @ op_b)))) @
% 109.69/16.25 (mult @ (mult @ op_b @ (mult @ op_b @ (mult @ op_b @ op_b))) @
% 109.69/16.25 (mult @ op_b @ (mult @ op_b @ (mult @ op_b @ (mult @ op_a @ op_a))))))
% 109.69/16.25 = (mult @ (ld @ op_b @ op_a) @ op_a))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl3656, zip_derived_cl120])).
% 109.69/16.25 thf(zip_derived_cl46, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X0 @ X1)) = (mult @ (mult @ X0 @ X0) @ X1))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl40, zip_derived_cl5])).
% 109.69/16.25 thf(zip_derived_cl46, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X0 @ X1)) = (mult @ (mult @ X0 @ X0) @ X1))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl40, zip_derived_cl5])).
% 109.69/16.25 thf(zip_derived_cl235, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ (mult @ X0 @ X0) @ (mult @ (mult @ X0 @ X0) @ X1))
% 109.69/16.25 = (mult @ (mult @ X0 @ (mult @ X0 @ (mult @ X0 @ X0))) @ X1))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl46, zip_derived_cl46])).
% 109.69/16.25 thf(zip_derived_cl46, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X0 @ X1)) = (mult @ (mult @ X0 @ X0) @ X1))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl40, zip_derived_cl5])).
% 109.69/16.25 thf(zip_derived_cl46, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X0 @ X1)) = (mult @ (mult @ X0 @ X0) @ X1))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl40, zip_derived_cl5])).
% 109.69/16.25 thf(zip_derived_cl240, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X0 @ (mult @ X0 @ (mult @ X0 @ X1))))
% 109.69/16.25 = (mult @ (mult @ X0 @ (mult @ X0 @ (mult @ X0 @ X0))) @ X1))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl235, zip_derived_cl46, zip_derived_cl46])).
% 109.69/16.25 thf(zip_derived_cl16, plain,
% 109.69/16.25 (((ld @ op_b @ unit)
% 109.69/16.25 = (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @ (mult @ op_b @ (mult @ op_b @ op_b))))))))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl1])).
% 109.69/16.25 thf(zip_derived_cl240, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X0 @ (mult @ X0 @ (mult @ X0 @ X1))))
% 109.69/16.25 = (mult @ (mult @ X0 @ (mult @ X0 @ (mult @ X0 @ X0))) @ X1))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl235, zip_derived_cl46, zip_derived_cl46])).
% 109.69/16.25 thf(zip_derived_cl2548, plain,
% 109.69/16.25 (![X0 : $i]: ((rd @ X0 @ (mult @ op_b @ X0)) = (ld @ op_b @ unit))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2444])).
% 109.69/16.25 thf(zip_derived_cl19, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((ld @ (rd @ X0 @ X1) @ X0) = (X1))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 109.69/16.25 thf(zip_derived_cl2711, plain,
% 109.69/16.25 (![X0 : $i]: ((ld @ (ld @ op_b @ unit) @ X0) = (mult @ op_b @ X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl2548, zip_derived_cl19])).
% 109.69/16.25 thf(zip_derived_cl6357, plain,
% 109.69/16.25 (((mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @ (mult @ op_b @ (mult @ op_a @ op_a)))))))))
% 109.69/16.25 = (mult @ (ld @ op_b @ op_a) @ op_a))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl6337, zip_derived_cl240, zip_derived_cl16,
% 109.69/16.25 zip_derived_cl240, zip_derived_cl2711])).
% 109.69/16.25 thf(zip_derived_cl120, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((ld @ (mult @ X1 @ X1) @ (mult @ X1 @ (mult @ X1 @ X0))) = (X0))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl91, zip_derived_cl5])).
% 109.69/16.25 thf(zip_derived_cl8171, plain,
% 109.69/16.25 (((ld @ (mult @ op_b @ op_b) @
% 109.69/16.25 (mult @ op_b @ (mult @ (ld @ op_b @ op_a) @ op_a)))
% 109.69/16.25 = (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @ (mult @ op_b @ (mult @ op_a @ op_a)))))))))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl6357, zip_derived_cl120])).
% 109.69/16.25 thf(zip_derived_cl2523, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((rd @ (ld @ op_b @ (mult @ X0 @ X0)) @ X0) = (ld @ op_b @ X0))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl2470, zip_derived_cl2295])).
% 109.69/16.25 thf(zip_derived_cl2, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c03])).
% 109.69/16.25 thf(zip_derived_cl5766, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ (ld @ op_b @ X0) @ X0) = (ld @ op_b @ (mult @ X0 @ X0)))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl2523, zip_derived_cl2])).
% 109.69/16.25 thf(zip_derived_cl0, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c01])).
% 109.69/16.25 thf(zip_derived_cl5813, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ op_b @ (mult @ (ld @ op_b @ X0) @ X0)) = (mult @ X0 @ X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl5766, zip_derived_cl0])).
% 109.69/16.25 thf(zip_derived_cl8237, plain,
% 109.69/16.25 (((ld @ (mult @ op_b @ op_b) @ (mult @ op_a @ op_a))
% 109.69/16.25 = (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @ (mult @ op_b @ (mult @ op_a @ op_a)))))))))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl8171, zip_derived_cl5813])).
% 109.69/16.25 thf(zip_derived_cl446, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((rd @ (mult @ X1 @ X0) @ (ld @ X1 @ X0)) = (mult @ X1 @ X1))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl201])).
% 109.69/16.25 thf(zip_derived_cl19, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((ld @ (rd @ X0 @ X1) @ X0) = (X1))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 109.69/16.25 thf(zip_derived_cl578, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((ld @ (mult @ X0 @ X0) @ (mult @ X0 @ X1)) = (ld @ X0 @ X1))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl446, zip_derived_cl19])).
% 109.69/16.25 thf(zip_derived_cl8289, plain,
% 109.69/16.25 (((ld @ (mult @ op_b @ op_b) @
% 109.69/16.25 (ld @ (mult @ op_b @ op_b) @ (mult @ op_a @ op_a)))
% 109.69/16.25 = (ld @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @ (mult @ op_b @ (mult @ op_a @ op_a)))))))))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl8237, zip_derived_cl578])).
% 109.69/16.25 thf(zip_derived_cl0, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c01])).
% 109.69/16.25 thf(zip_derived_cl578, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((ld @ (mult @ X0 @ X0) @ (mult @ X0 @ X1)) = (ld @ X0 @ X1))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl446, zip_derived_cl19])).
% 109.69/16.25 thf(zip_derived_cl2026, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((ld @ (mult @ X1 @ X1) @ X0) = (ld @ X1 @ (ld @ X1 @ X0)))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl578])).
% 109.69/16.25 thf(zip_derived_cl46, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X0 @ X1)) = (mult @ (mult @ X0 @ X0) @ X1))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl40, zip_derived_cl5])).
% 109.69/16.25 thf(zip_derived_cl1, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c02])).
% 109.69/16.25 thf(zip_derived_cl8351, plain,
% 109.69/16.25 (((ld @ (mult @ op_b @ (mult @ op_b @ (mult @ op_b @ op_b))) @
% 109.69/16.25 (mult @ op_a @ op_a))
% 109.69/16.25 = (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @ (mult @ op_b @ (mult @ op_a @ op_a)))))))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl8289, zip_derived_cl2026, zip_derived_cl46,
% 109.69/16.25 zip_derived_cl1])).
% 109.69/16.25 thf(zip_derived_cl0, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c01])).
% 109.69/16.25 thf(zip_derived_cl8584, plain,
% 109.69/16.25 (((mult @ (mult @ op_b @ (mult @ op_b @ (mult @ op_b @ op_b))) @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @
% 109.69/16.25 (mult @ op_b @ (mult @ op_b @ (mult @ op_b @ (mult @ op_a @ op_a)))))))
% 109.69/16.25 = (mult @ op_a @ op_a))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl8351, zip_derived_cl0])).
% 109.69/16.25 thf(zip_derived_cl46, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X0 @ X1)) = (mult @ (mult @ X0 @ X0) @ X1))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl40, zip_derived_cl5])).
% 109.69/16.25 thf(zip_derived_cl29, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((rd @ (mult @ X2 @ (mult @ X1 @ (mult @ X1 @ X0))) @ X0)
% 109.69/16.25 = (mult @ (mult @ X2 @ X1) @ X1))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl3])).
% 109.69/16.25 thf(zip_derived_cl221, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((rd @
% 109.69/16.25 (mult @ X2 @
% 109.69/16.25 (mult @ (mult @ X1 @ X1) @ (mult @ X1 @ (mult @ X1 @ X0)))) @
% 109.69/16.25 X0) = (mult @ (mult @ X2 @ (mult @ X1 @ X1)) @ (mult @ X1 @ X1)))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl46, zip_derived_cl29])).
% 109.69/16.25 thf(zip_derived_cl46, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X0 @ X1)) = (mult @ (mult @ X0 @ X0) @ X1))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl40, zip_derived_cl5])).
% 109.69/16.25 thf(zip_derived_cl245, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((rd @
% 109.69/16.25 (mult @ X2 @
% 109.69/16.25 (mult @ X1 @ (mult @ X1 @ (mult @ X1 @ (mult @ X1 @ X0))))) @
% 109.69/16.25 X0) = (mult @ (mult @ X2 @ (mult @ X1 @ X1)) @ (mult @ X1 @ X1)))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl221, zip_derived_cl46])).
% 109.69/16.25 thf(zip_derived_cl50, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X1 @ (mult @ X0 @ X0)) = (mult @ (mult @ X1 @ X0) @ X0))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl4])).
% 109.69/16.25 thf(zip_derived_cl46, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X0 @ X1)) = (mult @ (mult @ X0 @ X0) @ X1))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl40, zip_derived_cl5])).
% 109.69/16.25 thf(zip_derived_cl4755, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((rd @
% 109.69/16.25 (mult @ X2 @
% 109.69/16.25 (mult @ X1 @ (mult @ X1 @ (mult @ X1 @ (mult @ X1 @ X0))))) @
% 109.69/16.25 X0) = (mult @ X2 @ (mult @ X1 @ (mult @ X1 @ (mult @ X1 @ X1)))))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl245, zip_derived_cl50, zip_derived_cl46])).
% 109.69/16.25 thf(zip_derived_cl8826, plain,
% 109.69/16.25 (((rd @ (mult @ op_a @ op_a) @ (mult @ op_b @ (mult @ op_a @ op_a)))
% 109.69/16.25 = (mult @ (mult @ op_b @ (mult @ op_b @ (mult @ op_b @ op_b))) @
% 109.69/16.25 (mult @ op_b @ (mult @ op_b @ (mult @ op_b @ op_b)))))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl8584, zip_derived_cl4755])).
% 109.69/16.25 thf(zip_derived_cl2548, plain,
% 109.69/16.25 (![X0 : $i]: ((rd @ X0 @ (mult @ op_b @ X0)) = (ld @ op_b @ unit))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2444])).
% 109.69/16.25 thf(zip_derived_cl8858, plain,
% 109.69/16.25 (((ld @ op_b @ unit)
% 109.69/16.25 = (mult @ (mult @ op_b @ (mult @ op_b @ (mult @ op_b @ op_b))) @
% 109.69/16.25 (mult @ op_b @ (mult @ op_b @ (mult @ op_b @ op_b)))))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl8826, zip_derived_cl2548])).
% 109.69/16.25 thf(zip_derived_cl31, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((mult @ X2 @
% 109.69/16.25 (mult @ X1 @
% 109.69/16.25 (mult @ X1 @ (ld @ (mult @ (mult @ X2 @ X1) @ X1) @ X0))))
% 109.69/16.25 = (X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl0])).
% 109.69/16.25 thf(zip_derived_cl29, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((rd @ (mult @ X2 @ (mult @ X1 @ (mult @ X1 @ X0))) @ X0)
% 109.69/16.25 = (mult @ (mult @ X2 @ X1) @ X1))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl3])).
% 109.69/16.25 thf(zip_derived_cl278, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((rd @ (mult @ X2 @ X0) @
% 109.69/16.25 (mult @ X1 @ (ld @ (mult @ (mult @ X1 @ X1) @ X1) @ X0)))
% 109.69/16.25 = (mult @ (mult @ X2 @ X1) @ X1))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl31, zip_derived_cl29])).
% 109.69/16.25 thf(zip_derived_cl46, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X0 @ X1)) = (mult @ (mult @ X0 @ X0) @ X1))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl40, zip_derived_cl5])).
% 109.69/16.25 thf(zip_derived_cl330, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((rd @ (mult @ X2 @ X0) @
% 109.69/16.25 (mult @ X1 @ (ld @ (mult @ X1 @ (mult @ X1 @ X1)) @ X0)))
% 109.69/16.25 = (mult @ (mult @ X2 @ X1) @ X1))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl278, zip_derived_cl46])).
% 109.69/16.25 thf(zip_derived_cl50, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X1 @ (mult @ X0 @ X0)) = (mult @ (mult @ X1 @ X0) @ X0))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl4])).
% 109.69/16.25 thf(zip_derived_cl9836, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((rd @ (mult @ X2 @ X0) @
% 109.69/16.25 (mult @ X1 @ (ld @ (mult @ X1 @ (mult @ X1 @ X1)) @ X0)))
% 109.69/16.25 = (mult @ X2 @ (mult @ X1 @ X1)))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl330, zip_derived_cl50])).
% 109.69/16.25 thf(zip_derived_cl32888, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((rd @ (mult @ X0 @ X1) @
% 109.69/16.25 (mult @ (mult @ op_b @ (mult @ op_b @ (mult @ op_b @ op_b))) @
% 109.69/16.25 (ld @
% 109.69/16.25 (mult @ (mult @ op_b @ (mult @ op_b @ (mult @ op_b @ op_b))) @
% 109.69/16.25 (ld @ op_b @ unit)) @
% 109.69/16.25 X1)))
% 109.69/16.25 = (mult @ X0 @ (ld @ op_b @ unit)))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl8858, zip_derived_cl9836])).
% 109.69/16.25 thf(zip_derived_cl5, plain, (![X0 : $i]: ((mult @ unit @ X0) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c06])).
% 109.69/16.25 thf(zip_derived_cl6, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X1 @ (mult @ X1 @ X2)))
% 109.69/16.25 = (mult @ (mult @ (mult @ X0 @ X1) @ X1) @ X2))),
% 109.69/16.25 inference('cnf', [status(esa)], [c07])).
% 109.69/16.25 thf(zip_derived_cl6, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X1 @ (mult @ X1 @ X2)))
% 109.69/16.25 = (mult @ (mult @ (mult @ X0 @ X1) @ X1) @ X2))),
% 109.69/16.25 inference('cnf', [status(esa)], [c07])).
% 109.69/16.25 thf(zip_derived_cl38, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 109.69/16.25 ((mult @ (mult @ (mult @ X2 @ X1) @ X1) @
% 109.69/16.25 (mult @ X0 @ (mult @ X0 @ X3)))
% 109.69/16.25 = (mult @
% 109.69/16.25 (mult @ (mult @ X2 @ (mult @ X1 @ (mult @ X1 @ X0))) @ X0) @ X3))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl6])).
% 109.69/16.25 thf(zip_derived_cl6, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X1 @ (mult @ X1 @ X2)))
% 109.69/16.25 = (mult @ (mult @ (mult @ X0 @ X1) @ X1) @ X2))),
% 109.69/16.25 inference('cnf', [status(esa)], [c07])).
% 109.69/16.25 thf(zip_derived_cl45, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 109.69/16.25 ((mult @ X2 @
% 109.69/16.25 (mult @ X1 @ (mult @ X1 @ (mult @ X0 @ (mult @ X0 @ X3)))))
% 109.69/16.25 = (mult @
% 109.69/16.25 (mult @ (mult @ X2 @ (mult @ X1 @ (mult @ X1 @ X0))) @ X0) @ X3))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl38, zip_derived_cl6])).
% 109.69/16.25 thf(zip_derived_cl388, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((mult @ unit @
% 109.69/16.25 (mult @ X1 @ (mult @ X1 @ (mult @ X0 @ (mult @ X0 @ X2)))))
% 109.69/16.25 = (mult @ (mult @ (mult @ X1 @ (mult @ X1 @ X0)) @ X0) @ X2))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl45])).
% 109.69/16.25 thf(zip_derived_cl5, plain, (![X0 : $i]: ((mult @ unit @ X0) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c06])).
% 109.69/16.25 thf(zip_derived_cl414, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((mult @ X1 @ (mult @ X1 @ (mult @ X0 @ (mult @ X0 @ X2))))
% 109.69/16.25 = (mult @ (mult @ (mult @ X1 @ (mult @ X1 @ X0)) @ X0) @ X2))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl388, zip_derived_cl5])).
% 109.69/16.25 thf(zip_derived_cl46, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X0 @ X1)) = (mult @ (mult @ X0 @ X0) @ X1))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl40, zip_derived_cl5])).
% 109.69/16.25 thf(zip_derived_cl50, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X1 @ (mult @ X0 @ X0)) = (mult @ (mult @ X1 @ X0) @ X0))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl4])).
% 109.69/16.25 thf(zip_derived_cl347, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ (mult @ X1 @ X1) @ (mult @ X0 @ X0))
% 109.69/16.25 = (mult @ (mult @ X1 @ (mult @ X1 @ X0)) @ X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl46, zip_derived_cl50])).
% 109.69/16.25 thf(zip_derived_cl46, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X0 @ (mult @ X0 @ X1)) = (mult @ (mult @ X0 @ X0) @ X1))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl40, zip_derived_cl5])).
% 109.69/16.25 thf(zip_derived_cl358, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ X1 @ (mult @ X1 @ (mult @ X0 @ X0)))
% 109.69/16.25 = (mult @ (mult @ X1 @ (mult @ X1 @ X0)) @ X0))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl347, zip_derived_cl46])).
% 109.69/16.25 thf(zip_derived_cl21242, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((mult @ X1 @ (mult @ X1 @ (mult @ X0 @ (mult @ X0 @ X2))))
% 109.69/16.25 = (mult @ (mult @ X1 @ (mult @ X1 @ (mult @ X0 @ X0))) @ X2))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl414, zip_derived_cl358])).
% 109.69/16.25 thf(zip_derived_cl12036, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ (rd @ unit @ X0) @ (mult @ X0 @ X1)) = (X1))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl11983, zip_derived_cl0])).
% 109.69/16.25 thf(zip_derived_cl199, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 109.69/16.25 ((rd @
% 109.69/16.25 (mult @ X3 @
% 109.69/16.25 (mult @ X2 @ (mult @ X2 @ (mult @ X1 @ (mult @ X1 @ X0))))) @
% 109.69/16.25 X0) = (mult @ (mult @ X3 @ (mult @ X2 @ (mult @ X2 @ X1))) @ X1))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl176, zip_derived_cl6])).
% 109.69/16.25 thf(zip_derived_cl12091, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((rd @ (mult @ X2 @ (mult @ (rd @ unit @ X1) @ (mult @ X1 @ X0))) @ X0)
% 109.69/16.25 = (mult @
% 109.69/16.25 (mult @ X2 @
% 109.69/16.25 (mult @ (rd @ unit @ X1) @ (mult @ (rd @ unit @ X1) @ X1))) @
% 109.69/16.25 X1))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl12036, zip_derived_cl199])).
% 109.69/16.25 thf(zip_derived_cl12036, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((mult @ (rd @ unit @ X0) @ (mult @ X0 @ X1)) = (X1))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl11983, zip_derived_cl0])).
% 109.69/16.25 thf(zip_derived_cl3, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c04])).
% 109.69/16.25 thf(zip_derived_cl2, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c03])).
% 109.69/16.25 thf(zip_derived_cl4, plain, (![X0 : $i]: ((mult @ X0 @ unit) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c05])).
% 109.69/16.25 thf(zip_derived_cl12245, plain,
% 109.69/16.25 (![X1 : $i, X2 : $i]:
% 109.69/16.25 ((X2) = (mult @ (mult @ X2 @ (rd @ unit @ X1)) @ X1))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl12091, zip_derived_cl12036, zip_derived_cl3,
% 109.69/16.25 zip_derived_cl2, zip_derived_cl4])).
% 109.69/16.25 thf(zip_derived_cl12585, plain,
% 109.69/16.25 (![X0 : $i]: ((ld @ X0 @ unit) = (rd @ unit @ X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl12376, zip_derived_cl19])).
% 109.69/16.25 thf(zip_derived_cl22636, plain,
% 109.69/16.25 (![X1 : $i, X2 : $i]:
% 109.69/16.25 ((X2) = (mult @ (mult @ X2 @ (ld @ X1 @ unit)) @ X1))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl12245, zip_derived_cl12585])).
% 109.69/16.25 thf(zip_derived_cl3, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c04])).
% 109.69/16.25 thf(zip_derived_cl22662, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((rd @ X0 @ X1) = (mult @ X0 @ (ld @ X1 @ unit)))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl22636, zip_derived_cl3])).
% 109.69/16.25 thf(zip_derived_cl25, plain, (![X0 : $i]: ((rd @ X0 @ X0) = (unit))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl3])).
% 109.69/16.25 thf(zip_derived_cl4, plain, (![X0 : $i]: ((mult @ X0 @ unit) = (X0))),
% 109.69/16.25 inference('cnf', [status(esa)], [c05])).
% 109.69/16.25 thf(zip_derived_cl21242, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((mult @ X1 @ (mult @ X1 @ (mult @ X0 @ (mult @ X0 @ X2))))
% 109.69/16.25 = (mult @ (mult @ X1 @ (mult @ X1 @ (mult @ X0 @ X0))) @ X2))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl414, zip_derived_cl358])).
% 109.69/16.25 thf(zip_derived_cl337, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((mult @ X2 @
% 109.69/16.25 (mult @ X1 @
% 109.69/16.25 (mult @ X1 @ (ld @ (mult @ X2 @ (mult @ X1 @ X1)) @ X0))))
% 109.69/16.25 = (X0))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl31, zip_derived_cl50])).
% 109.69/16.25 thf(zip_derived_cl22662, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((rd @ X0 @ X1) = (mult @ X0 @ (ld @ X1 @ unit)))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl22636, zip_derived_cl3])).
% 109.69/16.25 thf(zip_derived_cl32971, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]:
% 109.69/16.25 ((rd @ (mult @ X0 @ X1) @ (mult @ op_b @ X1)) = (rd @ X0 @ op_b))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl32888, zip_derived_cl21242,
% 109.69/16.25 zip_derived_cl22662, zip_derived_cl25, zip_derived_cl4,
% 109.69/16.25 zip_derived_cl21242, zip_derived_cl337, zip_derived_cl22662])).
% 109.69/16.25 thf(zip_derived_cl59334, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((rd @ (mult @ X0 @ (ld @ (mult @ op_a @ op_b) @ unit)) @
% 109.69/16.25 (mult @ op_a @ (mult @ op_a @ op_a))) = (rd @ X0 @ op_b))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl45901, zip_derived_cl32971])).
% 109.69/16.25 thf(zip_derived_cl22662, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((rd @ X0 @ X1) = (mult @ X0 @ (ld @ X1 @ unit)))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl22636, zip_derived_cl3])).
% 109.69/16.25 thf(zip_derived_cl2341, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((rd @ X0 @ (mult @ op_a @ (mult @ op_a @ op_a))) = (mult @ X0 @ op_a))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl2264, zip_derived_cl3])).
% 109.69/16.25 thf(zip_derived_cl59476, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ (rd @ X0 @ (mult @ op_a @ op_b)) @ op_a) = (rd @ X0 @ op_b))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl59334, zip_derived_cl22662, zip_derived_cl2341])).
% 109.69/16.25 thf(zip_derived_cl12626, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((rd @ X0 @ (mult @ X1 @ X0)) = (ld @ X1 @ unit))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl12082, zip_derived_cl12585])).
% 109.69/16.25 thf(zip_derived_cl61880, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((rd @ op_a @ (rd @ X0 @ op_b))
% 109.69/16.25 = (ld @ (rd @ X0 @ (mult @ op_a @ op_b)) @ unit))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl59476, zip_derived_cl12626])).
% 109.69/16.25 thf(zip_derived_cl13586, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((rd @ X1 @ X0) = (ld @ (rd @ X0 @ X1) @ unit))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl12626])).
% 109.69/16.25 thf(zip_derived_cl22662, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((rd @ X0 @ X1) = (mult @ X0 @ (ld @ X1 @ unit)))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl22636, zip_derived_cl3])).
% 109.69/16.25 thf(zip_derived_cl23730, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 109.69/16.25 ((rd @ X2 @ (rd @ X0 @ X1)) = (mult @ X2 @ (rd @ X1 @ X0)))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl13586, zip_derived_cl22662])).
% 109.69/16.25 thf(zip_derived_cl13586, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((rd @ X1 @ X0) = (ld @ (rd @ X0 @ X1) @ unit))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl12626])).
% 109.69/16.25 thf(zip_derived_cl61973, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ op_a @ (rd @ op_b @ X0)) = (rd @ (mult @ op_a @ op_b) @ X0))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl61880, zip_derived_cl23730, zip_derived_cl13586])).
% 109.69/16.25 thf(zip_derived_cl12376, plain,
% 109.69/16.25 (![X1 : $i]: ((X1) = (rd @ unit @ (rd @ unit @ X1)))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl12352, zip_derived_cl3])).
% 109.69/16.25 thf(zip_derived_cl12585, plain,
% 109.69/16.25 (![X0 : $i]: ((ld @ X0 @ unit) = (rd @ unit @ X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl12376, zip_derived_cl19])).
% 109.69/16.25 thf(zip_derived_cl12585, plain,
% 109.69/16.25 (![X0 : $i]: ((ld @ X0 @ unit) = (rd @ unit @ X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl12376, zip_derived_cl19])).
% 109.69/16.25 thf(zip_derived_cl12627, plain,
% 109.69/16.25 (![X1 : $i]: ((X1) = (ld @ (ld @ X1 @ unit) @ unit))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl12376, zip_derived_cl12585, zip_derived_cl12585])).
% 109.69/16.25 thf(zip_derived_cl22662, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((rd @ X0 @ X1) = (mult @ X0 @ (ld @ X1 @ unit)))),
% 109.69/16.25 inference('s_sup+', [status(thm)], [zip_derived_cl22636, zip_derived_cl3])).
% 109.69/16.25 thf(zip_derived_cl23727, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((rd @ X1 @ (ld @ X0 @ unit)) = (mult @ X1 @ X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl12627, zip_derived_cl22662])).
% 109.69/16.25 thf(zip_derived_cl62139, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ op_a @ (rd @ op_b @ (ld @ X0 @ unit)))
% 109.69/16.25 = (mult @ (mult @ op_a @ op_b) @ X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl61973, zip_derived_cl23727])).
% 109.69/16.25 thf(zip_derived_cl23727, plain,
% 109.69/16.25 (![X0 : $i, X1 : $i]: ((rd @ X1 @ (ld @ X0 @ unit)) = (mult @ X1 @ X0))),
% 109.69/16.25 inference('s_sup+', [status(thm)],
% 109.69/16.25 [zip_derived_cl12627, zip_derived_cl22662])).
% 109.69/16.25 thf(zip_derived_cl62171, plain,
% 109.69/16.25 (![X0 : $i]:
% 109.69/16.25 ((mult @ op_a @ (mult @ op_b @ X0))
% 109.69/16.25 = (mult @ (mult @ op_a @ op_b) @ X0))),
% 109.69/16.25 inference('demod', [status(thm)],
% 109.69/16.25 [zip_derived_cl62139, zip_derived_cl23727])).
% 109.69/16.25 thf(zip_derived_cl62184, plain,
% 109.69/16.25 (((mult @ op_a @ (mult @ op_b @ a)) != (mult @ op_a @ (mult @ op_b @ a)))),
% 109.69/16.25 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl62171])).
% 109.69/16.25 thf(zip_derived_cl62185, plain, ($false),
% 109.69/16.25 inference('simplify', [status(thm)], [zip_derived_cl62184])).
% 109.69/16.25
% 109.69/16.25 % SZS output end Refutation
% 109.69/16.25
% 109.69/16.25
% 109.69/16.25 % Terminating...
% 109.69/16.29 % Runner terminated.
% 109.69/16.31 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------