TSTP Solution File: GRP660-10 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP660-10 : TPTP v8.1.2. Released v8.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.f0fZkyxmWB true
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:52:45 EDT 2023
% Result : Unsatisfiable 42.53s 6.65s
% Output : Refutation 42.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP660-10 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.12 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.f0fZkyxmWB true
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 00:53:41 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.34 % Python version: Python 3.6.8
% 0.13/0.34 % Running in FO mode
% 0.20/0.59 % Total configuration time : 435
% 0.20/0.59 % Estimated wc time : 1092
% 0.20/0.59 % Estimated cpu time (7 cpus) : 156.0
% 0.20/0.69 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.20/0.69 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.20/0.70 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.20/0.70 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.20/0.71 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.20/0.71 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.20/0.72 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 42.53/6.65 % Solved by fo/fo5.sh.
% 42.53/6.65 % done 733 iterations in 5.913s
% 42.53/6.65 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 42.53/6.65 % SZS output start Refutation
% 42.53/6.65 thf(ld_type, type, ld: $i > $i > $i).
% 42.53/6.65 thf(rd_type, type, rd: $i > $i > $i).
% 42.53/6.65 thf(x1_2_type, type, x1_2: $i > $i).
% 42.53/6.65 thf(mult_type, type, mult: $i > $i > $i).
% 42.53/6.65 thf(tuple_type, type, tuple: $i > $i > $i).
% 42.53/6.65 thf(x1_type, type, x1: $i > $i).
% 42.53/6.65 thf(f01, axiom, (( mult @ A @ ( ld @ A @ B ) ) = ( B ))).
% 42.53/6.65 thf(zip_derived_cl0, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f01])).
% 42.53/6.65 thf(f03, axiom, (( mult @ ( rd @ A @ B ) @ B ) = ( A ))).
% 42.53/6.65 thf(zip_derived_cl2, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f03])).
% 42.53/6.65 thf(zip_derived_cl2, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f03])).
% 42.53/6.65 thf(zip_derived_cl2, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f03])).
% 42.53/6.65 thf(f05, axiom,
% 42.53/6.65 (( mult @ ( mult @ ( mult @ A @ B ) @ C ) @ A ) =
% 42.53/6.65 ( mult @ A @ ( mult @ B @ ( mult @ C @ A ) ) ))).
% 42.53/6.65 thf(zip_derived_cl4, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((mult @ (mult @ (mult @ X0 @ X1) @ X2) @ X0)
% 42.53/6.65 = (mult @ X0 @ (mult @ X1 @ (mult @ X2 @ X0))))),
% 42.53/6.65 inference('cnf', [status(esa)], [f05])).
% 42.53/6.65 thf(f04, axiom, (( rd @ ( mult @ A @ B ) @ B ) = ( A ))).
% 42.53/6.65 thf(zip_derived_cl3, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f04])).
% 42.53/6.65 thf(zip_derived_cl13, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((rd @ (mult @ X0 @ (mult @ X2 @ (mult @ X1 @ X0))) @ X0)
% 42.53/6.65 = (mult @ (mult @ X0 @ X2) @ X1))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl3])).
% 42.53/6.65 thf(zip_derived_cl45, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((rd @ (mult @ X1 @ (mult @ X2 @ X0)) @ X1)
% 42.53/6.65 = (mult @ (mult @ X1 @ X2) @ (rd @ X0 @ X1)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 42.53/6.65 thf(zip_derived_cl152, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((rd @ (mult @ X1 @ X0) @ X1)
% 42.53/6.65 = (mult @ (mult @ X1 @ (rd @ X0 @ X2)) @ (rd @ X2 @ X1)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl45])).
% 42.53/6.65 thf(zip_derived_cl0, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f01])).
% 42.53/6.65 thf(zip_derived_cl2, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f03])).
% 42.53/6.65 thf(zip_derived_cl13, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((rd @ (mult @ X0 @ (mult @ X2 @ (mult @ X1 @ X0))) @ X0)
% 42.53/6.65 = (mult @ (mult @ X0 @ X2) @ X1))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl3])).
% 42.53/6.65 thf(zip_derived_cl42, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((rd @ (mult @ X2 @ X0) @ X2)
% 42.53/6.65 = (mult @ (mult @ X2 @ (rd @ X0 @ (mult @ X1 @ X2))) @ X1))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 42.53/6.65 thf(zip_derived_cl3, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f04])).
% 42.53/6.65 thf(zip_derived_cl1366, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((rd @ (rd @ (mult @ X0 @ X1) @ X0) @ X2)
% 42.53/6.65 = (mult @ X0 @ (rd @ X1 @ (mult @ X2 @ X0))))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl42, zip_derived_cl3])).
% 42.53/6.65 thf(f02, axiom, (( ld @ A @ ( mult @ A @ B ) ) = ( B ))).
% 42.53/6.65 thf(zip_derived_cl1, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f02])).
% 42.53/6.65 thf(zip_derived_cl1669, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((ld @ X1 @ (rd @ (rd @ (mult @ X1 @ X2) @ X1) @ X0))
% 42.53/6.65 = (rd @ X2 @ (mult @ X0 @ X1)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl1366, zip_derived_cl1])).
% 42.53/6.65 thf(zip_derived_cl4825, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((ld @ X1 @ (rd @ (rd @ X0 @ X1) @ X2))
% 42.53/6.65 = (rd @ (ld @ X1 @ X0) @ (mult @ X2 @ X1)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl1669])).
% 42.53/6.65 thf(zip_derived_cl0, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f01])).
% 42.53/6.65 thf(zip_derived_cl45, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((rd @ (mult @ X1 @ (mult @ X2 @ X0)) @ X1)
% 42.53/6.65 = (mult @ (mult @ X1 @ X2) @ (rd @ X0 @ X1)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 42.53/6.65 thf(zip_derived_cl3, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f04])).
% 42.53/6.65 thf(zip_derived_cl140, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((mult @ (mult @ (mult @ X1 @ X0) @ X1) @ (rd @ X0 @ (mult @ X1 @ X0)))
% 42.53/6.65 = (mult @ X1 @ X0))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl45, zip_derived_cl3])).
% 42.53/6.65 thf(zip_derived_cl328, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((mult @ (mult @ (mult @ X1 @ (ld @ X1 @ X0)) @ X1) @
% 42.53/6.65 (rd @ (ld @ X1 @ X0) @ X0)) = (mult @ X1 @ (ld @ X1 @ X0)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl140])).
% 42.53/6.65 thf(zip_derived_cl0, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f01])).
% 42.53/6.65 thf(zip_derived_cl0, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f01])).
% 42.53/6.65 thf(zip_derived_cl347, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((mult @ (mult @ X0 @ X1) @ (rd @ (ld @ X1 @ X0) @ X0)) = (X0))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl328, zip_derived_cl0, zip_derived_cl0])).
% 42.53/6.65 thf(zip_derived_cl4886, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((mult @ (mult @ (mult @ X0 @ X1) @ X1) @
% 42.53/6.65 (ld @ X1 @ (rd @ (rd @ (mult @ X0 @ X1) @ X1) @ X0)))
% 42.53/6.65 = (mult @ X0 @ X1))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl4825, zip_derived_cl347])).
% 42.53/6.65 thf(zip_derived_cl3, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f04])).
% 42.53/6.65 thf(zip_derived_cl4944, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((mult @ (mult @ (mult @ X0 @ X1) @ X1) @ (ld @ X1 @ (rd @ X0 @ X0)))
% 42.53/6.65 = (mult @ X0 @ X1))),
% 42.53/6.65 inference('demod', [status(thm)], [zip_derived_cl4886, zip_derived_cl3])).
% 42.53/6.65 thf(zip_derived_cl1, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f02])).
% 42.53/6.65 thf(zip_derived_cl5204, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((ld @ (mult @ (mult @ X1 @ X0) @ X0) @ (mult @ X1 @ X0))
% 42.53/6.65 = (ld @ X0 @ (rd @ X1 @ X1)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl4944, zip_derived_cl1])).
% 42.53/6.65 thf(zip_derived_cl5526, plain,
% 42.53/6.65 (![X0 : $i]:
% 42.53/6.65 ((ld @ (rd @ (mult @ X0 @ X0) @ X0) @ (mult @ X0 @ (rd @ X0 @ X0)))
% 42.53/6.65 = (ld @ (rd @ X0 @ X0) @ (rd @ X0 @ X0)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl152, zip_derived_cl5204])).
% 42.53/6.65 thf(zip_derived_cl3, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f04])).
% 42.53/6.65 thf(zip_derived_cl2, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f03])).
% 42.53/6.65 thf(zip_derived_cl140, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((mult @ (mult @ (mult @ X1 @ X0) @ X1) @ (rd @ X0 @ (mult @ X1 @ X0)))
% 42.53/6.65 = (mult @ X1 @ X0))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl45, zip_derived_cl3])).
% 42.53/6.65 thf(zip_derived_cl334, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((mult @ (mult @ (mult @ (rd @ X0 @ X1) @ X1) @ (rd @ X0 @ X1)) @
% 42.53/6.65 (rd @ X1 @ X0)) = (mult @ (rd @ X0 @ X1) @ X1))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl140])).
% 42.53/6.65 thf(zip_derived_cl2, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f03])).
% 42.53/6.65 thf(zip_derived_cl2, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f03])).
% 42.53/6.65 thf(zip_derived_cl353, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((mult @ (mult @ X0 @ (rd @ X0 @ X1)) @ (rd @ X1 @ X0)) = (X0))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl334, zip_derived_cl2, zip_derived_cl2])).
% 42.53/6.65 thf(zip_derived_cl3, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f04])).
% 42.53/6.65 thf(zip_derived_cl425, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((rd @ X0 @ (rd @ X1 @ X0)) = (mult @ X0 @ (rd @ X0 @ X1)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl353, zip_derived_cl3])).
% 42.53/6.65 thf(zip_derived_cl425, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((rd @ X0 @ (rd @ X1 @ X0)) = (mult @ X0 @ (rd @ X0 @ X1)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl353, zip_derived_cl3])).
% 42.53/6.65 thf(zip_derived_cl1, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f02])).
% 42.53/6.65 thf(zip_derived_cl600, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((ld @ X0 @ (rd @ X0 @ (rd @ X1 @ X0))) = (rd @ X0 @ X1))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl425, zip_derived_cl1])).
% 42.53/6.65 thf(zip_derived_cl5579, plain,
% 42.53/6.65 (![X0 : $i]: ((rd @ X0 @ X0) = (ld @ (rd @ X0 @ X0) @ (rd @ X0 @ X0)))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl5526, zip_derived_cl3, zip_derived_cl425,
% 42.53/6.65 zip_derived_cl600])).
% 42.53/6.65 thf(zip_derived_cl0, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f01])).
% 42.53/6.65 thf(zip_derived_cl5623, plain,
% 42.53/6.65 (![X0 : $i]: ((mult @ (rd @ X0 @ X0) @ (rd @ X0 @ X0)) = (rd @ X0 @ X0))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl5579, zip_derived_cl0])).
% 42.53/6.65 thf(zip_derived_cl2, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f03])).
% 42.53/6.65 thf(zip_derived_cl0, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f01])).
% 42.53/6.65 thf(zip_derived_cl4, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((mult @ (mult @ (mult @ X0 @ X1) @ X2) @ X0)
% 42.53/6.65 = (mult @ X0 @ (mult @ X1 @ (mult @ X2 @ X0))))),
% 42.53/6.65 inference('cnf', [status(esa)], [f05])).
% 42.53/6.65 thf(zip_derived_cl18, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((mult @ (mult @ X0 @ X2) @ X1)
% 42.53/6.65 = (mult @ X1 @ (mult @ (ld @ X1 @ X0) @ (mult @ X2 @ X1))))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl4])).
% 42.53/6.65 thf(zip_derived_cl86, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((mult @ (mult @ X2 @ (rd @ X0 @ X1)) @ X1)
% 42.53/6.65 = (mult @ X1 @ (mult @ (ld @ X1 @ X2) @ X0)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl18])).
% 42.53/6.65 thf(zip_derived_cl5724, plain,
% 42.53/6.65 (![X0 : $i]:
% 42.53/6.65 ((mult @ (rd @ X0 @ X0) @ X0)
% 42.53/6.65 = (mult @ X0 @ (mult @ (ld @ X0 @ (rd @ X0 @ X0)) @ X0)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl5623, zip_derived_cl86])).
% 42.53/6.65 thf(zip_derived_cl2, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f03])).
% 42.53/6.65 thf(zip_derived_cl5759, plain,
% 42.53/6.65 (![X0 : $i]:
% 42.53/6.65 ((X0) = (mult @ X0 @ (mult @ (ld @ X0 @ (rd @ X0 @ X0)) @ X0)))),
% 42.53/6.65 inference('demod', [status(thm)], [zip_derived_cl5724, zip_derived_cl2])).
% 42.53/6.65 thf(zip_derived_cl13, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((rd @ (mult @ X0 @ (mult @ X2 @ (mult @ X1 @ X0))) @ X0)
% 42.53/6.65 = (mult @ (mult @ X0 @ X2) @ X1))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl3])).
% 42.53/6.65 thf(zip_derived_cl5823, plain,
% 42.53/6.65 (![X0 : $i]:
% 42.53/6.65 ((rd @ (mult @ X0 @ X0) @ X0)
% 42.53/6.65 = (mult @ (mult @ X0 @ X0) @ (ld @ X0 @ (rd @ X0 @ X0))))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl5759, zip_derived_cl13])).
% 42.53/6.65 thf(zip_derived_cl3, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f04])).
% 42.53/6.65 thf(zip_derived_cl5884, plain,
% 42.53/6.65 (![X0 : $i]:
% 42.53/6.65 ((X0) = (mult @ (mult @ X0 @ X0) @ (ld @ X0 @ (rd @ X0 @ X0))))),
% 42.53/6.65 inference('demod', [status(thm)], [zip_derived_cl5823, zip_derived_cl3])).
% 42.53/6.65 thf(zip_derived_cl1, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f02])).
% 42.53/6.65 thf(zip_derived_cl5894, plain,
% 42.53/6.65 (![X0 : $i]: ((ld @ (mult @ X0 @ X0) @ X0) = (ld @ X0 @ (rd @ X0 @ X0)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl5884, zip_derived_cl1])).
% 42.53/6.65 thf(zip_derived_cl0, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f01])).
% 42.53/6.65 thf(zip_derived_cl3, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f04])).
% 42.53/6.65 thf(zip_derived_cl10, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((rd @ X0 @ (ld @ X1 @ X0)) = (X1))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl3])).
% 42.53/6.65 thf(zip_derived_cl3, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f04])).
% 42.53/6.65 thf(zip_derived_cl353, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((mult @ (mult @ X0 @ (rd @ X0 @ X1)) @ (rd @ X1 @ X0)) = (X0))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl334, zip_derived_cl2, zip_derived_cl2])).
% 42.53/6.65 thf(zip_derived_cl442, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((mult @ (mult @ X1 @ (rd @ X1 @ (mult @ X0 @ X1))) @ X0) = (X1))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl353])).
% 42.53/6.65 thf(zip_derived_cl3, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f04])).
% 42.53/6.65 thf(zip_derived_cl464, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((rd @ X0 @ X1) = (mult @ X0 @ (rd @ X0 @ (mult @ X1 @ X0))))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl442, zip_derived_cl3])).
% 42.53/6.65 thf(zip_derived_cl1, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f02])).
% 42.53/6.65 thf(zip_derived_cl529, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((ld @ X1 @ (rd @ X1 @ X0)) = (rd @ X1 @ (mult @ X0 @ X1)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl464, zip_derived_cl1])).
% 42.53/6.65 thf(zip_derived_cl2, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f03])).
% 42.53/6.65 thf(zip_derived_cl787, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((mult @ (ld @ X1 @ (rd @ X1 @ X0)) @ (mult @ X0 @ X1)) = (X1))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl529, zip_derived_cl2])).
% 42.53/6.65 thf(zip_derived_cl849, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((mult @ (ld @ X1 @ X0) @ (mult @ (ld @ X0 @ X1) @ X1)) = (X1))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl787])).
% 42.53/6.65 thf(zip_derived_cl1, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f02])).
% 42.53/6.65 thf(zip_derived_cl864, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((ld @ (ld @ X0 @ X1) @ X0) = (mult @ (ld @ X1 @ X0) @ X0))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl849, zip_derived_cl1])).
% 42.53/6.65 thf(zip_derived_cl6314, plain,
% 42.53/6.65 (![X0 : $i]:
% 42.53/6.65 ((ld @ (ld @ X0 @ (mult @ X0 @ X0)) @ X0)
% 42.53/6.65 = (mult @ (ld @ X0 @ (rd @ X0 @ X0)) @ X0))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl5894, zip_derived_cl864])).
% 42.53/6.65 thf(zip_derived_cl1, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f02])).
% 42.53/6.65 thf(zip_derived_cl6340, plain,
% 42.53/6.65 (![X0 : $i]: ((ld @ X0 @ X0) = (mult @ (ld @ X0 @ (rd @ X0 @ X0)) @ X0))),
% 42.53/6.65 inference('demod', [status(thm)], [zip_derived_cl6314, zip_derived_cl1])).
% 42.53/6.65 thf(zip_derived_cl5623, plain,
% 42.53/6.65 (![X0 : $i]: ((mult @ (rd @ X0 @ X0) @ (rd @ X0 @ X0)) = (rd @ X0 @ X0))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl5579, zip_derived_cl0])).
% 42.53/6.65 thf(zip_derived_cl2, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f03])).
% 42.53/6.65 thf(zip_derived_cl4, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((mult @ (mult @ (mult @ X0 @ X1) @ X2) @ X0)
% 42.53/6.65 = (mult @ X0 @ (mult @ X1 @ (mult @ X2 @ X0))))),
% 42.53/6.65 inference('cnf', [status(esa)], [f05])).
% 42.53/6.65 thf(zip_derived_cl20, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((mult @ (mult @ X0 @ X2) @ (rd @ X0 @ X1))
% 42.53/6.65 = (mult @ (rd @ X0 @ X1) @
% 42.53/6.65 (mult @ X1 @ (mult @ X2 @ (rd @ X0 @ X1)))))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 42.53/6.65 thf(zip_derived_cl5723, plain,
% 42.53/6.65 (![X0 : $i]:
% 42.53/6.65 ((mult @ (mult @ X0 @ (rd @ X0 @ X0)) @ (rd @ X0 @ X0))
% 42.53/6.65 = (mult @ (rd @ X0 @ X0) @ (mult @ X0 @ (rd @ X0 @ X0))))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl5623, zip_derived_cl20])).
% 42.53/6.65 thf(zip_derived_cl425, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((rd @ X0 @ (rd @ X1 @ X0)) = (mult @ X0 @ (rd @ X0 @ X1)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl353, zip_derived_cl3])).
% 42.53/6.65 thf(zip_derived_cl2, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f03])).
% 42.53/6.65 thf(zip_derived_cl425, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((rd @ X0 @ (rd @ X1 @ X0)) = (mult @ X0 @ (rd @ X0 @ X1)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl353, zip_derived_cl3])).
% 42.53/6.65 thf(zip_derived_cl5758, plain,
% 42.53/6.65 (![X0 : $i]:
% 42.53/6.65 ((X0) = (mult @ (rd @ X0 @ X0) @ (rd @ X0 @ (rd @ X0 @ X0))))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl5723, zip_derived_cl425, zip_derived_cl2,
% 42.53/6.65 zip_derived_cl425])).
% 42.53/6.65 thf(zip_derived_cl86, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((mult @ (mult @ X2 @ (rd @ X0 @ X1)) @ X1)
% 42.53/6.65 = (mult @ X1 @ (mult @ (ld @ X1 @ X2) @ X0)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl18])).
% 42.53/6.65 thf(zip_derived_cl1, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f02])).
% 42.53/6.65 thf(zip_derived_cl182, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((ld @ (mult @ X1 @ (rd @ X0 @ X2)) @
% 42.53/6.65 (mult @ X2 @ (mult @ (ld @ X2 @ X1) @ X0))) = (X2))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl86, zip_derived_cl1])).
% 42.53/6.65 thf(zip_derived_cl7209, plain,
% 42.53/6.65 (![X0 : $i]:
% 42.53/6.65 ((ld @ X0 @
% 42.53/6.65 (mult @ (rd @ X0 @ X0) @
% 42.53/6.65 (mult @ (ld @ (rd @ X0 @ X0) @ (rd @ X0 @ X0)) @ X0)))
% 42.53/6.65 = (rd @ X0 @ X0))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl5758, zip_derived_cl182])).
% 42.53/6.65 thf(zip_derived_cl5579, plain,
% 42.53/6.65 (![X0 : $i]: ((rd @ X0 @ X0) = (ld @ (rd @ X0 @ X0) @ (rd @ X0 @ X0)))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl5526, zip_derived_cl3, zip_derived_cl425,
% 42.53/6.65 zip_derived_cl600])).
% 42.53/6.65 thf(zip_derived_cl2, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f03])).
% 42.53/6.65 thf(zip_derived_cl2, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f03])).
% 42.53/6.65 thf(zip_derived_cl7252, plain,
% 42.53/6.65 (![X0 : $i]: ((ld @ X0 @ X0) = (rd @ X0 @ X0))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl7209, zip_derived_cl5579, zip_derived_cl2,
% 42.53/6.65 zip_derived_cl2])).
% 42.53/6.65 thf(zip_derived_cl9349, plain,
% 42.53/6.65 (![X0 : $i]: ((ld @ X0 @ X0) = (mult @ (ld @ X0 @ (ld @ X0 @ X0)) @ X0))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl6340, zip_derived_cl7252])).
% 42.53/6.65 thf(zip_derived_cl18, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((mult @ (mult @ X0 @ X2) @ X1)
% 42.53/6.65 = (mult @ X1 @ (mult @ (ld @ X1 @ X0) @ (mult @ X2 @ X1))))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl4])).
% 42.53/6.65 thf(zip_derived_cl13, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((rd @ (mult @ X0 @ (mult @ X2 @ (mult @ X1 @ X0))) @ X0)
% 42.53/6.65 = (mult @ (mult @ X0 @ X2) @ X1))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl3])).
% 42.53/6.65 thf(zip_derived_cl76, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((rd @ (mult @ (mult @ X1 @ X0) @ (mult @ (mult @ X2 @ X1) @ X0)) @
% 42.53/6.65 (mult @ X1 @ X0))
% 42.53/6.65 = (mult @ (mult @ (mult @ X1 @ X0) @ X0) @ (ld @ X0 @ X2)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl18, zip_derived_cl13])).
% 42.53/6.65 thf(zip_derived_cl10933, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((rd @
% 42.53/6.65 (mult @ (mult @ (ld @ X0 @ (ld @ X0 @ X0)) @ X0) @
% 42.53/6.65 (mult @ (mult @ X1 @ (ld @ X0 @ (ld @ X0 @ X0))) @ X0)) @
% 42.53/6.65 (ld @ X0 @ X0))
% 42.53/6.65 = (mult @ (mult @ (mult @ (ld @ X0 @ (ld @ X0 @ X0)) @ X0) @ X0) @
% 42.53/6.65 (ld @ X0 @ X1)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl9349, zip_derived_cl76])).
% 42.53/6.65 thf(zip_derived_cl9349, plain,
% 42.53/6.65 (![X0 : $i]: ((ld @ X0 @ X0) = (mult @ (ld @ X0 @ (ld @ X0 @ X0)) @ X0))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl6340, zip_derived_cl7252])).
% 42.53/6.65 thf(zip_derived_cl0, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f01])).
% 42.53/6.65 thf(zip_derived_cl13, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((rd @ (mult @ X0 @ (mult @ X2 @ (mult @ X1 @ X0))) @ X0)
% 42.53/6.65 = (mult @ (mult @ X0 @ X2) @ X1))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl3])).
% 42.53/6.65 thf(zip_derived_cl43, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((rd @ (mult @ (ld @ X1 @ X0) @ (mult @ X2 @ X0)) @ (ld @ X1 @ X0))
% 42.53/6.65 = (mult @ (mult @ (ld @ X1 @ X0) @ X2) @ X1))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl13])).
% 42.53/6.65 thf(zip_derived_cl9349, plain,
% 42.53/6.65 (![X0 : $i]: ((ld @ X0 @ X0) = (mult @ (ld @ X0 @ (ld @ X0 @ X0)) @ X0))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl6340, zip_derived_cl7252])).
% 42.53/6.65 thf(zip_derived_cl7252, plain,
% 42.53/6.65 (![X0 : $i]: ((ld @ X0 @ X0) = (rd @ X0 @ X0))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl7209, zip_derived_cl5579, zip_derived_cl2,
% 42.53/6.65 zip_derived_cl2])).
% 42.53/6.65 thf(zip_derived_cl2, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f03])).
% 42.53/6.65 thf(zip_derived_cl7267, plain,
% 42.53/6.65 (![X0 : $i]: ((mult @ (ld @ X0 @ X0) @ X0) = (X0))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl7252, zip_derived_cl2])).
% 42.53/6.65 thf(zip_derived_cl0, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f01])).
% 42.53/6.65 thf(zip_derived_cl11062, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((mult @
% 42.53/6.65 (mult @ (ld @ X0 @ X0) @ (mult @ X1 @ (ld @ X0 @ (ld @ X0 @ X0)))) @
% 42.53/6.65 X0) = (X1))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl10933, zip_derived_cl9349, zip_derived_cl43,
% 42.53/6.65 zip_derived_cl9349, zip_derived_cl7267, zip_derived_cl0])).
% 42.53/6.65 thf(zip_derived_cl25806, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((mult @ (mult @ (ld @ X1 @ X1) @ X0) @ X1)
% 42.53/6.65 = (rd @ X0 @ (ld @ X1 @ (ld @ X1 @ X1))))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl11062])).
% 42.53/6.65 thf(zip_derived_cl5884, plain,
% 42.53/6.65 (![X0 : $i]:
% 42.53/6.65 ((X0) = (mult @ (mult @ X0 @ X0) @ (ld @ X0 @ (rd @ X0 @ X0))))),
% 42.53/6.65 inference('demod', [status(thm)], [zip_derived_cl5823, zip_derived_cl3])).
% 42.53/6.65 thf(zip_derived_cl18, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((mult @ (mult @ X0 @ X2) @ X1)
% 42.53/6.65 = (mult @ X1 @ (mult @ (ld @ X1 @ X0) @ (mult @ X2 @ X1))))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl4])).
% 42.53/6.65 thf(zip_derived_cl1, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f02])).
% 42.53/6.65 thf(zip_derived_cl67, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((ld @ X0 @ (mult @ (mult @ X2 @ X1) @ X0))
% 42.53/6.65 = (mult @ (ld @ X0 @ X2) @ (mult @ X1 @ X0)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl18, zip_derived_cl1])).
% 42.53/6.65 thf(zip_derived_cl5960, plain,
% 42.53/6.65 (![X0 : $i]:
% 42.53/6.65 ((ld @ (ld @ X0 @ (rd @ X0 @ X0)) @ X0)
% 42.53/6.65 = (mult @ (ld @ (ld @ X0 @ (rd @ X0 @ X0)) @ X0) @
% 42.53/6.65 (mult @ X0 @ (ld @ X0 @ (rd @ X0 @ X0)))))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl5884, zip_derived_cl67])).
% 42.53/6.65 thf(zip_derived_cl529, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((ld @ X1 @ (rd @ X1 @ X0)) = (rd @ X1 @ (mult @ X0 @ X1)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl464, zip_derived_cl1])).
% 42.53/6.65 thf(zip_derived_cl2, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f03])).
% 42.53/6.65 thf(zip_derived_cl1, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f02])).
% 42.53/6.65 thf(zip_derived_cl8, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((ld @ (rd @ X0 @ X1) @ X0) = (X1))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 42.53/6.65 thf(zip_derived_cl788, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((ld @ (ld @ X1 @ (rd @ X1 @ X0)) @ X1) = (mult @ X0 @ X1))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl529, zip_derived_cl8])).
% 42.53/6.65 thf(zip_derived_cl788, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((ld @ (ld @ X1 @ (rd @ X1 @ X0)) @ X1) = (mult @ X0 @ X1))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl529, zip_derived_cl8])).
% 42.53/6.65 thf(zip_derived_cl0, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f01])).
% 42.53/6.65 thf(zip_derived_cl6002, plain,
% 42.53/6.65 (![X0 : $i]:
% 42.53/6.65 ((mult @ X0 @ X0) = (mult @ (mult @ X0 @ X0) @ (rd @ X0 @ X0)))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl5960, zip_derived_cl788, zip_derived_cl788,
% 42.53/6.65 zip_derived_cl0])).
% 42.53/6.65 thf(zip_derived_cl45, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((rd @ (mult @ X1 @ (mult @ X2 @ X0)) @ X1)
% 42.53/6.65 = (mult @ (mult @ X1 @ X2) @ (rd @ X0 @ X1)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 42.53/6.65 thf(zip_derived_cl2, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f03])).
% 42.53/6.65 thf(zip_derived_cl136, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((mult @ (mult @ (mult @ X0 @ X2) @ (rd @ X1 @ X0)) @ X0)
% 42.53/6.65 = (mult @ X0 @ (mult @ X2 @ X1)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl45, zip_derived_cl2])).
% 42.53/6.65 thf(zip_derived_cl6079, plain,
% 42.53/6.65 (![X0 : $i]:
% 42.53/6.65 ((mult @ (mult @ X0 @ X0) @ X0) = (mult @ X0 @ (mult @ X0 @ X0)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl6002, zip_derived_cl136])).
% 42.53/6.65 thf(zip_derived_cl67, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((ld @ X0 @ (mult @ (mult @ X2 @ X1) @ X0))
% 42.53/6.65 = (mult @ (ld @ X0 @ X2) @ (mult @ X1 @ X0)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl18, zip_derived_cl1])).
% 42.53/6.65 thf(zip_derived_cl6208, plain,
% 42.53/6.65 (![X0 : $i]:
% 42.53/6.65 ((ld @ X0 @ (mult @ X0 @ (mult @ X0 @ X0)))
% 42.53/6.65 = (mult @ (ld @ X0 @ X0) @ (mult @ X0 @ X0)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl6079, zip_derived_cl67])).
% 42.53/6.65 thf(zip_derived_cl1, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f02])).
% 42.53/6.65 thf(zip_derived_cl6260, plain,
% 42.53/6.65 (![X0 : $i]:
% 42.53/6.65 ((mult @ X0 @ X0) = (mult @ (ld @ X0 @ X0) @ (mult @ X0 @ X0)))),
% 42.53/6.65 inference('demod', [status(thm)], [zip_derived_cl6208, zip_derived_cl1])).
% 42.53/6.65 thf(zip_derived_cl3, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f04])).
% 42.53/6.65 thf(zip_derived_cl6712, plain,
% 42.53/6.65 (![X0 : $i]:
% 42.53/6.65 ((rd @ (mult @ X0 @ X0) @ (mult @ X0 @ X0)) = (ld @ X0 @ X0))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl6260, zip_derived_cl3])).
% 42.53/6.65 thf(zip_derived_cl5623, plain,
% 42.53/6.65 (![X0 : $i]: ((mult @ (rd @ X0 @ X0) @ (rd @ X0 @ X0)) = (rd @ X0 @ X0))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl5579, zip_derived_cl0])).
% 42.53/6.65 thf(zip_derived_cl7110, plain,
% 42.53/6.65 (![X0 : $i]:
% 42.53/6.65 ((mult @ (rd @ (mult @ X0 @ X0) @ (mult @ X0 @ X0)) @ (ld @ X0 @ X0))
% 42.53/6.65 = (rd @ (mult @ X0 @ X0) @ (mult @ X0 @ X0)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl6712, zip_derived_cl5623])).
% 42.53/6.65 thf(zip_derived_cl6712, plain,
% 42.53/6.65 (![X0 : $i]:
% 42.53/6.65 ((rd @ (mult @ X0 @ X0) @ (mult @ X0 @ X0)) = (ld @ X0 @ X0))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl6260, zip_derived_cl3])).
% 42.53/6.65 thf(zip_derived_cl6712, plain,
% 42.53/6.65 (![X0 : $i]:
% 42.53/6.65 ((rd @ (mult @ X0 @ X0) @ (mult @ X0 @ X0)) = (ld @ X0 @ X0))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl6260, zip_derived_cl3])).
% 42.53/6.65 thf(zip_derived_cl7140, plain,
% 42.53/6.65 (![X0 : $i]: ((mult @ (ld @ X0 @ X0) @ (ld @ X0 @ X0)) = (ld @ X0 @ X0))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl7110, zip_derived_cl6712, zip_derived_cl6712])).
% 42.53/6.65 thf(zip_derived_cl76, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((rd @ (mult @ (mult @ X1 @ X0) @ (mult @ (mult @ X2 @ X1) @ X0)) @
% 42.53/6.65 (mult @ X1 @ X0))
% 42.53/6.65 = (mult @ (mult @ (mult @ X1 @ X0) @ X0) @ (ld @ X0 @ X2)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl18, zip_derived_cl13])).
% 42.53/6.65 thf(zip_derived_cl10941, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((rd @
% 42.53/6.65 (mult @ (mult @ (ld @ X0 @ X0) @ (ld @ X0 @ X0)) @
% 42.53/6.65 (mult @ (mult @ X1 @ (ld @ X0 @ X0)) @ (ld @ X0 @ X0))) @
% 42.53/6.65 (ld @ X0 @ X0))
% 42.53/6.65 = (mult @
% 42.53/6.65 (mult @ (mult @ (ld @ X0 @ X0) @ (ld @ X0 @ X0)) @ (ld @ X0 @ X0)) @
% 42.53/6.65 (ld @ (ld @ X0 @ X0) @ X1)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl7140, zip_derived_cl76])).
% 42.53/6.65 thf(zip_derived_cl7140, plain,
% 42.53/6.65 (![X0 : $i]: ((mult @ (ld @ X0 @ X0) @ (ld @ X0 @ X0)) = (ld @ X0 @ X0))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl7110, zip_derived_cl6712, zip_derived_cl6712])).
% 42.53/6.65 thf(zip_derived_cl45, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((rd @ (mult @ X1 @ (mult @ X2 @ X0)) @ X1)
% 42.53/6.65 = (mult @ (mult @ X1 @ X2) @ (rd @ X0 @ X1)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 42.53/6.65 thf(zip_derived_cl6712, plain,
% 42.53/6.65 (![X0 : $i]:
% 42.53/6.65 ((rd @ (mult @ X0 @ X0) @ (mult @ X0 @ X0)) = (ld @ X0 @ X0))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl6260, zip_derived_cl3])).
% 42.53/6.65 thf(zip_derived_cl5579, plain,
% 42.53/6.65 (![X0 : $i]: ((rd @ X0 @ X0) = (ld @ (rd @ X0 @ X0) @ (rd @ X0 @ X0)))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl5526, zip_derived_cl3, zip_derived_cl425,
% 42.53/6.65 zip_derived_cl600])).
% 42.53/6.65 thf(zip_derived_cl10, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((rd @ X0 @ (ld @ X1 @ X0)) = (X1))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl3])).
% 42.53/6.65 thf(zip_derived_cl5624, plain,
% 42.53/6.65 (![X0 : $i]: ((rd @ (rd @ X0 @ X0) @ (rd @ X0 @ X0)) = (rd @ X0 @ X0))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl5579, zip_derived_cl10])).
% 42.53/6.65 thf(zip_derived_cl7112, plain,
% 42.53/6.65 (![X0 : $i]:
% 42.53/6.65 ((rd @ (rd @ (mult @ X0 @ X0) @ (mult @ X0 @ X0)) @ (ld @ X0 @ X0))
% 42.53/6.65 = (rd @ (mult @ X0 @ X0) @ (mult @ X0 @ X0)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl6712, zip_derived_cl5624])).
% 42.53/6.65 thf(zip_derived_cl6712, plain,
% 42.53/6.65 (![X0 : $i]:
% 42.53/6.65 ((rd @ (mult @ X0 @ X0) @ (mult @ X0 @ X0)) = (ld @ X0 @ X0))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl6260, zip_derived_cl3])).
% 42.53/6.65 thf(zip_derived_cl6712, plain,
% 42.53/6.65 (![X0 : $i]:
% 42.53/6.65 ((rd @ (mult @ X0 @ X0) @ (mult @ X0 @ X0)) = (ld @ X0 @ X0))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl6260, zip_derived_cl3])).
% 42.53/6.65 thf(zip_derived_cl7142, plain,
% 42.53/6.65 (![X0 : $i]: ((rd @ (ld @ X0 @ X0) @ (ld @ X0 @ X0)) = (ld @ X0 @ X0))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl7112, zip_derived_cl6712, zip_derived_cl6712])).
% 42.53/6.65 thf(zip_derived_cl7140, plain,
% 42.53/6.65 (![X0 : $i]: ((mult @ (ld @ X0 @ X0) @ (ld @ X0 @ X0)) = (ld @ X0 @ X0))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl7110, zip_derived_cl6712, zip_derived_cl6712])).
% 42.53/6.65 thf(zip_derived_cl7140, plain,
% 42.53/6.65 (![X0 : $i]: ((mult @ (ld @ X0 @ X0) @ (ld @ X0 @ X0)) = (ld @ X0 @ X0))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl7110, zip_derived_cl6712, zip_derived_cl6712])).
% 42.53/6.65 thf(zip_derived_cl0, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f01])).
% 42.53/6.65 thf(zip_derived_cl11070, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((mult @ (mult @ (ld @ X0 @ X0) @ (mult @ X1 @ (ld @ X0 @ X0))) @
% 42.53/6.65 (ld @ X0 @ X0)) = (X1))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl10941, zip_derived_cl7140, zip_derived_cl45,
% 42.53/6.65 zip_derived_cl7142, zip_derived_cl7140, zip_derived_cl7140,
% 42.53/6.65 zip_derived_cl0])).
% 42.53/6.65 thf(zip_derived_cl28034, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((mult @
% 42.53/6.65 (mult @ (ld @ X0 @ X0) @
% 42.53/6.65 (rd @ X1 @
% 42.53/6.65 (ld @ (ld @ X0 @ X0) @ (ld @ (ld @ X0 @ X0) @ (ld @ X0 @ X0))))) @
% 42.53/6.65 (ld @ X0 @ X0))
% 42.53/6.65 = (mult @ (ld @ (ld @ X0 @ X0) @ (ld @ X0 @ X0)) @ X1))),
% 42.53/6.65 inference('sup+', [status(thm)],
% 42.53/6.65 [zip_derived_cl25806, zip_derived_cl11070])).
% 42.53/6.65 thf(zip_derived_cl5623, plain,
% 42.53/6.65 (![X0 : $i]: ((mult @ (rd @ X0 @ X0) @ (rd @ X0 @ X0)) = (rd @ X0 @ X0))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl5579, zip_derived_cl0])).
% 42.53/6.65 thf(zip_derived_cl1, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f02])).
% 42.53/6.65 thf(zip_derived_cl347, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((mult @ (mult @ X0 @ X1) @ (rd @ (ld @ X1 @ X0) @ X0)) = (X0))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl328, zip_derived_cl0, zip_derived_cl0])).
% 42.53/6.65 thf(zip_derived_cl396, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((mult @ (mult @ (mult @ X1 @ X0) @ X1) @ (rd @ X0 @ (mult @ X1 @ X0)))
% 42.53/6.65 = (mult @ X1 @ X0))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl347])).
% 42.53/6.65 thf(zip_derived_cl529, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((ld @ X1 @ (rd @ X1 @ X0)) = (rd @ X1 @ (mult @ X0 @ X1)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl464, zip_derived_cl1])).
% 42.53/6.65 thf(zip_derived_cl1186, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((mult @ (mult @ (mult @ X1 @ X0) @ X1) @ (ld @ X0 @ (rd @ X0 @ X1)))
% 42.53/6.65 = (mult @ X1 @ X0))),
% 42.53/6.65 inference('demod', [status(thm)], [zip_derived_cl396, zip_derived_cl529])).
% 42.53/6.65 thf(zip_derived_cl5682, plain,
% 42.53/6.65 (![X0 : $i]:
% 42.53/6.65 ((mult @ (mult @ (rd @ X0 @ X0) @ (rd @ X0 @ X0)) @
% 42.53/6.65 (ld @ (rd @ X0 @ X0) @ (rd @ (rd @ X0 @ X0) @ (rd @ X0 @ X0))))
% 42.53/6.65 = (mult @ (rd @ X0 @ X0) @ (rd @ X0 @ X0)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl5623, zip_derived_cl1186])).
% 42.53/6.65 thf(zip_derived_cl5623, plain,
% 42.53/6.65 (![X0 : $i]: ((mult @ (rd @ X0 @ X0) @ (rd @ X0 @ X0)) = (rd @ X0 @ X0))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl5579, zip_derived_cl0])).
% 42.53/6.65 thf(zip_derived_cl0, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f01])).
% 42.53/6.65 thf(zip_derived_cl5623, plain,
% 42.53/6.65 (![X0 : $i]: ((mult @ (rd @ X0 @ X0) @ (rd @ X0 @ X0)) = (rd @ X0 @ X0))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl5579, zip_derived_cl0])).
% 42.53/6.65 thf(zip_derived_cl5736, plain,
% 42.53/6.65 (![X0 : $i]: ((rd @ (rd @ X0 @ X0) @ (rd @ X0 @ X0)) = (rd @ X0 @ X0))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl5682, zip_derived_cl5623, zip_derived_cl0,
% 42.53/6.65 zip_derived_cl5623])).
% 42.53/6.65 thf(zip_derived_cl7252, plain,
% 42.53/6.65 (![X0 : $i]: ((ld @ X0 @ X0) = (rd @ X0 @ X0))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl7209, zip_derived_cl5579, zip_derived_cl2,
% 42.53/6.65 zip_derived_cl2])).
% 42.53/6.65 thf(zip_derived_cl7252, plain,
% 42.53/6.65 (![X0 : $i]: ((ld @ X0 @ X0) = (rd @ X0 @ X0))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl7209, zip_derived_cl5579, zip_derived_cl2,
% 42.53/6.65 zip_derived_cl2])).
% 42.53/6.65 thf(zip_derived_cl7252, plain,
% 42.53/6.65 (![X0 : $i]: ((ld @ X0 @ X0) = (rd @ X0 @ X0))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl7209, zip_derived_cl5579, zip_derived_cl2,
% 42.53/6.65 zip_derived_cl2])).
% 42.53/6.65 thf(zip_derived_cl7252, plain,
% 42.53/6.65 (![X0 : $i]: ((ld @ X0 @ X0) = (rd @ X0 @ X0))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl7209, zip_derived_cl5579, zip_derived_cl2,
% 42.53/6.65 zip_derived_cl2])).
% 42.53/6.65 thf(zip_derived_cl8992, plain,
% 42.53/6.65 (![X0 : $i]: ((ld @ (ld @ X0 @ X0) @ (ld @ X0 @ X0)) = (ld @ X0 @ X0))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl5736, zip_derived_cl7252, zip_derived_cl7252,
% 42.53/6.65 zip_derived_cl7252, zip_derived_cl7252])).
% 42.53/6.65 thf(zip_derived_cl8992, plain,
% 42.53/6.65 (![X0 : $i]: ((ld @ (ld @ X0 @ X0) @ (ld @ X0 @ X0)) = (ld @ X0 @ X0))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl5736, zip_derived_cl7252, zip_derived_cl7252,
% 42.53/6.65 zip_derived_cl7252, zip_derived_cl7252])).
% 42.53/6.65 thf(zip_derived_cl86, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((mult @ (mult @ X2 @ (rd @ X0 @ X1)) @ X1)
% 42.53/6.65 = (mult @ X1 @ (mult @ (ld @ X1 @ X2) @ X0)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl18])).
% 42.53/6.65 thf(zip_derived_cl8992, plain,
% 42.53/6.65 (![X0 : $i]: ((ld @ (ld @ X0 @ X0) @ (ld @ X0 @ X0)) = (ld @ X0 @ X0))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl5736, zip_derived_cl7252, zip_derived_cl7252,
% 42.53/6.65 zip_derived_cl7252, zip_derived_cl7252])).
% 42.53/6.65 thf(zip_derived_cl8992, plain,
% 42.53/6.65 (![X0 : $i]: ((ld @ (ld @ X0 @ X0) @ (ld @ X0 @ X0)) = (ld @ X0 @ X0))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl5736, zip_derived_cl7252, zip_derived_cl7252,
% 42.53/6.65 zip_derived_cl7252, zip_derived_cl7252])).
% 42.53/6.65 thf(zip_derived_cl28172, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((mult @ (ld @ X0 @ X0) @ (mult @ (ld @ X0 @ X0) @ X1))
% 42.53/6.65 = (mult @ (ld @ X0 @ X0) @ X1))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl28034, zip_derived_cl8992, zip_derived_cl8992,
% 42.53/6.65 zip_derived_cl86, zip_derived_cl8992, zip_derived_cl8992])).
% 42.53/6.65 thf(zip_derived_cl33122, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((mult @ (ld @ X1 @ X1) @ X0)
% 42.53/6.65 = (mult @ (ld @ X1 @ X1) @ (ld @ (ld @ X1 @ X1) @ X0)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl28172])).
% 42.53/6.65 thf(zip_derived_cl0, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f01])).
% 42.53/6.65 thf(zip_derived_cl33159, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ (ld @ X1 @ X1) @ X0) = (X0))),
% 42.53/6.65 inference('demod', [status(thm)], [zip_derived_cl33122, zip_derived_cl0])).
% 42.53/6.65 thf(goal, conjecture,
% 42.53/6.65 (( tuple @ ( mult @ X0 @ ( x1 @ X0 ) ) @ ( mult @ ( x1_2 @ X0 ) @ X0 ) ) =
% 42.53/6.65 ( tuple @ ( x1 @ X0 ) @ ( x1_2 @ X0 ) ))).
% 42.53/6.65 thf(zf_stmt_0, negated_conjecture,
% 42.53/6.65 (( tuple @ ( mult @ X0 @ ( x1 @ X0 ) ) @ ( mult @ ( x1_2 @ X0 ) @ X0 ) ) !=
% 42.53/6.65 ( tuple @ ( x1 @ X0 ) @ ( x1_2 @ X0 ) )),
% 42.53/6.65 inference('cnf.neg', [status(esa)], [goal])).
% 42.53/6.65 thf(zip_derived_cl5, plain,
% 42.53/6.65 (![X0 : $i]:
% 42.53/6.65 ((tuple @ (mult @ X0 @ (x1 @ X0)) @ (mult @ (x1_2 @ X0) @ X0))
% 42.53/6.65 != (tuple @ (x1 @ X0) @ (x1_2 @ X0)))),
% 42.53/6.65 inference('cnf', [status(esa)], [zf_stmt_0])).
% 42.53/6.65 thf(zip_derived_cl33658, plain,
% 42.53/6.65 (![X0 : $i]:
% 42.53/6.65 ((tuple @ (x1 @ (ld @ X0 @ X0)) @
% 42.53/6.65 (mult @ (x1_2 @ (ld @ X0 @ X0)) @ (ld @ X0 @ X0)))
% 42.53/6.65 != (tuple @ (x1 @ (ld @ X0 @ X0)) @ (x1_2 @ (ld @ X0 @ X0))))),
% 42.53/6.65 inference('sup-', [status(thm)], [zip_derived_cl33159, zip_derived_cl5])).
% 42.53/6.65 thf(zip_derived_cl33159, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ (ld @ X1 @ X1) @ X0) = (X0))),
% 42.53/6.65 inference('demod', [status(thm)], [zip_derived_cl33122, zip_derived_cl0])).
% 42.53/6.65 thf(zip_derived_cl7267, plain,
% 42.53/6.65 (![X0 : $i]: ((mult @ (ld @ X0 @ X0) @ X0) = (X0))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl7252, zip_derived_cl2])).
% 42.53/6.65 thf(zip_derived_cl13, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.53/6.65 ((rd @ (mult @ X0 @ (mult @ X2 @ (mult @ X1 @ X0))) @ X0)
% 42.53/6.65 = (mult @ (mult @ X0 @ X2) @ X1))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl3])).
% 42.53/6.65 thf(zip_derived_cl7671, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((rd @ (mult @ X0 @ (mult @ X1 @ X0)) @ X0)
% 42.53/6.65 = (mult @ (mult @ X0 @ X1) @ (ld @ X0 @ X0)))),
% 42.53/6.65 inference('sup+', [status(thm)], [zip_derived_cl7267, zip_derived_cl13])).
% 42.53/6.65 thf(zip_derived_cl33601, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]:
% 42.53/6.65 ((rd @ (mult @ X1 @ (ld @ X0 @ X0)) @ (ld @ X0 @ X0))
% 42.53/6.65 = (mult @ (mult @ (ld @ X0 @ X0) @ X1) @
% 42.53/6.65 (ld @ (ld @ X0 @ X0) @ (ld @ X0 @ X0))))),
% 42.53/6.65 inference('sup+', [status(thm)],
% 42.53/6.65 [zip_derived_cl33159, zip_derived_cl7671])).
% 42.53/6.65 thf(zip_derived_cl3, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 42.53/6.65 inference('cnf', [status(esa)], [f04])).
% 42.53/6.65 thf(zip_derived_cl33159, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((mult @ (ld @ X1 @ X1) @ X0) = (X0))),
% 42.53/6.65 inference('demod', [status(thm)], [zip_derived_cl33122, zip_derived_cl0])).
% 42.53/6.65 thf(zip_derived_cl8992, plain,
% 42.53/6.65 (![X0 : $i]: ((ld @ (ld @ X0 @ X0) @ (ld @ X0 @ X0)) = (ld @ X0 @ X0))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl5736, zip_derived_cl7252, zip_derived_cl7252,
% 42.53/6.65 zip_derived_cl7252, zip_derived_cl7252])).
% 42.53/6.65 thf(zip_derived_cl33875, plain,
% 42.53/6.65 (![X0 : $i, X1 : $i]: ((X1) = (mult @ X1 @ (ld @ X0 @ X0)))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl33601, zip_derived_cl3, zip_derived_cl33159,
% 42.53/6.65 zip_derived_cl8992])).
% 42.53/6.65 thf(zip_derived_cl34794, plain,
% 42.53/6.65 (![X0 : $i]:
% 42.53/6.65 ((tuple @ (x1 @ (ld @ X0 @ X0)) @ (x1_2 @ (ld @ X0 @ X0)))
% 42.53/6.65 != (tuple @ (x1 @ (ld @ X0 @ X0)) @ (x1_2 @ (ld @ X0 @ X0))))),
% 42.53/6.65 inference('demod', [status(thm)],
% 42.53/6.65 [zip_derived_cl33658, zip_derived_cl33875])).
% 42.53/6.65 thf(zip_derived_cl34795, plain, ($false),
% 42.53/6.65 inference('simplify', [status(thm)], [zip_derived_cl34794])).
% 42.53/6.65
% 42.53/6.65 % SZS output end Refutation
% 42.53/6.65
% 42.53/6.65
% 42.53/6.65 % Terminating...
% 42.53/6.72 % Runner terminated.
% 42.53/6.73 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------