TSTP Solution File: GRP122-1 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP122-1 : TPTP v8.1.2. Released v1.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.D8bcdv4rbb true
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:50:01 EDT 2023
% Result : Unsatisfiable 17.89s 3.14s
% Output : Refutation 17.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP122-1 : TPTP v8.1.2. Released v1.2.0.
% 0.12/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.D8bcdv4rbb true
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.20/0.34 % WCLimit : 300
% 0.20/0.34 % DateTime : Tue Aug 29 00:02:26 EDT 2023
% 0.20/0.34 % CPUTime :
% 0.20/0.34 % Running portfolio for 300 s
% 0.20/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.34 % Number of cores: 8
% 0.20/0.34 % Python version: Python 3.6.8
% 0.20/0.35 % Running in FO mode
% 0.55/0.64 % Total configuration time : 435
% 0.55/0.64 % Estimated wc time : 1092
% 0.55/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.55/0.69 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.55/0.72 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.55/0.74 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.55/0.74 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.55/0.74 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.55/0.74 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.55/0.74 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 17.89/3.14 % Solved by fo/fo7.sh.
% 17.89/3.14 % done 488 iterations in 2.368s
% 17.89/3.14 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 17.89/3.14 % SZS output start Refutation
% 17.89/3.14 thf(a_type, type, a: $i).
% 17.89/3.14 thf(identity_type, type, identity: $i).
% 17.89/3.14 thf(b_type, type, b: $i).
% 17.89/3.14 thf(multiply_type, type, multiply: $i > $i > $i).
% 17.89/3.14 thf(c_type, type, c: $i).
% 17.89/3.14 thf(prove_order3, conjecture,
% 17.89/3.14 (( multiply @ ( multiply @ a @ b ) @ c ) =
% 17.89/3.14 ( multiply @ a @ ( multiply @ b @ c ) ))).
% 17.89/3.14 thf(zf_stmt_0, negated_conjecture,
% 17.89/3.14 (( multiply @ ( multiply @ a @ b ) @ c ) !=
% 17.89/3.14 ( multiply @ a @ ( multiply @ b @ c ) )),
% 17.89/3.14 inference('cnf.neg', [status(esa)], [prove_order3])).
% 17.89/3.14 thf(zip_derived_cl2, plain,
% 17.89/3.14 (((multiply @ (multiply @ a @ b) @ c)
% 17.89/3.14 != (multiply @ a @ (multiply @ b @ c)))),
% 17.89/3.14 inference('cnf', [status(esa)], [zf_stmt_0])).
% 17.89/3.14 thf(single_axiom2, axiom,
% 17.89/3.14 (( multiply @ identity @ identity ) = ( identity ))).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(single_axiom, axiom,
% 17.89/3.14 (( multiply @
% 17.89/3.14 Y @
% 17.89/3.14 ( multiply @
% 17.89/3.14 ( multiply @
% 17.89/3.14 Y @ ( multiply @ ( multiply @ Y @ Y ) @ ( multiply @ X @ Z ) ) ) @
% 17.89/3.14 ( multiply @ Z @ ( multiply @ Z @ Z ) ) ) ) =
% 17.89/3.14 ( X ))).
% 17.89/3.14 thf(zip_derived_cl0, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.89/3.14 ((multiply @ X1 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ X2))) @
% 17.89/3.14 (multiply @ X2 @ (multiply @ X2 @ X2))))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom])).
% 17.89/3.14 thf(zip_derived_cl5, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ X1 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ identity))) @
% 17.89/3.14 (multiply @ identity @ identity)))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl10, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ X1 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ identity))) @
% 17.89/3.14 identity))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl1])).
% 17.89/3.14 thf(zip_derived_cl23, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ identity))) @
% 17.89/3.14 identity))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl10])).
% 17.89/3.14 thf(zip_derived_cl23, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ identity))) @
% 17.89/3.14 identity))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl10])).
% 17.89/3.14 thf(zip_derived_cl26, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ identity @ X0) @ identity))
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ identity))))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl23, zip_derived_cl23])).
% 17.89/3.14 thf(zip_derived_cl26, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ identity @ X0) @ identity))
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ identity))))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl23, zip_derived_cl23])).
% 17.89/3.14 thf(zip_derived_cl45, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ identity))) @
% 17.89/3.14 identity))
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ (multiply @ identity @ X0) @ identity) @ identity))))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl26])).
% 17.89/3.14 thf(zip_derived_cl23, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ identity))) @
% 17.89/3.14 identity))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl10])).
% 17.89/3.14 thf(zip_derived_cl50, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((X0)
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ (multiply @ identity @ X0) @ identity) @ identity))))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl23])).
% 17.89/3.14 thf(zip_derived_cl23, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ identity))) @
% 17.89/3.14 identity))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl10])).
% 17.89/3.14 thf(zip_derived_cl60, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @ (multiply @ X0 @ identity))
% 17.89/3.14 = (multiply @ (multiply @ identity @ X0) @ identity))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl23])).
% 17.89/3.14 thf(zip_derived_cl0, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.89/3.14 ((multiply @ X1 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ X2))) @
% 17.89/3.14 (multiply @ X2 @ (multiply @ X2 @ X2))))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom])).
% 17.89/3.14 thf(zip_derived_cl50, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((X0)
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ (multiply @ identity @ X0) @ identity) @ identity))))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl23])).
% 17.89/3.14 thf(zip_derived_cl61, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ identity @ identity) @ (multiply @ X0 @ X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1)))
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity))))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl50])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl68, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ (multiply @ X0 @ X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1)))
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity))))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl61, zip_derived_cl1])).
% 17.89/3.14 thf(zip_derived_cl433, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ (multiply @ identity @ X0) @ X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1)))
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ identity)) @ identity))))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl60, zip_derived_cl68])).
% 17.89/3.14 thf(zip_derived_cl60, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @ (multiply @ X0 @ identity))
% 17.89/3.14 = (multiply @ (multiply @ identity @ X0) @ identity))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl23])).
% 17.89/3.14 thf(zip_derived_cl26, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ identity @ X0) @ identity))
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ identity))))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl23, zip_derived_cl23])).
% 17.89/3.14 thf(zip_derived_cl10, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ X1 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ identity))) @
% 17.89/3.14 identity))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl1])).
% 17.89/3.14 thf(zip_derived_cl36, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ (multiply @ identity @ identity) @
% 17.89/3.14 (multiply @ X0 @ identity)) @
% 17.89/3.14 identity)))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl10])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl26, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ identity @ X0) @ identity))
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ identity))))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl23, zip_derived_cl23])).
% 17.89/3.14 thf(zip_derived_cl53, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity))))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl36, zip_derived_cl1, zip_derived_cl26])).
% 17.89/3.14 thf(zip_derived_cl459, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ (multiply @ identity @ X0) @ X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1))) = (X0))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl433, zip_derived_cl60, zip_derived_cl53])).
% 17.89/3.14 thf(zip_derived_cl675, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ X0))) @
% 17.89/3.14 (multiply @ X0 @ (multiply @ X0 @ X0))) = (identity))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl459])).
% 17.89/3.14 thf(zip_derived_cl68, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ (multiply @ X0 @ X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1)))
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity))))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl61, zip_derived_cl1])).
% 17.89/3.14 thf(zip_derived_cl707, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ identity)) @
% 17.89/3.14 (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 17.89/3.14 (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 17.89/3.14 (multiply @ X0 @ (multiply @ X0 @ X0)))))
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ X0))) @
% 17.89/3.14 identity) @
% 17.89/3.14 identity))))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl675, zip_derived_cl68])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl60, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @ (multiply @ X0 @ identity))
% 17.89/3.14 = (multiply @ (multiply @ identity @ X0) @ identity))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl23])).
% 17.89/3.14 thf(zip_derived_cl60, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @ (multiply @ X0 @ identity))
% 17.89/3.14 = (multiply @ (multiply @ identity @ X0) @ identity))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl23])).
% 17.89/3.14 thf(zip_derived_cl60, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @ (multiply @ X0 @ identity))
% 17.89/3.14 = (multiply @ (multiply @ identity @ X0) @ identity))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl23])).
% 17.89/3.14 thf(zip_derived_cl60, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @ (multiply @ X0 @ identity))
% 17.89/3.14 = (multiply @ (multiply @ identity @ X0) @ identity))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl23])).
% 17.89/3.14 thf(zip_derived_cl10, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ X1 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ identity))) @
% 17.89/3.14 identity))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl1])).
% 17.89/3.14 thf(zip_derived_cl50, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((X0)
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ (multiply @ identity @ X0) @ identity) @ identity))))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl23])).
% 17.89/3.14 thf(zip_derived_cl62, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ identity @ identity) @
% 17.89/3.14 (multiply @ X0 @ identity))) @
% 17.89/3.14 identity)
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity))))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl50])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl69, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ identity))) @
% 17.89/3.14 identity)
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity))))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl62, zip_derived_cl1])).
% 17.89/3.14 thf(zip_derived_cl53, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity))))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl36, zip_derived_cl1, zip_derived_cl26])).
% 17.89/3.14 thf(zip_derived_cl745, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 17.89/3.14 (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 17.89/3.14 (multiply @ X0 @ (multiply @ X0 @ X0)))))
% 17.89/3.14 = (multiply @ identity @ (multiply @ identity @ X0)))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl707, zip_derived_cl1, zip_derived_cl1,
% 17.89/3.14 zip_derived_cl60, zip_derived_cl60, zip_derived_cl60,
% 17.89/3.14 zip_derived_cl60, zip_derived_cl69, zip_derived_cl53])).
% 17.89/3.14 thf(zip_derived_cl459, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ (multiply @ identity @ X0) @ X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1))) = (X0))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl433, zip_derived_cl60, zip_derived_cl53])).
% 17.89/3.14 thf(zip_derived_cl827, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ identity @ (multiply @ identity @ X0)) @
% 17.89/3.14 X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1)))
% 17.89/3.14 = (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 17.89/3.14 (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 17.89/3.14 (multiply @ X0 @ (multiply @ X0 @ X0)))))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl745, zip_derived_cl459])).
% 17.89/3.14 thf(zip_derived_cl459, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ (multiply @ identity @ X0) @ X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1))) = (X0))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl433, zip_derived_cl60, zip_derived_cl53])).
% 17.89/3.14 thf(zip_derived_cl847, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @ X0)
% 17.89/3.14 = (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 17.89/3.14 (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 17.89/3.14 (multiply @ X0 @ (multiply @ X0 @ X0)))))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl827, zip_derived_cl459])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl0, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.89/3.14 ((multiply @ X1 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ X2))) @
% 17.89/3.14 (multiply @ X2 @ (multiply @ X2 @ X2))))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom])).
% 17.89/3.14 thf(zip_derived_cl9, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ (multiply @ X0 @ X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1))))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 17.89/3.14 thf(zip_derived_cl847, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @ X0)
% 17.89/3.14 = (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 17.89/3.14 (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 17.89/3.14 (multiply @ X0 @ (multiply @ X0 @ X0)))))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl827, zip_derived_cl459])).
% 17.89/3.14 thf(zip_derived_cl9, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ (multiply @ X0 @ X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1))))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 17.89/3.14 thf(zip_derived_cl857, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X0 @ (multiply @ X0 @ X0))))) @
% 17.89/3.14 (multiply @ identity @ X0)))
% 17.89/3.14 = (X1))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl847, zip_derived_cl9])).
% 17.89/3.14 thf(zip_derived_cl1069, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ identity @ X0) @ (multiply @ identity @ X1)))
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ X1))))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl857])).
% 17.89/3.14 thf(zip_derived_cl459, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ (multiply @ identity @ X0) @ X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1))) = (X0))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl433, zip_derived_cl60, zip_derived_cl53])).
% 17.89/3.14 thf(zip_derived_cl1129, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ X1 @ X0))) @
% 17.89/3.14 X2))) @
% 17.89/3.14 (multiply @ X2 @ (multiply @ X2 @ X2)))
% 17.89/3.14 = (multiply @ (multiply @ identity @ X1) @
% 17.89/3.14 (multiply @ identity @ X0)))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl1069, zip_derived_cl459])).
% 17.89/3.14 thf(zip_derived_cl459, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ (multiply @ identity @ X0) @ X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1))) = (X0))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl433, zip_derived_cl60, zip_derived_cl53])).
% 17.89/3.14 thf(zip_derived_cl1221, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @ (multiply @ X1 @ X0))
% 17.89/3.14 = (multiply @ (multiply @ identity @ X1) @
% 17.89/3.14 (multiply @ identity @ X0)))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl1129, zip_derived_cl459])).
% 17.89/3.14 thf(zip_derived_cl847, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @ X0)
% 17.89/3.14 = (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 17.89/3.14 (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 17.89/3.14 (multiply @ X0 @ (multiply @ X0 @ X0)))))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl827, zip_derived_cl459])).
% 17.89/3.14 thf(zip_derived_cl675, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ X0))) @
% 17.89/3.14 (multiply @ X0 @ (multiply @ X0 @ X0))) = (identity))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl459])).
% 17.89/3.14 thf(zip_derived_cl862, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ (multiply @ X0 @ X0))))) @
% 17.89/3.14 (multiply @ identity @ X0)) = (identity))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl847, zip_derived_cl675])).
% 17.89/3.14 thf(zip_derived_cl1283, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ (multiply @ X0 @ X0)))) @
% 17.89/3.14 X0))
% 17.89/3.14 = (identity))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl1221, zip_derived_cl862])).
% 17.89/3.14 thf(zip_derived_cl459, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ (multiply @ identity @ X0) @ X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1))) = (X0))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl433, zip_derived_cl60, zip_derived_cl53])).
% 17.89/3.14 thf(zip_derived_cl1381, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1)))
% 17.89/3.14 = (multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ (multiply @ X0 @ X0)))) @
% 17.89/3.14 X0))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl1283, zip_derived_cl459])).
% 17.89/3.14 thf(zip_derived_cl68, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ (multiply @ X0 @ X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1)))
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity))))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl61, zip_derived_cl1])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl1412, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((identity)
% 17.89/3.14 = (multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ (multiply @ X0 @ X0)))) @
% 17.89/3.14 X0))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl1381, zip_derived_cl68, zip_derived_cl1,
% 17.89/3.14 zip_derived_cl1, zip_derived_cl1, zip_derived_cl1])).
% 17.89/3.14 thf(zip_derived_cl53, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity))))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl36, zip_derived_cl1, zip_derived_cl26])).
% 17.89/3.14 thf(zip_derived_cl1221, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @ (multiply @ X1 @ X0))
% 17.89/3.14 = (multiply @ (multiply @ identity @ X1) @
% 17.89/3.14 (multiply @ identity @ X0)))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl1129, zip_derived_cl459])).
% 17.89/3.14 thf(zip_derived_cl1295, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity)))))
% 17.89/3.14 = (multiply @ (multiply @ identity @ X1) @ X0))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl53, zip_derived_cl1221])).
% 17.89/3.14 thf(zip_derived_cl2222, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ (multiply @ X0 @ X0))) @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity)))))
% 17.89/3.14 = (identity))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl1412, zip_derived_cl1295])).
% 17.89/3.14 thf(zip_derived_cl1221, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @ (multiply @ X1 @ X0))
% 17.89/3.14 = (multiply @ (multiply @ identity @ X1) @
% 17.89/3.14 (multiply @ identity @ X0)))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl1129, zip_derived_cl459])).
% 17.89/3.14 thf(zip_derived_cl2251, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity)))))
% 17.89/3.14 = (identity))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl2222, zip_derived_cl1221])).
% 17.89/3.14 thf(zip_derived_cl459, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ (multiply @ identity @ X0) @ X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1))) = (X0))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl433, zip_derived_cl60, zip_derived_cl53])).
% 17.89/3.14 thf(zip_derived_cl3320, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1)))
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity)))))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl2251, zip_derived_cl459])).
% 17.89/3.14 thf(zip_derived_cl675, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ X0))) @
% 17.89/3.14 (multiply @ X0 @ (multiply @ X0 @ X0))) = (identity))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl459])).
% 17.89/3.14 thf(zip_derived_cl3387, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((identity)
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity)))))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl3320, zip_derived_cl675])).
% 17.89/3.14 thf(zip_derived_cl3456, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((identity)
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ identity @ X0) @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @ identity) @
% 17.89/3.14 identity)))))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl847, zip_derived_cl3387])).
% 17.89/3.14 thf(zip_derived_cl1221, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @ (multiply @ X1 @ X0))
% 17.89/3.14 = (multiply @ (multiply @ identity @ X1) @
% 17.89/3.14 (multiply @ identity @ X0)))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl1129, zip_derived_cl459])).
% 17.89/3.14 thf(zip_derived_cl3468, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((identity)
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ X0 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @ identity) @
% 17.89/3.14 identity)))))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl3456, zip_derived_cl1221])).
% 17.89/3.14 thf(zip_derived_cl459, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ (multiply @ identity @ X0) @ X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1))) = (X0))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl433, zip_derived_cl60, zip_derived_cl53])).
% 17.89/3.14 thf(zip_derived_cl3551, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1)))
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ X0 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @ identity) @
% 17.89/3.14 identity))))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl3468, zip_derived_cl459])).
% 17.89/3.14 thf(zip_derived_cl68, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ (multiply @ X0 @ X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1)))
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity))))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl61, zip_derived_cl1])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl3622, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((identity)
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ X0 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @ identity) @
% 17.89/3.14 identity))))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl3551, zip_derived_cl68, zip_derived_cl1,
% 17.89/3.14 zip_derived_cl1, zip_derived_cl1, zip_derived_cl1])).
% 17.89/3.14 thf(zip_derived_cl459, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ (multiply @ identity @ X0) @ X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1))) = (X0))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl433, zip_derived_cl60, zip_derived_cl53])).
% 17.89/3.14 thf(zip_derived_cl3670, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1)))
% 17.89/3.14 = (multiply @ X0 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @ identity) @
% 17.89/3.14 identity)))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl3622, zip_derived_cl459])).
% 17.89/3.14 thf(zip_derived_cl68, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ (multiply @ X0 @ X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1)))
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity))))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl61, zip_derived_cl1])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl3740, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((identity)
% 17.89/3.14 = (multiply @ X0 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @ identity) @
% 17.89/3.14 identity)))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl3670, zip_derived_cl68, zip_derived_cl1,
% 17.89/3.14 zip_derived_cl1, zip_derived_cl1, zip_derived_cl1])).
% 17.89/3.14 thf(zip_derived_cl53, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity))))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl36, zip_derived_cl1, zip_derived_cl26])).
% 17.89/3.14 thf(zip_derived_cl10, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ X1 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ identity))) @
% 17.89/3.14 identity))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl1])).
% 17.89/3.14 thf(zip_derived_cl847, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @ X0)
% 17.89/3.14 = (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 17.89/3.14 (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 17.89/3.14 (multiply @ X0 @ (multiply @ X0 @ X0)))))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl827, zip_derived_cl459])).
% 17.89/3.14 thf(zip_derived_cl53, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity))))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl36, zip_derived_cl1, zip_derived_cl26])).
% 17.89/3.14 thf(zip_derived_cl1221, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @ (multiply @ X1 @ X0))
% 17.89/3.14 = (multiply @ (multiply @ identity @ X1) @
% 17.89/3.14 (multiply @ identity @ X0)))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl1129, zip_derived_cl459])).
% 17.89/3.14 thf(zip_derived_cl1308, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity))) @
% 17.89/3.14 X1))
% 17.89/3.14 = (multiply @ X0 @ (multiply @ identity @ X1)))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl53, zip_derived_cl1221])).
% 17.89/3.14 thf(zip_derived_cl1308, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity))) @
% 17.89/3.14 X1))
% 17.89/3.14 = (multiply @ X0 @ (multiply @ identity @ X1)))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl53, zip_derived_cl1221])).
% 17.89/3.14 thf(zip_derived_cl459, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ (multiply @ identity @ X0) @ X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1))) = (X0))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl433, zip_derived_cl60, zip_derived_cl53])).
% 17.89/3.14 thf(zip_derived_cl1568, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @ (multiply @ X1 @ (multiply @ identity @ X0))) @
% 17.89/3.14 (multiply @ X0 @ (multiply @ X0 @ X0)))
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X1 @ identity) @ identity)))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl1308, zip_derived_cl459])).
% 17.89/3.14 thf(zip_derived_cl1653, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ X1 @ (multiply @ identity @ (multiply @ identity @ X0))) @
% 17.89/3.14 (multiply @ X0 @ (multiply @ X0 @ X0)))
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X1 @ identity) @ identity))) @
% 17.89/3.14 identity) @
% 17.89/3.14 identity)))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl1308, zip_derived_cl1568])).
% 17.89/3.14 thf(zip_derived_cl69, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ identity))) @
% 17.89/3.14 identity)
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity))))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl62, zip_derived_cl1])).
% 17.89/3.14 thf(zip_derived_cl69, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ identity))) @
% 17.89/3.14 identity)
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity))))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl62, zip_derived_cl1])).
% 17.89/3.14 thf(zip_derived_cl53, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity))))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl36, zip_derived_cl1, zip_derived_cl26])).
% 17.89/3.14 thf(zip_derived_cl1686, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ X1 @ (multiply @ identity @ (multiply @ identity @ X0))) @
% 17.89/3.14 (multiply @ X0 @ (multiply @ X0 @ X0)))
% 17.89/3.14 = (multiply @ (multiply @ X1 @ identity) @ identity))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl1653, zip_derived_cl69, zip_derived_cl69,
% 17.89/3.14 zip_derived_cl53])).
% 17.89/3.14 thf(zip_derived_cl1750, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ (multiply @ X0 @ X0))))) @
% 17.89/3.14 (multiply @ identity @ X0))
% 17.89/3.14 = (multiply @ (multiply @ X1 @ identity) @ identity))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl847, zip_derived_cl1686])).
% 17.89/3.14 thf(zip_derived_cl4571, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ identity @ identity) @
% 17.89/3.14 (multiply @ X0 @ identity))) @
% 17.89/3.14 identity) @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ identity @ identity) @
% 17.89/3.14 (multiply @ X0 @ identity))) @
% 17.89/3.14 identity) @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ identity @ identity) @
% 17.89/3.14 (multiply @ X0 @ identity))) @
% 17.89/3.14 identity)))))) @
% 17.89/3.14 X0) = (multiply @ (multiply @ X1 @ identity) @ identity))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl1750])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl69, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ identity))) @
% 17.89/3.14 identity)
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity))))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl62, zip_derived_cl1])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl69, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ identity))) @
% 17.89/3.14 identity)
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity))))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl62, zip_derived_cl1])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl69, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ identity))) @
% 17.89/3.14 identity)
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity))))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl62, zip_derived_cl1])).
% 17.89/3.14 thf(zip_derived_cl1221, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @ (multiply @ X1 @ X0))
% 17.89/3.14 = (multiply @ (multiply @ identity @ X1) @
% 17.89/3.14 (multiply @ identity @ X0)))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl1129, zip_derived_cl459])).
% 17.89/3.14 thf(zip_derived_cl1295, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity)))))
% 17.89/3.14 = (multiply @ (multiply @ identity @ X1) @ X0))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl53, zip_derived_cl1221])).
% 17.89/3.14 thf(zip_derived_cl2213, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity)))))
% 17.89/3.14 = (multiply @ (multiply @ identity @ (multiply @ identity @ X1)) @
% 17.89/3.14 X0))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl1221, zip_derived_cl1295])).
% 17.89/3.14 thf(zip_derived_cl2213, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity)))))
% 17.89/3.14 = (multiply @ (multiply @ identity @ (multiply @ identity @ X1)) @
% 17.89/3.14 X0))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl1221, zip_derived_cl1295])).
% 17.89/3.14 thf(zip_derived_cl2519, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ X0 @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ identity @ identity) @ identity))))) @
% 17.89/3.14 identity)))))
% 17.89/3.14 = (multiply @ (multiply @ identity @ (multiply @ identity @ X1)) @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ X0))))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl2213, zip_derived_cl2213])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl69, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ identity))) @
% 17.89/3.14 identity)
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity))))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl62, zip_derived_cl1])).
% 17.89/3.14 thf(zip_derived_cl53, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity))))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl36, zip_derived_cl1, zip_derived_cl26])).
% 17.89/3.14 thf(zip_derived_cl2554, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @ (multiply @ identity @ (multiply @ X1 @ X0)))
% 17.89/3.14 = (multiply @ (multiply @ identity @ (multiply @ identity @ X1)) @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ X0))))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl2519, zip_derived_cl1, zip_derived_cl1,
% 17.89/3.14 zip_derived_cl1, zip_derived_cl69, zip_derived_cl53])).
% 17.89/3.14 thf(zip_derived_cl2554, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @ (multiply @ identity @ (multiply @ X1 @ X0)))
% 17.89/3.14 = (multiply @ (multiply @ identity @ (multiply @ identity @ X1)) @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ X0))))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl2519, zip_derived_cl1, zip_derived_cl1,
% 17.89/3.14 zip_derived_cl1, zip_derived_cl69, zip_derived_cl53])).
% 17.89/3.14 thf(zip_derived_cl1221, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @ (multiply @ X1 @ X0))
% 17.89/3.14 = (multiply @ (multiply @ identity @ X1) @
% 17.89/3.14 (multiply @ identity @ X0)))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl1129, zip_derived_cl459])).
% 17.89/3.14 thf(zip_derived_cl1221, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @ (multiply @ X1 @ X0))
% 17.89/3.14 = (multiply @ (multiply @ identity @ X1) @
% 17.89/3.14 (multiply @ identity @ X0)))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl1129, zip_derived_cl459])).
% 17.89/3.14 thf(zip_derived_cl1308, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity))) @
% 17.89/3.14 X1))
% 17.89/3.14 = (multiply @ X0 @ (multiply @ identity @ X1)))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl53, zip_derived_cl1221])).
% 17.89/3.14 thf(zip_derived_cl1580, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X1 @ identity) @ identity)) @
% 17.89/3.14 X0)))
% 17.89/3.14 = (multiply @ X1 @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ X0))))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl1221, zip_derived_cl1308])).
% 17.89/3.14 thf(zip_derived_cl2379, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ (multiply @ X1 @ identity) @ identity) @
% 17.89/3.14 X0))))
% 17.89/3.14 = (multiply @ X1 @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ X0)))))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl1221, zip_derived_cl1580])).
% 17.89/3.14 thf(zip_derived_cl2379, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ (multiply @ X1 @ identity) @ identity) @
% 17.89/3.14 X0))))
% 17.89/3.14 = (multiply @ X1 @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ X0)))))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl1221, zip_derived_cl1580])).
% 17.89/3.14 thf(zip_derived_cl53, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity))))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl36, zip_derived_cl1, zip_derived_cl26])).
% 17.89/3.14 thf(zip_derived_cl4613, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ (multiply @ X0 @ X0)))) @
% 17.89/3.14 X0) = (multiply @ (multiply @ X1 @ identity) @ identity))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl4571, zip_derived_cl1, zip_derived_cl69,
% 17.89/3.14 zip_derived_cl1, zip_derived_cl69, zip_derived_cl1,
% 17.89/3.14 zip_derived_cl69, zip_derived_cl2554, zip_derived_cl2554,
% 17.89/3.14 zip_derived_cl2379, zip_derived_cl2379, zip_derived_cl53])).
% 17.89/3.14 thf(zip_derived_cl4613, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ (multiply @ X0 @ X0)))) @
% 17.89/3.14 X0) = (multiply @ (multiply @ X1 @ identity) @ identity))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl4571, zip_derived_cl1, zip_derived_cl69,
% 17.89/3.14 zip_derived_cl1, zip_derived_cl69, zip_derived_cl1,
% 17.89/3.14 zip_derived_cl69, zip_derived_cl2554, zip_derived_cl2554,
% 17.89/3.14 zip_derived_cl2379, zip_derived_cl2379, zip_derived_cl53])).
% 17.89/3.14 thf(zip_derived_cl4719, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ (multiply @ (multiply @ X0 @ identity) @ identity) @ X1)
% 17.89/3.14 = (multiply @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X0 @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @ (multiply @ X1 @ (multiply @ X1 @ X1))) @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1))) @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1))))))) @
% 17.89/3.14 identity) @
% 17.89/3.14 identity))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl4613, zip_derived_cl4613])).
% 17.89/3.14 thf(zip_derived_cl1221, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @ (multiply @ X1 @ X0))
% 17.89/3.14 = (multiply @ (multiply @ identity @ X1) @
% 17.89/3.14 (multiply @ identity @ X0)))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl1129, zip_derived_cl459])).
% 17.89/3.14 thf(zip_derived_cl1221, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @ (multiply @ X1 @ X0))
% 17.89/3.14 = (multiply @ (multiply @ identity @ X1) @
% 17.89/3.14 (multiply @ identity @ X0)))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl1129, zip_derived_cl459])).
% 17.89/3.14 thf(zip_derived_cl847, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @ X0)
% 17.89/3.14 = (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 17.89/3.14 (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 17.89/3.14 (multiply @ X0 @ (multiply @ X0 @ X0)))))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl827, zip_derived_cl459])).
% 17.89/3.14 thf(zip_derived_cl4737, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ (multiply @ (multiply @ X0 @ identity) @ identity) @ X1)
% 17.89/3.14 = (multiply @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X0 @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ X1)))) @
% 17.89/3.14 identity) @
% 17.89/3.14 identity))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl4719, zip_derived_cl1221, zip_derived_cl1221,
% 17.89/3.14 zip_derived_cl847])).
% 17.89/3.14 thf(zip_derived_cl5066, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ (multiply @ (multiply @ X1 @ identity) @ identity) @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity))
% 17.89/3.14 = (multiply @ (multiply @ (multiply @ X1 @ X0) @ identity) @
% 17.89/3.14 identity))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl53, zip_derived_cl4737])).
% 17.89/3.14 thf(zip_derived_cl5947, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((identity)
% 17.89/3.14 = (multiply @ X0 @
% 17.89/3.14 (multiply @ (multiply @ (multiply @ X0 @ identity) @ identity) @
% 17.89/3.14 (multiply @ (multiply @ (multiply @ X0 @ X0) @ identity) @
% 17.89/3.14 identity))))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl3740, zip_derived_cl5066])).
% 17.89/3.14 thf(zip_derived_cl10, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ X1 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ identity))) @
% 17.89/3.14 identity))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl1])).
% 17.89/3.14 thf(zip_derived_cl60, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @ (multiply @ X0 @ identity))
% 17.89/3.14 = (multiply @ (multiply @ identity @ X0) @ identity))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl23])).
% 17.89/3.14 thf(zip_derived_cl10, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ X1 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ identity))) @
% 17.89/3.14 identity))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl1])).
% 17.89/3.14 thf(zip_derived_cl77, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ X1 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ (multiply @ X1 @ X1) @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ identity)))) @
% 17.89/3.14 identity))
% 17.89/3.14 = (multiply @ identity @ X0))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl60, zip_derived_cl10])).
% 17.89/3.14 thf(zip_derived_cl188, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ X1 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @ (multiply @ (multiply @ X1 @ X1) @ X0)) @ identity))
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ identity @ identity) @
% 17.89/3.14 (multiply @ X0 @ identity)))))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl77])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl196, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ X1 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @ (multiply @ (multiply @ X1 @ X1) @ X0)) @ identity))
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ identity)))))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl188, zip_derived_cl1])).
% 17.89/3.14 thf(zip_derived_cl0, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.89/3.14 ((multiply @ X1 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ X2))) @
% 17.89/3.14 (multiply @ X2 @ (multiply @ X2 @ X2))))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom])).
% 17.89/3.14 thf(zip_derived_cl9, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ (multiply @ X0 @ X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1))))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 17.89/3.14 thf(zip_derived_cl1221, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @ (multiply @ X1 @ X0))
% 17.89/3.14 = (multiply @ (multiply @ identity @ X1) @
% 17.89/3.14 (multiply @ identity @ X0)))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl1129, zip_derived_cl459])).
% 17.89/3.14 thf(zip_derived_cl1305, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ X2))) @
% 17.89/3.14 (multiply @ X2 @ (multiply @ X2 @ X2))) @
% 17.89/3.14 X1))
% 17.89/3.14 = (multiply @ X0 @ (multiply @ identity @ X1)))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl1221])).
% 17.89/3.14 thf(zip_derived_cl847, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @ X0)
% 17.89/3.14 = (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 17.89/3.14 (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 17.89/3.14 (multiply @ X0 @ (multiply @ X0 @ X0)))))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl827, zip_derived_cl459])).
% 17.89/3.14 thf(zip_derived_cl0, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.89/3.14 ((multiply @ X1 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ X2))) @
% 17.89/3.14 (multiply @ X2 @ (multiply @ X2 @ X2))))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom])).
% 17.89/3.14 thf(zip_derived_cl855, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.89/3.14 ((multiply @ X2 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X2 @
% 17.89/3.14 (multiply @ (multiply @ X2 @ X2) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X0 @ (multiply @ X0 @ X0))))) @
% 17.89/3.14 (multiply @ identity @ X0)))
% 17.89/3.14 = (X1))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl847, zip_derived_cl0])).
% 17.89/3.14 thf(zip_derived_cl6707, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.89/3.14 ((multiply @ X2 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X2 @
% 17.89/3.14 (multiply @ (multiply @ X2 @ X2) @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ X1 @ X0))) @
% 17.89/3.14 (multiply @ X0 @ (multiply @ X0 @ X0))) @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ X1 @ X0))) @
% 17.89/3.14 (multiply @ X0 @ (multiply @ X0 @ X0)))))))) @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ X1 @ X0))) @
% 17.89/3.14 (multiply @ X0 @ (multiply @ X0 @ X0))))))
% 17.89/3.14 = (identity))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl1305, zip_derived_cl855])).
% 17.89/3.14 thf(zip_derived_cl1305, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ X2))) @
% 17.89/3.14 (multiply @ X2 @ (multiply @ X2 @ X2))) @
% 17.89/3.14 X1))
% 17.89/3.14 = (multiply @ X0 @ (multiply @ identity @ X1)))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl1221])).
% 17.89/3.14 thf(zip_derived_cl9, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ (multiply @ X0 @ X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1))))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 17.89/3.14 thf(zip_derived_cl9, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ (multiply @ X0 @ X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1))))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 17.89/3.14 thf(zip_derived_cl6967, plain,
% 17.89/3.14 (![X1 : $i, X2 : $i]:
% 17.89/3.14 ((multiply @ X2 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X2 @
% 17.89/3.14 (multiply @ (multiply @ X2 @ X2) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1)))) @
% 17.89/3.14 X1))
% 17.89/3.14 = (identity))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl6707, zip_derived_cl1305, zip_derived_cl9,
% 17.89/3.14 zip_derived_cl9])).
% 17.89/3.14 thf(zip_derived_cl855, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.89/3.14 ((multiply @ X2 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X2 @
% 17.89/3.14 (multiply @ (multiply @ X2 @ X2) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X0 @ (multiply @ X0 @ X0))))) @
% 17.89/3.14 (multiply @ identity @ X0)))
% 17.89/3.14 = (X1))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl847, zip_derived_cl0])).
% 17.89/3.14 thf(zip_derived_cl7024, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ X1 @
% 17.89/3.14 (multiply @ (multiply @ X1 @ identity) @ (multiply @ identity @ X0)))
% 17.89/3.14 = (multiply @ (multiply @ X1 @ X1) @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X1 @ X1)) @
% 17.89/3.14 (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 17.89/3.14 (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 17.89/3.14 (multiply @ X0 @ (multiply @ X0 @ X0)))))))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl6967, zip_derived_cl855])).
% 17.89/3.14 thf(zip_derived_cl847, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @ X0)
% 17.89/3.14 = (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 17.89/3.14 (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 17.89/3.14 (multiply @ X0 @ (multiply @ X0 @ X0)))))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl827, zip_derived_cl459])).
% 17.89/3.14 thf(zip_derived_cl7122, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ X1 @
% 17.89/3.14 (multiply @ (multiply @ X1 @ identity) @ (multiply @ identity @ X0)))
% 17.89/3.14 = (multiply @ (multiply @ X1 @ X1) @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X1 @ X1)) @
% 17.89/3.14 (multiply @ identity @ X0))))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl7024, zip_derived_cl847])).
% 17.89/3.14 thf(zip_derived_cl7189, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.89/3.14 ((multiply @ X2 @
% 17.89/3.14 (multiply @ (multiply @ X2 @ identity) @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ identity @ identity) @
% 17.89/3.14 (multiply @ X0 @ X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1))))))
% 17.89/3.14 = (multiply @ (multiply @ X2 @ X2) @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ (multiply @ X2 @ X2) @ (multiply @ X2 @ X2)) @ X0)))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl7122])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl9, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ (multiply @ X0 @ X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1))))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 17.89/3.14 thf(zip_derived_cl7227, plain,
% 17.89/3.14 (![X0 : $i, X2 : $i]:
% 17.89/3.14 ((multiply @ X2 @ (multiply @ (multiply @ X2 @ identity) @ X0))
% 17.89/3.14 = (multiply @ (multiply @ X2 @ X2) @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ (multiply @ X2 @ X2) @ (multiply @ X2 @ X2)) @ X0)))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl7189, zip_derived_cl1, zip_derived_cl9])).
% 17.89/3.14 thf(zip_derived_cl10, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ X1 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ identity))) @
% 17.89/3.14 identity))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl1])).
% 17.89/3.14 thf(zip_derived_cl7276, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ (multiply @ X1 @ X1) @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ (multiply @ X1 @ identity) @
% 17.89/3.14 (multiply @ X0 @ identity))) @
% 17.89/3.14 identity))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl7227, zip_derived_cl10])).
% 17.89/3.14 thf(zip_derived_cl10, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ X1 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ identity))) @
% 17.89/3.14 identity))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl1])).
% 17.89/3.14 thf(zip_derived_cl7372, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ X1 @ (multiply @ (multiply @ X1 @ X0) @ identity))
% 17.89/3.14 = (multiply @ X1 @
% 17.89/3.14 (multiply @ (multiply @ X1 @ identity) @
% 17.89/3.14 (multiply @ X0 @ identity))))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl7276, zip_derived_cl10])).
% 17.89/3.14 thf(zip_derived_cl7276, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ (multiply @ X1 @ X1) @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ (multiply @ X1 @ identity) @
% 17.89/3.14 (multiply @ X0 @ identity))) @
% 17.89/3.14 identity))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl7227, zip_derived_cl10])).
% 17.89/3.14 thf(zip_derived_cl7475, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ (multiply @ X1 @ X1) @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @ (multiply @ (multiply @ X1 @ X0) @ identity)) @
% 17.89/3.14 identity))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl7372, zip_derived_cl7276])).
% 17.89/3.14 thf(zip_derived_cl7926, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ (multiply @ X1 @ X1) @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ identity)))) @
% 17.89/3.14 identity)) @
% 17.89/3.14 identity))
% 17.89/3.14 = (multiply @
% 17.89/3.14 (multiply @ X1 @ (multiply @ (multiply @ X1 @ X1) @ X0)) @
% 17.89/3.14 identity))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl196, zip_derived_cl7475])).
% 17.89/3.14 thf(zip_derived_cl1221, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @ (multiply @ X1 @ X0))
% 17.89/3.14 = (multiply @ (multiply @ identity @ X1) @
% 17.89/3.14 (multiply @ identity @ X0)))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl1129, zip_derived_cl459])).
% 17.89/3.14 thf(zip_derived_cl2213, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity)))))
% 17.89/3.14 = (multiply @ (multiply @ identity @ (multiply @ identity @ X1)) @
% 17.89/3.14 X0))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl1221, zip_derived_cl1295])).
% 17.89/3.14 thf(zip_derived_cl2515, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity)))))
% 17.89/3.14 = (multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ X1))) @
% 17.89/3.14 X0))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl1221, zip_derived_cl2213])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl53, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity))))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl36, zip_derived_cl1, zip_derived_cl26])).
% 17.89/3.14 thf(zip_derived_cl8011, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ (multiply @ X1 @ X1) @
% 17.89/3.14 (multiply @ (multiply @ X1 @ X0) @ identity))
% 17.89/3.14 = (multiply @
% 17.89/3.14 (multiply @ X1 @ (multiply @ (multiply @ X1 @ X1) @ X0)) @
% 17.89/3.14 identity))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl7926, zip_derived_cl2515, zip_derived_cl1,
% 17.89/3.14 zip_derived_cl1, zip_derived_cl53])).
% 17.89/3.14 thf(zip_derived_cl0, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.89/3.14 ((multiply @ X1 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ X2))) @
% 17.89/3.14 (multiply @ X2 @ (multiply @ X2 @ X2))))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom])).
% 17.89/3.14 thf(zip_derived_cl675, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ X0))) @
% 17.89/3.14 (multiply @ X0 @ (multiply @ X0 @ X0))) = (identity))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl459])).
% 17.89/3.14 thf(zip_derived_cl855, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.89/3.14 ((multiply @ X2 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X2 @
% 17.89/3.14 (multiply @ (multiply @ X2 @ X2) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X0 @ (multiply @ X0 @ X0))))) @
% 17.89/3.14 (multiply @ identity @ X0)))
% 17.89/3.14 = (X1))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl847, zip_derived_cl0])).
% 17.89/3.14 thf(zip_derived_cl1883, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ X1 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @ (multiply @ (multiply @ X1 @ X1) @ identity)) @
% 17.89/3.14 (multiply @ identity @ X0)))
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ X0))))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl675, zip_derived_cl855])).
% 17.89/3.14 thf(zip_derived_cl1970, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.89/3.14 ((multiply @ X2 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X2 @ (multiply @ (multiply @ X2 @ X2) @ identity)) @ X0))
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ identity @ identity) @
% 17.89/3.14 (multiply @ X0 @ X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1)))))))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl1883])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl9, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ (multiply @ X0 @ X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1))))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 17.89/3.14 thf(zip_derived_cl1992, plain,
% 17.89/3.14 (![X0 : $i, X2 : $i]:
% 17.89/3.14 ((multiply @ X2 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X2 @ (multiply @ (multiply @ X2 @ X2) @ identity)) @ X0))
% 17.89/3.14 = (multiply @ identity @ (multiply @ identity @ X0)))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl1970, zip_derived_cl1, zip_derived_cl9])).
% 17.89/3.14 thf(zip_derived_cl8572, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ X0 @
% 17.89/3.14 (multiply @ (multiply @ X0 @ X0) @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity)))
% 17.89/3.14 = (multiply @ identity @ (multiply @ identity @ identity)))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl8011, zip_derived_cl1992])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl8655, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ X0 @
% 17.89/3.14 (multiply @ (multiply @ X0 @ X0) @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity)))
% 17.89/3.14 = (identity))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl8572, zip_derived_cl1, zip_derived_cl1])).
% 17.89/3.14 thf(zip_derived_cl459, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ (multiply @ identity @ X0) @ X1))) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X1 @ X1))) = (X0))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl433, zip_derived_cl60, zip_derived_cl53])).
% 17.89/3.14 thf(zip_derived_cl855, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.89/3.14 ((multiply @ X2 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X2 @
% 17.89/3.14 (multiply @ (multiply @ X2 @ X2) @
% 17.89/3.14 (multiply @ X1 @ (multiply @ X0 @ (multiply @ X0 @ X0))))) @
% 17.89/3.14 (multiply @ identity @ X0)))
% 17.89/3.14 = (X1))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl847, zip_derived_cl0])).
% 17.89/3.14 thf(zip_derived_cl1885, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.89/3.14 ((multiply @ X2 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X2 @ (multiply @ (multiply @ X2 @ X2) @ X0)) @
% 17.89/3.14 (multiply @ identity @ X1)))
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ identity @ X0) @ X1))))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl459, zip_derived_cl855])).
% 17.89/3.14 thf(zip_derived_cl8711, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ X1 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @ (multiply @ (multiply @ X1 @ X1) @ X0)) @ identity))
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ identity @ X0) @
% 17.89/3.14 (multiply @ (multiply @ identity @ identity) @
% 17.89/3.14 (multiply @ (multiply @ identity @ identity) @ identity))))))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl8655, zip_derived_cl1885])).
% 17.89/3.14 thf(zip_derived_cl8011, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ (multiply @ X1 @ X1) @
% 17.89/3.14 (multiply @ (multiply @ X1 @ X0) @ identity))
% 17.89/3.14 = (multiply @
% 17.89/3.14 (multiply @ X1 @ (multiply @ (multiply @ X1 @ X1) @ X0)) @
% 17.89/3.14 identity))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl7926, zip_derived_cl2515, zip_derived_cl1,
% 17.89/3.14 zip_derived_cl1, zip_derived_cl53])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl60, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @ (multiply @ X0 @ identity))
% 17.89/3.14 = (multiply @ (multiply @ identity @ X0) @ identity))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl23])).
% 17.89/3.14 thf(zip_derived_cl8803, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ X1 @
% 17.89/3.14 (multiply @ (multiply @ X1 @ X1) @
% 17.89/3.14 (multiply @ (multiply @ X1 @ X0) @ identity)))
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ X0 @ identity)))))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl8711, zip_derived_cl8011, zip_derived_cl1,
% 17.89/3.14 zip_derived_cl1, zip_derived_cl1, zip_derived_cl1,
% 17.89/3.14 zip_derived_cl60])).
% 17.89/3.14 thf(zip_derived_cl11895, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ X0 @
% 17.89/3.14 (multiply @ (multiply @ X0 @ X0) @ (multiply @ identity @ identity)))
% 17.89/3.14 = (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity) @
% 17.89/3.14 (multiply @ (multiply @ (multiply @ X0 @ X0) @ identity) @
% 17.89/3.14 identity)) @
% 17.89/3.14 identity)))))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl5947, zip_derived_cl8803])).
% 17.89/3.14 thf(zip_derived_cl1, plain,
% 17.89/3.14 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.14 thf(zip_derived_cl7372, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ X1 @ (multiply @ (multiply @ X1 @ X0) @ identity))
% 17.89/3.14 = (multiply @ X1 @
% 17.89/3.14 (multiply @ (multiply @ X1 @ identity) @
% 17.89/3.14 (multiply @ X0 @ identity))))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl7276, zip_derived_cl10])).
% 17.89/3.14 thf(zip_derived_cl7475, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ (multiply @ X1 @ X1) @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @ (multiply @ (multiply @ X1 @ X0) @ identity)) @
% 17.89/3.14 identity))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl7372, zip_derived_cl7276])).
% 17.89/3.14 thf(zip_derived_cl7933, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ (multiply @ X1 @ X1) @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @ (multiply @ (multiply @ X1 @ X0) @ identity)) @
% 17.89/3.14 identity)) @
% 17.89/3.14 identity))
% 17.89/3.14 = (multiply @ (multiply @ X1 @ identity) @
% 17.89/3.14 (multiply @ X0 @ identity)))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl7372, zip_derived_cl7475])).
% 17.89/3.14 thf(zip_derived_cl7372, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ X1 @ (multiply @ (multiply @ X1 @ X0) @ identity))
% 17.89/3.14 = (multiply @ X1 @
% 17.89/3.14 (multiply @ (multiply @ X1 @ identity) @
% 17.89/3.14 (multiply @ X0 @ identity))))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl7276, zip_derived_cl10])).
% 17.89/3.14 thf(zip_derived_cl7276, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ (multiply @ X1 @ X1) @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ (multiply @ X1 @ identity) @
% 17.89/3.14 (multiply @ X0 @ identity))) @
% 17.89/3.14 identity))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl7227, zip_derived_cl10])).
% 17.89/3.14 thf(zip_derived_cl8017, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ (multiply @ X1 @ X0) @ identity)
% 17.89/3.14 = (multiply @ (multiply @ X1 @ identity) @
% 17.89/3.14 (multiply @ X0 @ identity)))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl7933, zip_derived_cl7372, zip_derived_cl7276])).
% 17.89/3.14 thf(zip_derived_cl2379, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ (multiply @ X1 @ identity) @ identity) @
% 17.89/3.14 X0))))
% 17.89/3.14 = (multiply @ X1 @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ X0)))))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl1221, zip_derived_cl1580])).
% 17.89/3.14 thf(zip_derived_cl53, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ identity @
% 17.89/3.14 (multiply @ (multiply @ X0 @ identity) @ identity))))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl36, zip_derived_cl1, zip_derived_cl26])).
% 17.89/3.14 thf(zip_derived_cl11987, plain,
% 17.89/3.14 (![X0 : $i]:
% 17.89/3.14 ((multiply @ X0 @ (multiply @ (multiply @ X0 @ X0) @ identity))
% 17.89/3.14 = (multiply @ (multiply @ X0 @ identity) @
% 17.89/3.14 (multiply @ (multiply @ X0 @ X0) @ identity)))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl11895, zip_derived_cl1, zip_derived_cl8017,
% 17.89/3.14 zip_derived_cl2379, zip_derived_cl53])).
% 17.89/3.14 thf(zip_derived_cl0, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.89/3.14 ((multiply @ X1 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ X2))) @
% 17.89/3.14 (multiply @ X2 @ (multiply @ X2 @ X2))))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom])).
% 17.89/3.14 thf(zip_derived_cl12109, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ X1 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ (multiply @ X1 @ X1) @
% 17.89/3.14 (multiply @ X0 @ (multiply @ (multiply @ X0 @ X0) @ identity)))) @
% 17.89/3.14 (multiply @ (multiply @ (multiply @ X0 @ X0) @ identity) @
% 17.89/3.14 (multiply @ (multiply @ (multiply @ X0 @ X0) @ identity) @
% 17.89/3.14 (multiply @ (multiply @ X0 @ X0) @ identity)))))
% 17.89/3.14 = (multiply @ X0 @ identity))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl11987, zip_derived_cl0])).
% 17.89/3.14 thf(zip_derived_cl0, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.89/3.14 ((multiply @ X1 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ X2))) @
% 17.89/3.14 (multiply @ X2 @ (multiply @ X2 @ X2))))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom])).
% 17.89/3.14 thf(zip_derived_cl12195, plain,
% 17.89/3.14 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl12109, zip_derived_cl0])).
% 17.89/3.14 thf(zip_derived_cl0, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.89/3.14 ((multiply @ X1 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @
% 17.89/3.14 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ X2))) @
% 17.89/3.14 (multiply @ X2 @ (multiply @ X2 @ X2))))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('cnf', [status(esa)], [single_axiom])).
% 17.89/3.14 thf(zip_derived_cl12267, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ X1 @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @ (multiply @ (multiply @ X1 @ X1) @ X0)) @
% 17.89/3.14 (multiply @ identity @ (multiply @ identity @ identity))))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl12195, zip_derived_cl0])).
% 17.89/3.14 thf(zip_derived_cl12195, plain,
% 17.89/3.14 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl12109, zip_derived_cl0])).
% 17.89/3.14 thf(zip_derived_cl12195, plain,
% 17.89/3.14 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl12109, zip_derived_cl0])).
% 17.89/3.14 thf(zip_derived_cl12195, plain,
% 17.89/3.14 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl12109, zip_derived_cl0])).
% 17.89/3.14 thf(zip_derived_cl12310, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ X1 @
% 17.89/3.14 (multiply @ X1 @ (multiply @ (multiply @ X1 @ X1) @ X0))) = (
% 17.89/3.14 X0))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl12267, zip_derived_cl12195,
% 17.89/3.14 zip_derived_cl12195, zip_derived_cl12195])).
% 17.89/3.14 thf(zip_derived_cl7475, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ (multiply @ X1 @ X1) @
% 17.89/3.14 (multiply @
% 17.89/3.14 (multiply @ X1 @ (multiply @ (multiply @ X1 @ X0) @ identity)) @
% 17.89/3.14 identity))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('sup+', [status(thm)], [zip_derived_cl7372, zip_derived_cl7276])).
% 17.89/3.14 thf(zip_derived_cl8017, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ (multiply @ X1 @ X0) @ identity)
% 17.89/3.14 = (multiply @ (multiply @ X1 @ identity) @
% 17.89/3.14 (multiply @ X0 @ identity)))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl7933, zip_derived_cl7372, zip_derived_cl7276])).
% 17.89/3.14 thf(zip_derived_cl8078, plain,
% 17.89/3.14 (![X0 : $i, X1 : $i]:
% 17.89/3.14 ((multiply @ (multiply @ X1 @ X1) @
% 17.89/3.14 (multiply @ (multiply @ X1 @ identity) @
% 17.89/3.14 (multiply @ (multiply @ (multiply @ X1 @ X0) @ identity) @ identity)))
% 17.89/3.14 = (X0))),
% 17.89/3.14 inference('demod', [status(thm)],
% 17.89/3.14 [zip_derived_cl7475, zip_derived_cl8017])).
% 17.89/3.14 thf(zip_derived_cl12195, plain,
% 17.89/3.14 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl12109, zip_derived_cl0])).
% 17.89/3.14 thf(zip_derived_cl12195, plain,
% 17.89/3.14 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 17.89/3.14 inference('demod', [status(thm)], [zip_derived_cl12109, zip_derived_cl0])).
% 17.89/3.15 thf(zip_derived_cl12195, plain,
% 17.89/3.15 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 17.89/3.15 inference('demod', [status(thm)], [zip_derived_cl12109, zip_derived_cl0])).
% 17.89/3.15 thf(zip_derived_cl12248, plain,
% 17.89/3.15 (![X0 : $i, X1 : $i]:
% 17.89/3.15 ((multiply @ (multiply @ X1 @ X1) @
% 17.89/3.15 (multiply @ X1 @ (multiply @ X1 @ X0))) = (X0))),
% 17.89/3.15 inference('demod', [status(thm)],
% 17.89/3.15 [zip_derived_cl8078, zip_derived_cl12195, zip_derived_cl12195,
% 17.89/3.15 zip_derived_cl12195])).
% 17.89/3.15 thf(zip_derived_cl8655, plain,
% 17.89/3.15 (![X0 : $i]:
% 17.89/3.15 ((multiply @ X0 @
% 17.89/3.15 (multiply @ (multiply @ X0 @ X0) @
% 17.89/3.15 (multiply @ (multiply @ X0 @ identity) @ identity)))
% 17.89/3.15 = (identity))),
% 17.89/3.15 inference('demod', [status(thm)],
% 17.89/3.15 [zip_derived_cl8572, zip_derived_cl1, zip_derived_cl1])).
% 17.89/3.15 thf(zip_derived_cl855, plain,
% 17.89/3.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.89/3.15 ((multiply @ X2 @
% 17.89/3.15 (multiply @
% 17.89/3.15 (multiply @ X2 @
% 17.89/3.15 (multiply @ (multiply @ X2 @ X2) @
% 17.89/3.15 (multiply @ X1 @ (multiply @ X0 @ (multiply @ X0 @ X0))))) @
% 17.89/3.15 (multiply @ identity @ X0)))
% 17.89/3.15 = (X1))),
% 17.89/3.15 inference('sup+', [status(thm)], [zip_derived_cl847, zip_derived_cl0])).
% 17.89/3.15 thf(zip_derived_cl8697, plain,
% 17.89/3.15 (![X0 : $i, X1 : $i]:
% 17.89/3.15 ((multiply @ X1 @
% 17.89/3.15 (multiply @
% 17.89/3.15 (multiply @ X1 @
% 17.89/3.15 (multiply @ (multiply @ X1 @ X1) @
% 17.89/3.15 (multiply @ X0 @
% 17.89/3.15 (multiply @
% 17.89/3.15 (multiply @ (multiply @ identity @ identity) @
% 17.89/3.15 (multiply @ (multiply @ identity @ identity) @ identity)) @
% 17.89/3.15 (multiply @
% 17.89/3.15 (multiply @ (multiply @ identity @ identity) @
% 17.89/3.15 (multiply @ (multiply @ identity @ identity) @ identity)) @
% 17.89/3.15 (multiply @ (multiply @ identity @ identity) @
% 17.89/3.15 (multiply @ (multiply @ identity @ identity) @ identity))))))) @
% 17.89/3.15 identity))
% 17.89/3.15 = (X0))),
% 17.89/3.15 inference('sup+', [status(thm)], [zip_derived_cl8655, zip_derived_cl855])).
% 17.89/3.15 thf(zip_derived_cl1, plain,
% 17.89/3.15 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.15 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.15 thf(zip_derived_cl1, plain,
% 17.89/3.15 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.15 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.15 thf(zip_derived_cl1, plain,
% 17.89/3.15 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.15 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.15 thf(zip_derived_cl1, plain,
% 17.89/3.15 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.15 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.15 thf(zip_derived_cl1, plain,
% 17.89/3.15 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.15 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.15 thf(zip_derived_cl1, plain,
% 17.89/3.15 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.15 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.15 thf(zip_derived_cl1, plain,
% 17.89/3.15 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.15 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.15 thf(zip_derived_cl1, plain,
% 17.89/3.15 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.15 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.15 thf(zip_derived_cl1, plain,
% 17.89/3.15 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.15 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.15 thf(zip_derived_cl1, plain,
% 17.89/3.15 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.15 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.15 thf(zip_derived_cl1, plain,
% 17.89/3.15 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.15 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.15 thf(zip_derived_cl1, plain,
% 17.89/3.15 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.15 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.15 thf(zip_derived_cl1, plain,
% 17.89/3.15 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.15 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.15 thf(zip_derived_cl1, plain,
% 17.89/3.15 (((multiply @ identity @ identity) = (identity))),
% 17.89/3.15 inference('cnf', [status(esa)], [single_axiom2])).
% 17.89/3.15 thf(zip_derived_cl8011, plain,
% 17.89/3.15 (![X0 : $i, X1 : $i]:
% 17.89/3.15 ((multiply @ (multiply @ X1 @ X1) @
% 17.89/3.15 (multiply @ (multiply @ X1 @ X0) @ identity))
% 17.89/3.15 = (multiply @
% 17.89/3.15 (multiply @ X1 @ (multiply @ (multiply @ X1 @ X1) @ X0)) @
% 17.89/3.15 identity))),
% 17.89/3.15 inference('demod', [status(thm)],
% 17.89/3.15 [zip_derived_cl7926, zip_derived_cl2515, zip_derived_cl1,
% 17.89/3.15 zip_derived_cl1, zip_derived_cl53])).
% 17.89/3.15 thf(zip_derived_cl8017, plain,
% 17.89/3.15 (![X0 : $i, X1 : $i]:
% 17.89/3.15 ((multiply @ (multiply @ X1 @ X0) @ identity)
% 17.89/3.15 = (multiply @ (multiply @ X1 @ identity) @
% 17.89/3.15 (multiply @ X0 @ identity)))),
% 17.89/3.15 inference('demod', [status(thm)],
% 17.89/3.15 [zip_derived_cl7933, zip_derived_cl7372, zip_derived_cl7276])).
% 17.89/3.15 thf(zip_derived_cl8789, plain,
% 17.89/3.15 (![X0 : $i, X1 : $i]:
% 17.89/3.15 ((multiply @ X1 @
% 17.89/3.15 (multiply @ (multiply @ X1 @ X1) @
% 17.89/3.15 (multiply @ (multiply @ X1 @ identity) @
% 17.89/3.15 (multiply @ (multiply @ X0 @ identity) @ identity))))
% 17.89/3.15 = (X0))),
% 17.89/3.15 inference('demod', [status(thm)],
% 17.89/3.15 [zip_derived_cl8697, zip_derived_cl1, zip_derived_cl1,
% 17.89/3.15 zip_derived_cl1, zip_derived_cl1, zip_derived_cl1,
% 17.89/3.15 zip_derived_cl1, zip_derived_cl1, zip_derived_cl1,
% 17.89/3.15 zip_derived_cl1, zip_derived_cl1, zip_derived_cl1,
% 17.89/3.15 zip_derived_cl1, zip_derived_cl1, zip_derived_cl1,
% 17.89/3.15 zip_derived_cl8011, zip_derived_cl8017])).
% 17.89/3.15 thf(zip_derived_cl12195, plain,
% 17.89/3.15 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 17.89/3.15 inference('demod', [status(thm)], [zip_derived_cl12109, zip_derived_cl0])).
% 17.89/3.15 thf(zip_derived_cl12195, plain,
% 17.89/3.15 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 17.89/3.15 inference('demod', [status(thm)], [zip_derived_cl12109, zip_derived_cl0])).
% 17.89/3.15 thf(zip_derived_cl12195, plain,
% 17.89/3.15 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 17.89/3.15 inference('demod', [status(thm)], [zip_derived_cl12109, zip_derived_cl0])).
% 17.89/3.15 thf(zip_derived_cl12256, plain,
% 17.89/3.15 (![X0 : $i, X1 : $i]:
% 17.89/3.15 ((multiply @ X1 @
% 17.89/3.15 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X1 @ X0))) = (
% 17.89/3.15 X0))),
% 17.89/3.15 inference('demod', [status(thm)],
% 17.89/3.15 [zip_derived_cl8789, zip_derived_cl12195, zip_derived_cl12195,
% 17.89/3.15 zip_derived_cl12195])).
% 17.89/3.15 thf(zip_derived_cl12884, plain,
% 17.89/3.15 (![X0 : $i, X1 : $i]:
% 17.89/3.15 ((multiply @ (multiply @ X1 @ X1) @
% 17.89/3.15 (multiply @
% 17.89/3.15 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X1 @ X1)) @ X0))
% 17.89/3.15 = (multiply @ X1 @ (multiply @ X1 @ X0)))),
% 17.89/3.15 inference('sup+', [status(thm)],
% 17.89/3.15 [zip_derived_cl12248, zip_derived_cl12256])).
% 17.89/3.15 thf(zip_derived_cl12195, plain,
% 17.89/3.15 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 17.89/3.15 inference('demod', [status(thm)], [zip_derived_cl12109, zip_derived_cl0])).
% 17.89/3.15 thf(zip_derived_cl12248, plain,
% 17.89/3.15 (![X0 : $i, X1 : $i]:
% 17.89/3.15 ((multiply @ (multiply @ X1 @ X1) @
% 17.89/3.15 (multiply @ X1 @ (multiply @ X1 @ X0))) = (X0))),
% 17.89/3.15 inference('demod', [status(thm)],
% 17.89/3.15 [zip_derived_cl8078, zip_derived_cl12195, zip_derived_cl12195,
% 17.89/3.15 zip_derived_cl12195])).
% 17.89/3.15 thf(zip_derived_cl12595, plain,
% 17.89/3.15 (![X0 : $i]:
% 17.89/3.15 ((multiply @ (multiply @ X0 @ X0) @ (multiply @ X0 @ X0)) = (identity))),
% 17.89/3.15 inference('sup+', [status(thm)],
% 17.89/3.15 [zip_derived_cl12195, zip_derived_cl12248])).
% 17.89/3.15 thf(zip_derived_cl12595, plain,
% 17.89/3.15 (![X0 : $i]:
% 17.89/3.15 ((multiply @ (multiply @ X0 @ X0) @ (multiply @ X0 @ X0)) = (identity))),
% 17.89/3.15 inference('sup+', [status(thm)],
% 17.89/3.15 [zip_derived_cl12195, zip_derived_cl12248])).
% 17.89/3.15 thf(zip_derived_cl847, plain,
% 17.89/3.15 (![X0 : $i]:
% 17.89/3.15 ((multiply @ identity @ X0)
% 17.89/3.15 = (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 17.89/3.15 (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 17.89/3.15 (multiply @ X0 @ (multiply @ X0 @ X0)))))),
% 17.89/3.15 inference('demod', [status(thm)], [zip_derived_cl827, zip_derived_cl459])).
% 17.89/3.15 thf(zip_derived_cl12644, plain,
% 17.89/3.15 (![X0 : $i]:
% 17.89/3.15 ((multiply @ identity @ (multiply @ X0 @ X0))
% 17.89/3.15 = (multiply @
% 17.89/3.15 (multiply @ (multiply @ X0 @ X0) @
% 17.89/3.15 (multiply @ (multiply @ X0 @ X0) @ (multiply @ X0 @ X0))) @
% 17.89/3.15 (multiply @
% 17.89/3.15 (multiply @ (multiply @ X0 @ X0) @
% 17.89/3.15 (multiply @ (multiply @ X0 @ X0) @ (multiply @ X0 @ X0))) @
% 17.89/3.15 (multiply @ (multiply @ X0 @ X0) @ identity))))),
% 17.89/3.15 inference('sup+', [status(thm)], [zip_derived_cl12595, zip_derived_cl847])).
% 17.89/3.15 thf(zip_derived_cl12595, plain,
% 17.89/3.15 (![X0 : $i]:
% 17.89/3.15 ((multiply @ (multiply @ X0 @ X0) @ (multiply @ X0 @ X0)) = (identity))),
% 17.89/3.15 inference('sup+', [status(thm)],
% 17.89/3.15 [zip_derived_cl12195, zip_derived_cl12248])).
% 17.89/3.15 thf(zip_derived_cl12195, plain,
% 17.89/3.15 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 17.89/3.15 inference('demod', [status(thm)], [zip_derived_cl12109, zip_derived_cl0])).
% 17.89/3.15 thf(zip_derived_cl12595, plain,
% 17.89/3.15 (![X0 : $i]:
% 17.89/3.15 ((multiply @ (multiply @ X0 @ X0) @ (multiply @ X0 @ X0)) = (identity))),
% 17.89/3.15 inference('sup+', [status(thm)],
% 17.89/3.15 [zip_derived_cl12195, zip_derived_cl12248])).
% 17.89/3.15 thf(zip_derived_cl12195, plain,
% 17.89/3.15 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 17.89/3.15 inference('demod', [status(thm)], [zip_derived_cl12109, zip_derived_cl0])).
% 17.89/3.15 thf(zip_derived_cl12195, plain,
% 17.89/3.15 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 17.89/3.15 inference('demod', [status(thm)], [zip_derived_cl12109, zip_derived_cl0])).
% 17.89/3.15 thf(zip_derived_cl12595, plain,
% 17.89/3.15 (![X0 : $i]:
% 17.89/3.15 ((multiply @ (multiply @ X0 @ X0) @ (multiply @ X0 @ X0)) = (identity))),
% 17.89/3.15 inference('sup+', [status(thm)],
% 17.89/3.15 [zip_derived_cl12195, zip_derived_cl12248])).
% 17.89/3.15 thf(zip_derived_cl12195, plain,
% 17.89/3.15 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 17.89/3.15 inference('demod', [status(thm)], [zip_derived_cl12109, zip_derived_cl0])).
% 17.89/3.15 thf(zip_derived_cl12688, plain,
% 17.89/3.15 (![X0 : $i]:
% 17.89/3.15 ((multiply @ identity @ (multiply @ X0 @ X0)) = (multiply @ X0 @ X0))),
% 17.89/3.15 inference('demod', [status(thm)],
% 17.89/3.15 [zip_derived_cl12644, zip_derived_cl12595,
% 17.89/3.15 zip_derived_cl12195, zip_derived_cl12595,
% 17.89/3.15 zip_derived_cl12195, zip_derived_cl12195,
% 17.89/3.15 zip_derived_cl12595, zip_derived_cl12195])).
% 17.89/3.15 thf(zip_derived_cl9, plain,
% 17.89/3.15 (![X0 : $i, X1 : $i]:
% 17.89/3.15 ((multiply @ identity @
% 17.89/3.15 (multiply @
% 17.89/3.15 (multiply @ identity @ (multiply @ identity @ (multiply @ X0 @ X1))) @
% 17.89/3.15 (multiply @ X1 @ (multiply @ X1 @ X1))))
% 17.89/3.15 = (X0))),
% 17.89/3.15 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 17.89/3.15 thf(zip_derived_cl12741, plain,
% 17.89/3.15 (![X0 : $i]:
% 17.89/3.15 ((multiply @ identity @
% 17.89/3.15 (multiply @ (multiply @ identity @ (multiply @ X0 @ X0)) @
% 17.89/3.15 (multiply @ X0 @ (multiply @ X0 @ X0))))
% 17.89/3.15 = (X0))),
% 17.89/3.15 inference('sup+', [status(thm)], [zip_derived_cl12688, zip_derived_cl9])).
% 17.89/3.15 thf(zip_derived_cl12688, plain,
% 17.89/3.15 (![X0 : $i]:
% 17.89/3.15 ((multiply @ identity @ (multiply @ X0 @ X0)) = (multiply @ X0 @ X0))),
% 17.89/3.15 inference('demod', [status(thm)],
% 17.89/3.15 [zip_derived_cl12644, zip_derived_cl12595,
% 17.89/3.15 zip_derived_cl12195, zip_derived_cl12595,
% 17.89/3.15 zip_derived_cl12195, zip_derived_cl12195,
% 17.89/3.15 zip_derived_cl12595, zip_derived_cl12195])).
% 17.89/3.15 thf(zip_derived_cl12248, plain,
% 17.89/3.15 (![X0 : $i, X1 : $i]:
% 17.89/3.15 ((multiply @ (multiply @ X1 @ X1) @
% 17.89/3.15 (multiply @ X1 @ (multiply @ X1 @ X0))) = (X0))),
% 17.89/3.15 inference('demod', [status(thm)],
% 17.89/3.15 [zip_derived_cl8078, zip_derived_cl12195, zip_derived_cl12195,
% 17.89/3.15 zip_derived_cl12195])).
% 17.89/3.15 thf(zip_derived_cl12788, plain,
% 17.89/3.15 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 17.89/3.15 inference('demod', [status(thm)],
% 17.89/3.15 [zip_derived_cl12741, zip_derived_cl12688, zip_derived_cl12248])).
% 17.89/3.15 thf(zip_derived_cl12896, plain,
% 17.89/3.15 (![X0 : $i, X1 : $i]:
% 17.89/3.15 ((multiply @ (multiply @ X1 @ X1) @ X0)
% 17.89/3.15 = (multiply @ X1 @ (multiply @ X1 @ X0)))),
% 17.89/3.15 inference('demod', [status(thm)],
% 17.89/3.15 [zip_derived_cl12884, zip_derived_cl12595, zip_derived_cl12788])).
% 17.89/3.15 thf(zip_derived_cl12942, plain,
% 17.89/3.15 (![X0 : $i, X1 : $i]:
% 17.89/3.15 ((multiply @ X1 @
% 17.89/3.15 (multiply @ X1 @ (multiply @ X1 @ (multiply @ X1 @ X0)))) = (
% 17.89/3.15 X0))),
% 17.89/3.15 inference('demod', [status(thm)],
% 17.89/3.15 [zip_derived_cl12310, zip_derived_cl12896])).
% 17.89/3.15 thf(zip_derived_cl1885, plain,
% 17.89/3.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.89/3.15 ((multiply @ X2 @
% 17.89/3.15 (multiply @
% 17.89/3.15 (multiply @ X2 @ (multiply @ (multiply @ X2 @ X2) @ X0)) @
% 17.89/3.15 (multiply @ identity @ X1)))
% 17.89/3.15 = (multiply @ identity @
% 17.89/3.15 (multiply @ identity @
% 17.89/3.15 (multiply @ (multiply @ identity @ X0) @ X1))))),
% 17.89/3.15 inference('sup+', [status(thm)], [zip_derived_cl459, zip_derived_cl855])).
% 17.89/3.15 thf(zip_derived_cl12788, plain,
% 17.89/3.15 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 17.89/3.15 inference('demod', [status(thm)],
% 17.89/3.15 [zip_derived_cl12741, zip_derived_cl12688, zip_derived_cl12248])).
% 17.89/3.15 thf(zip_derived_cl12788, plain,
% 17.89/3.15 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 17.89/3.15 inference('demod', [status(thm)],
% 17.89/3.15 [zip_derived_cl12741, zip_derived_cl12688, zip_derived_cl12248])).
% 17.89/3.15 thf(zip_derived_cl12788, plain,
% 17.89/3.15 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 17.89/3.15 inference('demod', [status(thm)],
% 17.89/3.15 [zip_derived_cl12741, zip_derived_cl12688, zip_derived_cl12248])).
% 17.89/3.15 thf(zip_derived_cl12788, plain,
% 17.89/3.15 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 17.89/3.15 inference('demod', [status(thm)],
% 17.89/3.15 [zip_derived_cl12741, zip_derived_cl12688, zip_derived_cl12248])).
% 17.89/3.15 thf(zip_derived_cl12807, plain,
% 17.89/3.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.89/3.15 ((multiply @ X2 @
% 17.89/3.15 (multiply @
% 17.89/3.15 (multiply @ X2 @ (multiply @ (multiply @ X2 @ X2) @ X0)) @ X1))
% 17.89/3.15 = (multiply @ X0 @ X1))),
% 17.89/3.15 inference('demod', [status(thm)],
% 17.89/3.15 [zip_derived_cl1885, zip_derived_cl12788, zip_derived_cl12788,
% 17.89/3.15 zip_derived_cl12788, zip_derived_cl12788])).
% 17.89/3.15 thf(zip_derived_cl12896, plain,
% 17.89/3.15 (![X0 : $i, X1 : $i]:
% 17.89/3.15 ((multiply @ (multiply @ X1 @ X1) @ X0)
% 17.89/3.15 = (multiply @ X1 @ (multiply @ X1 @ X0)))),
% 17.89/3.15 inference('demod', [status(thm)],
% 17.89/3.15 [zip_derived_cl12884, zip_derived_cl12595, zip_derived_cl12788])).
% 17.89/3.15 thf(zip_derived_cl13229, plain,
% 17.89/3.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.89/3.15 ((multiply @ X2 @
% 17.89/3.15 (multiply @
% 17.89/3.15 (multiply @ X2 @ (multiply @ X2 @ (multiply @ X2 @ X0))) @ X1))
% 17.89/3.15 = (multiply @ X0 @ X1))),
% 17.89/3.15 inference('demod', [status(thm)],
% 17.89/3.15 [zip_derived_cl12807, zip_derived_cl12896])).
% 17.89/3.15 thf(zip_derived_cl13247, plain,
% 17.89/3.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.89/3.15 ((multiply @ X2 @ (multiply @ X0 @ X1))
% 17.89/3.15 = (multiply @ (multiply @ X2 @ X0) @ X1))),
% 17.89/3.15 inference('sup+', [status(thm)],
% 17.89/3.15 [zip_derived_cl12942, zip_derived_cl13229])).
% 17.89/3.15 thf(zip_derived_cl13293, plain,
% 17.89/3.15 (((multiply @ a @ (multiply @ b @ c))
% 17.89/3.15 != (multiply @ a @ (multiply @ b @ c)))),
% 17.89/3.15 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl13247])).
% 17.89/3.15 thf(zip_derived_cl13294, plain, ($false),
% 17.89/3.15 inference('simplify', [status(thm)], [zip_derived_cl13293])).
% 17.89/3.15
% 17.89/3.15 % SZS output end Refutation
% 17.89/3.15
% 17.89/3.15
% 17.89/3.15 % Terminating...
% 18.46/3.26 % Runner terminated.
% 18.46/3.27 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------