%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP119-1 : TPTP v9.2.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.ImJtmL000s true
% Computer : n012.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 Oct 2 04:35:39 PM UTC 2025
% Result : Unsatisfiable 111.32s 16.60s
% Output : Refutation 111.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP119-1 : TPTP v9.2.0. Bugfixed v1.2.1.
% 0.06/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.ImJtmL000s true
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 1 14:08:38 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Running portfolio for 300 s
% 0.12/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.35 % Number of cores: 8
% 0.12/0.35 % Python version: Python 3.6.8
% 0.12/0.35 % Running in FO mode
% 0.50/0.61 % Total configuration time : 435
% 0.50/0.61 % Estimated wc time : 1092
% 0.50/0.61 % Estimated cpu time (7 cpus) : 156.0
% 0.52/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.53/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.53/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.53/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.53/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.53/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.53/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 111.32/16.60 % Solved by fo/fo7.sh.
% 111.32/16.60 % done 750 iterations in 15.826s
% 111.32/16.60 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 111.32/16.60 % SZS output start Refutation
% 111.32/16.60 thf(a_type, type, a: $i).
% 111.32/16.60 thf(identity_type, type, identity: $i).
% 111.32/16.60 thf(multiply_type, type, multiply: $i > $i > $i).
% 111.32/16.60 thf(prove_order4, conjecture,
% 111.32/16.60 (( multiply @ a @ ( multiply @ a @ ( multiply @ a @ a ) ) ) = ( identity ))).
% 111.32/16.60 thf(zf_stmt_0, negated_conjecture,
% 111.32/16.60 (( multiply @ a @ ( multiply @ a @ ( multiply @ a @ a ) ) ) != ( identity )),
% 111.32/16.60 inference('cnf.neg', [status(esa)], [prove_order4])).
% 111.32/16.60 thf(zip_derived_cl2, plain,
% 111.32/16.60 (((multiply @ a @ (multiply @ a @ (multiply @ a @ a))) != (identity))),
% 111.32/16.60 inference('cnf', [status(esa)], [zf_stmt_0])).
% 111.32/16.60 thf(single_axiom2, axiom,
% 111.32/16.60 (( multiply @ identity @ identity ) = ( identity ))).
% 111.32/16.60 thf(zip_derived_cl1, plain,
% 111.32/16.60 (((multiply @ identity @ identity) = (identity))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom2])).
% 111.32/16.60 thf(single_axiom, axiom,
% 111.32/16.60 (( multiply @
% 111.32/16.60 Y @
% 111.32/16.60 ( multiply @
% 111.32/16.60 ( multiply @
% 111.32/16.60 Y @ ( multiply @ ( multiply @ Y @ Y ) @ ( multiply @ X @ Z ) ) ) @
% 111.32/16.60 ( multiply @ Z @ ( multiply @ Z @ Z ) ) ) ) =
% 111.32/16.60 ( X ))).
% 111.32/16.60 thf(zip_derived_cl0, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i, X2 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ X2))) @
% 111.32/16.60 (multiply @ X2 @ (multiply @ X2 @ X2))))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom])).
% 111.32/16.60 thf(zip_derived_cl5, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ identity))) @
% 111.32/16.60 (multiply @ identity @ identity)))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 111.32/16.60 thf(zip_derived_cl1, plain,
% 111.32/16.60 (((multiply @ identity @ identity) = (identity))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom2])).
% 111.32/16.60 thf(zip_derived_cl10, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ identity))) @
% 111.32/16.60 identity))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl1])).
% 111.32/16.60 thf(zip_derived_cl1, plain,
% 111.32/16.60 (((multiply @ identity @ identity) = (identity))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom2])).
% 111.32/16.60 thf(zip_derived_cl10, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ identity))) @
% 111.32/16.60 identity))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl1])).
% 111.32/16.60 thf(zip_derived_cl23, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity))) @
% 111.32/16.60 identity))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl10])).
% 111.32/16.60 thf(zip_derived_cl23, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity))) @
% 111.32/16.60 identity))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl10])).
% 111.32/16.60 thf(zip_derived_cl26, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ identity @ X0) @ identity))
% 111.32/16.60 = (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity))))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl23, zip_derived_cl23])).
% 111.32/16.60 thf(zip_derived_cl26, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ identity @ X0) @ identity))
% 111.32/16.60 = (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity))))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl23, zip_derived_cl23])).
% 111.32/16.60 thf(zip_derived_cl45, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity))) @
% 111.32/16.60 identity))
% 111.32/16.60 = (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ (multiply @ identity @ X0) @ identity) @ identity))))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl26])).
% 111.32/16.60 thf(zip_derived_cl23, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity))) @
% 111.32/16.60 identity))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl10])).
% 111.32/16.60 thf(zip_derived_cl50, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((X0)
% 111.32/16.60 = (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ (multiply @ identity @ X0) @ identity) @ identity))))),
% 111.32/16.60 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl23])).
% 111.32/16.60 thf(zip_derived_cl23, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity))) @
% 111.32/16.60 identity))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl10])).
% 111.32/16.60 thf(zip_derived_cl60, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @ (multiply @ X0 @ identity))
% 111.32/16.60 = (multiply @ (multiply @ identity @ X0) @ identity))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl23])).
% 111.32/16.60 thf(zip_derived_cl10, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ identity))) @
% 111.32/16.60 identity))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl1])).
% 111.32/16.60 thf(zip_derived_cl77, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity)))) @
% 111.32/16.60 identity))
% 111.32/16.60 = (multiply @ identity @ X0))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl60, zip_derived_cl10])).
% 111.32/16.60 thf(zip_derived_cl158, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @ (multiply @ (multiply @ X1 @ X1) @ X0)) @ identity))
% 111.32/16.60 = (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ identity @ identity) @
% 111.32/16.60 (multiply @ X0 @ identity)))))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl77])).
% 111.32/16.60 thf(zip_derived_cl1, plain,
% 111.32/16.60 (((multiply @ identity @ identity) = (identity))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom2])).
% 111.32/16.60 thf(zip_derived_cl166, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @ (multiply @ (multiply @ X1 @ X1) @ X0)) @ identity))
% 111.32/16.60 = (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity)))))),
% 111.32/16.60 inference('demod', [status(thm)], [zip_derived_cl158, zip_derived_cl1])).
% 111.32/16.60 thf(zip_derived_cl0, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i, X2 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ X2))) @
% 111.32/16.60 (multiply @ X2 @ (multiply @ X2 @ X2))))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom])).
% 111.32/16.60 thf(zip_derived_cl77, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity)))) @
% 111.32/16.60 identity))
% 111.32/16.60 = (multiply @ identity @ X0))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl60, zip_derived_cl10])).
% 111.32/16.60 thf(zip_derived_cl77, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity)))) @
% 111.32/16.60 identity))
% 111.32/16.60 = (multiply @ identity @ X0))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl60, zip_derived_cl10])).
% 111.32/16.60 thf(zip_derived_cl160, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @ (multiply @ identity @ X0))) @
% 111.32/16.60 identity))
% 111.32/16.60 = (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ identity @ identity) @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity))))))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl77, zip_derived_cl77])).
% 111.32/16.60 thf(zip_derived_cl1, plain,
% 111.32/16.60 (((multiply @ identity @ identity) = (identity))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom2])).
% 111.32/16.60 thf(zip_derived_cl168, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @ (multiply @ identity @ X0))) @
% 111.32/16.60 identity))
% 111.32/16.60 = (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity))))))),
% 111.32/16.60 inference('demod', [status(thm)], [zip_derived_cl160, zip_derived_cl1])).
% 111.32/16.60 thf(zip_derived_cl10, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ identity))) @
% 111.32/16.60 identity))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl1])).
% 111.32/16.60 thf(zip_derived_cl10, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ identity))) @
% 111.32/16.60 identity))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl1])).
% 111.32/16.60 thf(zip_derived_cl19, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ X1 @ (multiply @ (multiply @ X1 @ X0) @ identity))
% 111.32/16.60 = (multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X1 @ X1)) @
% 111.32/16.60 (multiply @ X0 @ identity))))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl10])).
% 111.32/16.60 thf(zip_derived_cl10, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ identity))) @
% 111.32/16.60 identity))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl1])).
% 111.32/16.60 thf(zip_derived_cl392, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @ (multiply @ (multiply @ X1 @ X0) @ identity)) @
% 111.32/16.60 identity))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl10])).
% 111.32/16.60 thf(zip_derived_cl492, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity))))) @
% 111.32/16.60 identity)) @
% 111.32/16.60 identity))
% 111.32/16.60 = (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @ (multiply @ identity @ X0))) @
% 111.32/16.60 identity))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl168, zip_derived_cl392])).
% 111.32/16.60 thf(zip_derived_cl60, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @ (multiply @ X0 @ identity))
% 111.32/16.60 = (multiply @ (multiply @ identity @ X0) @ identity))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl23])).
% 111.32/16.60 thf(zip_derived_cl60, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @ (multiply @ X0 @ identity))
% 111.32/16.60 = (multiply @ (multiply @ identity @ X0) @ identity))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl23])).
% 111.32/16.60 thf(zip_derived_cl10, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ identity))) @
% 111.32/16.60 identity))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl1])).
% 111.32/16.60 thf(zip_derived_cl50, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((X0)
% 111.32/16.60 = (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ (multiply @ identity @ X0) @ identity) @ identity))))),
% 111.32/16.60 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl23])).
% 111.32/16.60 thf(zip_derived_cl62, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ identity @ identity) @
% 111.32/16.60 (multiply @ X0 @ identity))) @
% 111.32/16.60 identity)
% 111.32/16.60 = (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity))))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl50])).
% 111.32/16.60 thf(zip_derived_cl1, plain,
% 111.32/16.60 (((multiply @ identity @ identity) = (identity))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom2])).
% 111.32/16.60 thf(zip_derived_cl69, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity))) @
% 111.32/16.60 identity)
% 111.32/16.60 = (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity))))),
% 111.32/16.60 inference('demod', [status(thm)], [zip_derived_cl62, zip_derived_cl1])).
% 111.32/16.60 thf(zip_derived_cl26, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ identity @ X0) @ identity))
% 111.32/16.60 = (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity))))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl23, zip_derived_cl23])).
% 111.32/16.60 thf(zip_derived_cl10, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ identity))) @
% 111.32/16.60 identity))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl1])).
% 111.32/16.60 thf(zip_derived_cl36, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ (multiply @ identity @ identity) @
% 111.32/16.60 (multiply @ X0 @ identity)) @
% 111.32/16.60 identity)))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl10])).
% 111.32/16.60 thf(zip_derived_cl1, plain,
% 111.32/16.60 (((multiply @ identity @ identity) = (identity))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom2])).
% 111.32/16.60 thf(zip_derived_cl26, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ identity @ X0) @ identity))
% 111.32/16.60 = (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity))))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl23, zip_derived_cl23])).
% 111.32/16.60 thf(zip_derived_cl53, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity))))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl36, zip_derived_cl1, zip_derived_cl26])).
% 111.32/16.60 thf(zip_derived_cl514, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @ (multiply @ X1 @ (multiply @ identity @ X0)) @ identity))
% 111.32/16.60 = (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @ (multiply @ identity @ X0))) @
% 111.32/16.60 identity))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl492, zip_derived_cl60, zip_derived_cl60,
% 111.32/16.60 zip_derived_cl69, zip_derived_cl53])).
% 111.32/16.60 thf(zip_derived_cl613, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i, X2 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ X2 @ X2) @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X2 @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ identity @ identity) @
% 111.32/16.60 (multiply @ X0 @ X1))) @
% 111.32/16.60 (multiply @ X1 @ (multiply @ X1 @ X1))))) @
% 111.32/16.60 identity))
% 111.32/16.60 = (multiply @
% 111.32/16.60 (multiply @ X2 @ (multiply @ (multiply @ X2 @ X2) @ X0)) @
% 111.32/16.60 identity))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl514])).
% 111.32/16.60 thf(zip_derived_cl1, plain,
% 111.32/16.60 (((multiply @ identity @ identity) = (identity))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom2])).
% 111.32/16.60 thf(zip_derived_cl1, plain,
% 111.32/16.60 (((multiply @ identity @ identity) = (identity))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom2])).
% 111.32/16.60 thf(zip_derived_cl0, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i, X2 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ X2))) @
% 111.32/16.60 (multiply @ X2 @ (multiply @ X2 @ X2))))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom])).
% 111.32/16.60 thf(zip_derived_cl9, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ identity @ (multiply @ identity @ (multiply @ X0 @ X1))) @
% 111.32/16.60 (multiply @ X1 @ (multiply @ X1 @ X1))))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 111.32/16.60 thf(zip_derived_cl622, plain,
% 111.32/16.60 (![X0 : $i, X2 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ X2 @ X2) @
% 111.32/16.60 (multiply @ (multiply @ X2 @ X0) @ identity))
% 111.32/16.60 = (multiply @
% 111.32/16.60 (multiply @ X2 @ (multiply @ (multiply @ X2 @ X2) @ X0)) @
% 111.32/16.60 identity))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl613, zip_derived_cl1, zip_derived_cl9])).
% 111.32/16.60 thf(zip_derived_cl893, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X0) @ identity)))
% 111.32/16.60 = (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity)))))),
% 111.32/16.60 inference('demod', [status(thm)], [zip_derived_cl166, zip_derived_cl622])).
% 111.32/16.60 thf(zip_derived_cl60, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @ (multiply @ X0 @ identity))
% 111.32/16.60 = (multiply @ (multiply @ identity @ X0) @ identity))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl23])).
% 111.32/16.60 thf(zip_derived_cl901, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity))) @
% 111.32/16.60 identity))
% 111.32/16.60 = (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X0) @ identity))) @
% 111.32/16.60 identity))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl893, zip_derived_cl60])).
% 111.32/16.60 thf(zip_derived_cl69, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity))) @
% 111.32/16.60 identity)
% 111.32/16.60 = (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity))))),
% 111.32/16.60 inference('demod', [status(thm)], [zip_derived_cl62, zip_derived_cl1])).
% 111.32/16.60 thf(zip_derived_cl53, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity))))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl36, zip_derived_cl1, zip_derived_cl26])).
% 111.32/16.60 thf(zip_derived_cl981, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((X0)
% 111.32/16.60 = (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X0) @ identity))) @
% 111.32/16.60 identity))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl901, zip_derived_cl69, zip_derived_cl53])).
% 111.32/16.60 thf(zip_derived_cl53, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity))))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl36, zip_derived_cl1, zip_derived_cl26])).
% 111.32/16.60 thf(zip_derived_cl77, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity)))) @
% 111.32/16.60 identity))
% 111.32/16.60 = (multiply @ identity @ X0))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl60, zip_derived_cl10])).
% 111.32/16.60 thf(zip_derived_cl514, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @ (multiply @ X1 @ (multiply @ identity @ X0)) @ identity))
% 111.32/16.60 = (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @ (multiply @ identity @ X0))) @
% 111.32/16.60 identity))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl492, zip_derived_cl60, zip_derived_cl60,
% 111.32/16.60 zip_derived_cl69, zip_derived_cl53])).
% 111.32/16.60 thf(zip_derived_cl597, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity))) @
% 111.32/16.60 identity)))
% 111.32/16.60 = (multiply @ identity @ X0))),
% 111.32/16.60 inference('demod', [status(thm)], [zip_derived_cl77, zip_derived_cl514])).
% 111.32/16.60 thf(zip_derived_cl893, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X0) @ identity)))
% 111.32/16.60 = (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity)))))),
% 111.32/16.60 inference('demod', [status(thm)], [zip_derived_cl166, zip_derived_cl622])).
% 111.32/16.60 thf(zip_derived_cl893, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X0) @ identity)))
% 111.32/16.60 = (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity)))))),
% 111.32/16.60 inference('demod', [status(thm)], [zip_derived_cl166, zip_derived_cl622])).
% 111.32/16.60 thf(zip_derived_cl622, plain,
% 111.32/16.60 (![X0 : $i, X2 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ X2 @ X2) @
% 111.32/16.60 (multiply @ (multiply @ X2 @ X0) @ identity))
% 111.32/16.60 = (multiply @
% 111.32/16.60 (multiply @ X2 @ (multiply @ (multiply @ X2 @ X2) @ X0)) @
% 111.32/16.60 identity))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl613, zip_derived_cl1, zip_derived_cl9])).
% 111.32/16.60 thf(zip_derived_cl915, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @ (multiply @ (multiply @ X1 @ X0) @ identity)) @
% 111.32/16.60 identity))
% 111.32/16.60 = (multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity)))) @
% 111.32/16.60 identity))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl893, zip_derived_cl622])).
% 111.32/16.60 thf(zip_derived_cl392, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @ (multiply @ (multiply @ X1 @ X0) @ identity)) @
% 111.32/16.60 identity))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl10])).
% 111.32/16.60 thf(zip_derived_cl989, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((X0)
% 111.32/16.60 = (multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity)))) @
% 111.32/16.60 identity))),
% 111.32/16.60 inference('demod', [status(thm)], [zip_derived_cl915, zip_derived_cl392])).
% 111.32/16.60 thf(zip_derived_cl989, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((X0)
% 111.32/16.60 = (multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity)))) @
% 111.32/16.60 identity))),
% 111.32/16.60 inference('demod', [status(thm)], [zip_derived_cl915, zip_derived_cl392])).
% 111.32/16.60 thf(zip_derived_cl1012, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity))))
% 111.32/16.60 = (multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ identity @ X0))) @
% 111.32/16.60 identity))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl989, zip_derived_cl989])).
% 111.32/16.60 thf(zip_derived_cl1067, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ identity @ (multiply @ X0 @ identity)) @
% 111.32/16.60 identity))))
% 111.32/16.60 = (multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X0) @ identity)))) @
% 111.32/16.60 identity))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl893, zip_derived_cl1012])).
% 111.32/16.60 thf(zip_derived_cl60, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @ (multiply @ X0 @ identity))
% 111.32/16.60 = (multiply @ (multiply @ identity @ X0) @ identity))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl23])).
% 111.32/16.60 thf(zip_derived_cl53, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity))))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl36, zip_derived_cl1, zip_derived_cl26])).
% 111.32/16.60 thf(zip_derived_cl1083, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ identity @ X0)
% 111.32/16.60 = (multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X0) @ identity)))) @
% 111.32/16.60 identity))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl1067, zip_derived_cl60, zip_derived_cl53])).
% 111.32/16.60 thf(zip_derived_cl1295, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity)))
% 111.32/16.60 = (multiply @ (multiply @ identity @ (multiply @ identity @ X0)) @
% 111.32/16.60 identity))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl597, zip_derived_cl1083])).
% 111.32/16.60 thf(zip_derived_cl53, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity))))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl36, zip_derived_cl1, zip_derived_cl26])).
% 111.32/16.60 thf(zip_derived_cl0, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i, X2 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ X2))) @
% 111.32/16.60 (multiply @ X2 @ (multiply @ X2 @ X2))))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom])).
% 111.32/16.60 thf(zip_derived_cl50, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((X0)
% 111.32/16.60 = (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ (multiply @ identity @ X0) @ identity) @ identity))))),
% 111.32/16.60 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl23])).
% 111.32/16.60 thf(zip_derived_cl61, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ identity @ identity) @ (multiply @ X0 @ X1))) @
% 111.32/16.60 (multiply @ X1 @ (multiply @ X1 @ X1)))
% 111.32/16.60 = (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity))))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl50])).
% 111.32/16.60 thf(zip_derived_cl1, plain,
% 111.32/16.60 (((multiply @ identity @ identity) = (identity))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom2])).
% 111.32/16.60 thf(zip_derived_cl68, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @
% 111.32/16.60 (multiply @ identity @ (multiply @ identity @ (multiply @ X0 @ X1))) @
% 111.32/16.60 (multiply @ X1 @ (multiply @ X1 @ X1)))
% 111.32/16.60 = (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity))))),
% 111.32/16.60 inference('demod', [status(thm)], [zip_derived_cl61, zip_derived_cl1])).
% 111.32/16.60 thf(zip_derived_cl3321, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ X0 @
% 111.32/16.60 (multiply @ (multiply @ (multiply @ X0 @ identity) @ identity) @
% 111.32/16.60 (multiply @ (multiply @ (multiply @ X0 @ identity) @ identity) @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity))))
% 111.32/16.60 = (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ identity @ identity) @ identity))))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl53, zip_derived_cl68])).
% 111.32/16.60 thf(zip_derived_cl1, plain,
% 111.32/16.60 (((multiply @ identity @ identity) = (identity))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom2])).
% 111.32/16.60 thf(zip_derived_cl1, plain,
% 111.32/16.60 (((multiply @ identity @ identity) = (identity))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom2])).
% 111.32/16.60 thf(zip_derived_cl1, plain,
% 111.32/16.60 (((multiply @ identity @ identity) = (identity))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom2])).
% 111.32/16.60 thf(zip_derived_cl1, plain,
% 111.32/16.60 (((multiply @ identity @ identity) = (identity))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom2])).
% 111.32/16.60 thf(zip_derived_cl3404, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ X0 @
% 111.32/16.60 (multiply @ (multiply @ (multiply @ X0 @ identity) @ identity) @
% 111.32/16.60 (multiply @ (multiply @ (multiply @ X0 @ identity) @ identity) @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity))))
% 111.32/16.60 = (identity))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl3321, zip_derived_cl1, zip_derived_cl1,
% 111.32/16.60 zip_derived_cl1, zip_derived_cl1])).
% 111.32/16.60 thf(zip_derived_cl622, plain,
% 111.32/16.60 (![X0 : $i, X2 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ X2 @ X2) @
% 111.32/16.60 (multiply @ (multiply @ X2 @ X0) @ identity))
% 111.32/16.60 = (multiply @
% 111.32/16.60 (multiply @ X2 @ (multiply @ (multiply @ X2 @ X2) @ X0)) @
% 111.32/16.60 identity))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl613, zip_derived_cl1, zip_derived_cl9])).
% 111.32/16.60 thf(zip_derived_cl981, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((X0)
% 111.32/16.60 = (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X0) @ identity))) @
% 111.32/16.60 identity))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl901, zip_derived_cl69, zip_derived_cl53])).
% 111.32/16.60 thf(zip_derived_cl1145, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ X1 @ X1) @ X0)
% 111.32/16.60 = (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X0) @ identity)))) @
% 111.32/16.60 identity))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl622, zip_derived_cl981])).
% 111.32/16.60 thf(zip_derived_cl3745, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ X0 @ X0) @
% 111.32/16.60 (multiply @ (multiply @ (multiply @ X0 @ identity) @ identity) @
% 111.32/16.60 (multiply @ (multiply @ (multiply @ X0 @ identity) @ identity) @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity))))
% 111.32/16.60 = (multiply @
% 111.32/16.60 (multiply @ X0 @
% 111.32/16.60 (multiply @ (multiply @ X0 @ X0) @
% 111.32/16.60 (multiply @ (multiply @ X0 @ X0) @
% 111.32/16.60 (multiply @ identity @ identity)))) @
% 111.32/16.60 identity))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl3404, zip_derived_cl1145])).
% 111.32/16.60 thf(zip_derived_cl1, plain,
% 111.32/16.60 (((multiply @ identity @ identity) = (identity))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom2])).
% 111.32/16.60 thf(zip_derived_cl1145, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ X1 @ X1) @ X0)
% 111.32/16.60 = (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X0) @ identity)))) @
% 111.32/16.60 identity))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl622, zip_derived_cl981])).
% 111.32/16.60 thf(zip_derived_cl981, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((X0)
% 111.32/16.60 = (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X0) @ identity))) @
% 111.32/16.60 identity))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl901, zip_derived_cl69, zip_derived_cl53])).
% 111.32/16.60 thf(zip_derived_cl1833, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X0) @ identity)))
% 111.32/16.60 = (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @ X0))) @
% 111.32/16.60 identity))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl1145, zip_derived_cl981])).
% 111.32/16.60 thf(zip_derived_cl622, plain,
% 111.32/16.60 (![X0 : $i, X2 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ X2 @ X2) @
% 111.32/16.60 (multiply @ (multiply @ X2 @ X0) @ identity))
% 111.32/16.60 = (multiply @
% 111.32/16.60 (multiply @ X2 @ (multiply @ (multiply @ X2 @ X2) @ X0)) @
% 111.32/16.60 identity))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl613, zip_derived_cl1, zip_derived_cl9])).
% 111.32/16.60 thf(zip_derived_cl392, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @ (multiply @ (multiply @ X1 @ X0) @ identity)) @
% 111.32/16.60 identity))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl10])).
% 111.32/16.60 thf(zip_derived_cl649, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ X0 @ X0) @
% 111.32/16.60 (multiply @ (multiply @ X0 @ X0) @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity)))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl622, zip_derived_cl392])).
% 111.32/16.60 thf(zip_derived_cl3900, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ X0 @ X0) @
% 111.32/16.60 (multiply @ (multiply @ (multiply @ X0 @ identity) @ identity) @
% 111.32/16.60 (multiply @ (multiply @ (multiply @ X0 @ identity) @ identity) @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity))))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl3745, zip_derived_cl1, zip_derived_cl1833,
% 111.32/16.60 zip_derived_cl649])).
% 111.32/16.60 thf(zip_derived_cl1, plain,
% 111.32/16.60 (((multiply @ identity @ identity) = (identity))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom2])).
% 111.32/16.60 thf(zip_derived_cl60, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @ (multiply @ X0 @ identity))
% 111.32/16.60 = (multiply @ (multiply @ identity @ X0) @ identity))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl23])).
% 111.32/16.60 thf(zip_derived_cl68, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @
% 111.32/16.60 (multiply @ identity @ (multiply @ identity @ (multiply @ X0 @ X1))) @
% 111.32/16.60 (multiply @ X1 @ (multiply @ X1 @ X1)))
% 111.32/16.60 = (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity))))),
% 111.32/16.60 inference('demod', [status(thm)], [zip_derived_cl61, zip_derived_cl1])).
% 111.32/16.60 thf(zip_derived_cl3387, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ (multiply @ identity @ X0) @ X1))) @
% 111.32/16.60 (multiply @ X1 @ (multiply @ X1 @ X1)))
% 111.32/16.60 = (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity)) @ identity))))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl60, zip_derived_cl68])).
% 111.32/16.60 thf(zip_derived_cl60, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @ (multiply @ X0 @ identity))
% 111.32/16.60 = (multiply @ (multiply @ identity @ X0) @ identity))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl23])).
% 111.32/16.60 thf(zip_derived_cl53, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity))))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl36, zip_derived_cl1, zip_derived_cl26])).
% 111.32/16.60 thf(zip_derived_cl3449, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ (multiply @ identity @ X0) @ X1))) @
% 111.32/16.60 (multiply @ X1 @ (multiply @ X1 @ X1))) = (X0))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl3387, zip_derived_cl60, zip_derived_cl53])).
% 111.32/16.60 thf(zip_derived_cl3601, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ identity @ X0))) @
% 111.32/16.60 (multiply @ X0 @ (multiply @ X0 @ X0))) = (identity))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl3449])).
% 111.32/16.60 thf(zip_derived_cl0, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i, X2 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ X2))) @
% 111.32/16.60 (multiply @ X2 @ (multiply @ X2 @ X2))))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom])).
% 111.32/16.60 thf(zip_derived_cl68, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @
% 111.32/16.60 (multiply @ identity @ (multiply @ identity @ (multiply @ X0 @ X1))) @
% 111.32/16.60 (multiply @ X1 @ (multiply @ X1 @ X1)))
% 111.32/16.60 = (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity))))),
% 111.32/16.60 inference('demod', [status(thm)], [zip_derived_cl61, zip_derived_cl1])).
% 111.32/16.60 thf(zip_derived_cl3322, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ identity @ X0) @
% 111.32/16.60 (multiply @ (multiply @ X1 @ (multiply @ X1 @ X1)) @
% 111.32/16.60 (multiply @ (multiply @ X1 @ (multiply @ X1 @ X1)) @
% 111.32/16.60 (multiply @ X1 @ (multiply @ X1 @ X1)))))
% 111.32/16.60 = (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ identity @ identity) @
% 111.32/16.60 (multiply @ X0 @ X1))) @
% 111.32/16.60 identity) @
% 111.32/16.60 identity))))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl68])).
% 111.32/16.60 thf(zip_derived_cl1, plain,
% 111.32/16.60 (((multiply @ identity @ identity) = (identity))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom2])).
% 111.32/16.60 thf(zip_derived_cl1295, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity)))
% 111.32/16.60 = (multiply @ (multiply @ identity @ (multiply @ identity @ X0)) @
% 111.32/16.60 identity))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl597, zip_derived_cl1083])).
% 111.32/16.60 thf(zip_derived_cl1295, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity)))
% 111.32/16.60 = (multiply @ (multiply @ identity @ (multiply @ identity @ X0)) @
% 111.32/16.60 identity))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl597, zip_derived_cl1083])).
% 111.32/16.60 thf(zip_derived_cl53, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity))))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl36, zip_derived_cl1, zip_derived_cl26])).
% 111.32/16.60 thf(zip_derived_cl3405, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ identity @ X0) @
% 111.32/16.60 (multiply @ (multiply @ X1 @ (multiply @ X1 @ X1)) @
% 111.32/16.60 (multiply @ (multiply @ X1 @ (multiply @ X1 @ X1)) @
% 111.32/16.60 (multiply @ X1 @ (multiply @ X1 @ X1)))))
% 111.32/16.60 = (multiply @ identity @ (multiply @ X0 @ X1)))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl3322, zip_derived_cl1, zip_derived_cl1295,
% 111.32/16.60 zip_derived_cl1295, zip_derived_cl53])).
% 111.32/16.60 thf(zip_derived_cl8665, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((identity)
% 111.32/16.60 = (multiply @ identity @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ (multiply @ X0 @ X0)))) @
% 111.32/16.60 X0)))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl3601, zip_derived_cl3405])).
% 111.32/16.60 thf(zip_derived_cl392, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @ (multiply @ (multiply @ X1 @ X0) @ identity)) @
% 111.32/16.60 identity))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl10])).
% 111.32/16.60 thf(zip_derived_cl8753, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ identity @ identity) @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ identity @ (multiply @ identity @ identity)) @ identity))
% 111.32/16.60 = (multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ (multiply @ X0 @ X0)))) @
% 111.32/16.60 X0))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl8665, zip_derived_cl392])).
% 111.32/16.60 thf(zip_derived_cl1, plain,
% 111.32/16.60 (((multiply @ identity @ identity) = (identity))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom2])).
% 111.32/16.60 thf(zip_derived_cl1, plain,
% 111.32/16.60 (((multiply @ identity @ identity) = (identity))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom2])).
% 111.32/16.60 thf(zip_derived_cl1, plain,
% 111.32/16.60 (((multiply @ identity @ identity) = (identity))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom2])).
% 111.32/16.60 thf(zip_derived_cl1, plain,
% 111.32/16.60 (((multiply @ identity @ identity) = (identity))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom2])).
% 111.32/16.60 thf(zip_derived_cl1, plain,
% 111.32/16.60 (((multiply @ identity @ identity) = (identity))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom2])).
% 111.32/16.60 thf(zip_derived_cl8829, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((identity)
% 111.32/16.60 = (multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ (multiply @ X0 @ X0)))) @
% 111.32/16.60 X0))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl8753, zip_derived_cl1, zip_derived_cl1,
% 111.32/16.60 zip_derived_cl1, zip_derived_cl1, zip_derived_cl1])).
% 111.32/16.60 thf(zip_derived_cl3449, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ (multiply @ identity @ X0) @ X1))) @
% 111.32/16.60 (multiply @ X1 @ (multiply @ X1 @ X1))) = (X0))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl3387, zip_derived_cl60, zip_derived_cl53])).
% 111.32/16.60 thf(zip_derived_cl3405, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ identity @ X0) @
% 111.32/16.60 (multiply @ (multiply @ X1 @ (multiply @ X1 @ X1)) @
% 111.32/16.60 (multiply @ (multiply @ X1 @ (multiply @ X1 @ X1)) @
% 111.32/16.60 (multiply @ X1 @ (multiply @ X1 @ X1)))))
% 111.32/16.60 = (multiply @ identity @ (multiply @ X0 @ X1)))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl3322, zip_derived_cl1, zip_derived_cl1295,
% 111.32/16.60 zip_derived_cl1295, zip_derived_cl53])).
% 111.32/16.60 thf(zip_derived_cl8666, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((X0)
% 111.32/16.60 = (multiply @ identity @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ identity @ X0) @
% 111.32/16.60 (multiply @ X1 @ (multiply @ X1 @ X1)))) @
% 111.32/16.60 X1)))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl3449, zip_derived_cl3405])).
% 111.32/16.60 thf(zip_derived_cl392, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @ (multiply @ (multiply @ X1 @ X0) @ identity)) @
% 111.32/16.60 identity))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl10])).
% 111.32/16.60 thf(zip_derived_cl9483, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ identity @ identity) @
% 111.32/16.60 (multiply @ (multiply @ identity @ (multiply @ X0 @ identity)) @
% 111.32/16.60 identity))
% 111.32/16.60 = (multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ identity @ X0) @
% 111.32/16.60 (multiply @ X1 @ (multiply @ X1 @ X1)))) @
% 111.32/16.60 X1))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl8666, zip_derived_cl392])).
% 111.32/16.60 thf(zip_derived_cl1, plain,
% 111.32/16.60 (((multiply @ identity @ identity) = (identity))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom2])).
% 111.32/16.60 thf(zip_derived_cl60, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @ (multiply @ X0 @ identity))
% 111.32/16.60 = (multiply @ (multiply @ identity @ X0) @ identity))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl23])).
% 111.32/16.60 thf(zip_derived_cl9622, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity)))
% 111.32/16.60 = (multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ identity @ X0) @
% 111.32/16.60 (multiply @ X1 @ (multiply @ X1 @ X1)))) @
% 111.32/16.60 X1))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl9483, zip_derived_cl1, zip_derived_cl60])).
% 111.32/16.60 thf(zip_derived_cl9983, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 111.32/16.60 (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 111.32/16.60 (multiply @ X0 @ (multiply @ X0 @ X0))))) @
% 111.32/16.60 identity) @
% 111.32/16.60 identity)))
% 111.32/16.60 = (multiply @ (multiply @ identity @ identity) @ X0))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl8829, zip_derived_cl9622])).
% 111.32/16.60 thf(zip_derived_cl60, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @ (multiply @ X0 @ identity))
% 111.32/16.60 = (multiply @ (multiply @ identity @ X0) @ identity))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl23])).
% 111.32/16.60 thf(zip_derived_cl60, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @ (multiply @ X0 @ identity))
% 111.32/16.60 = (multiply @ (multiply @ identity @ X0) @ identity))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl23])).
% 111.32/16.60 thf(zip_derived_cl53, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity))))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl36, zip_derived_cl1, zip_derived_cl26])).
% 111.32/16.60 thf(zip_derived_cl1, plain,
% 111.32/16.60 (((multiply @ identity @ identity) = (identity))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom2])).
% 111.32/16.60 thf(zip_derived_cl10025, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 111.32/16.60 (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 111.32/16.60 (multiply @ X0 @ (multiply @ X0 @ X0))))
% 111.32/16.60 = (multiply @ identity @ X0))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl9983, zip_derived_cl60, zip_derived_cl60,
% 111.32/16.60 zip_derived_cl53, zip_derived_cl1])).
% 111.32/16.60 thf(zip_derived_cl0, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i, X2 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ X2))) @
% 111.32/16.60 (multiply @ X2 @ (multiply @ X2 @ X2))))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom])).
% 111.32/16.60 thf(zip_derived_cl10219, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i, X2 : $i]:
% 111.32/16.60 ((multiply @ X2 @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X2 @
% 111.32/16.60 (multiply @ (multiply @ X2 @ X2) @
% 111.32/16.60 (multiply @ X1 @ (multiply @ X0 @ (multiply @ X0 @ X0))))) @
% 111.32/16.60 (multiply @ identity @ X0)))
% 111.32/16.60 = (X1))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl10025, zip_derived_cl0])).
% 111.32/16.60 thf(zip_derived_cl12242, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @ (multiply @ (multiply @ X1 @ X1) @ X0)) @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity))))
% 111.32/16.60 = (multiply @ X0 @ X0))),
% 111.32/16.60 inference('sup+', [status(thm)],
% 111.32/16.60 [zip_derived_cl3900, zip_derived_cl10219])).
% 111.32/16.60 thf(zip_derived_cl18909, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @ identity @ (multiply @ identity @ X0)))) @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity))) @
% 111.32/16.60 identity))))
% 111.32/16.60 = (multiply @ (multiply @ identity @ (multiply @ identity @ X0)) @
% 111.32/16.60 (multiply @ identity @ (multiply @ identity @ X0))))),
% 111.32/16.60 inference('sup+', [status(thm)],
% 111.32/16.60 [zip_derived_cl1295, zip_derived_cl12242])).
% 111.32/16.60 thf(zip_derived_cl1295, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity)))
% 111.32/16.60 = (multiply @ (multiply @ identity @ (multiply @ identity @ X0)) @
% 111.32/16.60 identity))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl597, zip_derived_cl1083])).
% 111.32/16.60 thf(zip_derived_cl53, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity))))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl36, zip_derived_cl1, zip_derived_cl26])).
% 111.32/16.60 thf(zip_derived_cl10025, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 111.32/16.60 (multiply @ (multiply @ X0 @ (multiply @ X0 @ X0)) @
% 111.32/16.60 (multiply @ X0 @ (multiply @ X0 @ X0))))
% 111.32/16.60 = (multiply @ identity @ X0))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl9983, zip_derived_cl60, zip_derived_cl60,
% 111.32/16.60 zip_derived_cl53, zip_derived_cl1])).
% 111.32/16.60 thf(zip_derived_cl3405, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ identity @ X0) @
% 111.32/16.60 (multiply @ (multiply @ X1 @ (multiply @ X1 @ X1)) @
% 111.32/16.60 (multiply @ (multiply @ X1 @ (multiply @ X1 @ X1)) @
% 111.32/16.60 (multiply @ X1 @ (multiply @ X1 @ X1)))))
% 111.32/16.60 = (multiply @ identity @ (multiply @ X0 @ X1)))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl3322, zip_derived_cl1, zip_derived_cl1295,
% 111.32/16.60 zip_derived_cl1295, zip_derived_cl53])).
% 111.32/16.60 thf(zip_derived_cl10240, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ identity @ X1) @ (multiply @ identity @ X0))
% 111.32/16.60 = (multiply @ identity @ (multiply @ X1 @ X0)))),
% 111.32/16.60 inference('sup+', [status(thm)],
% 111.32/16.60 [zip_derived_cl10025, zip_derived_cl3405])).
% 111.32/16.60 thf(zip_derived_cl10240, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ identity @ X1) @ (multiply @ identity @ X0))
% 111.32/16.60 = (multiply @ identity @ (multiply @ X1 @ X0)))),
% 111.32/16.60 inference('sup+', [status(thm)],
% 111.32/16.60 [zip_derived_cl10025, zip_derived_cl3405])).
% 111.32/16.60 thf(zip_derived_cl19004, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @ identity @ (multiply @ identity @ X0)))) @
% 111.32/16.60 X0))
% 111.32/16.60 = (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ X0))))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl18909, zip_derived_cl1295, zip_derived_cl53,
% 111.32/16.60 zip_derived_cl10240, zip_derived_cl10240])).
% 111.32/16.60 thf(zip_derived_cl3449, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ (multiply @ identity @ X0) @ X1))) @
% 111.32/16.60 (multiply @ X1 @ (multiply @ X1 @ X1))) = (X0))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl3387, zip_derived_cl60, zip_derived_cl53])).
% 111.32/16.60 thf(zip_derived_cl20460, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ X0))) @
% 111.32/16.60 X1))) @
% 111.32/16.60 (multiply @ X1 @ (multiply @ X1 @ X1)))
% 111.32/16.60 = (multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ identity @ identity) @
% 111.32/16.60 (multiply @ identity @ (multiply @ identity @ X0)))) @
% 111.32/16.60 X0))),
% 111.32/16.60 inference('sup+', [status(thm)],
% 111.32/16.60 [zip_derived_cl19004, zip_derived_cl3449])).
% 111.32/16.60 thf(zip_derived_cl3449, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ (multiply @ identity @ X0) @ X1))) @
% 111.32/16.60 (multiply @ X1 @ (multiply @ X1 @ X1))) = (X0))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl3387, zip_derived_cl60, zip_derived_cl53])).
% 111.32/16.60 thf(zip_derived_cl1, plain,
% 111.32/16.60 (((multiply @ identity @ identity) = (identity))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom2])).
% 111.32/16.60 thf(zip_derived_cl20675, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @ (multiply @ X0 @ X0))
% 111.32/16.60 = (multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ identity @ X0)))) @
% 111.32/16.60 X0))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl20460, zip_derived_cl3449, zip_derived_cl1])).
% 111.32/16.60 thf(zip_derived_cl20831, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ (multiply @ X0 @ identity) @ identity) @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity)))
% 111.32/16.60 = (multiply @ (multiply @ identity @ X0) @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity)))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl53, zip_derived_cl20675])).
% 111.32/16.60 thf(zip_derived_cl981, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((X0)
% 111.32/16.60 = (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X0) @ identity))) @
% 111.32/16.60 identity))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl901, zip_derived_cl69, zip_derived_cl53])).
% 111.32/16.60 thf(zip_derived_cl21065, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ (multiply @ X0 @ identity) @ identity) @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity))
% 111.32/16.60 = (multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ identity @ identity) @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ (multiply @ identity @ X0) @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity)) @
% 111.32/16.60 identity))) @
% 111.32/16.60 identity))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl20831, zip_derived_cl981])).
% 111.32/16.60 thf(zip_derived_cl1, plain,
% 111.32/16.60 (((multiply @ identity @ identity) = (identity))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom2])).
% 111.32/16.60 thf(zip_derived_cl3900, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ X0 @ X0) @
% 111.32/16.60 (multiply @ (multiply @ (multiply @ X0 @ identity) @ identity) @
% 111.32/16.60 (multiply @ (multiply @ (multiply @ X0 @ identity) @ identity) @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity))))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl3745, zip_derived_cl1, zip_derived_cl1833,
% 111.32/16.60 zip_derived_cl649])).
% 111.32/16.60 thf(zip_derived_cl3405, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ identity @ X0) @
% 111.32/16.60 (multiply @ (multiply @ X1 @ (multiply @ X1 @ X1)) @
% 111.32/16.60 (multiply @ (multiply @ X1 @ (multiply @ X1 @ X1)) @
% 111.32/16.60 (multiply @ X1 @ (multiply @ X1 @ X1)))))
% 111.32/16.60 = (multiply @ identity @ (multiply @ X0 @ X1)))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl3322, zip_derived_cl1, zip_derived_cl1295,
% 111.32/16.60 zip_derived_cl1295, zip_derived_cl53])).
% 111.32/16.60 thf(zip_derived_cl9, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ identity @ (multiply @ identity @ (multiply @ X0 @ X1))) @
% 111.32/16.60 (multiply @ X1 @ (multiply @ X1 @ X1))))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 111.32/16.60 thf(zip_derived_cl8659, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ X1 @ (multiply @ X0 @ (multiply @ X0 @ X0)))) @
% 111.32/16.60 X0)))
% 111.32/16.60 = (X1))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl3405, zip_derived_cl9])).
% 111.32/16.60 thf(zip_derived_cl9130, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @ (multiply @ identity @ X0) @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity))))
% 111.32/16.60 = (multiply @ X0 @ X0))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl3900, zip_derived_cl8659])).
% 111.32/16.60 thf(zip_derived_cl1295, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ identity)))
% 111.32/16.60 = (multiply @ (multiply @ identity @ (multiply @ identity @ X0)) @
% 111.32/16.60 identity))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl597, zip_derived_cl1083])).
% 111.32/16.60 thf(zip_derived_cl9278, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ identity @
% 111.32/16.60 (multiply @ identity @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ (multiply @ identity @ X0) @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity)) @
% 111.32/16.60 identity)))
% 111.32/16.60 = (multiply @ (multiply @ X0 @ X0) @ identity))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl9130, zip_derived_cl1295])).
% 111.32/16.60 thf(zip_derived_cl21312, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ (multiply @ X0 @ identity) @ identity) @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity))
% 111.32/16.60 = (multiply @ (multiply @ (multiply @ X0 @ X0) @ identity) @
% 111.32/16.60 identity))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl21065, zip_derived_cl1, zip_derived_cl9278])).
% 111.32/16.60 thf(zip_derived_cl3900, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ X0 @ X0) @
% 111.32/16.60 (multiply @ (multiply @ (multiply @ X0 @ identity) @ identity) @
% 111.32/16.60 (multiply @ (multiply @ (multiply @ X0 @ identity) @ identity) @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity))))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl3745, zip_derived_cl1, zip_derived_cl1833,
% 111.32/16.60 zip_derived_cl649])).
% 111.32/16.60 thf(zip_derived_cl21836, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ (multiply @ X0 @ X0) @
% 111.32/16.60 (multiply @ (multiply @ (multiply @ X0 @ identity) @ identity) @
% 111.32/16.60 (multiply @ (multiply @ (multiply @ X0 @ X0) @ identity) @ identity)))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('sup+', [status(thm)],
% 111.32/16.60 [zip_derived_cl21312, zip_derived_cl3900])).
% 111.32/16.60 thf(zip_derived_cl0, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i, X2 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ X2))) @
% 111.32/16.60 (multiply @ X2 @ (multiply @ X2 @ X2))))
% 111.32/16.60 = (X0))),
% 111.32/16.60 inference('cnf', [status(esa)], [single_axiom])).
% 111.32/16.60 thf(zip_derived_cl22231, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ X0 @
% 111.32/16.60 (multiply @ (multiply @ X0 @ X0) @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ (multiply @ (multiply @ X0 @ X0) @ identity) @
% 111.32/16.60 identity) @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ (multiply @ (multiply @ X0 @ X0) @ identity) @
% 111.32/16.60 identity) @
% 111.32/16.60 (multiply @ (multiply @ (multiply @ X0 @ X0) @ identity) @
% 111.32/16.60 identity)))))
% 111.32/16.60 = (multiply @ (multiply @ X0 @ identity) @ identity))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl21836, zip_derived_cl0])).
% 111.32/16.60 thf(zip_derived_cl3404, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ X0 @
% 111.32/16.60 (multiply @ (multiply @ (multiply @ X0 @ identity) @ identity) @
% 111.32/16.60 (multiply @ (multiply @ (multiply @ X0 @ identity) @ identity) @
% 111.32/16.60 (multiply @ (multiply @ X0 @ identity) @ identity))))
% 111.32/16.60 = (identity))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl3321, zip_derived_cl1, zip_derived_cl1,
% 111.32/16.60 zip_derived_cl1, zip_derived_cl1])).
% 111.32/16.60 thf(zip_derived_cl22360, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ X0 @ identity)
% 111.32/16.60 = (multiply @ (multiply @ X0 @ identity) @ identity))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl22231, zip_derived_cl3404])).
% 111.32/16.60 thf(zip_derived_cl22467, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X0) @ identity))) @
% 111.32/16.60 identity) = (multiply @ X0 @ identity))),
% 111.32/16.60 inference('sup+', [status(thm)], [zip_derived_cl981, zip_derived_cl22360])).
% 111.32/16.60 thf(zip_derived_cl981, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((X0)
% 111.32/16.60 = (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X0) @ identity))) @
% 111.32/16.60 identity))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl901, zip_derived_cl69, zip_derived_cl53])).
% 111.32/16.60 thf(zip_derived_cl22505, plain,
% 111.32/16.60 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl22467, zip_derived_cl981])).
% 111.32/16.60 thf(zip_derived_cl19004, plain,
% 111.32/16.60 (![X0 : $i, X1 : $i]:
% 111.32/16.60 ((multiply @ X1 @
% 111.32/16.60 (multiply @
% 111.32/16.60 (multiply @ X1 @
% 111.32/16.60 (multiply @ (multiply @ X1 @ X1) @
% 111.32/16.60 (multiply @ identity @ (multiply @ identity @ X0)))) @
% 111.32/16.60 X0))
% 111.32/16.60 = (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ X0 @ X0))))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl18909, zip_derived_cl1295, zip_derived_cl53,
% 111.32/16.60 zip_derived_cl10240, zip_derived_cl10240])).
% 111.32/16.60 thf(zip_derived_cl22677, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ X0 @
% 111.32/16.60 (multiply @ X0 @
% 111.32/16.60 (multiply @ (multiply @ X0 @ X0) @
% 111.32/16.60 (multiply @ identity @ (multiply @ identity @ identity)))))
% 111.32/16.60 = (multiply @ identity @
% 111.32/16.60 (multiply @ identity @ (multiply @ identity @ identity))))),
% 111.32/16.60 inference('sup+', [status(thm)],
% 111.32/16.60 [zip_derived_cl22505, zip_derived_cl19004])).
% 111.32/16.60 thf(zip_derived_cl22505, plain,
% 111.32/16.60 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl22467, zip_derived_cl981])).
% 111.32/16.60 thf(zip_derived_cl22505, plain,
% 111.32/16.60 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl22467, zip_derived_cl981])).
% 111.32/16.60 thf(zip_derived_cl22505, plain,
% 111.32/16.60 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl22467, zip_derived_cl981])).
% 111.32/16.60 thf(zip_derived_cl22505, plain,
% 111.32/16.60 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl22467, zip_derived_cl981])).
% 111.32/16.60 thf(zip_derived_cl22505, plain,
% 111.32/16.60 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl22467, zip_derived_cl981])).
% 111.32/16.60 thf(zip_derived_cl22505, plain,
% 111.32/16.60 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl22467, zip_derived_cl981])).
% 111.32/16.60 thf(zip_derived_cl22728, plain,
% 111.32/16.60 (![X0 : $i]:
% 111.32/16.60 ((multiply @ X0 @ (multiply @ X0 @ (multiply @ X0 @ X0))) = (identity))),
% 111.32/16.60 inference('demod', [status(thm)],
% 111.32/16.60 [zip_derived_cl22677, zip_derived_cl22505,
% 111.32/16.60 zip_derived_cl22505, zip_derived_cl22505,
% 111.32/16.60 zip_derived_cl22505, zip_derived_cl22505, zip_derived_cl22505])).
% 111.32/16.60 thf(zip_derived_cl22849, plain, (((identity) != (identity))),
% 111.32/16.60 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl22728])).
% 111.32/16.60 thf(zip_derived_cl22850, plain, ($false),
% 111.32/16.60 inference('simplify', [status(thm)], [zip_derived_cl22849])).
% 111.32/16.60
% 111.32/16.60 % SZS output end Refutation
% 111.32/16.60
% 111.32/16.60
% 111.32/16.60 % Terminating...
% 111.33/16.74 % Runner terminated.
% 111.33/16.76 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------