TSTP Solution File: BOO024-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : BOO024-1 : TPTP v8.1.2. Released v2.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.UvkWiqGlYF true
% Computer : n031.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 : Wed Aug 30 18:13:23 EDT 2023
% Result : Unsatisfiable 21.47s 3.66s
% Output : Refutation 21.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : BOO024-1 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.UvkWiqGlYF true
% 0.13/0.35 % Computer : n031.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 08:39:39 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.21/0.66 % Total configuration time : 435
% 0.21/0.66 % Estimated wc time : 1092
% 0.21/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 21.47/3.66 % Solved by fo/fo5.sh.
% 21.47/3.66 % done 1238 iterations in 2.878s
% 21.47/3.66 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 21.47/3.66 % SZS output start Refutation
% 21.47/3.66 thf(pixley_type, type, pixley: $i > $i > $i > $i).
% 21.47/3.66 thf(n1_type, type, n1: $i).
% 21.47/3.66 thf(add_type, type, add: $i > $i > $i).
% 21.47/3.66 thf(b_type, type, b: $i).
% 21.47/3.66 thf(multiply_type, type, multiply: $i > $i > $i).
% 21.47/3.66 thf(inverse_type, type, inverse: $i > $i).
% 21.47/3.66 thf(a_type, type, a: $i).
% 21.47/3.66 thf(prove_add_multiply, conjecture,
% 21.47/3.66 (( add @ ( multiply @ a @ b ) @ b ) = ( b ))).
% 21.47/3.66 thf(zf_stmt_0, negated_conjecture,
% 21.47/3.66 (( add @ ( multiply @ a @ b ) @ b ) != ( b )),
% 21.47/3.66 inference('cnf.neg', [status(esa)], [prove_add_multiply])).
% 21.47/3.66 thf(zip_derived_cl7, plain, (((add @ (multiply @ a @ b) @ b) != (b))),
% 21.47/3.66 inference('cnf', [status(esa)], [zf_stmt_0])).
% 21.47/3.66 thf(additive_inverse, axiom, (( add @ X @ ( inverse @ X ) ) = ( n1 ))).
% 21.47/3.66 thf(zip_derived_cl2, plain,
% 21.47/3.66 (![X0 : $i]: ((add @ X0 @ (inverse @ X0)) = (n1))),
% 21.47/3.66 inference('cnf', [status(esa)], [additive_inverse])).
% 21.47/3.66 thf(pixley_defn, axiom,
% 21.47/3.66 (( pixley @ X @ Y @ Z ) =
% 21.47/3.66 ( add @
% 21.47/3.66 ( multiply @ X @ ( inverse @ Y ) ) @
% 21.47/3.66 ( add @ ( multiply @ X @ Z ) @ ( multiply @ ( inverse @ Y ) @ Z ) ) ))).
% 21.47/3.66 thf(zip_derived_cl3, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((pixley @ X0 @ X1 @ X2)
% 21.47/3.66 = (add @ (multiply @ X0 @ (inverse @ X1)) @
% 21.47/3.66 (add @ (multiply @ X0 @ X2) @ (multiply @ (inverse @ X1) @ X2))))),
% 21.47/3.66 inference('cnf', [status(esa)], [pixley_defn])).
% 21.47/3.66 thf(multiply_add_property, axiom,
% 21.47/3.66 (( multiply @ X @ ( add @ Y @ Z ) ) =
% 21.47/3.66 ( add @ ( multiply @ Y @ X ) @ ( multiply @ Z @ X ) ))).
% 21.47/3.66 thf(zip_derived_cl1, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ X1 @ (add @ X0 @ X2))
% 21.47/3.66 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 21.47/3.66 inference('cnf', [status(esa)], [multiply_add_property])).
% 21.47/3.66 thf(zip_derived_cl25, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((pixley @ X0 @ X1 @ X2)
% 21.47/3.66 = (add @ (multiply @ X0 @ (inverse @ X1)) @
% 21.47/3.66 (multiply @ X2 @ (add @ X0 @ (inverse @ X1)))))),
% 21.47/3.66 inference('demod', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 21.47/3.66 thf(zip_derived_cl31, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((pixley @ X0 @ X0 @ X1)
% 21.47/3.66 = (add @ (multiply @ X0 @ (inverse @ X0)) @ (multiply @ X1 @ n1)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl25])).
% 21.47/3.66 thf(pixley1, axiom, (( pixley @ X @ X @ Y ) = ( Y ))).
% 21.47/3.66 thf(zip_derived_cl4, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((pixley @ X1 @ X1 @ X0) = (X0))),
% 21.47/3.66 inference('cnf', [status(esa)], [pixley1])).
% 21.47/3.66 thf(zip_derived_cl34, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((X1)
% 21.47/3.66 = (add @ (multiply @ X0 @ (inverse @ X0)) @ (multiply @ X1 @ n1)))),
% 21.47/3.66 inference('demod', [status(thm)], [zip_derived_cl31, zip_derived_cl4])).
% 21.47/3.66 thf(zip_derived_cl2, plain,
% 21.47/3.66 (![X0 : $i]: ((add @ X0 @ (inverse @ X0)) = (n1))),
% 21.47/3.66 inference('cnf', [status(esa)], [additive_inverse])).
% 21.47/3.66 thf(multiply_add, axiom, (( multiply @ ( add @ X @ Y ) @ Y ) = ( Y ))).
% 21.47/3.66 thf(zip_derived_cl0, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((multiply @ (add @ X1 @ X0) @ X0) = (X0))),
% 21.47/3.66 inference('cnf', [status(esa)], [multiply_add])).
% 21.47/3.66 thf(zip_derived_cl8, plain,
% 21.47/3.66 (![X0 : $i]: ((multiply @ n1 @ (inverse @ X0)) = (inverse @ X0))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 21.47/3.66 thf(zip_derived_cl1, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ X1 @ (add @ X0 @ X2))
% 21.47/3.66 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 21.47/3.66 inference('cnf', [status(esa)], [multiply_add_property])).
% 21.47/3.66 thf(zip_derived_cl11, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((multiply @ (inverse @ X0) @ (add @ X1 @ n1))
% 21.47/3.66 = (add @ (multiply @ X1 @ (inverse @ X0)) @ (inverse @ X0)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl1])).
% 21.47/3.66 thf(zip_derived_cl0, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((multiply @ (add @ X1 @ X0) @ X0) = (X0))),
% 21.47/3.66 inference('cnf', [status(esa)], [multiply_add])).
% 21.47/3.66 thf(zip_derived_cl1, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ X1 @ (add @ X0 @ X2))
% 21.47/3.66 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 21.47/3.66 inference('cnf', [status(esa)], [multiply_add_property])).
% 21.47/3.66 thf(zip_derived_cl10, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ X0 @ (add @ X2 @ (add @ X1 @ X0)))
% 21.47/3.66 = (add @ (multiply @ X2 @ X0) @ X0))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 21.47/3.66 thf(zip_derived_cl173, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ (inverse @ X1) @
% 21.47/3.66 (add @ X2 @ (multiply @ (inverse @ X1) @ (add @ X0 @ n1))))
% 21.47/3.66 = (add @ (multiply @ X2 @ (inverse @ X1)) @ (inverse @ X1)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl10])).
% 21.47/3.66 thf(zip_derived_cl11, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((multiply @ (inverse @ X0) @ (add @ X1 @ n1))
% 21.47/3.66 = (add @ (multiply @ X1 @ (inverse @ X0)) @ (inverse @ X0)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl1])).
% 21.47/3.66 thf(zip_derived_cl180, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ (inverse @ X1) @
% 21.47/3.66 (add @ X2 @ (multiply @ (inverse @ X1) @ (add @ X0 @ n1))))
% 21.47/3.66 = (multiply @ (inverse @ X1) @ (add @ X2 @ n1)))),
% 21.47/3.66 inference('demod', [status(thm)], [zip_derived_cl173, zip_derived_cl11])).
% 21.47/3.66 thf(zip_derived_cl10, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ X0 @ (add @ X2 @ (add @ X1 @ X0)))
% 21.47/3.66 = (add @ (multiply @ X2 @ X0) @ X0))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 21.47/3.66 thf(zip_derived_cl0, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((multiply @ (add @ X1 @ X0) @ X0) = (X0))),
% 21.47/3.66 inference('cnf', [status(esa)], [multiply_add])).
% 21.47/3.66 thf(zip_derived_cl8, plain,
% 21.47/3.66 (![X0 : $i]: ((multiply @ n1 @ (inverse @ X0)) = (inverse @ X0))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 21.47/3.66 thf(zip_derived_cl34, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((X1)
% 21.47/3.66 = (add @ (multiply @ X0 @ (inverse @ X0)) @ (multiply @ X1 @ n1)))),
% 21.47/3.66 inference('demod', [status(thm)], [zip_derived_cl31, zip_derived_cl4])).
% 21.47/3.66 thf(zip_derived_cl39, plain,
% 21.47/3.66 (![X0 : $i]: ((X0) = (add @ (inverse @ n1) @ (multiply @ X0 @ n1)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl34])).
% 21.47/3.66 thf(zip_derived_cl47, plain,
% 21.47/3.66 (![X0 : $i]: ((add @ X0 @ n1) = (add @ (inverse @ n1) @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl39])).
% 21.47/3.66 thf(zip_derived_cl47, plain,
% 21.47/3.66 (![X0 : $i]: ((add @ X0 @ n1) = (add @ (inverse @ n1) @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl39])).
% 21.47/3.66 thf(zip_derived_cl52, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((add @ X1 @ n1) = (add @ X0 @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl47, zip_derived_cl47])).
% 21.47/3.66 thf(zip_derived_cl0, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((multiply @ (add @ X1 @ X0) @ X0) = (X0))),
% 21.47/3.66 inference('cnf', [status(esa)], [multiply_add])).
% 21.47/3.66 thf(zip_derived_cl1, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ X1 @ (add @ X0 @ X2))
% 21.47/3.66 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 21.47/3.66 inference('cnf', [status(esa)], [multiply_add_property])).
% 21.47/3.66 thf(zip_derived_cl12, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ X0 @ (add @ (add @ X2 @ X0) @ X1))
% 21.47/3.66 = (add @ X0 @ (multiply @ X1 @ X0)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 21.47/3.66 thf(zip_derived_cl66, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((multiply @ X1 @ (add @ X0 @ n1)) = (add @ X1 @ (multiply @ n1 @ X1)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl52, zip_derived_cl12])).
% 21.47/3.66 thf(zip_derived_cl2, plain,
% 21.47/3.66 (![X0 : $i]: ((add @ X0 @ (inverse @ X0)) = (n1))),
% 21.47/3.66 inference('cnf', [status(esa)], [additive_inverse])).
% 21.47/3.66 thf(zip_derived_cl12, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ X0 @ (add @ (add @ X2 @ X0) @ X1))
% 21.47/3.66 = (add @ X0 @ (multiply @ X1 @ X0)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 21.47/3.66 thf(zip_derived_cl21, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((multiply @ X0 @ n1)
% 21.47/3.66 = (add @ X0 @ (multiply @ (inverse @ (add @ X1 @ X0)) @ X0)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl12])).
% 21.47/3.66 thf(zip_derived_cl151, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((multiply @ (multiply @ n1 @ X1) @ n1)
% 21.47/3.66 = (add @ (multiply @ n1 @ X1) @
% 21.47/3.66 (multiply @ (inverse @ (multiply @ X1 @ (add @ X0 @ n1))) @
% 21.47/3.66 (multiply @ n1 @ X1))))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl66, zip_derived_cl21])).
% 21.47/3.66 thf(zip_derived_cl11520, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ (multiply @ n1 @ (add @ X0 @ (add @ X1 @ n1))) @ n1)
% 21.47/3.66 = (add @ (add @ (multiply @ X0 @ n1) @ n1) @
% 21.47/3.66 (multiply @
% 21.47/3.66 (inverse @
% 21.47/3.66 (multiply @ (add @ X0 @ (add @ X1 @ n1)) @ (add @ X2 @ n1))) @
% 21.47/3.66 (multiply @ n1 @ (add @ X0 @ (add @ X1 @ n1))))))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl151])).
% 21.47/3.66 thf(zip_derived_cl52, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((add @ X1 @ n1) = (add @ X0 @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl47, zip_derived_cl47])).
% 21.47/3.66 thf(zip_derived_cl10, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ X0 @ (add @ X2 @ (add @ X1 @ X0)))
% 21.47/3.66 = (add @ (multiply @ X2 @ X0) @ X0))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 21.47/3.66 thf(zip_derived_cl62, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((multiply @ n1 @ (add @ X1 @ (add @ X0 @ n1)))
% 21.47/3.66 = (add @ (multiply @ X1 @ n1) @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl52, zip_derived_cl10])).
% 21.47/3.66 thf(zip_derived_cl52, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((add @ X1 @ n1) = (add @ X0 @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl47, zip_derived_cl47])).
% 21.47/3.66 thf(zip_derived_cl77, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((multiply @ n1 @ (add @ X1 @ (add @ X0 @ n1))) = (add @ X1 @ n1))),
% 21.47/3.66 inference('demod', [status(thm)], [zip_derived_cl62, zip_derived_cl52])).
% 21.47/3.66 thf(zip_derived_cl0, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((multiply @ (add @ X1 @ X0) @ X0) = (X0))),
% 21.47/3.66 inference('cnf', [status(esa)], [multiply_add])).
% 21.47/3.66 thf(zip_derived_cl52, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((add @ X1 @ n1) = (add @ X0 @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl47, zip_derived_cl47])).
% 21.47/3.66 thf(zip_derived_cl52, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((add @ X1 @ n1) = (add @ X0 @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl47, zip_derived_cl47])).
% 21.47/3.66 thf(zip_derived_cl52, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((add @ X1 @ n1) = (add @ X0 @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl47, zip_derived_cl47])).
% 21.47/3.66 thf(zip_derived_cl52, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((add @ X1 @ n1) = (add @ X0 @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl47, zip_derived_cl47])).
% 21.47/3.66 thf(zip_derived_cl52, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((add @ X1 @ n1) = (add @ X0 @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl47, zip_derived_cl47])).
% 21.47/3.66 thf(zip_derived_cl0, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((multiply @ (add @ X1 @ X0) @ X0) = (X0))),
% 21.47/3.66 inference('cnf', [status(esa)], [multiply_add])).
% 21.47/3.66 thf(zip_derived_cl1, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ X1 @ (add @ X0 @ X2))
% 21.47/3.66 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 21.47/3.66 inference('cnf', [status(esa)], [multiply_add_property])).
% 21.47/3.66 thf(zip_derived_cl0, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((multiply @ (add @ X1 @ X0) @ X0) = (X0))),
% 21.47/3.66 inference('cnf', [status(esa)], [multiply_add])).
% 21.47/3.66 thf(zip_derived_cl9, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ (multiply @ X2 @ (add @ X1 @ X0)) @ (multiply @ X0 @ X2))
% 21.47/3.66 = (multiply @ X0 @ X2))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 21.47/3.66 thf(zip_derived_cl98, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ (add @ X1 @ X0) @
% 21.47/3.66 (multiply @ X0 @ (add @ X2 @ (add @ X1 @ X0))))
% 21.47/3.66 = (multiply @ X0 @ (add @ X2 @ (add @ X1 @ X0))))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl9])).
% 21.47/3.66 thf(zip_derived_cl10, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ X0 @ (add @ X2 @ (add @ X1 @ X0)))
% 21.47/3.66 = (add @ (multiply @ X2 @ X0) @ X0))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 21.47/3.66 thf(zip_derived_cl10, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ X0 @ (add @ X2 @ (add @ X1 @ X0)))
% 21.47/3.66 = (add @ (multiply @ X2 @ X0) @ X0))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 21.47/3.66 thf(zip_derived_cl115, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ (add @ X1 @ X0) @ (add @ (multiply @ X2 @ X0) @ X0))
% 21.47/3.66 = (add @ (multiply @ X2 @ X0) @ X0))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl98, zip_derived_cl10, zip_derived_cl10])).
% 21.47/3.66 thf(zip_derived_cl204, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((multiply @ (add @ X0 @ n1) @ (add @ (multiply @ X1 @ n1) @ n1))
% 21.47/3.66 = (add @ (multiply @ X1 @ n1) @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl52, zip_derived_cl115])).
% 21.47/3.66 thf(zip_derived_cl52, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((add @ X1 @ n1) = (add @ X0 @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl47, zip_derived_cl47])).
% 21.47/3.66 thf(zip_derived_cl52, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((add @ X1 @ n1) = (add @ X0 @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl47, zip_derived_cl47])).
% 21.47/3.66 thf(zip_derived_cl223, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((multiply @ (add @ X0 @ n1) @ (add @ X1 @ n1)) = (add @ X1 @ n1))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl204, zip_derived_cl52, zip_derived_cl52])).
% 21.47/3.66 thf(zip_derived_cl264, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ (add @ X2 @ n1) @ (add @ X0 @ n1)) = (add @ X1 @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl52, zip_derived_cl223])).
% 21.47/3.66 thf(zip_derived_cl12, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ X0 @ (add @ (add @ X2 @ X0) @ X1))
% 21.47/3.66 = (add @ X0 @ (multiply @ X1 @ X0)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 21.47/3.66 thf(zip_derived_cl320, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((add @ X0 @ n1)
% 21.47/3.66 = (add @ (add @ X1 @ n1) @ (multiply @ n1 @ (add @ X1 @ n1))))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl264, zip_derived_cl12])).
% 21.47/3.66 thf(zip_derived_cl1172, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((add @ X2 @ n1)
% 21.47/3.66 = (add @ (add @ X1 @ n1) @ (multiply @ n1 @ (add @ X0 @ n1))))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl52, zip_derived_cl320])).
% 21.47/3.66 thf(zip_derived_cl0, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((multiply @ (add @ X1 @ X0) @ X0) = (X0))),
% 21.47/3.66 inference('cnf', [status(esa)], [multiply_add])).
% 21.47/3.66 thf(zip_derived_cl115, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ (add @ X1 @ X0) @ (add @ (multiply @ X2 @ X0) @ X0))
% 21.47/3.66 = (add @ (multiply @ X2 @ X0) @ X0))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl98, zip_derived_cl10, zip_derived_cl10])).
% 21.47/3.66 thf(zip_derived_cl197, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ (add @ X2 @ X0) @ (add @ X0 @ X0))
% 21.47/3.66 = (add @ (multiply @ (add @ X1 @ X0) @ X0) @ X0))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl115])).
% 21.47/3.66 thf(zip_derived_cl0, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((multiply @ (add @ X1 @ X0) @ X0) = (X0))),
% 21.47/3.66 inference('cnf', [status(esa)], [multiply_add])).
% 21.47/3.66 thf(zip_derived_cl218, plain,
% 21.47/3.66 (![X0 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ (add @ X2 @ X0) @ (add @ X0 @ X0)) = (add @ X0 @ X0))),
% 21.47/3.66 inference('demod', [status(thm)], [zip_derived_cl197, zip_derived_cl0])).
% 21.47/3.66 thf(zip_derived_cl9, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ (multiply @ X2 @ (add @ X1 @ X0)) @ (multiply @ X0 @ X2))
% 21.47/3.66 = (multiply @ X0 @ X2))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 21.47/3.66 thf(zip_derived_cl233, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((multiply @ (add @ X0 @ X0) @ (multiply @ X0 @ (add @ X1 @ X0)))
% 21.47/3.66 = (multiply @ X0 @ (add @ X1 @ X0)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl218, zip_derived_cl9])).
% 21.47/3.66 thf(zip_derived_cl115, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ (add @ X1 @ X0) @ (add @ (multiply @ X2 @ X0) @ X0))
% 21.47/3.66 = (add @ (multiply @ X2 @ X0) @ X0))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl98, zip_derived_cl10, zip_derived_cl10])).
% 21.47/3.66 thf(zip_derived_cl631, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ (add @ X2 @ (multiply @ X0 @ (add @ X1 @ X0))) @
% 21.47/3.66 (add @ (multiply @ X0 @ (add @ X1 @ X0)) @
% 21.47/3.66 (multiply @ X0 @ (add @ X1 @ X0))))
% 21.47/3.66 = (add @
% 21.47/3.66 (multiply @ (add @ X0 @ X0) @ (multiply @ X0 @ (add @ X1 @ X0))) @
% 21.47/3.66 (multiply @ X0 @ (add @ X1 @ X0))))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl233, zip_derived_cl115])).
% 21.47/3.66 thf(zip_derived_cl1, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ X1 @ (add @ X0 @ X2))
% 21.47/3.66 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 21.47/3.66 inference('cnf', [status(esa)], [multiply_add_property])).
% 21.47/3.66 thf(zip_derived_cl218, plain,
% 21.47/3.66 (![X0 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ (add @ X2 @ X0) @ (add @ X0 @ X0)) = (add @ X0 @ X0))),
% 21.47/3.66 inference('demod', [status(thm)], [zip_derived_cl197, zip_derived_cl0])).
% 21.47/3.66 thf(zip_derived_cl233, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((multiply @ (add @ X0 @ X0) @ (multiply @ X0 @ (add @ X1 @ X0)))
% 21.47/3.66 = (multiply @ X0 @ (add @ X1 @ X0)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl218, zip_derived_cl9])).
% 21.47/3.66 thf(zip_derived_cl1, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ X1 @ (add @ X0 @ X2))
% 21.47/3.66 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 21.47/3.66 inference('cnf', [status(esa)], [multiply_add_property])).
% 21.47/3.66 thf(zip_derived_cl218, plain,
% 21.47/3.66 (![X0 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ (add @ X2 @ X0) @ (add @ X0 @ X0)) = (add @ X0 @ X0))),
% 21.47/3.66 inference('demod', [status(thm)], [zip_derived_cl197, zip_derived_cl0])).
% 21.47/3.66 thf(zip_derived_cl671, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ (add @ X2 @ (multiply @ X0 @ (add @ X1 @ X0))) @
% 21.47/3.66 (add @ X0 @ X0)) = (add @ X0 @ X0))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl631, zip_derived_cl1, zip_derived_cl218,
% 21.47/3.66 zip_derived_cl233, zip_derived_cl1, zip_derived_cl218])).
% 21.47/3.66 thf(zip_derived_cl2074, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X3 : $i]:
% 21.47/3.66 ((multiply @
% 21.47/3.66 (add @ X3 @
% 21.47/3.66 (multiply @ (multiply @ n1 @ (add @ X1 @ n1)) @ (add @ X0 @ n1))) @
% 21.47/3.66 (add @ (multiply @ n1 @ (add @ X1 @ n1)) @
% 21.47/3.66 (multiply @ n1 @ (add @ X1 @ n1))))
% 21.47/3.66 = (add @ (multiply @ n1 @ (add @ X1 @ n1)) @
% 21.47/3.66 (multiply @ n1 @ (add @ X1 @ n1))))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl1172, zip_derived_cl671])).
% 21.47/3.66 thf(zip_derived_cl52, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((add @ X1 @ n1) = (add @ X0 @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl47, zip_derived_cl47])).
% 21.47/3.66 thf(zip_derived_cl34, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((X1)
% 21.47/3.66 = (add @ (multiply @ X0 @ (inverse @ X0)) @ (multiply @ X1 @ n1)))),
% 21.47/3.66 inference('demod', [status(thm)], [zip_derived_cl31, zip_derived_cl4])).
% 21.47/3.66 thf(zip_derived_cl218, plain,
% 21.47/3.66 (![X0 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ (add @ X2 @ X0) @ (add @ X0 @ X0)) = (add @ X0 @ X0))),
% 21.47/3.66 inference('demod', [status(thm)], [zip_derived_cl197, zip_derived_cl0])).
% 21.47/3.66 thf(zip_derived_cl245, plain,
% 21.47/3.66 (![X0 : $i]:
% 21.47/3.66 ((multiply @ X0 @ (add @ (multiply @ X0 @ n1) @ (multiply @ X0 @ n1)))
% 21.47/3.66 = (add @ (multiply @ X0 @ n1) @ (multiply @ X0 @ n1)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl34, zip_derived_cl218])).
% 21.47/3.66 thf(zip_derived_cl1, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ X1 @ (add @ X0 @ X2))
% 21.47/3.66 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 21.47/3.66 inference('cnf', [status(esa)], [multiply_add_property])).
% 21.47/3.66 thf(zip_derived_cl1, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ X1 @ (add @ X0 @ X2))
% 21.47/3.66 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 21.47/3.66 inference('cnf', [status(esa)], [multiply_add_property])).
% 21.47/3.66 thf(zip_derived_cl253, plain,
% 21.47/3.66 (![X0 : $i]:
% 21.47/3.66 ((multiply @ X0 @ (multiply @ n1 @ (add @ X0 @ X0)))
% 21.47/3.66 = (multiply @ n1 @ (add @ X0 @ X0)))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl245, zip_derived_cl1, zip_derived_cl1])).
% 21.47/3.66 thf(zip_derived_cl66, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((multiply @ X1 @ (add @ X0 @ n1)) = (add @ X1 @ (multiply @ n1 @ X1)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl52, zip_derived_cl12])).
% 21.47/3.66 thf(zip_derived_cl364, plain,
% 21.47/3.66 (![X0 : $i]:
% 21.47/3.66 ((multiply @ (multiply @ n1 @ (add @ n1 @ n1)) @ (add @ X0 @ n1))
% 21.47/3.66 = (add @ (multiply @ n1 @ (add @ n1 @ n1)) @
% 21.47/3.66 (multiply @ n1 @ (add @ n1 @ n1))))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl253, zip_derived_cl66])).
% 21.47/3.66 thf(zip_derived_cl1, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ X1 @ (add @ X0 @ X2))
% 21.47/3.66 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 21.47/3.66 inference('cnf', [status(esa)], [multiply_add_property])).
% 21.47/3.66 thf(zip_derived_cl218, plain,
% 21.47/3.66 (![X0 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ (add @ X2 @ X0) @ (add @ X0 @ X0)) = (add @ X0 @ X0))),
% 21.47/3.66 inference('demod', [status(thm)], [zip_derived_cl197, zip_derived_cl0])).
% 21.47/3.66 thf(zip_derived_cl379, plain,
% 21.47/3.66 (![X0 : $i]:
% 21.47/3.66 ((multiply @ (multiply @ n1 @ (add @ n1 @ n1)) @ (add @ X0 @ n1))
% 21.47/3.66 = (add @ n1 @ n1))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl364, zip_derived_cl1, zip_derived_cl218])).
% 21.47/3.66 thf(zip_derived_cl760, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((multiply @ (multiply @ n1 @ (add @ X0 @ n1)) @ (add @ X1 @ n1))
% 21.47/3.66 = (add @ n1 @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl52, zip_derived_cl379])).
% 21.47/3.66 thf(zip_derived_cl1, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ X1 @ (add @ X0 @ X2))
% 21.47/3.66 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 21.47/3.66 inference('cnf', [status(esa)], [multiply_add_property])).
% 21.47/3.66 thf(zip_derived_cl264, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ (add @ X2 @ n1) @ (add @ X0 @ n1)) = (add @ X1 @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl52, zip_derived_cl223])).
% 21.47/3.66 thf(zip_derived_cl1, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ X1 @ (add @ X0 @ X2))
% 21.47/3.66 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 21.47/3.66 inference('cnf', [status(esa)], [multiply_add_property])).
% 21.47/3.66 thf(zip_derived_cl264, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ (add @ X2 @ n1) @ (add @ X0 @ n1)) = (add @ X1 @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl52, zip_derived_cl223])).
% 21.47/3.66 thf(zip_derived_cl2155, plain,
% 21.47/3.66 (![X1 : $i, X3 : $i]:
% 21.47/3.66 ((multiply @ (add @ X3 @ (add @ n1 @ n1)) @ (add @ X1 @ n1))
% 21.47/3.66 = (add @ X1 @ n1))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl2074, zip_derived_cl760, zip_derived_cl1,
% 21.47/3.66 zip_derived_cl264, zip_derived_cl1, zip_derived_cl264])).
% 21.47/3.66 thf(zip_derived_cl2193, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ (add @ X2 @ (add @ X0 @ n1)) @ (add @ X1 @ n1))
% 21.47/3.66 = (add @ X1 @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl52, zip_derived_cl2155])).
% 21.47/3.66 thf(zip_derived_cl12, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ X0 @ (add @ (add @ X2 @ X0) @ X1))
% 21.47/3.66 = (add @ X0 @ (multiply @ X1 @ X0)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 21.47/3.66 thf(zip_derived_cl2220, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((add @ (add @ X2 @ (add @ X1 @ (add @ X0 @ n1))) @ n1)
% 21.47/3.66 = (add @ (add @ X1 @ (add @ X0 @ n1)) @
% 21.47/3.66 (multiply @ n1 @ (add @ X1 @ (add @ X0 @ n1)))))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl2193, zip_derived_cl12])).
% 21.47/3.66 thf(zip_derived_cl52, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((add @ X1 @ n1) = (add @ X0 @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl47, zip_derived_cl47])).
% 21.47/3.66 thf(zip_derived_cl77, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((multiply @ n1 @ (add @ X1 @ (add @ X0 @ n1))) = (add @ X1 @ n1))),
% 21.47/3.66 inference('demod', [status(thm)], [zip_derived_cl62, zip_derived_cl52])).
% 21.47/3.66 thf(zip_derived_cl2245, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((add @ X1 @ n1)
% 21.47/3.66 = (add @ (add @ X1 @ (add @ X0 @ n1)) @ (add @ X1 @ n1)))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl2220, zip_derived_cl52, zip_derived_cl77])).
% 21.47/3.66 thf(zip_derived_cl10, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ X0 @ (add @ X2 @ (add @ X1 @ X0)))
% 21.47/3.66 = (add @ (multiply @ X2 @ X0) @ X0))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 21.47/3.66 thf(zip_derived_cl2362, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((multiply @ n1 @ (add @ X0 @ n1))
% 21.47/3.66 = (add @ (multiply @ (add @ X0 @ (add @ X1 @ n1)) @ n1) @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl2245, zip_derived_cl10])).
% 21.47/3.66 thf(zip_derived_cl52, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((add @ X1 @ n1) = (add @ X0 @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl47, zip_derived_cl47])).
% 21.47/3.66 thf(zip_derived_cl2394, plain,
% 21.47/3.66 (![X0 : $i]: ((multiply @ n1 @ (add @ X0 @ n1)) = (add @ X0 @ n1))),
% 21.47/3.66 inference('demod', [status(thm)], [zip_derived_cl2362, zip_derived_cl52])).
% 21.47/3.66 thf(zip_derived_cl2428, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((multiply @ n1 @ (add @ X0 @ n1)) = (add @ X1 @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl52, zip_derived_cl2394])).
% 21.47/3.66 thf(zip_derived_cl77, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((multiply @ n1 @ (add @ X1 @ (add @ X0 @ n1))) = (add @ X1 @ n1))),
% 21.47/3.66 inference('demod', [status(thm)], [zip_derived_cl62, zip_derived_cl52])).
% 21.47/3.66 thf(zip_derived_cl66, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((multiply @ X1 @ (add @ X0 @ n1)) = (add @ X1 @ (multiply @ n1 @ X1)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl52, zip_derived_cl12])).
% 21.47/3.66 thf(zip_derived_cl136, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ (add @ X0 @ (add @ X1 @ n1)) @ (add @ X2 @ n1))
% 21.47/3.66 = (add @ (add @ X0 @ (add @ X1 @ n1)) @ (add @ X0 @ n1)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl77, zip_derived_cl66])).
% 21.47/3.66 thf(zip_derived_cl52, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((add @ X1 @ n1) = (add @ X0 @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl47, zip_derived_cl47])).
% 21.47/3.66 thf(zip_derived_cl2245, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((add @ X1 @ n1)
% 21.47/3.66 = (add @ (add @ X1 @ (add @ X0 @ n1)) @ (add @ X1 @ n1)))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl2220, zip_derived_cl52, zip_derived_cl77])).
% 21.47/3.66 thf(zip_derived_cl2371, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((add @ X1 @ n1)
% 21.47/3.66 = (add @ (add @ X1 @ (add @ X2 @ n1)) @ (add @ X0 @ n1)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl52, zip_derived_cl2245])).
% 21.47/3.66 thf(zip_derived_cl8457, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ (add @ X0 @ (add @ X1 @ n1)) @ (add @ X2 @ n1))
% 21.47/3.66 = (add @ X0 @ n1))),
% 21.47/3.66 inference('demod', [status(thm)], [zip_derived_cl136, zip_derived_cl2371])).
% 21.47/3.66 thf(zip_derived_cl77, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((multiply @ n1 @ (add @ X1 @ (add @ X0 @ n1))) = (add @ X1 @ n1))),
% 21.47/3.66 inference('demod', [status(thm)], [zip_derived_cl62, zip_derived_cl52])).
% 21.47/3.66 thf(zip_derived_cl1, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ X1 @ (add @ X0 @ X2))
% 21.47/3.66 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 21.47/3.66 inference('cnf', [status(esa)], [multiply_add_property])).
% 21.47/3.66 thf(zip_derived_cl11580, plain,
% 21.47/3.66 (![X0 : $i]:
% 21.47/3.66 ((n1)
% 21.47/3.66 = (multiply @ (add @ X0 @ n1) @
% 21.47/3.66 (add @ n1 @ (inverse @ (add @ X0 @ n1)))))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl11520, zip_derived_cl77, zip_derived_cl0,
% 21.47/3.66 zip_derived_cl2428, zip_derived_cl8457, zip_derived_cl77,
% 21.47/3.66 zip_derived_cl1])).
% 21.47/3.66 thf(zip_derived_cl25, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((pixley @ X0 @ X1 @ X2)
% 21.47/3.66 = (add @ (multiply @ X0 @ (inverse @ X1)) @
% 21.47/3.66 (multiply @ X2 @ (add @ X0 @ (inverse @ X1)))))),
% 21.47/3.66 inference('demod', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 21.47/3.66 thf(zip_derived_cl0, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((multiply @ (add @ X1 @ X0) @ X0) = (X0))),
% 21.47/3.66 inference('cnf', [status(esa)], [multiply_add])).
% 21.47/3.66 thf(zip_derived_cl26, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ (pixley @ X2 @ X1 @ X0) @
% 21.47/3.66 (multiply @ X0 @ (add @ X2 @ (inverse @ X1))))
% 21.47/3.66 = (multiply @ X0 @ (add @ X2 @ (inverse @ X1))))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl25, zip_derived_cl0])).
% 21.47/3.66 thf(zip_derived_cl11634, plain,
% 21.47/3.66 (![X0 : $i]:
% 21.47/3.66 ((multiply @ (pixley @ n1 @ (add @ X0 @ n1) @ (add @ X0 @ n1)) @ n1)
% 21.47/3.66 = (multiply @ (add @ X0 @ n1) @
% 21.47/3.66 (add @ n1 @ (inverse @ (add @ X0 @ n1)))))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl11580, zip_derived_cl26])).
% 21.47/3.66 thf(pixley2, axiom, (( pixley @ X @ Y @ Y ) = ( X ))).
% 21.47/3.66 thf(zip_derived_cl5, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((pixley @ X0 @ X1 @ X1) = (X0))),
% 21.47/3.66 inference('cnf', [status(esa)], [pixley2])).
% 21.47/3.66 thf(zip_derived_cl11580, plain,
% 21.47/3.66 (![X0 : $i]:
% 21.47/3.66 ((n1)
% 21.47/3.66 = (multiply @ (add @ X0 @ n1) @
% 21.47/3.66 (add @ n1 @ (inverse @ (add @ X0 @ n1)))))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl11520, zip_derived_cl77, zip_derived_cl0,
% 21.47/3.66 zip_derived_cl2428, zip_derived_cl8457, zip_derived_cl77,
% 21.47/3.66 zip_derived_cl1])).
% 21.47/3.66 thf(zip_derived_cl11691, plain, (((multiply @ n1 @ n1) = (n1))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl11634, zip_derived_cl5, zip_derived_cl11580])).
% 21.47/3.66 thf(zip_derived_cl39, plain,
% 21.47/3.66 (![X0 : $i]: ((X0) = (add @ (inverse @ n1) @ (multiply @ X0 @ n1)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl34])).
% 21.47/3.66 thf(zip_derived_cl11737, plain, (((n1) = (add @ (inverse @ n1) @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl11691, zip_derived_cl39])).
% 21.47/3.66 thf(zip_derived_cl52, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((add @ X1 @ n1) = (add @ X0 @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl47, zip_derived_cl47])).
% 21.47/3.66 thf(zip_derived_cl11811, plain, (![X0 : $i]: ((n1) = (add @ X0 @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl11737, zip_derived_cl52])).
% 21.47/3.66 thf(zip_derived_cl11811, plain, (![X0 : $i]: ((n1) = (add @ X0 @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl11737, zip_derived_cl52])).
% 21.47/3.66 thf(zip_derived_cl13022, plain,
% 21.47/3.66 (![X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ (inverse @ X1) @
% 21.47/3.66 (add @ X2 @ (multiply @ (inverse @ X1) @ n1)))
% 21.47/3.66 = (multiply @ (inverse @ X1) @ n1))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl180, zip_derived_cl11811, zip_derived_cl11811])).
% 21.47/3.66 thf(zip_derived_cl13053, plain,
% 21.47/3.66 (![X0 : $i]:
% 21.47/3.66 ((multiply @ (inverse @ X0) @ (inverse @ X0))
% 21.47/3.66 = (multiply @ (inverse @ X0) @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl34, zip_derived_cl13022])).
% 21.47/3.66 thf(zip_derived_cl2, plain,
% 21.47/3.66 (![X0 : $i]: ((add @ X0 @ (inverse @ X0)) = (n1))),
% 21.47/3.66 inference('cnf', [status(esa)], [additive_inverse])).
% 21.47/3.66 thf(zip_derived_cl21, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((multiply @ X0 @ n1)
% 21.47/3.66 = (add @ X0 @ (multiply @ (inverse @ (add @ X1 @ X0)) @ X0)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl12])).
% 21.47/3.66 thf(zip_derived_cl152, plain,
% 21.47/3.66 (![X0 : $i]:
% 21.47/3.66 ((multiply @ (inverse @ X0) @ n1)
% 21.47/3.66 = (add @ (inverse @ X0) @
% 21.47/3.66 (multiply @ (inverse @ n1) @ (inverse @ X0))))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl21])).
% 21.47/3.66 thf(zip_derived_cl13135, plain,
% 21.47/3.66 (((multiply @ (inverse @ n1) @ n1)
% 21.47/3.66 = (add @ (inverse @ n1) @ (multiply @ (inverse @ n1) @ n1)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl13053, zip_derived_cl152])).
% 21.47/3.66 thf(zip_derived_cl39, plain,
% 21.47/3.66 (![X0 : $i]: ((X0) = (add @ (inverse @ n1) @ (multiply @ X0 @ n1)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl34])).
% 21.47/3.66 thf(zip_derived_cl13152, plain,
% 21.47/3.66 (((multiply @ (inverse @ n1) @ n1) = (inverse @ n1))),
% 21.47/3.66 inference('demod', [status(thm)], [zip_derived_cl13135, zip_derived_cl39])).
% 21.47/3.66 thf(zip_derived_cl1, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ X1 @ (add @ X0 @ X2))
% 21.47/3.66 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 21.47/3.66 inference('cnf', [status(esa)], [multiply_add_property])).
% 21.47/3.66 thf(zip_derived_cl13155, plain,
% 21.47/3.66 (![X0 : $i]:
% 21.47/3.66 ((multiply @ n1 @ (add @ (inverse @ n1) @ X0))
% 21.47/3.66 = (add @ (inverse @ n1) @ (multiply @ X0 @ n1)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl13152, zip_derived_cl1])).
% 21.47/3.66 thf(zip_derived_cl39, plain,
% 21.47/3.66 (![X0 : $i]: ((X0) = (add @ (inverse @ n1) @ (multiply @ X0 @ n1)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl34])).
% 21.47/3.66 thf(zip_derived_cl13195, plain,
% 21.47/3.66 (![X0 : $i]: ((multiply @ n1 @ (add @ (inverse @ n1) @ X0)) = (X0))),
% 21.47/3.66 inference('demod', [status(thm)], [zip_derived_cl13155, zip_derived_cl39])).
% 21.47/3.66 thf(zip_derived_cl39, plain,
% 21.47/3.66 (![X0 : $i]: ((X0) = (add @ (inverse @ n1) @ (multiply @ X0 @ n1)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl34])).
% 21.47/3.66 thf(zip_derived_cl13195, plain,
% 21.47/3.66 (![X0 : $i]: ((multiply @ n1 @ (add @ (inverse @ n1) @ X0)) = (X0))),
% 21.47/3.66 inference('demod', [status(thm)], [zip_derived_cl13155, zip_derived_cl39])).
% 21.47/3.66 thf(zip_derived_cl13275, plain,
% 21.47/3.66 (![X0 : $i]: ((multiply @ n1 @ X0) = (multiply @ X0 @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl39, zip_derived_cl13195])).
% 21.47/3.66 thf(zip_derived_cl34, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((X1)
% 21.47/3.66 = (add @ (multiply @ X0 @ (inverse @ X0)) @ (multiply @ X1 @ n1)))),
% 21.47/3.66 inference('demod', [status(thm)], [zip_derived_cl31, zip_derived_cl4])).
% 21.47/3.66 thf(zip_derived_cl0, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((multiply @ (add @ X1 @ X0) @ X0) = (X0))),
% 21.47/3.66 inference('cnf', [status(esa)], [multiply_add])).
% 21.47/3.66 thf(zip_derived_cl35, plain,
% 21.47/3.66 (![X0 : $i]:
% 21.47/3.66 ((multiply @ X0 @ (multiply @ X0 @ n1)) = (multiply @ X0 @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl34, zip_derived_cl0])).
% 21.47/3.66 thf(zip_derived_cl13901, plain,
% 21.47/3.66 (![X0 : $i]:
% 21.47/3.66 ((multiply @ X0 @ (multiply @ n1 @ X0)) = (multiply @ X0 @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl13275, zip_derived_cl35])).
% 21.47/3.66 thf(zip_derived_cl14708, plain,
% 21.47/3.66 (![X0 : $i]:
% 21.47/3.66 ((multiply @ (add @ (inverse @ n1) @ X0) @ X0)
% 21.47/3.66 = (multiply @ (add @ (inverse @ n1) @ X0) @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)],
% 21.47/3.66 [zip_derived_cl13195, zip_derived_cl13901])).
% 21.47/3.66 thf(zip_derived_cl0, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((multiply @ (add @ X1 @ X0) @ X0) = (X0))),
% 21.47/3.66 inference('cnf', [status(esa)], [multiply_add])).
% 21.47/3.66 thf(zip_derived_cl14717, plain,
% 21.47/3.66 (![X0 : $i]: ((X0) = (multiply @ (add @ (inverse @ n1) @ X0) @ n1))),
% 21.47/3.66 inference('demod', [status(thm)], [zip_derived_cl14708, zip_derived_cl0])).
% 21.47/3.66 thf(zip_derived_cl13275, plain,
% 21.47/3.66 (![X0 : $i]: ((multiply @ n1 @ X0) = (multiply @ X0 @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl39, zip_derived_cl13195])).
% 21.47/3.66 thf(zip_derived_cl11737, plain, (((n1) = (add @ (inverse @ n1) @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl11691, zip_derived_cl39])).
% 21.47/3.66 thf(zip_derived_cl2428, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((multiply @ n1 @ (add @ X0 @ n1)) = (add @ X1 @ n1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl52, zip_derived_cl2394])).
% 21.47/3.66 thf(zip_derived_cl66, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((multiply @ X1 @ (add @ X0 @ n1)) = (add @ X1 @ (multiply @ n1 @ X1)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl52, zip_derived_cl12])).
% 21.47/3.66 thf(zip_derived_cl2578, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((multiply @ X1 @ (multiply @ n1 @ (add @ X0 @ n1)))
% 21.47/3.66 = (add @ X1 @ (multiply @ n1 @ X1)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl2428, zip_derived_cl66])).
% 21.47/3.66 thf(zip_derived_cl11851, plain,
% 21.47/3.66 (![X0 : $i]:
% 21.47/3.66 ((multiply @ X0 @ (multiply @ n1 @ n1))
% 21.47/3.66 = (add @ X0 @ (multiply @ n1 @ X0)))),
% 21.47/3.66 inference('sup+', [status(thm)],
% 21.47/3.66 [zip_derived_cl11737, zip_derived_cl2578])).
% 21.47/3.66 thf(zip_derived_cl11691, plain, (((multiply @ n1 @ n1) = (n1))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl11634, zip_derived_cl5, zip_derived_cl11580])).
% 21.47/3.66 thf(zip_derived_cl11910, plain,
% 21.47/3.66 (![X0 : $i]: ((multiply @ X0 @ n1) = (add @ X0 @ (multiply @ n1 @ X0)))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl11851, zip_derived_cl11691])).
% 21.47/3.66 thf(zip_derived_cl13972, plain,
% 21.47/3.66 (![X0 : $i]: ((multiply @ X0 @ n1) = (add @ X0 @ (multiply @ X0 @ n1)))),
% 21.47/3.66 inference('sup+', [status(thm)],
% 21.47/3.66 [zip_derived_cl13275, zip_derived_cl11910])).
% 21.47/3.66 thf(zip_derived_cl14972, plain,
% 21.47/3.66 (![X0 : $i]:
% 21.47/3.66 ((multiply @ (add @ (inverse @ n1) @ X0) @ n1)
% 21.47/3.66 = (add @ (add @ (inverse @ n1) @ X0) @ X0))),
% 21.47/3.66 inference('sup+', [status(thm)],
% 21.47/3.66 [zip_derived_cl14717, zip_derived_cl13972])).
% 21.47/3.66 thf(zip_derived_cl14717, plain,
% 21.47/3.66 (![X0 : $i]: ((X0) = (multiply @ (add @ (inverse @ n1) @ X0) @ n1))),
% 21.47/3.66 inference('demod', [status(thm)], [zip_derived_cl14708, zip_derived_cl0])).
% 21.47/3.66 thf(zip_derived_cl15021, plain,
% 21.47/3.66 (![X0 : $i]: ((X0) = (add @ (add @ (inverse @ n1) @ X0) @ X0))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl14972, zip_derived_cl14717])).
% 21.47/3.66 thf(zip_derived_cl12, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ X0 @ (add @ (add @ X2 @ X0) @ X1))
% 21.47/3.66 = (add @ X0 @ (multiply @ X1 @ X0)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 21.47/3.66 thf(zip_derived_cl15538, plain,
% 21.47/3.66 (![X0 : $i]: ((multiply @ X0 @ X0) = (add @ X0 @ (multiply @ X0 @ X0)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl15021, zip_derived_cl12])).
% 21.47/3.66 thf(zip_derived_cl14717, plain,
% 21.47/3.66 (![X0 : $i]: ((X0) = (multiply @ (add @ (inverse @ n1) @ X0) @ n1))),
% 21.47/3.66 inference('demod', [status(thm)], [zip_derived_cl14708, zip_derived_cl0])).
% 21.47/3.66 thf(zip_derived_cl34, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((X1)
% 21.47/3.66 = (add @ (multiply @ X0 @ (inverse @ X0)) @ (multiply @ X1 @ n1)))),
% 21.47/3.66 inference('demod', [status(thm)], [zip_derived_cl31, zip_derived_cl4])).
% 21.47/3.66 thf(zip_derived_cl9, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ (multiply @ X2 @ (add @ X1 @ X0)) @ (multiply @ X0 @ X2))
% 21.47/3.66 = (multiply @ X0 @ X2))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 21.47/3.66 thf(zip_derived_cl105, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((multiply @ (multiply @ X1 @ X0) @
% 21.47/3.66 (multiply @ (multiply @ X0 @ n1) @ X1))
% 21.47/3.66 = (multiply @ (multiply @ X0 @ n1) @ X1))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl34, zip_derived_cl9])).
% 21.47/3.66 thf(zip_derived_cl14946, plain,
% 21.47/3.66 (![X0 : $i]:
% 21.47/3.66 ((multiply @ X0 @
% 21.47/3.66 (multiply @ (multiply @ n1 @ n1) @ (add @ (inverse @ n1) @ X0)))
% 21.47/3.66 = (multiply @ (multiply @ n1 @ n1) @ (add @ (inverse @ n1) @ X0)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl14717, zip_derived_cl105])).
% 21.47/3.66 thf(zip_derived_cl11691, plain, (((multiply @ n1 @ n1) = (n1))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl11634, zip_derived_cl5, zip_derived_cl11580])).
% 21.47/3.66 thf(zip_derived_cl13195, plain,
% 21.47/3.66 (![X0 : $i]: ((multiply @ n1 @ (add @ (inverse @ n1) @ X0)) = (X0))),
% 21.47/3.66 inference('demod', [status(thm)], [zip_derived_cl13155, zip_derived_cl39])).
% 21.47/3.66 thf(zip_derived_cl11691, plain, (((multiply @ n1 @ n1) = (n1))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl11634, zip_derived_cl5, zip_derived_cl11580])).
% 21.47/3.66 thf(zip_derived_cl13195, plain,
% 21.47/3.66 (![X0 : $i]: ((multiply @ n1 @ (add @ (inverse @ n1) @ X0)) = (X0))),
% 21.47/3.66 inference('demod', [status(thm)], [zip_derived_cl13155, zip_derived_cl39])).
% 21.47/3.66 thf(zip_derived_cl15000, plain, (![X0 : $i]: ((multiply @ X0 @ X0) = (X0))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl14946, zip_derived_cl11691,
% 21.47/3.66 zip_derived_cl13195, zip_derived_cl11691, zip_derived_cl13195])).
% 21.47/3.66 thf(zip_derived_cl15000, plain, (![X0 : $i]: ((multiply @ X0 @ X0) = (X0))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl14946, zip_derived_cl11691,
% 21.47/3.66 zip_derived_cl13195, zip_derived_cl11691, zip_derived_cl13195])).
% 21.47/3.66 thf(zip_derived_cl15587, plain, (![X0 : $i]: ((X0) = (add @ X0 @ X0))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl15538, zip_derived_cl15000, zip_derived_cl15000])).
% 21.47/3.66 thf(zip_derived_cl1, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ X1 @ (add @ X0 @ X2))
% 21.47/3.66 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 21.47/3.66 inference('cnf', [status(esa)], [multiply_add_property])).
% 21.47/3.66 thf(zip_derived_cl15643, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((multiply @ X0 @ (add @ X1 @ X1)) = (multiply @ X1 @ X0))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl15587, zip_derived_cl1])).
% 21.47/3.66 thf(zip_derived_cl15587, plain, (![X0 : $i]: ((X0) = (add @ X0 @ X0))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl15538, zip_derived_cl15000, zip_derived_cl15000])).
% 21.47/3.66 thf(zip_derived_cl15681, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl15643, zip_derived_cl15587])).
% 21.47/3.66 thf(zip_derived_cl15970, plain, (((add @ (multiply @ b @ a) @ b) != (b))),
% 21.47/3.66 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl15681])).
% 21.47/3.66 thf(zip_derived_cl15681, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl15643, zip_derived_cl15587])).
% 21.47/3.66 thf(zip_derived_cl15587, plain, (![X0 : $i]: ((X0) = (add @ X0 @ X0))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl15538, zip_derived_cl15000, zip_derived_cl15000])).
% 21.47/3.66 thf(zip_derived_cl10, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ X0 @ (add @ X2 @ (add @ X1 @ X0)))
% 21.47/3.66 = (add @ (multiply @ X2 @ X0) @ X0))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 21.47/3.66 thf(zip_derived_cl15626, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((multiply @ X0 @ (add @ X1 @ X0))
% 21.47/3.66 = (add @ (multiply @ (add @ X1 @ X0) @ X0) @ X0))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl15587, zip_derived_cl10])).
% 21.47/3.66 thf(zip_derived_cl0, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((multiply @ (add @ X1 @ X0) @ X0) = (X0))),
% 21.47/3.66 inference('cnf', [status(esa)], [multiply_add])).
% 21.47/3.66 thf(zip_derived_cl15587, plain, (![X0 : $i]: ((X0) = (add @ X0 @ X0))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl15538, zip_derived_cl15000, zip_derived_cl15000])).
% 21.47/3.66 thf(zip_derived_cl15665, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ (add @ X1 @ X0)) = (X0))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl15626, zip_derived_cl0, zip_derived_cl15587])).
% 21.47/3.66 thf(zip_derived_cl1, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ X1 @ (add @ X0 @ X2))
% 21.47/3.66 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 21.47/3.66 inference('cnf', [status(esa)], [multiply_add_property])).
% 21.47/3.66 thf(zip_derived_cl10, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.47/3.66 ((multiply @ X0 @ (add @ X2 @ (add @ X1 @ X0)))
% 21.47/3.66 = (add @ (multiply @ X2 @ X0) @ X0))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 21.47/3.66 thf(zip_derived_cl17, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.47/3.66 ((multiply @ (multiply @ X0 @ X2) @
% 21.47/3.66 (add @ X3 @ (multiply @ X2 @ (add @ X1 @ X0))))
% 21.47/3.66 = (add @ (multiply @ X3 @ (multiply @ X0 @ X2)) @
% 21.47/3.66 (multiply @ X0 @ X2)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl10])).
% 21.47/3.66 thf(zip_derived_cl15710, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]:
% 21.47/3.66 ((multiply @ (multiply @ X0 @ X0) @ (add @ X1 @ X0))
% 21.47/3.66 = (add @ (multiply @ X1 @ (multiply @ X0 @ X0)) @
% 21.47/3.66 (multiply @ X0 @ X0)))),
% 21.47/3.66 inference('sup+', [status(thm)], [zip_derived_cl15665, zip_derived_cl17])).
% 21.47/3.66 thf(zip_derived_cl15000, plain, (![X0 : $i]: ((multiply @ X0 @ X0) = (X0))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl14946, zip_derived_cl11691,
% 21.47/3.66 zip_derived_cl13195, zip_derived_cl11691, zip_derived_cl13195])).
% 21.47/3.66 thf(zip_derived_cl15665, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ (add @ X1 @ X0)) = (X0))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl15626, zip_derived_cl0, zip_derived_cl15587])).
% 21.47/3.66 thf(zip_derived_cl15000, plain, (![X0 : $i]: ((multiply @ X0 @ X0) = (X0))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl14946, zip_derived_cl11691,
% 21.47/3.66 zip_derived_cl13195, zip_derived_cl11691, zip_derived_cl13195])).
% 21.47/3.66 thf(zip_derived_cl15000, plain, (![X0 : $i]: ((multiply @ X0 @ X0) = (X0))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl14946, zip_derived_cl11691,
% 21.47/3.66 zip_derived_cl13195, zip_derived_cl11691, zip_derived_cl13195])).
% 21.47/3.66 thf(zip_derived_cl15787, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((X0) = (add @ (multiply @ X1 @ X0) @ X0))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl15710, zip_derived_cl15000,
% 21.47/3.66 zip_derived_cl15665, zip_derived_cl15000, zip_derived_cl15000])).
% 21.47/3.66 thf(zip_derived_cl16186, plain,
% 21.47/3.66 (![X0 : $i, X1 : $i]: ((X1) = (add @ (multiply @ X1 @ X0) @ X1))),
% 21.47/3.66 inference('sup+', [status(thm)],
% 21.47/3.66 [zip_derived_cl15681, zip_derived_cl15787])).
% 21.47/3.66 thf(zip_derived_cl16223, plain, (((b) != (b))),
% 21.47/3.66 inference('demod', [status(thm)],
% 21.47/3.66 [zip_derived_cl15970, zip_derived_cl16186])).
% 21.47/3.66 thf(zip_derived_cl16224, plain, ($false),
% 21.47/3.66 inference('simplify', [status(thm)], [zip_derived_cl16223])).
% 21.47/3.66
% 21.47/3.66 % SZS output end Refutation
% 21.47/3.66
% 21.47/3.66
% 21.47/3.66 % Terminating...
% 22.19/3.78 % Runner terminated.
% 22.19/3.79 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------