%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : BOO025-1 : TPTP v9.2.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.D8IijGUzY9 true
% Computer : n020.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 04:29:49 PM UTC 2025
% Result : Unsatisfiable 5.92s 1.41s
% Output : Refutation 5.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : BOO025-1 : TPTP v9.2.0. Released v2.2.0.
% 0.10/0.12 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.D8IijGUzY9 true
% 0.10/0.32 % Computer : n020.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Wed Oct 1 13:54:23 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.10/0.32 % Running portfolio for 300 s
% 0.10/0.32 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.32 % Number of cores: 8
% 0.10/0.32 % Python version: Python 3.6.8
% 0.10/0.33 % Running in FO mode
% 0.49/0.59 % Total configuration time : 435
% 0.49/0.59 % Estimated wc time : 1092
% 0.49/0.59 % Estimated cpu time (7 cpus) : 156.0
% 0.58/0.69 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.58/0.69 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.58/0.69 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.58/0.69 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.58/0.69 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.58/0.69 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.58/0.69 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 5.92/1.41 % Solved by fo/fo4.sh.
% 5.92/1.41 % done 449 iterations in 0.683s
% 5.92/1.41 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 5.92/1.41 % SZS output start Refutation
% 5.92/1.41 thf(pixley_type, type, pixley: $i > $i > $i > $i).
% 5.92/1.41 thf(n1_type, type, n1: $i).
% 5.92/1.41 thf(add_type, type, add: $i > $i > $i).
% 5.92/1.41 thf(a_type, type, a: $i).
% 5.92/1.41 thf(multiply_type, type, multiply: $i > $i > $i).
% 5.92/1.41 thf(inverse_type, type, inverse: $i > $i).
% 5.92/1.41 thf(b_type, type, b: $i).
% 5.92/1.41 thf(prove_equal_identity, conjecture,
% 5.92/1.41 (( multiply @ b @ ( inverse @ b ) ) = ( multiply @ a @ ( inverse @ a ) ))).
% 5.92/1.41 thf(zf_stmt_0, negated_conjecture,
% 5.92/1.41 (( multiply @ b @ ( inverse @ b ) ) != ( multiply @ a @ ( inverse @ a ) )),
% 5.92/1.41 inference('cnf.neg', [status(esa)], [prove_equal_identity])).
% 5.92/1.41 thf(zip_derived_cl7, plain,
% 5.92/1.41 (((multiply @ b @ (inverse @ b)) != (multiply @ a @ (inverse @ a)))),
% 5.92/1.41 inference('cnf', [status(esa)], [zf_stmt_0])).
% 5.92/1.41 thf(additive_inverse, axiom, (( add @ X @ ( inverse @ X ) ) = ( n1 ))).
% 5.92/1.41 thf(zip_derived_cl2, plain,
% 5.92/1.41 (![X0 : $i]: ((add @ X0 @ (inverse @ X0)) = (n1))),
% 5.92/1.41 inference('cnf', [status(esa)], [additive_inverse])).
% 5.92/1.41 thf(pixley_defn, axiom,
% 5.92/1.41 (( pixley @ X @ Y @ Z ) =
% 5.92/1.41 ( add @
% 5.92/1.41 ( multiply @ X @ ( inverse @ Y ) ) @
% 5.92/1.41 ( add @ ( multiply @ X @ Z ) @ ( multiply @ ( inverse @ Y ) @ Z ) ) ))).
% 5.92/1.41 thf(zip_derived_cl3, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.92/1.41 ((pixley @ X0 @ X1 @ X2)
% 5.92/1.41 = (add @ (multiply @ X0 @ (inverse @ X1)) @
% 5.92/1.41 (add @ (multiply @ X0 @ X2) @ (multiply @ (inverse @ X1) @ X2))))),
% 5.92/1.41 inference('cnf', [status(esa)], [pixley_defn])).
% 5.92/1.41 thf(multiply_add_property, axiom,
% 5.92/1.41 (( multiply @ X @ ( add @ Y @ Z ) ) =
% 5.92/1.41 ( add @ ( multiply @ Y @ X ) @ ( multiply @ Z @ X ) ))).
% 5.92/1.41 thf(zip_derived_cl1, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.92/1.41 ((multiply @ X1 @ (add @ X0 @ X2))
% 5.92/1.41 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 5.92/1.41 inference('cnf', [status(esa)], [multiply_add_property])).
% 5.92/1.41 thf(zip_derived_cl34, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.92/1.41 ((pixley @ X0 @ X1 @ X2)
% 5.92/1.41 = (add @ (multiply @ X0 @ (inverse @ X1)) @
% 5.92/1.41 (multiply @ X2 @ (add @ X0 @ (inverse @ X1)))))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 5.92/1.41 thf(zip_derived_cl38, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((pixley @ X0 @ X0 @ X1)
% 5.92/1.41 = (add @ (multiply @ X0 @ (inverse @ X0)) @ (multiply @ X1 @ n1)))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl34])).
% 5.92/1.41 thf(pixley1, axiom, (( pixley @ X @ X @ Y ) = ( Y ))).
% 5.92/1.41 thf(zip_derived_cl4, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((pixley @ X1 @ X1 @ X0) = (X0))),
% 5.92/1.41 inference('cnf', [status(esa)], [pixley1])).
% 5.92/1.41 thf(zip_derived_cl44, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((X1)
% 5.92/1.41 = (add @ (multiply @ X0 @ (inverse @ X0)) @ (multiply @ X1 @ n1)))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl38, zip_derived_cl4])).
% 5.92/1.41 thf(zip_derived_cl2, plain,
% 5.92/1.41 (![X0 : $i]: ((add @ X0 @ (inverse @ X0)) = (n1))),
% 5.92/1.41 inference('cnf', [status(esa)], [additive_inverse])).
% 5.92/1.41 thf(multiply_add, axiom, (( multiply @ ( add @ X @ Y ) @ Y ) = ( Y ))).
% 5.92/1.41 thf(zip_derived_cl0, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((multiply @ (add @ X1 @ X0) @ X0) = (X0))),
% 5.92/1.41 inference('cnf', [status(esa)], [multiply_add])).
% 5.92/1.41 thf(zip_derived_cl8, plain,
% 5.92/1.41 (![X0 : $i]: ((multiply @ n1 @ (inverse @ X0)) = (inverse @ X0))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 5.92/1.41 thf(zip_derived_cl8, plain,
% 5.92/1.41 (![X0 : $i]: ((multiply @ n1 @ (inverse @ X0)) = (inverse @ X0))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 5.92/1.41 thf(zip_derived_cl1, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.92/1.41 ((multiply @ X1 @ (add @ X0 @ X2))
% 5.92/1.41 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 5.92/1.41 inference('cnf', [status(esa)], [multiply_add_property])).
% 5.92/1.41 thf(zip_derived_cl12, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((multiply @ (inverse @ X0) @ (add @ n1 @ X1))
% 5.92/1.41 = (add @ (inverse @ X0) @ (multiply @ X1 @ (inverse @ X0))))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl1])).
% 5.92/1.41 thf(zip_derived_cl19, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((multiply @ (inverse @ X0) @ (add @ n1 @ n1))
% 5.92/1.41 = (add @ (inverse @ X0) @ (inverse @ X0)))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl12])).
% 5.92/1.41 thf(zip_derived_cl0, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((multiply @ (add @ X1 @ X0) @ X0) = (X0))),
% 5.92/1.41 inference('cnf', [status(esa)], [multiply_add])).
% 5.92/1.41 thf(zip_derived_cl20, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((multiply @ (multiply @ (inverse @ X0) @ (add @ n1 @ n1)) @
% 5.92/1.41 (inverse @ X0)) = (inverse @ X0))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl0])).
% 5.92/1.41 thf(zip_derived_cl8, plain,
% 5.92/1.41 (![X0 : $i]: ((multiply @ n1 @ (inverse @ X0)) = (inverse @ X0))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 5.92/1.41 thf(zip_derived_cl1, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.92/1.41 ((multiply @ X1 @ (add @ X0 @ X2))
% 5.92/1.41 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 5.92/1.41 inference('cnf', [status(esa)], [multiply_add_property])).
% 5.92/1.41 thf(zip_derived_cl13, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((multiply @ (inverse @ X0) @ (add @ X1 @ n1))
% 5.92/1.41 = (add @ (multiply @ X1 @ (inverse @ X0)) @ (inverse @ X0)))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl1])).
% 5.92/1.41 thf(zip_derived_cl193, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((multiply @ (inverse @ X0) @
% 5.92/1.41 (add @ (multiply @ (inverse @ X0) @ (add @ n1 @ n1)) @ n1))
% 5.92/1.41 = (add @ (inverse @ X0) @ (inverse @ X0)))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl20, zip_derived_cl13])).
% 5.92/1.41 thf(zip_derived_cl0, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((multiply @ (add @ X1 @ X0) @ X0) = (X0))),
% 5.92/1.41 inference('cnf', [status(esa)], [multiply_add])).
% 5.92/1.41 thf(zip_derived_cl8, plain,
% 5.92/1.41 (![X0 : $i]: ((multiply @ n1 @ (inverse @ X0)) = (inverse @ X0))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 5.92/1.41 thf(zip_derived_cl44, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((X1)
% 5.92/1.41 = (add @ (multiply @ X0 @ (inverse @ X0)) @ (multiply @ X1 @ n1)))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl38, zip_derived_cl4])).
% 5.92/1.41 thf(zip_derived_cl47, plain,
% 5.92/1.41 (![X0 : $i]: ((X0) = (add @ (inverse @ n1) @ (multiply @ X0 @ n1)))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl44])).
% 5.92/1.41 thf(zip_derived_cl49, plain,
% 5.92/1.41 (![X0 : $i]: ((add @ X0 @ n1) = (add @ (inverse @ n1) @ n1))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl47])).
% 5.92/1.41 thf(zip_derived_cl49, plain,
% 5.92/1.41 (![X0 : $i]: ((add @ X0 @ n1) = (add @ (inverse @ n1) @ n1))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl47])).
% 5.92/1.41 thf(zip_derived_cl57, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((add @ X1 @ n1) = (add @ X0 @ n1))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl49, zip_derived_cl49])).
% 5.92/1.41 thf(zip_derived_cl204, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((multiply @ (inverse @ X0) @ (add @ X0 @ n1))
% 5.92/1.41 = (add @ (inverse @ X0) @ (inverse @ X0)))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl193, zip_derived_cl57])).
% 5.92/1.41 thf(zip_derived_cl2, plain,
% 5.92/1.41 (![X0 : $i]: ((add @ X0 @ (inverse @ X0)) = (n1))),
% 5.92/1.41 inference('cnf', [status(esa)], [additive_inverse])).
% 5.92/1.41 thf(zip_derived_cl1, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.92/1.41 ((multiply @ X1 @ (add @ X0 @ X2))
% 5.92/1.41 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 5.92/1.41 inference('cnf', [status(esa)], [multiply_add_property])).
% 5.92/1.41 thf(zip_derived_cl0, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((multiply @ (add @ X1 @ X0) @ X0) = (X0))),
% 5.92/1.41 inference('cnf', [status(esa)], [multiply_add])).
% 5.92/1.41 thf(zip_derived_cl9, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.92/1.41 ((multiply @ (multiply @ X2 @ (add @ X1 @ X0)) @ (multiply @ X0 @ X2))
% 5.92/1.41 = (multiply @ X0 @ X2))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 5.92/1.41 thf(zip_derived_cl165, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((multiply @ (multiply @ X0 @ n1) @ (multiply @ (inverse @ X1) @ X0))
% 5.92/1.41 = (multiply @ (inverse @ X1) @ X0))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl9])).
% 5.92/1.41 thf(zip_derived_cl251, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((multiply @ (multiply @ (add @ X0 @ n1) @ n1) @
% 5.92/1.41 (add @ (inverse @ X0) @ (inverse @ X0)))
% 5.92/1.41 = (multiply @ (inverse @ X0) @ (add @ X0 @ n1)))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl204, zip_derived_cl165])).
% 5.92/1.41 thf(zip_derived_cl0, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((multiply @ (add @ X1 @ X0) @ X0) = (X0))),
% 5.92/1.41 inference('cnf', [status(esa)], [multiply_add])).
% 5.92/1.41 thf(zip_derived_cl204, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((multiply @ (inverse @ X0) @ (add @ X0 @ n1))
% 5.92/1.41 = (add @ (inverse @ X0) @ (inverse @ X0)))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl193, zip_derived_cl57])).
% 5.92/1.41 thf(zip_derived_cl258, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((multiply @ n1 @ (add @ (inverse @ X0) @ (inverse @ X0)))
% 5.92/1.41 = (add @ (inverse @ X0) @ (inverse @ X0)))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl251, zip_derived_cl0, zip_derived_cl204])).
% 5.92/1.41 thf(zip_derived_cl44, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((X1)
% 5.92/1.41 = (add @ (multiply @ X0 @ (inverse @ X0)) @ (multiply @ X1 @ n1)))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl38, zip_derived_cl4])).
% 5.92/1.41 thf(zip_derived_cl0, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((multiply @ (add @ X1 @ X0) @ X0) = (X0))),
% 5.92/1.41 inference('cnf', [status(esa)], [multiply_add])).
% 5.92/1.41 thf(zip_derived_cl0, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((multiply @ (add @ X1 @ X0) @ X0) = (X0))),
% 5.92/1.41 inference('cnf', [status(esa)], [multiply_add])).
% 5.92/1.41 thf(zip_derived_cl9, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.92/1.41 ((multiply @ (multiply @ X2 @ (add @ X1 @ X0)) @ (multiply @ X0 @ X2))
% 5.92/1.41 = (multiply @ X0 @ X2))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 5.92/1.41 thf(zip_derived_cl160, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.92/1.41 ((multiply @ (add @ X1 @ X0) @
% 5.92/1.41 (multiply @ X0 @ (add @ X2 @ (add @ X1 @ X0))))
% 5.92/1.41 = (multiply @ X0 @ (add @ X2 @ (add @ X1 @ X0))))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl9])).
% 5.92/1.41 thf(zip_derived_cl0, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((multiply @ (add @ X1 @ X0) @ X0) = (X0))),
% 5.92/1.41 inference('cnf', [status(esa)], [multiply_add])).
% 5.92/1.41 thf(zip_derived_cl1, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.92/1.41 ((multiply @ X1 @ (add @ X0 @ X2))
% 5.92/1.41 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 5.92/1.41 inference('cnf', [status(esa)], [multiply_add_property])).
% 5.92/1.41 thf(zip_derived_cl10, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.92/1.41 ((multiply @ X0 @ (add @ X2 @ (add @ X1 @ X0)))
% 5.92/1.41 = (add @ (multiply @ X2 @ X0) @ X0))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 5.92/1.41 thf(zip_derived_cl10, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.92/1.41 ((multiply @ X0 @ (add @ X2 @ (add @ X1 @ X0)))
% 5.92/1.41 = (add @ (multiply @ X2 @ X0) @ X0))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 5.92/1.41 thf(zip_derived_cl184, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.92/1.41 ((multiply @ (add @ X1 @ X0) @ (add @ (multiply @ X2 @ X0) @ X0))
% 5.92/1.41 = (add @ (multiply @ X2 @ X0) @ X0))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl160, zip_derived_cl10, zip_derived_cl10])).
% 5.92/1.41 thf(zip_derived_cl354, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.92/1.41 ((multiply @ (add @ X2 @ X0) @ (add @ X0 @ X0))
% 5.92/1.41 = (add @ (multiply @ (add @ X1 @ X0) @ X0) @ X0))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl184])).
% 5.92/1.41 thf(zip_derived_cl0, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((multiply @ (add @ X1 @ X0) @ X0) = (X0))),
% 5.92/1.41 inference('cnf', [status(esa)], [multiply_add])).
% 5.92/1.41 thf(zip_derived_cl385, plain,
% 5.92/1.41 (![X0 : $i, X2 : $i]:
% 5.92/1.41 ((multiply @ (add @ X2 @ X0) @ (add @ X0 @ X0)) = (add @ X0 @ X0))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl354, zip_derived_cl0])).
% 5.92/1.41 thf(zip_derived_cl417, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((multiply @ X0 @ (add @ (multiply @ X0 @ n1) @ (multiply @ X0 @ n1)))
% 5.92/1.41 = (add @ (multiply @ X0 @ n1) @ (multiply @ X0 @ n1)))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl44, zip_derived_cl385])).
% 5.92/1.41 thf(zip_derived_cl1, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.92/1.41 ((multiply @ X1 @ (add @ X0 @ X2))
% 5.92/1.41 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 5.92/1.41 inference('cnf', [status(esa)], [multiply_add_property])).
% 5.92/1.41 thf(zip_derived_cl1, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.92/1.41 ((multiply @ X1 @ (add @ X0 @ X2))
% 5.92/1.41 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 5.92/1.41 inference('cnf', [status(esa)], [multiply_add_property])).
% 5.92/1.41 thf(zip_derived_cl429, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((multiply @ X0 @ (multiply @ n1 @ (add @ X0 @ X0)))
% 5.92/1.41 = (multiply @ n1 @ (add @ X0 @ X0)))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl417, zip_derived_cl1, zip_derived_cl1])).
% 5.92/1.41 thf(zip_derived_cl539, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((multiply @ (inverse @ X0) @ (add @ (inverse @ X0) @ (inverse @ X0)))
% 5.92/1.41 = (multiply @ n1 @ (add @ (inverse @ X0) @ (inverse @ X0))))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl258, zip_derived_cl429])).
% 5.92/1.41 thf(zip_derived_cl258, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((multiply @ n1 @ (add @ (inverse @ X0) @ (inverse @ X0)))
% 5.92/1.41 = (add @ (inverse @ X0) @ (inverse @ X0)))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl251, zip_derived_cl0, zip_derived_cl204])).
% 5.92/1.41 thf(zip_derived_cl547, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((multiply @ (inverse @ X0) @ (add @ (inverse @ X0) @ (inverse @ X0)))
% 5.92/1.41 = (add @ (inverse @ X0) @ (inverse @ X0)))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl539, zip_derived_cl258])).
% 5.92/1.41 thf(zip_derived_cl547, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((multiply @ (inverse @ X0) @ (add @ (inverse @ X0) @ (inverse @ X0)))
% 5.92/1.41 = (add @ (inverse @ X0) @ (inverse @ X0)))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl539, zip_derived_cl258])).
% 5.92/1.41 thf(zip_derived_cl34, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.92/1.41 ((pixley @ X0 @ X1 @ X2)
% 5.92/1.41 = (add @ (multiply @ X0 @ (inverse @ X1)) @
% 5.92/1.41 (multiply @ X2 @ (add @ X0 @ (inverse @ X1)))))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 5.92/1.41 thf(zip_derived_cl733, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((pixley @ (inverse @ X0) @ X0 @ (inverse @ X0))
% 5.92/1.41 = (add @ (multiply @ (inverse @ X0) @ (inverse @ X0)) @
% 5.92/1.41 (add @ (inverse @ X0) @ (inverse @ X0))))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl547, zip_derived_cl34])).
% 5.92/1.41 thf(pixley3, axiom, (( pixley @ X @ Y @ X ) = ( X ))).
% 5.92/1.41 thf(zip_derived_cl6, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((pixley @ X0 @ X1 @ X0) = (X0))),
% 5.92/1.41 inference('cnf', [status(esa)], [pixley3])).
% 5.92/1.41 thf(zip_derived_cl739, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((inverse @ X0)
% 5.92/1.41 = (add @ (multiply @ (inverse @ X0) @ (inverse @ X0)) @
% 5.92/1.41 (add @ (inverse @ X0) @ (inverse @ X0))))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl733, zip_derived_cl6])).
% 5.92/1.41 thf(zip_derived_cl10, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.92/1.41 ((multiply @ X0 @ (add @ X2 @ (add @ X1 @ X0)))
% 5.92/1.41 = (add @ (multiply @ X2 @ X0) @ X0))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 5.92/1.41 thf(zip_derived_cl803, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((multiply @ (inverse @ X0) @ (inverse @ X0))
% 5.92/1.41 = (add @
% 5.92/1.41 (multiply @ (multiply @ (inverse @ X0) @ (inverse @ X0)) @
% 5.92/1.41 (inverse @ X0)) @
% 5.92/1.41 (inverse @ X0)))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl739, zip_derived_cl10])).
% 5.92/1.41 thf(zip_derived_cl13, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((multiply @ (inverse @ X0) @ (add @ X1 @ n1))
% 5.92/1.41 = (add @ (multiply @ X1 @ (inverse @ X0)) @ (inverse @ X0)))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl1])).
% 5.92/1.41 thf(zip_derived_cl826, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((multiply @ (inverse @ X0) @
% 5.92/1.41 (add @ (multiply @ (inverse @ X0) @ (inverse @ X0)) @ n1))
% 5.92/1.41 = (multiply @ (inverse @ X0) @ (inverse @ X0)))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl803, zip_derived_cl13])).
% 5.92/1.41 thf(zip_derived_cl57, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((add @ X1 @ n1) = (add @ X0 @ n1))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl49, zip_derived_cl49])).
% 5.92/1.41 thf(zip_derived_cl57, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((add @ X1 @ n1) = (add @ X0 @ n1))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl49, zip_derived_cl49])).
% 5.92/1.41 thf(zip_derived_cl19, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((multiply @ (inverse @ X0) @ (add @ n1 @ n1))
% 5.92/1.41 = (add @ (inverse @ X0) @ (inverse @ X0)))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl12])).
% 5.92/1.41 thf(zip_derived_cl69, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((multiply @ (inverse @ X1) @ (add @ X0 @ n1))
% 5.92/1.41 = (add @ (inverse @ X1) @ (inverse @ X1)))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl57, zip_derived_cl19])).
% 5.92/1.41 thf(zip_derived_cl832, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((add @ (inverse @ X0) @ (inverse @ X0))
% 5.92/1.41 = (multiply @ (inverse @ X0) @ (inverse @ X0)))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl826, zip_derived_cl57, zip_derived_cl69])).
% 5.92/1.41 thf(zip_derived_cl832, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((add @ (inverse @ X0) @ (inverse @ X0))
% 5.92/1.41 = (multiply @ (inverse @ X0) @ (inverse @ X0)))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl826, zip_derived_cl57, zip_derived_cl69])).
% 5.92/1.41 thf(zip_derived_cl853, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((multiply @ (inverse @ X0) @
% 5.92/1.41 (multiply @ (inverse @ X0) @ (inverse @ X0)))
% 5.92/1.41 = (multiply @ (inverse @ X0) @ (inverse @ X0)))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl547, zip_derived_cl832, zip_derived_cl832])).
% 5.92/1.41 thf(zip_derived_cl739, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((inverse @ X0)
% 5.92/1.41 = (add @ (multiply @ (inverse @ X0) @ (inverse @ X0)) @
% 5.92/1.41 (add @ (inverse @ X0) @ (inverse @ X0))))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl733, zip_derived_cl6])).
% 5.92/1.41 thf(zip_derived_cl832, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((add @ (inverse @ X0) @ (inverse @ X0))
% 5.92/1.41 = (multiply @ (inverse @ X0) @ (inverse @ X0)))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl826, zip_derived_cl57, zip_derived_cl69])).
% 5.92/1.41 thf(zip_derived_cl1, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.92/1.41 ((multiply @ X1 @ (add @ X0 @ X2))
% 5.92/1.41 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 5.92/1.41 inference('cnf', [status(esa)], [multiply_add_property])).
% 5.92/1.41 thf(zip_derived_cl832, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((add @ (inverse @ X0) @ (inverse @ X0))
% 5.92/1.41 = (multiply @ (inverse @ X0) @ (inverse @ X0)))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl826, zip_derived_cl57, zip_derived_cl69])).
% 5.92/1.41 thf(zip_derived_cl855, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((inverse @ X0)
% 5.92/1.41 = (multiply @ (inverse @ X0) @
% 5.92/1.41 (multiply @ (inverse @ X0) @ (inverse @ X0))))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl739, zip_derived_cl832, zip_derived_cl1,
% 5.92/1.41 zip_derived_cl832])).
% 5.92/1.41 thf(zip_derived_cl1007, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((inverse @ X0) = (multiply @ (inverse @ X0) @ (inverse @ X0)))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl853, zip_derived_cl855])).
% 5.92/1.41 thf(zip_derived_cl2, plain,
% 5.92/1.41 (![X0 : $i]: ((add @ X0 @ (inverse @ X0)) = (n1))),
% 5.92/1.41 inference('cnf', [status(esa)], [additive_inverse])).
% 5.92/1.41 thf(zip_derived_cl12, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((multiply @ (inverse @ X0) @ (add @ n1 @ X1))
% 5.92/1.41 = (add @ (inverse @ X0) @ (multiply @ X1 @ (inverse @ X0))))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl1])).
% 5.92/1.41 thf(zip_derived_cl17, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((multiply @ (inverse @ X0) @ n1)
% 5.92/1.41 = (add @ (inverse @ X0) @
% 5.92/1.41 (multiply @ (inverse @ n1) @ (inverse @ X0))))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl12])).
% 5.92/1.41 thf(zip_derived_cl1027, plain,
% 5.92/1.41 (((multiply @ (inverse @ n1) @ n1)
% 5.92/1.41 = (add @ (inverse @ n1) @ (inverse @ n1)))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl1007, zip_derived_cl17])).
% 5.92/1.41 thf(zip_derived_cl832, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((add @ (inverse @ X0) @ (inverse @ X0))
% 5.92/1.41 = (multiply @ (inverse @ X0) @ (inverse @ X0)))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl826, zip_derived_cl57, zip_derived_cl69])).
% 5.92/1.41 thf(zip_derived_cl1007, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((inverse @ X0) = (multiply @ (inverse @ X0) @ (inverse @ X0)))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl853, zip_derived_cl855])).
% 5.92/1.41 thf(zip_derived_cl1009, plain,
% 5.92/1.41 (![X0 : $i]: ((add @ (inverse @ X0) @ (inverse @ X0)) = (inverse @ X0))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl832, zip_derived_cl1007])).
% 5.92/1.41 thf(zip_derived_cl1099, plain,
% 5.92/1.41 (((multiply @ (inverse @ n1) @ n1) = (inverse @ n1))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl1027, zip_derived_cl1009])).
% 5.92/1.41 thf(zip_derived_cl1, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.92/1.41 ((multiply @ X1 @ (add @ X0 @ X2))
% 5.92/1.41 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 5.92/1.41 inference('cnf', [status(esa)], [multiply_add_property])).
% 5.92/1.41 thf(zip_derived_cl1100, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((multiply @ n1 @ (add @ (inverse @ n1) @ X0))
% 5.92/1.41 = (add @ (inverse @ n1) @ (multiply @ X0 @ n1)))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl1099, zip_derived_cl1])).
% 5.92/1.41 thf(zip_derived_cl47, plain,
% 5.92/1.41 (![X0 : $i]: ((X0) = (add @ (inverse @ n1) @ (multiply @ X0 @ n1)))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl44])).
% 5.92/1.41 thf(zip_derived_cl1109, plain,
% 5.92/1.41 (![X0 : $i]: ((multiply @ n1 @ (add @ (inverse @ n1) @ X0)) = (X0))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl1100, zip_derived_cl47])).
% 5.92/1.41 thf(zip_derived_cl47, plain,
% 5.92/1.41 (![X0 : $i]: ((X0) = (add @ (inverse @ n1) @ (multiply @ X0 @ n1)))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl44])).
% 5.92/1.41 thf(zip_derived_cl1109, plain,
% 5.92/1.41 (![X0 : $i]: ((multiply @ n1 @ (add @ (inverse @ n1) @ X0)) = (X0))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl1100, zip_derived_cl47])).
% 5.92/1.41 thf(zip_derived_cl1265, plain,
% 5.92/1.41 (![X0 : $i]: ((multiply @ n1 @ X0) = (multiply @ X0 @ n1))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl47, zip_derived_cl1109])).
% 5.92/1.41 thf(zip_derived_cl44, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((X1)
% 5.92/1.41 = (add @ (multiply @ X0 @ (inverse @ X0)) @ (multiply @ X1 @ n1)))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl38, zip_derived_cl4])).
% 5.92/1.41 thf(zip_derived_cl0, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((multiply @ (add @ X1 @ X0) @ X0) = (X0))),
% 5.92/1.41 inference('cnf', [status(esa)], [multiply_add])).
% 5.92/1.41 thf(zip_derived_cl45, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((multiply @ X0 @ (multiply @ X0 @ n1)) = (multiply @ X0 @ n1))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl44, zip_derived_cl0])).
% 5.92/1.41 thf(zip_derived_cl1492, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((multiply @ X0 @ (multiply @ n1 @ X0)) = (multiply @ X0 @ n1))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl1265, zip_derived_cl45])).
% 5.92/1.41 thf(zip_derived_cl1681, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((multiply @ (add @ (inverse @ n1) @ X0) @ X0)
% 5.92/1.41 = (multiply @ (add @ (inverse @ n1) @ X0) @ n1))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl1109, zip_derived_cl1492])).
% 5.92/1.41 thf(zip_derived_cl0, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((multiply @ (add @ X1 @ X0) @ X0) = (X0))),
% 5.92/1.41 inference('cnf', [status(esa)], [multiply_add])).
% 5.92/1.41 thf(zip_derived_cl1690, plain,
% 5.92/1.41 (![X0 : $i]: ((X0) = (multiply @ (add @ (inverse @ n1) @ X0) @ n1))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl1681, zip_derived_cl0])).
% 5.92/1.41 thf(zip_derived_cl1265, plain,
% 5.92/1.41 (![X0 : $i]: ((multiply @ n1 @ X0) = (multiply @ X0 @ n1))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl47, zip_derived_cl1109])).
% 5.92/1.41 thf(zip_derived_cl57, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((add @ X1 @ n1) = (add @ X0 @ n1))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl49, zip_derived_cl49])).
% 5.92/1.41 thf(zip_derived_cl0, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((multiply @ (add @ X1 @ X0) @ X0) = (X0))),
% 5.92/1.41 inference('cnf', [status(esa)], [multiply_add])).
% 5.92/1.41 thf(zip_derived_cl1, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.92/1.41 ((multiply @ X1 @ (add @ X0 @ X2))
% 5.92/1.41 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 5.92/1.41 inference('cnf', [status(esa)], [multiply_add_property])).
% 5.92/1.41 thf(zip_derived_cl11, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.92/1.41 ((multiply @ X0 @ (add @ (add @ X2 @ X0) @ X1))
% 5.92/1.41 = (add @ X0 @ (multiply @ X1 @ X0)))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 5.92/1.41 thf(zip_derived_cl104, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((multiply @ X1 @ (add @ X0 @ n1)) = (add @ X1 @ (multiply @ n1 @ X1)))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl57, zip_derived_cl11])).
% 5.92/1.41 thf(zip_derived_cl57, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((add @ X1 @ n1) = (add @ X0 @ n1))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl49, zip_derived_cl49])).
% 5.92/1.41 thf(zip_derived_cl429, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((multiply @ X0 @ (multiply @ n1 @ (add @ X0 @ X0)))
% 5.92/1.41 = (multiply @ n1 @ (add @ X0 @ X0)))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl417, zip_derived_cl1, zip_derived_cl1])).
% 5.92/1.41 thf(zip_derived_cl540, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((multiply @ n1 @ (multiply @ n1 @ (add @ X0 @ n1)))
% 5.92/1.41 = (multiply @ n1 @ (add @ n1 @ n1)))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl57, zip_derived_cl429])).
% 5.92/1.41 thf(zip_derived_cl57, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((add @ X1 @ n1) = (add @ X0 @ n1))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl49, zip_derived_cl49])).
% 5.92/1.41 thf(zip_derived_cl1109, plain,
% 5.92/1.41 (![X0 : $i]: ((multiply @ n1 @ (add @ (inverse @ n1) @ X0)) = (X0))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl1100, zip_derived_cl47])).
% 5.92/1.41 thf(zip_derived_cl1261, plain,
% 5.92/1.41 (![X0 : $i]: ((multiply @ n1 @ (add @ X0 @ n1)) = (n1))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl57, zip_derived_cl1109])).
% 5.92/1.41 thf(zip_derived_cl2, plain,
% 5.92/1.41 (![X0 : $i]: ((add @ X0 @ (inverse @ X0)) = (n1))),
% 5.92/1.41 inference('cnf', [status(esa)], [additive_inverse])).
% 5.92/1.41 thf(zip_derived_cl1109, plain,
% 5.92/1.41 (![X0 : $i]: ((multiply @ n1 @ (add @ (inverse @ n1) @ X0)) = (X0))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl1100, zip_derived_cl47])).
% 5.92/1.41 thf(zip_derived_cl1260, plain,
% 5.92/1.41 (((multiply @ n1 @ n1) = (inverse @ (inverse @ n1)))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1109])).
% 5.92/1.41 thf(zip_derived_cl1261, plain,
% 5.92/1.41 (![X0 : $i]: ((multiply @ n1 @ (add @ X0 @ n1)) = (n1))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl57, zip_derived_cl1109])).
% 5.92/1.41 thf(zip_derived_cl1300, plain, (((inverse @ (inverse @ n1)) = (n1))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl540, zip_derived_cl1261, zip_derived_cl1260,
% 5.92/1.41 zip_derived_cl1261])).
% 5.92/1.41 thf(zip_derived_cl104, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((multiply @ X1 @ (add @ X0 @ n1)) = (add @ X1 @ (multiply @ n1 @ X1)))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl57, zip_derived_cl11])).
% 5.92/1.41 thf(zip_derived_cl13, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((multiply @ (inverse @ X0) @ (add @ X1 @ n1))
% 5.92/1.41 = (add @ (multiply @ X1 @ (inverse @ X0)) @ (inverse @ X0)))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl1])).
% 5.92/1.41 thf(zip_derived_cl127, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((add @ (inverse @ X0) @ (multiply @ n1 @ (inverse @ X0)))
% 5.92/1.41 = (add @ (multiply @ X1 @ (inverse @ X0)) @ (inverse @ X0)))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl104, zip_derived_cl13])).
% 5.92/1.41 thf(zip_derived_cl8, plain,
% 5.92/1.41 (![X0 : $i]: ((multiply @ n1 @ (inverse @ X0)) = (inverse @ X0))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 5.92/1.41 thf(zip_derived_cl142, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((add @ (inverse @ X0) @ (inverse @ X0))
% 5.92/1.41 = (add @ (multiply @ X1 @ (inverse @ X0)) @ (inverse @ X0)))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl127, zip_derived_cl8])).
% 5.92/1.41 thf(zip_derived_cl832, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((add @ (inverse @ X0) @ (inverse @ X0))
% 5.92/1.41 = (multiply @ (inverse @ X0) @ (inverse @ X0)))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl826, zip_derived_cl57, zip_derived_cl69])).
% 5.92/1.41 thf(zip_derived_cl850, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((multiply @ (inverse @ X0) @ (inverse @ X0))
% 5.92/1.41 = (add @ (multiply @ X1 @ (inverse @ X0)) @ (inverse @ X0)))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl142, zip_derived_cl832])).
% 5.92/1.41 thf(zip_derived_cl1007, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((inverse @ X0) = (multiply @ (inverse @ X0) @ (inverse @ X0)))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl853, zip_derived_cl855])).
% 5.92/1.41 thf(zip_derived_cl1010, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((inverse @ X0)
% 5.92/1.41 = (add @ (multiply @ X1 @ (inverse @ X0)) @ (inverse @ X0)))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl850, zip_derived_cl1007])).
% 5.92/1.41 thf(zip_derived_cl1344, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((inverse @ (inverse @ n1))
% 5.92/1.41 = (add @ (multiply @ X0 @ (inverse @ (inverse @ n1))) @ n1))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl1300, zip_derived_cl1010])).
% 5.92/1.41 thf(zip_derived_cl1300, plain, (((inverse @ (inverse @ n1)) = (n1))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl540, zip_derived_cl1261, zip_derived_cl1260,
% 5.92/1.41 zip_derived_cl1261])).
% 5.92/1.41 thf(zip_derived_cl1300, plain, (((inverse @ (inverse @ n1)) = (n1))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl540, zip_derived_cl1261, zip_derived_cl1260,
% 5.92/1.41 zip_derived_cl1261])).
% 5.92/1.41 thf(zip_derived_cl57, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((add @ X1 @ n1) = (add @ X0 @ n1))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl49, zip_derived_cl49])).
% 5.92/1.41 thf(zip_derived_cl1367, plain, (![X0 : $i]: ((n1) = (add @ X0 @ n1))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl1344, zip_derived_cl1300, zip_derived_cl1300,
% 5.92/1.41 zip_derived_cl57])).
% 5.92/1.41 thf(zip_derived_cl1378, plain,
% 5.92/1.41 (![X1 : $i]: ((multiply @ X1 @ n1) = (add @ X1 @ (multiply @ n1 @ X1)))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl104, zip_derived_cl1367])).
% 5.92/1.41 thf(zip_derived_cl1761, plain,
% 5.92/1.41 (![X0 : $i]: ((multiply @ X0 @ n1) = (add @ X0 @ (multiply @ X0 @ n1)))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl1265, zip_derived_cl1378])).
% 5.92/1.41 thf(zip_derived_cl1965, plain,
% 5.92/1.41 (![X0 : $i]:
% 5.92/1.41 ((multiply @ (add @ (inverse @ n1) @ X0) @ n1)
% 5.92/1.41 = (add @ (add @ (inverse @ n1) @ X0) @ X0))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl1690, zip_derived_cl1761])).
% 5.92/1.41 thf(zip_derived_cl1690, plain,
% 5.92/1.41 (![X0 : $i]: ((X0) = (multiply @ (add @ (inverse @ n1) @ X0) @ n1))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl1681, zip_derived_cl0])).
% 5.92/1.41 thf(zip_derived_cl1970, plain,
% 5.92/1.41 (![X0 : $i]: ((X0) = (add @ (add @ (inverse @ n1) @ X0) @ X0))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl1965, zip_derived_cl1690])).
% 5.92/1.41 thf(zip_derived_cl11, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.92/1.41 ((multiply @ X0 @ (add @ (add @ X2 @ X0) @ X1))
% 5.92/1.41 = (add @ X0 @ (multiply @ X1 @ X0)))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 5.92/1.41 thf(zip_derived_cl2000, plain,
% 5.92/1.41 (![X0 : $i]: ((multiply @ X0 @ X0) = (add @ X0 @ (multiply @ X0 @ X0)))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl1970, zip_derived_cl11])).
% 5.92/1.41 thf(zip_derived_cl1970, plain,
% 5.92/1.41 (![X0 : $i]: ((X0) = (add @ (add @ (inverse @ n1) @ X0) @ X0))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl1965, zip_derived_cl1690])).
% 5.92/1.41 thf(zip_derived_cl0, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((multiply @ (add @ X1 @ X0) @ X0) = (X0))),
% 5.92/1.41 inference('cnf', [status(esa)], [multiply_add])).
% 5.92/1.41 thf(zip_derived_cl1985, plain, (![X0 : $i]: ((multiply @ X0 @ X0) = (X0))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl1970, zip_derived_cl0])).
% 5.92/1.41 thf(zip_derived_cl1985, plain, (![X0 : $i]: ((multiply @ X0 @ X0) = (X0))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl1970, zip_derived_cl0])).
% 5.92/1.41 thf(zip_derived_cl2210, plain, (![X0 : $i]: ((X0) = (add @ X0 @ X0))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl2000, zip_derived_cl1985, zip_derived_cl1985])).
% 5.92/1.41 thf(zip_derived_cl1, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.92/1.41 ((multiply @ X1 @ (add @ X0 @ X2))
% 5.92/1.41 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 5.92/1.41 inference('cnf', [status(esa)], [multiply_add_property])).
% 5.92/1.41 thf(zip_derived_cl2229, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((multiply @ X0 @ (add @ X1 @ X1)) = (multiply @ X1 @ X0))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl2210, zip_derived_cl1])).
% 5.92/1.41 thf(zip_derived_cl2210, plain, (![X0 : $i]: ((X0) = (add @ X0 @ X0))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl2000, zip_derived_cl1985, zip_derived_cl1985])).
% 5.92/1.41 thf(zip_derived_cl2243, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl2229, zip_derived_cl2210])).
% 5.92/1.41 thf(zip_derived_cl1970, plain,
% 5.92/1.41 (![X0 : $i]: ((X0) = (add @ (add @ (inverse @ n1) @ X0) @ X0))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl1965, zip_derived_cl1690])).
% 5.92/1.41 thf(zip_derived_cl10, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.92/1.41 ((multiply @ X0 @ (add @ X2 @ (add @ X1 @ X0)))
% 5.92/1.41 = (add @ (multiply @ X2 @ X0) @ X0))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 5.92/1.41 thf(zip_derived_cl1987, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((multiply @ X0 @ (add @ X1 @ X0)) = (add @ (multiply @ X1 @ X0) @ X0))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl1970, zip_derived_cl10])).
% 5.92/1.41 thf(zip_derived_cl2210, plain, (![X0 : $i]: ((X0) = (add @ X0 @ X0))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl2000, zip_derived_cl1985, zip_derived_cl1985])).
% 5.92/1.41 thf(zip_derived_cl10, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.92/1.41 ((multiply @ X0 @ (add @ X2 @ (add @ X1 @ X0)))
% 5.92/1.41 = (add @ (multiply @ X2 @ X0) @ X0))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 5.92/1.41 thf(zip_derived_cl2221, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((multiply @ X0 @ (add @ X1 @ X0))
% 5.92/1.41 = (add @ (multiply @ (add @ X1 @ X0) @ X0) @ X0))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl2210, zip_derived_cl10])).
% 5.92/1.41 thf(zip_derived_cl0, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((multiply @ (add @ X1 @ X0) @ X0) = (X0))),
% 5.92/1.41 inference('cnf', [status(esa)], [multiply_add])).
% 5.92/1.41 thf(zip_derived_cl2210, plain, (![X0 : $i]: ((X0) = (add @ X0 @ X0))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl2000, zip_derived_cl1985, zip_derived_cl1985])).
% 5.92/1.41 thf(zip_derived_cl2237, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ (add @ X1 @ X0)) = (X0))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl2221, zip_derived_cl0, zip_derived_cl2210])).
% 5.92/1.41 thf(zip_derived_cl2445, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((X0) = (add @ (multiply @ X1 @ X0) @ X0))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl1987, zip_derived_cl2237])).
% 5.92/1.41 thf(zip_derived_cl2459, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((X1) = (add @ (multiply @ X1 @ X0) @ X1))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl2243, zip_derived_cl2445])).
% 5.92/1.41 thf(zip_derived_cl44, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((X1)
% 5.92/1.41 = (add @ (multiply @ X0 @ (inverse @ X0)) @ (multiply @ X1 @ n1)))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl38, zip_derived_cl4])).
% 5.92/1.41 thf(zip_derived_cl2648, plain, (![X0 : $i]: ((X0) = (multiply @ X0 @ n1))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl2459, zip_derived_cl44])).
% 5.92/1.41 thf(zip_derived_cl2676, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((X1) = (add @ (multiply @ X0 @ (inverse @ X0)) @ X1))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl44, zip_derived_cl2648])).
% 5.92/1.41 thf(zip_derived_cl2, plain,
% 5.92/1.41 (![X0 : $i]: ((add @ X0 @ (inverse @ X0)) = (n1))),
% 5.92/1.41 inference('cnf', [status(esa)], [additive_inverse])).
% 5.92/1.41 thf(zip_derived_cl2931, plain,
% 5.92/1.41 (![X0 : $i]: ((inverse @ (multiply @ X0 @ (inverse @ X0))) = (n1))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl2676, zip_derived_cl2])).
% 5.92/1.41 thf(zip_derived_cl8, plain,
% 5.92/1.41 (![X0 : $i]: ((multiply @ n1 @ (inverse @ X0)) = (inverse @ X0))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 5.92/1.41 thf(zip_derived_cl34, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.92/1.41 ((pixley @ X0 @ X1 @ X2)
% 5.92/1.41 = (add @ (multiply @ X0 @ (inverse @ X1)) @
% 5.92/1.41 (multiply @ X2 @ (add @ X0 @ (inverse @ X1)))))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 5.92/1.41 thf(zip_derived_cl42, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((pixley @ n1 @ X0 @ X1)
% 5.92/1.41 = (add @ (inverse @ X0) @
% 5.92/1.41 (multiply @ X1 @ (add @ n1 @ (inverse @ X0)))))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl34])).
% 5.92/1.41 thf(zip_derived_cl2931, plain,
% 5.92/1.41 (![X0 : $i]: ((inverse @ (multiply @ X0 @ (inverse @ X0))) = (n1))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl2676, zip_derived_cl2])).
% 5.92/1.41 thf(zip_derived_cl12, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((multiply @ (inverse @ X0) @ (add @ n1 @ X1))
% 5.92/1.41 = (add @ (inverse @ X0) @ (multiply @ X1 @ (inverse @ X0))))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl1])).
% 5.92/1.41 thf(zip_derived_cl34, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.92/1.41 ((pixley @ X0 @ X1 @ X2)
% 5.92/1.41 = (add @ (multiply @ X0 @ (inverse @ X1)) @
% 5.92/1.41 (multiply @ X2 @ (add @ X0 @ (inverse @ X1)))))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 5.92/1.41 thf(zip_derived_cl37, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((pixley @ n1 @ X1 @ (inverse @ X0))
% 5.92/1.41 = (add @ (multiply @ n1 @ (inverse @ X1)) @
% 5.92/1.41 (add @ (inverse @ X0) @
% 5.92/1.41 (multiply @ (inverse @ X1) @ (inverse @ X0)))))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl34])).
% 5.92/1.41 thf(zip_derived_cl8, plain,
% 5.92/1.41 (![X0 : $i]: ((multiply @ n1 @ (inverse @ X0)) = (inverse @ X0))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 5.92/1.41 thf(zip_derived_cl43, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((pixley @ n1 @ X1 @ (inverse @ X0))
% 5.92/1.41 = (add @ (inverse @ X1) @
% 5.92/1.41 (add @ (inverse @ X0) @
% 5.92/1.41 (multiply @ (inverse @ X1) @ (inverse @ X0)))))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl37, zip_derived_cl8])).
% 5.92/1.41 thf(zip_derived_cl2968, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((pixley @ n1 @ X1 @ (inverse @ (multiply @ X0 @ (inverse @ X0))))
% 5.92/1.41 = (add @ (inverse @ X1) @
% 5.92/1.41 (add @ (inverse @ (multiply @ X0 @ (inverse @ X0))) @
% 5.92/1.41 (multiply @ (inverse @ X1) @ n1))))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl2931, zip_derived_cl43])).
% 5.92/1.41 thf(zip_derived_cl2931, plain,
% 5.92/1.41 (![X0 : $i]: ((inverse @ (multiply @ X0 @ (inverse @ X0))) = (n1))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl2676, zip_derived_cl2])).
% 5.92/1.41 thf(zip_derived_cl6, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((pixley @ X0 @ X1 @ X0) = (X0))),
% 5.92/1.41 inference('cnf', [status(esa)], [pixley3])).
% 5.92/1.41 thf(zip_derived_cl2931, plain,
% 5.92/1.41 (![X0 : $i]: ((inverse @ (multiply @ X0 @ (inverse @ X0))) = (n1))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl2676, zip_derived_cl2])).
% 5.92/1.41 thf(zip_derived_cl2648, plain, (![X0 : $i]: ((X0) = (multiply @ X0 @ n1))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl2459, zip_derived_cl44])).
% 5.92/1.41 thf(zip_derived_cl2237, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ (add @ X1 @ X0)) = (X0))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl2221, zip_derived_cl0, zip_derived_cl2210])).
% 5.92/1.41 thf(zip_derived_cl2445, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((X0) = (add @ (multiply @ X1 @ X0) @ X0))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl1987, zip_derived_cl2237])).
% 5.92/1.41 thf(zip_derived_cl2467, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((add @ X1 @ X0) = (add @ X0 @ (add @ X1 @ X0)))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl2237, zip_derived_cl2445])).
% 5.92/1.41 thf(zip_derived_cl2997, plain,
% 5.92/1.41 (![X1 : $i]: ((n1) = (add @ n1 @ (inverse @ X1)))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl2968, zip_derived_cl2931, zip_derived_cl6,
% 5.92/1.41 zip_derived_cl2931, zip_derived_cl2648, zip_derived_cl2467])).
% 5.92/1.41 thf(zip_derived_cl2648, plain, (![X0 : $i]: ((X0) = (multiply @ X0 @ n1))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl2459, zip_derived_cl44])).
% 5.92/1.41 thf(zip_derived_cl3007, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((pixley @ n1 @ X0 @ X1) = (add @ (inverse @ X0) @ X1))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl42, zip_derived_cl2997, zip_derived_cl2648])).
% 5.92/1.41 thf(pixley2, axiom, (( pixley @ X @ Y @ Y ) = ( X ))).
% 5.92/1.41 thf(zip_derived_cl5, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((pixley @ X0 @ X1 @ X1) = (X0))),
% 5.92/1.41 inference('cnf', [status(esa)], [pixley2])).
% 5.92/1.41 thf(zip_derived_cl3138, plain,
% 5.92/1.41 (![X0 : $i]: ((add @ (inverse @ X0) @ X0) = (n1))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl3007, zip_derived_cl5])).
% 5.92/1.41 thf(zip_derived_cl34, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.92/1.41 ((pixley @ X0 @ X1 @ X2)
% 5.92/1.41 = (add @ (multiply @ X0 @ (inverse @ X1)) @
% 5.92/1.41 (multiply @ X2 @ (add @ X0 @ (inverse @ X1)))))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 5.92/1.41 thf(zip_derived_cl3160, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((pixley @ (inverse @ (inverse @ X0)) @ X0 @ X1)
% 5.92/1.41 = (add @ (multiply @ (inverse @ (inverse @ X0)) @ (inverse @ X0)) @
% 5.92/1.41 (multiply @ X1 @ n1)))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl3138, zip_derived_cl34])).
% 5.92/1.41 thf(zip_derived_cl2243, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl2229, zip_derived_cl2210])).
% 5.92/1.41 thf(zip_derived_cl2648, plain, (![X0 : $i]: ((X0) = (multiply @ X0 @ n1))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl2459, zip_derived_cl44])).
% 5.92/1.41 thf(zip_derived_cl2676, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((X1) = (add @ (multiply @ X0 @ (inverse @ X0)) @ X1))),
% 5.92/1.41 inference('demod', [status(thm)], [zip_derived_cl44, zip_derived_cl2648])).
% 5.92/1.41 thf(zip_derived_cl3172, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]:
% 5.92/1.41 ((pixley @ (inverse @ (inverse @ X0)) @ X0 @ X1) = (X1))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl3160, zip_derived_cl2243, zip_derived_cl2648,
% 5.92/1.41 zip_derived_cl2676])).
% 5.92/1.41 thf(zip_derived_cl5, plain,
% 5.92/1.41 (![X0 : $i, X1 : $i]: ((pixley @ X0 @ X1 @ X1) = (X0))),
% 5.92/1.41 inference('cnf', [status(esa)], [pixley2])).
% 5.92/1.41 thf(zip_derived_cl3337, plain,
% 5.92/1.41 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl3172, zip_derived_cl5])).
% 5.92/1.41 thf(zip_derived_cl3371, plain,
% 5.92/1.41 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (inverse @ n1))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl2931, zip_derived_cl3337])).
% 5.92/1.41 thf(zip_derived_cl3371, plain,
% 5.92/1.41 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (inverse @ n1))),
% 5.92/1.41 inference('sup+', [status(thm)], [zip_derived_cl2931, zip_derived_cl3337])).
% 5.92/1.41 thf(zip_derived_cl3394, plain, (((inverse @ n1) != (inverse @ n1))),
% 5.92/1.41 inference('demod', [status(thm)],
% 5.92/1.41 [zip_derived_cl7, zip_derived_cl3371, zip_derived_cl3371])).
% 5.92/1.41 thf(zip_derived_cl3395, plain, ($false),
% 5.92/1.41 inference('simplify', [status(thm)], [zip_derived_cl3394])).
% 5.92/1.41
% 5.92/1.41 % SZS output end Refutation
% 5.92/1.41
% 5.92/1.41
% 5.92/1.41 % Terminating...
% 6.53/1.51 % Runner terminated.
% 6.53/1.52 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------