TSTP Solution File: BOO026-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : BOO026-1 : TPTP v8.1.2. Released v2.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.698XgofLcl true
% Computer : n008.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 9.45s 2.09s
% Output : Refutation 9.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO026-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.698XgofLcl true
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 08:19:17 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.21/0.35 % Running in FO mode
% 0.21/0.62 % Total configuration time : 435
% 0.21/0.62 % Estimated wc time : 1092
% 0.21/0.62 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.69 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.74 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.74 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.74 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.74 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.74 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 9.45/2.09 % Solved by fo/fo5.sh.
% 9.45/2.09 % done 485 iterations in 1.319s
% 9.45/2.09 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 9.45/2.09 % SZS output start Refutation
% 9.45/2.09 thf(b_type, type, b: $i).
% 9.45/2.09 thf(a_type, type, a: $i).
% 9.45/2.09 thf(inverse_type, type, inverse: $i > $i).
% 9.45/2.09 thf(add_type, type, add: $i > $i > $i).
% 9.45/2.09 thf(n0_type, type, n0: $i).
% 9.45/2.09 thf(multiply_type, type, multiply: $i > $i > $i).
% 9.45/2.09 thf(n1_type, type, n1: $i).
% 9.45/2.09 thf(prove_multiply_add, conjecture,
% 9.45/2.09 (( multiply @ ( add @ a @ b ) @ b ) = ( b ))).
% 9.45/2.09 thf(zf_stmt_0, negated_conjecture,
% 9.45/2.09 (( multiply @ ( add @ a @ b ) @ b ) != ( b )),
% 9.45/2.09 inference('cnf.neg', [status(esa)], [prove_multiply_add])).
% 9.45/2.09 thf(zip_derived_cl10, plain, (((multiply @ (add @ a @ b) @ b) != (b))),
% 9.45/2.09 inference('cnf', [status(esa)], [zf_stmt_0])).
% 9.45/2.09 thf(additive_inverse, axiom, (( add @ X @ ( inverse @ X ) ) = ( n1 ))).
% 9.45/2.09 thf(zip_derived_cl1, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ X0 @ (inverse @ X0)) = (n1))),
% 9.45/2.09 inference('cnf', [status(esa)], [additive_inverse])).
% 9.45/2.09 thf(pixley1_dual, axiom,
% 9.45/2.09 (( multiply @
% 9.45/2.09 ( add @ X @ ( inverse @ X ) ) @
% 9.45/2.09 ( multiply @ ( add @ X @ Y ) @ ( add @ ( inverse @ X ) @ Y ) ) ) =
% 9.45/2.09 ( Y ))).
% 9.45/2.09 thf(zip_derived_cl7, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((multiply @ (add @ X1 @ (inverse @ X1)) @
% 9.45/2.09 (multiply @ (add @ X1 @ X0) @ (add @ (inverse @ X1) @ X0))) = (
% 9.45/2.09 X0))),
% 9.45/2.09 inference('cnf', [status(esa)], [pixley1_dual])).
% 9.45/2.09 thf(zip_derived_cl1, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ X0 @ (inverse @ X0)) = (n1))),
% 9.45/2.09 inference('cnf', [status(esa)], [additive_inverse])).
% 9.45/2.09 thf(add_multiply_property, axiom,
% 9.45/2.09 (( add @ X @ ( multiply @ Y @ Z ) ) =
% 9.45/2.09 ( multiply @ ( add @ Y @ X ) @ ( add @ Z @ X ) ))).
% 9.45/2.09 thf(zip_derived_cl2, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((add @ X1 @ (multiply @ X0 @ X2))
% 9.45/2.09 = (multiply @ (add @ X0 @ X1) @ (add @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [add_multiply_property])).
% 9.45/2.09 thf(multiplicative_inverse, axiom,
% 9.45/2.09 (( multiply @ X @ ( inverse @ X ) ) = ( n0 ))).
% 9.45/2.09 thf(zip_derived_cl3, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (n0))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiplicative_inverse])).
% 9.45/2.09 thf(zip_derived_cl155, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ n1 @ (add @ X0 @ n0)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl7, zip_derived_cl1, zip_derived_cl2,
% 9.45/2.09 zip_derived_cl3])).
% 9.45/2.09 thf(multiply_add_property, axiom,
% 9.45/2.09 (( multiply @ X @ ( add @ Y @ Z ) ) =
% 9.45/2.09 ( add @ ( multiply @ Y @ X ) @ ( multiply @ Z @ X ) ))).
% 9.45/2.09 thf(zip_derived_cl0, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((multiply @ X1 @ (add @ X0 @ X2))
% 9.45/2.09 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiply_add_property])).
% 9.45/2.09 thf(zip_derived_cl156, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((multiply @ (add @ X0 @ n0) @ (add @ n1 @ X1))
% 9.45/2.09 = (add @ X0 @ (multiply @ X1 @ (add @ X0 @ n0))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl155, zip_derived_cl0])).
% 9.45/2.09 thf(zip_derived_cl2, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((add @ X1 @ (multiply @ X0 @ X2))
% 9.45/2.09 = (multiply @ (add @ X0 @ X1) @ (add @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [add_multiply_property])).
% 9.45/2.09 thf(zip_derived_cl1058, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((add @ n0 @ (multiply @ X0 @ n1))
% 9.45/2.09 = (add @ X0 @ (multiply @ n0 @ (add @ X0 @ n0))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl156, zip_derived_cl2])).
% 9.45/2.09 thf(pixley1, axiom,
% 9.45/2.09 (( add @
% 9.45/2.09 ( multiply @ X @ ( inverse @ X ) ) @
% 9.45/2.09 ( add @ ( multiply @ X @ Y ) @ ( multiply @ ( inverse @ X ) @ Y ) ) ) =
% 9.45/2.09 ( Y ))).
% 9.45/2.09 thf(zip_derived_cl4, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((add @ (multiply @ X1 @ (inverse @ X1)) @
% 9.45/2.09 (add @ (multiply @ X1 @ X0) @ (multiply @ (inverse @ X1) @ X0)))
% 9.45/2.09 = (X0))),
% 9.45/2.09 inference('cnf', [status(esa)], [pixley1])).
% 9.45/2.09 thf(zip_derived_cl3, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (n0))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiplicative_inverse])).
% 9.45/2.09 thf(zip_derived_cl0, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((multiply @ X1 @ (add @ X0 @ X2))
% 9.45/2.09 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiply_add_property])).
% 9.45/2.09 thf(zip_derived_cl1, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ X0 @ (inverse @ X0)) = (n1))),
% 9.45/2.09 inference('cnf', [status(esa)], [additive_inverse])).
% 9.45/2.09 thf(zip_derived_cl19, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ n0 @ (multiply @ X0 @ n1)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl4, zip_derived_cl3, zip_derived_cl0,
% 9.45/2.09 zip_derived_cl1])).
% 9.45/2.09 thf(zip_derived_cl1079, plain,
% 9.45/2.09 (![X0 : $i]: ((X0) = (add @ X0 @ (multiply @ n0 @ (add @ X0 @ n0))))),
% 9.45/2.09 inference('demod', [status(thm)], [zip_derived_cl1058, zip_derived_cl19])).
% 9.45/2.09 thf(zip_derived_cl156, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((multiply @ (add @ X0 @ n0) @ (add @ n1 @ X1))
% 9.45/2.09 = (add @ X0 @ (multiply @ X1 @ (add @ X0 @ n0))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl155, zip_derived_cl0])).
% 9.45/2.09 thf(zip_derived_cl1093, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ (add @ X0 @ n0) @ (add @ n1 @ n0)) = (X0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl1079, zip_derived_cl156])).
% 9.45/2.09 thf(zip_derived_cl2, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((add @ X1 @ (multiply @ X0 @ X2))
% 9.45/2.09 = (multiply @ (add @ X0 @ X1) @ (add @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [add_multiply_property])).
% 9.45/2.09 thf(zip_derived_cl0, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((multiply @ X1 @ (add @ X0 @ X2))
% 9.45/2.09 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiply_add_property])).
% 9.45/2.09 thf(zip_derived_cl3, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (n0))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiplicative_inverse])).
% 9.45/2.09 thf(zip_derived_cl3, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (n0))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiplicative_inverse])).
% 9.45/2.09 thf(zip_derived_cl0, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((multiply @ X1 @ (add @ X0 @ X2))
% 9.45/2.09 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiply_add_property])).
% 9.45/2.09 thf(zip_derived_cl11, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((multiply @ (inverse @ X0) @ (add @ X1 @ X0))
% 9.45/2.09 = (add @ (multiply @ X1 @ (inverse @ X0)) @ n0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 9.45/2.09 thf(zip_derived_cl29, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((multiply @ (inverse @ X0) @ (add @ X0 @ X0)) = (add @ n0 @ n0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl11])).
% 9.45/2.09 thf(zip_derived_cl33, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((multiply @ (inverse @ (multiply @ X0 @ X1)) @
% 9.45/2.09 (multiply @ X1 @ (add @ X0 @ X0))) = (add @ n0 @ n0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl29])).
% 9.45/2.09 thf(zip_derived_cl40, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((multiply @ (inverse @ (multiply @ X0 @ (add @ X1 @ X0))) @
% 9.45/2.09 (add @ X0 @ (multiply @ X1 @ X0))) = (add @ n0 @ n0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl33])).
% 9.45/2.09 thf(zip_derived_cl2773, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((multiply @
% 9.45/2.09 (inverse @
% 9.45/2.09 (multiply @ (add @ n1 @ n0) @
% 9.45/2.09 (add @ (add @ X0 @ n0) @ (add @ n1 @ n0)))) @
% 9.45/2.09 (add @ (add @ n1 @ n0) @ X0)) = (add @ n0 @ n0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl1093, zip_derived_cl40])).
% 9.45/2.09 thf(zip_derived_cl1093, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ (add @ X0 @ n0) @ (add @ n1 @ n0)) = (X0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl1079, zip_derived_cl156])).
% 9.45/2.09 thf(zip_derived_cl2, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((add @ X1 @ (multiply @ X0 @ X2))
% 9.45/2.09 = (multiply @ (add @ X0 @ X1) @ (add @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [add_multiply_property])).
% 9.45/2.09 thf(zip_derived_cl0, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((multiply @ X1 @ (add @ X0 @ X2))
% 9.45/2.09 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiply_add_property])).
% 9.45/2.09 thf(zip_derived_cl13, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.45/2.09 ((multiply @ (add @ X0 @ X2) @ (add @ (add @ X1 @ X2) @ X3))
% 9.45/2.09 = (add @ (add @ X2 @ (multiply @ X1 @ X0)) @
% 9.45/2.09 (multiply @ X3 @ (add @ X0 @ X2))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 9.45/2.09 thf(zip_derived_cl1115, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((multiply @ (add @ n1 @ n0) @
% 9.45/2.09 (add @ (add @ X1 @ n0) @ (add @ X0 @ n0)))
% 9.45/2.09 = (add @ (add @ n0 @ (multiply @ X1 @ n1)) @ X0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl1093, zip_derived_cl13])).
% 9.45/2.09 thf(zip_derived_cl19, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ n0 @ (multiply @ X0 @ n1)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl4, zip_derived_cl3, zip_derived_cl0,
% 9.45/2.09 zip_derived_cl1])).
% 9.45/2.09 thf(zip_derived_cl1124, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((multiply @ (add @ n1 @ n0) @
% 9.45/2.09 (add @ (add @ X1 @ n0) @ (add @ X0 @ n0))) = (add @ X1 @ X0))),
% 9.45/2.09 inference('demod', [status(thm)], [zip_derived_cl1115, zip_derived_cl19])).
% 9.45/2.09 thf(zip_derived_cl2873, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((multiply @ (inverse @ (add @ X0 @ n1)) @
% 9.45/2.09 (add @ (add @ n1 @ n0) @ X0)) = (add @ n0 @ n0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl2773, zip_derived_cl1124])).
% 9.45/2.09 thf(zip_derived_cl2914, plain,
% 9.45/2.09 (((multiply @ (inverse @ (add @ (inverse @ (add @ n1 @ n0)) @ n1)) @ n1)
% 9.45/2.09 = (add @ n0 @ n0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2873])).
% 9.45/2.09 thf(zip_derived_cl19, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ n0 @ (multiply @ X0 @ n1)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl4, zip_derived_cl3, zip_derived_cl0,
% 9.45/2.09 zip_derived_cl1])).
% 9.45/2.09 thf(zip_derived_cl2, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((add @ X1 @ (multiply @ X0 @ X2))
% 9.45/2.09 = (multiply @ (add @ X0 @ X1) @ (add @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [add_multiply_property])).
% 9.45/2.09 thf(zip_derived_cl1, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ X0 @ (inverse @ X0)) = (n1))),
% 9.45/2.09 inference('cnf', [status(esa)], [additive_inverse])).
% 9.45/2.09 thf(zip_derived_cl1, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ X0 @ (inverse @ X0)) = (n1))),
% 9.45/2.09 inference('cnf', [status(esa)], [additive_inverse])).
% 9.45/2.09 thf(zip_derived_cl2, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((add @ X1 @ (multiply @ X0 @ X2))
% 9.45/2.09 = (multiply @ (add @ X0 @ X1) @ (add @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [add_multiply_property])).
% 9.45/2.09 thf(zip_derived_cl15, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((add @ (inverse @ X0) @ (multiply @ X1 @ X0))
% 9.45/2.09 = (multiply @ (add @ X1 @ (inverse @ X0)) @ n1))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 9.45/2.09 thf(zip_derived_cl95, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((add @ (inverse @ X0) @ (multiply @ X0 @ X0)) = (multiply @ n1 @ n1))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl15])).
% 9.45/2.09 thf(zip_derived_cl101, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((add @ (inverse @ (add @ X0 @ X1)) @
% 9.45/2.09 (add @ X1 @ (multiply @ X0 @ X0))) = (multiply @ n1 @ n1))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl95])).
% 9.45/2.09 thf(zip_derived_cl354, plain,
% 9.45/2.09 (((add @ (inverse @ (add @ n1 @ n0)) @ n1) = (multiply @ n1 @ n1))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl101])).
% 9.45/2.09 thf(zip_derived_cl2917, plain,
% 9.45/2.09 (((multiply @ (inverse @ (multiply @ n1 @ n1)) @ n1) = (add @ n0 @ n0))),
% 9.45/2.09 inference('demod', [status(thm)], [zip_derived_cl2914, zip_derived_cl354])).
% 9.45/2.09 thf(zip_derived_cl19, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ n0 @ (multiply @ X0 @ n1)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl4, zip_derived_cl3, zip_derived_cl0,
% 9.45/2.09 zip_derived_cl1])).
% 9.45/2.09 thf(zip_derived_cl2934, plain,
% 9.45/2.09 (((add @ n0 @ (add @ n0 @ n0)) = (inverse @ (multiply @ n1 @ n1)))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl2917, zip_derived_cl19])).
% 9.45/2.09 thf(zip_derived_cl2917, plain,
% 9.45/2.09 (((multiply @ (inverse @ (multiply @ n1 @ n1)) @ n1) = (add @ n0 @ n0))),
% 9.45/2.09 inference('demod', [status(thm)], [zip_derived_cl2914, zip_derived_cl354])).
% 9.45/2.09 thf(zip_derived_cl19, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ n0 @ (multiply @ X0 @ n1)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl4, zip_derived_cl3, zip_derived_cl0,
% 9.45/2.09 zip_derived_cl1])).
% 9.45/2.09 thf(zip_derived_cl11, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((multiply @ (inverse @ X0) @ (add @ X1 @ X0))
% 9.45/2.09 = (add @ (multiply @ X1 @ (inverse @ X0)) @ n0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 9.45/2.09 thf(zip_derived_cl155, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ n1 @ (add @ X0 @ n0)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl7, zip_derived_cl1, zip_derived_cl2,
% 9.45/2.09 zip_derived_cl3])).
% 9.45/2.09 thf(zip_derived_cl163, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((multiply @ n1 @ (multiply @ (inverse @ X0) @ (add @ X1 @ X0)))
% 9.45/2.09 = (multiply @ X1 @ (inverse @ X0)))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl155])).
% 9.45/2.09 thf(zip_derived_cl336, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((multiply @ n1 @ (multiply @ (inverse @ (multiply @ X0 @ n1)) @ X0))
% 9.45/2.09 = (multiply @ n0 @ (inverse @ (multiply @ X0 @ n1))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl163])).
% 9.45/2.09 thf(zip_derived_cl2948, plain,
% 9.45/2.09 (((multiply @ n1 @ (add @ n0 @ n0))
% 9.45/2.09 = (multiply @ n0 @ (inverse @ (multiply @ n1 @ n1))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl2917, zip_derived_cl336])).
% 9.45/2.09 thf(zip_derived_cl155, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ n1 @ (add @ X0 @ n0)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl7, zip_derived_cl1, zip_derived_cl2,
% 9.45/2.09 zip_derived_cl3])).
% 9.45/2.09 thf(zip_derived_cl2961, plain,
% 9.45/2.09 (((n0) = (multiply @ n0 @ (inverse @ (multiply @ n1 @ n1))))),
% 9.45/2.09 inference('demod', [status(thm)], [zip_derived_cl2948, zip_derived_cl155])).
% 9.45/2.09 thf(zip_derived_cl155, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ n1 @ (add @ X0 @ n0)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl7, zip_derived_cl1, zip_derived_cl2,
% 9.45/2.09 zip_derived_cl3])).
% 9.45/2.09 thf(zip_derived_cl156, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((multiply @ (add @ X0 @ n0) @ (add @ n1 @ X1))
% 9.45/2.09 = (add @ X0 @ (multiply @ X1 @ (add @ X0 @ n0))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl155, zip_derived_cl0])).
% 9.45/2.09 thf(zip_derived_cl1071, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((multiply @ (add @ X0 @ n0) @ (add @ n1 @ n1)) = (add @ X0 @ X0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl155, zip_derived_cl156])).
% 9.45/2.09 thf(zip_derived_cl0, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((multiply @ X1 @ (add @ X0 @ X2))
% 9.45/2.09 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiply_add_property])).
% 9.45/2.09 thf(zip_derived_cl1149, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((multiply @ X0 @ (add @ X1 @ X1))
% 9.45/2.09 = (multiply @ (add @ (multiply @ X1 @ X0) @ n0) @ (add @ n1 @ n1)))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl1071, zip_derived_cl0])).
% 9.45/2.09 thf(zip_derived_cl2973, plain,
% 9.45/2.09 (((multiply @ (inverse @ (multiply @ n1 @ n1)) @ (add @ n0 @ n0))
% 9.45/2.09 = (multiply @ (add @ n0 @ n0) @ (add @ n1 @ n1)))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl2961, zip_derived_cl1149])).
% 9.45/2.09 thf(zip_derived_cl1071, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((multiply @ (add @ X0 @ n0) @ (add @ n1 @ n1)) = (add @ X0 @ X0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl155, zip_derived_cl156])).
% 9.45/2.09 thf(zip_derived_cl2982, plain,
% 9.45/2.09 (((multiply @ (inverse @ (multiply @ n1 @ n1)) @ (add @ n0 @ n0))
% 9.45/2.09 = (add @ n0 @ n0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl2973, zip_derived_cl1071])).
% 9.45/2.09 thf(zip_derived_cl15, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((add @ (inverse @ X0) @ (multiply @ X1 @ X0))
% 9.45/2.09 = (multiply @ (add @ X1 @ (inverse @ X0)) @ n1))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 9.45/2.09 thf(zip_derived_cl19, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ n0 @ (multiply @ X0 @ n1)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl4, zip_derived_cl3, zip_derived_cl0,
% 9.45/2.09 zip_derived_cl1])).
% 9.45/2.09 thf(zip_derived_cl2, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((add @ X1 @ (multiply @ X0 @ X2))
% 9.45/2.09 = (multiply @ (add @ X0 @ X1) @ (add @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [add_multiply_property])).
% 9.45/2.09 thf(zip_derived_cl20, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((add @ (multiply @ X0 @ n1) @ (multiply @ n0 @ X1))
% 9.45/2.09 = (multiply @ X0 @ (add @ X1 @ (multiply @ X0 @ n1))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl2])).
% 9.45/2.09 thf(zip_derived_cl0, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((multiply @ X1 @ (add @ X0 @ X2))
% 9.45/2.09 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiply_add_property])).
% 9.45/2.09 thf(zip_derived_cl627, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((multiply @ n1 @ (add @ X0 @ n0))
% 9.45/2.09 = (multiply @ X0 @ (add @ n1 @ (multiply @ X0 @ n1))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl20, zip_derived_cl0])).
% 9.45/2.09 thf(zip_derived_cl155, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ n1 @ (add @ X0 @ n0)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl7, zip_derived_cl1, zip_derived_cl2,
% 9.45/2.09 zip_derived_cl3])).
% 9.45/2.09 thf(zip_derived_cl639, plain,
% 9.45/2.09 (![X0 : $i]: ((X0) = (multiply @ X0 @ (add @ n1 @ (multiply @ X0 @ n1))))),
% 9.45/2.09 inference('demod', [status(thm)], [zip_derived_cl627, zip_derived_cl155])).
% 9.45/2.09 thf(zip_derived_cl20, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((add @ (multiply @ X0 @ n1) @ (multiply @ n0 @ X1))
% 9.45/2.09 = (multiply @ X0 @ (add @ X1 @ (multiply @ X0 @ n1))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl2])).
% 9.45/2.09 thf(zip_derived_cl650, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ (multiply @ X0 @ n1) @ (multiply @ n0 @ n1)) = (X0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl639, zip_derived_cl20])).
% 9.45/2.09 thf(zip_derived_cl670, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((add @ (add @ (inverse @ X0) @ (multiply @ X1 @ X0)) @
% 9.45/2.09 (multiply @ n0 @ n1)) = (add @ X1 @ (inverse @ X0)))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl15, zip_derived_cl650])).
% 9.45/2.09 thf(zip_derived_cl4880, plain,
% 9.45/2.09 (((add @ (add @ (inverse @ (add @ n0 @ n0)) @ (add @ n0 @ n0)) @
% 9.45/2.09 (multiply @ n0 @ n1))
% 9.45/2.09 = (add @ (inverse @ (multiply @ n1 @ n1)) @
% 9.45/2.09 (inverse @ (add @ n0 @ n0))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl2982, zip_derived_cl670])).
% 9.45/2.09 thf(zip_derived_cl3, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (n0))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiplicative_inverse])).
% 9.45/2.09 thf(zip_derived_cl650, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ (multiply @ X0 @ n1) @ (multiply @ n0 @ n1)) = (X0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl639, zip_derived_cl20])).
% 9.45/2.09 thf(zip_derived_cl0, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((multiply @ X1 @ (add @ X0 @ X2))
% 9.45/2.09 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiply_add_property])).
% 9.45/2.09 thf(zip_derived_cl101, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((add @ (inverse @ (add @ X0 @ X1)) @
% 9.45/2.09 (add @ X1 @ (multiply @ X0 @ X0))) = (multiply @ n1 @ n1))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl95])).
% 9.45/2.09 thf(zip_derived_cl348, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((add @ (inverse @ (add @ X0 @ (multiply @ X1 @ X0))) @
% 9.45/2.09 (multiply @ X0 @ (add @ X1 @ X0))) = (multiply @ n1 @ n1))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl101])).
% 9.45/2.09 thf(zip_derived_cl3419, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((add @
% 9.45/2.09 (inverse @
% 9.45/2.09 (add @ (multiply @ n0 @ n1) @
% 9.45/2.09 (multiply @ (multiply @ X0 @ n1) @ (multiply @ n0 @ n1)))) @
% 9.45/2.09 (multiply @ (multiply @ n0 @ n1) @ X0)) = (multiply @ n1 @ n1))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl650, zip_derived_cl348])).
% 9.45/2.09 thf(zip_derived_cl650, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ (multiply @ X0 @ n1) @ (multiply @ n0 @ n1)) = (X0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl639, zip_derived_cl20])).
% 9.45/2.09 thf(zip_derived_cl0, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((multiply @ X1 @ (add @ X0 @ X2))
% 9.45/2.09 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiply_add_property])).
% 9.45/2.09 thf(zip_derived_cl2, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((add @ X1 @ (multiply @ X0 @ X2))
% 9.45/2.09 = (multiply @ (add @ X0 @ X1) @ (add @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [add_multiply_property])).
% 9.45/2.09 thf(zip_derived_cl16, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.45/2.09 ((add @ (multiply @ X0 @ X2) @ (multiply @ X3 @ (multiply @ X1 @ X2)))
% 9.45/2.09 = (multiply @ (add @ X3 @ (multiply @ X0 @ X2)) @
% 9.45/2.09 (multiply @ X2 @ (add @ X1 @ X0))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 9.45/2.09 thf(zip_derived_cl876, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((add @ (multiply @ n0 @ n1) @
% 9.45/2.09 (multiply @ (multiply @ X0 @ n1) @ (multiply @ X1 @ n1)))
% 9.45/2.09 = (multiply @ X0 @ (multiply @ n1 @ (add @ X1 @ n0))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl650, zip_derived_cl16])).
% 9.45/2.09 thf(zip_derived_cl155, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ n1 @ (add @ X0 @ n0)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl7, zip_derived_cl1, zip_derived_cl2,
% 9.45/2.09 zip_derived_cl3])).
% 9.45/2.09 thf(zip_derived_cl921, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((add @ (multiply @ n0 @ n1) @
% 9.45/2.09 (multiply @ (multiply @ X0 @ n1) @ (multiply @ X1 @ n1)))
% 9.45/2.09 = (multiply @ X0 @ X1))),
% 9.45/2.09 inference('demod', [status(thm)], [zip_derived_cl876, zip_derived_cl155])).
% 9.45/2.09 thf(zip_derived_cl3539, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((add @ (inverse @ (multiply @ X0 @ n0)) @
% 9.45/2.09 (multiply @ (multiply @ n0 @ n1) @ X0)) = (multiply @ n1 @ n1))),
% 9.45/2.09 inference('demod', [status(thm)], [zip_derived_cl3419, zip_derived_cl921])).
% 9.45/2.09 thf(zip_derived_cl3611, plain,
% 9.45/2.09 (((add @
% 9.45/2.09 (inverse @ (multiply @ (inverse @ (multiply @ n0 @ n1)) @ n0)) @ n0)
% 9.45/2.09 = (multiply @ n1 @ n1))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl3539])).
% 9.45/2.09 thf(zip_derived_cl155, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ n1 @ (add @ X0 @ n0)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl7, zip_derived_cl1, zip_derived_cl2,
% 9.45/2.09 zip_derived_cl3])).
% 9.45/2.09 thf(zip_derived_cl33, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((multiply @ (inverse @ (multiply @ X0 @ X1)) @
% 9.45/2.09 (multiply @ X1 @ (add @ X0 @ X0))) = (add @ n0 @ n0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl29])).
% 9.45/2.09 thf(zip_derived_cl162, plain,
% 9.45/2.09 (((multiply @ (inverse @ (multiply @ n0 @ n1)) @ n0) = (add @ n0 @ n0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl155, zip_derived_cl33])).
% 9.45/2.09 thf(zip_derived_cl3614, plain,
% 9.45/2.09 (((add @ (inverse @ (add @ n0 @ n0)) @ n0) = (multiply @ n1 @ n1))),
% 9.45/2.09 inference('demod', [status(thm)], [zip_derived_cl3611, zip_derived_cl162])).
% 9.45/2.09 thf(zip_derived_cl155, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ n1 @ (add @ X0 @ n0)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl7, zip_derived_cl1, zip_derived_cl2,
% 9.45/2.09 zip_derived_cl3])).
% 9.45/2.09 thf(zip_derived_cl3640, plain,
% 9.45/2.09 (((multiply @ n1 @ (multiply @ n1 @ n1)) = (inverse @ (add @ n0 @ n0)))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl3614, zip_derived_cl155])).
% 9.45/2.09 thf(zip_derived_cl2917, plain,
% 9.45/2.09 (((multiply @ (inverse @ (multiply @ n1 @ n1)) @ n1) = (add @ n0 @ n0))),
% 9.45/2.09 inference('demod', [status(thm)], [zip_derived_cl2914, zip_derived_cl354])).
% 9.45/2.09 thf(zip_derived_cl1149, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((multiply @ X0 @ (add @ X1 @ X1))
% 9.45/2.09 = (multiply @ (add @ (multiply @ X1 @ X0) @ n0) @ (add @ n1 @ n1)))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl1071, zip_derived_cl0])).
% 9.45/2.09 thf(zip_derived_cl2933, plain,
% 9.45/2.09 (((multiply @ n1 @
% 9.45/2.09 (add @ (inverse @ (multiply @ n1 @ n1)) @
% 9.45/2.09 (inverse @ (multiply @ n1 @ n1))))
% 9.45/2.09 = (multiply @ (add @ (add @ n0 @ n0) @ n0) @ (add @ n1 @ n1)))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl2917, zip_derived_cl1149])).
% 9.45/2.09 thf(zip_derived_cl3, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (n0))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiplicative_inverse])).
% 9.45/2.09 thf(zip_derived_cl1, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ X0 @ (inverse @ X0)) = (n1))),
% 9.45/2.09 inference('cnf', [status(esa)], [additive_inverse])).
% 9.45/2.09 thf(zip_derived_cl2, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((add @ X1 @ (multiply @ X0 @ X2))
% 9.45/2.09 = (multiply @ (add @ X0 @ X1) @ (add @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [add_multiply_property])).
% 9.45/2.09 thf(zip_derived_cl17, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((add @ (inverse @ X0) @ (multiply @ X0 @ X1))
% 9.45/2.09 = (multiply @ n1 @ (add @ X1 @ (inverse @ X0))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 9.45/2.09 thf(zip_derived_cl115, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((add @ (inverse @ X0) @ n0)
% 9.45/2.09 = (multiply @ n1 @ (add @ (inverse @ X0) @ (inverse @ X0))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl17])).
% 9.45/2.09 thf(zip_derived_cl1071, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((multiply @ (add @ X0 @ n0) @ (add @ n1 @ n1)) = (add @ X0 @ X0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl155, zip_derived_cl156])).
% 9.45/2.09 thf(zip_derived_cl2954, plain,
% 9.45/2.09 (((add @ (inverse @ (multiply @ n1 @ n1)) @ n0)
% 9.45/2.09 = (add @ (add @ n0 @ n0) @ (add @ n0 @ n0)))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl2933, zip_derived_cl115, zip_derived_cl1071])).
% 9.45/2.09 thf(zip_derived_cl348, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((add @ (inverse @ (add @ X0 @ (multiply @ X1 @ X0))) @
% 9.45/2.09 (multiply @ X0 @ (add @ X1 @ X0))) = (multiply @ n1 @ n1))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl101])).
% 9.45/2.09 thf(zip_derived_cl3436, plain,
% 9.45/2.09 (((add @
% 9.45/2.09 (inverse @
% 9.45/2.09 (add @ (add @ n0 @ n0) @
% 9.45/2.09 (multiply @ (add @ n0 @ n0) @ (add @ n0 @ n0)))) @
% 9.45/2.09 (multiply @ (add @ n0 @ n0) @
% 9.45/2.09 (add @ (inverse @ (multiply @ n1 @ n1)) @ n0)))
% 9.45/2.09 = (multiply @ n1 @ n1))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl2954, zip_derived_cl348])).
% 9.45/2.09 thf(zip_derived_cl2, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((add @ X1 @ (multiply @ X0 @ X2))
% 9.45/2.09 = (multiply @ (add @ X0 @ X1) @ (add @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [add_multiply_property])).
% 9.45/2.09 thf(zip_derived_cl2954, plain,
% 9.45/2.09 (((add @ (inverse @ (multiply @ n1 @ n1)) @ n0)
% 9.45/2.09 = (add @ (add @ n0 @ n0) @ (add @ n0 @ n0)))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl2933, zip_derived_cl115, zip_derived_cl1071])).
% 9.45/2.09 thf(zip_derived_cl19, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ n0 @ (multiply @ X0 @ n1)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl4, zip_derived_cl3, zip_derived_cl0,
% 9.45/2.09 zip_derived_cl1])).
% 9.45/2.09 thf(zip_derived_cl20, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((add @ (multiply @ X0 @ n1) @ (multiply @ n0 @ X1))
% 9.45/2.09 = (multiply @ X0 @ (add @ X1 @ (multiply @ X0 @ n1))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl2])).
% 9.45/2.09 thf(zip_derived_cl632, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((add @ (multiply @ X0 @ n1) @ (multiply @ n0 @ n0))
% 9.45/2.09 = (multiply @ X0 @ X0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl20])).
% 9.45/2.09 thf(zip_derived_cl2, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((add @ X1 @ (multiply @ X0 @ X2))
% 9.45/2.09 = (multiply @ (add @ X0 @ X1) @ (add @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [add_multiply_property])).
% 9.45/2.09 thf(zip_derived_cl695, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((add @ X0 @ (multiply @ X1 @ X1))
% 9.45/2.09 = (add @ (multiply @ (add @ X1 @ X0) @ n1) @ (multiply @ n0 @ n0)))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl632, zip_derived_cl2])).
% 9.45/2.09 thf(zip_derived_cl3123, plain,
% 9.45/2.09 (((add @ (add @ n0 @ n0) @ (multiply @ (add @ n0 @ n0) @ (add @ n0 @ n0)))
% 9.45/2.09 = (add @
% 9.45/2.09 (multiply @ (add @ (inverse @ (multiply @ n1 @ n1)) @ n0) @ n1) @
% 9.45/2.09 (multiply @ n0 @ n0)))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl2954, zip_derived_cl695])).
% 9.45/2.09 thf(zip_derived_cl2, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((add @ X1 @ (multiply @ X0 @ X2))
% 9.45/2.09 = (multiply @ (add @ X0 @ X1) @ (add @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [add_multiply_property])).
% 9.45/2.09 thf(zip_derived_cl695, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((add @ X0 @ (multiply @ X1 @ X1))
% 9.45/2.09 = (add @ (multiply @ (add @ X1 @ X0) @ n1) @ (multiply @ n0 @ n0)))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl632, zip_derived_cl2])).
% 9.45/2.09 thf(zip_derived_cl1, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ X0 @ (inverse @ X0)) = (n1))),
% 9.45/2.09 inference('cnf', [status(esa)], [additive_inverse])).
% 9.45/2.09 thf(zip_derived_cl3, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (n0))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiplicative_inverse])).
% 9.45/2.09 thf(zip_derived_cl0, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((multiply @ X1 @ (add @ X0 @ X2))
% 9.45/2.09 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiply_add_property])).
% 9.45/2.09 thf(zip_derived_cl12, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((multiply @ (inverse @ X0) @ (add @ X0 @ X1))
% 9.45/2.09 = (add @ n0 @ (multiply @ X1 @ (inverse @ X0))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 9.45/2.09 thf(zip_derived_cl70, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((multiply @ (inverse @ X0) @ n1)
% 9.45/2.09 = (add @ n0 @ (multiply @ (inverse @ X0) @ (inverse @ X0))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl12])).
% 9.45/2.09 thf(zip_derived_cl2917, plain,
% 9.45/2.09 (((multiply @ (inverse @ (multiply @ n1 @ n1)) @ n1) = (add @ n0 @ n0))),
% 9.45/2.09 inference('demod', [status(thm)], [zip_derived_cl2914, zip_derived_cl354])).
% 9.45/2.09 thf(zip_derived_cl3137, plain,
% 9.45/2.09 (((add @ (add @ n0 @ n0) @ (add @ n0 @ (multiply @ n0 @ n0)))
% 9.45/2.09 = (add @ n0 @ n0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl3123, zip_derived_cl2, zip_derived_cl695,
% 9.45/2.09 zip_derived_cl70, zip_derived_cl2917])).
% 9.45/2.09 thf(zip_derived_cl2, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((add @ X1 @ (multiply @ X0 @ X2))
% 9.45/2.09 = (multiply @ (add @ X0 @ X1) @ (add @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [add_multiply_property])).
% 9.45/2.09 thf(zip_derived_cl2961, plain,
% 9.45/2.09 (((n0) = (multiply @ n0 @ (inverse @ (multiply @ n1 @ n1))))),
% 9.45/2.09 inference('demod', [status(thm)], [zip_derived_cl2948, zip_derived_cl155])).
% 9.45/2.09 thf(zip_derived_cl3540, plain,
% 9.45/2.09 (((add @ (inverse @ (add @ n0 @ n0)) @ (add @ n0 @ n0))
% 9.45/2.09 = (multiply @ n1 @ n1))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl3436, zip_derived_cl2, zip_derived_cl3137,
% 9.45/2.09 zip_derived_cl2, zip_derived_cl2961])).
% 9.45/2.09 thf(zip_derived_cl3640, plain,
% 9.45/2.09 (((multiply @ n1 @ (multiply @ n1 @ n1)) = (inverse @ (add @ n0 @ n0)))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl3614, zip_derived_cl155])).
% 9.45/2.09 thf(zip_derived_cl3697, plain,
% 9.45/2.09 (((add @ (multiply @ n1 @ (multiply @ n1 @ n1)) @ (add @ n0 @ n0))
% 9.45/2.09 = (multiply @ n1 @ n1))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl3540, zip_derived_cl3640])).
% 9.45/2.09 thf(zip_derived_cl650, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ (multiply @ X0 @ n1) @ (multiply @ n0 @ n1)) = (X0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl639, zip_derived_cl20])).
% 9.45/2.09 thf(zip_derived_cl3640, plain,
% 9.45/2.09 (((multiply @ n1 @ (multiply @ n1 @ n1)) = (inverse @ (add @ n0 @ n0)))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl3614, zip_derived_cl155])).
% 9.45/2.09 thf(zip_derived_cl15, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((add @ (inverse @ X0) @ (multiply @ X1 @ X0))
% 9.45/2.09 = (multiply @ (add @ X1 @ (inverse @ X0)) @ n1))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 9.45/2.09 thf(zip_derived_cl4912, plain,
% 9.45/2.09 (((n1) = (multiply @ (add @ n1 @ (inverse @ (multiply @ n1 @ n1))) @ n1))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl4880, zip_derived_cl3640, zip_derived_cl3697,
% 9.45/2.09 zip_derived_cl650, zip_derived_cl3640, zip_derived_cl15])).
% 9.45/2.09 thf(zip_derived_cl4912, plain,
% 9.45/2.09 (((n1) = (multiply @ (add @ n1 @ (inverse @ (multiply @ n1 @ n1))) @ n1))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl4880, zip_derived_cl3640, zip_derived_cl3697,
% 9.45/2.09 zip_derived_cl650, zip_derived_cl3640, zip_derived_cl15])).
% 9.45/2.09 thf(zip_derived_cl19, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ n0 @ (multiply @ X0 @ n1)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl4, zip_derived_cl3, zip_derived_cl0,
% 9.45/2.09 zip_derived_cl1])).
% 9.45/2.09 thf(zip_derived_cl4939, plain,
% 9.45/2.09 (((add @ n0 @ n1) = (add @ n1 @ (inverse @ (multiply @ n1 @ n1))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl4912, zip_derived_cl19])).
% 9.45/2.09 thf(zip_derived_cl4966, plain, (((n1) = (multiply @ (add @ n0 @ n1) @ n1))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl4912, zip_derived_cl4939])).
% 9.45/2.09 thf(zip_derived_cl650, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ (multiply @ X0 @ n1) @ (multiply @ n0 @ n1)) = (X0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl639, zip_derived_cl20])).
% 9.45/2.09 thf(zip_derived_cl5020, plain,
% 9.45/2.09 (((add @ n1 @ (multiply @ n0 @ n1)) = (add @ n0 @ n1))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl4966, zip_derived_cl650])).
% 9.45/2.09 thf(zip_derived_cl0, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((multiply @ X1 @ (add @ X0 @ X2))
% 9.45/2.09 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiply_add_property])).
% 9.45/2.09 thf(zip_derived_cl2, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((add @ X1 @ (multiply @ X0 @ X2))
% 9.45/2.09 = (multiply @ (add @ X0 @ X1) @ (add @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [add_multiply_property])).
% 9.45/2.09 thf(zip_derived_cl18, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.45/2.09 ((add @ (multiply @ X0 @ X2) @ (multiply @ (multiply @ X1 @ X2) @ X3))
% 9.45/2.09 = (multiply @ (multiply @ X2 @ (add @ X1 @ X0)) @
% 9.45/2.09 (add @ X3 @ (multiply @ X0 @ X2))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 9.45/2.09 thf(zip_derived_cl5057, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((add @ (multiply @ n0 @ n1) @ (multiply @ (multiply @ X0 @ n1) @ n1))
% 9.45/2.09 = (multiply @ (multiply @ n1 @ (add @ X0 @ n0)) @ (add @ n0 @ n1)))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl5020, zip_derived_cl18])).
% 9.45/2.09 thf(zip_derived_cl0, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((multiply @ X1 @ (add @ X0 @ X2))
% 9.45/2.09 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiply_add_property])).
% 9.45/2.09 thf(zip_derived_cl19, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ n0 @ (multiply @ X0 @ n1)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl4, zip_derived_cl3, zip_derived_cl0,
% 9.45/2.09 zip_derived_cl1])).
% 9.45/2.09 thf(zip_derived_cl155, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ n1 @ (add @ X0 @ n0)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl7, zip_derived_cl1, zip_derived_cl2,
% 9.45/2.09 zip_derived_cl3])).
% 9.45/2.09 thf(zip_derived_cl5070, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ n1 @ X0) = (multiply @ X0 @ (add @ n0 @ n1)))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl5057, zip_derived_cl0, zip_derived_cl19,
% 9.45/2.09 zip_derived_cl155])).
% 9.45/2.09 thf(zip_derived_cl155, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ n1 @ (add @ X0 @ n0)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl7, zip_derived_cl1, zip_derived_cl2,
% 9.45/2.09 zip_derived_cl3])).
% 9.45/2.09 thf(zip_derived_cl0, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((multiply @ X1 @ (add @ X0 @ X2))
% 9.45/2.09 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiply_add_property])).
% 9.45/2.09 thf(zip_derived_cl159, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((multiply @ (add @ X0 @ n0) @ (add @ X1 @ n1))
% 9.45/2.09 = (add @ (multiply @ X1 @ (add @ X0 @ n0)) @ X0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl155, zip_derived_cl0])).
% 9.45/2.09 thf(zip_derived_cl155, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ n1 @ (add @ X0 @ n0)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl7, zip_derived_cl1, zip_derived_cl2,
% 9.45/2.09 zip_derived_cl3])).
% 9.45/2.09 thf(zip_derived_cl1487, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((multiply @ n1 @ (multiply @ (add @ n0 @ n0) @ (add @ X0 @ n1)))
% 9.45/2.09 = (multiply @ X0 @ (add @ n0 @ n0)))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl159, zip_derived_cl155])).
% 9.45/2.09 thf(zip_derived_cl5132, plain,
% 9.45/2.09 (((multiply @ n1 @ (multiply @ n1 @ (add @ n0 @ n0)))
% 9.45/2.09 = (multiply @ n0 @ (add @ n0 @ n0)))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl5070, zip_derived_cl1487])).
% 9.45/2.09 thf(zip_derived_cl155, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ n1 @ (add @ X0 @ n0)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl7, zip_derived_cl1, zip_derived_cl2,
% 9.45/2.09 zip_derived_cl3])).
% 9.45/2.09 thf(zip_derived_cl5157, plain,
% 9.45/2.09 (((multiply @ n1 @ n0) = (multiply @ n0 @ (add @ n0 @ n0)))),
% 9.45/2.09 inference('demod', [status(thm)], [zip_derived_cl5132, zip_derived_cl155])).
% 9.45/2.09 thf(zip_derived_cl5070, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ n1 @ X0) = (multiply @ X0 @ (add @ n0 @ n1)))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl5057, zip_derived_cl0, zip_derived_cl19,
% 9.45/2.09 zip_derived_cl155])).
% 9.45/2.09 thf(zip_derived_cl5020, plain,
% 9.45/2.09 (((add @ n1 @ (multiply @ n0 @ n1)) = (add @ n0 @ n1))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl4966, zip_derived_cl650])).
% 9.45/2.09 thf(zip_derived_cl639, plain,
% 9.45/2.09 (![X0 : $i]: ((X0) = (multiply @ X0 @ (add @ n1 @ (multiply @ X0 @ n1))))),
% 9.45/2.09 inference('demod', [status(thm)], [zip_derived_cl627, zip_derived_cl155])).
% 9.45/2.09 thf(zip_derived_cl5061, plain, (((n0) = (multiply @ n0 @ (add @ n0 @ n1)))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl5020, zip_derived_cl639])).
% 9.45/2.09 thf(zip_derived_cl5140, plain, (((n0) = (multiply @ n1 @ n0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl5070, zip_derived_cl5061])).
% 9.45/2.09 thf(zip_derived_cl5224, plain, (((n0) = (multiply @ n0 @ (add @ n0 @ n0)))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl5157, zip_derived_cl5140])).
% 9.45/2.09 thf(zip_derived_cl1079, plain,
% 9.45/2.09 (![X0 : $i]: ((X0) = (add @ X0 @ (multiply @ n0 @ (add @ X0 @ n0))))),
% 9.45/2.09 inference('demod', [status(thm)], [zip_derived_cl1058, zip_derived_cl19])).
% 9.45/2.09 thf(zip_derived_cl5253, plain, (((n0) = (add @ n0 @ n0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl5224, zip_derived_cl1079])).
% 9.45/2.09 thf(zip_derived_cl5253, plain, (((n0) = (add @ n0 @ n0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl5224, zip_derived_cl1079])).
% 9.45/2.09 thf(zip_derived_cl5290, plain, (((n0) = (inverse @ (multiply @ n1 @ n1)))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl2934, zip_derived_cl5253, zip_derived_cl5253])).
% 9.45/2.09 thf(zip_derived_cl354, plain,
% 9.45/2.09 (((add @ (inverse @ (add @ n1 @ n0)) @ n1) = (multiply @ n1 @ n1))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl101])).
% 9.45/2.09 thf(zip_derived_cl155, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ n1 @ (add @ X0 @ n0)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl7, zip_derived_cl1, zip_derived_cl2,
% 9.45/2.09 zip_derived_cl3])).
% 9.45/2.09 thf(zip_derived_cl15, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((add @ (inverse @ X0) @ (multiply @ X1 @ X0))
% 9.45/2.09 = (multiply @ (add @ X1 @ (inverse @ X0)) @ n1))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 9.45/2.09 thf(zip_derived_cl19, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ n0 @ (multiply @ X0 @ n1)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl4, zip_derived_cl3, zip_derived_cl0,
% 9.45/2.09 zip_derived_cl1])).
% 9.45/2.09 thf(zip_derived_cl83, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((add @ n0 @ (add @ (inverse @ X0) @ (multiply @ X1 @ X0)))
% 9.45/2.09 = (add @ X1 @ (inverse @ X0)))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl15, zip_derived_cl19])).
% 9.45/2.09 thf(zip_derived_cl161, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((add @ n0 @ (add @ (inverse @ (add @ X0 @ n0)) @ X0))
% 9.45/2.09 = (add @ n1 @ (inverse @ (add @ X0 @ n0))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl155, zip_derived_cl83])).
% 9.45/2.09 thf(zip_derived_cl458, plain,
% 9.45/2.09 (((add @ n0 @ (multiply @ n1 @ n1))
% 9.45/2.09 = (add @ n1 @ (inverse @ (add @ n1 @ n0))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl354, zip_derived_cl161])).
% 9.45/2.09 thf(zip_derived_cl19, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ n0 @ (multiply @ X0 @ n1)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl4, zip_derived_cl3, zip_derived_cl0,
% 9.45/2.09 zip_derived_cl1])).
% 9.45/2.09 thf(zip_derived_cl461, plain,
% 9.45/2.09 (((n1) = (add @ n1 @ (inverse @ (add @ n1 @ n0))))),
% 9.45/2.09 inference('demod', [status(thm)], [zip_derived_cl458, zip_derived_cl19])).
% 9.45/2.09 thf(pixley2_dual, axiom,
% 9.45/2.09 (( multiply @
% 9.45/2.09 ( add @ X @ ( inverse @ Y ) ) @
% 9.45/2.09 ( multiply @ ( add @ X @ Y ) @ ( add @ ( inverse @ Y ) @ Y ) ) ) =
% 9.45/2.09 ( X ))).
% 9.45/2.09 thf(zip_derived_cl8, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((multiply @ (add @ X0 @ (inverse @ X1)) @
% 9.45/2.09 (multiply @ (add @ X0 @ X1) @ (add @ (inverse @ X1) @ X1))) = (
% 9.45/2.09 X0))),
% 9.45/2.09 inference('cnf', [status(esa)], [pixley2_dual])).
% 9.45/2.09 thf(zip_derived_cl2, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((add @ X1 @ (multiply @ X0 @ X2))
% 9.45/2.09 = (multiply @ (add @ X0 @ X1) @ (add @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [add_multiply_property])).
% 9.45/2.09 thf(zip_derived_cl165, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((multiply @ (add @ X0 @ (inverse @ X1)) @
% 9.45/2.09 (add @ X1 @ (multiply @ X0 @ (inverse @ X1)))) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)], [zip_derived_cl8, zip_derived_cl2])).
% 9.45/2.09 thf(zip_derived_cl472, plain,
% 9.45/2.09 (((multiply @ n1 @
% 9.45/2.09 (add @ (add @ n1 @ n0) @ (multiply @ n1 @ (inverse @ (add @ n1 @ n0)))))
% 9.45/2.09 = (n1))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl461, zip_derived_cl165])).
% 9.45/2.09 thf(zip_derived_cl5253, plain, (((n0) = (add @ n0 @ n0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl5224, zip_derived_cl1079])).
% 9.45/2.09 thf(zip_derived_cl1093, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ (add @ X0 @ n0) @ (add @ n1 @ n0)) = (X0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl1079, zip_derived_cl156])).
% 9.45/2.09 thf(zip_derived_cl156, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((multiply @ (add @ X0 @ n0) @ (add @ n1 @ X1))
% 9.45/2.09 = (add @ X0 @ (multiply @ X1 @ (add @ X0 @ n0))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl155, zip_derived_cl0])).
% 9.45/2.09 thf(zip_derived_cl1117, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((multiply @ (add @ n1 @ n0) @ (add @ n1 @ (add @ X0 @ n0)))
% 9.45/2.09 = (add @ n1 @ X0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl1093, zip_derived_cl156])).
% 9.45/2.09 thf(zip_derived_cl5333, plain,
% 9.45/2.09 (((multiply @ (add @ n1 @ n0) @ (add @ n1 @ n0)) = (add @ n1 @ n0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl5253, zip_derived_cl1117])).
% 9.45/2.09 thf(zip_derived_cl1093, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ (add @ X0 @ n0) @ (add @ n1 @ n0)) = (X0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl1079, zip_derived_cl156])).
% 9.45/2.09 thf(zip_derived_cl5353, plain, (((n1) = (add @ n1 @ n0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl5333, zip_derived_cl1093])).
% 9.45/2.09 thf(zip_derived_cl5353, plain, (((n1) = (add @ n1 @ n0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl5333, zip_derived_cl1093])).
% 9.45/2.09 thf(zip_derived_cl3, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (n0))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiplicative_inverse])).
% 9.45/2.09 thf(zip_derived_cl5353, plain, (((n1) = (add @ n1 @ n0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl5333, zip_derived_cl1093])).
% 9.45/2.09 thf(zip_derived_cl5476, plain, (((multiply @ n1 @ n1) = (n1))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl472, zip_derived_cl5353, zip_derived_cl5353,
% 9.45/2.09 zip_derived_cl3, zip_derived_cl5353])).
% 9.45/2.09 thf(zip_derived_cl5774, plain, (((n0) = (inverse @ n1))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl5290, zip_derived_cl5476])).
% 9.45/2.09 thf(pixley2, axiom,
% 9.45/2.09 (( add @
% 9.45/2.09 ( multiply @ X @ ( inverse @ Y ) ) @
% 9.45/2.09 ( add @ ( multiply @ X @ Y ) @ ( multiply @ ( inverse @ Y ) @ Y ) ) ) =
% 9.45/2.09 ( X ))).
% 9.45/2.09 thf(zip_derived_cl5, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((add @ (multiply @ X0 @ (inverse @ X1)) @
% 9.45/2.09 (add @ (multiply @ X0 @ X1) @ (multiply @ (inverse @ X1) @ X1)))
% 9.45/2.09 = (X0))),
% 9.45/2.09 inference('cnf', [status(esa)], [pixley2])).
% 9.45/2.09 thf(zip_derived_cl0, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((multiply @ X1 @ (add @ X0 @ X2))
% 9.45/2.09 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiply_add_property])).
% 9.45/2.09 thf(zip_derived_cl52, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((add @ (multiply @ X0 @ (inverse @ X1)) @
% 9.45/2.09 (multiply @ X1 @ (add @ X0 @ (inverse @ X1)))) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl0])).
% 9.45/2.09 thf(zip_derived_cl5806, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((add @ (multiply @ X0 @ (inverse @ n1)) @
% 9.45/2.09 (multiply @ n1 @ (add @ X0 @ n0))) = (X0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl5774, zip_derived_cl52])).
% 9.45/2.09 thf(zip_derived_cl5774, plain, (((n0) = (inverse @ n1))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl5290, zip_derived_cl5476])).
% 9.45/2.09 thf(zip_derived_cl155, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ n1 @ (add @ X0 @ n0)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl7, zip_derived_cl1, zip_derived_cl2,
% 9.45/2.09 zip_derived_cl3])).
% 9.45/2.09 thf(zip_derived_cl5840, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ (multiply @ X0 @ n0) @ X0) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl5806, zip_derived_cl5774, zip_derived_cl155])).
% 9.45/2.09 thf(zip_derived_cl0, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((multiply @ X1 @ (add @ X0 @ X2))
% 9.45/2.09 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiply_add_property])).
% 9.45/2.09 thf(zip_derived_cl5946, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((multiply @ n0 @ (add @ (multiply @ X0 @ n0) @ X0))
% 9.45/2.09 = (multiply @ X0 @ n0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl5840, zip_derived_cl0])).
% 9.45/2.09 thf(zip_derived_cl5840, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ (multiply @ X0 @ n0) @ X0) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl5806, zip_derived_cl5774, zip_derived_cl155])).
% 9.45/2.09 thf(zip_derived_cl5967, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ n0 @ X0) = (multiply @ X0 @ n0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl5946, zip_derived_cl5840])).
% 9.45/2.09 thf(zip_derived_cl20, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((add @ (multiply @ X0 @ n1) @ (multiply @ n0 @ X1))
% 9.45/2.09 = (multiply @ X0 @ (add @ X1 @ (multiply @ X0 @ n1))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl2])).
% 9.45/2.09 thf(zip_derived_cl6689, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((add @ (multiply @ X0 @ n1) @ (multiply @ n0 @ n0))
% 9.45/2.09 = (multiply @ X0 @ (add @ n0 @ (multiply @ X0 @ n1))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl5967, zip_derived_cl20])).
% 9.45/2.09 thf(zip_derived_cl5224, plain, (((n0) = (multiply @ n0 @ (add @ n0 @ n0)))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl5157, zip_derived_cl5140])).
% 9.45/2.09 thf(zip_derived_cl5253, plain, (((n0) = (add @ n0 @ n0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl5224, zip_derived_cl1079])).
% 9.45/2.09 thf(zip_derived_cl5303, plain, (((n0) = (multiply @ n0 @ n0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl5224, zip_derived_cl5253])).
% 9.45/2.09 thf(zip_derived_cl650, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ (multiply @ X0 @ n1) @ (multiply @ n0 @ n1)) = (X0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl639, zip_derived_cl20])).
% 9.45/2.09 thf(zip_derived_cl5061, plain, (((n0) = (multiply @ n0 @ (add @ n0 @ n1)))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl5020, zip_derived_cl639])).
% 9.45/2.09 thf(zip_derived_cl4939, plain,
% 9.45/2.09 (((add @ n0 @ n1) = (add @ n1 @ (inverse @ (multiply @ n1 @ n1))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl4912, zip_derived_cl19])).
% 9.45/2.09 thf(zip_derived_cl5476, plain, (((multiply @ n1 @ n1) = (n1))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl472, zip_derived_cl5353, zip_derived_cl5353,
% 9.45/2.09 zip_derived_cl3, zip_derived_cl5353])).
% 9.45/2.09 thf(zip_derived_cl1, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ X0 @ (inverse @ X0)) = (n1))),
% 9.45/2.09 inference('cnf', [status(esa)], [additive_inverse])).
% 9.45/2.09 thf(zip_derived_cl5548, plain, (((add @ n0 @ n1) = (n1))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl4939, zip_derived_cl5476, zip_derived_cl1])).
% 9.45/2.09 thf(zip_derived_cl5618, plain, (((n0) = (multiply @ n0 @ n1))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl5061, zip_derived_cl5548])).
% 9.45/2.09 thf(zip_derived_cl5686, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ (multiply @ X0 @ n1) @ n0) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)], [zip_derived_cl650, zip_derived_cl5618])).
% 9.45/2.09 thf(zip_derived_cl19, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ n0 @ (multiply @ X0 @ n1)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl4, zip_derived_cl3, zip_derived_cl0,
% 9.45/2.09 zip_derived_cl1])).
% 9.45/2.09 thf(zip_derived_cl6721, plain, (![X0 : $i]: ((X0) = (multiply @ X0 @ X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl6689, zip_derived_cl5303, zip_derived_cl5686,
% 9.45/2.09 zip_derived_cl19])).
% 9.45/2.09 thf(zip_derived_cl2, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((add @ X1 @ (multiply @ X0 @ X2))
% 9.45/2.09 = (multiply @ (add @ X0 @ X1) @ (add @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [add_multiply_property])).
% 9.45/2.09 thf(zip_derived_cl6776, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((add @ X0 @ (multiply @ X1 @ X1)) = (add @ X1 @ X0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl6721, zip_derived_cl2])).
% 9.45/2.09 thf(zip_derived_cl6721, plain, (![X0 : $i]: ((X0) = (multiply @ X0 @ X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl6689, zip_derived_cl5303, zip_derived_cl5686,
% 9.45/2.09 zip_derived_cl19])).
% 9.45/2.09 thf(zip_derived_cl6802, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]: ((add @ X0 @ X1) = (add @ X1 @ X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl6776, zip_derived_cl6721])).
% 9.45/2.09 thf(zip_derived_cl6911, plain, (((multiply @ (add @ b @ a) @ b) != (b))),
% 9.45/2.09 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl6802])).
% 9.45/2.09 thf(zip_derived_cl5618, plain, (((n0) = (multiply @ n0 @ n1))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl5061, zip_derived_cl5548])).
% 9.45/2.09 thf(zip_derived_cl0, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((multiply @ X1 @ (add @ X0 @ X2))
% 9.45/2.09 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiply_add_property])).
% 9.45/2.09 thf(zip_derived_cl5694, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((multiply @ n1 @ (add @ n0 @ X0)) = (add @ n0 @ (multiply @ X0 @ n1)))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl5618, zip_derived_cl0])).
% 9.45/2.09 thf(zip_derived_cl19, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ n0 @ (multiply @ X0 @ n1)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl4, zip_derived_cl3, zip_derived_cl0,
% 9.45/2.09 zip_derived_cl1])).
% 9.45/2.09 thf(zip_derived_cl5716, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ n1 @ (add @ n0 @ X0)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)], [zip_derived_cl5694, zip_derived_cl19])).
% 9.45/2.09 thf(zip_derived_cl12, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((multiply @ (inverse @ X0) @ (add @ X0 @ X1))
% 9.45/2.09 = (add @ n0 @ (multiply @ X1 @ (inverse @ X0))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 9.45/2.09 thf(zip_derived_cl0, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((multiply @ X1 @ (add @ X0 @ X2))
% 9.45/2.09 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiply_add_property])).
% 9.45/2.09 thf(zip_derived_cl63, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((multiply @ (add @ X0 @ X1) @ (add @ (inverse @ X0) @ X2))
% 9.45/2.09 = (add @ (add @ n0 @ (multiply @ X1 @ (inverse @ X0))) @
% 9.45/2.09 (multiply @ X2 @ (add @ X0 @ X1))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl0])).
% 9.45/2.09 thf(zip_derived_cl7461, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((multiply @ (add @ n0 @ X0) @ (add @ (inverse @ n0) @ n1))
% 9.45/2.09 = (add @ (add @ n0 @ (multiply @ X0 @ (inverse @ n0))) @ X0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl5716, zip_derived_cl63])).
% 9.45/2.09 thf(zip_derived_cl5618, plain, (((n0) = (multiply @ n0 @ n1))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl5061, zip_derived_cl5548])).
% 9.45/2.09 thf(zip_derived_cl19, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ n0 @ (multiply @ X0 @ n1)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl4, zip_derived_cl3, zip_derived_cl0,
% 9.45/2.09 zip_derived_cl1])).
% 9.45/2.09 thf(zip_derived_cl11, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((multiply @ (inverse @ X0) @ (add @ X1 @ X0))
% 9.45/2.09 = (add @ (multiply @ X1 @ (inverse @ X0)) @ n0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 9.45/2.09 thf(zip_derived_cl28, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((multiply @ (inverse @ (multiply @ X0 @ n1)) @ X0)
% 9.45/2.09 = (add @ (multiply @ n0 @ (inverse @ (multiply @ X0 @ n1))) @ n0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl11])).
% 9.45/2.09 thf(zip_derived_cl5708, plain,
% 9.45/2.09 (((multiply @ (inverse @ (multiply @ n0 @ n1)) @ n0)
% 9.45/2.09 = (add @ (multiply @ n0 @ (inverse @ n0)) @ n0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl5618, zip_derived_cl28])).
% 9.45/2.09 thf(zip_derived_cl5618, plain, (((n0) = (multiply @ n0 @ n1))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl5061, zip_derived_cl5548])).
% 9.45/2.09 thf(zip_derived_cl3, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (n0))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiplicative_inverse])).
% 9.45/2.09 thf(zip_derived_cl5253, plain, (((n0) = (add @ n0 @ n0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl5224, zip_derived_cl1079])).
% 9.45/2.09 thf(zip_derived_cl5723, plain, (((multiply @ (inverse @ n0) @ n0) = (n0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl5708, zip_derived_cl5618, zip_derived_cl3,
% 9.45/2.09 zip_derived_cl5253])).
% 9.45/2.09 thf(zip_derived_cl5840, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ (multiply @ X0 @ n0) @ X0) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl5806, zip_derived_cl5774, zip_derived_cl155])).
% 9.45/2.09 thf(zip_derived_cl6029, plain,
% 9.45/2.09 (((add @ n0 @ (inverse @ n0)) = (inverse @ n0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl5723, zip_derived_cl5840])).
% 9.45/2.09 thf(zip_derived_cl1, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ X0 @ (inverse @ X0)) = (n1))),
% 9.45/2.09 inference('cnf', [status(esa)], [additive_inverse])).
% 9.45/2.09 thf(zip_derived_cl6033, plain, (((n1) = (inverse @ n0))),
% 9.45/2.09 inference('demod', [status(thm)], [zip_derived_cl6029, zip_derived_cl1])).
% 9.45/2.09 thf(zip_derived_cl3614, plain,
% 9.45/2.09 (((add @ (inverse @ (add @ n0 @ n0)) @ n0) = (multiply @ n1 @ n1))),
% 9.45/2.09 inference('demod', [status(thm)], [zip_derived_cl3611, zip_derived_cl162])).
% 9.45/2.09 thf(zip_derived_cl161, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((add @ n0 @ (add @ (inverse @ (add @ X0 @ n0)) @ X0))
% 9.45/2.09 = (add @ n1 @ (inverse @ (add @ X0 @ n0))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl155, zip_derived_cl83])).
% 9.45/2.09 thf(zip_derived_cl3655, plain,
% 9.45/2.09 (((add @ n0 @ (multiply @ n1 @ n1))
% 9.45/2.09 = (add @ n1 @ (inverse @ (add @ n0 @ n0))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl3614, zip_derived_cl161])).
% 9.45/2.09 thf(zip_derived_cl19, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ n0 @ (multiply @ X0 @ n1)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl4, zip_derived_cl3, zip_derived_cl0,
% 9.45/2.09 zip_derived_cl1])).
% 9.45/2.09 thf(zip_derived_cl3670, plain,
% 9.45/2.09 (((n1) = (add @ n1 @ (inverse @ (add @ n0 @ n0))))),
% 9.45/2.09 inference('demod', [status(thm)], [zip_derived_cl3655, zip_derived_cl19])).
% 9.45/2.09 thf(zip_derived_cl3640, plain,
% 9.45/2.09 (((multiply @ n1 @ (multiply @ n1 @ n1)) = (inverse @ (add @ n0 @ n0)))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl3614, zip_derived_cl155])).
% 9.45/2.09 thf(zip_derived_cl3699, plain,
% 9.45/2.09 (((n1) = (add @ n1 @ (multiply @ n1 @ (multiply @ n1 @ n1))))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl3670, zip_derived_cl3640])).
% 9.45/2.09 thf(zip_derived_cl5476, plain, (((multiply @ n1 @ n1) = (n1))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl472, zip_derived_cl5353, zip_derived_cl5353,
% 9.45/2.09 zip_derived_cl3, zip_derived_cl5353])).
% 9.45/2.09 thf(zip_derived_cl5476, plain, (((multiply @ n1 @ n1) = (n1))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl472, zip_derived_cl5353, zip_derived_cl5353,
% 9.45/2.09 zip_derived_cl3, zip_derived_cl5353])).
% 9.45/2.09 thf(zip_derived_cl5545, plain, (((n1) = (add @ n1 @ n1))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl3699, zip_derived_cl5476, zip_derived_cl5476])).
% 9.45/2.09 thf(zip_derived_cl5070, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ n1 @ X0) = (multiply @ X0 @ (add @ n0 @ n1)))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl5057, zip_derived_cl0, zip_derived_cl19,
% 9.45/2.09 zip_derived_cl155])).
% 9.45/2.09 thf(zip_derived_cl5548, plain, (((add @ n0 @ n1) = (n1))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl4939, zip_derived_cl5476, zip_derived_cl1])).
% 9.45/2.09 thf(zip_derived_cl5619, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ n1 @ X0) = (multiply @ X0 @ n1))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl5070, zip_derived_cl5548])).
% 9.45/2.09 thf(zip_derived_cl5716, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ n1 @ (add @ n0 @ X0)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)], [zip_derived_cl5694, zip_derived_cl19])).
% 9.45/2.09 thf(zip_derived_cl6033, plain, (((n1) = (inverse @ n0))),
% 9.45/2.09 inference('demod', [status(thm)], [zip_derived_cl6029, zip_derived_cl1])).
% 9.45/2.09 thf(zip_derived_cl19, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ n0 @ (multiply @ X0 @ n1)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl4, zip_derived_cl3, zip_derived_cl0,
% 9.45/2.09 zip_derived_cl1])).
% 9.45/2.09 thf(zip_derived_cl7520, plain, (![X0 : $i]: ((X0) = (add @ X0 @ X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl7461, zip_derived_cl6033, zip_derived_cl5545,
% 9.45/2.09 zip_derived_cl5619, zip_derived_cl5716, zip_derived_cl6033,
% 9.45/2.09 zip_derived_cl19])).
% 9.45/2.09 thf(zip_derived_cl0, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((multiply @ X1 @ (add @ X0 @ X2))
% 9.45/2.09 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiply_add_property])).
% 9.45/2.09 thf(zip_derived_cl7606, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((multiply @ X0 @ (add @ X1 @ X1)) = (multiply @ X1 @ X0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl7520, zip_derived_cl0])).
% 9.45/2.09 thf(zip_derived_cl7520, plain, (![X0 : $i]: ((X0) = (add @ X0 @ X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl7461, zip_derived_cl6033, zip_derived_cl5545,
% 9.45/2.09 zip_derived_cl5619, zip_derived_cl5716, zip_derived_cl6033,
% 9.45/2.09 zip_derived_cl19])).
% 9.45/2.09 thf(zip_derived_cl7641, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl7606, zip_derived_cl7520])).
% 9.45/2.09 thf(zip_derived_cl7955, plain, (((multiply @ b @ (add @ b @ a)) != (b))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl6911, zip_derived_cl7641])).
% 9.45/2.09 thf(zip_derived_cl6802, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]: ((add @ X0 @ X1) = (add @ X1 @ X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl6776, zip_derived_cl6721])).
% 9.45/2.09 thf(zip_derived_cl3, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (n0))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiplicative_inverse])).
% 9.45/2.09 thf(zip_derived_cl83, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((add @ n0 @ (add @ (inverse @ X0) @ (multiply @ X1 @ X0)))
% 9.45/2.09 = (add @ X1 @ (inverse @ X0)))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl15, zip_derived_cl19])).
% 9.45/2.09 thf(zip_derived_cl2, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((add @ X1 @ (multiply @ X0 @ X2))
% 9.45/2.09 = (multiply @ (add @ X0 @ X1) @ (add @ X2 @ X1)))),
% 9.45/2.09 inference('cnf', [status(esa)], [add_multiply_property])).
% 9.45/2.09 thf(zip_derived_cl127, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.09 ((add @ (add @ (inverse @ X0) @ (multiply @ X1 @ X0)) @
% 9.45/2.09 (multiply @ n0 @ X2))
% 9.45/2.09 = (multiply @ (add @ X1 @ (inverse @ X0)) @
% 9.45/2.09 (add @ X2 @ (add @ (inverse @ X0) @ (multiply @ X1 @ X0)))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl83, zip_derived_cl2])).
% 9.45/2.09 thf(zip_derived_cl7520, plain, (![X0 : $i]: ((X0) = (add @ X0 @ X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl7461, zip_derived_cl6033, zip_derived_cl5545,
% 9.45/2.09 zip_derived_cl5619, zip_derived_cl5716, zip_derived_cl6033,
% 9.45/2.09 zip_derived_cl19])).
% 9.45/2.09 thf(zip_derived_cl52, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((add @ (multiply @ X0 @ (inverse @ X1)) @
% 9.45/2.09 (multiply @ X1 @ (add @ X0 @ (inverse @ X1)))) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl0])).
% 9.45/2.09 thf(zip_derived_cl7587, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((add @ (multiply @ (inverse @ X0) @ (inverse @ X0)) @
% 9.45/2.09 (multiply @ X0 @ (inverse @ X0))) = (inverse @ X0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl7520, zip_derived_cl52])).
% 9.45/2.09 thf(zip_derived_cl6721, plain, (![X0 : $i]: ((X0) = (multiply @ X0 @ X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl6689, zip_derived_cl5303, zip_derived_cl5686,
% 9.45/2.09 zip_derived_cl19])).
% 9.45/2.09 thf(zip_derived_cl3, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (n0))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiplicative_inverse])).
% 9.45/2.09 thf(zip_derived_cl6802, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]: ((add @ X0 @ X1) = (add @ X1 @ X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl6776, zip_derived_cl6721])).
% 9.45/2.09 thf(zip_derived_cl7626, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ n0 @ (inverse @ X0)) = (inverse @ X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl7587, zip_derived_cl6721, zip_derived_cl3,
% 9.45/2.09 zip_derived_cl6802])).
% 9.45/2.09 thf(zip_derived_cl163, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((multiply @ n1 @ (multiply @ (inverse @ X0) @ (add @ X1 @ X0)))
% 9.45/2.09 = (multiply @ X1 @ (inverse @ X0)))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl155])).
% 9.45/2.09 thf(zip_derived_cl8192, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((multiply @ n1 @
% 9.45/2.09 (multiply @ (inverse @ (inverse @ X0)) @ (inverse @ X0)))
% 9.45/2.09 = (multiply @ n0 @ (inverse @ (inverse @ X0))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl7626, zip_derived_cl163])).
% 9.45/2.09 thf(zip_derived_cl7520, plain, (![X0 : $i]: ((X0) = (add @ X0 @ X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl7461, zip_derived_cl6033, zip_derived_cl5545,
% 9.45/2.09 zip_derived_cl5619, zip_derived_cl5716, zip_derived_cl6033,
% 9.45/2.09 zip_derived_cl19])).
% 9.45/2.09 thf(zip_derived_cl12, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((multiply @ (inverse @ X0) @ (add @ X0 @ X1))
% 9.45/2.09 = (add @ n0 @ (multiply @ X1 @ (inverse @ X0))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 9.45/2.09 thf(zip_derived_cl7564, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((multiply @ (inverse @ X0) @ X0)
% 9.45/2.09 = (add @ n0 @ (multiply @ X0 @ (inverse @ X0))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl7520, zip_derived_cl12])).
% 9.45/2.09 thf(zip_derived_cl3, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (n0))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiplicative_inverse])).
% 9.45/2.09 thf(zip_derived_cl7520, plain, (![X0 : $i]: ((X0) = (add @ X0 @ X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl7461, zip_derived_cl6033, zip_derived_cl5545,
% 9.45/2.09 zip_derived_cl5619, zip_derived_cl5716, zip_derived_cl6033,
% 9.45/2.09 zip_derived_cl19])).
% 9.45/2.09 thf(zip_derived_cl7613, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (n0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl7564, zip_derived_cl3, zip_derived_cl7520])).
% 9.45/2.09 thf(zip_derived_cl52, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((add @ (multiply @ X0 @ (inverse @ X1)) @
% 9.45/2.09 (multiply @ X1 @ (add @ X0 @ (inverse @ X1)))) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl0])).
% 9.45/2.09 thf(zip_derived_cl7664, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((add @ n0 @
% 9.45/2.09 (multiply @ X0 @ (add @ (inverse @ (inverse @ X0)) @ (inverse @ X0))))
% 9.45/2.09 = (inverse @ (inverse @ X0)))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl7613, zip_derived_cl52])).
% 9.45/2.09 thf(zip_derived_cl6721, plain, (![X0 : $i]: ((X0) = (multiply @ X0 @ X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl6689, zip_derived_cl5303, zip_derived_cl5686,
% 9.45/2.09 zip_derived_cl19])).
% 9.45/2.09 thf(zip_derived_cl17, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((add @ (inverse @ X0) @ (multiply @ X0 @ X1))
% 9.45/2.09 = (multiply @ n1 @ (add @ X1 @ (inverse @ X0))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 9.45/2.09 thf(zip_derived_cl6734, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((add @ (inverse @ X0) @ X0)
% 9.45/2.09 = (multiply @ n1 @ (add @ X0 @ (inverse @ X0))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl6721, zip_derived_cl17])).
% 9.45/2.09 thf(zip_derived_cl1, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ X0 @ (inverse @ X0)) = (n1))),
% 9.45/2.09 inference('cnf', [status(esa)], [additive_inverse])).
% 9.45/2.09 thf(zip_derived_cl6721, plain, (![X0 : $i]: ((X0) = (multiply @ X0 @ X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl6689, zip_derived_cl5303, zip_derived_cl5686,
% 9.45/2.09 zip_derived_cl19])).
% 9.45/2.09 thf(zip_derived_cl6781, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ (inverse @ X0) @ X0) = (n1))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl6734, zip_derived_cl1, zip_derived_cl6721])).
% 9.45/2.09 thf(zip_derived_cl19, plain,
% 9.45/2.09 (![X0 : $i]: ((add @ n0 @ (multiply @ X0 @ n1)) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl4, zip_derived_cl3, zip_derived_cl0,
% 9.45/2.09 zip_derived_cl1])).
% 9.45/2.09 thf(zip_derived_cl7706, plain,
% 9.45/2.09 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl7664, zip_derived_cl6781, zip_derived_cl19])).
% 9.45/2.09 thf(zip_derived_cl3, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (n0))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiplicative_inverse])).
% 9.45/2.09 thf(zip_derived_cl5140, plain, (((n0) = (multiply @ n1 @ n0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl5070, zip_derived_cl5061])).
% 9.45/2.09 thf(zip_derived_cl7706, plain,
% 9.45/2.09 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl7664, zip_derived_cl6781, zip_derived_cl19])).
% 9.45/2.09 thf(zip_derived_cl8218, plain, (![X0 : $i]: ((n0) = (multiply @ n0 @ X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl8192, zip_derived_cl7706, zip_derived_cl3,
% 9.45/2.09 zip_derived_cl5140, zip_derived_cl7706])).
% 9.45/2.09 thf(zip_derived_cl12, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((multiply @ (inverse @ X0) @ (add @ X0 @ X1))
% 9.45/2.09 = (add @ n0 @ (multiply @ X1 @ (inverse @ X0))))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 9.45/2.09 thf(zip_derived_cl52, plain,
% 9.45/2.09 (![X0 : $i, X1 : $i]:
% 9.45/2.09 ((add @ (multiply @ X0 @ (inverse @ X1)) @
% 9.45/2.09 (multiply @ X1 @ (add @ X0 @ (inverse @ X1)))) = (X0))),
% 9.45/2.09 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl0])).
% 9.45/2.09 thf(zip_derived_cl67, plain,
% 9.45/2.09 (![X0 : $i]:
% 9.45/2.09 ((add @ (multiply @ X0 @ (inverse @ (inverse @ X0))) @
% 9.45/2.09 (add @ n0 @ (multiply @ (inverse @ (inverse @ X0)) @ (inverse @ X0))))
% 9.45/2.09 = (X0))),
% 9.45/2.09 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl52])).
% 9.45/2.09 thf(zip_derived_cl7706, plain,
% 9.45/2.09 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl7664, zip_derived_cl6781, zip_derived_cl19])).
% 9.45/2.09 thf(zip_derived_cl6721, plain, (![X0 : $i]: ((X0) = (multiply @ X0 @ X0))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl6689, zip_derived_cl5303, zip_derived_cl5686,
% 9.45/2.09 zip_derived_cl19])).
% 9.45/2.09 thf(zip_derived_cl7706, plain,
% 9.45/2.09 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 9.45/2.09 inference('demod', [status(thm)],
% 9.45/2.09 [zip_derived_cl7664, zip_derived_cl6781, zip_derived_cl19])).
% 9.45/2.09 thf(zip_derived_cl3, plain,
% 9.45/2.09 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (n0))),
% 9.45/2.09 inference('cnf', [status(esa)], [multiplicative_inverse])).
% 9.45/2.10 thf(zip_derived_cl7520, plain, (![X0 : $i]: ((X0) = (add @ X0 @ X0))),
% 9.45/2.10 inference('demod', [status(thm)],
% 9.45/2.10 [zip_derived_cl7461, zip_derived_cl6033, zip_derived_cl5545,
% 9.45/2.10 zip_derived_cl5619, zip_derived_cl5716, zip_derived_cl6033,
% 9.45/2.10 zip_derived_cl19])).
% 9.45/2.10 thf(zip_derived_cl8223, plain, (![X0 : $i]: ((add @ X0 @ n0) = (X0))),
% 9.45/2.10 inference('demod', [status(thm)],
% 9.45/2.10 [zip_derived_cl67, zip_derived_cl7706, zip_derived_cl6721,
% 9.45/2.10 zip_derived_cl7706, zip_derived_cl3, zip_derived_cl7520])).
% 9.45/2.10 thf(zip_derived_cl8455, plain,
% 9.45/2.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.45/2.10 ((add @ (inverse @ X0) @ (multiply @ X1 @ X0))
% 9.45/2.10 = (multiply @ (add @ X1 @ (inverse @ X0)) @
% 9.45/2.10 (add @ X2 @ (add @ (inverse @ X0) @ (multiply @ X1 @ X0)))))),
% 9.45/2.10 inference('demod', [status(thm)],
% 9.45/2.10 [zip_derived_cl127, zip_derived_cl8218, zip_derived_cl8223])).
% 9.45/2.10 thf(zip_derived_cl8482, plain,
% 9.45/2.10 (![X0 : $i, X1 : $i]:
% 9.45/2.10 ((add @ (inverse @ (inverse @ X0)) @ (multiply @ X0 @ (inverse @ X0)))
% 9.45/2.10 = (multiply @ (add @ X0 @ (inverse @ (inverse @ X0))) @
% 9.45/2.10 (add @ X1 @ (add @ (inverse @ (inverse @ X0)) @ n0))))),
% 9.45/2.10 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl8455])).
% 9.45/2.10 thf(zip_derived_cl7706, plain,
% 9.45/2.10 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 9.45/2.10 inference('demod', [status(thm)],
% 9.45/2.10 [zip_derived_cl7664, zip_derived_cl6781, zip_derived_cl19])).
% 9.45/2.10 thf(zip_derived_cl3, plain,
% 9.45/2.10 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (n0))),
% 9.45/2.10 inference('cnf', [status(esa)], [multiplicative_inverse])).
% 9.45/2.10 thf(zip_derived_cl8223, plain, (![X0 : $i]: ((add @ X0 @ n0) = (X0))),
% 9.45/2.10 inference('demod', [status(thm)],
% 9.45/2.10 [zip_derived_cl67, zip_derived_cl7706, zip_derived_cl6721,
% 9.45/2.10 zip_derived_cl7706, zip_derived_cl3, zip_derived_cl7520])).
% 9.45/2.10 thf(zip_derived_cl7706, plain,
% 9.45/2.10 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 9.45/2.10 inference('demod', [status(thm)],
% 9.45/2.10 [zip_derived_cl7664, zip_derived_cl6781, zip_derived_cl19])).
% 9.45/2.10 thf(zip_derived_cl7520, plain, (![X0 : $i]: ((X0) = (add @ X0 @ X0))),
% 9.45/2.10 inference('demod', [status(thm)],
% 9.45/2.10 [zip_derived_cl7461, zip_derived_cl6033, zip_derived_cl5545,
% 9.45/2.10 zip_derived_cl5619, zip_derived_cl5716, zip_derived_cl6033,
% 9.45/2.10 zip_derived_cl19])).
% 9.45/2.10 thf(zip_derived_cl7706, plain,
% 9.45/2.10 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 9.45/2.10 inference('demod', [status(thm)],
% 9.45/2.10 [zip_derived_cl7664, zip_derived_cl6781, zip_derived_cl19])).
% 9.45/2.10 thf(zip_derived_cl8223, plain, (![X0 : $i]: ((add @ X0 @ n0) = (X0))),
% 9.45/2.10 inference('demod', [status(thm)],
% 9.45/2.10 [zip_derived_cl67, zip_derived_cl7706, zip_derived_cl6721,
% 9.45/2.10 zip_derived_cl7706, zip_derived_cl3, zip_derived_cl7520])).
% 9.45/2.10 thf(zip_derived_cl8515, plain,
% 9.45/2.10 (![X0 : $i, X1 : $i]: ((X0) = (multiply @ X0 @ (add @ X1 @ X0)))),
% 9.45/2.10 inference('demod', [status(thm)],
% 9.45/2.10 [zip_derived_cl8482, zip_derived_cl7706, zip_derived_cl3,
% 9.45/2.10 zip_derived_cl8223, zip_derived_cl7706, zip_derived_cl7520,
% 9.45/2.10 zip_derived_cl7706, zip_derived_cl8223])).
% 9.45/2.10 thf(zip_derived_cl8843, plain,
% 9.45/2.10 (![X0 : $i, X1 : $i]: ((X1) = (multiply @ X1 @ (add @ X1 @ X0)))),
% 9.45/2.10 inference('sup+', [status(thm)], [zip_derived_cl6802, zip_derived_cl8515])).
% 9.45/2.10 thf(zip_derived_cl9045, plain, (((b) != (b))),
% 9.45/2.10 inference('demod', [status(thm)],
% 9.45/2.10 [zip_derived_cl7955, zip_derived_cl8843])).
% 9.45/2.10 thf(zip_derived_cl9046, plain, ($false),
% 9.45/2.10 inference('simplify', [status(thm)], [zip_derived_cl9045])).
% 9.45/2.10
% 9.45/2.10 % SZS output end Refutation
% 9.45/2.10
% 9.45/2.10
% 9.45/2.10 % Terminating...
% 10.32/2.17 % Runner terminated.
% 10.32/2.18 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------