TSTP Solution File: BOO014-2 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : BOO014-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.37RR62voD1 true
% Computer : n006.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 18:13:19 EDT 2023
% Result : Unsatisfiable 9.95s 2.07s
% Output : Refutation 9.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO014-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.37RR62voD1 true
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 07:51:07 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.36 % Running in FO mode
% 0.21/0.65 % Total configuration time : 435
% 0.21/0.65 % Estimated wc time : 1092
% 0.21/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.73 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.21/0.78 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 9.95/2.07 % Solved by fo/fo5.sh.
% 9.95/2.07 % done 833 iterations in 1.282s
% 9.95/2.07 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 9.95/2.07 % SZS output start Refutation
% 9.95/2.07 thf(multiply_type, type, multiply: $i > $i > $i).
% 9.95/2.07 thf(d_type, type, d: $i).
% 9.95/2.07 thf(multiplicative_identity_type, type, multiplicative_identity: $i).
% 9.95/2.07 thf(a_type, type, a: $i).
% 9.95/2.07 thf(b_type, type, b: $i).
% 9.95/2.07 thf(c_type, type, c: $i).
% 9.95/2.07 thf(add_type, type, add: $i > $i > $i).
% 9.95/2.07 thf(inverse_type, type, inverse: $i > $i).
% 9.95/2.07 thf(additive_identity_type, type, additive_identity: $i).
% 9.95/2.07 thf(a_plus_b_is_c, axiom, (( add @ a @ b ) = ( c ))).
% 9.95/2.07 thf(zip_derived_cl14, plain, (((add @ a @ b) = (c))),
% 9.95/2.07 inference('cnf', [status(esa)], [a_plus_b_is_c])).
% 9.95/2.07 thf(additive_id2, axiom, (( add @ additive_identity @ X ) = ( X ))).
% 9.95/2.07 thf(zip_derived_cl13, plain,
% 9.95/2.07 (![X0 : $i]: ((add @ additive_identity @ X0) = (X0))),
% 9.95/2.07 inference('cnf', [status(esa)], [additive_id2])).
% 9.95/2.07 thf(commutativity_of_add, axiom, (( add @ X @ Y ) = ( add @ Y @ X ))).
% 9.95/2.07 thf(zip_derived_cl0, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]: ((add @ X1 @ X0) = (add @ X0 @ X1))),
% 9.95/2.07 inference('cnf', [status(esa)], [commutativity_of_add])).
% 9.95/2.07 thf(distributivity1, axiom,
% 9.95/2.07 (( add @ ( multiply @ X @ Y ) @ Z ) =
% 9.95/2.07 ( multiply @ ( add @ X @ Z ) @ ( add @ Y @ Z ) ))).
% 9.95/2.07 thf(zip_derived_cl2, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.95/2.07 ((add @ (multiply @ X0 @ X2) @ X1)
% 9.95/2.07 = (multiply @ (add @ X0 @ X1) @ (add @ X2 @ X1)))),
% 9.95/2.07 inference('cnf', [status(esa)], [distributivity1])).
% 9.95/2.07 thf(zip_derived_cl39, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.95/2.07 ((add @ (multiply @ X2 @ X0) @ X1)
% 9.95/2.07 = (multiply @ (add @ X2 @ X1) @ (add @ X1 @ X0)))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 9.95/2.07 thf(zip_derived_cl624, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]:
% 9.95/2.07 ((add @ (multiply @ additive_identity @ X1) @ X0)
% 9.95/2.07 = (multiply @ X0 @ (add @ X0 @ X1)))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl39])).
% 9.95/2.07 thf(zip_derived_cl13, plain,
% 9.95/2.07 (![X0 : $i]: ((add @ additive_identity @ X0) = (X0))),
% 9.95/2.07 inference('cnf', [status(esa)], [additive_id2])).
% 9.95/2.07 thf(multiplicative_inverse2, axiom,
% 9.95/2.07 (( multiply @ ( inverse @ X ) @ X ) = ( additive_identity ))).
% 9.95/2.07 thf(zip_derived_cl9, plain,
% 9.95/2.07 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (additive_identity))),
% 9.95/2.07 inference('cnf', [status(esa)], [multiplicative_inverse2])).
% 9.95/2.07 thf(distributivity3, axiom,
% 9.95/2.07 (( multiply @ ( add @ X @ Y ) @ Z ) =
% 9.95/2.07 ( add @ ( multiply @ X @ Z ) @ ( multiply @ Y @ Z ) ))).
% 9.95/2.07 thf(zip_derived_cl4, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.95/2.07 ((multiply @ (add @ X0 @ X2) @ X1)
% 9.95/2.07 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 9.95/2.07 inference('cnf', [status(esa)], [distributivity3])).
% 9.95/2.07 thf(zip_derived_cl100, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]:
% 9.95/2.07 ((multiply @ (add @ X1 @ (inverse @ X0)) @ X0)
% 9.95/2.07 = (add @ (multiply @ X1 @ X0) @ additive_identity))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl4])).
% 9.95/2.07 thf(additive_id1, axiom, (( add @ X @ additive_identity ) = ( X ))).
% 9.95/2.07 thf(zip_derived_cl12, plain,
% 9.95/2.07 (![X0 : $i]: ((add @ X0 @ additive_identity) = (X0))),
% 9.95/2.07 inference('cnf', [status(esa)], [additive_id1])).
% 9.95/2.07 thf(zip_derived_cl114, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]:
% 9.95/2.07 ((multiply @ (add @ X1 @ (inverse @ X0)) @ X0) = (multiply @ X1 @ X0))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl100, zip_derived_cl12])).
% 9.95/2.07 thf(zip_derived_cl481, plain,
% 9.95/2.07 (![X0 : $i]:
% 9.95/2.07 ((multiply @ (inverse @ X0) @ X0)
% 9.95/2.07 = (multiply @ additive_identity @ X0))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl114])).
% 9.95/2.07 thf(zip_derived_cl9, plain,
% 9.95/2.07 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (additive_identity))),
% 9.95/2.07 inference('cnf', [status(esa)], [multiplicative_inverse2])).
% 9.95/2.07 thf(zip_derived_cl494, plain,
% 9.95/2.07 (![X0 : $i]: ((additive_identity) = (multiply @ additive_identity @ X0))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl481, zip_derived_cl9])).
% 9.95/2.07 thf(zip_derived_cl13, plain,
% 9.95/2.07 (![X0 : $i]: ((add @ additive_identity @ X0) = (X0))),
% 9.95/2.07 inference('cnf', [status(esa)], [additive_id2])).
% 9.95/2.07 thf(zip_derived_cl656, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]: ((X0) = (multiply @ X0 @ (add @ X0 @ X1)))),
% 9.95/2.07 inference('demod', [status(thm)],
% 9.95/2.07 [zip_derived_cl624, zip_derived_cl494, zip_derived_cl13])).
% 9.95/2.07 thf(zip_derived_cl829, plain, (((a) = (multiply @ a @ c))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl656])).
% 9.95/2.07 thf(commutativity_of_multiply, axiom,
% 9.95/2.07 (( multiply @ X @ Y ) = ( multiply @ Y @ X ))).
% 9.95/2.07 thf(zip_derived_cl1, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 9.95/2.07 inference('cnf', [status(esa)], [commutativity_of_multiply])).
% 9.95/2.07 thf(zip_derived_cl839, plain, (((multiply @ c @ a) = (a))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl829, zip_derived_cl1])).
% 9.95/2.07 thf(multiplicative_inverse1, axiom,
% 9.95/2.07 (( multiply @ X @ ( inverse @ X ) ) = ( additive_identity ))).
% 9.95/2.07 thf(zip_derived_cl8, plain,
% 9.95/2.07 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (additive_identity))),
% 9.95/2.07 inference('cnf', [status(esa)], [multiplicative_inverse1])).
% 9.95/2.07 thf(additive_inverse2, axiom,
% 9.95/2.07 (( add @ ( inverse @ X ) @ X ) = ( multiplicative_identity ))).
% 9.95/2.07 thf(zip_derived_cl7, plain,
% 9.95/2.07 (![X0 : $i]: ((add @ (inverse @ X0) @ X0) = (multiplicative_identity))),
% 9.95/2.07 inference('cnf', [status(esa)], [additive_inverse2])).
% 9.95/2.07 thf(zip_derived_cl2, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.95/2.07 ((add @ (multiply @ X0 @ X2) @ X1)
% 9.95/2.07 = (multiply @ (add @ X0 @ X1) @ (add @ X2 @ X1)))),
% 9.95/2.07 inference('cnf', [status(esa)], [distributivity1])).
% 9.95/2.07 thf(zip_derived_cl43, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]:
% 9.95/2.07 ((add @ (multiply @ X1 @ (inverse @ X0)) @ X0)
% 9.95/2.07 = (multiply @ (add @ X1 @ X0) @ multiplicative_identity))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 9.95/2.07 thf(multiplicative_id1, axiom,
% 9.95/2.07 (( multiply @ X @ multiplicative_identity ) = ( X ))).
% 9.95/2.07 thf(zip_derived_cl10, plain,
% 9.95/2.07 (![X0 : $i]: ((multiply @ X0 @ multiplicative_identity) = (X0))),
% 9.95/2.07 inference('cnf', [status(esa)], [multiplicative_id1])).
% 9.95/2.07 thf(zip_derived_cl55, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]:
% 9.95/2.07 ((add @ (multiply @ X1 @ (inverse @ X0)) @ X0) = (add @ X1 @ X0))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl10])).
% 9.95/2.07 thf(zip_derived_cl161, plain,
% 9.95/2.07 (![X0 : $i]: ((add @ additive_identity @ X0) = (add @ X0 @ X0))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl55])).
% 9.95/2.07 thf(zip_derived_cl13, plain,
% 9.95/2.07 (![X0 : $i]: ((add @ additive_identity @ X0) = (X0))),
% 9.95/2.07 inference('cnf', [status(esa)], [additive_id2])).
% 9.95/2.07 thf(zip_derived_cl167, plain, (![X0 : $i]: ((X0) = (add @ X0 @ X0))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl161, zip_derived_cl13])).
% 9.95/2.07 thf(distributivity2, axiom,
% 9.95/2.07 (( add @ X @ ( multiply @ Y @ Z ) ) =
% 9.95/2.07 ( multiply @ ( add @ X @ Y ) @ ( add @ X @ Z ) ))).
% 9.95/2.07 thf(zip_derived_cl3, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.95/2.07 ((add @ X0 @ (multiply @ X1 @ X2))
% 9.95/2.07 = (multiply @ (add @ X0 @ X1) @ (add @ X0 @ X2)))),
% 9.95/2.07 inference('cnf', [status(esa)], [distributivity2])).
% 9.95/2.07 thf(zip_derived_cl1, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 9.95/2.07 inference('cnf', [status(esa)], [commutativity_of_multiply])).
% 9.95/2.07 thf(zip_derived_cl60, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.95/2.07 ((multiply @ (add @ X2 @ X0) @ (add @ X2 @ X1))
% 9.95/2.07 = (add @ X2 @ (multiply @ X1 @ X0)))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 9.95/2.07 thf(zip_derived_cl1392, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]:
% 9.95/2.07 ((multiply @ (add @ X0 @ X1) @ X0) = (add @ X0 @ (multiply @ X0 @ X1)))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl167, zip_derived_cl60])).
% 9.95/2.07 thf(zip_derived_cl0, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]: ((add @ X1 @ X0) = (add @ X0 @ X1))),
% 9.95/2.07 inference('cnf', [status(esa)], [commutativity_of_add])).
% 9.95/2.07 thf(zip_derived_cl12, plain,
% 9.95/2.07 (![X0 : $i]: ((add @ X0 @ additive_identity) = (X0))),
% 9.95/2.07 inference('cnf', [status(esa)], [additive_id1])).
% 9.95/2.07 thf(zip_derived_cl39, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.95/2.07 ((add @ (multiply @ X2 @ X0) @ X1)
% 9.95/2.07 = (multiply @ (add @ X2 @ X1) @ (add @ X1 @ X0)))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 9.95/2.07 thf(zip_derived_cl588, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]:
% 9.95/2.07 ((add @ (multiply @ X1 @ additive_identity) @ X0)
% 9.95/2.07 = (multiply @ (add @ X1 @ X0) @ X0))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl39])).
% 9.95/2.07 thf(zip_derived_cl13, plain,
% 9.95/2.07 (![X0 : $i]: ((add @ additive_identity @ X0) = (X0))),
% 9.95/2.07 inference('cnf', [status(esa)], [additive_id2])).
% 9.95/2.07 thf(additive_inverse1, axiom,
% 9.95/2.07 (( add @ X @ ( inverse @ X ) ) = ( multiplicative_identity ))).
% 9.95/2.07 thf(zip_derived_cl6, plain,
% 9.95/2.07 (![X0 : $i]: ((add @ X0 @ (inverse @ X0)) = (multiplicative_identity))),
% 9.95/2.07 inference('cnf', [status(esa)], [additive_inverse1])).
% 9.95/2.07 thf(zip_derived_cl17, plain,
% 9.95/2.07 (((inverse @ additive_identity) = (multiplicative_identity))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl6])).
% 9.95/2.07 thf(zip_derived_cl114, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]:
% 9.95/2.07 ((multiply @ (add @ X1 @ (inverse @ X0)) @ X0) = (multiply @ X1 @ X0))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl100, zip_derived_cl12])).
% 9.95/2.07 thf(zip_derived_cl485, plain,
% 9.95/2.07 (![X0 : $i]:
% 9.95/2.07 ((multiply @ (add @ X0 @ multiplicative_identity) @ additive_identity)
% 9.95/2.07 = (multiply @ X0 @ additive_identity))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl17, zip_derived_cl114])).
% 9.95/2.07 thf(multiplicative_id2, axiom,
% 9.95/2.07 (( multiply @ multiplicative_identity @ X ) = ( X ))).
% 9.95/2.07 thf(zip_derived_cl11, plain,
% 9.95/2.07 (![X0 : $i]: ((multiply @ multiplicative_identity @ X0) = (X0))),
% 9.95/2.07 inference('cnf', [status(esa)], [multiplicative_id2])).
% 9.95/2.07 thf(zip_derived_cl55, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]:
% 9.95/2.07 ((add @ (multiply @ X1 @ (inverse @ X0)) @ X0) = (add @ X1 @ X0))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl10])).
% 9.95/2.07 thf(zip_derived_cl164, plain,
% 9.95/2.07 (![X0 : $i]:
% 9.95/2.07 ((add @ (inverse @ X0) @ X0) = (add @ multiplicative_identity @ X0))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl55])).
% 9.95/2.07 thf(zip_derived_cl7, plain,
% 9.95/2.07 (![X0 : $i]: ((add @ (inverse @ X0) @ X0) = (multiplicative_identity))),
% 9.95/2.07 inference('cnf', [status(esa)], [additive_inverse2])).
% 9.95/2.07 thf(zip_derived_cl169, plain,
% 9.95/2.07 (![X0 : $i]:
% 9.95/2.07 ((multiplicative_identity) = (add @ multiplicative_identity @ X0))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl164, zip_derived_cl7])).
% 9.95/2.07 thf(zip_derived_cl0, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]: ((add @ X1 @ X0) = (add @ X0 @ X1))),
% 9.95/2.07 inference('cnf', [status(esa)], [commutativity_of_add])).
% 9.95/2.07 thf(zip_derived_cl187, plain,
% 9.95/2.07 (![X0 : $i]:
% 9.95/2.07 ((add @ X0 @ multiplicative_identity) = (multiplicative_identity))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl169, zip_derived_cl0])).
% 9.95/2.07 thf(zip_derived_cl11, plain,
% 9.95/2.07 (![X0 : $i]: ((multiply @ multiplicative_identity @ X0) = (X0))),
% 9.95/2.07 inference('cnf', [status(esa)], [multiplicative_id2])).
% 9.95/2.07 thf(zip_derived_cl497, plain,
% 9.95/2.07 (![X0 : $i]: ((additive_identity) = (multiply @ X0 @ additive_identity))),
% 9.95/2.07 inference('demod', [status(thm)],
% 9.95/2.07 [zip_derived_cl485, zip_derived_cl187, zip_derived_cl11])).
% 9.95/2.07 thf(zip_derived_cl13, plain,
% 9.95/2.07 (![X0 : $i]: ((add @ additive_identity @ X0) = (X0))),
% 9.95/2.07 inference('cnf', [status(esa)], [additive_id2])).
% 9.95/2.07 thf(zip_derived_cl635, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]: ((X0) = (multiply @ (add @ X1 @ X0) @ X0))),
% 9.95/2.07 inference('demod', [status(thm)],
% 9.95/2.07 [zip_derived_cl588, zip_derived_cl497, zip_derived_cl13])).
% 9.95/2.07 thf(zip_derived_cl769, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]: ((X1) = (multiply @ (add @ X1 @ X0) @ X1))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl635])).
% 9.95/2.07 thf(zip_derived_cl1454, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]: ((X0) = (add @ X0 @ (multiply @ X0 @ X1)))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl1392, zip_derived_cl769])).
% 9.95/2.07 thf(zip_derived_cl1537, plain, (((c) = (add @ c @ a))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl839, zip_derived_cl1454])).
% 9.95/2.07 thf(zip_derived_cl39, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.95/2.07 ((add @ (multiply @ X2 @ X0) @ X1)
% 9.95/2.07 = (multiply @ (add @ X2 @ X1) @ (add @ X1 @ X0)))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 9.95/2.07 thf(zip_derived_cl1581, plain,
% 9.95/2.07 (![X0 : $i]:
% 9.95/2.07 ((add @ (multiply @ X0 @ a) @ c) = (multiply @ (add @ X0 @ c) @ c))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl1537, zip_derived_cl39])).
% 9.95/2.07 thf(zip_derived_cl635, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]: ((X0) = (multiply @ (add @ X1 @ X0) @ X0))),
% 9.95/2.07 inference('demod', [status(thm)],
% 9.95/2.07 [zip_derived_cl588, zip_derived_cl497, zip_derived_cl13])).
% 9.95/2.07 thf(zip_derived_cl1596, plain,
% 9.95/2.07 (![X0 : $i]: ((add @ (multiply @ X0 @ a) @ c) = (c))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl1581, zip_derived_cl635])).
% 9.95/2.07 thf(zip_derived_cl7, plain,
% 9.95/2.07 (![X0 : $i]: ((add @ (inverse @ X0) @ X0) = (multiplicative_identity))),
% 9.95/2.07 inference('cnf', [status(esa)], [additive_inverse2])).
% 9.95/2.07 thf(zip_derived_cl2, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.95/2.07 ((add @ (multiply @ X0 @ X2) @ X1)
% 9.95/2.07 = (multiply @ (add @ X0 @ X1) @ (add @ X2 @ X1)))),
% 9.95/2.07 inference('cnf', [status(esa)], [distributivity1])).
% 9.95/2.07 thf(zip_derived_cl50, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]:
% 9.95/2.07 ((add @ (multiply @ (inverse @ X0) @ X1) @ X0)
% 9.95/2.07 = (multiply @ multiplicative_identity @ (add @ X1 @ X0)))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 9.95/2.07 thf(zip_derived_cl11, plain,
% 9.95/2.07 (![X0 : $i]: ((multiply @ multiplicative_identity @ X0) = (X0))),
% 9.95/2.07 inference('cnf', [status(esa)], [multiplicative_id2])).
% 9.95/2.07 thf(zip_derived_cl59, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]:
% 9.95/2.07 ((add @ (multiply @ (inverse @ X0) @ X1) @ X0) = (add @ X1 @ X0))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl50, zip_derived_cl11])).
% 9.95/2.07 thf(zip_derived_cl4229, plain, (((c) = (add @ a @ c))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl1596, zip_derived_cl59])).
% 9.95/2.07 thf(zip_derived_cl8, plain,
% 9.95/2.07 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (additive_identity))),
% 9.95/2.07 inference('cnf', [status(esa)], [multiplicative_inverse1])).
% 9.95/2.07 thf(zip_derived_cl4, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.95/2.07 ((multiply @ (add @ X0 @ X2) @ X1)
% 9.95/2.07 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 9.95/2.07 inference('cnf', [status(esa)], [distributivity3])).
% 9.95/2.07 thf(zip_derived_cl96, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]:
% 9.95/2.07 ((multiply @ (add @ X1 @ X0) @ (inverse @ X0))
% 9.95/2.07 = (add @ (multiply @ X1 @ (inverse @ X0)) @ additive_identity))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl4])).
% 9.95/2.07 thf(zip_derived_cl12, plain,
% 9.95/2.07 (![X0 : $i]: ((add @ X0 @ additive_identity) = (X0))),
% 9.95/2.07 inference('cnf', [status(esa)], [additive_id1])).
% 9.95/2.07 thf(zip_derived_cl112, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]:
% 9.95/2.07 ((multiply @ (add @ X1 @ X0) @ (inverse @ X0))
% 9.95/2.07 = (multiply @ X1 @ (inverse @ X0)))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl96, zip_derived_cl12])).
% 9.95/2.07 thf(zip_derived_cl7713, plain,
% 9.95/2.07 (((multiply @ c @ (inverse @ c)) = (multiply @ a @ (inverse @ c)))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl4229, zip_derived_cl112])).
% 9.95/2.07 thf(zip_derived_cl8, plain,
% 9.95/2.07 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (additive_identity))),
% 9.95/2.07 inference('cnf', [status(esa)], [multiplicative_inverse1])).
% 9.95/2.07 thf(zip_derived_cl7768, plain,
% 9.95/2.07 (((additive_identity) = (multiply @ a @ (inverse @ c)))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl7713, zip_derived_cl8])).
% 9.95/2.07 thf(zip_derived_cl6, plain,
% 9.95/2.07 (![X0 : $i]: ((add @ X0 @ (inverse @ X0)) = (multiplicative_identity))),
% 9.95/2.07 inference('cnf', [status(esa)], [additive_inverse1])).
% 9.95/2.07 thf(zip_derived_cl2, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.95/2.07 ((add @ (multiply @ X0 @ X2) @ X1)
% 9.95/2.07 = (multiply @ (add @ X0 @ X1) @ (add @ X2 @ X1)))),
% 9.95/2.07 inference('cnf', [status(esa)], [distributivity1])).
% 9.95/2.07 thf(zip_derived_cl48, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]:
% 9.95/2.07 ((add @ (multiply @ X0 @ X1) @ (inverse @ X0))
% 9.95/2.07 = (multiply @ multiplicative_identity @ (add @ X1 @ (inverse @ X0))))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl2])).
% 9.95/2.07 thf(zip_derived_cl11, plain,
% 9.95/2.07 (![X0 : $i]: ((multiply @ multiplicative_identity @ X0) = (X0))),
% 9.95/2.07 inference('cnf', [status(esa)], [multiplicative_id2])).
% 9.95/2.07 thf(zip_derived_cl57, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]:
% 9.95/2.07 ((add @ (multiply @ X0 @ X1) @ (inverse @ X0))
% 9.95/2.07 = (add @ X1 @ (inverse @ X0)))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl48, zip_derived_cl11])).
% 9.95/2.07 thf(zip_derived_cl7805, plain,
% 9.95/2.07 (((add @ additive_identity @ (inverse @ a))
% 9.95/2.07 = (add @ (inverse @ c) @ (inverse @ a)))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl7768, zip_derived_cl57])).
% 9.95/2.07 thf(zip_derived_cl13, plain,
% 9.95/2.07 (![X0 : $i]: ((add @ additive_identity @ X0) = (X0))),
% 9.95/2.07 inference('cnf', [status(esa)], [additive_id2])).
% 9.95/2.07 thf(zip_derived_cl7836, plain,
% 9.95/2.07 (((inverse @ a) = (add @ (inverse @ c) @ (inverse @ a)))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl7805, zip_derived_cl13])).
% 9.95/2.07 thf(a_inverse_times_b_inverse_is_d, axiom,
% 9.95/2.07 (( multiply @ ( inverse @ a ) @ ( inverse @ b ) ) = ( d ))).
% 9.95/2.07 thf(zip_derived_cl15, plain,
% 9.95/2.07 (((multiply @ (inverse @ a) @ (inverse @ b)) = (d))),
% 9.95/2.07 inference('cnf', [status(esa)], [a_inverse_times_b_inverse_is_d])).
% 9.95/2.07 thf(zip_derived_cl4, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.95/2.07 ((multiply @ (add @ X0 @ X2) @ X1)
% 9.95/2.07 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 9.95/2.07 inference('cnf', [status(esa)], [distributivity3])).
% 9.95/2.07 thf(zip_derived_cl101, plain,
% 9.95/2.07 (![X0 : $i]:
% 9.95/2.07 ((multiply @ (add @ X0 @ (inverse @ a)) @ (inverse @ b))
% 9.95/2.07 = (add @ (multiply @ X0 @ (inverse @ b)) @ d))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl15, zip_derived_cl4])).
% 9.95/2.07 thf(zip_derived_cl0, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]: ((add @ X1 @ X0) = (add @ X0 @ X1))),
% 9.95/2.07 inference('cnf', [status(esa)], [commutativity_of_add])).
% 9.95/2.07 thf(zip_derived_cl115, plain,
% 9.95/2.07 (![X0 : $i]:
% 9.95/2.07 ((multiply @ (add @ X0 @ (inverse @ a)) @ (inverse @ b))
% 9.95/2.07 = (add @ d @ (multiply @ X0 @ (inverse @ b))))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl101, zip_derived_cl0])).
% 9.95/2.07 thf(zip_derived_cl8776, plain,
% 9.95/2.07 (((multiply @ (inverse @ a) @ (inverse @ b))
% 9.95/2.07 = (add @ d @ (multiply @ (inverse @ c) @ (inverse @ b))))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl7836, zip_derived_cl115])).
% 9.95/2.07 thf(zip_derived_cl15, plain,
% 9.95/2.07 (((multiply @ (inverse @ a) @ (inverse @ b)) = (d))),
% 9.95/2.07 inference('cnf', [status(esa)], [a_inverse_times_b_inverse_is_d])).
% 9.95/2.07 thf(zip_derived_cl494, plain,
% 9.95/2.07 (![X0 : $i]: ((additive_identity) = (multiply @ additive_identity @ X0))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl481, zip_derived_cl9])).
% 9.95/2.07 thf(zip_derived_cl14, plain, (((add @ a @ b) = (c))),
% 9.95/2.07 inference('cnf', [status(esa)], [a_plus_b_is_c])).
% 9.95/2.07 thf(zip_derived_cl2, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.95/2.07 ((add @ (multiply @ X0 @ X2) @ X1)
% 9.95/2.07 = (multiply @ (add @ X0 @ X1) @ (add @ X2 @ X1)))),
% 9.95/2.07 inference('cnf', [status(esa)], [distributivity1])).
% 9.95/2.07 thf(zip_derived_cl45, plain,
% 9.95/2.07 (![X0 : $i]:
% 9.95/2.07 ((add @ (multiply @ X0 @ a) @ b) = (multiply @ (add @ X0 @ b) @ c))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl2])).
% 9.95/2.07 thf(zip_derived_cl1, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 9.95/2.07 inference('cnf', [status(esa)], [commutativity_of_multiply])).
% 9.95/2.07 thf(zip_derived_cl56, plain,
% 9.95/2.07 (![X0 : $i]:
% 9.95/2.07 ((add @ (multiply @ X0 @ a) @ b) = (multiply @ c @ (add @ X0 @ b)))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl1])).
% 9.95/2.07 thf(zip_derived_cl539, plain,
% 9.95/2.07 (((add @ additive_identity @ b)
% 9.95/2.07 = (multiply @ c @ (add @ additive_identity @ b)))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl494, zip_derived_cl56])).
% 9.95/2.07 thf(zip_derived_cl13, plain,
% 9.95/2.07 (![X0 : $i]: ((add @ additive_identity @ X0) = (X0))),
% 9.95/2.07 inference('cnf', [status(esa)], [additive_id2])).
% 9.95/2.07 thf(zip_derived_cl13, plain,
% 9.95/2.07 (![X0 : $i]: ((add @ additive_identity @ X0) = (X0))),
% 9.95/2.07 inference('cnf', [status(esa)], [additive_id2])).
% 9.95/2.07 thf(zip_derived_cl546, plain, (((b) = (multiply @ c @ b))),
% 9.95/2.07 inference('demod', [status(thm)],
% 9.95/2.07 [zip_derived_cl539, zip_derived_cl13, zip_derived_cl13])).
% 9.95/2.07 thf(zip_derived_cl6, plain,
% 9.95/2.07 (![X0 : $i]: ((add @ X0 @ (inverse @ X0)) = (multiplicative_identity))),
% 9.95/2.07 inference('cnf', [status(esa)], [additive_inverse1])).
% 9.95/2.07 thf(zip_derived_cl2, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.95/2.07 ((add @ (multiply @ X0 @ X2) @ X1)
% 9.95/2.07 = (multiply @ (add @ X0 @ X1) @ (add @ X2 @ X1)))),
% 9.95/2.07 inference('cnf', [status(esa)], [distributivity1])).
% 9.95/2.07 thf(zip_derived_cl41, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]:
% 9.95/2.07 ((add @ (multiply @ X1 @ X0) @ (inverse @ X0))
% 9.95/2.07 = (multiply @ (add @ X1 @ (inverse @ X0)) @ multiplicative_identity))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl2])).
% 9.95/2.07 thf(zip_derived_cl10, plain,
% 9.95/2.07 (![X0 : $i]: ((multiply @ X0 @ multiplicative_identity) = (X0))),
% 9.95/2.07 inference('cnf', [status(esa)], [multiplicative_id1])).
% 9.95/2.07 thf(zip_derived_cl53, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]:
% 9.95/2.07 ((add @ (multiply @ X1 @ X0) @ (inverse @ X0))
% 9.95/2.07 = (add @ X1 @ (inverse @ X0)))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl41, zip_derived_cl10])).
% 9.95/2.07 thf(zip_derived_cl1086, plain,
% 9.95/2.07 (((add @ b @ (inverse @ b)) = (add @ c @ (inverse @ b)))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl546, zip_derived_cl53])).
% 9.95/2.07 thf(zip_derived_cl6, plain,
% 9.95/2.07 (![X0 : $i]: ((add @ X0 @ (inverse @ X0)) = (multiplicative_identity))),
% 9.95/2.07 inference('cnf', [status(esa)], [additive_inverse1])).
% 9.95/2.07 thf(zip_derived_cl1103, plain,
% 9.95/2.07 (((multiplicative_identity) = (add @ c @ (inverse @ b)))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl1086, zip_derived_cl6])).
% 9.95/2.07 thf(zip_derived_cl8, plain,
% 9.95/2.07 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (additive_identity))),
% 9.95/2.07 inference('cnf', [status(esa)], [multiplicative_inverse1])).
% 9.95/2.07 thf(zip_derived_cl4, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.95/2.07 ((multiply @ (add @ X0 @ X2) @ X1)
% 9.95/2.07 = (add @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 9.95/2.07 inference('cnf', [status(esa)], [distributivity3])).
% 9.95/2.07 thf(zip_derived_cl105, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]:
% 9.95/2.07 ((multiply @ (add @ X0 @ X1) @ (inverse @ X0))
% 9.95/2.07 = (add @ additive_identity @ (multiply @ X1 @ (inverse @ X0))))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl4])).
% 9.95/2.07 thf(zip_derived_cl13, plain,
% 9.95/2.07 (![X0 : $i]: ((add @ additive_identity @ X0) = (X0))),
% 9.95/2.07 inference('cnf', [status(esa)], [additive_id2])).
% 9.95/2.07 thf(zip_derived_cl116, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]:
% 9.95/2.07 ((multiply @ (add @ X0 @ X1) @ (inverse @ X0))
% 9.95/2.07 = (multiply @ X1 @ (inverse @ X0)))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl105, zip_derived_cl13])).
% 9.95/2.07 thf(zip_derived_cl8183, plain,
% 9.95/2.07 (((multiply @ multiplicative_identity @ (inverse @ c))
% 9.95/2.07 = (multiply @ (inverse @ b) @ (inverse @ c)))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl1103, zip_derived_cl116])).
% 9.95/2.07 thf(zip_derived_cl11, plain,
% 9.95/2.07 (![X0 : $i]: ((multiply @ multiplicative_identity @ X0) = (X0))),
% 9.95/2.07 inference('cnf', [status(esa)], [multiplicative_id2])).
% 9.95/2.07 thf(zip_derived_cl8233, plain,
% 9.95/2.07 (((inverse @ c) = (multiply @ (inverse @ b) @ (inverse @ c)))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl8183, zip_derived_cl11])).
% 9.95/2.07 thf(zip_derived_cl1, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 9.95/2.07 inference('cnf', [status(esa)], [commutativity_of_multiply])).
% 9.95/2.07 thf(zip_derived_cl8319, plain,
% 9.95/2.07 (((multiply @ (inverse @ c) @ (inverse @ b)) = (inverse @ c))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl8233, zip_derived_cl1])).
% 9.95/2.07 thf(zip_derived_cl15, plain,
% 9.95/2.07 (((multiply @ (inverse @ a) @ (inverse @ b)) = (d))),
% 9.95/2.07 inference('cnf', [status(esa)], [a_inverse_times_b_inverse_is_d])).
% 9.95/2.07 thf(zip_derived_cl1454, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]: ((X0) = (add @ X0 @ (multiply @ X0 @ X1)))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl1392, zip_derived_cl769])).
% 9.95/2.07 thf(zip_derived_cl1531, plain, (((inverse @ a) = (add @ (inverse @ a) @ d))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl15, zip_derived_cl1454])).
% 9.95/2.07 thf(zip_derived_cl0, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]: ((add @ X1 @ X0) = (add @ X0 @ X1))),
% 9.95/2.07 inference('cnf', [status(esa)], [commutativity_of_add])).
% 9.95/2.07 thf(zip_derived_cl1605, plain, (((add @ d @ (inverse @ a)) = (inverse @ a))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl1531, zip_derived_cl0])).
% 9.95/2.07 thf(zip_derived_cl114, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]:
% 9.95/2.07 ((multiply @ (add @ X1 @ (inverse @ X0)) @ X0) = (multiply @ X1 @ X0))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl100, zip_derived_cl12])).
% 9.95/2.07 thf(zip_derived_cl1683, plain,
% 9.95/2.07 (((multiply @ (inverse @ a) @ a) = (multiply @ d @ a))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl1605, zip_derived_cl114])).
% 9.95/2.07 thf(zip_derived_cl9, plain,
% 9.95/2.07 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (additive_identity))),
% 9.95/2.07 inference('cnf', [status(esa)], [multiplicative_inverse2])).
% 9.95/2.07 thf(zip_derived_cl1692, plain, (((additive_identity) = (multiply @ d @ a))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl1683, zip_derived_cl9])).
% 9.95/2.07 thf(zip_derived_cl57, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]:
% 9.95/2.07 ((add @ (multiply @ X0 @ X1) @ (inverse @ X0))
% 9.95/2.07 = (add @ X1 @ (inverse @ X0)))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl48, zip_derived_cl11])).
% 9.95/2.07 thf(zip_derived_cl1695, plain,
% 9.95/2.07 (((add @ additive_identity @ (inverse @ d)) = (add @ a @ (inverse @ d)))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl1692, zip_derived_cl57])).
% 9.95/2.07 thf(zip_derived_cl13, plain,
% 9.95/2.07 (![X0 : $i]: ((add @ additive_identity @ X0) = (X0))),
% 9.95/2.07 inference('cnf', [status(esa)], [additive_id2])).
% 9.95/2.07 thf(zip_derived_cl1703, plain, (((inverse @ d) = (add @ a @ (inverse @ d)))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl1695, zip_derived_cl13])).
% 9.95/2.07 thf(zip_derived_cl656, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]: ((X0) = (multiply @ X0 @ (add @ X0 @ X1)))),
% 9.95/2.07 inference('demod', [status(thm)],
% 9.95/2.07 [zip_derived_cl624, zip_derived_cl494, zip_derived_cl13])).
% 9.95/2.07 thf(zip_derived_cl1710, plain, (((a) = (multiply @ a @ (inverse @ d)))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl1703, zip_derived_cl656])).
% 9.95/2.07 thf(zip_derived_cl14, plain, (((add @ a @ b) = (c))),
% 9.95/2.07 inference('cnf', [status(esa)], [a_plus_b_is_c])).
% 9.95/2.07 thf(zip_derived_cl2, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.95/2.07 ((add @ (multiply @ X0 @ X2) @ X1)
% 9.95/2.07 = (multiply @ (add @ X0 @ X1) @ (add @ X2 @ X1)))),
% 9.95/2.07 inference('cnf', [status(esa)], [distributivity1])).
% 9.95/2.07 thf(zip_derived_cl52, plain,
% 9.95/2.07 (![X0 : $i]:
% 9.95/2.07 ((add @ (multiply @ a @ X0) @ b) = (multiply @ c @ (add @ X0 @ b)))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl2])).
% 9.95/2.07 thf(zip_derived_cl1743, plain,
% 9.95/2.07 (((add @ a @ b) = (multiply @ c @ (add @ (inverse @ d) @ b)))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl1710, zip_derived_cl52])).
% 9.95/2.07 thf(zip_derived_cl14, plain, (((add @ a @ b) = (c))),
% 9.95/2.07 inference('cnf', [status(esa)], [a_plus_b_is_c])).
% 9.95/2.07 thf(zip_derived_cl0, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]: ((add @ X1 @ X0) = (add @ X0 @ X1))),
% 9.95/2.07 inference('cnf', [status(esa)], [commutativity_of_add])).
% 9.95/2.07 thf(zip_derived_cl1750, plain,
% 9.95/2.07 (((c) = (multiply @ c @ (add @ b @ (inverse @ d))))),
% 9.95/2.07 inference('demod', [status(thm)],
% 9.95/2.07 [zip_derived_cl1743, zip_derived_cl14, zip_derived_cl0])).
% 9.95/2.07 thf(zip_derived_cl15, plain,
% 9.95/2.07 (((multiply @ (inverse @ a) @ (inverse @ b)) = (d))),
% 9.95/2.07 inference('cnf', [status(esa)], [a_inverse_times_b_inverse_is_d])).
% 9.95/2.07 thf(zip_derived_cl167, plain, (![X0 : $i]: ((X0) = (add @ X0 @ X0))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl161, zip_derived_cl13])).
% 9.95/2.07 thf(zip_derived_cl60, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.95/2.07 ((multiply @ (add @ X2 @ X0) @ (add @ X2 @ X1))
% 9.95/2.07 = (add @ X2 @ (multiply @ X1 @ X0)))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 9.95/2.07 thf(zip_derived_cl1422, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]:
% 9.95/2.07 ((multiply @ X0 @ (add @ X0 @ X1)) = (add @ X0 @ (multiply @ X1 @ X0)))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl167, zip_derived_cl60])).
% 9.95/2.07 thf(zip_derived_cl656, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]: ((X0) = (multiply @ X0 @ (add @ X0 @ X1)))),
% 9.95/2.07 inference('demod', [status(thm)],
% 9.95/2.07 [zip_derived_cl624, zip_derived_cl494, zip_derived_cl13])).
% 9.95/2.07 thf(zip_derived_cl1472, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]: ((X0) = (add @ X0 @ (multiply @ X1 @ X0)))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl1422, zip_derived_cl656])).
% 9.95/2.07 thf(zip_derived_cl2374, plain, (((inverse @ b) = (add @ (inverse @ b) @ d))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl15, zip_derived_cl1472])).
% 9.95/2.07 thf(zip_derived_cl0, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]: ((add @ X1 @ X0) = (add @ X0 @ X1))),
% 9.95/2.07 inference('cnf', [status(esa)], [commutativity_of_add])).
% 9.95/2.07 thf(zip_derived_cl2402, plain, (((add @ d @ (inverse @ b)) = (inverse @ b))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl2374, zip_derived_cl0])).
% 9.95/2.07 thf(zip_derived_cl114, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]:
% 9.95/2.07 ((multiply @ (add @ X1 @ (inverse @ X0)) @ X0) = (multiply @ X1 @ X0))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl100, zip_derived_cl12])).
% 9.95/2.07 thf(zip_derived_cl2492, plain,
% 9.95/2.07 (((multiply @ (inverse @ b) @ b) = (multiply @ d @ b))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl2402, zip_derived_cl114])).
% 9.95/2.07 thf(zip_derived_cl9, plain,
% 9.95/2.07 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (additive_identity))),
% 9.95/2.07 inference('cnf', [status(esa)], [multiplicative_inverse2])).
% 9.95/2.07 thf(zip_derived_cl2503, plain, (((additive_identity) = (multiply @ d @ b))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl2492, zip_derived_cl9])).
% 9.95/2.07 thf(zip_derived_cl57, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]:
% 9.95/2.07 ((add @ (multiply @ X0 @ X1) @ (inverse @ X0))
% 9.95/2.07 = (add @ X1 @ (inverse @ X0)))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl48, zip_derived_cl11])).
% 9.95/2.07 thf(zip_derived_cl2506, plain,
% 9.95/2.07 (((add @ additive_identity @ (inverse @ d)) = (add @ b @ (inverse @ d)))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl2503, zip_derived_cl57])).
% 9.95/2.07 thf(zip_derived_cl13, plain,
% 9.95/2.07 (![X0 : $i]: ((add @ additive_identity @ X0) = (X0))),
% 9.95/2.07 inference('cnf', [status(esa)], [additive_id2])).
% 9.95/2.07 thf(zip_derived_cl2515, plain, (((inverse @ d) = (add @ b @ (inverse @ d)))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl2506, zip_derived_cl13])).
% 9.95/2.07 thf(zip_derived_cl2561, plain, (((c) = (multiply @ c @ (inverse @ d)))),
% 9.95/2.07 inference('demod', [status(thm)],
% 9.95/2.07 [zip_derived_cl1750, zip_derived_cl2515])).
% 9.95/2.07 thf(zip_derived_cl1472, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]: ((X0) = (add @ X0 @ (multiply @ X1 @ X0)))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl1422, zip_derived_cl656])).
% 9.95/2.07 thf(zip_derived_cl2599, plain, (((inverse @ d) = (add @ (inverse @ d) @ c))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl2561, zip_derived_cl1472])).
% 9.95/2.07 thf(zip_derived_cl0, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]: ((add @ X1 @ X0) = (add @ X0 @ X1))),
% 9.95/2.07 inference('cnf', [status(esa)], [commutativity_of_add])).
% 9.95/2.07 thf(zip_derived_cl2610, plain, (((add @ c @ (inverse @ d)) = (inverse @ d))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl2599, zip_derived_cl0])).
% 9.95/2.07 thf(zip_derived_cl114, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]:
% 9.95/2.07 ((multiply @ (add @ X1 @ (inverse @ X0)) @ X0) = (multiply @ X1 @ X0))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl100, zip_derived_cl12])).
% 9.95/2.07 thf(zip_derived_cl2684, plain,
% 9.95/2.07 (((multiply @ (inverse @ d) @ d) = (multiply @ c @ d))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl2610, zip_derived_cl114])).
% 9.95/2.07 thf(zip_derived_cl9, plain,
% 9.95/2.07 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (additive_identity))),
% 9.95/2.07 inference('cnf', [status(esa)], [multiplicative_inverse2])).
% 9.95/2.07 thf(zip_derived_cl2695, plain, (((additive_identity) = (multiply @ c @ d))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl2684, zip_derived_cl9])).
% 9.95/2.07 thf(zip_derived_cl57, plain,
% 9.95/2.07 (![X0 : $i, X1 : $i]:
% 9.95/2.07 ((add @ (multiply @ X0 @ X1) @ (inverse @ X0))
% 9.95/2.07 = (add @ X1 @ (inverse @ X0)))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl48, zip_derived_cl11])).
% 9.95/2.07 thf(zip_derived_cl2698, plain,
% 9.95/2.07 (((add @ additive_identity @ (inverse @ c)) = (add @ d @ (inverse @ c)))),
% 9.95/2.07 inference('sup+', [status(thm)], [zip_derived_cl2695, zip_derived_cl57])).
% 9.95/2.07 thf(zip_derived_cl13, plain,
% 9.95/2.07 (![X0 : $i]: ((add @ additive_identity @ X0) = (X0))),
% 9.95/2.07 inference('cnf', [status(esa)], [additive_id2])).
% 9.95/2.07 thf(zip_derived_cl2706, plain, (((inverse @ c) = (add @ d @ (inverse @ c)))),
% 9.95/2.07 inference('demod', [status(thm)], [zip_derived_cl2698, zip_derived_cl13])).
% 9.95/2.07 thf(zip_derived_cl8799, plain, (((d) = (inverse @ c))),
% 9.95/2.07 inference('demod', [status(thm)],
% 9.95/2.07 [zip_derived_cl8776, zip_derived_cl15, zip_derived_cl8319,
% 9.95/2.07 zip_derived_cl2706])).
% 9.95/2.07 thf(prove_c_inverse_is_d, conjecture, (( inverse @ c ) = ( d ))).
% 9.95/2.07 thf(zf_stmt_0, negated_conjecture, (( inverse @ c ) != ( d )),
% 9.95/2.07 inference('cnf.neg', [status(esa)], [prove_c_inverse_is_d])).
% 9.95/2.07 thf(zip_derived_cl16, plain, (((inverse @ c) != (d))),
% 9.95/2.07 inference('cnf', [status(esa)], [zf_stmt_0])).
% 9.95/2.07 thf(zip_derived_cl8800, plain, ($false),
% 9.95/2.07 inference('simplify_reflect-', [status(thm)],
% 9.95/2.07 [zip_derived_cl8799, zip_derived_cl16])).
% 9.95/2.07
% 9.95/2.07 % SZS output end Refutation
% 9.95/2.07
% 9.95/2.07
% 9.95/2.08 % Terminating...
% 10.39/2.18 % Runner terminated.
% 10.39/2.19 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------