TSTP Solution File: BOO015-4 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : BOO015-4 : TPTP v8.1.2. Released v1.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.CSNdVUjMNw 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 18:13:20 EDT 2023
% Result : Unsatisfiable 283.59s 41.38s
% Output : Refutation 283.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : BOO015-4 : TPTP v8.1.2. Released v1.1.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.CSNdVUjMNw true
% 0.15/0.35 % Computer : n006.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun Aug 27 07:59:07 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % Running portfolio for 300 s
% 0.15/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.36 % Number of cores: 8
% 0.22/0.36 % Python version: Python 3.6.8
% 0.22/0.36 % Running in FO mode
% 0.22/0.70 % Total configuration time : 435
% 0.22/0.70 % Estimated wc time : 1092
% 0.22/0.70 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.72 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.56/0.77 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.56/0.77 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.56/0.78 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.56/0.78 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 283.59/41.38 % Solved by fo/fo5.sh.
% 283.59/41.38 % done 5372 iterations in 40.577s
% 283.59/41.38 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 283.59/41.38 % SZS output start Refutation
% 283.59/41.38 thf(multiply_type, type, multiply: $i > $i > $i).
% 283.59/41.38 thf(b_type, type, b: $i).
% 283.59/41.38 thf(add_type, type, add: $i > $i > $i).
% 283.59/41.38 thf(inverse_type, type, inverse: $i > $i).
% 283.59/41.38 thf(a_type, type, a: $i).
% 283.59/41.38 thf(multiplicative_identity_type, type, multiplicative_identity: $i).
% 283.59/41.38 thf(additive_identity_type, type, additive_identity: $i).
% 283.59/41.38 thf(prove_c_inverse_is_d, conjecture,
% 283.59/41.38 (( inverse @ ( multiply @ a @ b ) ) =
% 283.59/41.38 ( add @ ( inverse @ a ) @ ( inverse @ b ) ))).
% 283.59/41.38 thf(zf_stmt_0, negated_conjecture,
% 283.59/41.38 (( inverse @ ( multiply @ a @ b ) ) !=
% 283.59/41.38 ( add @ ( inverse @ a ) @ ( inverse @ b ) )),
% 283.59/41.38 inference('cnf.neg', [status(esa)], [prove_c_inverse_is_d])).
% 283.59/41.38 thf(zip_derived_cl8, plain,
% 283.59/41.38 (((inverse @ (multiply @ a @ b)) != (add @ (inverse @ a) @ (inverse @ b)))),
% 283.59/41.38 inference('cnf', [status(esa)], [zf_stmt_0])).
% 283.59/41.38 thf(multiplicative_inverse1, axiom,
% 283.59/41.38 (( multiply @ X @ ( inverse @ X ) ) = ( additive_identity ))).
% 283.59/41.38 thf(zip_derived_cl7, plain,
% 283.59/41.38 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (additive_identity))),
% 283.59/41.38 inference('cnf', [status(esa)], [multiplicative_inverse1])).
% 283.59/41.38 thf(additive_inverse1, axiom,
% 283.59/41.38 (( add @ X @ ( inverse @ X ) ) = ( multiplicative_identity ))).
% 283.59/41.38 thf(zip_derived_cl6, plain,
% 283.59/41.38 (![X0 : $i]: ((add @ X0 @ (inverse @ X0)) = (multiplicative_identity))),
% 283.59/41.38 inference('cnf', [status(esa)], [additive_inverse1])).
% 283.59/41.38 thf(distributivity1, axiom,
% 283.59/41.38 (( add @ X @ ( multiply @ Y @ Z ) ) =
% 283.59/41.38 ( multiply @ ( add @ X @ Y ) @ ( add @ X @ Z ) ))).
% 283.59/41.38 thf(zip_derived_cl2, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.38 ((add @ X0 @ (multiply @ X1 @ X2))
% 283.59/41.38 = (multiply @ (add @ X0 @ X1) @ (add @ X0 @ X2)))),
% 283.59/41.38 inference('cnf', [status(esa)], [distributivity1])).
% 283.59/41.38 thf(zip_derived_cl33, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]:
% 283.59/41.38 ((add @ X1 @ (multiply @ (inverse @ X1) @ X0))
% 283.59/41.38 = (multiply @ multiplicative_identity @ (add @ X1 @ X0)))),
% 283.59/41.38 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl2])).
% 283.59/41.38 thf(multiplicative_id1, axiom,
% 283.59/41.38 (( multiply @ X @ multiplicative_identity ) = ( X ))).
% 283.59/41.38 thf(zip_derived_cl5, plain,
% 283.59/41.38 (![X0 : $i]: ((multiply @ X0 @ multiplicative_identity) = (X0))),
% 283.59/41.38 inference('cnf', [status(esa)], [multiplicative_id1])).
% 283.59/41.38 thf(commutativity_of_multiply, axiom,
% 283.59/41.38 (( multiply @ X @ Y ) = ( multiply @ Y @ X ))).
% 283.59/41.38 thf(zip_derived_cl1, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 283.59/41.38 inference('cnf', [status(esa)], [commutativity_of_multiply])).
% 283.59/41.38 thf(zip_derived_cl16, plain,
% 283.59/41.38 (![X0 : $i]: ((X0) = (multiply @ multiplicative_identity @ X0))),
% 283.59/41.38 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl1])).
% 283.59/41.38 thf(zip_derived_cl37, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]:
% 283.59/41.38 ((add @ X1 @ (multiply @ (inverse @ X1) @ X0)) = (add @ X1 @ X0))),
% 283.59/41.38 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl16])).
% 283.59/41.38 thf(zip_derived_cl140, plain,
% 283.59/41.38 (![X0 : $i]:
% 283.59/41.38 ((add @ X0 @ additive_identity)
% 283.59/41.38 = (add @ X0 @ (inverse @ (inverse @ X0))))),
% 283.59/41.38 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl37])).
% 283.59/41.38 thf(additive_id1, axiom, (( add @ X @ additive_identity ) = ( X ))).
% 283.59/41.38 thf(zip_derived_cl4, plain,
% 283.59/41.38 (![X0 : $i]: ((add @ X0 @ additive_identity) = (X0))),
% 283.59/41.38 inference('cnf', [status(esa)], [additive_id1])).
% 283.59/41.38 thf(zip_derived_cl144, plain,
% 283.59/41.38 (![X0 : $i]: ((X0) = (add @ X0 @ (inverse @ (inverse @ X0))))),
% 283.59/41.38 inference('demod', [status(thm)], [zip_derived_cl140, zip_derived_cl4])).
% 283.59/41.38 thf(zip_derived_cl7, plain,
% 283.59/41.38 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (additive_identity))),
% 283.59/41.38 inference('cnf', [status(esa)], [multiplicative_inverse1])).
% 283.59/41.38 thf(distributivity2, axiom,
% 283.59/41.38 (( multiply @ X @ ( add @ Y @ Z ) ) =
% 283.59/41.38 ( add @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ))).
% 283.59/41.38 thf(zip_derived_cl3, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.38 ((multiply @ X0 @ (add @ X1 @ X2))
% 283.59/41.38 = (add @ (multiply @ X0 @ X1) @ (multiply @ X0 @ X2)))),
% 283.59/41.38 inference('cnf', [status(esa)], [distributivity2])).
% 283.59/41.38 thf(zip_derived_cl52, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]:
% 283.59/41.38 ((multiply @ X1 @ (add @ (inverse @ X1) @ X0))
% 283.59/41.38 = (add @ additive_identity @ (multiply @ X1 @ X0)))),
% 283.59/41.38 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl3])).
% 283.59/41.38 thf(zip_derived_cl4, plain,
% 283.59/41.38 (![X0 : $i]: ((add @ X0 @ additive_identity) = (X0))),
% 283.59/41.38 inference('cnf', [status(esa)], [additive_id1])).
% 283.59/41.38 thf(commutativity_of_add, axiom, (( add @ X @ Y ) = ( add @ Y @ X ))).
% 283.59/41.38 thf(zip_derived_cl0, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]: ((add @ X1 @ X0) = (add @ X0 @ X1))),
% 283.59/41.38 inference('cnf', [status(esa)], [commutativity_of_add])).
% 283.59/41.38 thf(zip_derived_cl9, plain,
% 283.59/41.38 (![X0 : $i]: ((X0) = (add @ additive_identity @ X0))),
% 283.59/41.38 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 283.59/41.38 thf(zip_derived_cl57, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]:
% 283.59/41.38 ((multiply @ X1 @ (add @ (inverse @ X1) @ X0)) = (multiply @ X1 @ X0))),
% 283.59/41.38 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl9])).
% 283.59/41.38 thf(zip_derived_cl235, plain,
% 283.59/41.38 (![X0 : $i]:
% 283.59/41.38 ((multiply @ X0 @ (inverse @ X0))
% 283.59/41.38 = (multiply @ X0 @ (inverse @ (inverse @ (inverse @ X0)))))),
% 283.59/41.38 inference('sup+', [status(thm)], [zip_derived_cl144, zip_derived_cl57])).
% 283.59/41.38 thf(zip_derived_cl7, plain,
% 283.59/41.38 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (additive_identity))),
% 283.59/41.38 inference('cnf', [status(esa)], [multiplicative_inverse1])).
% 283.59/41.38 thf(zip_derived_cl244, plain,
% 283.59/41.38 (![X0 : $i]:
% 283.59/41.38 ((additive_identity)
% 283.59/41.38 = (multiply @ X0 @ (inverse @ (inverse @ (inverse @ X0)))))),
% 283.59/41.38 inference('demod', [status(thm)], [zip_derived_cl235, zip_derived_cl7])).
% 283.59/41.38 thf(zip_derived_cl6, plain,
% 283.59/41.38 (![X0 : $i]: ((add @ X0 @ (inverse @ X0)) = (multiplicative_identity))),
% 283.59/41.38 inference('cnf', [status(esa)], [additive_inverse1])).
% 283.59/41.38 thf(zip_derived_cl2, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.38 ((add @ X0 @ (multiply @ X1 @ X2))
% 283.59/41.38 = (multiply @ (add @ X0 @ X1) @ (add @ X0 @ X2)))),
% 283.59/41.38 inference('cnf', [status(esa)], [distributivity1])).
% 283.59/41.38 thf(zip_derived_cl28, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]:
% 283.59/41.38 ((add @ X0 @ (multiply @ X1 @ (inverse @ X0)))
% 283.59/41.38 = (multiply @ (add @ X0 @ X1) @ multiplicative_identity))),
% 283.59/41.38 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl2])).
% 283.59/41.38 thf(zip_derived_cl5, plain,
% 283.59/41.38 (![X0 : $i]: ((multiply @ X0 @ multiplicative_identity) = (X0))),
% 283.59/41.38 inference('cnf', [status(esa)], [multiplicative_id1])).
% 283.59/41.38 thf(zip_derived_cl35, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]:
% 283.59/41.38 ((add @ X0 @ (multiply @ X1 @ (inverse @ X0))) = (add @ X0 @ X1))),
% 283.59/41.38 inference('demod', [status(thm)], [zip_derived_cl28, zip_derived_cl5])).
% 283.59/41.38 thf(zip_derived_cl266, plain,
% 283.59/41.38 (![X0 : $i]:
% 283.59/41.38 ((add @ (inverse @ (inverse @ X0)) @ additive_identity)
% 283.59/41.38 = (add @ (inverse @ (inverse @ X0)) @ X0))),
% 283.59/41.38 inference('sup+', [status(thm)], [zip_derived_cl244, zip_derived_cl35])).
% 283.59/41.38 thf(zip_derived_cl4, plain,
% 283.59/41.38 (![X0 : $i]: ((add @ X0 @ additive_identity) = (X0))),
% 283.59/41.38 inference('cnf', [status(esa)], [additive_id1])).
% 283.59/41.38 thf(zip_derived_cl275, plain,
% 283.59/41.38 (![X0 : $i]:
% 283.59/41.38 ((inverse @ (inverse @ X0)) = (add @ (inverse @ (inverse @ X0)) @ X0))),
% 283.59/41.38 inference('demod', [status(thm)], [zip_derived_cl266, zip_derived_cl4])).
% 283.59/41.38 thf(zip_derived_cl0, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]: ((add @ X1 @ X0) = (add @ X0 @ X1))),
% 283.59/41.38 inference('cnf', [status(esa)], [commutativity_of_add])).
% 283.59/41.38 thf(zip_derived_cl296, plain,
% 283.59/41.38 (![X0 : $i]:
% 283.59/41.38 ((add @ X0 @ (inverse @ (inverse @ X0))) = (inverse @ (inverse @ X0)))),
% 283.59/41.38 inference('sup+', [status(thm)], [zip_derived_cl275, zip_derived_cl0])).
% 283.59/41.38 thf(zip_derived_cl144, plain,
% 283.59/41.38 (![X0 : $i]: ((X0) = (add @ X0 @ (inverse @ (inverse @ X0))))),
% 283.59/41.38 inference('demod', [status(thm)], [zip_derived_cl140, zip_derived_cl4])).
% 283.59/41.38 thf(zip_derived_cl309, plain,
% 283.59/41.38 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 283.59/41.38 inference('demod', [status(thm)], [zip_derived_cl296, zip_derived_cl144])).
% 283.59/41.38 thf(zip_derived_cl9, plain,
% 283.59/41.38 (![X0 : $i]: ((X0) = (add @ additive_identity @ X0))),
% 283.59/41.38 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 283.59/41.38 thf(zip_derived_cl0, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]: ((add @ X1 @ X0) = (add @ X0 @ X1))),
% 283.59/41.38 inference('cnf', [status(esa)], [commutativity_of_add])).
% 283.59/41.38 thf(zip_derived_cl2, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.38 ((add @ X0 @ (multiply @ X1 @ X2))
% 283.59/41.38 = (multiply @ (add @ X0 @ X1) @ (add @ X0 @ X2)))),
% 283.59/41.38 inference('cnf', [status(esa)], [distributivity1])).
% 283.59/41.38 thf(zip_derived_cl25, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.38 ((add @ X0 @ (multiply @ X2 @ X1))
% 283.59/41.38 = (multiply @ (add @ X0 @ X2) @ (add @ X1 @ X0)))),
% 283.59/41.38 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 283.59/41.38 thf(zip_derived_cl345, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]:
% 283.59/41.38 ((add @ X0 @ (multiply @ X1 @ additive_identity))
% 283.59/41.38 = (multiply @ (add @ X0 @ X1) @ X0))),
% 283.59/41.38 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl25])).
% 283.59/41.38 thf(zip_derived_cl9, plain,
% 283.59/41.38 (![X0 : $i]: ((X0) = (add @ additive_identity @ X0))),
% 283.59/41.38 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 283.59/41.38 thf(zip_derived_cl7, plain,
% 283.59/41.38 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (additive_identity))),
% 283.59/41.38 inference('cnf', [status(esa)], [multiplicative_inverse1])).
% 283.59/41.38 thf(zip_derived_cl3, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.38 ((multiply @ X0 @ (add @ X1 @ X2))
% 283.59/41.38 = (add @ (multiply @ X0 @ X1) @ (multiply @ X0 @ X2)))),
% 283.59/41.38 inference('cnf', [status(esa)], [distributivity2])).
% 283.59/41.38 thf(zip_derived_cl46, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]:
% 283.59/41.38 ((multiply @ X0 @ (add @ X1 @ (inverse @ X0)))
% 283.59/41.38 = (add @ (multiply @ X0 @ X1) @ additive_identity))),
% 283.59/41.38 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl3])).
% 283.59/41.38 thf(zip_derived_cl4, plain,
% 283.59/41.38 (![X0 : $i]: ((add @ X0 @ additive_identity) = (X0))),
% 283.59/41.38 inference('cnf', [status(esa)], [additive_id1])).
% 283.59/41.38 thf(zip_derived_cl55, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]:
% 283.59/41.38 ((multiply @ X0 @ (add @ X1 @ (inverse @ X0))) = (multiply @ X0 @ X1))),
% 283.59/41.38 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl4])).
% 283.59/41.38 thf(zip_derived_cl175, plain,
% 283.59/41.38 (![X0 : $i]:
% 283.59/41.38 ((multiply @ X0 @ (inverse @ X0))
% 283.59/41.38 = (multiply @ X0 @ additive_identity))),
% 283.59/41.38 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl55])).
% 283.59/41.38 thf(zip_derived_cl7, plain,
% 283.59/41.38 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (additive_identity))),
% 283.59/41.38 inference('cnf', [status(esa)], [multiplicative_inverse1])).
% 283.59/41.38 thf(zip_derived_cl182, plain,
% 283.59/41.38 (![X0 : $i]: ((additive_identity) = (multiply @ X0 @ additive_identity))),
% 283.59/41.38 inference('demod', [status(thm)], [zip_derived_cl175, zip_derived_cl7])).
% 283.59/41.38 thf(zip_derived_cl4, plain,
% 283.59/41.38 (![X0 : $i]: ((add @ X0 @ additive_identity) = (X0))),
% 283.59/41.38 inference('cnf', [status(esa)], [additive_id1])).
% 283.59/41.38 thf(zip_derived_cl363, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]: ((X0) = (multiply @ (add @ X0 @ X1) @ X0))),
% 283.59/41.38 inference('demod', [status(thm)],
% 283.59/41.38 [zip_derived_cl345, zip_derived_cl182, zip_derived_cl4])).
% 283.59/41.38 thf(zip_derived_cl1, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 283.59/41.38 inference('cnf', [status(esa)], [commutativity_of_multiply])).
% 283.59/41.38 thf(zip_derived_cl408, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ (add @ X0 @ X1)) = (X0))),
% 283.59/41.38 inference('sup+', [status(thm)], [zip_derived_cl363, zip_derived_cl1])).
% 283.59/41.38 thf(zip_derived_cl309, plain,
% 283.59/41.38 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 283.59/41.38 inference('demod', [status(thm)], [zip_derived_cl296, zip_derived_cl144])).
% 283.59/41.38 thf(zip_derived_cl7, plain,
% 283.59/41.38 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (additive_identity))),
% 283.59/41.38 inference('cnf', [status(esa)], [multiplicative_inverse1])).
% 283.59/41.38 thf(zip_derived_cl35, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]:
% 283.59/41.38 ((add @ X0 @ (multiply @ X1 @ (inverse @ X0))) = (add @ X0 @ X1))),
% 283.59/41.38 inference('demod', [status(thm)], [zip_derived_cl28, zip_derived_cl5])).
% 283.59/41.38 thf(zip_derived_cl65, plain,
% 283.59/41.38 (![X0 : $i]: ((add @ X0 @ additive_identity) = (add @ X0 @ X0))),
% 283.59/41.38 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl35])).
% 283.59/41.38 thf(zip_derived_cl4, plain,
% 283.59/41.38 (![X0 : $i]: ((add @ X0 @ additive_identity) = (X0))),
% 283.59/41.38 inference('cnf', [status(esa)], [additive_id1])).
% 283.59/41.38 thf(zip_derived_cl69, plain, (![X0 : $i]: ((X0) = (add @ X0 @ X0))),
% 283.59/41.38 inference('demod', [status(thm)], [zip_derived_cl65, zip_derived_cl4])).
% 283.59/41.38 thf(zip_derived_cl0, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]: ((add @ X1 @ X0) = (add @ X0 @ X1))),
% 283.59/41.38 inference('cnf', [status(esa)], [commutativity_of_add])).
% 283.59/41.38 thf(zip_derived_cl2, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.38 ((add @ X0 @ (multiply @ X1 @ X2))
% 283.59/41.38 = (multiply @ (add @ X0 @ X1) @ (add @ X0 @ X2)))),
% 283.59/41.38 inference('cnf', [status(esa)], [distributivity1])).
% 283.59/41.38 thf(zip_derived_cl30, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.38 ((add @ X0 @ (multiply @ X1 @ X2))
% 283.59/41.38 = (multiply @ (add @ X1 @ X0) @ (add @ X0 @ X2)))),
% 283.59/41.38 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 283.59/41.38 thf(zip_derived_cl512, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]:
% 283.59/41.38 ((add @ X0 @ (multiply @ X1 @ X0)) = (multiply @ (add @ X1 @ X0) @ X0))),
% 283.59/41.38 inference('sup+', [status(thm)], [zip_derived_cl69, zip_derived_cl30])).
% 283.59/41.38 thf(zip_derived_cl0, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]: ((add @ X1 @ X0) = (add @ X0 @ X1))),
% 283.59/41.38 inference('cnf', [status(esa)], [commutativity_of_add])).
% 283.59/41.38 thf(zip_derived_cl363, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]: ((X0) = (multiply @ (add @ X0 @ X1) @ X0))),
% 283.59/41.38 inference('demod', [status(thm)],
% 283.59/41.38 [zip_derived_cl345, zip_derived_cl182, zip_derived_cl4])).
% 283.59/41.38 thf(zip_derived_cl414, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]: ((X0) = (multiply @ (add @ X1 @ X0) @ X0))),
% 283.59/41.38 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl363])).
% 283.59/41.38 thf(zip_derived_cl538, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]: ((add @ X0 @ (multiply @ X1 @ X0)) = (X0))),
% 283.59/41.38 inference('demod', [status(thm)], [zip_derived_cl512, zip_derived_cl414])).
% 283.59/41.38 thf(zip_derived_cl57, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]:
% 283.59/41.38 ((multiply @ X1 @ (add @ (inverse @ X1) @ X0)) = (multiply @ X1 @ X0))),
% 283.59/41.38 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl9])).
% 283.59/41.38 thf(zip_derived_cl570, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]:
% 283.59/41.38 ((multiply @ X0 @ (inverse @ X0))
% 283.59/41.38 = (multiply @ X0 @ (multiply @ X1 @ (inverse @ X0))))),
% 283.59/41.38 inference('sup+', [status(thm)], [zip_derived_cl538, zip_derived_cl57])).
% 283.59/41.38 thf(zip_derived_cl7, plain,
% 283.59/41.38 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (additive_identity))),
% 283.59/41.38 inference('cnf', [status(esa)], [multiplicative_inverse1])).
% 283.59/41.38 thf(zip_derived_cl597, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]:
% 283.59/41.38 ((additive_identity)
% 283.59/41.38 = (multiply @ X0 @ (multiply @ X1 @ (inverse @ X0))))),
% 283.59/41.38 inference('demod', [status(thm)], [zip_derived_cl570, zip_derived_cl7])).
% 283.59/41.38 thf(zip_derived_cl1303, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]:
% 283.59/41.38 ((additive_identity)
% 283.59/41.38 = (multiply @ (inverse @ X0) @ (multiply @ X1 @ X0)))),
% 283.59/41.38 inference('sup+', [status(thm)], [zip_derived_cl309, zip_derived_cl597])).
% 283.59/41.38 thf(zip_derived_cl1936, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]:
% 283.59/41.38 ((additive_identity) = (multiply @ (inverse @ (add @ X0 @ X1)) @ X0))),
% 283.59/41.38 inference('sup+', [status(thm)], [zip_derived_cl408, zip_derived_cl1303])).
% 283.59/41.38 thf(zip_derived_cl35, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]:
% 283.59/41.38 ((add @ X0 @ (multiply @ X1 @ (inverse @ X0))) = (add @ X0 @ X1))),
% 283.59/41.38 inference('demod', [status(thm)], [zip_derived_cl28, zip_derived_cl5])).
% 283.59/41.38 thf(zip_derived_cl2523, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]:
% 283.59/41.38 ((add @ X1 @ additive_identity)
% 283.59/41.38 = (add @ X1 @ (inverse @ (add @ (inverse @ X1) @ X0))))),
% 283.59/41.38 inference('sup+', [status(thm)], [zip_derived_cl1936, zip_derived_cl35])).
% 283.59/41.38 thf(zip_derived_cl4, plain,
% 283.59/41.38 (![X0 : $i]: ((add @ X0 @ additive_identity) = (X0))),
% 283.59/41.38 inference('cnf', [status(esa)], [additive_id1])).
% 283.59/41.38 thf(zip_derived_cl2585, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]:
% 283.59/41.38 ((X1) = (add @ X1 @ (inverse @ (add @ (inverse @ X1) @ X0))))),
% 283.59/41.38 inference('demod', [status(thm)], [zip_derived_cl2523, zip_derived_cl4])).
% 283.59/41.38 thf(zip_derived_cl414, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]: ((X0) = (multiply @ (add @ X1 @ X0) @ X0))),
% 283.59/41.38 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl363])).
% 283.59/41.38 thf(zip_derived_cl5, plain,
% 283.59/41.38 (![X0 : $i]: ((multiply @ X0 @ multiplicative_identity) = (X0))),
% 283.59/41.38 inference('cnf', [status(esa)], [multiplicative_id1])).
% 283.59/41.38 thf(zip_derived_cl3, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.38 ((multiply @ X0 @ (add @ X1 @ X2))
% 283.59/41.38 = (add @ (multiply @ X0 @ X1) @ (multiply @ X0 @ X2)))),
% 283.59/41.38 inference('cnf', [status(esa)], [distributivity2])).
% 283.59/41.38 thf(zip_derived_cl0, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]: ((add @ X1 @ X0) = (add @ X0 @ X1))),
% 283.59/41.38 inference('cnf', [status(esa)], [commutativity_of_add])).
% 283.59/41.38 thf(zip_derived_cl39, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.38 ((add @ (multiply @ X2 @ X0) @ (multiply @ X2 @ X1))
% 283.59/41.38 = (multiply @ X2 @ (add @ X1 @ X0)))),
% 283.59/41.38 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 283.59/41.38 thf(zip_derived_cl667, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]:
% 283.59/41.38 ((add @ (multiply @ X0 @ X1) @ X0)
% 283.59/41.38 = (multiply @ X0 @ (add @ multiplicative_identity @ X1)))),
% 283.59/41.38 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl39])).
% 283.59/41.38 thf(zip_derived_cl16, plain,
% 283.59/41.38 (![X0 : $i]: ((X0) = (multiply @ multiplicative_identity @ X0))),
% 283.59/41.38 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl1])).
% 283.59/41.38 thf(zip_derived_cl35, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]:
% 283.59/41.38 ((add @ X0 @ (multiply @ X1 @ (inverse @ X0))) = (add @ X0 @ X1))),
% 283.59/41.38 inference('demod', [status(thm)], [zip_derived_cl28, zip_derived_cl5])).
% 283.59/41.38 thf(zip_derived_cl66, plain,
% 283.59/41.38 (![X0 : $i]:
% 283.59/41.38 ((add @ X0 @ (inverse @ X0)) = (add @ X0 @ multiplicative_identity))),
% 283.59/41.38 inference('sup+', [status(thm)], [zip_derived_cl16, zip_derived_cl35])).
% 283.59/41.38 thf(zip_derived_cl6, plain,
% 283.59/41.38 (![X0 : $i]: ((add @ X0 @ (inverse @ X0)) = (multiplicative_identity))),
% 283.59/41.38 inference('cnf', [status(esa)], [additive_inverse1])).
% 283.59/41.38 thf(zip_derived_cl70, plain,
% 283.59/41.38 (![X0 : $i]:
% 283.59/41.38 ((multiplicative_identity) = (add @ X0 @ multiplicative_identity))),
% 283.59/41.38 inference('demod', [status(thm)], [zip_derived_cl66, zip_derived_cl6])).
% 283.59/41.38 thf(zip_derived_cl0, plain,
% 283.59/41.38 (![X0 : $i, X1 : $i]: ((add @ X1 @ X0) = (add @ X0 @ X1))),
% 283.59/41.38 inference('cnf', [status(esa)], [commutativity_of_add])).
% 283.59/41.38 thf(zip_derived_cl82, plain,
% 283.59/41.39 (![X0 : $i]:
% 283.59/41.39 ((add @ multiplicative_identity @ X0) = (multiplicative_identity))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl70, zip_derived_cl0])).
% 283.59/41.39 thf(zip_derived_cl5, plain,
% 283.59/41.39 (![X0 : $i]: ((multiply @ X0 @ multiplicative_identity) = (X0))),
% 283.59/41.39 inference('cnf', [status(esa)], [multiplicative_id1])).
% 283.59/41.39 thf(zip_derived_cl705, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]: ((add @ (multiply @ X0 @ X1) @ X0) = (X0))),
% 283.59/41.39 inference('demod', [status(thm)],
% 283.59/41.39 [zip_derived_cl667, zip_derived_cl82, zip_derived_cl5])).
% 283.59/41.39 thf(zip_derived_cl752, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]: ((add @ X0 @ (add @ X1 @ X0)) = (add @ X1 @ X0))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl414, zip_derived_cl705])).
% 283.59/41.39 thf(zip_derived_cl4345, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((add @ (inverse @ (add @ (inverse @ X0) @ X1)) @ X0)
% 283.59/41.39 = (add @ X0 @ (inverse @ (add @ (inverse @ X0) @ X1))))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl2585, zip_derived_cl752])).
% 283.59/41.39 thf(zip_derived_cl2585, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((X1) = (add @ X1 @ (inverse @ (add @ (inverse @ X1) @ X0))))),
% 283.59/41.39 inference('demod', [status(thm)], [zip_derived_cl2523, zip_derived_cl4])).
% 283.59/41.39 thf(zip_derived_cl4416, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((add @ (inverse @ (add @ (inverse @ X0) @ X1)) @ X0) = (X0))),
% 283.59/41.39 inference('demod', [status(thm)],
% 283.59/41.39 [zip_derived_cl4345, zip_derived_cl2585])).
% 283.59/41.39 thf(zip_derived_cl6, plain,
% 283.59/41.39 (![X0 : $i]: ((add @ X0 @ (inverse @ X0)) = (multiplicative_identity))),
% 283.59/41.39 inference('cnf', [status(esa)], [additive_inverse1])).
% 283.59/41.39 thf(zip_derived_cl55, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((multiply @ X0 @ (add @ X1 @ (inverse @ X0))) = (multiply @ X0 @ X1))),
% 283.59/41.39 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl4])).
% 283.59/41.39 thf(zip_derived_cl3, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.39 ((multiply @ X0 @ (add @ X1 @ X2))
% 283.59/41.39 = (add @ (multiply @ X0 @ X1) @ (multiply @ X0 @ X2)))),
% 283.59/41.39 inference('cnf', [status(esa)], [distributivity2])).
% 283.59/41.39 thf(zip_derived_cl164, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.39 ((multiply @ X1 @ (add @ (add @ X0 @ (inverse @ X1)) @ X2))
% 283.59/41.39 = (add @ (multiply @ X1 @ X0) @ (multiply @ X1 @ X2)))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl55, zip_derived_cl3])).
% 283.59/41.39 thf(zip_derived_cl3, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.39 ((multiply @ X0 @ (add @ X1 @ X2))
% 283.59/41.39 = (add @ (multiply @ X0 @ X1) @ (multiply @ X0 @ X2)))),
% 283.59/41.39 inference('cnf', [status(esa)], [distributivity2])).
% 283.59/41.39 thf(zip_derived_cl186, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.39 ((multiply @ X1 @ (add @ (add @ X0 @ (inverse @ X1)) @ X2))
% 283.59/41.39 = (multiply @ X1 @ (add @ X0 @ X2)))),
% 283.59/41.39 inference('demod', [status(thm)], [zip_derived_cl164, zip_derived_cl3])).
% 283.59/41.39 thf(zip_derived_cl9842, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((multiply @ X0 @ multiplicative_identity)
% 283.59/41.39 = (multiply @ X0 @
% 283.59/41.39 (add @ X1 @ (inverse @ (add @ X1 @ (inverse @ X0))))))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl186])).
% 283.59/41.39 thf(zip_derived_cl5, plain,
% 283.59/41.39 (![X0 : $i]: ((multiply @ X0 @ multiplicative_identity) = (X0))),
% 283.59/41.39 inference('cnf', [status(esa)], [multiplicative_id1])).
% 283.59/41.39 thf(zip_derived_cl9901, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((X0)
% 283.59/41.39 = (multiply @ X0 @
% 283.59/41.39 (add @ X1 @ (inverse @ (add @ X1 @ (inverse @ X0))))))),
% 283.59/41.39 inference('demod', [status(thm)], [zip_derived_cl9842, zip_derived_cl5])).
% 283.59/41.39 thf(zip_derived_cl1, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 283.59/41.39 inference('cnf', [status(esa)], [commutativity_of_multiply])).
% 283.59/41.39 thf(zip_derived_cl705, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]: ((add @ (multiply @ X0 @ X1) @ X0) = (X0))),
% 283.59/41.39 inference('demod', [status(thm)],
% 283.59/41.39 [zip_derived_cl667, zip_derived_cl82, zip_derived_cl5])).
% 283.59/41.39 thf(zip_derived_cl741, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]: ((add @ (multiply @ X1 @ X0) @ X0) = (X0))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl705])).
% 283.59/41.39 thf(zip_derived_cl37, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((add @ X1 @ (multiply @ (inverse @ X1) @ X0)) = (add @ X1 @ X0))),
% 283.59/41.39 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl16])).
% 283.59/41.39 thf(zip_derived_cl25, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.39 ((add @ X0 @ (multiply @ X2 @ X1))
% 283.59/41.39 = (multiply @ (add @ X0 @ X2) @ (add @ X1 @ X0)))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 283.59/41.39 thf(zip_derived_cl340, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.39 ((add @ (multiply @ (inverse @ X1) @ X0) @ (multiply @ X2 @ X1))
% 283.59/41.39 = (multiply @ (add @ (multiply @ (inverse @ X1) @ X0) @ X2) @
% 283.59/41.39 (add @ X1 @ X0)))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl37, zip_derived_cl25])).
% 283.59/41.39 thf(zip_derived_cl14901, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((add @ (multiply @ (inverse @ X1) @ X0) @ (multiply @ X0 @ X1))
% 283.59/41.39 = (multiply @ X0 @ (add @ X1 @ X0)))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl741, zip_derived_cl340])).
% 283.59/41.39 thf(zip_derived_cl4, plain,
% 283.59/41.39 (![X0 : $i]: ((add @ X0 @ additive_identity) = (X0))),
% 283.59/41.39 inference('cnf', [status(esa)], [additive_id1])).
% 283.59/41.39 thf(zip_derived_cl25, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.39 ((add @ X0 @ (multiply @ X2 @ X1))
% 283.59/41.39 = (multiply @ (add @ X0 @ X2) @ (add @ X1 @ X0)))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 283.59/41.39 thf(zip_derived_cl352, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((add @ X0 @ (multiply @ additive_identity @ X1))
% 283.59/41.39 = (multiply @ X0 @ (add @ X1 @ X0)))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl25])).
% 283.59/41.39 thf(zip_derived_cl9, plain,
% 283.59/41.39 (![X0 : $i]: ((X0) = (add @ additive_identity @ X0))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 283.59/41.39 thf(zip_derived_cl6, plain,
% 283.59/41.39 (![X0 : $i]: ((add @ X0 @ (inverse @ X0)) = (multiplicative_identity))),
% 283.59/41.39 inference('cnf', [status(esa)], [additive_inverse1])).
% 283.59/41.39 thf(zip_derived_cl13, plain,
% 283.59/41.39 (((inverse @ additive_identity) = (multiplicative_identity))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl6])).
% 283.59/41.39 thf(zip_derived_cl55, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((multiply @ X0 @ (add @ X1 @ (inverse @ X0))) = (multiply @ X0 @ X1))),
% 283.59/41.39 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl4])).
% 283.59/41.39 thf(zip_derived_cl177, plain,
% 283.59/41.39 (![X0 : $i]:
% 283.59/41.39 ((multiply @ additive_identity @ (add @ X0 @ multiplicative_identity))
% 283.59/41.39 = (multiply @ additive_identity @ X0))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl55])).
% 283.59/41.39 thf(zip_derived_cl70, plain,
% 283.59/41.39 (![X0 : $i]:
% 283.59/41.39 ((multiplicative_identity) = (add @ X0 @ multiplicative_identity))),
% 283.59/41.39 inference('demod', [status(thm)], [zip_derived_cl66, zip_derived_cl6])).
% 283.59/41.39 thf(zip_derived_cl5, plain,
% 283.59/41.39 (![X0 : $i]: ((multiply @ X0 @ multiplicative_identity) = (X0))),
% 283.59/41.39 inference('cnf', [status(esa)], [multiplicative_id1])).
% 283.59/41.39 thf(zip_derived_cl184, plain,
% 283.59/41.39 (![X0 : $i]: ((additive_identity) = (multiply @ additive_identity @ X0))),
% 283.59/41.39 inference('demod', [status(thm)],
% 283.59/41.39 [zip_derived_cl177, zip_derived_cl70, zip_derived_cl5])).
% 283.59/41.39 thf(zip_derived_cl4, plain,
% 283.59/41.39 (![X0 : $i]: ((add @ X0 @ additive_identity) = (X0))),
% 283.59/41.39 inference('cnf', [status(esa)], [additive_id1])).
% 283.59/41.39 thf(zip_derived_cl367, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]: ((X0) = (multiply @ X0 @ (add @ X1 @ X0)))),
% 283.59/41.39 inference('demod', [status(thm)],
% 283.59/41.39 [zip_derived_cl352, zip_derived_cl184, zip_derived_cl4])).
% 283.59/41.39 thf(zip_derived_cl15018, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((add @ (multiply @ (inverse @ X1) @ X0) @ (multiply @ X0 @ X1))
% 283.59/41.39 = (X0))),
% 283.59/41.39 inference('demod', [status(thm)],
% 283.59/41.39 [zip_derived_cl14901, zip_derived_cl367])).
% 283.59/41.39 thf(zip_derived_cl86415, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((add @ (inverse @ X0) @
% 283.59/41.39 (multiply @
% 283.59/41.39 (add @ X1 @ (inverse @ (add @ X1 @ (inverse @ (inverse @ X0))))) @
% 283.59/41.39 X0))
% 283.59/41.39 = (add @ X1 @ (inverse @ (add @ X1 @ (inverse @ (inverse @ X0))))))),
% 283.59/41.39 inference('sup+', [status(thm)],
% 283.59/41.39 [zip_derived_cl9901, zip_derived_cl15018])).
% 283.59/41.39 thf(zip_derived_cl309, plain,
% 283.59/41.39 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 283.59/41.39 inference('demod', [status(thm)], [zip_derived_cl296, zip_derived_cl144])).
% 283.59/41.39 thf(zip_derived_cl1, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 283.59/41.39 inference('cnf', [status(esa)], [commutativity_of_multiply])).
% 283.59/41.39 thf(zip_derived_cl309, plain,
% 283.59/41.39 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 283.59/41.39 inference('demod', [status(thm)], [zip_derived_cl296, zip_derived_cl144])).
% 283.59/41.39 thf(zip_derived_cl6, plain,
% 283.59/41.39 (![X0 : $i]: ((add @ X0 @ (inverse @ X0)) = (multiplicative_identity))),
% 283.59/41.39 inference('cnf', [status(esa)], [additive_inverse1])).
% 283.59/41.39 thf(zip_derived_cl319, plain,
% 283.59/41.39 (![X0 : $i]: ((add @ (inverse @ X0) @ X0) = (multiplicative_identity))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl309, zip_derived_cl6])).
% 283.59/41.39 thf(zip_derived_cl25, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.39 ((add @ X0 @ (multiply @ X2 @ X1))
% 283.59/41.39 = (multiply @ (add @ X0 @ X2) @ (add @ X1 @ X0)))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 283.59/41.39 thf(zip_derived_cl377, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((add @ (inverse @ X0) @ (multiply @ X0 @ X1))
% 283.59/41.39 = (multiply @ multiplicative_identity @ (add @ X1 @ (inverse @ X0))))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl319, zip_derived_cl25])).
% 283.59/41.39 thf(zip_derived_cl16, plain,
% 283.59/41.39 (![X0 : $i]: ((X0) = (multiply @ multiplicative_identity @ X0))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl1])).
% 283.59/41.39 thf(zip_derived_cl389, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((add @ (inverse @ X0) @ (multiply @ X0 @ X1))
% 283.59/41.39 = (add @ X1 @ (inverse @ X0)))),
% 283.59/41.39 inference('demod', [status(thm)], [zip_derived_cl377, zip_derived_cl16])).
% 283.59/41.39 thf(zip_derived_cl55, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((multiply @ X0 @ (add @ X1 @ (inverse @ X0))) = (multiply @ X0 @ X1))),
% 283.59/41.39 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl4])).
% 283.59/41.39 thf(zip_derived_cl39, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.39 ((add @ (multiply @ X2 @ X0) @ (multiply @ X2 @ X1))
% 283.59/41.39 = (multiply @ X2 @ (add @ X1 @ X0)))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 283.59/41.39 thf(zip_derived_cl663, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.39 ((add @ (multiply @ X1 @ X2) @ (multiply @ X1 @ X0))
% 283.59/41.39 = (multiply @ X1 @ (add @ (add @ X0 @ (inverse @ X1)) @ X2)))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl55, zip_derived_cl39])).
% 283.59/41.39 thf(zip_derived_cl3, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.39 ((multiply @ X0 @ (add @ X1 @ X2))
% 283.59/41.39 = (add @ (multiply @ X0 @ X1) @ (multiply @ X0 @ X2)))),
% 283.59/41.39 inference('cnf', [status(esa)], [distributivity2])).
% 283.59/41.39 thf(zip_derived_cl701, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.39 ((multiply @ X1 @ (add @ X2 @ X0))
% 283.59/41.39 = (multiply @ X1 @ (add @ (add @ X0 @ (inverse @ X1)) @ X2)))),
% 283.59/41.39 inference('demod', [status(thm)], [zip_derived_cl663, zip_derived_cl3])).
% 283.59/41.39 thf(zip_derived_cl15018, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((add @ (multiply @ (inverse @ X1) @ X0) @ (multiply @ X0 @ X1))
% 283.59/41.39 = (X0))),
% 283.59/41.39 inference('demod', [status(thm)],
% 283.59/41.39 [zip_derived_cl14901, zip_derived_cl367])).
% 283.59/41.39 thf(zip_derived_cl48349, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.39 ((add @ (multiply @ (inverse @ X2) @ (add @ X1 @ X0)) @
% 283.59/41.39 (multiply @ (add @ (add @ X0 @ (inverse @ (inverse @ X2))) @ X1) @
% 283.59/41.39 X2))
% 283.59/41.39 = (add @ (add @ X0 @ (inverse @ (inverse @ X2))) @ X1))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl701, zip_derived_cl15018])).
% 283.59/41.39 thf(zip_derived_cl309, plain,
% 283.59/41.39 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 283.59/41.39 inference('demod', [status(thm)], [zip_derived_cl296, zip_derived_cl144])).
% 283.59/41.39 thf(zip_derived_cl367, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]: ((X0) = (multiply @ X0 @ (add @ X1 @ X0)))),
% 283.59/41.39 inference('demod', [status(thm)],
% 283.59/41.39 [zip_derived_cl352, zip_derived_cl184, zip_derived_cl4])).
% 283.59/41.39 thf(zip_derived_cl39, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.39 ((add @ (multiply @ X2 @ X0) @ (multiply @ X2 @ X1))
% 283.59/41.39 = (multiply @ X2 @ (add @ X1 @ X0)))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 283.59/41.39 thf(zip_derived_cl665, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.39 ((add @ (multiply @ X0 @ X1) @ X0)
% 283.59/41.39 = (multiply @ X0 @ (add @ (add @ X2 @ X0) @ X1)))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl367, zip_derived_cl39])).
% 283.59/41.39 thf(zip_derived_cl0, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]: ((add @ X1 @ X0) = (add @ X0 @ X1))),
% 283.59/41.39 inference('cnf', [status(esa)], [commutativity_of_add])).
% 283.59/41.39 thf(zip_derived_cl69, plain, (![X0 : $i]: ((X0) = (add @ X0 @ X0))),
% 283.59/41.39 inference('demod', [status(thm)], [zip_derived_cl65, zip_derived_cl4])).
% 283.59/41.39 thf(zip_derived_cl30, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.39 ((add @ X0 @ (multiply @ X1 @ X2))
% 283.59/41.39 = (multiply @ (add @ X1 @ X0) @ (add @ X0 @ X2)))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 283.59/41.39 thf(zip_derived_cl524, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((add @ X0 @ (multiply @ X0 @ X1)) = (multiply @ X0 @ (add @ X0 @ X1)))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl69, zip_derived_cl30])).
% 283.59/41.39 thf(zip_derived_cl408, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ (add @ X0 @ X1)) = (X0))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl363, zip_derived_cl1])).
% 283.59/41.39 thf(zip_derived_cl547, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]: ((add @ X0 @ (multiply @ X0 @ X1)) = (X0))),
% 283.59/41.39 inference('demod', [status(thm)], [zip_derived_cl524, zip_derived_cl408])).
% 283.59/41.39 thf(zip_derived_cl703, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.39 ((X0) = (multiply @ X0 @ (add @ (add @ X2 @ X0) @ X1)))),
% 283.59/41.39 inference('demod', [status(thm)],
% 283.59/41.39 [zip_derived_cl665, zip_derived_cl0, zip_derived_cl547])).
% 283.59/41.39 thf(zip_derived_cl538, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]: ((add @ X0 @ (multiply @ X1 @ X0)) = (X0))),
% 283.59/41.39 inference('demod', [status(thm)], [zip_derived_cl512, zip_derived_cl414])).
% 283.59/41.39 thf(zip_derived_cl414, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]: ((X0) = (multiply @ (add @ X1 @ X0) @ X0))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl363])).
% 283.59/41.39 thf(zip_derived_cl561, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((multiply @ X1 @ X0) = (multiply @ X0 @ (multiply @ X1 @ X0)))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl538, zip_derived_cl414])).
% 283.59/41.39 thf(zip_derived_cl14517, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.39 ((multiply @ X0 @ (add @ (add @ X2 @ X0) @ X1))
% 283.59/41.39 = (multiply @ (add @ (add @ X2 @ X0) @ X1) @ X0))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl703, zip_derived_cl561])).
% 283.59/41.39 thf(zip_derived_cl703, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.39 ((X0) = (multiply @ X0 @ (add @ (add @ X2 @ X0) @ X1)))),
% 283.59/41.39 inference('demod', [status(thm)],
% 283.59/41.39 [zip_derived_cl665, zip_derived_cl0, zip_derived_cl547])).
% 283.59/41.39 thf(zip_derived_cl14709, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.39 ((X0) = (multiply @ (add @ (add @ X2 @ X0) @ X1) @ X0))),
% 283.59/41.39 inference('demod', [status(thm)],
% 283.59/41.39 [zip_derived_cl14517, zip_derived_cl703])).
% 283.59/41.39 thf(zip_derived_cl37, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((add @ X1 @ (multiply @ (inverse @ X1) @ X0)) = (add @ X1 @ X0))),
% 283.59/41.39 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl16])).
% 283.59/41.39 thf(zip_derived_cl0, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]: ((add @ X1 @ X0) = (add @ X0 @ X1))),
% 283.59/41.39 inference('cnf', [status(esa)], [commutativity_of_add])).
% 283.59/41.39 thf(zip_derived_cl367, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]: ((X0) = (multiply @ X0 @ (add @ X1 @ X0)))),
% 283.59/41.39 inference('demod', [status(thm)],
% 283.59/41.39 [zip_derived_cl352, zip_derived_cl184, zip_derived_cl4])).
% 283.59/41.39 thf(zip_derived_cl538, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]: ((add @ X0 @ (multiply @ X1 @ X0)) = (X0))),
% 283.59/41.39 inference('demod', [status(thm)], [zip_derived_cl512, zip_derived_cl414])).
% 283.59/41.39 thf(zip_derived_cl577, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]: ((add @ (add @ X1 @ X0) @ X0) = (add @ X1 @ X0))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl367, zip_derived_cl538])).
% 283.59/41.39 thf(zip_derived_cl2707, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]: ((add @ (add @ X1 @ X0) @ X1) = (add @ X0 @ X1))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl577])).
% 283.59/41.39 thf(zip_derived_cl7285, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((add @ (add @ X1 @ X0) @ X1)
% 283.59/41.39 = (add @ (multiply @ (inverse @ X1) @ X0) @ X1))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl37, zip_derived_cl2707])).
% 283.59/41.39 thf(zip_derived_cl408, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ (add @ X0 @ X1)) = (X0))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl363, zip_derived_cl1])).
% 283.59/41.39 thf(zip_derived_cl538, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]: ((add @ X0 @ (multiply @ X1 @ X0)) = (X0))),
% 283.59/41.39 inference('demod', [status(thm)], [zip_derived_cl512, zip_derived_cl414])).
% 283.59/41.39 thf(zip_derived_cl574, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]: ((add @ (add @ X0 @ X1) @ X0) = (add @ X0 @ X1))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl408, zip_derived_cl538])).
% 283.59/41.39 thf(zip_derived_cl7327, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((add @ X1 @ X0) = (add @ (multiply @ (inverse @ X1) @ X0) @ X1))),
% 283.59/41.39 inference('demod', [status(thm)], [zip_derived_cl7285, zip_derived_cl574])).
% 283.59/41.39 thf(zip_derived_cl309, plain,
% 283.59/41.39 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 283.59/41.39 inference('demod', [status(thm)], [zip_derived_cl296, zip_derived_cl144])).
% 283.59/41.39 thf(zip_derived_cl48462, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.39 ((add @ X2 @ (add @ X1 @ X0)) = (add @ (add @ X0 @ X2) @ X1))),
% 283.59/41.39 inference('demod', [status(thm)],
% 283.59/41.39 [zip_derived_cl48349, zip_derived_cl309, zip_derived_cl14709,
% 283.59/41.39 zip_derived_cl7327, zip_derived_cl309])).
% 283.59/41.39 thf(zip_derived_cl0, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]: ((add @ X1 @ X0) = (add @ X0 @ X1))),
% 283.59/41.39 inference('cnf', [status(esa)], [commutativity_of_add])).
% 283.59/41.39 thf(zip_derived_cl48462, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 283.59/41.39 ((add @ X2 @ (add @ X1 @ X0)) = (add @ (add @ X0 @ X2) @ X1))),
% 283.59/41.39 inference('demod', [status(thm)],
% 283.59/41.39 [zip_derived_cl48349, zip_derived_cl309, zip_derived_cl14709,
% 283.59/41.39 zip_derived_cl7327, zip_derived_cl309])).
% 283.59/41.39 thf(zip_derived_cl309, plain,
% 283.59/41.39 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 283.59/41.39 inference('demod', [status(thm)], [zip_derived_cl296, zip_derived_cl144])).
% 283.59/41.39 thf(zip_derived_cl367, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]: ((X0) = (multiply @ X0 @ (add @ X1 @ X0)))),
% 283.59/41.39 inference('demod', [status(thm)],
% 283.59/41.39 [zip_derived_cl352, zip_derived_cl184, zip_derived_cl4])).
% 283.59/41.39 thf(zip_derived_cl1303, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((additive_identity)
% 283.59/41.39 = (multiply @ (inverse @ X0) @ (multiply @ X1 @ X0)))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl309, zip_derived_cl597])).
% 283.59/41.39 thf(zip_derived_cl1939, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((additive_identity) = (multiply @ (inverse @ (add @ X1 @ X0)) @ X0))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl367, zip_derived_cl1303])).
% 283.59/41.39 thf(zip_derived_cl35, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((add @ X0 @ (multiply @ X1 @ (inverse @ X0))) = (add @ X0 @ X1))),
% 283.59/41.39 inference('demod', [status(thm)], [zip_derived_cl28, zip_derived_cl5])).
% 283.59/41.39 thf(zip_derived_cl2614, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((add @ X0 @ additive_identity)
% 283.59/41.39 = (add @ X0 @ (inverse @ (add @ X1 @ (inverse @ X0)))))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl1939, zip_derived_cl35])).
% 283.59/41.39 thf(zip_derived_cl4, plain,
% 283.59/41.39 (![X0 : $i]: ((add @ X0 @ additive_identity) = (X0))),
% 283.59/41.39 inference('cnf', [status(esa)], [additive_id1])).
% 283.59/41.39 thf(zip_derived_cl2676, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((X0) = (add @ X0 @ (inverse @ (add @ X1 @ (inverse @ X0)))))),
% 283.59/41.39 inference('demod', [status(thm)], [zip_derived_cl2614, zip_derived_cl4])).
% 283.59/41.39 thf(zip_derived_cl752, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]: ((add @ X0 @ (add @ X1 @ X0)) = (add @ X1 @ X0))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl414, zip_derived_cl705])).
% 283.59/41.39 thf(zip_derived_cl5145, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((add @ (inverse @ (add @ X1 @ (inverse @ X0))) @ X0)
% 283.59/41.39 = (add @ X0 @ (inverse @ (add @ X1 @ (inverse @ X0)))))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl2676, zip_derived_cl752])).
% 283.59/41.39 thf(zip_derived_cl2676, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((X0) = (add @ X0 @ (inverse @ (add @ X1 @ (inverse @ X0)))))),
% 283.59/41.39 inference('demod', [status(thm)], [zip_derived_cl2614, zip_derived_cl4])).
% 283.59/41.39 thf(zip_derived_cl5208, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((add @ (inverse @ (add @ X1 @ (inverse @ X0))) @ X0) = (X0))),
% 283.59/41.39 inference('demod', [status(thm)],
% 283.59/41.39 [zip_derived_cl5145, zip_derived_cl2676])).
% 283.59/41.39 thf(zip_derived_cl10272, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((add @ (inverse @ (add @ X1 @ X0)) @ (inverse @ X0)) = (inverse @ X0))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl309, zip_derived_cl5208])).
% 283.59/41.39 thf(zip_derived_cl309, plain,
% 283.59/41.39 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 283.59/41.39 inference('demod', [status(thm)], [zip_derived_cl296, zip_derived_cl144])).
% 283.59/41.39 thf(zip_derived_cl86709, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((add @ X1 @ (inverse @ X0))
% 283.59/41.39 = (add @ X1 @ (inverse @ (add @ X1 @ X0))))),
% 283.59/41.39 inference('demod', [status(thm)],
% 283.59/41.39 [zip_derived_cl86415, zip_derived_cl309, zip_derived_cl1,
% 283.59/41.39 zip_derived_cl389, zip_derived_cl48462, zip_derived_cl0,
% 283.59/41.39 zip_derived_cl48462, zip_derived_cl10272, zip_derived_cl309])).
% 283.59/41.39 thf(zip_derived_cl55, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((multiply @ X0 @ (add @ X1 @ (inverse @ X0))) = (multiply @ X0 @ X1))),
% 283.59/41.39 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl4])).
% 283.59/41.39 thf(zip_derived_cl107544, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((multiply @ (add @ X1 @ X0) @ (add @ X1 @ (inverse @ X0)))
% 283.59/41.39 = (multiply @ (add @ X1 @ X0) @ X1))),
% 283.59/41.39 inference('sup+', [status(thm)], [zip_derived_cl86709, zip_derived_cl55])).
% 283.59/41.39 thf(zip_derived_cl363, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]: ((X0) = (multiply @ (add @ X0 @ X1) @ X0))),
% 283.59/41.39 inference('demod', [status(thm)],
% 283.59/41.39 [zip_derived_cl345, zip_derived_cl182, zip_derived_cl4])).
% 283.59/41.39 thf(zip_derived_cl107940, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((multiply @ (add @ X1 @ X0) @ (add @ X1 @ (inverse @ X0))) = (X1))),
% 283.59/41.39 inference('demod', [status(thm)],
% 283.59/41.39 [zip_derived_cl107544, zip_derived_cl363])).
% 283.59/41.39 thf(zip_derived_cl115245, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((multiply @ X0 @
% 283.59/41.39 (add @ (inverse @ (add @ (inverse @ X0) @ X1)) @ (inverse @ X0)))
% 283.59/41.39 = (inverse @ (add @ (inverse @ X0) @ X1)))),
% 283.59/41.39 inference('sup+', [status(thm)],
% 283.59/41.39 [zip_derived_cl4416, zip_derived_cl107940])).
% 283.59/41.39 thf(zip_derived_cl0, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]: ((add @ X1 @ X0) = (add @ X0 @ X1))),
% 283.59/41.39 inference('cnf', [status(esa)], [commutativity_of_add])).
% 283.59/41.39 thf(zip_derived_cl86709, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((add @ X1 @ (inverse @ X0))
% 283.59/41.39 = (add @ X1 @ (inverse @ (add @ X1 @ X0))))),
% 283.59/41.39 inference('demod', [status(thm)],
% 283.59/41.39 [zip_derived_cl86415, zip_derived_cl309, zip_derived_cl1,
% 283.59/41.39 zip_derived_cl389, zip_derived_cl48462, zip_derived_cl0,
% 283.59/41.39 zip_derived_cl48462, zip_derived_cl10272, zip_derived_cl309])).
% 283.59/41.39 thf(zip_derived_cl57, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((multiply @ X1 @ (add @ (inverse @ X1) @ X0)) = (multiply @ X1 @ X0))),
% 283.59/41.39 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl9])).
% 283.59/41.39 thf(zip_derived_cl115374, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((multiply @ X0 @ (inverse @ X1))
% 283.59/41.39 = (inverse @ (add @ (inverse @ X0) @ X1)))),
% 283.59/41.39 inference('demod', [status(thm)],
% 283.59/41.39 [zip_derived_cl115245, zip_derived_cl0, zip_derived_cl86709,
% 283.59/41.39 zip_derived_cl57])).
% 283.59/41.39 thf(zip_derived_cl309, plain,
% 283.59/41.39 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 283.59/41.39 inference('demod', [status(thm)], [zip_derived_cl296, zip_derived_cl144])).
% 283.59/41.39 thf(zip_derived_cl115961, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((add @ (inverse @ X1) @ X0)
% 283.59/41.39 = (inverse @ (multiply @ X1 @ (inverse @ X0))))),
% 283.59/41.39 inference('sup+', [status(thm)],
% 283.59/41.39 [zip_derived_cl115374, zip_derived_cl309])).
% 283.59/41.39 thf(zip_derived_cl119672, plain,
% 283.59/41.39 (![X0 : $i, X1 : $i]:
% 283.59/41.39 ((add @ (inverse @ X1) @ (inverse @ X0))
% 283.59/41.39 = (inverse @ (multiply @ X1 @ X0)))),
% 283.59/41.39 inference('sup+', [status(thm)],
% 283.59/41.39 [zip_derived_cl309, zip_derived_cl115961])).
% 283.59/41.39 thf(zip_derived_cl126184, plain,
% 283.59/41.39 (((inverse @ (multiply @ a @ b)) != (inverse @ (multiply @ a @ b)))),
% 283.59/41.39 inference('demod', [status(thm)], [zip_derived_cl8, zip_derived_cl119672])).
% 283.59/41.39 thf(zip_derived_cl126185, plain, ($false),
% 283.59/41.39 inference('simplify', [status(thm)], [zip_derived_cl126184])).
% 283.59/41.39
% 283.59/41.39 % SZS output end Refutation
% 283.59/41.39
% 283.59/41.39
% 283.59/41.39 % Terminating...
% 284.22/41.47 % Runner terminated.
% 284.22/41.48 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------