TSTP Solution File: BOO014-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : BOO014-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.T9dg4HyRaO 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 37.73s 6.02s
% Output : Refutation 37.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO014-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.T9dg4HyRaO true
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 08:33:07 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.21/0.62 % Total configuration time : 435
% 0.21/0.62 % Estimated wc time : 1092
% 0.21/0.62 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.72 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.72 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 37.73/6.02 % Solved by fo/fo5.sh.
% 37.73/6.02 % done 9906 iterations in 5.235s
% 37.73/6.02 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 37.73/6.02 % SZS output start Refutation
% 37.73/6.02 thf(sum_type, type, sum: $i > $i > $i > $o).
% 37.73/6.02 thf(x_inverse_times_y_inverse_type, type, x_inverse_times_y_inverse: $i).
% 37.73/6.02 thf(y_type, type, y: $i).
% 37.73/6.02 thf(x_plus_y_type, type, x_plus_y: $i).
% 37.73/6.02 thf(multiplicative_identity_type, type, multiplicative_identity: $i).
% 37.73/6.02 thf(inverse_type, type, inverse: $i > $i).
% 37.73/6.02 thf(x_type, type, x: $i).
% 37.73/6.02 thf(multiply_type, type, multiply: $i > $i > $i).
% 37.73/6.02 thf(product_type, type, product: $i > $i > $i > $o).
% 37.73/6.02 thf(add_type, type, add: $i > $i > $i).
% 37.73/6.02 thf(additive_identity_type, type, additive_identity: $i).
% 37.73/6.02 thf(closure_of_multiplication, axiom,
% 37.73/6.02 (product @ X @ Y @ ( multiply @ X @ Y ))).
% 37.73/6.02 thf(zip_derived_cl1, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 37.73/6.02 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 37.73/6.02 thf(commutativity_of_multiplication, axiom,
% 37.73/6.02 (( ~( product @ X @ Y @ Z ) ) | ( product @ Y @ X @ Z ))).
% 37.73/6.02 thf(zip_derived_cl3, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.02 (~ (product @ X0 @ X1 @ X2) | (product @ X1 @ X0 @ X2))),
% 37.73/6.02 inference('cnf', [status(esa)], [commutativity_of_multiplication])).
% 37.73/6.02 thf(zip_derived_cl50, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X1 @ X0))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl3])).
% 37.73/6.02 thf(x_inverse_times_y_inverse, conjecture,
% 37.73/6.02 (~( product @ ( inverse @ x ) @ ( inverse @ y ) @ x_inverse_times_y_inverse ))).
% 37.73/6.02 thf(zf_stmt_0, negated_conjecture,
% 37.73/6.02 (product @ ( inverse @ x ) @ ( inverse @ y ) @ x_inverse_times_y_inverse),
% 37.73/6.02 inference('cnf.neg', [status(esa)], [x_inverse_times_y_inverse])).
% 37.73/6.02 thf(zip_derived_cl23, plain,
% 37.73/6.02 ( (product @ (inverse @ x) @ (inverse @ y) @ x_inverse_times_y_inverse)),
% 37.73/6.02 inference('cnf', [status(esa)], [zf_stmt_0])).
% 37.73/6.02 thf(zip_derived_cl3, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.02 (~ (product @ X0 @ X1 @ X2) | (product @ X1 @ X0 @ X2))),
% 37.73/6.02 inference('cnf', [status(esa)], [commutativity_of_multiplication])).
% 37.73/6.02 thf(zip_derived_cl38, plain,
% 37.73/6.02 ( (product @ (inverse @ y) @ (inverse @ x) @ x_inverse_times_y_inverse)),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl3])).
% 37.73/6.02 thf(multiplicative_identity2, axiom,
% 37.73/6.02 (product @ X @ multiplicative_identity @ X)).
% 37.73/6.02 thf(zip_derived_cl7, plain,
% 37.73/6.02 (![X0 : $i]: (product @ X0 @ multiplicative_identity @ X0)),
% 37.73/6.02 inference('cnf', [status(esa)], [multiplicative_identity2])).
% 37.73/6.02 thf(distributivity1, axiom,
% 37.73/6.02 (( ~( product @ X @ Y @ V1 ) ) | ( ~( product @ X @ Z @ V2 ) ) |
% 37.73/6.02 ( ~( sum @ Y @ Z @ V3 ) ) | ( ~( product @ X @ V3 @ V4 ) ) |
% 37.73/6.02 ( sum @ V1 @ V2 @ V4 ))).
% 37.73/6.02 thf(zip_derived_cl8, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 37.73/6.02 (~ (product @ X0 @ X1 @ X2)
% 37.73/6.02 | ~ (product @ X0 @ X3 @ X4)
% 37.73/6.02 | ~ (sum @ X1 @ X3 @ X5)
% 37.73/6.02 | ~ (product @ X0 @ X5 @ X6)
% 37.73/6.02 | (sum @ X2 @ X4 @ X6))),
% 37.73/6.02 inference('cnf', [status(esa)], [distributivity1])).
% 37.73/6.02 thf(zip_derived_cl89, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 37.73/6.02 ( (sum @ X0 @ X3 @ X0)
% 37.73/6.02 | ~ (product @ X2 @ X1 @ X0)
% 37.73/6.02 | ~ (sum @ X1 @ X4 @ X1)
% 37.73/6.02 | ~ (product @ X2 @ X4 @ X3))),
% 37.73/6.02 inference('eq_fact', [status(thm)], [zip_derived_cl8])).
% 37.73/6.02 thf(zip_derived_cl651, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.02 (~ (product @ X0 @ X2 @ X1)
% 37.73/6.02 | ~ (sum @ multiplicative_identity @ X2 @ multiplicative_identity)
% 37.73/6.02 | (sum @ X0 @ X1 @ X0))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl89])).
% 37.73/6.02 thf(closure_of_addition, axiom, (sum @ X @ Y @ ( add @ X @ Y ))).
% 37.73/6.02 thf(zip_derived_cl0, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 37.73/6.02 inference('cnf', [status(esa)], [closure_of_addition])).
% 37.73/6.02 thf(additive_identity2, axiom, (sum @ X @ additive_identity @ X)).
% 37.73/6.02 thf(zip_derived_cl5, plain,
% 37.73/6.02 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 37.73/6.02 inference('cnf', [status(esa)], [additive_identity2])).
% 37.73/6.02 thf(distributivity5, axiom,
% 37.73/6.02 (( ~( sum @ X @ Y @ V1 ) ) | ( ~( sum @ X @ Z @ V2 ) ) |
% 37.73/6.02 ( ~( product @ Y @ Z @ V3 ) ) | ( ~( sum @ X @ V3 @ V4 ) ) |
% 37.73/6.02 ( product @ V1 @ V2 @ V4 ))).
% 37.73/6.02 thf(zip_derived_cl12, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 37.73/6.02 (~ (sum @ X0 @ X1 @ X2)
% 37.73/6.02 | ~ (sum @ X0 @ X3 @ X4)
% 37.73/6.02 | ~ (product @ X1 @ X3 @ X5)
% 37.73/6.02 | ~ (sum @ X0 @ X5 @ X6)
% 37.73/6.02 | (product @ X2 @ X4 @ X6))),
% 37.73/6.02 inference('cnf', [status(esa)], [distributivity5])).
% 37.73/6.02 thf(zip_derived_cl222, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 37.73/6.02 ( (product @ X0 @ X3 @ X0)
% 37.73/6.02 | ~ (sum @ X2 @ X1 @ X0)
% 37.73/6.02 | ~ (product @ X1 @ X4 @ X1)
% 37.73/6.02 | ~ (sum @ X2 @ X4 @ X3))),
% 37.73/6.02 inference('eq_fact', [status(thm)], [zip_derived_cl12])).
% 37.73/6.02 thf(zip_derived_cl2392, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.02 (~ (sum @ X0 @ X2 @ X1)
% 37.73/6.02 | ~ (product @ additive_identity @ X2 @ additive_identity)
% 37.73/6.02 | (product @ X0 @ X1 @ X0))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl222])).
% 37.73/6.02 thf(zip_derived_cl1, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 37.73/6.02 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 37.73/6.02 thf(zip_derived_cl5, plain,
% 37.73/6.02 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 37.73/6.02 inference('cnf', [status(esa)], [additive_identity2])).
% 37.73/6.02 thf(multiplicative_inverse2, axiom,
% 37.73/6.02 (product @ X @ ( inverse @ X ) @ additive_identity)).
% 37.73/6.02 thf(zip_derived_cl19, plain,
% 37.73/6.02 (![X0 : $i]: (product @ X0 @ (inverse @ X0) @ additive_identity)),
% 37.73/6.02 inference('cnf', [status(esa)], [multiplicative_inverse2])).
% 37.73/6.02 thf(zip_derived_cl1, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 37.73/6.02 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 37.73/6.02 thf(zip_derived_cl8, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 37.73/6.02 (~ (product @ X0 @ X1 @ X2)
% 37.73/6.02 | ~ (product @ X0 @ X3 @ X4)
% 37.73/6.02 | ~ (sum @ X1 @ X3 @ X5)
% 37.73/6.02 | ~ (product @ X0 @ X5 @ X6)
% 37.73/6.02 | (sum @ X2 @ X4 @ X6))),
% 37.73/6.02 inference('cnf', [status(esa)], [distributivity1])).
% 37.73/6.02 thf(zip_derived_cl81, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 37.73/6.02 ( (sum @ (multiply @ X1 @ X0) @ X3 @ X2)
% 37.73/6.02 | ~ (product @ X1 @ X4 @ X2)
% 37.73/6.02 | ~ (sum @ X0 @ X5 @ X4)
% 37.73/6.02 | ~ (product @ X1 @ X5 @ X3))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl8])).
% 37.73/6.02 thf(zip_derived_cl350, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.73/6.02 (~ (product @ X0 @ X2 @ X1)
% 37.73/6.02 | ~ (sum @ X3 @ X2 @ (inverse @ X0))
% 37.73/6.02 | (sum @ (multiply @ X0 @ X3) @ X1 @ additive_identity))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl81])).
% 37.73/6.02 thf(zip_derived_cl4944, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]:
% 37.73/6.02 ( (sum @ (multiply @ X0 @ (inverse @ X0)) @ X1 @ additive_identity)
% 37.73/6.02 | ~ (product @ X0 @ additive_identity @ X1))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl350])).
% 37.73/6.02 thf(zip_derived_cl1, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 37.73/6.02 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 37.73/6.02 thf(zip_derived_cl19, plain,
% 37.73/6.02 (![X0 : $i]: (product @ X0 @ (inverse @ X0) @ additive_identity)),
% 37.73/6.02 inference('cnf', [status(esa)], [multiplicative_inverse2])).
% 37.73/6.02 thf(multiplication_is_well_defined, axiom,
% 37.73/6.02 (( ~( product @ X @ Y @ U ) ) | ( ~( product @ X @ Y @ V ) ) |
% 37.73/6.02 ( ( U ) = ( V ) ))).
% 37.73/6.02 thf(zip_derived_cl21, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.73/6.02 (~ (product @ X0 @ X1 @ X2)
% 37.73/6.02 | ~ (product @ X0 @ X1 @ X3)
% 37.73/6.02 | ((X2) = (X3)))),
% 37.73/6.02 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 37.73/6.02 thf(zip_derived_cl100, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]:
% 37.73/6.02 (((additive_identity) = (X1)) | ~ (product @ X0 @ (inverse @ X0) @ X1))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl21])).
% 37.73/6.02 thf(zip_derived_cl134, plain,
% 37.73/6.02 (![X0 : $i]: ((additive_identity) = (multiply @ X0 @ (inverse @ X0)))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl100])).
% 37.73/6.02 thf(zip_derived_cl4956, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]:
% 37.73/6.02 ( (sum @ additive_identity @ X1 @ additive_identity)
% 37.73/6.02 | ~ (product @ X0 @ additive_identity @ X1))),
% 37.73/6.02 inference('demod', [status(thm)], [zip_derived_cl4944, zip_derived_cl134])).
% 37.73/6.02 thf(zip_derived_cl4968, plain,
% 37.73/6.02 (![X0 : $i]:
% 37.73/6.02 (sum @ additive_identity @ (multiply @ X0 @ additive_identity) @
% 37.73/6.02 additive_identity)),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl4956])).
% 37.73/6.02 thf(additive_identity1, axiom, (sum @ additive_identity @ X @ X)).
% 37.73/6.02 thf(zip_derived_cl4, plain,
% 37.73/6.02 (![X0 : $i]: (sum @ additive_identity @ X0 @ X0)),
% 37.73/6.02 inference('cnf', [status(esa)], [additive_identity1])).
% 37.73/6.02 thf(addition_is_well_defined, axiom,
% 37.73/6.02 (( ~( sum @ X @ Y @ U ) ) | ( ~( sum @ X @ Y @ V ) ) | ( ( U ) = ( V ) ))).
% 37.73/6.02 thf(zip_derived_cl20, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.73/6.02 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 37.73/6.02 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 37.73/6.02 thf(zip_derived_cl45, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]:
% 37.73/6.02 (((X0) = (X1)) | ~ (sum @ additive_identity @ X0 @ X1))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl20])).
% 37.73/6.02 thf(zip_derived_cl5579, plain,
% 37.73/6.02 (![X0 : $i]: ((multiply @ X0 @ additive_identity) = (additive_identity))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl4968, zip_derived_cl45])).
% 37.73/6.02 thf(zip_derived_cl50, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X1 @ X0))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl3])).
% 37.73/6.02 thf(zip_derived_cl5620, plain,
% 37.73/6.02 (![X0 : $i]: (product @ additive_identity @ X0 @ additive_identity)),
% 37.73/6.02 inference('sup+', [status(thm)], [zip_derived_cl5579, zip_derived_cl50])).
% 37.73/6.02 thf(zip_derived_cl5848, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.02 (~ (sum @ X0 @ X2 @ X1) | (product @ X0 @ X1 @ X0))),
% 37.73/6.02 inference('demod', [status(thm)],
% 37.73/6.02 [zip_derived_cl2392, zip_derived_cl5620])).
% 37.73/6.02 thf(zip_derived_cl6098, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (product @ X1 @ (add @ X1 @ X0) @ X1)),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl5848])).
% 37.73/6.02 thf(multiplicative_identity1, axiom,
% 37.73/6.02 (product @ multiplicative_identity @ X @ X)).
% 37.73/6.02 thf(zip_derived_cl6, plain,
% 37.73/6.02 (![X0 : $i]: (product @ multiplicative_identity @ X0 @ X0)),
% 37.73/6.02 inference('cnf', [status(esa)], [multiplicative_identity1])).
% 37.73/6.02 thf(zip_derived_cl21, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.73/6.02 (~ (product @ X0 @ X1 @ X2)
% 37.73/6.02 | ~ (product @ X0 @ X1 @ X3)
% 37.73/6.02 | ((X2) = (X3)))),
% 37.73/6.02 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 37.73/6.02 thf(zip_derived_cl101, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]:
% 37.73/6.02 (((X0) = (X1)) | ~ (product @ multiplicative_identity @ X0 @ X1))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl21])).
% 37.73/6.02 thf(zip_derived_cl7061, plain,
% 37.73/6.02 (![X0 : $i]:
% 37.73/6.02 ((add @ multiplicative_identity @ X0) = (multiplicative_identity))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl6098, zip_derived_cl101])).
% 37.73/6.02 thf(zip_derived_cl0, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 37.73/6.02 inference('cnf', [status(esa)], [closure_of_addition])).
% 37.73/6.02 thf(zip_derived_cl7135, plain,
% 37.73/6.02 (![X0 : $i]:
% 37.73/6.02 (sum @ multiplicative_identity @ X0 @ multiplicative_identity)),
% 37.73/6.02 inference('sup+', [status(thm)], [zip_derived_cl7061, zip_derived_cl0])).
% 37.73/6.02 thf(zip_derived_cl7215, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.02 (~ (product @ X0 @ X2 @ X1) | (sum @ X0 @ X1 @ X0))),
% 37.73/6.02 inference('demod', [status(thm)], [zip_derived_cl651, zip_derived_cl7135])).
% 37.73/6.02 thf(zip_derived_cl7335, plain,
% 37.73/6.02 ( (sum @ (inverse @ y) @ x_inverse_times_y_inverse @ (inverse @ y))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl7215])).
% 37.73/6.02 thf(zip_derived_cl350, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.73/6.02 (~ (product @ X0 @ X2 @ X1)
% 37.73/6.02 | ~ (sum @ X3 @ X2 @ (inverse @ X0))
% 37.73/6.02 | (sum @ (multiply @ X0 @ X3) @ X1 @ additive_identity))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl81])).
% 37.73/6.02 thf(zip_derived_cl7674, plain,
% 37.73/6.02 (![X0 : $i]:
% 37.73/6.02 ( (sum @ (multiply @ y @ (inverse @ y)) @ X0 @ additive_identity)
% 37.73/6.02 | ~ (product @ y @ x_inverse_times_y_inverse @ X0))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl7335, zip_derived_cl350])).
% 37.73/6.02 thf(zip_derived_cl134, plain,
% 37.73/6.02 (![X0 : $i]: ((additive_identity) = (multiply @ X0 @ (inverse @ X0)))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl100])).
% 37.73/6.02 thf(zip_derived_cl7689, plain,
% 37.73/6.02 (![X0 : $i]:
% 37.73/6.02 ( (sum @ additive_identity @ X0 @ additive_identity)
% 37.73/6.02 | ~ (product @ y @ x_inverse_times_y_inverse @ X0))),
% 37.73/6.02 inference('demod', [status(thm)], [zip_derived_cl7674, zip_derived_cl134])).
% 37.73/6.02 thf(zip_derived_cl8637, plain,
% 37.73/6.02 ( (sum @ additive_identity @
% 37.73/6.02 (multiply @ x_inverse_times_y_inverse @ y) @ additive_identity)),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl50, zip_derived_cl7689])).
% 37.73/6.02 thf(zip_derived_cl1, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 37.73/6.02 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 37.73/6.02 thf(x_plus_y, conjecture, (~( sum @ x @ y @ x_plus_y ))).
% 37.73/6.02 thf(zf_stmt_1, negated_conjecture, (sum @ x @ y @ x_plus_y),
% 37.73/6.02 inference('cnf.neg', [status(esa)], [x_plus_y])).
% 37.73/6.02 thf(zip_derived_cl22, plain, ( (sum @ x @ y @ x_plus_y)),
% 37.73/6.02 inference('cnf', [status(esa)], [zf_stmt_1])).
% 37.73/6.02 thf(distributivity2, axiom,
% 37.73/6.02 (( ~( product @ X @ Y @ V1 ) ) | ( ~( product @ X @ Z @ V2 ) ) |
% 37.73/6.02 ( ~( sum @ Y @ Z @ V3 ) ) | ( ~( sum @ V1 @ V2 @ V4 ) ) |
% 37.73/6.02 ( product @ X @ V3 @ V4 ))).
% 37.73/6.02 thf(zip_derived_cl9, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 37.73/6.02 (~ (product @ X0 @ X1 @ X2)
% 37.73/6.02 | ~ (product @ X0 @ X3 @ X4)
% 37.73/6.02 | ~ (sum @ X1 @ X3 @ X5)
% 37.73/6.02 | ~ (sum @ X2 @ X4 @ X6)
% 37.73/6.02 | (product @ X0 @ X5 @ X6))),
% 37.73/6.02 inference('cnf', [status(esa)], [distributivity2])).
% 37.73/6.02 thf(zip_derived_cl117, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.73/6.02 ( (product @ X1 @ x_plus_y @ X0)
% 37.73/6.02 | ~ (sum @ X3 @ X2 @ X0)
% 37.73/6.02 | ~ (product @ X1 @ y @ X2)
% 37.73/6.02 | ~ (product @ X1 @ x @ X3))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl9])).
% 37.73/6.02 thf(zip_derived_cl140, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.02 (~ (product @ X0 @ x @ X1)
% 37.73/6.02 | ~ (sum @ X1 @ (multiply @ X0 @ y) @ X2)
% 37.73/6.02 | (product @ X0 @ x_plus_y @ X2))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl117])).
% 37.73/6.02 thf(zip_derived_cl10832, plain,
% 37.73/6.02 (( (product @ x_inverse_times_y_inverse @ x_plus_y @ additive_identity)
% 37.73/6.02 | ~ (product @ x_inverse_times_y_inverse @ x @ additive_identity))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl8637, zip_derived_cl140])).
% 37.73/6.02 thf(zip_derived_cl50, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X1 @ X0))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl3])).
% 37.73/6.02 thf(zip_derived_cl23, plain,
% 37.73/6.02 ( (product @ (inverse @ x) @ (inverse @ y) @ x_inverse_times_y_inverse)),
% 37.73/6.02 inference('cnf', [status(esa)], [zf_stmt_0])).
% 37.73/6.02 thf(zip_derived_cl7215, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.02 (~ (product @ X0 @ X2 @ X1) | (sum @ X0 @ X1 @ X0))),
% 37.73/6.02 inference('demod', [status(thm)], [zip_derived_cl651, zip_derived_cl7135])).
% 37.73/6.02 thf(zip_derived_cl7334, plain,
% 37.73/6.02 ( (sum @ (inverse @ x) @ x_inverse_times_y_inverse @ (inverse @ x))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl7215])).
% 37.73/6.02 thf(zip_derived_cl350, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.73/6.02 (~ (product @ X0 @ X2 @ X1)
% 37.73/6.02 | ~ (sum @ X3 @ X2 @ (inverse @ X0))
% 37.73/6.02 | (sum @ (multiply @ X0 @ X3) @ X1 @ additive_identity))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl81])).
% 37.73/6.02 thf(zip_derived_cl7517, plain,
% 37.73/6.02 (![X0 : $i]:
% 37.73/6.02 ( (sum @ (multiply @ x @ (inverse @ x)) @ X0 @ additive_identity)
% 37.73/6.02 | ~ (product @ x @ x_inverse_times_y_inverse @ X0))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl7334, zip_derived_cl350])).
% 37.73/6.02 thf(zip_derived_cl134, plain,
% 37.73/6.02 (![X0 : $i]: ((additive_identity) = (multiply @ X0 @ (inverse @ X0)))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl100])).
% 37.73/6.02 thf(zip_derived_cl7532, plain,
% 37.73/6.02 (![X0 : $i]:
% 37.73/6.02 ( (sum @ additive_identity @ X0 @ additive_identity)
% 37.73/6.02 | ~ (product @ x @ x_inverse_times_y_inverse @ X0))),
% 37.73/6.02 inference('demod', [status(thm)], [zip_derived_cl7517, zip_derived_cl134])).
% 37.73/6.02 thf(zip_derived_cl8634, plain,
% 37.73/6.02 ( (sum @ additive_identity @
% 37.73/6.02 (multiply @ x_inverse_times_y_inverse @ x) @ additive_identity)),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl50, zip_derived_cl7532])).
% 37.73/6.02 thf(zip_derived_cl45, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]:
% 37.73/6.02 (((X0) = (X1)) | ~ (sum @ additive_identity @ X0 @ X1))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl20])).
% 37.73/6.02 thf(zip_derived_cl10572, plain,
% 37.73/6.02 (((multiply @ x_inverse_times_y_inverse @ x) = (additive_identity))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl8634, zip_derived_cl45])).
% 37.73/6.02 thf(zip_derived_cl1, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 37.73/6.02 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 37.73/6.02 thf(zip_derived_cl10593, plain,
% 37.73/6.02 ( (product @ x_inverse_times_y_inverse @ x @ additive_identity)),
% 37.73/6.02 inference('sup+', [status(thm)], [zip_derived_cl10572, zip_derived_cl1])).
% 37.73/6.02 thf(zip_derived_cl10852, plain,
% 37.73/6.02 ( (product @ x_inverse_times_y_inverse @ x_plus_y @ additive_identity)),
% 37.73/6.02 inference('demod', [status(thm)],
% 37.73/6.02 [zip_derived_cl10832, zip_derived_cl10593])).
% 37.73/6.02 thf(additive_inverse1, axiom,
% 37.73/6.02 (sum @ ( inverse @ X ) @ X @ multiplicative_identity)).
% 37.73/6.02 thf(zip_derived_cl16, plain,
% 37.73/6.02 (![X0 : $i]: (sum @ (inverse @ X0) @ X0 @ multiplicative_identity)),
% 37.73/6.02 inference('cnf', [status(esa)], [additive_inverse1])).
% 37.73/6.02 thf(zip_derived_cl7, plain,
% 37.73/6.02 (![X0 : $i]: (product @ X0 @ multiplicative_identity @ X0)),
% 37.73/6.02 inference('cnf', [status(esa)], [multiplicative_identity2])).
% 37.73/6.02 thf(zip_derived_cl81, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 37.73/6.02 ( (sum @ (multiply @ X1 @ X0) @ X3 @ X2)
% 37.73/6.02 | ~ (product @ X1 @ X4 @ X2)
% 37.73/6.02 | ~ (sum @ X0 @ X5 @ X4)
% 37.73/6.02 | ~ (product @ X1 @ X5 @ X3))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl8])).
% 37.73/6.02 thf(zip_derived_cl349, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.73/6.02 (~ (product @ X0 @ X2 @ X1)
% 37.73/6.02 | ~ (sum @ X3 @ X2 @ multiplicative_identity)
% 37.73/6.02 | (sum @ (multiply @ X0 @ X3) @ X1 @ X0))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl81])).
% 37.73/6.02 thf(zip_derived_cl4923, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.02 ( (sum @ (multiply @ X1 @ (inverse @ X0)) @ X2 @ X1)
% 37.73/6.02 | ~ (product @ X1 @ X0 @ X2))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl349])).
% 37.73/6.02 thf(zip_derived_cl17726, plain,
% 37.73/6.02 ( (sum @ (multiply @ x_inverse_times_y_inverse @ (inverse @ x_plus_y)) @
% 37.73/6.02 additive_identity @ x_inverse_times_y_inverse)),
% 37.73/6.02 inference('sup-', [status(thm)],
% 37.73/6.02 [zip_derived_cl10852, zip_derived_cl4923])).
% 37.73/6.02 thf(zip_derived_cl5, plain,
% 37.73/6.02 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 37.73/6.02 inference('cnf', [status(esa)], [additive_identity2])).
% 37.73/6.02 thf(zip_derived_cl20, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.73/6.02 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 37.73/6.02 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 37.73/6.02 thf(zip_derived_cl43, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]:
% 37.73/6.02 (((X0) = (X1)) | ~ (sum @ X0 @ additive_identity @ X1))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl20])).
% 37.73/6.02 thf(zip_derived_cl17777, plain,
% 37.73/6.02 (((multiply @ x_inverse_times_y_inverse @ (inverse @ x_plus_y))
% 37.73/6.02 = (x_inverse_times_y_inverse))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl17726, zip_derived_cl43])).
% 37.73/6.02 thf(zip_derived_cl50, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X1 @ X0))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl3])).
% 37.73/6.02 thf(zip_derived_cl1, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 37.73/6.02 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 37.73/6.02 thf(zip_derived_cl21, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.73/6.02 (~ (product @ X0 @ X1 @ X2)
% 37.73/6.02 | ~ (product @ X0 @ X1 @ X3)
% 37.73/6.02 | ((X2) = (X3)))),
% 37.73/6.02 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 37.73/6.02 thf(zip_derived_cl98, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.02 (((multiply @ X1 @ X0) = (X2)) | ~ (product @ X1 @ X0 @ X2))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl21])).
% 37.73/6.02 thf(zip_derived_cl297, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl50, zip_derived_cl98])).
% 37.73/6.02 thf(zip_derived_cl1, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 37.73/6.02 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 37.73/6.02 thf(zip_derived_cl7215, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.02 (~ (product @ X0 @ X2 @ X1) | (sum @ X0 @ X1 @ X0))),
% 37.73/6.02 inference('demod', [status(thm)], [zip_derived_cl651, zip_derived_cl7135])).
% 37.73/6.02 thf(zip_derived_cl7321, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (sum @ X1 @ (multiply @ X1 @ X0) @ X1)),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl7215])).
% 37.73/6.02 thf(zip_derived_cl0, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 37.73/6.02 inference('cnf', [status(esa)], [closure_of_addition])).
% 37.73/6.02 thf(commutativity_of_addition, axiom,
% 37.73/6.02 (( ~( sum @ X @ Y @ Z ) ) | ( sum @ Y @ X @ Z ))).
% 37.73/6.02 thf(zip_derived_cl2, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.02 (~ (sum @ X0 @ X1 @ X2) | (sum @ X1 @ X0 @ X2))),
% 37.73/6.02 inference('cnf', [status(esa)], [commutativity_of_addition])).
% 37.73/6.02 thf(zip_derived_cl25, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 37.73/6.02 thf(zip_derived_cl20, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.73/6.02 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 37.73/6.02 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 37.73/6.02 thf(zip_derived_cl42, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.02 (((add @ X1 @ X0) = (X2)) | ~ (sum @ X0 @ X1 @ X2))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl20])).
% 37.73/6.02 thf(zip_derived_cl9306, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: ((add @ (multiply @ X0 @ X1) @ X0) = (X0))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl7321, zip_derived_cl42])).
% 37.73/6.02 thf(zip_derived_cl9504, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: ((add @ (multiply @ X1 @ X0) @ X0) = (X0))),
% 37.73/6.02 inference('sup+', [status(thm)], [zip_derived_cl297, zip_derived_cl9306])).
% 37.73/6.02 thf(zip_derived_cl0, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 37.73/6.02 inference('cnf', [status(esa)], [closure_of_addition])).
% 37.73/6.02 thf(zip_derived_cl9799, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (sum @ (multiply @ X1 @ X0) @ X0 @ X0)),
% 37.73/6.02 inference('sup+', [status(thm)], [zip_derived_cl9504, zip_derived_cl0])).
% 37.73/6.02 thf(zip_derived_cl17815, plain,
% 37.73/6.02 ( (sum @ x_inverse_times_y_inverse @ (inverse @ x_plus_y) @
% 37.73/6.02 (inverse @ x_plus_y))),
% 37.73/6.02 inference('sup+', [status(thm)],
% 37.73/6.02 [zip_derived_cl17777, zip_derived_cl9799])).
% 37.73/6.02 thf(zip_derived_cl19, plain,
% 37.73/6.02 (![X0 : $i]: (product @ X0 @ (inverse @ X0) @ additive_identity)),
% 37.73/6.02 inference('cnf', [status(esa)], [multiplicative_inverse2])).
% 37.73/6.02 thf(zip_derived_cl5, plain,
% 37.73/6.02 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 37.73/6.02 inference('cnf', [status(esa)], [additive_identity2])).
% 37.73/6.02 thf(zip_derived_cl0, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 37.73/6.02 inference('cnf', [status(esa)], [closure_of_addition])).
% 37.73/6.02 thf(zip_derived_cl12, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 37.73/6.02 (~ (sum @ X0 @ X1 @ X2)
% 37.73/6.02 | ~ (sum @ X0 @ X3 @ X4)
% 37.73/6.02 | ~ (product @ X1 @ X3 @ X5)
% 37.73/6.02 | ~ (sum @ X0 @ X5 @ X6)
% 37.73/6.02 | (product @ X2 @ X4 @ X6))),
% 37.73/6.02 inference('cnf', [status(esa)], [distributivity5])).
% 37.73/6.02 thf(zip_derived_cl213, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 37.73/6.02 ( (product @ (add @ X1 @ X0) @ X3 @ X2)
% 37.73/6.02 | ~ (sum @ X1 @ X4 @ X2)
% 37.73/6.02 | ~ (product @ X0 @ X5 @ X4)
% 37.73/6.02 | ~ (sum @ X1 @ X5 @ X3))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl12])).
% 37.73/6.02 thf(zip_derived_cl1867, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.73/6.02 (~ (sum @ X0 @ X2 @ X1)
% 37.73/6.02 | ~ (product @ X3 @ X2 @ additive_identity)
% 37.73/6.02 | (product @ (add @ X0 @ X3) @ X1 @ X0))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl213])).
% 37.73/6.02 thf(zip_derived_cl22083, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.02 ( (product @ (add @ X1 @ X0) @ X2 @ X1)
% 37.73/6.02 | ~ (sum @ X1 @ (inverse @ X0) @ X2))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl1867])).
% 37.73/6.02 thf(zip_derived_cl22299, plain,
% 37.73/6.02 ( (product @ (add @ x_inverse_times_y_inverse @ x_plus_y) @
% 37.73/6.02 (inverse @ x_plus_y) @ x_inverse_times_y_inverse)),
% 37.73/6.02 inference('sup-', [status(thm)],
% 37.73/6.02 [zip_derived_cl17815, zip_derived_cl22083])).
% 37.73/6.02 thf(zip_derived_cl50, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X1 @ X0))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl3])).
% 37.73/6.02 thf(zip_derived_cl21, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.73/6.02 (~ (product @ X0 @ X1 @ X2)
% 37.73/6.02 | ~ (product @ X0 @ X1 @ X3)
% 37.73/6.02 | ((X2) = (X3)))),
% 37.73/6.02 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 37.73/6.02 thf(zip_derived_cl296, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.02 (((multiply @ X1 @ X0) = (X2)) | ~ (product @ X0 @ X1 @ X2))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl50, zip_derived_cl21])).
% 37.73/6.02 thf(zip_derived_cl24611, plain,
% 37.73/6.02 (((multiply @ (inverse @ x_plus_y) @
% 37.73/6.02 (add @ x_inverse_times_y_inverse @ x_plus_y))
% 37.73/6.02 = (x_inverse_times_y_inverse))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl22299, zip_derived_cl296])).
% 37.73/6.02 thf(zip_derived_cl5, plain,
% 37.73/6.02 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 37.73/6.02 inference('cnf', [status(esa)], [additive_identity2])).
% 37.73/6.02 thf(zip_derived_cl5579, plain,
% 37.73/6.02 (![X0 : $i]: ((multiply @ X0 @ additive_identity) = (additive_identity))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl4968, zip_derived_cl45])).
% 37.73/6.02 thf(zip_derived_cl1, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 37.73/6.02 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 37.73/6.02 thf(zip_derived_cl5618, plain,
% 37.73/6.02 (![X0 : $i]: (product @ X0 @ additive_identity @ additive_identity)),
% 37.73/6.02 inference('sup+', [status(thm)], [zip_derived_cl5579, zip_derived_cl1])).
% 37.73/6.02 thf(zip_derived_cl5, plain,
% 37.73/6.02 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 37.73/6.02 inference('cnf', [status(esa)], [additive_identity2])).
% 37.73/6.02 thf(zip_derived_cl22, plain, ( (sum @ x @ y @ x_plus_y)),
% 37.73/6.02 inference('cnf', [status(esa)], [zf_stmt_1])).
% 37.73/6.02 thf(zip_derived_cl2, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.02 (~ (sum @ X0 @ X1 @ X2) | (sum @ X1 @ X0 @ X2))),
% 37.73/6.02 inference('cnf', [status(esa)], [commutativity_of_addition])).
% 37.73/6.02 thf(zip_derived_cl30, plain, ( (sum @ y @ x @ x_plus_y)),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl2])).
% 37.73/6.02 thf(zip_derived_cl12, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 37.73/6.02 (~ (sum @ X0 @ X1 @ X2)
% 37.73/6.02 | ~ (sum @ X0 @ X3 @ X4)
% 37.73/6.02 | ~ (product @ X1 @ X3 @ X5)
% 37.73/6.02 | ~ (sum @ X0 @ X5 @ X6)
% 37.73/6.02 | (product @ X2 @ X4 @ X6))),
% 37.73/6.02 inference('cnf', [status(esa)], [distributivity5])).
% 37.73/6.02 thf(zip_derived_cl220, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.73/6.02 ( (product @ x_plus_y @ X1 @ X0)
% 37.73/6.02 | ~ (sum @ y @ X2 @ X0)
% 37.73/6.02 | ~ (product @ x @ X3 @ X2)
% 37.73/6.02 | ~ (sum @ y @ X3 @ X1))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl12])).
% 37.73/6.02 thf(zip_derived_cl2280, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]:
% 37.73/6.02 (~ (sum @ y @ X1 @ X0)
% 37.73/6.02 | ~ (product @ x @ X1 @ additive_identity)
% 37.73/6.02 | (product @ x_plus_y @ X0 @ y))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl220])).
% 37.73/6.02 thf(zip_derived_cl5837, plain,
% 37.73/6.02 (![X0 : $i]:
% 37.73/6.02 ( (product @ x_plus_y @ X0 @ y) | ~ (sum @ y @ additive_identity @ X0))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl5618, zip_derived_cl2280])).
% 37.73/6.02 thf(zip_derived_cl5984, plain, ( (product @ x_plus_y @ y @ y)),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl5837])).
% 37.73/6.02 thf(zip_derived_cl3, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.02 (~ (product @ X0 @ X1 @ X2) | (product @ X1 @ X0 @ X2))),
% 37.73/6.02 inference('cnf', [status(esa)], [commutativity_of_multiplication])).
% 37.73/6.02 thf(zip_derived_cl5987, plain, ( (product @ y @ x_plus_y @ y)),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl5984, zip_derived_cl3])).
% 37.73/6.02 thf(zip_derived_cl19, plain,
% 37.73/6.02 (![X0 : $i]: (product @ X0 @ (inverse @ X0) @ additive_identity)),
% 37.73/6.02 inference('cnf', [status(esa)], [multiplicative_inverse2])).
% 37.73/6.02 thf(zip_derived_cl0, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 37.73/6.02 inference('cnf', [status(esa)], [closure_of_addition])).
% 37.73/6.02 thf(zip_derived_cl0, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 37.73/6.02 inference('cnf', [status(esa)], [closure_of_addition])).
% 37.73/6.02 thf(zip_derived_cl9, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 37.73/6.02 (~ (product @ X0 @ X1 @ X2)
% 37.73/6.02 | ~ (product @ X0 @ X3 @ X4)
% 37.73/6.02 | ~ (sum @ X1 @ X3 @ X5)
% 37.73/6.02 | ~ (sum @ X2 @ X4 @ X6)
% 37.73/6.02 | (product @ X0 @ X5 @ X6))),
% 37.73/6.02 inference('cnf', [status(esa)], [distributivity2])).
% 37.73/6.02 thf(zip_derived_cl111, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 37.73/6.02 ( (product @ X3 @ (add @ X1 @ X0) @ X2)
% 37.73/6.02 | ~ (sum @ X5 @ X4 @ X2)
% 37.73/6.02 | ~ (product @ X3 @ X0 @ X4)
% 37.73/6.02 | ~ (product @ X3 @ X1 @ X5))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl9])).
% 37.73/6.02 thf(zip_derived_cl718, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 37.73/6.02 (~ (product @ X3 @ X2 @ X1)
% 37.73/6.02 | ~ (product @ X3 @ X4 @ X0)
% 37.73/6.02 | (product @ X3 @ (add @ X2 @ X4) @ (add @ X1 @ X0)))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl111])).
% 37.73/6.02 thf(zip_derived_cl9542, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.02 ( (product @ X0 @ (add @ (inverse @ X0) @ X2) @
% 37.73/6.02 (add @ additive_identity @ X1))
% 37.73/6.02 | ~ (product @ X0 @ X2 @ X1))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl718])).
% 37.73/6.02 thf(zip_derived_cl25, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 37.73/6.02 thf(zip_derived_cl43, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]:
% 37.73/6.02 (((X0) = (X1)) | ~ (sum @ X0 @ additive_identity @ X1))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl20])).
% 37.73/6.02 thf(zip_derived_cl55, plain,
% 37.73/6.02 (![X0 : $i]: ((X0) = (add @ additive_identity @ X0))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl43])).
% 37.73/6.02 thf(zip_derived_cl9569, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.02 ( (product @ X0 @ (add @ (inverse @ X0) @ X2) @ X1)
% 37.73/6.02 | ~ (product @ X0 @ X2 @ X1))),
% 37.73/6.02 inference('demod', [status(thm)], [zip_derived_cl9542, zip_derived_cl55])).
% 37.73/6.02 thf(zip_derived_cl18201, plain,
% 37.73/6.02 ( (product @ y @ (add @ (inverse @ y) @ x_plus_y) @ y)),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl5987, zip_derived_cl9569])).
% 37.73/6.02 thf(zip_derived_cl25, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 37.73/6.02 thf(zip_derived_cl0, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 37.73/6.02 inference('cnf', [status(esa)], [closure_of_addition])).
% 37.73/6.02 thf(zip_derived_cl20, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.73/6.02 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 37.73/6.02 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 37.73/6.02 thf(zip_derived_cl41, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.02 (((add @ X1 @ X0) = (X2)) | ~ (sum @ X1 @ X0 @ X2))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl20])).
% 37.73/6.02 thf(zip_derived_cl189, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: ((add @ X0 @ X1) = (add @ X1 @ X0))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl41])).
% 37.73/6.02 thf(zip_derived_cl18238, plain,
% 37.73/6.02 ( (product @ y @ (add @ x_plus_y @ (inverse @ y)) @ y)),
% 37.73/6.02 inference('demod', [status(thm)],
% 37.73/6.02 [zip_derived_cl18201, zip_derived_cl189])).
% 37.73/6.02 thf(zip_derived_cl0, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 37.73/6.02 inference('cnf', [status(esa)], [closure_of_addition])).
% 37.73/6.02 thf(zip_derived_cl16, plain,
% 37.73/6.02 (![X0 : $i]: (sum @ (inverse @ X0) @ X0 @ multiplicative_identity)),
% 37.73/6.02 inference('cnf', [status(esa)], [additive_inverse1])).
% 37.73/6.02 thf(zip_derived_cl16, plain,
% 37.73/6.02 (![X0 : $i]: (sum @ (inverse @ X0) @ X0 @ multiplicative_identity)),
% 37.73/6.02 inference('cnf', [status(esa)], [additive_inverse1])).
% 37.73/6.02 thf(zip_derived_cl12, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 37.73/6.02 (~ (sum @ X0 @ X1 @ X2)
% 37.73/6.02 | ~ (sum @ X0 @ X3 @ X4)
% 37.73/6.02 | ~ (product @ X1 @ X3 @ X5)
% 37.73/6.02 | ~ (sum @ X0 @ X5 @ X6)
% 37.73/6.02 | (product @ X2 @ X4 @ X6))),
% 37.73/6.02 inference('cnf', [status(esa)], [distributivity5])).
% 37.73/6.02 thf(zip_derived_cl218, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 37.73/6.02 ( (product @ multiplicative_identity @ X2 @ X1)
% 37.73/6.02 | ~ (sum @ (inverse @ X0) @ X3 @ X1)
% 37.73/6.02 | ~ (product @ X0 @ X4 @ X3)
% 37.73/6.02 | ~ (sum @ (inverse @ X0) @ X4 @ X2))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl12])).
% 37.73/6.02 thf(zip_derived_cl2154, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.02 (~ (sum @ (inverse @ X0) @ X2 @ X1)
% 37.73/6.02 | ~ (product @ X0 @ X2 @ X0)
% 37.73/6.02 | (product @ multiplicative_identity @ X1 @ multiplicative_identity))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl218])).
% 37.73/6.02 thf(zip_derived_cl17379, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]:
% 37.73/6.02 ( (product @ multiplicative_identity @ (add @ (inverse @ X1) @ X0) @
% 37.73/6.02 multiplicative_identity)
% 37.73/6.02 | ~ (product @ X1 @ X0 @ X1))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl2154])).
% 37.73/6.02 thf(zip_derived_cl37688, plain,
% 37.73/6.02 ( (product @ multiplicative_identity @
% 37.73/6.02 (add @ (inverse @ y) @ (add @ x_plus_y @ (inverse @ y))) @
% 37.73/6.02 multiplicative_identity)),
% 37.73/6.02 inference('sup-', [status(thm)],
% 37.73/6.02 [zip_derived_cl18238, zip_derived_cl17379])).
% 37.73/6.02 thf(zip_derived_cl189, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: ((add @ X0 @ X1) = (add @ X1 @ X0))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl41])).
% 37.73/6.02 thf(zip_derived_cl6098, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (product @ X1 @ (add @ X1 @ X0) @ X1)),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl5848])).
% 37.73/6.02 thf(zip_derived_cl296, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.02 (((multiply @ X1 @ X0) = (X2)) | ~ (product @ X0 @ X1 @ X2))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl50, zip_derived_cl21])).
% 37.73/6.02 thf(zip_derived_cl7020, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: ((multiply @ (add @ X0 @ X1) @ X0) = (X0))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl6098, zip_derived_cl296])).
% 37.73/6.02 thf(zip_derived_cl9306, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: ((add @ (multiply @ X0 @ X1) @ X0) = (X0))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl7321, zip_derived_cl42])).
% 37.73/6.02 thf(zip_derived_cl9512, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: ((add @ X0 @ (add @ X0 @ X1)) = (add @ X0 @ X1))),
% 37.73/6.02 inference('sup+', [status(thm)], [zip_derived_cl7020, zip_derived_cl9306])).
% 37.73/6.02 thf(zip_derived_cl12207, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: ((add @ X0 @ (add @ X1 @ X0)) = (add @ X0 @ X1))),
% 37.73/6.02 inference('sup+', [status(thm)], [zip_derived_cl189, zip_derived_cl9512])).
% 37.73/6.02 thf(zip_derived_cl189, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: ((add @ X0 @ X1) = (add @ X1 @ X0))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl41])).
% 37.73/6.02 thf(zip_derived_cl37708, plain,
% 37.73/6.02 ( (product @ multiplicative_identity @
% 37.73/6.02 (add @ x_plus_y @ (inverse @ y)) @ multiplicative_identity)),
% 37.73/6.02 inference('demod', [status(thm)],
% 37.73/6.02 [zip_derived_cl37688, zip_derived_cl12207, zip_derived_cl189])).
% 37.73/6.02 thf(zip_derived_cl0, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 37.73/6.02 inference('cnf', [status(esa)], [closure_of_addition])).
% 37.73/6.02 thf(zip_derived_cl23, plain,
% 37.73/6.02 ( (product @ (inverse @ x) @ (inverse @ y) @ x_inverse_times_y_inverse)),
% 37.73/6.02 inference('cnf', [status(esa)], [zf_stmt_0])).
% 37.73/6.02 thf(distributivity6, axiom,
% 37.73/6.02 (( ~( sum @ X @ Y @ V1 ) ) | ( ~( sum @ X @ Z @ V2 ) ) |
% 37.73/6.02 ( ~( product @ Y @ Z @ V3 ) ) | ( ~( product @ V1 @ V2 @ V4 ) ) |
% 37.73/6.02 ( sum @ X @ V3 @ V4 ))).
% 37.73/6.02 thf(zip_derived_cl13, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 37.73/6.02 (~ (sum @ X0 @ X1 @ X2)
% 37.73/6.02 | ~ (sum @ X0 @ X3 @ X4)
% 37.73/6.02 | ~ (product @ X1 @ X3 @ X5)
% 37.73/6.02 | ~ (product @ X2 @ X4 @ X6)
% 37.73/6.02 | (sum @ X0 @ X5 @ X6))),
% 37.73/6.02 inference('cnf', [status(esa)], [distributivity6])).
% 37.73/6.02 thf(zip_derived_cl245, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.73/6.02 ( (sum @ X1 @ x_inverse_times_y_inverse @ X0)
% 37.73/6.02 | ~ (product @ X3 @ X2 @ X0)
% 37.73/6.02 | ~ (sum @ X1 @ (inverse @ y) @ X2)
% 37.73/6.02 | ~ (sum @ X1 @ (inverse @ x) @ X3))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl13])).
% 37.73/6.02 thf(zip_derived_cl2878, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.02 (~ (sum @ X0 @ (inverse @ x) @ X1)
% 37.73/6.02 | ~ (product @ X1 @ (add @ X0 @ (inverse @ y)) @ X2)
% 37.73/6.02 | (sum @ X0 @ x_inverse_times_y_inverse @ X2))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl245])).
% 37.73/6.02 thf(zip_derived_cl39129, plain,
% 37.73/6.02 (( (sum @ x_plus_y @ x_inverse_times_y_inverse @ multiplicative_identity)
% 37.73/6.02 | ~ (sum @ x_plus_y @ (inverse @ x) @ multiplicative_identity))),
% 37.73/6.02 inference('sup-', [status(thm)],
% 37.73/6.02 [zip_derived_cl37708, zip_derived_cl2878])).
% 37.73/6.02 thf(zip_derived_cl22, plain, ( (sum @ x @ y @ x_plus_y)),
% 37.73/6.02 inference('cnf', [status(esa)], [zf_stmt_1])).
% 37.73/6.02 thf(zip_derived_cl5848, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.02 (~ (sum @ X0 @ X2 @ X1) | (product @ X0 @ X1 @ X0))),
% 37.73/6.02 inference('demod', [status(thm)],
% 37.73/6.02 [zip_derived_cl2392, zip_derived_cl5620])).
% 37.73/6.02 thf(zip_derived_cl6114, plain, ( (product @ x @ x_plus_y @ x)),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl5848])).
% 37.73/6.02 thf(zip_derived_cl9569, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.02 ( (product @ X0 @ (add @ (inverse @ X0) @ X2) @ X1)
% 37.73/6.02 | ~ (product @ X0 @ X2 @ X1))),
% 37.73/6.02 inference('demod', [status(thm)], [zip_derived_cl9542, zip_derived_cl55])).
% 37.73/6.02 thf(zip_derived_cl18199, plain,
% 37.73/6.02 ( (product @ x @ (add @ (inverse @ x) @ x_plus_y) @ x)),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl6114, zip_derived_cl9569])).
% 37.73/6.02 thf(zip_derived_cl189, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: ((add @ X0 @ X1) = (add @ X1 @ X0))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl41])).
% 37.73/6.02 thf(zip_derived_cl18236, plain,
% 37.73/6.02 ( (product @ x @ (add @ x_plus_y @ (inverse @ x)) @ x)),
% 37.73/6.02 inference('demod', [status(thm)],
% 37.73/6.02 [zip_derived_cl18199, zip_derived_cl189])).
% 37.73/6.02 thf(zip_derived_cl17379, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]:
% 37.73/6.02 ( (product @ multiplicative_identity @ (add @ (inverse @ X1) @ X0) @
% 37.73/6.02 multiplicative_identity)
% 37.73/6.02 | ~ (product @ X1 @ X0 @ X1))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl2154])).
% 37.73/6.02 thf(zip_derived_cl37685, plain,
% 37.73/6.02 ( (product @ multiplicative_identity @
% 37.73/6.02 (add @ (inverse @ x) @ (add @ x_plus_y @ (inverse @ x))) @
% 37.73/6.02 multiplicative_identity)),
% 37.73/6.02 inference('sup-', [status(thm)],
% 37.73/6.02 [zip_derived_cl18236, zip_derived_cl17379])).
% 37.73/6.02 thf(zip_derived_cl12207, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: ((add @ X0 @ (add @ X1 @ X0)) = (add @ X0 @ X1))),
% 37.73/6.02 inference('sup+', [status(thm)], [zip_derived_cl189, zip_derived_cl9512])).
% 37.73/6.02 thf(zip_derived_cl189, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: ((add @ X0 @ X1) = (add @ X1 @ X0))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl41])).
% 37.73/6.02 thf(zip_derived_cl37705, plain,
% 37.73/6.02 ( (product @ multiplicative_identity @
% 37.73/6.02 (add @ x_plus_y @ (inverse @ x)) @ multiplicative_identity)),
% 37.73/6.02 inference('demod', [status(thm)],
% 37.73/6.02 [zip_derived_cl37685, zip_derived_cl12207, zip_derived_cl189])).
% 37.73/6.02 thf(zip_derived_cl101, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]:
% 37.73/6.02 (((X0) = (X1)) | ~ (product @ multiplicative_identity @ X0 @ X1))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl21])).
% 37.73/6.02 thf(zip_derived_cl38407, plain,
% 37.73/6.02 (((add @ x_plus_y @ (inverse @ x)) = (multiplicative_identity))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl37705, zip_derived_cl101])).
% 37.73/6.02 thf(zip_derived_cl0, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 37.73/6.02 inference('cnf', [status(esa)], [closure_of_addition])).
% 37.73/6.02 thf(zip_derived_cl38511, plain,
% 37.73/6.02 ( (sum @ x_plus_y @ (inverse @ x) @ multiplicative_identity)),
% 37.73/6.02 inference('sup+', [status(thm)], [zip_derived_cl38407, zip_derived_cl0])).
% 37.73/6.02 thf(zip_derived_cl39185, plain,
% 37.73/6.02 ( (sum @ x_plus_y @ x_inverse_times_y_inverse @ multiplicative_identity)),
% 37.73/6.02 inference('demod', [status(thm)],
% 37.73/6.02 [zip_derived_cl39129, zip_derived_cl38511])).
% 37.73/6.02 thf(zip_derived_cl42, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.02 (((add @ X1 @ X0) = (X2)) | ~ (sum @ X0 @ X1 @ X2))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl20])).
% 37.73/6.02 thf(zip_derived_cl39195, plain,
% 37.73/6.02 (((add @ x_inverse_times_y_inverse @ x_plus_y)
% 37.73/6.02 = (multiplicative_identity))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl39185, zip_derived_cl42])).
% 37.73/6.02 thf(zip_derived_cl1, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 37.73/6.02 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 37.73/6.02 thf(zip_derived_cl7, plain,
% 37.73/6.02 (![X0 : $i]: (product @ X0 @ multiplicative_identity @ X0)),
% 37.73/6.02 inference('cnf', [status(esa)], [multiplicative_identity2])).
% 37.73/6.02 thf(zip_derived_cl21, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.73/6.02 (~ (product @ X0 @ X1 @ X2)
% 37.73/6.02 | ~ (product @ X0 @ X1 @ X3)
% 37.73/6.02 | ((X2) = (X3)))),
% 37.73/6.02 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 37.73/6.02 thf(zip_derived_cl99, plain,
% 37.73/6.02 (![X0 : $i, X1 : $i]:
% 37.73/6.02 (((X0) = (X1)) | ~ (product @ X0 @ multiplicative_identity @ X1))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl21])).
% 37.73/6.02 thf(zip_derived_cl120, plain,
% 37.73/6.02 (![X0 : $i]: ((X0) = (multiply @ X0 @ multiplicative_identity))),
% 37.73/6.02 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl99])).
% 37.73/6.02 thf(zip_derived_cl39375, plain,
% 37.73/6.02 (((inverse @ x_plus_y) = (x_inverse_times_y_inverse))),
% 37.73/6.02 inference('demod', [status(thm)],
% 37.73/6.02 [zip_derived_cl24611, zip_derived_cl39195, zip_derived_cl120])).
% 37.73/6.02 thf(prove_equation, conjecture,
% 37.73/6.02 (( inverse @ x_plus_y ) = ( x_inverse_times_y_inverse ))).
% 37.73/6.02 thf(zf_stmt_2, negated_conjecture,
% 37.73/6.02 (( inverse @ x_plus_y ) != ( x_inverse_times_y_inverse )),
% 37.73/6.02 inference('cnf.neg', [status(esa)], [prove_equation])).
% 37.73/6.02 thf(zip_derived_cl24, plain,
% 37.73/6.02 (((inverse @ x_plus_y) != (x_inverse_times_y_inverse))),
% 37.73/6.02 inference('cnf', [status(esa)], [zf_stmt_2])).
% 37.73/6.02 thf(zip_derived_cl39376, plain, ($false),
% 37.73/6.02 inference('simplify_reflect-', [status(thm)],
% 37.73/6.02 [zip_derived_cl39375, zip_derived_cl24])).
% 37.73/6.02
% 37.73/6.02 % SZS output end Refutation
% 37.73/6.02
% 37.73/6.02
% 37.73/6.02 % Terminating...
% 37.75/6.09 % Runner terminated.
% 37.76/6.10 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------