TSTP Solution File: BOO015-1 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : BOO015-1 : 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.yEoEJaXZE4 true
% Computer : n007.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 34.76s 5.63s
% Output : Refutation 34.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : BOO015-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.12/0.15 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.yEoEJaXZE4 true
% 0.16/0.37 % Computer : n007.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Sun Aug 27 07:57:27 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.16/0.37 % Running portfolio for 300 s
% 0.16/0.37 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.37 % Number of cores: 8
% 0.16/0.38 % Python version: Python 3.6.8
% 0.16/0.38 % Running in FO mode
% 0.23/0.64 % Total configuration time : 435
% 0.23/0.64 % Estimated wc time : 1092
% 0.23/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.23/0.72 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.23/0.73 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 1.27/0.76 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 1.27/0.76 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 1.27/0.76 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 1.27/0.77 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 1.27/0.77 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 34.76/5.63 % Solved by fo/fo5.sh.
% 34.76/5.63 % done 9146 iterations in 4.824s
% 34.76/5.63 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 34.76/5.63 % SZS output start Refutation
% 34.76/5.63 thf(sum_type, type, sum: $i > $i > $i > $o).
% 34.76/5.63 thf(x_inverse_plus_y_inverse_type, type, x_inverse_plus_y_inverse: $i).
% 34.76/5.63 thf(y_type, type, y: $i).
% 34.76/5.63 thf(x_times_y_type, type, x_times_y: $i).
% 34.76/5.63 thf(multiplicative_identity_type, type, multiplicative_identity: $i).
% 34.76/5.63 thf(inverse_type, type, inverse: $i > $i).
% 34.76/5.63 thf(x_type, type, x: $i).
% 34.76/5.63 thf(multiply_type, type, multiply: $i > $i > $i).
% 34.76/5.63 thf(product_type, type, product: $i > $i > $i > $o).
% 34.76/5.63 thf(add_type, type, add: $i > $i > $i).
% 34.76/5.63 thf(additive_identity_type, type, additive_identity: $i).
% 34.76/5.63 thf(x_times_y, conjecture, (~( product @ x @ y @ x_times_y ))).
% 34.76/5.63 thf(zf_stmt_0, negated_conjecture, (product @ x @ y @ x_times_y),
% 34.76/5.63 inference('cnf.neg', [status(esa)], [x_times_y])).
% 34.76/5.63 thf(zip_derived_cl22, plain, ( (product @ x @ y @ x_times_y)),
% 34.76/5.63 inference('cnf', [status(esa)], [zf_stmt_0])).
% 34.76/5.63 thf(commutativity_of_multiplication, axiom,
% 34.76/5.63 (( ~( product @ X @ Y @ Z ) ) | ( product @ Y @ X @ Z ))).
% 34.76/5.63 thf(zip_derived_cl3, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.76/5.63 (~ (product @ X0 @ X1 @ X2) | (product @ X1 @ X0 @ X2))),
% 34.76/5.63 inference('cnf', [status(esa)], [commutativity_of_multiplication])).
% 34.76/5.63 thf(zip_derived_cl38, plain, ( (product @ y @ x @ x_times_y)),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl3])).
% 34.76/5.63 thf(multiplicative_identity2, axiom,
% 34.76/5.63 (product @ X @ multiplicative_identity @ X)).
% 34.76/5.63 thf(zip_derived_cl7, plain,
% 34.76/5.63 (![X0 : $i]: (product @ X0 @ multiplicative_identity @ X0)),
% 34.76/5.63 inference('cnf', [status(esa)], [multiplicative_identity2])).
% 34.76/5.63 thf(distributivity1, axiom,
% 34.76/5.63 (( ~( product @ X @ Y @ V1 ) ) | ( ~( product @ X @ Z @ V2 ) ) |
% 34.76/5.63 ( ~( sum @ Y @ Z @ V3 ) ) | ( ~( product @ X @ V3 @ V4 ) ) |
% 34.76/5.63 ( sum @ V1 @ V2 @ V4 ))).
% 34.76/5.63 thf(zip_derived_cl8, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 34.76/5.63 (~ (product @ X0 @ X1 @ X2)
% 34.76/5.63 | ~ (product @ X0 @ X3 @ X4)
% 34.76/5.63 | ~ (sum @ X1 @ X3 @ X5)
% 34.76/5.63 | ~ (product @ X0 @ X5 @ X6)
% 34.76/5.63 | (sum @ X2 @ X4 @ X6))),
% 34.76/5.63 inference('cnf', [status(esa)], [distributivity1])).
% 34.76/5.63 thf(zip_derived_cl92, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 34.76/5.63 ( (sum @ X0 @ X3 @ X0)
% 34.76/5.63 | ~ (product @ X2 @ X1 @ X0)
% 34.76/5.63 | ~ (sum @ X1 @ X4 @ X1)
% 34.76/5.63 | ~ (product @ X2 @ X4 @ X3))),
% 34.76/5.63 inference('eq_fact', [status(thm)], [zip_derived_cl8])).
% 34.76/5.63 thf(zip_derived_cl564, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.76/5.63 (~ (product @ X0 @ X2 @ X1)
% 34.76/5.63 | ~ (sum @ multiplicative_identity @ X2 @ multiplicative_identity)
% 34.76/5.63 | (sum @ X0 @ X1 @ X0))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl92])).
% 34.76/5.63 thf(closure_of_addition, axiom, (sum @ X @ Y @ ( add @ X @ Y ))).
% 34.76/5.63 thf(zip_derived_cl0, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 34.76/5.63 inference('cnf', [status(esa)], [closure_of_addition])).
% 34.76/5.63 thf(additive_identity2, axiom, (sum @ X @ additive_identity @ X)).
% 34.76/5.63 thf(zip_derived_cl5, plain,
% 34.76/5.63 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 34.76/5.63 inference('cnf', [status(esa)], [additive_identity2])).
% 34.76/5.63 thf(distributivity5, axiom,
% 34.76/5.63 (( ~( sum @ X @ Y @ V1 ) ) | ( ~( sum @ X @ Z @ V2 ) ) |
% 34.76/5.63 ( ~( product @ Y @ Z @ V3 ) ) | ( ~( sum @ X @ V3 @ V4 ) ) |
% 34.76/5.63 ( product @ V1 @ V2 @ V4 ))).
% 34.76/5.63 thf(zip_derived_cl12, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 34.76/5.63 (~ (sum @ X0 @ X1 @ X2)
% 34.76/5.63 | ~ (sum @ X0 @ X3 @ X4)
% 34.76/5.63 | ~ (product @ X1 @ X3 @ X5)
% 34.76/5.63 | ~ (sum @ X0 @ X5 @ X6)
% 34.76/5.63 | (product @ X2 @ X4 @ X6))),
% 34.76/5.63 inference('cnf', [status(esa)], [distributivity5])).
% 34.76/5.63 thf(zip_derived_cl226, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 34.76/5.63 ( (product @ X0 @ X3 @ X0)
% 34.76/5.63 | ~ (sum @ X2 @ X1 @ X0)
% 34.76/5.63 | ~ (product @ X1 @ X4 @ X1)
% 34.76/5.63 | ~ (sum @ X2 @ X4 @ X3))),
% 34.76/5.63 inference('eq_fact', [status(thm)], [zip_derived_cl12])).
% 34.76/5.63 thf(zip_derived_cl2916, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.76/5.63 (~ (sum @ X0 @ X2 @ X1)
% 34.76/5.63 | ~ (product @ additive_identity @ X2 @ additive_identity)
% 34.76/5.63 | (product @ X0 @ X1 @ X0))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl226])).
% 34.76/5.63 thf(closure_of_multiplication, axiom,
% 34.76/5.63 (product @ X @ Y @ ( multiply @ X @ Y ))).
% 34.76/5.63 thf(zip_derived_cl1, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 34.76/5.63 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 34.76/5.63 thf(zip_derived_cl5, plain,
% 34.76/5.63 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 34.76/5.63 inference('cnf', [status(esa)], [additive_identity2])).
% 34.76/5.63 thf(multiplicative_inverse2, axiom,
% 34.76/5.63 (product @ X @ ( inverse @ X ) @ additive_identity)).
% 34.76/5.63 thf(zip_derived_cl19, plain,
% 34.76/5.63 (![X0 : $i]: (product @ X0 @ (inverse @ X0) @ additive_identity)),
% 34.76/5.63 inference('cnf', [status(esa)], [multiplicative_inverse2])).
% 34.76/5.63 thf(zip_derived_cl1, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 34.76/5.63 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 34.76/5.63 thf(zip_derived_cl8, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 34.76/5.63 (~ (product @ X0 @ X1 @ X2)
% 34.76/5.63 | ~ (product @ X0 @ X3 @ X4)
% 34.76/5.63 | ~ (sum @ X1 @ X3 @ X5)
% 34.76/5.63 | ~ (product @ X0 @ X5 @ X6)
% 34.76/5.63 | (sum @ X2 @ X4 @ X6))),
% 34.76/5.63 inference('cnf', [status(esa)], [distributivity1])).
% 34.76/5.63 thf(zip_derived_cl84, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 34.76/5.63 ( (sum @ (multiply @ X1 @ X0) @ X3 @ X2)
% 34.76/5.63 | ~ (product @ X1 @ X4 @ X2)
% 34.76/5.63 | ~ (sum @ X0 @ X5 @ X4)
% 34.76/5.63 | ~ (product @ X1 @ X5 @ X3))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl8])).
% 34.76/5.63 thf(zip_derived_cl344, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.76/5.63 (~ (product @ X0 @ X2 @ X1)
% 34.76/5.63 | ~ (sum @ X3 @ X2 @ (inverse @ X0))
% 34.76/5.63 | (sum @ (multiply @ X0 @ X3) @ X1 @ additive_identity))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl84])).
% 34.76/5.63 thf(zip_derived_cl5128, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]:
% 34.76/5.63 ( (sum @ (multiply @ X0 @ (inverse @ X0)) @ X1 @ additive_identity)
% 34.76/5.63 | ~ (product @ X0 @ additive_identity @ X1))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl344])).
% 34.76/5.63 thf(zip_derived_cl1, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 34.76/5.63 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 34.76/5.63 thf(zip_derived_cl19, plain,
% 34.76/5.63 (![X0 : $i]: (product @ X0 @ (inverse @ X0) @ additive_identity)),
% 34.76/5.63 inference('cnf', [status(esa)], [multiplicative_inverse2])).
% 34.76/5.63 thf(multiplication_is_well_defined, axiom,
% 34.76/5.63 (( ~( product @ X @ Y @ U ) ) | ( ~( product @ X @ Y @ V ) ) |
% 34.76/5.63 ( ( U ) = ( V ) ))).
% 34.76/5.63 thf(zip_derived_cl21, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.76/5.63 (~ (product @ X0 @ X1 @ X2)
% 34.76/5.63 | ~ (product @ X0 @ X1 @ X3)
% 34.76/5.63 | ((X2) = (X3)))),
% 34.76/5.63 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 34.76/5.63 thf(zip_derived_cl100, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]:
% 34.76/5.63 (((additive_identity) = (X1)) | ~ (product @ X0 @ (inverse @ X0) @ X1))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl21])).
% 34.76/5.63 thf(zip_derived_cl134, plain,
% 34.76/5.63 (![X0 : $i]: ((additive_identity) = (multiply @ X0 @ (inverse @ X0)))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl100])).
% 34.76/5.63 thf(zip_derived_cl5137, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]:
% 34.76/5.63 ( (sum @ additive_identity @ X1 @ additive_identity)
% 34.76/5.63 | ~ (product @ X0 @ additive_identity @ X1))),
% 34.76/5.63 inference('demod', [status(thm)], [zip_derived_cl5128, zip_derived_cl134])).
% 34.76/5.63 thf(zip_derived_cl5255, plain,
% 34.76/5.63 (![X0 : $i]:
% 34.76/5.63 (sum @ additive_identity @ (multiply @ X0 @ additive_identity) @
% 34.76/5.63 additive_identity)),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl5137])).
% 34.76/5.63 thf(additive_identity1, axiom, (sum @ additive_identity @ X @ X)).
% 34.76/5.63 thf(zip_derived_cl4, plain,
% 34.76/5.63 (![X0 : $i]: (sum @ additive_identity @ X0 @ X0)),
% 34.76/5.63 inference('cnf', [status(esa)], [additive_identity1])).
% 34.76/5.63 thf(addition_is_well_defined, axiom,
% 34.76/5.63 (( ~( sum @ X @ Y @ U ) ) | ( ~( sum @ X @ Y @ V ) ) | ( ( U ) = ( V ) ))).
% 34.76/5.63 thf(zip_derived_cl20, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.76/5.63 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 34.76/5.63 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 34.76/5.63 thf(zip_derived_cl45, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]:
% 34.76/5.63 (((X0) = (X1)) | ~ (sum @ additive_identity @ X0 @ X1))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl20])).
% 34.76/5.63 thf(zip_derived_cl5292, plain,
% 34.76/5.63 (![X0 : $i]: ((multiply @ X0 @ additive_identity) = (additive_identity))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl5255, zip_derived_cl45])).
% 34.76/5.63 thf(zip_derived_cl1, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 34.76/5.63 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 34.76/5.63 thf(zip_derived_cl3, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.76/5.63 (~ (product @ X0 @ X1 @ X2) | (product @ X1 @ X0 @ X2))),
% 34.76/5.63 inference('cnf', [status(esa)], [commutativity_of_multiplication])).
% 34.76/5.63 thf(zip_derived_cl50, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X1 @ X0))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl3])).
% 34.76/5.63 thf(zip_derived_cl5380, plain,
% 34.76/5.63 (![X0 : $i]: (product @ additive_identity @ X0 @ additive_identity)),
% 34.76/5.63 inference('sup+', [status(thm)], [zip_derived_cl5292, zip_derived_cl50])).
% 34.76/5.63 thf(zip_derived_cl5550, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.76/5.63 (~ (sum @ X0 @ X2 @ X1) | (product @ X0 @ X1 @ X0))),
% 34.76/5.63 inference('demod', [status(thm)],
% 34.76/5.63 [zip_derived_cl2916, zip_derived_cl5380])).
% 34.76/5.63 thf(zip_derived_cl5659, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (product @ X1 @ (add @ X1 @ X0) @ X1)),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl5550])).
% 34.76/5.63 thf(multiplicative_identity1, axiom,
% 34.76/5.63 (product @ multiplicative_identity @ X @ X)).
% 34.76/5.63 thf(zip_derived_cl6, plain,
% 34.76/5.63 (![X0 : $i]: (product @ multiplicative_identity @ X0 @ X0)),
% 34.76/5.63 inference('cnf', [status(esa)], [multiplicative_identity1])).
% 34.76/5.63 thf(zip_derived_cl21, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.76/5.63 (~ (product @ X0 @ X1 @ X2)
% 34.76/5.63 | ~ (product @ X0 @ X1 @ X3)
% 34.76/5.63 | ((X2) = (X3)))),
% 34.76/5.63 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 34.76/5.63 thf(zip_derived_cl101, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]:
% 34.76/5.63 (((X0) = (X1)) | ~ (product @ multiplicative_identity @ X0 @ X1))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl21])).
% 34.76/5.63 thf(zip_derived_cl6671, plain,
% 34.76/5.63 (![X0 : $i]:
% 34.76/5.63 ((add @ multiplicative_identity @ X0) = (multiplicative_identity))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl5659, zip_derived_cl101])).
% 34.76/5.63 thf(zip_derived_cl0, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 34.76/5.63 inference('cnf', [status(esa)], [closure_of_addition])).
% 34.76/5.63 thf(zip_derived_cl6758, plain,
% 34.76/5.63 (![X0 : $i]:
% 34.76/5.63 (sum @ multiplicative_identity @ X0 @ multiplicative_identity)),
% 34.76/5.63 inference('sup+', [status(thm)], [zip_derived_cl6671, zip_derived_cl0])).
% 34.76/5.63 thf(zip_derived_cl6952, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.76/5.63 (~ (product @ X0 @ X2 @ X1) | (sum @ X0 @ X1 @ X0))),
% 34.76/5.63 inference('demod', [status(thm)], [zip_derived_cl564, zip_derived_cl6758])).
% 34.76/5.63 thf(zip_derived_cl7088, plain, ( (sum @ y @ x_times_y @ y)),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl6952])).
% 34.76/5.63 thf(zip_derived_cl1, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 34.76/5.63 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 34.76/5.63 thf(multiplicative_inverse1, axiom,
% 34.76/5.63 (product @ ( inverse @ X ) @ X @ additive_identity)).
% 34.76/5.63 thf(zip_derived_cl18, plain,
% 34.76/5.63 (![X0 : $i]: (product @ (inverse @ X0) @ X0 @ additive_identity)),
% 34.76/5.63 inference('cnf', [status(esa)], [multiplicative_inverse1])).
% 34.76/5.63 thf(zip_derived_cl18, plain,
% 34.76/5.63 (![X0 : $i]: (product @ (inverse @ X0) @ X0 @ additive_identity)),
% 34.76/5.63 inference('cnf', [status(esa)], [multiplicative_inverse1])).
% 34.76/5.63 thf(zip_derived_cl8, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 34.76/5.63 (~ (product @ X0 @ X1 @ X2)
% 34.76/5.63 | ~ (product @ X0 @ X3 @ X4)
% 34.76/5.63 | ~ (sum @ X1 @ X3 @ X5)
% 34.76/5.63 | ~ (product @ X0 @ X5 @ X6)
% 34.76/5.63 | (sum @ X2 @ X4 @ X6))),
% 34.76/5.63 inference('cnf', [status(esa)], [distributivity1])).
% 34.76/5.63 thf(zip_derived_cl88, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 34.76/5.63 ( (sum @ additive_identity @ X2 @ X1)
% 34.76/5.63 | ~ (product @ (inverse @ X0) @ X3 @ X1)
% 34.76/5.63 | ~ (sum @ X0 @ X4 @ X3)
% 34.76/5.63 | ~ (product @ (inverse @ X0) @ X4 @ X2))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl8])).
% 34.76/5.63 thf(zip_derived_cl491, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.76/5.63 (~ (product @ (inverse @ X0) @ X2 @ X1)
% 34.76/5.63 | ~ (sum @ X0 @ X2 @ X0)
% 34.76/5.63 | (sum @ additive_identity @ X1 @ additive_identity))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl88])).
% 34.76/5.63 thf(zip_derived_cl2049, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]:
% 34.76/5.63 ( (sum @ additive_identity @ (multiply @ (inverse @ X1) @ X0) @
% 34.76/5.63 additive_identity)
% 34.76/5.63 | ~ (sum @ X1 @ X0 @ X1))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl491])).
% 34.76/5.63 thf(zip_derived_cl22350, plain,
% 34.76/5.63 ( (sum @ additive_identity @ (multiply @ (inverse @ y) @ x_times_y) @
% 34.76/5.63 additive_identity)),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl7088, zip_derived_cl2049])).
% 34.76/5.63 thf(zip_derived_cl50, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X1 @ X0))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl3])).
% 34.76/5.63 thf(zip_derived_cl1, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 34.76/5.63 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 34.76/5.63 thf(zip_derived_cl21, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.76/5.63 (~ (product @ X0 @ X1 @ X2)
% 34.76/5.63 | ~ (product @ X0 @ X1 @ X3)
% 34.76/5.63 | ((X2) = (X3)))),
% 34.76/5.63 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 34.76/5.63 thf(zip_derived_cl98, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.76/5.63 (((multiply @ X1 @ X0) = (X2)) | ~ (product @ X1 @ X0 @ X2))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl21])).
% 34.76/5.63 thf(zip_derived_cl305, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl50, zip_derived_cl98])).
% 34.76/5.63 thf(zip_derived_cl22360, plain,
% 34.76/5.63 ( (sum @ additive_identity @ (multiply @ x_times_y @ (inverse @ y)) @
% 34.76/5.63 additive_identity)),
% 34.76/5.63 inference('demod', [status(thm)],
% 34.76/5.63 [zip_derived_cl22350, zip_derived_cl305])).
% 34.76/5.63 thf(zip_derived_cl1, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 34.76/5.63 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 34.76/5.63 thf(x_inverse_plus_y_inverse, conjecture,
% 34.76/5.63 (~( sum @ ( inverse @ x ) @ ( inverse @ y ) @ x_inverse_plus_y_inverse ))).
% 34.76/5.63 thf(zf_stmt_1, negated_conjecture,
% 34.76/5.63 (sum @ ( inverse @ x ) @ ( inverse @ y ) @ x_inverse_plus_y_inverse),
% 34.76/5.63 inference('cnf.neg', [status(esa)], [x_inverse_plus_y_inverse])).
% 34.76/5.63 thf(zip_derived_cl23, plain,
% 34.76/5.63 ( (sum @ (inverse @ x) @ (inverse @ y) @ x_inverse_plus_y_inverse)),
% 34.76/5.63 inference('cnf', [status(esa)], [zf_stmt_1])).
% 34.76/5.63 thf(distributivity2, axiom,
% 34.76/5.63 (( ~( product @ X @ Y @ V1 ) ) | ( ~( product @ X @ Z @ V2 ) ) |
% 34.76/5.63 ( ~( sum @ Y @ Z @ V3 ) ) | ( ~( sum @ V1 @ V2 @ V4 ) ) |
% 34.76/5.63 ( product @ X @ V3 @ V4 ))).
% 34.76/5.63 thf(zip_derived_cl9, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 34.76/5.63 (~ (product @ X0 @ X1 @ X2)
% 34.76/5.63 | ~ (product @ X0 @ X3 @ X4)
% 34.76/5.63 | ~ (sum @ X1 @ X3 @ X5)
% 34.76/5.63 | ~ (sum @ X2 @ X4 @ X6)
% 34.76/5.63 | (product @ X0 @ X5 @ X6))),
% 34.76/5.63 inference('cnf', [status(esa)], [distributivity2])).
% 34.76/5.63 thf(zip_derived_cl115, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.76/5.63 ( (product @ X1 @ x_inverse_plus_y_inverse @ X0)
% 34.76/5.63 | ~ (sum @ X3 @ X2 @ X0)
% 34.76/5.63 | ~ (product @ X1 @ (inverse @ y) @ X2)
% 34.76/5.63 | ~ (product @ X1 @ (inverse @ x) @ X3))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl9])).
% 34.76/5.63 thf(zip_derived_cl901, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.76/5.63 (~ (product @ X0 @ (inverse @ x) @ X1)
% 34.76/5.63 | ~ (sum @ X1 @ (multiply @ X0 @ (inverse @ y)) @ X2)
% 34.76/5.63 | (product @ X0 @ x_inverse_plus_y_inverse @ X2))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl115])).
% 34.76/5.63 thf(zip_derived_cl22971, plain,
% 34.76/5.63 (( (product @ x_times_y @ x_inverse_plus_y_inverse @ additive_identity)
% 34.76/5.63 | ~ (product @ x_times_y @ (inverse @ x) @ additive_identity))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl22360, zip_derived_cl901])).
% 34.76/5.63 thf(zip_derived_cl5659, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (product @ X1 @ (add @ X1 @ X0) @ X1)),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl5550])).
% 34.76/5.63 thf(zip_derived_cl0, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 34.76/5.63 inference('cnf', [status(esa)], [closure_of_addition])).
% 34.76/5.63 thf(commutativity_of_addition, axiom,
% 34.76/5.63 (( ~( sum @ X @ Y @ Z ) ) | ( sum @ Y @ X @ Z ))).
% 34.76/5.63 thf(zip_derived_cl2, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.76/5.63 (~ (sum @ X0 @ X1 @ X2) | (sum @ X1 @ X0 @ X2))),
% 34.76/5.63 inference('cnf', [status(esa)], [commutativity_of_addition])).
% 34.76/5.63 thf(zip_derived_cl25, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 34.76/5.63 thf(zip_derived_cl1, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 34.76/5.63 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 34.76/5.63 thf(zip_derived_cl7, plain,
% 34.76/5.63 (![X0 : $i]: (product @ X0 @ multiplicative_identity @ X0)),
% 34.76/5.63 inference('cnf', [status(esa)], [multiplicative_identity2])).
% 34.76/5.63 thf(additive_inverse1, axiom,
% 34.76/5.63 (sum @ ( inverse @ X ) @ X @ multiplicative_identity)).
% 34.76/5.63 thf(zip_derived_cl16, plain,
% 34.76/5.63 (![X0 : $i]: (sum @ (inverse @ X0) @ X0 @ multiplicative_identity)),
% 34.76/5.63 inference('cnf', [status(esa)], [additive_inverse1])).
% 34.76/5.63 thf(zip_derived_cl19, plain,
% 34.76/5.63 (![X0 : $i]: (product @ X0 @ (inverse @ X0) @ additive_identity)),
% 34.76/5.63 inference('cnf', [status(esa)], [multiplicative_inverse2])).
% 34.76/5.63 thf(zip_derived_cl8, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 34.76/5.63 (~ (product @ X0 @ X1 @ X2)
% 34.76/5.63 | ~ (product @ X0 @ X3 @ X4)
% 34.76/5.63 | ~ (sum @ X1 @ X3 @ X5)
% 34.76/5.63 | ~ (product @ X0 @ X5 @ X6)
% 34.76/5.63 | (sum @ X2 @ X4 @ X6))),
% 34.76/5.63 inference('cnf', [status(esa)], [distributivity1])).
% 34.76/5.63 thf(zip_derived_cl86, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 34.76/5.63 ( (sum @ additive_identity @ X2 @ X1)
% 34.76/5.63 | ~ (product @ X0 @ X3 @ X1)
% 34.76/5.63 | ~ (sum @ (inverse @ X0) @ X4 @ X3)
% 34.76/5.63 | ~ (product @ X0 @ X4 @ X2))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl8])).
% 34.76/5.63 thf(zip_derived_cl419, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.76/5.63 (~ (product @ X0 @ X0 @ X1)
% 34.76/5.63 | ~ (product @ X0 @ multiplicative_identity @ X2)
% 34.76/5.63 | (sum @ additive_identity @ X1 @ X2))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl86])).
% 34.76/5.63 thf(zip_derived_cl505, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]:
% 34.76/5.63 ( (sum @ additive_identity @ X1 @ X0) | ~ (product @ X0 @ X0 @ X1))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl419])).
% 34.76/5.63 thf(zip_derived_cl512, plain,
% 34.76/5.63 (![X0 : $i]: (sum @ additive_identity @ (multiply @ X0 @ X0) @ X0)),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl505])).
% 34.76/5.63 thf(zip_derived_cl45, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]:
% 34.76/5.63 (((X0) = (X1)) | ~ (sum @ additive_identity @ X0 @ X1))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl20])).
% 34.76/5.63 thf(zip_derived_cl642, plain, (![X0 : $i]: ((multiply @ X0 @ X0) = (X0))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl512, zip_derived_cl45])).
% 34.76/5.63 thf(zip_derived_cl1, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 34.76/5.63 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 34.76/5.63 thf(zip_derived_cl648, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 34.76/5.63 inference('sup+', [status(thm)], [zip_derived_cl642, zip_derived_cl1])).
% 34.76/5.63 thf(zip_derived_cl1, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 34.76/5.63 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 34.76/5.63 thf(zip_derived_cl22, plain, ( (product @ x @ y @ x_times_y)),
% 34.76/5.63 inference('cnf', [status(esa)], [zf_stmt_0])).
% 34.76/5.63 thf(zip_derived_cl8, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 34.76/5.63 (~ (product @ X0 @ X1 @ X2)
% 34.76/5.63 | ~ (product @ X0 @ X3 @ X4)
% 34.76/5.63 | ~ (sum @ X1 @ X3 @ X5)
% 34.76/5.63 | ~ (product @ X0 @ X5 @ X6)
% 34.76/5.63 | (sum @ X2 @ X4 @ X6))),
% 34.76/5.63 inference('cnf', [status(esa)], [distributivity1])).
% 34.76/5.63 thf(zip_derived_cl89, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.76/5.63 ( (sum @ x_times_y @ X1 @ X0)
% 34.76/5.63 | ~ (product @ x @ X2 @ X0)
% 34.76/5.63 | ~ (sum @ y @ X3 @ X2)
% 34.76/5.63 | ~ (product @ x @ X3 @ X1))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl8])).
% 34.76/5.63 thf(zip_derived_cl140, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.76/5.63 (~ (product @ x @ X2 @ X1)
% 34.76/5.63 | ~ (sum @ y @ X2 @ X0)
% 34.76/5.63 | (sum @ x_times_y @ X1 @ (multiply @ x @ X0)))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl89])).
% 34.76/5.63 thf(zip_derived_cl1099, plain,
% 34.76/5.63 (![X0 : $i]:
% 34.76/5.63 ( (sum @ x_times_y @ x @ (multiply @ x @ X0)) | ~ (sum @ y @ x @ X0))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl648, zip_derived_cl140])).
% 34.76/5.63 thf(zip_derived_cl1260, plain,
% 34.76/5.63 ( (sum @ x_times_y @ x @ (multiply @ x @ (add @ x @ y)))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl1099])).
% 34.76/5.63 thf(zip_derived_cl25, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 34.76/5.63 thf(zip_derived_cl20, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.76/5.63 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 34.76/5.63 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 34.76/5.63 thf(zip_derived_cl42, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.76/5.63 (((add @ X1 @ X0) = (X2)) | ~ (sum @ X0 @ X1 @ X2))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl20])).
% 34.76/5.63 thf(zip_derived_cl1405, plain,
% 34.76/5.63 (((add @ x @ x_times_y) = (multiply @ x @ (add @ x @ y)))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl1260, zip_derived_cl42])).
% 34.76/5.63 thf(zip_derived_cl1, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 34.76/5.63 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 34.76/5.63 thf(zip_derived_cl2004, plain,
% 34.76/5.63 ( (product @ x @ (add @ x @ y) @ (add @ x @ x_times_y))),
% 34.76/5.63 inference('sup+', [status(thm)], [zip_derived_cl1405, zip_derived_cl1])).
% 34.76/5.63 thf(zip_derived_cl21, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.76/5.63 (~ (product @ X0 @ X1 @ X2)
% 34.76/5.63 | ~ (product @ X0 @ X1 @ X3)
% 34.76/5.63 | ((X2) = (X3)))),
% 34.76/5.63 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 34.76/5.63 thf(zip_derived_cl2061, plain,
% 34.76/5.63 (![X0 : $i]:
% 34.76/5.63 (((add @ x @ x_times_y) = (X0)) | ~ (product @ x @ (add @ x @ y) @ X0))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl2004, zip_derived_cl21])).
% 34.76/5.63 thf(zip_derived_cl6706, plain, (((add @ x @ x_times_y) = (x))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl5659, zip_derived_cl2061])).
% 34.76/5.63 thf(zip_derived_cl0, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 34.76/5.63 inference('cnf', [status(esa)], [closure_of_addition])).
% 34.76/5.63 thf(zip_derived_cl6798, plain, ( (sum @ x @ x_times_y @ x)),
% 34.76/5.63 inference('sup+', [status(thm)], [zip_derived_cl6706, zip_derived_cl0])).
% 34.76/5.63 thf(zip_derived_cl2049, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]:
% 34.76/5.63 ( (sum @ additive_identity @ (multiply @ (inverse @ X1) @ X0) @
% 34.76/5.63 additive_identity)
% 34.76/5.63 | ~ (sum @ X1 @ X0 @ X1))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl491])).
% 34.76/5.63 thf(zip_derived_cl22349, plain,
% 34.76/5.63 ( (sum @ additive_identity @ (multiply @ (inverse @ x) @ x_times_y) @
% 34.76/5.63 additive_identity)),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl6798, zip_derived_cl2049])).
% 34.76/5.63 thf(zip_derived_cl305, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl50, zip_derived_cl98])).
% 34.76/5.63 thf(zip_derived_cl22359, plain,
% 34.76/5.63 ( (sum @ additive_identity @ (multiply @ x_times_y @ (inverse @ x)) @
% 34.76/5.63 additive_identity)),
% 34.76/5.63 inference('demod', [status(thm)],
% 34.76/5.63 [zip_derived_cl22349, zip_derived_cl305])).
% 34.76/5.63 thf(zip_derived_cl45, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]:
% 34.76/5.63 (((X0) = (X1)) | ~ (sum @ additive_identity @ X0 @ X1))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl20])).
% 34.76/5.63 thf(zip_derived_cl22493, plain,
% 34.76/5.63 (((multiply @ x_times_y @ (inverse @ x)) = (additive_identity))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl22359, zip_derived_cl45])).
% 34.76/5.63 thf(zip_derived_cl1, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 34.76/5.63 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 34.76/5.63 thf(zip_derived_cl22523, plain,
% 34.76/5.63 ( (product @ x_times_y @ (inverse @ x) @ additive_identity)),
% 34.76/5.63 inference('sup+', [status(thm)], [zip_derived_cl22493, zip_derived_cl1])).
% 34.76/5.63 thf(zip_derived_cl22999, plain,
% 34.76/5.63 ( (product @ x_times_y @ x_inverse_plus_y_inverse @ additive_identity)),
% 34.76/5.63 inference('demod', [status(thm)],
% 34.76/5.63 [zip_derived_cl22971, zip_derived_cl22523])).
% 34.76/5.63 thf(zip_derived_cl16, plain,
% 34.76/5.63 (![X0 : $i]: (sum @ (inverse @ X0) @ X0 @ multiplicative_identity)),
% 34.76/5.63 inference('cnf', [status(esa)], [additive_inverse1])).
% 34.76/5.63 thf(zip_derived_cl6, plain,
% 34.76/5.63 (![X0 : $i]: (product @ multiplicative_identity @ X0 @ X0)),
% 34.76/5.63 inference('cnf', [status(esa)], [multiplicative_identity1])).
% 34.76/5.63 thf(zip_derived_cl1, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 34.76/5.63 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 34.76/5.63 thf(distributivity3, axiom,
% 34.76/5.63 (( ~( product @ Y @ X @ V1 ) ) | ( ~( product @ Z @ X @ V2 ) ) |
% 34.76/5.63 ( ~( sum @ Y @ Z @ V3 ) ) | ( ~( product @ V3 @ X @ V4 ) ) |
% 34.76/5.63 ( sum @ V1 @ V2 @ V4 ))).
% 34.76/5.63 thf(zip_derived_cl10, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 34.76/5.63 (~ (product @ X0 @ X1 @ X2)
% 34.76/5.63 | ~ (product @ X3 @ X1 @ X4)
% 34.76/5.63 | ~ (sum @ X0 @ X3 @ X5)
% 34.76/5.63 | ~ (product @ X5 @ X1 @ X6)
% 34.76/5.63 | (sum @ X2 @ X4 @ X6))),
% 34.76/5.63 inference('cnf', [status(esa)], [distributivity3])).
% 34.76/5.63 thf(zip_derived_cl152, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 34.76/5.63 ( (sum @ (multiply @ X1 @ X0) @ X3 @ X2)
% 34.76/5.63 | ~ (product @ X4 @ X0 @ X2)
% 34.76/5.63 | ~ (sum @ X1 @ X5 @ X4)
% 34.76/5.63 | ~ (product @ X5 @ X0 @ X3))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl10])).
% 34.76/5.63 thf(zip_derived_cl1205, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.76/5.63 (~ (product @ X2 @ X0 @ X1)
% 34.76/5.63 | ~ (sum @ X3 @ X2 @ multiplicative_identity)
% 34.76/5.63 | (sum @ (multiply @ X3 @ X0) @ X1 @ X0))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl152])).
% 34.76/5.63 thf(zip_derived_cl12428, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.76/5.63 ( (sum @ (multiply @ (inverse @ X0) @ X1) @ X2 @ X1)
% 34.76/5.63 | ~ (product @ X0 @ X1 @ X2))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl1205])).
% 34.76/5.63 thf(zip_derived_cl23009, plain,
% 34.76/5.63 ( (sum @ (multiply @ (inverse @ x_times_y) @ x_inverse_plus_y_inverse) @
% 34.76/5.63 additive_identity @ x_inverse_plus_y_inverse)),
% 34.76/5.63 inference('sup-', [status(thm)],
% 34.76/5.63 [zip_derived_cl22999, zip_derived_cl12428])).
% 34.76/5.63 thf(zip_derived_cl305, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl50, zip_derived_cl98])).
% 34.76/5.63 thf(zip_derived_cl23067, plain,
% 34.76/5.63 ( (sum @ (multiply @ x_inverse_plus_y_inverse @ (inverse @ x_times_y)) @
% 34.76/5.63 additive_identity @ x_inverse_plus_y_inverse)),
% 34.76/5.63 inference('demod', [status(thm)],
% 34.76/5.63 [zip_derived_cl23009, zip_derived_cl305])).
% 34.76/5.63 thf(zip_derived_cl5, plain,
% 34.76/5.63 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 34.76/5.63 inference('cnf', [status(esa)], [additive_identity2])).
% 34.76/5.63 thf(zip_derived_cl20, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.76/5.63 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 34.76/5.63 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 34.76/5.63 thf(zip_derived_cl43, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]:
% 34.76/5.63 (((X0) = (X1)) | ~ (sum @ X0 @ additive_identity @ X1))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl20])).
% 34.76/5.63 thf(zip_derived_cl24494, plain,
% 34.76/5.63 (((multiply @ x_inverse_plus_y_inverse @ (inverse @ x_times_y))
% 34.76/5.63 = (x_inverse_plus_y_inverse))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl23067, zip_derived_cl43])).
% 34.76/5.63 thf(zip_derived_cl1, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 34.76/5.63 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 34.76/5.63 thf(zip_derived_cl24576, plain,
% 34.76/5.63 ( (product @ x_inverse_plus_y_inverse @ (inverse @ x_times_y) @
% 34.76/5.63 x_inverse_plus_y_inverse)),
% 34.76/5.63 inference('sup+', [status(thm)], [zip_derived_cl24494, zip_derived_cl1])).
% 34.76/5.63 thf(zip_derived_cl19, plain,
% 34.76/5.63 (![X0 : $i]: (product @ X0 @ (inverse @ X0) @ additive_identity)),
% 34.76/5.63 inference('cnf', [status(esa)], [multiplicative_inverse2])).
% 34.76/5.63 thf(zip_derived_cl5, plain,
% 34.76/5.63 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 34.76/5.63 inference('cnf', [status(esa)], [additive_identity2])).
% 34.76/5.63 thf(zip_derived_cl0, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 34.76/5.63 inference('cnf', [status(esa)], [closure_of_addition])).
% 34.76/5.63 thf(distributivity4, axiom,
% 34.76/5.63 (( ~( product @ Y @ X @ V1 ) ) | ( ~( product @ Z @ X @ V2 ) ) |
% 34.76/5.63 ( ~( sum @ Y @ Z @ V3 ) ) | ( ~( sum @ V1 @ V2 @ V4 ) ) |
% 34.76/5.63 ( product @ V3 @ X @ V4 ))).
% 34.76/5.63 thf(zip_derived_cl11, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 34.76/5.63 (~ (product @ X0 @ X1 @ X2)
% 34.76/5.63 | ~ (product @ X3 @ X1 @ X4)
% 34.76/5.63 | ~ (sum @ X0 @ X3 @ X5)
% 34.76/5.63 | ~ (sum @ X2 @ X4 @ X6)
% 34.76/5.63 | (product @ X5 @ X1 @ X6))),
% 34.76/5.63 inference('cnf', [status(esa)], [distributivity4])).
% 34.76/5.63 thf(zip_derived_cl177, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 34.76/5.63 ( (product @ (add @ X1 @ X0) @ X3 @ X2)
% 34.76/5.63 | ~ (sum @ X5 @ X4 @ X2)
% 34.76/5.63 | ~ (product @ X0 @ X3 @ X4)
% 34.76/5.63 | ~ (product @ X1 @ X3 @ X5))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl11])).
% 34.76/5.63 thf(zip_derived_cl1631, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.76/5.63 (~ (product @ X2 @ X1 @ X0)
% 34.76/5.63 | ~ (product @ X3 @ X1 @ additive_identity)
% 34.76/5.63 | (product @ (add @ X2 @ X3) @ X1 @ X0))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl177])).
% 34.76/5.63 thf(zip_derived_cl15533, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.76/5.63 ( (product @ (add @ X2 @ X0) @ (inverse @ X0) @ X1)
% 34.76/5.63 | ~ (product @ X2 @ (inverse @ X0) @ X1))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl1631])).
% 34.76/5.63 thf(zip_derived_cl24716, plain,
% 34.76/5.63 ( (product @ (add @ x_inverse_plus_y_inverse @ x_times_y) @
% 34.76/5.63 (inverse @ x_times_y) @ x_inverse_plus_y_inverse)),
% 34.76/5.63 inference('sup-', [status(thm)],
% 34.76/5.63 [zip_derived_cl24576, zip_derived_cl15533])).
% 34.76/5.63 thf(zip_derived_cl50, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X1 @ X0))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl3])).
% 34.76/5.63 thf(zip_derived_cl21, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.76/5.63 (~ (product @ X0 @ X1 @ X2)
% 34.76/5.63 | ~ (product @ X0 @ X1 @ X3)
% 34.76/5.63 | ((X2) = (X3)))),
% 34.76/5.63 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 34.76/5.63 thf(zip_derived_cl304, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.76/5.63 (((multiply @ X1 @ X0) = (X2)) | ~ (product @ X0 @ X1 @ X2))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl50, zip_derived_cl21])).
% 34.76/5.63 thf(zip_derived_cl26418, plain,
% 34.76/5.63 (((multiply @ (inverse @ x_times_y) @
% 34.76/5.63 (add @ x_inverse_plus_y_inverse @ x_times_y))
% 34.76/5.63 = (x_inverse_plus_y_inverse))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl24716, zip_derived_cl304])).
% 34.76/5.63 thf(zip_derived_cl25, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 34.76/5.63 thf(zip_derived_cl23, plain,
% 34.76/5.63 ( (sum @ (inverse @ x) @ (inverse @ y) @ x_inverse_plus_y_inverse)),
% 34.76/5.63 inference('cnf', [status(esa)], [zf_stmt_1])).
% 34.76/5.63 thf(zip_derived_cl5550, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.76/5.63 (~ (sum @ X0 @ X2 @ X1) | (product @ X0 @ X1 @ X0))),
% 34.76/5.63 inference('demod', [status(thm)],
% 34.76/5.63 [zip_derived_cl2916, zip_derived_cl5380])).
% 34.76/5.63 thf(zip_derived_cl5669, plain,
% 34.76/5.63 ( (product @ (inverse @ x) @ x_inverse_plus_y_inverse @ (inverse @ x))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl5550])).
% 34.76/5.63 thf(additive_inverse2, axiom,
% 34.76/5.63 (sum @ X @ ( inverse @ X ) @ multiplicative_identity)).
% 34.76/5.63 thf(zip_derived_cl17, plain,
% 34.76/5.63 (![X0 : $i]: (sum @ X0 @ (inverse @ X0) @ multiplicative_identity)),
% 34.76/5.63 inference('cnf', [status(esa)], [additive_inverse2])).
% 34.76/5.63 thf(zip_derived_cl0, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 34.76/5.63 inference('cnf', [status(esa)], [closure_of_addition])).
% 34.76/5.63 thf(zip_derived_cl12, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 34.76/5.63 (~ (sum @ X0 @ X1 @ X2)
% 34.76/5.63 | ~ (sum @ X0 @ X3 @ X4)
% 34.76/5.63 | ~ (product @ X1 @ X3 @ X5)
% 34.76/5.63 | ~ (sum @ X0 @ X5 @ X6)
% 34.76/5.63 | (product @ X2 @ X4 @ X6))),
% 34.76/5.63 inference('cnf', [status(esa)], [distributivity5])).
% 34.76/5.63 thf(zip_derived_cl215, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 34.76/5.63 ( (product @ (add @ X1 @ X0) @ X3 @ X2)
% 34.76/5.63 | ~ (sum @ X1 @ X4 @ X2)
% 34.76/5.63 | ~ (product @ X0 @ X5 @ X4)
% 34.76/5.63 | ~ (sum @ X1 @ X5 @ X3))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl12])).
% 34.76/5.63 thf(zip_derived_cl2222, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.76/5.63 (~ (sum @ X0 @ X2 @ X1)
% 34.76/5.63 | ~ (product @ X3 @ X2 @ (inverse @ X0))
% 34.76/5.63 | (product @ (add @ X0 @ X3) @ X1 @ multiplicative_identity))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl215])).
% 34.76/5.63 thf(zip_derived_cl23703, plain,
% 34.76/5.63 (![X0 : $i]:
% 34.76/5.63 ( (product @ (add @ x @ (inverse @ x)) @ X0 @ multiplicative_identity)
% 34.76/5.63 | ~ (sum @ x @ x_inverse_plus_y_inverse @ X0))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl5669, zip_derived_cl2222])).
% 34.76/5.63 thf(zip_derived_cl0, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 34.76/5.63 inference('cnf', [status(esa)], [closure_of_addition])).
% 34.76/5.63 thf(zip_derived_cl17, plain,
% 34.76/5.63 (![X0 : $i]: (sum @ X0 @ (inverse @ X0) @ multiplicative_identity)),
% 34.76/5.63 inference('cnf', [status(esa)], [additive_inverse2])).
% 34.76/5.63 thf(zip_derived_cl20, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.76/5.63 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 34.76/5.63 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 34.76/5.63 thf(zip_derived_cl44, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]:
% 34.76/5.63 (((multiplicative_identity) = (X1))
% 34.76/5.63 | ~ (sum @ X0 @ (inverse @ X0) @ X1))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl20])).
% 34.76/5.63 thf(zip_derived_cl68, plain,
% 34.76/5.63 (![X0 : $i]: ((multiplicative_identity) = (add @ X0 @ (inverse @ X0)))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl44])).
% 34.76/5.63 thf(zip_derived_cl23714, plain,
% 34.76/5.63 (![X0 : $i]:
% 34.76/5.63 ( (product @ multiplicative_identity @ X0 @ multiplicative_identity)
% 34.76/5.63 | ~ (sum @ x @ x_inverse_plus_y_inverse @ X0))),
% 34.76/5.63 inference('demod', [status(thm)], [zip_derived_cl23703, zip_derived_cl68])).
% 34.76/5.63 thf(zip_derived_cl28248, plain,
% 34.76/5.63 ( (product @ multiplicative_identity @
% 34.76/5.63 (add @ x_inverse_plus_y_inverse @ x) @ multiplicative_identity)),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl23714])).
% 34.76/5.63 thf(zip_derived_cl101, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]:
% 34.76/5.63 (((X0) = (X1)) | ~ (product @ multiplicative_identity @ X0 @ X1))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl21])).
% 34.76/5.63 thf(zip_derived_cl28319, plain,
% 34.76/5.63 (((add @ x_inverse_plus_y_inverse @ x) = (multiplicative_identity))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl28248, zip_derived_cl101])).
% 34.76/5.63 thf(zip_derived_cl25, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 34.76/5.63 thf(zip_derived_cl28396, plain,
% 34.76/5.63 ( (sum @ x @ x_inverse_plus_y_inverse @ multiplicative_identity)),
% 34.76/5.63 inference('sup+', [status(thm)], [zip_derived_cl28319, zip_derived_cl25])).
% 34.76/5.63 thf(zip_derived_cl18, plain,
% 34.76/5.63 (![X0 : $i]: (product @ (inverse @ X0) @ X0 @ additive_identity)),
% 34.76/5.63 inference('cnf', [status(esa)], [multiplicative_inverse1])).
% 34.76/5.63 thf(zip_derived_cl5, plain,
% 34.76/5.63 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 34.76/5.63 inference('cnf', [status(esa)], [additive_identity2])).
% 34.76/5.63 thf(zip_derived_cl25, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 34.76/5.63 thf(zip_derived_cl12, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 34.76/5.63 (~ (sum @ X0 @ X1 @ X2)
% 34.76/5.63 | ~ (sum @ X0 @ X3 @ X4)
% 34.76/5.63 | ~ (product @ X1 @ X3 @ X5)
% 34.76/5.63 | ~ (sum @ X0 @ X5 @ X6)
% 34.76/5.63 | (product @ X2 @ X4 @ X6))),
% 34.76/5.63 inference('cnf', [status(esa)], [distributivity5])).
% 34.76/5.63 thf(zip_derived_cl216, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 34.76/5.63 ( (product @ (add @ X1 @ X0) @ X3 @ X2)
% 34.76/5.63 | ~ (sum @ X0 @ X4 @ X2)
% 34.76/5.63 | ~ (product @ X1 @ X5 @ X4)
% 34.76/5.63 | ~ (sum @ X0 @ X5 @ X3))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl12])).
% 34.76/5.63 thf(zip_derived_cl2307, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.76/5.63 (~ (sum @ X0 @ X2 @ X1)
% 34.76/5.63 | ~ (product @ X3 @ X2 @ additive_identity)
% 34.76/5.63 | (product @ (add @ X3 @ X0) @ X1 @ X0))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl216])).
% 34.76/5.63 thf(zip_derived_cl24964, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.76/5.63 ( (product @ (add @ (inverse @ X0) @ X1) @ X2 @ X1)
% 34.76/5.63 | ~ (sum @ X1 @ X0 @ X2))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl2307])).
% 34.76/5.63 thf(zip_derived_cl28508, plain,
% 34.76/5.63 ( (product @ (add @ (inverse @ x_inverse_plus_y_inverse) @ x) @
% 34.76/5.63 multiplicative_identity @ x)),
% 34.76/5.63 inference('sup-', [status(thm)],
% 34.76/5.63 [zip_derived_cl28396, zip_derived_cl24964])).
% 34.76/5.63 thf(zip_derived_cl7, plain,
% 34.76/5.63 (![X0 : $i]: (product @ X0 @ multiplicative_identity @ X0)),
% 34.76/5.63 inference('cnf', [status(esa)], [multiplicative_identity2])).
% 34.76/5.63 thf(zip_derived_cl21, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.76/5.63 (~ (product @ X0 @ X1 @ X2)
% 34.76/5.63 | ~ (product @ X0 @ X1 @ X3)
% 34.76/5.63 | ((X2) = (X3)))),
% 34.76/5.63 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 34.76/5.63 thf(zip_derived_cl99, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]:
% 34.76/5.63 (((X0) = (X1)) | ~ (product @ X0 @ multiplicative_identity @ X1))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl21])).
% 34.76/5.63 thf(zip_derived_cl28699, plain,
% 34.76/5.63 (((add @ (inverse @ x_inverse_plus_y_inverse) @ x) = (x))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl28508, zip_derived_cl99])).
% 34.76/5.63 thf(zip_derived_cl0, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 34.76/5.63 inference('cnf', [status(esa)], [closure_of_addition])).
% 34.76/5.63 thf(zip_derived_cl28753, plain,
% 34.76/5.63 ( (sum @ (inverse @ x_inverse_plus_y_inverse) @ x @ x)),
% 34.76/5.63 inference('sup+', [status(thm)], [zip_derived_cl28699, zip_derived_cl0])).
% 34.76/5.63 thf(zip_derived_cl22, plain, ( (product @ x @ y @ x_times_y)),
% 34.76/5.63 inference('cnf', [status(esa)], [zf_stmt_0])).
% 34.76/5.63 thf(distributivity6, axiom,
% 34.76/5.63 (( ~( sum @ X @ Y @ V1 ) ) | ( ~( sum @ X @ Z @ V2 ) ) |
% 34.76/5.63 ( ~( product @ Y @ Z @ V3 ) ) | ( ~( product @ V1 @ V2 @ V4 ) ) |
% 34.76/5.63 ( sum @ X @ V3 @ V4 ))).
% 34.76/5.63 thf(zip_derived_cl13, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 34.76/5.63 (~ (sum @ X0 @ X1 @ X2)
% 34.76/5.63 | ~ (sum @ X0 @ X3 @ X4)
% 34.76/5.63 | ~ (product @ X1 @ X3 @ X5)
% 34.76/5.63 | ~ (product @ X2 @ X4 @ X6)
% 34.76/5.63 | (sum @ X0 @ X5 @ X6))),
% 34.76/5.63 inference('cnf', [status(esa)], [distributivity6])).
% 34.76/5.63 thf(zip_derived_cl246, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.76/5.63 ( (sum @ X3 @ X0 @ X0)
% 34.76/5.63 | ~ (product @ X2 @ X1 @ X0)
% 34.76/5.63 | ~ (sum @ X3 @ X1 @ X1)
% 34.76/5.63 | ~ (sum @ X3 @ X2 @ X2))),
% 34.76/5.63 inference('eq_fact', [status(thm)], [zip_derived_cl13])).
% 34.76/5.63 thf(zip_derived_cl3471, plain,
% 34.76/5.63 (![X0 : $i]:
% 34.76/5.63 (~ (sum @ X0 @ x @ x)
% 34.76/5.63 | ~ (sum @ X0 @ y @ y)
% 34.76/5.63 | (sum @ X0 @ x_times_y @ x_times_y))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl246])).
% 34.76/5.63 thf(zip_derived_cl28838, plain,
% 34.76/5.63 (( (sum @ (inverse @ x_inverse_plus_y_inverse) @ x_times_y @ x_times_y)
% 34.76/5.63 | ~ (sum @ (inverse @ x_inverse_plus_y_inverse) @ y @ y))),
% 34.76/5.63 inference('sup-', [status(thm)],
% 34.76/5.63 [zip_derived_cl28753, zip_derived_cl3471])).
% 34.76/5.63 thf(zip_derived_cl25, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 34.76/5.63 thf(zip_derived_cl23, plain,
% 34.76/5.63 ( (sum @ (inverse @ x) @ (inverse @ y) @ x_inverse_plus_y_inverse)),
% 34.76/5.63 inference('cnf', [status(esa)], [zf_stmt_1])).
% 34.76/5.63 thf(zip_derived_cl2, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.76/5.63 (~ (sum @ X0 @ X1 @ X2) | (sum @ X1 @ X0 @ X2))),
% 34.76/5.63 inference('cnf', [status(esa)], [commutativity_of_addition])).
% 34.76/5.63 thf(zip_derived_cl30, plain,
% 34.76/5.63 ( (sum @ (inverse @ y) @ (inverse @ x) @ x_inverse_plus_y_inverse)),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl2])).
% 34.76/5.63 thf(zip_derived_cl5550, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.76/5.63 (~ (sum @ X0 @ X2 @ X1) | (product @ X0 @ X1 @ X0))),
% 34.76/5.63 inference('demod', [status(thm)],
% 34.76/5.63 [zip_derived_cl2916, zip_derived_cl5380])).
% 34.76/5.63 thf(zip_derived_cl5670, plain,
% 34.76/5.63 ( (product @ (inverse @ y) @ x_inverse_plus_y_inverse @ (inverse @ y))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl5550])).
% 34.76/5.63 thf(zip_derived_cl2222, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.76/5.63 (~ (sum @ X0 @ X2 @ X1)
% 34.76/5.63 | ~ (product @ X3 @ X2 @ (inverse @ X0))
% 34.76/5.63 | (product @ (add @ X0 @ X3) @ X1 @ multiplicative_identity))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl215])).
% 34.76/5.63 thf(zip_derived_cl23704, plain,
% 34.76/5.63 (![X0 : $i]:
% 34.76/5.63 ( (product @ (add @ y @ (inverse @ y)) @ X0 @ multiplicative_identity)
% 34.76/5.63 | ~ (sum @ y @ x_inverse_plus_y_inverse @ X0))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl5670, zip_derived_cl2222])).
% 34.76/5.63 thf(zip_derived_cl68, plain,
% 34.76/5.63 (![X0 : $i]: ((multiplicative_identity) = (add @ X0 @ (inverse @ X0)))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl44])).
% 34.76/5.63 thf(zip_derived_cl23715, plain,
% 34.76/5.63 (![X0 : $i]:
% 34.76/5.63 ( (product @ multiplicative_identity @ X0 @ multiplicative_identity)
% 34.76/5.63 | ~ (sum @ y @ x_inverse_plus_y_inverse @ X0))),
% 34.76/5.63 inference('demod', [status(thm)], [zip_derived_cl23704, zip_derived_cl68])).
% 34.76/5.63 thf(zip_derived_cl31220, plain,
% 34.76/5.63 ( (product @ multiplicative_identity @
% 34.76/5.63 (add @ x_inverse_plus_y_inverse @ y) @ multiplicative_identity)),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl23715])).
% 34.76/5.63 thf(zip_derived_cl101, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]:
% 34.76/5.63 (((X0) = (X1)) | ~ (product @ multiplicative_identity @ X0 @ X1))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl21])).
% 34.76/5.63 thf(zip_derived_cl31323, plain,
% 34.76/5.63 (((add @ x_inverse_plus_y_inverse @ y) = (multiplicative_identity))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl31220, zip_derived_cl101])).
% 34.76/5.63 thf(zip_derived_cl25, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 34.76/5.63 thf(zip_derived_cl31398, plain,
% 34.76/5.63 ( (sum @ y @ x_inverse_plus_y_inverse @ multiplicative_identity)),
% 34.76/5.63 inference('sup+', [status(thm)], [zip_derived_cl31323, zip_derived_cl25])).
% 34.76/5.63 thf(zip_derived_cl24964, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.76/5.63 ( (product @ (add @ (inverse @ X0) @ X1) @ X2 @ X1)
% 34.76/5.63 | ~ (sum @ X1 @ X0 @ X2))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl2307])).
% 34.76/5.63 thf(zip_derived_cl31558, plain,
% 34.76/5.63 ( (product @ (add @ (inverse @ x_inverse_plus_y_inverse) @ y) @
% 34.76/5.63 multiplicative_identity @ y)),
% 34.76/5.63 inference('sup-', [status(thm)],
% 34.76/5.63 [zip_derived_cl31398, zip_derived_cl24964])).
% 34.76/5.63 thf(zip_derived_cl99, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]:
% 34.76/5.63 (((X0) = (X1)) | ~ (product @ X0 @ multiplicative_identity @ X1))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl21])).
% 34.76/5.63 thf(zip_derived_cl32775, plain,
% 34.76/5.63 (((add @ (inverse @ x_inverse_plus_y_inverse) @ y) = (y))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl31558, zip_derived_cl99])).
% 34.76/5.63 thf(zip_derived_cl0, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 34.76/5.63 inference('cnf', [status(esa)], [closure_of_addition])).
% 34.76/5.63 thf(zip_derived_cl32861, plain,
% 34.76/5.63 ( (sum @ (inverse @ x_inverse_plus_y_inverse) @ y @ y)),
% 34.76/5.63 inference('sup+', [status(thm)], [zip_derived_cl32775, zip_derived_cl0])).
% 34.76/5.63 thf(zip_derived_cl32908, plain,
% 34.76/5.63 ( (sum @ (inverse @ x_inverse_plus_y_inverse) @ x_times_y @ x_times_y)),
% 34.76/5.63 inference('demod', [status(thm)],
% 34.76/5.63 [zip_derived_cl28838, zip_derived_cl32861])).
% 34.76/5.63 thf(zip_derived_cl22999, plain,
% 34.76/5.63 ( (product @ x_times_y @ x_inverse_plus_y_inverse @ additive_identity)),
% 34.76/5.63 inference('demod', [status(thm)],
% 34.76/5.63 [zip_derived_cl22971, zip_derived_cl22523])).
% 34.76/5.63 thf(zip_derived_cl16, plain,
% 34.76/5.63 (![X0 : $i]: (sum @ (inverse @ X0) @ X0 @ multiplicative_identity)),
% 34.76/5.63 inference('cnf', [status(esa)], [additive_inverse1])).
% 34.76/5.63 thf(zip_derived_cl7, plain,
% 34.76/5.63 (![X0 : $i]: (product @ X0 @ multiplicative_identity @ X0)),
% 34.76/5.63 inference('cnf', [status(esa)], [multiplicative_identity2])).
% 34.76/5.63 thf(zip_derived_cl84, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 34.76/5.63 ( (sum @ (multiply @ X1 @ X0) @ X3 @ X2)
% 34.76/5.63 | ~ (product @ X1 @ X4 @ X2)
% 34.76/5.63 | ~ (sum @ X0 @ X5 @ X4)
% 34.76/5.63 | ~ (product @ X1 @ X5 @ X3))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl8])).
% 34.76/5.63 thf(zip_derived_cl343, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.76/5.63 (~ (product @ X0 @ X2 @ X1)
% 34.76/5.63 | ~ (sum @ X3 @ X2 @ multiplicative_identity)
% 34.76/5.63 | (sum @ (multiply @ X0 @ X3) @ X1 @ X0))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl84])).
% 34.76/5.63 thf(zip_derived_cl5106, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.76/5.63 ( (sum @ (multiply @ X1 @ (inverse @ X0)) @ X2 @ X1)
% 34.76/5.63 | ~ (product @ X1 @ X0 @ X2))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl343])).
% 34.76/5.63 thf(zip_derived_cl23011, plain,
% 34.76/5.63 ( (sum @ (multiply @ x_times_y @ (inverse @ x_inverse_plus_y_inverse)) @
% 34.76/5.63 additive_identity @ x_times_y)),
% 34.76/5.63 inference('sup-', [status(thm)],
% 34.76/5.63 [zip_derived_cl22999, zip_derived_cl5106])).
% 34.76/5.63 thf(zip_derived_cl305, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl50, zip_derived_cl98])).
% 34.76/5.63 thf(zip_derived_cl23068, plain,
% 34.76/5.63 ( (sum @ (multiply @ (inverse @ x_inverse_plus_y_inverse) @ x_times_y) @
% 34.76/5.63 additive_identity @ x_times_y)),
% 34.76/5.63 inference('demod', [status(thm)],
% 34.76/5.63 [zip_derived_cl23011, zip_derived_cl305])).
% 34.76/5.63 thf(zip_derived_cl43, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]:
% 34.76/5.63 (((X0) = (X1)) | ~ (sum @ X0 @ additive_identity @ X1))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl20])).
% 34.76/5.63 thf(zip_derived_cl25541, plain,
% 34.76/5.63 (((multiply @ (inverse @ x_inverse_plus_y_inverse) @ x_times_y)
% 34.76/5.63 = (x_times_y))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl23068, zip_derived_cl43])).
% 34.76/5.63 thf(zip_derived_cl1, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 34.76/5.63 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 34.76/5.63 thf(zip_derived_cl6952, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.76/5.63 (~ (product @ X0 @ X2 @ X1) | (sum @ X0 @ X1 @ X0))),
% 34.76/5.63 inference('demod', [status(thm)], [zip_derived_cl564, zip_derived_cl6758])).
% 34.76/5.63 thf(zip_derived_cl7068, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (sum @ X1 @ (multiply @ X1 @ X0) @ X1)),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl6952])).
% 34.76/5.63 thf(zip_derived_cl20, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.76/5.63 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 34.76/5.63 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 34.76/5.63 thf(zip_derived_cl9163, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.76/5.63 (((X0) = (X2)) | ~ (sum @ X0 @ (multiply @ X0 @ X1) @ X2))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl7068, zip_derived_cl20])).
% 34.76/5.63 thf(zip_derived_cl25633, plain,
% 34.76/5.63 (![X0 : $i]:
% 34.76/5.63 (~ (sum @ (inverse @ x_inverse_plus_y_inverse) @ x_times_y @ X0)
% 34.76/5.63 | ((inverse @ x_inverse_plus_y_inverse) = (X0)))),
% 34.76/5.63 inference('sup-', [status(thm)],
% 34.76/5.63 [zip_derived_cl25541, zip_derived_cl9163])).
% 34.76/5.63 thf(zip_derived_cl33205, plain,
% 34.76/5.63 (((inverse @ x_inverse_plus_y_inverse) = (x_times_y))),
% 34.76/5.63 inference('sup-', [status(thm)],
% 34.76/5.63 [zip_derived_cl32908, zip_derived_cl25633])).
% 34.76/5.63 thf(zip_derived_cl33205, plain,
% 34.76/5.63 (((inverse @ x_inverse_plus_y_inverse) = (x_times_y))),
% 34.76/5.63 inference('sup-', [status(thm)],
% 34.76/5.63 [zip_derived_cl32908, zip_derived_cl25633])).
% 34.76/5.63 thf(zip_derived_cl68, plain,
% 34.76/5.63 (![X0 : $i]: ((multiplicative_identity) = (add @ X0 @ (inverse @ X0)))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl44])).
% 34.76/5.63 thf(zip_derived_cl1, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 34.76/5.63 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 34.76/5.63 thf(zip_derived_cl99, plain,
% 34.76/5.63 (![X0 : $i, X1 : $i]:
% 34.76/5.63 (((X0) = (X1)) | ~ (product @ X0 @ multiplicative_identity @ X1))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl21])).
% 34.76/5.63 thf(zip_derived_cl120, plain,
% 34.76/5.63 (![X0 : $i]: ((X0) = (multiply @ X0 @ multiplicative_identity))),
% 34.76/5.63 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl99])).
% 34.76/5.63 thf(zip_derived_cl33738, plain,
% 34.76/5.63 (((inverse @ (inverse @ x_inverse_plus_y_inverse))
% 34.76/5.63 = (x_inverse_plus_y_inverse))),
% 34.76/5.63 inference('demod', [status(thm)],
% 34.76/5.63 [zip_derived_cl26418, zip_derived_cl33205,
% 34.76/5.63 zip_derived_cl33205, zip_derived_cl68, zip_derived_cl120])).
% 34.76/5.63 thf(prove_equation, conjecture,
% 34.76/5.63 (( inverse @ x_times_y ) = ( x_inverse_plus_y_inverse ))).
% 34.76/5.63 thf(zf_stmt_2, negated_conjecture,
% 34.76/5.63 (( inverse @ x_times_y ) != ( x_inverse_plus_y_inverse )),
% 34.76/5.63 inference('cnf.neg', [status(esa)], [prove_equation])).
% 34.76/5.63 thf(zip_derived_cl24, plain,
% 34.76/5.63 (((inverse @ x_times_y) != (x_inverse_plus_y_inverse))),
% 34.76/5.63 inference('cnf', [status(esa)], [zf_stmt_2])).
% 34.76/5.63 thf(zip_derived_cl33205, plain,
% 34.76/5.63 (((inverse @ x_inverse_plus_y_inverse) = (x_times_y))),
% 34.76/5.63 inference('sup-', [status(thm)],
% 34.76/5.63 [zip_derived_cl32908, zip_derived_cl25633])).
% 34.76/5.63 thf(zip_derived_cl33221, plain,
% 34.76/5.63 (((inverse @ (inverse @ x_inverse_plus_y_inverse))
% 34.76/5.63 != (x_inverse_plus_y_inverse))),
% 34.76/5.63 inference('demod', [status(thm)], [zip_derived_cl24, zip_derived_cl33205])).
% 34.76/5.63 thf(zip_derived_cl33899, plain, ($false),
% 34.76/5.63 inference('simplify_reflect-', [status(thm)],
% 34.76/5.63 [zip_derived_cl33738, zip_derived_cl33221])).
% 34.76/5.63
% 34.76/5.63 % SZS output end Refutation
% 34.76/5.63
% 34.76/5.63
% 34.76/5.63 % Terminating...
% 35.14/5.70 % Runner terminated.
% 35.16/5.72 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------