TSTP Solution File: BOO008-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : BOO008-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.qEGedTgVa7 true
% Computer : n029.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 18:13:14 EDT 2023
% Result : Unsatisfiable 17.37s 3.13s
% Output : Refutation 17.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO008-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.qEGedTgVa7 true
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 08:59:25 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in FO mode
% 0.21/0.64 % Total configuration time : 435
% 0.21/0.64 % Estimated wc time : 1092
% 0.21/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.68 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 17.37/3.12 % /export/starexec/sandbox2/solver/bin/fo/fo1_lcnf.sh running for 50s
% 17.37/3.13 % Solved by fo/fo5.sh.
% 17.37/3.13 % done 5187 iterations in 2.308s
% 17.37/3.13 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 17.37/3.13 % SZS output start Refutation
% 17.37/3.13 thf(sum_type, type, sum: $i > $i > $i > $o).
% 17.37/3.13 thf(x__plus_y_plus_z_type, type, x__plus_y_plus_z: $i).
% 17.37/3.13 thf(x_type, type, x: $i).
% 17.37/3.13 thf(z_type, type, z: $i).
% 17.37/3.13 thf(x_plus_y__plus_z_type, type, x_plus_y__plus_z: $i).
% 17.37/3.13 thf(y_plus_z_type, type, y_plus_z: $i).
% 17.37/3.13 thf(multiplicative_identity_type, type, multiplicative_identity: $i).
% 17.37/3.13 thf(inverse_type, type, inverse: $i > $i).
% 17.37/3.13 thf(y_type, type, y: $i).
% 17.37/3.13 thf(multiply_type, type, multiply: $i > $i > $i).
% 17.37/3.13 thf(product_type, type, product: $i > $i > $i > $o).
% 17.37/3.13 thf(add_type, type, add: $i > $i > $i).
% 17.37/3.13 thf(x_plus_y_type, type, x_plus_y: $i).
% 17.37/3.13 thf(additive_identity_type, type, additive_identity: $i).
% 17.37/3.13 thf(y_plus_z, axiom, (sum @ y @ z @ y_plus_z)).
% 17.37/3.13 thf(zip_derived_cl22, plain, ( (sum @ y @ z @ y_plus_z)),
% 17.37/3.13 inference('cnf', [status(esa)], [y_plus_z])).
% 17.37/3.13 thf(commutativity_of_addition, axiom,
% 17.37/3.13 (( ~( sum @ X @ Y @ Z ) ) | ( sum @ Y @ X @ Z ))).
% 17.37/3.13 thf(zip_derived_cl2, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.37/3.13 (~ (sum @ X0 @ X1 @ X2) | (sum @ X1 @ X0 @ X2))),
% 17.37/3.13 inference('cnf', [status(esa)], [commutativity_of_addition])).
% 17.37/3.13 thf(zip_derived_cl32, plain, ( (sum @ z @ y @ y_plus_z)),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl2])).
% 17.37/3.13 thf(additive_identity2, axiom, (sum @ X @ additive_identity @ X)).
% 17.37/3.13 thf(zip_derived_cl5, plain,
% 17.37/3.13 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 17.37/3.13 inference('cnf', [status(esa)], [additive_identity2])).
% 17.37/3.13 thf(distributivity5, axiom,
% 17.37/3.13 (( ~( sum @ X @ Y @ V1 ) ) | ( ~( sum @ X @ Z @ V2 ) ) |
% 17.37/3.13 ( ~( product @ Y @ Z @ V3 ) ) | ( ~( sum @ X @ V3 @ V4 ) ) |
% 17.37/3.13 ( product @ V1 @ V2 @ V4 ))).
% 17.37/3.13 thf(zip_derived_cl12, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 17.37/3.13 (~ (sum @ X0 @ X1 @ X2)
% 17.37/3.13 | ~ (sum @ X0 @ X3 @ X4)
% 17.37/3.13 | ~ (product @ X1 @ X3 @ X5)
% 17.37/3.13 | ~ (sum @ X0 @ X5 @ X6)
% 17.37/3.13 | (product @ X2 @ X4 @ X6))),
% 17.37/3.13 inference('cnf', [status(esa)], [distributivity5])).
% 17.37/3.13 thf(zip_derived_cl143, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 17.37/3.13 ( (product @ X0 @ X3 @ X0)
% 17.37/3.13 | ~ (sum @ X2 @ X1 @ X0)
% 17.37/3.13 | ~ (product @ X1 @ X4 @ X1)
% 17.37/3.13 | ~ (sum @ X2 @ X4 @ X3))),
% 17.37/3.13 inference('eq_fact', [status(thm)], [zip_derived_cl12])).
% 17.37/3.13 thf(zip_derived_cl3377, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.37/3.13 (~ (sum @ X0 @ X2 @ X1)
% 17.37/3.13 | ~ (product @ additive_identity @ X2 @ additive_identity)
% 17.37/3.13 | (product @ X0 @ X1 @ X0))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl143])).
% 17.37/3.13 thf(closure_of_multiplication, axiom,
% 17.37/3.13 (product @ X @ Y @ ( multiply @ X @ Y ))).
% 17.37/3.13 thf(zip_derived_cl1, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 17.37/3.13 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 17.37/3.13 thf(zip_derived_cl5, plain,
% 17.37/3.13 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 17.37/3.13 inference('cnf', [status(esa)], [additive_identity2])).
% 17.37/3.13 thf(multiplicative_inverse2, axiom,
% 17.37/3.13 (product @ X @ ( inverse @ X ) @ additive_identity)).
% 17.37/3.13 thf(zip_derived_cl19, plain,
% 17.37/3.13 (![X0 : $i]: (product @ X0 @ (inverse @ X0) @ additive_identity)),
% 17.37/3.13 inference('cnf', [status(esa)], [multiplicative_inverse2])).
% 17.37/3.13 thf(zip_derived_cl1, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 17.37/3.13 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 17.37/3.13 thf(distributivity1, axiom,
% 17.37/3.13 (( ~( product @ X @ Y @ V1 ) ) | ( ~( product @ X @ Z @ V2 ) ) |
% 17.37/3.13 ( ~( sum @ Y @ Z @ V3 ) ) | ( ~( product @ X @ V3 @ V4 ) ) |
% 17.37/3.13 ( sum @ V1 @ V2 @ V4 ))).
% 17.37/3.13 thf(zip_derived_cl8, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 17.37/3.13 (~ (product @ X0 @ X1 @ X2)
% 17.37/3.13 | ~ (product @ X0 @ X3 @ X4)
% 17.37/3.13 | ~ (sum @ X1 @ X3 @ X5)
% 17.37/3.13 | ~ (product @ X0 @ X5 @ X6)
% 17.37/3.13 | (sum @ X2 @ X4 @ X6))),
% 17.37/3.13 inference('cnf', [status(esa)], [distributivity1])).
% 17.37/3.13 thf(zip_derived_cl67, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 17.37/3.13 ( (sum @ (multiply @ X1 @ X0) @ X3 @ X2)
% 17.37/3.13 | ~ (product @ X1 @ X4 @ X2)
% 17.37/3.13 | ~ (sum @ X0 @ X5 @ X4)
% 17.37/3.13 | ~ (product @ X1 @ X5 @ X3))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl8])).
% 17.37/3.13 thf(zip_derived_cl321, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 17.37/3.13 (~ (product @ X0 @ X2 @ X1)
% 17.37/3.13 | ~ (sum @ X3 @ X2 @ (inverse @ X0))
% 17.37/3.13 | (sum @ (multiply @ X0 @ X3) @ X1 @ additive_identity))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl67])).
% 17.37/3.13 thf(zip_derived_cl6184, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i]:
% 17.37/3.13 ( (sum @ (multiply @ X0 @ (inverse @ X0)) @ X1 @ additive_identity)
% 17.37/3.13 | ~ (product @ X0 @ additive_identity @ X1))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl321])).
% 17.37/3.13 thf(zip_derived_cl1, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 17.37/3.13 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 17.37/3.13 thf(zip_derived_cl19, plain,
% 17.37/3.13 (![X0 : $i]: (product @ X0 @ (inverse @ X0) @ additive_identity)),
% 17.37/3.13 inference('cnf', [status(esa)], [multiplicative_inverse2])).
% 17.37/3.13 thf(multiplication_is_well_defined, axiom,
% 17.37/3.13 (( ~( product @ X @ Y @ U ) ) | ( ~( product @ X @ Y @ V ) ) |
% 17.37/3.13 ( ( U ) = ( V ) ))).
% 17.37/3.13 thf(zip_derived_cl21, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 17.37/3.13 (~ (product @ X0 @ X1 @ X2)
% 17.37/3.13 | ~ (product @ X0 @ X1 @ X3)
% 17.37/3.13 | ((X2) = (X3)))),
% 17.37/3.13 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 17.37/3.13 thf(zip_derived_cl59, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i]:
% 17.37/3.13 (((additive_identity) = (X1)) | ~ (product @ X0 @ (inverse @ X0) @ X1))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl21])).
% 17.37/3.13 thf(zip_derived_cl241, plain,
% 17.37/3.13 (![X0 : $i]: ((additive_identity) = (multiply @ X0 @ (inverse @ X0)))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl59])).
% 17.37/3.13 thf(zip_derived_cl6197, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i]:
% 17.37/3.13 ( (sum @ additive_identity @ X1 @ additive_identity)
% 17.37/3.13 | ~ (product @ X0 @ additive_identity @ X1))),
% 17.37/3.13 inference('demod', [status(thm)], [zip_derived_cl6184, zip_derived_cl241])).
% 17.37/3.13 thf(zip_derived_cl6209, plain,
% 17.37/3.13 (![X0 : $i]:
% 17.37/3.13 (sum @ additive_identity @ (multiply @ X0 @ additive_identity) @
% 17.37/3.13 additive_identity)),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl6197])).
% 17.37/3.13 thf(additive_identity1, axiom, (sum @ additive_identity @ X @ X)).
% 17.37/3.13 thf(zip_derived_cl4, plain,
% 17.37/3.13 (![X0 : $i]: (sum @ additive_identity @ X0 @ X0)),
% 17.37/3.13 inference('cnf', [status(esa)], [additive_identity1])).
% 17.37/3.13 thf(addition_is_well_defined, axiom,
% 17.37/3.13 (( ~( sum @ X @ Y @ U ) ) | ( ~( sum @ X @ Y @ V ) ) | ( ( U ) = ( V ) ))).
% 17.37/3.13 thf(zip_derived_cl20, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 17.37/3.13 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 17.37/3.13 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 17.37/3.13 thf(zip_derived_cl48, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i]:
% 17.37/3.13 (((X0) = (X1)) | ~ (sum @ additive_identity @ X0 @ X1))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl20])).
% 17.37/3.13 thf(zip_derived_cl6281, plain,
% 17.37/3.13 (![X0 : $i]: ((multiply @ X0 @ additive_identity) = (additive_identity))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl6209, zip_derived_cl48])).
% 17.37/3.13 thf(zip_derived_cl1, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 17.37/3.13 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 17.37/3.13 thf(commutativity_of_multiplication, axiom,
% 17.37/3.13 (( ~( product @ X @ Y @ Z ) ) | ( product @ Y @ X @ Z ))).
% 17.37/3.13 thf(zip_derived_cl3, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.37/3.13 (~ (product @ X0 @ X1 @ X2) | (product @ X1 @ X0 @ X2))),
% 17.37/3.13 inference('cnf', [status(esa)], [commutativity_of_multiplication])).
% 17.37/3.13 thf(zip_derived_cl44, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X1 @ X0))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl3])).
% 17.37/3.13 thf(zip_derived_cl6327, plain,
% 17.37/3.13 (![X0 : $i]: (product @ additive_identity @ X0 @ additive_identity)),
% 17.37/3.13 inference('sup+', [status(thm)], [zip_derived_cl6281, zip_derived_cl44])).
% 17.37/3.13 thf(zip_derived_cl7221, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.37/3.13 (~ (sum @ X0 @ X2 @ X1) | (product @ X0 @ X1 @ X0))),
% 17.37/3.13 inference('demod', [status(thm)],
% 17.37/3.13 [zip_derived_cl3377, zip_derived_cl6327])).
% 17.37/3.13 thf(zip_derived_cl7703, plain, ( (product @ z @ y_plus_z @ z)),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl7221])).
% 17.37/3.13 thf(zip_derived_cl1, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 17.37/3.13 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 17.37/3.13 thf(multiplicative_identity2, axiom,
% 17.37/3.13 (product @ X @ multiplicative_identity @ X)).
% 17.37/3.13 thf(zip_derived_cl7, plain,
% 17.37/3.13 (![X0 : $i]: (product @ X0 @ multiplicative_identity @ X0)),
% 17.37/3.13 inference('cnf', [status(esa)], [multiplicative_identity2])).
% 17.37/3.13 thf(zip_derived_cl8, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 17.37/3.13 (~ (product @ X0 @ X1 @ X2)
% 17.37/3.13 | ~ (product @ X0 @ X3 @ X4)
% 17.37/3.13 | ~ (sum @ X1 @ X3 @ X5)
% 17.37/3.13 | ~ (product @ X0 @ X5 @ X6)
% 17.37/3.13 | (sum @ X2 @ X4 @ X6))),
% 17.37/3.13 inference('cnf', [status(esa)], [distributivity1])).
% 17.37/3.13 thf(zip_derived_cl73, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 17.37/3.13 ( (sum @ X0 @ X3 @ X0)
% 17.37/3.13 | ~ (product @ X2 @ X1 @ X0)
% 17.37/3.13 | ~ (sum @ X1 @ X4 @ X1)
% 17.37/3.13 | ~ (product @ X2 @ X4 @ X3))),
% 17.37/3.13 inference('eq_fact', [status(thm)], [zip_derived_cl8])).
% 17.37/3.13 thf(zip_derived_cl502, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.37/3.13 (~ (product @ X0 @ X2 @ X1)
% 17.37/3.13 | ~ (sum @ multiplicative_identity @ X2 @ multiplicative_identity)
% 17.37/3.13 | (sum @ X0 @ X1 @ X0))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl73])).
% 17.37/3.13 thf(closure_of_addition, axiom, (sum @ X @ Y @ ( add @ X @ Y ))).
% 17.37/3.13 thf(zip_derived_cl0, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 17.37/3.13 inference('cnf', [status(esa)], [closure_of_addition])).
% 17.37/3.13 thf(zip_derived_cl7221, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.37/3.13 (~ (sum @ X0 @ X2 @ X1) | (product @ X0 @ X1 @ X0))),
% 17.37/3.13 inference('demod', [status(thm)],
% 17.37/3.13 [zip_derived_cl3377, zip_derived_cl6327])).
% 17.37/3.13 thf(zip_derived_cl7694, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i]: (product @ X1 @ (add @ X1 @ X0) @ X1)),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl7221])).
% 17.37/3.13 thf(multiplicative_identity1, axiom,
% 17.37/3.13 (product @ multiplicative_identity @ X @ X)).
% 17.37/3.13 thf(zip_derived_cl6, plain,
% 17.37/3.13 (![X0 : $i]: (product @ multiplicative_identity @ X0 @ X0)),
% 17.37/3.13 inference('cnf', [status(esa)], [multiplicative_identity1])).
% 17.37/3.13 thf(zip_derived_cl21, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 17.37/3.13 (~ (product @ X0 @ X1 @ X2)
% 17.37/3.13 | ~ (product @ X0 @ X1 @ X3)
% 17.37/3.13 | ((X2) = (X3)))),
% 17.37/3.13 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 17.37/3.13 thf(zip_derived_cl60, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i]:
% 17.37/3.13 (((X0) = (X1)) | ~ (product @ multiplicative_identity @ X0 @ X1))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl21])).
% 17.37/3.13 thf(zip_derived_cl10967, plain,
% 17.37/3.13 (![X0 : $i]:
% 17.37/3.13 ((add @ multiplicative_identity @ X0) = (multiplicative_identity))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl7694, zip_derived_cl60])).
% 17.37/3.13 thf(zip_derived_cl0, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 17.37/3.13 inference('cnf', [status(esa)], [closure_of_addition])).
% 17.37/3.13 thf(zip_derived_cl11085, plain,
% 17.37/3.13 (![X0 : $i]:
% 17.37/3.13 (sum @ multiplicative_identity @ X0 @ multiplicative_identity)),
% 17.37/3.13 inference('sup+', [status(thm)], [zip_derived_cl10967, zip_derived_cl0])).
% 17.37/3.13 thf(zip_derived_cl11349, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.37/3.13 (~ (product @ X0 @ X2 @ X1) | (sum @ X0 @ X1 @ X0))),
% 17.37/3.13 inference('demod', [status(thm)],
% 17.37/3.13 [zip_derived_cl502, zip_derived_cl11085])).
% 17.37/3.13 thf(zip_derived_cl11878, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i]: (sum @ X1 @ (multiply @ X1 @ X0) @ X1)),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl11349])).
% 17.37/3.13 thf(zip_derived_cl1, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 17.37/3.13 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 17.37/3.13 thf(x_plus__y_plus_z, axiom, (sum @ x @ y_plus_z @ x__plus_y_plus_z)).
% 17.37/3.13 thf(zip_derived_cl23, plain, ( (sum @ x @ y_plus_z @ x__plus_y_plus_z)),
% 17.37/3.13 inference('cnf', [status(esa)], [x_plus__y_plus_z])).
% 17.37/3.13 thf(zip_derived_cl2, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.37/3.13 (~ (sum @ X0 @ X1 @ X2) | (sum @ X1 @ X0 @ X2))),
% 17.37/3.13 inference('cnf', [status(esa)], [commutativity_of_addition])).
% 17.37/3.13 thf(zip_derived_cl34, plain, ( (sum @ y_plus_z @ x @ x__plus_y_plus_z)),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl2])).
% 17.37/3.13 thf(distributivity2, axiom,
% 17.37/3.13 (( ~( product @ X @ Y @ V1 ) ) | ( ~( product @ X @ Z @ V2 ) ) |
% 17.37/3.13 ( ~( sum @ Y @ Z @ V3 ) ) | ( ~( sum @ V1 @ V2 @ V4 ) ) |
% 17.37/3.13 ( product @ X @ V3 @ V4 ))).
% 17.37/3.13 thf(zip_derived_cl9, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 17.37/3.13 (~ (product @ X0 @ X1 @ X2)
% 17.37/3.13 | ~ (product @ X0 @ X3 @ X4)
% 17.37/3.13 | ~ (sum @ X1 @ X3 @ X5)
% 17.37/3.13 | ~ (sum @ X2 @ X4 @ X6)
% 17.37/3.13 | (product @ X0 @ X5 @ X6))),
% 17.37/3.13 inference('cnf', [status(esa)], [distributivity2])).
% 17.37/3.13 thf(zip_derived_cl103, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 17.37/3.13 ( (product @ X1 @ x__plus_y_plus_z @ X0)
% 17.37/3.13 | ~ (sum @ X3 @ X2 @ X0)
% 17.37/3.13 | ~ (product @ X1 @ x @ X2)
% 17.37/3.13 | ~ (product @ X1 @ y_plus_z @ X3))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl34, zip_derived_cl9])).
% 17.37/3.13 thf(zip_derived_cl968, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.37/3.13 (~ (product @ X0 @ y_plus_z @ X1)
% 17.37/3.13 | ~ (sum @ X1 @ (multiply @ X0 @ x) @ X2)
% 17.37/3.13 | (product @ X0 @ x__plus_y_plus_z @ X2))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl103])).
% 17.37/3.13 thf(zip_derived_cl15403, plain,
% 17.37/3.13 (![X0 : $i]:
% 17.37/3.13 ( (product @ X0 @ x__plus_y_plus_z @ X0)
% 17.37/3.13 | ~ (product @ X0 @ y_plus_z @ X0))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl11878, zip_derived_cl968])).
% 17.37/3.13 thf(zip_derived_cl16834, plain, ( (product @ z @ x__plus_y_plus_z @ z)),
% 17.37/3.13 inference('sup-', [status(thm)],
% 17.37/3.13 [zip_derived_cl7703, zip_derived_cl15403])).
% 17.37/3.13 thf(x_plus_y__plus_z, axiom, (sum @ x_plus_y @ z @ x_plus_y__plus_z)).
% 17.37/3.13 thf(zip_derived_cl25, plain, ( (sum @ x_plus_y @ z @ x_plus_y__plus_z)),
% 17.37/3.13 inference('cnf', [status(esa)], [x_plus_y__plus_z])).
% 17.37/3.13 thf(zip_derived_cl2, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.37/3.13 (~ (sum @ X0 @ X1 @ X2) | (sum @ X1 @ X0 @ X2))),
% 17.37/3.13 inference('cnf', [status(esa)], [commutativity_of_addition])).
% 17.37/3.13 thf(zip_derived_cl35, plain, ( (sum @ z @ x_plus_y @ x_plus_y__plus_z)),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl2])).
% 17.37/3.13 thf(distributivity4, axiom,
% 17.37/3.13 (( ~( product @ Y @ X @ V1 ) ) | ( ~( product @ Z @ X @ V2 ) ) |
% 17.37/3.13 ( ~( sum @ Y @ Z @ V3 ) ) | ( ~( sum @ V1 @ V2 @ V4 ) ) |
% 17.37/3.13 ( product @ V3 @ X @ V4 ))).
% 17.37/3.13 thf(zip_derived_cl11, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 17.37/3.13 (~ (product @ X0 @ X1 @ X2)
% 17.37/3.13 | ~ (product @ X3 @ X1 @ X4)
% 17.37/3.13 | ~ (sum @ X0 @ X3 @ X5)
% 17.37/3.13 | ~ (sum @ X2 @ X4 @ X6)
% 17.37/3.13 | (product @ X5 @ X1 @ X6))),
% 17.37/3.13 inference('cnf', [status(esa)], [distributivity4])).
% 17.37/3.13 thf(zip_derived_cl128, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 17.37/3.13 ( (product @ X0 @ X3 @ X0)
% 17.37/3.13 | ~ (sum @ X2 @ X1 @ X0)
% 17.37/3.13 | ~ (product @ X1 @ X3 @ X1)
% 17.37/3.13 | ~ (product @ X2 @ X3 @ X2))),
% 17.37/3.13 inference('eq_fact', [status(thm)], [zip_derived_cl11])).
% 17.37/3.13 thf(zip_derived_cl2215, plain,
% 17.37/3.13 (![X0 : $i]:
% 17.37/3.13 (~ (product @ z @ X0 @ z)
% 17.37/3.13 | ~ (product @ x_plus_y @ X0 @ x_plus_y)
% 17.37/3.13 | (product @ x_plus_y__plus_z @ X0 @ x_plus_y__plus_z))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl35, zip_derived_cl128])).
% 17.37/3.13 thf(zip_derived_cl16888, plain,
% 17.37/3.13 (( (product @ x_plus_y__plus_z @ x__plus_y_plus_z @ x_plus_y__plus_z)
% 17.37/3.13 | ~ (product @ x_plus_y @ x__plus_y_plus_z @ x_plus_y))),
% 17.37/3.13 inference('sup-', [status(thm)],
% 17.37/3.13 [zip_derived_cl16834, zip_derived_cl2215])).
% 17.37/3.13 thf(x_plus_y, axiom, (sum @ x @ y @ x_plus_y)).
% 17.37/3.13 thf(zip_derived_cl24, plain, ( (sum @ x @ y @ x_plus_y)),
% 17.37/3.13 inference('cnf', [status(esa)], [x_plus_y])).
% 17.37/3.13 thf(zip_derived_cl23, plain, ( (sum @ x @ y_plus_z @ x__plus_y_plus_z)),
% 17.37/3.13 inference('cnf', [status(esa)], [x_plus__y_plus_z])).
% 17.37/3.13 thf(zip_derived_cl12, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 17.37/3.13 (~ (sum @ X0 @ X1 @ X2)
% 17.37/3.13 | ~ (sum @ X0 @ X3 @ X4)
% 17.37/3.13 | ~ (product @ X1 @ X3 @ X5)
% 17.37/3.13 | ~ (sum @ X0 @ X5 @ X6)
% 17.37/3.13 | (product @ X2 @ X4 @ X6))),
% 17.37/3.13 inference('cnf', [status(esa)], [distributivity5])).
% 17.37/3.13 thf(zip_derived_cl140, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 17.37/3.13 ( (product @ x__plus_y_plus_z @ X1 @ X0)
% 17.37/3.13 | ~ (sum @ x @ X2 @ X0)
% 17.37/3.13 | ~ (product @ y_plus_z @ X3 @ X2)
% 17.37/3.13 | ~ (sum @ x @ X3 @ X1))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl12])).
% 17.37/3.13 thf(zip_derived_cl3149, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i]:
% 17.37/3.13 (~ (sum @ x @ X1 @ X0)
% 17.37/3.13 | ~ (product @ y_plus_z @ X1 @ X1)
% 17.37/3.13 | (product @ x__plus_y_plus_z @ X0 @ X0))),
% 17.37/3.13 inference('eq_fact', [status(thm)], [zip_derived_cl140])).
% 17.37/3.13 thf(zip_derived_cl3746, plain,
% 17.37/3.13 (( (product @ x__plus_y_plus_z @ x_plus_y @ x_plus_y)
% 17.37/3.13 | ~ (product @ y_plus_z @ y @ y))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl3149])).
% 17.37/3.13 thf(zip_derived_cl5, plain,
% 17.37/3.13 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 17.37/3.13 inference('cnf', [status(esa)], [additive_identity2])).
% 17.37/3.13 thf(zip_derived_cl22, plain, ( (sum @ y @ z @ y_plus_z)),
% 17.37/3.13 inference('cnf', [status(esa)], [y_plus_z])).
% 17.37/3.13 thf(zip_derived_cl12, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 17.37/3.13 (~ (sum @ X0 @ X1 @ X2)
% 17.37/3.13 | ~ (sum @ X0 @ X3 @ X4)
% 17.37/3.13 | ~ (product @ X1 @ X3 @ X5)
% 17.37/3.13 | ~ (sum @ X0 @ X5 @ X6)
% 17.37/3.13 | (product @ X2 @ X4 @ X6))),
% 17.37/3.13 inference('cnf', [status(esa)], [distributivity5])).
% 17.37/3.13 thf(zip_derived_cl134, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 17.37/3.13 ( (product @ y_plus_z @ X1 @ X0)
% 17.37/3.13 | ~ (sum @ y @ X2 @ X0)
% 17.37/3.13 | ~ (product @ z @ X3 @ X2)
% 17.37/3.13 | ~ (sum @ y @ X3 @ X1))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl12])).
% 17.37/3.13 thf(zip_derived_cl2761, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i]:
% 17.37/3.13 (~ (sum @ y @ X1 @ X0)
% 17.37/3.13 | ~ (product @ z @ X1 @ X1)
% 17.37/3.13 | (product @ y_plus_z @ X0 @ X0))),
% 17.37/3.13 inference('eq_fact', [status(thm)], [zip_derived_cl134])).
% 17.37/3.13 thf(zip_derived_cl6244, plain,
% 17.37/3.13 (( (product @ y_plus_z @ y @ y)
% 17.37/3.13 | ~ (product @ z @ additive_identity @ additive_identity))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl2761])).
% 17.37/3.13 thf(zip_derived_cl6281, plain,
% 17.37/3.13 (![X0 : $i]: ((multiply @ X0 @ additive_identity) = (additive_identity))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl6209, zip_derived_cl48])).
% 17.37/3.13 thf(zip_derived_cl1, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 17.37/3.13 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 17.37/3.13 thf(zip_derived_cl6325, plain,
% 17.37/3.13 (![X0 : $i]: (product @ X0 @ additive_identity @ additive_identity)),
% 17.37/3.13 inference('sup+', [status(thm)], [zip_derived_cl6281, zip_derived_cl1])).
% 17.37/3.13 thf(zip_derived_cl6390, plain, ( (product @ y_plus_z @ y @ y)),
% 17.37/3.13 inference('demod', [status(thm)],
% 17.37/3.13 [zip_derived_cl6244, zip_derived_cl6325])).
% 17.37/3.13 thf(zip_derived_cl7333, plain,
% 17.37/3.13 ( (product @ x__plus_y_plus_z @ x_plus_y @ x_plus_y)),
% 17.37/3.13 inference('demod', [status(thm)],
% 17.37/3.13 [zip_derived_cl3746, zip_derived_cl6390])).
% 17.37/3.13 thf(zip_derived_cl3, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.37/3.13 (~ (product @ X0 @ X1 @ X2) | (product @ X1 @ X0 @ X2))),
% 17.37/3.13 inference('cnf', [status(esa)], [commutativity_of_multiplication])).
% 17.37/3.13 thf(zip_derived_cl7533, plain,
% 17.37/3.13 ( (product @ x_plus_y @ x__plus_y_plus_z @ x_plus_y)),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl7333, zip_derived_cl3])).
% 17.37/3.13 thf(zip_derived_cl16892, plain,
% 17.37/3.13 ( (product @ x_plus_y__plus_z @ x__plus_y_plus_z @ x_plus_y__plus_z)),
% 17.37/3.13 inference('demod', [status(thm)],
% 17.37/3.13 [zip_derived_cl16888, zip_derived_cl7533])).
% 17.37/3.13 thf(zip_derived_cl44, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X1 @ X0))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl3])).
% 17.37/3.13 thf(zip_derived_cl21, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 17.37/3.13 (~ (product @ X0 @ X1 @ X2)
% 17.37/3.13 | ~ (product @ X0 @ X1 @ X3)
% 17.37/3.13 | ((X2) = (X3)))),
% 17.37/3.13 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 17.37/3.13 thf(zip_derived_cl292, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.37/3.13 (((multiply @ X1 @ X0) = (X2)) | ~ (product @ X0 @ X1 @ X2))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl21])).
% 17.37/3.13 thf(zip_derived_cl16897, plain,
% 17.37/3.13 (((multiply @ x__plus_y_plus_z @ x_plus_y__plus_z) = (x_plus_y__plus_z))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl16892, zip_derived_cl292])).
% 17.37/3.13 thf(zip_derived_cl32, plain, ( (sum @ z @ y @ y_plus_z)),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl2])).
% 17.37/3.13 thf(zip_derived_cl35, plain, ( (sum @ z @ x_plus_y @ x_plus_y__plus_z)),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl2])).
% 17.37/3.13 thf(zip_derived_cl12, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 17.37/3.13 (~ (sum @ X0 @ X1 @ X2)
% 17.37/3.13 | ~ (sum @ X0 @ X3 @ X4)
% 17.37/3.13 | ~ (product @ X1 @ X3 @ X5)
% 17.37/3.13 | ~ (sum @ X0 @ X5 @ X6)
% 17.37/3.13 | (product @ X2 @ X4 @ X6))),
% 17.37/3.13 inference('cnf', [status(esa)], [distributivity5])).
% 17.37/3.13 thf(zip_derived_cl137, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 17.37/3.13 ( (product @ x_plus_y__plus_z @ X1 @ X0)
% 17.37/3.13 | ~ (sum @ z @ X2 @ X0)
% 17.37/3.13 | ~ (product @ x_plus_y @ X3 @ X2)
% 17.37/3.13 | ~ (sum @ z @ X3 @ X1))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl35, zip_derived_cl12])).
% 17.37/3.13 thf(zip_derived_cl2945, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i]:
% 17.37/3.13 (~ (sum @ z @ X1 @ X0)
% 17.37/3.13 | ~ (product @ x_plus_y @ X1 @ X1)
% 17.37/3.13 | (product @ x_plus_y__plus_z @ X0 @ X0))),
% 17.37/3.13 inference('eq_fact', [status(thm)], [zip_derived_cl137])).
% 17.37/3.13 thf(zip_derived_cl3410, plain,
% 17.37/3.13 (( (product @ x_plus_y__plus_z @ y_plus_z @ y_plus_z)
% 17.37/3.13 | ~ (product @ x_plus_y @ y @ y))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl2945])).
% 17.37/3.13 thf(zip_derived_cl24, plain, ( (sum @ x @ y @ x_plus_y)),
% 17.37/3.13 inference('cnf', [status(esa)], [x_plus_y])).
% 17.37/3.13 thf(zip_derived_cl2, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.37/3.13 (~ (sum @ X0 @ X1 @ X2) | (sum @ X1 @ X0 @ X2))),
% 17.37/3.13 inference('cnf', [status(esa)], [commutativity_of_addition])).
% 17.37/3.13 thf(zip_derived_cl33, plain, ( (sum @ y @ x @ x_plus_y)),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl2])).
% 17.37/3.13 thf(zip_derived_cl7221, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.37/3.13 (~ (sum @ X0 @ X2 @ X1) | (product @ X0 @ X1 @ X0))),
% 17.37/3.13 inference('demod', [status(thm)],
% 17.37/3.13 [zip_derived_cl3377, zip_derived_cl6327])).
% 17.37/3.13 thf(zip_derived_cl7701, plain, ( (product @ y @ x_plus_y @ y)),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl33, zip_derived_cl7221])).
% 17.37/3.13 thf(zip_derived_cl3, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.37/3.13 (~ (product @ X0 @ X1 @ X2) | (product @ X1 @ X0 @ X2))),
% 17.37/3.13 inference('cnf', [status(esa)], [commutativity_of_multiplication])).
% 17.37/3.13 thf(zip_derived_cl7893, plain, ( (product @ x_plus_y @ y @ y)),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl7701, zip_derived_cl3])).
% 17.37/3.13 thf(zip_derived_cl8083, plain,
% 17.37/3.13 ( (product @ x_plus_y__plus_z @ y_plus_z @ y_plus_z)),
% 17.37/3.13 inference('demod', [status(thm)],
% 17.37/3.13 [zip_derived_cl3410, zip_derived_cl7893])).
% 17.37/3.13 thf(zip_derived_cl3, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.37/3.13 (~ (product @ X0 @ X1 @ X2) | (product @ X1 @ X0 @ X2))),
% 17.37/3.13 inference('cnf', [status(esa)], [commutativity_of_multiplication])).
% 17.37/3.13 thf(zip_derived_cl8125, plain,
% 17.37/3.13 ( (product @ y_plus_z @ x_plus_y__plus_z @ y_plus_z)),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl8083, zip_derived_cl3])).
% 17.37/3.13 thf(zip_derived_cl34, plain, ( (sum @ y_plus_z @ x @ x__plus_y_plus_z)),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl2])).
% 17.37/3.13 thf(zip_derived_cl128, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 17.37/3.13 ( (product @ X0 @ X3 @ X0)
% 17.37/3.13 | ~ (sum @ X2 @ X1 @ X0)
% 17.37/3.13 | ~ (product @ X1 @ X3 @ X1)
% 17.37/3.13 | ~ (product @ X2 @ X3 @ X2))),
% 17.37/3.13 inference('eq_fact', [status(thm)], [zip_derived_cl11])).
% 17.37/3.13 thf(zip_derived_cl2216, plain,
% 17.37/3.13 (![X0 : $i]:
% 17.37/3.13 (~ (product @ y_plus_z @ X0 @ y_plus_z)
% 17.37/3.13 | ~ (product @ x @ X0 @ x)
% 17.37/3.13 | (product @ x__plus_y_plus_z @ X0 @ x__plus_y_plus_z))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl34, zip_derived_cl128])).
% 17.37/3.13 thf(zip_derived_cl8194, plain,
% 17.37/3.13 (( (product @ x__plus_y_plus_z @ x_plus_y__plus_z @ x__plus_y_plus_z)
% 17.37/3.13 | ~ (product @ x @ x_plus_y__plus_z @ x))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl8125, zip_derived_cl2216])).
% 17.37/3.13 thf(zip_derived_cl24, plain, ( (sum @ x @ y @ x_plus_y)),
% 17.37/3.13 inference('cnf', [status(esa)], [x_plus_y])).
% 17.37/3.13 thf(zip_derived_cl7221, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.37/3.13 (~ (sum @ X0 @ X2 @ X1) | (product @ X0 @ X1 @ X0))),
% 17.37/3.13 inference('demod', [status(thm)],
% 17.37/3.13 [zip_derived_cl3377, zip_derived_cl6327])).
% 17.37/3.13 thf(zip_derived_cl7708, plain, ( (product @ x @ x_plus_y @ x)),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl7221])).
% 17.37/3.13 thf(zip_derived_cl11878, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i]: (sum @ X1 @ (multiply @ X1 @ X0) @ X1)),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl11349])).
% 17.37/3.13 thf(zip_derived_cl1, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 17.37/3.13 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 17.37/3.13 thf(zip_derived_cl25, plain, ( (sum @ x_plus_y @ z @ x_plus_y__plus_z)),
% 17.37/3.13 inference('cnf', [status(esa)], [x_plus_y__plus_z])).
% 17.37/3.13 thf(zip_derived_cl9, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 17.37/3.13 (~ (product @ X0 @ X1 @ X2)
% 17.37/3.13 | ~ (product @ X0 @ X3 @ X4)
% 17.37/3.13 | ~ (sum @ X1 @ X3 @ X5)
% 17.37/3.13 | ~ (sum @ X2 @ X4 @ X6)
% 17.37/3.13 | (product @ X0 @ X5 @ X6))),
% 17.37/3.13 inference('cnf', [status(esa)], [distributivity2])).
% 17.37/3.13 thf(zip_derived_cl106, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 17.37/3.13 ( (product @ X1 @ x_plus_y__plus_z @ X0)
% 17.37/3.13 | ~ (sum @ X3 @ X2 @ X0)
% 17.37/3.13 | ~ (product @ X1 @ z @ X2)
% 17.37/3.13 | ~ (product @ X1 @ x_plus_y @ X3))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl9])).
% 17.37/3.13 thf(zip_derived_cl1091, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.37/3.13 (~ (product @ X0 @ x_plus_y @ X1)
% 17.37/3.13 | ~ (sum @ X1 @ (multiply @ X0 @ z) @ X2)
% 17.37/3.13 | (product @ X0 @ x_plus_y__plus_z @ X2))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl106])).
% 17.37/3.13 thf(zip_derived_cl15399, plain,
% 17.37/3.13 (![X0 : $i]:
% 17.37/3.13 ( (product @ X0 @ x_plus_y__plus_z @ X0)
% 17.37/3.13 | ~ (product @ X0 @ x_plus_y @ X0))),
% 17.37/3.13 inference('sup-', [status(thm)],
% 17.37/3.13 [zip_derived_cl11878, zip_derived_cl1091])).
% 17.37/3.13 thf(zip_derived_cl15874, plain, ( (product @ x @ x_plus_y__plus_z @ x)),
% 17.37/3.13 inference('sup-', [status(thm)],
% 17.37/3.13 [zip_derived_cl7708, zip_derived_cl15399])).
% 17.37/3.13 thf(zip_derived_cl15875, plain,
% 17.37/3.13 ( (product @ x__plus_y_plus_z @ x_plus_y__plus_z @ x__plus_y_plus_z)),
% 17.37/3.13 inference('demod', [status(thm)],
% 17.37/3.13 [zip_derived_cl8194, zip_derived_cl15874])).
% 17.37/3.13 thf(zip_derived_cl1, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 17.37/3.13 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 17.37/3.13 thf(zip_derived_cl21, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 17.37/3.13 (~ (product @ X0 @ X1 @ X2)
% 17.37/3.13 | ~ (product @ X0 @ X1 @ X3)
% 17.37/3.13 | ((X2) = (X3)))),
% 17.37/3.13 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 17.37/3.13 thf(zip_derived_cl57, plain,
% 17.37/3.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 17.37/3.13 (((multiply @ X1 @ X0) = (X2)) | ~ (product @ X1 @ X0 @ X2))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl21])).
% 17.37/3.13 thf(zip_derived_cl15967, plain,
% 17.37/3.13 (((multiply @ x__plus_y_plus_z @ x_plus_y__plus_z) = (x__plus_y_plus_z))),
% 17.37/3.13 inference('sup-', [status(thm)], [zip_derived_cl15875, zip_derived_cl57])).
% 17.37/3.13 thf(zip_derived_cl16949, plain, (((x__plus_y_plus_z) = (x_plus_y__plus_z))),
% 17.37/3.13 inference('demod', [status(thm)],
% 17.37/3.13 [zip_derived_cl16897, zip_derived_cl15967])).
% 17.37/3.13 thf(prove_equality, conjecture,
% 17.37/3.13 (( x__plus_y_plus_z ) = ( x_plus_y__plus_z ))).
% 17.37/3.13 thf(zf_stmt_0, negated_conjecture,
% 17.37/3.13 (( x__plus_y_plus_z ) != ( x_plus_y__plus_z )),
% 17.37/3.13 inference('cnf.neg', [status(esa)], [prove_equality])).
% 17.37/3.13 thf(zip_derived_cl26, plain, (((x__plus_y_plus_z) != (x_plus_y__plus_z))),
% 17.37/3.13 inference('cnf', [status(esa)], [zf_stmt_0])).
% 17.37/3.13 thf(zip_derived_cl16950, plain, ($false),
% 17.37/3.13 inference('simplify_reflect-', [status(thm)],
% 17.37/3.13 [zip_derived_cl16949, zip_derived_cl26])).
% 17.37/3.13
% 17.37/3.13 % SZS output end Refutation
% 17.37/3.13
% 17.37/3.13
% 17.37/3.13 % Terminating...
% 18.27/3.30 % Runner terminated.
% 18.27/3.32 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------