%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : BOO007-1 : TPTP v9.2.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.NdtG7PbDaN true
% Computer : n028.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 : Thu Oct 2 04:29:44 PM UTC 2025
% Result : Unsatisfiable 81.95s 14.40s
% Output : Refutation 81.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO007-1 : TPTP v9.2.0. Bugfixed v1.2.1.
% 0.00/0.12 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.NdtG7PbDaN true
% 0.09/0.32 % Computer : n028.cluster.edu
% 0.09/0.32 % Model : x86_64 x86_64
% 0.09/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.32 % Memory : 8042.1875MB
% 0.09/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.32 % CPULimit : 300
% 0.09/0.32 % WCLimit : 300
% 0.09/0.32 % DateTime : Wed Oct 1 13:56:08 EDT 2025
% 0.09/0.33 % CPUTime :
% 0.09/0.33 % Running portfolio for 300 s
% 0.09/0.33 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.33 % Number of cores: 8
% 0.09/0.33 % Python version: Python 3.6.8
% 0.09/0.33 % Running in FO mode
% 0.45/0.64 % Total configuration time : 435
% 0.45/0.64 % Estimated wc time : 1092
% 0.45/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.45/0.71 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.45/0.72 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.45/0.72 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.46/0.78 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.46/0.78 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.46/0.79 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.47/0.85 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 81.95/14.40 % Solved by fo/fo5.sh.
% 81.95/14.40 % done 13649 iterations in 13.569s
% 81.95/14.40 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 81.95/14.40 % SZS output start Refutation
% 81.95/14.40 thf(sum_type, type, sum: $i > $i > $i > $o).
% 81.95/14.40 thf(x_times__y_times_z_type, type, x_times__y_times_z: $i).
% 81.95/14.40 thf(x_type, type, x: $i).
% 81.95/14.40 thf(z_type, type, z: $i).
% 81.95/14.40 thf(x_times_y__times_z_type, type, x_times_y__times_z: $i).
% 81.95/14.40 thf(y_times_z_type, type, y_times_z: $i).
% 81.95/14.40 thf(multiplicative_identity_type, type, multiplicative_identity: $i).
% 81.95/14.40 thf(inverse_type, type, inverse: $i > $i).
% 81.95/14.40 thf(y_type, type, y: $i).
% 81.95/14.40 thf(multiply_type, type, multiply: $i > $i > $i).
% 81.95/14.40 thf(product_type, type, product: $i > $i > $i > $o).
% 81.95/14.40 thf(add_type, type, add: $i > $i > $i).
% 81.95/14.40 thf(x_times_y_type, type, x_times_y: $i).
% 81.95/14.40 thf(additive_identity_type, type, additive_identity: $i).
% 81.95/14.40 thf(y_times_z, axiom, (product @ y @ z @ y_times_z)).
% 81.95/14.40 thf(zip_derived_cl22, plain, ( (product @ y @ z @ y_times_z)),
% 81.95/14.40 inference('cnf', [status(esa)], [y_times_z])).
% 81.95/14.40 thf(x_times_y__times_z, axiom,
% 81.95/14.40 (product @ x_times_y @ z @ x_times_y__times_z)).
% 81.95/14.40 thf(zip_derived_cl25, plain,
% 81.95/14.40 ( (product @ x_times_y @ z @ x_times_y__times_z)),
% 81.95/14.40 inference('cnf', [status(esa)], [x_times_y__times_z])).
% 81.95/14.40 thf(distributivity3, axiom,
% 81.95/14.40 (( ~( product @ Y @ X @ V1 ) ) | ( ~( product @ Z @ X @ V2 ) ) |
% 81.95/14.40 ( ~( sum @ Y @ Z @ V3 ) ) | ( ~( product @ V3 @ X @ V4 ) ) |
% 81.95/14.40 ( sum @ V1 @ V2 @ V4 ))).
% 81.95/14.40 thf(zip_derived_cl10, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 81.95/14.40 (~ (product @ X0 @ X1 @ X2)
% 81.95/14.40 | ~ (product @ X3 @ X1 @ X4)
% 81.95/14.40 | ~ (sum @ X0 @ X3 @ X5)
% 81.95/14.40 | ~ (product @ X5 @ X1 @ X6)
% 81.95/14.40 | (sum @ X2 @ X4 @ X6))),
% 81.95/14.40 inference('cnf', [status(esa)], [distributivity3])).
% 81.95/14.40 thf(zip_derived_cl119, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 81.95/14.40 ( (sum @ x_times_y__times_z @ X1 @ X0)
% 81.95/14.40 | ~ (product @ X2 @ z @ X0)
% 81.95/14.40 | ~ (sum @ x_times_y @ X3 @ X2)
% 81.95/14.40 | ~ (product @ X3 @ z @ X1))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl10])).
% 81.95/14.40 thf(zip_derived_cl1519, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i]:
% 81.95/14.40 (~ (product @ X1 @ z @ X0)
% 81.95/14.40 | ~ (sum @ x_times_y @ X1 @ X1)
% 81.95/14.40 | (sum @ x_times_y__times_z @ X0 @ X0))),
% 81.95/14.40 inference('eq_fact', [status(thm)], [zip_derived_cl119])).
% 81.95/14.40 thf(zip_derived_cl1594, plain,
% 81.95/14.40 (( (sum @ x_times_y__times_z @ y_times_z @ y_times_z)
% 81.95/14.40 | ~ (sum @ x_times_y @ y @ y))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl1519])).
% 81.95/14.40 thf(multiplicative_identity2, axiom,
% 81.95/14.40 (product @ X @ multiplicative_identity @ X)).
% 81.95/14.40 thf(zip_derived_cl7, plain,
% 81.95/14.40 (![X0 : $i]: (product @ X0 @ multiplicative_identity @ X0)),
% 81.95/14.40 inference('cnf', [status(esa)], [multiplicative_identity2])).
% 81.95/14.40 thf(x_times_y, axiom, (product @ x @ y @ x_times_y)).
% 81.95/14.40 thf(zip_derived_cl24, plain, ( (product @ x @ y @ x_times_y)),
% 81.95/14.40 inference('cnf', [status(esa)], [x_times_y])).
% 81.95/14.40 thf(commutativity_of_multiplication, axiom,
% 81.95/14.40 (( ~( product @ X @ Y @ Z ) ) | ( product @ Y @ X @ Z ))).
% 81.95/14.40 thf(zip_derived_cl3, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i]:
% 81.95/14.40 (~ (product @ X0 @ X1 @ X2) | (product @ X1 @ X0 @ X2))),
% 81.95/14.40 inference('cnf', [status(esa)], [commutativity_of_multiplication])).
% 81.95/14.40 thf(zip_derived_cl39, plain, ( (product @ y @ x @ x_times_y)),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl3])).
% 81.95/14.40 thf(distributivity1, axiom,
% 81.95/14.40 (( ~( product @ X @ Y @ V1 ) ) | ( ~( product @ X @ Z @ V2 ) ) |
% 81.95/14.40 ( ~( sum @ Y @ Z @ V3 ) ) | ( ~( product @ X @ V3 @ V4 ) ) |
% 81.95/14.40 ( sum @ V1 @ V2 @ V4 ))).
% 81.95/14.40 thf(zip_derived_cl8, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 81.95/14.40 (~ (product @ X0 @ X1 @ X2)
% 81.95/14.40 | ~ (product @ X0 @ X3 @ X4)
% 81.95/14.40 | ~ (sum @ X1 @ X3 @ X5)
% 81.95/14.40 | ~ (product @ X0 @ X5 @ X6)
% 81.95/14.40 | (sum @ X2 @ X4 @ X6))),
% 81.95/14.40 inference('cnf', [status(esa)], [distributivity1])).
% 81.95/14.40 thf(zip_derived_cl71, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 81.95/14.40 ( (sum @ x_times_y @ X1 @ X0)
% 81.95/14.40 | ~ (product @ y @ X2 @ X0)
% 81.95/14.40 | ~ (sum @ x @ X3 @ X2)
% 81.95/14.40 | ~ (product @ y @ X3 @ X1))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl39, zip_derived_cl8])).
% 81.95/14.40 thf(zip_derived_cl513, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i]:
% 81.95/14.40 (~ (product @ y @ X1 @ X0)
% 81.95/14.40 | ~ (sum @ x @ X1 @ X1)
% 81.95/14.40 | (sum @ x_times_y @ X0 @ X0))),
% 81.95/14.40 inference('eq_fact', [status(thm)], [zip_derived_cl71])).
% 81.95/14.40 thf(zip_derived_cl2346, plain,
% 81.95/14.40 (( (sum @ x_times_y @ y @ y)
% 81.95/14.40 | ~ (sum @ x @ multiplicative_identity @ multiplicative_identity))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl513])).
% 81.95/14.40 thf(closure_of_addition, axiom, (sum @ X @ Y @ ( add @ X @ Y ))).
% 81.95/14.40 thf(zip_derived_cl0, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 81.95/14.40 inference('cnf', [status(esa)], [closure_of_addition])).
% 81.95/14.40 thf(additive_identity2, axiom, (sum @ X @ additive_identity @ X)).
% 81.95/14.40 thf(zip_derived_cl5, plain,
% 81.95/14.40 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 81.95/14.40 inference('cnf', [status(esa)], [additive_identity2])).
% 81.95/14.40 thf(distributivity5, axiom,
% 81.95/14.40 (( ~( sum @ X @ Y @ V1 ) ) | ( ~( sum @ X @ Z @ V2 ) ) |
% 81.95/14.40 ( ~( product @ Y @ Z @ V3 ) ) | ( ~( sum @ X @ V3 @ V4 ) ) |
% 81.95/14.40 ( product @ V1 @ V2 @ V4 ))).
% 81.95/14.40 thf(zip_derived_cl12, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 81.95/14.40 (~ (sum @ X0 @ X1 @ X2)
% 81.95/14.40 | ~ (sum @ X0 @ X3 @ X4)
% 81.95/14.40 | ~ (product @ X1 @ X3 @ X5)
% 81.95/14.40 | ~ (sum @ X0 @ X5 @ X6)
% 81.95/14.40 | (product @ X2 @ X4 @ X6))),
% 81.95/14.40 inference('cnf', [status(esa)], [distributivity5])).
% 81.95/14.40 thf(zip_derived_cl136, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 81.95/14.40 ( (product @ X0 @ X3 @ X0)
% 81.95/14.40 | ~ (sum @ X2 @ X1 @ X0)
% 81.95/14.40 | ~ (product @ X1 @ X4 @ X1)
% 81.95/14.40 | ~ (sum @ X2 @ X4 @ X3))),
% 81.95/14.40 inference('eq_fact', [status(thm)], [zip_derived_cl12])).
% 81.95/14.40 thf(zip_derived_cl2437, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i]:
% 81.95/14.40 (~ (sum @ X0 @ X2 @ X1)
% 81.95/14.40 | ~ (product @ additive_identity @ X2 @ additive_identity)
% 81.95/14.40 | (product @ X0 @ X1 @ X0))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl136])).
% 81.95/14.40 thf(closure_of_multiplication, axiom,
% 81.95/14.40 (product @ X @ Y @ ( multiply @ X @ Y ))).
% 81.95/14.40 thf(zip_derived_cl1, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 81.95/14.40 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 81.95/14.40 thf(zip_derived_cl5, plain,
% 81.95/14.40 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 81.95/14.40 inference('cnf', [status(esa)], [additive_identity2])).
% 81.95/14.40 thf(multiplicative_inverse2, axiom,
% 81.95/14.40 (product @ X @ ( inverse @ X ) @ additive_identity)).
% 81.95/14.40 thf(zip_derived_cl19, plain,
% 81.95/14.40 (![X0 : $i]: (product @ X0 @ (inverse @ X0) @ additive_identity)),
% 81.95/14.40 inference('cnf', [status(esa)], [multiplicative_inverse2])).
% 81.95/14.40 thf(zip_derived_cl1, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 81.95/14.40 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 81.95/14.40 thf(zip_derived_cl8, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 81.95/14.40 (~ (product @ X0 @ X1 @ X2)
% 81.95/14.40 | ~ (product @ X0 @ X3 @ X4)
% 81.95/14.40 | ~ (sum @ X1 @ X3 @ X5)
% 81.95/14.40 | ~ (product @ X0 @ X5 @ X6)
% 81.95/14.40 | (sum @ X2 @ X4 @ X6))),
% 81.95/14.40 inference('cnf', [status(esa)], [distributivity1])).
% 81.95/14.40 thf(zip_derived_cl65, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 81.95/14.40 ( (sum @ (multiply @ X1 @ X0) @ X3 @ X2)
% 81.95/14.40 | ~ (product @ X1 @ X4 @ X2)
% 81.95/14.40 | ~ (sum @ X0 @ X5 @ X4)
% 81.95/14.40 | ~ (product @ X1 @ X5 @ X3))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl8])).
% 81.95/14.40 thf(zip_derived_cl321, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 81.95/14.40 (~ (product @ X0 @ X2 @ X1)
% 81.95/14.40 | ~ (sum @ X3 @ X2 @ (inverse @ X0))
% 81.95/14.40 | (sum @ (multiply @ X0 @ X3) @ X1 @ additive_identity))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl65])).
% 81.95/14.40 thf(zip_derived_cl6305, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i]:
% 81.95/14.40 ( (sum @ (multiply @ X0 @ (inverse @ X0)) @ X1 @ additive_identity)
% 81.95/14.40 | ~ (product @ X0 @ additive_identity @ X1))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl321])).
% 81.95/14.40 thf(zip_derived_cl1, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 81.95/14.40 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 81.95/14.40 thf(zip_derived_cl19, plain,
% 81.95/14.40 (![X0 : $i]: (product @ X0 @ (inverse @ X0) @ additive_identity)),
% 81.95/14.40 inference('cnf', [status(esa)], [multiplicative_inverse2])).
% 81.95/14.40 thf(multiplication_is_well_defined, axiom,
% 81.95/14.40 (( ~( product @ X @ Y @ U ) ) | ( ~( product @ X @ Y @ V ) ) |
% 81.95/14.40 ( ( U ) = ( V ) ))).
% 81.95/14.40 thf(zip_derived_cl21, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 81.95/14.40 (~ (product @ X0 @ X1 @ X2)
% 81.95/14.40 | ~ (product @ X0 @ X1 @ X3)
% 81.95/14.40 | ((X2) = (X3)))),
% 81.95/14.40 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 81.95/14.40 thf(zip_derived_cl53, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i]:
% 81.95/14.40 (((additive_identity) = (X1)) | ~ (product @ X0 @ (inverse @ X0) @ X1))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl21])).
% 81.95/14.40 thf(zip_derived_cl223, plain,
% 81.95/14.40 (![X0 : $i]: ((additive_identity) = (multiply @ X0 @ (inverse @ X0)))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl53])).
% 81.95/14.40 thf(zip_derived_cl6318, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i]:
% 81.95/14.40 ( (sum @ additive_identity @ X1 @ additive_identity)
% 81.95/14.40 | ~ (product @ X0 @ additive_identity @ X1))),
% 81.95/14.40 inference('demod', [status(thm)], [zip_derived_cl6305, zip_derived_cl223])).
% 81.95/14.40 thf(zip_derived_cl6323, plain,
% 81.95/14.40 (![X0 : $i]:
% 81.95/14.40 (sum @ additive_identity @ (multiply @ X0 @ additive_identity) @
% 81.95/14.40 additive_identity)),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl6318])).
% 81.95/14.40 thf(additive_identity1, axiom, (sum @ additive_identity @ X @ X)).
% 81.95/14.40 thf(zip_derived_cl4, plain,
% 81.95/14.40 (![X0 : $i]: (sum @ additive_identity @ X0 @ X0)),
% 81.95/14.40 inference('cnf', [status(esa)], [additive_identity1])).
% 81.95/14.40 thf(addition_is_well_defined, axiom,
% 81.95/14.40 (( ~( sum @ X @ Y @ U ) ) | ( ~( sum @ X @ Y @ V ) ) | ( ( U ) = ( V ) ))).
% 81.95/14.40 thf(zip_derived_cl20, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 81.95/14.40 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 81.95/14.40 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 81.95/14.40 thf(zip_derived_cl48, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i]:
% 81.95/14.40 (((X0) = (X1)) | ~ (sum @ additive_identity @ X0 @ X1))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl20])).
% 81.95/14.40 thf(zip_derived_cl6360, plain,
% 81.95/14.40 (![X0 : $i]: ((multiply @ X0 @ additive_identity) = (additive_identity))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl6323, zip_derived_cl48])).
% 81.95/14.40 thf(zip_derived_cl1, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 81.95/14.40 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 81.95/14.40 thf(zip_derived_cl3, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i]:
% 81.95/14.40 (~ (product @ X0 @ X1 @ X2) | (product @ X1 @ X0 @ X2))),
% 81.95/14.40 inference('cnf', [status(esa)], [commutativity_of_multiplication])).
% 81.95/14.40 thf(zip_derived_cl43, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X1 @ X0))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl3])).
% 81.95/14.40 thf(zip_derived_cl6493, plain,
% 81.95/14.40 (![X0 : $i]: (product @ additive_identity @ X0 @ additive_identity)),
% 81.95/14.40 inference('sup+', [status(thm)], [zip_derived_cl6360, zip_derived_cl43])).
% 81.95/14.40 thf(zip_derived_cl6718, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i]:
% 81.95/14.40 (~ (sum @ X0 @ X2 @ X1) | (product @ X0 @ X1 @ X0))),
% 81.95/14.40 inference('demod', [status(thm)],
% 81.95/14.40 [zip_derived_cl2437, zip_derived_cl6493])).
% 81.95/14.40 thf(zip_derived_cl7046, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i]: (product @ X1 @ (add @ X1 @ X0) @ X1)),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl6718])).
% 81.95/14.40 thf(multiplicative_identity1, axiom,
% 81.95/14.40 (product @ multiplicative_identity @ X @ X)).
% 81.95/14.40 thf(zip_derived_cl6, plain,
% 81.95/14.40 (![X0 : $i]: (product @ multiplicative_identity @ X0 @ X0)),
% 81.95/14.40 inference('cnf', [status(esa)], [multiplicative_identity1])).
% 81.95/14.40 thf(zip_derived_cl21, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 81.95/14.40 (~ (product @ X0 @ X1 @ X2)
% 81.95/14.40 | ~ (product @ X0 @ X1 @ X3)
% 81.95/14.40 | ((X2) = (X3)))),
% 81.95/14.40 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 81.95/14.40 thf(zip_derived_cl54, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i]:
% 81.95/14.40 (((X0) = (X1)) | ~ (product @ multiplicative_identity @ X0 @ X1))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl21])).
% 81.95/14.40 thf(zip_derived_cl8098, plain,
% 81.95/14.40 (![X0 : $i]:
% 81.95/14.40 ((add @ multiplicative_identity @ X0) = (multiplicative_identity))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl7046, zip_derived_cl54])).
% 81.95/14.40 thf(zip_derived_cl0, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 81.95/14.40 inference('cnf', [status(esa)], [closure_of_addition])).
% 81.95/14.40 thf(commutativity_of_addition, axiom,
% 81.95/14.40 (( ~( sum @ X @ Y @ Z ) ) | ( sum @ Y @ X @ Z ))).
% 81.95/14.40 thf(zip_derived_cl2, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i]:
% 81.95/14.40 (~ (sum @ X0 @ X1 @ X2) | (sum @ X1 @ X0 @ X2))),
% 81.95/14.40 inference('cnf', [status(esa)], [commutativity_of_addition])).
% 81.95/14.40 thf(zip_derived_cl27, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 81.95/14.40 thf(zip_derived_cl8195, plain,
% 81.95/14.40 (![X0 : $i]:
% 81.95/14.40 (sum @ X0 @ multiplicative_identity @ multiplicative_identity)),
% 81.95/14.40 inference('sup+', [status(thm)], [zip_derived_cl8098, zip_derived_cl27])).
% 81.95/14.40 thf(zip_derived_cl8311, plain, ( (sum @ x_times_y @ y @ y)),
% 81.95/14.40 inference('demod', [status(thm)],
% 81.95/14.40 [zip_derived_cl2346, zip_derived_cl8195])).
% 81.95/14.40 thf(zip_derived_cl9037, plain,
% 81.95/14.40 ( (sum @ x_times_y__times_z @ y_times_z @ y_times_z)),
% 81.95/14.40 inference('demod', [status(thm)],
% 81.95/14.40 [zip_derived_cl1594, zip_derived_cl8311])).
% 81.95/14.40 thf(zip_derived_cl2, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i]:
% 81.95/14.40 (~ (sum @ X0 @ X1 @ X2) | (sum @ X1 @ X0 @ X2))),
% 81.95/14.40 inference('cnf', [status(esa)], [commutativity_of_addition])).
% 81.95/14.40 thf(zip_derived_cl9086, plain,
% 81.95/14.40 ( (sum @ y_times_z @ x_times_y__times_z @ y_times_z)),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl9037, zip_derived_cl2])).
% 81.95/14.40 thf(x_times__y_times_z, axiom,
% 81.95/14.40 (product @ x @ y_times_z @ x_times__y_times_z)).
% 81.95/14.40 thf(zip_derived_cl23, plain,
% 81.95/14.40 ( (product @ x @ y_times_z @ x_times__y_times_z)),
% 81.95/14.40 inference('cnf', [status(esa)], [x_times__y_times_z])).
% 81.95/14.40 thf(zip_derived_cl3, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i]:
% 81.95/14.40 (~ (product @ X0 @ X1 @ X2) | (product @ X1 @ X0 @ X2))),
% 81.95/14.40 inference('cnf', [status(esa)], [commutativity_of_multiplication])).
% 81.95/14.40 thf(zip_derived_cl40, plain,
% 81.95/14.40 ( (product @ y_times_z @ x @ x_times__y_times_z)),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl3])).
% 81.95/14.40 thf(distributivity8, axiom,
% 81.95/14.40 (( ~( sum @ Y @ X @ V1 ) ) | ( ~( sum @ Z @ X @ V2 ) ) |
% 81.95/14.40 ( ~( product @ Y @ Z @ V3 ) ) | ( ~( product @ V1 @ V2 @ V4 ) ) |
% 81.95/14.40 ( sum @ V3 @ X @ V4 ))).
% 81.95/14.40 thf(zip_derived_cl15, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 81.95/14.40 (~ (sum @ X0 @ X1 @ X2)
% 81.95/14.40 | ~ (sum @ X3 @ X1 @ X4)
% 81.95/14.40 | ~ (product @ X0 @ X3 @ X5)
% 81.95/14.40 | ~ (product @ X2 @ X4 @ X6)
% 81.95/14.40 | (sum @ X5 @ X1 @ X6))),
% 81.95/14.40 inference('cnf', [status(esa)], [distributivity8])).
% 81.95/14.40 thf(zip_derived_cl179, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 81.95/14.40 ( (sum @ X0 @ X3 @ X0)
% 81.95/14.40 | ~ (product @ X2 @ X1 @ X0)
% 81.95/14.40 | ~ (sum @ X1 @ X3 @ X1)
% 81.95/14.40 | ~ (sum @ X2 @ X3 @ X2))),
% 81.95/14.40 inference('eq_fact', [status(thm)], [zip_derived_cl15])).
% 81.95/14.40 thf(zip_derived_cl5373, plain,
% 81.95/14.40 (![X0 : $i]:
% 81.95/14.40 (~ (sum @ y_times_z @ X0 @ y_times_z)
% 81.95/14.40 | ~ (sum @ x @ X0 @ x)
% 81.95/14.40 | (sum @ x_times__y_times_z @ X0 @ x_times__y_times_z))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl40, zip_derived_cl179])).
% 81.95/14.40 thf(zip_derived_cl9247, plain,
% 81.95/14.40 (( (sum @ x_times__y_times_z @ x_times_y__times_z @ x_times__y_times_z)
% 81.95/14.40 | ~ (sum @ x @ x_times_y__times_z @ x))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl9086, zip_derived_cl5373])).
% 81.95/14.40 thf(zip_derived_cl7, plain,
% 81.95/14.40 (![X0 : $i]: (product @ X0 @ multiplicative_identity @ X0)),
% 81.95/14.40 inference('cnf', [status(esa)], [multiplicative_identity2])).
% 81.95/14.40 thf(zip_derived_cl24, plain, ( (product @ x @ y @ x_times_y)),
% 81.95/14.40 inference('cnf', [status(esa)], [x_times_y])).
% 81.95/14.40 thf(zip_derived_cl8, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 81.95/14.40 (~ (product @ X0 @ X1 @ X2)
% 81.95/14.40 | ~ (product @ X0 @ X3 @ X4)
% 81.95/14.40 | ~ (sum @ X1 @ X3 @ X5)
% 81.95/14.40 | ~ (product @ X0 @ X5 @ X6)
% 81.95/14.40 | (sum @ X2 @ X4 @ X6))),
% 81.95/14.40 inference('cnf', [status(esa)], [distributivity1])).
% 81.95/14.40 thf(zip_derived_cl73, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 81.95/14.40 ( (sum @ x_times_y @ X1 @ X0)
% 81.95/14.40 | ~ (product @ x @ X2 @ X0)
% 81.95/14.40 | ~ (sum @ y @ X3 @ X2)
% 81.95/14.40 | ~ (product @ x @ X3 @ X1))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl8])).
% 81.95/14.40 thf(zip_derived_cl611, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i]:
% 81.95/14.40 (~ (product @ x @ X1 @ X0)
% 81.95/14.40 | ~ (sum @ y @ X1 @ X1)
% 81.95/14.40 | (sum @ x_times_y @ X0 @ X0))),
% 81.95/14.40 inference('eq_fact', [status(thm)], [zip_derived_cl73])).
% 81.95/14.40 thf(zip_derived_cl2429, plain,
% 81.95/14.40 (( (sum @ x_times_y @ x @ x)
% 81.95/14.40 | ~ (sum @ y @ multiplicative_identity @ multiplicative_identity))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl611])).
% 81.95/14.40 thf(zip_derived_cl8195, plain,
% 81.95/14.40 (![X0 : $i]:
% 81.95/14.40 (sum @ X0 @ multiplicative_identity @ multiplicative_identity)),
% 81.95/14.40 inference('sup+', [status(thm)], [zip_derived_cl8098, zip_derived_cl27])).
% 81.95/14.40 thf(zip_derived_cl8313, plain, ( (sum @ x_times_y @ x @ x)),
% 81.95/14.40 inference('demod', [status(thm)],
% 81.95/14.40 [zip_derived_cl2429, zip_derived_cl8195])).
% 81.95/14.40 thf(zip_derived_cl2, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i]:
% 81.95/14.40 (~ (sum @ X0 @ X1 @ X2) | (sum @ X1 @ X0 @ X2))),
% 81.95/14.40 inference('cnf', [status(esa)], [commutativity_of_addition])).
% 81.95/14.40 thf(zip_derived_cl9292, plain, ( (sum @ x @ x_times_y @ x)),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl8313, zip_derived_cl2])).
% 81.95/14.40 thf(zip_derived_cl7046, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i]: (product @ X1 @ (add @ X1 @ X0) @ X1)),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl6718])).
% 81.95/14.40 thf(zip_derived_cl0, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 81.95/14.40 inference('cnf', [status(esa)], [closure_of_addition])).
% 81.95/14.40 thf(zip_derived_cl25, plain,
% 81.95/14.40 ( (product @ x_times_y @ z @ x_times_y__times_z)),
% 81.95/14.40 inference('cnf', [status(esa)], [x_times_y__times_z])).
% 81.95/14.40 thf(distributivity6, axiom,
% 81.95/14.40 (( ~( sum @ X @ Y @ V1 ) ) | ( ~( sum @ X @ Z @ V2 ) ) |
% 81.95/14.40 ( ~( product @ Y @ Z @ V3 ) ) | ( ~( product @ V1 @ V2 @ V4 ) ) |
% 81.95/14.40 ( sum @ X @ V3 @ V4 ))).
% 81.95/14.40 thf(zip_derived_cl13, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 81.95/14.40 (~ (sum @ X0 @ X1 @ X2)
% 81.95/14.40 | ~ (sum @ X0 @ X3 @ X4)
% 81.95/14.40 | ~ (product @ X1 @ X3 @ X5)
% 81.95/14.40 | ~ (product @ X2 @ X4 @ X6)
% 81.95/14.40 | (sum @ X0 @ X5 @ X6))),
% 81.95/14.40 inference('cnf', [status(esa)], [distributivity6])).
% 81.95/14.40 thf(zip_derived_cl148, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 81.95/14.40 ( (sum @ X1 @ x_times_y__times_z @ X0)
% 81.95/14.40 | ~ (product @ X3 @ X2 @ X0)
% 81.95/14.40 | ~ (sum @ X1 @ z @ X2)
% 81.95/14.40 | ~ (sum @ X1 @ x_times_y @ X3))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl13])).
% 81.95/14.40 thf(zip_derived_cl3428, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i]:
% 81.95/14.40 (~ (sum @ X0 @ x_times_y @ X1)
% 81.95/14.40 | ~ (product @ X1 @ (add @ X0 @ z) @ X2)
% 81.95/14.40 | (sum @ X0 @ x_times_y__times_z @ X2))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl148])).
% 81.95/14.40 thf(zip_derived_cl49884, plain,
% 81.95/14.40 (![X0 : $i]:
% 81.95/14.40 ( (sum @ X0 @ x_times_y__times_z @ X0) | ~ (sum @ X0 @ x_times_y @ X0))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl7046, zip_derived_cl3428])).
% 81.95/14.40 thf(zip_derived_cl52581, plain, ( (sum @ x @ x_times_y__times_z @ x)),
% 81.95/14.40 inference('sup-', [status(thm)],
% 81.95/14.40 [zip_derived_cl9292, zip_derived_cl49884])).
% 81.95/14.40 thf(zip_derived_cl53248, plain,
% 81.95/14.40 ( (sum @ x_times__y_times_z @ x_times_y__times_z @ x_times__y_times_z)),
% 81.95/14.40 inference('demod', [status(thm)],
% 81.95/14.40 [zip_derived_cl9247, zip_derived_cl52581])).
% 81.95/14.40 thf(zip_derived_cl7, plain,
% 81.95/14.40 (![X0 : $i]: (product @ X0 @ multiplicative_identity @ X0)),
% 81.95/14.40 inference('cnf', [status(esa)], [multiplicative_identity2])).
% 81.95/14.40 thf(zip_derived_cl22, plain, ( (product @ y @ z @ y_times_z)),
% 81.95/14.40 inference('cnf', [status(esa)], [y_times_z])).
% 81.95/14.40 thf(zip_derived_cl3, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i]:
% 81.95/14.40 (~ (product @ X0 @ X1 @ X2) | (product @ X1 @ X0 @ X2))),
% 81.95/14.40 inference('cnf', [status(esa)], [commutativity_of_multiplication])).
% 81.95/14.40 thf(zip_derived_cl38, plain, ( (product @ z @ y @ y_times_z)),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl3])).
% 81.95/14.40 thf(zip_derived_cl8, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 81.95/14.40 (~ (product @ X0 @ X1 @ X2)
% 81.95/14.40 | ~ (product @ X0 @ X3 @ X4)
% 81.95/14.40 | ~ (sum @ X1 @ X3 @ X5)
% 81.95/14.40 | ~ (product @ X0 @ X5 @ X6)
% 81.95/14.40 | (sum @ X2 @ X4 @ X6))),
% 81.95/14.40 inference('cnf', [status(esa)], [distributivity1])).
% 81.95/14.40 thf(zip_derived_cl72, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 81.95/14.40 ( (sum @ y_times_z @ X1 @ X0)
% 81.95/14.40 | ~ (product @ z @ X2 @ X0)
% 81.95/14.40 | ~ (sum @ y @ X3 @ X2)
% 81.95/14.40 | ~ (product @ z @ X3 @ X1))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl8])).
% 81.95/14.40 thf(zip_derived_cl572, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i]:
% 81.95/14.40 (~ (product @ z @ X1 @ X0)
% 81.95/14.40 | ~ (sum @ y @ X1 @ X1)
% 81.95/14.40 | (sum @ y_times_z @ X0 @ X0))),
% 81.95/14.40 inference('eq_fact', [status(thm)], [zip_derived_cl72])).
% 81.95/14.40 thf(zip_derived_cl2353, plain,
% 81.95/14.40 (( (sum @ y_times_z @ z @ z)
% 81.95/14.40 | ~ (sum @ y @ multiplicative_identity @ multiplicative_identity))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl572])).
% 81.95/14.40 thf(zip_derived_cl8195, plain,
% 81.95/14.40 (![X0 : $i]:
% 81.95/14.40 (sum @ X0 @ multiplicative_identity @ multiplicative_identity)),
% 81.95/14.40 inference('sup+', [status(thm)], [zip_derived_cl8098, zip_derived_cl27])).
% 81.95/14.40 thf(zip_derived_cl8312, plain, ( (sum @ y_times_z @ z @ z)),
% 81.95/14.40 inference('demod', [status(thm)],
% 81.95/14.40 [zip_derived_cl2353, zip_derived_cl8195])).
% 81.95/14.40 thf(zip_derived_cl2, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i]:
% 81.95/14.40 (~ (sum @ X0 @ X1 @ X2) | (sum @ X1 @ X0 @ X2))),
% 81.95/14.40 inference('cnf', [status(esa)], [commutativity_of_addition])).
% 81.95/14.40 thf(zip_derived_cl9252, plain, ( (sum @ z @ y_times_z @ z)),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl8312, zip_derived_cl2])).
% 81.95/14.40 thf(zip_derived_cl7046, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i]: (product @ X1 @ (add @ X1 @ X0) @ X1)),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl6718])).
% 81.95/14.40 thf(zip_derived_cl0, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 81.95/14.40 inference('cnf', [status(esa)], [closure_of_addition])).
% 81.95/14.40 thf(zip_derived_cl40, plain,
% 81.95/14.40 ( (product @ y_times_z @ x @ x_times__y_times_z)),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl3])).
% 81.95/14.40 thf(zip_derived_cl13, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 81.95/14.40 (~ (sum @ X0 @ X1 @ X2)
% 81.95/14.40 | ~ (sum @ X0 @ X3 @ X4)
% 81.95/14.40 | ~ (product @ X1 @ X3 @ X5)
% 81.95/14.40 | ~ (product @ X2 @ X4 @ X6)
% 81.95/14.40 | (sum @ X0 @ X5 @ X6))),
% 81.95/14.40 inference('cnf', [status(esa)], [distributivity6])).
% 81.95/14.40 thf(zip_derived_cl145, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 81.95/14.40 ( (sum @ X1 @ x_times__y_times_z @ X0)
% 81.95/14.40 | ~ (product @ X3 @ X2 @ X0)
% 81.95/14.40 | ~ (sum @ X1 @ x @ X2)
% 81.95/14.40 | ~ (sum @ X1 @ y_times_z @ X3))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl40, zip_derived_cl13])).
% 81.95/14.40 thf(zip_derived_cl3305, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i]:
% 81.95/14.40 (~ (sum @ X0 @ y_times_z @ X1)
% 81.95/14.40 | ~ (product @ X1 @ (add @ X0 @ x) @ X2)
% 81.95/14.40 | (sum @ X0 @ x_times__y_times_z @ X2))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl145])).
% 81.95/14.40 thf(zip_derived_cl47368, plain,
% 81.95/14.40 (![X0 : $i]:
% 81.95/14.40 ( (sum @ X0 @ x_times__y_times_z @ X0) | ~ (sum @ X0 @ y_times_z @ X0))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl7046, zip_derived_cl3305])).
% 81.95/14.40 thf(zip_derived_cl47400, plain, ( (sum @ z @ x_times__y_times_z @ z)),
% 81.95/14.40 inference('sup-', [status(thm)],
% 81.95/14.40 [zip_derived_cl9252, zip_derived_cl47368])).
% 81.95/14.40 thf(zip_derived_cl24, plain, ( (product @ x @ y @ x_times_y)),
% 81.95/14.40 inference('cnf', [status(esa)], [x_times_y])).
% 81.95/14.40 thf(zip_derived_cl23, plain,
% 81.95/14.40 ( (product @ x @ y_times_z @ x_times__y_times_z)),
% 81.95/14.40 inference('cnf', [status(esa)], [x_times__y_times_z])).
% 81.95/14.40 thf(zip_derived_cl8, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 81.95/14.40 (~ (product @ X0 @ X1 @ X2)
% 81.95/14.40 | ~ (product @ X0 @ X3 @ X4)
% 81.95/14.40 | ~ (sum @ X1 @ X3 @ X5)
% 81.95/14.40 | ~ (product @ X0 @ X5 @ X6)
% 81.95/14.40 | (sum @ X2 @ X4 @ X6))),
% 81.95/14.40 inference('cnf', [status(esa)], [distributivity1])).
% 81.95/14.40 thf(zip_derived_cl74, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 81.95/14.40 ( (sum @ x_times__y_times_z @ X1 @ X0)
% 81.95/14.40 | ~ (product @ x @ X2 @ X0)
% 81.95/14.40 | ~ (sum @ y_times_z @ X3 @ X2)
% 81.95/14.40 | ~ (product @ x @ X3 @ X1))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl8])).
% 81.95/14.40 thf(zip_derived_cl618, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i]:
% 81.95/14.40 (~ (product @ x @ X1 @ X0)
% 81.95/14.40 | ~ (sum @ y_times_z @ X1 @ X1)
% 81.95/14.40 | (sum @ x_times__y_times_z @ X0 @ X0))),
% 81.95/14.40 inference('eq_fact', [status(thm)], [zip_derived_cl74])).
% 81.95/14.40 thf(zip_derived_cl700, plain,
% 81.95/14.40 (( (sum @ x_times__y_times_z @ x_times_y @ x_times_y)
% 81.95/14.40 | ~ (sum @ y_times_z @ y @ y))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl618])).
% 81.95/14.40 thf(zip_derived_cl7, plain,
% 81.95/14.40 (![X0 : $i]: (product @ X0 @ multiplicative_identity @ X0)),
% 81.95/14.40 inference('cnf', [status(esa)], [multiplicative_identity2])).
% 81.95/14.40 thf(zip_derived_cl22, plain, ( (product @ y @ z @ y_times_z)),
% 81.95/14.40 inference('cnf', [status(esa)], [y_times_z])).
% 81.95/14.40 thf(zip_derived_cl8, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 81.95/14.40 (~ (product @ X0 @ X1 @ X2)
% 81.95/14.40 | ~ (product @ X0 @ X3 @ X4)
% 81.95/14.40 | ~ (sum @ X1 @ X3 @ X5)
% 81.95/14.40 | ~ (product @ X0 @ X5 @ X6)
% 81.95/14.40 | (sum @ X2 @ X4 @ X6))),
% 81.95/14.40 inference('cnf', [status(esa)], [distributivity1])).
% 81.95/14.40 thf(zip_derived_cl70, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 81.95/14.40 ( (sum @ y_times_z @ X1 @ X0)
% 81.95/14.40 | ~ (product @ y @ X2 @ X0)
% 81.95/14.40 | ~ (sum @ z @ X3 @ X2)
% 81.95/14.40 | ~ (product @ y @ X3 @ X1))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl8])).
% 81.95/14.40 thf(zip_derived_cl489, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i]:
% 81.95/14.40 (~ (product @ y @ X1 @ X0)
% 81.95/14.40 | ~ (sum @ z @ X1 @ X1)
% 81.95/14.40 | (sum @ y_times_z @ X0 @ X0))),
% 81.95/14.40 inference('eq_fact', [status(thm)], [zip_derived_cl70])).
% 81.95/14.40 thf(zip_derived_cl2326, plain,
% 81.95/14.40 (( (sum @ y_times_z @ y @ y)
% 81.95/14.40 | ~ (sum @ z @ multiplicative_identity @ multiplicative_identity))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl489])).
% 81.95/14.40 thf(zip_derived_cl8195, plain,
% 81.95/14.40 (![X0 : $i]:
% 81.95/14.40 (sum @ X0 @ multiplicative_identity @ multiplicative_identity)),
% 81.95/14.40 inference('sup+', [status(thm)], [zip_derived_cl8098, zip_derived_cl27])).
% 81.95/14.40 thf(zip_derived_cl8310, plain, ( (sum @ y_times_z @ y @ y)),
% 81.95/14.40 inference('demod', [status(thm)],
% 81.95/14.40 [zip_derived_cl2326, zip_derived_cl8195])).
% 81.95/14.40 thf(zip_derived_cl8779, plain,
% 81.95/14.40 ( (sum @ x_times__y_times_z @ x_times_y @ x_times_y)),
% 81.95/14.40 inference('demod', [status(thm)], [zip_derived_cl700, zip_derived_cl8310])).
% 81.95/14.40 thf(zip_derived_cl6718, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i]:
% 81.95/14.40 (~ (sum @ X0 @ X2 @ X1) | (product @ X0 @ X1 @ X0))),
% 81.95/14.40 inference('demod', [status(thm)],
% 81.95/14.40 [zip_derived_cl2437, zip_derived_cl6493])).
% 81.95/14.40 thf(zip_derived_cl8835, plain,
% 81.95/14.40 ( (product @ x_times__y_times_z @ x_times_y @ x_times__y_times_z)),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl8779, zip_derived_cl6718])).
% 81.95/14.40 thf(zip_derived_cl3, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i]:
% 81.95/14.40 (~ (product @ X0 @ X1 @ X2) | (product @ X1 @ X0 @ X2))),
% 81.95/14.40 inference('cnf', [status(esa)], [commutativity_of_multiplication])).
% 81.95/14.40 thf(zip_derived_cl8852, plain,
% 81.95/14.40 ( (product @ x_times_y @ x_times__y_times_z @ x_times__y_times_z)),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl8835, zip_derived_cl3])).
% 81.95/14.40 thf(zip_derived_cl25, plain,
% 81.95/14.40 ( (product @ x_times_y @ z @ x_times_y__times_z)),
% 81.95/14.40 inference('cnf', [status(esa)], [x_times_y__times_z])).
% 81.95/14.40 thf(zip_derived_cl65, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 81.95/14.40 ( (sum @ (multiply @ X1 @ X0) @ X3 @ X2)
% 81.95/14.40 | ~ (product @ X1 @ X4 @ X2)
% 81.95/14.40 | ~ (sum @ X0 @ X5 @ X4)
% 81.95/14.40 | ~ (product @ X1 @ X5 @ X3))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl8])).
% 81.95/14.40 thf(zip_derived_cl331, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i]:
% 81.95/14.40 (~ (product @ x_times_y @ X1 @ X0)
% 81.95/14.40 | ~ (sum @ X2 @ X1 @ z)
% 81.95/14.40 | (sum @ (multiply @ x_times_y @ X2) @ X0 @ x_times_y__times_z))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl65])).
% 81.95/14.40 thf(zip_derived_cl8921, plain,
% 81.95/14.40 (![X0 : $i]:
% 81.95/14.40 ( (sum @ (multiply @ x_times_y @ X0) @ x_times__y_times_z @
% 81.95/14.40 x_times_y__times_z)
% 81.95/14.40 | ~ (sum @ X0 @ x_times__y_times_z @ z))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl8852, zip_derived_cl331])).
% 81.95/14.40 thf(zip_derived_cl48086, plain,
% 81.95/14.40 ( (sum @ (multiply @ x_times_y @ z) @ x_times__y_times_z @
% 81.95/14.40 x_times_y__times_z)),
% 81.95/14.40 inference('sup-', [status(thm)],
% 81.95/14.40 [zip_derived_cl47400, zip_derived_cl8921])).
% 81.95/14.40 thf(zip_derived_cl1, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 81.95/14.40 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 81.95/14.40 thf(zip_derived_cl25, plain,
% 81.95/14.40 ( (product @ x_times_y @ z @ x_times_y__times_z)),
% 81.95/14.40 inference('cnf', [status(esa)], [x_times_y__times_z])).
% 81.95/14.40 thf(zip_derived_cl21, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 81.95/14.40 (~ (product @ X0 @ X1 @ X2)
% 81.95/14.40 | ~ (product @ X0 @ X1 @ X3)
% 81.95/14.40 | ((X2) = (X3)))),
% 81.95/14.40 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 81.95/14.40 thf(zip_derived_cl59, plain,
% 81.95/14.40 (![X0 : $i]:
% 81.95/14.40 (((x_times_y__times_z) = (X0)) | ~ (product @ x_times_y @ z @ X0))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl21])).
% 81.95/14.40 thf(zip_derived_cl83, plain,
% 81.95/14.40 (((x_times_y__times_z) = (multiply @ x_times_y @ z))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl59])).
% 81.95/14.40 thf(zip_derived_cl48100, plain,
% 81.95/14.40 ( (sum @ x_times_y__times_z @ x_times__y_times_z @ x_times_y__times_z)),
% 81.95/14.40 inference('demod', [status(thm)], [zip_derived_cl48086, zip_derived_cl83])).
% 81.95/14.40 thf(zip_derived_cl2, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i]:
% 81.95/14.40 (~ (sum @ X0 @ X1 @ X2) | (sum @ X1 @ X0 @ X2))),
% 81.95/14.40 inference('cnf', [status(esa)], [commutativity_of_addition])).
% 81.95/14.40 thf(zip_derived_cl48106, plain,
% 81.95/14.40 ( (sum @ x_times__y_times_z @ x_times_y__times_z @ x_times_y__times_z)),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl48100, zip_derived_cl2])).
% 81.95/14.40 thf(zip_derived_cl20, plain,
% 81.95/14.40 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 81.95/14.40 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 81.95/14.40 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 81.95/14.40 thf(zip_derived_cl48171, plain,
% 81.95/14.40 (![X0 : $i]:
% 81.95/14.40 (((x_times_y__times_z) = (X0))
% 81.95/14.40 | ~ (sum @ x_times__y_times_z @ x_times_y__times_z @ X0))),
% 81.95/14.40 inference('sup-', [status(thm)], [zip_derived_cl48106, zip_derived_cl20])).
% 81.95/14.40 thf(zip_derived_cl53388, plain,
% 81.95/14.40 (((x_times_y__times_z) = (x_times__y_times_z))),
% 81.95/14.40 inference('sup-', [status(thm)],
% 81.95/14.40 [zip_derived_cl53248, zip_derived_cl48171])).
% 81.95/14.40 thf(prove_equality, conjecture,
% 81.95/14.40 (( x_times__y_times_z ) = ( x_times_y__times_z ))).
% 81.95/14.40 thf(zf_stmt_0, negated_conjecture,
% 81.95/14.40 (( x_times__y_times_z ) != ( x_times_y__times_z )),
% 81.95/14.40 inference('cnf.neg', [status(esa)], [prove_equality])).
% 81.95/14.40 thf(zip_derived_cl26, plain,
% 81.95/14.40 (((x_times__y_times_z) != (x_times_y__times_z))),
% 81.95/14.40 inference('cnf', [status(esa)], [zf_stmt_0])).
% 81.95/14.40 thf(zip_derived_cl53393, plain, ($false),
% 81.95/14.40 inference('simplify_reflect-', [status(thm)],
% 81.95/14.40 [zip_derived_cl53388, zip_derived_cl26])).
% 81.95/14.40
% 81.95/14.40 % SZS output end Refutation
% 81.95/14.40
% 81.95/14.40
% 81.95/14.40 % Terminating...
% 81.95/14.50 % Runner terminated.
% 81.95/14.51 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------