%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : BOO014-3 : TPTP v9.2.0. Bugfixed v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.4UkjujxmsN true
% Computer : n009.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 04:29:47 PM UTC 2025
% Result : Unsatisfiable 96.39s 14.43s
% Output : Refutation 96.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : BOO014-3 : TPTP v9.2.0. Bugfixed v2.2.0.
% 0.13/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.4UkjujxmsN true
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 1 13:53:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.34 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.48/0.61 % Total configuration time : 435
% 0.48/0.61 % Estimated wc time : 1092
% 0.48/0.61 % Estimated cpu time (7 cpus) : 156.0
% 0.51/0.70 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.51/0.71 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.51/0.71 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.51/0.71 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.52/0.72 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.52/0.73 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.52/0.73 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 96.39/14.43 % Solved by fo/fo5.sh.
% 96.39/14.43 % done 17519 iterations in 13.673s
% 96.39/14.43 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 96.39/14.43 % SZS output start Refutation
% 96.39/14.43 thf(sum_type, type, sum: $i > $i > $i > $o).
% 96.39/14.43 thf(x_type, type, x: $i).
% 96.39/14.43 thf(x_inverse_times_y_inverse_type, type, x_inverse_times_y_inverse: $i).
% 96.39/14.43 thf(x_plus_y_type, type, x_plus_y: $i).
% 96.39/14.43 thf(multiplicative_identity_type, type, multiplicative_identity: $i).
% 96.39/14.43 thf(inverse_type, type, inverse: $i > $i).
% 96.39/14.43 thf(multiply_type, type, multiply: $i > $i > $i).
% 96.39/14.43 thf(product_type, type, product: $i > $i > $i > $o).
% 96.39/14.43 thf(add_type, type, add: $i > $i > $i).
% 96.39/14.43 thf(y_type, type, y: $i).
% 96.39/14.43 thf(additive_identity_type, type, additive_identity: $i).
% 96.39/14.43 thf(additive_identity2, axiom, (sum @ X @ additive_identity @ X)).
% 96.39/14.43 thf(zip_derived_cl5, plain,
% 96.39/14.43 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 96.39/14.43 inference('cnf', [status(esa)], [additive_identity2])).
% 96.39/14.43 thf(zip_derived_cl5, plain,
% 96.39/14.43 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 96.39/14.43 inference('cnf', [status(esa)], [additive_identity2])).
% 96.39/14.43 thf(x_plus_y, axiom, (sum @ x @ y @ x_plus_y)).
% 96.39/14.43 thf(zip_derived_cl24, plain, ( (sum @ x @ y @ x_plus_y)),
% 96.39/14.43 inference('cnf', [status(esa)], [x_plus_y])).
% 96.39/14.43 thf(commutativity_of_addition, axiom,
% 96.39/14.43 (( ~( sum @ X @ Y @ Z ) ) | ( sum @ Y @ X @ Z ))).
% 96.39/14.43 thf(zip_derived_cl2, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 96.39/14.43 (~ (sum @ X0 @ X1 @ X2) | (sum @ X1 @ X0 @ X2))),
% 96.39/14.43 inference('cnf', [status(esa)], [commutativity_of_addition])).
% 96.39/14.43 thf(zip_derived_cl38, plain, ( (sum @ y @ x @ x_plus_y)),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl2])).
% 96.39/14.43 thf(distributivity5, axiom,
% 96.39/14.43 (( ~( sum @ X @ Y @ V1 ) ) | ( ~( sum @ X @ Z @ V2 ) ) |
% 96.39/14.43 ( ~( product @ Y @ Z @ V3 ) ) | ( ~( sum @ X @ V3 @ V4 ) ) |
% 96.39/14.43 ( product @ V1 @ V2 @ V4 ))).
% 96.39/14.43 thf(zip_derived_cl12, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 96.39/14.43 (~ (sum @ X0 @ X1 @ X2)
% 96.39/14.43 | ~ (sum @ X0 @ X3 @ X4)
% 96.39/14.43 | ~ (product @ X1 @ X3 @ X5)
% 96.39/14.43 | ~ (sum @ X0 @ X5 @ X6)
% 96.39/14.43 | (product @ X2 @ X4 @ X6))),
% 96.39/14.43 inference('cnf', [status(esa)], [distributivity5])).
% 96.39/14.43 thf(zip_derived_cl131, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 96.39/14.43 ( (product @ x_plus_y @ X1 @ X0)
% 96.39/14.43 | ~ (sum @ y @ X2 @ X0)
% 96.39/14.43 | ~ (product @ x @ X3 @ X2)
% 96.39/14.43 | ~ (sum @ y @ X3 @ X1))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl12])).
% 96.39/14.43 thf(zip_derived_cl2197, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]:
% 96.39/14.43 (~ (sum @ y @ X1 @ X0)
% 96.39/14.43 | ~ (product @ x @ X1 @ X1)
% 96.39/14.43 | (product @ x_plus_y @ X0 @ X0))),
% 96.39/14.43 inference('eq_fact', [status(thm)], [zip_derived_cl131])).
% 96.39/14.43 thf(zip_derived_cl2391, plain,
% 96.39/14.43 (( (product @ x_plus_y @ y @ y)
% 96.39/14.43 | ~ (product @ x @ additive_identity @ additive_identity))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl2197])).
% 96.39/14.43 thf(closure_of_multiplication, axiom,
% 96.39/14.43 (product @ X @ Y @ ( multiply @ X @ Y ))).
% 96.39/14.43 thf(zip_derived_cl1, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 96.39/14.43 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 96.39/14.43 thf(zip_derived_cl5, plain,
% 96.39/14.43 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 96.39/14.43 inference('cnf', [status(esa)], [additive_identity2])).
% 96.39/14.43 thf(multiplicative_inverse2, axiom,
% 96.39/14.43 (product @ X @ ( inverse @ X ) @ additive_identity)).
% 96.39/14.43 thf(zip_derived_cl19, plain,
% 96.39/14.43 (![X0 : $i]: (product @ X0 @ (inverse @ X0) @ additive_identity)),
% 96.39/14.43 inference('cnf', [status(esa)], [multiplicative_inverse2])).
% 96.39/14.43 thf(zip_derived_cl1, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 96.39/14.43 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 96.39/14.43 thf(distributivity1, axiom,
% 96.39/14.43 (( ~( product @ X @ Y @ V1 ) ) | ( ~( product @ X @ Z @ V2 ) ) |
% 96.39/14.43 ( ~( sum @ Y @ Z @ V3 ) ) | ( ~( product @ X @ V3 @ V4 ) ) |
% 96.39/14.43 ( sum @ V1 @ V2 @ V4 ))).
% 96.39/14.43 thf(zip_derived_cl8, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 96.39/14.43 (~ (product @ X0 @ X1 @ X2)
% 96.39/14.43 | ~ (product @ X0 @ X3 @ X4)
% 96.39/14.43 | ~ (sum @ X1 @ X3 @ X5)
% 96.39/14.43 | ~ (product @ X0 @ X5 @ X6)
% 96.39/14.43 | (sum @ X2 @ X4 @ X6))),
% 96.39/14.43 inference('cnf', [status(esa)], [distributivity1])).
% 96.39/14.43 thf(zip_derived_cl71, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 96.39/14.43 ( (sum @ (multiply @ X1 @ X0) @ X3 @ X2)
% 96.39/14.43 | ~ (product @ X1 @ X4 @ X2)
% 96.39/14.43 | ~ (sum @ X0 @ X5 @ X4)
% 96.39/14.43 | ~ (product @ X1 @ X5 @ X3))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl8])).
% 96.39/14.43 thf(zip_derived_cl344, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 96.39/14.43 (~ (product @ X0 @ X2 @ X1)
% 96.39/14.43 | ~ (sum @ X3 @ X2 @ (inverse @ X0))
% 96.39/14.43 | (sum @ (multiply @ X0 @ X3) @ X1 @ additive_identity))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl71])).
% 96.39/14.43 thf(zip_derived_cl5591, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]:
% 96.39/14.43 ( (sum @ (multiply @ X0 @ (inverse @ X0)) @ X1 @ additive_identity)
% 96.39/14.43 | ~ (product @ X0 @ additive_identity @ X1))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl344])).
% 96.39/14.43 thf(zip_derived_cl1, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 96.39/14.43 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 96.39/14.43 thf(zip_derived_cl19, plain,
% 96.39/14.43 (![X0 : $i]: (product @ X0 @ (inverse @ X0) @ additive_identity)),
% 96.39/14.43 inference('cnf', [status(esa)], [multiplicative_inverse2])).
% 96.39/14.43 thf(multiplication_is_well_defined, axiom,
% 96.39/14.43 (( ~( product @ X @ Y @ U ) ) | ( ~( product @ X @ Y @ V ) ) |
% 96.39/14.43 ( ( U ) = ( V ) ))).
% 96.39/14.43 thf(zip_derived_cl21, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 96.39/14.43 (~ (product @ X0 @ X1 @ X2)
% 96.39/14.43 | ~ (product @ X0 @ X1 @ X3)
% 96.39/14.43 | ((X2) = (X3)))),
% 96.39/14.43 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 96.39/14.43 thf(zip_derived_cl58, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]:
% 96.39/14.43 (((additive_identity) = (X1)) | ~ (product @ X0 @ (inverse @ X0) @ X1))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl21])).
% 96.39/14.43 thf(zip_derived_cl199, plain,
% 96.39/14.43 (![X0 : $i]: ((additive_identity) = (multiply @ X0 @ (inverse @ X0)))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl58])).
% 96.39/14.43 thf(zip_derived_cl5609, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]:
% 96.39/14.43 ( (sum @ additive_identity @ X1 @ additive_identity)
% 96.39/14.43 | ~ (product @ X0 @ additive_identity @ X1))),
% 96.39/14.43 inference('demod', [status(thm)], [zip_derived_cl5591, zip_derived_cl199])).
% 96.39/14.43 thf(zip_derived_cl5614, plain,
% 96.39/14.43 (![X0 : $i]:
% 96.39/14.43 (sum @ additive_identity @ (multiply @ X0 @ additive_identity) @
% 96.39/14.43 additive_identity)),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl5609])).
% 96.39/14.43 thf(additive_identity1, axiom, (sum @ additive_identity @ X @ X)).
% 96.39/14.43 thf(zip_derived_cl4, plain,
% 96.39/14.43 (![X0 : $i]: (sum @ additive_identity @ X0 @ X0)),
% 96.39/14.43 inference('cnf', [status(esa)], [additive_identity1])).
% 96.39/14.43 thf(addition_is_well_defined, axiom,
% 96.39/14.43 (( ~( sum @ X @ Y @ U ) ) | ( ~( sum @ X @ Y @ V ) ) | ( ( U ) = ( V ) ))).
% 96.39/14.43 thf(zip_derived_cl20, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 96.39/14.43 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 96.39/14.43 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 96.39/14.43 thf(zip_derived_cl51, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]:
% 96.39/14.43 (((X0) = (X1)) | ~ (sum @ additive_identity @ X0 @ X1))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl20])).
% 96.39/14.43 thf(zip_derived_cl5670, plain,
% 96.39/14.43 (![X0 : $i]: ((multiply @ X0 @ additive_identity) = (additive_identity))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl5614, zip_derived_cl51])).
% 96.39/14.43 thf(zip_derived_cl1, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 96.39/14.43 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 96.39/14.43 thf(zip_derived_cl5706, plain,
% 96.39/14.43 (![X0 : $i]: (product @ X0 @ additive_identity @ additive_identity)),
% 96.39/14.43 inference('sup+', [status(thm)], [zip_derived_cl5670, zip_derived_cl1])).
% 96.39/14.43 thf(zip_derived_cl5748, plain, ( (product @ x_plus_y @ y @ y)),
% 96.39/14.43 inference('demod', [status(thm)],
% 96.39/14.43 [zip_derived_cl2391, zip_derived_cl5706])).
% 96.39/14.43 thf(closure_of_addition, axiom, (sum @ X @ Y @ ( add @ X @ Y ))).
% 96.39/14.43 thf(zip_derived_cl0, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 96.39/14.43 inference('cnf', [status(esa)], [closure_of_addition])).
% 96.39/14.43 thf(multiplicative_identity2, axiom,
% 96.39/14.43 (product @ X @ multiplicative_identity @ X)).
% 96.39/14.43 thf(zip_derived_cl7, plain,
% 96.39/14.43 (![X0 : $i]: (product @ X0 @ multiplicative_identity @ X0)),
% 96.39/14.43 inference('cnf', [status(esa)], [multiplicative_identity2])).
% 96.39/14.43 thf(zip_derived_cl38, plain, ( (sum @ y @ x @ x_plus_y)),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl2])).
% 96.39/14.43 thf(zip_derived_cl131, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 96.39/14.43 ( (product @ x_plus_y @ X1 @ X0)
% 96.39/14.43 | ~ (sum @ y @ X2 @ X0)
% 96.39/14.43 | ~ (product @ x @ X3 @ X2)
% 96.39/14.43 | ~ (sum @ y @ X3 @ X1))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl12])).
% 96.39/14.43 thf(zip_derived_cl2196, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]:
% 96.39/14.43 (~ (sum @ y @ X1 @ X0)
% 96.39/14.43 | ~ (product @ x @ X1 @ x)
% 96.39/14.43 | (product @ x_plus_y @ X0 @ x_plus_y))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl131])).
% 96.39/14.43 thf(zip_derived_cl2201, plain,
% 96.39/14.43 (![X0 : $i]:
% 96.39/14.43 ( (product @ x_plus_y @ X0 @ x_plus_y)
% 96.39/14.43 | ~ (sum @ y @ multiplicative_identity @ X0))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl2196])).
% 96.39/14.43 thf(zip_derived_cl2241, plain,
% 96.39/14.43 ( (product @ x_plus_y @ (add @ y @ multiplicative_identity) @ x_plus_y)),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl2201])).
% 96.39/14.43 thf(zip_derived_cl0, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 96.39/14.43 inference('cnf', [status(esa)], [closure_of_addition])).
% 96.39/14.43 thf(zip_derived_cl2, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 96.39/14.43 (~ (sum @ X0 @ X1 @ X2) | (sum @ X1 @ X0 @ X2))),
% 96.39/14.43 inference('cnf', [status(esa)], [commutativity_of_addition])).
% 96.39/14.43 thf(zip_derived_cl33, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 96.39/14.43 thf(zip_derived_cl7, plain,
% 96.39/14.43 (![X0 : $i]: (product @ X0 @ multiplicative_identity @ X0)),
% 96.39/14.43 inference('cnf', [status(esa)], [multiplicative_identity2])).
% 96.39/14.43 thf(zip_derived_cl8, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 96.39/14.43 (~ (product @ X0 @ X1 @ X2)
% 96.39/14.43 | ~ (product @ X0 @ X3 @ X4)
% 96.39/14.43 | ~ (sum @ X1 @ X3 @ X5)
% 96.39/14.43 | ~ (product @ X0 @ X5 @ X6)
% 96.39/14.43 | (sum @ X2 @ X4 @ X6))),
% 96.39/14.43 inference('cnf', [status(esa)], [distributivity1])).
% 96.39/14.43 thf(zip_derived_cl72, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 96.39/14.43 ( (sum @ X0 @ X2 @ X1)
% 96.39/14.43 | ~ (product @ X0 @ X3 @ X1)
% 96.39/14.43 | ~ (sum @ multiplicative_identity @ X4 @ X3)
% 96.39/14.43 | ~ (product @ X0 @ X4 @ X2))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl8])).
% 96.39/14.43 thf(zip_derived_cl393, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 96.39/14.43 (~ (product @ X2 @ X0 @ X1)
% 96.39/14.43 | ~ (product @ X2 @ (add @ X0 @ multiplicative_identity) @ X3)
% 96.39/14.43 | (sum @ X2 @ X1 @ X3))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl33, zip_derived_cl72])).
% 96.39/14.43 thf(zip_derived_cl6155, plain,
% 96.39/14.43 (![X0 : $i]:
% 96.39/14.43 ( (sum @ x_plus_y @ X0 @ x_plus_y) | ~ (product @ x_plus_y @ y @ X0))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl2241, zip_derived_cl393])).
% 96.39/14.43 thf(zip_derived_cl6330, plain, ( (sum @ x_plus_y @ y @ x_plus_y)),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl5748, zip_derived_cl6155])).
% 96.39/14.43 thf(zip_derived_cl2, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 96.39/14.43 (~ (sum @ X0 @ X1 @ X2) | (sum @ X1 @ X0 @ X2))),
% 96.39/14.43 inference('cnf', [status(esa)], [commutativity_of_addition])).
% 96.39/14.43 thf(zip_derived_cl6333, plain, ( (sum @ y @ x_plus_y @ x_plus_y)),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl6330, zip_derived_cl2])).
% 96.39/14.43 thf(multiplicative_inverse1, axiom,
% 96.39/14.43 (product @ ( inverse @ X ) @ X @ additive_identity)).
% 96.39/14.43 thf(zip_derived_cl18, plain,
% 96.39/14.43 (![X0 : $i]: (product @ (inverse @ X0) @ X0 @ additive_identity)),
% 96.39/14.43 inference('cnf', [status(esa)], [multiplicative_inverse1])).
% 96.39/14.43 thf(zip_derived_cl1, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 96.39/14.43 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 96.39/14.43 thf(zip_derived_cl71, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 96.39/14.43 ( (sum @ (multiply @ X1 @ X0) @ X3 @ X2)
% 96.39/14.43 | ~ (product @ X1 @ X4 @ X2)
% 96.39/14.43 | ~ (sum @ X0 @ X5 @ X4)
% 96.39/14.43 | ~ (product @ X1 @ X5 @ X3))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl8])).
% 96.39/14.43 thf(zip_derived_cl341, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 96.39/14.43 (~ (product @ X1 @ X3 @ X2)
% 96.39/14.43 | ~ (sum @ X4 @ X3 @ X0)
% 96.39/14.43 | (sum @ (multiply @ X1 @ X4) @ X2 @ (multiply @ X1 @ X0)))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl71])).
% 96.39/14.43 thf(zip_derived_cl5379, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 96.39/14.43 ( (sum @ (multiply @ (inverse @ X0) @ X2) @ additive_identity @
% 96.39/14.43 (multiply @ (inverse @ X0) @ X1))
% 96.39/14.43 | ~ (sum @ X2 @ X0 @ X1))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl341])).
% 96.39/14.43 thf(zip_derived_cl67201, plain,
% 96.39/14.43 ( (sum @ (multiply @ (inverse @ x_plus_y) @ y) @ additive_identity @
% 96.39/14.43 (multiply @ (inverse @ x_plus_y) @ x_plus_y))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl6333, zip_derived_cl5379])).
% 96.39/14.43 thf(zip_derived_cl1, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 96.39/14.43 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 96.39/14.43 thf(commutativity_of_multiplication, axiom,
% 96.39/14.43 (( ~( product @ X @ Y @ Z ) ) | ( product @ Y @ X @ Z ))).
% 96.39/14.43 thf(zip_derived_cl3, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 96.39/14.43 (~ (product @ X0 @ X1 @ X2) | (product @ X1 @ X0 @ X2))),
% 96.39/14.43 inference('cnf', [status(esa)], [commutativity_of_multiplication])).
% 96.39/14.43 thf(zip_derived_cl47, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X1 @ X0))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl3])).
% 96.39/14.43 thf(zip_derived_cl1, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 96.39/14.43 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 96.39/14.43 thf(zip_derived_cl21, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 96.39/14.43 (~ (product @ X0 @ X1 @ X2)
% 96.39/14.43 | ~ (product @ X0 @ X1 @ X3)
% 96.39/14.43 | ((X2) = (X3)))),
% 96.39/14.43 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 96.39/14.43 thf(zip_derived_cl56, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 96.39/14.43 (((multiply @ X1 @ X0) = (X2)) | ~ (product @ X1 @ X0 @ X2))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl21])).
% 96.39/14.43 thf(zip_derived_cl256, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl47, zip_derived_cl56])).
% 96.39/14.43 thf(zip_derived_cl1, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 96.39/14.43 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 96.39/14.43 thf(zip_derived_cl18, plain,
% 96.39/14.43 (![X0 : $i]: (product @ (inverse @ X0) @ X0 @ additive_identity)),
% 96.39/14.43 inference('cnf', [status(esa)], [multiplicative_inverse1])).
% 96.39/14.43 thf(zip_derived_cl21, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 96.39/14.43 (~ (product @ X0 @ X1 @ X2)
% 96.39/14.43 | ~ (product @ X0 @ X1 @ X3)
% 96.39/14.43 | ((X2) = (X3)))),
% 96.39/14.43 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 96.39/14.43 thf(zip_derived_cl60, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]:
% 96.39/14.43 (((additive_identity) = (X1)) | ~ (product @ (inverse @ X0) @ X0 @ X1))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl21])).
% 96.39/14.43 thf(zip_derived_cl205, plain,
% 96.39/14.43 (![X0 : $i]: ((additive_identity) = (multiply @ (inverse @ X0) @ X0))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl60])).
% 96.39/14.43 thf(zip_derived_cl67259, plain,
% 96.39/14.43 ( (sum @ (multiply @ y @ (inverse @ x_plus_y)) @ additive_identity @
% 96.39/14.43 additive_identity)),
% 96.39/14.43 inference('demod', [status(thm)],
% 96.39/14.43 [zip_derived_cl67201, zip_derived_cl256, zip_derived_cl205])).
% 96.39/14.43 thf(zip_derived_cl5, plain,
% 96.39/14.43 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 96.39/14.43 inference('cnf', [status(esa)], [additive_identity2])).
% 96.39/14.43 thf(zip_derived_cl20, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 96.39/14.43 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 96.39/14.43 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 96.39/14.43 thf(zip_derived_cl49, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]:
% 96.39/14.43 (((X0) = (X1)) | ~ (sum @ X0 @ additive_identity @ X1))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl20])).
% 96.39/14.43 thf(zip_derived_cl68831, plain,
% 96.39/14.43 (((multiply @ y @ (inverse @ x_plus_y)) = (additive_identity))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl67259, zip_derived_cl49])).
% 96.39/14.43 thf(zip_derived_cl256, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl47, zip_derived_cl56])).
% 96.39/14.43 thf(zip_derived_cl256, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl47, zip_derived_cl56])).
% 96.39/14.43 thf(zip_derived_cl1, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 96.39/14.43 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 96.39/14.43 thf(zip_derived_cl7, plain,
% 96.39/14.43 (![X0 : $i]: (product @ X0 @ multiplicative_identity @ X0)),
% 96.39/14.43 inference('cnf', [status(esa)], [multiplicative_identity2])).
% 96.39/14.43 thf(zip_derived_cl8, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 96.39/14.43 (~ (product @ X0 @ X1 @ X2)
% 96.39/14.43 | ~ (product @ X0 @ X3 @ X4)
% 96.39/14.43 | ~ (sum @ X1 @ X3 @ X5)
% 96.39/14.43 | ~ (product @ X0 @ X5 @ X6)
% 96.39/14.43 | (sum @ X2 @ X4 @ X6))),
% 96.39/14.43 inference('cnf', [status(esa)], [distributivity1])).
% 96.39/14.43 thf(zip_derived_cl78, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 96.39/14.43 ( (sum @ X0 @ X3 @ X0)
% 96.39/14.43 | ~ (product @ X2 @ X1 @ X0)
% 96.39/14.43 | ~ (sum @ X1 @ X4 @ X1)
% 96.39/14.43 | ~ (product @ X2 @ X4 @ X3))),
% 96.39/14.43 inference('eq_fact', [status(thm)], [zip_derived_cl8])).
% 96.39/14.43 thf(zip_derived_cl629, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 96.39/14.43 (~ (product @ X0 @ X2 @ X1)
% 96.39/14.43 | ~ (sum @ multiplicative_identity @ X2 @ multiplicative_identity)
% 96.39/14.43 | (sum @ X0 @ X1 @ X0))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl78])).
% 96.39/14.43 thf(zip_derived_cl0, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 96.39/14.43 inference('cnf', [status(esa)], [closure_of_addition])).
% 96.39/14.43 thf(zip_derived_cl5, plain,
% 96.39/14.43 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 96.39/14.43 inference('cnf', [status(esa)], [additive_identity2])).
% 96.39/14.43 thf(zip_derived_cl12, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 96.39/14.43 (~ (sum @ X0 @ X1 @ X2)
% 96.39/14.43 | ~ (sum @ X0 @ X3 @ X4)
% 96.39/14.43 | ~ (product @ X1 @ X3 @ X5)
% 96.39/14.43 | ~ (sum @ X0 @ X5 @ X6)
% 96.39/14.43 | (product @ X2 @ X4 @ X6))),
% 96.39/14.43 inference('cnf', [status(esa)], [distributivity5])).
% 96.39/14.43 thf(zip_derived_cl133, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 96.39/14.43 ( (product @ X0 @ X3 @ X0)
% 96.39/14.43 | ~ (sum @ X2 @ X1 @ X0)
% 96.39/14.43 | ~ (product @ X1 @ X4 @ X1)
% 96.39/14.43 | ~ (sum @ X2 @ X4 @ X3))),
% 96.39/14.43 inference('eq_fact', [status(thm)], [zip_derived_cl12])).
% 96.39/14.43 thf(zip_derived_cl2306, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 96.39/14.43 (~ (sum @ X0 @ X2 @ X1)
% 96.39/14.43 | ~ (product @ additive_identity @ X2 @ additive_identity)
% 96.39/14.43 | (product @ X0 @ X1 @ X0))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl133])).
% 96.39/14.43 thf(zip_derived_cl5670, plain,
% 96.39/14.43 (![X0 : $i]: ((multiply @ X0 @ additive_identity) = (additive_identity))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl5614, zip_derived_cl51])).
% 96.39/14.43 thf(zip_derived_cl47, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X1 @ X0))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl3])).
% 96.39/14.43 thf(zip_derived_cl5708, plain,
% 96.39/14.43 (![X0 : $i]: (product @ additive_identity @ X0 @ additive_identity)),
% 96.39/14.43 inference('sup+', [status(thm)], [zip_derived_cl5670, zip_derived_cl47])).
% 96.39/14.43 thf(zip_derived_cl6436, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 96.39/14.43 (~ (sum @ X0 @ X2 @ X1) | (product @ X0 @ X1 @ X0))),
% 96.39/14.43 inference('demod', [status(thm)],
% 96.39/14.43 [zip_derived_cl2306, zip_derived_cl5708])).
% 96.39/14.43 thf(zip_derived_cl6563, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]: (product @ X1 @ (add @ X1 @ X0) @ X1)),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl6436])).
% 96.39/14.43 thf(multiplicative_identity1, axiom,
% 96.39/14.43 (product @ multiplicative_identity @ X @ X)).
% 96.39/14.43 thf(zip_derived_cl6, plain,
% 96.39/14.43 (![X0 : $i]: (product @ multiplicative_identity @ X0 @ X0)),
% 96.39/14.43 inference('cnf', [status(esa)], [multiplicative_identity1])).
% 96.39/14.43 thf(zip_derived_cl21, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 96.39/14.43 (~ (product @ X0 @ X1 @ X2)
% 96.39/14.43 | ~ (product @ X0 @ X1 @ X3)
% 96.39/14.43 | ((X2) = (X3)))),
% 96.39/14.43 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 96.39/14.43 thf(zip_derived_cl59, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]:
% 96.39/14.43 (((X0) = (X1)) | ~ (product @ multiplicative_identity @ X0 @ X1))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl21])).
% 96.39/14.43 thf(zip_derived_cl7587, plain,
% 96.39/14.43 (![X0 : $i]:
% 96.39/14.43 ((add @ multiplicative_identity @ X0) = (multiplicative_identity))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl6563, zip_derived_cl59])).
% 96.39/14.43 thf(zip_derived_cl0, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 96.39/14.43 inference('cnf', [status(esa)], [closure_of_addition])).
% 96.39/14.43 thf(zip_derived_cl7685, plain,
% 96.39/14.43 (![X0 : $i]:
% 96.39/14.43 (sum @ multiplicative_identity @ X0 @ multiplicative_identity)),
% 96.39/14.43 inference('sup+', [status(thm)], [zip_derived_cl7587, zip_derived_cl0])).
% 96.39/14.43 thf(zip_derived_cl7833, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 96.39/14.43 (~ (product @ X0 @ X2 @ X1) | (sum @ X0 @ X1 @ X0))),
% 96.39/14.43 inference('demod', [status(thm)], [zip_derived_cl629, zip_derived_cl7685])).
% 96.39/14.43 thf(zip_derived_cl8463, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]: (sum @ X1 @ (multiply @ X1 @ X0) @ X1)),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl7833])).
% 96.39/14.43 thf(zip_derived_cl33, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 96.39/14.43 thf(zip_derived_cl20, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 96.39/14.43 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 96.39/14.43 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 96.39/14.43 thf(zip_derived_cl180, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 96.39/14.43 (((add @ X1 @ X0) = (X2)) | ~ (sum @ X0 @ X1 @ X2))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl33, zip_derived_cl20])).
% 96.39/14.43 thf(zip_derived_cl9462, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]: ((add @ (multiply @ X0 @ X1) @ X0) = (X0))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl8463, zip_derived_cl180])).
% 96.39/14.43 thf(zip_derived_cl9631, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]: ((add @ (multiply @ X1 @ X0) @ X0) = (X0))),
% 96.39/14.43 inference('sup+', [status(thm)], [zip_derived_cl256, zip_derived_cl9462])).
% 96.39/14.43 thf(zip_derived_cl6563, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]: (product @ X1 @ (add @ X1 @ X0) @ X1)),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl6436])).
% 96.39/14.43 thf(zip_derived_cl47, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X1 @ X0))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl3])).
% 96.39/14.43 thf(zip_derived_cl21, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 96.39/14.43 (~ (product @ X0 @ X1 @ X2)
% 96.39/14.43 | ~ (product @ X0 @ X1 @ X3)
% 96.39/14.43 | ((X2) = (X3)))),
% 96.39/14.43 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 96.39/14.43 thf(zip_derived_cl244, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 96.39/14.43 (((multiply @ X1 @ X0) = (X2)) | ~ (product @ X0 @ X1 @ X2))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl47, zip_derived_cl21])).
% 96.39/14.43 thf(zip_derived_cl7545, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]: ((multiply @ (add @ X0 @ X1) @ X0) = (X0))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl6563, zip_derived_cl244])).
% 96.39/14.43 thf(zip_derived_cl9842, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]:
% 96.39/14.43 ((multiply @ X0 @ (multiply @ X1 @ X0)) = (multiply @ X1 @ X0))),
% 96.39/14.43 inference('sup+', [status(thm)], [zip_derived_cl9631, zip_derived_cl7545])).
% 96.39/14.43 thf(zip_derived_cl12506, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]:
% 96.39/14.43 ((multiply @ X1 @ (multiply @ X1 @ X0)) = (multiply @ X0 @ X1))),
% 96.39/14.43 inference('sup+', [status(thm)], [zip_derived_cl256, zip_derived_cl9842])).
% 96.39/14.43 thf(zip_derived_cl68915, plain,
% 96.39/14.43 (((multiply @ y @ additive_identity)
% 96.39/14.43 = (multiply @ (inverse @ x_plus_y) @ y))),
% 96.39/14.43 inference('sup+', [status(thm)],
% 96.39/14.43 [zip_derived_cl68831, zip_derived_cl12506])).
% 96.39/14.43 thf(zip_derived_cl5670, plain,
% 96.39/14.43 (![X0 : $i]: ((multiply @ X0 @ additive_identity) = (additive_identity))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl5614, zip_derived_cl51])).
% 96.39/14.43 thf(zip_derived_cl68981, plain,
% 96.39/14.43 (((additive_identity) = (multiply @ (inverse @ x_plus_y) @ y))),
% 96.39/14.43 inference('demod', [status(thm)],
% 96.39/14.43 [zip_derived_cl68915, zip_derived_cl5670])).
% 96.39/14.43 thf(zip_derived_cl1, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 96.39/14.43 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 96.39/14.43 thf(additive_inverse1, axiom,
% 96.39/14.43 (sum @ ( inverse @ X ) @ X @ multiplicative_identity)).
% 96.39/14.43 thf(zip_derived_cl16, plain,
% 96.39/14.43 (![X0 : $i]: (sum @ (inverse @ X0) @ X0 @ multiplicative_identity)),
% 96.39/14.43 inference('cnf', [status(esa)], [additive_inverse1])).
% 96.39/14.43 thf(zip_derived_cl7, plain,
% 96.39/14.43 (![X0 : $i]: (product @ X0 @ multiplicative_identity @ X0)),
% 96.39/14.43 inference('cnf', [status(esa)], [multiplicative_identity2])).
% 96.39/14.43 thf(zip_derived_cl71, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 96.39/14.43 ( (sum @ (multiply @ X1 @ X0) @ X3 @ X2)
% 96.39/14.43 | ~ (product @ X1 @ X4 @ X2)
% 96.39/14.43 | ~ (sum @ X0 @ X5 @ X4)
% 96.39/14.43 | ~ (product @ X1 @ X5 @ X3))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl8])).
% 96.39/14.43 thf(zip_derived_cl343, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 96.39/14.43 (~ (product @ X0 @ X2 @ X1)
% 96.39/14.43 | ~ (sum @ X3 @ X2 @ multiplicative_identity)
% 96.39/14.43 | (sum @ (multiply @ X0 @ X3) @ X1 @ X0))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl71])).
% 96.39/14.43 thf(zip_derived_cl362, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 96.39/14.43 ( (sum @ (multiply @ X1 @ (inverse @ X0)) @ X2 @ X1)
% 96.39/14.43 | ~ (product @ X1 @ X0 @ X2))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl343])).
% 96.39/14.43 thf(zip_derived_cl674, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]:
% 96.39/14.43 (sum @ (multiply @ X1 @ (inverse @ X0)) @ (multiply @ X1 @ X0) @ X1)),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl362])).
% 96.39/14.43 thf(zip_derived_cl20, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 96.39/14.43 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 96.39/14.43 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 96.39/14.43 thf(zip_derived_cl8621, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 96.39/14.43 (((X0) = (X2))
% 96.39/14.43 | ~ (sum @ (multiply @ X0 @ (inverse @ X1)) @ (multiply @ X0 @ X1) @
% 96.39/14.43 X2))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl674, zip_derived_cl20])).
% 96.39/14.43 thf(zip_derived_cl69202, plain,
% 96.39/14.43 (![X0 : $i]:
% 96.39/14.43 (~ (sum @ (multiply @ (inverse @ x_plus_y) @ (inverse @ y)) @
% 96.39/14.43 additive_identity @ X0)
% 96.39/14.43 | ((inverse @ x_plus_y) = (X0)))),
% 96.39/14.43 inference('sup-', [status(thm)],
% 96.39/14.43 [zip_derived_cl68981, zip_derived_cl8621])).
% 96.39/14.43 thf(zip_derived_cl256, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl47, zip_derived_cl56])).
% 96.39/14.43 thf(zip_derived_cl69278, plain,
% 96.39/14.43 (![X0 : $i]:
% 96.39/14.43 (~ (sum @ (multiply @ (inverse @ y) @ (inverse @ x_plus_y)) @
% 96.39/14.43 additive_identity @ X0)
% 96.39/14.43 | ((inverse @ x_plus_y) = (X0)))),
% 96.39/14.43 inference('demod', [status(thm)],
% 96.39/14.43 [zip_derived_cl69202, zip_derived_cl256])).
% 96.39/14.43 thf(zip_derived_cl69727, plain,
% 96.39/14.43 (((inverse @ x_plus_y)
% 96.39/14.43 = (multiply @ (inverse @ y) @ (inverse @ x_plus_y)))),
% 96.39/14.43 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl69278])).
% 96.39/14.43 thf(zip_derived_cl1, plain,
% 96.39/14.43 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 96.39/14.43 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 96.39/14.43 thf(zip_derived_cl69729, plain,
% 96.39/14.43 ( (product @ (inverse @ y) @ (inverse @ x_plus_y) @ (inverse @ x_plus_y))),
% 96.39/14.44 inference('sup+', [status(thm)], [zip_derived_cl69727, zip_derived_cl1])).
% 96.39/14.44 thf(zip_derived_cl5, plain,
% 96.39/14.44 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 96.39/14.44 inference('cnf', [status(esa)], [additive_identity2])).
% 96.39/14.44 thf(zip_derived_cl5, plain,
% 96.39/14.44 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 96.39/14.44 inference('cnf', [status(esa)], [additive_identity2])).
% 96.39/14.44 thf(zip_derived_cl24, plain, ( (sum @ x @ y @ x_plus_y)),
% 96.39/14.44 inference('cnf', [status(esa)], [x_plus_y])).
% 96.39/14.44 thf(zip_derived_cl12, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 96.39/14.44 (~ (sum @ X0 @ X1 @ X2)
% 96.39/14.44 | ~ (sum @ X0 @ X3 @ X4)
% 96.39/14.44 | ~ (product @ X1 @ X3 @ X5)
% 96.39/14.44 | ~ (sum @ X0 @ X5 @ X6)
% 96.39/14.44 | (product @ X2 @ X4 @ X6))),
% 96.39/14.44 inference('cnf', [status(esa)], [distributivity5])).
% 96.39/14.44 thf(zip_derived_cl130, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 96.39/14.44 ( (product @ x_plus_y @ X1 @ X0)
% 96.39/14.44 | ~ (sum @ x @ X2 @ X0)
% 96.39/14.44 | ~ (product @ y @ X3 @ X2)
% 96.39/14.44 | ~ (sum @ x @ X3 @ X1))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl12])).
% 96.39/14.44 thf(zip_derived_cl2119, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i]:
% 96.39/14.44 (~ (sum @ x @ X1 @ X0)
% 96.39/14.44 | ~ (product @ y @ X1 @ X1)
% 96.39/14.44 | (product @ x_plus_y @ X0 @ X0))),
% 96.39/14.44 inference('eq_fact', [status(thm)], [zip_derived_cl130])).
% 96.39/14.44 thf(zip_derived_cl2378, plain,
% 96.39/14.44 (( (product @ x_plus_y @ x @ x)
% 96.39/14.44 | ~ (product @ y @ additive_identity @ additive_identity))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl2119])).
% 96.39/14.44 thf(zip_derived_cl5706, plain,
% 96.39/14.44 (![X0 : $i]: (product @ X0 @ additive_identity @ additive_identity)),
% 96.39/14.44 inference('sup+', [status(thm)], [zip_derived_cl5670, zip_derived_cl1])).
% 96.39/14.44 thf(zip_derived_cl5747, plain, ( (product @ x_plus_y @ x @ x)),
% 96.39/14.44 inference('demod', [status(thm)],
% 96.39/14.44 [zip_derived_cl2378, zip_derived_cl5706])).
% 96.39/14.44 thf(zip_derived_cl0, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 96.39/14.44 inference('cnf', [status(esa)], [closure_of_addition])).
% 96.39/14.44 thf(zip_derived_cl7, plain,
% 96.39/14.44 (![X0 : $i]: (product @ X0 @ multiplicative_identity @ X0)),
% 96.39/14.44 inference('cnf', [status(esa)], [multiplicative_identity2])).
% 96.39/14.44 thf(zip_derived_cl24, plain, ( (sum @ x @ y @ x_plus_y)),
% 96.39/14.44 inference('cnf', [status(esa)], [x_plus_y])).
% 96.39/14.44 thf(zip_derived_cl130, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 96.39/14.44 ( (product @ x_plus_y @ X1 @ X0)
% 96.39/14.44 | ~ (sum @ x @ X2 @ X0)
% 96.39/14.44 | ~ (product @ y @ X3 @ X2)
% 96.39/14.44 | ~ (sum @ x @ X3 @ X1))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl12])).
% 96.39/14.44 thf(zip_derived_cl2118, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i]:
% 96.39/14.44 (~ (sum @ x @ X1 @ X0)
% 96.39/14.44 | ~ (product @ y @ X1 @ y)
% 96.39/14.44 | (product @ x_plus_y @ X0 @ x_plus_y))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl130])).
% 96.39/14.44 thf(zip_derived_cl2123, plain,
% 96.39/14.44 (![X0 : $i]:
% 96.39/14.44 ( (product @ x_plus_y @ X0 @ x_plus_y)
% 96.39/14.44 | ~ (sum @ x @ multiplicative_identity @ X0))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl2118])).
% 96.39/14.44 thf(zip_derived_cl2129, plain,
% 96.39/14.44 ( (product @ x_plus_y @ (add @ x @ multiplicative_identity) @ x_plus_y)),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl2123])).
% 96.39/14.44 thf(zip_derived_cl393, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 96.39/14.44 (~ (product @ X2 @ X0 @ X1)
% 96.39/14.44 | ~ (product @ X2 @ (add @ X0 @ multiplicative_identity) @ X3)
% 96.39/14.44 | (sum @ X2 @ X1 @ X3))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl33, zip_derived_cl72])).
% 96.39/14.44 thf(zip_derived_cl6154, plain,
% 96.39/14.44 (![X0 : $i]:
% 96.39/14.44 ( (sum @ x_plus_y @ X0 @ x_plus_y) | ~ (product @ x_plus_y @ x @ X0))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl2129, zip_derived_cl393])).
% 96.39/14.44 thf(zip_derived_cl6208, plain, ( (sum @ x_plus_y @ x @ x_plus_y)),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl5747, zip_derived_cl6154])).
% 96.39/14.44 thf(zip_derived_cl2, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i, X2 : $i]:
% 96.39/14.44 (~ (sum @ X0 @ X1 @ X2) | (sum @ X1 @ X0 @ X2))),
% 96.39/14.44 inference('cnf', [status(esa)], [commutativity_of_addition])).
% 96.39/14.44 thf(zip_derived_cl6211, plain, ( (sum @ x @ x_plus_y @ x_plus_y)),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl6208, zip_derived_cl2])).
% 96.39/14.44 thf(zip_derived_cl5379, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i, X2 : $i]:
% 96.39/14.44 ( (sum @ (multiply @ (inverse @ X0) @ X2) @ additive_identity @
% 96.39/14.44 (multiply @ (inverse @ X0) @ X1))
% 96.39/14.44 | ~ (sum @ X2 @ X0 @ X1))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl341])).
% 96.39/14.44 thf(zip_derived_cl67196, plain,
% 96.39/14.44 ( (sum @ (multiply @ (inverse @ x_plus_y) @ x) @ additive_identity @
% 96.39/14.44 (multiply @ (inverse @ x_plus_y) @ x_plus_y))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl6211, zip_derived_cl5379])).
% 96.39/14.44 thf(zip_derived_cl256, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl47, zip_derived_cl56])).
% 96.39/14.44 thf(zip_derived_cl205, plain,
% 96.39/14.44 (![X0 : $i]: ((additive_identity) = (multiply @ (inverse @ X0) @ X0))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl60])).
% 96.39/14.44 thf(zip_derived_cl67254, plain,
% 96.39/14.44 ( (sum @ (multiply @ x @ (inverse @ x_plus_y)) @ additive_identity @
% 96.39/14.44 additive_identity)),
% 96.39/14.44 inference('demod', [status(thm)],
% 96.39/14.44 [zip_derived_cl67196, zip_derived_cl256, zip_derived_cl205])).
% 96.39/14.44 thf(zip_derived_cl49, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i]:
% 96.39/14.44 (((X0) = (X1)) | ~ (sum @ X0 @ additive_identity @ X1))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl20])).
% 96.39/14.44 thf(zip_derived_cl67335, plain,
% 96.39/14.44 (((multiply @ x @ (inverse @ x_plus_y)) = (additive_identity))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl67254, zip_derived_cl49])).
% 96.39/14.44 thf(zip_derived_cl12506, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i]:
% 96.39/14.44 ((multiply @ X1 @ (multiply @ X1 @ X0)) = (multiply @ X0 @ X1))),
% 96.39/14.44 inference('sup+', [status(thm)], [zip_derived_cl256, zip_derived_cl9842])).
% 96.39/14.44 thf(zip_derived_cl67418, plain,
% 96.39/14.44 (((multiply @ x @ additive_identity)
% 96.39/14.44 = (multiply @ (inverse @ x_plus_y) @ x))),
% 96.39/14.44 inference('sup+', [status(thm)],
% 96.39/14.44 [zip_derived_cl67335, zip_derived_cl12506])).
% 96.39/14.44 thf(zip_derived_cl5670, plain,
% 96.39/14.44 (![X0 : $i]: ((multiply @ X0 @ additive_identity) = (additive_identity))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl5614, zip_derived_cl51])).
% 96.39/14.44 thf(zip_derived_cl67484, plain,
% 96.39/14.44 (((additive_identity) = (multiply @ (inverse @ x_plus_y) @ x))),
% 96.39/14.44 inference('demod', [status(thm)],
% 96.39/14.44 [zip_derived_cl67418, zip_derived_cl5670])).
% 96.39/14.44 thf(zip_derived_cl8621, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i, X2 : $i]:
% 96.39/14.44 (((X0) = (X2))
% 96.39/14.44 | ~ (sum @ (multiply @ X0 @ (inverse @ X1)) @ (multiply @ X0 @ X1) @
% 96.39/14.44 X2))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl674, zip_derived_cl20])).
% 96.39/14.44 thf(zip_derived_cl67773, plain,
% 96.39/14.44 (![X0 : $i]:
% 96.39/14.44 (~ (sum @ (multiply @ (inverse @ x_plus_y) @ (inverse @ x)) @
% 96.39/14.44 additive_identity @ X0)
% 96.39/14.44 | ((inverse @ x_plus_y) = (X0)))),
% 96.39/14.44 inference('sup-', [status(thm)],
% 96.39/14.44 [zip_derived_cl67484, zip_derived_cl8621])).
% 96.39/14.44 thf(zip_derived_cl256, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl47, zip_derived_cl56])).
% 96.39/14.44 thf(zip_derived_cl67849, plain,
% 96.39/14.44 (![X0 : $i]:
% 96.39/14.44 (~ (sum @ (multiply @ (inverse @ x) @ (inverse @ x_plus_y)) @
% 96.39/14.44 additive_identity @ X0)
% 96.39/14.44 | ((inverse @ x_plus_y) = (X0)))),
% 96.39/14.44 inference('demod', [status(thm)],
% 96.39/14.44 [zip_derived_cl67773, zip_derived_cl256])).
% 96.39/14.44 thf(zip_derived_cl67925, plain,
% 96.39/14.44 (((inverse @ x_plus_y)
% 96.39/14.44 = (multiply @ (inverse @ x) @ (inverse @ x_plus_y)))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl67849])).
% 96.39/14.44 thf(zip_derived_cl8463, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i]: (sum @ X1 @ (multiply @ X1 @ X0) @ X1)),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl7833])).
% 96.39/14.44 thf(zip_derived_cl67949, plain,
% 96.39/14.44 ( (sum @ (inverse @ x) @ (inverse @ x_plus_y) @ (inverse @ x))),
% 96.39/14.44 inference('sup+', [status(thm)],
% 96.39/14.44 [zip_derived_cl67925, zip_derived_cl8463])).
% 96.39/14.44 thf(x_inverse_times_y_inverse, axiom,
% 96.39/14.44 (product @ ( inverse @ x ) @ ( inverse @ y ) @ x_inverse_times_y_inverse)).
% 96.39/14.44 thf(zip_derived_cl25, plain,
% 96.39/14.44 ( (product @ (inverse @ x) @ (inverse @ y) @ x_inverse_times_y_inverse)),
% 96.39/14.44 inference('cnf', [status(esa)], [x_inverse_times_y_inverse])).
% 96.39/14.44 thf(zip_derived_cl3, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i, X2 : $i]:
% 96.39/14.44 (~ (product @ X0 @ X1 @ X2) | (product @ X1 @ X0 @ X2))),
% 96.39/14.44 inference('cnf', [status(esa)], [commutativity_of_multiplication])).
% 96.39/14.44 thf(zip_derived_cl45, plain,
% 96.39/14.44 ( (product @ (inverse @ y) @ (inverse @ x) @ x_inverse_times_y_inverse)),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl3])).
% 96.39/14.44 thf(zip_derived_cl78, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 96.39/14.44 ( (sum @ X0 @ X3 @ X0)
% 96.39/14.44 | ~ (product @ X2 @ X1 @ X0)
% 96.39/14.44 | ~ (sum @ X1 @ X4 @ X1)
% 96.39/14.44 | ~ (product @ X2 @ X4 @ X3))),
% 96.39/14.44 inference('eq_fact', [status(thm)], [zip_derived_cl8])).
% 96.39/14.44 thf(zip_derived_cl635, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i]:
% 96.39/14.44 (~ (product @ (inverse @ y) @ X1 @ X0)
% 96.39/14.44 | ~ (sum @ (inverse @ x) @ X1 @ (inverse @ x))
% 96.39/14.44 | (sum @ x_inverse_times_y_inverse @ X0 @ x_inverse_times_y_inverse))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl45, zip_derived_cl78])).
% 96.39/14.44 thf(zip_derived_cl68750, plain,
% 96.39/14.44 (![X0 : $i]:
% 96.39/14.44 ( (sum @ x_inverse_times_y_inverse @ X0 @ x_inverse_times_y_inverse)
% 96.39/14.44 | ~ (product @ (inverse @ y) @ (inverse @ x_plus_y) @ X0))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl67949, zip_derived_cl635])).
% 96.39/14.44 thf(zip_derived_cl69931, plain,
% 96.39/14.44 ( (sum @ x_inverse_times_y_inverse @ (inverse @ x_plus_y) @
% 96.39/14.44 x_inverse_times_y_inverse)),
% 96.39/14.44 inference('sup-', [status(thm)],
% 96.39/14.44 [zip_derived_cl69729, zip_derived_cl68750])).
% 96.39/14.44 thf(zip_derived_cl7, plain,
% 96.39/14.44 (![X0 : $i]: (product @ X0 @ multiplicative_identity @ X0)),
% 96.39/14.44 inference('cnf', [status(esa)], [multiplicative_identity2])).
% 96.39/14.44 thf(zip_derived_cl8, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 96.39/14.44 (~ (product @ X0 @ X1 @ X2)
% 96.39/14.44 | ~ (product @ X0 @ X3 @ X4)
% 96.39/14.44 | ~ (sum @ X1 @ X3 @ X5)
% 96.39/14.44 | ~ (product @ X0 @ X5 @ X6)
% 96.39/14.44 | (sum @ X2 @ X4 @ X6))),
% 96.39/14.44 inference('cnf', [status(esa)], [distributivity1])).
% 96.39/14.44 thf(zip_derived_cl77, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 96.39/14.44 ( (sum @ X0 @ X0 @ X3)
% 96.39/14.44 | ~ (product @ X2 @ X4 @ X3)
% 96.39/14.44 | ~ (sum @ X1 @ X1 @ X4)
% 96.39/14.44 | ~ (product @ X2 @ X1 @ X0))),
% 96.39/14.44 inference('eq_fact', [status(thm)], [zip_derived_cl8])).
% 96.39/14.44 thf(zip_derived_cl592, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i, X2 : $i]:
% 96.39/14.44 (~ (product @ X2 @ X1 @ X0)
% 96.39/14.44 | ~ (sum @ X1 @ X1 @ X1)
% 96.39/14.44 | (sum @ X0 @ X0 @ X0))),
% 96.39/14.44 inference('eq_fact', [status(thm)], [zip_derived_cl77])).
% 96.39/14.44 thf(zip_derived_cl617, plain,
% 96.39/14.44 (![X0 : $i]:
% 96.39/14.44 ( (sum @ X0 @ X0 @ X0)
% 96.39/14.44 | ~ (sum @ multiplicative_identity @ multiplicative_identity @
% 96.39/14.44 multiplicative_identity))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl592])).
% 96.39/14.44 thf(zip_derived_cl5, plain,
% 96.39/14.44 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 96.39/14.44 inference('cnf', [status(esa)], [additive_identity2])).
% 96.39/14.44 thf(zip_derived_cl0, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 96.39/14.44 inference('cnf', [status(esa)], [closure_of_addition])).
% 96.39/14.44 thf(zip_derived_cl7, plain,
% 96.39/14.44 (![X0 : $i]: (product @ X0 @ multiplicative_identity @ X0)),
% 96.39/14.44 inference('cnf', [status(esa)], [multiplicative_identity2])).
% 96.39/14.44 thf(zip_derived_cl5, plain,
% 96.39/14.44 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 96.39/14.44 inference('cnf', [status(esa)], [additive_identity2])).
% 96.39/14.44 thf(zip_derived_cl12, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 96.39/14.44 (~ (sum @ X0 @ X1 @ X2)
% 96.39/14.44 | ~ (sum @ X0 @ X3 @ X4)
% 96.39/14.44 | ~ (product @ X1 @ X3 @ X5)
% 96.39/14.44 | ~ (sum @ X0 @ X5 @ X6)
% 96.39/14.44 | (product @ X2 @ X4 @ X6))),
% 96.39/14.44 inference('cnf', [status(esa)], [distributivity5])).
% 96.39/14.44 thf(zip_derived_cl126, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 96.39/14.44 ( (product @ X0 @ X2 @ X1)
% 96.39/14.44 | ~ (sum @ X0 @ X3 @ X1)
% 96.39/14.44 | ~ (product @ additive_identity @ X4 @ X3)
% 96.39/14.44 | ~ (sum @ X0 @ X4 @ X2))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl12])).
% 96.39/14.44 thf(zip_derived_cl1924, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i, X2 : $i]:
% 96.39/14.44 (~ (sum @ X1 @ multiplicative_identity @ X0)
% 96.39/14.44 | ~ (sum @ X1 @ additive_identity @ X2)
% 96.39/14.44 | (product @ X1 @ X0 @ X2))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl126])).
% 96.39/14.44 thf(zip_derived_cl2805, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i]:
% 96.39/14.44 ( (product @ X0 @ (add @ X0 @ multiplicative_identity) @ X1)
% 96.39/14.44 | ~ (sum @ X0 @ additive_identity @ X1))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl1924])).
% 96.39/14.44 thf(zip_derived_cl2863, plain,
% 96.39/14.44 (![X0 : $i]: (product @ X0 @ (add @ X0 @ multiplicative_identity) @ X0)),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl2805])).
% 96.39/14.44 thf(zip_derived_cl59, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i]:
% 96.39/14.44 (((X0) = (X1)) | ~ (product @ multiplicative_identity @ X0 @ X1))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl21])).
% 96.39/14.44 thf(zip_derived_cl2907, plain,
% 96.39/14.44 (((add @ multiplicative_identity @ multiplicative_identity)
% 96.39/14.44 = (multiplicative_identity))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl2863, zip_derived_cl59])).
% 96.39/14.44 thf(zip_derived_cl0, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 96.39/14.44 inference('cnf', [status(esa)], [closure_of_addition])).
% 96.39/14.44 thf(zip_derived_cl2968, plain,
% 96.39/14.44 ( (sum @ multiplicative_identity @ multiplicative_identity @
% 96.39/14.44 multiplicative_identity)),
% 96.39/14.44 inference('sup+', [status(thm)], [zip_derived_cl2907, zip_derived_cl0])).
% 96.39/14.44 thf(zip_derived_cl2974, plain, (![X0 : $i]: (sum @ X0 @ X0 @ X0)),
% 96.39/14.44 inference('demod', [status(thm)], [zip_derived_cl617, zip_derived_cl2968])).
% 96.39/14.44 thf(zip_derived_cl47, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X1 @ X0))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl3])).
% 96.39/14.44 thf(zip_derived_cl6, plain,
% 96.39/14.44 (![X0 : $i]: (product @ multiplicative_identity @ X0 @ X0)),
% 96.39/14.44 inference('cnf', [status(esa)], [multiplicative_identity1])).
% 96.39/14.44 thf(zip_derived_cl25, plain,
% 96.39/14.44 ( (product @ (inverse @ x) @ (inverse @ y) @ x_inverse_times_y_inverse)),
% 96.39/14.44 inference('cnf', [status(esa)], [x_inverse_times_y_inverse])).
% 96.39/14.44 thf(distributivity3, axiom,
% 96.39/14.44 (( ~( product @ Y @ X @ V1 ) ) | ( ~( product @ Z @ X @ V2 ) ) |
% 96.39/14.44 ( ~( sum @ Y @ Z @ V3 ) ) | ( ~( product @ V3 @ X @ V4 ) ) |
% 96.39/14.44 ( sum @ V1 @ V2 @ V4 ))).
% 96.39/14.44 thf(zip_derived_cl10, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 96.39/14.44 (~ (product @ X0 @ X1 @ X2)
% 96.39/14.44 | ~ (product @ X3 @ X1 @ X4)
% 96.39/14.44 | ~ (sum @ X0 @ X3 @ X5)
% 96.39/14.44 | ~ (product @ X5 @ X1 @ X6)
% 96.39/14.44 | (sum @ X2 @ X4 @ X6))),
% 96.39/14.44 inference('cnf', [status(esa)], [distributivity3])).
% 96.39/14.44 thf(zip_derived_cl114, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 96.39/14.44 ( (sum @ x_inverse_times_y_inverse @ X1 @ X0)
% 96.39/14.44 | ~ (product @ X2 @ (inverse @ y) @ X0)
% 96.39/14.44 | ~ (sum @ (inverse @ x) @ X3 @ X2)
% 96.39/14.44 | ~ (product @ X3 @ (inverse @ y) @ X1))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl10])).
% 96.39/14.44 thf(zip_derived_cl1363, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i]:
% 96.39/14.44 (~ (product @ X1 @ (inverse @ y) @ X0)
% 96.39/14.44 | ~ (sum @ (inverse @ x) @ X1 @ X1)
% 96.39/14.44 | (sum @ x_inverse_times_y_inverse @ X0 @ X0))),
% 96.39/14.44 inference('eq_fact', [status(thm)], [zip_derived_cl114])).
% 96.39/14.44 thf(zip_derived_cl1373, plain,
% 96.39/14.44 (( (sum @ x_inverse_times_y_inverse @ (inverse @ y) @ (inverse @ y))
% 96.39/14.44 | ~ (sum @ (inverse @ x) @ multiplicative_identity @
% 96.39/14.44 multiplicative_identity))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl1363])).
% 96.39/14.44 thf(zip_derived_cl7587, plain,
% 96.39/14.44 (![X0 : $i]:
% 96.39/14.44 ((add @ multiplicative_identity @ X0) = (multiplicative_identity))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl6563, zip_derived_cl59])).
% 96.39/14.44 thf(zip_derived_cl33, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 96.39/14.44 thf(zip_derived_cl7687, plain,
% 96.39/14.44 (![X0 : $i]:
% 96.39/14.44 (sum @ X0 @ multiplicative_identity @ multiplicative_identity)),
% 96.39/14.44 inference('sup+', [status(thm)], [zip_derived_cl7587, zip_derived_cl33])).
% 96.39/14.44 thf(zip_derived_cl7966, plain,
% 96.39/14.44 ( (sum @ x_inverse_times_y_inverse @ (inverse @ y) @ (inverse @ y))),
% 96.39/14.44 inference('demod', [status(thm)],
% 96.39/14.44 [zip_derived_cl1373, zip_derived_cl7687])).
% 96.39/14.44 thf(zip_derived_cl2, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i, X2 : $i]:
% 96.39/14.44 (~ (sum @ X0 @ X1 @ X2) | (sum @ X1 @ X0 @ X2))),
% 96.39/14.44 inference('cnf', [status(esa)], [commutativity_of_addition])).
% 96.39/14.44 thf(zip_derived_cl8106, plain,
% 96.39/14.44 ( (sum @ (inverse @ y) @ x_inverse_times_y_inverse @ (inverse @ y))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl7966, zip_derived_cl2])).
% 96.39/14.44 thf(zip_derived_cl19, plain,
% 96.39/14.44 (![X0 : $i]: (product @ X0 @ (inverse @ X0) @ additive_identity)),
% 96.39/14.44 inference('cnf', [status(esa)], [multiplicative_inverse2])).
% 96.39/14.44 thf(zip_derived_cl78, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 96.39/14.44 ( (sum @ X0 @ X3 @ X0)
% 96.39/14.44 | ~ (product @ X2 @ X1 @ X0)
% 96.39/14.44 | ~ (sum @ X1 @ X4 @ X1)
% 96.39/14.44 | ~ (product @ X2 @ X4 @ X3))),
% 96.39/14.44 inference('eq_fact', [status(thm)], [zip_derived_cl8])).
% 96.39/14.44 thf(zip_derived_cl630, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i, X2 : $i]:
% 96.39/14.44 (~ (product @ X0 @ X2 @ X1)
% 96.39/14.44 | ~ (sum @ (inverse @ X0) @ X2 @ (inverse @ X0))
% 96.39/14.44 | (sum @ additive_identity @ X1 @ additive_identity))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl78])).
% 96.39/14.44 thf(zip_derived_cl8251, plain,
% 96.39/14.44 (![X0 : $i]:
% 96.39/14.44 ( (sum @ additive_identity @ X0 @ additive_identity)
% 96.39/14.44 | ~ (product @ y @ x_inverse_times_y_inverse @ X0))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl8106, zip_derived_cl630])).
% 96.39/14.44 thf(zip_derived_cl8578, plain,
% 96.39/14.44 ( (sum @ additive_identity @
% 96.39/14.44 (multiply @ x_inverse_times_y_inverse @ y) @ additive_identity)),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl47, zip_derived_cl8251])).
% 96.39/14.44 thf(zip_derived_cl51, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i]:
% 96.39/14.44 (((X0) = (X1)) | ~ (sum @ additive_identity @ X0 @ X1))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl20])).
% 96.39/14.44 thf(zip_derived_cl10374, plain,
% 96.39/14.44 (((multiply @ x_inverse_times_y_inverse @ y) = (additive_identity))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl8578, zip_derived_cl51])).
% 96.39/14.44 thf(zip_derived_cl1, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 96.39/14.44 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 96.39/14.44 thf(zip_derived_cl10390, plain,
% 96.39/14.44 ( (product @ x_inverse_times_y_inverse @ y @ additive_identity)),
% 96.39/14.44 inference('sup+', [status(thm)], [zip_derived_cl10374, zip_derived_cl1])).
% 96.39/14.44 thf(zip_derived_cl47, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X1 @ X0))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl3])).
% 96.39/14.44 thf(zip_derived_cl7, plain,
% 96.39/14.44 (![X0 : $i]: (product @ X0 @ multiplicative_identity @ X0)),
% 96.39/14.44 inference('cnf', [status(esa)], [multiplicative_identity2])).
% 96.39/14.44 thf(zip_derived_cl25, plain,
% 96.39/14.44 ( (product @ (inverse @ x) @ (inverse @ y) @ x_inverse_times_y_inverse)),
% 96.39/14.44 inference('cnf', [status(esa)], [x_inverse_times_y_inverse])).
% 96.39/14.44 thf(zip_derived_cl8, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 96.39/14.44 (~ (product @ X0 @ X1 @ X2)
% 96.39/14.44 | ~ (product @ X0 @ X3 @ X4)
% 96.39/14.44 | ~ (sum @ X1 @ X3 @ X5)
% 96.39/14.44 | ~ (product @ X0 @ X5 @ X6)
% 96.39/14.44 | (sum @ X2 @ X4 @ X6))),
% 96.39/14.44 inference('cnf', [status(esa)], [distributivity1])).
% 96.39/14.44 thf(zip_derived_cl76, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 96.39/14.44 ( (sum @ x_inverse_times_y_inverse @ X1 @ X0)
% 96.39/14.44 | ~ (product @ (inverse @ x) @ X2 @ X0)
% 96.39/14.44 | ~ (sum @ (inverse @ y) @ X3 @ X2)
% 96.39/14.44 | ~ (product @ (inverse @ x) @ X3 @ X1))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl8])).
% 96.39/14.44 thf(zip_derived_cl572, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i]:
% 96.39/14.44 (~ (product @ (inverse @ x) @ X1 @ X0)
% 96.39/14.44 | ~ (sum @ (inverse @ y) @ X1 @ X1)
% 96.39/14.44 | (sum @ x_inverse_times_y_inverse @ X0 @ X0))),
% 96.39/14.44 inference('eq_fact', [status(thm)], [zip_derived_cl76])).
% 96.39/14.44 thf(zip_derived_cl660, plain,
% 96.39/14.44 (( (sum @ x_inverse_times_y_inverse @ (inverse @ x) @ (inverse @ x))
% 96.39/14.44 | ~ (sum @ (inverse @ y) @ multiplicative_identity @
% 96.39/14.44 multiplicative_identity))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl572])).
% 96.39/14.44 thf(zip_derived_cl7687, plain,
% 96.39/14.44 (![X0 : $i]:
% 96.39/14.44 (sum @ X0 @ multiplicative_identity @ multiplicative_identity)),
% 96.39/14.44 inference('sup+', [status(thm)], [zip_derived_cl7587, zip_derived_cl33])).
% 96.39/14.44 thf(zip_derived_cl7965, plain,
% 96.39/14.44 ( (sum @ x_inverse_times_y_inverse @ (inverse @ x) @ (inverse @ x))),
% 96.39/14.44 inference('demod', [status(thm)], [zip_derived_cl660, zip_derived_cl7687])).
% 96.39/14.44 thf(zip_derived_cl2, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i, X2 : $i]:
% 96.39/14.44 (~ (sum @ X0 @ X1 @ X2) | (sum @ X1 @ X0 @ X2))),
% 96.39/14.44 inference('cnf', [status(esa)], [commutativity_of_addition])).
% 96.39/14.44 thf(zip_derived_cl8071, plain,
% 96.39/14.44 ( (sum @ (inverse @ x) @ x_inverse_times_y_inverse @ (inverse @ x))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl7965, zip_derived_cl2])).
% 96.39/14.44 thf(zip_derived_cl630, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i, X2 : $i]:
% 96.39/14.44 (~ (product @ X0 @ X2 @ X1)
% 96.39/14.44 | ~ (sum @ (inverse @ X0) @ X2 @ (inverse @ X0))
% 96.39/14.44 | (sum @ additive_identity @ X1 @ additive_identity))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl78])).
% 96.39/14.44 thf(zip_derived_cl8206, plain,
% 96.39/14.44 (![X0 : $i]:
% 96.39/14.44 ( (sum @ additive_identity @ X0 @ additive_identity)
% 96.39/14.44 | ~ (product @ x @ x_inverse_times_y_inverse @ X0))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl8071, zip_derived_cl630])).
% 96.39/14.44 thf(zip_derived_cl8575, plain,
% 96.39/14.44 ( (sum @ additive_identity @
% 96.39/14.44 (multiply @ x_inverse_times_y_inverse @ x) @ additive_identity)),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl47, zip_derived_cl8206])).
% 96.39/14.44 thf(zip_derived_cl51, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i]:
% 96.39/14.44 (((X0) = (X1)) | ~ (sum @ additive_identity @ X0 @ X1))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl20])).
% 96.39/14.44 thf(zip_derived_cl10174, plain,
% 96.39/14.44 (((multiply @ x_inverse_times_y_inverse @ x) = (additive_identity))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl8575, zip_derived_cl51])).
% 96.39/14.44 thf(zip_derived_cl1, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 96.39/14.44 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 96.39/14.44 thf(zip_derived_cl10190, plain,
% 96.39/14.44 ( (product @ x_inverse_times_y_inverse @ x @ additive_identity)),
% 96.39/14.44 inference('sup+', [status(thm)], [zip_derived_cl10174, zip_derived_cl1])).
% 96.39/14.44 thf(zip_derived_cl38, plain, ( (sum @ y @ x @ x_plus_y)),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl2])).
% 96.39/14.44 thf(distributivity2, axiom,
% 96.39/14.44 (( ~( product @ X @ Y @ V1 ) ) | ( ~( product @ X @ Z @ V2 ) ) |
% 96.39/14.44 ( ~( sum @ Y @ Z @ V3 ) ) | ( ~( sum @ V1 @ V2 @ V4 ) ) |
% 96.39/14.44 ( product @ X @ V3 @ V4 ))).
% 96.39/14.44 thf(zip_derived_cl9, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 96.39/14.44 (~ (product @ X0 @ X1 @ X2)
% 96.39/14.44 | ~ (product @ X0 @ X3 @ X4)
% 96.39/14.44 | ~ (sum @ X1 @ X3 @ X5)
% 96.39/14.44 | ~ (sum @ X2 @ X4 @ X6)
% 96.39/14.44 | (product @ X0 @ X5 @ X6))),
% 96.39/14.44 inference('cnf', [status(esa)], [distributivity2])).
% 96.39/14.44 thf(zip_derived_cl107, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 96.39/14.44 ( (product @ X1 @ x_plus_y @ X0)
% 96.39/14.44 | ~ (sum @ X3 @ X2 @ X0)
% 96.39/14.44 | ~ (product @ X1 @ x @ X2)
% 96.39/14.44 | ~ (product @ X1 @ y @ X3))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl9])).
% 96.39/14.44 thf(zip_derived_cl10253, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i]:
% 96.39/14.44 (~ (product @ x_inverse_times_y_inverse @ y @ X0)
% 96.39/14.44 | ~ (sum @ X0 @ additive_identity @ X1)
% 96.39/14.44 | (product @ x_inverse_times_y_inverse @ x_plus_y @ X1))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl10190, zip_derived_cl107])).
% 96.39/14.44 thf(zip_derived_cl12614, plain,
% 96.39/14.44 (![X0 : $i]:
% 96.39/14.44 ( (product @ x_inverse_times_y_inverse @ x_plus_y @ X0)
% 96.39/14.44 | ~ (sum @ additive_identity @ additive_identity @ X0))),
% 96.39/14.44 inference('sup-', [status(thm)],
% 96.39/14.44 [zip_derived_cl10390, zip_derived_cl10253])).
% 96.39/14.44 thf(zip_derived_cl12617, plain,
% 96.39/14.44 ( (product @ x_inverse_times_y_inverse @ x_plus_y @ additive_identity)),
% 96.39/14.44 inference('sup-', [status(thm)],
% 96.39/14.44 [zip_derived_cl2974, zip_derived_cl12614])).
% 96.39/14.44 thf(zip_derived_cl362, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i, X2 : $i]:
% 96.39/14.44 ( (sum @ (multiply @ X1 @ (inverse @ X0)) @ X2 @ X1)
% 96.39/14.44 | ~ (product @ X1 @ X0 @ X2))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl343])).
% 96.39/14.44 thf(zip_derived_cl12630, plain,
% 96.39/14.44 ( (sum @ (multiply @ x_inverse_times_y_inverse @ (inverse @ x_plus_y)) @
% 96.39/14.44 additive_identity @ x_inverse_times_y_inverse)),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl12617, zip_derived_cl362])).
% 96.39/14.44 thf(zip_derived_cl49, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i]:
% 96.39/14.44 (((X0) = (X1)) | ~ (sum @ X0 @ additive_identity @ X1))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl20])).
% 96.39/14.44 thf(zip_derived_cl12845, plain,
% 96.39/14.44 (((multiply @ x_inverse_times_y_inverse @ (inverse @ x_plus_y))
% 96.39/14.44 = (x_inverse_times_y_inverse))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl12630, zip_derived_cl49])).
% 96.39/14.44 thf(zip_derived_cl256, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl47, zip_derived_cl56])).
% 96.39/14.44 thf(zip_derived_cl8463, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i]: (sum @ X1 @ (multiply @ X1 @ X0) @ X1)),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl7833])).
% 96.39/14.44 thf(zip_derived_cl2, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i, X2 : $i]:
% 96.39/14.44 (~ (sum @ X0 @ X1 @ X2) | (sum @ X1 @ X0 @ X2))),
% 96.39/14.44 inference('cnf', [status(esa)], [commutativity_of_addition])).
% 96.39/14.44 thf(zip_derived_cl9458, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i]: (sum @ (multiply @ X0 @ X1) @ X0 @ X0)),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl8463, zip_derived_cl2])).
% 96.39/14.44 thf(zip_derived_cl20, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 96.39/14.44 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 96.39/14.44 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 96.39/14.44 thf(zip_derived_cl11139, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i, X2 : $i]:
% 96.39/14.44 (((X0) = (X2)) | ~ (sum @ (multiply @ X0 @ X1) @ X0 @ X2))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl9458, zip_derived_cl20])).
% 96.39/14.44 thf(zip_derived_cl11269, plain,
% 96.39/14.44 (![X0 : $i, X1 : $i, X2 : $i]:
% 96.39/14.44 (~ (sum @ (multiply @ X1 @ X0) @ X0 @ X2) | ((X0) = (X2)))),
% 96.39/14.44 inference('sup-', [status(thm)], [zip_derived_cl256, zip_derived_cl11139])).
% 96.39/14.44 thf(zip_derived_cl12884, plain,
% 96.39/14.44 (![X0 : $i]:
% 96.39/14.44 (~ (sum @ x_inverse_times_y_inverse @ (inverse @ x_plus_y) @ X0)
% 96.39/14.44 | ((inverse @ x_plus_y) = (X0)))),
% 96.39/14.44 inference('sup-', [status(thm)],
% 96.39/14.44 [zip_derived_cl12845, zip_derived_cl11269])).
% 96.39/14.44 thf(zip_derived_cl70023, plain,
% 96.39/14.44 (((inverse @ x_plus_y) = (x_inverse_times_y_inverse))),
% 96.39/14.44 inference('sup-', [status(thm)],
% 96.39/14.44 [zip_derived_cl69931, zip_derived_cl12884])).
% 96.39/14.44 thf(prove_equation, conjecture,
% 96.39/14.44 (( inverse @ x_plus_y ) = ( x_inverse_times_y_inverse ))).
% 96.39/14.44 thf(zf_stmt_0, negated_conjecture,
% 96.39/14.44 (( inverse @ x_plus_y ) != ( x_inverse_times_y_inverse )),
% 96.39/14.44 inference('cnf.neg', [status(esa)], [prove_equation])).
% 96.39/14.44 thf(zip_derived_cl26, plain,
% 96.39/14.44 (((inverse @ x_plus_y) != (x_inverse_times_y_inverse))),
% 96.39/14.44 inference('cnf', [status(esa)], [zf_stmt_0])).
% 96.39/14.44 thf(zip_derived_cl70039, plain, ($false),
% 96.39/14.44 inference('simplify_reflect-', [status(thm)],
% 96.39/14.44 [zip_derived_cl70023, zip_derived_cl26])).
% 96.39/14.44
% 96.39/14.44 % SZS output end Refutation
% 96.39/14.44
% 96.39/14.44
% 96.39/14.44 % Terminating...
% 96.82/14.49 % Runner terminated.
% 96.82/14.50 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------