TSTP Solution File: RNG008-6 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : RNG008-6 : TPTP v8.1.2. Released v1.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.LglJ92Y126 true
% Computer : n005.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 Aug 31 14:06:17 EDT 2023
% Result : Unsatisfiable 145.27s 21.34s
% Output : Refutation 145.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : RNG008-6 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.12 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.LglJ92Y126 true
% 0.12/0.32 % Computer : n005.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Sun Aug 27 02:31:08 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % Running portfolio for 300 s
% 0.12/0.33 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Number of cores: 8
% 0.12/0.33 % Python version: Python 3.6.8
% 0.12/0.33 % Running in FO mode
% 0.18/0.61 % Total configuration time : 435
% 0.18/0.61 % Estimated wc time : 1092
% 0.18/0.61 % Estimated cpu time (7 cpus) : 156.0
% 0.18/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.18/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.18/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.18/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.18/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 1.31/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 1.31/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 145.27/21.34 % Solved by fo/fo5.sh.
% 145.27/21.34 % done 25985 iterations in 20.558s
% 145.27/21.34 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 145.27/21.34 % SZS output start Refutation
% 145.27/21.34 thf(multiply_type, type, multiply: $i > $i > $i).
% 145.27/21.34 thf(sum_type, type, sum: $i > $i > $i > $o).
% 145.27/21.34 thf(product_type, type, product: $i > $i > $i > $o).
% 145.27/21.34 thf(additive_identity_type, type, additive_identity: $i).
% 145.27/21.34 thf(b_type, type, b: $i).
% 145.27/21.34 thf(additive_inverse_type, type, additive_inverse: $i > $i).
% 145.27/21.34 thf(a_type, type, a: $i).
% 145.27/21.34 thf(add_type, type, add: $i > $i > $i).
% 145.27/21.34 thf(c_type, type, c: $i).
% 145.27/21.34 thf(prove_b_times_a_is_c, conjecture, (product @ b @ a @ c)).
% 145.27/21.34 thf(zf_stmt_0, negated_conjecture, (~( product @ b @ a @ c )),
% 145.27/21.34 inference('cnf.neg', [status(esa)], [prove_b_times_a_is_c])).
% 145.27/21.34 thf(zip_derived_cl21, plain, (~ (product @ b @ a @ c)),
% 145.27/21.34 inference('cnf', [status(esa)], [zf_stmt_0])).
% 145.27/21.34 thf(closure_of_multiplication, axiom,
% 145.27/21.34 (product @ X @ Y @ ( multiply @ X @ Y ))).
% 145.27/21.34 thf(zip_derived_cl2, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 145.27/21.34 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 145.27/21.34 thf(right_inverse, axiom,
% 145.27/21.34 (sum @ X @ ( additive_inverse @ X ) @ additive_identity)).
% 145.27/21.34 thf(zip_derived_cl5, plain,
% 145.27/21.34 (![X0 : $i]: (sum @ X0 @ (additive_inverse @ X0) @ additive_identity)),
% 145.27/21.34 inference('cnf', [status(esa)], [right_inverse])).
% 145.27/21.34 thf(x_times_identity_x_is_identity, axiom,
% 145.27/21.34 (product @ X @ additive_identity @ additive_identity)).
% 145.27/21.34 thf(zip_derived_cl17, plain,
% 145.27/21.34 (![X0 : $i]: (product @ X0 @ additive_identity @ additive_identity)),
% 145.27/21.34 inference('cnf', [status(esa)], [x_times_identity_x_is_identity])).
% 145.27/21.34 thf(x_squared_is_x, axiom, (product @ X @ X @ X)).
% 145.27/21.34 thf(zip_derived_cl19, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 145.27/21.34 inference('cnf', [status(esa)], [x_squared_is_x])).
% 145.27/21.34 thf(distributivity1, axiom,
% 145.27/21.34 (( ~( product @ X @ Y @ V1 ) ) | ( ~( product @ X @ Z @ V2 ) ) |
% 145.27/21.34 ( ~( sum @ Y @ Z @ V3 ) ) | ( ~( product @ X @ V3 @ V4 ) ) |
% 145.27/21.34 ( sum @ V1 @ V2 @ V4 ))).
% 145.27/21.34 thf(zip_derived_cl11, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 145.27/21.34 (~ (product @ X0 @ X1 @ X2)
% 145.27/21.34 | ~ (product @ X0 @ X3 @ X4)
% 145.27/21.34 | ~ (sum @ X1 @ X3 @ X5)
% 145.27/21.34 | ~ (product @ X0 @ X5 @ X6)
% 145.27/21.34 | (sum @ X2 @ X4 @ X6))),
% 145.27/21.34 inference('cnf', [status(esa)], [distributivity1])).
% 145.27/21.34 thf(zip_derived_cl90, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 145.27/21.34 ( (sum @ X0 @ X2 @ X1)
% 145.27/21.34 | ~ (product @ X0 @ X3 @ X1)
% 145.27/21.34 | ~ (sum @ X0 @ X4 @ X3)
% 145.27/21.34 | ~ (product @ X0 @ X4 @ X2))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl11])).
% 145.27/21.34 thf(zip_derived_cl1984, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 (~ (product @ X0 @ X2 @ X1)
% 145.27/21.34 | ~ (sum @ X0 @ X2 @ additive_identity)
% 145.27/21.34 | (sum @ X0 @ X1 @ additive_identity))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl90])).
% 145.27/21.34 thf(zip_derived_cl19939, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 ( (sum @ X0 @ X1 @ additive_identity)
% 145.27/21.34 | ~ (product @ X0 @ (additive_inverse @ X0) @ X1))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl1984])).
% 145.27/21.34 thf(zip_derived_cl21988, plain,
% 145.27/21.34 (![X0 : $i]:
% 145.27/21.34 (sum @ X0 @ (multiply @ X0 @ (additive_inverse @ X0)) @
% 145.27/21.34 additive_identity)),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl19939])).
% 145.27/21.34 thf(closure_of_addition, axiom, (sum @ X @ Y @ ( add @ X @ Y ))).
% 145.27/21.34 thf(zip_derived_cl3, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 145.27/21.34 inference('cnf', [status(esa)], [closure_of_addition])).
% 145.27/21.34 thf(commutativity_of_addition, axiom,
% 145.27/21.34 (( ~( sum @ X @ Y @ Z ) ) | ( sum @ Y @ X @ Z ))).
% 145.27/21.34 thf(zip_derived_cl8, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 (~ (sum @ X0 @ X1 @ X2) | (sum @ X1 @ X0 @ X2))),
% 145.27/21.34 inference('cnf', [status(esa)], [commutativity_of_addition])).
% 145.27/21.34 thf(zip_derived_cl43, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl8])).
% 145.27/21.34 thf(addition_is_well_defined, axiom,
% 145.27/21.34 (( ~( sum @ X @ Y @ U ) ) | ( ~( sum @ X @ Y @ V ) ) | ( ( U ) = ( V ) ))).
% 145.27/21.34 thf(zip_derived_cl15, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 145.27/21.34 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 145.27/21.34 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 145.27/21.34 thf(zip_derived_cl150, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 (((add @ X1 @ X0) = (X2)) | ~ (sum @ X0 @ X1 @ X2))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl43, zip_derived_cl15])).
% 145.27/21.34 thf(zip_derived_cl22011, plain,
% 145.27/21.34 (![X0 : $i]:
% 145.27/21.34 ((add @ (multiply @ X0 @ (additive_inverse @ X0)) @ X0)
% 145.27/21.34 = (additive_identity))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl21988, zip_derived_cl150])).
% 145.27/21.34 thf(zip_derived_cl43, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl8])).
% 145.27/21.34 thf(zip_derived_cl3, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 145.27/21.34 inference('cnf', [status(esa)], [closure_of_addition])).
% 145.27/21.34 thf(zip_derived_cl15, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 145.27/21.34 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 145.27/21.34 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 145.27/21.34 thf(zip_derived_cl49, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 (((add @ X1 @ X0) = (X2)) | ~ (sum @ X1 @ X0 @ X2))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl15])).
% 145.27/21.34 thf(zip_derived_cl178, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: ((add @ X0 @ X1) = (add @ X1 @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl43, zip_derived_cl49])).
% 145.27/21.34 thf(zip_derived_cl3, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 145.27/21.34 inference('cnf', [status(esa)], [closure_of_addition])).
% 145.27/21.34 thf(additive_identity1, axiom, (sum @ additive_identity @ X @ X)).
% 145.27/21.34 thf(zip_derived_cl0, plain,
% 145.27/21.34 (![X0 : $i]: (sum @ additive_identity @ X0 @ X0)),
% 145.27/21.34 inference('cnf', [status(esa)], [additive_identity1])).
% 145.27/21.34 thf(zip_derived_cl5, plain,
% 145.27/21.34 (![X0 : $i]: (sum @ X0 @ (additive_inverse @ X0) @ additive_identity)),
% 145.27/21.34 inference('cnf', [status(esa)], [right_inverse])).
% 145.27/21.34 thf(associativity_of_addition1, axiom,
% 145.27/21.34 (( ~( sum @ X @ Y @ U ) ) | ( ~( sum @ Y @ Z @ V ) ) |
% 145.27/21.34 ( ~( sum @ U @ Z @ W ) ) | ( sum @ X @ V @ W ))).
% 145.27/21.34 thf(zip_derived_cl6, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 145.27/21.34 (~ (sum @ X0 @ X1 @ X2)
% 145.27/21.34 | ~ (sum @ X1 @ X3 @ X4)
% 145.27/21.34 | ~ (sum @ X2 @ X3 @ X5)
% 145.27/21.34 | (sum @ X0 @ X4 @ X5))),
% 145.27/21.34 inference('cnf', [status(esa)], [associativity_of_addition1])).
% 145.27/21.34 thf(zip_derived_cl73, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 145.27/21.34 ( (sum @ X0 @ X2 @ X1)
% 145.27/21.34 | ~ (sum @ additive_identity @ X3 @ X1)
% 145.27/21.34 | ~ (sum @ (additive_inverse @ X0) @ X3 @ X2))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl6])).
% 145.27/21.34 thf(zip_derived_cl942, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 (~ (sum @ (additive_inverse @ X2) @ X0 @ X1) | (sum @ X2 @ X1 @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl73])).
% 145.27/21.34 thf(zip_derived_cl3086, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 (sum @ X1 @ (add @ (additive_inverse @ X1) @ X0) @ X0)),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl942])).
% 145.27/21.34 thf(zip_derived_cl150, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 (((add @ X1 @ X0) = (X2)) | ~ (sum @ X0 @ X1 @ X2))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl43, zip_derived_cl15])).
% 145.27/21.34 thf(zip_derived_cl3168, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 ((add @ (add @ (additive_inverse @ X1) @ X0) @ X1) = (X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl3086, zip_derived_cl150])).
% 145.27/21.34 thf(zip_derived_cl3243, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 ((add @ (add @ X1 @ (additive_inverse @ X0)) @ X0) = (X1))),
% 145.27/21.34 inference('sup+', [status(thm)], [zip_derived_cl178, zip_derived_cl3168])).
% 145.27/21.34 thf(zip_derived_cl22195, plain,
% 145.27/21.34 (![X0 : $i]:
% 145.27/21.34 ((add @ additive_identity @ X0)
% 145.27/21.34 = (multiply @ (additive_inverse @ X0) @
% 145.27/21.34 (additive_inverse @ (additive_inverse @ X0))))),
% 145.27/21.34 inference('sup+', [status(thm)],
% 145.27/21.34 [zip_derived_cl22011, zip_derived_cl3243])).
% 145.27/21.34 thf(zip_derived_cl3, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 145.27/21.34 inference('cnf', [status(esa)], [closure_of_addition])).
% 145.27/21.34 thf(zip_derived_cl0, plain,
% 145.27/21.34 (![X0 : $i]: (sum @ additive_identity @ X0 @ X0)),
% 145.27/21.34 inference('cnf', [status(esa)], [additive_identity1])).
% 145.27/21.34 thf(zip_derived_cl15, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 145.27/21.34 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 145.27/21.34 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 145.27/21.34 thf(zip_derived_cl52, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 (((X0) = (X1)) | ~ (sum @ additive_identity @ X0 @ X1))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl15])).
% 145.27/21.34 thf(zip_derived_cl101, plain,
% 145.27/21.34 (![X0 : $i]: ((X0) = (add @ additive_identity @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl52])).
% 145.27/21.34 thf(zip_derived_cl5, plain,
% 145.27/21.34 (![X0 : $i]: (sum @ X0 @ (additive_inverse @ X0) @ additive_identity)),
% 145.27/21.34 inference('cnf', [status(esa)], [right_inverse])).
% 145.27/21.34 thf(zip_derived_cl942, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 (~ (sum @ (additive_inverse @ X2) @ X0 @ X1) | (sum @ X2 @ X1 @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl73])).
% 145.27/21.34 thf(zip_derived_cl3089, plain,
% 145.27/21.34 (![X0 : $i]:
% 145.27/21.34 (sum @ X0 @ additive_identity @
% 145.27/21.34 (additive_inverse @ (additive_inverse @ X0)))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl942])).
% 145.27/21.34 thf(additive_identity2, axiom, (sum @ X @ additive_identity @ X)).
% 145.27/21.34 thf(zip_derived_cl1, plain,
% 145.27/21.34 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 145.27/21.34 inference('cnf', [status(esa)], [additive_identity2])).
% 145.27/21.34 thf(zip_derived_cl15, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 145.27/21.34 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 145.27/21.34 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 145.27/21.34 thf(zip_derived_cl50, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 (((X0) = (X1)) | ~ (sum @ X0 @ additive_identity @ X1))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl15])).
% 145.27/21.34 thf(zip_derived_cl3105, plain,
% 145.27/21.34 (![X0 : $i]: ((X0) = (additive_inverse @ (additive_inverse @ X0)))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl3089, zip_derived_cl50])).
% 145.27/21.34 thf(zip_derived_cl22238, plain,
% 145.27/21.34 (![X0 : $i]: ((X0) = (multiply @ (additive_inverse @ X0) @ X0))),
% 145.27/21.34 inference('demod', [status(thm)],
% 145.27/21.34 [zip_derived_cl22195, zip_derived_cl101, zip_derived_cl3105])).
% 145.27/21.34 thf(zip_derived_cl2, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 145.27/21.34 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 145.27/21.34 thf(zip_derived_cl22283, plain,
% 145.27/21.34 (![X0 : $i]: (product @ (additive_inverse @ X0) @ X0 @ X0)),
% 145.27/21.34 inference('sup+', [status(thm)], [zip_derived_cl22238, zip_derived_cl2])).
% 145.27/21.34 thf(zip_derived_cl5, plain,
% 145.27/21.34 (![X0 : $i]: (sum @ X0 @ (additive_inverse @ X0) @ additive_identity)),
% 145.27/21.34 inference('cnf', [status(esa)], [right_inverse])).
% 145.27/21.34 thf(identity_times_x_is_identity, axiom,
% 145.27/21.34 (product @ additive_identity @ X @ additive_identity)).
% 145.27/21.34 thf(zip_derived_cl18, plain,
% 145.27/21.34 (![X0 : $i]: (product @ additive_identity @ X0 @ additive_identity)),
% 145.27/21.34 inference('cnf', [status(esa)], [identity_times_x_is_identity])).
% 145.27/21.34 thf(zip_derived_cl19, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 145.27/21.34 inference('cnf', [status(esa)], [x_squared_is_x])).
% 145.27/21.34 thf(distributivity3, axiom,
% 145.27/21.34 (( ~( product @ Y @ X @ V1 ) ) | ( ~( product @ Z @ X @ V2 ) ) |
% 145.27/21.34 ( ~( sum @ Y @ Z @ V3 ) ) | ( ~( product @ V3 @ X @ V4 ) ) |
% 145.27/21.34 ( sum @ V1 @ V2 @ V4 ))).
% 145.27/21.34 thf(zip_derived_cl13, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 145.27/21.34 (~ (product @ X0 @ X1 @ X2)
% 145.27/21.34 | ~ (product @ X3 @ X1 @ X4)
% 145.27/21.34 | ~ (sum @ X0 @ X3 @ X5)
% 145.27/21.34 | ~ (product @ X5 @ X1 @ X6)
% 145.27/21.34 | (sum @ X2 @ X4 @ X6))),
% 145.27/21.34 inference('cnf', [status(esa)], [distributivity3])).
% 145.27/21.34 thf(zip_derived_cl113, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 145.27/21.34 ( (sum @ X0 @ X2 @ X1)
% 145.27/21.34 | ~ (product @ X3 @ X0 @ X1)
% 145.27/21.34 | ~ (sum @ X0 @ X4 @ X3)
% 145.27/21.34 | ~ (product @ X4 @ X0 @ X2))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl13])).
% 145.27/21.34 thf(zip_derived_cl2989, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 (~ (product @ X2 @ X0 @ X1)
% 145.27/21.34 | ~ (sum @ X0 @ X2 @ additive_identity)
% 145.27/21.34 | (sum @ X0 @ X1 @ additive_identity))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl113])).
% 145.27/21.34 thf(zip_derived_cl42526, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 ( (sum @ X0 @ X1 @ additive_identity)
% 145.27/21.34 | ~ (product @ (additive_inverse @ X0) @ X0 @ X1))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl2989])).
% 145.27/21.34 thf(zip_derived_cl57711, plain,
% 145.27/21.34 (![X0 : $i]: (sum @ X0 @ X0 @ additive_identity)),
% 145.27/21.34 inference('sup-', [status(thm)],
% 145.27/21.34 [zip_derived_cl22283, zip_derived_cl42526])).
% 145.27/21.34 thf(zip_derived_cl1, plain,
% 145.27/21.34 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 145.27/21.34 inference('cnf', [status(esa)], [additive_identity2])).
% 145.27/21.34 thf(zip_derived_cl3, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 145.27/21.34 inference('cnf', [status(esa)], [closure_of_addition])).
% 145.27/21.34 thf(associativity_of_addition2, axiom,
% 145.27/21.34 (( ~( sum @ X @ Y @ U ) ) | ( ~( sum @ Y @ Z @ V ) ) |
% 145.27/21.34 ( ~( sum @ X @ V @ W ) ) | ( sum @ U @ Z @ W ))).
% 145.27/21.34 thf(zip_derived_cl7, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 145.27/21.34 (~ (sum @ X0 @ X1 @ X2)
% 145.27/21.34 | ~ (sum @ X1 @ X3 @ X4)
% 145.27/21.34 | ~ (sum @ X0 @ X4 @ X5)
% 145.27/21.34 | (sum @ X2 @ X3 @ X5))),
% 145.27/21.34 inference('cnf', [status(esa)], [associativity_of_addition2])).
% 145.27/21.34 thf(zip_derived_cl79, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 145.27/21.34 ( (sum @ (add @ X1 @ X0) @ X3 @ X2)
% 145.27/21.34 | ~ (sum @ X1 @ X4 @ X2)
% 145.27/21.34 | ~ (sum @ X0 @ X3 @ X4))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl7])).
% 145.27/21.34 thf(zip_derived_cl1375, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 (~ (sum @ X2 @ X1 @ additive_identity)
% 145.27/21.34 | (sum @ (add @ X0 @ X2) @ X1 @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl79])).
% 145.27/21.34 thf(zip_derived_cl57773, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (sum @ (add @ X1 @ X0) @ X0 @ X1)),
% 145.27/21.34 inference('sup-', [status(thm)],
% 145.27/21.34 [zip_derived_cl57711, zip_derived_cl1375])).
% 145.27/21.34 thf(a_times_b_is_c, axiom, (product @ a @ b @ c)).
% 145.27/21.34 thf(zip_derived_cl20, plain, ( (product @ a @ b @ c)),
% 145.27/21.34 inference('cnf', [status(esa)], [a_times_b_is_c])).
% 145.27/21.34 thf(zip_derived_cl19, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 145.27/21.34 inference('cnf', [status(esa)], [x_squared_is_x])).
% 145.27/21.34 thf(zip_derived_cl2, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 145.27/21.34 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 145.27/21.34 thf(associativity_of_multiplication2, axiom,
% 145.27/21.34 (( ~( product @ X @ Y @ U ) ) | ( ~( product @ Y @ Z @ V ) ) |
% 145.27/21.34 ( ~( product @ X @ V @ W ) ) | ( product @ U @ Z @ W ))).
% 145.27/21.34 thf(zip_derived_cl10, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 145.27/21.34 (~ (product @ X0 @ X1 @ X2)
% 145.27/21.34 | ~ (product @ X1 @ X3 @ X4)
% 145.27/21.34 | ~ (product @ X0 @ X4 @ X5)
% 145.27/21.34 | (product @ X2 @ X3 @ X5))),
% 145.27/21.34 inference('cnf', [status(esa)], [associativity_of_multiplication2])).
% 145.27/21.34 thf(zip_derived_cl64, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 145.27/21.34 ( (product @ (multiply @ X1 @ X0) @ X3 @ X2)
% 145.27/21.34 | ~ (product @ X1 @ X4 @ X2)
% 145.27/21.34 | ~ (product @ X0 @ X3 @ X4))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl10])).
% 145.27/21.34 thf(zip_derived_cl538, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 (~ (product @ X2 @ X1 @ X0)
% 145.27/21.34 | (product @ (multiply @ X0 @ X2) @ X1 @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl64])).
% 145.27/21.34 thf(zip_derived_cl1568, plain, ( (product @ (multiply @ c @ a) @ b @ c)),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl538])).
% 145.27/21.34 thf(zip_derived_cl2, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 145.27/21.34 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 145.27/21.34 thf(multiplication_is_well_defined, axiom,
% 145.27/21.34 (( ~( product @ X @ Y @ U ) ) | ( ~( product @ X @ Y @ V ) ) |
% 145.27/21.34 ( ( U ) = ( V ) ))).
% 145.27/21.34 thf(zip_derived_cl16, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 145.27/21.34 (~ (product @ X0 @ X1 @ X2)
% 145.27/21.34 | ~ (product @ X0 @ X1 @ X3)
% 145.27/21.34 | ((X2) = (X3)))),
% 145.27/21.34 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 145.27/21.34 thf(zip_derived_cl23, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 (((multiply @ X1 @ X0) = (X2)) | ~ (product @ X1 @ X0 @ X2))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl16])).
% 145.27/21.34 thf(zip_derived_cl1588, plain, (((multiply @ (multiply @ c @ a) @ b) = (c))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl1568, zip_derived_cl23])).
% 145.27/21.34 thf(zip_derived_cl43, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl8])).
% 145.27/21.34 thf(zip_derived_cl19, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 145.27/21.34 inference('cnf', [status(esa)], [x_squared_is_x])).
% 145.27/21.34 thf(zip_derived_cl20, plain, ( (product @ a @ b @ c)),
% 145.27/21.34 inference('cnf', [status(esa)], [a_times_b_is_c])).
% 145.27/21.34 thf(zip_derived_cl20, plain, ( (product @ a @ b @ c)),
% 145.27/21.34 inference('cnf', [status(esa)], [a_times_b_is_c])).
% 145.27/21.34 thf(zip_derived_cl10, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 145.27/21.34 (~ (product @ X0 @ X1 @ X2)
% 145.27/21.34 | ~ (product @ X1 @ X3 @ X4)
% 145.27/21.34 | ~ (product @ X0 @ X4 @ X5)
% 145.27/21.34 | (product @ X2 @ X3 @ X5))),
% 145.27/21.34 inference('cnf', [status(esa)], [associativity_of_multiplication2])).
% 145.27/21.34 thf(zip_derived_cl67, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 ( (product @ c @ X1 @ X0)
% 145.27/21.34 | ~ (product @ a @ X2 @ X0)
% 145.27/21.34 | ~ (product @ b @ X1 @ X2))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl10])).
% 145.27/21.34 thf(zip_derived_cl187, plain,
% 145.27/21.34 (![X0 : $i]: (~ (product @ b @ X0 @ b) | (product @ c @ X0 @ c))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl67])).
% 145.27/21.34 thf(zip_derived_cl188, plain, ( (product @ c @ b @ c)),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl187])).
% 145.27/21.34 thf(zip_derived_cl2, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 145.27/21.34 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 145.27/21.34 thf(zip_derived_cl90, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 145.27/21.34 ( (sum @ X0 @ X2 @ X1)
% 145.27/21.34 | ~ (product @ X0 @ X3 @ X1)
% 145.27/21.34 | ~ (sum @ X0 @ X4 @ X3)
% 145.27/21.34 | ~ (product @ X0 @ X4 @ X2))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl11])).
% 145.27/21.34 thf(zip_derived_cl1983, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 145.27/21.34 (~ (product @ X1 @ X3 @ X2)
% 145.27/21.34 | ~ (sum @ X1 @ X3 @ X0)
% 145.27/21.34 | (sum @ X1 @ X2 @ (multiply @ X1 @ X0)))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl90])).
% 145.27/21.34 thf(zip_derived_cl19795, plain,
% 145.27/21.34 (![X0 : $i]:
% 145.27/21.34 ( (sum @ c @ c @ (multiply @ c @ X0)) | ~ (sum @ c @ b @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl188, zip_derived_cl1983])).
% 145.27/21.34 thf(zip_derived_cl19804, plain,
% 145.27/21.34 ( (sum @ c @ c @ (multiply @ c @ (add @ b @ c)))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl43, zip_derived_cl19795])).
% 145.27/21.34 thf(zip_derived_cl150, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 (((add @ X1 @ X0) = (X2)) | ~ (sum @ X0 @ X1 @ X2))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl43, zip_derived_cl15])).
% 145.27/21.34 thf(zip_derived_cl20243, plain,
% 145.27/21.34 (((add @ c @ c) = (multiply @ c @ (add @ b @ c)))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl19804, zip_derived_cl150])).
% 145.27/21.34 thf(zip_derived_cl2, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 145.27/21.34 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 145.27/21.34 thf(zip_derived_cl20274, plain,
% 145.27/21.34 ( (product @ c @ (add @ b @ c) @ (add @ c @ c))),
% 145.27/21.34 inference('sup+', [status(thm)], [zip_derived_cl20243, zip_derived_cl2])).
% 145.27/21.34 thf(zip_derived_cl2, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 145.27/21.34 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 145.27/21.34 thf(zip_derived_cl5, plain,
% 145.27/21.34 (![X0 : $i]: (sum @ X0 @ (additive_inverse @ X0) @ additive_identity)),
% 145.27/21.34 inference('cnf', [status(esa)], [right_inverse])).
% 145.27/21.34 thf(zip_derived_cl18, plain,
% 145.27/21.34 (![X0 : $i]: (product @ additive_identity @ X0 @ additive_identity)),
% 145.27/21.34 inference('cnf', [status(esa)], [identity_times_x_is_identity])).
% 145.27/21.34 thf(zip_derived_cl20, plain, ( (product @ a @ b @ c)),
% 145.27/21.34 inference('cnf', [status(esa)], [a_times_b_is_c])).
% 145.27/21.34 thf(zip_derived_cl20, plain, ( (product @ a @ b @ c)),
% 145.27/21.34 inference('cnf', [status(esa)], [a_times_b_is_c])).
% 145.27/21.34 thf(zip_derived_cl19, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 145.27/21.34 inference('cnf', [status(esa)], [x_squared_is_x])).
% 145.27/21.34 thf(associativity_of_multiplication1, axiom,
% 145.27/21.34 (( ~( product @ X @ Y @ U ) ) | ( ~( product @ Y @ Z @ V ) ) |
% 145.27/21.34 ( ~( product @ U @ Z @ W ) ) | ( product @ X @ V @ W ))).
% 145.27/21.34 thf(zip_derived_cl9, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 145.27/21.34 (~ (product @ X0 @ X1 @ X2)
% 145.27/21.34 | ~ (product @ X1 @ X3 @ X4)
% 145.27/21.34 | ~ (product @ X2 @ X3 @ X5)
% 145.27/21.34 | (product @ X0 @ X4 @ X5))),
% 145.27/21.34 inference('cnf', [status(esa)], [associativity_of_multiplication1])).
% 145.27/21.34 thf(zip_derived_cl55, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 145.27/21.34 ( (product @ X0 @ X2 @ X1)
% 145.27/21.34 | ~ (product @ X0 @ X3 @ X1)
% 145.27/21.34 | ~ (product @ X0 @ X3 @ X2))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl9])).
% 145.27/21.34 thf(zip_derived_cl208, plain,
% 145.27/21.34 (![X0 : $i]: (~ (product @ a @ b @ X0) | (product @ a @ X0 @ c))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl55])).
% 145.27/21.34 thf(zip_derived_cl213, plain, ( (product @ a @ c @ c)),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl208])).
% 145.27/21.34 thf(zip_derived_cl13, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 145.27/21.34 (~ (product @ X0 @ X1 @ X2)
% 145.27/21.34 | ~ (product @ X3 @ X1 @ X4)
% 145.27/21.34 | ~ (sum @ X0 @ X3 @ X5)
% 145.27/21.34 | ~ (product @ X5 @ X1 @ X6)
% 145.27/21.34 | (sum @ X2 @ X4 @ X6))),
% 145.27/21.34 inference('cnf', [status(esa)], [distributivity3])).
% 145.27/21.34 thf(zip_derived_cl218, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 145.27/21.34 ( (sum @ c @ X1 @ X0)
% 145.27/21.34 | ~ (product @ X2 @ c @ X0)
% 145.27/21.34 | ~ (sum @ a @ X3 @ X2)
% 145.27/21.34 | ~ (product @ X3 @ c @ X1))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl213, zip_derived_cl13])).
% 145.27/21.34 thf(zip_derived_cl4293, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 (~ (product @ X1 @ c @ X0)
% 145.27/21.34 | ~ (sum @ a @ X1 @ additive_identity)
% 145.27/21.34 | (sum @ c @ X0 @ additive_identity))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl218])).
% 145.27/21.34 thf(zip_derived_cl14577, plain,
% 145.27/21.34 (![X0 : $i]:
% 145.27/21.34 ( (sum @ c @ X0 @ additive_identity)
% 145.27/21.34 | ~ (product @ (additive_inverse @ a) @ c @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl4293])).
% 145.27/21.34 thf(zip_derived_cl14580, plain,
% 145.27/21.34 ( (sum @ c @ (multiply @ (additive_inverse @ a) @ c) @ additive_identity)),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl14577])).
% 145.27/21.34 thf(zip_derived_cl150, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 (((add @ X1 @ X0) = (X2)) | ~ (sum @ X0 @ X1 @ X2))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl43, zip_derived_cl15])).
% 145.27/21.34 thf(zip_derived_cl14585, plain,
% 145.27/21.34 (((add @ (multiply @ (additive_inverse @ a) @ c) @ c)
% 145.27/21.34 = (additive_identity))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl14580, zip_derived_cl150])).
% 145.27/21.34 thf(zip_derived_cl3105, plain,
% 145.27/21.34 (![X0 : $i]: ((X0) = (additive_inverse @ (additive_inverse @ X0)))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl3089, zip_derived_cl50])).
% 145.27/21.34 thf(zip_derived_cl3243, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 ((add @ (add @ X1 @ (additive_inverse @ X0)) @ X0) = (X1))),
% 145.27/21.34 inference('sup+', [status(thm)], [zip_derived_cl178, zip_derived_cl3168])).
% 145.27/21.34 thf(zip_derived_cl3336, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 ((add @ (add @ X1 @ X0) @ (additive_inverse @ X0)) = (X1))),
% 145.27/21.34 inference('sup+', [status(thm)], [zip_derived_cl3105, zip_derived_cl3243])).
% 145.27/21.34 thf(zip_derived_cl3105, plain,
% 145.27/21.34 (![X0 : $i]: ((X0) = (additive_inverse @ (additive_inverse @ X0)))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl3089, zip_derived_cl50])).
% 145.27/21.34 thf(zip_derived_cl3168, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 ((add @ (add @ (additive_inverse @ X1) @ X0) @ X1) = (X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl3086, zip_derived_cl150])).
% 145.27/21.34 thf(zip_derived_cl3249, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 ((add @ (add @ X0 @ X1) @ (additive_inverse @ X0)) = (X1))),
% 145.27/21.34 inference('sup+', [status(thm)], [zip_derived_cl3105, zip_derived_cl3168])).
% 145.27/21.34 thf(zip_derived_cl3608, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 ((add @ X0 @ (additive_inverse @ (add @ X0 @ X1)))
% 145.27/21.34 = (additive_inverse @ X1))),
% 145.27/21.34 inference('sup+', [status(thm)], [zip_derived_cl3336, zip_derived_cl3249])).
% 145.27/21.34 thf(zip_derived_cl14622, plain,
% 145.27/21.34 (((add @ (multiply @ (additive_inverse @ a) @ c) @
% 145.27/21.34 (additive_inverse @ additive_identity)) = (additive_inverse @ c))),
% 145.27/21.34 inference('sup+', [status(thm)],
% 145.27/21.34 [zip_derived_cl14585, zip_derived_cl3608])).
% 145.27/21.34 thf(left_inverse, axiom,
% 145.27/21.34 (sum @ ( additive_inverse @ X ) @ X @ additive_identity)).
% 145.27/21.34 thf(zip_derived_cl4, plain,
% 145.27/21.34 (![X0 : $i]: (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)),
% 145.27/21.34 inference('cnf', [status(esa)], [left_inverse])).
% 145.27/21.34 thf(zip_derived_cl50, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 (((X0) = (X1)) | ~ (sum @ X0 @ additive_identity @ X1))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl15])).
% 145.27/21.34 thf(zip_derived_cl100, plain,
% 145.27/21.34 (((additive_inverse @ additive_identity) = (additive_identity))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl50])).
% 145.27/21.34 thf(zip_derived_cl3, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 145.27/21.34 inference('cnf', [status(esa)], [closure_of_addition])).
% 145.27/21.34 thf(zip_derived_cl50, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 (((X0) = (X1)) | ~ (sum @ X0 @ additive_identity @ X1))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl15])).
% 145.27/21.34 thf(zip_derived_cl97, plain,
% 145.27/21.34 (![X0 : $i]: ((X0) = (add @ X0 @ additive_identity))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl50])).
% 145.27/21.34 thf(zip_derived_cl14643, plain,
% 145.27/21.34 (((multiply @ (additive_inverse @ a) @ c) = (additive_inverse @ c))),
% 145.27/21.34 inference('demod', [status(thm)],
% 145.27/21.34 [zip_derived_cl14622, zip_derived_cl100, zip_derived_cl97])).
% 145.27/21.34 thf(zip_derived_cl19, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 145.27/21.34 inference('cnf', [status(esa)], [x_squared_is_x])).
% 145.27/21.34 thf(zip_derived_cl2, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 145.27/21.34 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 145.27/21.34 thf(zip_derived_cl2, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 145.27/21.34 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 145.27/21.34 thf(zip_derived_cl9, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 145.27/21.34 (~ (product @ X0 @ X1 @ X2)
% 145.27/21.34 | ~ (product @ X1 @ X3 @ X4)
% 145.27/21.34 | ~ (product @ X2 @ X3 @ X5)
% 145.27/21.34 | (product @ X0 @ X4 @ X5))),
% 145.27/21.34 inference('cnf', [status(esa)], [associativity_of_multiplication1])).
% 145.27/21.34 thf(zip_derived_cl56, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 145.27/21.34 ( (product @ X1 @ X3 @ X2)
% 145.27/21.34 | ~ (product @ (multiply @ X1 @ X0) @ X4 @ X2)
% 145.27/21.34 | ~ (product @ X0 @ X4 @ X3))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl9])).
% 145.27/21.34 thf(zip_derived_cl235, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 145.27/21.34 (~ (product @ X1 @ X0 @ X3)
% 145.27/21.34 | (product @ X2 @ X3 @ (multiply @ (multiply @ X2 @ X1) @ X0)))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl56])).
% 145.27/21.34 thf(zip_derived_cl4510, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 (product @ X1 @ X0 @ (multiply @ (multiply @ X1 @ X0) @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl235])).
% 145.27/21.34 thf(zip_derived_cl23, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 (((multiply @ X1 @ X0) = (X2)) | ~ (product @ X1 @ X0 @ X2))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl16])).
% 145.27/21.34 thf(zip_derived_cl11962, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 ((multiply @ X1 @ X0) = (multiply @ (multiply @ X1 @ X0) @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl4510, zip_derived_cl23])).
% 145.27/21.34 thf(zip_derived_cl14678, plain,
% 145.27/21.34 (((multiply @ (additive_inverse @ a) @ c)
% 145.27/21.34 = (multiply @ (additive_inverse @ c) @ c))),
% 145.27/21.34 inference('sup+', [status(thm)],
% 145.27/21.34 [zip_derived_cl14643, zip_derived_cl11962])).
% 145.27/21.34 thf(zip_derived_cl14643, plain,
% 145.27/21.34 (((multiply @ (additive_inverse @ a) @ c) = (additive_inverse @ c))),
% 145.27/21.34 inference('demod', [status(thm)],
% 145.27/21.34 [zip_derived_cl14622, zip_derived_cl100, zip_derived_cl97])).
% 145.27/21.34 thf(zip_derived_cl14707, plain,
% 145.27/21.34 (((additive_inverse @ c) = (multiply @ (additive_inverse @ c) @ c))),
% 145.27/21.34 inference('demod', [status(thm)],
% 145.27/21.34 [zip_derived_cl14678, zip_derived_cl14643])).
% 145.27/21.34 thf(zip_derived_cl22238, plain,
% 145.27/21.34 (![X0 : $i]: ((X0) = (multiply @ (additive_inverse @ X0) @ X0))),
% 145.27/21.34 inference('demod', [status(thm)],
% 145.27/21.34 [zip_derived_cl22195, zip_derived_cl101, zip_derived_cl3105])).
% 145.27/21.34 thf(zip_derived_cl22255, plain, (((additive_inverse @ c) = (c))),
% 145.27/21.34 inference('demod', [status(thm)],
% 145.27/21.34 [zip_derived_cl14707, zip_derived_cl22238])).
% 145.27/21.34 thf(zip_derived_cl3, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 145.27/21.34 inference('cnf', [status(esa)], [closure_of_addition])).
% 145.27/21.34 thf(zip_derived_cl5, plain,
% 145.27/21.34 (![X0 : $i]: (sum @ X0 @ (additive_inverse @ X0) @ additive_identity)),
% 145.27/21.34 inference('cnf', [status(esa)], [right_inverse])).
% 145.27/21.34 thf(zip_derived_cl15, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 145.27/21.34 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 145.27/21.34 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 145.27/21.34 thf(zip_derived_cl51, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 (((additive_identity) = (X1))
% 145.27/21.34 | ~ (sum @ X0 @ (additive_inverse @ X0) @ X1))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl15])).
% 145.27/21.34 thf(zip_derived_cl133, plain,
% 145.27/21.34 (![X0 : $i]: ((additive_identity) = (add @ X0 @ (additive_inverse @ X0)))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl51])).
% 145.27/21.34 thf(zip_derived_cl22778, plain, (((additive_identity) = (add @ c @ c))),
% 145.27/21.34 inference('sup+', [status(thm)], [zip_derived_cl22255, zip_derived_cl133])).
% 145.27/21.34 thf(zip_derived_cl22878, plain,
% 145.27/21.34 ( (product @ c @ (add @ b @ c) @ additive_identity)),
% 145.27/21.34 inference('demod', [status(thm)],
% 145.27/21.34 [zip_derived_cl20274, zip_derived_cl22778])).
% 145.27/21.34 thf(zip_derived_cl17, plain,
% 145.27/21.34 (![X0 : $i]: (product @ X0 @ additive_identity @ additive_identity)),
% 145.27/21.34 inference('cnf', [status(esa)], [x_times_identity_x_is_identity])).
% 145.27/21.34 thf(zip_derived_cl64, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 145.27/21.34 ( (product @ (multiply @ X1 @ X0) @ X3 @ X2)
% 145.27/21.34 | ~ (product @ X1 @ X4 @ X2)
% 145.27/21.34 | ~ (product @ X0 @ X3 @ X4))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl10])).
% 145.27/21.34 thf(zip_derived_cl540, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 (~ (product @ X2 @ X1 @ additive_identity)
% 145.27/21.34 | (product @ (multiply @ X0 @ X2) @ X1 @ additive_identity))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl64])).
% 145.27/21.34 thf(zip_derived_cl24830, plain,
% 145.27/21.34 (![X0 : $i]:
% 145.27/21.34 (product @ (multiply @ X0 @ c) @ (add @ b @ c) @ additive_identity)),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl22878, zip_derived_cl540])).
% 145.27/21.34 thf(zip_derived_cl23, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 (((multiply @ X1 @ X0) = (X2)) | ~ (product @ X1 @ X0 @ X2))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl16])).
% 145.27/21.34 thf(zip_derived_cl33154, plain,
% 145.27/21.34 (![X0 : $i]:
% 145.27/21.34 ((multiply @ (multiply @ X0 @ c) @ (add @ b @ c))
% 145.27/21.34 = (additive_identity))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl24830, zip_derived_cl23])).
% 145.27/21.34 thf(zip_derived_cl2, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 145.27/21.34 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 145.27/21.34 thf(zip_derived_cl538, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 (~ (product @ X2 @ X1 @ X0)
% 145.27/21.34 | (product @ (multiply @ X0 @ X2) @ X1 @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl64])).
% 145.27/21.34 thf(zip_derived_cl1558, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 (product @ (multiply @ (multiply @ X1 @ X0) @ X1) @ X0 @
% 145.27/21.34 (multiply @ X1 @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl538])).
% 145.27/21.34 thf(zip_derived_cl23, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 (((multiply @ X1 @ X0) = (X2)) | ~ (product @ X1 @ X0 @ X2))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl16])).
% 145.27/21.34 thf(zip_derived_cl2065, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 ((multiply @ (multiply @ (multiply @ X1 @ X0) @ X1) @ X0)
% 145.27/21.34 = (multiply @ X1 @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl1558, zip_derived_cl23])).
% 145.27/21.34 thf(zip_derived_cl33360, plain,
% 145.27/21.34 (((multiply @ additive_identity @ c) = (multiply @ (add @ b @ c) @ c))),
% 145.27/21.34 inference('sup+', [status(thm)],
% 145.27/21.34 [zip_derived_cl33154, zip_derived_cl2065])).
% 145.27/21.34 thf(zip_derived_cl2, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 145.27/21.34 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 145.27/21.34 thf(zip_derived_cl18, plain,
% 145.27/21.34 (![X0 : $i]: (product @ additive_identity @ X0 @ additive_identity)),
% 145.27/21.34 inference('cnf', [status(esa)], [identity_times_x_is_identity])).
% 145.27/21.34 thf(zip_derived_cl16, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 145.27/21.34 (~ (product @ X0 @ X1 @ X2)
% 145.27/21.34 | ~ (product @ X0 @ X1 @ X3)
% 145.27/21.34 | ((X2) = (X3)))),
% 145.27/21.34 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 145.27/21.34 thf(zip_derived_cl25, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 (((additive_identity) = (X1))
% 145.27/21.34 | ~ (product @ additive_identity @ X0 @ X1))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl16])).
% 145.27/21.34 thf(zip_derived_cl40, plain,
% 145.27/21.34 (![X0 : $i]: ((additive_identity) = (multiply @ additive_identity @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl25])).
% 145.27/21.34 thf(zip_derived_cl33473, plain,
% 145.27/21.34 (((additive_identity) = (multiply @ (add @ b @ c) @ c))),
% 145.27/21.34 inference('demod', [status(thm)], [zip_derived_cl33360, zip_derived_cl40])).
% 145.27/21.34 thf(zip_derived_cl2, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 145.27/21.34 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 145.27/21.34 thf(zip_derived_cl235, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 145.27/21.34 (~ (product @ X1 @ X0 @ X3)
% 145.27/21.34 | (product @ X2 @ X3 @ (multiply @ (multiply @ X2 @ X1) @ X0)))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl56])).
% 145.27/21.34 thf(zip_derived_cl4511, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 (product @ X2 @ (multiply @ X1 @ X0) @
% 145.27/21.34 (multiply @ (multiply @ X2 @ X1) @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl235])).
% 145.27/21.34 thf(zip_derived_cl70048, plain,
% 145.27/21.34 (![X0 : $i]:
% 145.27/21.34 (product @ (add @ b @ c) @ (multiply @ c @ X0) @
% 145.27/21.34 (multiply @ additive_identity @ X0))),
% 145.27/21.34 inference('sup+', [status(thm)],
% 145.27/21.34 [zip_derived_cl33473, zip_derived_cl4511])).
% 145.27/21.34 thf(zip_derived_cl40, plain,
% 145.27/21.34 (![X0 : $i]: ((additive_identity) = (multiply @ additive_identity @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl25])).
% 145.27/21.34 thf(zip_derived_cl70188, plain,
% 145.27/21.34 (![X0 : $i]:
% 145.27/21.34 (product @ (add @ b @ c) @ (multiply @ c @ X0) @ additive_identity)),
% 145.27/21.34 inference('demod', [status(thm)], [zip_derived_cl70048, zip_derived_cl40])).
% 145.27/21.34 thf(zip_derived_cl2, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 145.27/21.34 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 145.27/21.34 thf(zip_derived_cl2, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 145.27/21.34 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 145.27/21.34 thf(zip_derived_cl20, plain, ( (product @ a @ b @ c)),
% 145.27/21.34 inference('cnf', [status(esa)], [a_times_b_is_c])).
% 145.27/21.34 thf(zip_derived_cl9, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 145.27/21.34 (~ (product @ X0 @ X1 @ X2)
% 145.27/21.34 | ~ (product @ X1 @ X3 @ X4)
% 145.27/21.34 | ~ (product @ X2 @ X3 @ X5)
% 145.27/21.34 | (product @ X0 @ X4 @ X5))),
% 145.27/21.34 inference('cnf', [status(esa)], [associativity_of_multiplication1])).
% 145.27/21.34 thf(zip_derived_cl59, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 ( (product @ a @ X1 @ X0)
% 145.27/21.34 | ~ (product @ c @ X2 @ X0)
% 145.27/21.34 | ~ (product @ b @ X2 @ X1))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl9])).
% 145.27/21.34 thf(zip_derived_cl162, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 (~ (product @ b @ X0 @ X1) | (product @ a @ X1 @ (multiply @ c @ X0)))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl59])).
% 145.27/21.34 thf(zip_derived_cl584, plain,
% 145.27/21.34 (![X0 : $i]: (product @ a @ (multiply @ b @ X0) @ (multiply @ c @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl162])).
% 145.27/21.34 thf(zip_derived_cl19, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 145.27/21.34 inference('cnf', [status(esa)], [x_squared_is_x])).
% 145.27/21.34 thf(zip_derived_cl56, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 145.27/21.34 ( (product @ X1 @ X3 @ X2)
% 145.27/21.34 | ~ (product @ (multiply @ X1 @ X0) @ X4 @ X2)
% 145.27/21.34 | ~ (product @ X0 @ X4 @ X3))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl9])).
% 145.27/21.34 thf(zip_derived_cl234, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 (~ (product @ X0 @ (multiply @ X1 @ X0) @ X2)
% 145.27/21.34 | (product @ X1 @ X2 @ (multiply @ X1 @ X0)))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl56])).
% 145.27/21.34 thf(zip_derived_cl4429, plain,
% 145.27/21.34 ( (product @ b @ (multiply @ c @ a) @ (multiply @ b @ a))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl584, zip_derived_cl234])).
% 145.27/21.34 thf(zip_derived_cl2, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 145.27/21.34 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 145.27/21.34 thf(zip_derived_cl55, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 145.27/21.34 ( (product @ X0 @ X2 @ X1)
% 145.27/21.34 | ~ (product @ X0 @ X3 @ X1)
% 145.27/21.34 | ~ (product @ X0 @ X3 @ X2))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl9])).
% 145.27/21.34 thf(zip_derived_cl211, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 (~ (product @ X2 @ X1 @ X0) | (product @ X2 @ X0 @ X0))),
% 145.27/21.34 inference('eq_fact', [status(thm)], [zip_derived_cl55])).
% 145.27/21.34 thf(zip_derived_cl254, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 (product @ X1 @ (multiply @ X1 @ X0) @ (multiply @ X1 @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl211])).
% 145.27/21.34 thf(zip_derived_cl13, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 145.27/21.34 (~ (product @ X0 @ X1 @ X2)
% 145.27/21.34 | ~ (product @ X3 @ X1 @ X4)
% 145.27/21.34 | ~ (sum @ X0 @ X3 @ X5)
% 145.27/21.34 | ~ (product @ X5 @ X1 @ X6)
% 145.27/21.34 | (sum @ X2 @ X4 @ X6))),
% 145.27/21.34 inference('cnf', [status(esa)], [distributivity3])).
% 145.27/21.34 thf(zip_derived_cl362, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 145.27/21.34 ( (sum @ (multiply @ X1 @ X0) @ X3 @ X2)
% 145.27/21.34 | ~ (product @ X4 @ (multiply @ X1 @ X0) @ X2)
% 145.27/21.34 | ~ (sum @ X1 @ X5 @ X4)
% 145.27/21.34 | ~ (product @ X5 @ (multiply @ X1 @ X0) @ X3))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl254, zip_derived_cl13])).
% 145.27/21.34 thf(zip_derived_cl5097, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 (~ (product @ X1 @ (multiply @ c @ a) @ X0)
% 145.27/21.34 | ~ (sum @ c @ X1 @ b)
% 145.27/21.34 | (sum @ (multiply @ c @ a) @ X0 @ (multiply @ b @ a)))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl4429, zip_derived_cl362])).
% 145.27/21.34 thf(zip_derived_cl97092, plain,
% 145.27/21.34 (( (sum @ (multiply @ c @ a) @ additive_identity @ (multiply @ b @ a))
% 145.27/21.34 | ~ (sum @ c @ (add @ b @ c) @ b))),
% 145.27/21.34 inference('sup-', [status(thm)],
% 145.27/21.34 [zip_derived_cl70188, zip_derived_cl5097])).
% 145.27/21.34 thf(zip_derived_cl43, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl8])).
% 145.27/21.34 thf(zip_derived_cl942, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 (~ (sum @ (additive_inverse @ X2) @ X0 @ X1) | (sum @ X2 @ X1 @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl73])).
% 145.27/21.34 thf(zip_derived_cl3087, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 (sum @ X0 @ (add @ X1 @ (additive_inverse @ X0)) @ X1)),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl43, zip_derived_cl942])).
% 145.27/21.34 thf(zip_derived_cl57711, plain,
% 145.27/21.34 (![X0 : $i]: (sum @ X0 @ X0 @ additive_identity)),
% 145.27/21.34 inference('sup-', [status(thm)],
% 145.27/21.34 [zip_derived_cl22283, zip_derived_cl42526])).
% 145.27/21.34 thf(zip_derived_cl150, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 (((add @ X1 @ X0) = (X2)) | ~ (sum @ X0 @ X1 @ X2))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl43, zip_derived_cl15])).
% 145.27/21.34 thf(zip_derived_cl57744, plain,
% 145.27/21.34 (![X0 : $i]: ((add @ X0 @ X0) = (additive_identity))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl57711, zip_derived_cl150])).
% 145.27/21.34 thf(zip_derived_cl3608, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 ((add @ X0 @ (additive_inverse @ (add @ X0 @ X1)))
% 145.27/21.34 = (additive_inverse @ X1))),
% 145.27/21.34 inference('sup+', [status(thm)], [zip_derived_cl3336, zip_derived_cl3249])).
% 145.27/21.34 thf(zip_derived_cl58113, plain,
% 145.27/21.34 (![X0 : $i]:
% 145.27/21.34 ((add @ X0 @ (additive_inverse @ additive_identity))
% 145.27/21.34 = (additive_inverse @ X0))),
% 145.27/21.34 inference('sup+', [status(thm)],
% 145.27/21.34 [zip_derived_cl57744, zip_derived_cl3608])).
% 145.27/21.34 thf(zip_derived_cl100, plain,
% 145.27/21.34 (((additive_inverse @ additive_identity) = (additive_identity))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl50])).
% 145.27/21.34 thf(zip_derived_cl97, plain,
% 145.27/21.34 (![X0 : $i]: ((X0) = (add @ X0 @ additive_identity))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl50])).
% 145.27/21.34 thf(zip_derived_cl58230, plain,
% 145.27/21.34 (![X0 : $i]: ((X0) = (additive_inverse @ X0))),
% 145.27/21.34 inference('demod', [status(thm)],
% 145.27/21.34 [zip_derived_cl58113, zip_derived_cl100, zip_derived_cl97])).
% 145.27/21.34 thf(zip_derived_cl58297, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (sum @ X0 @ (add @ X1 @ X0) @ X1)),
% 145.27/21.34 inference('demod', [status(thm)],
% 145.27/21.34 [zip_derived_cl3087, zip_derived_cl58230])).
% 145.27/21.34 thf(zip_derived_cl97131, plain,
% 145.27/21.34 ( (sum @ (multiply @ c @ a) @ additive_identity @ (multiply @ b @ a))),
% 145.27/21.34 inference('demod', [status(thm)],
% 145.27/21.34 [zip_derived_cl97092, zip_derived_cl58297])).
% 145.27/21.34 thf(zip_derived_cl50, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 (((X0) = (X1)) | ~ (sum @ X0 @ additive_identity @ X1))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl15])).
% 145.27/21.34 thf(zip_derived_cl105318, plain, (((multiply @ c @ a) = (multiply @ b @ a))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl97131, zip_derived_cl50])).
% 145.27/21.34 thf(zip_derived_cl20, plain, ( (product @ a @ b @ c)),
% 145.27/21.34 inference('cnf', [status(esa)], [a_times_b_is_c])).
% 145.27/21.34 thf(zip_derived_cl235, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 145.27/21.34 (~ (product @ X1 @ X0 @ X3)
% 145.27/21.34 | (product @ X2 @ X3 @ (multiply @ (multiply @ X2 @ X1) @ X0)))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl56])).
% 145.27/21.34 thf(zip_derived_cl4534, plain,
% 145.27/21.34 (![X0 : $i]: (product @ X0 @ c @ (multiply @ (multiply @ X0 @ a) @ b))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl235])).
% 145.27/21.34 thf(zip_derived_cl23, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 (((multiply @ X1 @ X0) = (X2)) | ~ (product @ X1 @ X0 @ X2))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl16])).
% 145.27/21.34 thf(zip_derived_cl7832, plain,
% 145.27/21.34 (![X0 : $i]: ((multiply @ X0 @ c) = (multiply @ (multiply @ X0 @ a) @ b))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl4534, zip_derived_cl23])).
% 145.27/21.34 thf(zip_derived_cl105352, plain, (((multiply @ b @ c) = (c))),
% 145.27/21.34 inference('demod', [status(thm)],
% 145.27/21.34 [zip_derived_cl1588, zip_derived_cl105318, zip_derived_cl7832])).
% 145.27/21.34 thf(zip_derived_cl2, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 145.27/21.34 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 145.27/21.34 thf(zip_derived_cl106192, plain, ( (product @ b @ c @ c)),
% 145.27/21.34 inference('sup+', [status(thm)], [zip_derived_cl105352, zip_derived_cl2])).
% 145.27/21.34 thf(zip_derived_cl213, plain, ( (product @ a @ c @ c)),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl208])).
% 145.27/21.34 thf(zip_derived_cl2, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 145.27/21.34 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 145.27/21.34 thf(zip_derived_cl13, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 145.27/21.34 (~ (product @ X0 @ X1 @ X2)
% 145.27/21.34 | ~ (product @ X3 @ X1 @ X4)
% 145.27/21.34 | ~ (sum @ X0 @ X3 @ X5)
% 145.27/21.34 | ~ (product @ X5 @ X1 @ X6)
% 145.27/21.34 | (sum @ X2 @ X4 @ X6))),
% 145.27/21.34 inference('cnf', [status(esa)], [distributivity3])).
% 145.27/21.34 thf(zip_derived_cl114, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 145.27/21.34 ( (sum @ (multiply @ X1 @ X0) @ X3 @ X2)
% 145.27/21.34 | ~ (product @ X4 @ X0 @ X2)
% 145.27/21.34 | ~ (sum @ X1 @ X5 @ X4)
% 145.27/21.34 | ~ (product @ X5 @ X0 @ X3))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 145.27/21.34 thf(zip_derived_cl3074, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 (~ (product @ X1 @ c @ X0)
% 145.27/21.34 | ~ (sum @ X2 @ X1 @ a)
% 145.27/21.34 | (sum @ (multiply @ X2 @ c) @ X0 @ c))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl213, zip_derived_cl114])).
% 145.27/21.34 thf(zip_derived_cl106625, plain,
% 145.27/21.34 (![X0 : $i]:
% 145.27/21.34 ( (sum @ (multiply @ X0 @ c) @ c @ c) | ~ (sum @ X0 @ b @ a))),
% 145.27/21.34 inference('sup-', [status(thm)],
% 145.27/21.34 [zip_derived_cl106192, zip_derived_cl3074])).
% 145.27/21.34 thf(zip_derived_cl110186, plain,
% 145.27/21.34 ( (sum @ (multiply @ (add @ a @ b) @ c) @ c @ c)),
% 145.27/21.34 inference('sup-', [status(thm)],
% 145.27/21.34 [zip_derived_cl57773, zip_derived_cl106625])).
% 145.27/21.34 thf(zip_derived_cl150, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 (((add @ X1 @ X0) = (X2)) | ~ (sum @ X0 @ X1 @ X2))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl43, zip_derived_cl15])).
% 145.27/21.34 thf(zip_derived_cl112121, plain,
% 145.27/21.34 (((add @ c @ (multiply @ (add @ a @ b) @ c)) = (c))),
% 145.27/21.34 inference('sup-', [status(thm)],
% 145.27/21.34 [zip_derived_cl110186, zip_derived_cl150])).
% 145.27/21.34 thf(zip_derived_cl3168, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 ((add @ (add @ (additive_inverse @ X1) @ X0) @ X1) = (X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl3086, zip_derived_cl150])).
% 145.27/21.34 thf(zip_derived_cl58230, plain,
% 145.27/21.34 (![X0 : $i]: ((X0) = (additive_inverse @ X0))),
% 145.27/21.34 inference('demod', [status(thm)],
% 145.27/21.34 [zip_derived_cl58113, zip_derived_cl100, zip_derived_cl97])).
% 145.27/21.34 thf(zip_derived_cl178, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: ((add @ X0 @ X1) = (add @ X1 @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl43, zip_derived_cl49])).
% 145.27/21.34 thf(zip_derived_cl58303, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: ((add @ X1 @ (add @ X1 @ X0)) = (X0))),
% 145.27/21.34 inference('demod', [status(thm)],
% 145.27/21.34 [zip_derived_cl3168, zip_derived_cl58230, zip_derived_cl178])).
% 145.27/21.34 thf(zip_derived_cl112180, plain,
% 145.27/21.34 (((add @ c @ c) = (multiply @ (add @ a @ b) @ c))),
% 145.27/21.34 inference('sup+', [status(thm)],
% 145.27/21.34 [zip_derived_cl112121, zip_derived_cl58303])).
% 145.27/21.34 thf(zip_derived_cl57744, plain,
% 145.27/21.34 (![X0 : $i]: ((add @ X0 @ X0) = (additive_identity))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl57711, zip_derived_cl150])).
% 145.27/21.34 thf(zip_derived_cl112205, plain,
% 145.27/21.34 (((additive_identity) = (multiply @ (add @ a @ b) @ c))),
% 145.27/21.34 inference('demod', [status(thm)],
% 145.27/21.34 [zip_derived_cl112180, zip_derived_cl57744])).
% 145.27/21.34 thf(zip_derived_cl4511, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 (product @ X2 @ (multiply @ X1 @ X0) @
% 145.27/21.34 (multiply @ (multiply @ X2 @ X1) @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl235])).
% 145.27/21.34 thf(zip_derived_cl23, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 (((multiply @ X1 @ X0) = (X2)) | ~ (product @ X1 @ X0 @ X2))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl16])).
% 145.27/21.34 thf(zip_derived_cl69654, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 ((multiply @ X2 @ (multiply @ X1 @ X0))
% 145.27/21.34 = (multiply @ (multiply @ X2 @ X1) @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl4511, zip_derived_cl23])).
% 145.27/21.34 thf(zip_derived_cl112283, plain,
% 145.27/21.34 (![X0 : $i]:
% 145.27/21.34 ((multiply @ (add @ a @ b) @ (multiply @ c @ X0))
% 145.27/21.34 = (multiply @ additive_identity @ X0))),
% 145.27/21.34 inference('sup+', [status(thm)],
% 145.27/21.34 [zip_derived_cl112205, zip_derived_cl69654])).
% 145.27/21.34 thf(zip_derived_cl40, plain,
% 145.27/21.34 (![X0 : $i]: ((additive_identity) = (multiply @ additive_identity @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl25])).
% 145.27/21.34 thf(zip_derived_cl112361, plain,
% 145.27/21.34 (![X0 : $i]:
% 145.27/21.34 ((multiply @ (add @ a @ b) @ (multiply @ c @ X0))
% 145.27/21.34 = (additive_identity))),
% 145.27/21.34 inference('demod', [status(thm)],
% 145.27/21.34 [zip_derived_cl112283, zip_derived_cl40])).
% 145.27/21.34 thf(zip_derived_cl2, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 145.27/21.34 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 145.27/21.34 thf(zip_derived_cl234, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 (~ (product @ X0 @ (multiply @ X1 @ X0) @ X2)
% 145.27/21.34 | (product @ X1 @ X2 @ (multiply @ X1 @ X0)))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl56])).
% 145.27/21.34 thf(zip_derived_cl4425, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 (product @ X1 @ (multiply @ X0 @ (multiply @ X1 @ X0)) @
% 145.27/21.34 (multiply @ X1 @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl234])).
% 145.27/21.34 thf(zip_derived_cl112529, plain,
% 145.27/21.34 ( (product @ c @ additive_identity @ (multiply @ c @ (add @ a @ b)))),
% 145.27/21.34 inference('sup+', [status(thm)],
% 145.27/21.34 [zip_derived_cl112361, zip_derived_cl4425])).
% 145.27/21.34 thf(zip_derived_cl17, plain,
% 145.27/21.34 (![X0 : $i]: (product @ X0 @ additive_identity @ additive_identity)),
% 145.27/21.34 inference('cnf', [status(esa)], [x_times_identity_x_is_identity])).
% 145.27/21.34 thf(zip_derived_cl16, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 145.27/21.34 (~ (product @ X0 @ X1 @ X2)
% 145.27/21.34 | ~ (product @ X0 @ X1 @ X3)
% 145.27/21.34 | ((X2) = (X3)))),
% 145.27/21.34 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 145.27/21.34 thf(zip_derived_cl24, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 (((additive_identity) = (X1))
% 145.27/21.34 | ~ (product @ X0 @ additive_identity @ X1))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl16])).
% 145.27/21.34 thf(zip_derived_cl114827, plain,
% 145.27/21.34 (((additive_identity) = (multiply @ c @ (add @ a @ b)))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl112529, zip_derived_cl24])).
% 145.27/21.34 thf(zip_derived_cl2, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 145.27/21.34 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 145.27/21.34 thf(zip_derived_cl114915, plain,
% 145.27/21.34 ( (product @ c @ (add @ a @ b) @ additive_identity)),
% 145.27/21.34 inference('sup+', [status(thm)], [zip_derived_cl114827, zip_derived_cl2])).
% 145.27/21.34 thf(zip_derived_cl188, plain, ( (product @ c @ b @ c)),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl187])).
% 145.27/21.34 thf(zip_derived_cl3, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 145.27/21.34 inference('cnf', [status(esa)], [closure_of_addition])).
% 145.27/21.34 thf(zip_derived_cl3, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 145.27/21.34 inference('cnf', [status(esa)], [closure_of_addition])).
% 145.27/21.34 thf(distributivity2, axiom,
% 145.27/21.34 (( ~( product @ X @ Y @ V1 ) ) | ( ~( product @ X @ Z @ V2 ) ) |
% 145.27/21.34 ( ~( sum @ Y @ Z @ V3 ) ) | ( ~( sum @ V1 @ V2 @ V4 ) ) |
% 145.27/21.34 ( product @ X @ V3 @ V4 ))).
% 145.27/21.34 thf(zip_derived_cl12, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 145.27/21.34 (~ (product @ X0 @ X1 @ X2)
% 145.27/21.34 | ~ (product @ X0 @ X3 @ X4)
% 145.27/21.34 | ~ (sum @ X1 @ X3 @ X5)
% 145.27/21.34 | ~ (sum @ X2 @ X4 @ X6)
% 145.27/21.34 | (product @ X0 @ X5 @ X6))),
% 145.27/21.34 inference('cnf', [status(esa)], [distributivity2])).
% 145.27/21.34 thf(zip_derived_cl107, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 145.27/21.34 ( (product @ X3 @ (add @ X1 @ X0) @ X2)
% 145.27/21.34 | ~ (sum @ X5 @ X4 @ X2)
% 145.27/21.34 | ~ (product @ X3 @ X0 @ X4)
% 145.27/21.34 | ~ (product @ X3 @ X1 @ X5))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl12])).
% 145.27/21.34 thf(zip_derived_cl2628, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 145.27/21.34 (~ (product @ X3 @ X2 @ X1)
% 145.27/21.34 | ~ (product @ X3 @ X4 @ X0)
% 145.27/21.34 | (product @ X3 @ (add @ X2 @ X4) @ (add @ X1 @ X0)))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl107])).
% 145.27/21.34 thf(zip_derived_cl37293, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 ( (product @ c @ (add @ b @ X1) @ (add @ c @ X0))
% 145.27/21.34 | ~ (product @ c @ X1 @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl188, zip_derived_cl2628])).
% 145.27/21.34 thf(zip_derived_cl139378, plain,
% 145.27/21.34 ( (product @ c @ (add @ b @ (add @ a @ b)) @
% 145.27/21.34 (add @ c @ additive_identity))),
% 145.27/21.34 inference('sup-', [status(thm)],
% 145.27/21.34 [zip_derived_cl114915, zip_derived_cl37293])).
% 145.27/21.34 thf(zip_derived_cl3243, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 ((add @ (add @ X1 @ (additive_inverse @ X0)) @ X0) = (X1))),
% 145.27/21.34 inference('sup+', [status(thm)], [zip_derived_cl178, zip_derived_cl3168])).
% 145.27/21.34 thf(zip_derived_cl58230, plain,
% 145.27/21.34 (![X0 : $i]: ((X0) = (additive_inverse @ X0))),
% 145.27/21.34 inference('demod', [status(thm)],
% 145.27/21.34 [zip_derived_cl58113, zip_derived_cl100, zip_derived_cl97])).
% 145.27/21.34 thf(zip_derived_cl178, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: ((add @ X0 @ X1) = (add @ X1 @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl43, zip_derived_cl49])).
% 145.27/21.34 thf(zip_derived_cl58316, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: ((add @ X0 @ (add @ X1 @ X0)) = (X1))),
% 145.27/21.34 inference('demod', [status(thm)],
% 145.27/21.34 [zip_derived_cl3243, zip_derived_cl58230, zip_derived_cl178])).
% 145.27/21.34 thf(zip_derived_cl97, plain,
% 145.27/21.34 (![X0 : $i]: ((X0) = (add @ X0 @ additive_identity))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl50])).
% 145.27/21.34 thf(zip_derived_cl139395, plain, ( (product @ c @ a @ c)),
% 145.27/21.34 inference('demod', [status(thm)],
% 145.27/21.34 [zip_derived_cl139378, zip_derived_cl58316, zip_derived_cl97])).
% 145.27/21.34 thf(zip_derived_cl2, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 145.27/21.34 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 145.27/21.34 thf(zip_derived_cl1568, plain, ( (product @ (multiply @ c @ a) @ b @ c)),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl538])).
% 145.27/21.34 thf(zip_derived_cl584, plain,
% 145.27/21.34 (![X0 : $i]: (product @ a @ (multiply @ b @ X0) @ (multiply @ c @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl162])).
% 145.27/21.34 thf(zip_derived_cl9, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 145.27/21.34 (~ (product @ X0 @ X1 @ X2)
% 145.27/21.34 | ~ (product @ X1 @ X3 @ X4)
% 145.27/21.34 | ~ (product @ X2 @ X3 @ X5)
% 145.27/21.34 | (product @ X0 @ X4 @ X5))),
% 145.27/21.34 inference('cnf', [status(esa)], [associativity_of_multiplication1])).
% 145.27/21.34 thf(zip_derived_cl607, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 145.27/21.34 ( (product @ a @ X2 @ X1)
% 145.27/21.34 | ~ (product @ (multiply @ c @ X0) @ X3 @ X1)
% 145.27/21.34 | ~ (product @ (multiply @ b @ X0) @ X3 @ X2))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl584, zip_derived_cl9])).
% 145.27/21.34 thf(zip_derived_cl6470, plain,
% 145.27/21.34 (![X0 : $i]:
% 145.27/21.34 (~ (product @ (multiply @ b @ a) @ b @ X0) | (product @ a @ X0 @ c))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl1568, zip_derived_cl607])).
% 145.27/21.34 thf(zip_derived_cl6488, plain,
% 145.27/21.34 ( (product @ a @ (multiply @ (multiply @ b @ a) @ b) @ c)),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl6470])).
% 145.27/21.34 thf(zip_derived_cl254, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 (product @ X1 @ (multiply @ X1 @ X0) @ (multiply @ X1 @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl211])).
% 145.27/21.34 thf(zip_derived_cl56, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 145.27/21.34 ( (product @ X1 @ X3 @ X2)
% 145.27/21.34 | ~ (product @ (multiply @ X1 @ X0) @ X4 @ X2)
% 145.27/21.34 | ~ (product @ X0 @ X4 @ X3))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl9])).
% 145.27/21.34 thf(zip_derived_cl372, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 145.27/21.34 (~ (product @ X1 @ (multiply @ (multiply @ X2 @ X1) @ X0) @ X3)
% 145.27/21.34 | (product @ X2 @ X3 @ (multiply @ (multiply @ X2 @ X1) @ X0)))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl254, zip_derived_cl56])).
% 145.27/21.34 thf(zip_derived_cl6521, plain,
% 145.27/21.34 ( (product @ b @ c @ (multiply @ (multiply @ b @ a) @ b))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl6488, zip_derived_cl372])).
% 145.27/21.34 thf(zip_derived_cl23, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 145.27/21.34 (((multiply @ X1 @ X0) = (X2)) | ~ (product @ X1 @ X0 @ X2))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl16])).
% 145.27/21.34 thf(zip_derived_cl6603, plain,
% 145.27/21.34 (((multiply @ b @ c) = (multiply @ (multiply @ b @ a) @ b))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl6521, zip_derived_cl23])).
% 145.27/21.34 thf(zip_derived_cl1558, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]:
% 145.27/21.34 (product @ (multiply @ (multiply @ X1 @ X0) @ X1) @ X0 @
% 145.27/21.34 (multiply @ X1 @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl538])).
% 145.27/21.34 thf(zip_derived_cl6659, plain,
% 145.27/21.34 ( (product @ (multiply @ b @ c) @ a @ (multiply @ b @ a))),
% 145.27/21.34 inference('sup+', [status(thm)], [zip_derived_cl6603, zip_derived_cl1558])).
% 145.27/21.34 thf(zip_derived_cl16, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 145.27/21.34 (~ (product @ X0 @ X1 @ X2)
% 145.27/21.34 | ~ (product @ X0 @ X1 @ X3)
% 145.27/21.34 | ((X2) = (X3)))),
% 145.27/21.34 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 145.27/21.34 thf(zip_derived_cl6906, plain,
% 145.27/21.34 (![X0 : $i]:
% 145.27/21.34 (((multiply @ b @ a) = (X0))
% 145.27/21.34 | ~ (product @ (multiply @ b @ c) @ a @ X0))),
% 145.27/21.34 inference('sup-', [status(thm)], [zip_derived_cl6659, zip_derived_cl16])).
% 145.27/21.34 thf(zip_derived_cl105352, plain, (((multiply @ b @ c) = (c))),
% 145.27/21.34 inference('demod', [status(thm)],
% 145.27/21.34 [zip_derived_cl1588, zip_derived_cl105318, zip_derived_cl7832])).
% 145.27/21.34 thf(zip_derived_cl106118, plain,
% 145.27/21.34 (![X0 : $i]: (((multiply @ b @ a) = (X0)) | ~ (product @ c @ a @ X0))),
% 145.27/21.34 inference('demod', [status(thm)],
% 145.27/21.34 [zip_derived_cl6906, zip_derived_cl105352])).
% 145.27/21.34 thf(zip_derived_cl139479, plain, (((multiply @ b @ a) = (c))),
% 145.27/21.34 inference('sup-', [status(thm)],
% 145.27/21.34 [zip_derived_cl139395, zip_derived_cl106118])).
% 145.27/21.34 thf(zip_derived_cl2, plain,
% 145.27/21.34 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 145.27/21.34 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 145.27/21.34 thf(zip_derived_cl140137, plain, ( (product @ b @ a @ c)),
% 145.27/21.34 inference('sup+', [status(thm)], [zip_derived_cl139479, zip_derived_cl2])).
% 145.27/21.34 thf(zip_derived_cl140617, plain, ($false),
% 145.27/21.34 inference('demod', [status(thm)],
% 145.27/21.34 [zip_derived_cl21, zip_derived_cl140137])).
% 145.27/21.34
% 145.27/21.34 % SZS output end Refutation
% 145.27/21.34
% 145.27/21.34
% 145.27/21.34 % Terminating...
% 145.27/21.42 % Runner terminated.
% 145.27/21.43 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------