TSTP Solution File: RNG007-1 by Zipperpin---2.1.9999
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%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : RNG007-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.i3uObcQoKf true
% Computer : n016.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 14:06:15 EDT 2023
% Result : Unsatisfiable 2.76s 1.30s
% Output : Refutation 2.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG007-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.i3uObcQoKf true
% 0.14/0.34 % Computer : n016.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 02:17:57 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.14/0.34 % Running portfolio for 300 s
% 0.14/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in FO mode
% 0.21/0.62 % Total configuration time : 435
% 0.21/0.62 % Estimated wc time : 1092
% 0.21/0.62 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.72 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.74 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 2.76/1.30 % Solved by fo/fo5.sh.
% 2.76/1.30 % done 1187 iterations in 0.530s
% 2.76/1.30 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 2.76/1.30 % SZS output start Refutation
% 2.76/1.30 thf(multiply_type, type, multiply: $i > $i > $i).
% 2.76/1.30 thf(sum_type, type, sum: $i > $i > $i > $o).
% 2.76/1.30 thf(product_type, type, product: $i > $i > $i > $o).
% 2.76/1.30 thf(additive_identity_type, type, additive_identity: $i).
% 2.76/1.30 thf(a_type, type, a: $i).
% 2.76/1.30 thf(additive_inverse_type, type, additive_inverse: $i > $i).
% 2.76/1.30 thf(add_type, type, add: $i > $i > $i).
% 2.76/1.30 thf(prove_a_plus_a_is_id, conjecture, (sum @ a @ a @ additive_identity)).
% 2.76/1.30 thf(zf_stmt_0, negated_conjecture, (~( sum @ a @ a @ additive_identity )),
% 2.76/1.30 inference('cnf.neg', [status(esa)], [prove_a_plus_a_is_id])).
% 2.76/1.30 thf(zip_derived_cl18, plain, (~ (sum @ a @ a @ additive_identity)),
% 2.76/1.30 inference('cnf', [status(esa)], [zf_stmt_0])).
% 2.76/1.30 thf(closure_of_multiplication, axiom,
% 2.76/1.30 (product @ X @ Y @ ( multiply @ X @ Y ))).
% 2.76/1.30 thf(zip_derived_cl2, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 2.76/1.30 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 2.76/1.30 thf(right_inverse, axiom,
% 2.76/1.30 (sum @ X @ ( additive_inverse @ X ) @ additive_identity)).
% 2.76/1.30 thf(zip_derived_cl5, plain,
% 2.76/1.30 (![X0 : $i]: (sum @ X0 @ (additive_inverse @ X0) @ additive_identity)),
% 2.76/1.30 inference('cnf', [status(esa)], [right_inverse])).
% 2.76/1.30 thf(additive_identity2, axiom, (sum @ X @ additive_identity @ X)).
% 2.76/1.30 thf(zip_derived_cl1, plain,
% 2.76/1.30 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 2.76/1.30 inference('cnf', [status(esa)], [additive_identity2])).
% 2.76/1.30 thf(zip_derived_cl2, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 2.76/1.30 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 2.76/1.30 thf(x_squared_is_x, axiom, (product @ X @ X @ X)).
% 2.76/1.30 thf(zip_derived_cl17, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 2.76/1.30 inference('cnf', [status(esa)], [x_squared_is_x])).
% 2.76/1.30 thf(zip_derived_cl17, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 2.76/1.30 inference('cnf', [status(esa)], [x_squared_is_x])).
% 2.76/1.30 thf(distributivity1, axiom,
% 2.76/1.30 (( ~( product @ X @ Y @ V1 ) ) | ( ~( product @ X @ Z @ V2 ) ) |
% 2.76/1.30 ( ~( sum @ Y @ Z @ V3 ) ) | ( ~( product @ X @ V3 @ V4 ) ) |
% 2.76/1.30 ( sum @ V1 @ V2 @ V4 ))).
% 2.76/1.30 thf(zip_derived_cl11, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 2.76/1.30 (~ (product @ X0 @ X1 @ X2)
% 2.76/1.30 | ~ (product @ X0 @ X3 @ X4)
% 2.76/1.30 | ~ (sum @ X1 @ X3 @ X5)
% 2.76/1.30 | ~ (product @ X0 @ X5 @ X6)
% 2.76/1.30 | (sum @ X2 @ X4 @ X6))),
% 2.76/1.30 inference('cnf', [status(esa)], [distributivity1])).
% 2.76/1.30 thf(zip_derived_cl71, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 2.76/1.30 ( (sum @ X0 @ X2 @ X1)
% 2.76/1.30 | ~ (product @ X0 @ X3 @ X1)
% 2.76/1.30 | ~ (sum @ X0 @ X4 @ X3)
% 2.76/1.30 | ~ (product @ X0 @ X4 @ X2))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl11])).
% 2.76/1.30 thf(zip_derived_cl1094, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.76/1.30 (~ (product @ X0 @ X2 @ X1)
% 2.76/1.30 | ~ (sum @ X0 @ X2 @ X0)
% 2.76/1.30 | (sum @ X0 @ X1 @ X0))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl71])).
% 2.76/1.30 thf(zip_derived_cl2404, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i]:
% 2.76/1.30 ( (sum @ X1 @ (multiply @ X1 @ X0) @ X1) | ~ (sum @ X1 @ X0 @ X1))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl1094])).
% 2.76/1.30 thf(zip_derived_cl2405, plain,
% 2.76/1.30 (![X0 : $i]: (sum @ X0 @ (multiply @ X0 @ additive_identity) @ X0)),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl2404])).
% 2.76/1.30 thf(closure_of_addition, axiom, (sum @ X @ Y @ ( add @ X @ Y ))).
% 2.76/1.30 thf(zip_derived_cl3, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 2.76/1.30 inference('cnf', [status(esa)], [closure_of_addition])).
% 2.76/1.30 thf(commutativity_of_addition, axiom,
% 2.76/1.30 (( ~( sum @ X @ Y @ Z ) ) | ( sum @ Y @ X @ Z ))).
% 2.76/1.30 thf(zip_derived_cl8, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.76/1.30 (~ (sum @ X0 @ X1 @ X2) | (sum @ X1 @ X0 @ X2))),
% 2.76/1.30 inference('cnf', [status(esa)], [commutativity_of_addition])).
% 2.76/1.30 thf(zip_derived_cl19, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl8])).
% 2.76/1.30 thf(left_inverse, axiom,
% 2.76/1.30 (sum @ ( additive_inverse @ X ) @ X @ additive_identity)).
% 2.76/1.30 thf(zip_derived_cl4, plain,
% 2.76/1.30 (![X0 : $i]: (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)),
% 2.76/1.30 inference('cnf', [status(esa)], [left_inverse])).
% 2.76/1.30 thf(associativity_of_addition2, axiom,
% 2.76/1.30 (( ~( sum @ X @ Y @ U ) ) | ( ~( sum @ Y @ Z @ V ) ) |
% 2.76/1.30 ( ~( sum @ X @ V @ W ) ) | ( sum @ U @ Z @ W ))).
% 2.76/1.30 thf(zip_derived_cl7, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 2.76/1.30 (~ (sum @ X0 @ X1 @ X2)
% 2.76/1.30 | ~ (sum @ X1 @ X3 @ X4)
% 2.76/1.30 | ~ (sum @ X0 @ X4 @ X5)
% 2.76/1.30 | (sum @ X2 @ X3 @ X5))),
% 2.76/1.30 inference('cnf', [status(esa)], [associativity_of_addition2])).
% 2.76/1.30 thf(zip_derived_cl57, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.76/1.30 ( (sum @ additive_identity @ X2 @ X1)
% 2.76/1.30 | ~ (sum @ (additive_inverse @ X0) @ X3 @ X1)
% 2.76/1.30 | ~ (sum @ X0 @ X2 @ X3))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl7])).
% 2.76/1.30 thf(zip_derived_cl588, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.76/1.30 (~ (sum @ X0 @ X2 @ X1)
% 2.76/1.30 | (sum @ additive_identity @ X2 @
% 2.76/1.30 (add @ X1 @ (additive_inverse @ X0))))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl57])).
% 2.76/1.30 thf(zip_derived_cl2430, plain,
% 2.76/1.30 (![X0 : $i]:
% 2.76/1.30 (sum @ additive_identity @ (multiply @ X0 @ additive_identity) @
% 2.76/1.30 (add @ X0 @ (additive_inverse @ X0)))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl2405, zip_derived_cl588])).
% 2.76/1.30 thf(zip_derived_cl3, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 2.76/1.30 inference('cnf', [status(esa)], [closure_of_addition])).
% 2.76/1.30 thf(zip_derived_cl5, plain,
% 2.76/1.30 (![X0 : $i]: (sum @ X0 @ (additive_inverse @ X0) @ additive_identity)),
% 2.76/1.30 inference('cnf', [status(esa)], [right_inverse])).
% 2.76/1.30 thf(addition_is_well_defined, axiom,
% 2.76/1.30 (( ~( sum @ X @ Y @ U ) ) | ( ~( sum @ X @ Y @ V ) ) | ( ( U ) = ( V ) ))).
% 2.76/1.30 thf(zip_derived_cl15, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.76/1.30 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 2.76/1.30 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 2.76/1.30 thf(zip_derived_cl46, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i]:
% 2.76/1.30 (((additive_identity) = (X1))
% 2.76/1.30 | ~ (sum @ X0 @ (additive_inverse @ X0) @ X1))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl15])).
% 2.76/1.30 thf(zip_derived_cl137, plain,
% 2.76/1.30 (![X0 : $i]: ((additive_identity) = (add @ X0 @ (additive_inverse @ X0)))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl46])).
% 2.76/1.30 thf(zip_derived_cl2468, plain,
% 2.76/1.30 (![X0 : $i]:
% 2.76/1.30 (sum @ additive_identity @ (multiply @ X0 @ additive_identity) @
% 2.76/1.30 additive_identity)),
% 2.76/1.30 inference('demod', [status(thm)], [zip_derived_cl2430, zip_derived_cl137])).
% 2.76/1.30 thf(additive_identity1, axiom, (sum @ additive_identity @ X @ X)).
% 2.76/1.30 thf(zip_derived_cl0, plain,
% 2.76/1.30 (![X0 : $i]: (sum @ additive_identity @ X0 @ X0)),
% 2.76/1.30 inference('cnf', [status(esa)], [additive_identity1])).
% 2.76/1.30 thf(zip_derived_cl15, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.76/1.30 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 2.76/1.30 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 2.76/1.30 thf(zip_derived_cl47, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i]:
% 2.76/1.30 (((X0) = (X1)) | ~ (sum @ additive_identity @ X0 @ X1))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl15])).
% 2.76/1.30 thf(zip_derived_cl2522, plain,
% 2.76/1.30 (![X0 : $i]: ((multiply @ X0 @ additive_identity) = (additive_identity))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl2468, zip_derived_cl47])).
% 2.76/1.30 thf(zip_derived_cl2, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 2.76/1.30 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 2.76/1.30 thf(zip_derived_cl2542, plain,
% 2.76/1.30 (![X0 : $i]: (product @ X0 @ additive_identity @ additive_identity)),
% 2.76/1.30 inference('sup+', [status(thm)], [zip_derived_cl2522, zip_derived_cl2])).
% 2.76/1.30 thf(zip_derived_cl71, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 2.76/1.30 ( (sum @ X0 @ X2 @ X1)
% 2.76/1.30 | ~ (product @ X0 @ X3 @ X1)
% 2.76/1.30 | ~ (sum @ X0 @ X4 @ X3)
% 2.76/1.30 | ~ (product @ X0 @ X4 @ X2))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl11])).
% 2.76/1.30 thf(zip_derived_cl2561, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.76/1.30 (~ (product @ X0 @ X2 @ X1)
% 2.76/1.30 | ~ (sum @ X0 @ X2 @ additive_identity)
% 2.76/1.30 | (sum @ X0 @ X1 @ additive_identity))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl2542, zip_derived_cl71])).
% 2.76/1.30 thf(zip_derived_cl2752, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i]:
% 2.76/1.30 ( (sum @ X0 @ X1 @ additive_identity)
% 2.76/1.30 | ~ (product @ X0 @ (additive_inverse @ X0) @ X1))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl2561])).
% 2.76/1.30 thf(zip_derived_cl2770, plain,
% 2.76/1.30 (![X0 : $i]:
% 2.76/1.30 (sum @ X0 @ (multiply @ X0 @ (additive_inverse @ X0)) @
% 2.76/1.30 additive_identity)),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl2752])).
% 2.76/1.30 thf(zip_derived_cl19, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl8])).
% 2.76/1.30 thf(zip_derived_cl15, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.76/1.30 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 2.76/1.30 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 2.76/1.30 thf(zip_derived_cl83, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.76/1.30 (((add @ X1 @ X0) = (X2)) | ~ (sum @ X0 @ X1 @ X2))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl15])).
% 2.76/1.30 thf(zip_derived_cl3052, plain,
% 2.76/1.30 (![X0 : $i]:
% 2.76/1.30 ((add @ (multiply @ X0 @ (additive_inverse @ X0)) @ X0)
% 2.76/1.30 = (additive_identity))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl2770, zip_derived_cl83])).
% 2.76/1.30 thf(zip_derived_cl19, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl8])).
% 2.76/1.30 thf(zip_derived_cl3, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 2.76/1.30 inference('cnf', [status(esa)], [closure_of_addition])).
% 2.76/1.30 thf(zip_derived_cl15, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.76/1.30 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 2.76/1.30 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 2.76/1.30 thf(zip_derived_cl44, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.76/1.30 (((add @ X1 @ X0) = (X2)) | ~ (sum @ X1 @ X0 @ X2))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl15])).
% 2.76/1.30 thf(zip_derived_cl236, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i]: ((add @ X0 @ X1) = (add @ X1 @ X0))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl44])).
% 2.76/1.30 thf(zip_derived_cl3, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 2.76/1.30 inference('cnf', [status(esa)], [closure_of_addition])).
% 2.76/1.30 thf(zip_derived_cl0, plain,
% 2.76/1.30 (![X0 : $i]: (sum @ additive_identity @ X0 @ X0)),
% 2.76/1.30 inference('cnf', [status(esa)], [additive_identity1])).
% 2.76/1.30 thf(zip_derived_cl5, plain,
% 2.76/1.30 (![X0 : $i]: (sum @ X0 @ (additive_inverse @ X0) @ additive_identity)),
% 2.76/1.30 inference('cnf', [status(esa)], [right_inverse])).
% 2.76/1.30 thf(associativity_of_addition1, axiom,
% 2.76/1.30 (( ~( sum @ X @ Y @ U ) ) | ( ~( sum @ Y @ Z @ V ) ) |
% 2.76/1.30 ( ~( sum @ U @ Z @ W ) ) | ( sum @ X @ V @ W ))).
% 2.76/1.30 thf(zip_derived_cl6, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 2.76/1.30 (~ (sum @ X0 @ X1 @ X2)
% 2.76/1.30 | ~ (sum @ X1 @ X3 @ X4)
% 2.76/1.30 | ~ (sum @ X2 @ X3 @ X5)
% 2.76/1.30 | (sum @ X0 @ X4 @ X5))),
% 2.76/1.30 inference('cnf', [status(esa)], [associativity_of_addition1])).
% 2.76/1.30 thf(zip_derived_cl27, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.76/1.30 ( (sum @ X0 @ X2 @ X1)
% 2.76/1.30 | ~ (sum @ additive_identity @ X3 @ X1)
% 2.76/1.30 | ~ (sum @ (additive_inverse @ X0) @ X3 @ X2))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl6])).
% 2.76/1.30 thf(zip_derived_cl164, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.76/1.30 (~ (sum @ (additive_inverse @ X2) @ X0 @ X1) | (sum @ X2 @ X1 @ X0))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl27])).
% 2.76/1.30 thf(zip_derived_cl268, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i]:
% 2.76/1.30 (sum @ X1 @ (add @ (additive_inverse @ X1) @ X0) @ X0)),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl164])).
% 2.76/1.30 thf(zip_derived_cl83, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.76/1.30 (((add @ X1 @ X0) = (X2)) | ~ (sum @ X0 @ X1 @ X2))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl15])).
% 2.76/1.30 thf(zip_derived_cl405, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i]:
% 2.76/1.30 ((add @ (add @ (additive_inverse @ X1) @ X0) @ X1) = (X0))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl268, zip_derived_cl83])).
% 2.76/1.30 thf(zip_derived_cl448, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i]:
% 2.76/1.30 ((add @ (add @ X1 @ (additive_inverse @ X0)) @ X0) = (X1))),
% 2.76/1.30 inference('sup+', [status(thm)], [zip_derived_cl236, zip_derived_cl405])).
% 2.76/1.30 thf(zip_derived_cl3174, plain,
% 2.76/1.30 (![X0 : $i]:
% 2.76/1.30 ((add @ additive_identity @ X0)
% 2.76/1.30 = (multiply @ (additive_inverse @ X0) @
% 2.76/1.30 (additive_inverse @ (additive_inverse @ X0))))),
% 2.76/1.30 inference('sup+', [status(thm)], [zip_derived_cl3052, zip_derived_cl448])).
% 2.76/1.30 thf(zip_derived_cl19, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl8])).
% 2.76/1.30 thf(zip_derived_cl1, plain,
% 2.76/1.30 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 2.76/1.30 inference('cnf', [status(esa)], [additive_identity2])).
% 2.76/1.30 thf(zip_derived_cl15, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.76/1.30 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 2.76/1.30 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 2.76/1.30 thf(zip_derived_cl45, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i]:
% 2.76/1.30 (((X0) = (X1)) | ~ (sum @ X0 @ additive_identity @ X1))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl15])).
% 2.76/1.30 thf(zip_derived_cl100, plain,
% 2.76/1.30 (![X0 : $i]: ((X0) = (add @ additive_identity @ X0))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl45])).
% 2.76/1.30 thf(zip_derived_cl5, plain,
% 2.76/1.30 (![X0 : $i]: (sum @ X0 @ (additive_inverse @ X0) @ additive_identity)),
% 2.76/1.30 inference('cnf', [status(esa)], [right_inverse])).
% 2.76/1.30 thf(zip_derived_cl164, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.76/1.30 (~ (sum @ (additive_inverse @ X2) @ X0 @ X1) | (sum @ X2 @ X1 @ X0))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl27])).
% 2.76/1.30 thf(zip_derived_cl271, plain,
% 2.76/1.30 (![X0 : $i]:
% 2.76/1.30 (sum @ X0 @ additive_identity @
% 2.76/1.30 (additive_inverse @ (additive_inverse @ X0)))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl164])).
% 2.76/1.30 thf(zip_derived_cl45, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i]:
% 2.76/1.30 (((X0) = (X1)) | ~ (sum @ X0 @ additive_identity @ X1))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl15])).
% 2.76/1.30 thf(zip_derived_cl317, plain,
% 2.76/1.30 (![X0 : $i]: ((X0) = (additive_inverse @ (additive_inverse @ X0)))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl271, zip_derived_cl45])).
% 2.76/1.30 thf(zip_derived_cl3198, plain,
% 2.76/1.30 (![X0 : $i]: ((X0) = (multiply @ (additive_inverse @ X0) @ X0))),
% 2.76/1.30 inference('demod', [status(thm)],
% 2.76/1.30 [zip_derived_cl3174, zip_derived_cl100, zip_derived_cl317])).
% 2.76/1.30 thf(zip_derived_cl2, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 2.76/1.30 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 2.76/1.30 thf(zip_derived_cl3207, plain,
% 2.76/1.30 (![X0 : $i]: (product @ (additive_inverse @ X0) @ X0 @ X0)),
% 2.76/1.30 inference('sup+', [status(thm)], [zip_derived_cl3198, zip_derived_cl2])).
% 2.76/1.30 thf(zip_derived_cl5, plain,
% 2.76/1.30 (![X0 : $i]: (sum @ X0 @ (additive_inverse @ X0) @ additive_identity)),
% 2.76/1.30 inference('cnf', [status(esa)], [right_inverse])).
% 2.76/1.30 thf(zip_derived_cl1, plain,
% 2.76/1.30 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 2.76/1.30 inference('cnf', [status(esa)], [additive_identity2])).
% 2.76/1.30 thf(zip_derived_cl2, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 2.76/1.30 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 2.76/1.30 thf(zip_derived_cl17, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 2.76/1.30 inference('cnf', [status(esa)], [x_squared_is_x])).
% 2.76/1.30 thf(zip_derived_cl17, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 2.76/1.30 inference('cnf', [status(esa)], [x_squared_is_x])).
% 2.76/1.30 thf(distributivity3, axiom,
% 2.76/1.30 (( ~( product @ Y @ X @ V1 ) ) | ( ~( product @ Z @ X @ V2 ) ) |
% 2.76/1.30 ( ~( sum @ Y @ Z @ V3 ) ) | ( ~( product @ V3 @ X @ V4 ) ) |
% 2.76/1.30 ( sum @ V1 @ V2 @ V4 ))).
% 2.76/1.30 thf(zip_derived_cl13, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 2.76/1.30 (~ (product @ X0 @ X1 @ X2)
% 2.76/1.30 | ~ (product @ X3 @ X1 @ X4)
% 2.76/1.30 | ~ (sum @ X0 @ X3 @ X5)
% 2.76/1.30 | ~ (product @ X5 @ X1 @ X6)
% 2.76/1.30 | (sum @ X2 @ X4 @ X6))),
% 2.76/1.30 inference('cnf', [status(esa)], [distributivity3])).
% 2.76/1.30 thf(zip_derived_cl111, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 2.76/1.30 ( (sum @ X0 @ X2 @ X1)
% 2.76/1.30 | ~ (product @ X3 @ X0 @ X1)
% 2.76/1.30 | ~ (sum @ X0 @ X4 @ X3)
% 2.76/1.30 | ~ (product @ X4 @ X0 @ X2))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl13])).
% 2.76/1.30 thf(zip_derived_cl1948, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.76/1.30 (~ (product @ X2 @ X0 @ X1)
% 2.76/1.30 | ~ (sum @ X0 @ X2 @ X0)
% 2.76/1.30 | (sum @ X0 @ X1 @ X0))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl111])).
% 2.76/1.30 thf(zip_derived_cl4217, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i]:
% 2.76/1.30 ( (sum @ X0 @ (multiply @ X1 @ X0) @ X0) | ~ (sum @ X0 @ X1 @ X0))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl1948])).
% 2.76/1.30 thf(zip_derived_cl4222, plain,
% 2.76/1.30 (![X0 : $i]: (sum @ X0 @ (multiply @ additive_identity @ X0) @ X0)),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl4217])).
% 2.76/1.30 thf(zip_derived_cl83, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.76/1.30 (((add @ X1 @ X0) = (X2)) | ~ (sum @ X0 @ X1 @ X2))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl15])).
% 2.76/1.30 thf(zip_derived_cl4239, plain,
% 2.76/1.30 (![X0 : $i]: ((add @ (multiply @ additive_identity @ X0) @ X0) = (X0))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl4222, zip_derived_cl83])).
% 2.76/1.30 thf(zip_derived_cl317, plain,
% 2.76/1.30 (![X0 : $i]: ((X0) = (additive_inverse @ (additive_inverse @ X0)))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl271, zip_derived_cl45])).
% 2.76/1.30 thf(zip_derived_cl448, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i]:
% 2.76/1.30 ((add @ (add @ X1 @ (additive_inverse @ X0)) @ X0) = (X1))),
% 2.76/1.30 inference('sup+', [status(thm)], [zip_derived_cl236, zip_derived_cl405])).
% 2.76/1.30 thf(zip_derived_cl579, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i]:
% 2.76/1.30 ((add @ (add @ X1 @ X0) @ (additive_inverse @ X0)) = (X1))),
% 2.76/1.30 inference('sup+', [status(thm)], [zip_derived_cl317, zip_derived_cl448])).
% 2.76/1.30 thf(zip_derived_cl4344, plain,
% 2.76/1.30 (![X0 : $i]:
% 2.76/1.30 ((add @ X0 @ (additive_inverse @ X0))
% 2.76/1.30 = (multiply @ additive_identity @ X0))),
% 2.76/1.30 inference('sup+', [status(thm)], [zip_derived_cl4239, zip_derived_cl579])).
% 2.76/1.30 thf(zip_derived_cl137, plain,
% 2.76/1.30 (![X0 : $i]: ((additive_identity) = (add @ X0 @ (additive_inverse @ X0)))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl46])).
% 2.76/1.30 thf(zip_derived_cl4383, plain,
% 2.76/1.30 (![X0 : $i]: ((additive_identity) = (multiply @ additive_identity @ X0))),
% 2.76/1.30 inference('demod', [status(thm)], [zip_derived_cl4344, zip_derived_cl137])).
% 2.76/1.30 thf(zip_derived_cl2, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 2.76/1.30 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 2.76/1.30 thf(zip_derived_cl4393, plain,
% 2.76/1.30 (![X0 : $i]: (product @ additive_identity @ X0 @ additive_identity)),
% 2.76/1.30 inference('sup+', [status(thm)], [zip_derived_cl4383, zip_derived_cl2])).
% 2.76/1.30 thf(zip_derived_cl111, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 2.76/1.30 ( (sum @ X0 @ X2 @ X1)
% 2.76/1.30 | ~ (product @ X3 @ X0 @ X1)
% 2.76/1.30 | ~ (sum @ X0 @ X4 @ X3)
% 2.76/1.30 | ~ (product @ X4 @ X0 @ X2))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl13])).
% 2.76/1.30 thf(zip_derived_cl4422, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.76/1.30 (~ (product @ X2 @ X0 @ X1)
% 2.76/1.30 | ~ (sum @ X0 @ X2 @ additive_identity)
% 2.76/1.30 | (sum @ X0 @ X1 @ additive_identity))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl4393, zip_derived_cl111])).
% 2.76/1.30 thf(zip_derived_cl4589, plain,
% 2.76/1.30 (![X0 : $i, X1 : $i]:
% 2.76/1.30 ( (sum @ X0 @ X1 @ additive_identity)
% 2.76/1.30 | ~ (product @ (additive_inverse @ X0) @ X0 @ X1))),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl4422])).
% 2.76/1.30 thf(zip_derived_cl4609, plain,
% 2.76/1.30 (![X0 : $i]: (sum @ X0 @ X0 @ additive_identity)),
% 2.76/1.30 inference('sup-', [status(thm)], [zip_derived_cl3207, zip_derived_cl4589])).
% 2.76/1.30 thf(zip_derived_cl4614, plain, ($false),
% 2.76/1.30 inference('demod', [status(thm)], [zip_derived_cl18, zip_derived_cl4609])).
% 2.76/1.30
% 2.76/1.30 % SZS output end Refutation
% 2.76/1.30
% 2.76/1.30
% 2.76/1.30 % Terminating...
% 3.57/1.36 % Runner terminated.
% 3.57/1.37 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------