TSTP Solution File: RNG004-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : RNG004-1 : 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.RBJxqKGZNC true
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 14:06:13 EDT 2023
% Result : Unsatisfiable 13.62s 3.07s
% Output : Refutation 13.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG004-1 : 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.RBJxqKGZNC true
% 0.16/0.34 % Computer : n029.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Sun Aug 27 02:36:25 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.16/0.35 % Running portfolio for 300 s
% 0.16/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.35 % Number of cores: 8
% 0.16/0.35 % Python version: Python 3.6.8
% 0.16/0.35 % Running in FO mode
% 0.22/0.63 % Total configuration time : 435
% 0.22/0.63 % Estimated wc time : 1092
% 0.22/0.63 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.70 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.71 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.74 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.75 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 1.25/0.78 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 1.25/0.78 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 13.62/3.07 % Solved by fo/fo5.sh.
% 13.62/3.07 % done 3423 iterations in 2.190s
% 13.62/3.07 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 13.62/3.07 % SZS output start Refutation
% 13.62/3.07 thf(multiply_type, type, multiply: $i > $i > $i).
% 13.62/3.07 thf(a_type, type, a: $i).
% 13.62/3.07 thf(sum_type, type, sum: $i > $i > $i > $o).
% 13.62/3.07 thf(product_type, type, product: $i > $i > $i > $o).
% 13.62/3.07 thf(c_type, type, c: $i).
% 13.62/3.07 thf(additive_identity_type, type, additive_identity: $i).
% 13.62/3.07 thf(b_type, type, b: $i).
% 13.62/3.07 thf(additive_inverse_type, type, additive_inverse: $i > $i).
% 13.62/3.07 thf(d_type, type, d: $i).
% 13.62/3.07 thf(add_type, type, add: $i > $i > $i).
% 13.62/3.07 thf(closure_of_addition, axiom, (sum @ X @ Y @ ( add @ X @ Y ))).
% 13.62/3.07 thf(zip_derived_cl3, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 13.62/3.07 inference('cnf', [status(esa)], [closure_of_addition])).
% 13.62/3.07 thf(commutativity_of_addition, axiom,
% 13.62/3.07 (( ~( sum @ X @ Y @ Z ) ) | ( sum @ Y @ X @ Z ))).
% 13.62/3.07 thf(zip_derived_cl8, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.62/3.07 (~ (sum @ X0 @ X1 @ X2) | (sum @ X1 @ X0 @ X2))),
% 13.62/3.07 inference('cnf', [status(esa)], [commutativity_of_addition])).
% 13.62/3.07 thf(zip_derived_cl20, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl8])).
% 13.62/3.07 thf(closure_of_multiplication, axiom,
% 13.62/3.07 (product @ X @ Y @ ( multiply @ X @ Y ))).
% 13.62/3.07 thf(zip_derived_cl2, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 13.62/3.07 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 13.62/3.07 thf(right_inverse, axiom,
% 13.62/3.07 (sum @ X @ ( additive_inverse @ X ) @ additive_identity)).
% 13.62/3.07 thf(zip_derived_cl5, plain,
% 13.62/3.07 (![X0 : $i]: (sum @ X0 @ (additive_inverse @ X0) @ additive_identity)),
% 13.62/3.07 inference('cnf', [status(esa)], [right_inverse])).
% 13.62/3.07 thf(zip_derived_cl2, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 13.62/3.07 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 13.62/3.07 thf(additive_identity2, axiom, (sum @ X @ additive_identity @ X)).
% 13.62/3.07 thf(zip_derived_cl1, plain,
% 13.62/3.07 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 13.62/3.07 inference('cnf', [status(esa)], [additive_identity2])).
% 13.62/3.07 thf(a_times_b, axiom, (product @ a @ b @ c)).
% 13.62/3.07 thf(zip_derived_cl17, plain, ( (product @ a @ b @ c)),
% 13.62/3.07 inference('cnf', [status(esa)], [a_times_b])).
% 13.62/3.07 thf(zip_derived_cl17, plain, ( (product @ a @ b @ c)),
% 13.62/3.07 inference('cnf', [status(esa)], [a_times_b])).
% 13.62/3.07 thf(distributivity3, axiom,
% 13.62/3.07 (( ~( product @ Y @ X @ V1 ) ) | ( ~( product @ Z @ X @ V2 ) ) |
% 13.62/3.07 ( ~( sum @ Y @ Z @ V3 ) ) | ( ~( product @ V3 @ X @ V4 ) ) |
% 13.62/3.07 ( sum @ V1 @ V2 @ V4 ))).
% 13.62/3.07 thf(zip_derived_cl13, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 13.62/3.07 (~ (product @ X0 @ X1 @ X2)
% 13.62/3.07 | ~ (product @ X3 @ X1 @ X4)
% 13.62/3.07 | ~ (sum @ X0 @ X3 @ X5)
% 13.62/3.07 | ~ (product @ X5 @ X1 @ X6)
% 13.62/3.07 | (sum @ X2 @ X4 @ X6))),
% 13.62/3.07 inference('cnf', [status(esa)], [distributivity3])).
% 13.62/3.07 thf(zip_derived_cl108, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.62/3.07 ( (sum @ c @ X1 @ X0)
% 13.62/3.07 | ~ (product @ X2 @ b @ X0)
% 13.62/3.07 | ~ (sum @ a @ X3 @ X2)
% 13.62/3.07 | ~ (product @ X3 @ b @ X1))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl13])).
% 13.62/3.07 thf(zip_derived_cl2047, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]:
% 13.62/3.07 (~ (product @ X1 @ b @ X0)
% 13.62/3.07 | ~ (sum @ a @ X1 @ a)
% 13.62/3.07 | (sum @ c @ X0 @ c))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl108])).
% 13.62/3.07 thf(zip_derived_cl2261, plain,
% 13.62/3.07 (![X0 : $i]:
% 13.62/3.07 ( (sum @ c @ X0 @ c) | ~ (product @ additive_identity @ b @ X0))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl2047])).
% 13.62/3.07 thf(zip_derived_cl2266, plain,
% 13.62/3.07 ( (sum @ c @ (multiply @ additive_identity @ b) @ c)),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl2261])).
% 13.62/3.07 thf(zip_derived_cl20, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl8])).
% 13.62/3.07 thf(addition_is_well_defined, axiom,
% 13.62/3.07 (( ~( sum @ X @ Y @ U ) ) | ( ~( sum @ X @ Y @ V ) ) | ( ( U ) = ( V ) ))).
% 13.62/3.07 thf(zip_derived_cl15, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.62/3.07 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 13.62/3.07 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 13.62/3.07 thf(zip_derived_cl43, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.62/3.07 (((add @ X1 @ X0) = (X2)) | ~ (sum @ X0 @ X1 @ X2))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl15])).
% 13.62/3.07 thf(zip_derived_cl2271, plain,
% 13.62/3.07 (((add @ (multiply @ additive_identity @ b) @ c) = (c))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl2266, zip_derived_cl43])).
% 13.62/3.07 thf(zip_derived_cl5, plain,
% 13.62/3.07 (![X0 : $i]: (sum @ X0 @ (additive_inverse @ X0) @ additive_identity)),
% 13.62/3.07 inference('cnf', [status(esa)], [right_inverse])).
% 13.62/3.07 thf(additive_identity1, axiom, (sum @ additive_identity @ X @ X)).
% 13.62/3.07 thf(zip_derived_cl0, plain,
% 13.62/3.07 (![X0 : $i]: (sum @ additive_identity @ X0 @ X0)),
% 13.62/3.07 inference('cnf', [status(esa)], [additive_identity1])).
% 13.62/3.07 thf(zip_derived_cl5, plain,
% 13.62/3.07 (![X0 : $i]: (sum @ X0 @ (additive_inverse @ X0) @ additive_identity)),
% 13.62/3.07 inference('cnf', [status(esa)], [right_inverse])).
% 13.62/3.07 thf(associativity_of_addition1, axiom,
% 13.62/3.07 (( ~( sum @ X @ Y @ U ) ) | ( ~( sum @ Y @ Z @ V ) ) |
% 13.62/3.07 ( ~( sum @ U @ Z @ W ) ) | ( sum @ X @ V @ W ))).
% 13.62/3.07 thf(zip_derived_cl6, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 13.62/3.07 (~ (sum @ X0 @ X1 @ X2)
% 13.62/3.07 | ~ (sum @ X1 @ X3 @ X4)
% 13.62/3.07 | ~ (sum @ X2 @ X3 @ X5)
% 13.62/3.07 | (sum @ X0 @ X4 @ X5))),
% 13.62/3.07 inference('cnf', [status(esa)], [associativity_of_addition1])).
% 13.62/3.07 thf(zip_derived_cl28, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.62/3.07 ( (sum @ X0 @ X2 @ X1)
% 13.62/3.07 | ~ (sum @ additive_identity @ X3 @ X1)
% 13.62/3.07 | ~ (sum @ (additive_inverse @ X0) @ X3 @ X2))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl6])).
% 13.62/3.07 thf(zip_derived_cl182, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.62/3.07 (~ (sum @ (additive_inverse @ X2) @ X0 @ X1) | (sum @ X2 @ X1 @ X0))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl28])).
% 13.62/3.07 thf(zip_derived_cl191, plain,
% 13.62/3.07 (![X0 : $i]:
% 13.62/3.07 (sum @ X0 @ additive_identity @
% 13.62/3.07 (additive_inverse @ (additive_inverse @ X0)))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl182])).
% 13.62/3.07 thf(zip_derived_cl1, plain,
% 13.62/3.07 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 13.62/3.07 inference('cnf', [status(esa)], [additive_identity2])).
% 13.62/3.07 thf(zip_derived_cl15, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.62/3.07 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 13.62/3.07 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 13.62/3.07 thf(zip_derived_cl44, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]:
% 13.62/3.07 (((X0) = (X1)) | ~ (sum @ X0 @ additive_identity @ X1))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl15])).
% 13.62/3.07 thf(zip_derived_cl211, plain,
% 13.62/3.07 (![X0 : $i]: ((X0) = (additive_inverse @ (additive_inverse @ X0)))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl191, zip_derived_cl44])).
% 13.62/3.07 thf(zip_derived_cl20, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl8])).
% 13.62/3.07 thf(zip_derived_cl3, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 13.62/3.07 inference('cnf', [status(esa)], [closure_of_addition])).
% 13.62/3.07 thf(zip_derived_cl15, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.62/3.07 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 13.62/3.07 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 13.62/3.07 thf(zip_derived_cl42, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.62/3.07 (((add @ X1 @ X0) = (X2)) | ~ (sum @ X1 @ X0 @ X2))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl15])).
% 13.62/3.07 thf(zip_derived_cl136, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]: ((add @ X0 @ X1) = (add @ X1 @ X0))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl42])).
% 13.62/3.07 thf(zip_derived_cl3, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 13.62/3.07 inference('cnf', [status(esa)], [closure_of_addition])).
% 13.62/3.07 thf(zip_derived_cl182, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.62/3.07 (~ (sum @ (additive_inverse @ X2) @ X0 @ X1) | (sum @ X2 @ X1 @ X0))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl28])).
% 13.62/3.07 thf(zip_derived_cl188, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]:
% 13.62/3.07 (sum @ X1 @ (add @ (additive_inverse @ X1) @ X0) @ X0)),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl182])).
% 13.62/3.07 thf(zip_derived_cl43, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.62/3.07 (((add @ X1 @ X0) = (X2)) | ~ (sum @ X0 @ X1 @ X2))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl15])).
% 13.62/3.07 thf(zip_derived_cl341, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]:
% 13.62/3.07 ((add @ (add @ (additive_inverse @ X1) @ X0) @ X1) = (X0))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl188, zip_derived_cl43])).
% 13.62/3.07 thf(zip_derived_cl380, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]:
% 13.62/3.07 ((add @ (add @ X1 @ (additive_inverse @ X0)) @ X0) = (X1))),
% 13.62/3.07 inference('sup+', [status(thm)], [zip_derived_cl136, zip_derived_cl341])).
% 13.62/3.07 thf(zip_derived_cl501, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]:
% 13.62/3.07 ((add @ (add @ X1 @ X0) @ (additive_inverse @ X0)) = (X1))),
% 13.62/3.07 inference('sup+', [status(thm)], [zip_derived_cl211, zip_derived_cl380])).
% 13.62/3.07 thf(zip_derived_cl2303, plain,
% 13.62/3.07 (((add @ c @ (additive_inverse @ c)) = (multiply @ additive_identity @ b))),
% 13.62/3.07 inference('sup+', [status(thm)], [zip_derived_cl2271, zip_derived_cl501])).
% 13.62/3.07 thf(zip_derived_cl3, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 13.62/3.07 inference('cnf', [status(esa)], [closure_of_addition])).
% 13.62/3.07 thf(zip_derived_cl5, plain,
% 13.62/3.07 (![X0 : $i]: (sum @ X0 @ (additive_inverse @ X0) @ additive_identity)),
% 13.62/3.07 inference('cnf', [status(esa)], [right_inverse])).
% 13.62/3.07 thf(zip_derived_cl15, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.62/3.07 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 13.62/3.07 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 13.62/3.07 thf(zip_derived_cl45, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]:
% 13.62/3.07 (((additive_identity) = (X1))
% 13.62/3.07 | ~ (sum @ X0 @ (additive_inverse @ X0) @ X1))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl15])).
% 13.62/3.07 thf(zip_derived_cl101, plain,
% 13.62/3.07 (![X0 : $i]: ((additive_identity) = (add @ X0 @ (additive_inverse @ X0)))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl45])).
% 13.62/3.07 thf(zip_derived_cl2317, plain,
% 13.62/3.07 (((additive_identity) = (multiply @ additive_identity @ b))),
% 13.62/3.07 inference('demod', [status(thm)], [zip_derived_cl2303, zip_derived_cl101])).
% 13.62/3.07 thf(zip_derived_cl2, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 13.62/3.07 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 13.62/3.07 thf(zip_derived_cl2323, plain,
% 13.62/3.07 ( (product @ additive_identity @ b @ additive_identity)),
% 13.62/3.07 inference('sup+', [status(thm)], [zip_derived_cl2317, zip_derived_cl2])).
% 13.62/3.07 thf(zip_derived_cl108, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.62/3.07 ( (sum @ c @ X1 @ X0)
% 13.62/3.07 | ~ (product @ X2 @ b @ X0)
% 13.62/3.07 | ~ (sum @ a @ X3 @ X2)
% 13.62/3.07 | ~ (product @ X3 @ b @ X1))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl13])).
% 13.62/3.07 thf(zip_derived_cl2357, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]:
% 13.62/3.07 (~ (product @ X1 @ b @ X0)
% 13.62/3.07 | ~ (sum @ a @ X1 @ additive_identity)
% 13.62/3.07 | (sum @ c @ X0 @ additive_identity))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl2323, zip_derived_cl108])).
% 13.62/3.07 thf(zip_derived_cl2540, plain,
% 13.62/3.07 (![X0 : $i]:
% 13.62/3.07 ( (sum @ c @ X0 @ additive_identity)
% 13.62/3.07 | ~ (product @ (additive_inverse @ a) @ b @ X0))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl2357])).
% 13.62/3.07 thf(zip_derived_cl2543, plain,
% 13.62/3.07 ( (sum @ c @ (multiply @ (additive_inverse @ a) @ b) @ additive_identity)),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl2540])).
% 13.62/3.07 thf(zip_derived_cl43, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.62/3.07 (((add @ X1 @ X0) = (X2)) | ~ (sum @ X0 @ X1 @ X2))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl15])).
% 13.62/3.07 thf(zip_derived_cl2553, plain,
% 13.62/3.07 (((add @ (multiply @ (additive_inverse @ a) @ b) @ c)
% 13.62/3.07 = (additive_identity))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl2543, zip_derived_cl43])).
% 13.62/3.07 thf(zip_derived_cl501, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]:
% 13.62/3.07 ((add @ (add @ X1 @ X0) @ (additive_inverse @ X0)) = (X1))),
% 13.62/3.07 inference('sup+', [status(thm)], [zip_derived_cl211, zip_derived_cl380])).
% 13.62/3.07 thf(zip_derived_cl211, plain,
% 13.62/3.07 (![X0 : $i]: ((X0) = (additive_inverse @ (additive_inverse @ X0)))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl191, zip_derived_cl44])).
% 13.62/3.07 thf(zip_derived_cl341, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]:
% 13.62/3.07 ((add @ (add @ (additive_inverse @ X1) @ X0) @ X1) = (X0))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl188, zip_derived_cl43])).
% 13.62/3.07 thf(zip_derived_cl386, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]:
% 13.62/3.07 ((add @ (add @ X0 @ X1) @ (additive_inverse @ X0)) = (X1))),
% 13.62/3.07 inference('sup+', [status(thm)], [zip_derived_cl211, zip_derived_cl341])).
% 13.62/3.07 thf(zip_derived_cl763, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]:
% 13.62/3.07 ((add @ X0 @ (additive_inverse @ (add @ X0 @ X1)))
% 13.62/3.07 = (additive_inverse @ X1))),
% 13.62/3.07 inference('sup+', [status(thm)], [zip_derived_cl501, zip_derived_cl386])).
% 13.62/3.07 thf(zip_derived_cl2614, plain,
% 13.62/3.07 (((add @ (multiply @ (additive_inverse @ a) @ b) @
% 13.62/3.07 (additive_inverse @ additive_identity)) = (additive_inverse @ c))),
% 13.62/3.07 inference('sup+', [status(thm)], [zip_derived_cl2553, zip_derived_cl763])).
% 13.62/3.07 thf(left_inverse, axiom,
% 13.62/3.07 (sum @ ( additive_inverse @ X ) @ X @ additive_identity)).
% 13.62/3.07 thf(zip_derived_cl4, plain,
% 13.62/3.07 (![X0 : $i]: (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)),
% 13.62/3.07 inference('cnf', [status(esa)], [left_inverse])).
% 13.62/3.07 thf(zip_derived_cl44, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]:
% 13.62/3.07 (((X0) = (X1)) | ~ (sum @ X0 @ additive_identity @ X1))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl15])).
% 13.62/3.07 thf(zip_derived_cl93, plain,
% 13.62/3.07 (((additive_inverse @ additive_identity) = (additive_identity))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl44])).
% 13.62/3.07 thf(zip_derived_cl3, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 13.62/3.07 inference('cnf', [status(esa)], [closure_of_addition])).
% 13.62/3.07 thf(zip_derived_cl44, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]:
% 13.62/3.07 (((X0) = (X1)) | ~ (sum @ X0 @ additive_identity @ X1))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl15])).
% 13.62/3.07 thf(zip_derived_cl89, plain,
% 13.62/3.07 (![X0 : $i]: ((X0) = (add @ X0 @ additive_identity))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl44])).
% 13.62/3.07 thf(zip_derived_cl2637, plain,
% 13.62/3.07 (((multiply @ (additive_inverse @ a) @ b) = (additive_inverse @ c))),
% 13.62/3.07 inference('demod', [status(thm)],
% 13.62/3.07 [zip_derived_cl2614, zip_derived_cl93, zip_derived_cl89])).
% 13.62/3.07 thf(zip_derived_cl2, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 13.62/3.07 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 13.62/3.07 thf(zip_derived_cl2652, plain,
% 13.62/3.07 ( (product @ (additive_inverse @ a) @ b @ (additive_inverse @ c))),
% 13.62/3.07 inference('sup+', [status(thm)], [zip_derived_cl2637, zip_derived_cl2])).
% 13.62/3.07 thf(a_inverse_times_b_inverse, axiom,
% 13.62/3.07 (product @ ( additive_inverse @ a ) @ ( additive_inverse @ b ) @ d)).
% 13.62/3.07 thf(zip_derived_cl18, plain,
% 13.62/3.07 ( (product @ (additive_inverse @ a) @ (additive_inverse @ b) @ d)),
% 13.62/3.07 inference('cnf', [status(esa)], [a_inverse_times_b_inverse])).
% 13.62/3.07 thf(zip_derived_cl5, plain,
% 13.62/3.07 (![X0 : $i]: (sum @ X0 @ (additive_inverse @ X0) @ additive_identity)),
% 13.62/3.07 inference('cnf', [status(esa)], [right_inverse])).
% 13.62/3.07 thf(distributivity2, axiom,
% 13.62/3.07 (( ~( product @ X @ Y @ V1 ) ) | ( ~( product @ X @ Z @ V2 ) ) |
% 13.62/3.07 ( ~( sum @ Y @ Z @ V3 ) ) | ( ~( sum @ V1 @ V2 @ V4 ) ) |
% 13.62/3.07 ( product @ X @ V3 @ V4 ))).
% 13.62/3.07 thf(zip_derived_cl12, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 13.62/3.07 (~ (product @ X0 @ X1 @ X2)
% 13.62/3.07 | ~ (product @ X0 @ X3 @ X4)
% 13.62/3.07 | ~ (sum @ X1 @ X3 @ X5)
% 13.62/3.07 | ~ (sum @ X2 @ X4 @ X6)
% 13.62/3.07 | (product @ X0 @ X5 @ X6))),
% 13.62/3.07 inference('cnf', [status(esa)], [distributivity2])).
% 13.62/3.07 thf(zip_derived_cl85, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 13.62/3.07 ( (product @ X2 @ additive_identity @ X1)
% 13.62/3.07 | ~ (sum @ X4 @ X3 @ X1)
% 13.62/3.07 | ~ (product @ X2 @ (additive_inverse @ X0) @ X3)
% 13.62/3.07 | ~ (product @ X2 @ X0 @ X4))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl12])).
% 13.62/3.07 thf(zip_derived_cl1655, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]:
% 13.62/3.07 (~ (product @ (additive_inverse @ a) @ b @ X0)
% 13.62/3.07 | ~ (sum @ X0 @ d @ X1)
% 13.62/3.07 | (product @ (additive_inverse @ a) @ additive_identity @ X1))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl85])).
% 13.62/3.07 thf(zip_derived_cl14967, plain,
% 13.62/3.07 (![X0 : $i]:
% 13.62/3.07 ( (product @ (additive_inverse @ a) @ additive_identity @ X0)
% 13.62/3.07 | ~ (sum @ (additive_inverse @ c) @ d @ X0))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl2652, zip_derived_cl1655])).
% 13.62/3.07 thf(zip_derived_cl14970, plain,
% 13.62/3.07 ( (product @ (additive_inverse @ a) @ additive_identity @
% 13.62/3.07 (add @ d @ (additive_inverse @ c)))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl14967])).
% 13.62/3.07 thf(zip_derived_cl2, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 13.62/3.07 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 13.62/3.07 thf(zip_derived_cl1, plain,
% 13.62/3.07 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 13.62/3.07 inference('cnf', [status(esa)], [additive_identity2])).
% 13.62/3.07 thf(zip_derived_cl18, plain,
% 13.62/3.07 ( (product @ (additive_inverse @ a) @ (additive_inverse @ b) @ d)),
% 13.62/3.07 inference('cnf', [status(esa)], [a_inverse_times_b_inverse])).
% 13.62/3.07 thf(zip_derived_cl18, plain,
% 13.62/3.07 ( (product @ (additive_inverse @ a) @ (additive_inverse @ b) @ d)),
% 13.62/3.07 inference('cnf', [status(esa)], [a_inverse_times_b_inverse])).
% 13.62/3.07 thf(distributivity1, axiom,
% 13.62/3.07 (( ~( product @ X @ Y @ V1 ) ) | ( ~( product @ X @ Z @ V2 ) ) |
% 13.62/3.07 ( ~( sum @ Y @ Z @ V3 ) ) | ( ~( product @ X @ V3 @ V4 ) ) |
% 13.62/3.07 ( sum @ V1 @ V2 @ V4 ))).
% 13.62/3.07 thf(zip_derived_cl11, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 13.62/3.07 (~ (product @ X0 @ X1 @ X2)
% 13.62/3.07 | ~ (product @ X0 @ X3 @ X4)
% 13.62/3.07 | ~ (sum @ X1 @ X3 @ X5)
% 13.62/3.07 | ~ (product @ X0 @ X5 @ X6)
% 13.62/3.07 | (sum @ X2 @ X4 @ X6))),
% 13.62/3.07 inference('cnf', [status(esa)], [distributivity1])).
% 13.62/3.07 thf(zip_derived_cl75, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.62/3.07 ( (sum @ d @ X1 @ X0)
% 13.62/3.07 | ~ (product @ (additive_inverse @ a) @ X2 @ X0)
% 13.62/3.07 | ~ (sum @ (additive_inverse @ b) @ X3 @ X2)
% 13.62/3.07 | ~ (product @ (additive_inverse @ a) @ X3 @ X1))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl11])).
% 13.62/3.07 thf(zip_derived_cl1255, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]:
% 13.62/3.07 (~ (product @ (additive_inverse @ a) @ X1 @ X0)
% 13.62/3.07 | ~ (sum @ (additive_inverse @ b) @ X1 @ (additive_inverse @ b))
% 13.62/3.07 | (sum @ d @ X0 @ d))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl75])).
% 13.62/3.07 thf(zip_derived_cl11129, plain,
% 13.62/3.07 (![X0 : $i]:
% 13.62/3.07 ( (sum @ d @ X0 @ d)
% 13.62/3.07 | ~ (product @ (additive_inverse @ a) @ additive_identity @ X0))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl1255])).
% 13.62/3.07 thf(zip_derived_cl11142, plain,
% 13.62/3.07 ( (sum @ d @ (multiply @ (additive_inverse @ a) @ additive_identity) @ d)),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl11129])).
% 13.62/3.07 thf(zip_derived_cl43, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.62/3.07 (((add @ X1 @ X0) = (X2)) | ~ (sum @ X0 @ X1 @ X2))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl15])).
% 13.62/3.07 thf(zip_derived_cl11147, plain,
% 13.62/3.07 (((add @ (multiply @ (additive_inverse @ a) @ additive_identity) @ d)
% 13.62/3.07 = (d))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl11142, zip_derived_cl43])).
% 13.62/3.07 thf(zip_derived_cl501, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]:
% 13.62/3.07 ((add @ (add @ X1 @ X0) @ (additive_inverse @ X0)) = (X1))),
% 13.62/3.07 inference('sup+', [status(thm)], [zip_derived_cl211, zip_derived_cl380])).
% 13.62/3.07 thf(zip_derived_cl11286, plain,
% 13.62/3.07 (((add @ d @ (additive_inverse @ d))
% 13.62/3.07 = (multiply @ (additive_inverse @ a) @ additive_identity))),
% 13.62/3.07 inference('sup+', [status(thm)], [zip_derived_cl11147, zip_derived_cl501])).
% 13.62/3.07 thf(zip_derived_cl101, plain,
% 13.62/3.07 (![X0 : $i]: ((additive_identity) = (add @ X0 @ (additive_inverse @ X0)))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl45])).
% 13.62/3.07 thf(zip_derived_cl11339, plain,
% 13.62/3.07 (((additive_identity)
% 13.62/3.07 = (multiply @ (additive_inverse @ a) @ additive_identity))),
% 13.62/3.07 inference('demod', [status(thm)],
% 13.62/3.07 [zip_derived_cl11286, zip_derived_cl101])).
% 13.62/3.07 thf(zip_derived_cl2, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 13.62/3.07 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 13.62/3.07 thf(zip_derived_cl11349, plain,
% 13.62/3.07 ( (product @ (additive_inverse @ a) @ additive_identity @
% 13.62/3.07 additive_identity)),
% 13.62/3.07 inference('sup+', [status(thm)], [zip_derived_cl11339, zip_derived_cl2])).
% 13.62/3.07 thf(multiplication_is_well_defined, axiom,
% 13.62/3.07 (( ~( product @ X @ Y @ U ) ) | ( ~( product @ X @ Y @ V ) ) |
% 13.62/3.07 ( ( U ) = ( V ) ))).
% 13.62/3.07 thf(zip_derived_cl16, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.62/3.07 (~ (product @ X0 @ X1 @ X2)
% 13.62/3.07 | ~ (product @ X0 @ X1 @ X3)
% 13.62/3.07 | ((X2) = (X3)))),
% 13.62/3.07 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 13.62/3.07 thf(zip_derived_cl11358, plain,
% 13.62/3.07 (![X0 : $i]:
% 13.62/3.07 (((additive_identity) = (X0))
% 13.62/3.07 | ~ (product @ (additive_inverse @ a) @ additive_identity @ X0))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl11349, zip_derived_cl16])).
% 13.62/3.07 thf(zip_derived_cl15016, plain,
% 13.62/3.07 (((additive_identity) = (add @ d @ (additive_inverse @ c)))),
% 13.62/3.07 inference('sup-', [status(thm)],
% 13.62/3.07 [zip_derived_cl14970, zip_derived_cl11358])).
% 13.62/3.07 thf(zip_derived_cl763, plain,
% 13.62/3.07 (![X0 : $i, X1 : $i]:
% 13.62/3.07 ((add @ X0 @ (additive_inverse @ (add @ X0 @ X1)))
% 13.62/3.07 = (additive_inverse @ X1))),
% 13.62/3.07 inference('sup+', [status(thm)], [zip_derived_cl501, zip_derived_cl386])).
% 13.62/3.07 thf(zip_derived_cl15032, plain,
% 13.62/3.07 (((add @ d @ (additive_inverse @ additive_identity))
% 13.62/3.07 = (additive_inverse @ (additive_inverse @ c)))),
% 13.62/3.07 inference('sup+', [status(thm)], [zip_derived_cl15016, zip_derived_cl763])).
% 13.62/3.07 thf(zip_derived_cl93, plain,
% 13.62/3.07 (((additive_inverse @ additive_identity) = (additive_identity))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl44])).
% 13.62/3.07 thf(zip_derived_cl89, plain,
% 13.62/3.07 (![X0 : $i]: ((X0) = (add @ X0 @ additive_identity))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl44])).
% 13.62/3.07 thf(zip_derived_cl211, plain,
% 13.62/3.07 (![X0 : $i]: ((X0) = (additive_inverse @ (additive_inverse @ X0)))),
% 13.62/3.07 inference('sup-', [status(thm)], [zip_derived_cl191, zip_derived_cl44])).
% 13.62/3.07 thf(zip_derived_cl15144, plain, (((d) = (c))),
% 13.62/3.07 inference('demod', [status(thm)],
% 13.62/3.07 [zip_derived_cl15032, zip_derived_cl93, zip_derived_cl89,
% 13.62/3.07 zip_derived_cl211])).
% 13.62/3.07 thf(prove_c_equals_d, conjecture, (( c ) = ( d ))).
% 13.62/3.07 thf(zf_stmt_0, negated_conjecture, (( c ) != ( d )),
% 13.62/3.07 inference('cnf.neg', [status(esa)], [prove_c_equals_d])).
% 13.62/3.07 thf(zip_derived_cl19, plain, (((c) != (d))),
% 13.62/3.07 inference('cnf', [status(esa)], [zf_stmt_0])).
% 13.62/3.07 thf(zip_derived_cl15145, plain, ($false),
% 13.62/3.07 inference('simplify_reflect-', [status(thm)],
% 13.62/3.07 [zip_derived_cl15144, zip_derived_cl19])).
% 13.62/3.07
% 13.62/3.07 % SZS output end Refutation
% 13.62/3.07
% 13.62/3.07
% 13.62/3.07 % Terminating...
% 16.34/3.66 % Runner terminated.
% 16.34/3.67 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------