%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : RNG004-2 : TPTP v9.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.gF3bFxOSam true
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:50:11 PM UTC 2025
% Result : Unsatisfiable 13.48s 3.90s
% Output : Refutation 13.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.17 % Problem : RNG004-2 : TPTP v9.2.0. Released v1.0.0.
% 0.14/0.19 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.gF3bFxOSam true
% 0.14/0.39 % Computer : n024.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8042.1875MB
% 0.14/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Wed Oct 1 17:20:23 EDT 2025
% 0.14/0.40 % CPUTime :
% 0.14/0.40 % Running portfolio for 300 s
% 0.14/0.40 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.40 % Number of cores: 8
% 0.14/0.40 % Python version: Python 3.6.8
% 0.14/0.40 % Running in FO mode
% 0.33/0.64 % Total configuration time : 435
% 0.33/0.64 % Estimated wc time : 1092
% 0.33/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.33/0.78 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.33/0.78 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.33/0.79 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.33/0.81 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.33/0.83 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.33/0.85 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.33/0.87 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 13.48/3.90 % Solved by fo/fo5.sh.
% 13.48/3.90 % done 3477 iterations in 2.954s
% 13.48/3.90 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 13.48/3.90 % SZS output start Refutation
% 13.48/3.90 thf(multiply_type, type, multiply: $i > $i > $i).
% 13.48/3.90 thf(sum_type, type, sum: $i > $i > $i > $o).
% 13.48/3.90 thf(b_type, type, b: $i).
% 13.48/3.90 thf(product_type, type, product: $i > $i > $i > $o).
% 13.48/3.90 thf(a_type, type, a: $i).
% 13.48/3.90 thf(additive_identity_type, type, additive_identity: $i).
% 13.48/3.90 thf(d_type, type, d: $i).
% 13.48/3.90 thf(c_type, type, c: $i).
% 13.48/3.90 thf(additive_inverse_type, type, additive_inverse: $i > $i).
% 13.48/3.90 thf(add_type, type, add: $i > $i > $i).
% 13.48/3.90 thf(closure_of_addition, axiom, (sum @ X @ Y @ ( add @ X @ Y ))).
% 13.48/3.90 thf(zip_derived_cl3, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 13.48/3.90 inference('cnf', [status(esa)], [closure_of_addition])).
% 13.48/3.90 thf(commutativity_of_addition, axiom,
% 13.48/3.90 (( ~( sum @ X @ Y @ Z ) ) | ( sum @ Y @ X @ Z ))).
% 13.48/3.90 thf(zip_derived_cl8, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.48/3.90 (~ (sum @ X0 @ X1 @ X2) | (sum @ X1 @ X0 @ X2))),
% 13.48/3.90 inference('cnf', [status(esa)], [commutativity_of_addition])).
% 13.48/3.90 thf(zip_derived_cl22, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl8])).
% 13.48/3.90 thf(closure_of_multiplication, axiom,
% 13.48/3.90 (product @ X @ Y @ ( multiply @ X @ Y ))).
% 13.48/3.90 thf(zip_derived_cl2, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 13.48/3.90 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 13.48/3.90 thf(right_inverse, axiom,
% 13.48/3.90 (sum @ X @ ( additive_inverse @ X ) @ additive_identity)).
% 13.48/3.90 thf(zip_derived_cl5, plain,
% 13.48/3.90 (![X0 : $i]: (sum @ X0 @ (additive_inverse @ X0) @ additive_identity)),
% 13.48/3.90 inference('cnf', [status(esa)], [right_inverse])).
% 13.48/3.90 thf(zip_derived_cl2, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 13.48/3.90 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 13.48/3.90 thf(additive_identity2, axiom, (sum @ X @ additive_identity @ X)).
% 13.48/3.90 thf(zip_derived_cl1, plain,
% 13.48/3.90 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 13.48/3.90 inference('cnf', [status(esa)], [additive_identity2])).
% 13.48/3.90 thf(a_times_b, axiom, (product @ a @ b @ c)).
% 13.48/3.90 thf(zip_derived_cl19, plain, ( (product @ a @ b @ c)),
% 13.48/3.90 inference('cnf', [status(esa)], [a_times_b])).
% 13.48/3.90 thf(zip_derived_cl19, plain, ( (product @ a @ b @ c)),
% 13.48/3.90 inference('cnf', [status(esa)], [a_times_b])).
% 13.48/3.90 thf(distributivity3, axiom,
% 13.48/3.90 (( ~( product @ Y @ X @ V1 ) ) | ( ~( product @ Z @ X @ V2 ) ) |
% 13.48/3.90 ( ~( sum @ Y @ Z @ V3 ) ) | ( ~( product @ V3 @ X @ V4 ) ) |
% 13.48/3.90 ( sum @ V1 @ V2 @ V4 ))).
% 13.48/3.90 thf(zip_derived_cl13, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 13.48/3.90 (~ (product @ X0 @ X1 @ X2)
% 13.48/3.90 | ~ (product @ X3 @ X1 @ X4)
% 13.48/3.90 | ~ (sum @ X0 @ X3 @ X5)
% 13.48/3.90 | ~ (product @ X5 @ X1 @ X6)
% 13.48/3.90 | (sum @ X2 @ X4 @ X6))),
% 13.48/3.90 inference('cnf', [status(esa)], [distributivity3])).
% 13.48/3.90 thf(zip_derived_cl125, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.48/3.90 ( (sum @ c @ X1 @ X0)
% 13.48/3.90 | ~ (product @ X2 @ b @ X0)
% 13.48/3.90 | ~ (sum @ a @ X3 @ X2)
% 13.48/3.90 | ~ (product @ X3 @ b @ X1))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl13])).
% 13.48/3.90 thf(zip_derived_cl1806, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i]:
% 13.48/3.90 (~ (product @ X1 @ b @ X0)
% 13.48/3.90 | ~ (sum @ a @ X1 @ a)
% 13.48/3.90 | (sum @ c @ X0 @ c))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl125])).
% 13.48/3.90 thf(zip_derived_cl1919, plain,
% 13.48/3.90 (![X0 : $i]:
% 13.48/3.90 ( (sum @ c @ X0 @ c) | ~ (product @ additive_identity @ b @ X0))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl1806])).
% 13.48/3.90 thf(zip_derived_cl1924, plain,
% 13.48/3.90 ( (sum @ c @ (multiply @ additive_identity @ b) @ c)),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl1919])).
% 13.48/3.90 thf(zip_derived_cl1, plain,
% 13.48/3.90 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 13.48/3.90 inference('cnf', [status(esa)], [additive_identity2])).
% 13.48/3.90 thf(cancellation1, axiom,
% 13.48/3.90 (( ~( sum @ X @ Y @ Z ) ) | ( ~( sum @ X @ W @ Z ) ) | ( ( Y ) = ( W ) ))).
% 13.48/3.90 thf(zip_derived_cl17, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.48/3.90 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X3 @ X2) | ((X1) = (X3)))),
% 13.48/3.90 inference('cnf', [status(esa)], [cancellation1])).
% 13.48/3.90 thf(zip_derived_cl57, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i]:
% 13.48/3.90 (((additive_identity) = (X1)) | ~ (sum @ X0 @ X1 @ X0))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl17])).
% 13.48/3.90 thf(zip_derived_cl1959, plain,
% 13.48/3.90 (((additive_identity) = (multiply @ additive_identity @ b))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl1924, zip_derived_cl57])).
% 13.48/3.90 thf(zip_derived_cl2, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 13.48/3.90 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 13.48/3.90 thf(zip_derived_cl1976, plain,
% 13.48/3.90 ( (product @ additive_identity @ b @ additive_identity)),
% 13.48/3.90 inference('sup+', [status(thm)], [zip_derived_cl1959, zip_derived_cl2])).
% 13.48/3.90 thf(zip_derived_cl125, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.48/3.90 ( (sum @ c @ X1 @ X0)
% 13.48/3.90 | ~ (product @ X2 @ b @ X0)
% 13.48/3.90 | ~ (sum @ a @ X3 @ X2)
% 13.48/3.90 | ~ (product @ X3 @ b @ X1))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl13])).
% 13.48/3.90 thf(zip_derived_cl1996, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i]:
% 13.48/3.90 (~ (product @ X1 @ b @ X0)
% 13.48/3.90 | ~ (sum @ a @ X1 @ additive_identity)
% 13.48/3.90 | (sum @ c @ X0 @ additive_identity))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl1976, zip_derived_cl125])).
% 13.48/3.90 thf(zip_derived_cl2058, plain,
% 13.48/3.90 (![X0 : $i]:
% 13.48/3.90 ( (sum @ c @ X0 @ additive_identity)
% 13.48/3.90 | ~ (product @ (additive_inverse @ a) @ b @ X0))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl1996])).
% 13.48/3.90 thf(zip_derived_cl2061, plain,
% 13.48/3.90 ( (sum @ c @ (multiply @ (additive_inverse @ a) @ b) @ additive_identity)),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl2058])).
% 13.48/3.90 thf(zip_derived_cl5, plain,
% 13.48/3.90 (![X0 : $i]: (sum @ X0 @ (additive_inverse @ X0) @ additive_identity)),
% 13.48/3.90 inference('cnf', [status(esa)], [right_inverse])).
% 13.48/3.90 thf(zip_derived_cl17, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.48/3.90 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X3 @ X2) | ((X1) = (X3)))),
% 13.48/3.90 inference('cnf', [status(esa)], [cancellation1])).
% 13.48/3.90 thf(zip_derived_cl58, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i]:
% 13.48/3.90 (((additive_inverse @ X0) = (X1))
% 13.48/3.90 | ~ (sum @ X0 @ X1 @ additive_identity))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl17])).
% 13.48/3.90 thf(zip_derived_cl2177, plain,
% 13.48/3.90 (((additive_inverse @ c) = (multiply @ (additive_inverse @ a) @ b))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl2061, zip_derived_cl58])).
% 13.48/3.90 thf(zip_derived_cl2, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 13.48/3.90 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 13.48/3.90 thf(zip_derived_cl2183, plain,
% 13.48/3.90 ( (product @ (additive_inverse @ a) @ b @ (additive_inverse @ c))),
% 13.48/3.90 inference('sup+', [status(thm)], [zip_derived_cl2177, zip_derived_cl2])).
% 13.48/3.90 thf(a_inverse_times_b_inverse, axiom,
% 13.48/3.90 (product @ ( additive_inverse @ a ) @ ( additive_inverse @ b ) @ d)).
% 13.48/3.90 thf(zip_derived_cl20, plain,
% 13.48/3.90 ( (product @ (additive_inverse @ a) @ (additive_inverse @ b) @ d)),
% 13.48/3.90 inference('cnf', [status(esa)], [a_inverse_times_b_inverse])).
% 13.48/3.90 thf(zip_derived_cl5, plain,
% 13.48/3.90 (![X0 : $i]: (sum @ X0 @ (additive_inverse @ X0) @ additive_identity)),
% 13.48/3.90 inference('cnf', [status(esa)], [right_inverse])).
% 13.48/3.90 thf(distributivity2, axiom,
% 13.48/3.90 (( ~( product @ X @ Y @ V1 ) ) | ( ~( product @ X @ Z @ V2 ) ) |
% 13.48/3.90 ( ~( sum @ Y @ Z @ V3 ) ) | ( ~( sum @ V1 @ V2 @ V4 ) ) |
% 13.48/3.90 ( product @ X @ V3 @ V4 ))).
% 13.48/3.90 thf(zip_derived_cl12, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 13.48/3.90 (~ (product @ X0 @ X1 @ X2)
% 13.48/3.90 | ~ (product @ X0 @ X3 @ X4)
% 13.48/3.90 | ~ (sum @ X1 @ X3 @ X5)
% 13.48/3.90 | ~ (sum @ X2 @ X4 @ X6)
% 13.48/3.90 | (product @ X0 @ X5 @ X6))),
% 13.48/3.90 inference('cnf', [status(esa)], [distributivity2])).
% 13.48/3.90 thf(zip_derived_cl119, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 13.48/3.90 ( (product @ X2 @ additive_identity @ X1)
% 13.48/3.90 | ~ (sum @ X4 @ X3 @ X1)
% 13.48/3.90 | ~ (product @ X2 @ (additive_inverse @ X0) @ X3)
% 13.48/3.90 | ~ (product @ X2 @ X0 @ X4))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl12])).
% 13.48/3.90 thf(zip_derived_cl1504, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i]:
% 13.48/3.90 (~ (product @ (additive_inverse @ a) @ b @ X0)
% 13.48/3.90 | ~ (sum @ X0 @ d @ X1)
% 13.48/3.90 | (product @ (additive_inverse @ a) @ additive_identity @ X1))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl119])).
% 13.48/3.90 thf(zip_derived_cl12323, plain,
% 13.48/3.90 (![X0 : $i]:
% 13.48/3.90 ( (product @ (additive_inverse @ a) @ additive_identity @ X0)
% 13.48/3.90 | ~ (sum @ (additive_inverse @ c) @ d @ X0))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl2183, zip_derived_cl1504])).
% 13.48/3.90 thf(zip_derived_cl12341, plain,
% 13.48/3.90 ( (product @ (additive_inverse @ a) @ additive_identity @
% 13.48/3.90 (add @ d @ (additive_inverse @ c)))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl12323])).
% 13.48/3.90 thf(zip_derived_cl2, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 13.48/3.90 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 13.48/3.90 thf(zip_derived_cl1, plain,
% 13.48/3.90 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 13.48/3.90 inference('cnf', [status(esa)], [additive_identity2])).
% 13.48/3.90 thf(zip_derived_cl20, plain,
% 13.48/3.90 ( (product @ (additive_inverse @ a) @ (additive_inverse @ b) @ d)),
% 13.48/3.90 inference('cnf', [status(esa)], [a_inverse_times_b_inverse])).
% 13.48/3.90 thf(zip_derived_cl20, plain,
% 13.48/3.90 ( (product @ (additive_inverse @ a) @ (additive_inverse @ b) @ d)),
% 13.48/3.90 inference('cnf', [status(esa)], [a_inverse_times_b_inverse])).
% 13.48/3.90 thf(distributivity1, axiom,
% 13.48/3.90 (( ~( product @ X @ Y @ V1 ) ) | ( ~( product @ X @ Z @ V2 ) ) |
% 13.48/3.90 ( ~( sum @ Y @ Z @ V3 ) ) | ( ~( product @ X @ V3 @ V4 ) ) |
% 13.48/3.90 ( sum @ V1 @ V2 @ V4 ))).
% 13.48/3.90 thf(zip_derived_cl11, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 13.48/3.90 (~ (product @ X0 @ X1 @ X2)
% 13.48/3.90 | ~ (product @ X0 @ X3 @ X4)
% 13.48/3.90 | ~ (sum @ X1 @ X3 @ X5)
% 13.48/3.90 | ~ (product @ X0 @ X5 @ X6)
% 13.48/3.90 | (sum @ X2 @ X4 @ X6))),
% 13.48/3.90 inference('cnf', [status(esa)], [distributivity1])).
% 13.48/3.90 thf(zip_derived_cl112, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.48/3.90 ( (sum @ d @ X1 @ X0)
% 13.48/3.90 | ~ (product @ (additive_inverse @ a) @ X2 @ X0)
% 13.48/3.90 | ~ (sum @ (additive_inverse @ b) @ X3 @ X2)
% 13.48/3.90 | ~ (product @ (additive_inverse @ a) @ X3 @ X1))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl11])).
% 13.48/3.90 thf(zip_derived_cl1184, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i]:
% 13.48/3.90 (~ (product @ (additive_inverse @ a) @ X1 @ X0)
% 13.48/3.90 | ~ (sum @ (additive_inverse @ b) @ X1 @ (additive_inverse @ b))
% 13.48/3.90 | (sum @ d @ X0 @ d))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl112])).
% 13.48/3.90 thf(zip_derived_cl7620, plain,
% 13.48/3.90 (![X0 : $i]:
% 13.48/3.90 ( (sum @ d @ X0 @ d)
% 13.48/3.90 | ~ (product @ (additive_inverse @ a) @ additive_identity @ X0))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl1184])).
% 13.48/3.90 thf(zip_derived_cl7629, plain,
% 13.48/3.90 ( (sum @ d @ (multiply @ (additive_inverse @ a) @ additive_identity) @ d)),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl7620])).
% 13.48/3.90 thf(zip_derived_cl57, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i]:
% 13.48/3.90 (((additive_identity) = (X1)) | ~ (sum @ X0 @ X1 @ X0))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl17])).
% 13.48/3.90 thf(zip_derived_cl7653, plain,
% 13.48/3.90 (((additive_identity)
% 13.48/3.90 = (multiply @ (additive_inverse @ a) @ additive_identity))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl7629, zip_derived_cl57])).
% 13.48/3.90 thf(zip_derived_cl2, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 13.48/3.90 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 13.48/3.90 thf(zip_derived_cl7701, plain,
% 13.48/3.90 ( (product @ (additive_inverse @ a) @ additive_identity @
% 13.48/3.90 additive_identity)),
% 13.48/3.90 inference('sup+', [status(thm)], [zip_derived_cl7653, zip_derived_cl2])).
% 13.48/3.90 thf(multiplication_is_well_defined, axiom,
% 13.48/3.90 (( ~( product @ X @ Y @ U ) ) | ( ~( product @ X @ Y @ V ) ) |
% 13.48/3.90 ( ( U ) = ( V ) ))).
% 13.48/3.90 thf(zip_derived_cl16, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.48/3.90 (~ (product @ X0 @ X1 @ X2)
% 13.48/3.90 | ~ (product @ X0 @ X1 @ X3)
% 13.48/3.90 | ((X2) = (X3)))),
% 13.48/3.90 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 13.48/3.90 thf(zip_derived_cl7707, plain,
% 13.48/3.90 (![X0 : $i]:
% 13.48/3.90 (((additive_identity) = (X0))
% 13.48/3.90 | ~ (product @ (additive_inverse @ a) @ additive_identity @ X0))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl7701, zip_derived_cl16])).
% 13.48/3.90 thf(zip_derived_cl12562, plain,
% 13.48/3.90 (((additive_identity) = (add @ d @ (additive_inverse @ c)))),
% 13.48/3.90 inference('sup-', [status(thm)],
% 13.48/3.90 [zip_derived_cl12341, zip_derived_cl7707])).
% 13.48/3.90 thf(zip_derived_cl3, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 13.48/3.90 inference('cnf', [status(esa)], [closure_of_addition])).
% 13.48/3.90 thf(additive_identity1, axiom, (sum @ additive_identity @ X @ X)).
% 13.48/3.90 thf(zip_derived_cl0, plain,
% 13.48/3.90 (![X0 : $i]: (sum @ additive_identity @ X0 @ X0)),
% 13.48/3.90 inference('cnf', [status(esa)], [additive_identity1])).
% 13.48/3.90 thf(zip_derived_cl5, plain,
% 13.48/3.90 (![X0 : $i]: (sum @ X0 @ (additive_inverse @ X0) @ additive_identity)),
% 13.48/3.90 inference('cnf', [status(esa)], [right_inverse])).
% 13.48/3.90 thf(associativity_of_addition1, axiom,
% 13.48/3.90 (( ~( sum @ X @ Y @ U ) ) | ( ~( sum @ Y @ Z @ V ) ) |
% 13.48/3.90 ( ~( sum @ U @ Z @ W ) ) | ( sum @ X @ V @ W ))).
% 13.48/3.90 thf(zip_derived_cl6, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 13.48/3.90 (~ (sum @ X0 @ X1 @ X2)
% 13.48/3.90 | ~ (sum @ X1 @ X3 @ X4)
% 13.48/3.90 | ~ (sum @ X2 @ X3 @ X5)
% 13.48/3.90 | (sum @ X0 @ X4 @ X5))),
% 13.48/3.90 inference('cnf', [status(esa)], [associativity_of_addition1])).
% 13.48/3.90 thf(zip_derived_cl30, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.48/3.90 ( (sum @ X0 @ X2 @ X1)
% 13.48/3.90 | ~ (sum @ additive_identity @ X3 @ X1)
% 13.48/3.90 | ~ (sum @ (additive_inverse @ X0) @ X3 @ X2))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl6])).
% 13.48/3.90 thf(zip_derived_cl200, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.48/3.90 (~ (sum @ (additive_inverse @ X2) @ X0 @ X1) | (sum @ X2 @ X1 @ X0))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl30])).
% 13.48/3.90 thf(zip_derived_cl347, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i]:
% 13.48/3.90 (sum @ X1 @ (add @ (additive_inverse @ X1) @ X0) @ X0)),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl200])).
% 13.48/3.90 thf(zip_derived_cl22, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl8])).
% 13.48/3.90 thf(zip_derived_cl17, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.48/3.90 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X3 @ X2) | ((X1) = (X3)))),
% 13.48/3.90 inference('cnf', [status(esa)], [cancellation1])).
% 13.48/3.90 thf(zip_derived_cl56, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.48/3.90 (((X1) = (X2)) | ~ (sum @ X0 @ X2 @ (add @ X1 @ X0)))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl17])).
% 13.48/3.90 thf(zip_derived_cl381, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i]:
% 13.48/3.90 ((X1) = (add @ (additive_inverse @ X0) @ (add @ X1 @ X0)))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl347, zip_derived_cl56])).
% 13.48/3.90 thf(zip_derived_cl22, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl8])).
% 13.48/3.90 thf(zip_derived_cl3, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 13.48/3.90 inference('cnf', [status(esa)], [closure_of_addition])).
% 13.48/3.90 thf(addition_is_well_defined, axiom,
% 13.48/3.90 (( ~( sum @ X @ Y @ U ) ) | ( ~( sum @ X @ Y @ V ) ) | ( ( U ) = ( V ) ))).
% 13.48/3.90 thf(zip_derived_cl15, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.48/3.90 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 13.48/3.90 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 13.48/3.90 thf(zip_derived_cl44, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.48/3.90 (((add @ X1 @ X0) = (X2)) | ~ (sum @ X1 @ X0 @ X2))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl15])).
% 13.48/3.90 thf(zip_derived_cl264, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i]: ((add @ X0 @ X1) = (add @ X1 @ X0))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl44])).
% 13.48/3.90 thf(zip_derived_cl599, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i]:
% 13.48/3.90 ((X0) = (add @ (add @ X0 @ X1) @ (additive_inverse @ X1)))),
% 13.48/3.90 inference('sup+', [status(thm)], [zip_derived_cl381, zip_derived_cl264])).
% 13.48/3.90 thf(zip_derived_cl12578, plain,
% 13.48/3.90 (((d)
% 13.48/3.90 = (add @ additive_identity @
% 13.48/3.90 (additive_inverse @ (additive_inverse @ c))))),
% 13.48/3.90 inference('sup+', [status(thm)], [zip_derived_cl12562, zip_derived_cl599])).
% 13.48/3.90 thf(zip_derived_cl5, plain,
% 13.48/3.90 (![X0 : $i]: (sum @ X0 @ (additive_inverse @ X0) @ additive_identity)),
% 13.48/3.90 inference('cnf', [status(esa)], [right_inverse])).
% 13.48/3.90 thf(left_inverse, axiom,
% 13.48/3.90 (sum @ ( additive_inverse @ X ) @ X @ additive_identity)).
% 13.48/3.90 thf(zip_derived_cl4, plain,
% 13.48/3.90 (![X0 : $i]: (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)),
% 13.48/3.90 inference('cnf', [status(esa)], [left_inverse])).
% 13.48/3.90 thf(zip_derived_cl17, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.48/3.90 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X3 @ X2) | ((X1) = (X3)))),
% 13.48/3.90 inference('cnf', [status(esa)], [cancellation1])).
% 13.48/3.90 thf(zip_derived_cl60, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i]:
% 13.48/3.90 (((X0) = (X1))
% 13.48/3.90 | ~ (sum @ (additive_inverse @ X0) @ X1 @ additive_identity))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl17])).
% 13.48/3.90 thf(zip_derived_cl175, plain,
% 13.48/3.90 (![X0 : $i]: ((X0) = (additive_inverse @ (additive_inverse @ X0)))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl60])).
% 13.48/3.90 thf(zip_derived_cl22, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl8])).
% 13.48/3.90 thf(zip_derived_cl1, plain,
% 13.48/3.90 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 13.48/3.90 inference('cnf', [status(esa)], [additive_identity2])).
% 13.48/3.90 thf(zip_derived_cl15, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.48/3.90 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 13.48/3.90 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 13.48/3.90 thf(zip_derived_cl46, plain,
% 13.48/3.90 (![X0 : $i, X1 : $i]:
% 13.48/3.90 (((X0) = (X1)) | ~ (sum @ X0 @ additive_identity @ X1))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl15])).
% 13.48/3.90 thf(zip_derived_cl94, plain,
% 13.48/3.90 (![X0 : $i]: ((X0) = (add @ additive_identity @ X0))),
% 13.48/3.90 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl46])).
% 13.48/3.90 thf(zip_derived_cl12686, plain, (((d) = (c))),
% 13.48/3.90 inference('demod', [status(thm)],
% 13.48/3.90 [zip_derived_cl12578, zip_derived_cl175, zip_derived_cl94])).
% 13.48/3.90 thf(prove_c_equals_d, conjecture, (( c ) = ( d ))).
% 13.48/3.90 thf(zf_stmt_0, negated_conjecture, (( c ) != ( d )),
% 13.48/3.90 inference('cnf.neg', [status(esa)], [prove_c_equals_d])).
% 13.48/3.90 thf(zip_derived_cl21, plain, (((c) != (d))),
% 13.48/3.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 13.48/3.90 thf(zip_derived_cl12687, plain, ($false),
% 13.48/3.90 inference('simplify_reflect-', [status(thm)],
% 13.48/3.90 [zip_derived_cl12686, zip_derived_cl21])).
% 13.48/3.90
% 13.48/3.90 % SZS output end Refutation
% 13.48/3.90
% 13.48/3.90
% 13.48/3.90 % Terminating...
% 13.94/4.05 % Runner terminated.
% 13.98/4.07 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------