TSTP Solution File: ARI696_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI696_1 : TPTP v8.1.2. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n018.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 : Wed Aug 30 17:48:51 EDT 2023
% Result : Theorem 4.30s 1.38s
% Output : Proof 5.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ARI696_1 : TPTP v8.1.2. Released v6.3.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 18:02:18 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.64 ________ _____
% 0.20/0.64 ___ __ \_________(_)________________________________
% 0.20/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.64
% 0.20/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.64 (2023-06-19)
% 0.20/0.64
% 0.20/0.64 (c) Philipp Rümmer, 2009-2023
% 0.20/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.64 Amanda Stjerna.
% 0.20/0.64 Free software under BSD-3-Clause.
% 0.20/0.64
% 0.20/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.64
% 0.20/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.65 Running up to 7 provers in parallel.
% 0.20/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.08/1.05 Prover 1: Preprocessing ...
% 2.08/1.05 Prover 5: Preprocessing ...
% 2.08/1.05 Prover 6: Preprocessing ...
% 2.08/1.05 Prover 4: Preprocessing ...
% 2.08/1.05 Prover 0: Preprocessing ...
% 2.08/1.05 Prover 3: Preprocessing ...
% 2.08/1.06 Prover 2: Preprocessing ...
% 2.98/1.13 Prover 3: Constructing countermodel ...
% 2.98/1.13 Prover 5: Constructing countermodel ...
% 2.98/1.13 Prover 0: Constructing countermodel ...
% 2.98/1.13 Prover 6: Constructing countermodel ...
% 2.98/1.13 Prover 1: Constructing countermodel ...
% 2.98/1.13 Prover 4: Constructing countermodel ...
% 2.98/1.13 Prover 2: Constructing countermodel ...
% 4.30/1.38 Prover 3: proved (713ms)
% 4.30/1.38
% 4.30/1.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.30/1.38
% 4.30/1.38 Prover 2: proved (715ms)
% 4.30/1.38
% 4.30/1.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.30/1.38
% 4.30/1.38 Prover 5: proved (711ms)
% 4.30/1.38
% 4.30/1.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.30/1.38
% 4.30/1.38 Prover 6: proved (709ms)
% 4.30/1.38
% 4.30/1.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.30/1.38
% 4.30/1.39 Prover 0: proved (717ms)
% 4.30/1.39
% 4.30/1.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.30/1.39
% 4.30/1.39 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.30/1.39 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.30/1.39 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.30/1.39 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.30/1.39 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.30/1.41 Prover 7: Preprocessing ...
% 4.30/1.41 Prover 11: Preprocessing ...
% 4.30/1.42 Prover 13: Preprocessing ...
% 4.30/1.42 Prover 8: Preprocessing ...
% 4.30/1.42 Prover 10: Preprocessing ...
% 4.30/1.43 Prover 11: Constructing countermodel ...
% 4.30/1.43 Prover 7: Constructing countermodel ...
% 4.30/1.43 Prover 4: Found proof (size 17)
% 4.99/1.43 Prover 4: proved (762ms)
% 4.99/1.43 Prover 7: stopped
% 5.01/1.43 Prover 11: stopped
% 5.01/1.43 Prover 1: Found proof (size 17)
% 5.01/1.43 Prover 1: proved (771ms)
% 5.01/1.43 Prover 13: Constructing countermodel ...
% 5.01/1.43 Prover 13: stopped
% 5.01/1.44 Prover 10: Constructing countermodel ...
% 5.01/1.44 Prover 10: stopped
% 5.01/1.44 Prover 8: Constructing countermodel ...
% 5.01/1.44 Prover 8: stopped
% 5.01/1.44
% 5.01/1.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.01/1.44
% 5.01/1.45 % SZS output start Proof for theBenchmark
% 5.01/1.45 Assumptions after simplification:
% 5.01/1.45 ---------------------------------
% 5.01/1.45
% 5.01/1.45 (conj)
% 5.01/1.46 ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ? [v4: int] : ?
% 5.01/1.46 [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ?
% 5.01/1.46 [v10: int] : ? [v11: int] : ( ~
% 5.01/1.46 ($difference($difference($difference($sum($sum($difference($difference($sum($difference($difference($difference($difference($difference(v11,
% 5.01/1.46 v10), v9), $product(2, v8)), v7), v6), v5), v4),
% 5.01/1.46 $product(2, v3)), v2), v1), $product(2, v0)), $product(2, d)),
% 5.01/1.46 $product(2, c)) = b) & $product(v8, a) = v11 & $product(v5, a) = v7 &
% 5.01/1.46 $product(v2, a) = v9 & $product(v0, a) = v1 & $product(d, c) = v10 &
% 5.01/1.46 $product(d, b) = v0 & $product(d, a) = v8 & $product(c, c) = v6 &
% 5.01/1.46 $product(c, b) = v2 & $product(c, a) = v5 & $product(b, a) = v4 &
% 5.01/1.46 $product(a, a) = v3)
% 5.01/1.46
% 5.01/1.46 (eq)
% 5.01/1.46 ? [v0: int] : ? [v1: int] : ? [v2: int] : ($product(v1, $sum(a, -2)) = v2 &
% 5.01/1.46 $product($difference($difference($difference($product(-1, d), c), b), a),
% 5.01/1.46 $sum(c, 2)) = $sum($sum(v2, v0), b) & $product($sum(b, a),
% 5.01/1.46 $sum($difference(c, d), 1)) = v1 & $product(a, a) = v0)
% 5.01/1.46
% 5.01/1.46 Those formulas are unsatisfiable:
% 5.01/1.46 ---------------------------------
% 5.01/1.46
% 5.01/1.46 Begin of proof
% 5.01/1.46 |
% 5.01/1.46 | DELTA: instantiating (eq) with fresh symbols all_2_0, all_2_1, all_2_2 gives:
% 5.01/1.47 | (1) $product(all_2_1, $sum(a, -2)) = all_2_0 &
% 5.01/1.47 | $product($difference($difference($difference($product(-1, d), c), b),
% 5.01/1.47 | a), $sum(c, 2)) = $sum($sum(all_2_0, all_2_2), b) &
% 5.01/1.47 | $product($sum(b, a), $sum($difference(c, d), 1)) = all_2_1 &
% 5.01/1.47 | $product(a, a) = all_2_2
% 5.01/1.47 |
% 5.01/1.47 | ALPHA: (1) implies:
% 5.01/1.47 | (2) $product(a, a) = all_2_2
% 5.01/1.47 | (3) $product($sum(b, a), $sum($difference(c, d), 1)) = all_2_1
% 5.01/1.47 | (4) $product($difference($difference($difference($product(-1, d), c), b),
% 5.01/1.47 | a), $sum(c, 2)) = $sum($sum(all_2_0, all_2_2), b)
% 5.01/1.47 | (5) $product(all_2_1, $sum(a, -2)) = all_2_0
% 5.01/1.47 |
% 5.01/1.47 | DELTA: instantiating (conj) with fresh symbols all_4_0, all_4_1, all_4_2,
% 5.01/1.47 | all_4_3, all_4_4, all_4_5, all_4_6, all_4_7, all_4_8, all_4_9,
% 5.01/1.47 | all_4_10, all_4_11 gives:
% 5.01/1.47 | (6) ~
% 5.01/1.47 | ($difference($difference($difference($sum($sum($difference($difference($sum($difference($difference($difference($difference($difference(all_4_0,
% 5.01/1.47 | all_4_1), all_4_2), $product(2, all_4_3)),
% 5.01/1.47 | all_4_4), all_4_5), all_4_6), all_4_7),
% 5.01/1.47 | $product(2, all_4_8)), all_4_9), all_4_10), $product(2,
% 5.01/1.47 | all_4_11)), $product(2, d)), $product(2, c)) = b) &
% 5.01/1.47 | $product(all_4_3, a) = all_4_0 & $product(all_4_6, a) = all_4_4 &
% 5.01/1.47 | $product(all_4_9, a) = all_4_2 & $product(all_4_11, a) = all_4_10 &
% 5.01/1.47 | $product(d, c) = all_4_1 & $product(d, b) = all_4_11 & $product(d, a) =
% 5.01/1.47 | all_4_3 & $product(c, c) = all_4_5 & $product(c, b) = all_4_9 &
% 5.01/1.47 | $product(c, a) = all_4_6 & $product(b, a) = all_4_7 & $product(a, a) =
% 5.01/1.47 | all_4_8
% 5.01/1.47 |
% 5.01/1.47 | ALPHA: (6) implies:
% 5.01/1.47 | (7) ~
% 5.01/1.47 | ($difference($difference($difference($sum($sum($difference($difference($sum($difference($difference($difference($difference($difference(all_4_0,
% 5.01/1.47 | all_4_1), all_4_2), $product(2, all_4_3)),
% 5.01/1.47 | all_4_4), all_4_5), all_4_6), all_4_7),
% 5.01/1.47 | $product(2, all_4_8)), all_4_9), all_4_10), $product(2,
% 5.01/1.47 | all_4_11)), $product(2, d)), $product(2, c)) = b)
% 5.01/1.47 | (8) $product(a, a) = all_4_8
% 5.01/1.47 | (9) $product(b, a) = all_4_7
% 5.01/1.47 | (10) $product(c, a) = all_4_6
% 5.01/1.47 | (11) $product(c, b) = all_4_9
% 5.01/1.47 | (12) $product(c, c) = all_4_5
% 5.01/1.47 | (13) $product(d, a) = all_4_3
% 5.01/1.48 | (14) $product(d, b) = all_4_11
% 5.01/1.48 | (15) $product(d, c) = all_4_1
% 5.01/1.48 | (16) $product(all_4_11, a) = all_4_10
% 5.01/1.48 | (17) $product(all_4_9, a) = all_4_2
% 5.01/1.48 | (18) $product(all_4_6, a) = all_4_4
% 5.01/1.48 | (19) $product(all_4_3, a) = all_4_0
% 5.01/1.48 |
% 5.01/1.48 | THEORY_AXIOM GroebnerMultiplication:
% 5.01/1.48 | (20) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4:
% 5.01/1.48 | int] : ! [v5: int] : ! [v6: int] : ! [v7: int] : ! [v8: int] :
% 5.01/1.48 | ! [v9: int] : ! [v10: int] : ! [v11: int] : ! [v12: int] : ! [v13:
% 5.01/1.48 | int] : ! [v14: int] : ! [v15: int] : ! [v16: int] : ! [v17: int]
% 5.01/1.48 | :
% 5.01/1.48 | ($sum($difference($difference($difference($difference($difference($sum($sum($difference($sum($difference($difference($difference($difference($difference(v17,
% 5.01/1.48 | v16), v15), $product(3, v14)), v13),
% 5.01/1.48 | v12), $product(2, v11)), v10), $product(2,
% 5.01/1.48 | v9)), v8), $product(3, v7)), v5), $product(2,
% 5.01/1.48 | v4)), $product(2, v3)), $product(2, v2)), v0) = 0 | ~
% 5.01/1.48 | ($product(v14, v0) = v17) | ~ ($product(v11, v0) = v13) | ~
% 5.01/1.48 | ($product(v9, v0) = v15) | ~ ($product(v7, v0) = v8) | ~
% 5.01/1.48 | ($product(v5, $sum(v0, -2)) = v6) | ~
% 5.01/1.48 | ($product($difference($difference($difference($product(-1, v3), v2),
% 5.01/1.48 | v1), v0), $sum(v2, 2)) = $sum($sum(v6, v4), v1)) | ~
% 5.01/1.48 | ($product(v3, v2) = v16) | ~ ($product(v3, v1) = v7) | ~
% 5.01/1.48 | ($product(v3, v0) = v14) | ~ ($product(v2, v2) = v12) | ~
% 5.01/1.48 | ($product(v2, v1) = v9) | ~ ($product(v2, v0) = v11) | ~
% 5.01/1.48 | ($product($sum(v1, v0), $sum($difference(v2, v3), 1)) = v5) | ~
% 5.01/1.48 | ($product(v1, v0) = v10) | ~ ($product(v0, v0) = v4))
% 5.01/1.48 |
% 5.01/1.48 | GROUND_INST: instantiating (20) with a, b, c, d, all_2_2, all_2_1, all_2_0,
% 5.01/1.48 | all_4_11, all_4_10, all_4_9, all_4_7, all_4_6, all_4_5, all_4_4,
% 5.01/1.48 | all_4_3, all_4_2, all_4_1, all_4_0, simplifying with (2), (3),
% 5.01/1.48 | (4), (5), (9), (10), (11), (12), (13), (14), (15), (16), (17),
% 5.01/1.48 | (18), (19) gives:
% 5.01/1.48 | (21) $sum($difference($difference($difference($difference($difference($sum($sum($difference($sum($difference($difference($difference($difference($difference(all_4_0,
% 5.01/1.48 | all_4_1), all_4_2), $product(3,
% 5.01/1.48 | all_4_3)), all_4_4), all_4_5), $product(2,
% 5.01/1.48 | all_4_6)), all_4_7), $product(2, all_4_9)),
% 5.01/1.48 | all_4_10), $product(3, all_4_11)), all_2_1), $product(2,
% 5.01/1.48 | all_2_2)), $product(2, d)), $product(2, c)), a) = 0
% 5.01/1.48 |
% 5.01/1.48 | THEORY_AXIOM GroebnerMultiplication:
% 5.01/1.49 | (22) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4:
% 5.01/1.49 | int] : ! [v5: int] : ! [v6: int] : ! [v7: int] : ! [v8: int] :
% 5.01/1.49 | ($difference($sum($sum($difference($difference(v8, v7), v6), v5), v4),
% 5.01/1.49 | v1) = v0 | ~ ($product(v3, v1) = v5) | ~ ($product(v3, v0) = v8)
% 5.01/1.49 | | ~ ($product(v2, v1) = v6) | ~ ($product(v2, v0) = v7) | ~
% 5.01/1.49 | ($product($sum(v1, v0), $sum($difference(v2, v3), 1)) = v4))
% 5.01/1.49 |
% 5.01/1.49 | GROUND_INST: instantiating (22) with a, b, c, d, all_2_1, all_4_11, all_4_9,
% 5.01/1.49 | all_4_6, all_4_3, simplifying with (3), (10), (11), (13), (14)
% 5.01/1.49 | gives:
% 5.01/1.49 | (23) $difference($sum($sum($difference($difference(all_4_3, all_4_6),
% 5.01/1.49 | all_4_9), all_4_11), all_2_1), b) = a
% 5.01/1.49 |
% 5.01/1.49 | THEORY_AXIOM GroebnerMultiplication:
% 5.01/1.49 | (24) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4:
% 5.01/1.49 | int] : ! [v5: int] : ! [v6: int] : ! [v7: int] : ! [v8: int] :
% 5.01/1.49 | ! [v9: int] : ! [v10: int] : ! [v11: int] : ! [v12: int] : ! [v13:
% 5.01/1.49 | int] : ! [v14: int] : ! [v15: int] :
% 5.01/1.49 | ($sum($sum($sum($difference($difference($difference(v15, v14), v12),
% 5.01/1.49 | v10), v8), v6), $product(2, v5)) = v4 | ~ ($product(v13,
% 5.01/1.49 | v0) = v15) | ~ ($product(v11, v0) = v12) | ~ ($product(v9, v0)
% 5.01/1.49 | = v14) | ~ ($product(v7, v0) = v8) | ~ ($product(v5, $sum(v0,
% 5.01/1.49 | -2)) = v6) | ~
% 5.01/1.49 | ($product($difference($difference($difference($product(-1, v3), v2),
% 5.01/1.49 | v1), v0), $sum(v2, 2)) = $sum($sum(v6, v4), v1)) | ~
% 5.01/1.49 | ($product(v3, v1) = v7) | ~ ($product(v3, v0) = v13) | ~
% 5.01/1.49 | ($product(v2, v1) = v9) | ~ ($product(v2, v0) = v11) | ~
% 5.01/1.49 | ($product($sum(v1, v0), $sum($difference(v2, v3), 1)) = v5) | ~
% 5.01/1.49 | ($product(v1, v0) = v10) | ~ ($product(v0, v0) = v4))
% 5.01/1.49 |
% 5.01/1.49 | GROUND_INST: instantiating (24) with a, b, c, d, all_2_2, all_2_1, all_2_0,
% 5.01/1.49 | all_4_11, all_4_10, all_4_9, all_4_7, all_4_6, all_4_4, all_4_3,
% 5.01/1.49 | all_4_2, all_4_0, simplifying with (2), (3), (4), (5), (9), (10),
% 5.01/1.49 | (11), (13), (14), (16), (17), (18), (19) gives:
% 5.01/1.49 | (25) $sum($sum($sum($difference($difference($difference(all_4_0, all_4_2),
% 5.01/1.49 | all_4_4), all_4_7), all_4_10), all_2_0), $product(2,
% 5.01/1.49 | all_2_1)) = all_2_2
% 5.01/1.49 |
% 5.01/1.49 | THEORY_AXIOM GroebnerMultiplication:
% 5.01/1.49 | (26) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~
% 5.01/1.49 | ($product(v0, v0) = v2) | ~ ($product(v0, v0) = v1))
% 5.01/1.49 |
% 5.01/1.49 | GROUND_INST: instantiating (26) with a, all_2_2, all_4_8, simplifying with
% 5.01/1.49 | (2), (8) gives:
% 5.01/1.49 | (27) all_4_8 = all_2_2
% 5.01/1.49 |
% 5.01/1.49 | COMBINE_EQS: (21), (25) imply:
% 5.01/1.49 | (28) $sum($sum($sum($sum($sum($sum($difference($difference($sum($sum(all_4_1,
% 5.01/1.49 | $product(3, all_4_3)), all_4_5), $product(2,
% 5.01/1.49 | all_4_6)), $product(2, all_4_9)), $product(3,
% 5.01/1.49 | all_4_11)), all_2_0), $product(3, all_2_1)), all_2_2),
% 5.01/1.49 | $product(2, d)), $product(2, c)) = a
% 5.01/1.49 |
% 5.01/1.49 | COMBINE_EQS: (23), (28) imply:
% 5.01/1.49 | (29) $sum($sum($sum($sum($sum($sum($sum($sum($sum(all_4_1, all_4_5),
% 5.01/1.49 | all_4_6), all_4_9), all_2_0), all_2_2), $product(2,
% 5.01/1.49 | d)), $product(2, c)), $product(3, b)), $product(2, a)) = 0
% 5.01/1.49 |
% 5.01/1.49 | REDUCE: (7), (23), (25), (27), (29) imply:
% 5.01/1.49 | (30) $false
% 5.01/1.50 |
% 5.01/1.50 | CLOSE: (30) is inconsistent.
% 5.01/1.50 |
% 5.01/1.50 End of proof
% 5.01/1.50 % SZS output end Proof for theBenchmark
% 5.01/1.50
% 5.01/1.50 853ms
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