TSTP Solution File: ARI708_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI708_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 : n023.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 17:48:53 EDT 2023
% Result : Theorem 3.68s 1.24s
% Output : Proof 3.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ARI708_1 : TPTP v8.1.2. Released v6.3.0.
% 0.03/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n023.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 : Tue Aug 29 18:37:24 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.54/0.62 ________ _____
% 0.54/0.62 ___ __ \_________(_)________________________________
% 0.54/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.54/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.54/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.54/0.62
% 0.54/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.54/0.62 (2023-06-19)
% 0.54/0.62
% 0.54/0.62 (c) Philipp Rümmer, 2009-2023
% 0.54/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.54/0.62 Amanda Stjerna.
% 0.54/0.62 Free software under BSD-3-Clause.
% 0.54/0.62
% 0.54/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.54/0.62
% 0.54/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.70/0.64 Running up to 7 provers in parallel.
% 0.70/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.70/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.70/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.70/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.70/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.70/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.70/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.08/1.01 Prover 0: Preprocessing ...
% 2.08/1.01 Prover 2: Preprocessing ...
% 2.08/1.01 Prover 6: Preprocessing ...
% 2.08/1.01 Prover 4: Preprocessing ...
% 2.08/1.01 Prover 1: Preprocessing ...
% 2.08/1.01 Prover 5: Preprocessing ...
% 2.08/1.01 Prover 3: Preprocessing ...
% 2.39/1.07 Prover 3: Constructing countermodel ...
% 2.39/1.07 Prover 2: Constructing countermodel ...
% 2.39/1.07 Prover 0: Constructing countermodel ...
% 2.39/1.07 Prover 4: Constructing countermodel ...
% 2.39/1.07 Prover 6: Constructing countermodel ...
% 2.39/1.07 Prover 1: Constructing countermodel ...
% 2.39/1.07 Prover 5: Constructing countermodel ...
% 3.68/1.24 Prover 3: proved (593ms)
% 3.68/1.24 Prover 0: proved (595ms)
% 3.68/1.24 Prover 5: proved (591ms)
% 3.68/1.24 Prover 2: proved (594ms)
% 3.68/1.24 Prover 6: proved (590ms)
% 3.68/1.24
% 3.68/1.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.68/1.24
% 3.68/1.24
% 3.68/1.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.68/1.24
% 3.68/1.24
% 3.68/1.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.68/1.24
% 3.68/1.24
% 3.68/1.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.68/1.24
% 3.68/1.24
% 3.68/1.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.68/1.24
% 3.79/1.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.79/1.25 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.79/1.25 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.79/1.25 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.79/1.25 Prover 7: Preprocessing ...
% 3.79/1.25 Prover 10: Preprocessing ...
% 3.79/1.26 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.79/1.26 Prover 8: Preprocessing ...
% 3.79/1.26 Prover 1: Found proof (size 9)
% 3.79/1.26 Prover 1: proved (618ms)
% 3.79/1.26 Prover 11: Preprocessing ...
% 3.79/1.27 Prover 13: Preprocessing ...
% 3.79/1.27 Prover 8: Constructing countermodel ...
% 3.79/1.27 Prover 4: Found proof (size 9)
% 3.79/1.27 Prover 4: proved (626ms)
% 3.79/1.27 Prover 8: stopped
% 3.79/1.27 Prover 10: Constructing countermodel ...
% 3.79/1.27 Prover 10: stopped
% 3.79/1.27 Prover 11: Constructing countermodel ...
% 3.79/1.27 Prover 11: stopped
% 3.79/1.28 Prover 13: Constructing countermodel ...
% 3.79/1.28 Prover 7: Constructing countermodel ...
% 3.79/1.28 Prover 13: stopped
% 3.79/1.28 Prover 7: stopped
% 3.79/1.28
% 3.79/1.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.79/1.28
% 3.79/1.28 % SZS output start Proof for theBenchmark
% 3.79/1.28 Assumptions after simplification:
% 3.79/1.28 ---------------------------------
% 3.79/1.28
% 3.79/1.28 (conj)
% 3.79/1.29 ? [v0: int] : ? [v1: int] : ( ~ ($difference($sum($product(2, v1),
% 3.79/1.29 $product(2, v0)), b) = a) & $product(d, d) = v1 & $product(c, c) = v0)
% 3.79/1.29
% 3.79/1.29 (eq1)
% 3.79/1.29 $product($sum(d, c), $sum(d, c)) = a
% 3.79/1.29
% 3.79/1.29 (eq2)
% 3.79/1.29 $product($difference(c, d), $difference(c, d)) = b
% 3.79/1.29
% 3.79/1.29 Those formulas are unsatisfiable:
% 3.79/1.29 ---------------------------------
% 3.79/1.29
% 3.79/1.29 Begin of proof
% 3.79/1.29 |
% 3.79/1.29 | DELTA: instantiating (conj) with fresh symbols all_3_0, all_3_1 gives:
% 3.79/1.29 | (1) ~ ($difference($sum($product(2, all_3_0), $product(2, all_3_1)), b) =
% 3.79/1.29 | a) & $product(d, d) = all_3_0 & $product(c, c) = all_3_1
% 3.79/1.30 |
% 3.79/1.30 | ALPHA: (1) implies:
% 3.79/1.30 | (2) ~ ($difference($sum($product(2, all_3_0), $product(2, all_3_1)), b) =
% 3.79/1.30 | a)
% 3.79/1.30 | (3) $product(c, c) = all_3_1
% 3.79/1.30 | (4) $product(d, d) = all_3_0
% 3.79/1.30 |
% 3.79/1.30 | THEORY_AXIOM GroebnerMultiplication:
% 3.79/1.30 | (5) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4:
% 3.79/1.30 | int] : ! [v5: int] : ($difference($sum($product(2, v5), $product(2,
% 3.79/1.30 | v4)), v3) = v0 | ~ ($product($difference(v1, v2),
% 3.79/1.30 | $difference(v1, v2)) = v3) | ~ ($product($sum(v2, v1), $sum(v2,
% 3.79/1.30 | v1)) = v0) | ~ ($product(v2, v2) = v5) | ~ ($product(v1, v1)
% 3.79/1.30 | = v4))
% 3.79/1.30 |
% 3.79/1.30 | GROUND_INST: instantiating (5) with a, c, d, b, all_3_1, all_3_0, simplifying
% 3.79/1.30 | with (3), (4), (eq1), (eq2) gives:
% 3.79/1.30 | (6) $difference($sum($product(2, all_3_0), $product(2, all_3_1)), b) = a
% 3.79/1.30 |
% 3.79/1.30 | COL_REDUCE: introducing fresh symbol sc_8_0_0 defined by:
% 3.79/1.30 | (7) $difference($difference($sum(all_3_0, all_3_1), b), a) = sc_8_0_0
% 3.79/1.30 |
% 3.79/1.30 | COMBINE_EQS: (6), (7) imply:
% 3.79/1.30 | (8) $sum($sum(b, a), $product(2, sc_8_0_0)) = 0
% 3.79/1.30 |
% 3.79/1.30 | COMBINE_EQS: (7), (8) imply:
% 3.79/1.30 | (9) $sum($sum(all_3_0, all_3_1), sc_8_0_0) = 0
% 3.79/1.30 |
% 3.79/1.30 | REDUCE: (2), (8), (9) imply:
% 3.79/1.30 | (10) $false
% 3.79/1.30 |
% 3.79/1.30 | CLOSE: (10) is inconsistent.
% 3.79/1.30 |
% 3.79/1.30 End of proof
% 3.79/1.31 % SZS output end Proof for theBenchmark
% 3.79/1.31
% 3.79/1.31 680ms
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