TSTP Solution File: ARI660_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI660_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 : n002.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 17:48:43 EDT 2023
% Result : Theorem 3.88s 1.45s
% Output : Proof 4.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ARI660_1 : TPTP v8.1.2. Released v6.3.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 18:07:05 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.63 ________ _____
% 0.20/0.63 ___ __ \_________(_)________________________________
% 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.63
% 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.63 (2023-06-19)
% 0.20/0.63
% 0.20/0.63 (c) Philipp Rümmer, 2009-2023
% 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.63 Amanda Stjerna.
% 0.20/0.63 Free software under BSD-3-Clause.
% 0.20/0.63
% 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.63
% 0.20/0.63 Loading /export/starexec/sandbox2/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 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
% 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 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 1.85/1.08 Prover 0: Preprocessing ...
% 1.85/1.08 Prover 2: Preprocessing ...
% 1.85/1.08 Prover 3: Preprocessing ...
% 1.85/1.08 Prover 5: Preprocessing ...
% 1.85/1.08 Prover 6: Preprocessing ...
% 1.85/1.08 Prover 1: Preprocessing ...
% 1.85/1.08 Prover 4: Preprocessing ...
% 2.22/1.15 Prover 4: Constructing countermodel ...
% 2.22/1.15 Prover 6: Constructing countermodel ...
% 2.22/1.15 Prover 5: Constructing countermodel ...
% 2.22/1.15 Prover 1: Constructing countermodel ...
% 2.22/1.15 Prover 0: Constructing countermodel ...
% 2.22/1.15 Prover 2: Constructing countermodel ...
% 2.22/1.15 Prover 3: Constructing countermodel ...
% 3.88/1.44 Prover 5: proved (778ms)
% 3.88/1.44 Prover 2: proved (779ms)
% 3.88/1.44 Prover 3: proved (775ms)
% 3.88/1.45
% 3.88/1.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.88/1.45
% 3.88/1.45
% 3.88/1.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.88/1.45
% 3.88/1.45
% 3.88/1.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.88/1.45
% 3.88/1.45 Prover 0: stopped
% 3.88/1.45 Prover 6: stopped
% 3.88/1.45 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.88/1.46 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.88/1.46 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.88/1.46 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.88/1.46 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.88/1.46 Prover 10: Preprocessing ...
% 3.88/1.47 Prover 7: Preprocessing ...
% 3.88/1.47 Prover 8: Preprocessing ...
% 3.88/1.47 Prover 11: Preprocessing ...
% 3.88/1.47 Prover 10: Constructing countermodel ...
% 3.88/1.48 Prover 7: Constructing countermodel ...
% 3.88/1.49 Prover 8: Constructing countermodel ...
% 3.88/1.49 Prover 13: Preprocessing ...
% 3.88/1.50 Prover 1: Found proof (size 31)
% 3.88/1.50 Prover 11: Constructing countermodel ...
% 3.88/1.50 Prover 1: proved (839ms)
% 3.88/1.50 Prover 7: stopped
% 4.47/1.50 Prover 8: stopped
% 4.47/1.50 Prover 10: stopped
% 4.47/1.50 Prover 11: stopped
% 4.47/1.51 Prover 4: Found proof (size 31)
% 4.47/1.51 Prover 4: proved (840ms)
% 4.47/1.51 Prover 13: Constructing countermodel ...
% 4.47/1.51 Prover 13: stopped
% 4.47/1.51
% 4.47/1.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.47/1.51
% 4.47/1.52 % SZS output start Proof for theBenchmark
% 4.47/1.52 Assumptions after simplification:
% 4.47/1.52 ---------------------------------
% 4.47/1.52
% 4.47/1.52 (conj)
% 4.47/1.54 ? [v0: int] : ? [v1: int] : ($product(v0, a) = v1 & $product(a, a) = v0 &
% 4.47/1.54 (($lesseq(v1, 10) & $lesseq(3, a)) | ($lesseq(11, v1) & $lesseq(a, 2))))
% 4.47/1.54
% 4.47/1.54 Those formulas are unsatisfiable:
% 4.47/1.54 ---------------------------------
% 4.47/1.54
% 4.47/1.54 Begin of proof
% 4.47/1.54 |
% 4.47/1.54 | DELTA: instantiating (conj) with fresh symbols all_2_0, all_2_1 gives:
% 4.47/1.55 | (1) $product(all_2_1, a) = all_2_0 & $product(a, a) = all_2_1 &
% 4.47/1.55 | (($lesseq(all_2_0, 10) & $lesseq(3, a)) | ($lesseq(11, all_2_0) &
% 4.47/1.55 | $lesseq(a, 2)))
% 4.47/1.55 |
% 4.47/1.55 | ALPHA: (1) implies:
% 4.47/1.55 | (2) $product(a, a) = all_2_1
% 4.47/1.55 | (3) $product(all_2_1, a) = all_2_0
% 4.47/1.55 | (4) ($lesseq(all_2_0, 10) & $lesseq(3, a)) | ($lesseq(11, all_2_0) &
% 4.47/1.55 | $lesseq(a, 2))
% 4.47/1.55 |
% 4.47/1.55 | THEORY_AXIOM GroebnerMultiplication:
% 4.47/1.55 | (5) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | ~ ($product(v0,
% 4.47/1.55 | v0) = v1))
% 4.47/1.55 |
% 4.47/1.55 | GROUND_INST: instantiating (5) with a, all_2_1, simplifying with (2) gives:
% 4.47/1.55 | (6) $lesseq(0, all_2_1)
% 4.47/1.55 |
% 4.47/1.55 | BETA: splitting (4) gives:
% 4.47/1.55 |
% 4.47/1.55 | Case 1:
% 4.47/1.55 | |
% 4.47/1.55 | | (7) $lesseq(all_2_0, 10) & $lesseq(3, a)
% 4.47/1.55 | |
% 4.47/1.55 | | ALPHA: (7) implies:
% 4.47/1.55 | | (8) $lesseq(3, a)
% 4.47/1.55 | | (9) $lesseq(all_2_0, 10)
% 4.47/1.55 | |
% 4.47/1.55 | | THEORY_AXIOM GroebnerMultiplication:
% 4.47/1.56 | | (10) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(v1, 8)) | ~ ($lesseq(3,
% 4.47/1.56 | | v0)) | ~ ($product(v0, v0) = v1))
% 4.47/1.56 | |
% 4.47/1.56 | | GROUND_INST: instantiating (10) with a, all_2_1, simplifying with (2) gives:
% 4.47/1.56 | | (11) ~ ($lesseq(all_2_1, 8)) | ~ ($lesseq(3, a))
% 4.47/1.56 | |
% 4.47/1.56 | | BETA: splitting (11) gives:
% 4.47/1.56 | |
% 4.47/1.56 | | Case 1:
% 4.47/1.56 | | |
% 4.47/1.56 | | | (12) $lesseq(a, 2)
% 4.47/1.56 | | |
% 4.47/1.56 | | | COMBINE_INEQS: (8), (12) imply:
% 4.47/1.56 | | | (13) $false
% 4.47/1.56 | | |
% 4.47/1.56 | | | CLOSE: (13) is inconsistent.
% 4.47/1.56 | | |
% 4.47/1.56 | | Case 2:
% 4.47/1.56 | | |
% 4.47/1.56 | | | (14) $lesseq(9, all_2_1)
% 4.47/1.56 | | |
% 4.47/1.56 | | | THEORY_AXIOM GroebnerMultiplication:
% 4.47/1.56 | | | (15) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1,
% 4.47/1.56 | | | $difference($product(3, v1), v2))) | ~ ($lesseq(0, v1)) |
% 4.47/1.56 | | | ~ ($lesseq(3, v0)) | ~ ($product(v1, v0) = v2))
% 4.47/1.56 | | |
% 4.47/1.56 | | | GROUND_INST: instantiating (15) with a, all_2_1, all_2_0, simplifying with
% 4.47/1.56 | | | (3) gives:
% 4.47/1.56 | | | (16) ~ ($lesseq(1, $difference($product(3, all_2_1), all_2_0))) | ~
% 4.47/1.56 | | | ($lesseq(0, all_2_1)) | ~ ($lesseq(3, a))
% 4.47/1.56 | | |
% 4.47/1.56 | | | BETA: splitting (16) gives:
% 4.47/1.56 | | |
% 4.47/1.56 | | | Case 1:
% 4.47/1.56 | | | |
% 4.47/1.56 | | | | (17) $lesseq(all_2_1, -1)
% 4.47/1.56 | | | |
% 4.47/1.56 | | | | COMBINE_INEQS: (6), (17) imply:
% 4.47/1.56 | | | | (18) $false
% 4.47/1.56 | | | |
% 4.47/1.57 | | | | CLOSE: (18) is inconsistent.
% 4.47/1.57 | | | |
% 4.47/1.57 | | | Case 2:
% 4.47/1.57 | | | |
% 4.47/1.57 | | | | (19) ~ ($lesseq(1, $difference($product(3, all_2_1), all_2_0))) | ~
% 4.47/1.57 | | | | ($lesseq(3, a))
% 4.47/1.57 | | | |
% 4.47/1.57 | | | | BETA: splitting (19) gives:
% 4.47/1.57 | | | |
% 4.47/1.57 | | | | Case 1:
% 4.47/1.57 | | | | |
% 4.47/1.57 | | | | | (20) $lesseq(a, 2)
% 4.47/1.57 | | | | |
% 4.47/1.57 | | | | | COMBINE_INEQS: (8), (20) imply:
% 4.47/1.57 | | | | | (21) $false
% 4.47/1.57 | | | | |
% 4.47/1.57 | | | | | CLOSE: (21) is inconsistent.
% 4.47/1.57 | | | | |
% 4.47/1.57 | | | | Case 2:
% 4.47/1.57 | | | | |
% 4.47/1.57 | | | | | (22) $lesseq(0, $difference(all_2_0, $product(3, all_2_1)))
% 4.47/1.57 | | | | |
% 4.47/1.57 | | | | | COMBINE_INEQS: (9), (22) imply:
% 4.47/1.57 | | | | | (23) $lesseq(all_2_1, 3)
% 4.47/1.57 | | | | |
% 4.47/1.57 | | | | | SIMP: (23) implies:
% 4.47/1.57 | | | | | (24) $lesseq(all_2_1, 3)
% 4.47/1.57 | | | | |
% 4.47/1.57 | | | | | COMBINE_INEQS: (14), (24) imply:
% 4.47/1.57 | | | | | (25) $false
% 4.47/1.57 | | | | |
% 4.47/1.57 | | | | | CLOSE: (25) is inconsistent.
% 4.47/1.57 | | | | |
% 4.47/1.57 | | | | End of split
% 4.47/1.57 | | | |
% 4.47/1.57 | | | End of split
% 4.47/1.57 | | |
% 4.47/1.57 | | End of split
% 4.47/1.57 | |
% 4.47/1.57 | Case 2:
% 4.47/1.57 | |
% 4.47/1.57 | | (26) $lesseq(11, all_2_0) & $lesseq(a, 2)
% 4.47/1.57 | |
% 4.47/1.57 | | ALPHA: (26) implies:
% 4.47/1.57 | | (27) $lesseq(a, 2)
% 4.47/1.57 | | (28) $lesseq(11, all_2_0)
% 4.47/1.57 | |
% 4.47/1.57 | | THEORY_AXIOM GroebnerMultiplication:
% 4.47/1.57 | | (29) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(9, v2)) |
% 4.47/1.57 | | ~ ($lesseq(v0, 2)) | ~ ($product(v1, v0) = v2) | ~ ($product(v0,
% 4.47/1.57 | | v0) = v1))
% 4.47/1.57 | |
% 4.47/1.57 | | GROUND_INST: instantiating (29) with a, all_2_1, all_2_0, simplifying with
% 4.47/1.57 | | (2), (3) gives:
% 4.47/1.57 | | (30) ~ ($lesseq(9, all_2_0)) | ~ ($lesseq(a, 2))
% 4.47/1.57 | |
% 4.47/1.57 | | BETA: splitting (30) gives:
% 4.47/1.57 | |
% 4.47/1.57 | | Case 1:
% 4.47/1.57 | | |
% 4.47/1.57 | | | (31) $lesseq(3, a)
% 4.47/1.57 | | |
% 4.47/1.57 | | | COMBINE_INEQS: (27), (31) imply:
% 4.47/1.58 | | | (32) $false
% 4.47/1.58 | | |
% 4.47/1.58 | | | CLOSE: (32) is inconsistent.
% 4.47/1.58 | | |
% 4.47/1.58 | | Case 2:
% 4.47/1.58 | | |
% 4.47/1.58 | | | (33) $lesseq(all_2_0, 8)
% 4.47/1.58 | | |
% 4.47/1.58 | | | COMBINE_INEQS: (28), (33) imply:
% 4.47/1.58 | | | (34) $false
% 4.47/1.58 | | |
% 4.47/1.58 | | | CLOSE: (34) is inconsistent.
% 4.47/1.58 | | |
% 4.47/1.58 | | End of split
% 4.47/1.58 | |
% 4.47/1.58 | End of split
% 4.47/1.58 |
% 4.47/1.58 End of proof
% 4.47/1.58 % SZS output end Proof for theBenchmark
% 4.47/1.58
% 4.47/1.58 943ms
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