TSTP Solution File: ARI680_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI680_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 : n021.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 17:48:47 EDT 2023
% Result : Theorem 3.13s 1.17s
% Output : Proof 3.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ARI680_1 : TPTP v8.1.2. Released v6.3.0.
% 0.07/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n021.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 17:47:14 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.62 ___ __ \_________(_)________________________________
% 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62
% 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.63 (2023-06-19)
% 0.21/0.63
% 0.21/0.63 (c) Philipp Rümmer, 2009-2023
% 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.63 Amanda Stjerna.
% 0.21/0.63 Free software under BSD-3-Clause.
% 0.21/0.63
% 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.63
% 0.21/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.64 Running up to 7 provers in parallel.
% 0.68/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.68/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.68/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.68/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.68/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.68/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.68/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.92/1.01 Prover 3: Preprocessing ...
% 1.92/1.01 Prover 4: Preprocessing ...
% 1.92/1.01 Prover 0: Preprocessing ...
% 1.92/1.01 Prover 2: Preprocessing ...
% 1.92/1.01 Prover 5: Preprocessing ...
% 1.92/1.01 Prover 1: Preprocessing ...
% 1.92/1.02 Prover 6: Preprocessing ...
% 2.28/1.07 Prover 4: Constructing countermodel ...
% 2.28/1.07 Prover 1: Constructing countermodel ...
% 2.28/1.07 Prover 2: Constructing countermodel ...
% 2.28/1.07 Prover 3: Constructing countermodel ...
% 2.28/1.07 Prover 5: Constructing countermodel ...
% 2.28/1.07 Prover 0: Constructing countermodel ...
% 2.28/1.07 Prover 6: Constructing countermodel ...
% 3.13/1.17 Prover 2: proved (519ms)
% 3.13/1.17 Prover 5: proved (516ms)
% 3.13/1.17 Prover 6: proved (515ms)
% 3.13/1.17 Prover 0: proved (519ms)
% 3.13/1.17 Prover 3: proved (518ms)
% 3.13/1.17
% 3.13/1.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.13/1.17
% 3.13/1.17
% 3.13/1.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.13/1.17
% 3.13/1.17
% 3.13/1.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.13/1.17
% 3.13/1.17
% 3.13/1.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.13/1.17
% 3.13/1.17
% 3.13/1.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.13/1.17
% 3.24/1.17 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.24/1.17 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.24/1.17 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.24/1.17 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.24/1.17 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.24/1.19 Prover 8: Preprocessing ...
% 3.24/1.19 Prover 11: Preprocessing ...
% 3.24/1.19 Prover 4: Found proof (size 14)
% 3.24/1.19 Prover 4: proved (541ms)
% 3.24/1.19 Prover 13: Preprocessing ...
% 3.24/1.19 Prover 10: Preprocessing ...
% 3.24/1.19 Prover 8: Constructing countermodel ...
% 3.24/1.19 Prover 7: Preprocessing ...
% 3.24/1.19 Prover 1: Found proof (size 14)
% 3.24/1.19 Prover 1: proved (549ms)
% 3.24/1.19 Prover 8: stopped
% 3.24/1.20 Prover 11: Constructing countermodel ...
% 3.24/1.20 Prover 11: stopped
% 3.24/1.20 Prover 13: Constructing countermodel ...
% 3.24/1.20 Prover 10: Constructing countermodel ...
% 3.24/1.20 Prover 7: Constructing countermodel ...
% 3.24/1.20 Prover 13: stopped
% 3.24/1.20 Prover 10: stopped
% 3.24/1.20 Prover 7: stopped
% 3.24/1.20
% 3.24/1.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.24/1.20
% 3.24/1.21 % SZS output start Proof for theBenchmark
% 3.24/1.21 Assumptions after simplification:
% 3.24/1.21 ---------------------------------
% 3.24/1.21
% 3.24/1.21 (conj)
% 3.24/1.22 ? [v0: int] : ($lesseq(-3, $difference($product(-1, v0), $product(7, a))) &
% 3.24/1.22 $product($product(3, x), y) = v0)
% 3.24/1.22
% 3.24/1.22 (conj_001)
% 3.24/1.22 $lesseq(2, x)
% 3.24/1.22
% 3.24/1.22 (conj_002)
% 3.24/1.22 $lesseq(2, y)
% 3.24/1.22
% 3.24/1.22 (conj_003)
% 3.24/1.22 $lesseq(0, a)
% 3.24/1.22
% 3.24/1.22 Those formulas are unsatisfiable:
% 3.24/1.22 ---------------------------------
% 3.24/1.22
% 3.24/1.22 Begin of proof
% 3.24/1.22 |
% 3.24/1.22 | DELTA: instantiating (conj) with fresh symbol all_3_0 gives:
% 3.24/1.22 | (1) $lesseq(-3, $difference($product(-1, all_3_0), $product(7, a))) &
% 3.24/1.22 | $product($product(3, x), y) = all_3_0
% 3.24/1.22 |
% 3.24/1.22 | ALPHA: (1) implies:
% 3.24/1.23 | (2) $lesseq(-3, $difference($product(-1, all_3_0), $product(7, a)))
% 3.24/1.23 | (3) $product($product(3, x), y) = all_3_0
% 3.24/1.23 |
% 3.24/1.23 | THEORY_AXIOM GroebnerMultiplication:
% 3.24/1.23 | (4) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(v2, 11)) | ~
% 3.24/1.23 | ($lesseq(2, v1)) | ~ ($lesseq(2, v0)) | ~ ($product($product(3,
% 3.24/1.23 | v0), v1) = v2))
% 3.24/1.23 |
% 3.24/1.23 | GROUND_INST: instantiating (4) with x, y, all_3_0, simplifying with (3) gives:
% 3.24/1.23 | (5) ~ ($lesseq(all_3_0, 11)) | ~ ($lesseq(2, y)) | ~ ($lesseq(2, x))
% 3.24/1.23 |
% 3.24/1.23 | BETA: splitting (5) gives:
% 3.24/1.23 |
% 3.24/1.23 | Case 1:
% 3.24/1.23 | |
% 3.24/1.23 | | (6) $lesseq(y, 1)
% 3.24/1.23 | |
% 3.24/1.23 | | COMBINE_INEQS: (6), (conj_002) imply:
% 3.24/1.23 | | (7) $false
% 3.24/1.23 | |
% 3.24/1.23 | | CLOSE: (7) is inconsistent.
% 3.24/1.23 | |
% 3.24/1.23 | Case 2:
% 3.24/1.23 | |
% 3.24/1.23 | | (8) ~ ($lesseq(all_3_0, 11)) | ~ ($lesseq(2, x))
% 3.24/1.23 | |
% 3.24/1.23 | | BETA: splitting (8) gives:
% 3.24/1.23 | |
% 3.24/1.23 | | Case 1:
% 3.24/1.23 | | |
% 3.24/1.23 | | | (9) $lesseq(x, 1)
% 3.24/1.23 | | |
% 3.24/1.23 | | | COMBINE_INEQS: (9), (conj_001) imply:
% 3.24/1.23 | | | (10) $false
% 3.24/1.23 | | |
% 3.24/1.23 | | | CLOSE: (10) is inconsistent.
% 3.24/1.23 | | |
% 3.24/1.23 | | Case 2:
% 3.24/1.23 | | |
% 3.24/1.23 | | | (11) $lesseq(12, all_3_0)
% 3.24/1.23 | | |
% 3.24/1.23 | | | COMBINE_INEQS: (2), (11) imply:
% 3.24/1.24 | | | (12) $lesseq(a, -2)
% 3.24/1.24 | | |
% 3.24/1.24 | | | SIMP: (12) implies:
% 3.24/1.24 | | | (13) $lesseq(a, -2)
% 3.24/1.24 | | |
% 3.24/1.24 | | | COMBINE_INEQS: (13), (conj_003) imply:
% 3.24/1.24 | | | (14) $false
% 3.24/1.24 | | |
% 3.24/1.24 | | | CLOSE: (14) is inconsistent.
% 3.24/1.24 | | |
% 3.24/1.24 | | End of split
% 3.24/1.24 | |
% 3.24/1.24 | End of split
% 3.24/1.24 |
% 3.24/1.24 End of proof
% 3.24/1.24 % SZS output end Proof for theBenchmark
% 3.24/1.24
% 3.24/1.24 610ms
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