TSTP Solution File: ARI656_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI656_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 : n027.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 17:48:42 EDT 2023
% Result : Theorem 3.34s 1.31s
% Output : Proof 3.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ARI656_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 : n027.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 18:46:23 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.58/0.66 ________ _____
% 0.58/0.66 ___ __ \_________(_)________________________________
% 0.58/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.58/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.58/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.58/0.66
% 0.58/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.58/0.66 (2023-06-19)
% 0.58/0.66
% 0.58/0.66 (c) Philipp Rümmer, 2009-2023
% 0.58/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.58/0.66 Amanda Stjerna.
% 0.58/0.66 Free software under BSD-3-Clause.
% 0.58/0.66
% 0.58/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.58/0.66
% 0.58/0.66 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.58/0.68 Running up to 7 provers in parallel.
% 0.58/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.58/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.58/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.58/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.58/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.58/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.58/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.03/1.06 Prover 0: Preprocessing ...
% 2.03/1.06 Prover 6: Preprocessing ...
% 2.03/1.06 Prover 1: Preprocessing ...
% 2.03/1.06 Prover 3: Preprocessing ...
% 2.03/1.06 Prover 5: Preprocessing ...
% 2.03/1.06 Prover 2: Preprocessing ...
% 2.03/1.06 Prover 4: Preprocessing ...
% 2.38/1.11 Prover 1: Constructing countermodel ...
% 2.38/1.11 Prover 3: Constructing countermodel ...
% 2.38/1.11 Prover 6: Constructing countermodel ...
% 2.38/1.11 Prover 4: Constructing countermodel ...
% 2.38/1.11 Prover 5: Constructing countermodel ...
% 2.38/1.11 Prover 0: Constructing countermodel ...
% 2.38/1.11 Prover 2: Constructing countermodel ...
% 3.34/1.31 Prover 5: proved (622ms)
% 3.34/1.31 Prover 3: proved (624ms)
% 3.34/1.31 Prover 6: proved (621ms)
% 3.34/1.31 Prover 2: proved (624ms)
% 3.34/1.31
% 3.34/1.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.34/1.31
% 3.34/1.32
% 3.34/1.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.34/1.32
% 3.34/1.32 Prover 0: proved (625ms)
% 3.34/1.32
% 3.34/1.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.34/1.32
% 3.34/1.32
% 3.34/1.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.34/1.32
% 3.34/1.32
% 3.34/1.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.34/1.32
% 3.34/1.32 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.34/1.32 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.34/1.33 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.34/1.33 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.34/1.33 Prover 8: Preprocessing ...
% 3.34/1.33 Prover 7: Preprocessing ...
% 3.34/1.33 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.34/1.34 Prover 8: Constructing countermodel ...
% 3.34/1.34 Prover 7: Constructing countermodel ...
% 3.34/1.34 Prover 4: Found proof (size 12)
% 3.34/1.34 Prover 4: proved (649ms)
% 3.34/1.34 Prover 1: Found proof (size 12)
% 3.34/1.34 Prover 1: proved (651ms)
% 3.34/1.34 Prover 8: stopped
% 3.34/1.34 Prover 7: stopped
% 3.34/1.34 Prover 10: Preprocessing ...
% 3.34/1.34 Prover 13: Preprocessing ...
% 3.34/1.34 Prover 11: Preprocessing ...
% 3.34/1.35 Prover 10: Constructing countermodel ...
% 3.34/1.35 Prover 10: stopped
% 3.34/1.35 Prover 13: Constructing countermodel ...
% 3.34/1.35 Prover 13: stopped
% 3.34/1.35 Prover 11: Constructing countermodel ...
% 3.34/1.35 Prover 11: stopped
% 3.34/1.35
% 3.34/1.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.34/1.35
% 3.34/1.35 % SZS output start Proof for theBenchmark
% 3.34/1.36 Assumptions after simplification:
% 3.34/1.36 ---------------------------------
% 3.34/1.36
% 3.34/1.36 (conj)
% 3.85/1.36 $lesseq(c, b)
% 3.85/1.36
% 3.85/1.36 (conj_001)
% 3.85/1.36 $lesseq(0, a)
% 3.85/1.36
% 3.85/1.36 (conj_002)
% 3.85/1.37 ? [v0: int] : ? [v1: int] : ($lesseq(1, $difference(v1, v0)) & $product(a,
% 3.85/1.37 c) = v1 & $product(a, b) = v0)
% 3.85/1.37
% 3.85/1.37 Those formulas are unsatisfiable:
% 3.85/1.37 ---------------------------------
% 3.85/1.37
% 3.85/1.37 Begin of proof
% 3.85/1.37 |
% 3.85/1.37 | DELTA: instantiating (conj_002) with fresh symbols all_3_0, all_3_1 gives:
% 3.85/1.37 | (1) $lesseq(1, $difference(all_3_0, all_3_1)) & $product(a, c) = all_3_0 &
% 3.85/1.37 | $product(a, b) = all_3_1
% 3.85/1.37 |
% 3.85/1.37 | ALPHA: (1) implies:
% 3.85/1.37 | (2) $lesseq(1, $difference(all_3_0, all_3_1))
% 3.85/1.37 | (3) $product(a, b) = all_3_1
% 3.85/1.37 | (4) $product(a, c) = all_3_0
% 3.85/1.37 |
% 3.85/1.37 | THEORY_AXIOM GroebnerMultiplication:
% 3.85/1.37 | (5) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4:
% 3.85/1.38 | int] : ( ~ ($lesseq(1, $difference(v4, v3))) | ~ ($lesseq(0, v2)) |
% 3.85/1.38 | ~ ($lesseq(v1, v0)) | ~ ($product(v2, v1) = v4) | ~ ($product(v2,
% 3.85/1.38 | v0) = v3))
% 3.85/1.38 |
% 3.85/1.38 | GROUND_INST: instantiating (5) with b, c, a, all_3_1, all_3_0, simplifying
% 3.85/1.38 | with (3), (4) gives:
% 3.85/1.38 | (6) ~ ($lesseq(1, $difference(all_3_0, all_3_1))) | ~ ($lesseq(0, a)) |
% 3.85/1.38 | ~ ($lesseq(c, b))
% 3.85/1.38 |
% 3.85/1.38 | BETA: splitting (6) gives:
% 3.85/1.38 |
% 3.85/1.38 | Case 1:
% 3.85/1.38 | |
% 3.85/1.38 | | (7) $lesseq(a, -1)
% 3.85/1.38 | |
% 3.85/1.38 | | COMBINE_INEQS: (7), (conj_001) imply:
% 3.85/1.38 | | (8) $false
% 3.85/1.38 | |
% 3.85/1.38 | | CLOSE: (8) is inconsistent.
% 3.85/1.38 | |
% 3.85/1.38 | Case 2:
% 3.85/1.38 | |
% 3.85/1.38 | | (9) ~ ($lesseq(1, $difference(all_3_0, all_3_1))) | ~ ($lesseq(c, b))
% 3.85/1.38 | |
% 3.85/1.38 | | BETA: splitting (9) gives:
% 3.85/1.38 | |
% 3.85/1.38 | | Case 1:
% 3.85/1.38 | | |
% 3.85/1.38 | | | (10) $lesseq(1, $difference(c, b))
% 3.85/1.38 | | |
% 3.85/1.38 | | | COMBINE_INEQS: (10), (conj) imply:
% 3.85/1.38 | | | (11) $false
% 3.85/1.38 | | |
% 3.85/1.38 | | | CLOSE: (11) is inconsistent.
% 3.85/1.38 | | |
% 3.85/1.38 | | Case 2:
% 3.85/1.38 | | |
% 3.85/1.38 | | | (12) $lesseq(all_3_0, all_3_1)
% 3.85/1.38 | | |
% 3.85/1.38 | | | COMBINE_INEQS: (2), (12) imply:
% 3.85/1.38 | | | (13) $false
% 3.85/1.38 | | |
% 3.85/1.38 | | | CLOSE: (13) is inconsistent.
% 3.85/1.38 | | |
% 3.85/1.38 | | End of split
% 3.85/1.38 | |
% 3.85/1.38 | End of split
% 3.85/1.38 |
% 3.85/1.38 End of proof
% 3.85/1.38 % SZS output end Proof for theBenchmark
% 3.85/1.38
% 3.85/1.38 720ms
%------------------------------------------------------------------------------