TSTP Solution File: SYN358+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SYN358+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n017.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 : Fri Sep 1 03:27:21 EDT 2023
% Result : Theorem 2.60s 1.15s
% Output : Proof 3.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN358+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 19:19:26 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.67/0.97 Prover 1: Preprocessing ...
% 1.67/0.97 Prover 4: Preprocessing ...
% 2.11/1.01 Prover 6: Preprocessing ...
% 2.11/1.01 Prover 5: Preprocessing ...
% 2.11/1.01 Prover 3: Preprocessing ...
% 2.11/1.01 Prover 0: Preprocessing ...
% 2.11/1.01 Prover 2: Preprocessing ...
% 2.11/1.06 Prover 1: Constructing countermodel ...
% 2.11/1.06 Prover 2: Constructing countermodel ...
% 2.11/1.06 Prover 3: Constructing countermodel ...
% 2.11/1.06 Prover 5: Constructing countermodel ...
% 2.11/1.07 Prover 6: Proving ...
% 2.11/1.07 Prover 4: Constructing countermodel ...
% 2.60/1.07 Prover 0: Proving ...
% 2.60/1.15 Prover 2: proved (527ms)
% 2.60/1.15
% 2.60/1.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.60/1.15
% 2.60/1.15 Prover 5: proved (528ms)
% 2.60/1.15
% 2.60/1.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.60/1.15
% 2.60/1.15 Prover 3: stopped
% 2.60/1.15 Prover 0: stopped
% 2.60/1.15 Prover 6: stopped
% 2.60/1.15 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 2.60/1.15 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 2.60/1.15 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 2.60/1.16 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 2.60/1.16 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 2.60/1.16 Prover 8: Preprocessing ...
% 2.60/1.16 Prover 7: Preprocessing ...
% 2.60/1.17 Prover 10: Preprocessing ...
% 3.25/1.18 Prover 13: Preprocessing ...
% 3.25/1.18 Prover 4: Found proof (size 9)
% 3.25/1.18 Prover 4: proved (553ms)
% 3.25/1.18 Prover 11: Preprocessing ...
% 3.25/1.18 Prover 7: Constructing countermodel ...
% 3.25/1.18 Prover 10: Constructing countermodel ...
% 3.25/1.18 Prover 1: Found proof (size 14)
% 3.25/1.18 Prover 1: proved (566ms)
% 3.25/1.18 Prover 7: stopped
% 3.25/1.19 Prover 8: Warning: ignoring some quantifiers
% 3.25/1.19 Prover 8: Constructing countermodel ...
% 3.25/1.19 Prover 10: stopped
% 3.25/1.19 Prover 8: stopped
% 3.25/1.19 Prover 11: Constructing countermodel ...
% 3.25/1.20 Prover 11: stopped
% 3.25/1.20 Prover 13: Constructing countermodel ...
% 3.25/1.20 Prover 13: stopped
% 3.42/1.20
% 3.42/1.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.42/1.20
% 3.42/1.20 % SZS output start Proof for theBenchmark
% 3.42/1.20 Assumptions after simplification:
% 3.42/1.20 ---------------------------------
% 3.42/1.20
% 3.42/1.20 (x2109)
% 3.51/1.24 ? [v0: $i] : ? [v1: int] : ? [v2: $i] : ? [v3: int] : ($i(v2) & $i(v0) &
% 3.51/1.24 ((v3 = 0 & big_q(v2) = 0 & p & ! [v4: $i] : ( ~ (big_q(v4) = 0) | ~
% 3.51/1.24 $i(v4))) | (v1 = 0 & big_q(v0) = 0 & p & ! [v4: $i] : ( ~ (big_q(v4)
% 3.51/1.24 = 0) | ~ $i(v4)))))
% 3.51/1.24
% 3.51/1.24 Those formulas are unsatisfiable:
% 3.51/1.24 ---------------------------------
% 3.51/1.24
% 3.51/1.24 Begin of proof
% 3.51/1.24 |
% 3.51/1.24 | DELTA: instantiating (x2109) with fresh symbols all_3_0, all_3_1, all_3_2,
% 3.51/1.24 | all_3_3 gives:
% 3.51/1.25 | (1) $i(all_3_1) & $i(all_3_3) & ((all_3_0 = 0 & big_q(all_3_1) = 0 & p & !
% 3.51/1.25 | [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0))) | (all_3_2 = 0 &
% 3.51/1.25 | big_q(all_3_3) = 0 & p & ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~
% 3.51/1.25 | $i(v0))))
% 3.51/1.25 |
% 3.51/1.25 | ALPHA: (1) implies:
% 3.51/1.25 | (2) $i(all_3_3)
% 3.51/1.25 | (3) $i(all_3_1)
% 3.51/1.25 | (4) (all_3_0 = 0 & big_q(all_3_1) = 0 & p & ! [v0: $i] : ( ~ (big_q(v0) =
% 3.51/1.25 | 0) | ~ $i(v0))) | (all_3_2 = 0 & big_q(all_3_3) = 0 & p & !
% 3.51/1.25 | [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0)))
% 3.51/1.25 |
% 3.51/1.25 | BETA: splitting (4) gives:
% 3.51/1.25 |
% 3.51/1.25 | Case 1:
% 3.51/1.25 | |
% 3.51/1.25 | | (5) all_3_0 = 0 & big_q(all_3_1) = 0 & p & ! [v0: $i] : ( ~ (big_q(v0) =
% 3.51/1.25 | | 0) | ~ $i(v0))
% 3.51/1.25 | |
% 3.51/1.25 | | ALPHA: (5) implies:
% 3.51/1.25 | | (6) big_q(all_3_1) = 0
% 3.51/1.25 | | (7) ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0))
% 3.51/1.25 | |
% 3.51/1.25 | | GROUND_INST: instantiating (7) with all_3_1, simplifying with (3), (6)
% 3.51/1.25 | | gives:
% 3.51/1.25 | | (8) $false
% 3.51/1.25 | |
% 3.51/1.25 | | CLOSE: (8) is inconsistent.
% 3.51/1.25 | |
% 3.51/1.26 | Case 2:
% 3.51/1.26 | |
% 3.51/1.26 | | (9) all_3_2 = 0 & big_q(all_3_3) = 0 & p & ! [v0: $i] : ( ~ (big_q(v0) =
% 3.51/1.26 | | 0) | ~ $i(v0))
% 3.51/1.26 | |
% 3.51/1.26 | | ALPHA: (9) implies:
% 3.51/1.26 | | (10) big_q(all_3_3) = 0
% 3.51/1.26 | | (11) ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0))
% 3.51/1.26 | |
% 3.51/1.26 | | GROUND_INST: instantiating (11) with all_3_3, simplifying with (2), (10)
% 3.51/1.26 | | gives:
% 3.51/1.26 | | (12) $false
% 3.51/1.26 | |
% 3.51/1.26 | | CLOSE: (12) is inconsistent.
% 3.51/1.26 | |
% 3.51/1.26 | End of split
% 3.51/1.26 |
% 3.51/1.26 End of proof
% 3.51/1.26 % SZS output end Proof for theBenchmark
% 3.51/1.26
% 3.51/1.26 661ms
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