TSTP Solution File: LAT382+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : LAT382+1 : TPTP v8.1.2. Released v4.0.0.
% 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 : Thu Aug 31 06:25:17 EDT 2023
% Result : Theorem 7.30s 1.80s
% Output : Proof 10.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LAT382+1 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Aug 24 03:48:24 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.63 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.47/1.07 Prover 1: Preprocessing ...
% 2.47/1.07 Prover 4: Preprocessing ...
% 2.96/1.11 Prover 3: Preprocessing ...
% 2.96/1.11 Prover 5: Preprocessing ...
% 2.96/1.11 Prover 2: Preprocessing ...
% 2.96/1.11 Prover 0: Preprocessing ...
% 2.96/1.11 Prover 6: Preprocessing ...
% 5.21/1.45 Prover 5: Constructing countermodel ...
% 5.21/1.45 Prover 2: Constructing countermodel ...
% 6.20/1.63 Prover 3: Constructing countermodel ...
% 6.20/1.65 Prover 1: Constructing countermodel ...
% 6.20/1.66 Prover 6: Proving ...
% 7.30/1.80 Prover 2: proved (1162ms)
% 7.30/1.80
% 7.30/1.80 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.30/1.80
% 7.30/1.80 Prover 6: stopped
% 7.30/1.80 Prover 5: stopped
% 7.30/1.81 Prover 3: stopped
% 7.30/1.81 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.30/1.81 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.30/1.81 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.30/1.81 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.04/1.88 Prover 4: Constructing countermodel ...
% 8.59/1.92 Prover 11: Preprocessing ...
% 8.59/1.92 Prover 7: Preprocessing ...
% 8.59/1.92 Prover 8: Preprocessing ...
% 8.59/1.97 Prover 10: Preprocessing ...
% 9.07/1.97 Prover 0: Proving ...
% 9.07/1.97 Prover 0: stopped
% 9.07/1.99 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.07/2.00 Prover 1: gave up
% 9.07/2.00 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 9.07/2.00 Prover 7: Constructing countermodel ...
% 9.07/2.03 Prover 13: Preprocessing ...
% 9.07/2.04 Prover 16: Preprocessing ...
% 9.07/2.06 Prover 10: Constructing countermodel ...
% 9.83/2.11 Prover 13: Constructing countermodel ...
% 9.83/2.13 Prover 16: Constructing countermodel ...
% 9.83/2.13 Prover 8: Warning: ignoring some quantifiers
% 9.83/2.14 Prover 8: Constructing countermodel ...
% 9.83/2.18 Prover 7: Found proof (size 16)
% 9.83/2.18 Prover 7: proved (371ms)
% 9.83/2.18 Prover 4: stopped
% 9.83/2.18 Prover 13: stopped
% 9.83/2.18 Prover 8: stopped
% 9.83/2.18 Prover 10: stopped
% 9.83/2.18 Prover 16: stopped
% 10.83/2.25 Prover 11: Constructing countermodel ...
% 10.83/2.26 Prover 11: stopped
% 10.83/2.26
% 10.83/2.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.83/2.26
% 10.83/2.26 % SZS output start Proof for theBenchmark
% 10.83/2.27 Assumptions after simplification:
% 10.83/2.27 ---------------------------------
% 10.83/2.27
% 10.83/2.27 (mASymm)
% 10.83/2.27 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 10.83/2.27 sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aElement0(v1) | ~
% 10.83/2.27 aElement0(v0))
% 10.83/2.27
% 10.83/2.27 (mDefInf)
% 10.83/2.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2)
% 10.83/2.28 | ~ $i(v1) | ~ $i(v0) | ~ aInfimumOfIn0(v2, v1, v0) | ~
% 10.83/2.28 aLowerBoundOfIn0(v3, v1, v0) | ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) |
% 10.83/2.28 sdtlseqdt0(v3, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) |
% 10.83/2.28 ~ $i(v1) | ~ $i(v0) | ~ aInfimumOfIn0(v2, v1, v0) | ~ aSubsetOf0(v1, v0)
% 10.83/2.28 | ~ aSet0(v0) | aLowerBoundOfIn0(v2, v1, v0)) & ! [v0: $i] : ! [v1: $i] :
% 10.83/2.28 ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aInfimumOfIn0(v2, v1,
% 10.83/2.28 v0) | ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aElementOf0(v2, v0)) & !
% 10.83/2.28 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 10.83/2.28 aLowerBoundOfIn0(v2, v1, v0) | ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2,
% 10.83/2.28 v0) | ~ aSet0(v0) | aInfimumOfIn0(v2, v1, v0) | ? [v3: $i] : ($i(v3) &
% 10.83/2.28 aLowerBoundOfIn0(v3, v1, v0) & ~ sdtlseqdt0(v3, v2)))
% 10.83/2.28
% 10.83/2.28 (mEOfElem)
% 10.83/2.28 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) |
% 10.83/2.28 ~ aSet0(v0) | aElement0(v1))
% 10.83/2.28
% 10.83/2.28 (m__)
% 10.83/2.28 ~ (xv = xu) & $i(xv) & $i(xu)
% 10.83/2.28
% 10.83/2.28 (m__773)
% 10.83/2.28 $i(xT) & aSet0(xT)
% 10.83/2.28
% 10.83/2.28 (m__773_01)
% 10.83/2.28 $i(xS) & $i(xT) & aSubsetOf0(xS, xT)
% 10.83/2.28
% 10.83/2.28 (m__792)
% 10.83/2.28 $i(xv) & $i(xu) & $i(xS) & $i(xT) & aInfimumOfIn0(xv, xS, xT) &
% 10.83/2.28 aInfimumOfIn0(xu, xS, xT)
% 10.83/2.28
% 10.83/2.28 Further assumptions not needed in the proof:
% 10.83/2.28 --------------------------------------------
% 10.83/2.28 mARefl, mDefEmpty, mDefLB, mDefSub, mDefSup, mDefUB, mElmSort, mLessRel,
% 10.83/2.28 mSetSort, mSupUn, mTrans
% 10.83/2.28
% 10.83/2.28 Those formulas are unsatisfiable:
% 10.83/2.28 ---------------------------------
% 10.83/2.28
% 10.83/2.28 Begin of proof
% 10.83/2.28 |
% 10.83/2.28 | ALPHA: (m__) implies:
% 10.83/2.28 | (1) ~ (xv = xu)
% 10.83/2.28 |
% 10.83/2.28 | ALPHA: (m__792) implies:
% 10.83/2.28 | (2) aInfimumOfIn0(xu, xS, xT)
% 10.83/2.28 | (3) aInfimumOfIn0(xv, xS, xT)
% 10.83/2.28 | (4) $i(xu)
% 10.83/2.28 | (5) $i(xv)
% 10.83/2.28 |
% 10.83/2.28 | ALPHA: (m__773_01) implies:
% 10.83/2.29 | (6) aSubsetOf0(xS, xT)
% 10.83/2.29 | (7) $i(xS)
% 10.83/2.29 |
% 10.83/2.29 | ALPHA: (m__773) implies:
% 10.83/2.29 | (8) aSet0(xT)
% 10.83/2.29 | (9) $i(xT)
% 10.83/2.29 |
% 10.83/2.29 | ALPHA: (mDefInf) implies:
% 10.83/2.29 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 10.83/2.29 | $i(v0) | ~ aInfimumOfIn0(v2, v1, v0) | ~ aSubsetOf0(v1, v0) | ~
% 10.83/2.29 | aSet0(v0) | aElementOf0(v2, v0))
% 10.83/2.29 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 10.83/2.29 | $i(v0) | ~ aInfimumOfIn0(v2, v1, v0) | ~ aSubsetOf0(v1, v0) | ~
% 10.83/2.29 | aSet0(v0) | aLowerBoundOfIn0(v2, v1, v0))
% 10.83/2.29 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) |
% 10.83/2.29 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aInfimumOfIn0(v2, v1, v0) | ~
% 10.83/2.29 | aLowerBoundOfIn0(v3, v1, v0) | ~ aSubsetOf0(v1, v0) | ~ aSet0(v0)
% 10.83/2.29 | | sdtlseqdt0(v3, v2))
% 10.83/2.29 |
% 10.83/2.29 | GROUND_INST: instantiating (11) with xT, xS, xu, simplifying with (2), (4),
% 10.83/2.29 | (6), (7), (8), (9) gives:
% 10.83/2.29 | (13) aLowerBoundOfIn0(xu, xS, xT)
% 10.83/2.29 |
% 10.83/2.29 | GROUND_INST: instantiating (10) with xT, xS, xu, simplifying with (2), (4),
% 10.83/2.29 | (6), (7), (8), (9) gives:
% 10.83/2.29 | (14) aElementOf0(xu, xT)
% 10.83/2.29 |
% 10.83/2.29 | GROUND_INST: instantiating (11) with xT, xS, xv, simplifying with (3), (5),
% 10.83/2.29 | (6), (7), (8), (9) gives:
% 10.83/2.29 | (15) aLowerBoundOfIn0(xv, xS, xT)
% 10.83/2.29 |
% 10.83/2.29 | GROUND_INST: instantiating (10) with xT, xS, xv, simplifying with (3), (5),
% 10.83/2.29 | (6), (7), (8), (9) gives:
% 10.83/2.29 | (16) aElementOf0(xv, xT)
% 10.83/2.29 |
% 10.83/2.29 | GROUND_INST: instantiating (mEOfElem) with xT, xu, simplifying with (4), (8),
% 10.83/2.29 | (9), (14) gives:
% 10.83/2.29 | (17) aElement0(xu)
% 10.83/2.29 |
% 10.83/2.29 | GROUND_INST: instantiating (mEOfElem) with xT, xv, simplifying with (5), (8),
% 10.83/2.29 | (9), (16) gives:
% 10.83/2.29 | (18) aElement0(xv)
% 10.83/2.29 |
% 10.83/2.30 | GROUND_INST: instantiating (12) with xT, xS, xv, xu, simplifying with (3),
% 10.83/2.30 | (4), (5), (6), (7), (8), (9), (13) gives:
% 10.83/2.30 | (19) sdtlseqdt0(xu, xv)
% 10.83/2.30 |
% 10.83/2.30 | GROUND_INST: instantiating (12) with xT, xS, xu, xv, simplifying with (2),
% 10.83/2.30 | (4), (5), (6), (7), (8), (9), (15) gives:
% 10.83/2.30 | (20) sdtlseqdt0(xv, xu)
% 10.83/2.30 |
% 10.83/2.30 | GROUND_INST: instantiating (mASymm) with xu, xv, simplifying with (4), (5),
% 10.83/2.30 | (17), (18), (19), (20) gives:
% 10.83/2.30 | (21) xv = xu
% 10.83/2.30 |
% 10.83/2.30 | REDUCE: (1), (21) imply:
% 10.83/2.30 | (22) $false
% 10.83/2.30 |
% 10.83/2.30 | CLOSE: (22) is inconsistent.
% 10.83/2.30 |
% 10.83/2.30 End of proof
% 10.83/2.30 % SZS output end Proof for theBenchmark
% 10.83/2.30
% 10.83/2.30 1684ms
%------------------------------------------------------------------------------