TSTP Solution File: NUM519+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM519+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 : n023.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 11:48:20 EDT 2023
% Result : Theorem 8.49s 1.85s
% Output : Proof 12.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM519+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n023.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 : Fri Aug 25 15:16:41 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.62/0.60 ________ _____
% 0.62/0.60 ___ __ \_________(_)________________________________
% 0.62/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.62/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.62/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.62/0.60
% 0.62/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.62/0.60 (2023-06-19)
% 0.62/0.60
% 0.62/0.60 (c) Philipp Rümmer, 2009-2023
% 0.62/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.62/0.60 Amanda Stjerna.
% 0.62/0.60 Free software under BSD-3-Clause.
% 0.62/0.60
% 0.62/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.62/0.60
% 0.62/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.62/0.61 Running up to 7 provers in parallel.
% 0.62/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.62/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.62/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.62/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.62/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.62/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.62/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.42/1.17 Prover 4: Preprocessing ...
% 3.42/1.17 Prover 1: Preprocessing ...
% 3.88/1.21 Prover 2: Preprocessing ...
% 3.88/1.21 Prover 6: Preprocessing ...
% 3.88/1.21 Prover 5: Preprocessing ...
% 3.88/1.21 Prover 3: Preprocessing ...
% 3.88/1.21 Prover 0: Preprocessing ...
% 7.82/1.79 Prover 6: Constructing countermodel ...
% 7.82/1.79 Prover 3: Constructing countermodel ...
% 8.49/1.84 Prover 3: proved (1218ms)
% 8.49/1.84 Prover 6: proved (1214ms)
% 8.49/1.84
% 8.49/1.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.49/1.85
% 8.49/1.85
% 8.49/1.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.49/1.85
% 8.49/1.85 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.49/1.85 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.49/1.85 Prover 5: Constructing countermodel ...
% 8.49/1.85 Prover 5: stopped
% 8.49/1.87 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.07/1.94 Prover 1: Constructing countermodel ...
% 9.07/1.96 Prover 7: Preprocessing ...
% 9.65/1.98 Prover 8: Preprocessing ...
% 9.65/1.98 Prover 10: Preprocessing ...
% 10.67/2.16 Prover 2: Constructing countermodel ...
% 10.67/2.16 Prover 2: stopped
% 10.67/2.18 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.28/2.21 Prover 1: Found proof (size 20)
% 11.28/2.22 Prover 1: proved (1595ms)
% 11.28/2.26 Prover 10: Constructing countermodel ...
% 11.28/2.27 Prover 11: Preprocessing ...
% 11.28/2.27 Prover 8: Warning: ignoring some quantifiers
% 12.00/2.29 Prover 8: Constructing countermodel ...
% 12.08/2.30 Prover 0: Constructing countermodel ...
% 12.08/2.30 Prover 0: stopped
% 12.08/2.30 Prover 10: stopped
% 12.08/2.30 Prover 8: stopped
% 12.19/2.31 Prover 7: Constructing countermodel ...
% 12.22/2.33 Prover 7: stopped
% 12.22/2.34 Prover 11: stopped
% 12.22/2.35 Prover 4: Constructing countermodel ...
% 12.22/2.37 Prover 4: stopped
% 12.22/2.37
% 12.22/2.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.22/2.37
% 12.22/2.38 % SZS output start Proof for theBenchmark
% 12.22/2.38 Assumptions after simplification:
% 12.22/2.38 ---------------------------------
% 12.22/2.38
% 12.22/2.38 (m__2449)
% 12.22/2.41 $i(xr) & $i(xm) & $i(xn) & ? [v0: any] : ? [v1: any] : (doDivides0(xr, xm) =
% 12.22/2.41 v1 & doDivides0(xr, xn) = v0 & (v1 = 0 | v0 = 0))
% 12.22/2.41
% 12.22/2.41 (m__2487)
% 12.74/2.41 $i(xr) & $i(xn) & ? [v0: int] : ( ~ (v0 = 0) & doDivides0(xr, xn) = v0)
% 12.74/2.41
% 12.74/2.41 (m__2698)
% 12.74/2.41 $i(xr) & $i(xm) & ? [v0: int] : ( ~ (v0 = 0) & doDivides0(xr, xm) = v0)
% 12.74/2.41
% 12.74/2.41 (function-axioms)
% 12.74/2.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.74/2.42 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0:
% 12.74/2.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 12.74/2.42 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & !
% 12.74/2.42 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 12.74/2.42 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & !
% 12.74/2.42 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.74/2.42 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0:
% 12.74/2.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 12.74/2.42 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & !
% 12.74/2.42 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.74/2.42 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 12.74/2.42 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) |
% 12.74/2.42 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.74/2.42 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~
% 12.74/2.42 (isPrime0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.74/2.42 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1)
% 12.74/2.42 | ~ (aNaturalNumber0(v2) = v0))
% 12.74/2.42
% 12.74/2.42 Further assumptions not needed in the proof:
% 12.74/2.42 --------------------------------------------
% 12.74/2.42 mAMDistr, mAddAsso, mAddCanc, mAddComm, mDefDiff, mDefDiv, mDefLE, mDefPrime,
% 12.74/2.42 mDefQuot, mDivAsso, mDivLE, mDivMin, mDivSum, mDivTrans, mIH, mIH_03, mLEAsym,
% 12.74/2.42 mLENTr, mLERefl, mLETotal, mLETran, mMonAdd, mMonMul, mMonMul2, mMulAsso,
% 12.74/2.42 mMulCanc, mMulComm, mNatSort, mPrimDiv, mSortsB, mSortsB_02, mSortsC,
% 12.74/2.42 mSortsC_01, mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, m_MulZero, m__, m__1799,
% 12.74/2.42 m__1837, m__1860, m__1870, m__2075, m__2287, m__2306, m__2315, m__2327, m__2342,
% 12.74/2.42 m__2362, m__2377
% 12.74/2.42
% 12.74/2.42 Those formulas are unsatisfiable:
% 12.74/2.42 ---------------------------------
% 12.74/2.42
% 12.74/2.42 Begin of proof
% 12.74/2.42 |
% 12.74/2.42 | ALPHA: (m__2449) implies:
% 12.74/2.42 | (1) ? [v0: any] : ? [v1: any] : (doDivides0(xr, xm) = v1 & doDivides0(xr,
% 12.74/2.42 | xn) = v0 & (v1 = 0 | v0 = 0))
% 12.74/2.42 |
% 12.74/2.42 | ALPHA: (m__2487) implies:
% 12.74/2.42 | (2) ? [v0: int] : ( ~ (v0 = 0) & doDivides0(xr, xn) = v0)
% 12.74/2.42 |
% 12.74/2.42 | ALPHA: (m__2698) implies:
% 12.74/2.42 | (3) ? [v0: int] : ( ~ (v0 = 0) & doDivides0(xr, xm) = v0)
% 12.74/2.42 |
% 12.74/2.42 | ALPHA: (function-axioms) implies:
% 12.74/2.43 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 12.74/2.43 | ! [v3: $i] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~
% 12.74/2.43 | (doDivides0(v3, v2) = v0))
% 12.74/2.43 |
% 12.74/2.43 | DELTA: instantiating (2) with fresh symbol all_38_0 gives:
% 12.74/2.43 | (5) ~ (all_38_0 = 0) & doDivides0(xr, xn) = all_38_0
% 12.74/2.43 |
% 12.74/2.43 | ALPHA: (5) implies:
% 12.74/2.43 | (6) ~ (all_38_0 = 0)
% 12.74/2.43 | (7) doDivides0(xr, xn) = all_38_0
% 12.74/2.43 |
% 12.74/2.43 | DELTA: instantiating (3) with fresh symbol all_40_0 gives:
% 12.74/2.43 | (8) ~ (all_40_0 = 0) & doDivides0(xr, xm) = all_40_0
% 12.74/2.43 |
% 12.74/2.43 | ALPHA: (8) implies:
% 12.74/2.43 | (9) ~ (all_40_0 = 0)
% 12.74/2.43 | (10) doDivides0(xr, xm) = all_40_0
% 12.74/2.43 |
% 12.74/2.43 | DELTA: instantiating (1) with fresh symbols all_48_0, all_48_1 gives:
% 12.74/2.43 | (11) doDivides0(xr, xm) = all_48_0 & doDivides0(xr, xn) = all_48_1 &
% 12.74/2.43 | (all_48_0 = 0 | all_48_1 = 0)
% 12.74/2.43 |
% 12.74/2.43 | ALPHA: (11) implies:
% 12.74/2.43 | (12) doDivides0(xr, xn) = all_48_1
% 12.74/2.43 | (13) doDivides0(xr, xm) = all_48_0
% 12.74/2.43 | (14) all_48_0 = 0 | all_48_1 = 0
% 12.74/2.43 |
% 12.74/2.43 | GROUND_INST: instantiating (4) with all_38_0, all_48_1, xn, xr, simplifying
% 12.74/2.43 | with (7), (12) gives:
% 12.74/2.43 | (15) all_48_1 = all_38_0
% 12.74/2.43 |
% 12.74/2.43 | GROUND_INST: instantiating (4) with all_40_0, all_48_0, xm, xr, simplifying
% 12.74/2.43 | with (10), (13) gives:
% 12.74/2.43 | (16) all_48_0 = all_40_0
% 12.74/2.43 |
% 12.74/2.43 | BETA: splitting (14) gives:
% 12.74/2.43 |
% 12.74/2.43 | Case 1:
% 12.74/2.43 | |
% 12.74/2.43 | | (17) all_48_0 = 0
% 12.74/2.43 | |
% 12.74/2.43 | | COMBINE_EQS: (16), (17) imply:
% 12.74/2.43 | | (18) all_40_0 = 0
% 12.74/2.43 | |
% 12.74/2.43 | | SIMP: (18) implies:
% 12.74/2.43 | | (19) all_40_0 = 0
% 12.74/2.43 | |
% 12.74/2.43 | | REDUCE: (9), (19) imply:
% 12.74/2.43 | | (20) $false
% 12.74/2.43 | |
% 12.74/2.43 | | CLOSE: (20) is inconsistent.
% 12.74/2.43 | |
% 12.74/2.43 | Case 2:
% 12.74/2.43 | |
% 12.74/2.43 | | (21) all_48_1 = 0
% 12.74/2.43 | |
% 12.74/2.43 | | COMBINE_EQS: (15), (21) imply:
% 12.74/2.43 | | (22) all_38_0 = 0
% 12.74/2.44 | |
% 12.74/2.44 | | REDUCE: (6), (22) imply:
% 12.74/2.44 | | (23) $false
% 12.74/2.44 | |
% 12.74/2.44 | | CLOSE: (23) is inconsistent.
% 12.74/2.44 | |
% 12.74/2.44 | End of split
% 12.74/2.44 |
% 12.74/2.44 End of proof
% 12.74/2.44 % SZS output end Proof for theBenchmark
% 12.74/2.44
% 12.74/2.44 1833ms
%------------------------------------------------------------------------------