TSTP Solution File: NUM443+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM443+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n012.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 11:47:47 EDT 2023
% Result : Theorem 14.12s 2.67s
% Output : Proof 19.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM443+4 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n012.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 : Fri Aug 25 17:57:26 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.03/1.23 Prover 1: Preprocessing ...
% 4.03/1.23 Prover 4: Preprocessing ...
% 4.03/1.27 Prover 3: Preprocessing ...
% 4.03/1.27 Prover 5: Preprocessing ...
% 4.03/1.27 Prover 2: Preprocessing ...
% 4.03/1.27 Prover 6: Preprocessing ...
% 4.03/1.27 Prover 0: Preprocessing ...
% 10.53/2.14 Prover 1: Constructing countermodel ...
% 10.53/2.17 Prover 5: Constructing countermodel ...
% 10.53/2.17 Prover 6: Proving ...
% 10.53/2.19 Prover 3: Constructing countermodel ...
% 11.11/2.24 Prover 2: Proving ...
% 14.12/2.66 Prover 4: Constructing countermodel ...
% 14.12/2.67 Prover 3: proved (2037ms)
% 14.12/2.67 Prover 0: Proving ...
% 14.12/2.67
% 14.12/2.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.12/2.67
% 14.12/2.67 Prover 5: stopped
% 14.12/2.68 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.12/2.68 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.12/2.68 Prover 6: stopped
% 14.12/2.68 Prover 0: stopped
% 14.80/2.69 Prover 2: stopped
% 14.90/2.70 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 14.90/2.70 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.90/2.70 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 15.70/2.83 Prover 10: Preprocessing ...
% 15.70/2.84 Prover 11: Preprocessing ...
% 15.70/2.84 Prover 8: Preprocessing ...
% 15.70/2.84 Prover 7: Preprocessing ...
% 15.70/2.85 Prover 13: Preprocessing ...
% 17.17/3.08 Prover 10: Constructing countermodel ...
% 17.76/3.10 Prover 7: Constructing countermodel ...
% 17.76/3.11 Prover 8: Warning: ignoring some quantifiers
% 17.76/3.12 Prover 8: Constructing countermodel ...
% 17.76/3.17 Prover 13: Constructing countermodel ...
% 18.45/3.18 Prover 1: Found proof (size 132)
% 18.45/3.18 Prover 1: proved (2559ms)
% 18.45/3.18 Prover 10: stopped
% 18.45/3.18 Prover 4: stopped
% 18.45/3.18 Prover 7: stopped
% 18.54/3.19 Prover 13: stopped
% 18.54/3.19 Prover 8: stopped
% 19.04/3.35 Prover 11: Constructing countermodel ...
% 19.04/3.37 Prover 11: stopped
% 19.04/3.37
% 19.04/3.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.04/3.37
% 19.38/3.40 % SZS output start Proof for theBenchmark
% 19.38/3.41 Assumptions after simplification:
% 19.38/3.41 ---------------------------------
% 19.38/3.41
% 19.38/3.41 (mAddComm)
% 19.38/3.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 19.38/3.44 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 19.38/3.44 (sdtpldt0(v1, v0) = v5 & aInteger0(v1) = v4 & aInteger0(v0) = v3 & $i(v5) &
% 19.38/3.44 ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 19.38/3.44
% 19.38/3.44 (mDivisor)
% 19.38/3.44 $i(sz00) & ! [v0: $i] : ( ~ (aInteger0(v0) = 0) | ~ $i(v0) | ( ! [v1: $i] :
% 19.38/3.44 ! [v2: int] : (v2 = 0 | v1 = sz00 | ~ (aDivisorOf0(v1, v0) = v2) | ~
% 19.38/3.44 $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & aInteger0(v1) = v3) | ! [v3: $i]
% 19.38/3.44 : ( ~ (sdtasdt0(v1, v3) = v0) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0)
% 19.38/3.44 & aInteger0(v3) = v4))) & ! [v1: $i] : ( ~ (aDivisorOf0(v1, v0) =
% 19.38/3.44 0) | ~ $i(v1) | ( ~ (v1 = sz00) & aInteger0(v1) = 0 & ? [v2: $i] :
% 19.38/3.44 (sdtasdt0(v1, v2) = v0 & aInteger0(v2) = 0 & $i(v2))))))
% 19.38/3.44
% 19.38/3.44 (mEquModSym)
% 19.38/3.44 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = sz00 | ~
% 19.38/3.44 (sdteqdtlpzmzozddtrp0(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 19.38/3.44 ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: any] :
% 19.38/3.44 (sdteqdtlpzmzozddtrp0(v1, v0, v2) = v6 & aInteger0(v2) = v5 & aInteger0(v1)
% 19.38/3.44 = v4 & aInteger0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v6
% 19.38/3.44 = 0)))
% 19.38/3.44
% 19.38/3.44 (mEquModTrn)
% 19.38/3.45 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 19.38/3.45 int] : (v4 = 0 | v2 = sz00 | ~ (sdteqdtlpzmzozddtrp0(v0, v3, v2) = v4) | ~
% 19.38/3.45 (sdteqdtlpzmzozddtrp0(v0, v1, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 19.38/3.45 ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : ?
% 19.38/3.45 [v9: any] : (sdteqdtlpzmzozddtrp0(v1, v3, v2) = v9 & aInteger0(v3) = v8 &
% 19.38/3.45 aInteger0(v2) = v7 & aInteger0(v1) = v6 & aInteger0(v0) = v5 & ( ~ (v9 =
% 19.38/3.45 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0))))
% 19.38/3.45
% 19.38/3.45 (mIntMult)
% 19.38/3.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 19.38/3.45 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 19.38/3.45 (aInteger0(v2) = v5 & aInteger0(v1) = v4 & aInteger0(v0) = v3 & ( ~ (v4 = 0)
% 19.38/3.45 | ~ (v3 = 0) | v5 = 0)))
% 19.38/3.45
% 19.38/3.45 (mIntNeg)
% 19.38/3.45 ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ? [v2: any] :
% 19.38/3.45 ? [v3: any] : (aInteger0(v1) = v3 & aInteger0(v0) = v2 & ( ~ (v2 = 0) | v3
% 19.38/3.45 = 0)))
% 19.38/3.45
% 19.38/3.45 (mIntPlus)
% 19.38/3.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 19.38/3.45 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 19.38/3.45 (aInteger0(v2) = v5 & aInteger0(v1) = v4 & aInteger0(v0) = v3 & ( ~ (v4 = 0)
% 19.38/3.45 | ~ (v3 = 0) | v5 = 0)))
% 19.38/3.45
% 19.38/3.45 (mMulComm)
% 19.38/3.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 19.38/3.45 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 19.38/3.45 (sdtasdt0(v1, v0) = v5 & aInteger0(v1) = v4 & aInteger0(v0) = v3 & $i(v5) &
% 19.38/3.45 ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 19.38/3.45
% 19.38/3.45 (m__)
% 19.38/3.45 $i(xc) & $i(xb) & $i(xq) & $i(xa) & ? [v0: $i] : ? [v1: $i] : ? [v2: int] :
% 19.38/3.45 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v2
% 19.38/3.45 = 0) & szAzrzSzezqlpdtcmdtrp0(xa, xq) = v0 & stldt0(v0) = v3 & aSet0(v0) =
% 19.38/3.45 0 & aElementOf0(xc, v3) = v6 & aElementOf0(xc, v0) = 0 & aElementOf0(xb, v3)
% 19.38/3.45 = 0 & aElementOf0(xb, v0) = v2 & sdteqdtlpzmzozddtrp0(xc, xb, xq) = 0 &
% 19.38/3.45 aDivisorOf0(xq, v5) = 0 & sdtpldt0(xc, v4) = v5 & smndt0(xb) = v4 &
% 19.38/3.45 smndt0(xa) = v1 & $i(v5) & $i(v4) & $i(v3) & $i(v1) & $i(v0) & ! [v7: $i] :
% 19.38/3.45 ! [v8: int] : (v8 = 0 | ~ (aElementOf0(v7, v0) = v8) | ~ $i(v7) | ? [v9:
% 19.38/3.45 any] : ? [v10: $i] : ? [v11: any] : ? [v12: any] :
% 19.38/3.45 (sdteqdtlpzmzozddtrp0(v7, xa, xq) = v12 & aDivisorOf0(xq, v10) = v11 &
% 19.38/3.45 sdtpldt0(v7, v1) = v10 & aInteger0(v7) = v9 & $i(v10) & ( ~ (v9 = 0) | (
% 19.38/3.45 ~ (v12 = 0) & ~ (v11 = 0) & ! [v13: $i] : ( ~ (sdtasdt0(xq, v13) =
% 19.38/3.45 v10) | ~ $i(v13) | ? [v14: int] : ( ~ (v14 = 0) &
% 19.38/3.45 aInteger0(v13) = v14)))))) & ! [v7: $i] : ( ~ (aElementOf0(v7,
% 19.38/3.45 v0) = 0) | ~ $i(v7) | ? [v8: $i] : (sdteqdtlpzmzozddtrp0(v7, xa, xq)
% 19.38/3.45 = 0 & aDivisorOf0(xq, v8) = 0 & sdtpldt0(v7, v1) = v8 & aInteger0(v7) =
% 19.38/3.45 0 & $i(v8) & ? [v9: $i] : (sdtasdt0(xq, v9) = v8 & aInteger0(v9) = 0 &
% 19.38/3.45 $i(v9)))) & ? [v7: $i] : (sdtasdt0(xq, v7) = v5 & aInteger0(v7) = 0 &
% 19.38/3.45 $i(v7)))
% 19.38/3.45
% 19.38/3.45 (m__1962)
% 19.38/3.45 ~ (xq = sz00) & aInteger0(xq) = 0 & aInteger0(xa) = 0 & $i(xq) & $i(xa) &
% 19.38/3.45 $i(sz00)
% 19.38/3.45
% 19.38/3.45 (m__2010)
% 19.38/3.46 aInteger0(xc) = 0 & aInteger0(xb) = 0 & $i(xc) & $i(xb)
% 19.38/3.46
% 19.38/3.46 (function-axioms)
% 19.38/3.46 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 19.38/3.46 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v1)
% 19.38/3.46 | ~ (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 19.38/3.46 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (szAzrzSzezqlpdtcmdtrp0(v3, v2) = v1)
% 19.38/3.46 | ~ (szAzrzSzezqlpdtcmdtrp0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 19.38/3.46 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtslmnbsdt0(v3, v2) = v1) | ~
% 19.38/3.46 (sdtslmnbsdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 19.38/3.46 [v3: $i] : (v1 = v0 | ~ (sdtbsmnsldt0(v3, v2) = v1) | ~ (sdtbsmnsldt0(v3,
% 19.38/3.46 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 19.38/3.46 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (aSubsetOf0(v3, v2) = v1) | ~
% 19.38/3.46 (aSubsetOf0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 19.38/3.46 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 19.38/3.46 (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) & ! [v0:
% 19.38/3.46 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 19.38/3.46 : (v1 = v0 | ~ (aDivisorOf0(v3, v2) = v1) | ~ (aDivisorOf0(v3, v2) = v0)) &
% 19.38/3.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 19.38/3.46 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 19.38/3.46 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) |
% 19.38/3.46 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 19.38/3.46 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isFinite0(v2) = v1) | ~
% 19.38/3.46 (isFinite0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 19.38/3.46 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isClosed0(v2) = v1) | ~
% 19.38/3.46 (isClosed0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 19.38/3.46 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isOpen0(v2) = v1) | ~
% 19.38/3.46 (isOpen0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 19.38/3.46 ~ (stldt0(v2) = v1) | ~ (stldt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 19.38/3.46 [v2: $i] : (v1 = v0 | ~ (sbsmnsldt0(v2) = v1) | ~ (sbsmnsldt0(v2) = v0)) &
% 19.38/3.46 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 =
% 19.38/3.46 v0 | ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) & ! [v0: MultipleValueBool]
% 19.38/3.46 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isPrime0(v2) = v1)
% 19.38/3.46 | ~ (isPrime0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 19.38/3.46 v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) & ! [v0:
% 19.38/3.46 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 19.38/3.46 ~ (aInteger0(v2) = v1) | ~ (aInteger0(v2) = v0))
% 19.38/3.46
% 19.38/3.46 Further assumptions not needed in the proof:
% 19.38/3.46 --------------------------------------------
% 19.38/3.46 mAddAsso, mAddNeg, mAddZero, mArSeq, mClosed, mComplement, mDistrib, mElements,
% 19.38/3.46 mEquMod, mEquModMul, mEquModRef, mFinSet, mIntOne, mIntZero, mIntegers,
% 19.38/3.46 mInterOpen, mIntersection, mMulAsso, mMulMinOne, mMulOne, mMulZero, mOpen,
% 19.38/3.46 mPrime, mPrimeDivisor, mSets, mSubset, mUnion, mUnionClosed, mUnionOpen,
% 19.38/3.46 mUnionSClosed, mUnionSet, mZeroDiv
% 19.38/3.46
% 19.38/3.46 Those formulas are unsatisfiable:
% 19.38/3.46 ---------------------------------
% 19.38/3.46
% 19.38/3.46 Begin of proof
% 19.38/3.46 |
% 19.38/3.46 | ALPHA: (mDivisor) implies:
% 19.38/3.46 | (1) ! [v0: $i] : ( ~ (aInteger0(v0) = 0) | ~ $i(v0) | ( ! [v1: $i] : !
% 19.38/3.46 | [v2: int] : (v2 = 0 | v1 = sz00 | ~ (aDivisorOf0(v1, v0) = v2) |
% 19.38/3.46 | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & aInteger0(v1) = v3) | !
% 19.38/3.46 | [v3: $i] : ( ~ (sdtasdt0(v1, v3) = v0) | ~ $i(v3) | ? [v4: int]
% 19.38/3.46 | : ( ~ (v4 = 0) & aInteger0(v3) = v4))) & ! [v1: $i] : ( ~
% 19.38/3.46 | (aDivisorOf0(v1, v0) = 0) | ~ $i(v1) | ( ~ (v1 = sz00) &
% 19.38/3.46 | aInteger0(v1) = 0 & ? [v2: $i] : (sdtasdt0(v1, v2) = v0 &
% 19.38/3.46 | aInteger0(v2) = 0 & $i(v2))))))
% 19.38/3.46 |
% 19.38/3.46 | ALPHA: (mEquModSym) implies:
% 19.38/3.47 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = sz00 | ~
% 19.38/3.47 | (sdteqdtlpzmzozddtrp0(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 19.38/3.47 | $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: any] :
% 19.38/3.47 | (sdteqdtlpzmzozddtrp0(v1, v0, v2) = v6 & aInteger0(v2) = v5 &
% 19.38/3.47 | aInteger0(v1) = v4 & aInteger0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 =
% 19.38/3.47 | 0) | ~ (v3 = 0) | v6 = 0)))
% 19.38/3.47 |
% 19.38/3.47 | ALPHA: (mEquModTrn) implies:
% 19.38/3.47 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 19.38/3.47 | (v4 = 0 | v2 = sz00 | ~ (sdteqdtlpzmzozddtrp0(v0, v3, v2) = v4) | ~
% 19.38/3.47 | (sdteqdtlpzmzozddtrp0(v0, v1, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~
% 19.38/3.47 | $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ?
% 19.38/3.47 | [v8: any] : ? [v9: any] : (sdteqdtlpzmzozddtrp0(v1, v3, v2) = v9 &
% 19.38/3.47 | aInteger0(v3) = v8 & aInteger0(v2) = v7 & aInteger0(v1) = v6 &
% 19.38/3.47 | aInteger0(v0) = v5 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~
% 19.38/3.47 | (v6 = 0) | ~ (v5 = 0))))
% 19.38/3.47 |
% 19.38/3.47 | ALPHA: (m__1962) implies:
% 19.38/3.47 | (4) ~ (xq = sz00)
% 19.38/3.47 | (5) aInteger0(xa) = 0
% 19.38/3.47 | (6) aInteger0(xq) = 0
% 19.38/3.47 |
% 19.38/3.47 | ALPHA: (m__2010) implies:
% 19.38/3.47 | (7) aInteger0(xb) = 0
% 19.38/3.47 |
% 19.38/3.47 | ALPHA: (m__) implies:
% 19.38/3.47 | (8) $i(xa)
% 19.38/3.47 | (9) $i(xq)
% 19.38/3.47 | (10) $i(xb)
% 19.38/3.47 | (11) $i(xc)
% 19.38/3.47 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: $i] : ? [v4: $i] :
% 19.38/3.47 | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v2 = 0) &
% 19.38/3.47 | szAzrzSzezqlpdtcmdtrp0(xa, xq) = v0 & stldt0(v0) = v3 & aSet0(v0) =
% 19.38/3.47 | 0 & aElementOf0(xc, v3) = v6 & aElementOf0(xc, v0) = 0 &
% 19.38/3.47 | aElementOf0(xb, v3) = 0 & aElementOf0(xb, v0) = v2 &
% 19.38/3.47 | sdteqdtlpzmzozddtrp0(xc, xb, xq) = 0 & aDivisorOf0(xq, v5) = 0 &
% 19.38/3.47 | sdtpldt0(xc, v4) = v5 & smndt0(xb) = v4 & smndt0(xa) = v1 & $i(v5) &
% 19.38/3.47 | $i(v4) & $i(v3) & $i(v1) & $i(v0) & ! [v7: $i] : ! [v8: int] : (v8
% 19.38/3.47 | = 0 | ~ (aElementOf0(v7, v0) = v8) | ~ $i(v7) | ? [v9: any] :
% 19.38/3.47 | ? [v10: $i] : ? [v11: any] : ? [v12: any] :
% 19.38/3.47 | (sdteqdtlpzmzozddtrp0(v7, xa, xq) = v12 & aDivisorOf0(xq, v10) =
% 19.38/3.47 | v11 & sdtpldt0(v7, v1) = v10 & aInteger0(v7) = v9 & $i(v10) & (
% 19.38/3.47 | ~ (v9 = 0) | ( ~ (v12 = 0) & ~ (v11 = 0) & ! [v13: $i] : ( ~
% 19.38/3.47 | (sdtasdt0(xq, v13) = v10) | ~ $i(v13) | ? [v14: int] : (
% 19.38/3.47 | ~ (v14 = 0) & aInteger0(v13) = v14)))))) & ! [v7: $i] :
% 19.38/3.47 | ( ~ (aElementOf0(v7, v0) = 0) | ~ $i(v7) | ? [v8: $i] :
% 19.38/3.47 | (sdteqdtlpzmzozddtrp0(v7, xa, xq) = 0 & aDivisorOf0(xq, v8) = 0 &
% 19.38/3.47 | sdtpldt0(v7, v1) = v8 & aInteger0(v7) = 0 & $i(v8) & ? [v9: $i]
% 19.38/3.47 | : (sdtasdt0(xq, v9) = v8 & aInteger0(v9) = 0 & $i(v9)))) & ?
% 19.38/3.47 | [v7: $i] : (sdtasdt0(xq, v7) = v5 & aInteger0(v7) = 0 & $i(v7)))
% 19.38/3.47 |
% 19.38/3.47 | ALPHA: (function-axioms) implies:
% 19.38/3.47 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 19.38/3.47 | : (v1 = v0 | ~ (aInteger0(v2) = v1) | ~ (aInteger0(v2) = v0))
% 19.38/3.47 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 19.38/3.47 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sdteqdtlpzmzozddtrp0(v4,
% 19.38/3.47 | v3, v2) = v1) | ~ (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v0))
% 19.38/3.47 |
% 19.38/3.47 | DELTA: instantiating (12) with fresh symbols all_41_0, all_41_1, all_41_2,
% 19.38/3.47 | all_41_3, all_41_4, all_41_5, all_41_6 gives:
% 19.81/3.48 | (15) ~ (all_41_0 = 0) & ~ (all_41_4 = 0) & szAzrzSzezqlpdtcmdtrp0(xa, xq)
% 19.81/3.48 | = all_41_6 & stldt0(all_41_6) = all_41_3 & aSet0(all_41_6) = 0 &
% 19.81/3.48 | aElementOf0(xc, all_41_3) = all_41_0 & aElementOf0(xc, all_41_6) = 0 &
% 19.81/3.48 | aElementOf0(xb, all_41_3) = 0 & aElementOf0(xb, all_41_6) = all_41_4 &
% 19.81/3.48 | sdteqdtlpzmzozddtrp0(xc, xb, xq) = 0 & aDivisorOf0(xq, all_41_1) = 0 &
% 19.81/3.48 | sdtpldt0(xc, all_41_2) = all_41_1 & smndt0(xb) = all_41_2 & smndt0(xa)
% 19.81/3.48 | = all_41_5 & $i(all_41_1) & $i(all_41_2) & $i(all_41_3) & $i(all_41_5)
% 19.81/3.48 | & $i(all_41_6) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 19.81/3.48 | (aElementOf0(v0, all_41_6) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 19.81/3.48 | [v3: $i] : ? [v4: any] : ? [v5: any] : (sdteqdtlpzmzozddtrp0(v0,
% 19.81/3.48 | xa, xq) = v5 & aDivisorOf0(xq, v3) = v4 & sdtpldt0(v0, all_41_5)
% 19.81/3.48 | = v3 & aInteger0(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | ( ~ (v5 = 0) &
% 19.81/3.48 | ~ (v4 = 0) & ! [v6: $i] : ( ~ (sdtasdt0(xq, v6) = v3) | ~
% 19.81/3.48 | $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & aInteger0(v6) =
% 19.81/3.48 | v7)))))) & ! [v0: $i] : ( ~ (aElementOf0(v0, all_41_6) =
% 19.81/3.48 | 0) | ~ $i(v0) | ? [v1: $i] : (sdteqdtlpzmzozddtrp0(v0, xa, xq) =
% 19.81/3.48 | 0 & aDivisorOf0(xq, v1) = 0 & sdtpldt0(v0, all_41_5) = v1 &
% 19.81/3.48 | aInteger0(v0) = 0 & $i(v1) & ? [v2: $i] : (sdtasdt0(xq, v2) = v1
% 19.81/3.48 | & aInteger0(v2) = 0 & $i(v2)))) & ? [v0: $i] : (sdtasdt0(xq,
% 19.81/3.48 | v0) = all_41_1 & aInteger0(v0) = 0 & $i(v0))
% 19.81/3.48 |
% 19.81/3.48 | ALPHA: (15) implies:
% 19.81/3.48 | (16) ~ (all_41_4 = 0)
% 19.81/3.48 | (17) $i(all_41_2)
% 19.81/3.48 | (18) $i(all_41_1)
% 19.81/3.48 | (19) smndt0(xa) = all_41_5
% 19.81/3.48 | (20) smndt0(xb) = all_41_2
% 19.81/3.48 | (21) sdtpldt0(xc, all_41_2) = all_41_1
% 19.81/3.48 | (22) aDivisorOf0(xq, all_41_1) = 0
% 19.81/3.48 | (23) sdteqdtlpzmzozddtrp0(xc, xb, xq) = 0
% 19.81/3.48 | (24) aElementOf0(xb, all_41_6) = all_41_4
% 19.81/3.48 | (25) aElementOf0(xc, all_41_6) = 0
% 19.81/3.48 | (26) ! [v0: $i] : ( ~ (aElementOf0(v0, all_41_6) = 0) | ~ $i(v0) | ?
% 19.81/3.48 | [v1: $i] : (sdteqdtlpzmzozddtrp0(v0, xa, xq) = 0 & aDivisorOf0(xq,
% 19.81/3.48 | v1) = 0 & sdtpldt0(v0, all_41_5) = v1 & aInteger0(v0) = 0 &
% 19.81/3.48 | $i(v1) & ? [v2: $i] : (sdtasdt0(xq, v2) = v1 & aInteger0(v2) = 0
% 19.81/3.48 | & $i(v2))))
% 19.81/3.48 | (27) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aElementOf0(v0, all_41_6) =
% 19.81/3.48 | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : ?
% 19.81/3.48 | [v5: any] : (sdteqdtlpzmzozddtrp0(v0, xa, xq) = v5 & aDivisorOf0(xq,
% 19.81/3.48 | v3) = v4 & sdtpldt0(v0, all_41_5) = v3 & aInteger0(v0) = v2 &
% 19.81/3.48 | $i(v3) & ( ~ (v2 = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & ! [v6: $i] :
% 19.81/3.48 | ( ~ (sdtasdt0(xq, v6) = v3) | ~ $i(v6) | ? [v7: int] : ( ~
% 19.81/3.48 | (v7 = 0) & aInteger0(v6) = v7))))))
% 19.81/3.48 | (28) ? [v0: $i] : (sdtasdt0(xq, v0) = all_41_1 & aInteger0(v0) = 0 &
% 19.81/3.48 | $i(v0))
% 19.81/3.48 |
% 19.81/3.48 | DELTA: instantiating (28) with fresh symbol all_44_0 gives:
% 19.81/3.48 | (29) sdtasdt0(xq, all_44_0) = all_41_1 & aInteger0(all_44_0) = 0 &
% 19.81/3.48 | $i(all_44_0)
% 19.81/3.48 |
% 19.81/3.48 | ALPHA: (29) implies:
% 19.81/3.48 | (30) $i(all_44_0)
% 19.81/3.48 | (31) aInteger0(all_44_0) = 0
% 19.81/3.48 | (32) sdtasdt0(xq, all_44_0) = all_41_1
% 19.81/3.48 |
% 19.81/3.48 | GROUND_INST: instantiating (mIntNeg) with xa, all_41_5, simplifying with (8),
% 19.81/3.48 | (19) gives:
% 19.81/3.48 | (33) ? [v0: any] : ? [v1: any] : (aInteger0(all_41_5) = v1 &
% 19.81/3.48 | aInteger0(xa) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 19.81/3.48 |
% 19.81/3.48 | GROUND_INST: instantiating (mIntNeg) with xb, all_41_2, simplifying with (10),
% 19.81/3.48 | (20) gives:
% 19.81/3.48 | (34) ? [v0: any] : ? [v1: any] : (aInteger0(all_41_2) = v1 &
% 19.81/3.48 | aInteger0(xb) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 19.81/3.48 |
% 19.81/3.49 | GROUND_INST: instantiating (mAddComm) with xc, all_41_2, all_41_1, simplifying
% 19.81/3.49 | with (11), (17), (21) gives:
% 19.81/3.49 | (35) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(all_41_2, xc) =
% 19.81/3.49 | v2 & aInteger0(all_41_2) = v1 & aInteger0(xc) = v0 & $i(v2) & ( ~
% 19.81/3.49 | (v1 = 0) | ~ (v0 = 0) | v2 = all_41_1))
% 19.81/3.49 |
% 19.81/3.49 | GROUND_INST: instantiating (mIntPlus) with xc, all_41_2, all_41_1, simplifying
% 19.81/3.49 | with (11), (17), (21) gives:
% 19.81/3.49 | (36) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aInteger0(all_41_1) = v2
% 19.81/3.49 | & aInteger0(all_41_2) = v1 & aInteger0(xc) = v0 & ( ~ (v1 = 0) | ~
% 19.81/3.49 | (v0 = 0) | v2 = 0))
% 19.81/3.49 |
% 19.81/3.49 | GROUND_INST: instantiating (mMulComm) with xq, all_44_0, all_41_1, simplifying
% 19.81/3.49 | with (9), (30), (32) gives:
% 19.81/3.49 | (37) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(all_44_0, xq) =
% 19.81/3.49 | v2 & aInteger0(all_44_0) = v1 & aInteger0(xq) = v0 & $i(v2) & ( ~
% 19.81/3.49 | (v1 = 0) | ~ (v0 = 0) | v2 = all_41_1))
% 19.81/3.49 |
% 19.81/3.49 | GROUND_INST: instantiating (mIntMult) with xq, all_44_0, all_41_1, simplifying
% 19.81/3.49 | with (9), (30), (32) gives:
% 19.81/3.49 | (38) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aInteger0(all_44_0) = v1
% 19.81/3.49 | & aInteger0(all_41_1) = v2 & aInteger0(xq) = v0 & ( ~ (v1 = 0) | ~
% 19.81/3.49 | (v0 = 0) | v2 = 0))
% 19.81/3.49 |
% 19.81/3.49 | GROUND_INST: instantiating (2) with xc, xb, xq, simplifying with (9), (10),
% 19.81/3.49 | (11), (23) gives:
% 19.81/3.49 | (39) xq = sz00 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any]
% 19.81/3.49 | : (sdteqdtlpzmzozddtrp0(xb, xc, xq) = v3 & aInteger0(xc) = v0 &
% 19.81/3.49 | aInteger0(xb) = v1 & aInteger0(xq) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0)
% 19.81/3.49 | | ~ (v0 = 0) | v3 = 0))
% 19.81/3.49 |
% 19.81/3.49 | GROUND_INST: instantiating (27) with xb, all_41_4, simplifying with (10), (24)
% 19.81/3.49 | gives:
% 19.81/3.49 | (40) all_41_4 = 0 | ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3:
% 19.81/3.49 | any] : (sdteqdtlpzmzozddtrp0(xb, xa, xq) = v3 & aDivisorOf0(xq, v1)
% 19.81/3.49 | = v2 & sdtpldt0(xb, all_41_5) = v1 & aInteger0(xb) = v0 & $i(v1) & (
% 19.81/3.49 | ~ (v0 = 0) | ( ~ (v3 = 0) & ~ (v2 = 0) & ! [v4: $i] : ( ~
% 19.81/3.49 | (sdtasdt0(xq, v4) = v1) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 =
% 19.81/3.49 | 0) & aInteger0(v4) = v5)))))
% 19.81/3.49 |
% 19.81/3.49 | GROUND_INST: instantiating (26) with xc, simplifying with (11), (25) gives:
% 19.81/3.49 | (41) ? [v0: $i] : (sdteqdtlpzmzozddtrp0(xc, xa, xq) = 0 & aDivisorOf0(xq,
% 19.81/3.49 | v0) = 0 & sdtpldt0(xc, all_41_5) = v0 & aInteger0(xc) = 0 & $i(v0)
% 19.81/3.49 | & ? [v1: $i] : (sdtasdt0(xq, v1) = v0 & aInteger0(v1) = 0 &
% 19.81/3.49 | $i(v1)))
% 19.81/3.49 |
% 19.81/3.49 | DELTA: instantiating (34) with fresh symbols all_64_0, all_64_1 gives:
% 19.81/3.49 | (42) aInteger0(all_41_2) = all_64_0 & aInteger0(xb) = all_64_1 & ( ~
% 19.81/3.49 | (all_64_1 = 0) | all_64_0 = 0)
% 19.81/3.49 |
% 19.81/3.49 | ALPHA: (42) implies:
% 19.81/3.49 | (43) aInteger0(xb) = all_64_1
% 19.81/3.49 |
% 19.81/3.49 | DELTA: instantiating (33) with fresh symbols all_66_0, all_66_1 gives:
% 19.81/3.49 | (44) aInteger0(all_41_5) = all_66_0 & aInteger0(xa) = all_66_1 & ( ~
% 19.81/3.49 | (all_66_1 = 0) | all_66_0 = 0)
% 19.81/3.49 |
% 19.81/3.49 | ALPHA: (44) implies:
% 19.81/3.49 | (45) aInteger0(xa) = all_66_1
% 19.81/3.49 |
% 19.81/3.49 | DELTA: instantiating (38) with fresh symbols all_70_0, all_70_1, all_70_2
% 19.81/3.49 | gives:
% 19.81/3.49 | (46) aInteger0(all_44_0) = all_70_1 & aInteger0(all_41_1) = all_70_0 &
% 19.81/3.49 | aInteger0(xq) = all_70_2 & ( ~ (all_70_1 = 0) | ~ (all_70_2 = 0) |
% 19.81/3.49 | all_70_0 = 0)
% 19.81/3.49 |
% 19.81/3.49 | ALPHA: (46) implies:
% 19.81/3.49 | (47) aInteger0(xq) = all_70_2
% 19.81/3.49 | (48) aInteger0(all_41_1) = all_70_0
% 19.81/3.49 | (49) aInteger0(all_44_0) = all_70_1
% 19.81/3.50 | (50) ~ (all_70_1 = 0) | ~ (all_70_2 = 0) | all_70_0 = 0
% 19.81/3.50 |
% 19.81/3.50 | DELTA: instantiating (36) with fresh symbols all_72_0, all_72_1, all_72_2
% 19.81/3.50 | gives:
% 19.81/3.50 | (51) aInteger0(all_41_1) = all_72_0 & aInteger0(all_41_2) = all_72_1 &
% 19.81/3.50 | aInteger0(xc) = all_72_2 & ( ~ (all_72_1 = 0) | ~ (all_72_2 = 0) |
% 19.81/3.50 | all_72_0 = 0)
% 19.81/3.50 |
% 19.81/3.50 | ALPHA: (51) implies:
% 19.81/3.50 | (52) aInteger0(xc) = all_72_2
% 19.81/3.50 | (53) aInteger0(all_41_1) = all_72_0
% 19.81/3.50 |
% 19.81/3.50 | DELTA: instantiating (37) with fresh symbols all_74_0, all_74_1, all_74_2
% 19.81/3.50 | gives:
% 19.81/3.50 | (54) sdtasdt0(all_44_0, xq) = all_74_0 & aInteger0(all_44_0) = all_74_1 &
% 19.81/3.50 | aInteger0(xq) = all_74_2 & $i(all_74_0) & ( ~ (all_74_1 = 0) | ~
% 19.81/3.50 | (all_74_2 = 0) | all_74_0 = all_41_1)
% 19.81/3.50 |
% 19.81/3.50 | ALPHA: (54) implies:
% 19.81/3.50 | (55) aInteger0(xq) = all_74_2
% 19.81/3.50 | (56) aInteger0(all_44_0) = all_74_1
% 19.81/3.50 |
% 19.81/3.50 | DELTA: instantiating (35) with fresh symbols all_76_0, all_76_1, all_76_2
% 19.81/3.50 | gives:
% 19.81/3.50 | (57) sdtpldt0(all_41_2, xc) = all_76_0 & aInteger0(all_41_2) = all_76_1 &
% 19.81/3.50 | aInteger0(xc) = all_76_2 & $i(all_76_0) & ( ~ (all_76_1 = 0) | ~
% 19.81/3.50 | (all_76_2 = 0) | all_76_0 = all_41_1)
% 19.81/3.50 |
% 19.81/3.50 | ALPHA: (57) implies:
% 19.81/3.50 | (58) aInteger0(xc) = all_76_2
% 19.81/3.50 |
% 19.81/3.50 | DELTA: instantiating (41) with fresh symbol all_78_0 gives:
% 19.81/3.50 | (59) sdteqdtlpzmzozddtrp0(xc, xa, xq) = 0 & aDivisorOf0(xq, all_78_0) = 0 &
% 19.81/3.50 | sdtpldt0(xc, all_41_5) = all_78_0 & aInteger0(xc) = 0 & $i(all_78_0) &
% 19.81/3.50 | ? [v0: $i] : (sdtasdt0(xq, v0) = all_78_0 & aInteger0(v0) = 0 &
% 19.81/3.50 | $i(v0))
% 19.81/3.50 |
% 19.81/3.50 | ALPHA: (59) implies:
% 19.81/3.50 | (60) aInteger0(xc) = 0
% 19.81/3.50 | (61) sdteqdtlpzmzozddtrp0(xc, xa, xq) = 0
% 19.81/3.50 |
% 19.81/3.50 | BETA: splitting (39) gives:
% 19.81/3.50 |
% 19.81/3.50 | Case 1:
% 19.81/3.50 | |
% 19.81/3.50 | | (62) xq = sz00
% 19.81/3.50 | |
% 19.81/3.50 | | REDUCE: (4), (62) imply:
% 19.81/3.50 | | (63) $false
% 19.81/3.50 | |
% 19.81/3.50 | | CLOSE: (63) is inconsistent.
% 19.81/3.50 | |
% 19.81/3.50 | Case 2:
% 19.81/3.50 | |
% 19.81/3.50 | | (64) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 19.81/3.50 | | (sdteqdtlpzmzozddtrp0(xb, xc, xq) = v3 & aInteger0(xc) = v0 &
% 19.81/3.50 | | aInteger0(xb) = v1 & aInteger0(xq) = v2 & ( ~ (v2 = 0) | ~ (v1 =
% 19.81/3.50 | | 0) | ~ (v0 = 0) | v3 = 0))
% 19.81/3.50 | |
% 19.81/3.50 | | DELTA: instantiating (64) with fresh symbols all_86_0, all_86_1, all_86_2,
% 19.81/3.50 | | all_86_3 gives:
% 19.81/3.50 | | (65) sdteqdtlpzmzozddtrp0(xb, xc, xq) = all_86_0 & aInteger0(xc) =
% 19.81/3.50 | | all_86_3 & aInteger0(xb) = all_86_2 & aInteger0(xq) = all_86_1 & ( ~
% 19.81/3.50 | | (all_86_1 = 0) | ~ (all_86_2 = 0) | ~ (all_86_3 = 0) | all_86_0
% 19.81/3.50 | | = 0)
% 19.81/3.50 | |
% 19.81/3.50 | | ALPHA: (65) implies:
% 19.81/3.50 | | (66) aInteger0(xq) = all_86_1
% 19.81/3.50 | | (67) aInteger0(xb) = all_86_2
% 19.81/3.50 | | (68) aInteger0(xc) = all_86_3
% 19.81/3.50 | | (69) sdteqdtlpzmzozddtrp0(xb, xc, xq) = all_86_0
% 19.81/3.50 | | (70) ~ (all_86_1 = 0) | ~ (all_86_2 = 0) | ~ (all_86_3 = 0) | all_86_0
% 19.81/3.50 | | = 0
% 19.81/3.50 | |
% 19.81/3.50 | | BETA: splitting (40) gives:
% 19.81/3.50 | |
% 19.81/3.50 | | Case 1:
% 19.81/3.50 | | |
% 19.81/3.50 | | | (71) all_41_4 = 0
% 19.81/3.50 | | |
% 19.81/3.50 | | | REDUCE: (16), (71) imply:
% 19.81/3.50 | | | (72) $false
% 19.81/3.50 | | |
% 19.81/3.50 | | | CLOSE: (72) is inconsistent.
% 19.81/3.50 | | |
% 19.81/3.50 | | Case 2:
% 19.81/3.50 | | |
% 19.81/3.50 | | | (73) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: any] :
% 19.81/3.50 | | | (sdteqdtlpzmzozddtrp0(xb, xa, xq) = v3 & aDivisorOf0(xq, v1) = v2
% 19.81/3.50 | | | & sdtpldt0(xb, all_41_5) = v1 & aInteger0(xb) = v0 & $i(v1) & (
% 19.81/3.50 | | | ~ (v0 = 0) | ( ~ (v3 = 0) & ~ (v2 = 0) & ! [v4: $i] : ( ~
% 19.81/3.50 | | | (sdtasdt0(xq, v4) = v1) | ~ $i(v4) | ? [v5: int] : ( ~
% 19.81/3.50 | | | (v5 = 0) & aInteger0(v4) = v5)))))
% 19.81/3.50 | | |
% 19.81/3.50 | | | DELTA: instantiating (73) with fresh symbols all_91_0, all_91_1, all_91_2,
% 19.81/3.50 | | | all_91_3 gives:
% 19.81/3.51 | | | (74) sdteqdtlpzmzozddtrp0(xb, xa, xq) = all_91_0 & aDivisorOf0(xq,
% 19.81/3.51 | | | all_91_2) = all_91_1 & sdtpldt0(xb, all_41_5) = all_91_2 &
% 19.81/3.51 | | | aInteger0(xb) = all_91_3 & $i(all_91_2) & ( ~ (all_91_3 = 0) | ( ~
% 19.81/3.51 | | | (all_91_0 = 0) & ~ (all_91_1 = 0) & ! [v0: $i] : ( ~
% 19.81/3.51 | | | (sdtasdt0(xq, v0) = all_91_2) | ~ $i(v0) | ? [v1: int] : (
% 19.81/3.51 | | | ~ (v1 = 0) & aInteger0(v0) = v1))))
% 19.81/3.51 | | |
% 19.81/3.51 | | | ALPHA: (74) implies:
% 19.81/3.51 | | | (75) aInteger0(xb) = all_91_3
% 19.81/3.51 | | | (76) sdteqdtlpzmzozddtrp0(xb, xa, xq) = all_91_0
% 19.81/3.51 | | | (77) ~ (all_91_3 = 0) | ( ~ (all_91_0 = 0) & ~ (all_91_1 = 0) & !
% 19.81/3.51 | | | [v0: $i] : ( ~ (sdtasdt0(xq, v0) = all_91_2) | ~ $i(v0) | ?
% 19.81/3.51 | | | [v1: int] : ( ~ (v1 = 0) & aInteger0(v0) = v1)))
% 19.81/3.51 | | |
% 19.81/3.51 | | | GROUND_INST: instantiating (13) with 0, all_66_1, xa, simplifying with
% 19.81/3.51 | | | (5), (45) gives:
% 19.81/3.51 | | | (78) all_66_1 = 0
% 19.81/3.51 | | |
% 19.81/3.51 | | | GROUND_INST: instantiating (13) with 0, all_74_2, xq, simplifying with
% 19.81/3.51 | | | (6), (55) gives:
% 19.81/3.51 | | | (79) all_74_2 = 0
% 19.81/3.51 | | |
% 19.81/3.51 | | | GROUND_INST: instantiating (13) with all_74_2, all_86_1, xq, simplifying
% 19.81/3.51 | | | with (55), (66) gives:
% 19.81/3.51 | | | (80) all_86_1 = all_74_2
% 19.81/3.51 | | |
% 19.81/3.51 | | | GROUND_INST: instantiating (13) with all_70_2, all_86_1, xq, simplifying
% 19.81/3.51 | | | with (47), (66) gives:
% 19.81/3.51 | | | (81) all_86_1 = all_70_2
% 19.81/3.51 | | |
% 19.81/3.51 | | | GROUND_INST: instantiating (13) with all_64_1, all_86_2, xb, simplifying
% 19.81/3.51 | | | with (43), (67) gives:
% 19.81/3.51 | | | (82) all_86_2 = all_64_1
% 19.81/3.51 | | |
% 19.81/3.51 | | | GROUND_INST: instantiating (13) with 0, all_91_3, xb, simplifying with
% 19.81/3.51 | | | (7), (75) gives:
% 19.81/3.51 | | | (83) all_91_3 = 0
% 19.81/3.51 | | |
% 19.81/3.51 | | | GROUND_INST: instantiating (13) with all_86_2, all_91_3, xb, simplifying
% 19.81/3.51 | | | with (67), (75) gives:
% 19.81/3.51 | | | (84) all_91_3 = all_86_2
% 19.81/3.51 | | |
% 19.81/3.51 | | | GROUND_INST: instantiating (13) with 0, all_86_3, xc, simplifying with
% 19.81/3.51 | | | (60), (68) gives:
% 19.81/3.51 | | | (85) all_86_3 = 0
% 19.81/3.51 | | |
% 19.81/3.51 | | | GROUND_INST: instantiating (13) with all_76_2, all_86_3, xc, simplifying
% 19.81/3.51 | | | with (58), (68) gives:
% 19.81/3.51 | | | (86) all_86_3 = all_76_2
% 19.81/3.51 | | |
% 19.81/3.51 | | | GROUND_INST: instantiating (13) with all_72_2, all_86_3, xc, simplifying
% 19.81/3.51 | | | with (52), (68) gives:
% 19.81/3.51 | | | (87) all_86_3 = all_72_2
% 19.81/3.51 | | |
% 19.81/3.51 | | | GROUND_INST: instantiating (13) with all_70_0, all_72_0, all_41_1,
% 19.81/3.51 | | | simplifying with (48), (53) gives:
% 19.81/3.51 | | | (88) all_72_0 = all_70_0
% 19.81/3.51 | | |
% 19.81/3.51 | | | GROUND_INST: instantiating (13) with 0, all_74_1, all_44_0, simplifying
% 19.81/3.51 | | | with (31), (56) gives:
% 19.81/3.51 | | | (89) all_74_1 = 0
% 19.81/3.51 | | |
% 19.81/3.51 | | | GROUND_INST: instantiating (13) with all_70_1, all_74_1, all_44_0,
% 19.81/3.51 | | | simplifying with (49), (56) gives:
% 19.81/3.51 | | | (90) all_74_1 = all_70_1
% 19.81/3.51 | | |
% 19.81/3.51 | | | COMBINE_EQS: (83), (84) imply:
% 19.81/3.51 | | | (91) all_86_2 = 0
% 19.81/3.51 | | |
% 19.81/3.51 | | | SIMP: (91) implies:
% 19.81/3.51 | | | (92) all_86_2 = 0
% 19.81/3.51 | | |
% 19.81/3.51 | | | COMBINE_EQS: (80), (81) imply:
% 19.81/3.51 | | | (93) all_74_2 = all_70_2
% 19.81/3.51 | | |
% 19.81/3.51 | | | SIMP: (93) implies:
% 19.81/3.51 | | | (94) all_74_2 = all_70_2
% 19.81/3.51 | | |
% 19.81/3.51 | | | COMBINE_EQS: (82), (92) imply:
% 19.81/3.51 | | | (95) all_64_1 = 0
% 19.81/3.51 | | |
% 19.81/3.51 | | | SIMP: (95) implies:
% 19.81/3.51 | | | (96) all_64_1 = 0
% 19.81/3.51 | | |
% 19.81/3.51 | | | COMBINE_EQS: (86), (87) imply:
% 19.81/3.51 | | | (97) all_76_2 = all_72_2
% 19.81/3.51 | | |
% 19.81/3.51 | | | COMBINE_EQS: (85), (86) imply:
% 19.81/3.51 | | | (98) all_76_2 = 0
% 19.81/3.51 | | |
% 19.81/3.51 | | | COMBINE_EQS: (97), (98) imply:
% 19.81/3.51 | | | (99) all_72_2 = 0
% 19.81/3.51 | | |
% 19.81/3.51 | | | SIMP: (99) implies:
% 19.81/3.51 | | | (100) all_72_2 = 0
% 19.81/3.51 | | |
% 19.81/3.51 | | | COMBINE_EQS: (89), (90) imply:
% 19.81/3.51 | | | (101) all_70_1 = 0
% 19.81/3.51 | | |
% 19.81/3.51 | | | COMBINE_EQS: (79), (94) imply:
% 19.81/3.51 | | | (102) all_70_2 = 0
% 19.81/3.51 | | |
% 19.81/3.51 | | | COMBINE_EQS: (81), (102) imply:
% 19.81/3.51 | | | (103) all_86_1 = 0
% 19.81/3.51 | | |
% 19.81/3.51 | | | BETA: splitting (50) gives:
% 19.81/3.51 | | |
% 19.81/3.51 | | | Case 1:
% 19.81/3.51 | | | |
% 19.81/3.51 | | | | (104) ~ (all_70_1 = 0)
% 19.81/3.51 | | | |
% 19.81/3.51 | | | | REDUCE: (101), (104) imply:
% 19.81/3.51 | | | | (105) $false
% 19.81/3.51 | | | |
% 19.81/3.51 | | | | CLOSE: (105) is inconsistent.
% 19.81/3.51 | | | |
% 19.81/3.51 | | | Case 2:
% 19.81/3.51 | | | |
% 19.81/3.51 | | | | (106) ~ (all_70_2 = 0) | all_70_0 = 0
% 19.81/3.51 | | | |
% 19.81/3.51 | | | | BETA: splitting (106) gives:
% 19.81/3.51 | | | |
% 19.81/3.51 | | | | Case 1:
% 19.81/3.51 | | | | |
% 19.81/3.51 | | | | | (107) ~ (all_70_2 = 0)
% 19.81/3.51 | | | | |
% 19.81/3.51 | | | | | REDUCE: (102), (107) imply:
% 19.81/3.51 | | | | | (108) $false
% 19.81/3.51 | | | | |
% 19.81/3.51 | | | | | CLOSE: (108) is inconsistent.
% 19.81/3.51 | | | | |
% 19.81/3.51 | | | | Case 2:
% 19.81/3.51 | | | | |
% 19.81/3.51 | | | | | (109) all_70_0 = 0
% 19.81/3.51 | | | | |
% 19.81/3.51 | | | | | REDUCE: (48), (109) imply:
% 19.81/3.51 | | | | | (110) aInteger0(all_41_1) = 0
% 19.81/3.51 | | | | |
% 19.81/3.51 | | | | | BETA: splitting (77) gives:
% 19.81/3.51 | | | | |
% 19.81/3.51 | | | | | Case 1:
% 19.81/3.51 | | | | | |
% 19.81/3.51 | | | | | | (111) ~ (all_91_3 = 0)
% 19.81/3.51 | | | | | |
% 19.81/3.51 | | | | | | REDUCE: (83), (111) imply:
% 19.81/3.51 | | | | | | (112) $false
% 19.81/3.51 | | | | | |
% 19.81/3.51 | | | | | | CLOSE: (112) is inconsistent.
% 19.81/3.51 | | | | | |
% 19.81/3.51 | | | | | Case 2:
% 19.81/3.51 | | | | | |
% 19.81/3.51 | | | | | | (113) ~ (all_91_0 = 0) & ~ (all_91_1 = 0) & ! [v0: $i] : ( ~
% 19.81/3.51 | | | | | | (sdtasdt0(xq, v0) = all_91_2) | ~ $i(v0) | ? [v1: int]
% 19.81/3.51 | | | | | | : ( ~ (v1 = 0) & aInteger0(v0) = v1))
% 19.81/3.51 | | | | | |
% 19.81/3.51 | | | | | | ALPHA: (113) implies:
% 19.81/3.51 | | | | | | (114) ~ (all_91_0 = 0)
% 19.81/3.51 | | | | | |
% 19.81/3.51 | | | | | | BETA: splitting (70) gives:
% 19.81/3.51 | | | | | |
% 19.81/3.51 | | | | | | Case 1:
% 19.81/3.51 | | | | | | |
% 19.81/3.51 | | | | | | | (115) ~ (all_86_1 = 0)
% 19.81/3.51 | | | | | | |
% 19.81/3.51 | | | | | | | REDUCE: (103), (115) imply:
% 19.81/3.51 | | | | | | | (116) $false
% 19.81/3.51 | | | | | | |
% 19.81/3.51 | | | | | | | CLOSE: (116) is inconsistent.
% 19.81/3.51 | | | | | | |
% 19.81/3.51 | | | | | | Case 2:
% 19.81/3.51 | | | | | | |
% 19.81/3.52 | | | | | | | (117) ~ (all_86_2 = 0) | ~ (all_86_3 = 0) | all_86_0 = 0
% 19.81/3.52 | | | | | | |
% 19.81/3.52 | | | | | | | BETA: splitting (117) gives:
% 19.81/3.52 | | | | | | |
% 19.81/3.52 | | | | | | | Case 1:
% 19.81/3.52 | | | | | | | |
% 19.81/3.52 | | | | | | | | (118) ~ (all_86_2 = 0)
% 19.81/3.52 | | | | | | | |
% 19.81/3.52 | | | | | | | | REDUCE: (92), (118) imply:
% 19.81/3.52 | | | | | | | | (119) $false
% 19.81/3.52 | | | | | | | |
% 19.81/3.52 | | | | | | | | CLOSE: (119) is inconsistent.
% 19.81/3.52 | | | | | | | |
% 19.81/3.52 | | | | | | | Case 2:
% 19.81/3.52 | | | | | | | |
% 19.81/3.52 | | | | | | | | (120) ~ (all_86_3 = 0) | all_86_0 = 0
% 19.81/3.52 | | | | | | | |
% 19.81/3.52 | | | | | | | | BETA: splitting (120) gives:
% 19.81/3.52 | | | | | | | |
% 19.81/3.52 | | | | | | | | Case 1:
% 19.81/3.52 | | | | | | | | |
% 19.81/3.52 | | | | | | | | | (121) ~ (all_86_3 = 0)
% 19.81/3.52 | | | | | | | | |
% 19.81/3.52 | | | | | | | | | REDUCE: (85), (121) imply:
% 19.81/3.52 | | | | | | | | | (122) $false
% 19.81/3.52 | | | | | | | | |
% 19.81/3.52 | | | | | | | | | CLOSE: (122) is inconsistent.
% 19.81/3.52 | | | | | | | | |
% 19.81/3.52 | | | | | | | | Case 2:
% 19.81/3.52 | | | | | | | | |
% 19.81/3.52 | | | | | | | | | (123) all_86_0 = 0
% 19.81/3.52 | | | | | | | | |
% 19.81/3.52 | | | | | | | | | REDUCE: (69), (123) imply:
% 19.81/3.52 | | | | | | | | | (124) sdteqdtlpzmzozddtrp0(xb, xc, xq) = 0
% 19.81/3.52 | | | | | | | | |
% 19.81/3.52 | | | | | | | | | GROUND_INST: instantiating (1) with all_41_1, simplifying with
% 19.81/3.52 | | | | | | | | | (18), (110) gives:
% 19.81/3.52 | | | | | | | | | (125) ! [v0: $i] : ! [v1: int] : (v1 = 0 | v0 = sz00 | ~
% 19.81/3.52 | | | | | | | | | (aDivisorOf0(v0, all_41_1) = v1) | ~ $i(v0) | ?
% 19.81/3.52 | | | | | | | | | [v2: int] : ( ~ (v2 = 0) & aInteger0(v0) = v2) | !
% 19.81/3.52 | | | | | | | | | [v2: $i] : ( ~ (sdtasdt0(v0, v2) = all_41_1) | ~
% 19.81/3.52 | | | | | | | | | $i(v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 19.81/3.52 | | | | | | | | | aInteger0(v2) = v3))) & ! [v0: $i] : ( ~
% 19.81/3.52 | | | | | | | | | (aDivisorOf0(v0, all_41_1) = 0) | ~ $i(v0) | ( ~
% 19.81/3.52 | | | | | | | | | (v0 = sz00) & aInteger0(v0) = 0 & ? [v1: $i] :
% 19.81/3.52 | | | | | | | | | (sdtasdt0(v0, v1) = all_41_1 & aInteger0(v1) = 0
% 19.81/3.52 | | | | | | | | | & $i(v1))))
% 19.81/3.52 | | | | | | | | |
% 19.81/3.52 | | | | | | | | | ALPHA: (125) implies:
% 19.81/3.52 | | | | | | | | | (126) ! [v0: $i] : ( ~ (aDivisorOf0(v0, all_41_1) = 0) |
% 19.81/3.52 | | | | | | | | | ~ $i(v0) | ( ~ (v0 = sz00) & aInteger0(v0) = 0 & ?
% 19.81/3.52 | | | | | | | | | [v1: $i] : (sdtasdt0(v0, v1) = all_41_1 &
% 19.81/3.52 | | | | | | | | | aInteger0(v1) = 0 & $i(v1))))
% 19.81/3.52 | | | | | | | | |
% 19.81/3.52 | | | | | | | | | GROUND_INST: instantiating (3) with xb, xc, xq, xa, all_91_0,
% 19.81/3.52 | | | | | | | | | simplifying with (8), (9), (10), (11), (76), (124)
% 19.81/3.52 | | | | | | | | | gives:
% 19.81/3.52 | | | | | | | | | (127) all_91_0 = 0 | xq = sz00 | ? [v0: any] : ? [v1:
% 19.81/3.52 | | | | | | | | | any] : ? [v2: any] : ? [v3: any] : ? [v4: any] :
% 19.81/3.52 | | | | | | | | | (sdteqdtlpzmzozddtrp0(xc, xa, xq) = v4 &
% 19.81/3.52 | | | | | | | | | aInteger0(xc) = v1 & aInteger0(xb) = v0 &
% 19.81/3.52 | | | | | | | | | aInteger0(xq) = v2 & aInteger0(xa) = v3 & ( ~ (v4 =
% 19.81/3.52 | | | | | | | | | 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) |
% 19.81/3.52 | | | | | | | | | ~ (v0 = 0)))
% 19.81/3.52 | | | | | | | | |
% 19.81/3.52 | | | | | | | | | GROUND_INST: instantiating (126) with xq, simplifying with (9),
% 19.81/3.52 | | | | | | | | | (22) gives:
% 19.81/3.52 | | | | | | | | | (128) ~ (xq = sz00) & aInteger0(xq) = 0 & ? [v0: $i] :
% 19.81/3.52 | | | | | | | | | (sdtasdt0(xq, v0) = all_41_1 & aInteger0(v0) = 0 &
% 19.81/3.52 | | | | | | | | | $i(v0))
% 19.81/3.52 | | | | | | | | |
% 19.81/3.52 | | | | | | | | | BETA: splitting (127) gives:
% 19.81/3.52 | | | | | | | | |
% 19.81/3.52 | | | | | | | | | Case 1:
% 19.81/3.52 | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | (129) xq = sz00
% 19.81/3.52 | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | REDUCE: (4), (129) imply:
% 19.81/3.52 | | | | | | | | | | (130) $false
% 19.81/3.52 | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | CLOSE: (130) is inconsistent.
% 19.81/3.52 | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | Case 2:
% 19.81/3.52 | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | (131) all_91_0 = 0 | ? [v0: any] : ? [v1: any] : ?
% 19.81/3.52 | | | | | | | | | | [v2: any] : ? [v3: any] : ? [v4: any] :
% 19.81/3.52 | | | | | | | | | | (sdteqdtlpzmzozddtrp0(xc, xa, xq) = v4 &
% 19.81/3.52 | | | | | | | | | | aInteger0(xc) = v1 & aInteger0(xb) = v0 &
% 19.81/3.52 | | | | | | | | | | aInteger0(xq) = v2 & aInteger0(xa) = v3 & ( ~ (v4
% 19.81/3.52 | | | | | | | | | | = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 =
% 19.81/3.52 | | | | | | | | | | 0) | ~ (v0 = 0)))
% 19.81/3.52 | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | BETA: splitting (131) gives:
% 19.81/3.52 | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | Case 1:
% 19.81/3.52 | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | (132) all_91_0 = 0
% 19.81/3.52 | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | REDUCE: (114), (132) imply:
% 19.81/3.52 | | | | | | | | | | | (133) $false
% 19.81/3.52 | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | CLOSE: (133) is inconsistent.
% 19.81/3.52 | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | Case 2:
% 19.81/3.52 | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | (134) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 19.81/3.52 | | | | | | | | | | | [v3: any] : ? [v4: any] :
% 19.81/3.52 | | | | | | | | | | | (sdteqdtlpzmzozddtrp0(xc, xa, xq) = v4 &
% 19.81/3.52 | | | | | | | | | | | aInteger0(xc) = v1 & aInteger0(xb) = v0 &
% 19.81/3.52 | | | | | | | | | | | aInteger0(xq) = v2 & aInteger0(xa) = v3 & ( ~
% 19.81/3.52 | | | | | | | | | | | (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1
% 19.81/3.52 | | | | | | | | | | | = 0) | ~ (v0 = 0)))
% 19.81/3.52 | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | DELTA: instantiating (134) with fresh symbols all_257_0,
% 19.81/3.52 | | | | | | | | | | | all_257_1, all_257_2, all_257_3, all_257_4 gives:
% 19.81/3.52 | | | | | | | | | | | (135) sdteqdtlpzmzozddtrp0(xc, xa, xq) = all_257_0 &
% 19.81/3.52 | | | | | | | | | | | aInteger0(xc) = all_257_3 & aInteger0(xb) =
% 19.81/3.52 | | | | | | | | | | | all_257_4 & aInteger0(xq) = all_257_2 &
% 19.81/3.52 | | | | | | | | | | | aInteger0(xa) = all_257_1 & ( ~ (all_257_0 = 0) |
% 19.81/3.52 | | | | | | | | | | | ~ (all_257_1 = 0) | ~ (all_257_2 = 0) | ~
% 19.81/3.52 | | | | | | | | | | | (all_257_3 = 0) | ~ (all_257_4 = 0))
% 19.81/3.52 | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | ALPHA: (135) implies:
% 19.81/3.52 | | | | | | | | | | | (136) aInteger0(xa) = all_257_1
% 19.81/3.52 | | | | | | | | | | | (137) aInteger0(xq) = all_257_2
% 19.81/3.52 | | | | | | | | | | | (138) aInteger0(xb) = all_257_4
% 19.81/3.52 | | | | | | | | | | | (139) aInteger0(xc) = all_257_3
% 19.81/3.52 | | | | | | | | | | | (140) sdteqdtlpzmzozddtrp0(xc, xa, xq) = all_257_0
% 19.81/3.52 | | | | | | | | | | | (141) ~ (all_257_0 = 0) | ~ (all_257_1 = 0) | ~
% 19.81/3.52 | | | | | | | | | | | (all_257_2 = 0) | ~ (all_257_3 = 0) | ~
% 19.81/3.52 | | | | | | | | | | | (all_257_4 = 0)
% 19.81/3.52 | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_257_1, xa,
% 19.81/3.52 | | | | | | | | | | | simplifying with (5), (136) gives:
% 19.81/3.52 | | | | | | | | | | | (142) all_257_1 = 0
% 19.81/3.52 | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_257_2, xq,
% 19.81/3.52 | | | | | | | | | | | simplifying with (6), (137) gives:
% 19.81/3.52 | | | | | | | | | | | (143) all_257_2 = 0
% 19.81/3.52 | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_257_4, xb,
% 19.81/3.52 | | | | | | | | | | | simplifying with (7), (138) gives:
% 19.81/3.52 | | | | | | | | | | | (144) all_257_4 = 0
% 19.81/3.52 | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_257_3, xc,
% 19.81/3.52 | | | | | | | | | | | simplifying with (60), (139) gives:
% 19.81/3.52 | | | | | | | | | | | (145) all_257_3 = 0
% 19.81/3.52 | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_257_0, xq, xa, xc,
% 19.81/3.52 | | | | | | | | | | | simplifying with (61), (140) gives:
% 19.81/3.52 | | | | | | | | | | | (146) all_257_0 = 0
% 19.81/3.52 | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | BETA: splitting (141) gives:
% 19.81/3.52 | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | Case 1:
% 19.81/3.52 | | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | | (147) ~ (all_257_0 = 0)
% 19.81/3.52 | | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | | REDUCE: (146), (147) imply:
% 19.81/3.52 | | | | | | | | | | | | (148) $false
% 19.81/3.52 | | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | | CLOSE: (148) is inconsistent.
% 19.81/3.52 | | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | Case 2:
% 19.81/3.52 | | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | | (149) ~ (all_257_1 = 0) | ~ (all_257_2 = 0) | ~
% 19.81/3.52 | | | | | | | | | | | | (all_257_3 = 0) | ~ (all_257_4 = 0)
% 19.81/3.52 | | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | | BETA: splitting (149) gives:
% 19.81/3.52 | | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | | Case 1:
% 19.81/3.52 | | | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | | | (150) ~ (all_257_1 = 0)
% 19.81/3.52 | | | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | | | REDUCE: (142), (150) imply:
% 19.81/3.52 | | | | | | | | | | | | | (151) $false
% 19.81/3.52 | | | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | | | CLOSE: (151) is inconsistent.
% 19.81/3.52 | | | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | | Case 2:
% 19.81/3.52 | | | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | | | (152) ~ (all_257_2 = 0) | ~ (all_257_3 = 0) | ~
% 19.81/3.52 | | | | | | | | | | | | | (all_257_4 = 0)
% 19.81/3.52 | | | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | | | BETA: splitting (152) gives:
% 19.81/3.52 | | | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | | | Case 1:
% 19.81/3.52 | | | | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | | | | (153) ~ (all_257_2 = 0)
% 19.81/3.52 | | | | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | | | | REDUCE: (143), (153) imply:
% 19.81/3.52 | | | | | | | | | | | | | | (154) $false
% 19.81/3.52 | | | | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | | | | CLOSE: (154) is inconsistent.
% 19.81/3.52 | | | | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | | | Case 2:
% 19.81/3.52 | | | | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | | | | (155) ~ (all_257_3 = 0) | ~ (all_257_4 = 0)
% 19.81/3.52 | | | | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 19.81/3.52 | | | | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | | | | Case 1:
% 19.81/3.52 | | | | | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | | | | | (156) ~ (all_257_3 = 0)
% 19.81/3.52 | | | | | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | | | | | REDUCE: (145), (156) imply:
% 19.81/3.52 | | | | | | | | | | | | | | | (157) $false
% 19.81/3.52 | | | | | | | | | | | | | | |
% 19.81/3.52 | | | | | | | | | | | | | | | CLOSE: (157) is inconsistent.
% 19.81/3.52 | | | | | | | | | | | | | | |
% 19.81/3.53 | | | | | | | | | | | | | | Case 2:
% 19.81/3.53 | | | | | | | | | | | | | | |
% 19.81/3.53 | | | | | | | | | | | | | | | (158) ~ (all_257_4 = 0)
% 19.81/3.53 | | | | | | | | | | | | | | |
% 19.81/3.53 | | | | | | | | | | | | | | | REDUCE: (144), (158) imply:
% 19.81/3.53 | | | | | | | | | | | | | | | (159) $false
% 19.81/3.53 | | | | | | | | | | | | | | |
% 19.81/3.53 | | | | | | | | | | | | | | | CLOSE: (159) is inconsistent.
% 19.81/3.53 | | | | | | | | | | | | | | |
% 19.81/3.53 | | | | | | | | | | | | | | End of split
% 19.81/3.53 | | | | | | | | | | | | | |
% 19.81/3.53 | | | | | | | | | | | | | End of split
% 19.81/3.53 | | | | | | | | | | | | |
% 19.81/3.53 | | | | | | | | | | | | End of split
% 19.81/3.53 | | | | | | | | | | | |
% 19.81/3.53 | | | | | | | | | | | End of split
% 19.81/3.53 | | | | | | | | | | |
% 19.81/3.53 | | | | | | | | | | End of split
% 19.81/3.53 | | | | | | | | | |
% 19.81/3.53 | | | | | | | | | End of split
% 19.81/3.53 | | | | | | | | |
% 19.81/3.53 | | | | | | | | End of split
% 19.81/3.53 | | | | | | | |
% 19.81/3.53 | | | | | | | End of split
% 19.81/3.53 | | | | | | |
% 19.81/3.53 | | | | | | End of split
% 19.81/3.53 | | | | | |
% 19.81/3.53 | | | | | End of split
% 19.81/3.53 | | | | |
% 19.81/3.53 | | | | End of split
% 19.81/3.53 | | | |
% 19.81/3.53 | | | End of split
% 19.81/3.53 | | |
% 19.81/3.53 | | End of split
% 19.81/3.53 | |
% 19.81/3.53 | End of split
% 19.81/3.53 |
% 19.81/3.53 End of proof
% 19.81/3.53 % SZS output end Proof for theBenchmark
% 19.81/3.53
% 19.81/3.53 2925ms
%------------------------------------------------------------------------------