TSTP Solution File: RNG099+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG099+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n010.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 13:57:51 EDT 2023
% Result : Theorem 13.62s 2.70s
% Output : Proof 41.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG099+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 02:35:19 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.60 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.88/1.13 Prover 1: Preprocessing ...
% 2.88/1.13 Prover 4: Preprocessing ...
% 3.24/1.17 Prover 3: Preprocessing ...
% 3.24/1.17 Prover 5: Preprocessing ...
% 3.24/1.17 Prover 0: Preprocessing ...
% 3.24/1.17 Prover 2: Preprocessing ...
% 3.24/1.17 Prover 6: Preprocessing ...
% 8.30/1.88 Prover 1: Constructing countermodel ...
% 8.30/1.89 Prover 3: Constructing countermodel ...
% 8.30/1.90 Prover 6: Proving ...
% 8.81/2.01 Prover 5: Proving ...
% 8.81/2.02 Prover 4: Constructing countermodel ...
% 8.81/2.04 Prover 2: Proving ...
% 9.75/2.18 Prover 0: Proving ...
% 13.62/2.70 Prover 0: proved (2086ms)
% 13.62/2.70
% 13.62/2.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.62/2.70
% 13.62/2.70 Prover 3: stopped
% 13.62/2.72 Prover 2: stopped
% 14.08/2.72 Prover 6: stopped
% 14.08/2.72 Prover 5: stopped
% 14.08/2.74 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.08/2.74 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.08/2.74 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.08/2.74 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 14.08/2.74 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.08/2.78 Prover 7: Preprocessing ...
% 15.02/2.81 Prover 10: Preprocessing ...
% 15.02/2.82 Prover 13: Preprocessing ...
% 15.02/2.83 Prover 8: Preprocessing ...
% 15.02/2.83 Prover 11: Preprocessing ...
% 16.26/2.97 Prover 10: Constructing countermodel ...
% 16.35/2.99 Prover 7: Constructing countermodel ...
% 16.35/3.00 Prover 8: Warning: ignoring some quantifiers
% 16.54/3.01 Prover 8: Constructing countermodel ...
% 16.64/3.03 Prover 13: Warning: ignoring some quantifiers
% 16.64/3.05 Prover 13: Constructing countermodel ...
% 17.34/3.15 Prover 11: Constructing countermodel ...
% 39.58/6.07 Prover 1: Found proof (size 305)
% 39.58/6.07 Prover 1: proved (5452ms)
% 39.58/6.07 Prover 13: stopped
% 39.58/6.07 Prover 4: stopped
% 39.58/6.07 Prover 7: stopped
% 39.58/6.07 Prover 11: stopped
% 39.58/6.07 Prover 10: stopped
% 39.58/6.07 Prover 8: stopped
% 39.58/6.07
% 39.58/6.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 39.58/6.07
% 40.03/6.16 % SZS output start Proof for theBenchmark
% 40.03/6.17 Assumptions after simplification:
% 40.03/6.17 ---------------------------------
% 40.03/6.17
% 40.03/6.17 (mAddAsso)
% 40.03/6.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 40.03/6.19 (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 40.03/6.19 | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ?
% 40.03/6.19 [v9: $i] : (sdtpldt0(v1, v2) = v8 & sdtpldt0(v0, v8) = v9 & aElement0(v2) =
% 40.03/6.19 v7 & aElement0(v1) = v6 & aElement0(v0) = v5 & $i(v9) & $i(v8) & ( ~ (v7 =
% 40.03/6.19 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = v4)))
% 40.03/6.19
% 40.03/6.19 (mAddComm)
% 40.03/6.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 40.03/6.19 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 40.03/6.19 (sdtpldt0(v1, v0) = v5 & aElement0(v1) = v4 & aElement0(v0) = v3 & $i(v5) &
% 40.03/6.20 ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 40.03/6.20
% 40.03/6.20 (mDefMod)
% 40.03/6.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 40.03/6.20 any] : ( ~ (aElementOf0(v4, v2) = v5) | ~ (sdtpldt0(v0, v3) = v4) | ~
% 40.03/6.20 (smndt0(v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ?
% 40.03/6.20 [v7: any] : ? [v8: any] : ? [v9: any] : (sdteqdtlpzmzozddtrp0(v0, v1, v2)
% 40.03/6.20 = v9 & aIdeal0(v2) = v8 & aElement0(v1) = v7 & aElement0(v0) = v6 & ( ~
% 40.03/6.20 (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | (( ~ (v9 = 0) | v5 = 0) & ( ~ (v5
% 40.03/6.20 = 0) | v9 = 0)))))
% 40.03/6.20
% 40.03/6.20 (mEOfElem)
% 40.03/6.20 ! [v0: $i] : ( ~ (aSet0(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: int] :
% 40.03/6.20 (v2 = 0 | ~ (aElement0(v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0)
% 40.03/6.20 & aElementOf0(v1, v0) = v3)))
% 40.03/6.20
% 40.03/6.20 (mIdeSum)
% 40.03/6.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~
% 40.03/6.20 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 40.03/6.20 (aIdeal0(v2) = v5 & aIdeal0(v1) = v4 & aIdeal0(v0) = v3 & ( ~ (v4 = 0) | ~
% 40.03/6.20 (v3 = 0) | v5 = 0)))
% 40.03/6.20
% 40.03/6.20 (mMulComm)
% 40.03/6.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 40.03/6.20 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 40.03/6.20 (sdtasdt0(v1, v0) = v5 & aElement0(v1) = v4 & aElement0(v0) = v3 & $i(v5) &
% 40.03/6.20 ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 40.03/6.20
% 40.03/6.20 (mSortsB)
% 40.03/6.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 40.03/6.20 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 40.03/6.20 (aElement0(v2) = v5 & aElement0(v1) = v4 & aElement0(v0) = v3 & ( ~ (v4 = 0)
% 40.03/6.20 | ~ (v3 = 0) | v5 = 0)))
% 40.03/6.20
% 40.03/6.20 (mSortsB_02)
% 40.03/6.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 40.03/6.21 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 40.03/6.21 (aElement0(v2) = v5 & aElement0(v1) = v4 & aElement0(v0) = v3 & ( ~ (v4 = 0)
% 40.03/6.21 | ~ (v3 = 0) | v5 = 0)))
% 40.03/6.21
% 40.03/6.21 (mSortsU)
% 40.03/6.21 ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ? [v2: any] :
% 40.03/6.21 ? [v3: any] : (aElement0(v1) = v3 & aElement0(v0) = v2 & ( ~ (v2 = 0) | v3
% 40.03/6.21 = 0)))
% 40.03/6.21
% 40.03/6.21 (m__)
% 40.03/6.21 $i(xy) & $i(xx) & $i(xJ) & $i(xI) & ? [v0: $i] : ? [v1: $i] : (smndt0(xy) =
% 40.03/6.21 v1 & smndt0(xx) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: any] : ( ~
% 40.03/6.21 (sdteqdtlpzmzozddtrp0(v2, xy, xJ) = v3) | ~ $i(v2) | ? [v4: any] : ?
% 40.03/6.21 [v5: $i] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: any] :
% 40.03/6.21 (sdteqdtlpzmzozddtrp0(v2, xx, xI) = v7 & aElementOf0(v8, xJ) = v9 &
% 40.03/6.21 aElementOf0(v5, xI) = v6 & sdtpldt0(v2, v1) = v8 & sdtpldt0(v2, v0) = v5
% 40.03/6.21 & aElement0(v2) = v4 & $i(v8) & $i(v5) & ( ~ (v4 = 0) | ( ~ (v9 = 0) &
% 40.03/6.21 ~ (v3 = 0)) | ( ~ (v7 = 0) & ~ (v6 = 0))))))
% 40.03/6.21
% 40.03/6.21 (m__1205)
% 40.03/6.21 aIdeal0(xJ) = 0 & aIdeal0(xI) = 0 & aSet0(xJ) = 0 & aSet0(xI) = 0 & $i(xJ) &
% 40.03/6.21 $i(xI) & ! [v0: $i] : ( ~ (aElementOf0(v0, xJ) = 0) | ~ $i(v0) | ( ! [v1:
% 40.03/6.21 $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ? [v3:
% 40.03/6.21 any] : ? [v4: any] : (aElementOf0(v2, xJ) = v4 & aElement0(v1) = v3 &
% 40.03/6.21 ( ~ (v3 = 0) | v4 = 0))) & ! [v1: $i] : ( ~ (aElementOf0(v1, xJ) = 0)
% 40.03/6.21 | ~ $i(v1) | ? [v2: $i] : (aElementOf0(v2, xJ) = 0 & sdtpldt0(v0, v1)
% 40.03/6.21 = v2 & $i(v2))))) & ! [v0: $i] : ( ~ (aElementOf0(v0, xI) = 0) | ~
% 40.03/6.21 $i(v0) | ( ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~
% 40.03/6.21 $i(v1) | ? [v3: any] : ? [v4: any] : (aElementOf0(v2, xI) = v4 &
% 40.03/6.21 aElement0(v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v1: $i] : ( ~
% 40.03/6.21 (aElementOf0(v1, xI) = 0) | ~ $i(v1) | ? [v2: $i] : (aElementOf0(v2,
% 40.03/6.21 xI) = 0 & sdtpldt0(v0, v1) = v2 & $i(v2)))))
% 40.03/6.21
% 40.03/6.21 (m__1205_03)
% 40.03/6.21 $i(xJ) & $i(xI) & ? [v0: $i] : (sdtpldt1(xI, xJ) = v0 & $i(v0) & ! [v1: $i]
% 40.03/6.21 : ! [v2: any] : ( ~ (aElementOf0(v1, v0) = v2) | ~ $i(v1) | ? [v3: int] :
% 40.03/6.21 ( ~ (v3 = 0) & aElement0(v1) = v3) | (v2 = 0 & ? [v3: $i] : ? [v4: $i] :
% 40.03/6.21 (aElementOf0(v4, xJ) = 0 & aElementOf0(v3, xI) = 0 & sdtpldt0(v3, v4) =
% 40.03/6.21 v1 & $i(v4) & $i(v3)))))
% 40.03/6.21
% 40.03/6.21 (m__1217)
% 40.03/6.21 aElement0(xy) = 0 & aElement0(xx) = 0 & $i(xy) & $i(xx)
% 40.03/6.21
% 40.03/6.21 (m__1294)
% 40.03/6.22 aElementOf0(xb, xJ) = 0 & aElementOf0(xa, xI) = 0 & sdtpldt0(xa, xb) = sz10 &
% 40.03/6.22 $i(xb) & $i(xa) & $i(xJ) & $i(xI) & $i(sz10)
% 40.03/6.22
% 40.03/6.22 (m__1319)
% 40.03/6.22 $i(xw) & $i(xb) & $i(xa) & $i(xy) & $i(xx) & ? [v0: $i] : ? [v1: $i] :
% 40.03/6.22 (sdtasdt0(xy, xa) = v0 & sdtasdt0(xx, xb) = v1 & sdtpldt0(v0, v1) = xw &
% 40.03/6.22 $i(v1) & $i(v0))
% 40.03/6.22
% 40.03/6.22 (m__1332)
% 40.03/6.22 $i(xw) & $i(xx) & $i(xI) & ? [v0: $i] : ? [v1: $i] : (aElementOf0(v1, xI) =
% 40.03/6.22 0 & sdtpldt0(xw, v0) = v1 & smndt0(xx) = v0 & $i(v1) & $i(v0))
% 40.03/6.22
% 40.03/6.22 (m__1409)
% 40.03/6.22 $i(xw) & $i(xy) & $i(xJ) & ? [v0: $i] : ? [v1: $i] : (aElementOf0(v1, xJ) =
% 40.03/6.22 0 & sdtpldt0(xw, v0) = v1 & smndt0(xy) = v0 & $i(v1) & $i(v0))
% 40.03/6.22
% 40.03/6.22 (function-axioms)
% 40.03/6.22 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 40.03/6.22 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v1)
% 40.03/6.22 | ~ (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 40.03/6.22 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasasdt0(v3, v2) = v1) | ~
% 40.03/6.22 (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 40.03/6.22 [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) | ~ (sdtpldt1(v3, v2) = v0))
% 40.03/6.22 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 40.03/6.22 [v3: $i] : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2)
% 40.03/6.22 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 40.03/6.22 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] :
% 40.03/6.22 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1)
% 40.03/6.22 | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 40.03/6.22 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aIdeal0(v2) = v1) | ~
% 40.03/6.22 (aIdeal0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 40.03/6.22 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aSet0(v2) = v1) | ~
% 40.03/6.22 (aSet0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 40.03/6.22 (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 40.03/6.22 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) |
% 40.03/6.22 ~ (aElement0(v2) = v0))
% 40.03/6.22
% 40.03/6.22 Further assumptions not needed in the proof:
% 40.03/6.22 --------------------------------------------
% 40.03/6.22 mAMDistr, mAddInvr, mAddZero, mCancel, mDefIdeal, mDefSInt, mDefSSum, mElmSort,
% 40.03/6.22 mIdeInt, mMulAsso, mMulMnOne, mMulUnit, mMulZero, mSetEq, mSetSort, mSortsC,
% 40.03/6.22 mSortsC_01, mUnNeZr
% 40.03/6.22
% 40.03/6.22 Those formulas are unsatisfiable:
% 40.03/6.22 ---------------------------------
% 40.03/6.22
% 40.03/6.22 Begin of proof
% 40.03/6.22 |
% 40.03/6.22 | ALPHA: (m__1205) implies:
% 40.03/6.22 | (1) aSet0(xI) = 0
% 40.03/6.23 | (2) aSet0(xJ) = 0
% 40.03/6.23 | (3) aIdeal0(xI) = 0
% 40.03/6.23 | (4) aIdeal0(xJ) = 0
% 40.03/6.23 | (5) ! [v0: $i] : ( ~ (aElementOf0(v0, xI) = 0) | ~ $i(v0) | ( ! [v1: $i]
% 40.03/6.23 | : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ? [v3:
% 40.03/6.23 | any] : ? [v4: any] : (aElementOf0(v2, xI) = v4 & aElement0(v1)
% 40.03/6.23 | = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v1: $i] : ( ~
% 40.03/6.23 | (aElementOf0(v1, xI) = 0) | ~ $i(v1) | ? [v2: $i] :
% 40.03/6.23 | (aElementOf0(v2, xI) = 0 & sdtpldt0(v0, v1) = v2 & $i(v2)))))
% 40.03/6.23 | (6) ! [v0: $i] : ( ~ (aElementOf0(v0, xJ) = 0) | ~ $i(v0) | ( ! [v1: $i]
% 40.03/6.23 | : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ? [v3:
% 40.03/6.23 | any] : ? [v4: any] : (aElementOf0(v2, xJ) = v4 & aElement0(v1)
% 40.03/6.23 | = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v1: $i] : ( ~
% 40.03/6.23 | (aElementOf0(v1, xJ) = 0) | ~ $i(v1) | ? [v2: $i] :
% 40.03/6.23 | (aElementOf0(v2, xJ) = 0 & sdtpldt0(v0, v1) = v2 & $i(v2)))))
% 40.03/6.23 |
% 40.03/6.23 | ALPHA: (m__1205_03) implies:
% 40.03/6.23 | (7) ? [v0: $i] : (sdtpldt1(xI, xJ) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 40.03/6.23 | any] : ( ~ (aElementOf0(v1, v0) = v2) | ~ $i(v1) | ? [v3: int] :
% 40.03/6.23 | ( ~ (v3 = 0) & aElement0(v1) = v3) | (v2 = 0 & ? [v3: $i] : ?
% 40.03/6.23 | [v4: $i] : (aElementOf0(v4, xJ) = 0 & aElementOf0(v3, xI) = 0 &
% 40.03/6.23 | sdtpldt0(v3, v4) = v1 & $i(v4) & $i(v3)))))
% 40.03/6.23 |
% 40.03/6.23 | ALPHA: (m__1217) implies:
% 40.03/6.23 | (8) aElement0(xx) = 0
% 40.03/6.23 | (9) aElement0(xy) = 0
% 40.03/6.23 |
% 40.03/6.23 | ALPHA: (m__1294) implies:
% 40.03/6.23 | (10) sdtpldt0(xa, xb) = sz10
% 40.03/6.23 | (11) aElementOf0(xa, xI) = 0
% 40.03/6.23 | (12) aElementOf0(xb, xJ) = 0
% 40.03/6.23 |
% 40.03/6.23 | ALPHA: (m__1319) implies:
% 40.03/6.23 | (13) $i(xa)
% 40.03/6.23 | (14) $i(xb)
% 40.03/6.23 | (15) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xy, xa) = v0 & sdtasdt0(xx, xb)
% 40.03/6.23 | = v1 & sdtpldt0(v0, v1) = xw & $i(v1) & $i(v0))
% 40.03/6.23 |
% 40.03/6.23 | ALPHA: (m__1332) implies:
% 40.03/6.23 | (16) ? [v0: $i] : ? [v1: $i] : (aElementOf0(v1, xI) = 0 & sdtpldt0(xw,
% 40.03/6.23 | v0) = v1 & smndt0(xx) = v0 & $i(v1) & $i(v0))
% 40.03/6.23 |
% 40.03/6.23 | ALPHA: (m__1409) implies:
% 40.03/6.23 | (17) $i(xw)
% 40.03/6.23 | (18) ? [v0: $i] : ? [v1: $i] : (aElementOf0(v1, xJ) = 0 & sdtpldt0(xw,
% 40.03/6.23 | v0) = v1 & smndt0(xy) = v0 & $i(v1) & $i(v0))
% 40.03/6.23 |
% 40.03/6.23 | ALPHA: (m__) implies:
% 40.03/6.23 | (19) $i(xI)
% 40.03/6.23 | (20) $i(xJ)
% 40.03/6.23 | (21) $i(xx)
% 40.03/6.23 | (22) $i(xy)
% 40.03/6.23 | (23) ? [v0: $i] : ? [v1: $i] : (smndt0(xy) = v1 & smndt0(xx) = v0 &
% 40.03/6.23 | $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: any] : ( ~
% 40.03/6.23 | (sdteqdtlpzmzozddtrp0(v2, xy, xJ) = v3) | ~ $i(v2) | ? [v4: any]
% 40.03/6.23 | : ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ?
% 40.03/6.23 | [v9: any] : (sdteqdtlpzmzozddtrp0(v2, xx, xI) = v7 &
% 40.03/6.23 | aElementOf0(v8, xJ) = v9 & aElementOf0(v5, xI) = v6 &
% 40.03/6.23 | sdtpldt0(v2, v1) = v8 & sdtpldt0(v2, v0) = v5 & aElement0(v2) =
% 40.03/6.23 | v4 & $i(v8) & $i(v5) & ( ~ (v4 = 0) | ( ~ (v9 = 0) & ~ (v3 =
% 40.03/6.23 | 0)) | ( ~ (v7 = 0) & ~ (v6 = 0))))))
% 40.03/6.23 |
% 40.03/6.23 | ALPHA: (function-axioms) implies:
% 40.03/6.24 | (24) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 40.03/6.24 | : (v1 = v0 | ~ (aElement0(v2) = v1) | ~ (aElement0(v2) = v0))
% 40.03/6.24 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) =
% 40.03/6.24 | v1) | ~ (smndt0(v2) = v0))
% 40.03/6.24 | (26) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 40.03/6.24 | : (v1 = v0 | ~ (aIdeal0(v2) = v1) | ~ (aIdeal0(v2) = v0))
% 40.03/6.24 | (27) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 40.03/6.24 | : ! [v3: $i] : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~
% 40.03/6.24 | (aElementOf0(v3, v2) = v0))
% 40.03/6.24 | (28) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 40.03/6.24 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sdteqdtlpzmzozddtrp0(v4,
% 40.03/6.24 | v3, v2) = v1) | ~ (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v0))
% 40.03/6.24 |
% 40.03/6.24 | DELTA: instantiating (15) with fresh symbols all_26_0, all_26_1 gives:
% 40.03/6.24 | (29) sdtasdt0(xy, xa) = all_26_1 & sdtasdt0(xx, xb) = all_26_0 &
% 40.03/6.24 | sdtpldt0(all_26_1, all_26_0) = xw & $i(all_26_0) & $i(all_26_1)
% 40.03/6.24 |
% 40.03/6.24 | ALPHA: (29) implies:
% 40.03/6.24 | (30) $i(all_26_1)
% 40.03/6.24 | (31) $i(all_26_0)
% 40.03/6.24 | (32) sdtpldt0(all_26_1, all_26_0) = xw
% 40.03/6.24 | (33) sdtasdt0(xx, xb) = all_26_0
% 40.03/6.24 | (34) sdtasdt0(xy, xa) = all_26_1
% 40.03/6.24 |
% 40.03/6.24 | DELTA: instantiating (16) with fresh symbols all_28_0, all_28_1 gives:
% 40.03/6.24 | (35) aElementOf0(all_28_0, xI) = 0 & sdtpldt0(xw, all_28_1) = all_28_0 &
% 40.03/6.24 | smndt0(xx) = all_28_1 & $i(all_28_0) & $i(all_28_1)
% 40.03/6.24 |
% 40.03/6.24 | ALPHA: (35) implies:
% 40.03/6.24 | (36) $i(all_28_0)
% 40.03/6.24 | (37) smndt0(xx) = all_28_1
% 40.03/6.24 | (38) sdtpldt0(xw, all_28_1) = all_28_0
% 40.03/6.24 | (39) aElementOf0(all_28_0, xI) = 0
% 40.03/6.24 |
% 40.03/6.24 | DELTA: instantiating (18) with fresh symbols all_30_0, all_30_1 gives:
% 40.03/6.24 | (40) aElementOf0(all_30_0, xJ) = 0 & sdtpldt0(xw, all_30_1) = all_30_0 &
% 40.03/6.24 | smndt0(xy) = all_30_1 & $i(all_30_0) & $i(all_30_1)
% 40.03/6.24 |
% 40.03/6.24 | ALPHA: (40) implies:
% 40.03/6.24 | (41) $i(all_30_0)
% 40.03/6.24 | (42) smndt0(xy) = all_30_1
% 40.03/6.24 | (43) sdtpldt0(xw, all_30_1) = all_30_0
% 40.03/6.24 | (44) aElementOf0(all_30_0, xJ) = 0
% 40.03/6.24 |
% 40.03/6.24 | DELTA: instantiating (7) with fresh symbol all_32_0 gives:
% 40.03/6.24 | (45) sdtpldt1(xI, xJ) = all_32_0 & $i(all_32_0) & ! [v0: $i] : ! [v1:
% 40.03/6.24 | any] : ( ~ (aElementOf0(v0, all_32_0) = v1) | ~ $i(v0) | ? [v2:
% 40.03/6.24 | int] : ( ~ (v2 = 0) & aElement0(v0) = v2) | (v1 = 0 & ? [v2: $i]
% 40.03/6.24 | : ? [v3: $i] : (aElementOf0(v3, xJ) = 0 & aElementOf0(v2, xI) = 0
% 40.03/6.24 | & sdtpldt0(v2, v3) = v0 & $i(v3) & $i(v2))))
% 40.03/6.24 |
% 40.03/6.24 | ALPHA: (45) implies:
% 40.03/6.24 | (46) sdtpldt1(xI, xJ) = all_32_0
% 40.03/6.24 |
% 40.03/6.24 | DELTA: instantiating (23) with fresh symbols all_38_0, all_38_1 gives:
% 40.03/6.24 | (47) smndt0(xy) = all_38_0 & smndt0(xx) = all_38_1 & $i(all_38_0) &
% 40.03/6.24 | $i(all_38_1) & ! [v0: $i] : ! [v1: any] : ( ~
% 40.03/6.24 | (sdteqdtlpzmzozddtrp0(v0, xy, xJ) = v1) | ~ $i(v0) | ? [v2: any] :
% 40.03/6.24 | ? [v3: $i] : ? [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7:
% 40.03/6.24 | any] : (sdteqdtlpzmzozddtrp0(v0, xx, xI) = v5 & aElementOf0(v6,
% 40.03/6.24 | xJ) = v7 & aElementOf0(v3, xI) = v4 & sdtpldt0(v0, all_38_0) =
% 40.03/6.24 | v6 & sdtpldt0(v0, all_38_1) = v3 & aElement0(v0) = v2 & $i(v6) &
% 40.03/6.24 | $i(v3) & ( ~ (v2 = 0) | ( ~ (v7 = 0) & ~ (v1 = 0)) | ( ~ (v5 = 0)
% 40.03/6.24 | & ~ (v4 = 0)))))
% 40.03/6.24 |
% 40.03/6.24 | ALPHA: (47) implies:
% 40.03/6.25 | (48) $i(all_38_1)
% 40.03/6.25 | (49) $i(all_38_0)
% 40.03/6.25 | (50) smndt0(xx) = all_38_1
% 40.03/6.25 | (51) smndt0(xy) = all_38_0
% 40.03/6.25 | (52) ! [v0: $i] : ! [v1: any] : ( ~ (sdteqdtlpzmzozddtrp0(v0, xy, xJ) =
% 40.03/6.25 | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : ?
% 40.03/6.25 | [v5: any] : ? [v6: $i] : ? [v7: any] : (sdteqdtlpzmzozddtrp0(v0,
% 40.03/6.25 | xx, xI) = v5 & aElementOf0(v6, xJ) = v7 & aElementOf0(v3, xI) =
% 40.03/6.25 | v4 & sdtpldt0(v0, all_38_0) = v6 & sdtpldt0(v0, all_38_1) = v3 &
% 40.03/6.25 | aElement0(v0) = v2 & $i(v6) & $i(v3) & ( ~ (v2 = 0) | ( ~ (v7 = 0)
% 40.03/6.25 | & ~ (v1 = 0)) | ( ~ (v5 = 0) & ~ (v4 = 0)))))
% 40.03/6.25 |
% 40.03/6.25 | GROUND_INST: instantiating (25) with all_28_1, all_38_1, xx, simplifying with
% 40.03/6.25 | (37), (50) gives:
% 40.03/6.25 | (53) all_38_1 = all_28_1
% 40.03/6.25 |
% 40.03/6.25 | GROUND_INST: instantiating (25) with all_30_1, all_38_0, xy, simplifying with
% 40.03/6.25 | (42), (51) gives:
% 40.03/6.25 | (54) all_38_0 = all_30_1
% 40.03/6.25 |
% 40.03/6.25 | REDUCE: (49), (54) imply:
% 40.03/6.25 | (55) $i(all_30_1)
% 40.03/6.25 |
% 40.03/6.25 | REDUCE: (48), (53) imply:
% 40.03/6.25 | (56) $i(all_28_1)
% 40.03/6.25 |
% 40.03/6.25 | GROUND_INST: instantiating (mSortsU) with xx, all_28_1, simplifying with (21),
% 40.03/6.25 | (37) gives:
% 40.03/6.25 | (57) ? [v0: any] : ? [v1: any] : (aElement0(all_28_1) = v1 &
% 40.03/6.25 | aElement0(xx) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 40.03/6.25 |
% 40.03/6.25 | GROUND_INST: instantiating (mSortsU) with xy, all_30_1, simplifying with (22),
% 40.03/6.25 | (42) gives:
% 40.03/6.25 | (58) ? [v0: any] : ? [v1: any] : (aElement0(all_30_1) = v1 &
% 40.03/6.25 | aElement0(xy) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 40.03/6.25 |
% 40.03/6.25 | GROUND_INST: instantiating (mAddComm) with xa, xb, sz10, simplifying with
% 40.03/6.25 | (10), (13), (14) gives:
% 40.03/6.25 | (59) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(xb, xa) = v2 &
% 40.03/6.25 | aElement0(xb) = v1 & aElement0(xa) = v0 & $i(v2) & ( ~ (v1 = 0) | ~
% 40.03/6.25 | (v0 = 0) | v2 = sz10))
% 40.03/6.25 |
% 40.03/6.25 | GROUND_INST: instantiating (mSortsB) with xa, xb, sz10, simplifying with (10),
% 40.03/6.25 | (13), (14) gives:
% 40.03/6.25 | (60) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aElement0(xb) = v1 &
% 40.03/6.25 | aElement0(xa) = v0 & aElement0(sz10) = v2 & ( ~ (v1 = 0) | ~ (v0 =
% 40.03/6.25 | 0) | v2 = 0))
% 40.03/6.25 |
% 40.03/6.25 | GROUND_INST: instantiating (mAddComm) with xw, all_28_1, all_28_0, simplifying
% 40.03/6.25 | with (17), (38), (56) gives:
% 40.03/6.25 | (61) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(all_28_1, xw) =
% 40.03/6.25 | v2 & aElement0(all_28_1) = v1 & aElement0(xw) = v0 & $i(v2) & ( ~
% 40.03/6.25 | (v1 = 0) | ~ (v0 = 0) | v2 = all_28_0))
% 40.03/6.25 |
% 40.03/6.25 | GROUND_INST: instantiating (mSortsB) with xw, all_28_1, all_28_0, simplifying
% 40.03/6.25 | with (17), (38), (56) gives:
% 40.03/6.25 | (62) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aElement0(all_28_0) = v2
% 40.03/6.25 | & aElement0(all_28_1) = v1 & aElement0(xw) = v0 & ( ~ (v1 = 0) | ~
% 40.03/6.25 | (v0 = 0) | v2 = 0))
% 40.03/6.25 |
% 40.03/6.26 | GROUND_INST: instantiating (mAddComm) with xw, all_30_1, all_30_0, simplifying
% 40.03/6.26 | with (17), (43), (55) gives:
% 40.03/6.26 | (63) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(all_30_1, xw) =
% 40.03/6.26 | v2 & aElement0(all_30_1) = v1 & aElement0(xw) = v0 & $i(v2) & ( ~
% 40.03/6.26 | (v1 = 0) | ~ (v0 = 0) | v2 = all_30_0))
% 40.03/6.26 |
% 40.03/6.26 | GROUND_INST: instantiating (mSortsB) with xw, all_30_1, all_30_0, simplifying
% 40.03/6.26 | with (17), (43), (55) gives:
% 40.03/6.26 | (64) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aElement0(all_30_0) = v2
% 40.03/6.26 | & aElement0(all_30_1) = v1 & aElement0(xw) = v0 & ( ~ (v1 = 0) | ~
% 40.03/6.26 | (v0 = 0) | v2 = 0))
% 40.03/6.26 |
% 40.03/6.26 | GROUND_INST: instantiating (mAddAsso) with all_26_1, all_26_0, all_30_1, xw,
% 40.03/6.26 | all_30_0, simplifying with (30), (31), (32), (43), (55) gives:
% 40.03/6.26 | (65) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: $i]
% 40.03/6.26 | : (sdtpldt0(all_26_0, all_30_1) = v3 & sdtpldt0(all_26_1, v3) = v4 &
% 40.03/6.26 | aElement0(all_30_1) = v2 & aElement0(all_26_0) = v1 &
% 40.03/6.26 | aElement0(all_26_1) = v0 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 =
% 40.03/6.26 | 0) | ~ (v0 = 0) | v4 = all_30_0))
% 40.03/6.26 |
% 40.03/6.26 | GROUND_INST: instantiating (mAddAsso) with all_26_1, all_26_0, all_28_1, xw,
% 40.03/6.26 | all_28_0, simplifying with (30), (31), (32), (38), (56) gives:
% 40.03/6.26 | (66) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: $i]
% 40.03/6.26 | : (sdtpldt0(all_26_0, all_28_1) = v3 & sdtpldt0(all_26_1, v3) = v4 &
% 40.03/6.26 | aElement0(all_28_1) = v2 & aElement0(all_26_0) = v1 &
% 40.03/6.26 | aElement0(all_26_1) = v0 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 =
% 40.03/6.26 | 0) | ~ (v0 = 0) | v4 = all_28_0))
% 40.03/6.26 |
% 40.03/6.26 | GROUND_INST: instantiating (mAddComm) with all_26_1, all_26_0, xw, simplifying
% 40.03/6.26 | with (30), (31), (32) gives:
% 40.03/6.26 | (67) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(all_26_0,
% 40.03/6.26 | all_26_1) = v2 & aElement0(all_26_0) = v1 & aElement0(all_26_1) =
% 40.03/6.26 | v0 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xw))
% 40.03/6.26 |
% 40.03/6.26 | GROUND_INST: instantiating (mSortsB) with all_26_1, all_26_0, xw, simplifying
% 40.03/6.26 | with (30), (31), (32) gives:
% 40.03/6.26 | (68) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aElement0(all_26_0) = v1
% 40.03/6.26 | & aElement0(all_26_1) = v0 & aElement0(xw) = v2 & ( ~ (v1 = 0) | ~
% 40.03/6.26 | (v0 = 0) | v2 = 0))
% 40.03/6.26 |
% 40.03/6.26 | GROUND_INST: instantiating (mMulComm) with xx, xb, all_26_0, simplifying with
% 40.03/6.26 | (14), (21), (33) gives:
% 40.03/6.26 | (69) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xb, xx) = v2 &
% 40.03/6.26 | aElement0(xb) = v1 & aElement0(xx) = v0 & $i(v2) & ( ~ (v1 = 0) | ~
% 40.03/6.26 | (v0 = 0) | v2 = all_26_0))
% 40.03/6.26 |
% 40.03/6.26 | GROUND_INST: instantiating (mSortsB_02) with xx, xb, all_26_0, simplifying
% 40.03/6.26 | with (14), (21), (33) gives:
% 40.03/6.26 | (70) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aElement0(all_26_0) = v2
% 40.03/6.26 | & aElement0(xb) = v1 & aElement0(xx) = v0 & ( ~ (v1 = 0) | ~ (v0 =
% 40.03/6.26 | 0) | v2 = 0))
% 40.03/6.26 |
% 40.03/6.26 | GROUND_INST: instantiating (mMulComm) with xy, xa, all_26_1, simplifying with
% 40.03/6.26 | (13), (22), (34) gives:
% 40.03/6.27 | (71) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xa, xy) = v2 &
% 40.03/6.27 | aElement0(xa) = v1 & aElement0(xy) = v0 & $i(v2) & ( ~ (v1 = 0) | ~
% 40.03/6.27 | (v0 = 0) | v2 = all_26_1))
% 40.03/6.27 |
% 40.03/6.27 | GROUND_INST: instantiating (mSortsB_02) with xy, xa, all_26_1, simplifying
% 40.03/6.27 | with (13), (22), (34) gives:
% 40.03/6.27 | (72) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aElement0(all_26_1) = v2
% 40.03/6.27 | & aElement0(xa) = v1 & aElement0(xy) = v0 & ( ~ (v1 = 0) | ~ (v0 =
% 40.03/6.27 | 0) | v2 = 0))
% 40.03/6.27 |
% 40.03/6.27 | GROUND_INST: instantiating (5) with xa, simplifying with (11), (13) gives:
% 40.03/6.27 | (73) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, xa) = v1) | ~ $i(v0) |
% 40.03/6.27 | ? [v2: any] : ? [v3: any] : (aElementOf0(v1, xI) = v3 &
% 40.03/6.27 | aElement0(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~
% 40.03/6.27 | (aElementOf0(v0, xI) = 0) | ~ $i(v0) | ? [v1: $i] :
% 40.03/6.27 | (aElementOf0(v1, xI) = 0 & sdtpldt0(xa, v0) = v1 & $i(v1)))
% 40.03/6.27 |
% 40.03/6.27 | ALPHA: (73) implies:
% 40.03/6.27 | (74) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, xa) = v1) | ~ $i(v0) |
% 40.03/6.27 | ? [v2: any] : ? [v3: any] : (aElementOf0(v1, xI) = v3 &
% 40.03/6.27 | aElement0(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 40.03/6.27 |
% 40.03/6.27 | GROUND_INST: instantiating (6) with xb, simplifying with (12), (14) gives:
% 40.03/6.27 | (75) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, xb) = v1) | ~ $i(v0) |
% 40.03/6.27 | ? [v2: any] : ? [v3: any] : (aElementOf0(v1, xJ) = v3 &
% 40.03/6.27 | aElement0(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~
% 40.03/6.27 | (aElementOf0(v0, xJ) = 0) | ~ $i(v0) | ? [v1: $i] :
% 40.03/6.27 | (aElementOf0(v1, xJ) = 0 & sdtpldt0(xb, v0) = v1 & $i(v1)))
% 40.03/6.27 |
% 40.03/6.27 | ALPHA: (75) implies:
% 40.03/6.27 | (76) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, xb) = v1) | ~ $i(v0) |
% 40.03/6.27 | ? [v2: any] : ? [v3: any] : (aElementOf0(v1, xJ) = v3 &
% 40.03/6.27 | aElement0(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 40.03/6.27 |
% 40.03/6.27 | GROUND_INST: instantiating (mDefMod) with xw, xx, xI, all_28_1, all_28_0, 0,
% 40.03/6.27 | simplifying with (17), (19), (21), (37), (38), (39) gives:
% 40.03/6.27 | (77) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 40.03/6.27 | (sdteqdtlpzmzozddtrp0(xw, xx, xI) = v3 & aIdeal0(xI) = v2 &
% 40.03/6.27 | aElement0(xw) = v0 & aElement0(xx) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)
% 40.03/6.27 | | ~ (v0 = 0) | v3 = 0))
% 40.03/6.27 |
% 40.03/6.27 | GROUND_INST: instantiating (5) with all_28_0, simplifying with (36), (39)
% 40.03/6.27 | gives:
% 40.03/6.27 | (78) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, all_28_0) = v1) | ~
% 40.03/6.27 | $i(v0) | ? [v2: any] : ? [v3: any] : (aElementOf0(v1, xI) = v3 &
% 40.03/6.27 | aElement0(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~
% 40.03/6.27 | (aElementOf0(v0, xI) = 0) | ~ $i(v0) | ? [v1: $i] :
% 40.03/6.27 | (aElementOf0(v1, xI) = 0 & sdtpldt0(all_28_0, v0) = v1 & $i(v1)))
% 40.03/6.27 |
% 40.03/6.27 | ALPHA: (78) implies:
% 40.03/6.27 | (79) ! [v0: $i] : ( ~ (aElementOf0(v0, xI) = 0) | ~ $i(v0) | ? [v1: $i]
% 40.03/6.27 | : (aElementOf0(v1, xI) = 0 & sdtpldt0(all_28_0, v0) = v1 & $i(v1)))
% 40.03/6.27 |
% 40.58/6.27 | GROUND_INST: instantiating (mDefMod) with xw, xy, xJ, all_30_1, all_30_0, 0,
% 40.58/6.27 | simplifying with (17), (20), (22), (42), (43), (44) gives:
% 40.58/6.27 | (80) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 40.58/6.27 | (sdteqdtlpzmzozddtrp0(xw, xy, xJ) = v3 & aIdeal0(xJ) = v2 &
% 40.58/6.27 | aElement0(xw) = v0 & aElement0(xy) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)
% 40.58/6.27 | | ~ (v0 = 0) | v3 = 0))
% 40.58/6.27 |
% 40.58/6.27 | GROUND_INST: instantiating (6) with all_30_0, simplifying with (41), (44)
% 40.58/6.27 | gives:
% 40.58/6.27 | (81) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, all_30_0) = v1) | ~
% 40.58/6.27 | $i(v0) | ? [v2: any] : ? [v3: any] : (aElementOf0(v1, xJ) = v3 &
% 40.58/6.27 | aElement0(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~
% 40.58/6.27 | (aElementOf0(v0, xJ) = 0) | ~ $i(v0) | ? [v1: $i] :
% 40.58/6.27 | (aElementOf0(v1, xJ) = 0 & sdtpldt0(all_30_0, v0) = v1 & $i(v1)))
% 40.58/6.27 |
% 40.58/6.27 | ALPHA: (81) implies:
% 40.58/6.27 | (82) ! [v0: $i] : ( ~ (aElementOf0(v0, xJ) = 0) | ~ $i(v0) | ? [v1: $i]
% 40.58/6.27 | : (aElementOf0(v1, xJ) = 0 & sdtpldt0(all_30_0, v0) = v1 & $i(v1)))
% 40.58/6.27 |
% 40.58/6.27 | GROUND_INST: instantiating (mEOfElem) with xI, simplifying with (1), (19)
% 40.58/6.27 | gives:
% 40.58/6.27 | (83) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aElement0(v0) = v1) | ~
% 40.58/6.27 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & aElementOf0(v0, xI) = v2))
% 40.58/6.27 |
% 40.58/6.28 | GROUND_INST: instantiating (mEOfElem) with xJ, simplifying with (2), (20)
% 40.58/6.28 | gives:
% 40.58/6.28 | (84) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aElement0(v0) = v1) | ~
% 40.58/6.28 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & aElementOf0(v0, xJ) = v2))
% 40.58/6.28 |
% 40.58/6.28 | GROUND_INST: instantiating (mIdeSum) with xI, xJ, all_32_0, simplifying with
% 40.58/6.28 | (19), (20), (46) gives:
% 40.58/6.28 | (85) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aIdeal0(all_32_0) = v2 &
% 40.85/6.28 | aIdeal0(xJ) = v1 & aIdeal0(xI) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) |
% 40.85/6.28 | v2 = 0))
% 40.85/6.28 |
% 40.85/6.28 | GROUND_INST: instantiating (82) with all_30_0, simplifying with (41), (44)
% 40.85/6.28 | gives:
% 40.85/6.28 | (86) ? [v0: $i] : (aElementOf0(v0, xJ) = 0 & sdtpldt0(all_30_0, all_30_0)
% 40.85/6.28 | = v0 & $i(v0))
% 40.85/6.28 |
% 40.85/6.28 | GROUND_INST: instantiating (76) with xx, all_26_0, simplifying with (21), (33)
% 40.85/6.28 | gives:
% 40.85/6.28 | (87) ? [v0: any] : ? [v1: any] : (aElementOf0(all_26_0, xJ) = v1 &
% 40.85/6.28 | aElement0(xx) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 40.85/6.28 |
% 40.85/6.28 | GROUND_INST: instantiating (79) with xa, simplifying with (11), (13) gives:
% 40.85/6.28 | (88) ? [v0: $i] : (aElementOf0(v0, xI) = 0 & sdtpldt0(all_28_0, xa) = v0 &
% 40.85/6.28 | $i(v0))
% 40.85/6.28 |
% 40.85/6.28 | GROUND_INST: instantiating (74) with xy, all_26_1, simplifying with (22), (34)
% 40.85/6.28 | gives:
% 40.85/6.28 | (89) ? [v0: any] : ? [v1: any] : (aElementOf0(all_26_1, xI) = v1 &
% 40.85/6.28 | aElement0(xy) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 40.85/6.28 |
% 40.85/6.28 | DELTA: instantiating (58) with fresh symbols all_63_0, all_63_1 gives:
% 40.85/6.28 | (90) aElement0(all_30_1) = all_63_0 & aElement0(xy) = all_63_1 & ( ~
% 40.85/6.28 | (all_63_1 = 0) | all_63_0 = 0)
% 40.85/6.28 |
% 40.85/6.28 | ALPHA: (90) implies:
% 40.85/6.28 | (91) aElement0(xy) = all_63_1
% 40.85/6.28 |
% 40.85/6.28 | DELTA: instantiating (57) with fresh symbols all_65_0, all_65_1 gives:
% 40.85/6.28 | (92) aElement0(all_28_1) = all_65_0 & aElement0(xx) = all_65_1 & ( ~
% 40.85/6.28 | (all_65_1 = 0) | all_65_0 = 0)
% 40.85/6.28 |
% 40.85/6.28 | ALPHA: (92) implies:
% 40.85/6.28 | (93) aElement0(xx) = all_65_1
% 40.85/6.28 |
% 40.85/6.28 | DELTA: instantiating (62) with fresh symbols all_69_0, all_69_1, all_69_2
% 40.85/6.28 | gives:
% 40.85/6.28 | (94) aElement0(all_28_0) = all_69_0 & aElement0(all_28_1) = all_69_1 &
% 40.85/6.28 | aElement0(xw) = all_69_2 & ( ~ (all_69_1 = 0) | ~ (all_69_2 = 0) |
% 40.85/6.28 | all_69_0 = 0)
% 40.85/6.28 |
% 40.85/6.28 | ALPHA: (94) implies:
% 40.85/6.28 | (95) aElement0(xw) = all_69_2
% 40.85/6.28 |
% 40.85/6.28 | DELTA: instantiating (85) with fresh symbols all_71_0, all_71_1, all_71_2
% 40.85/6.28 | gives:
% 40.85/6.28 | (96) aIdeal0(all_32_0) = all_71_0 & aIdeal0(xJ) = all_71_1 & aIdeal0(xI) =
% 40.85/6.28 | all_71_2 & ( ~ (all_71_1 = 0) | ~ (all_71_2 = 0) | all_71_0 = 0)
% 40.85/6.28 |
% 40.85/6.28 | ALPHA: (96) implies:
% 40.85/6.28 | (97) aIdeal0(xI) = all_71_2
% 40.85/6.28 | (98) aIdeal0(xJ) = all_71_1
% 40.85/6.28 | (99) ~ (all_71_1 = 0) | ~ (all_71_2 = 0) | all_71_0 = 0
% 40.85/6.28 |
% 40.85/6.28 | DELTA: instantiating (60) with fresh symbols all_73_0, all_73_1, all_73_2
% 40.85/6.28 | gives:
% 40.85/6.28 | (100) aElement0(xb) = all_73_1 & aElement0(xa) = all_73_2 & aElement0(sz10)
% 40.85/6.28 | = all_73_0 & ( ~ (all_73_1 = 0) | ~ (all_73_2 = 0) | all_73_0 = 0)
% 40.85/6.28 |
% 40.85/6.28 | ALPHA: (100) implies:
% 40.85/6.28 | (101) aElement0(xa) = all_73_2
% 40.85/6.28 | (102) aElement0(xb) = all_73_1
% 40.85/6.28 |
% 40.85/6.28 | DELTA: instantiating (70) with fresh symbols all_75_0, all_75_1, all_75_2
% 40.85/6.28 | gives:
% 40.85/6.28 | (103) aElement0(all_26_0) = all_75_0 & aElement0(xb) = all_75_1 &
% 40.85/6.28 | aElement0(xx) = all_75_2 & ( ~ (all_75_1 = 0) | ~ (all_75_2 = 0) |
% 40.85/6.28 | all_75_0 = 0)
% 40.85/6.28 |
% 40.85/6.28 | ALPHA: (103) implies:
% 40.85/6.28 | (104) aElement0(xx) = all_75_2
% 40.85/6.28 | (105) aElement0(xb) = all_75_1
% 40.85/6.28 | (106) aElement0(all_26_0) = all_75_0
% 40.85/6.28 | (107) ~ (all_75_1 = 0) | ~ (all_75_2 = 0) | all_75_0 = 0
% 40.85/6.28 |
% 40.85/6.28 | DELTA: instantiating (64) with fresh symbols all_77_0, all_77_1, all_77_2
% 40.85/6.28 | gives:
% 40.85/6.28 | (108) aElement0(all_30_0) = all_77_0 & aElement0(all_30_1) = all_77_1 &
% 40.85/6.28 | aElement0(xw) = all_77_2 & ( ~ (all_77_1 = 0) | ~ (all_77_2 = 0) |
% 40.85/6.28 | all_77_0 = 0)
% 40.85/6.28 |
% 40.85/6.28 | ALPHA: (108) implies:
% 40.85/6.28 | (109) aElement0(xw) = all_77_2
% 40.85/6.28 |
% 40.85/6.28 | DELTA: instantiating (68) with fresh symbols all_79_0, all_79_1, all_79_2
% 40.85/6.28 | gives:
% 40.85/6.28 | (110) aElement0(all_26_0) = all_79_1 & aElement0(all_26_1) = all_79_2 &
% 40.85/6.28 | aElement0(xw) = all_79_0 & ( ~ (all_79_1 = 0) | ~ (all_79_2 = 0) |
% 40.85/6.28 | all_79_0 = 0)
% 40.85/6.28 |
% 40.85/6.28 | ALPHA: (110) implies:
% 40.85/6.28 | (111) aElement0(xw) = all_79_0
% 40.85/6.28 | (112) aElement0(all_26_1) = all_79_2
% 40.85/6.28 | (113) aElement0(all_26_0) = all_79_1
% 40.85/6.28 | (114) ~ (all_79_1 = 0) | ~ (all_79_2 = 0) | all_79_0 = 0
% 40.85/6.28 |
% 40.85/6.28 | DELTA: instantiating (72) with fresh symbols all_81_0, all_81_1, all_81_2
% 40.85/6.28 | gives:
% 40.85/6.28 | (115) aElement0(all_26_1) = all_81_0 & aElement0(xa) = all_81_1 &
% 40.85/6.28 | aElement0(xy) = all_81_2 & ( ~ (all_81_1 = 0) | ~ (all_81_2 = 0) |
% 40.85/6.28 | all_81_0 = 0)
% 40.85/6.28 |
% 40.85/6.28 | ALPHA: (115) implies:
% 40.85/6.28 | (116) aElement0(xy) = all_81_2
% 40.85/6.28 | (117) aElement0(xa) = all_81_1
% 40.85/6.28 | (118) aElement0(all_26_1) = all_81_0
% 40.85/6.28 | (119) ~ (all_81_1 = 0) | ~ (all_81_2 = 0) | all_81_0 = 0
% 40.85/6.28 |
% 40.85/6.28 | DELTA: instantiating (63) with fresh symbols all_83_0, all_83_1, all_83_2
% 40.85/6.28 | gives:
% 40.85/6.28 | (120) sdtpldt0(all_30_1, xw) = all_83_0 & aElement0(all_30_1) = all_83_1 &
% 40.85/6.28 | aElement0(xw) = all_83_2 & $i(all_83_0) & ( ~ (all_83_1 = 0) | ~
% 40.85/6.28 | (all_83_2 = 0) | all_83_0 = all_30_0)
% 40.85/6.28 |
% 40.85/6.28 | ALPHA: (120) implies:
% 40.85/6.28 | (121) aElement0(xw) = all_83_2
% 40.85/6.28 |
% 40.85/6.28 | DELTA: instantiating (59) with fresh symbols all_85_0, all_85_1, all_85_2
% 40.85/6.28 | gives:
% 40.85/6.28 | (122) sdtpldt0(xb, xa) = all_85_0 & aElement0(xb) = all_85_1 &
% 40.85/6.28 | aElement0(xa) = all_85_2 & $i(all_85_0) & ( ~ (all_85_1 = 0) | ~
% 40.85/6.28 | (all_85_2 = 0) | all_85_0 = sz10)
% 40.85/6.28 |
% 40.85/6.28 | ALPHA: (122) implies:
% 40.85/6.28 | (123) aElement0(xa) = all_85_2
% 40.85/6.28 | (124) aElement0(xb) = all_85_1
% 40.85/6.28 |
% 40.85/6.28 | DELTA: instantiating (67) with fresh symbols all_87_0, all_87_1, all_87_2
% 40.85/6.28 | gives:
% 40.85/6.28 | (125) sdtpldt0(all_26_0, all_26_1) = all_87_0 & aElement0(all_26_0) =
% 40.85/6.28 | all_87_1 & aElement0(all_26_1) = all_87_2 & $i(all_87_0) & ( ~
% 40.85/6.28 | (all_87_1 = 0) | ~ (all_87_2 = 0) | all_87_0 = xw)
% 40.85/6.28 |
% 40.85/6.28 | ALPHA: (125) implies:
% 40.85/6.28 | (126) aElement0(all_26_1) = all_87_2
% 40.85/6.29 | (127) aElement0(all_26_0) = all_87_1
% 40.85/6.29 |
% 40.85/6.29 | DELTA: instantiating (71) with fresh symbols all_89_0, all_89_1, all_89_2
% 40.85/6.29 | gives:
% 40.85/6.29 | (128) sdtasdt0(xa, xy) = all_89_0 & aElement0(xa) = all_89_1 &
% 40.85/6.29 | aElement0(xy) = all_89_2 & $i(all_89_0) & ( ~ (all_89_1 = 0) | ~
% 40.85/6.29 | (all_89_2 = 0) | all_89_0 = all_26_1)
% 40.85/6.29 |
% 40.85/6.29 | ALPHA: (128) implies:
% 40.85/6.29 | (129) aElement0(xy) = all_89_2
% 40.85/6.29 | (130) aElement0(xa) = all_89_1
% 40.85/6.29 |
% 40.85/6.29 | DELTA: instantiating (61) with fresh symbols all_91_0, all_91_1, all_91_2
% 40.85/6.29 | gives:
% 40.85/6.29 | (131) sdtpldt0(all_28_1, xw) = all_91_0 & aElement0(all_28_1) = all_91_1 &
% 40.85/6.29 | aElement0(xw) = all_91_2 & $i(all_91_0) & ( ~ (all_91_1 = 0) | ~
% 40.85/6.29 | (all_91_2 = 0) | all_91_0 = all_28_0)
% 40.85/6.29 |
% 40.85/6.29 | ALPHA: (131) implies:
% 40.85/6.29 | (132) aElement0(xw) = all_91_2
% 40.85/6.29 |
% 40.85/6.29 | DELTA: instantiating (69) with fresh symbols all_93_0, all_93_1, all_93_2
% 40.85/6.29 | gives:
% 40.85/6.29 | (133) sdtasdt0(xb, xx) = all_93_0 & aElement0(xb) = all_93_1 &
% 40.85/6.29 | aElement0(xx) = all_93_2 & $i(all_93_0) & ( ~ (all_93_1 = 0) | ~
% 40.85/6.29 | (all_93_2 = 0) | all_93_0 = all_26_0)
% 40.85/6.29 |
% 40.85/6.29 | ALPHA: (133) implies:
% 40.85/6.29 | (134) aElement0(xx) = all_93_2
% 40.85/6.29 | (135) aElement0(xb) = all_93_1
% 40.85/6.29 |
% 40.85/6.29 | DELTA: instantiating (86) with fresh symbol all_95_0 gives:
% 40.85/6.29 | (136) aElementOf0(all_95_0, xJ) = 0 & sdtpldt0(all_30_0, all_30_0) =
% 40.85/6.29 | all_95_0 & $i(all_95_0)
% 40.85/6.29 |
% 40.85/6.29 | ALPHA: (136) implies:
% 40.85/6.29 | (137) sdtpldt0(all_30_0, all_30_0) = all_95_0
% 40.85/6.29 |
% 40.85/6.29 | DELTA: instantiating (80) with fresh symbols all_99_0, all_99_1, all_99_2,
% 40.85/6.29 | all_99_3 gives:
% 40.85/6.29 | (138) sdteqdtlpzmzozddtrp0(xw, xy, xJ) = all_99_0 & aIdeal0(xJ) = all_99_1
% 40.85/6.29 | & aElement0(xw) = all_99_3 & aElement0(xy) = all_99_2 & ( ~ (all_99_1
% 40.85/6.29 | = 0) | ~ (all_99_2 = 0) | ~ (all_99_3 = 0) | all_99_0 = 0)
% 40.85/6.29 |
% 40.85/6.29 | ALPHA: (138) implies:
% 40.85/6.29 | (139) aElement0(xy) = all_99_2
% 40.85/6.29 | (140) aElement0(xw) = all_99_3
% 40.85/6.29 | (141) aIdeal0(xJ) = all_99_1
% 40.85/6.29 | (142) sdteqdtlpzmzozddtrp0(xw, xy, xJ) = all_99_0
% 40.85/6.29 | (143) ~ (all_99_1 = 0) | ~ (all_99_2 = 0) | ~ (all_99_3 = 0) | all_99_0
% 40.85/6.29 | = 0
% 40.85/6.29 |
% 40.85/6.29 | DELTA: instantiating (77) with fresh symbols all_101_0, all_101_1, all_101_2,
% 40.85/6.29 | all_101_3 gives:
% 40.85/6.29 | (144) sdteqdtlpzmzozddtrp0(xw, xx, xI) = all_101_0 & aIdeal0(xI) =
% 40.85/6.29 | all_101_1 & aElement0(xw) = all_101_3 & aElement0(xx) = all_101_2 & (
% 40.85/6.29 | ~ (all_101_1 = 0) | ~ (all_101_2 = 0) | ~ (all_101_3 = 0) |
% 40.85/6.29 | all_101_0 = 0)
% 40.85/6.29 |
% 40.85/6.29 | ALPHA: (144) implies:
% 40.85/6.29 | (145) aElement0(xx) = all_101_2
% 40.85/6.29 | (146) aElement0(xw) = all_101_3
% 40.85/6.29 | (147) aIdeal0(xI) = all_101_1
% 40.85/6.29 | (148) sdteqdtlpzmzozddtrp0(xw, xx, xI) = all_101_0
% 40.85/6.29 | (149) ~ (all_101_1 = 0) | ~ (all_101_2 = 0) | ~ (all_101_3 = 0) |
% 40.85/6.29 | all_101_0 = 0
% 40.85/6.29 |
% 40.85/6.29 | DELTA: instantiating (87) with fresh symbols all_109_0, all_109_1 gives:
% 40.85/6.29 | (150) aElementOf0(all_26_0, xJ) = all_109_0 & aElement0(xx) = all_109_1 & (
% 40.85/6.29 | ~ (all_109_1 = 0) | all_109_0 = 0)
% 40.85/6.29 |
% 40.85/6.29 | ALPHA: (150) implies:
% 40.85/6.29 | (151) aElement0(xx) = all_109_1
% 40.85/6.29 |
% 40.85/6.29 | DELTA: instantiating (88) with fresh symbol all_111_0 gives:
% 40.85/6.29 | (152) aElementOf0(all_111_0, xI) = 0 & sdtpldt0(all_28_0, xa) = all_111_0 &
% 40.85/6.29 | $i(all_111_0)
% 40.85/6.29 |
% 40.85/6.29 | ALPHA: (152) implies:
% 40.85/6.29 | (153) sdtpldt0(all_28_0, xa) = all_111_0
% 40.85/6.29 |
% 40.85/6.29 | DELTA: instantiating (66) with fresh symbols all_113_0, all_113_1, all_113_2,
% 40.85/6.29 | all_113_3, all_113_4 gives:
% 40.85/6.29 | (154) sdtpldt0(all_26_0, all_28_1) = all_113_1 & sdtpldt0(all_26_1,
% 40.85/6.29 | all_113_1) = all_113_0 & aElement0(all_28_1) = all_113_2 &
% 40.85/6.29 | aElement0(all_26_0) = all_113_3 & aElement0(all_26_1) = all_113_4 &
% 40.85/6.29 | $i(all_113_0) & $i(all_113_1) & ( ~ (all_113_2 = 0) | ~ (all_113_3 =
% 40.85/6.29 | 0) | ~ (all_113_4 = 0) | all_113_0 = all_28_0)
% 40.85/6.29 |
% 40.85/6.29 | ALPHA: (154) implies:
% 40.85/6.29 | (155) aElement0(all_26_1) = all_113_4
% 40.85/6.29 | (156) aElement0(all_26_0) = all_113_3
% 40.85/6.29 |
% 40.85/6.29 | DELTA: instantiating (65) with fresh symbols all_115_0, all_115_1, all_115_2,
% 40.85/6.29 | all_115_3, all_115_4 gives:
% 40.85/6.29 | (157) sdtpldt0(all_26_0, all_30_1) = all_115_1 & sdtpldt0(all_26_1,
% 40.85/6.29 | all_115_1) = all_115_0 & aElement0(all_30_1) = all_115_2 &
% 40.85/6.29 | aElement0(all_26_0) = all_115_3 & aElement0(all_26_1) = all_115_4 &
% 40.85/6.29 | $i(all_115_0) & $i(all_115_1) & ( ~ (all_115_2 = 0) | ~ (all_115_3 =
% 40.85/6.29 | 0) | ~ (all_115_4 = 0) | all_115_0 = all_30_0)
% 40.85/6.29 |
% 40.85/6.29 | ALPHA: (157) implies:
% 40.85/6.29 | (158) aElement0(all_26_1) = all_115_4
% 40.85/6.29 | (159) aElement0(all_26_0) = all_115_3
% 40.85/6.29 |
% 40.85/6.29 | DELTA: instantiating (89) with fresh symbols all_121_0, all_121_1 gives:
% 40.85/6.29 | (160) aElementOf0(all_26_1, xI) = all_121_0 & aElement0(xy) = all_121_1 & (
% 40.85/6.29 | ~ (all_121_1 = 0) | all_121_0 = 0)
% 40.85/6.29 |
% 40.85/6.29 | ALPHA: (160) implies:
% 40.85/6.29 | (161) aElement0(xy) = all_121_1
% 40.85/6.29 |
% 40.85/6.29 | GROUND_INST: instantiating (24) with 0, all_101_2, xx, simplifying with (8),
% 40.85/6.29 | (145) gives:
% 40.85/6.29 | (162) all_101_2 = 0
% 40.85/6.29 |
% 40.85/6.29 | GROUND_INST: instantiating (24) with all_93_2, all_101_2, xx, simplifying with
% 40.85/6.29 | (134), (145) gives:
% 40.85/6.29 | (163) all_101_2 = all_93_2
% 40.85/6.29 |
% 40.85/6.29 | GROUND_INST: instantiating (24) with all_75_2, all_101_2, xx, simplifying with
% 40.85/6.29 | (104), (145) gives:
% 40.85/6.29 | (164) all_101_2 = all_75_2
% 40.85/6.29 |
% 40.85/6.29 | GROUND_INST: instantiating (24) with all_93_2, all_109_1, xx, simplifying with
% 40.85/6.29 | (134), (151) gives:
% 40.85/6.29 | (165) all_109_1 = all_93_2
% 40.85/6.29 |
% 40.85/6.29 | GROUND_INST: instantiating (24) with all_65_1, all_109_1, xx, simplifying with
% 40.85/6.29 | (93), (151) gives:
% 40.85/6.29 | (166) all_109_1 = all_65_1
% 40.85/6.29 |
% 40.85/6.29 | GROUND_INST: instantiating (24) with all_63_1, all_89_2, xy, simplifying with
% 40.85/6.29 | (91), (129) gives:
% 40.85/6.29 | (167) all_89_2 = all_63_1
% 40.85/6.29 |
% 40.85/6.29 | GROUND_INST: instantiating (24) with 0, all_99_2, xy, simplifying with (9),
% 40.85/6.29 | (139) gives:
% 40.85/6.29 | (168) all_99_2 = 0
% 40.85/6.29 |
% 40.85/6.29 | GROUND_INST: instantiating (24) with all_89_2, all_99_2, xy, simplifying with
% 40.85/6.29 | (129), (139) gives:
% 40.85/6.29 | (169) all_99_2 = all_89_2
% 40.85/6.29 |
% 40.85/6.29 | GROUND_INST: instantiating (24) with all_89_2, all_121_1, xy, simplifying with
% 40.85/6.29 | (129), (161) gives:
% 40.85/6.29 | (170) all_121_1 = all_89_2
% 40.85/6.29 |
% 40.85/6.29 | GROUND_INST: instantiating (24) with all_81_2, all_121_1, xy, simplifying with
% 40.85/6.29 | (116), (161) gives:
% 40.85/6.29 | (171) all_121_1 = all_81_2
% 40.85/6.29 |
% 40.85/6.29 | GROUND_INST: instantiating (24) with all_81_1, all_85_2, xa, simplifying with
% 40.85/6.29 | (117), (123) gives:
% 40.85/6.29 | (172) all_85_2 = all_81_1
% 40.85/6.29 |
% 40.85/6.29 | GROUND_INST: instantiating (24) with all_85_2, all_89_1, xa, simplifying with
% 40.85/6.29 | (123), (130) gives:
% 40.85/6.29 | (173) all_89_1 = all_85_2
% 40.85/6.29 |
% 40.85/6.29 | GROUND_INST: instantiating (24) with all_73_2, all_89_1, xa, simplifying with
% 40.85/6.29 | (101), (130) gives:
% 40.85/6.29 | (174) all_89_1 = all_73_2
% 40.85/6.29 |
% 40.85/6.29 | GROUND_INST: instantiating (24) with all_73_1, all_85_1, xb, simplifying with
% 40.85/6.29 | (102), (124) gives:
% 40.85/6.29 | (175) all_85_1 = all_73_1
% 40.85/6.29 |
% 40.85/6.29 | GROUND_INST: instantiating (24) with all_85_1, all_93_1, xb, simplifying with
% 40.85/6.29 | (124), (135) gives:
% 40.85/6.29 | (176) all_93_1 = all_85_1
% 40.85/6.29 |
% 40.85/6.29 | GROUND_INST: instantiating (24) with all_75_1, all_93_1, xb, simplifying with
% 40.85/6.29 | (105), (135) gives:
% 40.85/6.29 | (177) all_93_1 = all_75_1
% 40.85/6.29 |
% 40.85/6.30 | GROUND_INST: instantiating (24) with all_91_2, all_99_3, xw, simplifying with
% 40.85/6.30 | (132), (140) gives:
% 40.85/6.30 | (178) all_99_3 = all_91_2
% 40.85/6.30 |
% 40.85/6.30 | GROUND_INST: instantiating (24) with all_83_2, all_99_3, xw, simplifying with
% 40.85/6.30 | (121), (140) gives:
% 40.85/6.30 | (179) all_99_3 = all_83_2
% 40.85/6.30 |
% 40.85/6.30 | GROUND_INST: instantiating (24) with all_69_2, all_99_3, xw, simplifying with
% 40.85/6.30 | (95), (140) gives:
% 40.85/6.30 | (180) all_99_3 = all_69_2
% 40.85/6.30 |
% 40.85/6.30 | GROUND_INST: instantiating (24) with all_83_2, all_101_3, xw, simplifying with
% 40.85/6.30 | (121), (146) gives:
% 40.85/6.30 | (181) all_101_3 = all_83_2
% 40.85/6.30 |
% 40.85/6.30 | GROUND_INST: instantiating (24) with all_79_0, all_101_3, xw, simplifying with
% 40.85/6.30 | (111), (146) gives:
% 40.85/6.30 | (182) all_101_3 = all_79_0
% 40.85/6.30 |
% 40.85/6.30 | GROUND_INST: instantiating (24) with all_77_2, all_101_3, xw, simplifying with
% 40.85/6.30 | (109), (146) gives:
% 40.85/6.30 | (183) all_101_3 = all_77_2
% 40.85/6.30 |
% 40.85/6.30 | GROUND_INST: instantiating (24) with all_87_2, all_113_4, all_26_1,
% 40.85/6.30 | simplifying with (126), (155) gives:
% 40.85/6.30 | (184) all_113_4 = all_87_2
% 40.85/6.30 |
% 40.85/6.30 | GROUND_INST: instantiating (24) with all_81_0, all_113_4, all_26_1,
% 40.85/6.30 | simplifying with (118), (155) gives:
% 40.85/6.30 | (185) all_113_4 = all_81_0
% 40.85/6.30 |
% 40.85/6.30 | GROUND_INST: instantiating (24) with all_113_4, all_115_4, all_26_1,
% 40.85/6.30 | simplifying with (155), (158) gives:
% 40.85/6.30 | (186) all_115_4 = all_113_4
% 40.85/6.30 |
% 40.85/6.30 | GROUND_INST: instantiating (24) with all_79_2, all_115_4, all_26_1,
% 40.85/6.30 | simplifying with (112), (158) gives:
% 40.85/6.30 | (187) all_115_4 = all_79_2
% 40.85/6.30 |
% 40.85/6.30 | GROUND_INST: instantiating (24) with all_79_1, all_87_1, all_26_0, simplifying
% 40.85/6.30 | with (113), (127) gives:
% 40.85/6.30 | (188) all_87_1 = all_79_1
% 40.85/6.30 |
% 40.85/6.30 | GROUND_INST: instantiating (24) with all_113_3, all_115_3, all_26_0,
% 40.85/6.30 | simplifying with (156), (159) gives:
% 40.85/6.30 | (189) all_115_3 = all_113_3
% 40.85/6.30 |
% 40.85/6.30 | GROUND_INST: instantiating (24) with all_87_1, all_115_3, all_26_0,
% 40.85/6.30 | simplifying with (127), (159) gives:
% 40.85/6.30 | (190) all_115_3 = all_87_1
% 40.85/6.30 |
% 40.85/6.30 | GROUND_INST: instantiating (24) with all_75_0, all_115_3, all_26_0,
% 40.85/6.30 | simplifying with (106), (159) gives:
% 40.85/6.30 | (191) all_115_3 = all_75_0
% 40.85/6.30 |
% 40.85/6.30 | GROUND_INST: instantiating (26) with 0, all_101_1, xI, simplifying with (3),
% 40.85/6.30 | (147) gives:
% 40.85/6.30 | (192) all_101_1 = 0
% 40.85/6.30 |
% 40.85/6.30 | GROUND_INST: instantiating (26) with all_71_2, all_101_1, xI, simplifying with
% 40.85/6.30 | (97), (147) gives:
% 40.85/6.30 | (193) all_101_1 = all_71_2
% 40.85/6.30 |
% 40.85/6.30 | GROUND_INST: instantiating (26) with 0, all_99_1, xJ, simplifying with (4),
% 40.85/6.30 | (141) gives:
% 40.85/6.30 | (194) all_99_1 = 0
% 40.85/6.30 |
% 40.85/6.30 | GROUND_INST: instantiating (26) with all_71_1, all_99_1, xJ, simplifying with
% 40.85/6.30 | (98), (141) gives:
% 40.85/6.30 | (195) all_99_1 = all_71_1
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (170), (171) imply:
% 40.85/6.30 | (196) all_89_2 = all_81_2
% 40.85/6.30 |
% 40.85/6.30 | SIMP: (196) implies:
% 40.85/6.30 | (197) all_89_2 = all_81_2
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (189), (190) imply:
% 40.85/6.30 | (198) all_113_3 = all_87_1
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (189), (191) imply:
% 40.85/6.30 | (199) all_113_3 = all_75_0
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (186), (187) imply:
% 40.85/6.30 | (200) all_113_4 = all_79_2
% 40.85/6.30 |
% 40.85/6.30 | SIMP: (200) implies:
% 40.85/6.30 | (201) all_113_4 = all_79_2
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (198), (199) imply:
% 40.85/6.30 | (202) all_87_1 = all_75_0
% 40.85/6.30 |
% 40.85/6.30 | SIMP: (202) implies:
% 40.85/6.30 | (203) all_87_1 = all_75_0
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (184), (201) imply:
% 40.85/6.30 | (204) all_87_2 = all_79_2
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (184), (185) imply:
% 40.85/6.30 | (205) all_87_2 = all_81_0
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (165), (166) imply:
% 40.85/6.30 | (206) all_93_2 = all_65_1
% 40.85/6.30 |
% 40.85/6.30 | SIMP: (206) implies:
% 40.85/6.30 | (207) all_93_2 = all_65_1
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (192), (193) imply:
% 40.85/6.30 | (208) all_71_2 = 0
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (163), (164) imply:
% 40.85/6.30 | (209) all_93_2 = all_75_2
% 40.85/6.30 |
% 40.85/6.30 | SIMP: (209) implies:
% 40.85/6.30 | (210) all_93_2 = all_75_2
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (162), (164) imply:
% 40.85/6.30 | (211) all_75_2 = 0
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (182), (183) imply:
% 40.85/6.30 | (212) all_79_0 = all_77_2
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (181), (182) imply:
% 40.85/6.30 | (213) all_83_2 = all_79_0
% 40.85/6.30 |
% 40.85/6.30 | SIMP: (213) implies:
% 40.85/6.30 | (214) all_83_2 = all_79_0
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (194), (195) imply:
% 40.85/6.30 | (215) all_71_1 = 0
% 40.85/6.30 |
% 40.85/6.30 | SIMP: (215) implies:
% 40.85/6.30 | (216) all_71_1 = 0
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (168), (169) imply:
% 40.85/6.30 | (217) all_89_2 = 0
% 40.85/6.30 |
% 40.85/6.30 | SIMP: (217) implies:
% 40.85/6.30 | (218) all_89_2 = 0
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (178), (179) imply:
% 40.85/6.30 | (219) all_91_2 = all_83_2
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (178), (180) imply:
% 40.85/6.30 | (220) all_91_2 = all_69_2
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (176), (177) imply:
% 40.85/6.30 | (221) all_85_1 = all_75_1
% 40.85/6.30 |
% 40.85/6.30 | SIMP: (221) implies:
% 40.85/6.30 | (222) all_85_1 = all_75_1
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (207), (210) imply:
% 40.85/6.30 | (223) all_75_2 = all_65_1
% 40.85/6.30 |
% 40.85/6.30 | SIMP: (223) implies:
% 40.85/6.30 | (224) all_75_2 = all_65_1
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (219), (220) imply:
% 40.85/6.30 | (225) all_83_2 = all_69_2
% 40.85/6.30 |
% 40.85/6.30 | SIMP: (225) implies:
% 40.85/6.30 | (226) all_83_2 = all_69_2
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (173), (174) imply:
% 40.85/6.30 | (227) all_85_2 = all_73_2
% 40.85/6.30 |
% 40.85/6.30 | SIMP: (227) implies:
% 40.85/6.30 | (228) all_85_2 = all_73_2
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (167), (197) imply:
% 40.85/6.30 | (229) all_81_2 = all_63_1
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (197), (218) imply:
% 40.85/6.30 | (230) all_81_2 = 0
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (188), (203) imply:
% 40.85/6.30 | (231) all_79_1 = all_75_0
% 40.85/6.30 |
% 40.85/6.30 | SIMP: (231) implies:
% 40.85/6.30 | (232) all_79_1 = all_75_0
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (204), (205) imply:
% 40.85/6.30 | (233) all_81_0 = all_79_2
% 40.85/6.30 |
% 40.85/6.30 | SIMP: (233) implies:
% 40.85/6.30 | (234) all_81_0 = all_79_2
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (175), (222) imply:
% 40.85/6.30 | (235) all_75_1 = all_73_1
% 40.85/6.30 |
% 40.85/6.30 | SIMP: (235) implies:
% 40.85/6.30 | (236) all_75_1 = all_73_1
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (172), (228) imply:
% 40.85/6.30 | (237) all_81_1 = all_73_2
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (214), (226) imply:
% 40.85/6.30 | (238) all_79_0 = all_69_2
% 40.85/6.30 |
% 40.85/6.30 | SIMP: (238) implies:
% 40.85/6.30 | (239) all_79_0 = all_69_2
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (229), (230) imply:
% 40.85/6.30 | (240) all_63_1 = 0
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (212), (239) imply:
% 40.85/6.30 | (241) all_77_2 = all_69_2
% 40.85/6.30 |
% 40.85/6.30 | SIMP: (241) implies:
% 40.85/6.30 | (242) all_77_2 = all_69_2
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (211), (224) imply:
% 40.85/6.30 | (243) all_65_1 = 0
% 40.85/6.30 |
% 40.85/6.30 | COMBINE_EQS: (182), (239) imply:
% 40.85/6.30 | (244) all_101_3 = all_69_2
% 40.85/6.30 |
% 40.85/6.30 | BETA: splitting (99) gives:
% 40.85/6.30 |
% 40.85/6.30 | Case 1:
% 40.85/6.30 | |
% 40.85/6.30 | | (245) ~ (all_71_1 = 0)
% 40.85/6.30 | |
% 40.85/6.30 | | REDUCE: (216), (245) imply:
% 40.85/6.30 | | (246) $false
% 40.85/6.31 | |
% 40.85/6.31 | | CLOSE: (246) is inconsistent.
% 40.85/6.31 | |
% 40.85/6.31 | Case 2:
% 40.85/6.31 | |
% 40.85/6.31 | | (247) ~ (all_71_2 = 0) | all_71_0 = 0
% 40.85/6.31 | |
% 40.85/6.31 | | BETA: splitting (247) gives:
% 40.85/6.31 | |
% 40.85/6.31 | | Case 1:
% 40.85/6.31 | | |
% 40.85/6.31 | | | (248) ~ (all_71_2 = 0)
% 40.85/6.31 | | |
% 40.85/6.31 | | | REDUCE: (208), (248) imply:
% 40.85/6.31 | | | (249) $false
% 40.85/6.31 | | |
% 40.85/6.31 | | | CLOSE: (249) is inconsistent.
% 40.85/6.31 | | |
% 40.85/6.31 | | Case 2:
% 40.85/6.31 | | |
% 40.85/6.31 | | |
% 40.85/6.31 | | | GROUND_INST: instantiating (83) with xa, all_73_2, simplifying with (13),
% 40.85/6.31 | | | (101) gives:
% 40.85/6.31 | | | (250) all_73_2 = 0 | ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(xa, xI)
% 40.85/6.31 | | | = v0)
% 40.85/6.31 | | |
% 40.85/6.31 | | | GROUND_INST: instantiating (84) with xb, all_73_1, simplifying with (14),
% 40.85/6.31 | | | (102) gives:
% 40.85/6.31 | | | (251) all_73_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(xb, xJ)
% 40.85/6.31 | | | = v0)
% 40.85/6.31 | | |
% 40.85/6.31 | | | GROUND_INST: instantiating (mAddAsso) with xw, all_28_1, xa, all_28_0,
% 40.85/6.31 | | | all_111_0, simplifying with (13), (17), (38), (56), (153)
% 40.85/6.31 | | | gives:
% 40.85/6.31 | | | (252) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ?
% 40.85/6.31 | | | [v4: $i] : (sdtpldt0(all_28_1, xa) = v3 & sdtpldt0(xw, v3) = v4 &
% 40.85/6.31 | | | aElement0(all_28_1) = v1 & aElement0(xw) = v0 & aElement0(xa) =
% 40.85/6.31 | | | v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)
% 40.85/6.31 | | | | v4 = all_111_0))
% 40.85/6.31 | | |
% 41.01/6.31 | | | GROUND_INST: instantiating (mAddAsso) with xw, all_30_1, all_30_0,
% 41.01/6.31 | | | all_30_0, all_95_0, simplifying with (17), (41), (43), (55),
% 41.01/6.31 | | | (137) gives:
% 41.01/6.31 | | | (253) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ?
% 41.01/6.31 | | | [v4: $i] : (sdtpldt0(all_30_1, all_30_0) = v3 & sdtpldt0(xw, v3)
% 41.01/6.31 | | | = v4 & aElement0(all_30_0) = v2 & aElement0(all_30_1) = v1 &
% 41.01/6.31 | | | aElement0(xw) = v0 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 =
% 41.01/6.31 | | | 0) | ~ (v0 = 0) | v4 = all_95_0))
% 41.01/6.31 | | |
% 41.01/6.31 | | | GROUND_INST: instantiating (52) with xw, all_99_0, simplifying with (17),
% 41.01/6.31 | | | (142) gives:
% 41.01/6.31 | | | (254) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : ?
% 41.01/6.31 | | | [v4: $i] : ? [v5: any] : (sdteqdtlpzmzozddtrp0(xw, xx, xI) = v3
% 41.01/6.31 | | | & aElementOf0(v4, xJ) = v5 & aElementOf0(v1, xI) = v2 &
% 41.01/6.31 | | | sdtpldt0(xw, all_38_0) = v4 & sdtpldt0(xw, all_38_1) = v1 &
% 41.01/6.31 | | | aElement0(xw) = v0 & $i(v4) & $i(v1) & ( ~ (v0 = 0) | ( ~ (v5 =
% 41.01/6.31 | | | 0) & ~ (all_99_0 = 0)) | ( ~ (v3 = 0) & ~ (v2 = 0))))
% 41.01/6.31 | | |
% 41.01/6.31 | | | DELTA: instantiating (253) with fresh symbols all_333_0, all_333_1,
% 41.01/6.31 | | | all_333_2, all_333_3, all_333_4 gives:
% 41.01/6.31 | | | (255) sdtpldt0(all_30_1, all_30_0) = all_333_1 & sdtpldt0(xw,
% 41.01/6.31 | | | all_333_1) = all_333_0 & aElement0(all_30_0) = all_333_2 &
% 41.01/6.31 | | | aElement0(all_30_1) = all_333_3 & aElement0(xw) = all_333_4 &
% 41.01/6.31 | | | $i(all_333_0) & $i(all_333_1) & ( ~ (all_333_2 = 0) | ~
% 41.01/6.31 | | | (all_333_3 = 0) | ~ (all_333_4 = 0) | all_333_0 = all_95_0)
% 41.01/6.31 | | |
% 41.01/6.31 | | | ALPHA: (255) implies:
% 41.01/6.31 | | | (256) aElement0(xw) = all_333_4
% 41.01/6.31 | | |
% 41.01/6.31 | | | DELTA: instantiating (252) with fresh symbols all_345_0, all_345_1,
% 41.01/6.31 | | | all_345_2, all_345_3, all_345_4 gives:
% 41.01/6.31 | | | (257) sdtpldt0(all_28_1, xa) = all_345_1 & sdtpldt0(xw, all_345_1) =
% 41.01/6.31 | | | all_345_0 & aElement0(all_28_1) = all_345_3 & aElement0(xw) =
% 41.01/6.31 | | | all_345_4 & aElement0(xa) = all_345_2 & $i(all_345_0) &
% 41.01/6.31 | | | $i(all_345_1) & ( ~ (all_345_2 = 0) | ~ (all_345_3 = 0) | ~
% 41.01/6.31 | | | (all_345_4 = 0) | all_345_0 = all_111_0)
% 41.01/6.31 | | |
% 41.01/6.31 | | | ALPHA: (257) implies:
% 41.01/6.31 | | | (258) aElement0(xw) = all_345_4
% 41.01/6.31 | | |
% 41.01/6.31 | | | DELTA: instantiating (254) with fresh symbols all_363_0, all_363_1,
% 41.01/6.31 | | | all_363_2, all_363_3, all_363_4, all_363_5 gives:
% 41.01/6.31 | | | (259) sdteqdtlpzmzozddtrp0(xw, xx, xI) = all_363_2 &
% 41.01/6.31 | | | aElementOf0(all_363_1, xJ) = all_363_0 & aElementOf0(all_363_4,
% 41.01/6.31 | | | xI) = all_363_3 & sdtpldt0(xw, all_38_0) = all_363_1 &
% 41.01/6.31 | | | sdtpldt0(xw, all_38_1) = all_363_4 & aElement0(xw) = all_363_5 &
% 41.01/6.31 | | | $i(all_363_1) & $i(all_363_4) & ( ~ (all_363_5 = 0) | ( ~
% 41.01/6.31 | | | (all_363_0 = 0) & ~ (all_99_0 = 0)) | ( ~ (all_363_2 = 0) &
% 41.01/6.31 | | | ~ (all_363_3 = 0)))
% 41.01/6.31 | | |
% 41.01/6.31 | | | ALPHA: (259) implies:
% 41.01/6.31 | | | (260) aElement0(xw) = all_363_5
% 41.01/6.31 | | | (261) sdteqdtlpzmzozddtrp0(xw, xx, xI) = all_363_2
% 41.01/6.31 | | | (262) ~ (all_363_5 = 0) | ( ~ (all_363_0 = 0) & ~ (all_99_0 = 0)) | (
% 41.01/6.31 | | | ~ (all_363_2 = 0) & ~ (all_363_3 = 0))
% 41.01/6.31 | | |
% 41.01/6.31 | | | BETA: splitting (250) gives:
% 41.01/6.31 | | |
% 41.01/6.31 | | | Case 1:
% 41.01/6.31 | | | |
% 41.01/6.31 | | | | (263) all_73_2 = 0
% 41.01/6.31 | | | |
% 41.01/6.31 | | | | COMBINE_EQS: (237), (263) imply:
% 41.01/6.31 | | | | (264) all_81_1 = 0
% 41.01/6.31 | | | |
% 41.01/6.31 | | | | BETA: splitting (251) gives:
% 41.01/6.31 | | | |
% 41.01/6.31 | | | | Case 1:
% 41.01/6.31 | | | | |
% 41.01/6.31 | | | | | (265) all_73_1 = 0
% 41.01/6.31 | | | | |
% 41.01/6.31 | | | | | COMBINE_EQS: (236), (265) imply:
% 41.01/6.31 | | | | | (266) all_75_1 = 0
% 41.01/6.31 | | | | |
% 41.01/6.31 | | | | | BETA: splitting (107) gives:
% 41.01/6.31 | | | | |
% 41.01/6.31 | | | | | Case 1:
% 41.01/6.31 | | | | | |
% 41.01/6.31 | | | | | | (267) ~ (all_75_1 = 0)
% 41.01/6.31 | | | | | |
% 41.01/6.31 | | | | | | REDUCE: (266), (267) imply:
% 41.01/6.31 | | | | | | (268) $false
% 41.01/6.31 | | | | | |
% 41.01/6.31 | | | | | | CLOSE: (268) is inconsistent.
% 41.01/6.31 | | | | | |
% 41.01/6.31 | | | | | Case 2:
% 41.01/6.31 | | | | | |
% 41.01/6.31 | | | | | | (269) ~ (all_75_2 = 0) | all_75_0 = 0
% 41.01/6.31 | | | | | |
% 41.01/6.31 | | | | | | BETA: splitting (269) gives:
% 41.01/6.31 | | | | | |
% 41.01/6.31 | | | | | | Case 1:
% 41.01/6.31 | | | | | | |
% 41.01/6.31 | | | | | | | (270) ~ (all_75_2 = 0)
% 41.01/6.31 | | | | | | |
% 41.01/6.31 | | | | | | | REDUCE: (211), (270) imply:
% 41.01/6.31 | | | | | | | (271) $false
% 41.01/6.31 | | | | | | |
% 41.01/6.31 | | | | | | | CLOSE: (271) is inconsistent.
% 41.01/6.31 | | | | | | |
% 41.01/6.31 | | | | | | Case 2:
% 41.01/6.31 | | | | | | |
% 41.01/6.31 | | | | | | | (272) all_75_0 = 0
% 41.01/6.31 | | | | | | |
% 41.01/6.31 | | | | | | | COMBINE_EQS: (232), (272) imply:
% 41.01/6.31 | | | | | | | (273) all_79_1 = 0
% 41.01/6.31 | | | | | | |
% 41.01/6.31 | | | | | | | BETA: splitting (114) gives:
% 41.01/6.31 | | | | | | |
% 41.01/6.31 | | | | | | | Case 1:
% 41.01/6.31 | | | | | | | |
% 41.01/6.31 | | | | | | | | (274) ~ (all_79_1 = 0)
% 41.01/6.31 | | | | | | | |
% 41.01/6.31 | | | | | | | | REDUCE: (273), (274) imply:
% 41.01/6.31 | | | | | | | | (275) $false
% 41.01/6.31 | | | | | | | |
% 41.01/6.31 | | | | | | | | CLOSE: (275) is inconsistent.
% 41.01/6.31 | | | | | | | |
% 41.01/6.31 | | | | | | | Case 2:
% 41.01/6.31 | | | | | | | |
% 41.01/6.31 | | | | | | | | (276) ~ (all_79_2 = 0) | all_79_0 = 0
% 41.01/6.31 | | | | | | | |
% 41.01/6.31 | | | | | | | | BETA: splitting (276) gives:
% 41.01/6.31 | | | | | | | |
% 41.01/6.31 | | | | | | | | Case 1:
% 41.01/6.31 | | | | | | | | |
% 41.01/6.31 | | | | | | | | | (277) ~ (all_79_2 = 0)
% 41.01/6.31 | | | | | | | | |
% 41.01/6.31 | | | | | | | | | BETA: splitting (119) gives:
% 41.01/6.31 | | | | | | | | |
% 41.01/6.31 | | | | | | | | | Case 1:
% 41.01/6.31 | | | | | | | | | |
% 41.01/6.31 | | | | | | | | | | (278) ~ (all_81_1 = 0)
% 41.01/6.31 | | | | | | | | | |
% 41.01/6.31 | | | | | | | | | | REDUCE: (264), (278) imply:
% 41.01/6.31 | | | | | | | | | | (279) $false
% 41.01/6.31 | | | | | | | | | |
% 41.01/6.31 | | | | | | | | | | CLOSE: (279) is inconsistent.
% 41.01/6.31 | | | | | | | | | |
% 41.01/6.31 | | | | | | | | | Case 2:
% 41.01/6.31 | | | | | | | | | |
% 41.01/6.31 | | | | | | | | | | (280) ~ (all_81_2 = 0) | all_81_0 = 0
% 41.01/6.31 | | | | | | | | | |
% 41.01/6.31 | | | | | | | | | | BETA: splitting (280) gives:
% 41.01/6.31 | | | | | | | | | |
% 41.01/6.31 | | | | | | | | | | Case 1:
% 41.01/6.31 | | | | | | | | | | |
% 41.01/6.31 | | | | | | | | | | | (281) ~ (all_81_2 = 0)
% 41.01/6.31 | | | | | | | | | | |
% 41.01/6.31 | | | | | | | | | | | REDUCE: (230), (281) imply:
% 41.01/6.31 | | | | | | | | | | | (282) $false
% 41.01/6.31 | | | | | | | | | | |
% 41.01/6.31 | | | | | | | | | | | CLOSE: (282) is inconsistent.
% 41.01/6.31 | | | | | | | | | | |
% 41.01/6.31 | | | | | | | | | | Case 2:
% 41.01/6.31 | | | | | | | | | | |
% 41.01/6.31 | | | | | | | | | | | (283) all_81_0 = 0
% 41.01/6.31 | | | | | | | | | | |
% 41.01/6.31 | | | | | | | | | | | COMBINE_EQS: (234), (283) imply:
% 41.01/6.31 | | | | | | | | | | | (284) all_79_2 = 0
% 41.01/6.31 | | | | | | | | | | |
% 41.01/6.31 | | | | | | | | | | | SIMP: (284) implies:
% 41.01/6.31 | | | | | | | | | | | (285) all_79_2 = 0
% 41.01/6.31 | | | | | | | | | | |
% 41.01/6.31 | | | | | | | | | | | REDUCE: (277), (285) imply:
% 41.01/6.31 | | | | | | | | | | | (286) $false
% 41.01/6.31 | | | | | | | | | | |
% 41.01/6.31 | | | | | | | | | | | CLOSE: (286) is inconsistent.
% 41.01/6.31 | | | | | | | | | | |
% 41.01/6.31 | | | | | | | | | | End of split
% 41.01/6.31 | | | | | | | | | |
% 41.01/6.31 | | | | | | | | | End of split
% 41.01/6.31 | | | | | | | | |
% 41.01/6.31 | | | | | | | | Case 2:
% 41.01/6.31 | | | | | | | | |
% 41.01/6.31 | | | | | | | | | (287) all_79_0 = 0
% 41.01/6.31 | | | | | | | | |
% 41.01/6.31 | | | | | | | | | COMBINE_EQS: (239), (287) imply:
% 41.01/6.31 | | | | | | | | | (288) all_69_2 = 0
% 41.01/6.31 | | | | | | | | |
% 41.01/6.31 | | | | | | | | | SIMP: (288) implies:
% 41.01/6.31 | | | | | | | | | (289) all_69_2 = 0
% 41.01/6.31 | | | | | | | | |
% 41.01/6.31 | | | | | | | | | COMBINE_EQS: (180), (289) imply:
% 41.01/6.32 | | | | | | | | | (290) all_99_3 = 0
% 41.01/6.32 | | | | | | | | |
% 41.01/6.32 | | | | | | | | | COMBINE_EQS: (244), (289) imply:
% 41.01/6.32 | | | | | | | | | (291) all_101_3 = 0
% 41.01/6.32 | | | | | | | | |
% 41.01/6.32 | | | | | | | | | REDUCE: (95), (289) imply:
% 41.01/6.32 | | | | | | | | | (292) aElement0(xw) = 0
% 41.01/6.32 | | | | | | | | |
% 41.01/6.32 | | | | | | | | | BETA: splitting (143) gives:
% 41.01/6.32 | | | | | | | | |
% 41.01/6.32 | | | | | | | | | Case 1:
% 41.01/6.32 | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | (293) ~ (all_99_1 = 0)
% 41.01/6.32 | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | REDUCE: (194), (293) imply:
% 41.01/6.32 | | | | | | | | | | (294) $false
% 41.01/6.32 | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | CLOSE: (294) is inconsistent.
% 41.01/6.32 | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | Case 2:
% 41.01/6.32 | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | (295) ~ (all_99_2 = 0) | ~ (all_99_3 = 0) | all_99_0 =
% 41.01/6.32 | | | | | | | | | | 0
% 41.01/6.32 | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | BETA: splitting (149) gives:
% 41.01/6.32 | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | Case 1:
% 41.01/6.32 | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | (296) ~ (all_101_1 = 0)
% 41.01/6.32 | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | REDUCE: (192), (296) imply:
% 41.01/6.32 | | | | | | | | | | | (297) $false
% 41.01/6.32 | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | CLOSE: (297) is inconsistent.
% 41.01/6.32 | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | Case 2:
% 41.01/6.32 | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | (298) ~ (all_101_2 = 0) | ~ (all_101_3 = 0) |
% 41.01/6.32 | | | | | | | | | | | all_101_0 = 0
% 41.01/6.32 | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | BETA: splitting (298) gives:
% 41.01/6.32 | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | Case 1:
% 41.01/6.32 | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | (299) ~ (all_101_2 = 0)
% 41.01/6.32 | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | REDUCE: (162), (299) imply:
% 41.01/6.32 | | | | | | | | | | | | (300) $false
% 41.01/6.32 | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | CLOSE: (300) is inconsistent.
% 41.01/6.32 | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | Case 2:
% 41.01/6.32 | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | (301) ~ (all_101_3 = 0) | all_101_0 = 0
% 41.01/6.32 | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | BETA: splitting (295) gives:
% 41.01/6.32 | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | Case 1:
% 41.01/6.32 | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | (302) ~ (all_99_2 = 0)
% 41.01/6.32 | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | REDUCE: (168), (302) imply:
% 41.01/6.32 | | | | | | | | | | | | | (303) $false
% 41.01/6.32 | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | CLOSE: (303) is inconsistent.
% 41.01/6.32 | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | Case 2:
% 41.01/6.32 | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | (304) ~ (all_99_3 = 0) | all_99_0 = 0
% 41.01/6.32 | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | BETA: splitting (304) gives:
% 41.01/6.32 | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | Case 1:
% 41.01/6.32 | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | (305) ~ (all_99_3 = 0)
% 41.01/6.32 | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | REDUCE: (290), (305) imply:
% 41.01/6.32 | | | | | | | | | | | | | | (306) $false
% 41.01/6.32 | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | CLOSE: (306) is inconsistent.
% 41.01/6.32 | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | Case 2:
% 41.01/6.32 | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | (307) all_99_0 = 0
% 41.01/6.32 | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 41.01/6.32 | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | Case 1:
% 41.01/6.32 | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | (308) ~ (all_101_3 = 0)
% 41.01/6.32 | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | REDUCE: (291), (308) imply:
% 41.01/6.32 | | | | | | | | | | | | | | | (309) $false
% 41.01/6.32 | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | CLOSE: (309) is inconsistent.
% 41.01/6.32 | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | Case 2:
% 41.01/6.32 | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | (310) all_101_0 = 0
% 41.01/6.32 | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | REDUCE: (148), (310) imply:
% 41.01/6.32 | | | | | | | | | | | | | | | (311) sdteqdtlpzmzozddtrp0(xw, xx, xI) = 0
% 41.01/6.32 | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_345_4, all_363_5, xw,
% 41.01/6.32 | | | | | | | | | | | | | | | simplifying with (258), (260) gives:
% 41.01/6.32 | | | | | | | | | | | | | | | (312) all_363_5 = all_345_4
% 41.01/6.32 | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_333_4, all_363_5, xw,
% 41.01/6.32 | | | | | | | | | | | | | | | simplifying with (256), (260) gives:
% 41.01/6.32 | | | | | | | | | | | | | | | (313) all_363_5 = all_333_4
% 41.01/6.32 | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with 0, all_363_5, xw,
% 41.01/6.32 | | | | | | | | | | | | | | | simplifying with (260), (292) gives:
% 41.01/6.32 | | | | | | | | | | | | | | | (314) all_363_5 = 0
% 41.01/6.32 | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with 0, all_363_2, xI, xx, xw,
% 41.01/6.32 | | | | | | | | | | | | | | | simplifying with (261), (311) gives:
% 41.01/6.32 | | | | | | | | | | | | | | | (315) all_363_2 = 0
% 41.01/6.32 | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | COMBINE_EQS: (312), (313) imply:
% 41.01/6.32 | | | | | | | | | | | | | | | (316) all_345_4 = all_333_4
% 41.01/6.32 | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | COMBINE_EQS: (312), (314) imply:
% 41.01/6.32 | | | | | | | | | | | | | | | (317) all_345_4 = 0
% 41.01/6.32 | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | COMBINE_EQS: (316), (317) imply:
% 41.01/6.32 | | | | | | | | | | | | | | | (318) all_333_4 = 0
% 41.01/6.32 | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | BETA: splitting (262) gives:
% 41.01/6.32 | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | Case 1:
% 41.01/6.32 | | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | | (319) ~ (all_363_5 = 0)
% 41.01/6.32 | | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | | REDUCE: (314), (319) imply:
% 41.01/6.32 | | | | | | | | | | | | | | | | (320) $false
% 41.01/6.32 | | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | | CLOSE: (320) is inconsistent.
% 41.01/6.32 | | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | Case 2:
% 41.01/6.32 | | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | | (321) ( ~ (all_363_0 = 0) & ~ (all_99_0 = 0)) | ( ~
% 41.01/6.32 | | | | | | | | | | | | | | | | (all_363_2 = 0) & ~ (all_363_3 = 0))
% 41.01/6.32 | | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | | BETA: splitting (321) gives:
% 41.01/6.32 | | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | | Case 1:
% 41.01/6.32 | | | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | | | (322) ~ (all_363_0 = 0) & ~ (all_99_0 = 0)
% 41.01/6.32 | | | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | | | ALPHA: (322) implies:
% 41.01/6.32 | | | | | | | | | | | | | | | | | (323) ~ (all_99_0 = 0)
% 41.01/6.32 | | | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | | | REDUCE: (307), (323) imply:
% 41.01/6.32 | | | | | | | | | | | | | | | | | (324) $false
% 41.01/6.32 | | | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | | | CLOSE: (324) is inconsistent.
% 41.01/6.32 | | | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | | Case 2:
% 41.01/6.32 | | | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | | | (325) ~ (all_363_2 = 0) & ~ (all_363_3 = 0)
% 41.01/6.32 | | | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | | | ALPHA: (325) implies:
% 41.01/6.32 | | | | | | | | | | | | | | | | | (326) ~ (all_363_2 = 0)
% 41.01/6.32 | | | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | | | REDUCE: (315), (326) imply:
% 41.01/6.32 | | | | | | | | | | | | | | | | | (327) $false
% 41.01/6.32 | | | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | | | CLOSE: (327) is inconsistent.
% 41.01/6.32 | | | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | | End of split
% 41.01/6.32 | | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | | End of split
% 41.01/6.32 | | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | | End of split
% 41.01/6.32 | | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | | End of split
% 41.01/6.32 | | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | | End of split
% 41.01/6.32 | | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | | End of split
% 41.01/6.32 | | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | | End of split
% 41.01/6.32 | | | | | | | | | |
% 41.01/6.32 | | | | | | | | | End of split
% 41.01/6.32 | | | | | | | | |
% 41.01/6.32 | | | | | | | | End of split
% 41.01/6.32 | | | | | | | |
% 41.01/6.32 | | | | | | | End of split
% 41.01/6.32 | | | | | | |
% 41.01/6.32 | | | | | | End of split
% 41.01/6.32 | | | | | |
% 41.01/6.32 | | | | | End of split
% 41.01/6.32 | | | | |
% 41.01/6.32 | | | | Case 2:
% 41.01/6.32 | | | | |
% 41.01/6.32 | | | | | (328) ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(xb, xJ) = v0)
% 41.01/6.32 | | | | |
% 41.01/6.32 | | | | | DELTA: instantiating (328) with fresh symbol all_459_0 gives:
% 41.01/6.32 | | | | | (329) ~ (all_459_0 = 0) & aElementOf0(xb, xJ) = all_459_0
% 41.01/6.32 | | | | |
% 41.01/6.32 | | | | | ALPHA: (329) implies:
% 41.01/6.32 | | | | | (330) ~ (all_459_0 = 0)
% 41.01/6.32 | | | | | (331) aElementOf0(xb, xJ) = all_459_0
% 41.01/6.32 | | | | |
% 41.01/6.32 | | | | | GROUND_INST: instantiating (27) with 0, all_459_0, xJ, xb, simplifying
% 41.01/6.32 | | | | | with (12), (331) gives:
% 41.01/6.32 | | | | | (332) all_459_0 = 0
% 41.01/6.32 | | | | |
% 41.01/6.32 | | | | | REDUCE: (330), (332) imply:
% 41.01/6.32 | | | | | (333) $false
% 41.01/6.32 | | | | |
% 41.01/6.32 | | | | | CLOSE: (333) is inconsistent.
% 41.01/6.32 | | | | |
% 41.01/6.32 | | | | End of split
% 41.01/6.32 | | | |
% 41.01/6.32 | | | Case 2:
% 41.01/6.32 | | | |
% 41.01/6.32 | | | | (334) ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(xa, xI) = v0)
% 41.01/6.32 | | | |
% 41.01/6.32 | | | | DELTA: instantiating (334) with fresh symbol all_451_0 gives:
% 41.01/6.32 | | | | (335) ~ (all_451_0 = 0) & aElementOf0(xa, xI) = all_451_0
% 41.01/6.32 | | | |
% 41.01/6.32 | | | | ALPHA: (335) implies:
% 41.01/6.32 | | | | (336) ~ (all_451_0 = 0)
% 41.01/6.32 | | | | (337) aElementOf0(xa, xI) = all_451_0
% 41.01/6.32 | | | |
% 41.01/6.32 | | | | GROUND_INST: instantiating (27) with 0, all_451_0, xI, xa, simplifying
% 41.01/6.32 | | | | with (11), (337) gives:
% 41.01/6.32 | | | | (338) all_451_0 = 0
% 41.01/6.32 | | | |
% 41.01/6.32 | | | | REDUCE: (336), (338) imply:
% 41.01/6.32 | | | | (339) $false
% 41.01/6.32 | | | |
% 41.01/6.32 | | | | CLOSE: (339) is inconsistent.
% 41.01/6.32 | | | |
% 41.01/6.32 | | | End of split
% 41.01/6.32 | | |
% 41.01/6.32 | | End of split
% 41.01/6.32 | |
% 41.01/6.32 | End of split
% 41.01/6.32 |
% 41.01/6.32 End of proof
% 41.01/6.32 % SZS output end Proof for theBenchmark
% 41.01/6.32
% 41.01/6.32 5729ms
%------------------------------------------------------------------------------