TSTP Solution File: NUM453+6 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM453+6 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n032.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 11:47:51 EDT 2023
% Result : Theorem 47.46s 7.03s
% Output : Proof 154.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : NUM453+6 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Fri Aug 25 10:28:12 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.16/0.52 ________ _____
% 0.16/0.52 ___ __ \_________(_)________________________________
% 0.16/0.52 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.16/0.52 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.16/0.52 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.16/0.52
% 0.16/0.52 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.16/0.52 (2023-06-19)
% 0.16/0.52
% 0.16/0.52 (c) Philipp Rümmer, 2009-2023
% 0.16/0.52 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.16/0.52 Amanda Stjerna.
% 0.16/0.52 Free software under BSD-3-Clause.
% 0.16/0.52
% 0.16/0.52 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.16/0.52
% 0.16/0.52 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.16/0.53 Running up to 7 provers in parallel.
% 0.16/0.54 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.16/0.54 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.16/0.54 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.16/0.54 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.16/0.54 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.16/0.54 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.16/0.54 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.41/1.26 Prover 1: Preprocessing ...
% 4.41/1.26 Prover 4: Preprocessing ...
% 4.65/1.29 Prover 5: Preprocessing ...
% 4.65/1.29 Prover 0: Preprocessing ...
% 4.65/1.29 Prover 6: Preprocessing ...
% 4.65/1.29 Prover 3: Preprocessing ...
% 4.65/1.29 Prover 2: Preprocessing ...
% 13.35/2.51 Prover 1: Constructing countermodel ...
% 13.35/2.53 Prover 3: Constructing countermodel ...
% 13.35/2.55 Prover 6: Proving ...
% 13.35/2.56 Prover 5: Proving ...
% 15.08/2.75 Prover 2: Proving ...
% 19.96/3.37 Prover 4: Constructing countermodel ...
% 20.82/3.47 Prover 0: Proving ...
% 47.46/7.01 Prover 6: proved (6465ms)
% 47.46/7.01
% 47.46/7.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 47.46/7.03
% 47.46/7.03 Prover 0: stopped
% 47.46/7.03 Prover 2: stopped
% 47.46/7.05 Prover 5: stopped
% 47.46/7.06 Prover 3: stopped
% 47.46/7.07 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 47.46/7.07 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 47.46/7.07 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 47.46/7.07 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 47.46/7.08 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 48.80/7.21 Prover 8: Preprocessing ...
% 48.80/7.23 Prover 7: Preprocessing ...
% 48.80/7.23 Prover 10: Preprocessing ...
% 49.38/7.30 Prover 11: Preprocessing ...
% 49.84/7.33 Prover 13: Preprocessing ...
% 50.83/7.45 Prover 8: Warning: ignoring some quantifiers
% 50.83/7.45 Prover 7: Warning: ignoring some quantifiers
% 50.83/7.47 Prover 8: Constructing countermodel ...
% 50.83/7.47 Prover 10: Warning: ignoring some quantifiers
% 50.83/7.47 Prover 7: Constructing countermodel ...
% 51.11/7.49 Prover 10: Constructing countermodel ...
% 52.16/7.71 Prover 13: Warning: ignoring some quantifiers
% 52.16/7.72 Prover 13: Constructing countermodel ...
% 55.88/8.14 Prover 11: Constructing countermodel ...
% 82.61/11.68 Prover 13: stopped
% 83.08/11.69 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 83.77/11.80 Prover 16: Preprocessing ...
% 84.25/12.03 Prover 16: Warning: ignoring some quantifiers
% 84.25/12.03 Prover 16: Constructing countermodel ...
% 114.94/15.88 Prover 1: stopped
% 114.94/15.89 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 115.60/15.97 Prover 19: Preprocessing ...
% 118.24/16.42 Prover 19: Warning: ignoring some quantifiers
% 118.24/16.44 Prover 19: Constructing countermodel ...
% 123.27/17.02 Prover 16: stopped
% 140.13/19.47 Prover 19: stopped
% 153.83/21.75 Prover 10: Found proof (size 323)
% 153.83/21.75 Prover 10: proved (14706ms)
% 153.92/21.76 Prover 4: stopped
% 153.92/21.76 Prover 7: stopped
% 153.92/21.76 Prover 8: stopped
% 153.92/21.76 Prover 11: stopped
% 153.92/21.76
% 153.92/21.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 153.92/21.76
% 153.92/21.78 % SZS output start Proof for theBenchmark
% 153.92/21.79 Assumptions after simplification:
% 153.92/21.79 ---------------------------------
% 153.92/21.79
% 153.92/21.79 (mAddAsso)
% 154.17/21.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 154.17/21.82 (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 154.17/21.82 | ~ $i(v0) | ~ aInteger0(v2) | ~ aInteger0(v1) | ~ aInteger0(v0) | ?
% 154.17/21.82 [v5: $i] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4 & $i(v5) &
% 154.17/21.82 $i(v4)))
% 154.17/21.82
% 154.17/21.82 (mAddComm)
% 154.17/21.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 154.17/21.82 $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) | (sdtpldt0(v1, v0)
% 154.17/21.82 = v2 & $i(v2)))
% 154.17/21.82
% 154.17/21.82 (mAddNeg)
% 154.17/21.82 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = sz00 | ~
% 154.17/21.82 (sdtpldt0(v1, v0) = v2) | ~ (smndt0(v0) = v1) | ~ $i(v0) | ~
% 154.17/21.82 aInteger0(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v1,
% 154.17/21.82 v0) = v2) | ~ (smndt0(v0) = v1) | ~ $i(v0) | ~ aInteger0(v0) |
% 154.17/21.82 sdtpldt0(v0, v1) = sz00)
% 154.17/21.82
% 154.17/21.82 (mAddZero)
% 154.17/21.82 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1)
% 154.17/21.82 | ~ $i(v0) | ~ aInteger0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 154.17/21.82 (sdtpldt0(sz00, v0) = v1) | ~ $i(v0) | ~ aInteger0(v0) | sdtpldt0(v0,
% 154.17/21.82 sz00) = v0)
% 154.17/21.82
% 154.17/21.82 (mArSeq)
% 154.17/21.83 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 |
% 154.17/21.83 v1 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1)
% 154.17/21.83 | ~ $i(v0) | ~ aSet0(v3) | ~ aInteger0(v1) | ~ aInteger0(v0) | ? [v4:
% 154.17/21.83 $i] : ($i(v4) & ( ~ aElementOf0(v4, v3) | ~ sdteqdtlpzmzozddtrp0(v4, v0,
% 154.17/21.83 v1) | ~ aInteger0(v4)) & (aElementOf0(v4, v3) |
% 154.17/21.83 (sdteqdtlpzmzozddtrp0(v4, v0, v1) & aInteger0(v4))))) & ! [v0: $i] : !
% 154.17/21.83 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = sz00 | ~
% 154.17/21.83 (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 154.17/21.83 ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aInteger0(v1) | ~ aInteger0(v0) |
% 154.17/21.83 sdteqdtlpzmzozddtrp0(v3, v0, v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 154.17/21.83 : ! [v3: $i] : (v1 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) | ~
% 154.17/21.83 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~
% 154.17/21.83 aInteger0(v1) | ~ aInteger0(v0) | aInteger0(v3)) & ! [v0: $i] : ! [v1:
% 154.17/21.83 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = sz00 | ~
% 154.17/21.83 (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 154.17/21.83 ~ $i(v0) | ~ sdteqdtlpzmzozddtrp0(v3, v0, v1) | ~ aInteger0(v3) | ~
% 154.17/21.83 aInteger0(v1) | ~ aInteger0(v0) | aElementOf0(v3, v2)) & ! [v0: $i] : !
% 154.17/21.83 [v1: $i] : ! [v2: $i] : (v1 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2)
% 154.17/21.83 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) |
% 154.17/21.83 aSet0(v2))
% 154.17/21.83
% 154.17/21.83 (mEquModRef)
% 154.17/21.83 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ $i(v1) | ~ $i(v0) | ~
% 154.17/21.83 aInteger0(v1) | ~ aInteger0(v0) | sdteqdtlpzmzozddtrp0(v0, v0, v1))
% 154.17/21.83
% 154.17/21.83 (mIntMult)
% 154.17/21.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 154.17/21.84 $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) | aInteger0(v2))
% 154.17/21.84
% 154.17/21.84 (mIntNeg)
% 154.17/21.84 ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ~
% 154.17/21.84 aInteger0(v0) | aInteger0(v1))
% 154.17/21.84
% 154.17/21.84 (mIntOne)
% 154.17/21.84 $i(sz10) & aInteger0(sz10)
% 154.17/21.84
% 154.17/21.84 (mIntPlus)
% 154.17/21.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 154.17/21.84 $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) | aInteger0(v2))
% 154.17/21.84
% 154.17/21.84 (mIntZero)
% 154.17/21.84 $i(sz00) & aInteger0(sz00)
% 154.17/21.84
% 154.17/21.84 (mMulMinOne)
% 154.17/21.84 $i(sz10) & ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 154.17/21.84 $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ aInteger0(v1) |
% 154.17/21.84 (sdtasdt0(v1, v0) = v2 & smndt0(v1) = v2 & $i(v2))))
% 154.17/21.84
% 154.17/21.84 (mPrimeDivisor)
% 154.17/21.84 $i(sz10) & ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : (v1 = v0
% 154.17/21.84 | v1 = sz10 | ~ $i(v1) | ~ aInteger0(v1) | ? [v2: $i] : ($i(v2) &
% 154.17/21.84 isPrime0(v2) & aDivisorOf0(v2, v1))) & ! [v1: $i] : ( ~ $i(v1) | ~
% 154.17/21.84 isPrime0(v1) | ~ aDivisorOf0(v1, v0) | ~ aInteger0(v0)) & ! [v1: $i] :
% 154.17/21.84 ( ~ $i(v1) | ~ isPrime0(v1) | ~ aDivisorOf0(v1, sz10) | ~
% 154.17/21.84 aInteger0(sz10)))
% 154.17/21.84
% 154.17/21.84 (mSubset)
% 154.17/21.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 154.17/21.85 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) |
% 154.17/21.85 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) |
% 154.17/21.85 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i]
% 154.17/21.85 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) |
% 154.17/21.85 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)))
% 154.17/21.85
% 154.17/21.85 (m__)
% 154.17/21.85 $i(xp) & $i(sz10) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ((v2 = sz10 &
% 154.17/21.85 sdtpldt0(sz10, v1) = sz10 & smndt0(xp) = v1 & $i(v1)) | (v0 = sz10 &
% 154.17/21.85 sdtpldt0(sz10, xp) = sz10))
% 154.17/21.85
% 154.17/21.85 (m__2079)
% 154.17/21.85 $i(cS2076) & $i(xS) & $i(sz10) & ? [v0: $i] : ? [v1: $i] : (stldt0(v0) =
% 154.17/21.85 cS2076 & sbsmnsldt0(xS) = v0 & smndt0(sz10) = v1 & $i(v1) & $i(v0) &
% 154.17/21.85 aElementOf0(v1, cS2076) & aElementOf0(sz10, cS2076) & aSet0(v0) &
% 154.17/21.85 aSet0(cS2076) & ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 154.17/21.85 aElementOf0(v3, xS) | ~ aElementOf0(v2, v3) | ~ aInteger0(v2) |
% 154.17/21.85 aElementOf0(v2, v0)) & ! [v2: $i] : (v2 = v1 | v2 = sz10 | ~ $i(v2) | ~
% 154.17/21.85 aElementOf0(v2, cS2076)) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2,
% 154.17/21.85 v0) | ~ aElementOf0(v2, cS2076)) & ! [v2: $i] : ( ~ $i(v2) | ~
% 154.17/21.85 aElementOf0(v2, v0) | aInteger0(v2)) & ! [v2: $i] : ( ~ $i(v2) | ~
% 154.17/21.85 aElementOf0(v2, v0) | ? [v3: $i] : ($i(v3) & aElementOf0(v3, xS) &
% 154.17/21.85 aElementOf0(v2, v3))) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2,
% 154.17/21.85 cS2076) | aInteger0(v2)) & ! [v2: $i] : ( ~ $i(v2) | ~ aInteger0(v2) |
% 154.17/21.85 aElementOf0(v2, v0) | aElementOf0(v2, cS2076)))
% 154.17/21.85
% 154.17/21.85 (m__2144)
% 154.17/21.86 $i(xS) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : (stldt0(v0) = v1 &
% 154.17/21.86 sbsmnsldt0(xS) = v0 & $i(v1) & $i(v0) & isClosed0(v0) & isOpen0(v1) &
% 154.17/21.86 aSet0(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (smndt0(v2) = v3) | ~ $i(v2) |
% 154.17/21.86 ~ aElementOf0(v2, v1) | ? [v4: $i] : ? [v5: $i] : ( ~ (v4 = sz00) &
% 154.17/21.86 szAzrzSzezqlpdtcmdtrp0(v2, v4) = v5 & $i(v5) & $i(v4) & aSubsetOf0(v5,
% 154.17/21.86 v1) & aSet0(v5) & aInteger0(v4) & ! [v6: $i] : ! [v7: $i] : ! [v8:
% 154.17/21.86 $i] : ( ~ (sdtasdt0(v4, v8) = v7) | ~ (sdtpldt0(v6, v3) = v7) | ~
% 154.17/21.86 $i(v8) | ~ $i(v6) | ~ aInteger0(v8) | ~ aInteger0(v6) |
% 154.17/21.86 aElementOf0(v6, v5)) & ! [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6,
% 154.17/21.86 v3) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v5) |
% 154.17/21.86 sdteqdtlpzmzozddtrp0(v6, v2, v4)) & ! [v6: $i] : ! [v7: $i] : ( ~
% 154.17/21.86 (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v5) |
% 154.17/21.86 aDivisorOf0(v4, v7)) & ! [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6,
% 154.17/21.86 v3) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v5) | aInteger0(v6)) &
% 154.17/21.86 ! [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~
% 154.17/21.86 aElementOf0(v6, v5) | ? [v8: $i] : (sdtasdt0(v4, v8) = v7 & $i(v8) &
% 154.17/21.86 $i(v7) & aInteger0(v8))) & ! [v6: $i] : ! [v7: $i] : ( ~
% 154.17/21.86 (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~ sdteqdtlpzmzozddtrp0(v6, v2,
% 154.17/21.86 v4) | ~ aInteger0(v6) | aElementOf0(v6, v5)) & ! [v6: $i] : !
% 154.17/21.86 [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~ aDivisorOf0(v4,
% 154.17/21.86 v7) | ~ aInteger0(v6) | aElementOf0(v6, v5)) & ! [v6: $i] : ( ~
% 154.17/21.86 $i(v6) | ~ aElementOf0(v6, v5) | aElementOf0(v6, v1)))) & ! [v2: $i]
% 154.17/21.86 : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ aElementOf0(v3, xS) | ~
% 154.17/21.86 aElementOf0(v2, v3) | ~ aInteger0(v2) | aElementOf0(v2, v0)) & ! [v2:
% 154.17/21.86 $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | ~ aElementOf0(v2, v0)) & !
% 154.17/21.86 [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | aInteger0(v2)) & ! [v2:
% 154.17/21.86 $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v0) | aInteger0(v2)) & ! [v2: $i] :
% 154.17/21.86 ( ~ $i(v2) | ~ aElementOf0(v2, v0) | ? [v3: $i] : ($i(v3) &
% 154.17/21.86 aElementOf0(v3, xS) & aElementOf0(v2, v3))) & ! [v2: $i] : ( ~ $i(v2) |
% 154.17/21.86 ~ aInteger0(v2) | aElementOf0(v2, v1) | aElementOf0(v2, v0)))
% 154.17/21.86
% 154.17/21.86 (m__2171)
% 154.17/21.87 $i(xp) & $i(xS) & $i(sz10) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 154.17/21.87 $i] : ? [v3: $i] : ( ~ (xp = sz00) & szAzrzSzezqlpdtcmdtrp0(sz10, xp) = v0
% 154.17/21.87 & stldt0(v2) = v3 & sbsmnsldt0(xS) = v2 & smndt0(sz10) = v1 & $i(v3) &
% 154.17/21.87 $i(v2) & $i(v1) & $i(v0) & aSubsetOf0(v0, v3) & aSet0(v2) & aSet0(v0) &
% 154.17/21.87 aInteger0(xp) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtasdt0(xp,
% 154.17/21.87 v6) = v5) | ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v6) | ~ $i(v4) | ~
% 154.17/21.87 aInteger0(v6) | ~ aInteger0(v4) | aElementOf0(v4, v0)) & ! [v4: $i] : !
% 154.17/21.87 [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aElementOf0(v4, v0)
% 154.17/21.87 | sdteqdtlpzmzozddtrp0(v4, sz10, xp)) & ! [v4: $i] : ! [v5: $i] : ( ~
% 154.17/21.87 (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aElementOf0(v4, v0) |
% 154.17/21.87 aDivisorOf0(xp, v5)) & ! [v4: $i] : ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) =
% 154.17/21.87 v5) | ~ $i(v4) | ~ aElementOf0(v4, v0) | aInteger0(v4)) & ! [v4: $i]
% 154.17/21.87 : ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aElementOf0(v4,
% 154.17/21.87 v0) | ? [v6: $i] : (sdtasdt0(xp, v6) = v5 & $i(v6) & $i(v5) &
% 154.17/21.87 aInteger0(v6))) & ! [v4: $i] : ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) =
% 154.17/21.87 v5) | ~ $i(v4) | ~ sdteqdtlpzmzozddtrp0(v4, sz10, xp) | ~
% 154.17/21.87 aInteger0(v4) | aElementOf0(v4, v0)) & ! [v4: $i] : ! [v5: $i] : ( ~
% 154.17/21.87 (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aDivisorOf0(xp, v5) | ~
% 154.17/21.87 aInteger0(v4) | aElementOf0(v4, v0)) & ! [v4: $i] : ! [v5: $i] : ( ~
% 154.17/21.87 $i(v5) | ~ $i(v4) | ~ aElementOf0(v5, xS) | ~ aElementOf0(v4, v5) | ~
% 154.17/21.87 aInteger0(v4) | aElementOf0(v4, v2)) & ! [v4: $i] : ( ~ $i(v4) | ~
% 154.17/21.87 aElementOf0(v4, v3) | ~ aElementOf0(v4, v2)) & ! [v4: $i] : ( ~ $i(v4) |
% 154.17/21.87 ~ aElementOf0(v4, v3) | aInteger0(v4)) & ! [v4: $i] : ( ~ $i(v4) | ~
% 154.17/21.87 aElementOf0(v4, v2) | aInteger0(v4)) & ! [v4: $i] : ( ~ $i(v4) | ~
% 154.17/21.87 aElementOf0(v4, v2) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, xS) &
% 154.17/21.87 aElementOf0(v4, v5))) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4,
% 154.17/21.87 v0) | aElementOf0(v4, v3)) & ! [v4: $i] : ( ~ $i(v4) | ~ aInteger0(v4)
% 154.17/21.87 | aElementOf0(v4, v3) | aElementOf0(v4, v2)))
% 154.17/21.87
% 154.17/21.87 (m__2232)
% 154.17/21.87 $i(xp) & $i(sz10) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 154.17/21.87 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 154.17/21.87 (szAzrzSzezqlpdtcmdtrp0(sz10, xp) = v3 & sdtasdt0(xp, v8) = v2 & sdtasdt0(xp,
% 154.17/21.87 v7) = v6 & sdtpldt0(v5, v1) = v6 & sdtpldt0(v0, v1) = v2 & sdtpldt0(sz10,
% 154.17/21.87 v4) = v5 & sdtpldt0(sz10, xp) = v0 & smndt0(xp) = v4 & smndt0(sz10) = v1 &
% 154.17/21.87 $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 154.17/21.87 $i(v0) & aElementOf0(v5, v3) & aElementOf0(v0, v3) &
% 154.17/21.87 sdteqdtlpzmzozddtrp0(v5, sz10, xp) & sdteqdtlpzmzozddtrp0(v0, sz10, xp) &
% 154.17/21.87 aDivisorOf0(xp, v6) & aDivisorOf0(xp, v2) & aInteger0(v8) & aInteger0(v7))
% 154.17/21.87
% 154.17/21.87 (function-axioms)
% 154.17/21.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.17/21.88 (szAzrzSzezqlpdtcmdtrp0(v3, v2) = v1) | ~ (szAzrzSzezqlpdtcmdtrp0(v3, v2) =
% 154.17/21.88 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 154.17/21.88 ~ (sdtslmnbsdt0(v3, v2) = v1) | ~ (sdtslmnbsdt0(v3, v2) = v0)) & ! [v0:
% 154.17/21.88 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.17/21.88 (sdtbsmnsldt0(v3, v2) = v1) | ~ (sdtbsmnsldt0(v3, v2) = v0)) & ! [v0: $i]
% 154.17/21.88 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) =
% 154.17/21.88 v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 154.17/21.88 $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3,
% 154.17/21.88 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 154.17/21.88 (stldt0(v2) = v1) | ~ (stldt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 154.17/21.88 [v2: $i] : (v1 = v0 | ~ (sbsmnsldt0(v2) = v1) | ~ (sbsmnsldt0(v2) = v0)) &
% 154.17/21.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~
% 154.17/21.88 (smndt0(v2) = v0))
% 154.17/21.88
% 154.17/21.88 Further assumptions not needed in the proof:
% 154.17/21.88 --------------------------------------------
% 154.17/21.88 mArSeqClosed, mClosed, mComplement, mDistrib, mDivisor, mElements, mEquMod,
% 154.17/21.88 mEquModMul, mEquModSym, mEquModTrn, mFinSet, mIntegers, mInterOpen,
% 154.17/21.88 mIntersection, mMulAsso, mMulComm, mMulOne, mMulZero, mOpen, mPrime, mSets,
% 154.17/21.88 mUnion, mUnionClosed, mUnionOpen, mUnionSClosed, mUnionSet, mZeroDiv, m__2046,
% 154.17/21.88 m__2117
% 154.17/21.88
% 154.17/21.88 Those formulas are unsatisfiable:
% 154.17/21.88 ---------------------------------
% 154.17/21.88
% 154.17/21.88 Begin of proof
% 154.17/21.88 |
% 154.17/21.88 | ALPHA: (mIntZero) implies:
% 154.17/21.88 | (1) aInteger0(sz00)
% 154.17/21.88 |
% 154.17/21.88 | ALPHA: (mIntOne) implies:
% 154.17/21.88 | (2) aInteger0(sz10)
% 154.17/21.88 |
% 154.17/21.88 | ALPHA: (mAddZero) implies:
% 154.17/21.88 | (3) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) |
% 154.17/21.88 | ~ $i(v0) | ~ aInteger0(v0))
% 154.17/21.88 |
% 154.17/21.88 | ALPHA: (mAddNeg) implies:
% 154.17/21.88 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = sz00 | ~ (sdtpldt0(v1,
% 154.17/21.88 | v0) = v2) | ~ (smndt0(v0) = v1) | ~ $i(v0) | ~ aInteger0(v0))
% 154.17/21.88 |
% 154.17/21.88 | ALPHA: (mMulMinOne) implies:
% 154.17/21.88 | (5) ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] :
% 154.17/21.88 | ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ aInteger0(v1) |
% 154.17/21.88 | (sdtasdt0(v1, v0) = v2 & smndt0(v1) = v2 & $i(v2))))
% 154.17/21.88 |
% 154.17/21.88 | ALPHA: (mEquModRef) implies:
% 154.17/21.88 | (6) ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ $i(v1) | ~ $i(v0) | ~
% 154.17/21.88 | aInteger0(v1) | ~ aInteger0(v0) | sdteqdtlpzmzozddtrp0(v0, v0, v1))
% 154.17/21.88 |
% 154.17/21.88 | ALPHA: (mPrimeDivisor) implies:
% 154.17/21.88 | (7) ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : (v1 = v0 | v1
% 154.17/21.88 | = sz10 | ~ $i(v1) | ~ aInteger0(v1) | ? [v2: $i] : ($i(v2) &
% 154.17/21.88 | isPrime0(v2) & aDivisorOf0(v2, v1))) & ! [v1: $i] : ( ~ $i(v1) |
% 154.17/21.88 | ~ isPrime0(v1) | ~ aDivisorOf0(v1, v0) | ~ aInteger0(v0)) & !
% 154.17/21.88 | [v1: $i] : ( ~ $i(v1) | ~ isPrime0(v1) | ~ aDivisorOf0(v1, sz10) |
% 154.17/21.88 | ~ aInteger0(sz10)))
% 154.17/21.88 |
% 154.17/21.88 | ALPHA: (mSubset) implies:
% 154.17/21.88 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 154.17/21.88 | $i(v0) | ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~
% 154.17/21.88 | aSet0(v0) | aElementOf0(v2, v0))
% 154.17/21.88 |
% 154.17/21.88 | ALPHA: (mArSeq) implies:
% 154.17/21.89 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = sz00 | ~
% 154.17/21.89 | (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 154.17/21.89 | $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aInteger0(v1) | ~
% 154.17/21.89 | aInteger0(v0) | aInteger0(v3))
% 154.17/21.89 |
% 154.17/21.89 | ALPHA: (m__2079) implies:
% 154.17/21.89 | (10) ? [v0: $i] : ? [v1: $i] : (stldt0(v0) = cS2076 & sbsmnsldt0(xS) = v0
% 154.17/21.89 | & smndt0(sz10) = v1 & $i(v1) & $i(v0) & aElementOf0(v1, cS2076) &
% 154.17/21.89 | aElementOf0(sz10, cS2076) & aSet0(v0) & aSet0(cS2076) & ! [v2: $i]
% 154.17/21.89 | : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ aElementOf0(v3, xS) | ~
% 154.17/21.89 | aElementOf0(v2, v3) | ~ aInteger0(v2) | aElementOf0(v2, v0)) & !
% 154.17/21.89 | [v2: $i] : (v2 = v1 | v2 = sz10 | ~ $i(v2) | ~ aElementOf0(v2,
% 154.17/21.89 | cS2076)) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v0) |
% 154.17/21.89 | ~ aElementOf0(v2, cS2076)) & ! [v2: $i] : ( ~ $i(v2) | ~
% 154.17/21.89 | aElementOf0(v2, v0) | aInteger0(v2)) & ! [v2: $i] : ( ~ $i(v2) |
% 154.17/21.89 | ~ aElementOf0(v2, v0) | ? [v3: $i] : ($i(v3) & aElementOf0(v3,
% 154.17/21.89 | xS) & aElementOf0(v2, v3))) & ! [v2: $i] : ( ~ $i(v2) | ~
% 154.17/21.89 | aElementOf0(v2, cS2076) | aInteger0(v2)) & ! [v2: $i] : ( ~
% 154.17/21.89 | $i(v2) | ~ aInteger0(v2) | aElementOf0(v2, v0) | aElementOf0(v2,
% 154.17/21.89 | cS2076)))
% 154.17/21.89 |
% 154.17/21.89 | ALPHA: (m__2144) implies:
% 154.17/21.90 | (11) ? [v0: $i] : ? [v1: $i] : (stldt0(v0) = v1 & sbsmnsldt0(xS) = v0 &
% 154.17/21.90 | $i(v1) & $i(v0) & isClosed0(v0) & isOpen0(v1) & aSet0(v0) & ! [v2:
% 154.17/21.90 | $i] : ! [v3: $i] : ( ~ (smndt0(v2) = v3) | ~ $i(v2) | ~
% 154.17/21.90 | aElementOf0(v2, v1) | ? [v4: $i] : ? [v5: $i] : ( ~ (v4 = sz00)
% 154.17/21.90 | & szAzrzSzezqlpdtcmdtrp0(v2, v4) = v5 & $i(v5) & $i(v4) &
% 154.17/21.90 | aSubsetOf0(v5, v1) & aSet0(v5) & aInteger0(v4) & ! [v6: $i] :
% 154.17/21.90 | ! [v7: $i] : ! [v8: $i] : ( ~ (sdtasdt0(v4, v8) = v7) | ~
% 154.17/21.90 | (sdtpldt0(v6, v3) = v7) | ~ $i(v8) | ~ $i(v6) | ~
% 154.17/21.90 | aInteger0(v8) | ~ aInteger0(v6) | aElementOf0(v6, v5)) & !
% 154.17/21.90 | [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6)
% 154.17/21.90 | | ~ aElementOf0(v6, v5) | sdteqdtlpzmzozddtrp0(v6, v2, v4)) &
% 154.17/21.90 | ! [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~
% 154.17/21.90 | $i(v6) | ~ aElementOf0(v6, v5) | aDivisorOf0(v4, v7)) & !
% 154.17/21.90 | [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6)
% 154.17/21.90 | | ~ aElementOf0(v6, v5) | aInteger0(v6)) & ! [v6: $i] : !
% 154.17/21.90 | [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~
% 154.17/21.90 | aElementOf0(v6, v5) | ? [v8: $i] : (sdtasdt0(v4, v8) = v7 &
% 154.17/21.90 | $i(v8) & $i(v7) & aInteger0(v8))) & ! [v6: $i] : ! [v7:
% 154.17/21.90 | $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~
% 154.17/21.90 | sdteqdtlpzmzozddtrp0(v6, v2, v4) | ~ aInteger0(v6) |
% 154.17/21.90 | aElementOf0(v6, v5)) & ! [v6: $i] : ! [v7: $i] : ( ~
% 154.17/21.90 | (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~ aDivisorOf0(v4, v7) |
% 154.17/21.90 | ~ aInteger0(v6) | aElementOf0(v6, v5)) & ! [v6: $i] : ( ~
% 154.17/21.90 | $i(v6) | ~ aElementOf0(v6, v5) | aElementOf0(v6, v1)))) & !
% 154.17/21.90 | [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ aElementOf0(v3,
% 154.17/21.90 | xS) | ~ aElementOf0(v2, v3) | ~ aInteger0(v2) |
% 154.17/21.90 | aElementOf0(v2, v0)) & ! [v2: $i] : ( ~ $i(v2) | ~
% 154.17/21.90 | aElementOf0(v2, v1) | ~ aElementOf0(v2, v0)) & ! [v2: $i] : ( ~
% 154.17/21.90 | $i(v2) | ~ aElementOf0(v2, v1) | aInteger0(v2)) & ! [v2: $i] : (
% 154.17/21.90 | ~ $i(v2) | ~ aElementOf0(v2, v0) | aInteger0(v2)) & ! [v2: $i] :
% 154.17/21.90 | ( ~ $i(v2) | ~ aElementOf0(v2, v0) | ? [v3: $i] : ($i(v3) &
% 154.17/21.90 | aElementOf0(v3, xS) & aElementOf0(v2, v3))) & ! [v2: $i] : ( ~
% 154.17/21.90 | $i(v2) | ~ aInteger0(v2) | aElementOf0(v2, v1) | aElementOf0(v2,
% 154.17/21.90 | v0)))
% 154.17/21.90 |
% 154.17/21.90 | ALPHA: (m__2171) implies:
% 154.17/21.90 | (12) $i(sz00)
% 154.17/21.90 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (xp =
% 154.17/21.90 | sz00) & szAzrzSzezqlpdtcmdtrp0(sz10, xp) = v0 & stldt0(v2) = v3 &
% 154.17/21.90 | sbsmnsldt0(xS) = v2 & smndt0(sz10) = v1 & $i(v3) & $i(v2) & $i(v1) &
% 154.17/21.90 | $i(v0) & aSubsetOf0(v0, v3) & aSet0(v2) & aSet0(v0) & aInteger0(xp)
% 154.17/21.90 | & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtasdt0(xp, v6) =
% 154.17/21.90 | v5) | ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v6) | ~ $i(v4) | ~
% 154.17/21.90 | aInteger0(v6) | ~ aInteger0(v4) | aElementOf0(v4, v0)) & ! [v4:
% 154.17/21.90 | $i] : ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~
% 154.17/21.90 | aElementOf0(v4, v0) | sdteqdtlpzmzozddtrp0(v4, sz10, xp)) & !
% 154.17/21.90 | [v4: $i] : ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) |
% 154.17/21.90 | ~ aElementOf0(v4, v0) | aDivisorOf0(xp, v5)) & ! [v4: $i] : !
% 154.17/21.90 | [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~
% 154.17/21.90 | aElementOf0(v4, v0) | aInteger0(v4)) & ! [v4: $i] : ! [v5: $i] :
% 154.17/21.90 | ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aElementOf0(v4, v0) |
% 154.17/21.90 | ? [v6: $i] : (sdtasdt0(xp, v6) = v5 & $i(v6) & $i(v5) &
% 154.17/21.90 | aInteger0(v6))) & ! [v4: $i] : ! [v5: $i] : ( ~ (sdtpldt0(v4,
% 154.17/21.90 | v1) = v5) | ~ $i(v4) | ~ sdteqdtlpzmzozddtrp0(v4, sz10, xp)
% 154.17/21.90 | | ~ aInteger0(v4) | aElementOf0(v4, v0)) & ! [v4: $i] : ! [v5:
% 154.17/21.90 | $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aDivisorOf0(xp,
% 154.17/21.90 | v5) | ~ aInteger0(v4) | aElementOf0(v4, v0)) & ! [v4: $i] : !
% 154.17/21.90 | [v5: $i] : ( ~ $i(v5) | ~ $i(v4) | ~ aElementOf0(v5, xS) | ~
% 154.17/21.90 | aElementOf0(v4, v5) | ~ aInteger0(v4) | aElementOf0(v4, v2)) & !
% 154.17/21.90 | [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v3) | ~ aElementOf0(v4,
% 154.17/21.90 | v2)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v3) |
% 154.17/21.90 | aInteger0(v4)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v2)
% 154.17/21.90 | | aInteger0(v4)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4,
% 154.17/21.90 | v2) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, xS) &
% 154.17/21.90 | aElementOf0(v4, v5))) & ! [v4: $i] : ( ~ $i(v4) | ~
% 154.17/21.90 | aElementOf0(v4, v0) | aElementOf0(v4, v3)) & ! [v4: $i] : ( ~
% 154.17/21.91 | $i(v4) | ~ aInteger0(v4) | aElementOf0(v4, v3) | aElementOf0(v4,
% 154.17/21.91 | v2)))
% 154.17/21.91 |
% 154.17/21.91 | ALPHA: (m__2232) implies:
% 154.17/21.91 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 154.17/21.91 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 154.17/21.91 | (szAzrzSzezqlpdtcmdtrp0(sz10, xp) = v3 & sdtasdt0(xp, v8) = v2 &
% 154.17/21.91 | sdtasdt0(xp, v7) = v6 & sdtpldt0(v5, v1) = v6 & sdtpldt0(v0, v1) =
% 154.17/21.91 | v2 & sdtpldt0(sz10, v4) = v5 & sdtpldt0(sz10, xp) = v0 & smndt0(xp)
% 154.17/21.91 | = v4 & smndt0(sz10) = v1 & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 154.17/21.91 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v5, v3) &
% 154.17/21.91 | aElementOf0(v0, v3) & sdteqdtlpzmzozddtrp0(v5, sz10, xp) &
% 154.17/21.91 | sdteqdtlpzmzozddtrp0(v0, sz10, xp) & aDivisorOf0(xp, v6) &
% 154.17/21.91 | aDivisorOf0(xp, v2) & aInteger0(v8) & aInteger0(v7))
% 154.17/21.91 |
% 154.17/21.91 | ALPHA: (m__) implies:
% 154.17/21.91 | (15) $i(sz10)
% 154.17/21.91 | (16) $i(xp)
% 154.17/21.91 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ((v2 = sz10 & sdtpldt0(sz10,
% 154.17/21.91 | v1) = sz10 & smndt0(xp) = v1 & $i(v1)) | (v0 = sz10 &
% 154.17/21.91 | sdtpldt0(sz10, xp) = sz10))
% 154.17/21.91 |
% 154.17/21.91 | ALPHA: (function-axioms) implies:
% 154.17/21.91 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) =
% 154.17/21.91 | v1) | ~ (smndt0(v2) = v0))
% 154.17/21.91 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 154.17/21.91 | (sbsmnsldt0(v2) = v1) | ~ (sbsmnsldt0(v2) = v0))
% 154.17/21.91 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (stldt0(v2) =
% 154.17/21.91 | v1) | ~ (stldt0(v2) = v0))
% 154.17/21.91 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.17/21.91 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 154.17/21.91 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.17/21.91 | (szAzrzSzezqlpdtcmdtrp0(v3, v2) = v1) | ~
% 154.17/21.91 | (szAzrzSzezqlpdtcmdtrp0(v3, v2) = v0))
% 154.17/21.91 |
% 154.17/21.91 | DELTA: instantiating (17) with fresh symbols all_36_0, all_36_1, all_36_2
% 154.17/21.91 | gives:
% 154.17/21.91 | (23) (all_36_0 = sz10 & sdtpldt0(sz10, all_36_1) = sz10 & smndt0(xp) =
% 154.17/21.91 | all_36_1 & $i(all_36_1)) | (all_36_2 = sz10 & sdtpldt0(sz10, xp) =
% 154.17/21.91 | sz10)
% 154.17/21.91 |
% 154.17/21.91 | DELTA: instantiating (5) with fresh symbol all_37_0 gives:
% 154.17/21.91 | (24) smndt0(sz10) = all_37_0 & $i(all_37_0) & ! [v0: $i] : ! [v1: $i] : (
% 154.17/21.91 | ~ (sdtasdt0(all_37_0, v0) = v1) | ~ $i(v0) | ~ aInteger0(v0) |
% 154.17/21.91 | (sdtasdt0(v0, all_37_0) = v1 & smndt0(v0) = v1 & $i(v1)))
% 154.17/21.91 |
% 154.17/21.91 | ALPHA: (24) implies:
% 154.17/21.91 | (25) smndt0(sz10) = all_37_0
% 154.17/21.91 |
% 154.17/21.91 | DELTA: instantiating (7) with fresh symbol all_40_0 gives:
% 154.17/21.92 | (26) smndt0(sz10) = all_40_0 & $i(all_40_0) & ! [v0: any] : (v0 = all_40_0
% 154.17/21.92 | | v0 = sz10 | ~ $i(v0) | ~ aInteger0(v0) | ? [v1: $i] : ($i(v1) &
% 154.17/21.92 | isPrime0(v1) & aDivisorOf0(v1, v0))) & ! [v0: $i] : ( ~ $i(v0) |
% 154.17/21.92 | ~ isPrime0(v0) | ~ aDivisorOf0(v0, all_40_0) | ~
% 154.17/21.92 | aInteger0(all_40_0)) & ! [v0: $i] : ( ~ $i(v0) | ~ isPrime0(v0) |
% 154.17/21.92 | ~ aDivisorOf0(v0, sz10) | ~ aInteger0(sz10))
% 154.17/21.92 |
% 154.17/21.92 | ALPHA: (26) implies:
% 154.17/21.92 | (27) $i(all_40_0)
% 154.17/21.92 | (28) smndt0(sz10) = all_40_0
% 154.17/21.92 | (29) ! [v0: any] : (v0 = all_40_0 | v0 = sz10 | ~ $i(v0) | ~
% 154.17/21.92 | aInteger0(v0) | ? [v1: $i] : ($i(v1) & isPrime0(v1) &
% 154.17/21.92 | aDivisorOf0(v1, v0)))
% 154.17/21.92 |
% 154.17/21.92 | DELTA: instantiating (14) with fresh symbols all_43_0, all_43_1, all_43_2,
% 154.17/21.92 | all_43_3, all_43_4, all_43_5, all_43_6, all_43_7, all_43_8 gives:
% 154.17/21.92 | (30) szAzrzSzezqlpdtcmdtrp0(sz10, xp) = all_43_5 & sdtasdt0(xp, all_43_0) =
% 154.17/21.92 | all_43_6 & sdtasdt0(xp, all_43_1) = all_43_2 & sdtpldt0(all_43_3,
% 154.17/21.92 | all_43_7) = all_43_2 & sdtpldt0(all_43_8, all_43_7) = all_43_6 &
% 154.17/21.92 | sdtpldt0(sz10, all_43_4) = all_43_3 & sdtpldt0(sz10, xp) = all_43_8 &
% 154.17/21.92 | smndt0(xp) = all_43_4 & smndt0(sz10) = all_43_7 & $i(all_43_0) &
% 154.17/21.92 | $i(all_43_1) & $i(all_43_2) & $i(all_43_3) & $i(all_43_4) &
% 154.17/21.92 | $i(all_43_5) & $i(all_43_6) & $i(all_43_7) & $i(all_43_8) &
% 154.17/21.92 | aElementOf0(all_43_3, all_43_5) & aElementOf0(all_43_8, all_43_5) &
% 154.17/21.92 | sdteqdtlpzmzozddtrp0(all_43_3, sz10, xp) &
% 154.17/21.92 | sdteqdtlpzmzozddtrp0(all_43_8, sz10, xp) & aDivisorOf0(xp, all_43_2) &
% 154.17/21.92 | aDivisorOf0(xp, all_43_6) & aInteger0(all_43_0) & aInteger0(all_43_1)
% 154.17/21.92 |
% 154.17/21.92 | ALPHA: (30) implies:
% 154.17/21.92 | (31) aInteger0(all_43_1)
% 154.17/21.92 | (32) aInteger0(all_43_0)
% 154.17/21.92 | (33) aElementOf0(all_43_8, all_43_5)
% 154.17/21.92 | (34) aElementOf0(all_43_3, all_43_5)
% 154.17/21.92 | (35) $i(all_43_8)
% 154.17/21.92 | (36) $i(all_43_4)
% 154.17/21.92 | (37) $i(all_43_3)
% 154.17/21.92 | (38) $i(all_43_1)
% 154.17/21.92 | (39) $i(all_43_0)
% 154.17/21.92 | (40) smndt0(sz10) = all_43_7
% 154.17/21.92 | (41) smndt0(xp) = all_43_4
% 154.17/21.92 | (42) sdtpldt0(sz10, xp) = all_43_8
% 154.17/21.92 | (43) sdtpldt0(sz10, all_43_4) = all_43_3
% 154.17/21.92 | (44) sdtpldt0(all_43_8, all_43_7) = all_43_6
% 154.17/21.92 | (45) sdtpldt0(all_43_3, all_43_7) = all_43_2
% 154.17/21.92 | (46) sdtasdt0(xp, all_43_1) = all_43_2
% 154.17/21.92 | (47) sdtasdt0(xp, all_43_0) = all_43_6
% 154.17/21.92 | (48) szAzrzSzezqlpdtcmdtrp0(sz10, xp) = all_43_5
% 154.17/21.92 |
% 154.17/21.92 | DELTA: instantiating (10) with fresh symbols all_45_0, all_45_1 gives:
% 154.17/21.93 | (49) stldt0(all_45_1) = cS2076 & sbsmnsldt0(xS) = all_45_1 & smndt0(sz10) =
% 154.17/21.93 | all_45_0 & $i(all_45_0) & $i(all_45_1) & aElementOf0(all_45_0, cS2076)
% 154.17/21.93 | & aElementOf0(sz10, cS2076) & aSet0(all_45_1) & aSet0(cS2076) & !
% 154.17/21.93 | [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1,
% 154.17/21.93 | xS) | ~ aElementOf0(v0, v1) | ~ aInteger0(v0) | aElementOf0(v0,
% 154.17/21.93 | all_45_1)) & ! [v0: any] : (v0 = all_45_0 | v0 = sz10 | ~ $i(v0)
% 154.17/21.93 | | ~ aElementOf0(v0, cS2076)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 154.17/21.93 | aElementOf0(v0, all_45_1) | ~ aElementOf0(v0, cS2076)) & ! [v0:
% 154.17/21.93 | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_45_1) | aInteger0(v0)) &
% 154.17/21.93 | ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_45_1) | ? [v1: $i] :
% 154.17/21.93 | ($i(v1) & aElementOf0(v1, xS) & aElementOf0(v0, v1))) & ! [v0: $i]
% 154.17/21.93 | : ( ~ $i(v0) | ~ aElementOf0(v0, cS2076) | aInteger0(v0)) & ! [v0:
% 154.17/21.93 | $i] : ( ~ $i(v0) | ~ aInteger0(v0) | aElementOf0(v0, all_45_1) |
% 154.17/21.93 | aElementOf0(v0, cS2076))
% 154.17/21.93 |
% 154.17/21.93 | ALPHA: (49) implies:
% 154.17/21.93 | (50) aSet0(cS2076)
% 154.17/21.93 | (51) smndt0(sz10) = all_45_0
% 154.17/21.93 | (52) sbsmnsldt0(xS) = all_45_1
% 154.17/21.93 | (53) stldt0(all_45_1) = cS2076
% 154.17/21.93 | (54) ! [v0: any] : (v0 = all_45_0 | v0 = sz10 | ~ $i(v0) | ~
% 154.17/21.93 | aElementOf0(v0, cS2076))
% 154.17/21.93 |
% 154.17/21.93 | DELTA: instantiating (13) with fresh symbols all_48_0, all_48_1, all_48_2,
% 154.17/21.93 | all_48_3 gives:
% 154.17/21.93 | (55) ~ (xp = sz00) & szAzrzSzezqlpdtcmdtrp0(sz10, xp) = all_48_3 &
% 154.17/21.93 | stldt0(all_48_1) = all_48_0 & sbsmnsldt0(xS) = all_48_1 & smndt0(sz10)
% 154.17/21.93 | = all_48_2 & $i(all_48_0) & $i(all_48_1) & $i(all_48_2) & $i(all_48_3)
% 154.17/21.93 | & aSubsetOf0(all_48_3, all_48_0) & aSet0(all_48_1) & aSet0(all_48_3) &
% 154.17/21.93 | aInteger0(xp) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 154.17/21.93 | (sdtasdt0(xp, v2) = v1) | ~ (sdtpldt0(v0, all_48_2) = v1) | ~
% 154.17/21.93 | $i(v2) | ~ $i(v0) | ~ aInteger0(v2) | ~ aInteger0(v0) |
% 154.17/21.93 | aElementOf0(v0, all_48_3)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 154.17/21.93 | (sdtpldt0(v0, all_48_2) = v1) | ~ $i(v0) | ~ aElementOf0(v0,
% 154.17/21.93 | all_48_3) | sdteqdtlpzmzozddtrp0(v0, sz10, xp)) & ! [v0: $i] : !
% 154.17/21.93 | [v1: $i] : ( ~ (sdtpldt0(v0, all_48_2) = v1) | ~ $i(v0) | ~
% 154.17/21.93 | aElementOf0(v0, all_48_3) | aDivisorOf0(xp, v1)) & ! [v0: $i] : !
% 154.17/21.93 | [v1: $i] : ( ~ (sdtpldt0(v0, all_48_2) = v1) | ~ $i(v0) | ~
% 154.17/21.93 | aElementOf0(v0, all_48_3) | aInteger0(v0)) & ! [v0: $i] : ! [v1:
% 154.17/21.93 | $i] : ( ~ (sdtpldt0(v0, all_48_2) = v1) | ~ $i(v0) | ~
% 154.17/21.93 | aElementOf0(v0, all_48_3) | ? [v2: $i] : (sdtasdt0(xp, v2) = v1 &
% 154.17/21.93 | $i(v2) & $i(v1) & aInteger0(v2))) & ! [v0: $i] : ! [v1: $i] : (
% 154.17/21.93 | ~ (sdtpldt0(v0, all_48_2) = v1) | ~ $i(v0) | ~
% 154.17/21.93 | sdteqdtlpzmzozddtrp0(v0, sz10, xp) | ~ aInteger0(v0) |
% 154.17/21.93 | aElementOf0(v0, all_48_3)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 154.17/21.93 | (sdtpldt0(v0, all_48_2) = v1) | ~ $i(v0) | ~ aDivisorOf0(xp, v1) |
% 154.17/21.93 | ~ aInteger0(v0) | aElementOf0(v0, all_48_3)) & ! [v0: $i] : !
% 154.17/21.93 | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, xS) | ~
% 154.17/21.93 | aElementOf0(v0, v1) | ~ aInteger0(v0) | aElementOf0(v0, all_48_1))
% 154.17/21.93 | & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_48_0) | ~
% 154.17/21.93 | aElementOf0(v0, all_48_1)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 154.17/21.93 | aElementOf0(v0, all_48_0) | aInteger0(v0)) & ! [v0: $i] : ( ~
% 154.17/21.93 | $i(v0) | ~ aElementOf0(v0, all_48_1) | aInteger0(v0)) & ! [v0: $i]
% 154.17/21.93 | : ( ~ $i(v0) | ~ aElementOf0(v0, all_48_1) | ? [v1: $i] : ($i(v1) &
% 154.17/21.93 | aElementOf0(v1, xS) & aElementOf0(v0, v1))) & ! [v0: $i] : ( ~
% 154.17/21.93 | $i(v0) | ~ aElementOf0(v0, all_48_3) | aElementOf0(v0, all_48_0)) &
% 154.17/21.93 | ! [v0: $i] : ( ~ $i(v0) | ~ aInteger0(v0) | aElementOf0(v0,
% 154.17/21.94 | all_48_0) | aElementOf0(v0, all_48_1))
% 154.17/21.94 |
% 154.17/21.94 | ALPHA: (55) implies:
% 154.17/21.94 | (56) ~ (xp = sz00)
% 154.17/21.94 | (57) aInteger0(xp)
% 154.17/21.94 | (58) aSubsetOf0(all_48_3, all_48_0)
% 154.17/21.94 | (59) $i(all_48_3)
% 154.17/21.94 | (60) $i(all_48_0)
% 154.17/21.94 | (61) smndt0(sz10) = all_48_2
% 154.17/21.94 | (62) sbsmnsldt0(xS) = all_48_1
% 154.17/21.94 | (63) stldt0(all_48_1) = all_48_0
% 154.17/21.94 | (64) szAzrzSzezqlpdtcmdtrp0(sz10, xp) = all_48_3
% 154.17/21.94 | (65) ! [v0: $i] : ( ~ $i(v0) | ~ aInteger0(v0) | aElementOf0(v0,
% 154.17/21.94 | all_48_0) | aElementOf0(v0, all_48_1))
% 154.17/21.94 |
% 154.17/21.94 | DELTA: instantiating (11) with fresh symbols all_51_0, all_51_1 gives:
% 154.17/21.94 | (66) stldt0(all_51_1) = all_51_0 & sbsmnsldt0(xS) = all_51_1 & $i(all_51_0)
% 154.17/21.94 | & $i(all_51_1) & isClosed0(all_51_1) & isOpen0(all_51_0) &
% 154.17/21.94 | aSet0(all_51_1) & ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) |
% 154.17/21.94 | ~ $i(v0) | ~ aElementOf0(v0, all_51_0) | ? [v2: $i] : ? [v3: $i]
% 154.17/21.94 | : ( ~ (v2 = sz00) & szAzrzSzezqlpdtcmdtrp0(v0, v2) = v3 & $i(v3) &
% 154.17/21.94 | $i(v2) & aSubsetOf0(v3, all_51_0) & aSet0(v3) & aInteger0(v2) & !
% 154.17/21.94 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtasdt0(v2, v6) = v5)
% 154.17/21.94 | | ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v6) | ~ $i(v4) | ~
% 154.17/21.94 | aInteger0(v6) | ~ aInteger0(v4) | aElementOf0(v4, v3)) & !
% 154.17/21.94 | [v4: $i] : ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) |
% 154.17/21.94 | ~ aElementOf0(v4, v3) | sdteqdtlpzmzozddtrp0(v4, v0, v2)) & !
% 154.17/21.94 | [v4: $i] : ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) |
% 154.17/21.94 | ~ aElementOf0(v4, v3) | aDivisorOf0(v2, v5)) & ! [v4: $i] : !
% 154.17/21.94 | [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~
% 154.17/21.94 | aElementOf0(v4, v3) | aInteger0(v4)) & ! [v4: $i] : ! [v5: $i]
% 154.17/21.94 | : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aElementOf0(v4, v3)
% 154.17/21.94 | | ? [v6: $i] : (sdtasdt0(v2, v6) = v5 & $i(v6) & $i(v5) &
% 154.17/21.94 | aInteger0(v6))) & ! [v4: $i] : ! [v5: $i] : ( ~
% 154.17/21.94 | (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~
% 154.17/21.94 | sdteqdtlpzmzozddtrp0(v4, v0, v2) | ~ aInteger0(v4) |
% 154.17/21.94 | aElementOf0(v4, v3)) & ! [v4: $i] : ! [v5: $i] : ( ~
% 154.17/21.94 | (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aDivisorOf0(v2, v5) |
% 154.17/21.94 | ~ aInteger0(v4) | aElementOf0(v4, v3)) & ! [v4: $i] : ( ~
% 154.17/21.94 | $i(v4) | ~ aElementOf0(v4, v3) | aElementOf0(v4, all_51_0)))) &
% 154.17/21.94 | ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 154.17/21.94 | aElementOf0(v1, xS) | ~ aElementOf0(v0, v1) | ~ aInteger0(v0) |
% 154.17/21.94 | aElementOf0(v0, all_51_1)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 154.17/21.94 | aElementOf0(v0, all_51_0) | ~ aElementOf0(v0, all_51_1)) & ! [v0:
% 154.17/21.94 | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_51_0) | aInteger0(v0)) &
% 154.17/21.94 | ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_51_1) |
% 154.17/21.94 | aInteger0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0,
% 154.17/21.94 | all_51_1) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, xS) &
% 154.17/21.94 | aElementOf0(v0, v1))) & ! [v0: $i] : ( ~ $i(v0) | ~
% 154.17/21.94 | aInteger0(v0) | aElementOf0(v0, all_51_0) | aElementOf0(v0,
% 154.17/21.94 | all_51_1))
% 154.17/21.94 |
% 154.17/21.94 | ALPHA: (66) implies:
% 154.17/21.94 | (67) sbsmnsldt0(xS) = all_51_1
% 154.17/21.94 | (68) stldt0(all_51_1) = all_51_0
% 154.17/21.94 |
% 154.17/21.94 | GROUND_INST: instantiating (18) with all_40_0, all_43_7, sz10, simplifying
% 154.17/21.94 | with (28), (40) gives:
% 154.17/21.94 | (69) all_43_7 = all_40_0
% 154.17/21.94 |
% 154.17/21.94 | GROUND_INST: instantiating (18) with all_45_0, all_48_2, sz10, simplifying
% 154.17/21.94 | with (51), (61) gives:
% 154.17/21.94 | (70) all_48_2 = all_45_0
% 154.17/21.94 |
% 154.17/21.94 | GROUND_INST: instantiating (18) with all_43_7, all_48_2, sz10, simplifying
% 154.17/21.94 | with (40), (61) gives:
% 154.17/21.94 | (71) all_48_2 = all_43_7
% 154.17/21.94 |
% 154.17/21.94 | GROUND_INST: instantiating (18) with all_37_0, all_48_2, sz10, simplifying
% 154.17/21.94 | with (25), (61) gives:
% 154.17/21.94 | (72) all_48_2 = all_37_0
% 154.17/21.94 |
% 154.17/21.94 | GROUND_INST: instantiating (19) with all_48_1, all_51_1, xS, simplifying with
% 154.17/21.94 | (62), (67) gives:
% 154.17/21.94 | (73) all_51_1 = all_48_1
% 154.17/21.94 |
% 154.17/21.94 | GROUND_INST: instantiating (19) with all_45_1, all_51_1, xS, simplifying with
% 154.17/21.94 | (52), (67) gives:
% 154.17/21.94 | (74) all_51_1 = all_45_1
% 154.17/21.94 |
% 154.17/21.95 | GROUND_INST: instantiating (22) with all_43_5, all_48_3, xp, sz10, simplifying
% 154.17/21.95 | with (48), (64) gives:
% 154.17/21.95 | (75) all_48_3 = all_43_5
% 154.17/21.95 |
% 154.17/21.95 | COMBINE_EQS: (73), (74) imply:
% 154.17/21.95 | (76) all_48_1 = all_45_1
% 154.17/21.95 |
% 154.17/21.95 | COMBINE_EQS: (70), (71) imply:
% 154.17/21.95 | (77) all_45_0 = all_43_7
% 154.17/21.95 |
% 154.17/21.95 | COMBINE_EQS: (70), (72) imply:
% 154.17/21.95 | (78) all_45_0 = all_37_0
% 154.17/21.95 |
% 154.17/21.95 | COMBINE_EQS: (77), (78) imply:
% 154.17/21.95 | (79) all_43_7 = all_37_0
% 154.17/21.95 |
% 154.17/21.95 | SIMP: (79) implies:
% 154.17/21.95 | (80) all_43_7 = all_37_0
% 154.17/21.95 |
% 154.17/21.95 | COMBINE_EQS: (69), (80) imply:
% 154.17/21.95 | (81) all_40_0 = all_37_0
% 154.17/21.95 |
% 154.17/21.95 | REDUCE: (68), (74) imply:
% 154.17/21.95 | (82) stldt0(all_45_1) = all_51_0
% 154.17/21.95 |
% 154.17/21.95 | REDUCE: (63), (76) imply:
% 154.17/21.95 | (83) stldt0(all_45_1) = all_48_0
% 154.17/21.95 |
% 154.17/21.95 | REDUCE: (45), (80) imply:
% 154.17/21.95 | (84) sdtpldt0(all_43_3, all_37_0) = all_43_2
% 154.17/21.95 |
% 154.17/21.95 | REDUCE: (44), (80) imply:
% 154.17/21.95 | (85) sdtpldt0(all_43_8, all_37_0) = all_43_6
% 154.17/21.95 |
% 154.17/21.95 | REDUCE: (59), (75) imply:
% 154.17/21.95 | (86) $i(all_43_5)
% 154.17/21.95 |
% 154.17/21.95 | REDUCE: (27), (81) imply:
% 154.17/21.95 | (87) $i(all_37_0)
% 154.17/21.95 |
% 154.17/21.95 | REDUCE: (58), (75) imply:
% 154.17/21.95 | (88) aSubsetOf0(all_43_5, all_48_0)
% 154.17/21.95 |
% 154.17/21.95 | GROUND_INST: instantiating (20) with cS2076, all_51_0, all_45_1, simplifying
% 154.17/21.95 | with (53), (82) gives:
% 154.17/21.95 | (89) all_51_0 = cS2076
% 154.17/21.95 |
% 154.17/21.95 | GROUND_INST: instantiating (20) with all_48_0, all_51_0, all_45_1, simplifying
% 154.17/21.95 | with (82), (83) gives:
% 154.17/21.95 | (90) all_51_0 = all_48_0
% 154.17/21.95 |
% 154.17/21.95 | COMBINE_EQS: (89), (90) imply:
% 154.17/21.95 | (91) all_48_0 = cS2076
% 154.17/21.95 |
% 154.17/21.95 | REDUCE: (60), (91) imply:
% 154.17/21.95 | (92) $i(cS2076)
% 154.17/21.95 |
% 154.17/21.95 | REDUCE: (88), (91) imply:
% 154.17/21.95 | (93) aSubsetOf0(all_43_5, cS2076)
% 154.17/21.95 |
% 154.17/21.95 | GROUND_INST: instantiating (29) with sz00, simplifying with (1), (12) gives:
% 154.17/21.95 | (94) all_40_0 = sz00 | sz10 = sz00 | ? [v0: $i] : ($i(v0) & isPrime0(v0) &
% 154.17/21.95 | aDivisorOf0(v0, sz00))
% 154.17/21.95 |
% 154.17/21.95 | GROUND_INST: instantiating (65) with sz00, simplifying with (1), (12) gives:
% 154.17/21.95 | (95) aElementOf0(sz00, all_48_0) | aElementOf0(sz00, all_48_1)
% 154.17/21.95 |
% 154.17/21.95 | GROUND_INST: instantiating (8) with cS2076, all_43_5, all_43_8, simplifying
% 154.17/21.95 | with (33), (35), (50), (86), (92), (93) gives:
% 154.17/21.95 | (96) aElementOf0(all_43_8, cS2076)
% 154.17/21.95 |
% 154.17/21.95 | GROUND_INST: instantiating (mIntNeg) with sz10, all_37_0, simplifying with
% 154.17/21.95 | (2), (15), (25) gives:
% 154.17/21.95 | (97) aInteger0(all_37_0)
% 154.17/21.95 |
% 154.17/21.95 | GROUND_INST: instantiating (mIntNeg) with xp, all_43_4, simplifying with (16),
% 154.17/21.95 | (41), (57) gives:
% 154.17/21.95 | (98) aInteger0(all_43_4)
% 154.17/21.95 |
% 154.17/21.95 | GROUND_INST: instantiating (mIntPlus) with sz10, xp, all_43_8, simplifying
% 154.17/21.95 | with (2), (15), (16), (42), (57) gives:
% 154.17/21.95 | (99) aInteger0(all_43_8)
% 154.17/21.95 |
% 154.17/21.95 | GROUND_INST: instantiating (mAddComm) with sz10, xp, all_43_8, simplifying
% 154.17/21.95 | with (2), (15), (16), (42), (57) gives:
% 154.17/21.95 | (100) sdtpldt0(xp, sz10) = all_43_8 & $i(all_43_8)
% 154.17/21.95 |
% 154.17/21.95 | ALPHA: (100) implies:
% 154.17/21.95 | (101) sdtpldt0(xp, sz10) = all_43_8
% 154.17/21.95 |
% 154.17/21.95 | GROUND_INST: instantiating (mIntMult) with xp, all_43_1, all_43_2, simplifying
% 154.17/21.95 | with (16), (31), (38), (46), (57) gives:
% 154.17/21.95 | (102) aInteger0(all_43_2)
% 154.17/21.95 |
% 154.17/21.95 | GROUND_INST: instantiating (mIntMult) with xp, all_43_0, all_43_6, simplifying
% 154.17/21.95 | with (16), (32), (39), (47), (57) gives:
% 154.17/21.95 | (103) aInteger0(all_43_6)
% 154.17/21.95 |
% 154.17/21.95 | GROUND_INST: instantiating (9) with sz10, xp, all_43_5, all_43_3, simplifying
% 154.17/21.95 | with (2), (15), (16), (34), (37), (48), (57), (86) gives:
% 154.17/21.95 | (104) xp = sz00 | aInteger0(all_43_3)
% 154.17/21.95 |
% 154.17/21.95 | BETA: splitting (104) gives:
% 154.17/21.95 |
% 154.17/21.95 | Case 1:
% 154.17/21.95 | |
% 154.17/21.95 | | (105) aInteger0(all_43_3)
% 154.17/21.95 | |
% 154.17/21.95 | | GROUND_INST: instantiating (mAddAsso) with sz10, xp, all_37_0, all_43_8,
% 154.17/21.95 | | all_43_6, simplifying with (2), (15), (16), (42), (57), (85),
% 154.17/21.95 | | (87), (97) gives:
% 154.17/21.95 | | (106) ? [v0: $i] : (sdtpldt0(xp, all_37_0) = v0 & sdtpldt0(sz10, v0) =
% 154.17/21.95 | | all_43_6 & $i(v0) & $i(all_43_6))
% 154.17/21.95 | |
% 154.17/21.95 | | GROUND_INST: instantiating (mAddComm) with all_43_8, all_37_0, all_43_6,
% 154.17/21.95 | | simplifying with (35), (85), (87), (97), (99) gives:
% 154.17/21.95 | | (107) sdtpldt0(all_37_0, all_43_8) = all_43_6 & $i(all_43_6)
% 154.17/21.95 | |
% 154.17/21.95 | | ALPHA: (107) implies:
% 154.17/21.95 | | (108) sdtpldt0(all_37_0, all_43_8) = all_43_6
% 154.17/21.95 | |
% 154.17/21.95 | | GROUND_INST: instantiating (29) with all_43_8, simplifying with (35), (99)
% 154.17/21.95 | | gives:
% 154.17/21.96 | | (109) all_43_8 = all_40_0 | all_43_8 = sz10 | ? [v0: $i] : ($i(v0) &
% 154.17/21.96 | | isPrime0(v0) & aDivisorOf0(v0, all_43_8))
% 154.17/21.96 | |
% 154.17/21.96 | | GROUND_INST: instantiating (mAddAsso) with sz10, all_43_4, all_37_0,
% 154.17/21.96 | | all_43_3, all_43_2, simplifying with (2), (15), (36), (43),
% 154.17/21.96 | | (84), (87), (97), (98) gives:
% 154.17/21.96 | | (110) ? [v0: $i] : (sdtpldt0(all_43_4, all_37_0) = v0 & sdtpldt0(sz10,
% 154.17/21.96 | | v0) = all_43_2 & $i(v0) & $i(all_43_2))
% 154.17/21.96 | |
% 154.17/21.96 | | GROUND_INST: instantiating (mAddComm) with sz10, all_43_4, all_43_3,
% 154.17/21.96 | | simplifying with (2), (15), (36), (43), (98) gives:
% 154.17/21.96 | | (111) sdtpldt0(all_43_4, sz10) = all_43_3 & $i(all_43_3)
% 154.17/21.96 | |
% 154.17/21.96 | | ALPHA: (111) implies:
% 154.17/21.96 | | (112) sdtpldt0(all_43_4, sz10) = all_43_3
% 154.17/21.96 | |
% 154.17/21.96 | | GROUND_INST: instantiating (29) with all_43_4, simplifying with (36), (98)
% 154.17/21.96 | | gives:
% 154.17/21.96 | | (113) all_43_4 = all_40_0 | all_43_4 = sz10 | ? [v0: $i] : ($i(v0) &
% 154.17/21.96 | | isPrime0(v0) & aDivisorOf0(v0, all_43_4))
% 154.17/21.96 | |
% 154.17/21.96 | | GROUND_INST: instantiating (mAddComm) with all_43_3, all_37_0, all_43_2,
% 154.17/21.96 | | simplifying with (37), (84), (87), (97), (105) gives:
% 154.17/21.96 | | (114) sdtpldt0(all_37_0, all_43_3) = all_43_2 & $i(all_43_2)
% 154.17/21.96 | |
% 154.17/21.96 | | ALPHA: (114) implies:
% 154.17/21.96 | | (115) $i(all_43_2)
% 154.17/21.96 | | (116) sdtpldt0(all_37_0, all_43_3) = all_43_2
% 154.17/21.96 | |
% 154.17/21.96 | | GROUND_INST: instantiating (6) with all_43_2, xp, simplifying with (16),
% 154.17/21.96 | | (57), (102), (115) gives:
% 154.17/21.96 | | (117) xp = sz00 | sdteqdtlpzmzozddtrp0(all_43_2, all_43_2, xp)
% 154.17/21.96 | |
% 154.17/21.96 | | GROUND_INST: instantiating (54) with all_43_8, simplifying with (35), (96)
% 154.17/21.96 | | gives:
% 154.17/21.96 | | (118) all_45_0 = all_43_8 | all_43_8 = sz10
% 154.17/21.96 | |
% 154.17/21.96 | | GROUND_INST: instantiating (mAddAsso) with xp, sz10, all_37_0, all_43_8,
% 154.17/21.96 | | all_43_6, simplifying with (2), (15), (16), (57), (85), (87),
% 154.17/21.96 | | (97), (101) gives:
% 154.17/21.96 | | (119) ? [v0: $i] : (sdtpldt0(xp, v0) = all_43_6 & sdtpldt0(sz10,
% 154.17/21.96 | | all_37_0) = v0 & $i(v0) & $i(all_43_6))
% 154.17/21.96 | |
% 154.17/21.96 | | DELTA: instantiating (110) with fresh symbol all_129_0 gives:
% 154.17/21.96 | | (120) sdtpldt0(all_43_4, all_37_0) = all_129_0 & sdtpldt0(sz10,
% 154.17/21.96 | | all_129_0) = all_43_2 & $i(all_129_0) & $i(all_43_2)
% 154.17/21.96 | |
% 154.17/21.96 | | ALPHA: (120) implies:
% 154.17/21.96 | | (121) sdtpldt0(sz10, all_129_0) = all_43_2
% 154.17/21.96 | | (122) sdtpldt0(all_43_4, all_37_0) = all_129_0
% 154.17/21.96 | |
% 154.17/21.96 | | DELTA: instantiating (106) with fresh symbol all_131_0 gives:
% 154.17/21.96 | | (123) sdtpldt0(xp, all_37_0) = all_131_0 & sdtpldt0(sz10, all_131_0) =
% 154.17/21.96 | | all_43_6 & $i(all_131_0) & $i(all_43_6)
% 154.17/21.96 | |
% 154.17/21.96 | | ALPHA: (123) implies:
% 154.17/21.96 | | (124) sdtpldt0(sz10, all_131_0) = all_43_6
% 154.17/21.96 | | (125) sdtpldt0(xp, all_37_0) = all_131_0
% 154.17/21.96 | |
% 154.17/21.96 | | DELTA: instantiating (119) with fresh symbol all_133_0 gives:
% 154.17/21.96 | | (126) sdtpldt0(xp, all_133_0) = all_43_6 & sdtpldt0(sz10, all_37_0) =
% 154.17/21.96 | | all_133_0 & $i(all_133_0) & $i(all_43_6)
% 154.17/21.96 | |
% 154.17/21.96 | | ALPHA: (126) implies:
% 154.17/21.96 | | (127) sdtpldt0(sz10, all_37_0) = all_133_0
% 154.17/21.96 | | (128) sdtpldt0(xp, all_133_0) = all_43_6
% 154.17/21.96 | |
% 154.17/21.96 | | BETA: splitting (117) gives:
% 154.17/21.96 | |
% 154.17/21.96 | | Case 1:
% 154.17/21.96 | | |
% 154.17/21.96 | | |
% 154.17/21.96 | | | GROUND_INST: instantiating (mIntPlus) with sz10, all_37_0, all_133_0,
% 154.17/21.96 | | | simplifying with (2), (15), (87), (97), (127) gives:
% 154.17/21.96 | | | (129) aInteger0(all_133_0)
% 154.17/21.96 | | |
% 154.17/21.96 | | | GROUND_INST: instantiating (mAddComm) with sz10, all_37_0, all_133_0,
% 154.17/21.96 | | | simplifying with (2), (15), (87), (97), (127) gives:
% 154.17/21.96 | | | (130) sdtpldt0(all_37_0, sz10) = all_133_0 & $i(all_133_0)
% 154.17/21.96 | | |
% 154.17/21.96 | | | ALPHA: (130) implies:
% 154.17/21.96 | | | (131) sdtpldt0(all_37_0, sz10) = all_133_0
% 154.17/21.96 | | |
% 154.17/21.96 | | | GROUND_INST: instantiating (mIntPlus) with xp, all_37_0, all_131_0,
% 154.17/21.96 | | | simplifying with (16), (57), (87), (97), (125) gives:
% 154.17/21.96 | | | (132) aInteger0(all_131_0)
% 154.17/21.96 | | |
% 154.17/21.96 | | | GROUND_INST: instantiating (mAddComm) with xp, all_37_0, all_131_0,
% 154.17/21.96 | | | simplifying with (16), (57), (87), (97), (125) gives:
% 154.17/21.96 | | | (133) sdtpldt0(all_37_0, xp) = all_131_0 & $i(all_131_0)
% 154.17/21.96 | | |
% 154.17/21.96 | | | ALPHA: (133) implies:
% 154.17/21.96 | | | (134) $i(all_131_0)
% 154.17/21.96 | | | (135) sdtpldt0(all_37_0, xp) = all_131_0
% 154.17/21.96 | | |
% 154.17/21.96 | | | GROUND_INST: instantiating (mAddAsso) with all_43_4, sz10, all_37_0,
% 154.17/21.96 | | | all_43_3, all_43_2, simplifying with (2), (15), (36), (84),
% 154.17/21.96 | | | (87), (97), (98), (112) gives:
% 154.17/21.96 | | | (136) ? [v0: $i] : (sdtpldt0(all_43_4, v0) = all_43_2 & sdtpldt0(sz10,
% 154.17/21.96 | | | all_37_0) = v0 & $i(v0) & $i(all_43_2))
% 154.17/21.96 | | |
% 154.17/21.96 | | | GROUND_INST: instantiating (mIntPlus) with all_43_4, all_37_0, all_129_0,
% 154.17/21.96 | | | simplifying with (36), (87), (97), (98), (122) gives:
% 154.17/21.96 | | | (137) aInteger0(all_129_0)
% 154.17/21.96 | | |
% 154.17/21.96 | | | GROUND_INST: instantiating (mAddComm) with all_43_4, all_37_0, all_129_0,
% 154.17/21.96 | | | simplifying with (36), (87), (97), (98), (122) gives:
% 154.17/21.96 | | | (138) sdtpldt0(all_37_0, all_43_4) = all_129_0 & $i(all_129_0)
% 154.17/21.96 | | |
% 154.17/21.96 | | | ALPHA: (138) implies:
% 154.17/21.96 | | | (139) $i(all_129_0)
% 154.17/21.96 | | |
% 154.17/21.96 | | | DELTA: instantiating (136) with fresh symbol all_181_0 gives:
% 154.17/21.96 | | | (140) sdtpldt0(all_43_4, all_181_0) = all_43_2 & sdtpldt0(sz10,
% 154.17/21.96 | | | all_37_0) = all_181_0 & $i(all_181_0) & $i(all_43_2)
% 154.17/21.96 | | |
% 154.17/21.96 | | | ALPHA: (140) implies:
% 154.17/21.97 | | | (141) sdtpldt0(sz10, all_37_0) = all_181_0
% 154.17/21.97 | | | (142) sdtpldt0(all_43_4, all_181_0) = all_43_2
% 154.17/21.97 | | |
% 154.17/21.97 | | | GROUND_INST: instantiating (21) with all_133_0, all_181_0, all_37_0, sz10,
% 154.17/21.97 | | | simplifying with (127), (141) gives:
% 154.17/21.97 | | | (143) all_181_0 = all_133_0
% 154.17/21.97 | | |
% 154.17/21.97 | | | REDUCE: (142), (143) imply:
% 154.17/21.97 | | | (144) sdtpldt0(all_43_4, all_133_0) = all_43_2
% 154.17/21.97 | | |
% 154.17/21.97 | | | BETA: splitting (23) gives:
% 154.17/21.97 | | |
% 154.17/21.97 | | | Case 1:
% 154.17/21.97 | | | |
% 154.17/21.97 | | | | (145) all_36_0 = sz10 & sdtpldt0(sz10, all_36_1) = sz10 & smndt0(xp)
% 154.17/21.97 | | | | = all_36_1 & $i(all_36_1)
% 154.17/21.97 | | | |
% 154.17/21.97 | | | | ALPHA: (145) implies:
% 154.17/21.97 | | | | (146) smndt0(xp) = all_36_1
% 154.17/21.97 | | | | (147) sdtpldt0(sz10, all_36_1) = sz10
% 154.17/21.97 | | | |
% 154.17/21.97 | | | | GROUND_INST: instantiating (18) with all_43_4, all_36_1, xp, simplifying
% 154.17/21.97 | | | | with (41), (146) gives:
% 154.17/21.97 | | | | (148) all_43_4 = all_36_1
% 154.17/21.97 | | | |
% 154.17/21.97 | | | | REDUCE: (144), (148) imply:
% 154.17/21.97 | | | | (149) sdtpldt0(all_36_1, all_133_0) = all_43_2
% 154.17/21.97 | | | |
% 154.17/21.97 | | | | REDUCE: (122), (148) imply:
% 154.17/21.97 | | | | (150) sdtpldt0(all_36_1, all_37_0) = all_129_0
% 154.17/21.97 | | | |
% 154.17/21.97 | | | | REDUCE: (112), (148) imply:
% 154.17/21.97 | | | | (151) sdtpldt0(all_36_1, sz10) = all_43_3
% 154.17/21.97 | | | |
% 154.17/21.97 | | | | REDUCE: (43), (148) imply:
% 154.17/21.97 | | | | (152) sdtpldt0(sz10, all_36_1) = all_43_3
% 154.17/21.97 | | | |
% 154.17/21.97 | | | | REDUCE: (36), (148) imply:
% 154.17/21.97 | | | | (153) $i(all_36_1)
% 154.17/21.97 | | | |
% 154.17/21.97 | | | | REDUCE: (98), (148) imply:
% 154.17/21.97 | | | | (154) aInteger0(all_36_1)
% 154.17/21.97 | | | |
% 154.17/21.97 | | | | GROUND_INST: instantiating (21) with sz10, all_43_3, all_36_1, sz10,
% 154.17/21.97 | | | | simplifying with (147), (152) gives:
% 154.17/21.97 | | | | (155) all_43_3 = sz10
% 154.17/21.97 | | | |
% 154.17/21.97 | | | | REDUCE: (116), (155) imply:
% 154.17/21.97 | | | | (156) sdtpldt0(all_37_0, sz10) = all_43_2
% 154.17/21.97 | | | |
% 154.17/21.97 | | | | REDUCE: (151), (155) imply:
% 154.17/21.97 | | | | (157) sdtpldt0(all_36_1, sz10) = sz10
% 154.17/21.97 | | | |
% 154.17/21.97 | | | | GROUND_INST: instantiating (21) with all_133_0, all_43_2, sz10,
% 154.17/21.97 | | | | all_37_0, simplifying with (131), (156) gives:
% 154.17/21.97 | | | | (158) all_133_0 = all_43_2
% 154.17/21.97 | | | |
% 154.17/21.97 | | | | REDUCE: (149), (158) imply:
% 154.17/21.97 | | | | (159) sdtpldt0(all_36_1, all_43_2) = all_43_2
% 154.17/21.97 | | | |
% 154.17/21.97 | | | | REDUCE: (128), (158) imply:
% 154.17/21.97 | | | | (160) sdtpldt0(xp, all_43_2) = all_43_6
% 154.17/21.97 | | | |
% 154.17/21.97 | | | | BETA: splitting (95) gives:
% 154.17/21.97 | | | |
% 154.17/21.97 | | | | Case 1:
% 154.17/21.97 | | | | |
% 154.17/21.97 | | | | | (161) aElementOf0(sz00, all_48_0)
% 154.17/21.97 | | | | |
% 154.17/21.97 | | | | | REDUCE: (91), (161) imply:
% 154.17/21.97 | | | | | (162) aElementOf0(sz00, cS2076)
% 154.17/21.97 | | | | |
% 154.17/21.97 | | | | | GROUND_INST: instantiating (6) with all_131_0, xp, simplifying with
% 154.17/21.97 | | | | | (16), (57), (132), (134) gives:
% 154.17/21.97 | | | | | (163) xp = sz00 | sdteqdtlpzmzozddtrp0(all_131_0, all_131_0, xp)
% 154.17/21.97 | | | | |
% 154.17/21.97 | | | | | GROUND_INST: instantiating (54) with sz00, simplifying with (12),
% 154.17/21.97 | | | | | (162) gives:
% 154.17/21.97 | | | | | (164) all_45_0 = sz00 | sz10 = sz00
% 154.17/21.97 | | | | |
% 154.17/21.97 | | | | | GROUND_INST: instantiating (mAddAsso) with sz10, all_36_1, all_129_0,
% 154.17/21.97 | | | | | sz10, all_43_2, simplifying with (2), (15), (121), (137),
% 154.17/21.97 | | | | | (139), (147), (153), (154) gives:
% 154.17/21.97 | | | | | (165) ? [v0: $i] : (sdtpldt0(all_36_1, all_129_0) = v0 &
% 154.17/21.97 | | | | | sdtpldt0(sz10, v0) = all_43_2 & $i(v0) & $i(all_43_2))
% 154.17/21.97 | | | | |
% 154.17/21.97 | | | | | GROUND_INST: instantiating (mAddAsso) with all_36_1, sz10, xp, sz10,
% 154.17/21.97 | | | | | all_43_8, simplifying with (2), (15), (16), (42), (57),
% 154.17/21.97 | | | | | (153), (154), (157) gives:
% 154.17/21.97 | | | | | (166) ? [v0: $i] : (sdtpldt0(all_36_1, v0) = all_43_8 &
% 154.17/21.97 | | | | | sdtpldt0(sz10, xp) = v0 & $i(v0) & $i(all_43_8))
% 154.17/21.97 | | | | |
% 154.17/21.97 | | | | | GROUND_INST: instantiating (4) with sz10, all_37_0, all_43_2,
% 154.17/21.97 | | | | | simplifying with (2), (15), (25), (156) gives:
% 154.17/21.97 | | | | | (167) all_43_2 = sz00
% 154.17/21.97 | | | | |
% 154.17/21.97 | | | | | DELTA: instantiating (165) with fresh symbol all_243_0 gives:
% 154.17/21.97 | | | | | (168) sdtpldt0(all_36_1, all_129_0) = all_243_0 & sdtpldt0(sz10,
% 154.17/21.97 | | | | | all_243_0) = all_43_2 & $i(all_243_0) & $i(all_43_2)
% 154.17/21.97 | | | | |
% 154.17/21.97 | | | | | ALPHA: (168) implies:
% 154.17/21.97 | | | | | (169) $i(all_243_0)
% 154.17/21.97 | | | | | (170) sdtpldt0(sz10, all_243_0) = all_43_2
% 154.17/21.97 | | | | | (171) sdtpldt0(all_36_1, all_129_0) = all_243_0
% 154.17/21.97 | | | | |
% 154.17/21.97 | | | | | DELTA: instantiating (166) with fresh symbol all_247_0 gives:
% 154.17/21.97 | | | | | (172) sdtpldt0(all_36_1, all_247_0) = all_43_8 & sdtpldt0(sz10, xp)
% 154.17/21.97 | | | | | = all_247_0 & $i(all_247_0) & $i(all_43_8)
% 154.17/21.97 | | | | |
% 154.17/21.97 | | | | | ALPHA: (172) implies:
% 154.17/21.97 | | | | | (173) $i(all_247_0)
% 154.17/21.97 | | | | | (174) sdtpldt0(sz10, xp) = all_247_0
% 154.17/21.97 | | | | | (175) sdtpldt0(all_36_1, all_247_0) = all_43_8
% 154.17/21.97 | | | | |
% 154.17/21.97 | | | | | REDUCE: (159), (167) imply:
% 154.17/21.97 | | | | | (176) sdtpldt0(all_36_1, sz00) = sz00
% 154.17/21.97 | | | | |
% 154.17/21.97 | | | | | REDUCE: (160), (167) imply:
% 154.17/21.97 | | | | | (177) sdtpldt0(xp, sz00) = all_43_6
% 154.17/21.97 | | | | |
% 154.17/21.97 | | | | | REDUCE: (167), (170) imply:
% 154.17/21.97 | | | | | (178) sdtpldt0(sz10, all_243_0) = sz00
% 154.17/21.97 | | | | |
% 154.17/21.97 | | | | | BETA: splitting (163) gives:
% 154.17/21.97 | | | | |
% 154.17/21.97 | | | | | Case 1:
% 154.17/21.97 | | | | | |
% 154.17/21.97 | | | | | |
% 154.17/21.97 | | | | | | GROUND_INST: instantiating (21) with all_43_8, all_247_0, xp, sz10,
% 154.17/21.97 | | | | | | simplifying with (42), (174) gives:
% 154.17/21.97 | | | | | | (179) all_247_0 = all_43_8
% 154.17/21.97 | | | | | |
% 154.17/21.97 | | | | | | REDUCE: (175), (179) imply:
% 154.17/21.97 | | | | | | (180) sdtpldt0(all_36_1, all_43_8) = all_43_8
% 154.17/21.97 | | | | | |
% 154.17/21.97 | | | | | | BETA: splitting (94) gives:
% 154.17/21.97 | | | | | |
% 154.17/21.97 | | | | | | Case 1:
% 154.17/21.97 | | | | | | |
% 154.17/21.97 | | | | | | | (181) all_40_0 = sz00
% 154.17/21.97 | | | | | | |
% 154.17/21.97 | | | | | | | COMBINE_EQS: (81), (181) imply:
% 154.17/21.97 | | | | | | | (182) all_37_0 = sz00
% 154.17/21.97 | | | | | | |
% 154.17/21.97 | | | | | | | SIMP: (182) implies:
% 154.17/21.97 | | | | | | | (183) all_37_0 = sz00
% 154.17/21.97 | | | | | | |
% 154.17/21.97 | | | | | | | COMBINE_EQS: (78), (183) imply:
% 154.17/21.97 | | | | | | | (184) all_45_0 = sz00
% 154.17/21.97 | | | | | | |
% 154.17/21.97 | | | | | | | REDUCE: (85), (183) imply:
% 154.17/21.97 | | | | | | | (185) sdtpldt0(all_43_8, sz00) = all_43_6
% 154.17/21.97 | | | | | | |
% 154.17/21.97 | | | | | | | REDUCE: (108), (183) imply:
% 154.17/21.97 | | | | | | | (186) sdtpldt0(sz00, all_43_8) = all_43_6
% 154.17/21.97 | | | | | | |
% 154.17/21.97 | | | | | | | REDUCE: (135), (183) imply:
% 154.17/21.97 | | | | | | | (187) sdtpldt0(sz00, xp) = all_131_0
% 154.17/21.97 | | | | | | |
% 154.17/21.97 | | | | | | | REDUCE: (150), (183) imply:
% 154.17/21.97 | | | | | | | (188) sdtpldt0(all_36_1, sz00) = all_129_0
% 154.17/21.98 | | | | | | |
% 154.17/21.98 | | | | | | | REDUCE: (125), (183) imply:
% 154.17/21.98 | | | | | | | (189) sdtpldt0(xp, sz00) = all_131_0
% 154.17/21.98 | | | | | | |
% 154.17/21.98 | | | | | | | GROUND_INST: instantiating (21) with all_43_6, all_131_0, sz00,
% 154.17/21.98 | | | | | | | xp, simplifying with (177), (189) gives:
% 154.17/21.98 | | | | | | | (190) all_131_0 = all_43_6
% 154.17/21.98 | | | | | | |
% 154.17/21.98 | | | | | | | GROUND_INST: instantiating (21) with sz00, all_129_0, sz00,
% 154.17/21.98 | | | | | | | all_36_1, simplifying with (176), (188) gives:
% 154.17/21.98 | | | | | | | (191) all_129_0 = sz00
% 154.17/21.98 | | | | | | |
% 154.17/21.98 | | | | | | | REDUCE: (171), (191) imply:
% 154.17/21.98 | | | | | | | (192) sdtpldt0(all_36_1, sz00) = all_243_0
% 154.17/21.98 | | | | | | |
% 154.17/21.98 | | | | | | | REDUCE: (187), (190) imply:
% 154.17/21.98 | | | | | | | (193) sdtpldt0(sz00, xp) = all_43_6
% 154.17/21.98 | | | | | | |
% 154.17/21.98 | | | | | | | GROUND_INST: instantiating (21) with sz00, all_243_0, sz00,
% 154.17/21.98 | | | | | | | all_36_1, simplifying with (176), (192) gives:
% 154.17/21.98 | | | | | | | (194) all_243_0 = sz00
% 154.17/21.98 | | | | | | |
% 154.17/21.98 | | | | | | | REDUCE: (178), (194) imply:
% 154.17/21.98 | | | | | | | (195) sdtpldt0(sz10, sz00) = sz00
% 154.17/21.98 | | | | | | |
% 154.17/21.98 | | | | | | | BETA: splitting (118) gives:
% 154.17/21.98 | | | | | | |
% 154.17/21.98 | | | | | | | Case 1:
% 154.17/21.98 | | | | | | | |
% 154.17/21.98 | | | | | | | | (196) all_45_0 = all_43_8
% 154.17/21.98 | | | | | | | |
% 154.17/21.98 | | | | | | | | COMBINE_EQS: (184), (196) imply:
% 154.17/21.98 | | | | | | | | (197) all_43_8 = sz00
% 154.17/21.98 | | | | | | | |
% 154.17/21.98 | | | | | | | | SIMP: (197) implies:
% 154.17/21.98 | | | | | | | | (198) all_43_8 = sz00
% 154.17/21.98 | | | | | | | |
% 154.17/21.98 | | | | | | | | REDUCE: (186), (198) imply:
% 154.17/21.98 | | | | | | | | (199) sdtpldt0(sz00, sz00) = all_43_6
% 154.17/21.98 | | | | | | | |
% 154.17/21.98 | | | | | | | | GROUND_INST: instantiating (3) with sz00, all_43_6, simplifying
% 154.17/21.98 | | | | | | | | with (1), (12), (199) gives:
% 154.17/21.98 | | | | | | | | (200) all_43_6 = sz00
% 154.17/21.98 | | | | | | | |
% 154.17/21.98 | | | | | | | | GROUND_INST: instantiating (3) with xp, all_43_6, simplifying
% 154.17/21.98 | | | | | | | | with (16), (57), (193) gives:
% 154.17/21.98 | | | | | | | | (201) all_43_6 = xp
% 154.17/21.98 | | | | | | | |
% 154.17/21.98 | | | | | | | | COMBINE_EQS: (200), (201) imply:
% 154.17/21.98 | | | | | | | | (202) xp = sz00
% 154.17/21.98 | | | | | | | |
% 154.17/21.98 | | | | | | | | SIMP: (202) implies:
% 154.17/21.98 | | | | | | | | (203) xp = sz00
% 154.17/21.98 | | | | | | | |
% 154.17/21.98 | | | | | | | | REDUCE: (56), (203) imply:
% 154.17/21.98 | | | | | | | | (204) $false
% 154.17/21.98 | | | | | | | |
% 154.17/21.98 | | | | | | | | CLOSE: (204) is inconsistent.
% 154.17/21.98 | | | | | | | |
% 154.17/21.98 | | | | | | | Case 2:
% 154.17/21.98 | | | | | | | |
% 154.17/21.98 | | | | | | | | (205) all_43_8 = sz10
% 154.17/21.98 | | | | | | | |
% 154.17/21.98 | | | | | | | | REDUCE: (185), (205) imply:
% 154.17/21.98 | | | | | | | | (206) sdtpldt0(sz10, sz00) = all_43_6
% 154.17/21.98 | | | | | | | |
% 154.17/21.98 | | | | | | | | GROUND_INST: instantiating (21) with sz00, all_43_6, sz00, sz10,
% 154.17/21.98 | | | | | | | | simplifying with (195), (206) gives:
% 154.17/21.98 | | | | | | | | (207) all_43_6 = sz00
% 154.17/21.98 | | | | | | | |
% 154.17/21.98 | | | | | | | | REDUCE: (193), (207) imply:
% 154.17/21.98 | | | | | | | | (208) sdtpldt0(sz00, xp) = sz00
% 154.17/21.98 | | | | | | | |
% 154.17/21.98 | | | | | | | | REF_CLOSE: (3), (16), (56), (57), (208) are inconsistent by
% 154.17/21.98 | | | | | | | | sub-proof #1.
% 154.17/21.98 | | | | | | | |
% 154.17/21.98 | | | | | | | End of split
% 154.17/21.98 | | | | | | |
% 154.17/21.98 | | | | | | Case 2:
% 154.17/21.98 | | | | | | |
% 154.17/21.98 | | | | | | | (209) ~ (all_40_0 = sz00)
% 154.17/21.98 | | | | | | |
% 154.17/21.98 | | | | | | | REDUCE: (81), (209) imply:
% 154.17/21.98 | | | | | | | (210) ~ (all_37_0 = sz00)
% 154.17/21.98 | | | | | | |
% 154.17/21.98 | | | | | | | BETA: splitting (164) gives:
% 154.17/21.98 | | | | | | |
% 154.17/21.98 | | | | | | | Case 1:
% 154.17/21.98 | | | | | | | |
% 154.17/21.98 | | | | | | | | (211) all_45_0 = sz00
% 154.17/21.98 | | | | | | | |
% 154.17/21.98 | | | | | | | | COMBINE_EQS: (78), (211) imply:
% 154.17/21.98 | | | | | | | | (212) all_37_0 = sz00
% 154.17/21.98 | | | | | | | |
% 154.17/21.98 | | | | | | | | SIMP: (212) implies:
% 154.17/21.98 | | | | | | | | (213) all_37_0 = sz00
% 154.17/21.98 | | | | | | | |
% 154.17/21.98 | | | | | | | | REDUCE: (210), (213) imply:
% 154.17/21.98 | | | | | | | | (214) $false
% 154.17/21.98 | | | | | | | |
% 154.17/21.98 | | | | | | | | CLOSE: (214) is inconsistent.
% 154.17/21.98 | | | | | | | |
% 154.17/21.98 | | | | | | | Case 2:
% 154.17/21.98 | | | | | | | |
% 154.17/21.98 | | | | | | | | (215) sz10 = sz00
% 154.17/21.98 | | | | | | | |
% 154.17/21.98 | | | | | | | | REDUCE: (178), (215) imply:
% 154.17/21.98 | | | | | | | | (216) sdtpldt0(sz00, all_243_0) = sz00
% 154.17/21.98 | | | | | | | |
% 154.17/21.98 | | | | | | | | REDUCE: (42), (215) imply:
% 154.17/21.98 | | | | | | | | (217) sdtpldt0(sz00, xp) = all_43_8
% 154.17/21.98 | | | | | | | |
% 154.17/21.98 | | | | | | | | BETA: splitting (118) gives:
% 154.17/21.98 | | | | | | | |
% 154.17/21.98 | | | | | | | | Case 1:
% 154.17/21.98 | | | | | | | | |
% 154.17/21.98 | | | | | | | | | (218) all_45_0 = all_43_8
% 154.17/21.98 | | | | | | | | |
% 154.17/21.98 | | | | | | | | | COMBINE_EQS: (78), (218) imply:
% 154.17/21.98 | | | | | | | | | (219) all_43_8 = all_37_0
% 154.17/21.98 | | | | | | | | |
% 154.17/21.98 | | | | | | | | | REDUCE: (180), (219) imply:
% 154.17/21.98 | | | | | | | | | (220) sdtpldt0(all_36_1, all_37_0) = all_37_0
% 154.17/21.98 | | | | | | | | |
% 154.17/21.98 | | | | | | | | | GROUND_INST: instantiating (21) with all_129_0, all_37_0,
% 154.17/21.98 | | | | | | | | | all_37_0, all_36_1, simplifying with (150), (220)
% 154.17/21.98 | | | | | | | | | gives:
% 154.17/21.98 | | | | | | | | | (221) all_129_0 = all_37_0
% 154.17/21.98 | | | | | | | | |
% 154.17/21.98 | | | | | | | | | REDUCE: (171), (221) imply:
% 154.17/21.98 | | | | | | | | | (222) sdtpldt0(all_36_1, all_37_0) = all_243_0
% 154.17/21.98 | | | | | | | | |
% 154.17/21.98 | | | | | | | | | GROUND_INST: instantiating (21) with all_37_0, all_243_0,
% 154.17/21.98 | | | | | | | | | all_37_0, all_36_1, simplifying with (220), (222)
% 154.17/21.98 | | | | | | | | | gives:
% 154.17/21.98 | | | | | | | | | (223) all_243_0 = all_37_0
% 154.17/21.98 | | | | | | | | |
% 154.17/21.98 | | | | | | | | | REDUCE: (216), (223) imply:
% 154.17/21.98 | | | | | | | | | (224) sdtpldt0(sz00, all_37_0) = sz00
% 154.17/21.98 | | | | | | | | |
% 154.17/21.98 | | | | | | | | | GROUND_INST: instantiating (3) with all_37_0, sz00, simplifying
% 154.17/21.98 | | | | | | | | | with (87), (97), (224) gives:
% 154.17/21.98 | | | | | | | | | (225) all_37_0 = sz00
% 154.17/21.98 | | | | | | | | |
% 154.17/21.98 | | | | | | | | | COMBINE_EQS: (78), (225) imply:
% 154.17/21.98 | | | | | | | | | (226) all_45_0 = sz00
% 154.17/21.98 | | | | | | | | |
% 154.17/21.98 | | | | | | | | | BETA: splitting (118) gives:
% 154.17/21.98 | | | | | | | | |
% 154.17/21.98 | | | | | | | | | Case 1:
% 154.17/21.98 | | | | | | | | | |
% 154.17/21.98 | | | | | | | | | |
% 154.17/21.98 | | | | | | | | | | COMBINE_EQS: (218), (226) imply:
% 154.17/21.98 | | | | | | | | | | (227) all_43_8 = sz00
% 154.17/21.98 | | | | | | | | | |
% 154.17/21.98 | | | | | | | | | | REDUCE: (217), (227) imply:
% 154.17/21.98 | | | | | | | | | | (228) sdtpldt0(sz00, xp) = sz00
% 154.17/21.98 | | | | | | | | | |
% 154.17/21.98 | | | | | | | | | | REF_CLOSE: (3), (16), (56), (57), (228) are inconsistent by
% 154.17/21.98 | | | | | | | | | | sub-proof #1.
% 154.17/21.98 | | | | | | | | | |
% 154.17/21.98 | | | | | | | | | Case 2:
% 154.17/21.98 | | | | | | | | | |
% 154.17/21.98 | | | | | | | | | | (229) all_43_8 = sz10
% 154.17/21.98 | | | | | | | | | | (230) ~ (all_45_0 = all_43_8)
% 154.17/21.98 | | | | | | | | | |
% 154.17/21.98 | | | | | | | | | | COMBINE_EQS: (215), (229) imply:
% 154.17/21.98 | | | | | | | | | | (231) all_43_8 = sz00
% 154.17/21.98 | | | | | | | | | |
% 154.17/21.98 | | | | | | | | | | REDUCE: (226), (230), (231) imply:
% 154.17/21.98 | | | | | | | | | | (232) $false
% 154.17/21.98 | | | | | | | | | |
% 154.17/21.98 | | | | | | | | | | CLOSE: (232) is inconsistent.
% 154.17/21.98 | | | | | | | | | |
% 154.17/21.98 | | | | | | | | | End of split
% 154.17/21.98 | | | | | | | | |
% 154.17/21.98 | | | | | | | | Case 2:
% 154.17/21.98 | | | | | | | | |
% 154.17/21.98 | | | | | | | | | (233) all_43_8 = sz10
% 154.17/21.98 | | | | | | | | |
% 154.17/21.98 | | | | | | | | | COMBINE_EQS: (215), (233) imply:
% 154.17/21.98 | | | | | | | | | (234) all_43_8 = sz00
% 154.17/21.98 | | | | | | | | |
% 154.17/21.98 | | | | | | | | | REDUCE: (217), (234) imply:
% 154.17/21.98 | | | | | | | | | (235) sdtpldt0(sz00, xp) = sz00
% 154.17/21.98 | | | | | | | | |
% 154.17/21.98 | | | | | | | | | REF_CLOSE: (3), (16), (56), (57), (235) are inconsistent by
% 154.17/21.98 | | | | | | | | | sub-proof #1.
% 154.17/21.98 | | | | | | | | |
% 154.17/21.98 | | | | | | | | End of split
% 154.17/21.98 | | | | | | | |
% 154.17/21.98 | | | | | | | End of split
% 154.17/21.99 | | | | | | |
% 154.17/21.99 | | | | | | End of split
% 154.17/21.99 | | | | | |
% 154.17/21.99 | | | | | Case 2:
% 154.17/21.99 | | | | | |
% 154.17/21.99 | | | | | | (236) xp = sz00
% 154.17/21.99 | | | | | |
% 154.17/21.99 | | | | | | REDUCE: (56), (236) imply:
% 154.17/21.99 | | | | | | (237) $false
% 154.17/21.99 | | | | | |
% 154.17/21.99 | | | | | | CLOSE: (237) is inconsistent.
% 154.17/21.99 | | | | | |
% 154.17/21.99 | | | | | End of split
% 154.17/21.99 | | | | |
% 154.17/21.99 | | | | Case 2:
% 154.17/21.99 | | | | |
% 154.17/21.99 | | | | | (238) ~ aElementOf0(sz00, all_48_0)
% 154.17/21.99 | | | | |
% 154.17/21.99 | | | | | REDUCE: (91), (238) imply:
% 154.17/21.99 | | | | | (239) ~ aElementOf0(sz00, cS2076)
% 154.17/21.99 | | | | |
% 154.17/21.99 | | | | | GROUND_INST: instantiating (mAddComm) with sz10, all_129_0, all_43_2,
% 154.17/21.99 | | | | | simplifying with (2), (15), (121), (137), (139) gives:
% 154.17/21.99 | | | | | (240) sdtpldt0(all_129_0, sz10) = all_43_2 & $i(all_43_2)
% 154.17/21.99 | | | | |
% 154.17/21.99 | | | | | GROUND_INST: instantiating (6) with all_131_0, xp, simplifying with
% 154.17/21.99 | | | | | (16), (57), (132), (134) gives:
% 154.17/21.99 | | | | | (241) xp = sz00 | sdteqdtlpzmzozddtrp0(all_131_0, all_131_0, xp)
% 154.17/21.99 | | | | |
% 154.17/21.99 | | | | | GROUND_INST: instantiating (mAddAsso) with sz10, all_36_1, all_129_0,
% 154.17/21.99 | | | | | sz10, all_43_2, simplifying with (2), (15), (121), (137),
% 154.17/21.99 | | | | | (139), (147), (153), (154) gives:
% 154.17/21.99 | | | | | (242) ? [v0: $i] : (sdtpldt0(all_36_1, all_129_0) = v0 &
% 154.17/21.99 | | | | | sdtpldt0(sz10, v0) = all_43_2 & $i(v0) & $i(all_43_2))
% 154.17/21.99 | | | | |
% 154.17/21.99 | | | | | GROUND_INST: instantiating (mAddComm) with xp, all_43_2, all_43_6,
% 154.17/21.99 | | | | | simplifying with (16), (57), (102), (115), (160) gives:
% 154.17/21.99 | | | | | (243) sdtpldt0(all_43_2, xp) = all_43_6 & $i(all_43_6)
% 154.17/21.99 | | | | |
% 154.17/21.99 | | | | | ALPHA: (243) implies:
% 154.17/21.99 | | | | | (244) sdtpldt0(all_43_2, xp) = all_43_6
% 154.17/21.99 | | | | |
% 154.17/21.99 | | | | | GROUND_INST: instantiating (mAddAsso) with all_36_1, sz10, xp, sz10,
% 154.17/21.99 | | | | | all_43_8, simplifying with (2), (15), (16), (42), (57),
% 154.17/21.99 | | | | | (153), (154), (157) gives:
% 154.17/21.99 | | | | | (245) ? [v0: $i] : (sdtpldt0(all_36_1, v0) = all_43_8 &
% 154.17/21.99 | | | | | sdtpldt0(sz10, xp) = v0 & $i(v0) & $i(all_43_8))
% 154.17/21.99 | | | | |
% 154.17/21.99 | | | | | GROUND_INST: instantiating (mAddComm) with all_36_1, all_43_2,
% 154.17/21.99 | | | | | all_43_2, simplifying with (102), (115), (153), (154),
% 154.17/21.99 | | | | | (159) gives:
% 154.17/21.99 | | | | | (246) sdtpldt0(all_43_2, all_36_1) = all_43_2
% 154.17/21.99 | | | | |
% 154.17/21.99 | | | | | GROUND_INST: instantiating (4) with sz10, all_37_0, all_43_2,
% 154.17/21.99 | | | | | simplifying with (2), (15), (25), (156) gives:
% 154.17/21.99 | | | | | (247) all_43_2 = sz00
% 154.17/21.99 | | | | |
% 154.17/21.99 | | | | | DELTA: instantiating (245) with fresh symbol all_241_0 gives:
% 154.17/21.99 | | | | | (248) sdtpldt0(all_36_1, all_241_0) = all_43_8 & sdtpldt0(sz10, xp)
% 154.17/21.99 | | | | | = all_241_0 & $i(all_241_0) & $i(all_43_8)
% 154.17/21.99 | | | | |
% 154.17/21.99 | | | | | ALPHA: (248) implies:
% 154.17/21.99 | | | | | (249) sdtpldt0(sz10, xp) = all_241_0
% 154.17/21.99 | | | | | (250) sdtpldt0(all_36_1, all_241_0) = all_43_8
% 154.17/21.99 | | | | |
% 154.17/21.99 | | | | | DELTA: instantiating (242) with fresh symbol all_249_0 gives:
% 154.17/21.99 | | | | | (251) sdtpldt0(all_36_1, all_129_0) = all_249_0 & sdtpldt0(sz10,
% 154.17/21.99 | | | | | all_249_0) = all_43_2 & $i(all_249_0) & $i(all_43_2)
% 154.17/21.99 | | | | |
% 154.17/21.99 | | | | | ALPHA: (251) implies:
% 154.17/21.99 | | | | | (252) $i(all_249_0)
% 154.17/21.99 | | | | | (253) sdtpldt0(all_36_1, all_129_0) = all_249_0
% 154.17/21.99 | | | | |
% 154.17/21.99 | | | | | REDUCE: (246), (247) imply:
% 154.17/21.99 | | | | | (254) sdtpldt0(sz00, all_36_1) = sz00
% 154.17/21.99 | | | | |
% 154.17/21.99 | | | | | REDUCE: (244), (247) imply:
% 154.17/21.99 | | | | | (255) sdtpldt0(sz00, xp) = all_43_6
% 154.17/21.99 | | | | |
% 154.17/21.99 | | | | | REDUCE: (156), (247) imply:
% 154.17/21.99 | | | | | (256) sdtpldt0(all_37_0, sz10) = sz00
% 154.17/21.99 | | | | |
% 154.17/21.99 | | | | | BETA: splitting (241) gives:
% 154.17/21.99 | | | | |
% 154.17/21.99 | | | | | Case 1:
% 154.17/21.99 | | | | | |
% 154.17/21.99 | | | | | |
% 154.17/21.99 | | | | | | GROUND_INST: instantiating (21) with all_43_8, all_241_0, xp, sz10,
% 154.17/21.99 | | | | | | simplifying with (42), (249) gives:
% 154.17/21.99 | | | | | | (257) all_241_0 = all_43_8
% 154.17/21.99 | | | | | |
% 154.17/21.99 | | | | | | REDUCE: (250), (257) imply:
% 154.17/21.99 | | | | | | (258) sdtpldt0(all_36_1, all_43_8) = all_43_8
% 154.17/21.99 | | | | | |
% 154.17/21.99 | | | | | | BETA: splitting (109) gives:
% 154.17/21.99 | | | | | |
% 154.17/21.99 | | | | | | Case 1:
% 154.17/21.99 | | | | | | |
% 154.17/21.99 | | | | | | | (259) all_43_8 = all_40_0
% 154.17/21.99 | | | | | | |
% 154.17/21.99 | | | | | | | COMBINE_EQS: (81), (259) imply:
% 154.17/21.99 | | | | | | | (260) all_43_8 = all_37_0
% 154.17/21.99 | | | | | | |
% 154.17/21.99 | | | | | | | REDUCE: (258), (260) imply:
% 154.17/21.99 | | | | | | | (261) sdtpldt0(all_36_1, all_37_0) = all_37_0
% 154.17/21.99 | | | | | | |
% 154.17/21.99 | | | | | | | REDUCE: (96), (260) imply:
% 154.17/21.99 | | | | | | | (262) aElementOf0(all_37_0, cS2076)
% 154.17/21.99 | | | | | | |
% 154.17/21.99 | | | | | | | GROUND_INST: instantiating (21) with all_129_0, all_37_0,
% 154.17/21.99 | | | | | | | all_37_0, all_36_1, simplifying with (150), (261)
% 154.17/21.99 | | | | | | | gives:
% 154.17/21.99 | | | | | | | (263) all_129_0 = all_37_0
% 154.17/21.99 | | | | | | |
% 154.17/21.99 | | | | | | | REDUCE: (253), (263) imply:
% 154.17/21.99 | | | | | | | (264) sdtpldt0(all_36_1, all_37_0) = all_249_0
% 154.17/21.99 | | | | | | |
% 154.17/21.99 | | | | | | | GROUND_INST: instantiating (21) with all_37_0, all_249_0,
% 154.17/21.99 | | | | | | | all_37_0, all_36_1, simplifying with (261), (264)
% 154.17/21.99 | | | | | | | gives:
% 154.17/21.99 | | | | | | | (265) all_249_0 = all_37_0
% 154.17/21.99 | | | | | | |
% 154.17/21.99 | | | | | | | BETA: splitting (113) gives:
% 154.17/21.99 | | | | | | |
% 154.17/21.99 | | | | | | | Case 1:
% 154.17/21.99 | | | | | | | |
% 154.17/21.99 | | | | | | | | (266) all_43_4 = all_40_0
% 154.17/21.99 | | | | | | | |
% 154.17/21.99 | | | | | | | | COMBINE_EQS: (148), (266) imply:
% 154.17/21.99 | | | | | | | | (267) all_40_0 = all_36_1
% 154.17/21.99 | | | | | | | |
% 154.17/21.99 | | | | | | | | COMBINE_EQS: (81), (267) imply:
% 154.17/21.99 | | | | | | | | (268) all_37_0 = all_36_1
% 154.17/21.99 | | | | | | | |
% 154.17/21.99 | | | | | | | | SIMP: (268) implies:
% 154.17/21.99 | | | | | | | | (269) all_37_0 = all_36_1
% 154.17/21.99 | | | | | | | |
% 154.17/21.99 | | | | | | | | REDUCE: (262), (269) imply:
% 154.17/21.99 | | | | | | | | (270) aElementOf0(all_36_1, cS2076)
% 154.17/21.99 | | | | | | | |
% 154.17/21.99 | | | | | | | | GROUND_INST: instantiating (3) with all_36_1, sz00, simplifying
% 154.17/21.99 | | | | | | | | with (153), (154), (254) gives:
% 154.17/21.99 | | | | | | | | (271) all_36_1 = sz00
% 154.17/21.99 | | | | | | | |
% 154.17/21.99 | | | | | | | | REDUCE: (270), (271) imply:
% 154.17/21.99 | | | | | | | | (272) aElementOf0(sz00, cS2076)
% 154.17/21.99 | | | | | | | |
% 154.17/21.99 | | | | | | | | PRED_UNIFY: (239), (272) imply:
% 154.17/21.99 | | | | | | | | (273) $false
% 154.17/21.99 | | | | | | | |
% 154.17/21.99 | | | | | | | | CLOSE: (273) is inconsistent.
% 154.17/21.99 | | | | | | | |
% 154.17/21.99 | | | | | | | Case 2:
% 154.17/21.99 | | | | | | | |
% 154.17/21.99 | | | | | | | |
% 154.17/21.99 | | | | | | | | GROUND_INST: instantiating (3) with xp, all_43_6, simplifying
% 154.17/21.99 | | | | | | | | with (16), (57), (255) gives:
% 154.17/21.99 | | | | | | | | (274) all_43_6 = xp
% 154.17/21.99 | | | | | | | |
% 154.17/21.99 | | | | | | | | GROUND_INST: instantiating (mAddAsso) with sz00, all_36_1, xp,
% 154.17/21.99 | | | | | | | | sz00, all_43_6, simplifying with (1), (12), (16),
% 154.17/21.99 | | | | | | | | (57), (153), (154), (254), (255) gives:
% 154.17/21.99 | | | | | | | | (275) ? [v0: $i] : (sdtpldt0(all_36_1, xp) = v0 &
% 154.17/21.99 | | | | | | | | sdtpldt0(sz00, v0) = all_43_6 & $i(v0) &
% 154.17/21.99 | | | | | | | | $i(all_43_6))
% 154.17/21.99 | | | | | | | |
% 154.17/21.99 | | | | | | | | GROUND_INST: instantiating (3) with all_36_1, sz00, simplifying
% 154.17/21.99 | | | | | | | | with (153), (154), (254) gives:
% 154.17/21.99 | | | | | | | | (276) all_36_1 = sz00
% 154.17/21.99 | | | | | | | |
% 154.17/21.99 | | | | | | | | DELTA: instantiating (275) with fresh symbol all_1020_0 gives:
% 154.17/21.99 | | | | | | | | (277) sdtpldt0(all_36_1, xp) = all_1020_0 & sdtpldt0(sz00,
% 154.17/21.99 | | | | | | | | all_1020_0) = all_43_6 & $i(all_1020_0) &
% 154.17/21.99 | | | | | | | | $i(all_43_6)
% 154.17/21.99 | | | | | | | |
% 154.17/21.99 | | | | | | | | ALPHA: (277) implies:
% 154.17/21.99 | | | | | | | | (278) $i(all_43_6)
% 154.17/21.99 | | | | | | | |
% 154.17/21.99 | | | | | | | | REDUCE: (146), (276) imply:
% 154.17/21.99 | | | | | | | | (279) smndt0(xp) = sz00
% 154.17/21.99 | | | | | | | |
% 154.17/21.99 | | | | | | | | GROUND_INST: instantiating (4) with xp, sz00, all_43_6,
% 154.17/21.99 | | | | | | | | simplifying with (16), (57), (255), (279) gives:
% 154.17/21.99 | | | | | | | | (280) all_43_6 = sz00
% 154.17/21.99 | | | | | | | |
% 154.17/21.99 | | | | | | | | COMBINE_EQS: (274), (280) imply:
% 154.17/22.00 | | | | | | | | (281) xp = sz00
% 154.17/22.00 | | | | | | | |
% 154.17/22.00 | | | | | | | | REDUCE: (56), (281) imply:
% 154.17/22.00 | | | | | | | | (282) $false
% 154.17/22.00 | | | | | | | |
% 154.17/22.00 | | | | | | | | CLOSE: (282) is inconsistent.
% 154.17/22.00 | | | | | | | |
% 154.17/22.00 | | | | | | | End of split
% 154.17/22.00 | | | | | | |
% 154.17/22.00 | | | | | | Case 2:
% 154.17/22.00 | | | | | | |
% 154.17/22.00 | | | | | | | (283) ~ (all_43_8 = all_40_0)
% 154.17/22.00 | | | | | | |
% 154.17/22.00 | | | | | | | REDUCE: (81), (283) imply:
% 154.17/22.00 | | | | | | | (284) ~ (all_43_8 = all_37_0)
% 154.17/22.00 | | | | | | |
% 154.17/22.00 | | | | | | | BETA: splitting (118) gives:
% 154.17/22.00 | | | | | | |
% 154.17/22.00 | | | | | | | Case 1:
% 154.17/22.00 | | | | | | | |
% 154.17/22.00 | | | | | | | | (285) all_45_0 = all_43_8
% 154.17/22.00 | | | | | | | |
% 154.17/22.00 | | | | | | | | COMBINE_EQS: (78), (285) imply:
% 154.17/22.00 | | | | | | | | (286) all_43_8 = all_37_0
% 154.17/22.00 | | | | | | | |
% 154.17/22.00 | | | | | | | | REDUCE: (284), (286) imply:
% 154.17/22.00 | | | | | | | | (287) $false
% 154.17/22.00 | | | | | | | |
% 154.17/22.00 | | | | | | | | CLOSE: (287) is inconsistent.
% 154.17/22.00 | | | | | | | |
% 154.17/22.00 | | | | | | | Case 2:
% 154.17/22.00 | | | | | | | |
% 154.17/22.00 | | | | | | | | (288) all_43_8 = sz10
% 154.17/22.00 | | | | | | | |
% 154.17/22.00 | | | | | | | | REDUCE: (108), (288) imply:
% 154.17/22.00 | | | | | | | | (289) sdtpldt0(all_37_0, sz10) = all_43_6
% 154.17/22.00 | | | | | | | |
% 154.17/22.00 | | | | | | | | GROUND_INST: instantiating (21) with sz00, all_43_6, sz10,
% 154.17/22.00 | | | | | | | | all_37_0, simplifying with (256), (289) gives:
% 154.17/22.00 | | | | | | | | (290) all_43_6 = sz00
% 154.17/22.00 | | | | | | | |
% 154.17/22.00 | | | | | | | | REDUCE: (255), (290) imply:
% 154.17/22.00 | | | | | | | | (291) sdtpldt0(sz00, xp) = sz00
% 154.17/22.00 | | | | | | | |
% 154.17/22.00 | | | | | | | | REF_CLOSE: (3), (16), (56), (57), (291) are inconsistent by
% 154.17/22.00 | | | | | | | | sub-proof #1.
% 154.17/22.00 | | | | | | | |
% 154.17/22.00 | | | | | | | End of split
% 154.17/22.00 | | | | | | |
% 154.17/22.00 | | | | | | End of split
% 154.17/22.00 | | | | | |
% 154.17/22.00 | | | | | Case 2:
% 154.17/22.00 | | | | | |
% 154.17/22.00 | | | | | | (292) xp = sz00
% 154.17/22.00 | | | | | |
% 154.17/22.00 | | | | | | REDUCE: (56), (292) imply:
% 154.17/22.00 | | | | | | (293) $false
% 154.17/22.00 | | | | | |
% 154.17/22.00 | | | | | | CLOSE: (293) is inconsistent.
% 154.17/22.00 | | | | | |
% 154.17/22.00 | | | | | End of split
% 154.17/22.00 | | | | |
% 154.17/22.00 | | | | End of split
% 154.17/22.00 | | | |
% 154.17/22.00 | | | Case 2:
% 154.17/22.00 | | | |
% 154.17/22.00 | | | | (294) all_36_2 = sz10 & sdtpldt0(sz10, xp) = sz10
% 154.17/22.00 | | | |
% 154.17/22.00 | | | | ALPHA: (294) implies:
% 154.17/22.00 | | | | (295) sdtpldt0(sz10, xp) = sz10
% 154.17/22.00 | | | |
% 154.17/22.00 | | | | GROUND_INST: instantiating (21) with all_43_8, sz10, xp, sz10,
% 154.17/22.00 | | | | simplifying with (42), (295) gives:
% 154.17/22.00 | | | | (296) all_43_8 = sz10
% 154.17/22.00 | | | |
% 154.17/22.00 | | | | REDUCE: (108), (296) imply:
% 154.17/22.00 | | | | (297) sdtpldt0(all_37_0, sz10) = all_43_6
% 154.17/22.00 | | | |
% 154.17/22.00 | | | | GROUND_INST: instantiating (21) with all_133_0, all_43_6, sz10,
% 154.17/22.00 | | | | all_37_0, simplifying with (131), (297) gives:
% 154.17/22.00 | | | | (298) all_133_0 = all_43_6
% 154.17/22.00 | | | |
% 154.17/22.00 | | | | REDUCE: (128), (298) imply:
% 154.17/22.00 | | | | (299) sdtpldt0(xp, all_43_6) = all_43_6
% 154.17/22.00 | | | |
% 154.17/22.00 | | | | GROUND_INST: instantiating (mAddComm) with sz10, all_131_0, all_43_6,
% 154.17/22.00 | | | | simplifying with (2), (15), (124), (132), (134) gives:
% 154.17/22.00 | | | | (300) sdtpldt0(all_131_0, sz10) = all_43_6 & $i(all_43_6)
% 154.17/22.00 | | | |
% 154.17/22.00 | | | | ALPHA: (300) implies:
% 154.17/22.00 | | | | (301) $i(all_43_6)
% 154.17/22.00 | | | |
% 154.17/22.00 | | | | GROUND_INST: instantiating (mAddComm) with xp, all_43_6, all_43_6,
% 154.17/22.00 | | | | simplifying with (16), (57), (103), (299), (301) gives:
% 154.17/22.00 | | | | (302) sdtpldt0(all_43_6, xp) = all_43_6
% 154.17/22.00 | | | |
% 154.17/22.00 | | | | GROUND_INST: instantiating (4) with sz10, all_37_0, all_43_6,
% 154.17/22.00 | | | | simplifying with (2), (15), (25), (297) gives:
% 154.17/22.00 | | | | (303) all_43_6 = sz00
% 154.17/22.00 | | | |
% 154.17/22.00 | | | | REDUCE: (302), (303) imply:
% 154.17/22.00 | | | | (304) sdtpldt0(sz00, xp) = sz00
% 154.17/22.00 | | | |
% 154.17/22.00 | | | | REF_CLOSE: (3), (16), (56), (57), (304) are inconsistent by sub-proof
% 154.17/22.00 | | | | #1.
% 154.17/22.00 | | | |
% 154.17/22.00 | | | End of split
% 154.17/22.00 | | |
% 154.17/22.00 | | Case 2:
% 154.17/22.00 | | |
% 154.17/22.00 | | | (305) xp = sz00
% 154.17/22.00 | | |
% 154.17/22.00 | | | REDUCE: (56), (305) imply:
% 154.17/22.00 | | | (306) $false
% 154.17/22.00 | | |
% 154.17/22.00 | | | CLOSE: (306) is inconsistent.
% 154.17/22.00 | | |
% 154.17/22.00 | | End of split
% 154.17/22.00 | |
% 154.17/22.00 | Case 2:
% 154.17/22.00 | |
% 154.17/22.00 | | (307) xp = sz00
% 154.17/22.00 | |
% 154.17/22.00 | | REDUCE: (56), (307) imply:
% 154.17/22.00 | | (308) $false
% 154.17/22.00 | |
% 154.17/22.00 | | CLOSE: (308) is inconsistent.
% 154.17/22.00 | |
% 154.17/22.00 | End of split
% 154.17/22.00 |
% 154.17/22.00 End of proof
% 154.17/22.00
% 154.17/22.00 Sub-proof #1 shows that the following formulas are inconsistent:
% 154.17/22.00 ----------------------------------------------------------------
% 154.41/22.00 (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~
% 154.41/22.00 $i(v0) | ~ aInteger0(v0))
% 154.41/22.00 (2) aInteger0(xp)
% 154.41/22.00 (3) sdtpldt0(sz00, xp) = sz00
% 154.41/22.00 (4) $i(xp)
% 154.41/22.00 (5) ~ (xp = sz00)
% 154.41/22.00
% 154.41/22.00 Begin of proof
% 154.41/22.00 |
% 154.41/22.00 | GROUND_INST: instantiating (1) with xp, sz00, simplifying with (2), (3), (4)
% 154.41/22.00 | gives:
% 154.41/22.00 | (6) xp = sz00
% 154.41/22.00 |
% 154.41/22.00 | REDUCE: (5), (6) imply:
% 154.41/22.00 | (7) $false
% 154.41/22.00 |
% 154.41/22.00 | CLOSE: (7) is inconsistent.
% 154.41/22.00 |
% 154.41/22.00 End of proof
% 154.41/22.00 % SZS output end Proof for theBenchmark
% 154.41/22.00
% 154.41/22.00 21481ms
%------------------------------------------------------------------------------