TSTP Solution File: NUM453+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM453+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n005.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 11:47:50 EDT 2023
% Result : Theorem 95.49s 13.16s
% Output : Proof 104.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM453+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 15:10:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.04/1.28 Prover 1: Preprocessing ...
% 4.04/1.28 Prover 4: Preprocessing ...
% 4.37/1.33 Prover 6: Preprocessing ...
% 4.37/1.33 Prover 0: Preprocessing ...
% 4.37/1.33 Prover 5: Preprocessing ...
% 4.37/1.33 Prover 2: Preprocessing ...
% 4.37/1.33 Prover 3: Preprocessing ...
% 11.43/2.29 Prover 1: Constructing countermodel ...
% 11.43/2.32 Prover 3: Constructing countermodel ...
% 11.43/2.34 Prover 5: Constructing countermodel ...
% 12.23/2.40 Prover 6: Proving ...
% 12.61/2.46 Prover 2: Proving ...
% 13.71/2.72 Prover 4: Constructing countermodel ...
% 15.27/2.81 Prover 0: Proving ...
% 72.44/10.28 Prover 2: stopped
% 72.44/10.28 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 74.03/10.37 Prover 7: Preprocessing ...
% 75.62/10.57 Prover 7: Constructing countermodel ...
% 95.49/13.16 Prover 0: proved (12392ms)
% 95.49/13.16
% 95.49/13.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 95.49/13.16
% 95.49/13.16 Prover 5: stopped
% 95.49/13.17 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 95.49/13.17 Prover 6: stopped
% 95.49/13.18 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 95.49/13.18 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 96.25/13.27 Prover 10: Preprocessing ...
% 96.25/13.28 Prover 11: Preprocessing ...
% 96.25/13.28 Prover 8: Preprocessing ...
% 97.47/13.40 Prover 8: Warning: ignoring some quantifiers
% 97.47/13.40 Prover 10: Constructing countermodel ...
% 97.47/13.40 Prover 8: Constructing countermodel ...
% 98.54/13.61 Prover 11: Constructing countermodel ...
% 102.52/14.06 Prover 3: stopped
% 102.52/14.07 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 102.52/14.14 Prover 13: Preprocessing ...
% 103.85/14.20 Prover 7: Found proof (size 176)
% 103.85/14.21 Prover 7: proved (3917ms)
% 103.85/14.21 Prover 10: stopped
% 103.85/14.21 Prover 8: stopped
% 103.85/14.21 Prover 11: stopped
% 103.85/14.21 Prover 1: stopped
% 103.85/14.21 Prover 4: stopped
% 103.85/14.24 Prover 13: Constructing countermodel ...
% 103.85/14.24 Prover 13: stopped
% 103.85/14.24
% 103.85/14.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 103.85/14.24
% 104.06/14.26 % SZS output start Proof for theBenchmark
% 104.06/14.26 Assumptions after simplification:
% 104.06/14.26 ---------------------------------
% 104.06/14.26
% 104.06/14.26 (mAddAsso)
% 104.06/14.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 104.06/14.29 (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 104.06/14.29 | ~ $i(v0) | ~ aInteger0(v2) | ~ aInteger0(v1) | ~ aInteger0(v0) | ?
% 104.06/14.29 [v5: $i] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4 & $i(v5) &
% 104.06/14.29 $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 104.06/14.29 $i] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ (sdtpldt0(v0, v3) = v4) | ~ $i(v2) |
% 104.06/14.29 ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v2) | ~ aInteger0(v1) | ~
% 104.06/14.29 aInteger0(v0) | ? [v5: $i] : (sdtpldt0(v5, v2) = v4 & sdtpldt0(v0, v1) = v5
% 104.06/14.29 & $i(v5) & $i(v4)))
% 104.06/14.29
% 104.06/14.29 (mAddComm)
% 104.06/14.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v1, v0) = v2) | ~
% 104.06/14.29 $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) | (sdtpldt0(v0, v1)
% 104.06/14.29 = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 104.06/14.29 (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~
% 104.06/14.29 aInteger0(v0) | (sdtpldt0(v1, v0) = v2 & $i(v2)))
% 104.06/14.29
% 104.06/14.29 (mAddNeg)
% 104.06/14.29 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ~
% 104.06/14.29 aInteger0(v0) | (sdtpldt0(v1, v0) = sz00 & sdtpldt0(v0, v1) = sz00))
% 104.06/14.29
% 104.06/14.29 (mAddZero)
% 104.06/14.29 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1)
% 104.06/14.30 | ~ $i(v0) | ~ aInteger0(v0)) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~
% 104.06/14.30 (sdtpldt0(sz00, v0) = v1) | ~ $i(v0) | ~ aInteger0(v0)) & ! [v0: $i] : !
% 104.06/14.30 [v1: $i] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ $i(v0) | ~ aInteger0(v0) |
% 104.06/14.30 sdtpldt0(sz00, v0) = v0) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(sz00,
% 104.06/14.30 v0) = v1) | ~ $i(v0) | ~ aInteger0(v0) | sdtpldt0(v0, sz00) = v0)
% 104.06/14.30
% 104.06/14.30 (mArSeqClosed)
% 104.06/14.30 $i(cS1395) & $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = sz00 |
% 104.06/14.30 ~ (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 104.06/14.30 aInteger0(v1) | ~ aInteger0(v0) | isClosed0(v2)) & ! [v0: $i] : ! [v1:
% 104.06/14.30 $i] : ! [v2: $i] : (v1 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) |
% 104.06/14.30 ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) | aSubsetOf0(v2,
% 104.06/14.30 cS1395))
% 104.06/14.30
% 104.06/14.30 (mDistrib)
% 104.06/14.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 104.06/14.31 $i] : ( ~ (sdtasdt0(v1, v2) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~
% 104.06/14.31 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 104.06/14.31 aInteger0(v2) | ~ aInteger0(v1) | ~ aInteger0(v0) | ? [v6: $i] : ? [v7:
% 104.06/14.31 $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v9, v2) = v5 & sdtasdt0(v0,
% 104.06/14.31 v6) = v7 & sdtasdt0(v0, v1) = v8 & sdtpldt0(v8, v3) = v7 & sdtpldt0(v1,
% 104.06/14.31 v2) = v6 & sdtpldt0(v0, v1) = v9 & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 104.06/14.31 $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 104.06/14.31 $i] : ! [v5: $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3)
% 104.06/14.31 | ~ (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 104.06/14.31 aInteger0(v2) | ~ aInteger0(v1) | ~ aInteger0(v0) | ? [v6: $i] : ? [v7:
% 104.06/14.31 $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v7, v2) = v8 & sdtasdt0(v1,
% 104.06/14.31 v2) = v9 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v4, v9) = v8 & sdtpldt0(v1,
% 104.06/14.31 v2) = v6 & sdtpldt0(v0, v1) = v7 & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 104.06/14.31 $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 104.06/14.31 $i] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) |
% 104.06/14.31 ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v2) | ~ aInteger0(v1) | ~
% 104.06/14.31 aInteger0(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ?
% 104.06/14.31 [v9: $i] : (sdtasdt0(v1, v2) = v9 & sdtasdt0(v0, v5) = v6 & sdtasdt0(v0, v2)
% 104.06/14.31 = v8 & sdtasdt0(v0, v1) = v7 & sdtpldt0(v8, v9) = v4 & sdtpldt0(v7, v8) =
% 104.06/14.31 v6 & sdtpldt0(v1, v2) = v5 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 104.06/14.31 $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 104.06/14.31 $i] : ( ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) |
% 104.06/14.31 ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v2) | ~ aInteger0(v1) | ~
% 104.06/14.31 aInteger0(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ?
% 104.06/14.31 [v9: $i] : (sdtasdt0(v7, v2) = v8 & sdtasdt0(v1, v2) = v9 & sdtasdt0(v0, v2)
% 104.06/14.31 = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v6, v9) = v8 & sdtpldt0(v5, v6) =
% 104.06/14.31 v4 & sdtpldt0(v0, v1) = v7 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 104.06/14.31 $i(v4)))
% 104.06/14.31
% 104.06/14.31 (mEquModRef)
% 104.06/14.31 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ $i(v1) | ~ $i(v0) | ~
% 104.06/14.31 aInteger0(v1) | ~ aInteger0(v0) | sdteqdtlpzmzozddtrp0(v0, v0, v1))
% 104.06/14.31
% 104.06/14.31 (mIntNeg)
% 104.06/14.31 ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ~
% 104.06/14.31 aInteger0(v0) | aInteger0(v1))
% 104.06/14.31
% 104.06/14.31 (mIntOne)
% 104.06/14.31 $i(sz10) & aInteger0(sz10)
% 104.06/14.31
% 104.06/14.31 (mIntZero)
% 104.06/14.31 $i(sz00) & aInteger0(sz00)
% 104.06/14.31
% 104.06/14.31 (mMulAsso)
% 104.06/14.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 104.06/14.31 (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 104.06/14.31 | ~ $i(v0) | ~ aInteger0(v2) | ~ aInteger0(v1) | ~ aInteger0(v0) | ?
% 104.06/14.31 [v5: $i] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4 & $i(v5) &
% 104.06/14.31 $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 104.06/14.31 $i] : ( ~ (sdtasdt0(v1, v2) = v3) | ~ (sdtasdt0(v0, v3) = v4) | ~ $i(v2) |
% 104.06/14.31 ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v2) | ~ aInteger0(v1) | ~
% 104.06/14.31 aInteger0(v0) | ? [v5: $i] : (sdtasdt0(v5, v2) = v4 & sdtasdt0(v0, v1) = v5
% 104.06/14.31 & $i(v5) & $i(v4)))
% 104.06/14.31
% 104.06/14.31 (mMulMinOne)
% 104.06/14.32 $i(sz10) & ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 104.06/14.32 $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ~ aInteger0(v1) |
% 104.06/14.32 (sdtasdt0(v0, v1) = v2 & smndt0(v1) = v2 & $i(v2))) & ! [v1: $i] : !
% 104.06/14.32 [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ aInteger0(v1) |
% 104.06/14.32 (sdtasdt0(v1, v0) = v2 & smndt0(v1) = v2 & $i(v2))) & ! [v1: $i] : !
% 104.06/14.32 [v2: $i] : ( ~ (smndt0(v1) = v2) | ~ $i(v1) | ~ aInteger0(v1) |
% 104.06/14.32 (sdtasdt0(v1, v0) = v2 & sdtasdt0(v0, v1) = v2 & $i(v2))))
% 104.06/14.32
% 104.06/14.32 (mMulZero)
% 104.06/14.32 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) =
% 104.06/14.32 v1) | ~ $i(v0) | ~ aInteger0(v0)) & ! [v0: $i] : ! [v1: $i] : (v1 =
% 104.06/14.32 sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ $i(v0) | ~ aInteger0(v0)) & !
% 104.06/14.32 [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ $i(v0) | ~
% 104.06/14.32 aInteger0(v0) | sdtasdt0(sz00, v0) = sz00) & ! [v0: $i] : ! [v1: $i] : ( ~
% 104.06/14.32 (sdtasdt0(sz00, v0) = v1) | ~ $i(v0) | ~ aInteger0(v0) | sdtasdt0(v0,
% 104.06/14.32 sz00) = sz00)
% 104.06/14.32
% 104.06/14.32 (mPrimeDivisor)
% 104.06/14.32 $i(sz10) & ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : (v1 = v0
% 104.06/14.32 | v1 = sz10 | ~ $i(v1) | ~ aInteger0(v1) | ? [v2: $i] : ($i(v2) &
% 104.06/14.32 isPrime0(v2) & aDivisorOf0(v2, v1))) & ! [v1: $i] : ( ~ $i(v1) | ~
% 104.06/14.32 isPrime0(v1) | ~ aDivisorOf0(v1, v0) | ~ aInteger0(v0)) & ! [v1: $i] :
% 104.06/14.32 ( ~ $i(v1) | ~ isPrime0(v1) | ~ aDivisorOf0(v1, sz10) | ~
% 104.06/14.32 aInteger0(sz10)))
% 104.06/14.32
% 104.06/14.32 (m__)
% 104.06/14.32 $i(xp) & $i(sz10) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ((v2 = sz10 &
% 104.06/14.32 sdtpldt0(sz10, v1) = sz10 & smndt0(xp) = v1 & $i(v1)) | (v0 = sz10 &
% 104.06/14.32 sdtpldt0(sz10, xp) = sz10))
% 104.06/14.32
% 104.06/14.32 (m__2046)
% 104.06/14.32 xS = cS2043 & $i(cS2043)
% 104.06/14.32
% 104.06/14.32 (m__2079)
% 104.06/14.32 $i(cS2076) & $i(xS) & ? [v0: $i] : (stldt0(v0) = cS2076 & sbsmnsldt0(xS) = v0
% 104.06/14.32 & $i(v0))
% 104.06/14.32
% 104.06/14.32 (m__2144)
% 104.06/14.32 $i(xS) & ? [v0: $i] : ? [v1: $i] : (stldt0(v0) = v1 & sbsmnsldt0(xS) = v0 &
% 104.06/14.32 $i(v1) & $i(v0) & isClosed0(v0) & isOpen0(v1))
% 104.06/14.32
% 104.06/14.32 (m__2171)
% 104.06/14.32 $i(xp) & $i(xS) & $i(sz10) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 104.06/14.32 $i] : ( ~ (xp = sz00) & szAzrzSzezqlpdtcmdtrp0(sz10, xp) = v0 & stldt0(v1) =
% 104.06/14.32 v2 & sbsmnsldt0(xS) = v1 & $i(v2) & $i(v1) & $i(v0) & aSubsetOf0(v0, v2) &
% 104.06/14.32 aInteger0(xp))
% 104.06/14.32
% 104.06/14.32 (m__2232)
% 104.06/14.33 $i(xp) & $i(sz10) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 104.06/14.33 (szAzrzSzezqlpdtcmdtrp0(sz10, xp) = v1 & sdtpldt0(sz10, v2) = v3 &
% 104.06/14.33 sdtpldt0(sz10, xp) = v0 & smndt0(xp) = v2 & $i(v3) & $i(v2) & $i(v1) &
% 104.06/14.33 $i(v0) & aElementOf0(v3, v1) & aElementOf0(v0, v1))
% 104.06/14.33
% 104.06/14.33 (function-axioms)
% 104.06/14.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 104.06/14.33 (szAzrzSzezqlpdtcmdtrp0(v3, v2) = v1) | ~ (szAzrzSzezqlpdtcmdtrp0(v3, v2) =
% 104.06/14.33 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 104.06/14.33 ~ (sdtslmnbsdt0(v3, v2) = v1) | ~ (sdtslmnbsdt0(v3, v2) = v0)) & ! [v0:
% 104.06/14.33 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 104.06/14.33 (sdtbsmnsldt0(v3, v2) = v1) | ~ (sdtbsmnsldt0(v3, v2) = v0)) & ! [v0: $i]
% 104.06/14.33 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) =
% 104.06/14.33 v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 104.06/14.33 $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3,
% 104.06/14.33 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 104.06/14.33 (stldt0(v2) = v1) | ~ (stldt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 104.06/14.33 [v2: $i] : (v1 = v0 | ~ (sbsmnsldt0(v2) = v1) | ~ (sbsmnsldt0(v2) = v0)) &
% 104.06/14.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~
% 104.06/14.33 (smndt0(v2) = v0))
% 104.06/14.33
% 104.06/14.33 Further assumptions not needed in the proof:
% 104.06/14.33 --------------------------------------------
% 104.06/14.33 mArSeq, mClosed, mComplement, mDivisor, mElements, mEquMod, mEquModMul,
% 104.06/14.33 mEquModSym, mEquModTrn, mFinSet, mIntMult, mIntPlus, mIntegers, mInterOpen,
% 104.06/14.33 mIntersection, mMulComm, mMulOne, mOpen, mPrime, mSets, mSubset, mUnion,
% 104.06/14.33 mUnionClosed, mUnionOpen, mUnionSClosed, mUnionSet, mZeroDiv, m__2117
% 104.06/14.33
% 104.06/14.33 Those formulas are unsatisfiable:
% 104.06/14.33 ---------------------------------
% 104.06/14.33
% 104.06/14.33 Begin of proof
% 104.06/14.33 |
% 104.06/14.33 | ALPHA: (mIntZero) implies:
% 104.06/14.33 | (1) aInteger0(sz00)
% 104.06/14.33 |
% 104.06/14.33 | ALPHA: (mIntOne) implies:
% 104.06/14.33 | (2) aInteger0(sz10)
% 104.06/14.33 |
% 104.06/14.33 | ALPHA: (mAddAsso) implies:
% 104.06/14.33 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 104.06/14.33 | ~ (sdtpldt0(v1, v2) = v3) | ~ (sdtpldt0(v0, v3) = v4) | ~ $i(v2) |
% 104.06/14.33 | ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v2) | ~ aInteger0(v1) | ~
% 104.06/14.33 | aInteger0(v0) | ? [v5: $i] : (sdtpldt0(v5, v2) = v4 & sdtpldt0(v0,
% 104.06/14.33 | v1) = v5 & $i(v5) & $i(v4)))
% 104.06/14.33 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 104.06/14.33 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) |
% 104.06/14.33 | ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v2) | ~ aInteger0(v1) | ~
% 104.06/14.33 | aInteger0(v0) | ? [v5: $i] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0,
% 104.06/14.33 | v5) = v4 & $i(v5) & $i(v4)))
% 104.06/14.33 |
% 104.06/14.33 | ALPHA: (mAddComm) implies:
% 104.06/14.34 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) |
% 104.06/14.34 | ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) |
% 104.06/14.34 | (sdtpldt0(v1, v0) = v2 & $i(v2)))
% 104.06/14.34 |
% 104.06/14.34 | ALPHA: (mAddZero) implies:
% 104.06/14.34 | (6) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) |
% 104.06/14.34 | ~ $i(v0) | ~ aInteger0(v0))
% 104.06/14.34 | (7) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) |
% 104.06/14.34 | ~ $i(v0) | ~ aInteger0(v0))
% 104.06/14.34 |
% 104.06/14.34 | ALPHA: (mAddNeg) implies:
% 104.06/14.34 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ~
% 104.06/14.34 | aInteger0(v0) | (sdtpldt0(v1, v0) = sz00 & sdtpldt0(v0, v1) = sz00))
% 104.06/14.34 |
% 104.06/14.34 | ALPHA: (mMulAsso) implies:
% 104.06/14.34 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 104.06/14.34 | ~ (sdtasdt0(v1, v2) = v3) | ~ (sdtasdt0(v0, v3) = v4) | ~ $i(v2) |
% 104.06/14.34 | ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v2) | ~ aInteger0(v1) | ~
% 104.06/14.34 | aInteger0(v0) | ? [v5: $i] : (sdtasdt0(v5, v2) = v4 & sdtasdt0(v0,
% 104.06/14.34 | v1) = v5 & $i(v5) & $i(v4)))
% 104.06/14.34 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 104.06/14.34 | ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) |
% 104.06/14.34 | ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v2) | ~ aInteger0(v1) | ~
% 104.06/14.34 | aInteger0(v0) | ? [v5: $i] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0,
% 104.06/14.34 | v5) = v4 & $i(v5) & $i(v4)))
% 104.06/14.34 |
% 104.06/14.34 | ALPHA: (mDistrib) implies:
% 104.06/14.34 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 104.06/14.34 | ( ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) |
% 104.06/14.34 | ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v2) | ~ aInteger0(v1) | ~
% 104.06/14.34 | aInteger0(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 104.06/14.34 | $i] : ? [v9: $i] : (sdtasdt0(v7, v2) = v8 & sdtasdt0(v1, v2) = v9
% 104.06/14.34 | & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v6, v9)
% 104.06/14.34 | = v8 & sdtpldt0(v5, v6) = v4 & sdtpldt0(v0, v1) = v7 & $i(v9) &
% 104.06/14.34 | $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4)))
% 104.50/14.34 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 104.50/14.34 | ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) |
% 104.50/14.34 | ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v2) | ~ aInteger0(v1) | ~
% 104.50/14.34 | aInteger0(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 104.50/14.34 | $i] : ? [v9: $i] : (sdtasdt0(v1, v2) = v9 & sdtasdt0(v0, v5) = v6
% 104.50/14.34 | & sdtasdt0(v0, v2) = v8 & sdtasdt0(v0, v1) = v7 & sdtpldt0(v8, v9)
% 104.50/14.34 | = v4 & sdtpldt0(v7, v8) = v6 & sdtpldt0(v1, v2) = v5 & $i(v9) &
% 104.50/14.34 | $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4)))
% 104.50/14.34 |
% 104.50/14.34 | ALPHA: (mMulZero) implies:
% 104.50/14.34 | (13) ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1)
% 104.50/14.34 | | ~ $i(v0) | ~ aInteger0(v0))
% 104.50/14.34 |
% 104.50/14.34 | ALPHA: (mMulMinOne) implies:
% 104.50/14.35 | (14) ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i]
% 104.50/14.35 | : ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ~ aInteger0(v1) |
% 104.50/14.35 | (sdtasdt0(v0, v1) = v2 & smndt0(v1) = v2 & $i(v2))) & ! [v1: $i]
% 104.50/14.35 | : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~
% 104.50/14.35 | aInteger0(v1) | (sdtasdt0(v1, v0) = v2 & smndt0(v1) = v2 &
% 104.50/14.35 | $i(v2))) & ! [v1: $i] : ! [v2: $i] : ( ~ (smndt0(v1) = v2) |
% 104.50/14.35 | ~ $i(v1) | ~ aInteger0(v1) | (sdtasdt0(v1, v0) = v2 &
% 104.50/14.35 | sdtasdt0(v0, v1) = v2 & $i(v2))))
% 104.50/14.35 |
% 104.50/14.35 | ALPHA: (mEquModRef) implies:
% 104.50/14.35 | (15) ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ $i(v1) | ~ $i(v0) | ~
% 104.50/14.35 | aInteger0(v1) | ~ aInteger0(v0) | sdteqdtlpzmzozddtrp0(v0, v0, v1))
% 104.50/14.35 |
% 104.50/14.35 | ALPHA: (mPrimeDivisor) implies:
% 104.50/14.35 | (16) ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : (v1 = v0 |
% 104.50/14.35 | v1 = sz10 | ~ $i(v1) | ~ aInteger0(v1) | ? [v2: $i] : ($i(v2) &
% 104.50/14.35 | isPrime0(v2) & aDivisorOf0(v2, v1))) & ! [v1: $i] : ( ~ $i(v1)
% 104.50/14.35 | | ~ isPrime0(v1) | ~ aDivisorOf0(v1, v0) | ~ aInteger0(v0)) &
% 104.50/14.35 | ! [v1: $i] : ( ~ $i(v1) | ~ isPrime0(v1) | ~ aDivisorOf0(v1, sz10)
% 104.50/14.35 | | ~ aInteger0(sz10)))
% 104.50/14.35 |
% 104.50/14.35 | ALPHA: (mArSeqClosed) implies:
% 104.50/14.35 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = sz00 | ~
% 104.50/14.35 | (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 104.50/14.35 | aInteger0(v1) | ~ aInteger0(v0) | isClosed0(v2))
% 104.50/14.35 |
% 104.50/14.35 | ALPHA: (m__2046) implies:
% 104.50/14.35 | (18) xS = cS2043
% 104.50/14.35 |
% 104.50/14.35 | ALPHA: (m__2079) implies:
% 104.50/14.35 | (19) ? [v0: $i] : (stldt0(v0) = cS2076 & sbsmnsldt0(xS) = v0 & $i(v0))
% 104.50/14.35 |
% 104.50/14.35 | ALPHA: (m__2144) implies:
% 104.50/14.35 | (20) ? [v0: $i] : ? [v1: $i] : (stldt0(v0) = v1 & sbsmnsldt0(xS) = v0 &
% 104.50/14.35 | $i(v1) & $i(v0) & isClosed0(v0) & isOpen0(v1))
% 104.50/14.35 |
% 104.50/14.35 | ALPHA: (m__2171) implies:
% 104.50/14.35 | (21) $i(sz00)
% 104.50/14.35 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (xp = sz00) &
% 104.50/14.35 | szAzrzSzezqlpdtcmdtrp0(sz10, xp) = v0 & stldt0(v1) = v2 &
% 104.50/14.35 | sbsmnsldt0(xS) = v1 & $i(v2) & $i(v1) & $i(v0) & aSubsetOf0(v0, v2)
% 104.50/14.35 | & aInteger0(xp))
% 104.50/14.35 |
% 104.50/14.35 | ALPHA: (m__2232) implies:
% 104.50/14.35 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 104.50/14.35 | (szAzrzSzezqlpdtcmdtrp0(sz10, xp) = v1 & sdtpldt0(sz10, v2) = v3 &
% 104.50/14.35 | sdtpldt0(sz10, xp) = v0 & smndt0(xp) = v2 & $i(v3) & $i(v2) & $i(v1)
% 104.50/14.35 | & $i(v0) & aElementOf0(v3, v1) & aElementOf0(v0, v1))
% 104.50/14.35 |
% 104.50/14.35 | ALPHA: (m__) implies:
% 104.50/14.35 | (24) $i(sz10)
% 104.50/14.35 | (25) $i(xp)
% 104.50/14.35 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ((v2 = sz10 & sdtpldt0(sz10,
% 104.50/14.35 | v1) = sz10 & smndt0(xp) = v1 & $i(v1)) | (v0 = sz10 &
% 104.50/14.35 | sdtpldt0(sz10, xp) = sz10))
% 104.50/14.35 |
% 104.50/14.35 | ALPHA: (function-axioms) implies:
% 104.50/14.35 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) =
% 104.50/14.35 | v1) | ~ (smndt0(v2) = v0))
% 104.50/14.35 | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 104.50/14.35 | (sbsmnsldt0(v2) = v1) | ~ (sbsmnsldt0(v2) = v0))
% 104.50/14.35 | (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (stldt0(v2) =
% 104.50/14.36 | v1) | ~ (stldt0(v2) = v0))
% 104.50/14.36 | (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 104.50/14.36 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 104.50/14.36 | (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 104.50/14.36 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 104.50/14.36 | (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 104.50/14.36 | (szAzrzSzezqlpdtcmdtrp0(v3, v2) = v1) | ~
% 104.50/14.36 | (szAzrzSzezqlpdtcmdtrp0(v3, v2) = v0))
% 104.50/14.36 |
% 104.50/14.36 | DELTA: instantiating (19) with fresh symbol all_36_0 gives:
% 104.50/14.36 | (33) stldt0(all_36_0) = cS2076 & sbsmnsldt0(xS) = all_36_0 & $i(all_36_0)
% 104.50/14.36 |
% 104.50/14.36 | ALPHA: (33) implies:
% 104.50/14.36 | (34) sbsmnsldt0(xS) = all_36_0
% 104.50/14.36 | (35) stldt0(all_36_0) = cS2076
% 104.50/14.36 |
% 104.50/14.36 | DELTA: instantiating (20) with fresh symbols all_38_0, all_38_1 gives:
% 104.50/14.36 | (36) stldt0(all_38_1) = all_38_0 & sbsmnsldt0(xS) = all_38_1 & $i(all_38_0)
% 104.50/14.36 | & $i(all_38_1) & isClosed0(all_38_1) & isOpen0(all_38_0)
% 104.50/14.36 |
% 104.50/14.36 | ALPHA: (36) implies:
% 104.50/14.36 | (37) sbsmnsldt0(xS) = all_38_1
% 104.50/14.36 | (38) stldt0(all_38_1) = all_38_0
% 104.50/14.36 |
% 104.50/14.36 | DELTA: instantiating (26) with fresh symbols all_40_0, all_40_1, all_40_2
% 104.50/14.36 | gives:
% 104.50/14.36 | (39) (all_40_0 = sz10 & sdtpldt0(sz10, all_40_1) = sz10 & smndt0(xp) =
% 104.50/14.36 | all_40_1 & $i(all_40_1)) | (all_40_2 = sz10 & sdtpldt0(sz10, xp) =
% 104.50/14.36 | sz10)
% 104.50/14.36 |
% 104.50/14.36 | DELTA: instantiating (22) with fresh symbols all_41_0, all_41_1, all_41_2
% 104.50/14.36 | gives:
% 104.50/14.36 | (40) ~ (xp = sz00) & szAzrzSzezqlpdtcmdtrp0(sz10, xp) = all_41_2 &
% 104.50/14.36 | stldt0(all_41_1) = all_41_0 & sbsmnsldt0(xS) = all_41_1 & $i(all_41_0)
% 104.50/14.36 | & $i(all_41_1) & $i(all_41_2) & aSubsetOf0(all_41_2, all_41_0) &
% 104.50/14.36 | aInteger0(xp)
% 104.50/14.36 |
% 104.50/14.36 | ALPHA: (40) implies:
% 104.50/14.36 | (41) ~ (xp = sz00)
% 104.50/14.36 | (42) aInteger0(xp)
% 104.50/14.36 | (43) sbsmnsldt0(xS) = all_41_1
% 104.50/14.36 | (44) szAzrzSzezqlpdtcmdtrp0(sz10, xp) = all_41_2
% 104.50/14.36 |
% 104.50/14.36 | DELTA: instantiating (23) with fresh symbols all_43_0, all_43_1, all_43_2,
% 104.50/14.36 | all_43_3 gives:
% 104.50/14.36 | (45) szAzrzSzezqlpdtcmdtrp0(sz10, xp) = all_43_2 & sdtpldt0(sz10, all_43_1)
% 104.50/14.36 | = all_43_0 & sdtpldt0(sz10, xp) = all_43_3 & smndt0(xp) = all_43_1 &
% 104.50/14.36 | $i(all_43_0) & $i(all_43_1) & $i(all_43_2) & $i(all_43_3) &
% 104.50/14.36 | aElementOf0(all_43_0, all_43_2) & aElementOf0(all_43_3, all_43_2)
% 104.50/14.36 |
% 104.50/14.36 | ALPHA: (45) implies:
% 104.50/14.36 | (46) smndt0(xp) = all_43_1
% 104.50/14.36 | (47) sdtpldt0(sz10, xp) = all_43_3
% 104.50/14.36 | (48) szAzrzSzezqlpdtcmdtrp0(sz10, xp) = all_43_2
% 104.50/14.36 |
% 104.50/14.36 | DELTA: instantiating (16) with fresh symbol all_45_0 gives:
% 104.50/14.36 | (49) smndt0(sz10) = all_45_0 & $i(all_45_0) & ! [v0: any] : (v0 = all_45_0
% 104.50/14.36 | | v0 = sz10 | ~ $i(v0) | ~ aInteger0(v0) | ? [v1: $i] : ($i(v1) &
% 104.50/14.36 | isPrime0(v1) & aDivisorOf0(v1, v0))) & ! [v0: $i] : ( ~ $i(v0) |
% 104.50/14.36 | ~ isPrime0(v0) | ~ aDivisorOf0(v0, all_45_0) | ~
% 104.50/14.36 | aInteger0(all_45_0)) & ! [v0: $i] : ( ~ $i(v0) | ~ isPrime0(v0) |
% 104.50/14.36 | ~ aDivisorOf0(v0, sz10) | ~ aInteger0(sz10))
% 104.50/14.36 |
% 104.50/14.36 | ALPHA: (49) implies:
% 104.50/14.36 | (50) smndt0(sz10) = all_45_0
% 104.50/14.36 |
% 104.50/14.36 | DELTA: instantiating (14) with fresh symbol all_48_0 gives:
% 104.50/14.37 | (51) smndt0(sz10) = all_48_0 & $i(all_48_0) & ! [v0: $i] : ! [v1: $i] : (
% 104.50/14.37 | ~ (sdtasdt0(v0, all_48_0) = v1) | ~ $i(v0) | ~ aInteger0(v0) |
% 104.50/14.37 | (sdtasdt0(all_48_0, v0) = v1 & smndt0(v0) = v1 & $i(v1))) & ! [v0:
% 104.50/14.37 | $i] : ! [v1: $i] : ( ~ (sdtasdt0(all_48_0, v0) = v1) | ~ $i(v0) |
% 104.50/14.37 | ~ aInteger0(v0) | (sdtasdt0(v0, all_48_0) = v1 & smndt0(v0) = v1 &
% 104.50/14.37 | $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~
% 104.50/14.37 | $i(v0) | ~ aInteger0(v0) | (sdtasdt0(v0, all_48_0) = v1 &
% 104.50/14.37 | sdtasdt0(all_48_0, v0) = v1 & $i(v1)))
% 104.50/14.37 |
% 104.50/14.37 | ALPHA: (51) implies:
% 104.50/14.37 | (52) smndt0(sz10) = all_48_0
% 104.50/14.37 | (53) ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ~
% 104.50/14.37 | aInteger0(v0) | (sdtasdt0(v0, all_48_0) = v1 & sdtasdt0(all_48_0,
% 104.50/14.37 | v0) = v1 & $i(v1)))
% 104.50/14.37 |
% 104.50/14.37 | REDUCE: (18), (43) imply:
% 104.50/14.37 | (54) sbsmnsldt0(cS2043) = all_41_1
% 104.50/14.37 |
% 104.50/14.37 | REDUCE: (18), (37) imply:
% 104.50/14.37 | (55) sbsmnsldt0(cS2043) = all_38_1
% 104.50/14.37 |
% 104.50/14.37 | REDUCE: (18), (34) imply:
% 104.50/14.37 | (56) sbsmnsldt0(cS2043) = all_36_0
% 104.50/14.37 |
% 104.50/14.37 | GROUND_INST: instantiating (27) with all_45_0, all_48_0, sz10, simplifying
% 104.50/14.37 | with (50), (52) gives:
% 104.50/14.37 | (57) all_48_0 = all_45_0
% 104.50/14.37 |
% 104.50/14.37 | GROUND_INST: instantiating (28) with all_38_1, all_41_1, cS2043, simplifying
% 104.50/14.37 | with (54), (55) gives:
% 104.50/14.37 | (58) all_41_1 = all_38_1
% 104.50/14.37 |
% 104.50/14.37 | GROUND_INST: instantiating (28) with all_36_0, all_41_1, cS2043, simplifying
% 104.50/14.37 | with (54), (56) gives:
% 104.50/14.37 | (59) all_41_1 = all_36_0
% 104.50/14.37 |
% 104.50/14.37 | GROUND_INST: instantiating (29) with cS2076, all_38_0, all_36_0, simplifying
% 104.50/14.37 | with (35) gives:
% 104.50/14.37 | (60) all_38_0 = cS2076 | ~ (stldt0(all_36_0) = all_38_0)
% 104.50/14.37 |
% 104.50/14.37 | GROUND_INST: instantiating (32) with all_41_2, all_43_2, xp, sz10, simplifying
% 104.50/14.37 | with (44), (48) gives:
% 104.50/14.37 | (61) all_43_2 = all_41_2
% 104.50/14.37 |
% 104.50/14.37 | COMBINE_EQS: (58), (59) imply:
% 104.50/14.37 | (62) all_38_1 = all_36_0
% 104.50/14.37 |
% 104.50/14.37 | SIMP: (62) implies:
% 104.50/14.37 | (63) all_38_1 = all_36_0
% 104.50/14.37 |
% 104.50/14.37 | REDUCE: (38), (63) imply:
% 104.50/14.37 | (64) stldt0(all_36_0) = all_38_0
% 104.50/14.37 |
% 104.50/14.37 | BETA: splitting (60) gives:
% 104.50/14.37 |
% 104.50/14.37 | Case 1:
% 104.50/14.37 | |
% 104.50/14.37 | | (65) ~ (stldt0(all_36_0) = all_38_0)
% 104.50/14.37 | |
% 104.50/14.37 | | PRED_UNIFY: (64), (65) imply:
% 104.50/14.37 | | (66) $false
% 104.50/14.37 | |
% 104.50/14.37 | | CLOSE: (66) is inconsistent.
% 104.50/14.37 | |
% 104.50/14.37 | Case 2:
% 104.50/14.37 | |
% 104.50/14.37 | |
% 104.50/14.37 | | GROUND_INST: instantiating (mIntNeg) with sz10, all_45_0, simplifying with
% 104.50/14.37 | | (2), (24), (50) gives:
% 104.50/14.37 | | (67) aInteger0(all_45_0)
% 104.50/14.37 | |
% 104.50/14.37 | | GROUND_INST: instantiating (53) with sz10, all_45_0, simplifying with (2),
% 104.50/14.37 | | (24), (50) gives:
% 104.50/14.38 | | (68) sdtasdt0(all_48_0, sz10) = all_45_0 & sdtasdt0(sz10, all_48_0) =
% 104.50/14.38 | | all_45_0 & $i(all_45_0)
% 104.50/14.38 | |
% 104.50/14.38 | | ALPHA: (68) implies:
% 104.50/14.38 | | (69) $i(all_45_0)
% 104.50/14.38 | | (70) sdtasdt0(sz10, all_48_0) = all_45_0
% 104.50/14.38 | | (71) sdtasdt0(all_48_0, sz10) = all_45_0
% 104.50/14.38 | |
% 104.50/14.38 | | GROUND_INST: instantiating (8) with sz10, all_45_0, simplifying with (2),
% 104.50/14.38 | | (24), (50) gives:
% 104.50/14.38 | | (72) sdtpldt0(all_45_0, sz10) = sz00 & sdtpldt0(sz10, all_45_0) = sz00
% 104.50/14.38 | |
% 104.50/14.38 | | ALPHA: (72) implies:
% 104.50/14.38 | | (73) sdtpldt0(sz10, all_45_0) = sz00
% 104.50/14.38 | | (74) sdtpldt0(all_45_0, sz10) = sz00
% 104.50/14.38 | |
% 104.50/14.38 | | GROUND_INST: instantiating (mIntNeg) with xp, all_43_1, simplifying with
% 104.50/14.38 | | (25), (42), (46) gives:
% 104.50/14.38 | | (75) aInteger0(all_43_1)
% 104.50/14.38 | |
% 104.50/14.38 | | GROUND_INST: instantiating (53) with xp, all_43_1, simplifying with (25),
% 104.50/14.38 | | (42), (46) gives:
% 104.50/14.38 | | (76) sdtasdt0(all_48_0, xp) = all_43_1 & sdtasdt0(xp, all_48_0) =
% 104.50/14.38 | | all_43_1 & $i(all_43_1)
% 104.50/14.38 | |
% 104.50/14.38 | | ALPHA: (76) implies:
% 104.50/14.38 | | (77) sdtasdt0(xp, all_48_0) = all_43_1
% 104.50/14.38 | | (78) sdtasdt0(all_48_0, xp) = all_43_1
% 104.50/14.38 | |
% 104.50/14.38 | | GROUND_INST: instantiating (8) with xp, all_43_1, simplifying with (25),
% 104.50/14.38 | | (42), (46) gives:
% 104.50/14.38 | | (79) sdtpldt0(all_43_1, xp) = sz00 & sdtpldt0(xp, all_43_1) = sz00
% 104.50/14.38 | |
% 104.50/14.38 | | ALPHA: (79) implies:
% 104.50/14.38 | | (80) sdtpldt0(all_43_1, xp) = sz00
% 104.50/14.38 | |
% 104.50/14.38 | | GROUND_INST: instantiating (5) with sz10, xp, all_43_3, simplifying with
% 104.50/14.38 | | (2), (24), (25), (42), (47) gives:
% 104.50/14.38 | | (81) sdtpldt0(xp, sz10) = all_43_3 & $i(all_43_3)
% 104.50/14.38 | |
% 104.50/14.38 | | ALPHA: (81) implies:
% 104.50/14.38 | | (82) sdtpldt0(xp, sz10) = all_43_3
% 104.50/14.38 | |
% 104.50/14.38 | | GROUND_INST: instantiating (17) with sz10, xp, all_41_2, simplifying with
% 104.50/14.38 | | (2), (24), (25), (42), (44) gives:
% 104.50/14.38 | | (83) xp = sz00 | isClosed0(all_41_2)
% 104.50/14.38 | |
% 104.50/14.38 | | REDUCE: (57), (78) imply:
% 104.50/14.38 | | (84) sdtasdt0(all_45_0, xp) = all_43_1
% 104.50/14.38 | |
% 104.50/14.38 | | REDUCE: (57), (71) imply:
% 104.50/14.38 | | (85) sdtasdt0(all_45_0, sz10) = all_45_0
% 104.50/14.38 | |
% 104.50/14.38 | | REDUCE: (57), (77) imply:
% 104.50/14.38 | | (86) sdtasdt0(xp, all_45_0) = all_43_1
% 104.50/14.38 | |
% 104.50/14.38 | | REDUCE: (57), (70) imply:
% 104.50/14.38 | | (87) sdtasdt0(sz10, all_45_0) = all_45_0
% 104.50/14.38 | |
% 104.50/14.38 | | BETA: splitting (83) gives:
% 104.50/14.38 | |
% 104.50/14.38 | | Case 1:
% 104.50/14.38 | | |
% 104.50/14.38 | | |
% 104.50/14.38 | | | GROUND_INST: instantiating (15) with xp, all_45_0, simplifying with (25),
% 104.50/14.38 | | | (42), (67), (69) gives:
% 104.50/14.38 | | | (88) all_45_0 = sz00 | sdteqdtlpzmzozddtrp0(xp, xp, all_45_0)
% 104.50/14.38 | | |
% 104.50/14.38 | | | ALPHA: (76) implies:
% 104.50/14.38 | | | (89) $i(all_43_1)
% 104.50/14.38 | | |
% 104.50/14.38 | | | GROUND_INST: instantiating (4) with xp, sz10, all_45_0, sz10, sz00,
% 104.50/14.38 | | | simplifying with (2), (24), (25), (42), (67), (69), (73)
% 104.50/14.38 | | | gives:
% 104.50/14.39 | | | (90) ~ (sdtpldt0(xp, sz10) = sz10) | ? [v0: $i] : (sdtpldt0(xp, v0) =
% 104.50/14.39 | | | sz00 & sdtpldt0(sz10, all_45_0) = v0 & $i(v0) & $i(sz00))
% 104.50/14.39 | | |
% 104.50/14.39 | | | GROUND_INST: instantiating (7) with xp, sz00, simplifying with (25), (42)
% 104.50/14.39 | | | gives:
% 104.50/14.39 | | | (91) xp = sz00 | ~ (sdtpldt0(xp, sz00) = sz00)
% 104.50/14.39 | | |
% 104.50/14.39 | | | GROUND_INST: instantiating (5) with sz00, xp, sz00, simplifying with (1),
% 104.50/14.39 | | | (21), (25), (42) gives:
% 104.50/14.39 | | | (92) ~ (sdtpldt0(sz00, xp) = sz00) | sdtpldt0(xp, sz00) = sz00
% 104.50/14.39 | | |
% 104.50/14.39 | | | GROUND_INST: instantiating (3) with all_45_0, sz10, all_43_1, sz10, sz00,
% 104.50/14.39 | | | simplifying with (2), (24), (67), (69), (74), (75), (89)
% 104.50/14.39 | | | gives:
% 104.50/14.39 | | | (93) ~ (sdtpldt0(sz10, all_43_1) = sz10) | ? [v0: $i] : (sdtpldt0(v0,
% 104.50/14.39 | | | all_43_1) = sz00 & sdtpldt0(all_45_0, sz10) = v0 & $i(v0) &
% 104.50/14.39 | | | $i(sz00))
% 104.50/14.39 | | |
% 104.50/14.39 | | | GROUND_INST: instantiating (3) with all_45_0, sz10, xp, sz10, sz00,
% 104.50/14.39 | | | simplifying with (2), (24), (25), (42), (67), (69), (74)
% 104.50/14.39 | | | gives:
% 104.50/14.39 | | | (94) ~ (sdtpldt0(sz10, xp) = sz10) | ? [v0: $i] : (sdtpldt0(v0, xp) =
% 104.50/14.39 | | | sz00 & sdtpldt0(all_45_0, sz10) = v0 & $i(v0) & $i(sz00))
% 104.50/14.39 | | |
% 104.50/14.39 | | | GROUND_INST: instantiating (12) with xp, sz10, all_45_0, sz10, all_45_0,
% 104.50/14.39 | | | simplifying with (2), (24), (25), (42), (67), (69), (87)
% 104.50/14.39 | | | gives:
% 104.75/14.39 | | | (95) ~ (sdtpldt0(xp, sz10) = sz10) | ? [v0: $i] : ? [v1: $i] : ?
% 104.75/14.39 | | | [v2: $i] : ? [v3: $i] : ? [v4: $i] : (sdtasdt0(xp, v0) = v1 &
% 104.75/14.39 | | | sdtasdt0(xp, all_45_0) = v3 & sdtasdt0(xp, sz10) = v2 &
% 104.75/14.39 | | | sdtasdt0(sz10, all_45_0) = v4 & sdtpldt0(v3, v4) = all_45_0 &
% 104.75/14.39 | | | sdtpldt0(v2, v3) = v1 & sdtpldt0(sz10, all_45_0) = v0 & $i(v4) &
% 104.75/14.39 | | | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 104.75/14.39 | | |
% 104.75/14.39 | | | GROUND_INST: instantiating (10) with all_43_1, sz10, sz10, all_43_1,
% 104.75/14.39 | | | all_43_1, simplifying with (2), (24), (75), (89) gives:
% 104.75/14.39 | | | (96) ~ (sdtasdt0(all_43_1, sz10) = all_43_1) | ? [v0: $i] :
% 104.75/14.39 | | | (sdtasdt0(all_43_1, v0) = all_43_1 & sdtasdt0(sz10, sz10) = v0 &
% 104.75/14.39 | | | $i(v0))
% 104.75/14.39 | | |
% 104.75/14.39 | | | GROUND_INST: instantiating (9) with xp, all_45_0, sz10, all_45_0,
% 104.75/14.39 | | | all_43_1, simplifying with (2), (24), (25), (42), (67), (69),
% 104.75/14.39 | | | (85), (86) gives:
% 104.75/14.39 | | | (97) ? [v0: $i] : (sdtasdt0(v0, sz10) = all_43_1 & sdtasdt0(xp,
% 104.75/14.39 | | | all_45_0) = v0 & $i(v0) & $i(all_43_1))
% 104.75/14.39 | | |
% 104.75/14.39 | | | GROUND_INST: instantiating (11) with all_45_0, sz10, all_43_1, sz10,
% 104.75/14.39 | | | all_45_0, simplifying with (2), (24), (67), (69), (75), (85),
% 104.75/14.39 | | | (89) gives:
% 104.75/14.40 | | | (98) ~ (sdtpldt0(sz10, all_43_1) = sz10) | ? [v0: $i] : ? [v1: $i] :
% 104.75/14.40 | | | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (sdtasdt0(v2, all_43_1)
% 104.75/14.40 | | | = v3 & sdtasdt0(all_45_0, all_43_1) = v1 & sdtasdt0(all_45_0,
% 104.75/14.40 | | | sz10) = v0 & sdtasdt0(sz10, all_43_1) = v4 & sdtpldt0(v1, v4)
% 104.75/14.40 | | | = v3 & sdtpldt0(v0, v1) = all_45_0 & sdtpldt0(all_45_0, sz10) =
% 104.75/14.40 | | | v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 104.75/14.40 | | |
% 104.75/14.40 | | | GROUND_INST: instantiating (10) with sz10, all_45_0, xp, all_45_0,
% 104.75/14.40 | | | all_43_1, simplifying with (2), (24), (25), (42), (67), (69),
% 104.75/14.40 | | | (84), (87) gives:
% 104.75/14.40 | | | (99) ? [v0: $i] : (sdtasdt0(all_45_0, xp) = v0 & sdtasdt0(sz10, v0) =
% 104.75/14.40 | | | all_43_1 & $i(v0) & $i(all_43_1))
% 104.75/14.40 | | |
% 104.75/14.40 | | | GROUND_INST: instantiating (13) with xp, all_43_1, simplifying with (25),
% 104.75/14.40 | | | (42) gives:
% 104.75/14.40 | | | (100) all_43_1 = sz00 | ~ (sdtasdt0(sz00, xp) = all_43_1)
% 104.75/14.40 | | |
% 104.75/14.40 | | | DELTA: instantiating (99) with fresh symbol all_115_0 gives:
% 104.75/14.40 | | | (101) sdtasdt0(all_45_0, xp) = all_115_0 & sdtasdt0(sz10, all_115_0) =
% 104.75/14.40 | | | all_43_1 & $i(all_115_0) & $i(all_43_1)
% 104.75/14.40 | | |
% 104.75/14.40 | | | ALPHA: (101) implies:
% 104.75/14.40 | | | (102) sdtasdt0(all_45_0, xp) = all_115_0
% 104.75/14.40 | | |
% 104.75/14.40 | | | DELTA: instantiating (97) with fresh symbol all_119_0 gives:
% 104.75/14.40 | | | (103) sdtasdt0(all_119_0, sz10) = all_43_1 & sdtasdt0(xp, all_45_0) =
% 104.75/14.40 | | | all_119_0 & $i(all_119_0) & $i(all_43_1)
% 104.75/14.40 | | |
% 104.75/14.40 | | | ALPHA: (103) implies:
% 104.75/14.40 | | | (104) sdtasdt0(xp, all_45_0) = all_119_0
% 104.75/14.40 | | | (105) sdtasdt0(all_119_0, sz10) = all_43_1
% 104.75/14.40 | | |
% 104.75/14.40 | | | BETA: splitting (91) gives:
% 104.75/14.40 | | |
% 104.75/14.40 | | | Case 1:
% 104.75/14.40 | | | |
% 104.75/14.40 | | | | (106) ~ (sdtpldt0(xp, sz00) = sz00)
% 104.75/14.40 | | | |
% 104.75/14.40 | | | | BETA: splitting (90) gives:
% 104.75/14.40 | | | |
% 104.75/14.40 | | | | Case 1:
% 104.75/14.40 | | | | |
% 104.75/14.40 | | | | | (107) ~ (sdtpldt0(xp, sz10) = sz10)
% 104.75/14.40 | | | | |
% 104.75/14.40 | | | | | BETA: splitting (92) gives:
% 104.75/14.40 | | | | |
% 104.75/14.40 | | | | | Case 1:
% 104.75/14.40 | | | | | |
% 104.75/14.40 | | | | | | (108) ~ (sdtpldt0(sz00, xp) = sz00)
% 104.75/14.40 | | | | | |
% 104.75/14.40 | | | | | | BETA: splitting (94) gives:
% 104.75/14.40 | | | | | |
% 104.75/14.40 | | | | | | Case 1:
% 104.75/14.40 | | | | | | |
% 104.75/14.40 | | | | | | | (109) ~ (sdtpldt0(sz10, xp) = sz10)
% 104.75/14.40 | | | | | | |
% 104.75/14.40 | | | | | | | GROUND_INST: instantiating (31) with all_43_1, all_119_0,
% 104.75/14.40 | | | | | | | all_45_0, xp, simplifying with (86), (104) gives:
% 104.75/14.40 | | | | | | | (110) all_119_0 = all_43_1
% 104.75/14.40 | | | | | | |
% 104.75/14.40 | | | | | | | GROUND_INST: instantiating (31) with all_43_1, all_115_0, xp,
% 104.75/14.40 | | | | | | | all_45_0, simplifying with (84), (102) gives:
% 104.75/14.40 | | | | | | | (111) all_115_0 = all_43_1
% 104.75/14.40 | | | | | | |
% 104.75/14.40 | | | | | | | PRED_UNIFY: (80), (108) imply:
% 104.75/14.40 | | | | | | | (112) ~ (all_43_1 = sz00)
% 104.75/14.40 | | | | | | |
% 104.75/14.40 | | | | | | | REDUCE: (105), (110) imply:
% 104.75/14.40 | | | | | | | (113) sdtasdt0(all_43_1, sz10) = all_43_1
% 104.75/14.40 | | | | | | |
% 104.75/14.40 | | | | | | | BETA: splitting (39) gives:
% 104.75/14.40 | | | | | | |
% 104.75/14.40 | | | | | | | Case 1:
% 104.75/14.40 | | | | | | | |
% 104.75/14.40 | | | | | | | | (114) all_40_0 = sz10 & sdtpldt0(sz10, all_40_1) = sz10 &
% 104.75/14.40 | | | | | | | | smndt0(xp) = all_40_1 & $i(all_40_1)
% 104.75/14.40 | | | | | | | |
% 104.75/14.40 | | | | | | | | ALPHA: (114) implies:
% 104.75/14.40 | | | | | | | | (115) smndt0(xp) = all_40_1
% 104.75/14.40 | | | | | | | | (116) sdtpldt0(sz10, all_40_1) = sz10
% 104.75/14.40 | | | | | | | |
% 104.75/14.40 | | | | | | | | BETA: splitting (100) gives:
% 104.75/14.40 | | | | | | | |
% 104.75/14.40 | | | | | | | | Case 1:
% 104.75/14.40 | | | | | | | | |
% 104.75/14.40 | | | | | | | | | (117) ~ (sdtasdt0(sz00, xp) = all_43_1)
% 104.75/14.40 | | | | | | | | |
% 104.75/14.40 | | | | | | | | | BETA: splitting (96) gives:
% 104.75/14.40 | | | | | | | | |
% 104.75/14.40 | | | | | | | | | Case 1:
% 104.75/14.40 | | | | | | | | | |
% 104.75/14.40 | | | | | | | | | | (118) ~ (sdtasdt0(all_43_1, sz10) = all_43_1)
% 104.75/14.40 | | | | | | | | | |
% 104.75/14.40 | | | | | | | | | | PRED_UNIFY: (113), (118) imply:
% 104.75/14.40 | | | | | | | | | | (119) $false
% 104.75/14.40 | | | | | | | | | |
% 104.75/14.40 | | | | | | | | | | CLOSE: (119) is inconsistent.
% 104.75/14.40 | | | | | | | | | |
% 104.75/14.40 | | | | | | | | | Case 2:
% 104.75/14.40 | | | | | | | | | |
% 104.75/14.40 | | | | | | | | | |
% 104.75/14.40 | | | | | | | | | | GROUND_INST: instantiating (27) with all_43_1, all_40_1, xp,
% 104.75/14.40 | | | | | | | | | | simplifying with (46), (115) gives:
% 104.75/14.40 | | | | | | | | | | (120) all_43_1 = all_40_1
% 104.75/14.40 | | | | | | | | | |
% 104.75/14.40 | | | | | | | | | | PRED_UNIFY: (84), (117) imply:
% 104.75/14.40 | | | | | | | | | | (121) ~ (all_45_0 = sz00)
% 104.75/14.40 | | | | | | | | | |
% 104.75/14.40 | | | | | | | | | | REDUCE: (112), (120) imply:
% 104.75/14.40 | | | | | | | | | | (122) ~ (all_40_1 = sz00)
% 104.75/14.40 | | | | | | | | | |
% 104.75/14.40 | | | | | | | | | | REDUCE: (75), (120) imply:
% 104.75/14.40 | | | | | | | | | | (123) aInteger0(all_40_1)
% 104.75/14.40 | | | | | | | | | |
% 104.75/14.40 | | | | | | | | | | BETA: splitting (93) gives:
% 104.75/14.40 | | | | | | | | | |
% 104.75/14.40 | | | | | | | | | | Case 1:
% 104.75/14.40 | | | | | | | | | | |
% 104.75/14.40 | | | | | | | | | | | (124) ~ (sdtpldt0(sz10, all_43_1) = sz10)
% 104.75/14.40 | | | | | | | | | | |
% 104.75/14.40 | | | | | | | | | | | REDUCE: (120), (124) imply:
% 104.75/14.40 | | | | | | | | | | | (125) ~ (sdtpldt0(sz10, all_40_1) = sz10)
% 104.75/14.40 | | | | | | | | | | |
% 104.75/14.40 | | | | | | | | | | | PRED_UNIFY: (116), (125) imply:
% 104.75/14.40 | | | | | | | | | | | (126) $false
% 104.75/14.40 | | | | | | | | | | |
% 104.75/14.40 | | | | | | | | | | | CLOSE: (126) is inconsistent.
% 104.75/14.40 | | | | | | | | | | |
% 104.75/14.40 | | | | | | | | | | Case 2:
% 104.75/14.40 | | | | | | | | | | |
% 104.75/14.40 | | | | | | | | | | | (127) sdtpldt0(sz10, all_43_1) = sz10
% 104.75/14.40 | | | | | | | | | | | (128) ? [v0: $i] : (sdtpldt0(v0, all_43_1) = sz00 &
% 104.75/14.40 | | | | | | | | | | | sdtpldt0(all_45_0, sz10) = v0 & $i(v0) &
% 104.75/14.40 | | | | | | | | | | | $i(sz00))
% 104.75/14.40 | | | | | | | | | | |
% 104.75/14.40 | | | | | | | | | | | DELTA: instantiating (128) with fresh symbol all_300_0
% 104.75/14.40 | | | | | | | | | | | gives:
% 104.75/14.40 | | | | | | | | | | | (129) sdtpldt0(all_300_0, all_43_1) = sz00 &
% 104.75/14.40 | | | | | | | | | | | sdtpldt0(all_45_0, sz10) = all_300_0 &
% 104.75/14.40 | | | | | | | | | | | $i(all_300_0) & $i(sz00)
% 104.75/14.40 | | | | | | | | | | |
% 104.75/14.40 | | | | | | | | | | | ALPHA: (129) implies:
% 104.75/14.40 | | | | | | | | | | | (130) sdtpldt0(all_45_0, sz10) = all_300_0
% 104.75/14.40 | | | | | | | | | | | (131) sdtpldt0(all_300_0, all_43_1) = sz00
% 104.75/14.40 | | | | | | | | | | |
% 104.75/14.40 | | | | | | | | | | | REDUCE: (120), (131) imply:
% 104.75/14.41 | | | | | | | | | | | (132) sdtpldt0(all_300_0, all_40_1) = sz00
% 104.75/14.41 | | | | | | | | | | |
% 104.75/14.41 | | | | | | | | | | | BETA: splitting (98) gives:
% 104.75/14.41 | | | | | | | | | | |
% 104.75/14.41 | | | | | | | | | | | Case 1:
% 104.75/14.41 | | | | | | | | | | | |
% 104.75/14.41 | | | | | | | | | | | | (133) ~ (sdtpldt0(sz10, all_43_1) = sz10)
% 104.75/14.41 | | | | | | | | | | | |
% 104.75/14.41 | | | | | | | | | | | | REDUCE: (120), (133) imply:
% 104.75/14.41 | | | | | | | | | | | | (134) ~ (sdtpldt0(sz10, all_40_1) = sz10)
% 104.75/14.41 | | | | | | | | | | | |
% 104.75/14.41 | | | | | | | | | | | | PRED_UNIFY: (116), (134) imply:
% 104.75/14.41 | | | | | | | | | | | | (135) $false
% 104.75/14.41 | | | | | | | | | | | |
% 104.75/14.41 | | | | | | | | | | | | CLOSE: (135) is inconsistent.
% 104.75/14.41 | | | | | | | | | | | |
% 104.75/14.41 | | | | | | | | | | | Case 2:
% 104.75/14.41 | | | | | | | | | | | |
% 104.75/14.41 | | | | | | | | | | | | (136) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 104.75/14.41 | | | | | | | | | | | | $i] : ? [v4: $i] : (sdtasdt0(v2, all_43_1) = v3
% 104.75/14.41 | | | | | | | | | | | | & sdtasdt0(all_45_0, all_43_1) = v1 &
% 104.75/14.41 | | | | | | | | | | | | sdtasdt0(all_45_0, sz10) = v0 & sdtasdt0(sz10,
% 104.75/14.41 | | | | | | | | | | | | all_43_1) = v4 & sdtpldt0(v1, v4) = v3 &
% 104.75/14.41 | | | | | | | | | | | | sdtpldt0(v0, v1) = all_45_0 & sdtpldt0(all_45_0,
% 104.75/14.41 | | | | | | | | | | | | sz10) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1)
% 104.75/14.41 | | | | | | | | | | | | & $i(v0))
% 104.75/14.41 | | | | | | | | | | | |
% 104.75/14.41 | | | | | | | | | | | | DELTA: instantiating (136) with fresh symbols all_310_0,
% 104.75/14.41 | | | | | | | | | | | | all_310_1, all_310_2, all_310_3, all_310_4 gives:
% 104.75/14.41 | | | | | | | | | | | | (137) sdtasdt0(all_310_2, all_43_1) = all_310_1 &
% 104.75/14.41 | | | | | | | | | | | | sdtasdt0(all_45_0, all_43_1) = all_310_3 &
% 104.75/14.41 | | | | | | | | | | | | sdtasdt0(all_45_0, sz10) = all_310_4 &
% 104.75/14.41 | | | | | | | | | | | | sdtasdt0(sz10, all_43_1) = all_310_0 &
% 104.75/14.41 | | | | | | | | | | | | sdtpldt0(all_310_3, all_310_0) = all_310_1 &
% 104.75/14.41 | | | | | | | | | | | | sdtpldt0(all_310_4, all_310_3) = all_45_0 &
% 104.75/14.41 | | | | | | | | | | | | sdtpldt0(all_45_0, sz10) = all_310_2 &
% 104.75/14.41 | | | | | | | | | | | | $i(all_310_0) & $i(all_310_1) & $i(all_310_2) &
% 104.75/14.41 | | | | | | | | | | | | $i(all_310_3) & $i(all_310_4)
% 104.75/14.41 | | | | | | | | | | | |
% 104.75/14.41 | | | | | | | | | | | | ALPHA: (137) implies:
% 104.75/14.41 | | | | | | | | | | | | (138) sdtpldt0(all_45_0, sz10) = all_310_2
% 104.75/14.41 | | | | | | | | | | | |
% 104.75/14.41 | | | | | | | | | | | | BETA: splitting (88) gives:
% 104.75/14.41 | | | | | | | | | | | |
% 104.75/14.41 | | | | | | | | | | | | Case 1:
% 104.75/14.41 | | | | | | | | | | | | |
% 104.75/14.41 | | | | | | | | | | | | |
% 104.75/14.41 | | | | | | | | | | | | | GROUND_INST: instantiating (30) with sz00, all_310_2, sz10,
% 104.75/14.41 | | | | | | | | | | | | | all_45_0, simplifying with (74), (138) gives:
% 104.75/14.41 | | | | | | | | | | | | | (139) all_310_2 = sz00
% 104.75/14.41 | | | | | | | | | | | | |
% 104.75/14.41 | | | | | | | | | | | | | GROUND_INST: instantiating (30) with all_300_0, all_310_2,
% 104.75/14.41 | | | | | | | | | | | | | sz10, all_45_0, simplifying with (130), (138)
% 104.75/14.41 | | | | | | | | | | | | | gives:
% 104.75/14.41 | | | | | | | | | | | | | (140) all_310_2 = all_300_0
% 104.75/14.41 | | | | | | | | | | | | |
% 104.75/14.41 | | | | | | | | | | | | | COMBINE_EQS: (139), (140) imply:
% 104.75/14.41 | | | | | | | | | | | | | (141) all_300_0 = sz00
% 104.75/14.41 | | | | | | | | | | | | |
% 104.75/14.41 | | | | | | | | | | | | | SIMP: (141) implies:
% 104.75/14.41 | | | | | | | | | | | | | (142) all_300_0 = sz00
% 104.75/14.41 | | | | | | | | | | | | |
% 104.75/14.41 | | | | | | | | | | | | | REDUCE: (132), (142) imply:
% 104.75/14.41 | | | | | | | | | | | | | (143) sdtpldt0(sz00, all_40_1) = sz00
% 104.75/14.41 | | | | | | | | | | | | |
% 104.75/14.41 | | | | | | | | | | | | | GROUND_INST: instantiating (53) with xp, all_40_1, simplifying
% 104.75/14.41 | | | | | | | | | | | | | with (25), (42), (115) gives:
% 104.75/14.41 | | | | | | | | | | | | | (144) sdtasdt0(all_48_0, xp) = all_40_1 & sdtasdt0(xp,
% 104.75/14.41 | | | | | | | | | | | | | all_48_0) = all_40_1 & $i(all_40_1)
% 104.75/14.41 | | | | | | | | | | | | |
% 104.75/14.41 | | | | | | | | | | | | | ALPHA: (144) implies:
% 104.75/14.41 | | | | | | | | | | | | | (145) $i(all_40_1)
% 104.75/14.41 | | | | | | | | | | | | |
% 104.75/14.41 | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_40_1, sz00, simplifying
% 104.75/14.41 | | | | | | | | | | | | | with (123), (143), (145) gives:
% 104.75/14.41 | | | | | | | | | | | | | (146) all_40_1 = sz00
% 104.75/14.41 | | | | | | | | | | | | |
% 104.75/14.41 | | | | | | | | | | | | | REDUCE: (122), (146) imply:
% 104.75/14.41 | | | | | | | | | | | | | (147) $false
% 104.75/14.41 | | | | | | | | | | | | |
% 104.75/14.41 | | | | | | | | | | | | | CLOSE: (147) is inconsistent.
% 104.75/14.41 | | | | | | | | | | | | |
% 104.75/14.41 | | | | | | | | | | | | Case 2:
% 104.75/14.41 | | | | | | | | | | | | |
% 104.75/14.41 | | | | | | | | | | | | | (148) all_45_0 = sz00
% 104.75/14.41 | | | | | | | | | | | | |
% 104.75/14.41 | | | | | | | | | | | | | REDUCE: (121), (148) imply:
% 104.75/14.41 | | | | | | | | | | | | | (149) $false
% 104.75/14.41 | | | | | | | | | | | | |
% 104.75/14.41 | | | | | | | | | | | | | CLOSE: (149) is inconsistent.
% 104.75/14.41 | | | | | | | | | | | | |
% 104.75/14.41 | | | | | | | | | | | | End of split
% 104.75/14.41 | | | | | | | | | | | |
% 104.75/14.41 | | | | | | | | | | | End of split
% 104.75/14.41 | | | | | | | | | | |
% 104.75/14.41 | | | | | | | | | | End of split
% 104.75/14.41 | | | | | | | | | |
% 104.75/14.41 | | | | | | | | | End of split
% 104.75/14.41 | | | | | | | | |
% 104.75/14.41 | | | | | | | | Case 2:
% 104.75/14.41 | | | | | | | | |
% 104.75/14.41 | | | | | | | | | (150) all_43_1 = sz00
% 104.75/14.41 | | | | | | | | |
% 104.75/14.41 | | | | | | | | | REDUCE: (112), (150) imply:
% 104.75/14.41 | | | | | | | | | (151) $false
% 104.75/14.41 | | | | | | | | |
% 104.75/14.41 | | | | | | | | | CLOSE: (151) is inconsistent.
% 104.75/14.41 | | | | | | | | |
% 104.75/14.41 | | | | | | | | End of split
% 104.75/14.41 | | | | | | | |
% 104.75/14.41 | | | | | | | Case 2:
% 104.75/14.41 | | | | | | | |
% 104.75/14.41 | | | | | | | | (152) all_40_2 = sz10 & sdtpldt0(sz10, xp) = sz10
% 104.75/14.41 | | | | | | | |
% 104.75/14.41 | | | | | | | | ALPHA: (152) implies:
% 104.75/14.41 | | | | | | | | (153) sdtpldt0(sz10, xp) = sz10
% 104.75/14.41 | | | | | | | |
% 104.75/14.41 | | | | | | | | PRED_UNIFY: (109), (153) imply:
% 104.75/14.41 | | | | | | | | (154) $false
% 104.75/14.41 | | | | | | | |
% 104.75/14.41 | | | | | | | | CLOSE: (154) is inconsistent.
% 104.75/14.41 | | | | | | | |
% 104.75/14.41 | | | | | | | End of split
% 104.75/14.41 | | | | | | |
% 104.75/14.41 | | | | | | Case 2:
% 104.75/14.41 | | | | | | |
% 104.75/14.41 | | | | | | | (155) sdtpldt0(sz10, xp) = sz10
% 104.75/14.41 | | | | | | |
% 104.75/14.41 | | | | | | | GROUND_INST: instantiating (30) with all_43_3, sz10, xp, sz10,
% 104.75/14.41 | | | | | | | simplifying with (47), (155) gives:
% 104.75/14.41 | | | | | | | (156) all_43_3 = sz10
% 104.75/14.41 | | | | | | |
% 104.75/14.41 | | | | | | | PRED_UNIFY: (82), (107) imply:
% 104.75/14.41 | | | | | | | (157) ~ (all_43_3 = sz10)
% 104.75/14.41 | | | | | | |
% 104.75/14.41 | | | | | | | REDUCE: (156), (157) imply:
% 104.75/14.41 | | | | | | | (158) $false
% 104.75/14.41 | | | | | | |
% 104.75/14.41 | | | | | | | CLOSE: (158) is inconsistent.
% 104.75/14.41 | | | | | | |
% 104.75/14.41 | | | | | | End of split
% 104.75/14.41 | | | | | |
% 104.75/14.41 | | | | | Case 2:
% 104.75/14.41 | | | | | |
% 104.75/14.41 | | | | | | (159) sdtpldt0(xp, sz00) = sz00
% 104.75/14.41 | | | | | |
% 104.75/14.41 | | | | | | PRED_UNIFY: (106), (159) imply:
% 104.75/14.41 | | | | | | (160) $false
% 104.75/14.41 | | | | | |
% 104.75/14.41 | | | | | | CLOSE: (160) is inconsistent.
% 104.75/14.41 | | | | | |
% 104.75/14.41 | | | | | End of split
% 104.75/14.41 | | | | |
% 104.75/14.41 | | | | Case 2:
% 104.75/14.41 | | | | |
% 104.75/14.41 | | | | | (161) sdtpldt0(xp, sz10) = sz10
% 104.75/14.41 | | | | | (162) ? [v0: $i] : (sdtpldt0(xp, v0) = sz00 & sdtpldt0(sz10,
% 104.75/14.41 | | | | | all_45_0) = v0 & $i(v0) & $i(sz00))
% 104.75/14.41 | | | | |
% 104.75/14.41 | | | | | DELTA: instantiating (162) with fresh symbol all_147_0 gives:
% 104.75/14.41 | | | | | (163) sdtpldt0(xp, all_147_0) = sz00 & sdtpldt0(sz10, all_45_0) =
% 104.75/14.41 | | | | | all_147_0 & $i(all_147_0) & $i(sz00)
% 104.75/14.41 | | | | |
% 104.75/14.41 | | | | | ALPHA: (163) implies:
% 104.75/14.41 | | | | | (164) sdtpldt0(sz10, all_45_0) = all_147_0
% 104.75/14.41 | | | | | (165) sdtpldt0(xp, all_147_0) = sz00
% 104.75/14.41 | | | | |
% 104.75/14.41 | | | | | BETA: splitting (95) gives:
% 104.75/14.41 | | | | |
% 104.75/14.41 | | | | | Case 1:
% 104.75/14.41 | | | | | |
% 104.75/14.41 | | | | | | (166) ~ (sdtpldt0(xp, sz10) = sz10)
% 104.75/14.41 | | | | | |
% 104.75/14.41 | | | | | | PRED_UNIFY: (161), (166) imply:
% 104.75/14.41 | | | | | | (167) $false
% 104.75/14.41 | | | | | |
% 104.75/14.41 | | | | | | CLOSE: (167) is inconsistent.
% 104.75/14.41 | | | | | |
% 104.75/14.41 | | | | | Case 2:
% 104.75/14.41 | | | | | |
% 104.75/14.41 | | | | | | (168) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 104.75/14.41 | | | | | | [v4: $i] : (sdtasdt0(xp, v0) = v1 & sdtasdt0(xp, all_45_0)
% 104.75/14.41 | | | | | | = v3 & sdtasdt0(xp, sz10) = v2 & sdtasdt0(sz10, all_45_0)
% 104.75/14.41 | | | | | | = v4 & sdtpldt0(v3, v4) = all_45_0 & sdtpldt0(v2, v3) =
% 104.75/14.41 | | | | | | v1 & sdtpldt0(sz10, all_45_0) = v0 & $i(v4) & $i(v3) &
% 104.75/14.41 | | | | | | $i(v2) & $i(v1) & $i(v0))
% 104.75/14.41 | | | | | |
% 104.75/14.41 | | | | | | DELTA: instantiating (168) with fresh symbols all_176_0, all_176_1,
% 104.75/14.41 | | | | | | all_176_2, all_176_3, all_176_4 gives:
% 104.75/14.41 | | | | | | (169) sdtasdt0(xp, all_176_4) = all_176_3 & sdtasdt0(xp,
% 104.75/14.41 | | | | | | all_45_0) = all_176_1 & sdtasdt0(xp, sz10) = all_176_2 &
% 104.75/14.41 | | | | | | sdtasdt0(sz10, all_45_0) = all_176_0 & sdtpldt0(all_176_1,
% 104.75/14.41 | | | | | | all_176_0) = all_45_0 & sdtpldt0(all_176_2, all_176_1) =
% 104.75/14.41 | | | | | | all_176_3 & sdtpldt0(sz10, all_45_0) = all_176_4 &
% 104.75/14.41 | | | | | | $i(all_176_0) & $i(all_176_1) & $i(all_176_2) &
% 104.75/14.41 | | | | | | $i(all_176_3) & $i(all_176_4)
% 104.75/14.41 | | | | | |
% 104.75/14.41 | | | | | | ALPHA: (169) implies:
% 104.75/14.41 | | | | | | (170) sdtpldt0(sz10, all_45_0) = all_176_4
% 104.75/14.41 | | | | | |
% 104.75/14.42 | | | | | | GROUND_INST: instantiating (30) with sz00, all_176_4, all_45_0,
% 104.75/14.42 | | | | | | sz10, simplifying with (73), (170) gives:
% 104.75/14.42 | | | | | | (171) all_176_4 = sz00
% 104.75/14.42 | | | | | |
% 104.75/14.42 | | | | | | GROUND_INST: instantiating (30) with all_147_0, all_176_4, all_45_0,
% 104.75/14.42 | | | | | | sz10, simplifying with (164), (170) gives:
% 104.75/14.42 | | | | | | (172) all_176_4 = all_147_0
% 104.75/14.42 | | | | | |
% 104.75/14.42 | | | | | | PRED_UNIFY: (106), (165) imply:
% 104.75/14.42 | | | | | | (173) ~ (all_147_0 = sz00)
% 104.75/14.42 | | | | | |
% 104.75/14.42 | | | | | | COMBINE_EQS: (171), (172) imply:
% 104.75/14.42 | | | | | | (174) all_147_0 = sz00
% 104.75/14.42 | | | | | |
% 104.75/14.42 | | | | | | REDUCE: (173), (174) imply:
% 104.75/14.42 | | | | | | (175) $false
% 104.75/14.42 | | | | | |
% 104.75/14.42 | | | | | | CLOSE: (175) is inconsistent.
% 104.75/14.42 | | | | | |
% 104.75/14.42 | | | | | End of split
% 104.75/14.42 | | | | |
% 104.75/14.42 | | | | End of split
% 104.75/14.42 | | | |
% 104.75/14.42 | | | Case 2:
% 104.75/14.42 | | | |
% 104.75/14.42 | | | | (176) xp = sz00
% 104.75/14.42 | | | |
% 104.75/14.42 | | | | REDUCE: (41), (176) imply:
% 104.75/14.42 | | | | (177) $false
% 104.75/14.42 | | | |
% 104.75/14.42 | | | | CLOSE: (177) is inconsistent.
% 104.75/14.42 | | | |
% 104.75/14.42 | | | End of split
% 104.75/14.42 | | |
% 104.75/14.42 | | Case 2:
% 104.75/14.42 | | |
% 104.75/14.42 | | | (178) xp = sz00
% 104.75/14.42 | | |
% 104.75/14.42 | | | REDUCE: (41), (178) imply:
% 104.75/14.42 | | | (179) $false
% 104.75/14.42 | | |
% 104.75/14.42 | | | CLOSE: (179) is inconsistent.
% 104.75/14.42 | | |
% 104.75/14.42 | | End of split
% 104.75/14.42 | |
% 104.75/14.42 | End of split
% 104.75/14.42 |
% 104.75/14.42 End of proof
% 104.75/14.42 % SZS output end Proof for theBenchmark
% 104.75/14.42
% 104.75/14.42 13811ms
%------------------------------------------------------------------------------