TSTP Solution File: NUM494+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM494+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 11:48:09 EDT 2023
% Result : Theorem 15.42s 2.94s
% Output : Proof 27.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM494+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.36 % Computer : n022.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Aug 25 15:21:10 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.63 ________ _____
% 0.21/0.63 ___ __ \_________(_)________________________________
% 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.63
% 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.63 (2023-06-19)
% 0.21/0.63
% 0.21/0.63 (c) Philipp Rümmer, 2009-2023
% 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.63 Amanda Stjerna.
% 0.21/0.63 Free software under BSD-3-Clause.
% 0.21/0.63
% 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.63
% 0.21/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.64 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.92/1.24 Prover 1: Preprocessing ...
% 3.92/1.24 Prover 4: Preprocessing ...
% 3.92/1.27 Prover 2: Preprocessing ...
% 3.92/1.27 Prover 0: Preprocessing ...
% 3.92/1.27 Prover 6: Preprocessing ...
% 3.92/1.27 Prover 3: Preprocessing ...
% 3.92/1.27 Prover 5: Preprocessing ...
% 9.79/2.04 Prover 1: Constructing countermodel ...
% 9.79/2.07 Prover 3: Constructing countermodel ...
% 10.33/2.11 Prover 6: Proving ...
% 10.33/2.18 Prover 5: Constructing countermodel ...
% 12.44/2.38 Prover 2: Proving ...
% 13.11/2.46 Prover 4: Constructing countermodel ...
% 13.11/2.47 Prover 0: Proving ...
% 15.42/2.93 Prover 3: proved (2283ms)
% 15.42/2.93
% 15.42/2.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.42/2.94
% 15.42/2.94 Prover 5: stopped
% 15.42/2.94 Prover 6: stopped
% 15.42/2.94 Prover 2: stopped
% 15.42/2.95 Prover 0: stopped
% 15.42/2.96 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 15.42/2.96 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 15.42/2.96 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 15.42/2.96 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 15.42/2.96 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 17.84/3.11 Prover 11: Preprocessing ...
% 17.84/3.12 Prover 8: Preprocessing ...
% 17.84/3.13 Prover 10: Preprocessing ...
% 17.84/3.13 Prover 13: Preprocessing ...
% 17.84/3.13 Prover 7: Preprocessing ...
% 19.60/3.33 Prover 8: Warning: ignoring some quantifiers
% 19.60/3.33 Prover 8: Constructing countermodel ...
% 19.60/3.34 Prover 10: Constructing countermodel ...
% 20.16/3.39 Prover 7: Constructing countermodel ...
% 20.87/3.53 Prover 13: Constructing countermodel ...
% 21.66/3.63 Prover 11: Constructing countermodel ...
% 26.01/4.26 Prover 10: Found proof (size 102)
% 26.01/4.26 Prover 10: proved (1320ms)
% 26.01/4.26 Prover 4: stopped
% 26.01/4.26 Prover 7: stopped
% 26.01/4.26 Prover 13: stopped
% 26.01/4.26 Prover 1: stopped
% 26.01/4.26 Prover 8: stopped
% 26.01/4.26 Prover 11: stopped
% 26.01/4.27
% 26.01/4.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.01/4.27
% 26.01/4.27 % SZS output start Proof for theBenchmark
% 26.49/4.28 Assumptions after simplification:
% 26.49/4.28 ---------------------------------
% 26.49/4.28
% 26.49/4.28 (mAddAsso)
% 26.49/4.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 26.49/4.30 (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 26.49/4.30 | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 26.49/4.30 aNaturalNumber0(v0) | ? [v5: $i] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0,
% 26.49/4.30 v5) = v4 & $i(v5) & $i(v4)))
% 26.49/4.30
% 26.49/4.30 (mAddComm)
% 26.49/4.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 26.49/4.31 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) |
% 26.49/4.31 (sdtpldt0(v1, v0) = v2 & $i(v2)))
% 26.49/4.31
% 26.49/4.31 (mDefDiff)
% 26.49/4.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 26.49/4.31 (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ $i(v3) | ~ $i(v1)
% 26.49/4.31 | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~
% 26.49/4.31 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] :
% 26.49/4.31 ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~
% 26.49/4.31 (sdtpldt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 26.49/4.31 sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & !
% 26.49/4.31 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtmndt0(v1, v0) =
% 26.49/4.31 v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 26.49/4.31 sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) |
% 26.49/4.31 aNaturalNumber0(v2))
% 26.49/4.31
% 26.49/4.31 (mMonAdd)
% 26.49/4.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 26.49/4.31 (sdtpldt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 26.49/4.31 sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 26.49/4.31 aNaturalNumber0(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v6 =
% 26.49/4.31 v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 &
% 26.49/4.31 sdtpldt0(v1, v2) = v6 & $i(v6) & $i(v5) & $i(v4) & sdtlseqdt0(v4, v5) &
% 26.49/4.31 sdtlseqdt0(v3, v6)))
% 26.49/4.31
% 26.49/4.31 (mPrimDiv)
% 26.49/4.31 $i(sz10) & $i(sz00) & ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ $i(v0) | ~
% 26.49/4.31 aNaturalNumber0(v0) | ? [v1: $i] : ($i(v1) & isPrime0(v1) & doDivides0(v1,
% 26.49/4.31 v0) & aNaturalNumber0(v1)))
% 26.49/4.31
% 26.49/4.31 (mSortsB)
% 26.49/4.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 26.49/4.31 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) |
% 26.49/4.31 aNaturalNumber0(v2))
% 26.49/4.31
% 26.49/4.31 (m__)
% 26.49/4.31 $i(xr) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 26.49/4.31 ? [v3: $i] : (sdtpldt0(v2, xp) = v3 & sdtpldt0(v0, xp) = v1 & sdtpldt0(xr, xm)
% 26.49/4.31 = v0 & sdtpldt0(xn, xm) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v3 = v1
% 26.49/4.31 | ( ~ sdtlseqdt0(v1, v3) & ! [v4: $i] : ( ~ (sdtpldt0(v1, v4) = v3) | ~
% 26.49/4.31 $i(v4) | ~ aNaturalNumber0(v4)))))
% 26.49/4.31
% 26.49/4.31 (m__1799)
% 27.06/4.33 $i(xp) & $i(xm) & $i(xn) & $i(sz10) & $i(sz00) & ? [v0: $i] : ? [v1: $i] :
% 27.06/4.33 (sdtpldt0(v0, xp) = v1 & sdtpldt0(xn, xm) = v0 & $i(v1) & $i(v0) & ! [v2: $i]
% 27.06/4.33 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v4 = sz10 | v4 =
% 27.06/4.33 sz00 | ~ (sdtpldt0(v5, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4)
% 27.06/4.33 | ~ $i(v3) | ~ $i(v2) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~
% 27.06/4.33 aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | doDivides0(v4, v3) |
% 27.06/4.33 doDivides0(v4, v2) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10:
% 27.06/4.33 $i] : ($i(v9) & $i(v8) & ((v10 = v4 & ~ (v8 = v4) & ~ (v8 = sz10) &
% 27.06/4.33 sdtasdt0(v8, v9) = v4 & doDivides0(v8, v4) & aNaturalNumber0(v9) &
% 27.06/4.33 aNaturalNumber0(v8)) | (sdtasdt0(v2, v3) = v7 & $i(v7) & ~
% 27.06/4.33 doDivides0(v4, v7) & ! [v11: $i] : ( ~ (sdtasdt0(v4, v11) = v7) |
% 27.06/4.33 ~ $i(v11) | ~ aNaturalNumber0(v11)))))) & ! [v2: $i] : ! [v3:
% 27.06/4.33 $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v4 = sz10 | v4 = sz00 |
% 27.06/4.33 ~ (sdtpldt0(v5, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~
% 27.06/4.33 $i(v3) | ~ $i(v2) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~
% 27.06/4.33 aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | doDivides0(v4, v3) | ?
% 27.06/4.33 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ?
% 27.06/4.33 [v12: $i] : ($i(v11) & $i(v10) & $i(v8) & ((v12 = v4 & ~ (v10 = v4) & ~
% 27.06/4.33 (v10 = sz10) & sdtasdt0(v10, v11) = v4 & doDivides0(v10, v4) &
% 27.06/4.33 aNaturalNumber0(v11) & aNaturalNumber0(v10)) | (v9 = v2 &
% 27.06/4.33 sdtasdt0(v4, v8) = v2 & aNaturalNumber0(v8)) | (sdtasdt0(v2, v3) =
% 27.06/4.33 v7 & $i(v7) & ~ doDivides0(v4, v7) & ! [v13: $i] : ( ~
% 27.06/4.33 (sdtasdt0(v4, v13) = v7) | ~ $i(v13) | ~
% 27.06/4.33 aNaturalNumber0(v13)))))) & ! [v2: $i] : ! [v3: $i] : ! [v4:
% 27.06/4.33 $i] : ! [v5: $i] : ! [v6: $i] : (v4 = sz10 | v4 = sz00 | ~
% 27.06/4.33 (sdtpldt0(v5, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~
% 27.06/4.33 $i(v3) | ~ $i(v2) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~
% 27.06/4.33 aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | doDivides0(v4, v2) | ?
% 27.06/4.33 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ?
% 27.06/4.33 [v12: $i] : ($i(v11) & $i(v10) & $i(v8) & ((v12 = v4 & ~ (v10 = v4) & ~
% 27.06/4.33 (v10 = sz10) & sdtasdt0(v10, v11) = v4 & doDivides0(v10, v4) &
% 27.06/4.33 aNaturalNumber0(v11) & aNaturalNumber0(v10)) | (v9 = v3 &
% 27.06/4.33 sdtasdt0(v4, v8) = v3 & aNaturalNumber0(v8)) | (sdtasdt0(v2, v3) =
% 27.06/4.33 v7 & $i(v7) & ~ doDivides0(v4, v7) & ! [v13: $i] : ( ~
% 27.06/4.33 (sdtasdt0(v4, v13) = v7) | ~ $i(v13) | ~
% 27.06/4.33 aNaturalNumber0(v13)))))) & ! [v2: $i] : ! [v3: $i] : ! [v4:
% 27.06/4.33 $i] : ! [v5: $i] : ! [v6: $i] : (v4 = sz10 | v4 = sz00 | ~
% 27.06/4.33 (sdtpldt0(v5, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~
% 27.06/4.33 $i(v3) | ~ $i(v2) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~
% 27.06/4.33 aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v7: $i] : ? [v8: $i] :
% 27.06/4.33 ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] :
% 27.06/4.33 ? [v14: $i] : ($i(v13) & $i(v12) & $i(v10) & $i(v8) & ((v14 = v4 & ~ (v12
% 27.06/4.33 = v4) & ~ (v12 = sz10) & sdtasdt0(v12, v13) = v4 &
% 27.06/4.33 doDivides0(v12, v4) & aNaturalNumber0(v13) & aNaturalNumber0(v12)) |
% 27.06/4.33 (v11 = v2 & sdtasdt0(v4, v10) = v2 & aNaturalNumber0(v10)) | (v9 = v3
% 27.06/4.33 & sdtasdt0(v4, v8) = v3 & aNaturalNumber0(v8)) | (sdtasdt0(v2, v3) =
% 27.06/4.33 v7 & $i(v7) & ~ doDivides0(v4, v7) & ! [v15: $i] : ( ~
% 27.06/4.33 (sdtasdt0(v4, v15) = v7) | ~ $i(v15) | ~
% 27.06/4.33 aNaturalNumber0(v15)))))) & ! [v2: $i] : ! [v3: $i] : ! [v4:
% 27.06/4.33 $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtpldt0(v5, v4) = v6) | ~
% 27.06/4.33 (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 27.06/4.33 isPrime0(v4) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~
% 27.06/4.33 aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | doDivides0(v4, v3) |
% 27.06/4.33 doDivides0(v4, v2) | ? [v7: $i] : (sdtasdt0(v2, v3) = v7 & $i(v7) & ~
% 27.06/4.33 doDivides0(v4, v7) & ! [v8: $i] : ( ~ (sdtasdt0(v4, v8) = v7) | ~
% 27.06/4.33 $i(v8) | ~ aNaturalNumber0(v8)))) & ! [v2: $i] : ! [v3: $i] : !
% 27.06/4.33 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtpldt0(v5, v4) = v6) | ~
% 27.06/4.33 (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 27.06/4.33 isPrime0(v4) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~
% 27.06/4.33 aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | doDivides0(v4, v3) | ?
% 27.06/4.33 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v8) & ((v9 = v2 & sdtasdt0(v4,
% 27.06/4.33 v8) = v2 & aNaturalNumber0(v8)) | (sdtasdt0(v2, v3) = v7 & $i(v7)
% 27.06/4.33 & ~ doDivides0(v4, v7) & ! [v10: $i] : ( ~ (sdtasdt0(v4, v10) =
% 27.06/4.33 v7) | ~ $i(v10) | ~ aNaturalNumber0(v10)))))) & ! [v2: $i] :
% 27.06/4.33 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtpldt0(v5, v4)
% 27.06/4.33 = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 27.06/4.33 ~ isPrime0(v4) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~
% 27.06/4.33 aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | doDivides0(v4, v2) | ?
% 27.06/4.33 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v8) & ((v9 = v3 & sdtasdt0(v4,
% 27.06/4.33 v8) = v3 & aNaturalNumber0(v8)) | (sdtasdt0(v2, v3) = v7 & $i(v7)
% 27.06/4.33 & ~ doDivides0(v4, v7) & ! [v10: $i] : ( ~ (sdtasdt0(v4, v10) =
% 27.06/4.33 v7) | ~ $i(v10) | ~ aNaturalNumber0(v10)))))) & ! [v2: $i] :
% 27.06/4.33 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtpldt0(v5, v4)
% 27.06/4.33 = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 27.06/4.33 ~ isPrime0(v4) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~
% 27.06/4.33 aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v7: $i] : ? [v8: $i] :
% 27.06/4.33 ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ($i(v10) & $i(v8) & ((v11 = v2
% 27.06/4.33 & sdtasdt0(v4, v10) = v2 & aNaturalNumber0(v10)) | (v9 = v3 &
% 27.06/4.33 sdtasdt0(v4, v8) = v3 & aNaturalNumber0(v8)) | (sdtasdt0(v2, v3) =
% 27.06/4.33 v7 & $i(v7) & ~ doDivides0(v4, v7) & ! [v12: $i] : ( ~
% 27.06/4.33 (sdtasdt0(v4, v12) = v7) | ~ $i(v12) | ~
% 27.06/4.33 aNaturalNumber0(v12)))))))
% 27.06/4.33
% 27.06/4.33 (m__1837)
% 27.06/4.33 $i(xp) & $i(xm) & $i(xn) & aNaturalNumber0(xp) & aNaturalNumber0(xm) &
% 27.06/4.33 aNaturalNumber0(xn)
% 27.06/4.33
% 27.06/4.33 (m__1860)
% 27.06/4.33 $i(xp) & $i(xm) & $i(xn) & $i(sz10) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : (
% 27.06/4.33 ~ (xp = sz10) & ~ (xp = sz00) & sdtasdt0(xp, v1) = v0 & sdtasdt0(xn, xm) =
% 27.06/4.33 v0 & $i(v1) & $i(v0) & isPrime0(xp) & doDivides0(xp, v0) &
% 27.06/4.33 aNaturalNumber0(v1) & ! [v2: $i] : ! [v3: $i] : (v2 = xp | v2 = sz10 | ~
% 27.06/4.33 (sdtasdt0(v2, v3) = xp) | ~ $i(v3) | ~ $i(v2) | ~ aNaturalNumber0(v3) |
% 27.06/4.33 ~ aNaturalNumber0(v2)) & ! [v2: $i] : (v2 = xp | v2 = sz10 | ~ $i(v2) |
% 27.06/4.33 ~ doDivides0(v2, xp) | ~ aNaturalNumber0(v2)))
% 27.06/4.33
% 27.06/4.33 (m__1870)
% 27.06/4.33 $i(xp) & $i(xn) & ? [v0: $i] : (sdtpldt0(xp, v0) = xn & $i(v0) &
% 27.06/4.33 sdtlseqdt0(xp, xn) & aNaturalNumber0(v0))
% 27.06/4.33
% 27.06/4.33 (m__1883)
% 27.06/4.33 sdtmndt0(xn, xp) = xr & sdtpldt0(xp, xr) = xn & $i(xr) & $i(xp) & $i(xn) &
% 27.06/4.33 aNaturalNumber0(xr)
% 27.06/4.33
% 27.06/4.33 (m__1894)
% 27.06/4.33 $i(xr) & $i(xn) & ? [v0: $i] : ( ~ (xr = xn) & sdtpldt0(xr, v0) = xn & $i(v0)
% 27.06/4.33 & sdtlseqdt0(xr, xn) & aNaturalNumber0(v0))
% 27.06/4.33
% 27.06/4.33 (function-axioms)
% 27.06/4.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 27.06/4.33 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: $i] : !
% 27.06/4.33 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) |
% 27.06/4.33 ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 27.06/4.33 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 27.06/4.33 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 27.06/4.33 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 27.06/4.33
% 27.06/4.33 Further assumptions not needed in the proof:
% 27.06/4.33 --------------------------------------------
% 27.06/4.33 mAMDistr, mAddCanc, mDefDiv, mDefLE, mDefPrime, mDefQuot, mDivAsso, mDivLE,
% 27.06/4.33 mDivMin, mDivSum, mDivTrans, mIH, mIH_03, mLEAsym, mLENTr, mLERefl, mLETotal,
% 27.06/4.33 mLETran, mMonMul, mMonMul2, mMulAsso, mMulCanc, mMulComm, mNatSort, mSortsB_02,
% 27.06/4.33 mSortsC, mSortsC_01, mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, m_MulZero,
% 27.06/4.33 m__1913
% 27.06/4.33
% 27.06/4.33 Those formulas are unsatisfiable:
% 27.06/4.33 ---------------------------------
% 27.06/4.33
% 27.06/4.33 Begin of proof
% 27.06/4.33 |
% 27.06/4.33 | ALPHA: (mDefDiff) implies:
% 27.06/4.34 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 27.06/4.34 | (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ $i(v3) | ~
% 27.06/4.34 | $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) |
% 27.06/4.34 | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 27.06/4.34 |
% 27.06/4.34 | ALPHA: (mPrimDiv) implies:
% 27.06/4.34 | (2) ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ $i(v0) | ~
% 27.06/4.34 | aNaturalNumber0(v0) | ? [v1: $i] : ($i(v1) & isPrime0(v1) &
% 27.06/4.34 | doDivides0(v1, v0) & aNaturalNumber0(v1)))
% 27.06/4.34 |
% 27.06/4.34 | ALPHA: (m__1837) implies:
% 27.06/4.34 | (3) aNaturalNumber0(xn)
% 27.06/4.34 | (4) aNaturalNumber0(xm)
% 27.06/4.34 | (5) aNaturalNumber0(xp)
% 27.06/4.34 |
% 27.06/4.34 | ALPHA: (m__1799) implies:
% 27.06/4.35 | (6) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(v0, xp) = v1 & sdtpldt0(xn, xm) =
% 27.06/4.35 | v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 27.06/4.35 | [v5: $i] : ! [v6: $i] : (v4 = sz10 | v4 = sz00 | ~ (sdtpldt0(v5,
% 27.06/4.35 | v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3)
% 27.06/4.35 | | ~ $i(v2) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~
% 27.06/4.35 | aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | doDivides0(v4, v3) |
% 27.06/4.35 | doDivides0(v4, v2) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 27.06/4.35 | [v10: $i] : ($i(v9) & $i(v8) & ((v10 = v4 & ~ (v8 = v4) & ~ (v8 =
% 27.06/4.35 | sz10) & sdtasdt0(v8, v9) = v4 & doDivides0(v8, v4) &
% 27.06/4.35 | aNaturalNumber0(v9) & aNaturalNumber0(v8)) | (sdtasdt0(v2,
% 27.06/4.35 | v3) = v7 & $i(v7) & ~ doDivides0(v4, v7) & ! [v11: $i] :
% 27.06/4.35 | ( ~ (sdtasdt0(v4, v11) = v7) | ~ $i(v11) | ~
% 27.06/4.35 | aNaturalNumber0(v11)))))) & ! [v2: $i] : ! [v3: $i] : !
% 27.06/4.35 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v4 = sz10 | v4 = sz00 | ~
% 27.06/4.35 | (sdtpldt0(v5, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) |
% 27.06/4.35 | ~ $i(v3) | ~ $i(v2) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) |
% 27.06/4.35 | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | doDivides0(v4,
% 27.06/4.35 | v3) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ?
% 27.06/4.35 | [v11: $i] : ? [v12: $i] : ($i(v11) & $i(v10) & $i(v8) & ((v12 = v4
% 27.06/4.35 | & ~ (v10 = v4) & ~ (v10 = sz10) & sdtasdt0(v10, v11) = v4 &
% 27.06/4.35 | doDivides0(v10, v4) & aNaturalNumber0(v11) &
% 27.06/4.35 | aNaturalNumber0(v10)) | (v9 = v2 & sdtasdt0(v4, v8) = v2 &
% 27.06/4.35 | aNaturalNumber0(v8)) | (sdtasdt0(v2, v3) = v7 & $i(v7) & ~
% 27.06/4.35 | doDivides0(v4, v7) & ! [v13: $i] : ( ~ (sdtasdt0(v4, v13) =
% 27.06/4.35 | v7) | ~ $i(v13) | ~ aNaturalNumber0(v13)))))) & ! [v2:
% 27.06/4.35 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v4 =
% 27.06/4.35 | sz10 | v4 = sz00 | ~ (sdtpldt0(v5, v4) = v6) | ~ (sdtpldt0(v2,
% 27.06/4.35 | v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ iLess0(v6,
% 27.06/4.35 | v1) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~
% 27.06/4.35 | aNaturalNumber0(v2) | doDivides0(v4, v2) | ? [v7: $i] : ? [v8:
% 27.06/4.35 | $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] :
% 27.06/4.35 | ($i(v11) & $i(v10) & $i(v8) & ((v12 = v4 & ~ (v10 = v4) & ~ (v10
% 27.06/4.35 | = sz10) & sdtasdt0(v10, v11) = v4 & doDivides0(v10, v4) &
% 27.06/4.35 | aNaturalNumber0(v11) & aNaturalNumber0(v10)) | (v9 = v3 &
% 27.06/4.35 | sdtasdt0(v4, v8) = v3 & aNaturalNumber0(v8)) | (sdtasdt0(v2,
% 27.06/4.35 | v3) = v7 & $i(v7) & ~ doDivides0(v4, v7) & ! [v13: $i] :
% 27.06/4.35 | ( ~ (sdtasdt0(v4, v13) = v7) | ~ $i(v13) | ~
% 27.06/4.35 | aNaturalNumber0(v13)))))) & ! [v2: $i] : ! [v3: $i] : !
% 27.06/4.35 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v4 = sz10 | v4 = sz00 | ~
% 27.06/4.35 | (sdtpldt0(v5, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) |
% 27.06/4.35 | ~ $i(v3) | ~ $i(v2) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) |
% 27.06/4.35 | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v7: $i] : ?
% 27.06/4.35 | [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i]
% 27.06/4.35 | : ? [v13: $i] : ? [v14: $i] : ($i(v13) & $i(v12) & $i(v10) &
% 27.06/4.35 | $i(v8) & ((v14 = v4 & ~ (v12 = v4) & ~ (v12 = sz10) &
% 27.06/4.35 | sdtasdt0(v12, v13) = v4 & doDivides0(v12, v4) &
% 27.06/4.35 | aNaturalNumber0(v13) & aNaturalNumber0(v12)) | (v11 = v2 &
% 27.06/4.35 | sdtasdt0(v4, v10) = v2 & aNaturalNumber0(v10)) | (v9 = v3 &
% 27.06/4.35 | sdtasdt0(v4, v8) = v3 & aNaturalNumber0(v8)) | (sdtasdt0(v2,
% 27.06/4.35 | v3) = v7 & $i(v7) & ~ doDivides0(v4, v7) & ! [v15: $i] :
% 27.06/4.35 | ( ~ (sdtasdt0(v4, v15) = v7) | ~ $i(v15) | ~
% 27.06/4.35 | aNaturalNumber0(v15)))))) & ! [v2: $i] : ! [v3: $i] : !
% 27.06/4.35 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtpldt0(v5, v4) = v6) |
% 27.06/4.35 | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 27.06/4.35 | isPrime0(v4) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~
% 27.06/4.35 | aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | doDivides0(v4, v3) |
% 27.06/4.35 | doDivides0(v4, v2) | ? [v7: $i] : (sdtasdt0(v2, v3) = v7 & $i(v7)
% 27.06/4.35 | & ~ doDivides0(v4, v7) & ! [v8: $i] : ( ~ (sdtasdt0(v4, v8) =
% 27.06/4.35 | v7) | ~ $i(v8) | ~ aNaturalNumber0(v8)))) & ! [v2: $i] :
% 27.06/4.35 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 27.06/4.35 | (sdtpldt0(v5, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) |
% 27.06/4.35 | ~ $i(v3) | ~ $i(v2) | ~ isPrime0(v4) | ~ iLess0(v6, v1) | ~
% 27.06/4.35 | aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~
% 27.06/4.35 | aNaturalNumber0(v2) | doDivides0(v4, v3) | ? [v7: $i] : ? [v8:
% 27.06/4.35 | $i] : ? [v9: $i] : ($i(v8) & ((v9 = v2 & sdtasdt0(v4, v8) = v2 &
% 27.06/4.35 | aNaturalNumber0(v8)) | (sdtasdt0(v2, v3) = v7 & $i(v7) & ~
% 27.06/4.35 | doDivides0(v4, v7) & ! [v10: $i] : ( ~ (sdtasdt0(v4, v10) =
% 27.06/4.35 | v7) | ~ $i(v10) | ~ aNaturalNumber0(v10)))))) & ! [v2:
% 27.06/4.35 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 27.06/4.35 | (sdtpldt0(v5, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) |
% 27.06/4.35 | ~ $i(v3) | ~ $i(v2) | ~ isPrime0(v4) | ~ iLess0(v6, v1) | ~
% 27.06/4.35 | aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~
% 27.06/4.35 | aNaturalNumber0(v2) | doDivides0(v4, v2) | ? [v7: $i] : ? [v8:
% 27.06/4.35 | $i] : ? [v9: $i] : ($i(v8) & ((v9 = v3 & sdtasdt0(v4, v8) = v3 &
% 27.06/4.35 | aNaturalNumber0(v8)) | (sdtasdt0(v2, v3) = v7 & $i(v7) & ~
% 27.06/4.35 | doDivides0(v4, v7) & ! [v10: $i] : ( ~ (sdtasdt0(v4, v10) =
% 27.06/4.35 | v7) | ~ $i(v10) | ~ aNaturalNumber0(v10)))))) & ! [v2:
% 27.06/4.35 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 27.06/4.35 | (sdtpldt0(v5, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) |
% 27.06/4.35 | ~ $i(v3) | ~ $i(v2) | ~ isPrime0(v4) | ~ iLess0(v6, v1) | ~
% 27.06/4.35 | aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~
% 27.06/4.35 | aNaturalNumber0(v2) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 27.06/4.35 | [v10: $i] : ? [v11: $i] : ($i(v10) & $i(v8) & ((v11 = v2 &
% 27.06/4.35 | sdtasdt0(v4, v10) = v2 & aNaturalNumber0(v10)) | (v9 = v3 &
% 27.06/4.35 | sdtasdt0(v4, v8) = v3 & aNaturalNumber0(v8)) | (sdtasdt0(v2,
% 27.06/4.35 | v3) = v7 & $i(v7) & ~ doDivides0(v4, v7) & ! [v12: $i] :
% 27.06/4.35 | ( ~ (sdtasdt0(v4, v12) = v7) | ~ $i(v12) | ~
% 27.06/4.35 | aNaturalNumber0(v12)))))))
% 27.06/4.35 |
% 27.06/4.35 | ALPHA: (m__1860) implies:
% 27.06/4.35 | (7) ? [v0: $i] : ? [v1: $i] : ( ~ (xp = sz10) & ~ (xp = sz00) &
% 27.06/4.35 | sdtasdt0(xp, v1) = v0 & sdtasdt0(xn, xm) = v0 & $i(v1) & $i(v0) &
% 27.06/4.35 | isPrime0(xp) & doDivides0(xp, v0) & aNaturalNumber0(v1) & ! [v2: $i]
% 27.06/4.35 | : ! [v3: $i] : (v2 = xp | v2 = sz10 | ~ (sdtasdt0(v2, v3) = xp) |
% 27.06/4.35 | ~ $i(v3) | ~ $i(v2) | ~ aNaturalNumber0(v3) | ~
% 27.06/4.35 | aNaturalNumber0(v2)) & ! [v2: $i] : (v2 = xp | v2 = sz10 | ~
% 27.06/4.35 | $i(v2) | ~ doDivides0(v2, xp) | ~ aNaturalNumber0(v2)))
% 27.06/4.35 |
% 27.06/4.35 | ALPHA: (m__1870) implies:
% 27.06/4.35 | (8) ? [v0: $i] : (sdtpldt0(xp, v0) = xn & $i(v0) & sdtlseqdt0(xp, xn) &
% 27.06/4.35 | aNaturalNumber0(v0))
% 27.06/4.35 |
% 27.06/4.35 | ALPHA: (m__1883) implies:
% 27.06/4.35 | (9) aNaturalNumber0(xr)
% 27.06/4.35 | (10) sdtpldt0(xp, xr) = xn
% 27.06/4.35 | (11) sdtmndt0(xn, xp) = xr
% 27.06/4.35 |
% 27.06/4.35 | ALPHA: (m__1894) implies:
% 27.06/4.35 | (12) ? [v0: $i] : ( ~ (xr = xn) & sdtpldt0(xr, v0) = xn & $i(v0) &
% 27.06/4.35 | sdtlseqdt0(xr, xn) & aNaturalNumber0(v0))
% 27.06/4.35 |
% 27.06/4.35 | ALPHA: (m__) implies:
% 27.06/4.35 | (13) $i(xn)
% 27.06/4.35 | (14) $i(xm)
% 27.06/4.35 | (15) $i(xp)
% 27.06/4.35 | (16) $i(xr)
% 27.06/4.35 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtpldt0(v2,
% 27.06/4.35 | xp) = v3 & sdtpldt0(v0, xp) = v1 & sdtpldt0(xr, xm) = v0 &
% 27.06/4.35 | sdtpldt0(xn, xm) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v3 = v1
% 27.06/4.35 | | ( ~ sdtlseqdt0(v1, v3) & ! [v4: $i] : ( ~ (sdtpldt0(v1, v4) =
% 27.06/4.35 | v3) | ~ $i(v4) | ~ aNaturalNumber0(v4)))))
% 27.06/4.35 |
% 27.06/4.35 | ALPHA: (function-axioms) implies:
% 27.06/4.35 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 27.06/4.35 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 27.06/4.36 |
% 27.06/4.36 | DELTA: instantiating (8) with fresh symbol all_38_0 gives:
% 27.06/4.36 | (19) sdtpldt0(xp, all_38_0) = xn & $i(all_38_0) & sdtlseqdt0(xp, xn) &
% 27.06/4.36 | aNaturalNumber0(all_38_0)
% 27.06/4.36 |
% 27.06/4.36 | ALPHA: (19) implies:
% 27.06/4.36 | (20) aNaturalNumber0(all_38_0)
% 27.06/4.36 | (21) sdtlseqdt0(xp, xn)
% 27.06/4.36 | (22) $i(all_38_0)
% 27.06/4.36 | (23) sdtpldt0(xp, all_38_0) = xn
% 27.06/4.36 |
% 27.06/4.36 | DELTA: instantiating (12) with fresh symbol all_40_0 gives:
% 27.06/4.36 | (24) ~ (xr = xn) & sdtpldt0(xr, all_40_0) = xn & $i(all_40_0) &
% 27.06/4.36 | sdtlseqdt0(xr, xn) & aNaturalNumber0(all_40_0)
% 27.06/4.36 |
% 27.06/4.36 | ALPHA: (24) implies:
% 27.06/4.36 | (25) ~ (xr = xn)
% 27.06/4.36 | (26) aNaturalNumber0(all_40_0)
% 27.06/4.36 | (27) sdtlseqdt0(xr, xn)
% 27.06/4.36 | (28) $i(all_40_0)
% 27.06/4.36 | (29) sdtpldt0(xr, all_40_0) = xn
% 27.06/4.36 |
% 27.06/4.36 | DELTA: instantiating (17) with fresh symbols all_44_0, all_44_1, all_44_2,
% 27.06/4.36 | all_44_3 gives:
% 27.06/4.36 | (30) sdtpldt0(all_44_1, xp) = all_44_0 & sdtpldt0(all_44_3, xp) = all_44_2
% 27.06/4.36 | & sdtpldt0(xr, xm) = all_44_3 & sdtpldt0(xn, xm) = all_44_1 &
% 27.06/4.36 | $i(all_44_0) & $i(all_44_1) & $i(all_44_2) & $i(all_44_3) & (all_44_0
% 27.06/4.36 | = all_44_2 | ( ~ sdtlseqdt0(all_44_2, all_44_0) & ! [v0: $i] : ( ~
% 27.06/4.36 | (sdtpldt0(all_44_2, v0) = all_44_0) | ~ $i(v0) | ~
% 27.06/4.36 | aNaturalNumber0(v0))))
% 27.06/4.36 |
% 27.06/4.36 | ALPHA: (30) implies:
% 27.06/4.36 | (31) sdtpldt0(xn, xm) = all_44_1
% 27.06/4.36 | (32) sdtpldt0(xr, xm) = all_44_3
% 27.06/4.36 | (33) sdtpldt0(all_44_3, xp) = all_44_2
% 27.06/4.36 | (34) sdtpldt0(all_44_1, xp) = all_44_0
% 27.06/4.36 | (35) all_44_0 = all_44_2 | ( ~ sdtlseqdt0(all_44_2, all_44_0) & ! [v0: $i]
% 27.06/4.36 | : ( ~ (sdtpldt0(all_44_2, v0) = all_44_0) | ~ $i(v0) | ~
% 27.06/4.36 | aNaturalNumber0(v0)))
% 27.06/4.36 |
% 27.06/4.36 | DELTA: instantiating (7) with fresh symbols all_46_0, all_46_1 gives:
% 27.06/4.36 | (36) ~ (xp = sz10) & ~ (xp = sz00) & sdtasdt0(xp, all_46_0) = all_46_1 &
% 27.06/4.36 | sdtasdt0(xn, xm) = all_46_1 & $i(all_46_0) & $i(all_46_1) &
% 27.06/4.36 | isPrime0(xp) & doDivides0(xp, all_46_1) & aNaturalNumber0(all_46_0) &
% 27.06/4.36 | ! [v0: $i] : ! [v1: $i] : (v0 = xp | v0 = sz10 | ~ (sdtasdt0(v0, v1)
% 27.06/4.36 | = xp) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~
% 27.06/4.36 | aNaturalNumber0(v0)) & ! [v0: $i] : (v0 = xp | v0 = sz10 | ~
% 27.06/4.36 | $i(v0) | ~ doDivides0(v0, xp) | ~ aNaturalNumber0(v0))
% 27.06/4.36 |
% 27.06/4.36 | ALPHA: (36) implies:
% 27.06/4.36 | (37) ~ (xp = sz00)
% 27.06/4.36 | (38) ~ (xp = sz10)
% 27.06/4.36 |
% 27.06/4.36 | DELTA: instantiating (6) with fresh symbols all_49_0, all_49_1 gives:
% 27.25/4.37 | (39) sdtpldt0(all_49_1, xp) = all_49_0 & sdtpldt0(xn, xm) = all_49_1 &
% 27.25/4.37 | $i(all_49_0) & $i(all_49_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 27.25/4.37 | : ! [v3: $i] : ! [v4: $i] : (v2 = sz10 | v2 = sz00 | ~
% 27.25/4.37 | (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) |
% 27.25/4.37 | ~ $i(v1) | ~ $i(v0) | ~ iLess0(v4, all_49_0) | ~
% 27.25/4.37 | aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 27.25/4.37 | aNaturalNumber0(v0) | doDivides0(v2, v1) | doDivides0(v2, v0) | ?
% 27.25/4.37 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ($i(v7) &
% 27.25/4.37 | $i(v6) & ((v8 = v2 & ~ (v6 = v2) & ~ (v6 = sz10) & sdtasdt0(v6,
% 27.25/4.37 | v7) = v2 & doDivides0(v6, v2) & aNaturalNumber0(v7) &
% 27.25/4.37 | aNaturalNumber0(v6)) | (sdtasdt0(v0, v1) = v5 & $i(v5) & ~
% 27.25/4.37 | doDivides0(v2, v5) & ! [v9: $i] : ( ~ (sdtasdt0(v2, v9) = v5)
% 27.25/4.37 | | ~ $i(v9) | ~ aNaturalNumber0(v9)))))) & ! [v0: $i] : !
% 27.25/4.37 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = sz10 | v2 =
% 27.25/4.37 | sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~
% 27.25/4.37 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ iLess0(v4, all_49_0) | ~
% 27.25/4.37 | aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 27.25/4.37 | aNaturalNumber0(v0) | doDivides0(v2, v1) | ? [v5: $i] : ? [v6: $i]
% 27.25/4.37 | : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ($i(v9) &
% 27.25/4.37 | $i(v8) & $i(v6) & ((v10 = v2 & ~ (v8 = v2) & ~ (v8 = sz10) &
% 27.25/4.37 | sdtasdt0(v8, v9) = v2 & doDivides0(v8, v2) &
% 27.25/4.37 | aNaturalNumber0(v9) & aNaturalNumber0(v8)) | (v7 = v0 &
% 27.25/4.37 | sdtasdt0(v2, v6) = v0 & aNaturalNumber0(v6)) | (sdtasdt0(v0,
% 27.25/4.37 | v1) = v5 & $i(v5) & ~ doDivides0(v2, v5) & ! [v11: $i] : (
% 27.25/4.37 | ~ (sdtasdt0(v2, v11) = v5) | ~ $i(v11) | ~
% 27.25/4.37 | aNaturalNumber0(v11)))))) & ! [v0: $i] : ! [v1: $i] : !
% 27.25/4.37 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = sz10 | v2 = sz00 | ~
% 27.25/4.37 | (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) |
% 27.25/4.37 | ~ $i(v1) | ~ $i(v0) | ~ iLess0(v4, all_49_0) | ~
% 27.25/4.37 | aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 27.25/4.37 | aNaturalNumber0(v0) | doDivides0(v2, v0) | ? [v5: $i] : ? [v6: $i]
% 27.25/4.37 | : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ($i(v9) &
% 27.25/4.37 | $i(v8) & $i(v6) & ((v10 = v2 & ~ (v8 = v2) & ~ (v8 = sz10) &
% 27.25/4.37 | sdtasdt0(v8, v9) = v2 & doDivides0(v8, v2) &
% 27.25/4.37 | aNaturalNumber0(v9) & aNaturalNumber0(v8)) | (v7 = v1 &
% 27.25/4.37 | sdtasdt0(v2, v6) = v1 & aNaturalNumber0(v6)) | (sdtasdt0(v0,
% 27.25/4.37 | v1) = v5 & $i(v5) & ~ doDivides0(v2, v5) & ! [v11: $i] : (
% 27.25/4.37 | ~ (sdtasdt0(v2, v11) = v5) | ~ $i(v11) | ~
% 27.25/4.37 | aNaturalNumber0(v11)))))) & ! [v0: $i] : ! [v1: $i] : !
% 27.25/4.37 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = sz10 | v2 = sz00 | ~
% 27.25/4.37 | (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) |
% 27.25/4.37 | ~ $i(v1) | ~ $i(v0) | ~ iLess0(v4, all_49_0) | ~
% 27.25/4.37 | aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 27.25/4.37 | aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 27.25/4.37 | [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i]
% 27.25/4.37 | : ($i(v11) & $i(v10) & $i(v8) & $i(v6) & ((v12 = v2 & ~ (v10 = v2)
% 27.25/4.37 | & ~ (v10 = sz10) & sdtasdt0(v10, v11) = v2 & doDivides0(v10,
% 27.25/4.37 | v2) & aNaturalNumber0(v11) & aNaturalNumber0(v10)) | (v9 =
% 27.25/4.37 | v0 & sdtasdt0(v2, v8) = v0 & aNaturalNumber0(v8)) | (v7 = v1 &
% 27.25/4.37 | sdtasdt0(v2, v6) = v1 & aNaturalNumber0(v6)) | (sdtasdt0(v0,
% 27.25/4.37 | v1) = v5 & $i(v5) & ~ doDivides0(v2, v5) & ! [v13: $i] : (
% 27.25/4.37 | ~ (sdtasdt0(v2, v13) = v5) | ~ $i(v13) | ~
% 27.25/4.37 | aNaturalNumber0(v13)))))) & ! [v0: $i] : ! [v1: $i] : !
% 27.25/4.37 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v3, v2) = v4) |
% 27.25/4.37 | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 27.25/4.37 | isPrime0(v2) | ~ iLess0(v4, all_49_0) | ~ aNaturalNumber0(v2) | ~
% 27.25/4.37 | aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) |
% 27.25/4.37 | doDivides0(v2, v0) | ? [v5: $i] : (sdtasdt0(v0, v1) = v5 & $i(v5) &
% 27.25/4.37 | ~ doDivides0(v2, v5) & ! [v6: $i] : ( ~ (sdtasdt0(v2, v6) = v5)
% 27.25/4.37 | | ~ $i(v6) | ~ aNaturalNumber0(v6)))) & ! [v0: $i] : ! [v1:
% 27.25/4.37 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v3,
% 27.25/4.37 | v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) |
% 27.25/4.37 | ~ $i(v0) | ~ isPrime0(v2) | ~ iLess0(v4, all_49_0) | ~
% 27.25/4.37 | aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 27.25/4.37 | aNaturalNumber0(v0) | doDivides0(v2, v1) | ? [v5: $i] : ? [v6: $i]
% 27.25/4.37 | : ? [v7: $i] : ($i(v6) & ((v7 = v0 & sdtasdt0(v2, v6) = v0 &
% 27.25/4.37 | aNaturalNumber0(v6)) | (sdtasdt0(v0, v1) = v5 & $i(v5) & ~
% 27.25/4.37 | doDivides0(v2, v5) & ! [v8: $i] : ( ~ (sdtasdt0(v2, v8) = v5)
% 27.25/4.37 | | ~ $i(v8) | ~ aNaturalNumber0(v8)))))) & ! [v0: $i] : !
% 27.25/4.37 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v3,
% 27.25/4.37 | v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) |
% 27.25/4.37 | ~ $i(v0) | ~ isPrime0(v2) | ~ iLess0(v4, all_49_0) | ~
% 27.25/4.37 | aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 27.25/4.37 | aNaturalNumber0(v0) | doDivides0(v2, v0) | ? [v5: $i] : ? [v6: $i]
% 27.25/4.37 | : ? [v7: $i] : ($i(v6) & ((v7 = v1 & sdtasdt0(v2, v6) = v1 &
% 27.25/4.37 | aNaturalNumber0(v6)) | (sdtasdt0(v0, v1) = v5 & $i(v5) & ~
% 27.25/4.37 | doDivides0(v2, v5) & ! [v8: $i] : ( ~ (sdtasdt0(v2, v8) = v5)
% 27.25/4.37 | | ~ $i(v8) | ~ aNaturalNumber0(v8)))))) & ! [v0: $i] : !
% 27.25/4.37 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v3,
% 27.25/4.37 | v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) |
% 27.25/4.37 | ~ $i(v0) | ~ isPrime0(v2) | ~ iLess0(v4, all_49_0) | ~
% 27.25/4.37 | aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 27.25/4.37 | aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 27.25/4.37 | [v8: $i] : ? [v9: $i] : ($i(v8) & $i(v6) & ((v9 = v0 & sdtasdt0(v2,
% 27.25/4.37 | v8) = v0 & aNaturalNumber0(v8)) | (v7 = v1 & sdtasdt0(v2,
% 27.25/4.37 | v6) = v1 & aNaturalNumber0(v6)) | (sdtasdt0(v0, v1) = v5 &
% 27.25/4.37 | $i(v5) & ~ doDivides0(v2, v5) & ! [v10: $i] : ( ~
% 27.25/4.37 | (sdtasdt0(v2, v10) = v5) | ~ $i(v10) | ~
% 27.25/4.37 | aNaturalNumber0(v10))))))
% 27.25/4.37 |
% 27.25/4.37 | ALPHA: (39) implies:
% 27.25/4.37 | (40) sdtpldt0(xn, xm) = all_49_1
% 27.25/4.37 | (41) sdtpldt0(all_49_1, xp) = all_49_0
% 27.25/4.37 |
% 27.25/4.37 | GROUND_INST: instantiating (18) with all_44_1, all_49_1, xm, xn, simplifying
% 27.25/4.37 | with (31), (40) gives:
% 27.25/4.37 | (42) all_49_1 = all_44_1
% 27.25/4.37 |
% 27.25/4.37 | REDUCE: (41), (42) imply:
% 27.25/4.37 | (43) sdtpldt0(all_44_1, xp) = all_49_0
% 27.25/4.37 |
% 27.25/4.37 | GROUND_INST: instantiating (18) with all_44_0, all_49_0, xp, all_44_1,
% 27.25/4.37 | simplifying with (34), (43) gives:
% 27.25/4.37 | (44) all_49_0 = all_44_0
% 27.25/4.37 |
% 27.25/4.37 | GROUND_INST: instantiating (2) with xp, simplifying with (5), (15) gives:
% 27.25/4.37 | (45) xp = sz10 | xp = sz00 | ? [v0: $i] : ($i(v0) & isPrime0(v0) &
% 27.25/4.37 | doDivides0(v0, xp) & aNaturalNumber0(v0))
% 27.25/4.37 |
% 27.25/4.37 | GROUND_INST: instantiating (mSortsB) with xn, xm, all_44_1, simplifying with
% 27.25/4.37 | (3), (4), (13), (14), (31) gives:
% 27.25/4.37 | (46) aNaturalNumber0(all_44_1)
% 27.25/4.37 |
% 27.25/4.37 | GROUND_INST: instantiating (mAddComm) with xn, xm, all_44_1, simplifying with
% 27.25/4.37 | (3), (4), (13), (14), (31) gives:
% 27.25/4.37 | (47) sdtpldt0(xm, xn) = all_44_1 & $i(all_44_1)
% 27.25/4.37 |
% 27.25/4.37 | ALPHA: (47) implies:
% 27.25/4.37 | (48) sdtpldt0(xm, xn) = all_44_1
% 27.25/4.37 |
% 27.25/4.38 | GROUND_INST: instantiating (mAddAsso) with xp, xr, xm, xn, all_44_1,
% 27.25/4.38 | simplifying with (4), (5), (9), (10), (14), (15), (16), (31)
% 27.25/4.38 | gives:
% 27.25/4.38 | (49) ? [v0: $i] : (sdtpldt0(xr, xm) = v0 & sdtpldt0(xp, v0) = all_44_1 &
% 27.25/4.38 | $i(v0) & $i(all_44_1))
% 27.25/4.38 |
% 27.25/4.38 | GROUND_INST: instantiating (mAddAsso) with xp, all_38_0, xm, xn, all_44_1,
% 27.25/4.38 | simplifying with (4), (5), (14), (15), (20), (22), (23), (31)
% 27.25/4.38 | gives:
% 27.25/4.38 | (50) ? [v0: $i] : (sdtpldt0(all_38_0, xm) = v0 & sdtpldt0(xp, v0) =
% 27.25/4.38 | all_44_1 & $i(v0) & $i(all_44_1))
% 27.25/4.38 |
% 27.25/4.38 | GROUND_INST: instantiating (mAddComm) with xp, all_38_0, xn, simplifying with
% 27.25/4.38 | (5), (15), (20), (22), (23) gives:
% 27.25/4.38 | (51) sdtpldt0(all_38_0, xp) = xn & $i(xn)
% 27.25/4.38 |
% 27.25/4.38 | GROUND_INST: instantiating (mMonAdd) with xr, xn, xm, all_44_3, simplifying
% 27.25/4.38 | with (3), (4), (9), (13), (14), (16), (27), (32) gives:
% 27.25/4.38 | (52) xr = xn | ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ( ~ (v2 =
% 27.25/4.38 | all_44_3) & ~ (v1 = v0) & sdtpldt0(xm, xr) = v0 & sdtpldt0(xm,
% 27.25/4.38 | xn) = v1 & sdtpldt0(xn, xm) = v2 & $i(v2) & $i(v1) & $i(v0) &
% 27.25/4.38 | sdtlseqdt0(v0, v1) & sdtlseqdt0(all_44_3, v2))
% 27.25/4.38 |
% 27.25/4.38 | GROUND_INST: instantiating (mSortsB) with xr, xm, all_44_3, simplifying with
% 27.25/4.38 | (4), (9), (14), (16), (32) gives:
% 27.25/4.38 | (53) aNaturalNumber0(all_44_3)
% 27.25/4.38 |
% 27.25/4.38 | GROUND_INST: instantiating (mAddComm) with xr, xm, all_44_3, simplifying with
% 27.25/4.38 | (4), (9), (14), (16), (32) gives:
% 27.25/4.38 | (54) sdtpldt0(xm, xr) = all_44_3 & $i(all_44_3)
% 27.25/4.38 |
% 27.25/4.38 | ALPHA: (54) implies:
% 27.25/4.38 | (55) sdtpldt0(xm, xr) = all_44_3
% 27.25/4.38 |
% 27.25/4.38 | GROUND_INST: instantiating (mAddComm) with xr, all_40_0, xn, simplifying with
% 27.25/4.38 | (9), (16), (26), (28), (29) gives:
% 27.25/4.38 | (56) sdtpldt0(all_40_0, xr) = xn & $i(xn)
% 27.25/4.38 |
% 27.25/4.38 | GROUND_INST: instantiating (1) with xp, xn, xr, all_38_0, simplifying with
% 27.25/4.38 | (3), (5), (11), (13), (15), (20), (21), (22), (23) gives:
% 27.25/4.38 | (57) all_38_0 = xr
% 27.25/4.38 |
% 27.25/4.38 | DELTA: instantiating (49) with fresh symbol all_78_0 gives:
% 27.25/4.38 | (58) sdtpldt0(xr, xm) = all_78_0 & sdtpldt0(xp, all_78_0) = all_44_1 &
% 27.25/4.38 | $i(all_78_0) & $i(all_44_1)
% 27.25/4.38 |
% 27.25/4.38 | ALPHA: (58) implies:
% 27.25/4.38 | (59) $i(all_78_0)
% 27.25/4.38 | (60) sdtpldt0(xp, all_78_0) = all_44_1
% 27.25/4.38 | (61) sdtpldt0(xr, xm) = all_78_0
% 27.25/4.38 |
% 27.25/4.38 | DELTA: instantiating (50) with fresh symbol all_84_0 gives:
% 27.25/4.38 | (62) sdtpldt0(all_38_0, xm) = all_84_0 & sdtpldt0(xp, all_84_0) = all_44_1
% 27.25/4.38 | & $i(all_84_0) & $i(all_44_1)
% 27.25/4.38 |
% 27.25/4.38 | ALPHA: (62) implies:
% 27.25/4.38 | (63) sdtpldt0(all_38_0, xm) = all_84_0
% 27.25/4.38 |
% 27.25/4.38 | REDUCE: (57), (63) imply:
% 27.25/4.38 | (64) sdtpldt0(xr, xm) = all_84_0
% 27.25/4.38 |
% 27.25/4.38 | BETA: splitting (52) gives:
% 27.25/4.38 |
% 27.25/4.38 | Case 1:
% 27.25/4.38 | |
% 27.25/4.38 | | (65) xr = xn
% 27.25/4.38 | |
% 27.25/4.38 | | REDUCE: (25), (65) imply:
% 27.25/4.38 | | (66) $false
% 27.25/4.38 | |
% 27.25/4.38 | | CLOSE: (66) is inconsistent.
% 27.25/4.38 | |
% 27.25/4.38 | Case 2:
% 27.25/4.38 | |
% 27.25/4.38 | | (67) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ( ~ (v2 = all_44_3) & ~
% 27.25/4.38 | | (v1 = v0) & sdtpldt0(xm, xr) = v0 & sdtpldt0(xm, xn) = v1 &
% 27.25/4.38 | | sdtpldt0(xn, xm) = v2 & $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v0,
% 27.25/4.38 | | v1) & sdtlseqdt0(all_44_3, v2))
% 27.25/4.38 | |
% 27.25/4.38 | | DELTA: instantiating (67) with fresh symbols all_92_0, all_92_1, all_92_2
% 27.25/4.38 | | gives:
% 27.25/4.38 | | (68) ~ (all_92_0 = all_44_3) & ~ (all_92_1 = all_92_2) & sdtpldt0(xm,
% 27.25/4.38 | | xr) = all_92_2 & sdtpldt0(xm, xn) = all_92_1 & sdtpldt0(xn, xm) =
% 27.25/4.38 | | all_92_0 & $i(all_92_0) & $i(all_92_1) & $i(all_92_2) &
% 27.25/4.38 | | sdtlseqdt0(all_92_2, all_92_1) & sdtlseqdt0(all_44_3, all_92_0)
% 27.25/4.38 | |
% 27.25/4.38 | | ALPHA: (68) implies:
% 27.25/4.38 | | (69) ~ (all_92_1 = all_92_2)
% 27.25/4.38 | | (70) sdtlseqdt0(all_44_3, all_92_0)
% 27.25/4.38 | | (71) $i(all_92_1)
% 27.25/4.38 | | (72) sdtpldt0(xn, xm) = all_92_0
% 27.25/4.38 | | (73) sdtpldt0(xm, xn) = all_92_1
% 27.25/4.38 | | (74) sdtpldt0(xm, xr) = all_92_2
% 27.25/4.38 | |
% 27.25/4.38 | | BETA: splitting (45) gives:
% 27.25/4.38 | |
% 27.25/4.38 | | Case 1:
% 27.25/4.38 | | |
% 27.25/4.38 | | | (75) xp = sz00
% 27.25/4.38 | | |
% 27.25/4.39 | | | REDUCE: (37), (75) imply:
% 27.25/4.39 | | | (76) $false
% 27.25/4.39 | | |
% 27.25/4.39 | | | CLOSE: (76) is inconsistent.
% 27.25/4.39 | | |
% 27.25/4.39 | | Case 2:
% 27.25/4.39 | | |
% 27.25/4.39 | | | (77) xp = sz10 | ? [v0: $i] : ($i(v0) & isPrime0(v0) & doDivides0(v0,
% 27.25/4.39 | | | xp) & aNaturalNumber0(v0))
% 27.25/4.39 | | |
% 27.25/4.39 | | | BETA: splitting (77) gives:
% 27.25/4.39 | | |
% 27.25/4.39 | | | Case 1:
% 27.25/4.39 | | | |
% 27.25/4.39 | | | | (78) xp = sz10
% 27.25/4.39 | | | |
% 27.25/4.39 | | | | REDUCE: (38), (78) imply:
% 27.25/4.39 | | | | (79) $false
% 27.25/4.39 | | | |
% 27.25/4.39 | | | | CLOSE: (79) is inconsistent.
% 27.25/4.39 | | | |
% 27.25/4.39 | | | Case 2:
% 27.25/4.39 | | | |
% 27.25/4.39 | | | |
% 27.25/4.39 | | | | GROUND_INST: instantiating (18) with all_44_1, all_92_0, xm, xn,
% 27.25/4.39 | | | | simplifying with (31), (72) gives:
% 27.25/4.39 | | | | (80) all_92_0 = all_44_1
% 27.25/4.39 | | | |
% 27.25/4.39 | | | | GROUND_INST: instantiating (18) with all_44_1, all_92_1, xn, xm,
% 27.25/4.39 | | | | simplifying with (48), (73) gives:
% 27.25/4.39 | | | | (81) all_92_1 = all_44_1
% 27.25/4.39 | | | |
% 27.25/4.39 | | | | GROUND_INST: instantiating (18) with all_44_3, all_92_2, xr, xm,
% 27.25/4.39 | | | | simplifying with (55), (74) gives:
% 27.25/4.39 | | | | (82) all_92_2 = all_44_3
% 27.25/4.39 | | | |
% 27.25/4.39 | | | | GROUND_INST: instantiating (18) with all_44_3, all_84_0, xm, xr,
% 27.25/4.39 | | | | simplifying with (32), (64) gives:
% 27.25/4.39 | | | | (83) all_84_0 = all_44_3
% 27.25/4.39 | | | |
% 27.25/4.39 | | | | GROUND_INST: instantiating (18) with all_78_0, all_84_0, xm, xr,
% 27.25/4.39 | | | | simplifying with (61), (64) gives:
% 27.25/4.39 | | | | (84) all_84_0 = all_78_0
% 27.25/4.39 | | | |
% 27.25/4.39 | | | | COMBINE_EQS: (83), (84) imply:
% 27.25/4.39 | | | | (85) all_78_0 = all_44_3
% 27.25/4.39 | | | |
% 27.25/4.39 | | | | SIMP: (85) implies:
% 27.25/4.39 | | | | (86) all_78_0 = all_44_3
% 27.25/4.39 | | | |
% 27.25/4.39 | | | | REDUCE: (69), (81), (82) imply:
% 27.25/4.39 | | | | (87) ~ (all_44_1 = all_44_3)
% 27.25/4.39 | | | |
% 27.25/4.39 | | | | REDUCE: (60), (86) imply:
% 27.25/4.39 | | | | (88) sdtpldt0(xp, all_44_3) = all_44_1
% 27.25/4.39 | | | |
% 27.25/4.39 | | | | REDUCE: (71), (81) imply:
% 27.25/4.39 | | | | (89) $i(all_44_1)
% 27.25/4.39 | | | |
% 27.25/4.39 | | | | REDUCE: (59), (86) imply:
% 27.25/4.39 | | | | (90) $i(all_44_3)
% 27.25/4.39 | | | |
% 27.25/4.39 | | | | REDUCE: (70), (80) imply:
% 27.25/4.39 | | | | (91) sdtlseqdt0(all_44_3, all_44_1)
% 27.25/4.39 | | | |
% 27.25/4.39 | | | | GROUND_INST: instantiating (mAddComm) with all_44_1, xp, all_44_0,
% 27.25/4.39 | | | | simplifying with (5), (15), (34), (46), (89) gives:
% 27.25/4.39 | | | | (92) sdtpldt0(xp, all_44_1) = all_44_0 & $i(all_44_0)
% 27.25/4.39 | | | |
% 27.25/4.39 | | | | ALPHA: (92) implies:
% 27.25/4.39 | | | | (93) sdtpldt0(xp, all_44_1) = all_44_0
% 27.25/4.39 | | | |
% 27.25/4.39 | | | | GROUND_INST: instantiating (mMonAdd) with all_44_3, all_44_1, xp,
% 27.25/4.39 | | | | all_44_2, simplifying with (5), (15), (33), (46), (53),
% 27.25/4.39 | | | | (89), (90), (91) gives:
% 27.25/4.39 | | | | (94) all_44_1 = all_44_3 | ? [v0: $i] : ? [v1: $i] : ? [v2: any] :
% 27.25/4.39 | | | | ( ~ (v2 = all_44_2) & ~ (v1 = v0) & sdtpldt0(all_44_1, xp) = v2
% 27.25/4.39 | | | | & sdtpldt0(xp, all_44_1) = v1 & sdtpldt0(xp, all_44_3) = v0 &
% 27.25/4.39 | | | | $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1) &
% 27.25/4.39 | | | | sdtlseqdt0(all_44_2, v2))
% 27.25/4.39 | | | |
% 27.25/4.39 | | | | GROUND_INST: instantiating (mAddAsso) with xp, all_44_3, xp, all_44_1,
% 27.25/4.39 | | | | all_44_0, simplifying with (5), (15), (34), (53), (88),
% 27.25/4.39 | | | | (90) gives:
% 27.25/4.39 | | | | (95) ? [v0: $i] : (sdtpldt0(all_44_3, xp) = v0 & sdtpldt0(xp, v0) =
% 27.25/4.39 | | | | all_44_0 & $i(v0) & $i(all_44_0))
% 27.25/4.39 | | | |
% 27.25/4.39 | | | | GROUND_INST: instantiating (mAddComm) with xp, all_44_3, all_44_1,
% 27.25/4.39 | | | | simplifying with (5), (15), (53), (88), (90) gives:
% 27.25/4.39 | | | | (96) sdtpldt0(all_44_3, xp) = all_44_1 & $i(all_44_1)
% 27.25/4.39 | | | |
% 27.25/4.39 | | | | ALPHA: (96) implies:
% 27.25/4.39 | | | | (97) sdtpldt0(all_44_3, xp) = all_44_1
% 27.25/4.39 | | | |
% 27.25/4.39 | | | | DELTA: instantiating (95) with fresh symbol all_172_0 gives:
% 27.25/4.39 | | | | (98) sdtpldt0(all_44_3, xp) = all_172_0 & sdtpldt0(xp, all_172_0) =
% 27.25/4.39 | | | | all_44_0 & $i(all_172_0) & $i(all_44_0)
% 27.25/4.39 | | | |
% 27.25/4.39 | | | | ALPHA: (98) implies:
% 27.25/4.39 | | | | (99) sdtpldt0(all_44_3, xp) = all_172_0
% 27.25/4.39 | | | |
% 27.25/4.39 | | | | BETA: splitting (94) gives:
% 27.25/4.39 | | | |
% 27.25/4.39 | | | | Case 1:
% 27.25/4.39 | | | | |
% 27.25/4.39 | | | | | (100) all_44_1 = all_44_3
% 27.25/4.39 | | | | |
% 27.25/4.39 | | | | | REDUCE: (87), (100) imply:
% 27.25/4.39 | | | | | (101) $false
% 27.25/4.39 | | | | |
% 27.25/4.39 | | | | | CLOSE: (101) is inconsistent.
% 27.25/4.39 | | | | |
% 27.25/4.39 | | | | Case 2:
% 27.25/4.39 | | | | |
% 27.25/4.39 | | | | | (102) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ( ~ (v2 =
% 27.25/4.39 | | | | | all_44_2) & ~ (v1 = v0) & sdtpldt0(all_44_1, xp) = v2 &
% 27.25/4.39 | | | | | sdtpldt0(xp, all_44_1) = v1 & sdtpldt0(xp, all_44_3) = v0 &
% 27.25/4.39 | | | | | $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1) &
% 27.25/4.39 | | | | | sdtlseqdt0(all_44_2, v2))
% 27.25/4.39 | | | | |
% 27.25/4.39 | | | | | DELTA: instantiating (102) with fresh symbols all_192_0, all_192_1,
% 27.25/4.39 | | | | | all_192_2 gives:
% 27.25/4.39 | | | | | (103) ~ (all_192_0 = all_44_2) & ~ (all_192_1 = all_192_2) &
% 27.25/4.39 | | | | | sdtpldt0(all_44_1, xp) = all_192_0 & sdtpldt0(xp, all_44_1) =
% 27.25/4.39 | | | | | all_192_1 & sdtpldt0(xp, all_44_3) = all_192_2 &
% 27.25/4.39 | | | | | $i(all_192_0) & $i(all_192_1) & $i(all_192_2) &
% 27.25/4.39 | | | | | sdtlseqdt0(all_192_2, all_192_1) & sdtlseqdt0(all_44_2,
% 27.25/4.39 | | | | | all_192_0)
% 27.25/4.39 | | | | |
% 27.25/4.39 | | | | | ALPHA: (103) implies:
% 27.25/4.39 | | | | | (104) ~ (all_192_1 = all_192_2)
% 27.25/4.39 | | | | | (105) sdtlseqdt0(all_44_2, all_192_0)
% 27.25/4.39 | | | | | (106) sdtpldt0(xp, all_44_3) = all_192_2
% 27.25/4.39 | | | | | (107) sdtpldt0(xp, all_44_1) = all_192_1
% 27.25/4.39 | | | | | (108) sdtpldt0(all_44_1, xp) = all_192_0
% 27.25/4.39 | | | | |
% 27.25/4.39 | | | | | GROUND_INST: instantiating (18) with all_44_1, all_192_2, all_44_3,
% 27.25/4.39 | | | | | xp, simplifying with (88), (106) gives:
% 27.25/4.39 | | | | | (109) all_192_2 = all_44_1
% 27.25/4.39 | | | | |
% 27.25/4.39 | | | | | GROUND_INST: instantiating (18) with all_44_0, all_192_1, all_44_1,
% 27.25/4.39 | | | | | xp, simplifying with (93), (107) gives:
% 27.25/4.39 | | | | | (110) all_192_1 = all_44_0
% 27.25/4.39 | | | | |
% 27.25/4.39 | | | | | GROUND_INST: instantiating (18) with all_44_2, all_172_0, xp,
% 27.25/4.39 | | | | | all_44_3, simplifying with (33), (99) gives:
% 27.25/4.39 | | | | | (111) all_172_0 = all_44_2
% 27.25/4.39 | | | | |
% 27.25/4.39 | | | | | GROUND_INST: instantiating (18) with all_44_1, all_172_0, xp,
% 27.25/4.39 | | | | | all_44_3, simplifying with (97), (99) gives:
% 27.25/4.39 | | | | | (112) all_172_0 = all_44_1
% 27.25/4.39 | | | | |
% 27.25/4.39 | | | | | GROUND_INST: instantiating (18) with all_44_0, all_192_0, xp,
% 27.25/4.39 | | | | | all_44_1, simplifying with (34), (108) gives:
% 27.25/4.39 | | | | | (113) all_192_0 = all_44_0
% 27.25/4.39 | | | | |
% 27.25/4.39 | | | | | COMBINE_EQS: (111), (112) imply:
% 27.25/4.39 | | | | | (114) all_44_1 = all_44_2
% 27.25/4.39 | | | | |
% 27.25/4.39 | | | | | SIMP: (114) implies:
% 27.25/4.39 | | | | | (115) all_44_1 = all_44_2
% 27.25/4.39 | | | | |
% 27.25/4.39 | | | | | COMBINE_EQS: (109), (115) imply:
% 27.25/4.39 | | | | | (116) all_192_2 = all_44_2
% 27.25/4.39 | | | | |
% 27.25/4.39 | | | | | REDUCE: (104), (110), (116) imply:
% 27.25/4.40 | | | | | (117) ~ (all_44_0 = all_44_2)
% 27.25/4.40 | | | | |
% 27.25/4.40 | | | | | REDUCE: (105), (113) imply:
% 27.25/4.40 | | | | | (118) sdtlseqdt0(all_44_2, all_44_0)
% 27.25/4.40 | | | | |
% 27.25/4.40 | | | | | BETA: splitting (35) gives:
% 27.25/4.40 | | | | |
% 27.25/4.40 | | | | | Case 1:
% 27.25/4.40 | | | | | |
% 27.25/4.40 | | | | | | (119) all_44_0 = all_44_2
% 27.25/4.40 | | | | | |
% 27.25/4.40 | | | | | | REDUCE: (117), (119) imply:
% 27.25/4.40 | | | | | | (120) $false
% 27.25/4.40 | | | | | |
% 27.25/4.40 | | | | | | CLOSE: (120) is inconsistent.
% 27.25/4.40 | | | | | |
% 27.25/4.40 | | | | | Case 2:
% 27.25/4.40 | | | | | |
% 27.25/4.40 | | | | | | (121) ~ sdtlseqdt0(all_44_2, all_44_0) & ! [v0: $i] : ( ~
% 27.25/4.40 | | | | | | (sdtpldt0(all_44_2, v0) = all_44_0) | ~ $i(v0) | ~
% 27.25/4.40 | | | | | | aNaturalNumber0(v0))
% 27.25/4.40 | | | | | |
% 27.25/4.40 | | | | | | ALPHA: (121) implies:
% 27.25/4.40 | | | | | | (122) ~ sdtlseqdt0(all_44_2, all_44_0)
% 27.25/4.40 | | | | | |
% 27.25/4.40 | | | | | | PRED_UNIFY: (118), (122) imply:
% 27.25/4.40 | | | | | | (123) $false
% 27.25/4.40 | | | | | |
% 27.25/4.40 | | | | | | CLOSE: (123) is inconsistent.
% 27.25/4.40 | | | | | |
% 27.25/4.40 | | | | | End of split
% 27.25/4.40 | | | | |
% 27.25/4.40 | | | | End of split
% 27.25/4.40 | | | |
% 27.25/4.40 | | | End of split
% 27.25/4.40 | | |
% 27.25/4.40 | | End of split
% 27.25/4.40 | |
% 27.25/4.40 | End of split
% 27.25/4.40 |
% 27.25/4.40 End of proof
% 27.25/4.40 % SZS output end Proof for theBenchmark
% 27.25/4.40
% 27.25/4.40 3769ms
%------------------------------------------------------------------------------