TSTP Solution File: RNG046+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG046+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 : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 13:57:32 EDT 2023
% Result : Theorem 8.89s 1.93s
% Output : Proof 12.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG046+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 : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 03:03:26 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.64/0.62 ________ _____
% 0.64/0.62 ___ __ \_________(_)________________________________
% 0.64/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.64/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.64/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.64/0.62
% 0.64/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.64/0.62 (2023-06-19)
% 0.64/0.62
% 0.64/0.62 (c) Philipp Rümmer, 2009-2023
% 0.64/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.64/0.62 Amanda Stjerna.
% 0.64/0.62 Free software under BSD-3-Clause.
% 0.64/0.62
% 0.64/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.64/0.62
% 0.64/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.64/0.63 Running up to 7 provers in parallel.
% 0.69/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.69/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.69/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.69/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.69/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.69/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.69/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.62/1.08 Prover 1: Preprocessing ...
% 2.62/1.08 Prover 4: Preprocessing ...
% 2.62/1.12 Prover 0: Preprocessing ...
% 2.62/1.12 Prover 2: Preprocessing ...
% 2.62/1.12 Prover 6: Preprocessing ...
% 2.62/1.12 Prover 5: Preprocessing ...
% 2.62/1.12 Prover 3: Preprocessing ...
% 5.43/1.48 Prover 3: Constructing countermodel ...
% 5.43/1.48 Prover 1: Constructing countermodel ...
% 5.43/1.50 Prover 6: Constructing countermodel ...
% 6.10/1.58 Prover 4: Constructing countermodel ...
% 6.10/1.60 Prover 5: Constructing countermodel ...
% 7.08/1.70 Prover 0: Proving ...
% 7.08/1.74 Prover 2: Proving ...
% 8.89/1.92 Prover 0: proved (1286ms)
% 8.89/1.93
% 8.89/1.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.89/1.93
% 8.89/1.93 Prover 3: stopped
% 8.89/1.93 Prover 2: stopped
% 8.89/1.94 Prover 5: stopped
% 8.89/1.94 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.89/1.94 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.89/1.94 Prover 6: stopped
% 8.89/1.95 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.89/1.95 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.89/1.95 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.24/1.98 Prover 7: Preprocessing ...
% 9.24/1.98 Prover 10: Preprocessing ...
% 9.24/2.01 Prover 11: Preprocessing ...
% 9.24/2.01 Prover 13: Preprocessing ...
% 9.24/2.01 Prover 8: Preprocessing ...
% 9.98/2.08 Prover 10: Constructing countermodel ...
% 9.98/2.08 Prover 8: Warning: ignoring some quantifiers
% 9.98/2.09 Prover 8: Constructing countermodel ...
% 10.38/2.14 Prover 13: Constructing countermodel ...
% 10.58/2.17 Prover 11: Constructing countermodel ...
% 10.58/2.17 Prover 7: Constructing countermodel ...
% 10.58/2.19 Prover 10: gave up
% 10.58/2.19 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 10.58/2.22 Prover 16: Preprocessing ...
% 11.16/2.25 Prover 4: Found proof (size 89)
% 11.16/2.25 Prover 4: proved (1604ms)
% 11.16/2.25 Prover 13: stopped
% 11.16/2.25 Prover 1: stopped
% 11.16/2.25 Prover 8: stopped
% 11.16/2.25 Prover 11: stopped
% 11.16/2.25 Prover 16: stopped
% 11.16/2.25 Prover 7: stopped
% 11.16/2.26
% 11.16/2.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.16/2.26
% 11.16/2.28 % SZS output start Proof for theBenchmark
% 11.16/2.28 Assumptions after simplification:
% 11.16/2.28 ---------------------------------
% 11.16/2.28
% 11.16/2.28 (mMNeg)
% 11.53/2.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (smndt0(v1) = v2)
% 11.53/2.31 | ~ (sdtasdt0(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ?
% 11.53/2.32 [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 11.53/2.32 (smndt0(v6) = v7 & smndt0(v0) = v8 & sdtasdt0(v8, v1) = v9 & sdtasdt0(v0,
% 11.53/2.32 v1) = v6 & aScalar0(v1) = v5 & aScalar0(v0) = v4 & $i(v9) & $i(v8) &
% 11.53/2.32 $i(v7) & $i(v6) & ( ~ (v5 = 0) | ~ (v4 = 0) | (v9 = v3 & v7 = v3)))) & !
% 11.53/2.32 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (smndt0(v0) = v2) |
% 11.53/2.32 ~ (sdtasdt0(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5:
% 11.53/2.32 any] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (smndt0(v8)
% 11.53/2.32 = v9 & smndt0(v1) = v6 & sdtasdt0(v0, v6) = v7 & sdtasdt0(v0, v1) = v8 &
% 11.53/2.32 aScalar0(v1) = v5 & aScalar0(v0) = v4 & $i(v9) & $i(v8) & $i(v7) & $i(v6)
% 11.53/2.32 & ( ~ (v5 = 0) | ~ (v4 = 0) | (v9 = v3 & v7 = v3)))) & ! [v0: $i] : !
% 11.53/2.32 [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 11.53/2.32 ? [v3: any] : ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 11.53/2.32 [v8: $i] : ? [v9: $i] : (smndt0(v2) = v7 & smndt0(v1) = v5 & smndt0(v0) =
% 11.53/2.32 v8 & sdtasdt0(v8, v1) = v9 & sdtasdt0(v0, v5) = v6 & aScalar0(v1) = v4 &
% 11.53/2.32 aScalar0(v0) = v3 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & ( ~ (v4 =
% 11.53/2.32 0) | ~ (v3 = 0) | (v9 = v6 & v7 = v6))))
% 11.53/2.32
% 11.53/2.32 (mMulSc)
% 11.53/2.32 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 11.53/2.32 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 11.53/2.32 (aScalar0(v2) = v5 & aScalar0(v1) = v4 & aScalar0(v0) = v3 & ( ~ (v4 = 0) |
% 11.53/2.32 ~ (v3 = 0) | v5 = 0)))
% 11.53/2.32
% 11.53/2.32 (mNegSc)
% 11.53/2.32 ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ? [v2: any] :
% 11.53/2.32 ? [v3: any] : (aScalar0(v1) = v3 & aScalar0(v0) = v2 & ( ~ (v2 = 0) | v3 =
% 11.53/2.32 0))) & ! [v0: $i] : ( ~ (aScalar0(v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 11.53/2.32 (smndt0(v0) = v1 & aScalar0(v1) = 0 & $i(v1)))
% 11.53/2.32
% 11.53/2.32 (mScZero)
% 11.53/2.33 $i(sz0z00) & ? [v0: $i] : (smndt0(sz0z00) = v0 & $i(v0) & ! [v1: $i] : !
% 11.53/2.33 [v2: $i] : ( ~ (smndt0(v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] :
% 11.53/2.33 ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 11.53/2.33 [v10: $i] : (smndt0(v2) = v10 & sdtasdt0(v1, sz0z00) = v6 &
% 11.53/2.33 sdtasdt0(sz0z00, v1) = v7 & sdtpldt0(v2, v1) = v9 & sdtpldt0(v1, v2) =
% 11.53/2.33 v8 & sdtpldt0(v1, sz0z00) = v4 & sdtpldt0(sz0z00, v1) = v5 &
% 11.53/2.33 aScalar0(v1) = v3 & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5)
% 11.53/2.33 & $i(v4) & ( ~ (v3 = 0) | (v10 = v1 & v9 = sz0z00 & v8 = sz0z00 & v7 =
% 11.53/2.33 sz0z00 & v6 = sz0z00 & v5 = v1 & v4 = v1 & v0 = sz0z00)))) & ! [v1:
% 11.53/2.33 $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, sz0z00) = v2) | ~ $i(v1) | ? [v3:
% 11.53/2.33 any] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 11.53/2.33 $i] : ? [v9: $i] : ? [v10: $i] : (smndt0(v7) = v10 & smndt0(v1) = v7 &
% 11.53/2.33 sdtasdt0(sz0z00, v1) = v6 & sdtpldt0(v7, v1) = v9 & sdtpldt0(v1, v7) =
% 11.53/2.33 v8 & sdtpldt0(v1, sz0z00) = v4 & sdtpldt0(sz0z00, v1) = v5 &
% 11.53/2.33 aScalar0(v1) = v3 & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5)
% 11.53/2.33 & $i(v4) & ( ~ (v3 = 0) | (v10 = v1 & v9 = sz0z00 & v8 = sz0z00 & v6 =
% 11.53/2.33 sz0z00 & v5 = v1 & v4 = v1 & v2 = sz0z00 & v0 = sz0z00)))) & ! [v1:
% 11.53/2.33 $i] : ! [v2: $i] : ( ~ (sdtasdt0(sz0z00, v1) = v2) | ~ $i(v1) | ? [v3:
% 11.53/2.33 any] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 11.53/2.33 $i] : ? [v9: $i] : ? [v10: $i] : (smndt0(v7) = v10 & smndt0(v1) = v7 &
% 11.53/2.33 sdtasdt0(v1, sz0z00) = v6 & sdtpldt0(v7, v1) = v9 & sdtpldt0(v1, v7) =
% 11.53/2.33 v8 & sdtpldt0(v1, sz0z00) = v4 & sdtpldt0(sz0z00, v1) = v5 &
% 11.53/2.33 aScalar0(v1) = v3 & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5)
% 11.53/2.33 & $i(v4) & ( ~ (v3 = 0) | (v10 = v1 & v9 = sz0z00 & v8 = sz0z00 & v6 =
% 11.53/2.33 sz0z00 & v5 = v1 & v4 = v1 & v2 = sz0z00 & v0 = sz0z00)))) & ! [v1:
% 11.53/2.33 $i] : ! [v2: $i] : ( ~ (sdtpldt0(v1, sz0z00) = v2) | ~ $i(v1) | ? [v3:
% 11.53/2.33 any] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 11.53/2.33 $i] : ? [v9: $i] : ? [v10: $i] : (smndt0(v7) = v10 & smndt0(v1) = v7 &
% 11.53/2.33 sdtasdt0(v1, sz0z00) = v5 & sdtasdt0(sz0z00, v1) = v6 & sdtpldt0(v7, v1)
% 11.53/2.33 = v9 & sdtpldt0(v1, v7) = v8 & sdtpldt0(sz0z00, v1) = v4 & aScalar0(v1)
% 11.53/2.33 = v3 & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & (
% 11.53/2.33 ~ (v3 = 0) | (v10 = v1 & v9 = sz0z00 & v8 = sz0z00 & v6 = sz0z00 & v5
% 11.53/2.33 = sz0z00 & v4 = v1 & v2 = v1 & v0 = sz0z00)))) & ! [v1: $i] : !
% 11.53/2.33 [v2: $i] : ( ~ (sdtpldt0(sz0z00, v1) = v2) | ~ $i(v1) | ? [v3: any] : ?
% 11.53/2.33 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9:
% 11.53/2.33 $i] : ? [v10: $i] : (smndt0(v7) = v10 & smndt0(v1) = v7 & sdtasdt0(v1,
% 11.53/2.33 sz0z00) = v5 & sdtasdt0(sz0z00, v1) = v6 & sdtpldt0(v7, v1) = v9 &
% 11.53/2.33 sdtpldt0(v1, v7) = v8 & sdtpldt0(v1, sz0z00) = v4 & aScalar0(v1) = v3 &
% 11.53/2.33 $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & ( ~ (v3
% 11.53/2.33 = 0) | (v10 = v1 & v9 = sz0z00 & v8 = sz0z00 & v6 = sz0z00 & v5 =
% 11.53/2.33 sz0z00 & v4 = v1 & v2 = v1 & v0 = sz0z00)))) & ! [v1: $i] : (v0 =
% 11.53/2.33 sz0z00 | ~ (aScalar0(v1) = 0) | ~ $i(v1)) & ! [v1: $i] : ( ~
% 11.53/2.33 (aScalar0(v1) = 0) | ~ $i(v1) | ? [v2: $i] : (smndt0(v2) = v1 &
% 11.53/2.33 smndt0(v1) = v2 & sdtasdt0(v1, sz0z00) = sz0z00 & sdtasdt0(sz0z00, v1) =
% 11.53/2.33 sz0z00 & sdtpldt0(v2, v1) = sz0z00 & sdtpldt0(v1, v2) = sz0z00 &
% 11.53/2.33 sdtpldt0(v1, sz0z00) = v1 & sdtpldt0(sz0z00, v1) = v1 & $i(v2))))
% 11.53/2.33
% 11.53/2.33 (m__)
% 11.53/2.34 $i(xy) & $i(xx) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~
% 11.53/2.34 (v3 = v2) & smndt0(xy) = v1 & smndt0(xx) = v0 & sdtasdt0(v0, v1) = v2 &
% 11.53/2.34 sdtasdt0(xx, xy) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 11.53/2.34
% 11.53/2.34 (m__799)
% 11.53/2.34 aScalar0(xy) = 0 & aScalar0(xx) = 0 & $i(xy) & $i(xx)
% 11.53/2.34
% 11.53/2.34 (function-axioms)
% 11.53/2.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.53/2.34 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 11.53/2.34 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) |
% 11.53/2.34 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.53/2.34 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (iLess0(v3,
% 11.53/2.34 v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 11.53/2.34 [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) & ! [v0:
% 11.53/2.34 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 11.53/2.34 ~ (aScalar0(v2) = v1) | ~ (aScalar0(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 11.53/2.34 : ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 11.53/2.34 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 11.53/2.34 $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) =
% 11.53/2.34 v0))
% 11.53/2.34
% 11.53/2.34 Further assumptions not needed in the proof:
% 11.53/2.34 --------------------------------------------
% 11.53/2.34 mArith, mDistr, mDistr2, mIH, mIHOrd, mNatExtr, mNatSort, mSZeroSc, mScSort,
% 11.53/2.34 mSuccEqu, mSuccNat, mSumSc, mZeroNat
% 11.53/2.34
% 11.53/2.34 Those formulas are unsatisfiable:
% 11.53/2.34 ---------------------------------
% 11.53/2.34
% 11.53/2.34 Begin of proof
% 11.53/2.34 |
% 11.53/2.34 | ALPHA: (mNegSc) implies:
% 11.53/2.34 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ? [v2:
% 11.53/2.34 | any] : ? [v3: any] : (aScalar0(v1) = v3 & aScalar0(v0) = v2 & ( ~
% 11.53/2.34 | (v2 = 0) | v3 = 0)))
% 11.53/2.34 |
% 11.53/2.34 | ALPHA: (mScZero) implies:
% 11.53/2.35 | (2) ? [v0: $i] : (smndt0(sz0z00) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i]
% 11.53/2.35 | : ( ~ (smndt0(v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : ?
% 11.53/2.35 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 11.53/2.35 | ? [v10: $i] : (smndt0(v2) = v10 & sdtasdt0(v1, sz0z00) = v6 &
% 11.53/2.35 | sdtasdt0(sz0z00, v1) = v7 & sdtpldt0(v2, v1) = v9 & sdtpldt0(v1,
% 11.53/2.35 | v2) = v8 & sdtpldt0(v1, sz0z00) = v4 & sdtpldt0(sz0z00, v1) =
% 11.53/2.35 | v5 & aScalar0(v1) = v3 & $i(v10) & $i(v9) & $i(v8) & $i(v7) &
% 11.53/2.35 | $i(v6) & $i(v5) & $i(v4) & ( ~ (v3 = 0) | (v10 = v1 & v9 = sz0z00
% 11.53/2.35 | & v8 = sz0z00 & v7 = sz0z00 & v6 = sz0z00 & v5 = v1 & v4 = v1
% 11.53/2.35 | & v0 = sz0z00)))) & ! [v1: $i] : ! [v2: $i] : ( ~
% 11.53/2.35 | (sdtasdt0(v1, sz0z00) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4:
% 11.53/2.35 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ?
% 11.53/2.35 | [v9: $i] : ? [v10: $i] : (smndt0(v7) = v10 & smndt0(v1) = v7 &
% 11.53/2.35 | sdtasdt0(sz0z00, v1) = v6 & sdtpldt0(v7, v1) = v9 & sdtpldt0(v1,
% 11.53/2.35 | v7) = v8 & sdtpldt0(v1, sz0z00) = v4 & sdtpldt0(sz0z00, v1) =
% 11.53/2.35 | v5 & aScalar0(v1) = v3 & $i(v10) & $i(v9) & $i(v8) & $i(v7) &
% 11.53/2.35 | $i(v6) & $i(v5) & $i(v4) & ( ~ (v3 = 0) | (v10 = v1 & v9 = sz0z00
% 11.53/2.35 | & v8 = sz0z00 & v6 = sz0z00 & v5 = v1 & v4 = v1 & v2 = sz0z00
% 11.53/2.35 | & v0 = sz0z00)))) & ! [v1: $i] : ! [v2: $i] : ( ~
% 11.53/2.35 | (sdtasdt0(sz0z00, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4:
% 11.53/2.35 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ?
% 11.53/2.35 | [v9: $i] : ? [v10: $i] : (smndt0(v7) = v10 & smndt0(v1) = v7 &
% 11.53/2.35 | sdtasdt0(v1, sz0z00) = v6 & sdtpldt0(v7, v1) = v9 & sdtpldt0(v1,
% 11.53/2.35 | v7) = v8 & sdtpldt0(v1, sz0z00) = v4 & sdtpldt0(sz0z00, v1) =
% 11.53/2.35 | v5 & aScalar0(v1) = v3 & $i(v10) & $i(v9) & $i(v8) & $i(v7) &
% 11.53/2.35 | $i(v6) & $i(v5) & $i(v4) & ( ~ (v3 = 0) | (v10 = v1 & v9 = sz0z00
% 11.53/2.35 | & v8 = sz0z00 & v6 = sz0z00 & v5 = v1 & v4 = v1 & v2 = sz0z00
% 11.53/2.36 | & v0 = sz0z00)))) & ! [v1: $i] : ! [v2: $i] : ( ~
% 11.53/2.36 | (sdtpldt0(v1, sz0z00) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4:
% 11.53/2.36 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ?
% 11.53/2.36 | [v9: $i] : ? [v10: $i] : (smndt0(v7) = v10 & smndt0(v1) = v7 &
% 11.53/2.36 | sdtasdt0(v1, sz0z00) = v5 & sdtasdt0(sz0z00, v1) = v6 &
% 11.53/2.36 | sdtpldt0(v7, v1) = v9 & sdtpldt0(v1, v7) = v8 & sdtpldt0(sz0z00,
% 11.53/2.36 | v1) = v4 & aScalar0(v1) = v3 & $i(v10) & $i(v9) & $i(v8) &
% 11.53/2.36 | $i(v7) & $i(v6) & $i(v5) & $i(v4) & ( ~ (v3 = 0) | (v10 = v1 & v9
% 11.53/2.36 | = sz0z00 & v8 = sz0z00 & v6 = sz0z00 & v5 = sz0z00 & v4 = v1
% 11.53/2.36 | & v2 = v1 & v0 = sz0z00)))) & ! [v1: $i] : ! [v2: $i] : ( ~
% 11.53/2.36 | (sdtpldt0(sz0z00, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4:
% 11.53/2.36 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ?
% 11.53/2.36 | [v9: $i] : ? [v10: $i] : (smndt0(v7) = v10 & smndt0(v1) = v7 &
% 11.53/2.36 | sdtasdt0(v1, sz0z00) = v5 & sdtasdt0(sz0z00, v1) = v6 &
% 11.53/2.36 | sdtpldt0(v7, v1) = v9 & sdtpldt0(v1, v7) = v8 & sdtpldt0(v1,
% 11.53/2.36 | sz0z00) = v4 & aScalar0(v1) = v3 & $i(v10) & $i(v9) & $i(v8) &
% 11.53/2.36 | $i(v7) & $i(v6) & $i(v5) & $i(v4) & ( ~ (v3 = 0) | (v10 = v1 & v9
% 11.53/2.36 | = sz0z00 & v8 = sz0z00 & v6 = sz0z00 & v5 = sz0z00 & v4 = v1
% 11.53/2.36 | & v2 = v1 & v0 = sz0z00)))) & ! [v1: $i] : (v0 = sz0z00 | ~
% 11.53/2.36 | (aScalar0(v1) = 0) | ~ $i(v1)) & ! [v1: $i] : ( ~ (aScalar0(v1) =
% 11.53/2.36 | 0) | ~ $i(v1) | ? [v2: $i] : (smndt0(v2) = v1 & smndt0(v1) = v2
% 11.53/2.36 | & sdtasdt0(v1, sz0z00) = sz0z00 & sdtasdt0(sz0z00, v1) = sz0z00 &
% 11.53/2.36 | sdtpldt0(v2, v1) = sz0z00 & sdtpldt0(v1, v2) = sz0z00 &
% 11.53/2.36 | sdtpldt0(v1, sz0z00) = v1 & sdtpldt0(sz0z00, v1) = v1 & $i(v2))))
% 11.53/2.36 |
% 11.53/2.36 | ALPHA: (mMNeg) implies:
% 11.89/2.36 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) |
% 11.89/2.36 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 11.89/2.36 | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (smndt0(v2) =
% 11.89/2.36 | v7 & smndt0(v1) = v5 & smndt0(v0) = v8 & sdtasdt0(v8, v1) = v9 &
% 11.89/2.36 | sdtasdt0(v0, v5) = v6 & aScalar0(v1) = v4 & aScalar0(v0) = v3 &
% 11.89/2.36 | $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & ( ~ (v4 = 0) | ~ (v3
% 11.89/2.36 | = 0) | (v9 = v6 & v7 = v6))))
% 11.89/2.36 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (smndt0(v0)
% 11.89/2.36 | = v2) | ~ (sdtasdt0(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ?
% 11.89/2.36 | [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 11.89/2.36 | ? [v9: $i] : (smndt0(v8) = v9 & smndt0(v1) = v6 & sdtasdt0(v0, v6) =
% 11.89/2.36 | v7 & sdtasdt0(v0, v1) = v8 & aScalar0(v1) = v5 & aScalar0(v0) = v4
% 11.89/2.36 | & $i(v9) & $i(v8) & $i(v7) & $i(v6) & ( ~ (v5 = 0) | ~ (v4 = 0) |
% 11.89/2.36 | (v9 = v3 & v7 = v3))))
% 11.89/2.36 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (smndt0(v1)
% 11.89/2.36 | = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ?
% 11.89/2.36 | [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 11.89/2.36 | ? [v9: $i] : (smndt0(v6) = v7 & smndt0(v0) = v8 & sdtasdt0(v8, v1) =
% 11.89/2.36 | v9 & sdtasdt0(v0, v1) = v6 & aScalar0(v1) = v5 & aScalar0(v0) = v4
% 11.89/2.36 | & $i(v9) & $i(v8) & $i(v7) & $i(v6) & ( ~ (v5 = 0) | ~ (v4 = 0) |
% 11.89/2.36 | (v9 = v3 & v7 = v3))))
% 11.89/2.36 |
% 11.89/2.36 | ALPHA: (m__799) implies:
% 11.89/2.36 | (6) aScalar0(xx) = 0
% 11.89/2.36 | (7) aScalar0(xy) = 0
% 11.89/2.36 |
% 11.89/2.36 | ALPHA: (m__) implies:
% 11.89/2.36 | (8) $i(xx)
% 11.89/2.36 | (9) $i(xy)
% 11.89/2.37 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2)
% 11.89/2.37 | & smndt0(xy) = v1 & smndt0(xx) = v0 & sdtasdt0(v0, v1) = v2 &
% 11.89/2.37 | sdtasdt0(xx, xy) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 11.89/2.37 |
% 11.89/2.37 | ALPHA: (function-axioms) implies:
% 11.89/2.37 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 11.89/2.37 | : (v1 = v0 | ~ (aScalar0(v2) = v1) | ~ (aScalar0(v2) = v0))
% 11.89/2.37 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) =
% 11.89/2.37 | v1) | ~ (smndt0(v2) = v0))
% 11.89/2.37 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.89/2.37 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 11.89/2.37 |
% 11.89/2.37 | DELTA: instantiating (10) with fresh symbols all_15_0, all_15_1, all_15_2,
% 11.89/2.37 | all_15_3 gives:
% 11.89/2.37 | (14) ~ (all_15_0 = all_15_1) & smndt0(xy) = all_15_2 & smndt0(xx) =
% 11.89/2.37 | all_15_3 & sdtasdt0(all_15_3, all_15_2) = all_15_1 & sdtasdt0(xx, xy)
% 11.89/2.37 | = all_15_0 & $i(all_15_0) & $i(all_15_1) & $i(all_15_2) & $i(all_15_3)
% 11.89/2.37 |
% 11.89/2.37 | ALPHA: (14) implies:
% 11.89/2.37 | (15) ~ (all_15_0 = all_15_1)
% 11.89/2.37 | (16) $i(all_15_3)
% 11.89/2.37 | (17) $i(all_15_2)
% 11.89/2.37 | (18) sdtasdt0(xx, xy) = all_15_0
% 11.89/2.37 | (19) sdtasdt0(all_15_3, all_15_2) = all_15_1
% 11.89/2.37 | (20) smndt0(xx) = all_15_3
% 11.89/2.37 | (21) smndt0(xy) = all_15_2
% 11.89/2.37 |
% 11.89/2.37 | DELTA: instantiating (2) with fresh symbol all_17_0 gives:
% 11.89/2.38 | (22) smndt0(sz0z00) = all_17_0 & $i(all_17_0) & ! [v0: $i] : ! [v1: $i] :
% 11.89/2.38 | ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ?
% 11.89/2.38 | [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 11.89/2.38 | ? [v9: $i] : (smndt0(v1) = v9 & sdtasdt0(v0, sz0z00) = v5 &
% 11.89/2.38 | sdtasdt0(sz0z00, v0) = v6 & sdtpldt0(v1, v0) = v8 & sdtpldt0(v0,
% 11.89/2.38 | v1) = v7 & sdtpldt0(v0, sz0z00) = v3 & sdtpldt0(sz0z00, v0) = v4
% 11.89/2.38 | & aScalar0(v0) = v2 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 11.89/2.38 | $i(v4) & $i(v3) & ( ~ (v2 = 0) | (v9 = v0 & v8 = sz0z00 & v7 =
% 11.89/2.38 | sz0z00 & v6 = sz0z00 & v5 = sz0z00 & v4 = v0 & v3 = v0 &
% 11.89/2.38 | all_17_0 = sz0z00)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 11.89/2.38 | (sdtasdt0(v0, sz0z00) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i]
% 11.89/2.38 | : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 11.89/2.38 | $i] : ? [v9: $i] : (smndt0(v6) = v9 & smndt0(v0) = v6 &
% 11.89/2.38 | sdtasdt0(sz0z00, v0) = v5 & sdtpldt0(v6, v0) = v8 & sdtpldt0(v0,
% 11.89/2.38 | v6) = v7 & sdtpldt0(v0, sz0z00) = v3 & sdtpldt0(sz0z00, v0) = v4
% 11.89/2.38 | & aScalar0(v0) = v2 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 11.89/2.38 | $i(v4) & $i(v3) & ( ~ (v2 = 0) | (v9 = v0 & v8 = sz0z00 & v7 =
% 11.89/2.38 | sz0z00 & v5 = sz0z00 & v4 = v0 & v3 = v0 & v1 = sz0z00 &
% 11.89/2.38 | all_17_0 = sz0z00)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 11.89/2.38 | (sdtasdt0(sz0z00, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i]
% 11.89/2.38 | : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 11.89/2.38 | $i] : ? [v9: $i] : (smndt0(v6) = v9 & smndt0(v0) = v6 &
% 11.89/2.38 | sdtasdt0(v0, sz0z00) = v5 & sdtpldt0(v6, v0) = v8 & sdtpldt0(v0,
% 11.89/2.38 | v6) = v7 & sdtpldt0(v0, sz0z00) = v3 & sdtpldt0(sz0z00, v0) = v4
% 11.89/2.38 | & aScalar0(v0) = v2 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 11.89/2.38 | $i(v4) & $i(v3) & ( ~ (v2 = 0) | (v9 = v0 & v8 = sz0z00 & v7 =
% 11.89/2.38 | sz0z00 & v5 = sz0z00 & v4 = v0 & v3 = v0 & v1 = sz0z00 &
% 12.00/2.38 | all_17_0 = sz0z00)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 12.00/2.38 | (sdtpldt0(v0, sz0z00) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i]
% 12.00/2.38 | : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 12.00/2.38 | $i] : ? [v9: $i] : (smndt0(v6) = v9 & smndt0(v0) = v6 &
% 12.00/2.38 | sdtasdt0(v0, sz0z00) = v4 & sdtasdt0(sz0z00, v0) = v5 &
% 12.00/2.38 | sdtpldt0(v6, v0) = v8 & sdtpldt0(v0, v6) = v7 & sdtpldt0(sz0z00,
% 12.00/2.38 | v0) = v3 & aScalar0(v0) = v2 & $i(v9) & $i(v8) & $i(v7) & $i(v6)
% 12.00/2.38 | & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | (v9 = v0 & v8 = sz0z00
% 12.00/2.38 | & v7 = sz0z00 & v5 = sz0z00 & v4 = sz0z00 & v3 = v0 & v1 = v0
% 12.00/2.38 | & all_17_0 = sz0z00)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 12.00/2.38 | (sdtpldt0(sz0z00, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i]
% 12.00/2.38 | : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 12.00/2.38 | $i] : ? [v9: $i] : (smndt0(v6) = v9 & smndt0(v0) = v6 &
% 12.00/2.38 | sdtasdt0(v0, sz0z00) = v4 & sdtasdt0(sz0z00, v0) = v5 &
% 12.00/2.38 | sdtpldt0(v6, v0) = v8 & sdtpldt0(v0, v6) = v7 & sdtpldt0(v0,
% 12.00/2.38 | sz0z00) = v3 & aScalar0(v0) = v2 & $i(v9) & $i(v8) & $i(v7) &
% 12.00/2.38 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | (v9 = v0 & v8 =
% 12.00/2.38 | sz0z00 & v7 = sz0z00 & v5 = sz0z00 & v4 = sz0z00 & v3 = v0 &
% 12.00/2.38 | v1 = v0 & all_17_0 = sz0z00)))) & ! [v0: $i] : (all_17_0 =
% 12.00/2.38 | sz0z00 | ~ (aScalar0(v0) = 0) | ~ $i(v0)) & ! [v0: $i] : ( ~
% 12.00/2.38 | (aScalar0(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (smndt0(v1) = v0 &
% 12.00/2.38 | smndt0(v0) = v1 & sdtasdt0(v0, sz0z00) = sz0z00 & sdtasdt0(sz0z00,
% 12.00/2.38 | v0) = sz0z00 & sdtpldt0(v1, v0) = sz0z00 & sdtpldt0(v0, v1) =
% 12.00/2.38 | sz0z00 & sdtpldt0(v0, sz0z00) = v0 & sdtpldt0(sz0z00, v0) = v0 &
% 12.00/2.38 | $i(v1)))
% 12.00/2.38 |
% 12.00/2.38 | ALPHA: (22) implies:
% 12.00/2.38 | (23) ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ?
% 12.00/2.38 | [v2: any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 12.00/2.38 | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (smndt0(v1) = v9 &
% 12.00/2.38 | sdtasdt0(v0, sz0z00) = v5 & sdtasdt0(sz0z00, v0) = v6 &
% 12.00/2.38 | sdtpldt0(v1, v0) = v8 & sdtpldt0(v0, v1) = v7 & sdtpldt0(v0,
% 12.00/2.38 | sz0z00) = v3 & sdtpldt0(sz0z00, v0) = v4 & aScalar0(v0) = v2 &
% 12.00/2.38 | $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~
% 12.00/2.38 | (v2 = 0) | (v9 = v0 & v8 = sz0z00 & v7 = sz0z00 & v6 = sz0z00 &
% 12.00/2.38 | v5 = sz0z00 & v4 = v0 & v3 = v0 & all_17_0 = sz0z00))))
% 12.00/2.38 |
% 12.00/2.38 | GROUND_INST: instantiating (3) with xx, xy, all_15_0, simplifying with (8),
% 12.00/2.38 | (9), (18) gives:
% 12.00/2.39 | (24) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 12.00/2.39 | : ? [v5: $i] : ? [v6: $i] : (smndt0(all_15_0) = v4 & smndt0(xy) = v2
% 12.00/2.39 | & smndt0(xx) = v5 & sdtasdt0(v5, xy) = v6 & sdtasdt0(xx, v2) = v3 &
% 12.00/2.39 | aScalar0(xy) = v1 & aScalar0(xx) = v0 & $i(v6) & $i(v5) & $i(v4) &
% 12.00/2.39 | $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | (v6 = v3 & v4 = v3)))
% 12.00/2.39 |
% 12.00/2.39 | GROUND_INST: instantiating (mMulSc) with xx, xy, all_15_0, simplifying with
% 12.00/2.39 | (8), (9), (18) gives:
% 12.00/2.39 | (25) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aScalar0(all_15_0) = v2
% 12.00/2.39 | & aScalar0(xy) = v1 & aScalar0(xx) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)
% 12.00/2.39 | | v2 = 0))
% 12.00/2.39 |
% 12.00/2.39 | GROUND_INST: instantiating (4) with xx, all_15_2, all_15_3, all_15_1,
% 12.00/2.39 | simplifying with (8), (17), (19), (20) gives:
% 12.00/2.39 | (26) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 12.00/2.39 | : ? [v5: $i] : (smndt0(v4) = v5 & smndt0(all_15_2) = v2 &
% 12.00/2.39 | sdtasdt0(xx, v2) = v3 & sdtasdt0(xx, all_15_2) = v4 &
% 12.00/2.39 | aScalar0(all_15_2) = v1 & aScalar0(xx) = v0 & $i(v5) & $i(v4) &
% 12.00/2.39 | $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | (v5 = all_15_1 & v3 =
% 12.00/2.39 | all_15_1)))
% 12.00/2.39 |
% 12.00/2.39 | GROUND_INST: instantiating (23) with xx, all_15_3, simplifying with (8), (20)
% 12.00/2.39 | gives:
% 12.00/2.39 | (27) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 12.00/2.39 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (smndt0(all_15_3) = v7 &
% 12.00/2.39 | sdtasdt0(xx, sz0z00) = v3 & sdtasdt0(sz0z00, xx) = v4 &
% 12.00/2.39 | sdtpldt0(all_15_3, xx) = v6 & sdtpldt0(xx, all_15_3) = v5 &
% 12.00/2.39 | sdtpldt0(xx, sz0z00) = v1 & sdtpldt0(sz0z00, xx) = v2 & aScalar0(xx)
% 12.00/2.39 | = v0 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1)
% 12.00/2.39 | & ( ~ (v0 = 0) | (v7 = xx & v6 = sz0z00 & v5 = sz0z00 & v4 = sz0z00
% 12.00/2.39 | & v3 = sz0z00 & v2 = xx & v1 = xx & all_17_0 = sz0z00)))
% 12.00/2.39 |
% 12.00/2.39 | GROUND_INST: instantiating (1) with xx, all_15_3, simplifying with (8), (20)
% 12.00/2.39 | gives:
% 12.00/2.39 | (28) ? [v0: any] : ? [v1: any] : (aScalar0(all_15_3) = v1 & aScalar0(xx)
% 12.00/2.39 | = v0 & ( ~ (v0 = 0) | v1 = 0))
% 12.00/2.39 |
% 12.00/2.39 | GROUND_INST: instantiating (5) with all_15_3, xy, all_15_2, all_15_1,
% 12.00/2.39 | simplifying with (9), (16), (19), (21) gives:
% 12.00/2.39 | (29) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 12.00/2.39 | : ? [v5: $i] : (smndt0(v2) = v3 & smndt0(all_15_3) = v4 &
% 12.00/2.39 | sdtasdt0(v4, xy) = v5 & sdtasdt0(all_15_3, xy) = v2 &
% 12.00/2.39 | aScalar0(all_15_3) = v0 & aScalar0(xy) = v1 & $i(v5) & $i(v4) &
% 12.00/2.39 | $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | (v5 = all_15_1 & v3 =
% 12.00/2.39 | all_15_1)))
% 12.00/2.39 |
% 12.00/2.39 | GROUND_INST: instantiating (23) with xy, all_15_2, simplifying with (9), (21)
% 12.00/2.39 | gives:
% 12.00/2.39 | (30) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 12.00/2.39 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (smndt0(all_15_2) = v7 &
% 12.00/2.39 | sdtasdt0(xy, sz0z00) = v3 & sdtasdt0(sz0z00, xy) = v4 &
% 12.00/2.39 | sdtpldt0(all_15_2, xy) = v6 & sdtpldt0(xy, all_15_2) = v5 &
% 12.00/2.39 | sdtpldt0(xy, sz0z00) = v1 & sdtpldt0(sz0z00, xy) = v2 & aScalar0(xy)
% 12.00/2.39 | = v0 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1)
% 12.00/2.39 | & ( ~ (v0 = 0) | (v7 = xy & v6 = sz0z00 & v5 = sz0z00 & v4 = sz0z00
% 12.00/2.39 | & v3 = sz0z00 & v2 = xy & v1 = xy & all_17_0 = sz0z00)))
% 12.00/2.39 |
% 12.00/2.39 | GROUND_INST: instantiating (1) with xy, all_15_2, simplifying with (9), (21)
% 12.00/2.39 | gives:
% 12.00/2.39 | (31) ? [v0: any] : ? [v1: any] : (aScalar0(all_15_2) = v1 & aScalar0(xy)
% 12.00/2.39 | = v0 & ( ~ (v0 = 0) | v1 = 0))
% 12.00/2.39 |
% 12.00/2.39 | DELTA: instantiating (31) with fresh symbols all_34_0, all_34_1 gives:
% 12.00/2.40 | (32) aScalar0(all_15_2) = all_34_0 & aScalar0(xy) = all_34_1 & ( ~
% 12.00/2.40 | (all_34_1 = 0) | all_34_0 = 0)
% 12.00/2.40 |
% 12.00/2.40 | ALPHA: (32) implies:
% 12.00/2.40 | (33) aScalar0(xy) = all_34_1
% 12.00/2.40 |
% 12.00/2.40 | DELTA: instantiating (28) with fresh symbols all_38_0, all_38_1 gives:
% 12.00/2.40 | (34) aScalar0(all_15_3) = all_38_0 & aScalar0(xx) = all_38_1 & ( ~
% 12.00/2.40 | (all_38_1 = 0) | all_38_0 = 0)
% 12.00/2.40 |
% 12.00/2.40 | ALPHA: (34) implies:
% 12.00/2.40 | (35) aScalar0(xx) = all_38_1
% 12.00/2.40 | (36) aScalar0(all_15_3) = all_38_0
% 12.00/2.40 | (37) ~ (all_38_1 = 0) | all_38_0 = 0
% 12.00/2.40 |
% 12.00/2.40 | DELTA: instantiating (25) with fresh symbols all_42_0, all_42_1, all_42_2
% 12.00/2.40 | gives:
% 12.00/2.40 | (38) aScalar0(all_15_0) = all_42_0 & aScalar0(xy) = all_42_1 & aScalar0(xx)
% 12.00/2.40 | = all_42_2 & ( ~ (all_42_1 = 0) | ~ (all_42_2 = 0) | all_42_0 = 0)
% 12.00/2.40 |
% 12.00/2.40 | ALPHA: (38) implies:
% 12.00/2.40 | (39) aScalar0(xx) = all_42_2
% 12.00/2.40 | (40) aScalar0(xy) = all_42_1
% 12.00/2.40 |
% 12.00/2.40 | DELTA: instantiating (29) with fresh symbols all_52_0, all_52_1, all_52_2,
% 12.00/2.40 | all_52_3, all_52_4, all_52_5 gives:
% 12.00/2.40 | (41) smndt0(all_52_3) = all_52_2 & smndt0(all_15_3) = all_52_1 &
% 12.00/2.40 | sdtasdt0(all_52_1, xy) = all_52_0 & sdtasdt0(all_15_3, xy) = all_52_3
% 12.00/2.40 | & aScalar0(all_15_3) = all_52_5 & aScalar0(xy) = all_52_4 &
% 12.00/2.40 | $i(all_52_0) & $i(all_52_1) & $i(all_52_2) & $i(all_52_3) & ( ~
% 12.00/2.40 | (all_52_4 = 0) | ~ (all_52_5 = 0) | (all_52_0 = all_15_1 & all_52_2
% 12.00/2.40 | = all_15_1))
% 12.00/2.40 |
% 12.00/2.40 | ALPHA: (41) implies:
% 12.00/2.40 | (42) aScalar0(xy) = all_52_4
% 12.00/2.40 | (43) aScalar0(all_15_3) = all_52_5
% 12.00/2.40 | (44) sdtasdt0(all_52_1, xy) = all_52_0
% 12.00/2.40 | (45) smndt0(all_15_3) = all_52_1
% 12.00/2.40 | (46) ~ (all_52_4 = 0) | ~ (all_52_5 = 0) | (all_52_0 = all_15_1 &
% 12.00/2.40 | all_52_2 = all_15_1)
% 12.00/2.40 |
% 12.00/2.40 | DELTA: instantiating (26) with fresh symbols all_54_0, all_54_1, all_54_2,
% 12.00/2.40 | all_54_3, all_54_4, all_54_5 gives:
% 12.00/2.40 | (47) smndt0(all_54_1) = all_54_0 & smndt0(all_15_2) = all_54_3 &
% 12.00/2.40 | sdtasdt0(xx, all_54_3) = all_54_2 & sdtasdt0(xx, all_15_2) = all_54_1
% 12.00/2.40 | & aScalar0(all_15_2) = all_54_4 & aScalar0(xx) = all_54_5 &
% 12.00/2.40 | $i(all_54_0) & $i(all_54_1) & $i(all_54_2) & $i(all_54_3) & ( ~
% 12.00/2.40 | (all_54_4 = 0) | ~ (all_54_5 = 0) | (all_54_0 = all_15_1 & all_54_2
% 12.00/2.40 | = all_15_1))
% 12.00/2.40 |
% 12.00/2.40 | ALPHA: (47) implies:
% 12.00/2.40 | (48) aScalar0(xx) = all_54_5
% 12.00/2.40 |
% 12.00/2.40 | DELTA: instantiating (24) with fresh symbols all_56_0, all_56_1, all_56_2,
% 12.00/2.40 | all_56_3, all_56_4, all_56_5, all_56_6 gives:
% 12.00/2.40 | (49) smndt0(all_15_0) = all_56_2 & smndt0(xy) = all_56_4 & smndt0(xx) =
% 12.00/2.40 | all_56_1 & sdtasdt0(all_56_1, xy) = all_56_0 & sdtasdt0(xx, all_56_4)
% 12.00/2.40 | = all_56_3 & aScalar0(xy) = all_56_5 & aScalar0(xx) = all_56_6 &
% 12.00/2.40 | $i(all_56_0) & $i(all_56_1) & $i(all_56_2) & $i(all_56_3) &
% 12.00/2.40 | $i(all_56_4) & ( ~ (all_56_5 = 0) | ~ (all_56_6 = 0) | (all_56_0 =
% 12.00/2.40 | all_56_3 & all_56_2 = all_56_3))
% 12.00/2.40 |
% 12.00/2.40 | ALPHA: (49) implies:
% 12.00/2.40 | (50) aScalar0(xx) = all_56_6
% 12.00/2.40 | (51) aScalar0(xy) = all_56_5
% 12.00/2.40 |
% 12.00/2.40 | DELTA: instantiating (30) with fresh symbols all_60_0, all_60_1, all_60_2,
% 12.00/2.40 | all_60_3, all_60_4, all_60_5, all_60_6, all_60_7 gives:
% 12.00/2.40 | (52) smndt0(all_15_2) = all_60_0 & sdtasdt0(xy, sz0z00) = all_60_4 &
% 12.00/2.40 | sdtasdt0(sz0z00, xy) = all_60_3 & sdtpldt0(all_15_2, xy) = all_60_1 &
% 12.00/2.40 | sdtpldt0(xy, all_15_2) = all_60_2 & sdtpldt0(xy, sz0z00) = all_60_6 &
% 12.00/2.40 | sdtpldt0(sz0z00, xy) = all_60_5 & aScalar0(xy) = all_60_7 &
% 12.00/2.40 | $i(all_60_0) & $i(all_60_1) & $i(all_60_2) & $i(all_60_3) &
% 12.00/2.40 | $i(all_60_4) & $i(all_60_5) & $i(all_60_6) & ( ~ (all_60_7 = 0) |
% 12.00/2.40 | (all_60_0 = xy & all_60_1 = sz0z00 & all_60_2 = sz0z00 & all_60_3 =
% 12.00/2.40 | sz0z00 & all_60_4 = sz0z00 & all_60_5 = xy & all_60_6 = xy &
% 12.00/2.40 | all_17_0 = sz0z00))
% 12.00/2.40 |
% 12.00/2.40 | ALPHA: (52) implies:
% 12.00/2.40 | (53) aScalar0(xy) = all_60_7
% 12.00/2.40 |
% 12.00/2.40 | DELTA: instantiating (27) with fresh symbols all_64_0, all_64_1, all_64_2,
% 12.00/2.40 | all_64_3, all_64_4, all_64_5, all_64_6, all_64_7 gives:
% 12.00/2.40 | (54) smndt0(all_15_3) = all_64_0 & sdtasdt0(xx, sz0z00) = all_64_4 &
% 12.00/2.40 | sdtasdt0(sz0z00, xx) = all_64_3 & sdtpldt0(all_15_3, xx) = all_64_1 &
% 12.00/2.40 | sdtpldt0(xx, all_15_3) = all_64_2 & sdtpldt0(xx, sz0z00) = all_64_6 &
% 12.00/2.40 | sdtpldt0(sz0z00, xx) = all_64_5 & aScalar0(xx) = all_64_7 &
% 12.00/2.40 | $i(all_64_0) & $i(all_64_1) & $i(all_64_2) & $i(all_64_3) &
% 12.00/2.40 | $i(all_64_4) & $i(all_64_5) & $i(all_64_6) & ( ~ (all_64_7 = 0) |
% 12.00/2.40 | (all_64_0 = xx & all_64_1 = sz0z00 & all_64_2 = sz0z00 & all_64_3 =
% 12.00/2.40 | sz0z00 & all_64_4 = sz0z00 & all_64_5 = xx & all_64_6 = xx &
% 12.00/2.40 | all_17_0 = sz0z00))
% 12.00/2.40 |
% 12.00/2.40 | ALPHA: (54) implies:
% 12.00/2.40 | (55) aScalar0(xx) = all_64_7
% 12.00/2.40 | (56) smndt0(all_15_3) = all_64_0
% 12.00/2.40 | (57) ~ (all_64_7 = 0) | (all_64_0 = xx & all_64_1 = sz0z00 & all_64_2 =
% 12.00/2.40 | sz0z00 & all_64_3 = sz0z00 & all_64_4 = sz0z00 & all_64_5 = xx &
% 12.00/2.40 | all_64_6 = xx & all_17_0 = sz0z00)
% 12.00/2.40 |
% 12.00/2.40 | GROUND_INST: instantiating (11) with 0, all_56_6, xx, simplifying with (6),
% 12.00/2.40 | (50) gives:
% 12.00/2.40 | (58) all_56_6 = 0
% 12.00/2.40 |
% 12.00/2.40 | GROUND_INST: instantiating (11) with all_54_5, all_56_6, xx, simplifying with
% 12.00/2.40 | (48), (50) gives:
% 12.00/2.40 | (59) all_56_6 = all_54_5
% 12.00/2.40 |
% 12.00/2.40 | GROUND_INST: instantiating (11) with all_42_2, all_56_6, xx, simplifying with
% 12.00/2.40 | (39), (50) gives:
% 12.00/2.40 | (60) all_56_6 = all_42_2
% 12.00/2.40 |
% 12.00/2.40 | GROUND_INST: instantiating (11) with all_54_5, all_64_7, xx, simplifying with
% 12.00/2.40 | (48), (55) gives:
% 12.00/2.40 | (61) all_64_7 = all_54_5
% 12.00/2.40 |
% 12.00/2.41 | GROUND_INST: instantiating (11) with all_38_1, all_64_7, xx, simplifying with
% 12.00/2.41 | (35), (55) gives:
% 12.00/2.41 | (62) all_64_7 = all_38_1
% 12.00/2.41 |
% 12.00/2.41 | GROUND_INST: instantiating (11) with 0, all_42_1, xy, simplifying with (7),
% 12.00/2.41 | (40) gives:
% 12.00/2.41 | (63) all_42_1 = 0
% 12.00/2.41 |
% 12.00/2.41 | GROUND_INST: instantiating (11) with all_42_1, all_52_4, xy, simplifying with
% 12.00/2.41 | (40), (42) gives:
% 12.00/2.41 | (64) all_52_4 = all_42_1
% 12.00/2.41 |
% 12.00/2.41 | GROUND_INST: instantiating (11) with all_52_4, all_56_5, xy, simplifying with
% 12.00/2.41 | (42), (51) gives:
% 12.00/2.41 | (65) all_56_5 = all_52_4
% 12.00/2.41 |
% 12.00/2.41 | GROUND_INST: instantiating (11) with all_56_5, all_60_7, xy, simplifying with
% 12.00/2.41 | (51), (53) gives:
% 12.00/2.41 | (66) all_60_7 = all_56_5
% 12.00/2.41 |
% 12.00/2.41 | GROUND_INST: instantiating (11) with all_34_1, all_60_7, xy, simplifying with
% 12.00/2.41 | (33), (53) gives:
% 12.00/2.41 | (67) all_60_7 = all_34_1
% 12.00/2.41 |
% 12.00/2.41 | GROUND_INST: instantiating (11) with all_38_0, all_52_5, all_15_3, simplifying
% 12.00/2.41 | with (36), (43) gives:
% 12.00/2.41 | (68) all_52_5 = all_38_0
% 12.00/2.41 |
% 12.00/2.41 | GROUND_INST: instantiating (12) with all_52_1, all_64_0, all_15_3, simplifying
% 12.00/2.41 | with (45), (56) gives:
% 12.00/2.41 | (69) all_64_0 = all_52_1
% 12.00/2.41 |
% 12.00/2.41 | COMBINE_EQS: (61), (62) imply:
% 12.00/2.41 | (70) all_54_5 = all_38_1
% 12.00/2.41 |
% 12.00/2.41 | SIMP: (70) implies:
% 12.00/2.41 | (71) all_54_5 = all_38_1
% 12.00/2.41 |
% 12.00/2.41 | COMBINE_EQS: (66), (67) imply:
% 12.00/2.41 | (72) all_56_5 = all_34_1
% 12.00/2.41 |
% 12.00/2.41 | SIMP: (72) implies:
% 12.00/2.41 | (73) all_56_5 = all_34_1
% 12.00/2.41 |
% 12.00/2.41 | COMBINE_EQS: (65), (73) imply:
% 12.00/2.41 | (74) all_52_4 = all_34_1
% 12.00/2.41 |
% 12.00/2.41 | SIMP: (74) implies:
% 12.00/2.41 | (75) all_52_4 = all_34_1
% 12.00/2.41 |
% 12.00/2.41 | COMBINE_EQS: (59), (60) imply:
% 12.00/2.41 | (76) all_54_5 = all_42_2
% 12.00/2.41 |
% 12.00/2.41 | SIMP: (76) implies:
% 12.00/2.41 | (77) all_54_5 = all_42_2
% 12.00/2.41 |
% 12.00/2.41 | COMBINE_EQS: (58), (60) imply:
% 12.00/2.41 | (78) all_42_2 = 0
% 12.00/2.41 |
% 12.00/2.41 | COMBINE_EQS: (71), (77) imply:
% 12.00/2.41 | (79) all_42_2 = all_38_1
% 12.00/2.41 |
% 12.00/2.41 | SIMP: (79) implies:
% 12.00/2.41 | (80) all_42_2 = all_38_1
% 12.00/2.41 |
% 12.00/2.41 | COMBINE_EQS: (64), (75) imply:
% 12.00/2.41 | (81) all_42_1 = all_34_1
% 12.00/2.41 |
% 12.00/2.41 | SIMP: (81) implies:
% 12.00/2.41 | (82) all_42_1 = all_34_1
% 12.00/2.41 |
% 12.00/2.41 | COMBINE_EQS: (63), (82) imply:
% 12.00/2.41 | (83) all_34_1 = 0
% 12.00/2.41 |
% 12.00/2.41 | COMBINE_EQS: (78), (80) imply:
% 12.00/2.41 | (84) all_38_1 = 0
% 12.00/2.41 |
% 12.00/2.41 | COMBINE_EQS: (75), (83) imply:
% 12.00/2.41 | (85) all_52_4 = 0
% 12.00/2.41 |
% 12.00/2.41 | COMBINE_EQS: (62), (84) imply:
% 12.00/2.41 | (86) all_64_7 = 0
% 12.00/2.41 |
% 12.00/2.41 | BETA: splitting (37) gives:
% 12.00/2.41 |
% 12.00/2.41 | Case 1:
% 12.00/2.41 | |
% 12.00/2.41 | | (87) ~ (all_38_1 = 0)
% 12.00/2.41 | |
% 12.00/2.41 | | REDUCE: (84), (87) imply:
% 12.00/2.41 | | (88) $false
% 12.00/2.41 | |
% 12.00/2.41 | | CLOSE: (88) is inconsistent.
% 12.00/2.41 | |
% 12.00/2.41 | Case 2:
% 12.00/2.41 | |
% 12.00/2.41 | | (89) all_38_0 = 0
% 12.00/2.41 | |
% 12.00/2.41 | | COMBINE_EQS: (68), (89) imply:
% 12.00/2.41 | | (90) all_52_5 = 0
% 12.00/2.41 | |
% 12.00/2.41 | | BETA: splitting (46) gives:
% 12.00/2.41 | |
% 12.00/2.41 | | Case 1:
% 12.00/2.41 | | |
% 12.00/2.41 | | | (91) ~ (all_52_4 = 0)
% 12.00/2.41 | | |
% 12.00/2.41 | | | REDUCE: (85), (91) imply:
% 12.00/2.41 | | | (92) $false
% 12.00/2.41 | | |
% 12.00/2.41 | | | CLOSE: (92) is inconsistent.
% 12.00/2.41 | | |
% 12.00/2.41 | | Case 2:
% 12.00/2.41 | | |
% 12.00/2.41 | | | (93) ~ (all_52_5 = 0) | (all_52_0 = all_15_1 & all_52_2 = all_15_1)
% 12.00/2.41 | | |
% 12.00/2.41 | | | BETA: splitting (57) gives:
% 12.00/2.41 | | |
% 12.00/2.41 | | | Case 1:
% 12.00/2.41 | | | |
% 12.00/2.41 | | | | (94) ~ (all_64_7 = 0)
% 12.00/2.41 | | | |
% 12.00/2.41 | | | | REDUCE: (86), (94) imply:
% 12.00/2.41 | | | | (95) $false
% 12.00/2.41 | | | |
% 12.00/2.41 | | | | CLOSE: (95) is inconsistent.
% 12.00/2.41 | | | |
% 12.00/2.41 | | | Case 2:
% 12.00/2.41 | | | |
% 12.00/2.41 | | | | (96) all_64_0 = xx & all_64_1 = sz0z00 & all_64_2 = sz0z00 & all_64_3
% 12.00/2.41 | | | | = sz0z00 & all_64_4 = sz0z00 & all_64_5 = xx & all_64_6 = xx &
% 12.00/2.41 | | | | all_17_0 = sz0z00
% 12.00/2.41 | | | |
% 12.00/2.41 | | | | ALPHA: (96) implies:
% 12.00/2.41 | | | | (97) all_64_0 = xx
% 12.00/2.41 | | | |
% 12.00/2.41 | | | | COMBINE_EQS: (69), (97) imply:
% 12.00/2.41 | | | | (98) all_52_1 = xx
% 12.00/2.41 | | | |
% 12.00/2.41 | | | | REDUCE: (44), (98) imply:
% 12.00/2.41 | | | | (99) sdtasdt0(xx, xy) = all_52_0
% 12.00/2.41 | | | |
% 12.00/2.41 | | | | BETA: splitting (93) gives:
% 12.00/2.41 | | | |
% 12.00/2.41 | | | | Case 1:
% 12.00/2.41 | | | | |
% 12.00/2.41 | | | | | (100) ~ (all_52_5 = 0)
% 12.00/2.41 | | | | |
% 12.00/2.41 | | | | | REDUCE: (90), (100) imply:
% 12.00/2.41 | | | | | (101) $false
% 12.00/2.41 | | | | |
% 12.00/2.41 | | | | | CLOSE: (101) is inconsistent.
% 12.00/2.41 | | | | |
% 12.00/2.41 | | | | Case 2:
% 12.00/2.41 | | | | |
% 12.00/2.41 | | | | | (102) all_52_0 = all_15_1 & all_52_2 = all_15_1
% 12.00/2.41 | | | | |
% 12.00/2.41 | | | | | ALPHA: (102) implies:
% 12.00/2.41 | | | | | (103) all_52_0 = all_15_1
% 12.00/2.41 | | | | |
% 12.00/2.41 | | | | | REDUCE: (99), (103) imply:
% 12.00/2.41 | | | | | (104) sdtasdt0(xx, xy) = all_15_1
% 12.00/2.41 | | | | |
% 12.00/2.41 | | | | | GROUND_INST: instantiating (13) with all_15_0, all_15_1, xy, xx,
% 12.00/2.41 | | | | | simplifying with (18), (104) gives:
% 12.00/2.41 | | | | | (105) all_15_0 = all_15_1
% 12.00/2.41 | | | | |
% 12.00/2.42 | | | | | REDUCE: (15), (105) imply:
% 12.00/2.42 | | | | | (106) $false
% 12.00/2.42 | | | | |
% 12.00/2.42 | | | | | CLOSE: (106) is inconsistent.
% 12.00/2.42 | | | | |
% 12.00/2.42 | | | | End of split
% 12.00/2.42 | | | |
% 12.00/2.42 | | | End of split
% 12.00/2.42 | | |
% 12.00/2.42 | | End of split
% 12.00/2.42 | |
% 12.00/2.42 | End of split
% 12.00/2.42 |
% 12.00/2.42 End of proof
% 12.00/2.42 % SZS output end Proof for theBenchmark
% 12.00/2.42
% 12.00/2.42 1795ms
%------------------------------------------------------------------------------