%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG048+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 : n021.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 24.36s 4.02s % Output : Proof 24.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG048+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n021.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Sun Aug 27 03:08:57 EDT 2023 % 0.12/0.34 % CPUTime : % 0.18/0.59 ________ _____ % 0.18/0.59 ___ __ \_________(_)________________________________ % 0.18/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.59 % 0.18/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.59 (2023-06-19) % 0.18/0.59 % 0.18/0.59 (c) Philipp Rümmer, 2009-2023 % 0.18/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.59 Amanda Stjerna. % 0.18/0.59 Free software under BSD-3-Clause. % 0.18/0.59 % 0.18/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.59 % 0.18/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.18/0.61 Running up to 7 provers in parallel. % 0.18/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.18/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.18/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.18/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.18/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.18/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.18/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.29/1.14 Prover 4: Preprocessing ... % 3.29/1.14 Prover 1: Preprocessing ... % 3.29/1.18 Prover 6: Preprocessing ... % 3.29/1.18 Prover 2: Preprocessing ... % 3.29/1.19 Prover 5: Preprocessing ... % 3.29/1.19 Prover 0: Preprocessing ... % 3.29/1.19 Prover 3: Preprocessing ... % 8.26/1.84 Prover 1: Constructing countermodel ... % 8.75/1.92 Prover 3: Constructing countermodel ... % 8.75/1.96 Prover 6: Proving ... % 10.54/2.18 Prover 3: gave up % 10.54/2.18 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.54/2.20 Prover 5: Constructing countermodel ... % 11.03/2.27 Prover 7: Preprocessing ... % 11.03/2.30 Prover 2: Proving ... % 11.03/2.32 Prover 1: gave up % 11.77/2.34 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.77/2.39 Prover 4: Constructing countermodel ... % 12.25/2.40 Prover 8: Preprocessing ... % 12.79/2.49 Prover 0: Proving ... % 13.05/2.51 Prover 7: Constructing countermodel ... % 13.05/2.53 Prover 8: Warning: ignoring some quantifiers % 13.31/2.54 Prover 8: Constructing countermodel ... % 18.88/3.31 Prover 8: gave up % 19.15/3.33 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 19.28/3.41 Prover 9: Preprocessing ... % 24.15/3.98 Prover 7: Found proof (size 152) % 24.15/3.98 Prover 7: proved (1808ms) % 24.15/3.99 Prover 5: stopped % 24.15/3.99 Prover 4: stopped % 24.15/3.99 Prover 0: stopped % 24.15/3.99 Prover 6: stopped % 24.15/3.99 Prover 2: stopped % 24.15/4.01 Prover 9: Constructing countermodel ... % 24.15/4.01 Prover 9: stopped % 24.15/4.01 % 24.36/4.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 24.36/4.02 % 24.36/4.03 % SZS output start Proof for theBenchmark % 24.36/4.03 Assumptions after simplification: % 24.36/4.03 --------------------------------- % 24.36/4.03 % 24.36/4.03 (mDefInit) % 24.44/4.07 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ (aDimensionOf0(v0) = % 24.44/4.07 v1) | ~ $i(v0) | ~ aVector0(v0) | ? [v2: $i] : (sziznziztdt0(v0) = v2 & % 24.44/4.07 $i(v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtlbdtrb0(v2, v4) % 24.44/4.07 = v5) | ~ (aDimensionOf0(v2) = v3) | ~ $i(v4) | ~ % 24.44/4.07 aNaturalNumber0(v4) | (sdtlbdtrb0(v0, v4) = v5 & $i(v5))) & ! [v3: $i] % 24.44/4.07 : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtlbdtrb0(v0, v4) = v5) | ~ % 24.44/4.07 (aDimensionOf0(v2) = v3) | ~ $i(v4) | ~ aNaturalNumber0(v4) | % 24.44/4.07 (sdtlbdtrb0(v2, v4) = v5 & $i(v5))) & ! [v3: $i] : ! [v4: $i] : (v3 = % 24.44/4.07 v2 | ~ (aDimensionOf0(v3) = v4) | ~ $i(v3) | ~ aVector0(v3) | ? [v5: % 24.44/4.07 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ($i(v6) & (( ~ (v8 = % 24.44/4.07 v7) & sdtlbdtrb0(v3, v6) = v7 & sdtlbdtrb0(v0, v6) = v8 & $i(v8) % 24.44/4.07 & $i(v7) & aNaturalNumber0(v6)) | ( ~ (v5 = v1) & szszuzczcdt0(v4) % 24.44/4.07 = v5 & $i(v5))))) & ! [v3: $i] : ( ~ (aDimensionOf0(v2) = v3) | % 24.44/4.07 aVector0(v2)) & ! [v3: $i] : ( ~ (aDimensionOf0(v2) = v3) | % 24.44/4.07 (szszuzczcdt0(v3) = v1 & $i(v1))))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 24.44/4.07 (sziznziztdt0(v0) = v1) | ~ $i(v0) | ~ aVector0(v0) | ? [v2: $i] : % 24.44/4.07 (aDimensionOf0(v0) = v2 & $i(v2) & (v2 = sz00 | ( ! [v3: $i] : ! [v4: $i] : % 24.44/4.07 ! [v5: $i] : ( ~ (sdtlbdtrb0(v1, v4) = v5) | ~ (aDimensionOf0(v1) = % 24.44/4.07 v3) | ~ $i(v4) | ~ $i(v1) | ~ aNaturalNumber0(v4) | % 24.44/4.07 (sdtlbdtrb0(v0, v4) = v5 & $i(v5))) & ! [v3: $i] : ! [v4: $i] : ! % 24.44/4.07 [v5: $i] : ( ~ (sdtlbdtrb0(v0, v4) = v5) | ~ (aDimensionOf0(v1) = v3) % 24.44/4.07 | ~ $i(v4) | ~ $i(v1) | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1, % 24.44/4.07 v4) = v5 & $i(v5))) & ! [v3: $i] : ! [v4: $i] : (v3 = v1 | ~ % 24.44/4.07 (aDimensionOf0(v3) = v4) | ~ $i(v3) | ~ aVector0(v3) | ? [v5: $i] % 24.44/4.07 : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ($i(v6) & (( ~ (v8 = v7) % 24.44/4.07 & sdtlbdtrb0(v3, v6) = v7 & sdtlbdtrb0(v0, v6) = v8 & $i(v8) & % 24.44/4.07 $i(v7) & aNaturalNumber0(v6)) | ( ~ (v5 = v2) & % 24.44/4.07 szszuzczcdt0(v4) = v5 & $i(v5))))) & ! [v3: $i] : ( ~ % 24.44/4.07 (aDimensionOf0(v1) = v3) | ~ $i(v1) | szszuzczcdt0(v3) = v2) & ! % 24.44/4.07 [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~ $i(v1) | % 24.44/4.07 aVector0(v1)))))) % 24.44/4.07 % 24.44/4.07 (mDefSPN) % 24.44/4.07 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 24.44/4.07 : ! [v5: $i] : (v2 = sz00 | ~ (sdtlbdtrb0(v1, v2) = v4) | ~ (sdtlbdtrb0(v0, % 24.44/4.07 v2) = v3) | ~ (aDimensionOf0(v1) = v2) | ~ (aDimensionOf0(v0) = v2) | % 24.44/4.07 ~ (sdtasdt0(v3, v4) = v5) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ % 24.44/4.07 aVector0(v0) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 24.44/4.07 (sdtasasdt0(v7, v8) = v9 & sdtasasdt0(v0, v1) = v6 & sziznziztdt0(v1) = v8 & % 24.44/4.07 sziznziztdt0(v0) = v7 & sdtpldt0(v9, v5) = v6 & $i(v9) & $i(v8) & $i(v7) & % 24.44/4.07 $i(v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 24.44/4.07 $i] : ( ~ (sdtasasdt0(v2, v3) = v4) | ~ (sziznziztdt0(v1) = v3) | ~ % 24.44/4.07 (sziznziztdt0(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ % 24.44/4.07 aVector0(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? % 24.44/4.07 [v9: $i] : ? [v10: $i] : ? [v11: $i] : (aDimensionOf0(v1) = v6 & $i(v6) & % 24.44/4.07 (v6 = sz00 | (v11 = v7 & sdtasasdt0(v0, v1) = v7 & sdtlbdtrb0(v1, v6) = v9 % 24.44/4.07 & sdtlbdtrb0(v0, v5) = v8 & aDimensionOf0(v0) = v5 & sdtasdt0(v8, v9) % 24.44/4.07 = v10 & sdtpldt0(v4, v10) = v7 & $i(v10) & $i(v9) & $i(v8) & $i(v7) & % 24.44/4.07 $i(v5)) | ( ~ (v6 = v5) & aDimensionOf0(v0) = v5 & $i(v5))))) & ! % 24.44/4.07 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~ % 24.44/4.07 $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) | ? [v3: $i] : ? % 24.44/4.07 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: % 24.44/4.07 $i] : ? [v10: $i] : ? [v11: $i] : (aDimensionOf0(v1) = v4 & $i(v4) & (v4 % 24.44/4.07 = sz00 | (v11 = v2 & sdtasasdt0(v5, v6) = v7 & sziznziztdt0(v1) = v6 & % 24.44/4.07 sziznziztdt0(v0) = v5 & sdtlbdtrb0(v1, v4) = v9 & sdtlbdtrb0(v0, v3) = % 24.44/4.07 v8 & aDimensionOf0(v0) = v3 & sdtasdt0(v8, v9) = v10 & sdtpldt0(v7, % 24.44/4.07 v10) = v2 & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & % 24.44/4.07 $i(v3) & $i(v2)) | ( ~ (v4 = v3) & aDimensionOf0(v0) = v3 & $i(v3))))) % 24.44/4.07 % 24.44/4.07 (mDefSPZ) % 24.44/4.08 $i(sz0z00) & $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = sz0z00 % 24.44/4.08 | ~ (sdtasasdt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | % 24.44/4.08 ~ aVector0(v0) | ? [v3: $i] : ? [v4: $i] : (aDimensionOf0(v1) = v4 & % 24.44/4.08 $i(v4) & ( ~ (v4 = sz00) | ( ~ (v3 = sz00) & aDimensionOf0(v0) = v3 & % 24.44/4.08 $i(v3))))) % 24.44/4.08 % 24.44/4.08 (mDimNat) % 24.44/4.08 ! [v0: $i] : ! [v1: $i] : ( ~ (aDimensionOf0(v0) = v1) | ~ $i(v0) | ~ % 24.44/4.08 aVector0(v0) | aNaturalNumber0(v1)) % 24.44/4.08 % 24.44/4.08 (mElmSc) % 24.44/4.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(v0, v1) = v2) | ~ % 24.44/4.08 $i(v1) | ~ $i(v0) | ~ aVector0(v0) | ~ aNaturalNumber0(v1) | % 24.44/4.08 aScalar0(v2)) % 24.44/4.08 % 24.44/4.08 (mEqInit) % 24.44/4.08 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 24.44/4.08 : ! [v5: $i] : (v5 = v3 | ~ (sziznziztdt0(v1) = v4) | ~ (sziznziztdt0(v0) = % 24.44/4.08 v2) | ~ (aDimensionOf0(v4) = v5) | ~ (aDimensionOf0(v2) = v3) | ~ % 24.44/4.08 $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) | ? [v6: $i] : ? % 24.44/4.08 [v7: $i] : (aDimensionOf0(v1) = v7 & $i(v7) & (v7 = sz00 | ( ~ (v7 = v6) & % 24.44/4.08 aDimensionOf0(v0) = v6 & $i(v6))))) & ! [v0: $i] : ! [v1: $i] : ! % 24.44/4.08 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = sz00 | ~ (sziznziztdt0(v0) = v3) % 24.44/4.08 | ~ (aDimensionOf0(v3) = v4) | ~ (aDimensionOf0(v1) = v2) | ~ $i(v1) | ~ % 24.44/4.08 $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) | ? [v5: $i] : ? [v6: $i] : ? % 24.44/4.08 [v7: $i] : ((v7 = v4 & sziznziztdt0(v1) = v6 & aDimensionOf0(v6) = v4 & % 24.44/4.08 $i(v6) & $i(v4)) | ( ~ (v5 = v2) & aDimensionOf0(v0) = v5 & $i(v5)))) & % 24.44/4.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 24.44/4.08 (sziznziztdt0(v1) = v3) | ~ (aDimensionOf0(v3) = v4) | ~ % 24.44/4.08 (aDimensionOf0(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ % 24.44/4.08 aVector0(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ((v7 = v4 & % 24.44/4.08 sziznziztdt0(v0) = v6 & aDimensionOf0(v6) = v4 & $i(v6) & $i(v4)) | % 24.44/4.08 (aDimensionOf0(v1) = v5 & $i(v5) & ( ~ (v5 = v2) | v2 = sz00)))) & ! [v0: % 24.44/4.08 $i] : ! [v1: $i] : ! [v2: $i] : (v2 = sz00 | ~ (aDimensionOf0(v1) = v2) | % 24.44/4.08 ~ (aDimensionOf0(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ % 24.44/4.08 aVector0(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (sziznziztdt0(v1) = % 24.44/4.08 v5 & sziznziztdt0(v0) = v3 & aDimensionOf0(v5) = v4 & aDimensionOf0(v3) = % 24.44/4.08 v4 & $i(v5) & $i(v4) & $i(v3))) % 24.44/4.08 % 24.44/4.08 (mIH) % 24.44/4.08 ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) | ~ % 24.44/4.08 aNaturalNumber0(v0) | iLess0(v0, v1)) % 24.44/4.08 % 24.44/4.08 (mLETot) % 24.44/4.08 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ % 24.44/4.08 aScalar0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1)) % 24.44/4.08 % 24.44/4.08 (mMDNeg) % 24.44/4.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 24.44/4.08 (smndt0(v1) = v3) | ~ (smndt0(v0) = v2) | ~ (sdtasdt0(v2, v3) = v4) | ~ % 24.44/4.08 $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | (sdtasdt0(v0, v1) = % 24.44/4.08 v4 & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 24.44/4.08 (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ % 24.44/4.08 aScalar0(v0) | ? [v3: $i] : ? [v4: $i] : (smndt0(v1) = v4 & smndt0(v0) = % 24.44/4.08 v3 & sdtasdt0(v3, v4) = v2 & $i(v4) & $i(v3) & $i(v2))) % 24.44/4.08 % 24.44/4.08 (mMulSc) % 24.44/4.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 24.44/4.08 $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | aScalar0(v2)) % 24.44/4.08 % 24.44/4.08 (mPosMon) % 24.44/4.09 $i(sz0z00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = % 24.44/4.09 v2) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(sz0z00, v1) | ~ % 24.44/4.09 sdtlseqdt0(sz0z00, v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | % 24.44/4.09 sdtlseqdt0(sz0z00, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 24.44/4.09 (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(sz0z00, v1) % 24.44/4.09 | ~ sdtlseqdt0(sz0z00, v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v3: % 24.44/4.09 $i] : (sdtpldt0(v0, v1) = v3 & $i(v3) & sdtlseqdt0(sz0z00, v3))) & ! [v0: % 24.44/4.09 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | % 24.44/4.09 ~ $i(v0) | ~ sdtlseqdt0(sz0z00, v1) | ~ sdtlseqdt0(sz0z00, v0) | ~ % 24.44/4.09 aScalar0(v1) | ~ aScalar0(v0) | sdtlseqdt0(sz0z00, v2)) & ! [v0: $i] : ! % 24.44/4.09 [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 24.44/4.09 ~ sdtlseqdt0(sz0z00, v1) | ~ sdtlseqdt0(sz0z00, v0) | ~ aScalar0(v1) | ~ % 24.44/4.09 aScalar0(v0) | ? [v3: $i] : (sdtasdt0(v0, v1) = v3 & $i(v3) & % 24.44/4.09 sdtlseqdt0(sz0z00, v3))) % 24.44/4.09 % 24.44/4.09 (mSZeroSc) % 24.44/4.09 $i(sz0z00) & aScalar0(sz0z00) % 24.44/4.09 % 24.44/4.09 (mScPr) % 24.44/4.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~ % 24.44/4.09 $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) | aScalar0(v2) | ? % 24.44/4.09 [v3: $i] : ? [v4: $i] : ( ~ (v4 = v3) & aDimensionOf0(v1) = v4 & % 24.44/4.09 aDimensionOf0(v0) = v3 & $i(v4) & $i(v3))) % 24.44/4.09 % 24.44/4.09 (mSqPos) % 24.44/4.09 $i(sz0z00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, v0) = v1) | ~ % 24.44/4.09 $i(v0) | ~ aScalar0(v0) | sdtlseqdt0(sz0z00, v1)) % 24.44/4.09 % 24.44/4.09 (m__) % 24.44/4.09 $i(sz0z00) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasasdt0(v0, v0) = % 24.44/4.09 v2 & aDimensionOf0(v0) = v1 & $i(v2) & $i(v1) & $i(v0) & aVector0(v0) & ~ % 24.44/4.09 sdtlseqdt0(sz0z00, v2) & ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasasdt0(v3, v3) % 24.44/4.09 = v4) | ~ $i(v3) | ~ aVector0(v3) | sdtlseqdt0(sz0z00, v4) | ? [v5: % 24.44/4.09 $i] : (aDimensionOf0(v3) = v5 & $i(v5) & ~ iLess0(v5, v1))) & ! [v3: % 24.44/4.09 $i] : ! [v4: $i] : ( ~ (aDimensionOf0(v3) = v4) | ~ $i(v3) | ~ % 24.44/4.09 aVector0(v3) | ~ iLess0(v4, v1) | ? [v5: $i] : (sdtasasdt0(v3, v3) = v5 % 24.44/4.09 & $i(v5) & sdtlseqdt0(sz0z00, v5)))) % 24.44/4.09 % 24.44/4.09 (function-axioms) % 24.44/4.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 24.44/4.09 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 24.44/4.09 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) % 24.44/4.09 | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 24.44/4.09 ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = % 24.44/4.09 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 24.44/4.09 ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 24.44/4.09 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sziznziztdt0(v2) = v1) | ~ % 24.44/4.09 (sziznziztdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 24.44/4.09 v0 | ~ (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) & ! [v0: % 24.44/4.09 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ % 24.44/4.09 (smndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 24.44/4.09 (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0)) % 24.44/4.09 % 24.44/4.09 Further assumptions not needed in the proof: % 24.44/4.09 -------------------------------------------- % 24.44/4.09 mArith, mDistr, mDistr2, mIHOrd, mLEASm, mLEMon, mLEMonM, mLERef, mLETrn, mLess, % 24.44/4.09 mMNeg, mNatExtr, mNatSort, mNegSc, mScSort, mScZero, mSqrt, mSuccEqu, mSuccNat, % 24.44/4.09 mSumSc, mVcSort, mZeroNat % 24.44/4.09 % 24.44/4.09 Those formulas are unsatisfiable: % 24.44/4.09 --------------------------------- % 24.44/4.09 % 24.44/4.09 Begin of proof % 24.44/4.09 | % 24.44/4.09 | ALPHA: (mSZeroSc) implies: % 24.44/4.09 | (1) aScalar0(sz0z00) % 24.44/4.09 | % 24.44/4.09 | ALPHA: (mMDNeg) implies: % 24.44/4.09 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | % 24.44/4.09 | ~ $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v3: % 24.44/4.09 | $i] : ? [v4: $i] : (smndt0(v1) = v4 & smndt0(v0) = v3 & % 24.44/4.09 | sdtasdt0(v3, v4) = v2 & $i(v4) & $i(v3) & $i(v2))) % 24.44/4.09 | % 24.44/4.09 | ALPHA: (mPosMon) implies: % 24.44/4.10 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | % 24.44/4.10 | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(sz0z00, v1) | ~ % 24.44/4.10 | sdtlseqdt0(sz0z00, v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | % 24.44/4.10 | sdtlseqdt0(sz0z00, v2)) % 24.44/4.10 | % 24.44/4.10 | ALPHA: (mSqPos) implies: % 24.44/4.10 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, v0) = v1) | ~ $i(v0) | % 24.44/4.10 | ~ aScalar0(v0) | sdtlseqdt0(sz0z00, v1)) % 24.44/4.10 | % 24.44/4.10 | ALPHA: (mDefInit) implies: % 24.44/4.10 | (5) ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ (aDimensionOf0(v0) = v1) | % 24.44/4.10 | ~ $i(v0) | ~ aVector0(v0) | ? [v2: $i] : (sziznziztdt0(v0) = v2 & % 24.44/4.10 | $i(v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 24.44/4.10 | (sdtlbdtrb0(v2, v4) = v5) | ~ (aDimensionOf0(v2) = v3) | ~ % 24.44/4.10 | $i(v4) | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v0, v4) = v5 & % 24.44/4.10 | $i(v5))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 24.44/4.10 | (sdtlbdtrb0(v0, v4) = v5) | ~ (aDimensionOf0(v2) = v3) | ~ % 24.44/4.10 | $i(v4) | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v2, v4) = v5 & % 24.44/4.10 | $i(v5))) & ! [v3: $i] : ! [v4: $i] : (v3 = v2 | ~ % 24.44/4.10 | (aDimensionOf0(v3) = v4) | ~ $i(v3) | ~ aVector0(v3) | ? [v5: % 24.44/4.10 | $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ($i(v6) & (( ~ % 24.44/4.10 | (v8 = v7) & sdtlbdtrb0(v3, v6) = v7 & sdtlbdtrb0(v0, v6) = % 24.44/4.10 | v8 & $i(v8) & $i(v7) & aNaturalNumber0(v6)) | ( ~ (v5 = v1) % 24.44/4.10 | & szszuzczcdt0(v4) = v5 & $i(v5))))) & ! [v3: $i] : ( ~ % 24.44/4.10 | (aDimensionOf0(v2) = v3) | aVector0(v2)) & ! [v3: $i] : ( ~ % 24.44/4.10 | (aDimensionOf0(v2) = v3) | (szszuzczcdt0(v3) = v1 & $i(v1))))) % 24.44/4.10 | % 24.44/4.10 | ALPHA: (mEqInit) implies: % 24.44/4.10 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = sz00 | ~ % 24.44/4.10 | (aDimensionOf0(v1) = v2) | ~ (aDimensionOf0(v0) = v2) | ~ $i(v1) | % 24.44/4.10 | ~ $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) | ? [v3: $i] : ? [v4: % 24.44/4.10 | $i] : ? [v5: $i] : (sziznziztdt0(v1) = v5 & sziznziztdt0(v0) = v3 % 24.44/4.10 | & aDimensionOf0(v5) = v4 & aDimensionOf0(v3) = v4 & $i(v5) & $i(v4) % 24.44/4.10 | & $i(v3))) % 24.44/4.10 | % 24.44/4.10 | ALPHA: (mDefSPZ) implies: % 24.44/4.10 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = sz0z00 | ~ % 24.44/4.10 | (sdtasasdt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | % 24.44/4.10 | ~ aVector0(v0) | ? [v3: $i] : ? [v4: $i] : (aDimensionOf0(v1) = v4 % 24.44/4.10 | & $i(v4) & ( ~ (v4 = sz00) | ( ~ (v3 = sz00) & aDimensionOf0(v0) = % 24.44/4.10 | v3 & $i(v3))))) % 24.44/4.10 | % 24.44/4.10 | ALPHA: (mDefSPN) implies: % 24.44/4.10 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasasdt0(v0, v1) = v2) % 24.44/4.10 | | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) | ? [v3: % 24.44/4.10 | $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? % 24.44/4.10 | [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : % 24.44/4.10 | (aDimensionOf0(v1) = v4 & $i(v4) & (v4 = sz00 | (v11 = v2 & % 24.44/4.10 | sdtasasdt0(v5, v6) = v7 & sziznziztdt0(v1) = v6 & % 24.44/4.10 | sziznziztdt0(v0) = v5 & sdtlbdtrb0(v1, v4) = v9 & % 24.44/4.10 | sdtlbdtrb0(v0, v3) = v8 & aDimensionOf0(v0) = v3 & sdtasdt0(v8, % 24.44/4.10 | v9) = v10 & sdtpldt0(v7, v10) = v2 & $i(v10) & $i(v9) & % 24.44/4.10 | $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v3) & $i(v2)) | ( ~ (v4 % 24.44/4.10 | = v3) & aDimensionOf0(v0) = v3 & $i(v3))))) % 24.44/4.10 | % 24.44/4.10 | ALPHA: (m__) implies: % 24.44/4.10 | (9) $i(sz0z00) % 24.44/4.10 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasasdt0(v0, v0) = v2 & % 24.44/4.10 | aDimensionOf0(v0) = v1 & $i(v2) & $i(v1) & $i(v0) & aVector0(v0) & % 24.44/4.11 | ~ sdtlseqdt0(sz0z00, v2) & ! [v3: $i] : ! [v4: $i] : ( ~ % 24.44/4.11 | (sdtasasdt0(v3, v3) = v4) | ~ $i(v3) | ~ aVector0(v3) | % 24.44/4.11 | sdtlseqdt0(sz0z00, v4) | ? [v5: $i] : (aDimensionOf0(v3) = v5 & % 24.44/4.11 | $i(v5) & ~ iLess0(v5, v1))) & ! [v3: $i] : ! [v4: $i] : ( ~ % 24.44/4.11 | (aDimensionOf0(v3) = v4) | ~ $i(v3) | ~ aVector0(v3) | ~ % 24.44/4.11 | iLess0(v4, v1) | ? [v5: $i] : (sdtasasdt0(v3, v3) = v5 & $i(v5) & % 24.44/4.11 | sdtlseqdt0(sz0z00, v5)))) % 24.44/4.11 | % 24.44/4.11 | ALPHA: (function-axioms) implies: % 24.44/4.11 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 24.44/4.11 | (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) % 24.44/4.11 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 24.44/4.11 | (sziznziztdt0(v2) = v1) | ~ (sziznziztdt0(v2) = v0)) % 24.44/4.11 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 24.44/4.11 | (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) = v0)) % 24.44/4.11 | % 24.44/4.11 | DELTA: instantiating (10) with fresh symbols all_32_0, all_32_1, all_32_2 % 24.44/4.11 | gives: % 24.44/4.11 | (14) sdtasasdt0(all_32_2, all_32_2) = all_32_0 & aDimensionOf0(all_32_2) = % 24.44/4.11 | all_32_1 & $i(all_32_0) & $i(all_32_1) & $i(all_32_2) & % 24.44/4.11 | aVector0(all_32_2) & ~ sdtlseqdt0(sz0z00, all_32_0) & ! [v0: $i] : % 24.44/4.11 | ! [v1: $i] : ( ~ (sdtasasdt0(v0, v0) = v1) | ~ $i(v0) | ~ % 24.44/4.11 | aVector0(v0) | sdtlseqdt0(sz0z00, v1) | ? [v2: $i] : % 24.44/4.11 | (aDimensionOf0(v0) = v2 & $i(v2) & ~ iLess0(v2, all_32_1))) & ! % 24.44/4.11 | [v0: $i] : ! [v1: $i] : ( ~ (aDimensionOf0(v0) = v1) | ~ $i(v0) | ~ % 24.44/4.11 | aVector0(v0) | ~ iLess0(v1, all_32_1) | ? [v2: $i] : % 24.44/4.11 | (sdtasasdt0(v0, v0) = v2 & $i(v2) & sdtlseqdt0(sz0z00, v2))) % 24.44/4.11 | % 24.44/4.11 | ALPHA: (14) implies: % 24.44/4.11 | (15) ~ sdtlseqdt0(sz0z00, all_32_0) % 24.44/4.11 | (16) aVector0(all_32_2) % 24.44/4.11 | (17) $i(all_32_2) % 24.44/4.11 | (18) aDimensionOf0(all_32_2) = all_32_1 % 24.44/4.11 | (19) sdtasasdt0(all_32_2, all_32_2) = all_32_0 % 24.44/4.11 | (20) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasasdt0(v0, v0) = v1) | ~ $i(v0) % 24.44/4.11 | | ~ aVector0(v0) | sdtlseqdt0(sz0z00, v1) | ? [v2: $i] : % 24.44/4.11 | (aDimensionOf0(v0) = v2 & $i(v2) & ~ iLess0(v2, all_32_1))) % 24.44/4.11 | % 24.44/4.11 | GROUND_INST: instantiating (mLETot) with sz0z00, sz0z00, simplifying with (1), % 24.44/4.11 | (9) gives: % 24.44/4.11 | (21) sdtlseqdt0(sz0z00, sz0z00) % 24.44/4.11 | % 24.44/4.11 | GROUND_INST: instantiating (6) with all_32_2, all_32_2, all_32_1, simplifying % 24.44/4.11 | with (16), (17), (18) gives: % 24.44/4.11 | (22) all_32_1 = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 24.44/4.11 | (sziznziztdt0(all_32_2) = v2 & sziznziztdt0(all_32_2) = v0 & % 24.44/4.11 | aDimensionOf0(v2) = v1 & aDimensionOf0(v0) = v1 & $i(v2) & $i(v1) & % 24.44/4.11 | $i(v0)) % 24.44/4.11 | % 24.44/4.11 | GROUND_INST: instantiating (5) with all_32_2, all_32_1, simplifying with (16), % 24.44/4.11 | (17), (18) gives: % 24.44/4.12 | (23) all_32_1 = sz00 | ? [v0: $i] : (sziznziztdt0(all_32_2) = v0 & $i(v0) % 24.44/4.12 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlbdtrb0(v0, v2) % 24.44/4.12 | = v3) | ~ (aDimensionOf0(v0) = v1) | ~ $i(v2) | ~ % 24.44/4.12 | aNaturalNumber0(v2) | (sdtlbdtrb0(all_32_2, v2) = v3 & $i(v3))) & % 24.44/4.12 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlbdtrb0(all_32_2, % 24.44/4.12 | v2) = v3) | ~ (aDimensionOf0(v0) = v1) | ~ $i(v2) | ~ % 24.44/4.12 | aNaturalNumber0(v2) | (sdtlbdtrb0(v0, v2) = v3 & $i(v3))) & ! % 24.44/4.12 | [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (aDimensionOf0(v1) = v2) | ~ % 24.44/4.12 | $i(v1) | ~ aVector0(v1) | ? [v3: any] : ? [v4: $i] : ? [v5: % 24.44/4.12 | $i] : ? [v6: $i] : ($i(v4) & (( ~ (v6 = v5) & sdtlbdtrb0(v1, % 24.44/4.12 | v4) = v5 & sdtlbdtrb0(all_32_2, v4) = v6 & $i(v6) & $i(v5) % 24.44/4.12 | & aNaturalNumber0(v4)) | ( ~ (v3 = all_32_1) & % 24.44/4.12 | szszuzczcdt0(v2) = v3 & $i(v3))))) & ! [v1: $i] : ( ~ % 24.44/4.12 | (aDimensionOf0(v0) = v1) | aVector0(v0)) & ! [v1: $i] : ( ~ % 24.44/4.12 | (aDimensionOf0(v0) = v1) | (szszuzczcdt0(v1) = all_32_1 & % 24.44/4.12 | $i(all_32_1)))) % 24.44/4.12 | % 24.44/4.12 | GROUND_INST: instantiating (mDimNat) with all_32_2, all_32_1, simplifying with % 24.44/4.12 | (16), (17), (18) gives: % 24.44/4.12 | (24) aNaturalNumber0(all_32_1) % 24.44/4.12 | % 24.85/4.12 | GROUND_INST: instantiating (7) with all_32_2, all_32_2, all_32_0, simplifying % 24.85/4.12 | with (16), (17), (19) gives: % 24.85/4.12 | (25) all_32_0 = sz0z00 | ? [v0: $i] : ? [v1: $i] : % 24.85/4.12 | (aDimensionOf0(all_32_2) = v1 & $i(v1) & ( ~ (v1 = sz00) | ( ~ (v0 = % 24.85/4.12 | sz00) & aDimensionOf0(all_32_2) = v0 & $i(v0)))) % 24.85/4.12 | % 24.85/4.12 | GROUND_INST: instantiating (8) with all_32_2, all_32_2, all_32_0, simplifying % 24.85/4.12 | with (16), (17), (19) gives: % 24.85/4.12 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 24.85/4.12 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : % 24.85/4.12 | (aDimensionOf0(all_32_2) = v1 & $i(v1) & (v1 = sz00 | (v8 = all_32_0 & % 24.85/4.12 | sdtasasdt0(v2, v3) = v4 & sziznziztdt0(all_32_2) = v3 & % 24.85/4.12 | sziznziztdt0(all_32_2) = v2 & sdtlbdtrb0(all_32_2, v1) = v6 & % 24.85/4.12 | sdtlbdtrb0(all_32_2, v0) = v5 & aDimensionOf0(all_32_2) = v0 & % 24.85/4.12 | sdtasdt0(v5, v6) = v7 & sdtpldt0(v4, v7) = all_32_0 & $i(v7) & % 24.85/4.12 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v0) & % 24.85/4.12 | $i(all_32_0)) | ( ~ (v1 = v0) & aDimensionOf0(all_32_2) = v0 & % 24.85/4.12 | $i(v0)))) % 24.85/4.12 | % 24.85/4.12 | GROUND_INST: instantiating (20) with all_32_2, all_32_0, simplifying with % 24.85/4.12 | (15), (16), (17), (19) gives: % 24.85/4.12 | (27) ? [v0: $i] : (aDimensionOf0(all_32_2) = v0 & $i(v0) & ~ iLess0(v0, % 24.85/4.12 | all_32_1)) % 24.85/4.12 | % 24.85/4.12 | DELTA: instantiating (27) with fresh symbol all_44_0 gives: % 24.85/4.12 | (28) aDimensionOf0(all_32_2) = all_44_0 & $i(all_44_0) & ~ % 24.85/4.12 | iLess0(all_44_0, all_32_1) % 24.85/4.12 | % 24.85/4.12 | ALPHA: (28) implies: % 24.85/4.12 | (29) aDimensionOf0(all_32_2) = all_44_0 % 24.85/4.12 | % 24.85/4.12 | DELTA: instantiating (26) with fresh symbols all_46_0, all_46_1, all_46_2, % 24.85/4.12 | all_46_3, all_46_4, all_46_5, all_46_6, all_46_7, all_46_8 gives: % 24.85/4.12 | (30) aDimensionOf0(all_32_2) = all_46_7 & $i(all_46_7) & (all_46_7 = sz00 | % 24.85/4.12 | (all_46_0 = all_32_0 & sdtasasdt0(all_46_6, all_46_5) = all_46_4 & % 24.85/4.12 | sziznziztdt0(all_32_2) = all_46_5 & sziznziztdt0(all_32_2) = % 24.85/4.12 | all_46_6 & sdtlbdtrb0(all_32_2, all_46_7) = all_46_2 & % 24.85/4.12 | sdtlbdtrb0(all_32_2, all_46_8) = all_46_3 & % 24.85/4.12 | aDimensionOf0(all_32_2) = all_46_8 & sdtasdt0(all_46_3, all_46_2) % 24.85/4.12 | = all_46_1 & sdtpldt0(all_46_4, all_46_1) = all_32_0 & % 24.85/4.12 | $i(all_46_1) & $i(all_46_2) & $i(all_46_3) & $i(all_46_4) & % 24.85/4.12 | $i(all_46_5) & $i(all_46_6) & $i(all_46_8) & $i(all_32_0)) | ( ~ % 24.85/4.12 | (all_46_7 = all_46_8) & aDimensionOf0(all_32_2) = all_46_8 & % 24.85/4.12 | $i(all_46_8))) % 24.85/4.12 | % 24.85/4.12 | ALPHA: (30) implies: % 24.85/4.12 | (31) aDimensionOf0(all_32_2) = all_46_7 % 24.85/4.12 | (32) all_46_7 = sz00 | (all_46_0 = all_32_0 & sdtasasdt0(all_46_6, % 24.85/4.12 | all_46_5) = all_46_4 & sziznziztdt0(all_32_2) = all_46_5 & % 24.85/4.12 | sziznziztdt0(all_32_2) = all_46_6 & sdtlbdtrb0(all_32_2, all_46_7) = % 24.85/4.12 | all_46_2 & sdtlbdtrb0(all_32_2, all_46_8) = all_46_3 & % 24.85/4.12 | aDimensionOf0(all_32_2) = all_46_8 & sdtasdt0(all_46_3, all_46_2) = % 24.85/4.12 | all_46_1 & sdtpldt0(all_46_4, all_46_1) = all_32_0 & $i(all_46_1) & % 24.85/4.12 | $i(all_46_2) & $i(all_46_3) & $i(all_46_4) & $i(all_46_5) & % 24.85/4.12 | $i(all_46_6) & $i(all_46_8) & $i(all_32_0)) | ( ~ (all_46_7 = % 24.85/4.12 | all_46_8) & aDimensionOf0(all_32_2) = all_46_8 & $i(all_46_8)) % 24.85/4.12 | % 24.85/4.12 | PRED_UNIFY: (15), (21) imply: % 24.85/4.12 | (33) ~ (all_32_0 = sz0z00) % 24.85/4.12 | % 24.85/4.12 | GROUND_INST: instantiating (11) with all_32_1, all_46_7, all_32_2, simplifying % 24.85/4.12 | with (18), (31) gives: % 24.85/4.12 | (34) all_46_7 = all_32_1 % 24.85/4.12 | % 24.85/4.12 | GROUND_INST: instantiating (11) with all_44_0, all_46_7, all_32_2, simplifying % 24.85/4.12 | with (29), (31) gives: % 24.85/4.12 | (35) all_46_7 = all_44_0 % 24.85/4.12 | % 24.85/4.12 | COMBINE_EQS: (34), (35) imply: % 24.85/4.12 | (36) all_44_0 = all_32_1 % 24.85/4.12 | % 24.85/4.12 | BETA: splitting (25) gives: % 24.85/4.12 | % 24.85/4.12 | Case 1: % 24.85/4.12 | | % 24.85/4.12 | | (37) all_32_0 = sz0z00 % 24.85/4.12 | | % 24.85/4.12 | | REDUCE: (33), (37) imply: % 24.85/4.12 | | (38) $false % 24.85/4.13 | | % 24.85/4.13 | | CLOSE: (38) is inconsistent. % 24.85/4.13 | | % 24.85/4.13 | Case 2: % 24.85/4.13 | | % 24.85/4.13 | | (39) ? [v0: $i] : ? [v1: $i] : (aDimensionOf0(all_32_2) = v1 & $i(v1) & % 24.85/4.13 | | ( ~ (v1 = sz00) | ( ~ (v0 = sz00) & aDimensionOf0(all_32_2) = v0 & % 24.85/4.13 | | $i(v0)))) % 24.85/4.13 | | % 24.85/4.13 | | DELTA: instantiating (39) with fresh symbols all_60_0, all_60_1 gives: % 24.85/4.13 | | (40) aDimensionOf0(all_32_2) = all_60_0 & $i(all_60_0) & ( ~ (all_60_0 = % 24.85/4.13 | | sz00) | ( ~ (all_60_1 = sz00) & aDimensionOf0(all_32_2) = % 24.85/4.13 | | all_60_1 & $i(all_60_1))) % 24.85/4.13 | | % 24.85/4.13 | | ALPHA: (40) implies: % 24.85/4.13 | | (41) aDimensionOf0(all_32_2) = all_60_0 % 24.85/4.13 | | (42) ~ (all_60_0 = sz00) | ( ~ (all_60_1 = sz00) & % 24.85/4.13 | | aDimensionOf0(all_32_2) = all_60_1 & $i(all_60_1)) % 24.85/4.13 | | % 24.85/4.13 | | BETA: splitting (42) gives: % 24.85/4.13 | | % 24.85/4.13 | | Case 1: % 24.85/4.13 | | | % 24.85/4.13 | | | (43) ~ (all_60_0 = sz00) % 24.85/4.13 | | | % 24.85/4.13 | | | GROUND_INST: instantiating (11) with all_32_1, all_60_0, all_32_2, % 24.85/4.13 | | | simplifying with (18), (41) gives: % 24.85/4.13 | | | (44) all_60_0 = all_32_1 % 24.85/4.13 | | | % 24.85/4.13 | | | REDUCE: (43), (44) imply: % 24.85/4.13 | | | (45) ~ (all_32_1 = sz00) % 24.85/4.13 | | | % 24.85/4.13 | | | BETA: splitting (32) gives: % 24.85/4.13 | | | % 24.85/4.13 | | | Case 1: % 24.85/4.13 | | | | % 24.85/4.13 | | | | (46) all_46_7 = sz00 % 24.85/4.13 | | | | % 24.85/4.13 | | | | COMBINE_EQS: (34), (46) imply: % 24.85/4.13 | | | | (47) all_32_1 = sz00 % 24.85/4.13 | | | | % 24.85/4.13 | | | | SIMP: (47) implies: % 24.85/4.13 | | | | (48) all_32_1 = sz00 % 24.85/4.13 | | | | % 24.85/4.13 | | | | REDUCE: (45), (48) imply: % 24.85/4.13 | | | | (49) $false % 24.85/4.13 | | | | % 24.85/4.13 | | | | CLOSE: (49) is inconsistent. % 24.85/4.13 | | | | % 24.85/4.13 | | | Case 2: % 24.85/4.13 | | | | % 24.85/4.13 | | | | (50) ~ (all_46_7 = sz00) % 24.85/4.13 | | | | (51) (all_46_0 = all_32_0 & sdtasasdt0(all_46_6, all_46_5) = all_46_4 % 24.85/4.13 | | | | & sziznziztdt0(all_32_2) = all_46_5 & sziznziztdt0(all_32_2) = % 24.85/4.13 | | | | all_46_6 & sdtlbdtrb0(all_32_2, all_46_7) = all_46_2 & % 24.85/4.13 | | | | sdtlbdtrb0(all_32_2, all_46_8) = all_46_3 & % 24.85/4.13 | | | | aDimensionOf0(all_32_2) = all_46_8 & sdtasdt0(all_46_3, % 24.85/4.13 | | | | all_46_2) = all_46_1 & sdtpldt0(all_46_4, all_46_1) = % 24.85/4.13 | | | | all_32_0 & $i(all_46_1) & $i(all_46_2) & $i(all_46_3) & % 24.85/4.13 | | | | $i(all_46_4) & $i(all_46_5) & $i(all_46_6) & $i(all_46_8) & % 24.85/4.13 | | | | $i(all_32_0)) | ( ~ (all_46_7 = all_46_8) & % 24.85/4.13 | | | | aDimensionOf0(all_32_2) = all_46_8 & $i(all_46_8)) % 24.85/4.13 | | | | % 24.85/4.13 | | | | BETA: splitting (22) gives: % 24.85/4.13 | | | | % 24.85/4.13 | | | | Case 1: % 24.85/4.13 | | | | | % 24.85/4.13 | | | | | (52) all_32_1 = sz00 % 24.85/4.13 | | | | | % 24.85/4.13 | | | | | REDUCE: (45), (52) imply: % 24.85/4.13 | | | | | (53) $false % 24.85/4.13 | | | | | % 24.85/4.13 | | | | | CLOSE: (53) is inconsistent. % 24.85/4.13 | | | | | % 24.85/4.13 | | | | Case 2: % 24.85/4.13 | | | | | % 24.85/4.13 | | | | | (54) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 24.85/4.13 | | | | | (sziznziztdt0(all_32_2) = v2 & sziznziztdt0(all_32_2) = v0 & % 24.85/4.13 | | | | | aDimensionOf0(v2) = v1 & aDimensionOf0(v0) = v1 & $i(v2) & % 24.85/4.13 | | | | | $i(v1) & $i(v0)) % 24.85/4.13 | | | | | % 24.85/4.13 | | | | | DELTA: instantiating (54) with fresh symbols all_77_0, all_77_1, % 24.85/4.13 | | | | | all_77_2 gives: % 24.85/4.13 | | | | | (55) sziznziztdt0(all_32_2) = all_77_0 & sziznziztdt0(all_32_2) = % 24.85/4.13 | | | | | all_77_2 & aDimensionOf0(all_77_0) = all_77_1 & % 24.85/4.13 | | | | | aDimensionOf0(all_77_2) = all_77_1 & $i(all_77_0) & % 24.85/4.13 | | | | | $i(all_77_1) & $i(all_77_2) % 24.85/4.13 | | | | | % 24.85/4.13 | | | | | ALPHA: (55) implies: % 24.85/4.13 | | | | | (56) $i(all_77_1) % 24.85/4.13 | | | | | (57) aDimensionOf0(all_77_2) = all_77_1 % 24.85/4.13 | | | | | (58) sziznziztdt0(all_32_2) = all_77_2 % 24.85/4.13 | | | | | (59) sziznziztdt0(all_32_2) = all_77_0 % 24.85/4.13 | | | | | % 24.85/4.13 | | | | | BETA: splitting (23) gives: % 24.85/4.13 | | | | | % 24.85/4.13 | | | | | Case 1: % 24.85/4.13 | | | | | | % 24.85/4.13 | | | | | | (60) all_32_1 = sz00 % 24.85/4.13 | | | | | | % 24.85/4.13 | | | | | | REDUCE: (45), (60) imply: % 24.85/4.13 | | | | | | (61) $false % 24.85/4.13 | | | | | | % 24.85/4.13 | | | | | | CLOSE: (61) is inconsistent. % 24.85/4.13 | | | | | | % 24.85/4.13 | | | | | Case 2: % 24.85/4.13 | | | | | | % 24.85/4.13 | | | | | | (62) ? [v0: $i] : (sziznziztdt0(all_32_2) = v0 & $i(v0) & ! % 24.85/4.13 | | | | | | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlbdtrb0(v0, % 24.85/4.13 | | | | | | v2) = v3) | ~ (aDimensionOf0(v0) = v1) | ~ $i(v2) % 24.85/4.13 | | | | | | | ~ aNaturalNumber0(v2) | (sdtlbdtrb0(all_32_2, v2) = % 24.85/4.13 | | | | | | v3 & $i(v3))) & ! [v1: $i] : ! [v2: $i] : ! [v3: % 24.85/4.13 | | | | | | $i] : ( ~ (sdtlbdtrb0(all_32_2, v2) = v3) | ~ % 24.85/4.13 | | | | | | (aDimensionOf0(v0) = v1) | ~ $i(v2) | ~ % 24.85/4.13 | | | | | | aNaturalNumber0(v2) | (sdtlbdtrb0(v0, v2) = v3 & % 24.85/4.13 | | | | | | $i(v3))) & ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 24.85/4.13 | | | | | | (aDimensionOf0(v1) = v2) | ~ $i(v1) | ~ aVector0(v1) | % 24.85/4.13 | | | | | | ? [v3: any] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 24.85/4.13 | | | | | | ($i(v4) & (( ~ (v6 = v5) & sdtlbdtrb0(v1, v4) = v5 & % 24.85/4.13 | | | | | | sdtlbdtrb0(all_32_2, v4) = v6 & $i(v6) & $i(v5) & % 24.85/4.13 | | | | | | aNaturalNumber0(v4)) | ( ~ (v3 = all_32_1) & % 24.85/4.13 | | | | | | szszuzczcdt0(v2) = v3 & $i(v3))))) & ! [v1: $i] : % 24.85/4.13 | | | | | | ( ~ (aDimensionOf0(v0) = v1) | aVector0(v0)) & ! [v1: $i] % 24.85/4.13 | | | | | | : ( ~ (aDimensionOf0(v0) = v1) | (szszuzczcdt0(v1) = % 24.85/4.13 | | | | | | all_32_1 & $i(all_32_1)))) % 24.85/4.13 | | | | | | % 24.85/4.13 | | | | | | DELTA: instantiating (62) with fresh symbol all_82_0 gives: % 24.85/4.13 | | | | | | (63) sziznziztdt0(all_32_2) = all_82_0 & $i(all_82_0) & ! [v0: % 24.85/4.14 | | | | | | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 24.85/4.14 | | | | | | (sdtlbdtrb0(all_82_0, v1) = v2) | ~ % 24.85/4.14 | | | | | | (aDimensionOf0(all_82_0) = v0) | ~ $i(v1) | ~ % 24.85/4.14 | | | | | | aNaturalNumber0(v1) | (sdtlbdtrb0(all_32_2, v1) = v2 & % 24.85/4.14 | | | | | | $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 24.85/4.14 | | | | | | (sdtlbdtrb0(all_32_2, v1) = v2) | ~ % 24.85/4.14 | | | | | | (aDimensionOf0(all_82_0) = v0) | ~ $i(v1) | ~ % 24.85/4.14 | | | | | | aNaturalNumber0(v1) | (sdtlbdtrb0(all_82_0, v1) = v2 & % 24.85/4.14 | | | | | | $i(v2))) & ! [v0: any] : ! [v1: $i] : (v0 = all_82_0 | % 24.85/4.14 | | | | | | ~ (aDimensionOf0(v0) = v1) | ~ $i(v0) | ~ aVector0(v0) % 24.85/4.14 | | | | | | | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 24.85/4.14 | | | | | | ($i(v3) & (( ~ (v5 = v4) & sdtlbdtrb0(v0, v3) = v4 & % 24.85/4.14 | | | | | | sdtlbdtrb0(all_32_2, v3) = v5 & $i(v5) & $i(v4) & % 24.85/4.14 | | | | | | aNaturalNumber0(v3)) | ( ~ (v2 = all_32_1) & % 24.85/4.14 | | | | | | szszuzczcdt0(v1) = v2 & $i(v2))))) & ! [v0: $i] : ( % 24.85/4.14 | | | | | | ~ (aDimensionOf0(all_82_0) = v0) | aVector0(all_82_0)) & % 24.85/4.14 | | | | | | ! [v0: $i] : ( ~ (aDimensionOf0(all_82_0) = v0) | % 24.85/4.14 | | | | | | (szszuzczcdt0(v0) = all_32_1 & $i(all_32_1))) % 24.85/4.14 | | | | | | % 24.85/4.14 | | | | | | ALPHA: (63) implies: % 24.85/4.14 | | | | | | (64) sziznziztdt0(all_32_2) = all_82_0 % 24.85/4.14 | | | | | | (65) ! [v0: $i] : ( ~ (aDimensionOf0(all_82_0) = v0) | % 24.85/4.14 | | | | | | (szszuzczcdt0(v0) = all_32_1 & $i(all_32_1))) % 24.85/4.14 | | | | | | (66) ! [v0: $i] : ( ~ (aDimensionOf0(all_82_0) = v0) | % 24.85/4.14 | | | | | | aVector0(all_82_0)) % 24.85/4.14 | | | | | | % 24.85/4.14 | | | | | | BETA: splitting (51) gives: % 24.85/4.14 | | | | | | % 24.85/4.14 | | | | | | Case 1: % 24.85/4.14 | | | | | | | % 24.85/4.14 | | | | | | | (67) all_46_0 = all_32_0 & sdtasasdt0(all_46_6, all_46_5) = % 24.85/4.14 | | | | | | | all_46_4 & sziznziztdt0(all_32_2) = all_46_5 & % 24.85/4.14 | | | | | | | sziznziztdt0(all_32_2) = all_46_6 & sdtlbdtrb0(all_32_2, % 24.85/4.14 | | | | | | | all_46_7) = all_46_2 & sdtlbdtrb0(all_32_2, all_46_8) = % 24.85/4.14 | | | | | | | all_46_3 & aDimensionOf0(all_32_2) = all_46_8 & % 24.85/4.14 | | | | | | | sdtasdt0(all_46_3, all_46_2) = all_46_1 & % 24.85/4.14 | | | | | | | sdtpldt0(all_46_4, all_46_1) = all_32_0 & $i(all_46_1) & % 24.85/4.14 | | | | | | | $i(all_46_2) & $i(all_46_3) & $i(all_46_4) & $i(all_46_5) % 24.85/4.14 | | | | | | | & $i(all_46_6) & $i(all_46_8) & $i(all_32_0) % 24.85/4.14 | | | | | | | % 24.85/4.14 | | | | | | | ALPHA: (67) implies: % 24.85/4.14 | | | | | | | (68) $i(all_46_8) % 24.85/4.14 | | | | | | | (69) $i(all_46_5) % 24.85/4.14 | | | | | | | (70) $i(all_46_4) % 24.85/4.14 | | | | | | | (71) $i(all_46_2) % 24.85/4.14 | | | | | | | (72) sdtpldt0(all_46_4, all_46_1) = all_32_0 % 24.85/4.14 | | | | | | | (73) sdtasdt0(all_46_3, all_46_2) = all_46_1 % 24.85/4.14 | | | | | | | (74) aDimensionOf0(all_32_2) = all_46_8 % 24.85/4.14 | | | | | | | (75) sdtlbdtrb0(all_32_2, all_46_8) = all_46_3 % 24.85/4.14 | | | | | | | (76) sdtlbdtrb0(all_32_2, all_46_7) = all_46_2 % 24.85/4.14 | | | | | | | (77) sziznziztdt0(all_32_2) = all_46_6 % 24.85/4.14 | | | | | | | (78) sziznziztdt0(all_32_2) = all_46_5 % 24.85/4.14 | | | | | | | (79) sdtasasdt0(all_46_6, all_46_5) = all_46_4 % 24.85/4.14 | | | | | | | % 24.85/4.14 | | | | | | | REDUCE: (34), (76) imply: % 24.85/4.14 | | | | | | | (80) sdtlbdtrb0(all_32_2, all_32_1) = all_46_2 % 24.85/4.14 | | | | | | | % 24.85/4.14 | | | | | | | GROUND_INST: instantiating (11) with all_32_1, all_46_8, all_32_2, % 24.85/4.14 | | | | | | | simplifying with (18), (74) gives: % 24.85/4.14 | | | | | | | (81) all_46_8 = all_32_1 % 24.85/4.14 | | | | | | | % 24.85/4.14 | | | | | | | GROUND_INST: instantiating (13) with all_46_2, all_46_3, all_32_1, % 24.85/4.14 | | | | | | | all_32_2, simplifying with (80) gives: % 24.85/4.14 | | | | | | | (82) all_46_2 = all_46_3 | ~ (sdtlbdtrb0(all_32_2, all_32_1) = % 24.85/4.14 | | | | | | | all_46_3) % 24.85/4.14 | | | | | | | % 24.85/4.14 | | | | | | | GROUND_INST: instantiating (12) with all_77_2, all_77_0, all_32_2, % 24.85/4.14 | | | | | | | simplifying with (58), (59) gives: % 24.85/4.14 | | | | | | | (83) all_77_0 = all_77_2 % 24.85/4.14 | | | | | | | % 24.85/4.14 | | | | | | | GROUND_INST: instantiating (12) with all_46_5, all_77_0, all_32_2, % 24.85/4.14 | | | | | | | simplifying with (59), (78) gives: % 24.85/4.14 | | | | | | | (84) all_77_0 = all_46_5 % 24.85/4.14 | | | | | | | % 24.85/4.14 | | | | | | | GROUND_INST: instantiating (12) with all_77_0, all_82_0, all_32_2, % 24.85/4.14 | | | | | | | simplifying with (59), (64) gives: % 24.85/4.14 | | | | | | | (85) all_82_0 = all_77_0 % 24.85/4.14 | | | | | | | % 24.85/4.14 | | | | | | | GROUND_INST: instantiating (12) with all_46_6, all_82_0, all_32_2, % 24.85/4.14 | | | | | | | simplifying with (64), (77) gives: % 24.85/4.14 | | | | | | | (86) all_82_0 = all_46_6 % 24.85/4.14 | | | | | | | % 24.85/4.14 | | | | | | | COMBINE_EQS: (85), (86) imply: % 24.85/4.14 | | | | | | | (87) all_77_0 = all_46_6 % 24.85/4.14 | | | | | | | % 24.85/4.14 | | | | | | | SIMP: (87) implies: % 24.85/4.14 | | | | | | | (88) all_77_0 = all_46_6 % 24.85/4.14 | | | | | | | % 24.85/4.14 | | | | | | | COMBINE_EQS: (83), (88) imply: % 24.85/4.14 | | | | | | | (89) all_77_2 = all_46_6 % 24.85/4.14 | | | | | | | % 24.85/4.14 | | | | | | | COMBINE_EQS: (83), (84) imply: % 24.85/4.14 | | | | | | | (90) all_77_2 = all_46_5 % 24.85/4.14 | | | | | | | % 24.85/4.14 | | | | | | | COMBINE_EQS: (89), (90) imply: % 24.85/4.14 | | | | | | | (91) all_46_5 = all_46_6 % 24.85/4.14 | | | | | | | % 24.85/4.14 | | | | | | | SIMP: (91) implies: % 24.85/4.14 | | | | | | | (92) all_46_5 = all_46_6 % 24.85/4.14 | | | | | | | % 24.85/4.14 | | | | | | | REDUCE: (79), (92) imply: % 24.85/4.14 | | | | | | | (93) sdtasasdt0(all_46_6, all_46_6) = all_46_4 % 24.85/4.14 | | | | | | | % 24.85/4.14 | | | | | | | REDUCE: (75), (81) imply: % 24.85/4.14 | | | | | | | (94) sdtlbdtrb0(all_32_2, all_32_1) = all_46_3 % 24.85/4.14 | | | | | | | % 24.85/4.14 | | | | | | | REDUCE: (57), (89) imply: % 24.85/4.14 | | | | | | | (95) aDimensionOf0(all_46_6) = all_77_1 % 24.85/4.14 | | | | | | | % 24.85/4.14 | | | | | | | REDUCE: (69), (92) imply: % 24.85/4.14 | | | | | | | (96) $i(all_46_6) % 24.85/4.14 | | | | | | | % 24.85/4.14 | | | | | | | REDUCE: (68), (81) imply: % 24.85/4.14 | | | | | | | (97) $i(all_32_1) % 24.85/4.14 | | | | | | | % 24.85/4.14 | | | | | | | BETA: splitting (82) gives: % 24.85/4.14 | | | | | | | % 24.85/4.14 | | | | | | | Case 1: % 24.85/4.14 | | | | | | | | % 24.85/4.14 | | | | | | | | (98) ~ (sdtlbdtrb0(all_32_2, all_32_1) = all_46_3) % 24.85/4.14 | | | | | | | | % 24.85/4.14 | | | | | | | | PRED_UNIFY: (94), (98) imply: % 24.85/4.14 | | | | | | | | (99) $false % 24.85/4.14 | | | | | | | | % 24.85/4.14 | | | | | | | | CLOSE: (99) is inconsistent. % 24.85/4.14 | | | | | | | | % 24.85/4.14 | | | | | | | Case 2: % 24.85/4.14 | | | | | | | | % 24.85/4.14 | | | | | | | | (100) all_46_2 = all_46_3 % 24.85/4.14 | | | | | | | | % 24.85/4.14 | | | | | | | | REDUCE: (73), (100) imply: % 24.85/4.14 | | | | | | | | (101) sdtasdt0(all_46_3, all_46_3) = all_46_1 % 24.85/4.14 | | | | | | | | % 24.85/4.14 | | | | | | | | REDUCE: (71), (100) imply: % 24.85/4.14 | | | | | | | | (102) $i(all_46_3) % 24.85/4.14 | | | | | | | | % 24.85/4.14 | | | | | | | | GROUND_INST: instantiating (66) with all_77_1 gives: % 24.85/4.14 | | | | | | | | (103) ~ (aDimensionOf0(all_82_0) = all_77_1) | % 24.85/4.14 | | | | | | | | aVector0(all_82_0) % 24.85/4.14 | | | | | | | | % 24.85/4.14 | | | | | | | | GROUND_INST: instantiating (65) with all_77_1 gives: % 24.85/4.14 | | | | | | | | (104) ~ (aDimensionOf0(all_82_0) = all_77_1) | % 24.85/4.14 | | | | | | | | (szszuzczcdt0(all_77_1) = all_32_1 & $i(all_32_1)) % 24.85/4.14 | | | | | | | | % 24.85/4.14 | | | | | | | | GROUND_INST: instantiating (mElmSc) with all_32_2, all_32_1, % 24.85/4.14 | | | | | | | | all_46_3, simplifying with (16), (17), (24), (94), % 24.85/4.14 | | | | | | | | (97) gives: % 24.85/4.14 | | | | | | | | (105) aScalar0(all_46_3) % 24.85/4.14 | | | | | | | | % 24.85/4.14 | | | | | | | | BETA: splitting (103) gives: % 24.85/4.14 | | | | | | | | % 24.85/4.14 | | | | | | | | Case 1: % 24.85/4.14 | | | | | | | | | % 24.85/4.14 | | | | | | | | | (106) ~ (aDimensionOf0(all_82_0) = all_77_1) % 24.85/4.14 | | | | | | | | | % 24.85/4.14 | | | | | | | | | REDUCE: (86), (106) imply: % 24.85/4.14 | | | | | | | | | (107) ~ (aDimensionOf0(all_46_6) = all_77_1) % 24.85/4.14 | | | | | | | | | % 24.85/4.15 | | | | | | | | | PRED_UNIFY: (95), (107) imply: % 24.85/4.15 | | | | | | | | | (108) $false % 24.85/4.15 | | | | | | | | | % 24.85/4.15 | | | | | | | | | CLOSE: (108) is inconsistent. % 24.85/4.15 | | | | | | | | | % 24.85/4.15 | | | | | | | | Case 2: % 24.85/4.15 | | | | | | | | | % 24.85/4.15 | | | | | | | | | (109) aVector0(all_82_0) % 24.85/4.15 | | | | | | | | | (110) aDimensionOf0(all_82_0) = all_77_1 % 24.85/4.15 | | | | | | | | | % 24.85/4.15 | | | | | | | | | REDUCE: (86), (109) imply: % 24.85/4.15 | | | | | | | | | (111) aVector0(all_46_6) % 24.85/4.15 | | | | | | | | | % 24.85/4.15 | | | | | | | | | BETA: splitting (104) gives: % 24.85/4.15 | | | | | | | | | % 24.85/4.15 | | | | | | | | | Case 1: % 24.85/4.15 | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | (112) ~ (aDimensionOf0(all_82_0) = all_77_1) % 24.85/4.15 | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | REDUCE: (86), (112) imply: % 24.85/4.15 | | | | | | | | | | (113) ~ (aDimensionOf0(all_46_6) = all_77_1) % 24.85/4.15 | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | PRED_UNIFY: (95), (113) imply: % 24.85/4.15 | | | | | | | | | | (114) $false % 24.85/4.15 | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | CLOSE: (114) is inconsistent. % 24.85/4.15 | | | | | | | | | | % 24.85/4.15 | | | | | | | | | Case 2: % 24.85/4.15 | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | (115) szszuzczcdt0(all_77_1) = all_32_1 & $i(all_32_1) % 24.85/4.15 | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | ALPHA: (115) implies: % 24.85/4.15 | | | | | | | | | | (116) szszuzczcdt0(all_77_1) = all_32_1 % 24.85/4.15 | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | GROUND_INST: instantiating (mMulSc) with all_46_3, all_46_3, % 24.85/4.15 | | | | | | | | | | all_46_1, simplifying with (101), (102), (105) % 24.85/4.15 | | | | | | | | | | gives: % 24.85/4.15 | | | | | | | | | | (117) aScalar0(all_46_1) % 24.85/4.15 | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | GROUND_INST: instantiating (2) with all_46_3, all_46_3, % 24.85/4.15 | | | | | | | | | | all_46_1, simplifying with (101), (102), (105) % 24.85/4.15 | | | | | | | | | | gives: % 24.85/4.15 | | | | | | | | | | (118) ? [v0: $i] : ? [v1: $i] : (smndt0(all_46_3) = v1 % 24.85/4.15 | | | | | | | | | | & smndt0(all_46_3) = v0 & sdtasdt0(v0, v1) = % 24.85/4.15 | | | | | | | | | | all_46_1 & $i(v1) & $i(v0) & $i(all_46_1)) % 24.85/4.15 | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | GROUND_INST: instantiating (4) with all_46_3, all_46_1, % 24.85/4.15 | | | | | | | | | | simplifying with (101), (102), (105) gives: % 24.85/4.15 | | | | | | | | | | (119) sdtlseqdt0(sz0z00, all_46_1) % 24.85/4.15 | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | GROUND_INST: instantiating (mScPr) with all_46_6, all_46_6, % 24.85/4.15 | | | | | | | | | | all_46_4, simplifying with (93), (96), (111) % 24.85/4.15 | | | | | | | | | | gives: % 24.85/4.15 | | | | | | | | | | (120) aScalar0(all_46_4) | ? [v0: $i] : ? [v1: $i] : ( % 24.85/4.15 | | | | | | | | | | ~ (v1 = v0) & aDimensionOf0(all_46_6) = v1 & % 24.85/4.15 | | | | | | | | | | aDimensionOf0(all_46_6) = v0 & $i(v1) & $i(v0)) % 24.85/4.15 | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | GROUND_INST: instantiating (8) with all_46_6, all_46_6, % 24.85/4.15 | | | | | | | | | | all_46_4, simplifying with (93), (96), (111) % 24.85/4.15 | | | | | | | | | | gives: % 24.85/4.15 | | | | | | | | | | (121) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 24.85/4.15 | | | | | | | | | | $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 24.85/4.15 | | | | | | | | | | ? [v7: $i] : ? [v8: int] : % 24.85/4.15 | | | | | | | | | | (aDimensionOf0(all_46_6) = v1 & $i(v1) & (v1 = sz00 % 24.85/4.15 | | | | | | | | | | | (v8 = all_46_4 & sdtasasdt0(v2, v3) = v4 & % 24.85/4.15 | | | | | | | | | | sziznziztdt0(all_46_6) = v3 & % 24.85/4.15 | | | | | | | | | | sziznziztdt0(all_46_6) = v2 & % 24.85/4.15 | | | | | | | | | | sdtlbdtrb0(all_46_6, v1) = v6 & % 24.85/4.15 | | | | | | | | | | sdtlbdtrb0(all_46_6, v0) = v5 & % 24.85/4.15 | | | | | | | | | | aDimensionOf0(all_46_6) = v0 & sdtasdt0(v5, % 24.85/4.15 | | | | | | | | | | v6) = v7 & sdtpldt0(v4, v7) = all_46_4 & % 24.85/4.15 | | | | | | | | | | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 24.85/4.15 | | | | | | | | | | $i(v2) & $i(v0) & $i(all_46_4)) | ( ~ (v1 = % 24.85/4.15 | | | | | | | | | | v0) & aDimensionOf0(all_46_6) = v0 & % 24.85/4.15 | | | | | | | | | | $i(v0)))) % 24.85/4.15 | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | GROUND_INST: instantiating (20) with all_46_6, all_46_4, % 24.85/4.15 | | | | | | | | | | simplifying with (93), (96), (111) gives: % 24.85/4.15 | | | | | | | | | | (122) sdtlseqdt0(sz0z00, all_46_4) | ? [v0: $i] : % 24.85/4.15 | | | | | | | | | | (aDimensionOf0(all_46_6) = v0 & $i(v0) & ~ % 24.85/4.15 | | | | | | | | | | iLess0(v0, all_32_1)) % 24.85/4.15 | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | GROUND_INST: instantiating (mDimNat) with all_46_6, all_77_1, % 24.85/4.15 | | | | | | | | | | simplifying with (95), (96), (111) gives: % 24.85/4.15 | | | | | | | | | | (123) aNaturalNumber0(all_77_1) % 24.85/4.15 | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | GROUND_INST: instantiating (mIH) with all_77_1, all_32_1, % 24.85/4.15 | | | | | | | | | | simplifying with (56), (116) gives: % 24.85/4.15 | | | | | | | | | | (124) ~ aNaturalNumber0(all_77_1) | iLess0(all_77_1, % 24.85/4.15 | | | | | | | | | | all_32_1) % 24.85/4.15 | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | DELTA: instantiating (118) with fresh symbols all_137_0, % 24.85/4.15 | | | | | | | | | | all_137_1 gives: % 24.85/4.15 | | | | | | | | | | (125) smndt0(all_46_3) = all_137_0 & smndt0(all_46_3) = % 24.85/4.15 | | | | | | | | | | all_137_1 & sdtasdt0(all_137_1, all_137_0) = % 24.85/4.15 | | | | | | | | | | all_46_1 & $i(all_137_0) & $i(all_137_1) & % 24.85/4.15 | | | | | | | | | | $i(all_46_1) % 24.85/4.15 | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | ALPHA: (125) implies: % 24.85/4.15 | | | | | | | | | | (126) $i(all_46_1) % 24.85/4.15 | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | DELTA: instantiating (121) with fresh symbols all_142_0, % 24.85/4.15 | | | | | | | | | | all_142_1, all_142_2, all_142_3, all_142_4, % 24.85/4.15 | | | | | | | | | | all_142_5, all_142_6, all_142_7, all_142_8 gives: % 24.85/4.15 | | | | | | | | | | (127) aDimensionOf0(all_46_6) = all_142_7 & $i(all_142_7) % 24.85/4.15 | | | | | | | | | | & (all_142_7 = sz00 | (all_142_0 = all_46_4 & % 24.85/4.15 | | | | | | | | | | sdtasasdt0(all_142_6, all_142_5) = all_142_4 & % 24.85/4.15 | | | | | | | | | | sziznziztdt0(all_46_6) = all_142_5 & % 24.85/4.15 | | | | | | | | | | sziznziztdt0(all_46_6) = all_142_6 & % 24.85/4.15 | | | | | | | | | | sdtlbdtrb0(all_46_6, all_142_7) = all_142_2 & % 24.85/4.15 | | | | | | | | | | sdtlbdtrb0(all_46_6, all_142_8) = all_142_3 & % 24.85/4.15 | | | | | | | | | | aDimensionOf0(all_46_6) = all_142_8 & % 24.85/4.15 | | | | | | | | | | sdtasdt0(all_142_3, all_142_2) = all_142_1 & % 24.85/4.15 | | | | | | | | | | sdtpldt0(all_142_4, all_142_1) = all_46_4 & % 24.85/4.15 | | | | | | | | | | $i(all_142_1) & $i(all_142_2) & $i(all_142_3) & % 24.85/4.15 | | | | | | | | | | $i(all_142_4) & $i(all_142_5) & $i(all_142_6) & % 24.85/4.15 | | | | | | | | | | $i(all_142_8) & $i(all_46_4)) | ( ~ (all_142_7 % 24.85/4.15 | | | | | | | | | | = all_142_8) & aDimensionOf0(all_46_6) = % 24.85/4.15 | | | | | | | | | | all_142_8 & $i(all_142_8))) % 24.85/4.15 | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | ALPHA: (127) implies: % 24.85/4.15 | | | | | | | | | | (128) aDimensionOf0(all_46_6) = all_142_7 % 24.85/4.15 | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | BETA: splitting (124) gives: % 24.85/4.15 | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | Case 1: % 24.85/4.15 | | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | | (129) ~ aNaturalNumber0(all_77_1) % 24.85/4.15 | | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | | PRED_UNIFY: (123), (129) imply: % 24.85/4.15 | | | | | | | | | | | (130) $false % 24.85/4.15 | | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | | CLOSE: (130) is inconsistent. % 24.85/4.15 | | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | Case 2: % 24.85/4.15 | | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | | (131) iLess0(all_77_1, all_32_1) % 24.85/4.15 | | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | | BETA: splitting (120) gives: % 24.85/4.15 | | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | | Case 1: % 24.85/4.15 | | | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | | | (132) aScalar0(all_46_4) % 24.85/4.15 | | | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_77_1, all_142_7, % 24.85/4.15 | | | | | | | | | | | | all_46_6, simplifying with (95), (128) gives: % 24.85/4.15 | | | | | | | | | | | | (133) all_142_7 = all_77_1 % 24.85/4.15 | | | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | | | BETA: splitting (122) gives: % 24.85/4.15 | | | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | | | Case 1: % 24.85/4.15 | | | | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | | | | (134) sdtlseqdt0(sz0z00, all_46_4) % 24.85/4.15 | | | | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_46_4, all_46_1, % 24.85/4.15 | | | | | | | | | | | | | all_32_0, simplifying with (15), (70), (72), % 24.85/4.15 | | | | | | | | | | | | | (117), (119), (126), (132), (134) gives: % 24.85/4.15 | | | | | | | | | | | | | (135) $false % 24.85/4.15 | | | | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | | | | CLOSE: (135) is inconsistent. % 24.85/4.15 | | | | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | | | Case 2: % 24.85/4.15 | | | | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | | | | (136) ? [v0: $i] : (aDimensionOf0(all_46_6) = v0 & % 24.85/4.15 | | | | | | | | | | | | | $i(v0) & ~ iLess0(v0, all_32_1)) % 24.85/4.15 | | | | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | | | | DELTA: instantiating (136) with fresh symbol all_172_0 % 24.85/4.15 | | | | | | | | | | | | | gives: % 24.85/4.15 | | | | | | | | | | | | | (137) aDimensionOf0(all_46_6) = all_172_0 & % 24.85/4.15 | | | | | | | | | | | | | $i(all_172_0) & ~ iLess0(all_172_0, all_32_1) % 24.85/4.15 | | | | | | | | | | | | | % 24.85/4.15 | | | | | | | | | | | | | ALPHA: (137) implies: % 24.85/4.15 | | | | | | | | | | | | | (138) ~ iLess0(all_172_0, all_32_1) % 24.85/4.15 | | | | | | | | | | | | | (139) aDimensionOf0(all_46_6) = all_172_0 % 24.85/4.15 | | | | | | | | | | | | | % 24.85/4.16 | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_77_1, all_172_0, % 24.85/4.16 | | | | | | | | | | | | | all_46_6, simplifying with (95), (139) gives: % 24.85/4.16 | | | | | | | | | | | | | (140) all_172_0 = all_77_1 % 24.85/4.16 | | | | | | | | | | | | | % 24.85/4.16 | | | | | | | | | | | | | PRED_UNIFY: (131), (138) imply: % 24.85/4.16 | | | | | | | | | | | | | (141) ~ (all_172_0 = all_77_1) % 24.85/4.16 | | | | | | | | | | | | | % 24.85/4.16 | | | | | | | | | | | | | REDUCE: (140), (141) imply: % 24.85/4.16 | | | | | | | | | | | | | (142) $false % 24.85/4.16 | | | | | | | | | | | | | % 24.85/4.16 | | | | | | | | | | | | | CLOSE: (142) is inconsistent. % 24.85/4.16 | | | | | | | | | | | | | % 24.85/4.16 | | | | | | | | | | | | End of split % 24.85/4.16 | | | | | | | | | | | | % 24.85/4.16 | | | | | | | | | | | Case 2: % 24.85/4.16 | | | | | | | | | | | | % 24.85/4.16 | | | | | | | | | | | | (143) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & % 24.85/4.16 | | | | | | | | | | | | aDimensionOf0(all_46_6) = v1 & % 24.85/4.16 | | | | | | | | | | | | aDimensionOf0(all_46_6) = v0 & $i(v1) & $i(v0)) % 24.85/4.16 | | | | | | | | | | | | % 24.85/4.16 | | | | | | | | | | | | DELTA: instantiating (143) with fresh symbols all_164_0, % 24.85/4.16 | | | | | | | | | | | | all_164_1 gives: % 24.85/4.16 | | | | | | | | | | | | (144) ~ (all_164_0 = all_164_1) & % 24.85/4.16 | | | | | | | | | | | | aDimensionOf0(all_46_6) = all_164_0 & % 24.85/4.16 | | | | | | | | | | | | aDimensionOf0(all_46_6) = all_164_1 & % 24.85/4.16 | | | | | | | | | | | | $i(all_164_0) & $i(all_164_1) % 24.85/4.16 | | | | | | | | | | | | % 24.85/4.16 | | | | | | | | | | | | ALPHA: (144) implies: % 24.85/4.16 | | | | | | | | | | | | (145) ~ (all_164_0 = all_164_1) % 24.85/4.16 | | | | | | | | | | | | (146) aDimensionOf0(all_46_6) = all_164_1 % 24.85/4.16 | | | | | | | | | | | | (147) aDimensionOf0(all_46_6) = all_164_0 % 24.85/4.16 | | | | | | | | | | | | % 24.85/4.16 | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_77_1, all_164_1, % 24.85/4.16 | | | | | | | | | | | | all_46_6, simplifying with (95), (146) gives: % 24.85/4.16 | | | | | | | | | | | | (148) all_164_1 = all_77_1 % 24.85/4.16 | | | | | | | | | | | | % 24.85/4.16 | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_164_1, all_164_0, % 24.85/4.16 | | | | | | | | | | | | all_46_6, simplifying with (146), (147) gives: % 24.85/4.16 | | | | | | | | | | | | (149) all_164_0 = all_164_1 % 24.85/4.16 | | | | | | | | | | | | % 24.85/4.16 | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_142_7, all_164_0, % 24.85/4.16 | | | | | | | | | | | | all_46_6, simplifying with (128), (147) gives: % 24.85/4.16 | | | | | | | | | | | | (150) all_164_0 = all_142_7 % 24.85/4.16 | | | | | | | | | | | | % 24.85/4.16 | | | | | | | | | | | | COMBINE_EQS: (149), (150) imply: % 24.85/4.16 | | | | | | | | | | | | (151) all_164_1 = all_142_7 % 24.85/4.16 | | | | | | | | | | | | % 24.85/4.16 | | | | | | | | | | | | SIMP: (151) implies: % 24.85/4.16 | | | | | | | | | | | | (152) all_164_1 = all_142_7 % 24.85/4.16 | | | | | | | | | | | | % 24.85/4.16 | | | | | | | | | | | | COMBINE_EQS: (148), (152) imply: % 24.85/4.16 | | | | | | | | | | | | (153) all_142_7 = all_77_1 % 24.85/4.16 | | | | | | | | | | | | % 24.85/4.16 | | | | | | | | | | | | COMBINE_EQS: (150), (153) imply: % 24.85/4.16 | | | | | | | | | | | | (154) all_164_0 = all_77_1 % 24.85/4.16 | | | | | | | | | | | | % 24.85/4.16 | | | | | | | | | | | | REDUCE: (145), (148), (154) imply: % 24.85/4.16 | | | | | | | | | | | | (155) $false % 24.85/4.16 | | | | | | | | | | | | % 24.85/4.16 | | | | | | | | | | | | CLOSE: (155) is inconsistent. % 24.85/4.16 | | | | | | | | | | | | % 24.85/4.16 | | | | | | | | | | | End of split % 24.85/4.16 | | | | | | | | | | | % 24.85/4.16 | | | | | | | | | | End of split % 24.85/4.16 | | | | | | | | | | % 24.85/4.16 | | | | | | | | | End of split % 24.85/4.16 | | | | | | | | | % 24.85/4.16 | | | | | | | | End of split % 24.85/4.16 | | | | | | | | % 24.85/4.16 | | | | | | | End of split % 24.85/4.16 | | | | | | | % 24.85/4.16 | | | | | | Case 2: % 24.85/4.16 | | | | | | | % 24.85/4.16 | | | | | | | (156) ~ (all_46_7 = all_46_8) & aDimensionOf0(all_32_2) = % 24.85/4.16 | | | | | | | all_46_8 & $i(all_46_8) % 24.85/4.16 | | | | | | | % 24.85/4.16 | | | | | | | ALPHA: (156) implies: % 24.85/4.16 | | | | | | | (157) ~ (all_46_7 = all_46_8) % 24.85/4.16 | | | | | | | (158) aDimensionOf0(all_32_2) = all_46_8 % 24.85/4.16 | | | | | | | % 24.85/4.16 | | | | | | | REDUCE: (34), (157) imply: % 24.85/4.16 | | | | | | | (159) ~ (all_46_8 = all_32_1) % 24.85/4.16 | | | | | | | % 24.85/4.16 | | | | | | | SIMP: (159) implies: % 24.85/4.16 | | | | | | | (160) ~ (all_46_8 = all_32_1) % 24.85/4.16 | | | | | | | % 24.85/4.16 | | | | | | | GROUND_INST: instantiating (11) with all_32_1, all_46_8, all_32_2, % 24.85/4.16 | | | | | | | simplifying with (18), (158) gives: % 24.85/4.16 | | | | | | | (161) all_46_8 = all_32_1 % 24.85/4.16 | | | | | | | % 24.85/4.16 | | | | | | | REDUCE: (160), (161) imply: % 24.85/4.16 | | | | | | | (162) $false % 24.85/4.16 | | | | | | | % 24.85/4.16 | | | | | | | CLOSE: (162) is inconsistent. % 24.85/4.16 | | | | | | | % 24.85/4.16 | | | | | | End of split % 24.85/4.16 | | | | | | % 24.85/4.16 | | | | | End of split % 24.85/4.16 | | | | | % 24.85/4.16 | | | | End of split % 24.85/4.16 | | | | % 24.85/4.16 | | | End of split % 24.85/4.16 | | | % 24.85/4.16 | | Case 2: % 24.85/4.16 | | | % 24.85/4.16 | | | (163) all_60_0 = sz00 % 24.85/4.16 | | | (164) ~ (all_60_1 = sz00) & aDimensionOf0(all_32_2) = all_60_1 & % 24.85/4.16 | | | $i(all_60_1) % 24.85/4.16 | | | % 24.85/4.16 | | | ALPHA: (164) implies: % 24.85/4.16 | | | (165) ~ (all_60_1 = sz00) % 24.85/4.16 | | | (166) aDimensionOf0(all_32_2) = all_60_1 % 24.85/4.16 | | | % 24.85/4.16 | | | REDUCE: (41), (163) imply: % 24.85/4.16 | | | (167) aDimensionOf0(all_32_2) = sz00 % 24.85/4.16 | | | % 24.85/4.16 | | | GROUND_INST: instantiating (11) with sz00, all_60_1, all_32_2, simplifying % 24.85/4.16 | | | with (166), (167) gives: % 24.85/4.16 | | | (168) all_60_1 = sz00 % 24.85/4.16 | | | % 24.85/4.16 | | | REDUCE: (165), (168) imply: % 24.85/4.16 | | | (169) $false % 24.85/4.16 | | | % 24.85/4.16 | | | CLOSE: (169) is inconsistent. % 24.85/4.16 | | | % 24.85/4.16 | | End of split % 24.85/4.16 | | % 24.85/4.16 | End of split % 24.85/4.16 | % 24.85/4.16 End of proof % 24.85/4.16 % SZS output end Proof for theBenchmark % 24.85/4.16 % 24.85/4.16 3568ms %------------------------------------------------------------------------------