%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG065+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 : n009.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 13:57:38 EDT 2023 % Result : Theorem 138.89s 19.07s % Output : Proof 139.87s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : RNG065+1 : TPTP v8.1.2. Released v4.0.0. % 0.06/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n009.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 02:10:50 EDT 2023 % 0.12/0.33 % CPUTime : % 0.50/0.59 ________ _____ % 0.50/0.59 ___ __ \_________(_)________________________________ % 0.50/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.50/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.50/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.50/0.59 % 0.50/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.50/0.59 (2023-06-19) % 0.50/0.59 % 0.50/0.59 (c) Philipp Rümmer, 2009-2023 % 0.50/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.50/0.59 Amanda Stjerna. % 0.50/0.59 Free software under BSD-3-Clause. % 0.50/0.59 % 0.50/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.50/0.59 % 0.50/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.50/0.60 Running up to 7 provers in parallel. % 0.50/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.50/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.50/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.50/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.50/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.50/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.50/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.27/1.23 Prover 1: Preprocessing ... % 3.27/1.23 Prover 4: Preprocessing ... % 3.86/1.27 Prover 3: Preprocessing ... % 3.86/1.27 Prover 0: Preprocessing ... % 3.86/1.27 Prover 6: Preprocessing ... % 3.86/1.27 Prover 5: Preprocessing ... % 3.86/1.27 Prover 2: Preprocessing ... % 9.41/2.02 Prover 3: Constructing countermodel ... % 9.80/2.03 Prover 1: Constructing countermodel ... % 9.80/2.04 Prover 6: Proving ... % 10.94/2.20 Prover 5: Constructing countermodel ... % 11.75/2.30 Prover 4: Constructing countermodel ... % 12.77/2.42 Prover 0: Proving ... % 12.77/2.46 Prover 2: Proving ... % 73.26/10.28 Prover 2: stopped % 73.26/10.28 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 73.84/10.36 Prover 7: Preprocessing ... % 76.14/10.62 Prover 7: Constructing countermodel ... % 101.88/13.94 Prover 5: stopped % 101.88/13.94 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 102.41/14.06 Prover 8: Preprocessing ... % 103.49/14.15 Prover 8: Warning: ignoring some quantifiers % 103.49/14.15 Prover 8: Constructing countermodel ... % 117.39/15.95 Prover 1: stopped % 117.39/15.96 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 117.39/16.02 Prover 9: Preprocessing ... % 121.66/16.48 Prover 9: Constructing countermodel ... % 131.08/17.88 Prover 6: stopped % 131.08/17.88 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 132.25/18.01 Prover 10: Preprocessing ... % 132.69/18.11 Prover 10: Constructing countermodel ... % 138.23/18.80 Prover 10: Found proof (size 199) % 138.23/18.80 Prover 10: proved (922ms) % 138.23/18.80 Prover 9: stopped % 138.23/18.80 Prover 0: stopped % 138.23/18.80 Prover 7: stopped % 138.23/18.81 Prover 8: stopped % 138.23/18.83 Prover 4: stopped % 138.89/19.07 Prover 3: stopped % 138.89/19.07 % 138.89/19.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 138.89/19.07 % 139.05/19.15 % SZS output start Proof for theBenchmark % 139.05/19.15 Assumptions after simplification: % 139.05/19.15 --------------------------------- % 139.05/19.15 % 139.05/19.15 (mArith) % 139.29/19.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 139.29/19.19 (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 139.29/19.19 | ~ $i(v0) | ~ aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v5: % 139.29/19.19 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(v6, v2) = v7 & % 139.29/19.19 sdtasdt0(v1, v2) = v8 & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v8) = v7 & % 139.29/19.19 sdtasdt0(v0, v1) = v6 & sdtpldt0(v1, v2) = v5 & sdtpldt0(v1, v0) = v3 & % 139.29/19.19 sdtpldt0(v0, v5) = v4 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 139.29/19.19 $i(v3))) % 139.29/19.19 % 139.29/19.19 (mDefInit) % 139.29/19.19 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sziznziztdt0(v0) = v1) | ~ $i(v0) % 139.29/19.19 | ~ aVector0(v0) | ? [v2: $i] : (aDimensionOf0(v0) = v2 & $i(v2) & (v2 = % 139.29/19.19 sz00 | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtlbdtrb0(v0, % 139.29/19.19 v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~ $i(v4) | ~ $i(v1) % 139.29/19.19 | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1, v4) = v5 & $i(v5))) & ! % 139.29/19.19 [v3: $i] : ! [v4: $i] : (v3 = v1 | ~ (aDimensionOf0(v3) = v4) | ~ % 139.29/19.19 $i(v3) | ~ aVector0(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 139.29/19.19 ? [v8: $i] : ($i(v6) & (( ~ (v8 = v7) & sdtlbdtrb0(v3, v6) = v7 & % 139.29/19.19 sdtlbdtrb0(v0, v6) = v8 & $i(v8) & $i(v7) & % 139.29/19.19 aNaturalNumber0(v6)) | ( ~ (v5 = v2) & szszuzczcdt0(v4) = v5 & % 139.29/19.19 $i(v5))))) & ! [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~ % 139.29/19.19 $i(v1) | szszuzczcdt0(v3) = v2) & ! [v3: $i] : ( ~ % 139.29/19.19 (aDimensionOf0(v1) = v3) | ~ $i(v1) | aVector0(v1)))))) % 139.29/19.19 % 139.29/19.19 (mDistr) % 139.37/19.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 139.37/19.20 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ % 139.37/19.20 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 139.37/19.20 aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v6: $i] : ? [v7: $i] % 139.37/19.20 : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v7, v2) = v8 & sdtasdt0(v1, v2) = v9 % 139.37/19.20 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v4, v9) = v8 & sdtpldt0(v1, v2) = v6 & % 139.37/19.20 sdtpldt0(v0, v1) = v7 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5))) % 139.37/19.20 % 139.37/19.20 (mEqInit) % 139.37/19.20 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 139.37/19.20 (sziznziztdt0(v1) = v3) | ~ (sziznziztdt0(v0) = v2) | ~ $i(v1) | ~ $i(v0) % 139.37/19.20 | ~ aVector0(v1) | ~ aVector0(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: % 139.37/19.20 $i] : ? [v7: $i] : ((v7 = v6 & aDimensionOf0(v3) = v6 & aDimensionOf0(v2) % 139.37/19.20 = v6 & $i(v6)) | (aDimensionOf0(v1) = v5 & $i(v5) & (v5 = sz00 | ( ~ (v5 % 139.37/19.20 = v4) & aDimensionOf0(v0) = v4 & $i(v4)))))) % 139.37/19.20 % 139.37/19.20 (mLEMon) % 139.37/19.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 139.37/19.21 $i] : ( ~ (sdtpldt0(v1, v3) = v5) | ~ (sdtpldt0(v0, v2) = v4) | ~ $i(v3) | % 139.37/19.21 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v2, v3) | ~ % 139.37/19.21 sdtlseqdt0(v0, v1) | ~ aScalar0(v3) | ~ aScalar0(v2) | ~ aScalar0(v1) | % 139.37/19.21 ~ aScalar0(v0) | sdtlseqdt0(v4, v5)) % 139.37/19.21 % 139.37/19.21 (mLETrn) % 139.37/19.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 139.37/19.21 ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aScalar0(v2) | ~ % 139.37/19.21 aScalar0(v1) | ~ aScalar0(v0) | sdtlseqdt0(v0, v2)) % 139.37/19.21 % 139.37/19.21 (mMNeg) % 139.37/19.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (smndt0(v0) = v2) % 139.37/19.21 | ~ (sdtasdt0(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ % 139.37/19.21 aScalar0(v0) | ? [v4: $i] : ? [v5: $i] : (smndt0(v5) = v3 & smndt0(v1) = % 139.37/19.21 v4 & sdtasdt0(v0, v4) = v3 & sdtasdt0(v0, v1) = v5 & $i(v5) & $i(v4) & % 139.37/19.21 $i(v3))) % 139.37/19.21 % 139.37/19.21 (mMulSc) % 139.37/19.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 139.37/19.21 $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | aScalar0(v2)) % 139.37/19.21 % 139.37/19.21 (mNegSc) % 139.37/19.21 ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ~ % 139.37/19.21 aScalar0(v0) | aScalar0(v1)) % 139.37/19.21 % 139.37/19.21 (mSumSc) % 139.37/19.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 139.37/19.21 $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | aScalar0(v2)) % 139.37/19.21 % 139.37/19.21 (m__) % 139.37/19.22 $i(xS) & $i(xP) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 139.37/19.22 $i] : ? [v4: $i] : (sdtasdt0(xS, xS) = v3 & sdtasdt0(xP, xP) = v0 & % 139.37/19.22 sdtasdt0(xR, xR) = v2 & sdtpldt0(v2, v3) = v4 & sdtpldt0(v0, v0) = v1 & % 139.37/19.22 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~ sdtlseqdt0(v1, v4)) % 139.37/19.22 % 139.37/19.22 (m__1652) % 139.48/19.22 $i(xs) & ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : ! % 139.48/19.22 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2, v2) % 139.48/19.22 = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4) = v5) | ~ % 139.48/19.22 $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1) | ? [v6: $i] : ? % 139.48/19.22 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ((sdtasasdt0(v1, v2) = v8 & % 139.48/19.22 sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8) & sdtlseqdt0(v9, v5)) | % 139.48/19.22 (aDimensionOf0(v1) = v6 & $i(v6) & ( ~ iLess0(v6, v0) | ( ~ (v7 = v6) & % 139.48/19.22 aDimensionOf0(v2) = v7 & $i(v7))))))) % 139.48/19.22 % 139.48/19.22 (m__1678) % 139.48/19.22 $i(xt) & $i(xs) & aVector0(xt) & aVector0(xs) % 139.48/19.22 % 139.48/19.22 (m__1678_01) % 139.48/19.22 $i(xt) & $i(xs) & ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) = % 139.48/19.22 v0 & $i(v0)) % 139.48/19.22 % 139.48/19.22 (m__1692) % 139.48/19.22 $i(xs) & $i(sz00) & ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 & % 139.48/19.22 $i(v0)) % 139.48/19.22 % 139.48/19.22 (m__1709) % 139.48/19.22 sziznziztdt0(xs) = xp & $i(xp) & $i(xs) & aVector0(xp) % 139.48/19.22 % 139.48/19.22 (m__1726) % 139.48/19.22 sziznziztdt0(xt) = xq & $i(xq) & $i(xt) & aVector0(xq) % 139.48/19.22 % 139.48/19.22 (m__1746) % 139.48/19.22 $i(xA) & $i(xs) & ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) = % 139.48/19.22 v0 & $i(v0) & aScalar0(xA)) % 139.48/19.22 % 139.48/19.22 (m__1766) % 139.48/19.22 $i(xB) & $i(xt) & ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) = % 139.48/19.22 v0 & $i(v0) & aScalar0(xB)) % 139.48/19.22 % 139.48/19.22 (m__1892) % 139.48/19.22 sdtasdt0(xC, xG) = xR & $i(xR) & $i(xG) & $i(xC) & aScalar0(xR) % 139.48/19.22 % 139.48/19.22 (m__1911) % 139.48/19.22 sdtasdt0(xE, xH) = xP & $i(xP) & $i(xH) & $i(xE) & aScalar0(xP) % 139.48/19.22 % 139.48/19.22 (m__1930) % 139.48/19.23 sdtasdt0(xF, xD) = xS & $i(xS) & $i(xF) & $i(xD) & aScalar0(xS) % 139.48/19.23 % 139.48/19.23 (m__1949) % 139.48/19.23 sdtasdt0(xR, xS) = xN & $i(xN) & $i(xS) & $i(xR) & aScalar0(xN) % 139.48/19.23 % 139.48/19.23 (m__2004) % 139.48/19.23 $i(xN) & $i(xP) & ? [v0: $i] : (sdtasdt0(xP, xP) = v0 & $i(v0) & % 139.48/19.23 sdtlseqdt0(v0, xN)) % 139.48/19.23 % 139.48/19.23 (m__2144) % 139.48/19.23 $i(xN) & $i(xS) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 139.48/19.23 (smndt0(xN) = v1 & smndt0(xS) = v0 & sdtasdt0(v0, v0) = v2 & sdtasdt0(v0, xR) % 139.48/19.23 = v1 & sdtasdt0(xS, xS) = v2 & sdtasdt0(xR, v0) = v1 & $i(v2) & $i(v1) & % 139.48/19.23 $i(v0)) % 139.48/19.23 % 139.48/19.23 (m__2180) % 139.48/19.23 $i(xN) & $i(xS) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 139.48/19.23 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (smndt0(xN) = % 139.48/19.23 v4 & smndt0(xS) = v0 & sdtasdt0(v1, v1) = v2 & sdtasdt0(xS, xS) = v6 & % 139.48/19.23 sdtasdt0(xR, xR) = v3 & sdtpldt0(v5, v7) = v2 & sdtpldt0(v4, v6) = v7 & % 139.48/19.23 sdtpldt0(v3, v4) = v5 & sdtpldt0(xR, v0) = v1 & $i(v7) & $i(v6) & $i(v5) & % 139.48/19.23 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 139.48/19.23 % 139.48/19.23 (m__2221) % 139.48/19.23 $i(xN) & $i(xS) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 139.48/19.23 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (smndt0(xN) = % 139.48/19.23 v4 & smndt0(xS) = v0 & sdtasdt0(v1, v1) = v2 & sdtasdt0(xS, xS) = v6 & % 139.48/19.23 sdtasdt0(xR, xR) = v3 & sdtpldt0(v6, v4) = v7 & sdtpldt0(v5, v7) = v2 & % 139.48/19.23 sdtpldt0(v3, v4) = v5 & sdtpldt0(xR, v0) = v1 & $i(v7) & $i(v6) & $i(v5) & % 139.48/19.23 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 139.48/19.23 % 139.48/19.23 (m__2262) % 139.48/19.23 $i(xN) & $i(xS) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 139.48/19.23 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (smndt0(xN) = % 139.48/19.23 v6 & smndt0(xS) = v0 & sdtasdt0(v1, v1) = v2 & sdtasdt0(xS, xS) = v4 & % 139.48/19.23 sdtasdt0(xR, xR) = v3 & sdtpldt0(v7, v6) = v2 & sdtpldt0(v5, v6) = v7 & % 139.48/19.23 sdtpldt0(v3, v4) = v5 & sdtpldt0(xR, v0) = v1 & $i(v7) & $i(v6) & $i(v5) & % 139.48/19.23 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 139.48/19.24 % 139.48/19.24 (m__2303) % 139.48/19.24 $i(xN) & $i(xS) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 139.48/19.24 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (smndt0(xS) = v0 & % 139.48/19.24 sdtasdt0(v1, v1) = v2 & sdtasdt0(xS, xS) = v6 & sdtasdt0(xR, xR) = v5 & % 139.48/19.24 sdtpldt0(v5, v6) = v4 & sdtpldt0(v3, xN) = v4 & sdtpldt0(v2, xN) = v3 & % 139.48/19.24 sdtpldt0(xR, v0) = v1 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) % 139.48/19.24 & $i(v0)) % 139.48/19.24 % 139.48/19.24 (m__2318) % 139.48/19.24 $i(xS) & $i(xR) & $i(sz0z00) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 139.48/19.24 (smndt0(xS) = v0 & sdtasdt0(v1, v1) = v2 & sdtpldt0(xR, v0) = v1 & $i(v2) & % 139.48/19.24 $i(v1) & $i(v0) & sdtlseqdt0(sz0z00, v2)) % 139.48/19.24 % 139.48/19.24 (m__2348) % 139.48/19.24 $i(xN) & $i(xS) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 139.48/19.24 $i] : (sdtasdt0(xS, xS) = v2 & sdtasdt0(xR, xR) = v1 & sdtpldt0(v1, v2) = v3 % 139.48/19.24 & sdtpldt0(xN, xN) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v0, % 139.48/19.24 v3)) % 139.48/19.24 % 139.48/19.24 (function-axioms) % 139.48/19.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 139.48/19.24 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 139.48/19.24 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) % 139.48/19.24 | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 139.48/19.24 ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = % 139.48/19.24 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 139.48/19.24 ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 139.48/19.24 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sziznziztdt0(v2) = v1) | ~ % 139.48/19.24 (sziznziztdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 139.48/19.24 v0 | ~ (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) & ! [v0: % 139.48/19.24 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ % 139.48/19.24 (smndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 139.48/19.24 (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0)) % 139.48/19.24 % 139.48/19.24 Further assumptions not needed in the proof: % 139.48/19.24 -------------------------------------------- % 139.48/19.24 mDefSPN, mDefSPZ, mDimNat, mDistr2, mElmSc, mIH, mIHOrd, mLEASm, mLEMonM, % 139.48/19.24 mLERef, mLETot, mLess, mMDNeg, mNatExtr, mNatSort, mPosMon, mSZeroSc, mScPr, % 139.48/19.24 mScSort, mScSqPos, mScZero, mSqPos, mSqrt, mSuccEqu, mSuccNat, mVcSort, % 139.48/19.24 mZeroNat, m__1783, m__1800, m__1820, m__1837, m__1854, m__1873, m__1967 % 139.48/19.24 % 139.48/19.24 Those formulas are unsatisfiable: % 139.48/19.24 --------------------------------- % 139.48/19.24 % 139.48/19.24 Begin of proof % 139.48/19.24 | % 139.48/19.25 | ALPHA: (mDefInit) implies: % 139.48/19.25 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (sziznziztdt0(v0) = v1) | ~ $i(v0) | % 139.48/19.25 | ~ aVector0(v0) | ? [v2: $i] : (aDimensionOf0(v0) = v2 & $i(v2) & (v2 % 139.48/19.25 | = sz00 | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 139.48/19.25 | (sdtlbdtrb0(v0, v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~ % 139.48/19.25 | $i(v4) | ~ $i(v1) | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1, % 139.48/19.25 | v4) = v5 & $i(v5))) & ! [v3: $i] : ! [v4: $i] : (v3 = % 139.48/19.25 | v1 | ~ (aDimensionOf0(v3) = v4) | ~ $i(v3) | ~ % 139.48/19.25 | aVector0(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? % 139.48/19.25 | [v8: $i] : ($i(v6) & (( ~ (v8 = v7) & sdtlbdtrb0(v3, v6) = v7 % 139.48/19.25 | & sdtlbdtrb0(v0, v6) = v8 & $i(v8) & $i(v7) & % 139.48/19.25 | aNaturalNumber0(v6)) | ( ~ (v5 = v2) & szszuzczcdt0(v4) % 139.48/19.25 | = v5 & $i(v5))))) & ! [v3: $i] : ( ~ % 139.48/19.25 | (aDimensionOf0(v1) = v3) | ~ $i(v1) | szszuzczcdt0(v3) = v2) % 139.48/19.25 | & ! [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~ $i(v1) | % 139.48/19.25 | aVector0(v1)))))) % 139.48/19.25 | % 139.48/19.25 | ALPHA: (mEqInit) implies: % 139.48/19.25 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 139.48/19.25 | (sziznziztdt0(v1) = v3) | ~ (sziznziztdt0(v0) = v2) | ~ $i(v1) | ~ % 139.48/19.25 | $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) | ? [v4: $i] : ? [v5: % 139.48/19.25 | $i] : ? [v6: $i] : ? [v7: $i] : ((v7 = v6 & aDimensionOf0(v3) = % 139.48/19.25 | v6 & aDimensionOf0(v2) = v6 & $i(v6)) | (aDimensionOf0(v1) = v5 & % 139.48/19.25 | $i(v5) & (v5 = sz00 | ( ~ (v5 = v4) & aDimensionOf0(v0) = v4 & % 139.48/19.25 | $i(v4)))))) % 139.48/19.25 | % 139.48/19.25 | ALPHA: (m__1678) implies: % 139.48/19.25 | (3) aVector0(xs) % 139.48/19.25 | (4) aVector0(xt) % 139.48/19.25 | % 139.48/19.25 | ALPHA: (m__1652) implies: % 139.48/19.25 | (5) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 139.48/19.25 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2, % 139.48/19.25 | v2) = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4) % 139.48/19.25 | = v5) | ~ $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1) % 139.48/19.25 | | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 139.48/19.25 | ((sdtasasdt0(v1, v2) = v8 & sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8) % 139.48/19.25 | & sdtlseqdt0(v9, v5)) | (aDimensionOf0(v1) = v6 & $i(v6) & ( ~ % 139.48/19.25 | iLess0(v6, v0) | ( ~ (v7 = v6) & aDimensionOf0(v2) = v7 & % 139.48/19.25 | $i(v7))))))) % 139.48/19.25 | % 139.48/19.25 | ALPHA: (m__1678_01) implies: % 139.48/19.25 | (6) ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) = v0 & % 139.48/19.26 | $i(v0)) % 139.48/19.26 | % 139.48/19.26 | ALPHA: (m__1692) implies: % 139.48/19.26 | (7) ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 & $i(v0)) % 139.48/19.26 | % 139.48/19.26 | ALPHA: (m__1709) implies: % 139.48/19.26 | (8) sziznziztdt0(xs) = xp % 139.48/19.26 | % 139.48/19.26 | ALPHA: (m__1726) implies: % 139.48/19.26 | (9) sziznziztdt0(xt) = xq % 139.48/19.26 | % 139.48/19.26 | ALPHA: (m__1746) implies: % 139.48/19.26 | (10) $i(xs) % 139.48/19.26 | (11) ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) = v0 & % 139.48/19.26 | $i(v0) & aScalar0(xA)) % 139.48/19.26 | % 139.48/19.26 | ALPHA: (m__1766) implies: % 139.48/19.26 | (12) $i(xt) % 139.48/19.26 | (13) ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) = v0 & % 139.48/19.26 | $i(v0) & aScalar0(xB)) % 139.48/19.26 | % 139.48/19.26 | ALPHA: (m__1892) implies: % 139.48/19.26 | (14) aScalar0(xR) % 139.48/19.26 | % 139.48/19.26 | ALPHA: (m__1911) implies: % 139.48/19.26 | (15) aScalar0(xP) % 139.48/19.26 | % 139.48/19.26 | ALPHA: (m__1930) implies: % 139.48/19.26 | (16) aScalar0(xS) % 139.48/19.26 | % 139.48/19.26 | ALPHA: (m__1949) implies: % 139.48/19.26 | (17) aScalar0(xN) % 139.48/19.26 | (18) sdtasdt0(xR, xS) = xN % 139.48/19.26 | % 139.48/19.26 | ALPHA: (m__2004) implies: % 139.48/19.26 | (19) ? [v0: $i] : (sdtasdt0(xP, xP) = v0 & $i(v0) & sdtlseqdt0(v0, xN)) % 139.48/19.26 | % 139.48/19.26 | ALPHA: (m__2144) implies: % 139.48/19.26 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (smndt0(xN) = v1 & % 139.48/19.26 | smndt0(xS) = v0 & sdtasdt0(v0, v0) = v2 & sdtasdt0(v0, xR) = v1 & % 139.48/19.26 | sdtasdt0(xS, xS) = v2 & sdtasdt0(xR, v0) = v1 & $i(v2) & $i(v1) & % 139.48/19.26 | $i(v0)) % 139.48/19.26 | % 139.48/19.26 | ALPHA: (m__2180) implies: % 139.48/19.26 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 139.48/19.26 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (smndt0(xN) = v4 & smndt0(xS) % 139.48/19.26 | = v0 & sdtasdt0(v1, v1) = v2 & sdtasdt0(xS, xS) = v6 & sdtasdt0(xR, % 139.48/19.26 | xR) = v3 & sdtpldt0(v5, v7) = v2 & sdtpldt0(v4, v6) = v7 & % 139.48/19.26 | sdtpldt0(v3, v4) = v5 & sdtpldt0(xR, v0) = v1 & $i(v7) & $i(v6) & % 139.48/19.26 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 139.48/19.26 | % 139.48/19.26 | ALPHA: (m__2221) implies: % 139.48/19.26 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 139.48/19.26 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (smndt0(xN) = v4 & smndt0(xS) % 139.48/19.26 | = v0 & sdtasdt0(v1, v1) = v2 & sdtasdt0(xS, xS) = v6 & sdtasdt0(xR, % 139.48/19.26 | xR) = v3 & sdtpldt0(v6, v4) = v7 & sdtpldt0(v5, v7) = v2 & % 139.48/19.26 | sdtpldt0(v3, v4) = v5 & sdtpldt0(xR, v0) = v1 & $i(v7) & $i(v6) & % 139.48/19.26 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 139.48/19.26 | % 139.48/19.26 | ALPHA: (m__2262) implies: % 139.48/19.26 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 139.48/19.26 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (smndt0(xN) = v6 & smndt0(xS) % 139.48/19.26 | = v0 & sdtasdt0(v1, v1) = v2 & sdtasdt0(xS, xS) = v4 & sdtasdt0(xR, % 139.48/19.26 | xR) = v3 & sdtpldt0(v7, v6) = v2 & sdtpldt0(v5, v6) = v7 & % 139.48/19.26 | sdtpldt0(v3, v4) = v5 & sdtpldt0(xR, v0) = v1 & $i(v7) & $i(v6) & % 139.48/19.26 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 139.48/19.26 | % 139.48/19.26 | ALPHA: (m__2303) implies: % 139.48/19.27 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 139.48/19.27 | ? [v5: $i] : ? [v6: $i] : (smndt0(xS) = v0 & sdtasdt0(v1, v1) = v2 & % 139.48/19.27 | sdtasdt0(xS, xS) = v6 & sdtasdt0(xR, xR) = v5 & sdtpldt0(v5, v6) = % 139.48/19.27 | v4 & sdtpldt0(v3, xN) = v4 & sdtpldt0(v2, xN) = v3 & sdtpldt0(xR, % 139.48/19.27 | v0) = v1 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 139.48/19.27 | $i(v0)) % 139.48/19.27 | % 139.48/19.27 | ALPHA: (m__2318) implies: % 139.48/19.27 | (25) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (smndt0(xS) = v0 & % 139.48/19.27 | sdtasdt0(v1, v1) = v2 & sdtpldt0(xR, v0) = v1 & $i(v2) & $i(v1) & % 139.48/19.27 | $i(v0) & sdtlseqdt0(sz0z00, v2)) % 139.48/19.27 | % 139.48/19.27 | ALPHA: (m__2348) implies: % 139.48/19.27 | (26) $i(xN) % 139.48/19.27 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(xS, % 139.48/19.27 | xS) = v2 & sdtasdt0(xR, xR) = v1 & sdtpldt0(v1, v2) = v3 & % 139.48/19.27 | sdtpldt0(xN, xN) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 139.48/19.27 | sdtlseqdt0(v0, v3)) % 139.48/19.27 | % 139.48/19.27 | ALPHA: (m__) implies: % 139.48/19.27 | (28) $i(xR) % 139.48/19.27 | (29) $i(xP) % 139.48/19.27 | (30) $i(xS) % 139.48/19.27 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 139.48/19.27 | (sdtasdt0(xS, xS) = v3 & sdtasdt0(xP, xP) = v0 & sdtasdt0(xR, xR) = v2 % 139.48/19.27 | & sdtpldt0(v2, v3) = v4 & sdtpldt0(v0, v0) = v1 & $i(v4) & $i(v3) & % 139.48/19.27 | $i(v2) & $i(v1) & $i(v0) & ~ sdtlseqdt0(v1, v4)) % 139.48/19.27 | % 139.48/19.27 | ALPHA: (function-axioms) implies: % 139.48/19.27 | (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = % 139.48/19.27 | v1) | ~ (smndt0(v2) = v0)) % 139.48/19.27 | (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 139.48/19.27 | (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) % 139.48/19.27 | (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 139.48/19.27 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 139.48/19.27 | (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 139.48/19.27 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 139.48/19.27 | % 139.48/19.27 | DELTA: instantiating (6) with fresh symbol all_33_0 gives: % 139.48/19.27 | (36) aDimensionOf0(xt) = all_33_0 & aDimensionOf0(xs) = all_33_0 & % 139.48/19.27 | $i(all_33_0) % 139.48/19.27 | % 139.48/19.27 | ALPHA: (36) implies: % 139.48/19.27 | (37) aDimensionOf0(xs) = all_33_0 % 139.48/19.27 | (38) aDimensionOf0(xt) = all_33_0 % 139.48/19.27 | % 139.48/19.27 | DELTA: instantiating (19) with fresh symbol all_35_0 gives: % 139.48/19.27 | (39) sdtasdt0(xP, xP) = all_35_0 & $i(all_35_0) & sdtlseqdt0(all_35_0, xN) % 139.48/19.27 | % 139.48/19.27 | ALPHA: (39) implies: % 139.48/19.27 | (40) sdtlseqdt0(all_35_0, xN) % 139.48/19.27 | (41) sdtasdt0(xP, xP) = all_35_0 % 139.48/19.27 | % 139.48/19.27 | DELTA: instantiating (7) with fresh symbol all_37_0 gives: % 139.48/19.28 | (42) ~ (all_37_0 = sz00) & aDimensionOf0(xs) = all_37_0 & $i(all_37_0) % 139.48/19.28 | % 139.48/19.28 | ALPHA: (42) implies: % 139.48/19.28 | (43) ~ (all_37_0 = sz00) % 139.48/19.28 | (44) aDimensionOf0(xs) = all_37_0 % 139.48/19.28 | % 139.48/19.28 | DELTA: instantiating (11) with fresh symbol all_39_0 gives: % 139.48/19.28 | (45) sdtlbdtrb0(xs, all_39_0) = xA & aDimensionOf0(xs) = all_39_0 & % 139.48/19.28 | $i(all_39_0) & aScalar0(xA) % 139.48/19.28 | % 139.48/19.28 | ALPHA: (45) implies: % 139.48/19.28 | (46) aDimensionOf0(xs) = all_39_0 % 139.48/19.28 | % 139.48/19.28 | DELTA: instantiating (13) with fresh symbol all_41_0 gives: % 139.48/19.28 | (47) sdtlbdtrb0(xt, all_41_0) = xB & aDimensionOf0(xt) = all_41_0 & % 139.48/19.28 | $i(all_41_0) & aScalar0(xB) % 139.48/19.28 | % 139.48/19.28 | ALPHA: (47) implies: % 139.48/19.28 | (48) aDimensionOf0(xt) = all_41_0 % 139.48/19.28 | % 139.48/19.28 | DELTA: instantiating (25) with fresh symbols all_45_0, all_45_1, all_45_2 % 139.48/19.28 | gives: % 139.48/19.28 | (49) smndt0(xS) = all_45_2 & sdtasdt0(all_45_1, all_45_1) = all_45_0 & % 139.48/19.28 | sdtpldt0(xR, all_45_2) = all_45_1 & $i(all_45_0) & $i(all_45_1) & % 139.48/19.28 | $i(all_45_2) & sdtlseqdt0(sz0z00, all_45_0) % 139.48/19.28 | % 139.48/19.28 | ALPHA: (49) implies: % 139.48/19.28 | (50) smndt0(xS) = all_45_2 % 139.48/19.28 | % 139.48/19.28 | DELTA: instantiating (20) with fresh symbols all_47_0, all_47_1, all_47_2 % 139.48/19.28 | gives: % 139.48/19.28 | (51) smndt0(xN) = all_47_1 & smndt0(xS) = all_47_2 & sdtasdt0(all_47_2, % 139.48/19.28 | all_47_2) = all_47_0 & sdtasdt0(all_47_2, xR) = all_47_1 & % 139.48/19.28 | sdtasdt0(xS, xS) = all_47_0 & sdtasdt0(xR, all_47_2) = all_47_1 & % 139.48/19.28 | $i(all_47_0) & $i(all_47_1) & $i(all_47_2) % 139.48/19.28 | % 139.48/19.28 | ALPHA: (51) implies: % 139.48/19.28 | (52) sdtasdt0(xS, xS) = all_47_0 % 139.48/19.28 | (53) sdtasdt0(all_47_2, xR) = all_47_1 % 139.48/19.28 | (54) smndt0(xS) = all_47_2 % 139.48/19.28 | (55) smndt0(xN) = all_47_1 % 139.48/19.28 | % 139.48/19.28 | DELTA: instantiating (27) with fresh symbols all_49_0, all_49_1, all_49_2, % 139.48/19.28 | all_49_3 gives: % 139.48/19.28 | (56) sdtasdt0(xS, xS) = all_49_1 & sdtasdt0(xR, xR) = all_49_2 & % 139.48/19.28 | sdtpldt0(all_49_2, all_49_1) = all_49_0 & sdtpldt0(xN, xN) = all_49_3 % 139.48/19.28 | & $i(all_49_0) & $i(all_49_1) & $i(all_49_2) & $i(all_49_3) & % 139.48/19.28 | sdtlseqdt0(all_49_3, all_49_0) % 139.48/19.28 | % 139.48/19.28 | ALPHA: (56) implies: % 139.48/19.28 | (57) sdtlseqdt0(all_49_3, all_49_0) % 139.48/19.28 | (58) sdtpldt0(xN, xN) = all_49_3 % 139.48/19.28 | (59) sdtpldt0(all_49_2, all_49_1) = all_49_0 % 139.48/19.28 | (60) sdtasdt0(xR, xR) = all_49_2 % 139.48/19.28 | (61) sdtasdt0(xS, xS) = all_49_1 % 139.48/19.28 | % 139.48/19.28 | DELTA: instantiating (31) with fresh symbols all_51_0, all_51_1, all_51_2, % 139.48/19.28 | all_51_3, all_51_4 gives: % 139.48/19.28 | (62) sdtasdt0(xS, xS) = all_51_1 & sdtasdt0(xP, xP) = all_51_4 & % 139.48/19.28 | sdtasdt0(xR, xR) = all_51_2 & sdtpldt0(all_51_2, all_51_1) = all_51_0 % 139.48/19.28 | & sdtpldt0(all_51_4, all_51_4) = all_51_3 & $i(all_51_0) & % 139.48/19.28 | $i(all_51_1) & $i(all_51_2) & $i(all_51_3) & $i(all_51_4) & ~ % 139.48/19.28 | sdtlseqdt0(all_51_3, all_51_0) % 139.48/19.28 | % 139.48/19.28 | ALPHA: (62) implies: % 139.48/19.28 | (63) ~ sdtlseqdt0(all_51_3, all_51_0) % 139.48/19.28 | (64) $i(all_51_2) % 139.48/19.28 | (65) sdtpldt0(all_51_4, all_51_4) = all_51_3 % 139.48/19.28 | (66) sdtpldt0(all_51_2, all_51_1) = all_51_0 % 139.48/19.28 | (67) sdtasdt0(xR, xR) = all_51_2 % 139.48/19.28 | (68) sdtasdt0(xP, xP) = all_51_4 % 139.48/19.28 | (69) sdtasdt0(xS, xS) = all_51_1 % 139.48/19.28 | % 139.48/19.28 | DELTA: instantiating (24) with fresh symbols all_53_0, all_53_1, all_53_2, % 139.48/19.28 | all_53_3, all_53_4, all_53_5, all_53_6 gives: % 139.48/19.28 | (70) smndt0(xS) = all_53_6 & sdtasdt0(all_53_5, all_53_5) = all_53_4 & % 139.48/19.28 | sdtasdt0(xS, xS) = all_53_0 & sdtasdt0(xR, xR) = all_53_1 & % 139.48/19.28 | sdtpldt0(all_53_1, all_53_0) = all_53_2 & sdtpldt0(all_53_3, xN) = % 139.48/19.28 | all_53_2 & sdtpldt0(all_53_4, xN) = all_53_3 & sdtpldt0(xR, all_53_6) % 139.48/19.28 | = all_53_5 & $i(all_53_0) & $i(all_53_1) & $i(all_53_2) & $i(all_53_3) % 139.48/19.28 | & $i(all_53_4) & $i(all_53_5) & $i(all_53_6) % 139.48/19.28 | % 139.48/19.28 | ALPHA: (70) implies: % 139.48/19.28 | (71) sdtpldt0(all_53_1, all_53_0) = all_53_2 % 139.48/19.29 | (72) sdtasdt0(xR, xR) = all_53_1 % 139.48/19.29 | (73) sdtasdt0(xS, xS) = all_53_0 % 139.48/19.29 | (74) smndt0(xS) = all_53_6 % 139.48/19.29 | % 139.48/19.29 | DELTA: instantiating (21) with fresh symbols all_55_0, all_55_1, all_55_2, % 139.48/19.29 | all_55_3, all_55_4, all_55_5, all_55_6, all_55_7 gives: % 139.48/19.29 | (75) smndt0(xN) = all_55_3 & smndt0(xS) = all_55_7 & sdtasdt0(all_55_6, % 139.48/19.29 | all_55_6) = all_55_5 & sdtasdt0(xS, xS) = all_55_1 & sdtasdt0(xR, % 139.48/19.29 | xR) = all_55_4 & sdtpldt0(all_55_2, all_55_0) = all_55_5 & % 139.48/19.29 | sdtpldt0(all_55_3, all_55_1) = all_55_0 & sdtpldt0(all_55_4, all_55_3) % 139.48/19.29 | = all_55_2 & sdtpldt0(xR, all_55_7) = all_55_6 & $i(all_55_0) & % 139.48/19.29 | $i(all_55_1) & $i(all_55_2) & $i(all_55_3) & $i(all_55_4) & % 139.48/19.29 | $i(all_55_5) & $i(all_55_6) & $i(all_55_7) % 139.48/19.29 | % 139.48/19.29 | ALPHA: (75) implies: % 139.48/19.29 | (76) sdtasdt0(xR, xR) = all_55_4 % 139.48/19.29 | (77) sdtasdt0(xS, xS) = all_55_1 % 139.48/19.29 | (78) smndt0(xS) = all_55_7 % 139.48/19.29 | (79) smndt0(xN) = all_55_3 % 139.48/19.29 | % 139.48/19.29 | DELTA: instantiating (22) with fresh symbols all_57_0, all_57_1, all_57_2, % 139.48/19.29 | all_57_3, all_57_4, all_57_5, all_57_6, all_57_7 gives: % 139.48/19.29 | (80) smndt0(xN) = all_57_3 & smndt0(xS) = all_57_7 & sdtasdt0(all_57_6, % 139.48/19.29 | all_57_6) = all_57_5 & sdtasdt0(xS, xS) = all_57_1 & sdtasdt0(xR, % 139.48/19.29 | xR) = all_57_4 & sdtpldt0(all_57_1, all_57_3) = all_57_0 & % 139.48/19.29 | sdtpldt0(all_57_2, all_57_0) = all_57_5 & sdtpldt0(all_57_4, all_57_3) % 139.48/19.29 | = all_57_2 & sdtpldt0(xR, all_57_7) = all_57_6 & $i(all_57_0) & % 139.48/19.29 | $i(all_57_1) & $i(all_57_2) & $i(all_57_3) & $i(all_57_4) & % 139.48/19.29 | $i(all_57_5) & $i(all_57_6) & $i(all_57_7) % 139.48/19.29 | % 139.48/19.29 | ALPHA: (80) implies: % 139.48/19.29 | (81) sdtasdt0(xR, xR) = all_57_4 % 139.48/19.29 | (82) sdtasdt0(xS, xS) = all_57_1 % 139.48/19.29 | (83) smndt0(xS) = all_57_7 % 139.48/19.29 | (84) smndt0(xN) = all_57_3 % 139.48/19.29 | % 139.48/19.29 | DELTA: instantiating (23) with fresh symbols all_59_0, all_59_1, all_59_2, % 139.48/19.29 | all_59_3, all_59_4, all_59_5, all_59_6, all_59_7 gives: % 139.48/19.29 | (85) smndt0(xN) = all_59_1 & smndt0(xS) = all_59_7 & sdtasdt0(all_59_6, % 139.48/19.29 | all_59_6) = all_59_5 & sdtasdt0(xS, xS) = all_59_3 & sdtasdt0(xR, % 139.48/19.29 | xR) = all_59_4 & sdtpldt0(all_59_0, all_59_1) = all_59_5 & % 139.48/19.29 | sdtpldt0(all_59_2, all_59_1) = all_59_0 & sdtpldt0(all_59_4, all_59_3) % 139.48/19.29 | = all_59_2 & sdtpldt0(xR, all_59_7) = all_59_6 & $i(all_59_0) & % 139.48/19.29 | $i(all_59_1) & $i(all_59_2) & $i(all_59_3) & $i(all_59_4) & % 139.48/19.29 | $i(all_59_5) & $i(all_59_6) & $i(all_59_7) % 139.48/19.29 | % 139.48/19.29 | ALPHA: (85) implies: % 139.48/19.29 | (86) sdtpldt0(all_59_4, all_59_3) = all_59_2 % 139.48/19.29 | (87) sdtpldt0(all_59_2, all_59_1) = all_59_0 % 139.48/19.29 | (88) sdtasdt0(xR, xR) = all_59_4 % 139.48/19.29 | (89) sdtasdt0(xS, xS) = all_59_3 % 139.48/19.29 | (90) smndt0(xS) = all_59_7 % 139.48/19.29 | (91) smndt0(xN) = all_59_1 % 139.48/19.29 | % 139.48/19.29 | DELTA: instantiating (5) with fresh symbol all_61_0 gives: % 139.48/19.29 | (92) aDimensionOf0(xs) = all_61_0 & $i(all_61_0) & ! [v0: $i] : ! [v1: % 139.48/19.29 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasasdt0(v1, % 139.48/19.29 | v1) = v3) | ~ (sdtasasdt0(v0, v0) = v2) | ~ (sdtasdt0(v2, v3) % 139.48/19.29 | = v4) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) % 139.48/19.29 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 139.48/19.29 | ((sdtasasdt0(v0, v1) = v7 & sdtasdt0(v7, v7) = v8 & $i(v8) & $i(v7) % 139.48/19.29 | & sdtlseqdt0(v8, v4)) | (aDimensionOf0(v0) = v5 & $i(v5) & ( ~ % 139.48/19.29 | iLess0(v5, all_61_0) | ( ~ (v6 = v5) & aDimensionOf0(v1) = v6 % 139.48/19.29 | & $i(v6)))))) % 139.48/19.29 | % 139.48/19.29 | ALPHA: (92) implies: % 139.48/19.29 | (93) aDimensionOf0(xs) = all_61_0 % 139.48/19.29 | % 139.48/19.30 | GROUND_INST: instantiating (35) with all_49_2, all_53_1, xR, xR, simplifying % 139.48/19.30 | with (60), (72) gives: % 139.48/19.30 | (94) all_53_1 = all_49_2 % 139.48/19.30 | % 139.48/19.30 | GROUND_INST: instantiating (35) with all_51_2, all_57_4, xR, xR, simplifying % 139.48/19.30 | with (67), (81) gives: % 139.48/19.30 | (95) all_57_4 = all_51_2 % 139.48/19.30 | % 139.48/19.30 | GROUND_INST: instantiating (35) with all_57_4, all_59_4, xR, xR, simplifying % 139.48/19.30 | with (81), (88) gives: % 139.48/19.30 | (96) all_59_4 = all_57_4 % 139.48/19.30 | % 139.48/19.30 | GROUND_INST: instantiating (35) with all_55_4, all_59_4, xR, xR, simplifying % 139.48/19.30 | with (76), (88) gives: % 139.48/19.30 | (97) all_59_4 = all_55_4 % 139.48/19.30 | % 139.48/19.30 | GROUND_INST: instantiating (35) with all_53_1, all_59_4, xR, xR, simplifying % 139.48/19.30 | with (72), (88) gives: % 139.48/19.30 | (98) all_59_4 = all_53_1 % 139.48/19.30 | % 139.48/19.30 | GROUND_INST: instantiating (35) with all_35_0, all_51_4, xP, xP, simplifying % 139.48/19.30 | with (41), (68) gives: % 139.48/19.30 | (99) all_51_4 = all_35_0 % 139.48/19.30 | % 139.48/19.30 | GROUND_INST: instantiating (35) with all_49_1, all_53_0, xS, xS, simplifying % 139.48/19.30 | with (61), (73) gives: % 139.48/19.30 | (100) all_53_0 = all_49_1 % 139.48/19.30 | % 139.48/19.30 | GROUND_INST: instantiating (35) with all_53_0, all_55_1, xS, xS, simplifying % 139.48/19.30 | with (73), (77) gives: % 139.87/19.30 | (101) all_55_1 = all_53_0 % 139.87/19.30 | % 139.87/19.30 | GROUND_INST: instantiating (35) with all_53_0, all_57_1, xS, xS, simplifying % 139.87/19.30 | with (73), (82) gives: % 139.87/19.30 | (102) all_57_1 = all_53_0 % 139.87/19.30 | % 139.87/19.30 | GROUND_INST: instantiating (35) with all_51_1, all_57_1, xS, xS, simplifying % 139.87/19.30 | with (69), (82) gives: % 139.87/19.30 | (103) all_57_1 = all_51_1 % 139.87/19.30 | % 139.87/19.30 | GROUND_INST: instantiating (35) with all_55_1, all_59_3, xS, xS, simplifying % 139.87/19.30 | with (77), (89) gives: % 139.87/19.30 | (104) all_59_3 = all_55_1 % 139.87/19.30 | % 139.87/19.30 | GROUND_INST: instantiating (35) with all_47_0, all_59_3, xS, xS, simplifying % 139.87/19.30 | with (52), (89) gives: % 139.87/19.30 | (105) all_59_3 = all_47_0 % 139.87/19.30 | % 139.87/19.30 | GROUND_INST: instantiating (32) with all_53_6, all_55_7, xS, simplifying with % 139.87/19.30 | (74), (78) gives: % 139.87/19.30 | (106) all_55_7 = all_53_6 % 139.87/19.30 | % 139.87/19.30 | GROUND_INST: instantiating (32) with all_47_2, all_55_7, xS, simplifying with % 139.87/19.30 | (54), (78) gives: % 139.87/19.30 | (107) all_55_7 = all_47_2 % 139.87/19.30 | % 139.87/19.30 | GROUND_INST: instantiating (32) with all_53_6, all_57_7, xS, simplifying with % 139.87/19.30 | (74), (83) gives: % 139.87/19.30 | (108) all_57_7 = all_53_6 % 139.87/19.30 | % 139.87/19.30 | GROUND_INST: instantiating (32) with all_57_7, all_59_7, xS, simplifying with % 139.87/19.30 | (83), (90) gives: % 139.87/19.30 | (109) all_59_7 = all_57_7 % 139.87/19.30 | % 139.87/19.30 | GROUND_INST: instantiating (32) with all_45_2, all_59_7, xS, simplifying with % 139.87/19.30 | (50), (90) gives: % 139.87/19.30 | (110) all_59_7 = all_45_2 % 139.87/19.30 | % 139.87/19.30 | GROUND_INST: instantiating (32) with all_47_1, all_57_3, xN, simplifying with % 139.87/19.30 | (55), (84) gives: % 139.87/19.30 | (111) all_57_3 = all_47_1 % 139.87/19.30 | % 139.87/19.30 | GROUND_INST: instantiating (32) with all_57_3, all_59_1, xN, simplifying with % 139.87/19.30 | (84), (91) gives: % 139.87/19.30 | (112) all_59_1 = all_57_3 % 139.87/19.30 | % 139.87/19.30 | GROUND_INST: instantiating (32) with all_55_3, all_59_1, xN, simplifying with % 139.87/19.30 | (79), (91) gives: % 139.87/19.30 | (113) all_59_1 = all_55_3 % 139.87/19.30 | % 139.87/19.30 | GROUND_INST: instantiating (33) with all_33_0, all_39_0, xs, simplifying with % 139.87/19.30 | (37), (46) gives: % 139.87/19.30 | (114) all_39_0 = all_33_0 % 139.87/19.30 | % 139.87/19.30 | GROUND_INST: instantiating (33) with all_39_0, all_61_0, xs, simplifying with % 139.87/19.30 | (46), (93) gives: % 139.87/19.30 | (115) all_61_0 = all_39_0 % 139.87/19.30 | % 139.87/19.30 | GROUND_INST: instantiating (33) with all_37_0, all_61_0, xs, simplifying with % 139.87/19.30 | (44), (93) gives: % 139.87/19.30 | (116) all_61_0 = all_37_0 % 139.87/19.30 | % 139.87/19.30 | GROUND_INST: instantiating (33) with all_33_0, all_41_0, xt, simplifying with % 139.87/19.31 | (38), (48) gives: % 139.87/19.31 | (117) all_41_0 = all_33_0 % 139.87/19.31 | % 139.87/19.31 | COMBINE_EQS: (115), (116) imply: % 139.87/19.31 | (118) all_39_0 = all_37_0 % 139.87/19.31 | % 139.87/19.31 | SIMP: (118) implies: % 139.87/19.31 | (119) all_39_0 = all_37_0 % 139.87/19.31 | % 139.87/19.31 | COMBINE_EQS: (112), (113) imply: % 139.87/19.31 | (120) all_57_3 = all_55_3 % 139.87/19.31 | % 139.87/19.31 | SIMP: (120) implies: % 139.87/19.31 | (121) all_57_3 = all_55_3 % 139.87/19.31 | % 139.87/19.31 | COMBINE_EQS: (104), (105) imply: % 139.87/19.31 | (122) all_55_1 = all_47_0 % 139.87/19.31 | % 139.87/19.31 | SIMP: (122) implies: % 139.87/19.31 | (123) all_55_1 = all_47_0 % 139.87/19.31 | % 139.87/19.31 | COMBINE_EQS: (96), (97) imply: % 139.87/19.31 | (124) all_57_4 = all_55_4 % 139.87/19.31 | % 139.87/19.31 | SIMP: (124) implies: % 139.87/19.31 | (125) all_57_4 = all_55_4 % 139.87/19.31 | % 139.87/19.31 | COMBINE_EQS: (97), (98) imply: % 139.87/19.31 | (126) all_55_4 = all_53_1 % 139.87/19.31 | % 139.87/19.31 | COMBINE_EQS: (109), (110) imply: % 139.87/19.31 | (127) all_57_7 = all_45_2 % 139.87/19.31 | % 139.87/19.31 | SIMP: (127) implies: % 139.87/19.31 | (128) all_57_7 = all_45_2 % 139.87/19.31 | % 139.87/19.31 | COMBINE_EQS: (102), (103) imply: % 139.87/19.31 | (129) all_53_0 = all_51_1 % 139.87/19.31 | % 139.87/19.31 | SIMP: (129) implies: % 139.87/19.31 | (130) all_53_0 = all_51_1 % 139.87/19.31 | % 139.87/19.31 | COMBINE_EQS: (111), (121) imply: % 139.87/19.31 | (131) all_55_3 = all_47_1 % 139.87/19.31 | % 139.87/19.31 | SIMP: (131) implies: % 139.87/19.31 | (132) all_55_3 = all_47_1 % 139.87/19.31 | % 139.87/19.31 | COMBINE_EQS: (95), (125) imply: % 139.87/19.31 | (133) all_55_4 = all_51_2 % 139.87/19.31 | % 139.87/19.31 | SIMP: (133) implies: % 139.87/19.31 | (134) all_55_4 = all_51_2 % 139.87/19.31 | % 139.87/19.31 | COMBINE_EQS: (108), (128) imply: % 139.87/19.31 | (135) all_53_6 = all_45_2 % 139.87/19.31 | % 139.87/19.31 | SIMP: (135) implies: % 139.87/19.31 | (136) all_53_6 = all_45_2 % 139.87/19.31 | % 139.87/19.31 | COMBINE_EQS: (101), (123) imply: % 139.87/19.31 | (137) all_53_0 = all_47_0 % 139.87/19.31 | % 139.87/19.31 | SIMP: (137) implies: % 139.87/19.31 | (138) all_53_0 = all_47_0 % 139.87/19.31 | % 139.87/19.31 | COMBINE_EQS: (126), (134) imply: % 139.87/19.31 | (139) all_53_1 = all_51_2 % 139.87/19.31 | % 139.87/19.31 | SIMP: (139) implies: % 139.87/19.31 | (140) all_53_1 = all_51_2 % 139.87/19.31 | % 139.87/19.31 | COMBINE_EQS: (106), (107) imply: % 139.87/19.31 | (141) all_53_6 = all_47_2 % 139.87/19.31 | % 139.87/19.31 | SIMP: (141) implies: % 139.87/19.31 | (142) all_53_6 = all_47_2 % 139.87/19.31 | % 139.87/19.31 | COMBINE_EQS: (100), (130) imply: % 139.87/19.31 | (143) all_51_1 = all_49_1 % 139.87/19.31 | % 139.87/19.31 | COMBINE_EQS: (130), (138) imply: % 139.87/19.31 | (144) all_51_1 = all_47_0 % 139.87/19.31 | % 139.87/19.31 | COMBINE_EQS: (94), (140) imply: % 139.87/19.31 | (145) all_51_2 = all_49_2 % 139.87/19.31 | % 139.87/19.31 | COMBINE_EQS: (136), (142) imply: % 139.87/19.31 | (146) all_47_2 = all_45_2 % 139.87/19.31 | % 139.87/19.31 | SIMP: (146) implies: % 139.87/19.31 | (147) all_47_2 = all_45_2 % 139.87/19.31 | % 139.87/19.31 | COMBINE_EQS: (143), (144) imply: % 139.87/19.31 | (148) all_49_1 = all_47_0 % 139.87/19.31 | % 139.87/19.31 | SIMP: (148) implies: % 139.87/19.31 | (149) all_49_1 = all_47_0 % 139.87/19.31 | % 139.87/19.31 | COMBINE_EQS: (114), (119) imply: % 139.87/19.31 | (150) all_37_0 = all_33_0 % 139.87/19.31 | % 139.87/19.31 | COMBINE_EQS: (134), (145) imply: % 139.87/19.31 | (151) all_55_4 = all_49_2 % 139.87/19.31 | % 139.87/19.31 | COMBINE_EQS: (97), (151) imply: % 139.87/19.31 | (152) all_59_4 = all_49_2 % 139.87/19.31 | % 139.87/19.31 | COMBINE_EQS: (113), (132) imply: % 139.87/19.31 | (153) all_59_1 = all_47_1 % 139.87/19.31 | % 139.87/19.31 | REDUCE: (43), (150) imply: % 139.87/19.31 | (154) ~ (all_33_0 = sz00) % 139.87/19.31 | % 139.87/19.31 | REDUCE: (53), (147) imply: % 139.87/19.31 | (155) sdtasdt0(all_45_2, xR) = all_47_1 % 139.87/19.31 | % 139.87/19.31 | REDUCE: (87), (153) imply: % 139.87/19.31 | (156) sdtpldt0(all_59_2, all_47_1) = all_59_0 % 139.87/19.31 | % 139.87/19.31 | REDUCE: (86), (105), (152) imply: % 139.87/19.31 | (157) sdtpldt0(all_49_2, all_47_0) = all_59_2 % 139.87/19.31 | % 139.87/19.31 | REDUCE: (71), (94), (138) imply: % 139.87/19.31 | (158) sdtpldt0(all_49_2, all_47_0) = all_53_2 % 139.87/19.31 | % 139.87/19.31 | REDUCE: (66), (144), (145) imply: % 139.87/19.31 | (159) sdtpldt0(all_49_2, all_47_0) = all_51_0 % 139.87/19.31 | % 139.87/19.31 | REDUCE: (65), (99) imply: % 139.87/19.31 | (160) sdtpldt0(all_35_0, all_35_0) = all_51_3 % 139.87/19.31 | % 139.87/19.31 | REDUCE: (59), (149) imply: % 139.87/19.31 | (161) sdtpldt0(all_49_2, all_47_0) = all_49_0 % 139.87/19.31 | % 139.87/19.31 | REDUCE: (64), (145) imply: % 139.87/19.31 | (162) $i(all_49_2) % 139.87/19.32 | % 139.87/19.32 | GROUND_INST: instantiating (34) with all_51_0, all_53_2, all_47_0, all_49_2, % 139.87/19.32 | simplifying with (158), (159) gives: % 139.87/19.32 | (163) all_53_2 = all_51_0 % 139.87/19.32 | % 139.87/19.32 | GROUND_INST: instantiating (34) with all_53_2, all_59_2, all_47_0, all_49_2, % 139.87/19.32 | simplifying with (157), (158) gives: % 139.87/19.32 | (164) all_59_2 = all_53_2 % 139.87/19.32 | % 139.87/19.32 | GROUND_INST: instantiating (34) with all_49_0, all_59_2, all_47_0, all_49_2, % 139.87/19.32 | simplifying with (157), (161) gives: % 139.87/19.32 | (165) all_59_2 = all_49_0 % 139.87/19.32 | % 139.87/19.32 | COMBINE_EQS: (164), (165) imply: % 139.87/19.32 | (166) all_53_2 = all_49_0 % 139.87/19.32 | % 139.87/19.32 | SIMP: (166) implies: % 139.87/19.32 | (167) all_53_2 = all_49_0 % 139.87/19.32 | % 139.87/19.32 | COMBINE_EQS: (163), (167) imply: % 139.87/19.32 | (168) all_51_0 = all_49_0 % 139.87/19.32 | % 139.87/19.32 | SIMP: (168) implies: % 139.87/19.32 | (169) all_51_0 = all_49_0 % 139.87/19.32 | % 139.87/19.32 | REDUCE: (156), (165) imply: % 139.87/19.32 | (170) sdtpldt0(all_49_0, all_47_1) = all_59_0 % 139.87/19.32 | % 139.87/19.32 | REDUCE: (63), (169) imply: % 139.87/19.32 | (171) ~ sdtlseqdt0(all_51_3, all_49_0) % 139.87/19.32 | % 139.87/19.32 | GROUND_INST: instantiating (mSumSc) with xN, xN, all_49_3, simplifying with % 139.87/19.32 | (17), (26), (58) gives: % 139.87/19.32 | (172) aScalar0(all_49_3) % 139.87/19.32 | % 139.87/19.32 | GROUND_INST: instantiating (mMulSc) with xR, xR, all_49_2, simplifying with % 139.87/19.32 | (14), (28), (60) gives: % 139.87/19.32 | (173) aScalar0(all_49_2) % 139.87/19.32 | % 139.87/19.32 | GROUND_INST: instantiating (mDistr) with xR, xS, xS, xN, xN, all_49_3, % 139.87/19.32 | simplifying with (14), (16), (18), (28), (30), (58) gives: % 139.87/19.32 | (174) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v1, % 139.87/19.32 | xS) = v2 & sdtasdt0(xS, xS) = v3 & sdtasdt0(xR, v0) = all_49_3 & % 139.87/19.32 | sdtpldt0(xN, v3) = v2 & sdtpldt0(xS, xS) = v0 & sdtpldt0(xR, xS) = % 139.87/19.32 | v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_49_3)) % 139.87/19.32 | % 139.87/19.32 | GROUND_INST: instantiating (mDistr) with xP, xP, xP, all_35_0, all_35_0, % 139.87/19.32 | all_51_3, simplifying with (15), (29), (41), (160) gives: % 139.87/19.32 | (175) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v1, % 139.87/19.32 | xP) = v2 & sdtasdt0(xP, v0) = all_51_3 & sdtasdt0(xP, xP) = v3 & % 139.87/19.32 | sdtpldt0(all_35_0, v3) = v2 & sdtpldt0(xP, xP) = v1 & sdtpldt0(xP, % 139.87/19.32 | xP) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_51_3)) % 139.87/19.32 | % 139.87/19.32 | GROUND_INST: instantiating (mMulSc) with xP, xP, all_35_0, simplifying with % 139.87/19.32 | (15), (29), (41) gives: % 139.87/19.32 | (176) aScalar0(all_35_0) % 139.87/19.32 | % 139.87/19.32 | GROUND_INST: instantiating (mMulSc) with xS, xS, all_47_0, simplifying with % 139.87/19.32 | (16), (30), (52) gives: % 139.87/19.32 | (177) aScalar0(all_47_0) % 139.87/19.32 | % 139.87/19.32 | GROUND_INST: instantiating (mMNeg) with xS, xR, all_45_2, all_47_1, % 139.87/19.32 | simplifying with (14), (16), (28), (30), (50), (155) gives: % 139.87/19.32 | (178) ? [v0: $i] : ? [v1: $i] : (smndt0(v1) = all_47_1 & smndt0(xR) = v0 % 139.87/19.32 | & sdtasdt0(xS, v0) = all_47_1 & sdtasdt0(xS, xR) = v1 & $i(v1) & % 139.87/19.32 | $i(v0) & $i(all_47_1)) % 139.87/19.32 | % 139.87/19.32 | GROUND_INST: instantiating (mNegSc) with xN, all_47_1, simplifying with (17), % 139.87/19.32 | (26), (55) gives: % 139.87/19.32 | (179) aScalar0(all_47_1) % 139.87/19.32 | % 139.87/19.32 | GROUND_INST: instantiating (1) with xs, xp, simplifying with (3), (8), (10) % 139.87/19.32 | gives: % 139.87/19.33 | (180) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & (v0 = sz00 | ( ! % 139.87/19.33 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlbdtrb0(xs, v2) % 139.87/19.33 | = v3) | ~ (aDimensionOf0(xp) = v1) | ~ $i(v2) | ~ $i(xp) % 139.87/19.33 | | ~ aNaturalNumber0(v2) | (sdtlbdtrb0(xp, v2) = v3 & % 139.87/19.33 | $i(v3))) & ! [v1: $i] : ! [v2: $i] : (v1 = xp | ~ % 139.87/19.33 | (aDimensionOf0(v1) = v2) | ~ $i(v1) | ~ aVector0(v1) | ? % 139.87/19.33 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ($i(v4) % 139.87/19.33 | & (( ~ (v6 = v5) & sdtlbdtrb0(v1, v4) = v5 & sdtlbdtrb0(xs, % 139.87/19.33 | v4) = v6 & $i(v6) & $i(v5) & aNaturalNumber0(v4)) | ( % 139.87/19.33 | ~ (v3 = v0) & szszuzczcdt0(v2) = v3 & $i(v3))))) & ! % 139.87/19.33 | [v1: $i] : ( ~ (aDimensionOf0(xp) = v1) | ~ $i(xp) | % 139.87/19.33 | szszuzczcdt0(v1) = v0) & ! [v1: $i] : ( ~ (aDimensionOf0(xp) % 139.87/19.33 | = v1) | ~ $i(xp) | aVector0(xp))))) % 139.87/19.33 | % 139.87/19.33 | GROUND_INST: instantiating (2) with xt, xs, xq, xp, simplifying with (3), (4), % 139.87/19.33 | (8), (9), (10), (12) gives: % 139.87/19.33 | (181) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ((v3 = v2 & % 139.87/19.33 | aDimensionOf0(xq) = v2 & aDimensionOf0(xp) = v2 & $i(v2)) | % 139.87/19.33 | (aDimensionOf0(xs) = v1 & $i(v1) & (v1 = sz00 | ( ~ (v1 = v0) & % 139.87/19.33 | aDimensionOf0(xt) = v0 & $i(v0))))) % 139.87/19.33 | % 139.87/19.33 | GROUND_INST: instantiating (1) with xt, xq, simplifying with (4), (9), (12) % 139.87/19.33 | gives: % 139.87/19.33 | (182) ? [v0: $i] : (aDimensionOf0(xt) = v0 & $i(v0) & (v0 = sz00 | ( ! % 139.87/19.33 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlbdtrb0(xt, v2) % 139.87/19.33 | = v3) | ~ (aDimensionOf0(xq) = v1) | ~ $i(v2) | ~ $i(xq) % 139.87/19.33 | | ~ aNaturalNumber0(v2) | (sdtlbdtrb0(xq, v2) = v3 & % 139.87/19.33 | $i(v3))) & ! [v1: $i] : ! [v2: $i] : (v1 = xq | ~ % 139.87/19.33 | (aDimensionOf0(v1) = v2) | ~ $i(v1) | ~ aVector0(v1) | ? % 139.87/19.33 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ($i(v4) % 139.87/19.33 | & (( ~ (v6 = v5) & sdtlbdtrb0(v1, v4) = v5 & sdtlbdtrb0(xt, % 139.87/19.33 | v4) = v6 & $i(v6) & $i(v5) & aNaturalNumber0(v4)) | ( % 139.87/19.33 | ~ (v3 = v0) & szszuzczcdt0(v2) = v3 & $i(v3))))) & ! % 139.87/19.33 | [v1: $i] : ( ~ (aDimensionOf0(xq) = v1) | ~ $i(xq) | % 139.87/19.33 | szszuzczcdt0(v1) = v0) & ! [v1: $i] : ( ~ (aDimensionOf0(xq) % 139.87/19.33 | = v1) | ~ $i(xq) | aVector0(xq))))) % 139.87/19.33 | % 139.87/19.33 | DELTA: instantiating (178) with fresh symbols all_85_0, all_85_1 gives: % 139.87/19.33 | (183) smndt0(all_85_0) = all_47_1 & smndt0(xR) = all_85_1 & sdtasdt0(xS, % 139.87/19.33 | all_85_1) = all_47_1 & sdtasdt0(xS, xR) = all_85_0 & $i(all_85_0) & % 139.87/19.33 | $i(all_85_1) & $i(all_47_1) % 139.87/19.33 | % 139.87/19.33 | ALPHA: (183) implies: % 139.87/19.33 | (184) $i(all_47_1) % 139.87/19.33 | % 139.87/19.33 | DELTA: instantiating (181) with fresh symbols all_90_0, all_90_1, all_90_2, % 139.87/19.33 | all_90_3 gives: % 139.87/19.33 | (185) (all_90_0 = all_90_1 & aDimensionOf0(xq) = all_90_1 & % 139.87/19.33 | aDimensionOf0(xp) = all_90_1 & $i(all_90_1)) | (aDimensionOf0(xs) = % 139.87/19.33 | all_90_2 & $i(all_90_2) & (all_90_2 = sz00 | ( ~ (all_90_2 = % 139.87/19.33 | all_90_3) & aDimensionOf0(xt) = all_90_3 & $i(all_90_3)))) % 139.87/19.33 | % 139.87/19.33 | DELTA: instantiating (175) with fresh symbols all_91_0, all_91_1, all_91_2, % 139.87/19.33 | all_91_3 gives: % 139.87/19.33 | (186) sdtasdt0(all_91_2, xP) = all_91_1 & sdtasdt0(xP, all_91_3) = all_51_3 % 139.87/19.33 | & sdtasdt0(xP, xP) = all_91_0 & sdtpldt0(all_35_0, all_91_0) = % 139.87/19.33 | all_91_1 & sdtpldt0(xP, xP) = all_91_2 & sdtpldt0(xP, xP) = all_91_3 % 139.87/19.33 | & $i(all_91_0) & $i(all_91_1) & $i(all_91_2) & $i(all_91_3) & % 139.87/19.33 | $i(all_51_3) % 139.87/19.33 | % 139.87/19.33 | ALPHA: (186) implies: % 139.87/19.33 | (187) $i(all_91_1) % 139.87/19.33 | (188) $i(all_91_0) % 139.87/19.33 | (189) sdtpldt0(all_35_0, all_91_0) = all_91_1 % 139.87/19.33 | (190) sdtasdt0(xP, xP) = all_91_0 % 139.87/19.33 | % 139.87/19.33 | DELTA: instantiating (174) with fresh symbols all_93_0, all_93_1, all_93_2, % 139.87/19.33 | all_93_3 gives: % 139.87/19.33 | (191) sdtasdt0(all_93_2, xS) = all_93_1 & sdtasdt0(xS, xS) = all_93_0 & % 139.87/19.33 | sdtasdt0(xR, all_93_3) = all_49_3 & sdtpldt0(xN, all_93_0) = all_93_1 % 139.87/19.33 | & sdtpldt0(xS, xS) = all_93_3 & sdtpldt0(xR, xS) = all_93_2 & % 139.87/19.33 | $i(all_93_0) & $i(all_93_1) & $i(all_93_2) & $i(all_93_3) & % 139.87/19.33 | $i(all_49_3) % 139.87/19.33 | % 139.87/19.33 | ALPHA: (191) implies: % 139.87/19.33 | (192) $i(all_49_3) % 139.87/19.33 | (193) $i(all_93_0) % 139.87/19.33 | (194) sdtasdt0(xS, xS) = all_93_0 % 139.87/19.33 | % 139.87/19.33 | DELTA: instantiating (182) with fresh symbol all_96_0 gives: % 139.87/19.34 | (195) aDimensionOf0(xt) = all_96_0 & $i(all_96_0) & (all_96_0 = sz00 | ( ! % 139.87/19.34 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(xt, v1) = % 139.87/19.34 | v2) | ~ (aDimensionOf0(xq) = v0) | ~ $i(v1) | ~ $i(xq) | % 139.87/19.34 | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(xq, v1) = v2 & $i(v2))) & % 139.87/19.34 | ! [v0: $i] : ! [v1: $i] : (v0 = xq | ~ (aDimensionOf0(v0) = v1) % 139.87/19.34 | | ~ $i(v0) | ~ aVector0(v0) | ? [v2: any] : ? [v3: $i] : ? % 139.87/19.34 | [v4: $i] : ? [v5: $i] : ($i(v3) & (( ~ (v5 = v4) & % 139.87/19.34 | sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xt, v3) = v5 & % 139.87/19.34 | $i(v5) & $i(v4) & aNaturalNumber0(v3)) | ( ~ (v2 = % 139.87/19.34 | all_96_0) & szszuzczcdt0(v1) = v2 & $i(v2))))) & ! % 139.87/19.34 | [v0: $i] : ( ~ (aDimensionOf0(xq) = v0) | ~ $i(xq) | % 139.87/19.34 | szszuzczcdt0(v0) = all_96_0) & ! [v0: $i] : ( ~ % 139.87/19.34 | (aDimensionOf0(xq) = v0) | ~ $i(xq) | aVector0(xq)))) % 139.87/19.34 | % 139.87/19.34 | ALPHA: (195) implies: % 139.87/19.34 | (196) aDimensionOf0(xt) = all_96_0 % 139.87/19.34 | % 139.87/19.34 | DELTA: instantiating (180) with fresh symbol all_98_0 gives: % 139.87/19.34 | (197) aDimensionOf0(xs) = all_98_0 & $i(all_98_0) & (all_98_0 = sz00 | ( ! % 139.87/19.34 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(xs, v1) = % 139.87/19.34 | v2) | ~ (aDimensionOf0(xp) = v0) | ~ $i(v1) | ~ $i(xp) | % 139.87/19.34 | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(xp, v1) = v2 & $i(v2))) & % 139.87/19.34 | ! [v0: $i] : ! [v1: $i] : (v0 = xp | ~ (aDimensionOf0(v0) = v1) % 139.87/19.34 | | ~ $i(v0) | ~ aVector0(v0) | ? [v2: any] : ? [v3: $i] : ? % 139.87/19.34 | [v4: $i] : ? [v5: $i] : ($i(v3) & (( ~ (v5 = v4) & % 139.87/19.34 | sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xs, v3) = v5 & % 139.87/19.34 | $i(v5) & $i(v4) & aNaturalNumber0(v3)) | ( ~ (v2 = % 139.87/19.34 | all_98_0) & szszuzczcdt0(v1) = v2 & $i(v2))))) & ! % 139.87/19.34 | [v0: $i] : ( ~ (aDimensionOf0(xp) = v0) | ~ $i(xp) | % 139.87/19.34 | szszuzczcdt0(v0) = all_98_0) & ! [v0: $i] : ( ~ % 139.87/19.34 | (aDimensionOf0(xp) = v0) | ~ $i(xp) | aVector0(xp)))) % 139.87/19.34 | % 139.87/19.34 | ALPHA: (197) implies: % 139.87/19.34 | (198) aDimensionOf0(xs) = all_98_0 % 139.87/19.34 | % 139.87/19.34 | GROUND_INST: instantiating (35) with all_35_0, all_91_0, xP, xP, simplifying % 139.87/19.34 | with (41), (190) gives: % 139.87/19.34 | (199) all_91_0 = all_35_0 % 139.87/19.34 | % 139.87/19.34 | GROUND_INST: instantiating (35) with all_47_0, all_93_0, xS, xS, simplifying % 139.87/19.34 | with (52), (194) gives: % 139.87/19.34 | (200) all_93_0 = all_47_0 % 139.87/19.34 | % 139.87/19.34 | GROUND_INST: instantiating (33) with all_33_0, all_98_0, xs, simplifying with % 139.87/19.34 | (37), (198) gives: % 139.87/19.34 | (201) all_98_0 = all_33_0 % 139.87/19.34 | % 139.87/19.34 | GROUND_INST: instantiating (33) with all_33_0, all_96_0, xt, simplifying with % 139.87/19.34 | (38), (196) gives: % 139.87/19.34 | (202) all_96_0 = all_33_0 % 139.87/19.34 | % 139.87/19.34 | REDUCE: (189), (199) imply: % 139.87/19.34 | (203) sdtpldt0(all_35_0, all_35_0) = all_91_1 % 139.87/19.34 | % 139.87/19.34 | REDUCE: (193), (200) imply: % 139.87/19.34 | (204) $i(all_47_0) % 139.87/19.34 | % 139.87/19.34 | REDUCE: (188), (199) imply: % 139.87/19.34 | (205) $i(all_35_0) % 139.87/19.34 | % 139.87/19.34 | BETA: splitting (185) gives: % 139.87/19.34 | % 139.87/19.34 | Case 1: % 139.87/19.34 | | % 139.87/19.34 | | % 139.87/19.34 | | GROUND_INST: instantiating (34) with all_51_3, all_91_1, all_35_0, all_35_0, % 139.87/19.34 | | simplifying with (160), (203) gives: % 139.87/19.34 | | (206) all_91_1 = all_51_3 % 139.87/19.34 | | % 139.87/19.34 | | REDUCE: (187), (206) imply: % 139.87/19.34 | | (207) $i(all_51_3) % 139.87/19.34 | | % 139.87/19.34 | | GROUND_INST: instantiating (mSumSc) with all_35_0, all_35_0, all_51_3, % 139.87/19.34 | | simplifying with (160), (176), (205) gives: % 139.87/19.34 | | (208) aScalar0(all_51_3) % 139.87/19.34 | | % 139.87/19.34 | | GROUND_INST: instantiating (mLEMon) with all_35_0, xN, all_35_0, xN, % 139.87/19.34 | | all_51_3, all_49_3, simplifying with (17), (26), (40), (58), % 139.87/19.34 | | (160), (176), (205) gives: % 139.87/19.34 | | (209) sdtlseqdt0(all_51_3, all_49_3) % 139.87/19.34 | | % 139.87/19.34 | | GROUND_INST: instantiating (mArith) with all_49_2, all_47_0, all_47_1, % 139.87/19.34 | | all_49_0, all_59_0, simplifying with (161), (162), (170), % 139.87/19.34 | | (173), (177), (179), (184), (204) gives: % 139.87/19.35 | | (210) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 139.87/19.35 | | (sdtasdt0(v1, all_47_1) = v2 & sdtasdt0(all_49_2, v3) = v2 & % 139.87/19.35 | | sdtasdt0(all_49_2, all_47_0) = v1 & sdtasdt0(all_47_0, all_49_2) % 139.87/19.35 | | = v1 & sdtasdt0(all_47_0, all_47_1) = v3 & sdtpldt0(all_49_2, v0) % 139.87/19.35 | | = all_59_0 & sdtpldt0(all_47_0, all_49_2) = all_49_0 & % 139.87/19.35 | | sdtpldt0(all_47_0, all_47_1) = v0 & $i(v3) & $i(v2) & $i(v1) & % 139.87/19.35 | | $i(v0) & $i(all_59_0) & $i(all_49_0)) % 139.87/19.35 | | % 139.87/19.35 | | GROUND_INST: instantiating (mSumSc) with all_49_2, all_47_0, all_49_0, % 139.87/19.35 | | simplifying with (161), (162), (173), (177), (204) gives: % 139.87/19.35 | | (211) aScalar0(all_49_0) % 139.87/19.35 | | % 139.87/19.35 | | DELTA: instantiating (210) with fresh symbols all_155_0, all_155_1, % 139.87/19.35 | | all_155_2, all_155_3 gives: % 139.87/19.35 | | (212) sdtasdt0(all_155_2, all_47_1) = all_155_1 & sdtasdt0(all_49_2, % 139.87/19.35 | | all_155_0) = all_155_1 & sdtasdt0(all_49_2, all_47_0) = all_155_2 % 139.87/19.35 | | & sdtasdt0(all_47_0, all_49_2) = all_155_2 & sdtasdt0(all_47_0, % 139.87/19.35 | | all_47_1) = all_155_0 & sdtpldt0(all_49_2, all_155_3) = all_59_0 % 139.87/19.35 | | & sdtpldt0(all_47_0, all_49_2) = all_49_0 & sdtpldt0(all_47_0, % 139.87/19.35 | | all_47_1) = all_155_3 & $i(all_155_0) & $i(all_155_1) & % 139.87/19.35 | | $i(all_155_2) & $i(all_155_3) & $i(all_59_0) & $i(all_49_0) % 139.87/19.35 | | % 139.87/19.35 | | ALPHA: (212) implies: % 139.87/19.35 | | (213) $i(all_49_0) % 139.87/19.35 | | % 139.87/19.35 | | GROUND_INST: instantiating (mLETrn) with all_51_3, all_49_3, all_49_0, % 139.87/19.35 | | simplifying with (57), (171), (172), (192), (207), (208), % 139.87/19.35 | | (209), (211), (213) gives: % 139.87/19.35 | | (214) $false % 139.87/19.35 | | % 139.87/19.35 | | CLOSE: (214) is inconsistent. % 139.87/19.35 | | % 139.87/19.35 | Case 2: % 139.87/19.35 | | % 139.87/19.35 | | (215) aDimensionOf0(xs) = all_90_2 & $i(all_90_2) & (all_90_2 = sz00 | ( % 139.87/19.35 | | ~ (all_90_2 = all_90_3) & aDimensionOf0(xt) = all_90_3 & % 139.87/19.35 | | $i(all_90_3))) % 139.87/19.35 | | % 139.87/19.35 | | ALPHA: (215) implies: % 139.87/19.35 | | (216) aDimensionOf0(xs) = all_90_2 % 139.87/19.35 | | (217) all_90_2 = sz00 | ( ~ (all_90_2 = all_90_3) & aDimensionOf0(xt) = % 139.87/19.35 | | all_90_3 & $i(all_90_3)) % 139.87/19.35 | | % 139.87/19.35 | | GROUND_INST: instantiating (33) with all_33_0, all_90_2, xs, simplifying % 139.87/19.35 | | with (37), (216) gives: % 139.87/19.35 | | (218) all_90_2 = all_33_0 % 139.87/19.35 | | % 139.87/19.35 | | BETA: splitting (217) gives: % 139.87/19.35 | | % 139.87/19.35 | | Case 1: % 139.87/19.35 | | | % 139.87/19.35 | | | (219) all_90_2 = sz00 % 139.87/19.35 | | | % 139.87/19.35 | | | COMBINE_EQS: (218), (219) imply: % 139.87/19.35 | | | (220) all_33_0 = sz00 % 139.87/19.35 | | | % 139.87/19.35 | | | SIMP: (220) implies: % 139.87/19.35 | | | (221) all_33_0 = sz00 % 139.87/19.35 | | | % 139.87/19.35 | | | REDUCE: (154), (221) imply: % 139.87/19.35 | | | (222) $false % 139.87/19.35 | | | % 139.87/19.35 | | | CLOSE: (222) is inconsistent. % 139.87/19.35 | | | % 139.87/19.35 | | Case 2: % 139.87/19.35 | | | % 139.87/19.35 | | | (223) ~ (all_90_2 = all_90_3) & aDimensionOf0(xt) = all_90_3 & % 139.87/19.35 | | | $i(all_90_3) % 139.87/19.35 | | | % 139.87/19.35 | | | ALPHA: (223) implies: % 139.87/19.35 | | | (224) ~ (all_90_2 = all_90_3) % 139.87/19.35 | | | (225) aDimensionOf0(xt) = all_90_3 % 139.87/19.35 | | | % 139.87/19.35 | | | REDUCE: (218), (224) imply: % 139.87/19.35 | | | (226) ~ (all_90_3 = all_33_0) % 139.87/19.35 | | | % 139.87/19.35 | | | SIMP: (226) implies: % 139.87/19.35 | | | (227) ~ (all_90_3 = all_33_0) % 139.87/19.35 | | | % 139.87/19.35 | | | GROUND_INST: instantiating (33) with all_33_0, all_90_3, xt, simplifying % 139.87/19.35 | | | with (38), (225) gives: % 139.87/19.35 | | | (228) all_90_3 = all_33_0 % 139.87/19.35 | | | % 139.87/19.35 | | | REDUCE: (227), (228) imply: % 139.87/19.35 | | | (229) $false % 139.87/19.35 | | | % 139.87/19.35 | | | CLOSE: (229) is inconsistent. % 139.87/19.35 | | | % 139.87/19.35 | | End of split % 139.87/19.35 | | % 139.87/19.35 | End of split % 139.87/19.35 | % 139.87/19.35 End of proof % 139.87/19.35 % SZS output end Proof for theBenchmark % 139.87/19.35 % 139.87/19.35 18763ms %------------------------------------------------------------------------------