%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG065+2 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n011.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 13:57:39 EDT 2023 % Result : Theorem 141.53s 19.69s % Output : Proof 142.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : RNG065+2 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n011.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sun Aug 27 01:43:09 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.47/1.22 Prover 4: Preprocessing ... % 3.47/1.22 Prover 1: Preprocessing ... % 3.78/1.27 Prover 3: Preprocessing ... % 3.78/1.27 Prover 6: Preprocessing ... % 3.78/1.27 Prover 0: Preprocessing ... % 3.78/1.28 Prover 5: Preprocessing ... % 3.78/1.28 Prover 2: Preprocessing ... % 10.17/2.10 Prover 1: Constructing countermodel ... % 10.17/2.10 Prover 3: Constructing countermodel ... % 10.17/2.12 Prover 6: Proving ... % 11.40/2.26 Prover 5: Constructing countermodel ... % 12.09/2.39 Prover 2: Proving ... % 12.42/2.40 Prover 4: Constructing countermodel ... % 12.84/2.46 Prover 0: Proving ... % 72.75/10.36 Prover 2: stopped % 72.75/10.36 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 74.38/10.52 Prover 7: Preprocessing ... % 76.13/10.78 Prover 7: Constructing countermodel ... % 100.45/13.99 Prover 5: stopped % 101.18/14.00 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 101.18/14.09 Prover 8: Preprocessing ... % 101.90/14.22 Prover 8: Warning: ignoring some quantifiers % 101.90/14.24 Prover 8: Constructing countermodel ... % 115.88/16.00 Prover 1: stopped % 115.88/16.01 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 116.66/16.10 Prover 9: Preprocessing ... % 120.48/16.53 Prover 9: Constructing countermodel ... % 130.34/17.90 Prover 6: stopped % 130.34/17.91 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 132.02/18.05 Prover 10: Preprocessing ... % 132.95/18.16 Prover 10: Constructing countermodel ... % 140.08/19.09 Prover 10: Found proof (size 186) % 140.08/19.10 Prover 10: proved (1186ms) % 140.08/19.10 Prover 0: stopped % 140.08/19.10 Prover 9: stopped % 140.08/19.10 Prover 8: stopped % 140.08/19.10 Prover 7: stopped % 140.08/19.11 Prover 4: stopped % 141.53/19.69 Prover 3: stopped % 141.53/19.69 % 141.53/19.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 141.53/19.69 % 141.53/19.73 % SZS output start Proof for theBenchmark % 141.53/19.73 Assumptions after simplification: % 141.53/19.73 --------------------------------- % 141.53/19.73 % 141.53/19.73 (mArith) % 141.53/19.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 141.53/19.76 (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 141.53/19.76 | ~ $i(v0) | ~ aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v5: % 141.53/19.76 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(v6, v2) = v7 & % 141.53/19.76 sdtasdt0(v1, v2) = v8 & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v8) = v7 & % 141.53/19.76 sdtasdt0(v0, v1) = v6 & sdtpldt0(v1, v2) = v5 & sdtpldt0(v1, v0) = v3 & % 141.53/19.76 sdtpldt0(v0, v5) = v4 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 141.53/19.76 $i(v3))) % 141.53/19.76 % 141.53/19.76 (mDefInit) % 141.53/19.77 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sziznziztdt0(v0) = v1) | ~ $i(v0) % 141.53/19.77 | ~ aVector0(v0) | ? [v2: $i] : (aDimensionOf0(v0) = v2 & $i(v2) & (v2 = % 141.53/19.77 sz00 | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtlbdtrb0(v0, % 141.53/19.77 v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~ $i(v4) | ~ $i(v1) % 141.53/19.77 | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1, v4) = v5 & $i(v5))) & ! % 141.53/19.77 [v3: $i] : ! [v4: $i] : (v3 = v1 | ~ (aDimensionOf0(v3) = v4) | ~ % 141.53/19.77 $i(v3) | ~ aVector0(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 141.53/19.77 ? [v8: $i] : ($i(v6) & (( ~ (v8 = v7) & sdtlbdtrb0(v3, v6) = v7 & % 141.53/19.77 sdtlbdtrb0(v0, v6) = v8 & $i(v8) & $i(v7) & % 141.53/19.77 aNaturalNumber0(v6)) | ( ~ (v5 = v2) & szszuzczcdt0(v4) = v5 & % 141.53/19.77 $i(v5))))) & ! [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~ % 141.53/19.77 $i(v1) | szszuzczcdt0(v3) = v2) & ! [v3: $i] : ( ~ % 141.53/19.77 (aDimensionOf0(v1) = v3) | ~ $i(v1) | aVector0(v1)))))) % 141.53/19.77 % 141.53/19.77 (mDistr) % 141.53/19.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 141.53/19.77 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ % 141.53/19.77 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 141.53/19.77 aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v6: $i] : ? [v7: $i] % 141.53/19.77 : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v7, v2) = v8 & sdtasdt0(v1, v2) = v9 % 141.53/19.77 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v4, v9) = v8 & sdtpldt0(v1, v2) = v6 & % 141.53/19.77 sdtpldt0(v0, v1) = v7 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5))) % 141.53/19.77 % 141.53/19.77 (mLEMon) % 141.53/19.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 141.53/19.78 $i] : ( ~ (sdtpldt0(v1, v3) = v5) | ~ (sdtpldt0(v0, v2) = v4) | ~ $i(v3) | % 141.53/19.78 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v2, v3) | ~ % 141.53/19.78 sdtlseqdt0(v0, v1) | ~ aScalar0(v3) | ~ aScalar0(v2) | ~ aScalar0(v1) | % 141.53/19.78 ~ aScalar0(v0) | sdtlseqdt0(v4, v5)) % 141.53/19.78 % 141.53/19.78 (mLETrn) % 141.53/19.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 141.53/19.78 ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aScalar0(v2) | ~ % 141.53/19.78 aScalar0(v1) | ~ aScalar0(v0) | sdtlseqdt0(v0, v2)) % 141.53/19.78 % 141.53/19.78 (mMNeg) % 141.53/19.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (smndt0(v0) = v2) % 141.53/19.78 | ~ (sdtasdt0(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ % 141.53/19.78 aScalar0(v0) | ? [v4: $i] : ? [v5: $i] : (smndt0(v5) = v3 & smndt0(v1) = % 141.53/19.78 v4 & sdtasdt0(v0, v4) = v3 & sdtasdt0(v0, v1) = v5 & $i(v5) & $i(v4) & % 141.53/19.78 $i(v3))) % 141.53/19.78 % 141.53/19.78 (mMulSc) % 141.53/19.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 141.53/19.78 $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | aScalar0(v2)) % 141.53/19.78 % 141.53/19.78 (mNegSc) % 141.53/19.78 ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ~ % 141.53/19.78 aScalar0(v0) | aScalar0(v1)) % 141.53/19.78 % 141.53/19.78 (mSumSc) % 141.53/19.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 141.53/19.79 $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | aScalar0(v2)) % 141.53/19.79 % 141.53/19.79 (m__) % 141.53/19.79 $i(xS) & $i(xP) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 141.53/19.79 $i] : ? [v4: $i] : (sdtasdt0(xS, xS) = v3 & sdtasdt0(xP, xP) = v0 & % 141.53/19.79 sdtasdt0(xR, xR) = v2 & sdtpldt0(v2, v3) = v4 & sdtpldt0(v0, v0) = v1 & % 141.53/19.79 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~ sdtlseqdt0(v1, v4)) % 141.53/19.79 % 141.53/19.79 (m__1652) % 141.53/19.79 $i(xs) & ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : ! % 141.53/19.79 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2, v2) % 141.53/19.79 = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4) = v5) | ~ % 141.53/19.79 $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1) | ? [v6: $i] : ? % 141.53/19.79 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ((sdtasasdt0(v1, v2) = v8 & % 141.53/19.79 sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8) & sdtlseqdt0(v9, v5)) | % 141.53/19.79 (aDimensionOf0(v1) = v6 & $i(v6) & ( ~ iLess0(v6, v0) | ( ~ (v7 = v6) & % 141.53/19.79 aDimensionOf0(v2) = v7 & $i(v7))))))) % 141.53/19.79 % 141.53/19.79 (m__1678) % 141.53/19.79 $i(xt) & $i(xs) & aVector0(xt) & aVector0(xs) % 141.53/19.79 % 141.53/19.79 (m__1678_01) % 142.03/19.79 $i(xt) & $i(xs) & ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) = % 142.03/19.79 v0 & $i(v0)) % 142.03/19.79 % 142.03/19.79 (m__1692) % 142.03/19.79 $i(xs) & $i(sz00) & ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 & % 142.03/19.79 $i(v0)) % 142.03/19.79 % 142.03/19.79 (m__1709) % 142.03/19.80 $i(xp) & $i(xs) & ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xs) = xp & % 142.03/19.80 aDimensionOf0(xp) = v0 & aDimensionOf0(xs) = v1 & szszuzczcdt0(v0) = v1 & % 142.03/19.80 $i(v1) & $i(v0) & aVector0(xp) & ! [v2: $i] : ! [v3: $i] : ( ~ % 142.03/19.80 (sdtlbdtrb0(xp, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) | % 142.03/19.80 (sdtlbdtrb0(xs, v2) = v3 & $i(v3)))) % 142.03/19.80 % 142.03/19.80 (m__1726) % 142.03/19.80 $i(xq) & $i(xt) & ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xt) = xq & % 142.03/19.80 aDimensionOf0(xq) = v0 & aDimensionOf0(xt) = v1 & szszuzczcdt0(v0) = v1 & % 142.03/19.80 $i(v1) & $i(v0) & aVector0(xq) & ! [v2: $i] : ! [v3: $i] : ( ~ % 142.03/19.80 (sdtlbdtrb0(xt, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) | % 142.03/19.80 (sdtlbdtrb0(xq, v2) = v3 & $i(v3)))) % 142.03/19.80 % 142.03/19.80 (m__1746) % 142.03/19.80 $i(xA) & $i(xs) & ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) = % 142.03/19.80 v0 & $i(v0) & aScalar0(xA)) % 142.03/19.80 % 142.03/19.80 (m__1766) % 142.03/19.80 $i(xB) & $i(xt) & ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) = % 142.03/19.80 v0 & $i(v0) & aScalar0(xB)) % 142.03/19.80 % 142.03/19.80 (m__1892) % 142.03/19.80 sdtasdt0(xC, xG) = xR & $i(xR) & $i(xG) & $i(xC) & aScalar0(xR) % 142.03/19.80 % 142.03/19.80 (m__1911) % 142.03/19.80 sdtasdt0(xE, xH) = xP & $i(xP) & $i(xH) & $i(xE) & aScalar0(xP) % 142.03/19.80 % 142.03/19.80 (m__1930) % 142.03/19.80 sdtasdt0(xF, xD) = xS & $i(xS) & $i(xF) & $i(xD) & aScalar0(xS) % 142.03/19.80 % 142.03/19.80 (m__1949) % 142.03/19.80 sdtasdt0(xR, xS) = xN & $i(xN) & $i(xS) & $i(xR) & aScalar0(xN) % 142.03/19.80 % 142.03/19.80 (m__2004) % 142.03/19.80 $i(xN) & $i(xP) & ? [v0: $i] : (sdtasdt0(xP, xP) = v0 & $i(v0) & % 142.03/19.80 sdtlseqdt0(v0, xN)) % 142.03/19.80 % 142.03/19.80 (m__2144) % 142.03/19.80 $i(xN) & $i(xS) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 142.03/19.80 (smndt0(xN) = v1 & smndt0(xS) = v0 & sdtasdt0(v0, v0) = v2 & sdtasdt0(v0, xR) % 142.03/19.80 = v1 & sdtasdt0(xS, xS) = v2 & sdtasdt0(xR, v0) = v1 & $i(v2) & $i(v1) & % 142.03/19.80 $i(v0)) % 142.03/19.80 % 142.03/19.81 (m__2180) % 142.03/19.81 $i(xN) & $i(xS) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 142.03/19.81 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (smndt0(xN) = % 142.03/19.81 v4 & smndt0(xS) = v0 & sdtasdt0(v1, v1) = v2 & sdtasdt0(xS, xS) = v6 & % 142.03/19.81 sdtasdt0(xR, xR) = v3 & sdtpldt0(v5, v7) = v2 & sdtpldt0(v4, v6) = v7 & % 142.03/19.81 sdtpldt0(v3, v4) = v5 & sdtpldt0(xR, v0) = v1 & $i(v7) & $i(v6) & $i(v5) & % 142.03/19.81 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 142.03/19.81 % 142.03/19.81 (m__2221) % 142.03/19.81 $i(xN) & $i(xS) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 142.03/19.81 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (smndt0(xN) = % 142.03/19.81 v4 & smndt0(xS) = v0 & sdtasdt0(v1, v1) = v2 & sdtasdt0(xS, xS) = v6 & % 142.03/19.81 sdtasdt0(xR, xR) = v3 & sdtpldt0(v6, v4) = v7 & sdtpldt0(v5, v7) = v2 & % 142.03/19.81 sdtpldt0(v3, v4) = v5 & sdtpldt0(xR, v0) = v1 & $i(v7) & $i(v6) & $i(v5) & % 142.03/19.81 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 142.03/19.81 % 142.03/19.81 (m__2262) % 142.03/19.81 $i(xN) & $i(xS) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 142.03/19.81 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (smndt0(xN) = % 142.03/19.81 v6 & smndt0(xS) = v0 & sdtasdt0(v1, v1) = v2 & sdtasdt0(xS, xS) = v4 & % 142.03/19.81 sdtasdt0(xR, xR) = v3 & sdtpldt0(v7, v6) = v2 & sdtpldt0(v5, v6) = v7 & % 142.03/19.81 sdtpldt0(v3, v4) = v5 & sdtpldt0(xR, v0) = v1 & $i(v7) & $i(v6) & $i(v5) & % 142.03/19.81 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 142.03/19.81 % 142.03/19.81 (m__2303) % 142.03/19.81 $i(xN) & $i(xS) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 142.03/19.81 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (smndt0(xS) = v0 & % 142.03/19.81 sdtasdt0(v1, v1) = v2 & sdtasdt0(xS, xS) = v6 & sdtasdt0(xR, xR) = v5 & % 142.03/19.81 sdtpldt0(v5, v6) = v4 & sdtpldt0(v3, xN) = v4 & sdtpldt0(v2, xN) = v3 & % 142.03/19.81 sdtpldt0(xR, v0) = v1 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) % 142.03/19.81 & $i(v0)) % 142.03/19.81 % 142.03/19.81 (m__2318) % 142.03/19.82 $i(xS) & $i(xR) & $i(sz0z00) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 142.03/19.82 (smndt0(xS) = v0 & sdtasdt0(v1, v1) = v2 & sdtpldt0(xR, v0) = v1 & $i(v2) & % 142.03/19.82 $i(v1) & $i(v0) & sdtlseqdt0(sz0z00, v2)) % 142.03/19.82 % 142.03/19.82 (m__2348) % 142.03/19.82 $i(xN) & $i(xS) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 142.03/19.82 $i] : (sdtasdt0(xS, xS) = v2 & sdtasdt0(xR, xR) = v1 & sdtpldt0(v1, v2) = v3 % 142.03/19.82 & sdtpldt0(xN, xN) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v0, % 142.03/19.82 v3)) % 142.03/19.82 % 142.03/19.82 (function-axioms) % 142.03/19.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 142.03/19.82 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 142.03/19.82 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) % 142.03/19.82 | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 142.03/19.82 ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = % 142.03/19.82 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 142.03/19.82 ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 142.03/19.82 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sziznziztdt0(v2) = v1) | ~ % 142.03/19.82 (sziznziztdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 142.03/19.82 v0 | ~ (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) & ! [v0: % 142.03/19.82 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ % 142.03/19.82 (smndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 142.03/19.82 (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0)) % 142.03/19.82 % 142.03/19.82 Further assumptions not needed in the proof: % 142.03/19.82 -------------------------------------------- % 142.03/19.82 mDefSPN, mDefSPZ, mDimNat, mDistr2, mElmSc, mEqInit, mIH, mIHOrd, mLEASm, % 142.03/19.82 mLEMonM, mLERef, mLETot, mLess, mMDNeg, mNatExtr, mNatSort, mPosMon, mSZeroSc, % 142.03/19.82 mScPr, mScSort, mScSqPos, mScZero, mSqPos, mSqrt, mSuccEqu, mSuccNat, mVcSort, % 142.03/19.82 mZeroNat, m__1783, m__1800, m__1820, m__1837, m__1854, m__1873, m__1967 % 142.03/19.82 % 142.03/19.82 Those formulas are unsatisfiable: % 142.03/19.82 --------------------------------- % 142.03/19.82 % 142.03/19.82 Begin of proof % 142.03/19.82 | % 142.03/19.82 | ALPHA: (mDefInit) implies: % 142.03/19.83 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (sziznziztdt0(v0) = v1) | ~ $i(v0) | % 142.03/19.83 | ~ aVector0(v0) | ? [v2: $i] : (aDimensionOf0(v0) = v2 & $i(v2) & (v2 % 142.03/19.83 | = sz00 | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 142.03/19.83 | (sdtlbdtrb0(v0, v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~ % 142.03/19.83 | $i(v4) | ~ $i(v1) | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1, % 142.03/19.83 | v4) = v5 & $i(v5))) & ! [v3: $i] : ! [v4: $i] : (v3 = % 142.03/19.83 | v1 | ~ (aDimensionOf0(v3) = v4) | ~ $i(v3) | ~ % 142.03/19.83 | aVector0(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? % 142.03/19.83 | [v8: $i] : ($i(v6) & (( ~ (v8 = v7) & sdtlbdtrb0(v3, v6) = v7 % 142.03/19.83 | & sdtlbdtrb0(v0, v6) = v8 & $i(v8) & $i(v7) & % 142.03/19.83 | aNaturalNumber0(v6)) | ( ~ (v5 = v2) & szszuzczcdt0(v4) % 142.03/19.83 | = v5 & $i(v5))))) & ! [v3: $i] : ( ~ % 142.03/19.83 | (aDimensionOf0(v1) = v3) | ~ $i(v1) | szszuzczcdt0(v3) = v2) % 142.03/19.83 | & ! [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~ $i(v1) | % 142.03/19.83 | aVector0(v1)))))) % 142.03/19.83 | % 142.03/19.83 | ALPHA: (m__1678) implies: % 142.03/19.83 | (2) aVector0(xt) % 142.03/19.83 | % 142.03/19.83 | ALPHA: (m__1652) implies: % 142.03/19.83 | (3) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 142.03/19.83 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2, % 142.03/19.83 | v2) = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4) % 142.03/19.83 | = v5) | ~ $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1) % 142.03/19.83 | | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 142.03/19.83 | ((sdtasasdt0(v1, v2) = v8 & sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8) % 142.03/19.83 | & sdtlseqdt0(v9, v5)) | (aDimensionOf0(v1) = v6 & $i(v6) & ( ~ % 142.03/19.83 | iLess0(v6, v0) | ( ~ (v7 = v6) & aDimensionOf0(v2) = v7 & % 142.03/19.83 | $i(v7))))))) % 142.03/19.83 | % 142.03/19.83 | ALPHA: (m__1678_01) implies: % 142.03/19.83 | (4) ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) = v0 & % 142.03/19.83 | $i(v0)) % 142.03/19.83 | % 142.03/19.83 | ALPHA: (m__1692) implies: % 142.03/19.83 | (5) ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 & $i(v0)) % 142.03/19.83 | % 142.03/19.83 | ALPHA: (m__1709) implies: % 142.03/19.83 | (6) ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xs) = xp & aDimensionOf0(xp) % 142.03/19.83 | = v0 & aDimensionOf0(xs) = v1 & szszuzczcdt0(v0) = v1 & $i(v1) & % 142.03/19.83 | $i(v0) & aVector0(xp) & ! [v2: $i] : ! [v3: $i] : ( ~ % 142.03/19.83 | (sdtlbdtrb0(xp, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) | % 142.03/19.83 | (sdtlbdtrb0(xs, v2) = v3 & $i(v3)))) % 142.03/19.83 | % 142.03/19.83 | ALPHA: (m__1726) implies: % 142.03/19.83 | (7) ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xt) = xq & aDimensionOf0(xq) % 142.03/19.83 | = v0 & aDimensionOf0(xt) = v1 & szszuzczcdt0(v0) = v1 & $i(v1) & % 142.03/19.83 | $i(v0) & aVector0(xq) & ! [v2: $i] : ! [v3: $i] : ( ~ % 142.03/19.83 | (sdtlbdtrb0(xt, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) | % 142.03/19.83 | (sdtlbdtrb0(xq, v2) = v3 & $i(v3)))) % 142.03/19.83 | % 142.03/19.83 | ALPHA: (m__1746) implies: % 142.03/19.83 | (8) ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) = v0 & % 142.03/19.83 | $i(v0) & aScalar0(xA)) % 142.03/19.83 | % 142.03/19.83 | ALPHA: (m__1766) implies: % 142.03/19.83 | (9) $i(xt) % 142.03/19.83 | (10) ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) = v0 & % 142.03/19.83 | $i(v0) & aScalar0(xB)) % 142.03/19.83 | % 142.03/19.83 | ALPHA: (m__1892) implies: % 142.03/19.83 | (11) aScalar0(xR) % 142.03/19.83 | % 142.03/19.83 | ALPHA: (m__1911) implies: % 142.03/19.83 | (12) aScalar0(xP) % 142.03/19.83 | % 142.03/19.83 | ALPHA: (m__1930) implies: % 142.03/19.83 | (13) aScalar0(xS) % 142.03/19.83 | % 142.03/19.83 | ALPHA: (m__1949) implies: % 142.03/19.83 | (14) aScalar0(xN) % 142.03/19.83 | (15) sdtasdt0(xR, xS) = xN % 142.03/19.83 | % 142.03/19.83 | ALPHA: (m__2004) implies: % 142.03/19.84 | (16) ? [v0: $i] : (sdtasdt0(xP, xP) = v0 & $i(v0) & sdtlseqdt0(v0, xN)) % 142.03/19.84 | % 142.03/19.84 | ALPHA: (m__2144) implies: % 142.03/19.84 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (smndt0(xN) = v1 & % 142.03/19.84 | smndt0(xS) = v0 & sdtasdt0(v0, v0) = v2 & sdtasdt0(v0, xR) = v1 & % 142.03/19.84 | sdtasdt0(xS, xS) = v2 & sdtasdt0(xR, v0) = v1 & $i(v2) & $i(v1) & % 142.03/19.84 | $i(v0)) % 142.03/19.84 | % 142.03/19.84 | ALPHA: (m__2180) implies: % 142.03/19.84 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 142.03/19.84 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (smndt0(xN) = v4 & smndt0(xS) % 142.03/19.84 | = v0 & sdtasdt0(v1, v1) = v2 & sdtasdt0(xS, xS) = v6 & sdtasdt0(xR, % 142.03/19.84 | xR) = v3 & sdtpldt0(v5, v7) = v2 & sdtpldt0(v4, v6) = v7 & % 142.03/19.84 | sdtpldt0(v3, v4) = v5 & sdtpldt0(xR, v0) = v1 & $i(v7) & $i(v6) & % 142.03/19.84 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 142.03/19.84 | % 142.03/19.84 | ALPHA: (m__2221) implies: % 142.03/19.84 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 142.03/19.84 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (smndt0(xN) = v4 & smndt0(xS) % 142.03/19.84 | = v0 & sdtasdt0(v1, v1) = v2 & sdtasdt0(xS, xS) = v6 & sdtasdt0(xR, % 142.03/19.84 | xR) = v3 & sdtpldt0(v6, v4) = v7 & sdtpldt0(v5, v7) = v2 & % 142.03/19.84 | sdtpldt0(v3, v4) = v5 & sdtpldt0(xR, v0) = v1 & $i(v7) & $i(v6) & % 142.03/19.84 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 142.03/19.84 | % 142.03/19.84 | ALPHA: (m__2262) implies: % 142.03/19.84 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 142.03/19.84 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (smndt0(xN) = v6 & smndt0(xS) % 142.03/19.84 | = v0 & sdtasdt0(v1, v1) = v2 & sdtasdt0(xS, xS) = v4 & sdtasdt0(xR, % 142.03/19.84 | xR) = v3 & sdtpldt0(v7, v6) = v2 & sdtpldt0(v5, v6) = v7 & % 142.03/19.84 | sdtpldt0(v3, v4) = v5 & sdtpldt0(xR, v0) = v1 & $i(v7) & $i(v6) & % 142.03/19.84 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 142.03/19.84 | % 142.03/19.84 | ALPHA: (m__2303) implies: % 142.03/19.84 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 142.03/19.84 | ? [v5: $i] : ? [v6: $i] : (smndt0(xS) = v0 & sdtasdt0(v1, v1) = v2 & % 142.03/19.84 | sdtasdt0(xS, xS) = v6 & sdtasdt0(xR, xR) = v5 & sdtpldt0(v5, v6) = % 142.03/19.84 | v4 & sdtpldt0(v3, xN) = v4 & sdtpldt0(v2, xN) = v3 & sdtpldt0(xR, % 142.03/19.84 | v0) = v1 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 142.03/19.84 | $i(v0)) % 142.03/19.84 | % 142.03/19.84 | ALPHA: (m__2318) implies: % 142.03/19.84 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (smndt0(xS) = v0 & % 142.03/19.84 | sdtasdt0(v1, v1) = v2 & sdtpldt0(xR, v0) = v1 & $i(v2) & $i(v1) & % 142.03/19.84 | $i(v0) & sdtlseqdt0(sz0z00, v2)) % 142.03/19.84 | % 142.03/19.84 | ALPHA: (m__2348) implies: % 142.03/19.84 | (23) $i(xN) % 142.03/19.84 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(xS, % 142.03/19.84 | xS) = v2 & sdtasdt0(xR, xR) = v1 & sdtpldt0(v1, v2) = v3 & % 142.03/19.84 | sdtpldt0(xN, xN) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 142.03/19.84 | sdtlseqdt0(v0, v3)) % 142.03/19.84 | % 142.03/19.84 | ALPHA: (m__) implies: % 142.03/19.84 | (25) $i(xR) % 142.03/19.84 | (26) $i(xP) % 142.03/19.85 | (27) $i(xS) % 142.03/19.85 | (28) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 142.03/19.85 | (sdtasdt0(xS, xS) = v3 & sdtasdt0(xP, xP) = v0 & sdtasdt0(xR, xR) = v2 % 142.03/19.85 | & sdtpldt0(v2, v3) = v4 & sdtpldt0(v0, v0) = v1 & $i(v4) & $i(v3) & % 142.03/19.85 | $i(v2) & $i(v1) & $i(v0) & ~ sdtlseqdt0(v1, v4)) % 142.03/19.85 | % 142.03/19.85 | ALPHA: (function-axioms) implies: % 142.03/19.85 | (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = % 142.03/19.85 | v1) | ~ (smndt0(v2) = v0)) % 142.03/19.85 | (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 142.03/19.85 | (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) % 142.03/19.85 | (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 142.03/19.85 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 142.03/19.85 | (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 142.03/19.85 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 142.03/19.85 | % 142.03/19.85 | DELTA: instantiating (4) with fresh symbol all_33_0 gives: % 142.03/19.85 | (33) aDimensionOf0(xt) = all_33_0 & aDimensionOf0(xs) = all_33_0 & % 142.03/19.85 | $i(all_33_0) % 142.03/19.85 | % 142.03/19.85 | ALPHA: (33) implies: % 142.03/19.85 | (34) aDimensionOf0(xs) = all_33_0 % 142.03/19.85 | (35) aDimensionOf0(xt) = all_33_0 % 142.03/19.85 | % 142.03/19.85 | DELTA: instantiating (16) with fresh symbol all_35_0 gives: % 142.03/19.85 | (36) sdtasdt0(xP, xP) = all_35_0 & $i(all_35_0) & sdtlseqdt0(all_35_0, xN) % 142.03/19.85 | % 142.03/19.85 | ALPHA: (36) implies: % 142.03/19.85 | (37) sdtlseqdt0(all_35_0, xN) % 142.03/19.85 | (38) sdtasdt0(xP, xP) = all_35_0 % 142.03/19.85 | % 142.03/19.85 | DELTA: instantiating (5) with fresh symbol all_37_0 gives: % 142.03/19.85 | (39) ~ (all_37_0 = sz00) & aDimensionOf0(xs) = all_37_0 & $i(all_37_0) % 142.03/19.85 | % 142.03/19.85 | ALPHA: (39) implies: % 142.03/19.85 | (40) ~ (all_37_0 = sz00) % 142.03/19.85 | (41) aDimensionOf0(xs) = all_37_0 % 142.03/19.85 | % 142.03/19.85 | DELTA: instantiating (10) with fresh symbol all_39_0 gives: % 142.03/19.85 | (42) sdtlbdtrb0(xt, all_39_0) = xB & aDimensionOf0(xt) = all_39_0 & % 142.03/19.85 | $i(all_39_0) & aScalar0(xB) % 142.03/19.85 | % 142.03/19.85 | ALPHA: (42) implies: % 142.03/19.85 | (43) aDimensionOf0(xt) = all_39_0 % 142.03/19.85 | % 142.03/19.85 | DELTA: instantiating (8) with fresh symbol all_41_0 gives: % 142.03/19.85 | (44) sdtlbdtrb0(xs, all_41_0) = xA & aDimensionOf0(xs) = all_41_0 & % 142.03/19.85 | $i(all_41_0) & aScalar0(xA) % 142.03/19.85 | % 142.03/19.85 | ALPHA: (44) implies: % 142.03/19.85 | (45) aDimensionOf0(xs) = all_41_0 % 142.03/19.85 | % 142.03/19.85 | DELTA: instantiating (22) with fresh symbols all_45_0, all_45_1, all_45_2 % 142.03/19.85 | gives: % 142.03/19.85 | (46) smndt0(xS) = all_45_2 & sdtasdt0(all_45_1, all_45_1) = all_45_0 & % 142.03/19.85 | sdtpldt0(xR, all_45_2) = all_45_1 & $i(all_45_0) & $i(all_45_1) & % 142.03/19.85 | $i(all_45_2) & sdtlseqdt0(sz0z00, all_45_0) % 142.03/19.85 | % 142.03/19.85 | ALPHA: (46) implies: % 142.03/19.85 | (47) smndt0(xS) = all_45_2 % 142.03/19.85 | % 142.03/19.85 | DELTA: instantiating (24) with fresh symbols all_47_0, all_47_1, all_47_2, % 142.03/19.85 | all_47_3 gives: % 142.03/19.85 | (48) sdtasdt0(xS, xS) = all_47_1 & sdtasdt0(xR, xR) = all_47_2 & % 142.03/19.85 | sdtpldt0(all_47_2, all_47_1) = all_47_0 & sdtpldt0(xN, xN) = all_47_3 % 142.03/19.85 | & $i(all_47_0) & $i(all_47_1) & $i(all_47_2) & $i(all_47_3) & % 142.03/19.85 | sdtlseqdt0(all_47_3, all_47_0) % 142.03/19.85 | % 142.03/19.85 | ALPHA: (48) implies: % 142.03/19.85 | (49) sdtlseqdt0(all_47_3, all_47_0) % 142.03/19.85 | (50) sdtpldt0(xN, xN) = all_47_3 % 142.03/19.85 | (51) sdtpldt0(all_47_2, all_47_1) = all_47_0 % 142.03/19.85 | (52) sdtasdt0(xR, xR) = all_47_2 % 142.03/19.85 | (53) sdtasdt0(xS, xS) = all_47_1 % 142.03/19.85 | % 142.03/19.85 | DELTA: instantiating (17) with fresh symbols all_49_0, all_49_1, all_49_2 % 142.03/19.85 | gives: % 142.03/19.86 | (54) smndt0(xN) = all_49_1 & smndt0(xS) = all_49_2 & sdtasdt0(all_49_2, % 142.03/19.86 | all_49_2) = all_49_0 & sdtasdt0(all_49_2, xR) = all_49_1 & % 142.03/19.86 | sdtasdt0(xS, xS) = all_49_0 & sdtasdt0(xR, all_49_2) = all_49_1 & % 142.03/19.86 | $i(all_49_0) & $i(all_49_1) & $i(all_49_2) % 142.03/19.86 | % 142.03/19.86 | ALPHA: (54) implies: % 142.03/19.86 | (55) sdtasdt0(xS, xS) = all_49_0 % 142.03/19.86 | (56) sdtasdt0(all_49_2, xR) = all_49_1 % 142.03/19.86 | (57) smndt0(xS) = all_49_2 % 142.03/19.86 | (58) smndt0(xN) = all_49_1 % 142.03/19.86 | % 142.03/19.86 | DELTA: instantiating (28) with fresh symbols all_51_0, all_51_1, all_51_2, % 142.03/19.86 | all_51_3, all_51_4 gives: % 142.03/19.86 | (59) sdtasdt0(xS, xS) = all_51_1 & sdtasdt0(xP, xP) = all_51_4 & % 142.03/19.86 | sdtasdt0(xR, xR) = all_51_2 & sdtpldt0(all_51_2, all_51_1) = all_51_0 % 142.03/19.86 | & sdtpldt0(all_51_4, all_51_4) = all_51_3 & $i(all_51_0) & % 142.03/19.86 | $i(all_51_1) & $i(all_51_2) & $i(all_51_3) & $i(all_51_4) & ~ % 142.03/19.86 | sdtlseqdt0(all_51_3, all_51_0) % 142.03/19.86 | % 142.03/19.86 | ALPHA: (59) implies: % 142.03/19.86 | (60) ~ sdtlseqdt0(all_51_3, all_51_0) % 142.03/19.86 | (61) $i(all_51_2) % 142.03/19.86 | (62) sdtpldt0(all_51_4, all_51_4) = all_51_3 % 142.03/19.86 | (63) sdtpldt0(all_51_2, all_51_1) = all_51_0 % 142.03/19.86 | (64) sdtasdt0(xR, xR) = all_51_2 % 142.03/19.86 | (65) sdtasdt0(xP, xP) = all_51_4 % 142.03/19.86 | (66) sdtasdt0(xS, xS) = all_51_1 % 142.03/19.86 | % 142.03/19.86 | DELTA: instantiating (7) with fresh symbols all_53_0, all_53_1 gives: % 142.03/19.86 | (67) sziznziztdt0(xt) = xq & aDimensionOf0(xq) = all_53_1 & % 142.03/19.86 | aDimensionOf0(xt) = all_53_0 & szszuzczcdt0(all_53_1) = all_53_0 & % 142.03/19.86 | $i(all_53_0) & $i(all_53_1) & aVector0(xq) & ! [v0: $i] : ! [v1: $i] % 142.03/19.86 | : ( ~ (sdtlbdtrb0(xt, v0) = v1) | ~ $i(v0) | ~ aNaturalNumber0(v0) | % 142.03/19.86 | (sdtlbdtrb0(xq, v0) = v1 & $i(v1))) % 142.03/19.86 | % 142.03/19.86 | ALPHA: (67) implies: % 142.03/19.86 | (68) aDimensionOf0(xt) = all_53_0 % 142.03/19.86 | (69) sziznziztdt0(xt) = xq % 142.03/19.86 | % 142.03/19.86 | DELTA: instantiating (6) with fresh symbols all_56_0, all_56_1 gives: % 142.03/19.86 | (70) sziznziztdt0(xs) = xp & aDimensionOf0(xp) = all_56_1 & % 142.03/19.86 | aDimensionOf0(xs) = all_56_0 & szszuzczcdt0(all_56_1) = all_56_0 & % 142.03/19.86 | $i(all_56_0) & $i(all_56_1) & aVector0(xp) & ! [v0: $i] : ! [v1: $i] % 142.03/19.86 | : ( ~ (sdtlbdtrb0(xp, v0) = v1) | ~ $i(v0) | ~ aNaturalNumber0(v0) | % 142.03/19.86 | (sdtlbdtrb0(xs, v0) = v1 & $i(v1))) % 142.03/19.86 | % 142.03/19.86 | ALPHA: (70) implies: % 142.03/19.86 | (71) aDimensionOf0(xs) = all_56_0 % 142.03/19.86 | % 142.03/19.86 | DELTA: instantiating (21) with fresh symbols all_59_0, all_59_1, all_59_2, % 142.03/19.86 | all_59_3, all_59_4, all_59_5, all_59_6 gives: % 142.03/19.86 | (72) smndt0(xS) = all_59_6 & sdtasdt0(all_59_5, all_59_5) = all_59_4 & % 142.03/19.86 | sdtasdt0(xS, xS) = all_59_0 & sdtasdt0(xR, xR) = all_59_1 & % 142.03/19.86 | sdtpldt0(all_59_1, all_59_0) = all_59_2 & sdtpldt0(all_59_3, xN) = % 142.03/19.86 | all_59_2 & sdtpldt0(all_59_4, xN) = all_59_3 & sdtpldt0(xR, all_59_6) % 142.03/19.86 | = all_59_5 & $i(all_59_0) & $i(all_59_1) & $i(all_59_2) & $i(all_59_3) % 142.03/19.86 | & $i(all_59_4) & $i(all_59_5) & $i(all_59_6) % 142.03/19.86 | % 142.03/19.86 | ALPHA: (72) implies: % 142.03/19.86 | (73) sdtpldt0(all_59_1, all_59_0) = all_59_2 % 142.03/19.86 | (74) sdtasdt0(xR, xR) = all_59_1 % 142.03/19.86 | (75) sdtasdt0(xS, xS) = all_59_0 % 142.03/19.86 | (76) smndt0(xS) = all_59_6 % 142.03/19.86 | % 142.03/19.86 | DELTA: instantiating (18) with fresh symbols all_61_0, all_61_1, all_61_2, % 142.03/19.86 | all_61_3, all_61_4, all_61_5, all_61_6, all_61_7 gives: % 142.03/19.86 | (77) smndt0(xN) = all_61_3 & smndt0(xS) = all_61_7 & sdtasdt0(all_61_6, % 142.03/19.86 | all_61_6) = all_61_5 & sdtasdt0(xS, xS) = all_61_1 & sdtasdt0(xR, % 142.03/19.86 | xR) = all_61_4 & sdtpldt0(all_61_2, all_61_0) = all_61_5 & % 142.03/19.86 | sdtpldt0(all_61_3, all_61_1) = all_61_0 & sdtpldt0(all_61_4, all_61_3) % 142.03/19.86 | = all_61_2 & sdtpldt0(xR, all_61_7) = all_61_6 & $i(all_61_0) & % 142.03/19.86 | $i(all_61_1) & $i(all_61_2) & $i(all_61_3) & $i(all_61_4) & % 142.03/19.86 | $i(all_61_5) & $i(all_61_6) & $i(all_61_7) % 142.03/19.86 | % 142.03/19.86 | ALPHA: (77) implies: % 142.03/19.87 | (78) sdtasdt0(xR, xR) = all_61_4 % 142.03/19.87 | (79) sdtasdt0(xS, xS) = all_61_1 % 142.03/19.87 | (80) smndt0(xS) = all_61_7 % 142.03/19.87 | (81) smndt0(xN) = all_61_3 % 142.03/19.87 | % 142.03/19.87 | DELTA: instantiating (19) with fresh symbols all_63_0, all_63_1, all_63_2, % 142.03/19.87 | all_63_3, all_63_4, all_63_5, all_63_6, all_63_7 gives: % 142.03/19.87 | (82) smndt0(xN) = all_63_3 & smndt0(xS) = all_63_7 & sdtasdt0(all_63_6, % 142.03/19.87 | all_63_6) = all_63_5 & sdtasdt0(xS, xS) = all_63_1 & sdtasdt0(xR, % 142.03/19.87 | xR) = all_63_4 & sdtpldt0(all_63_1, all_63_3) = all_63_0 & % 142.03/19.87 | sdtpldt0(all_63_2, all_63_0) = all_63_5 & sdtpldt0(all_63_4, all_63_3) % 142.03/19.87 | = all_63_2 & sdtpldt0(xR, all_63_7) = all_63_6 & $i(all_63_0) & % 142.03/19.87 | $i(all_63_1) & $i(all_63_2) & $i(all_63_3) & $i(all_63_4) & % 142.03/19.87 | $i(all_63_5) & $i(all_63_6) & $i(all_63_7) % 142.03/19.87 | % 142.03/19.87 | ALPHA: (82) implies: % 142.03/19.87 | (83) sdtasdt0(xR, xR) = all_63_4 % 142.03/19.87 | (84) sdtasdt0(xS, xS) = all_63_1 % 142.03/19.87 | (85) smndt0(xS) = all_63_7 % 142.03/19.87 | (86) smndt0(xN) = all_63_3 % 142.03/19.87 | % 142.03/19.87 | DELTA: instantiating (20) with fresh symbols all_65_0, all_65_1, all_65_2, % 142.03/19.87 | all_65_3, all_65_4, all_65_5, all_65_6, all_65_7 gives: % 142.03/19.87 | (87) smndt0(xN) = all_65_1 & smndt0(xS) = all_65_7 & sdtasdt0(all_65_6, % 142.03/19.87 | all_65_6) = all_65_5 & sdtasdt0(xS, xS) = all_65_3 & sdtasdt0(xR, % 142.03/19.87 | xR) = all_65_4 & sdtpldt0(all_65_0, all_65_1) = all_65_5 & % 142.03/19.87 | sdtpldt0(all_65_2, all_65_1) = all_65_0 & sdtpldt0(all_65_4, all_65_3) % 142.03/19.87 | = all_65_2 & sdtpldt0(xR, all_65_7) = all_65_6 & $i(all_65_0) & % 142.03/19.87 | $i(all_65_1) & $i(all_65_2) & $i(all_65_3) & $i(all_65_4) & % 142.03/19.87 | $i(all_65_5) & $i(all_65_6) & $i(all_65_7) % 142.03/19.87 | % 142.03/19.87 | ALPHA: (87) implies: % 142.03/19.87 | (88) sdtpldt0(all_65_4, all_65_3) = all_65_2 % 142.03/19.87 | (89) sdtpldt0(all_65_2, all_65_1) = all_65_0 % 142.03/19.87 | (90) sdtasdt0(xR, xR) = all_65_4 % 142.03/19.87 | (91) sdtasdt0(xS, xS) = all_65_3 % 142.03/19.87 | (92) smndt0(xS) = all_65_7 % 142.03/19.87 | (93) smndt0(xN) = all_65_1 % 142.03/19.87 | % 142.03/19.87 | DELTA: instantiating (3) with fresh symbol all_67_0 gives: % 142.03/19.87 | (94) aDimensionOf0(xs) = all_67_0 & $i(all_67_0) & ! [v0: $i] : ! [v1: % 142.03/19.87 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasasdt0(v1, % 142.03/19.87 | v1) = v3) | ~ (sdtasasdt0(v0, v0) = v2) | ~ (sdtasdt0(v2, v3) % 142.03/19.87 | = v4) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) % 142.03/19.87 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 142.03/19.87 | ((sdtasasdt0(v0, v1) = v7 & sdtasdt0(v7, v7) = v8 & $i(v8) & $i(v7) % 142.03/19.87 | & sdtlseqdt0(v8, v4)) | (aDimensionOf0(v0) = v5 & $i(v5) & ( ~ % 142.03/19.87 | iLess0(v5, all_67_0) | ( ~ (v6 = v5) & aDimensionOf0(v1) = v6 % 142.03/19.87 | & $i(v6)))))) % 142.03/19.87 | % 142.03/19.87 | ALPHA: (94) implies: % 142.03/19.87 | (95) aDimensionOf0(xs) = all_67_0 % 142.03/19.87 | % 142.03/19.87 | GROUND_INST: instantiating (32) with all_51_2, all_59_1, xR, xR, simplifying % 142.03/19.87 | with (64), (74) gives: % 142.03/19.87 | (96) all_59_1 = all_51_2 % 142.03/19.87 | % 142.03/19.87 | GROUND_INST: instantiating (32) with all_47_2, all_63_4, xR, xR, simplifying % 142.03/19.87 | with (52), (83) gives: % 142.03/19.87 | (97) all_63_4 = all_47_2 % 142.03/19.87 | % 142.03/19.87 | GROUND_INST: instantiating (32) with all_63_4, all_65_4, xR, xR, simplifying % 142.03/19.87 | with (83), (90) gives: % 142.03/19.87 | (98) all_65_4 = all_63_4 % 142.03/19.87 | % 142.03/19.87 | GROUND_INST: instantiating (32) with all_61_4, all_65_4, xR, xR, simplifying % 142.03/19.87 | with (78), (90) gives: % 142.03/19.87 | (99) all_65_4 = all_61_4 % 142.03/19.88 | % 142.03/19.88 | GROUND_INST: instantiating (32) with all_59_1, all_65_4, xR, xR, simplifying % 142.03/19.88 | with (74), (90) gives: % 142.03/19.88 | (100) all_65_4 = all_59_1 % 142.03/19.88 | % 142.03/19.88 | GROUND_INST: instantiating (32) with all_35_0, all_51_4, xP, xP, simplifying % 142.03/19.88 | with (38), (65) gives: % 142.03/19.88 | (101) all_51_4 = all_35_0 % 142.03/19.88 | % 142.03/19.88 | GROUND_INST: instantiating (32) with all_47_1, all_59_0, xS, xS, simplifying % 142.03/19.88 | with (53), (75) gives: % 142.03/19.88 | (102) all_59_0 = all_47_1 % 142.03/19.88 | % 142.03/19.88 | GROUND_INST: instantiating (32) with all_59_0, all_61_1, xS, xS, simplifying % 142.03/19.88 | with (75), (79) gives: % 142.03/19.88 | (103) all_61_1 = all_59_0 % 142.03/19.88 | % 142.03/19.88 | GROUND_INST: instantiating (32) with all_61_1, all_63_1, xS, xS, simplifying % 142.03/19.88 | with (79), (84) gives: % 142.03/19.88 | (104) all_63_1 = all_61_1 % 142.03/19.88 | % 142.03/19.88 | GROUND_INST: instantiating (32) with all_51_1, all_63_1, xS, xS, simplifying % 142.03/19.88 | with (66), (84) gives: % 142.03/19.88 | (105) all_63_1 = all_51_1 % 142.03/19.88 | % 142.03/19.88 | GROUND_INST: instantiating (32) with all_59_0, all_65_3, xS, xS, simplifying % 142.03/19.88 | with (75), (91) gives: % 142.03/19.88 | (106) all_65_3 = all_59_0 % 142.03/19.88 | % 142.03/19.88 | GROUND_INST: instantiating (32) with all_49_0, all_65_3, xS, xS, simplifying % 142.03/19.88 | with (55), (91) gives: % 142.03/19.88 | (107) all_65_3 = all_49_0 % 142.03/19.88 | % 142.03/19.88 | GROUND_INST: instantiating (29) with all_45_2, all_59_6, xS, simplifying with % 142.03/19.88 | (47), (76) gives: % 142.03/19.88 | (108) all_59_6 = all_45_2 % 142.03/19.88 | % 142.03/19.88 | GROUND_INST: instantiating (29) with all_59_6, all_63_7, xS, simplifying with % 142.03/19.88 | (76), (85) gives: % 142.03/19.88 | (109) all_63_7 = all_59_6 % 142.03/19.88 | % 142.03/19.88 | GROUND_INST: instantiating (29) with all_49_2, all_63_7, xS, simplifying with % 142.03/19.88 | (57), (85) gives: % 142.03/19.88 | (110) all_63_7 = all_49_2 % 142.03/19.88 | % 142.03/19.88 | GROUND_INST: instantiating (29) with all_63_7, all_65_7, xS, simplifying with % 142.03/19.88 | (85), (92) gives: % 142.03/19.88 | (111) all_65_7 = all_63_7 % 142.03/19.88 | % 142.03/19.88 | GROUND_INST: instantiating (29) with all_61_7, all_65_7, xS, simplifying with % 142.03/19.88 | (80), (92) gives: % 142.03/19.88 | (112) all_65_7 = all_61_7 % 142.03/19.88 | % 142.03/19.88 | GROUND_INST: instantiating (29) with all_49_1, all_63_3, xN, simplifying with % 142.03/19.88 | (58), (86) gives: % 142.03/19.88 | (113) all_63_3 = all_49_1 % 142.03/19.88 | % 142.03/19.88 | GROUND_INST: instantiating (29) with all_63_3, all_65_1, xN, simplifying with % 142.03/19.88 | (86), (93) gives: % 142.03/19.88 | (114) all_65_1 = all_63_3 % 142.03/19.88 | % 142.03/19.88 | GROUND_INST: instantiating (29) with all_61_3, all_65_1, xN, simplifying with % 142.03/19.88 | (81), (93) gives: % 142.03/19.88 | (115) all_65_1 = all_61_3 % 142.03/19.88 | % 142.03/19.88 | GROUND_INST: instantiating (30) with all_37_0, all_41_0, xs, simplifying with % 142.03/19.88 | (41), (45) gives: % 142.03/19.88 | (116) all_41_0 = all_37_0 % 142.03/19.88 | % 142.60/19.88 | GROUND_INST: instantiating (30) with all_41_0, all_56_0, xs, simplifying with % 142.60/19.88 | (45), (71) gives: % 142.60/19.88 | (117) all_56_0 = all_41_0 % 142.60/19.88 | % 142.60/19.88 | GROUND_INST: instantiating (30) with all_56_0, all_67_0, xs, simplifying with % 142.60/19.88 | (71), (95) gives: % 142.60/19.88 | (118) all_67_0 = all_56_0 % 142.60/19.88 | % 142.60/19.88 | GROUND_INST: instantiating (30) with all_33_0, all_67_0, xs, simplifying with % 142.60/19.88 | (34), (95) gives: % 142.60/19.88 | (119) all_67_0 = all_33_0 % 142.60/19.88 | % 142.60/19.88 | GROUND_INST: instantiating (30) with all_39_0, all_53_0, xt, simplifying with % 142.60/19.88 | (43), (68) gives: % 142.60/19.88 | (120) all_53_0 = all_39_0 % 142.60/19.88 | % 142.60/19.88 | GROUND_INST: instantiating (30) with all_33_0, all_53_0, xt, simplifying with % 142.60/19.88 | (35), (68) gives: % 142.60/19.88 | (121) all_53_0 = all_33_0 % 142.60/19.88 | % 142.60/19.88 | COMBINE_EQS: (118), (119) imply: % 142.60/19.88 | (122) all_56_0 = all_33_0 % 142.60/19.88 | % 142.60/19.88 | SIMP: (122) implies: % 142.60/19.88 | (123) all_56_0 = all_33_0 % 142.60/19.88 | % 142.60/19.88 | COMBINE_EQS: (114), (115) imply: % 142.60/19.88 | (124) all_63_3 = all_61_3 % 142.60/19.88 | % 142.60/19.88 | SIMP: (124) implies: % 142.60/19.88 | (125) all_63_3 = all_61_3 % 142.60/19.88 | % 142.60/19.88 | COMBINE_EQS: (106), (107) imply: % 142.60/19.88 | (126) all_59_0 = all_49_0 % 142.60/19.88 | % 142.60/19.88 | SIMP: (126) implies: % 142.60/19.88 | (127) all_59_0 = all_49_0 % 142.60/19.88 | % 142.60/19.88 | COMBINE_EQS: (98), (99) imply: % 142.60/19.89 | (128) all_63_4 = all_61_4 % 142.60/19.89 | % 142.60/19.89 | SIMP: (128) implies: % 142.60/19.89 | (129) all_63_4 = all_61_4 % 142.60/19.89 | % 142.60/19.89 | COMBINE_EQS: (99), (100) imply: % 142.60/19.89 | (130) all_61_4 = all_59_1 % 142.60/19.89 | % 142.60/19.89 | COMBINE_EQS: (111), (112) imply: % 142.60/19.89 | (131) all_63_7 = all_61_7 % 142.60/19.89 | % 142.60/19.89 | SIMP: (131) implies: % 142.60/19.89 | (132) all_63_7 = all_61_7 % 142.60/19.89 | % 142.60/19.89 | COMBINE_EQS: (104), (105) imply: % 142.60/19.89 | (133) all_61_1 = all_51_1 % 142.60/19.89 | % 142.60/19.89 | SIMP: (133) implies: % 142.60/19.89 | (134) all_61_1 = all_51_1 % 142.60/19.89 | % 142.60/19.89 | COMBINE_EQS: (113), (125) imply: % 142.60/19.89 | (135) all_61_3 = all_49_1 % 142.60/19.89 | % 142.60/19.89 | COMBINE_EQS: (97), (129) imply: % 142.60/19.89 | (136) all_61_4 = all_47_2 % 142.60/19.89 | % 142.60/19.89 | SIMP: (136) implies: % 142.60/19.89 | (137) all_61_4 = all_47_2 % 142.60/19.89 | % 142.60/19.89 | COMBINE_EQS: (110), (132) imply: % 142.60/19.89 | (138) all_61_7 = all_49_2 % 142.60/19.89 | % 142.60/19.89 | COMBINE_EQS: (109), (132) imply: % 142.60/19.89 | (139) all_61_7 = all_59_6 % 142.60/19.89 | % 142.60/19.89 | COMBINE_EQS: (103), (134) imply: % 142.60/19.89 | (140) all_59_0 = all_51_1 % 142.60/19.89 | % 142.60/19.89 | SIMP: (140) implies: % 142.60/19.89 | (141) all_59_0 = all_51_1 % 142.60/19.89 | % 142.60/19.89 | COMBINE_EQS: (130), (137) imply: % 142.60/19.89 | (142) all_59_1 = all_47_2 % 142.60/19.89 | % 142.60/19.89 | SIMP: (142) implies: % 142.60/19.89 | (143) all_59_1 = all_47_2 % 142.60/19.89 | % 142.60/19.89 | COMBINE_EQS: (138), (139) imply: % 142.60/19.89 | (144) all_59_6 = all_49_2 % 142.60/19.89 | % 142.60/19.89 | SIMP: (144) implies: % 142.60/19.89 | (145) all_59_6 = all_49_2 % 142.60/19.89 | % 142.60/19.89 | COMBINE_EQS: (102), (141) imply: % 142.60/19.89 | (146) all_51_1 = all_47_1 % 142.60/19.89 | % 142.60/19.89 | COMBINE_EQS: (127), (141) imply: % 142.60/19.89 | (147) all_51_1 = all_49_0 % 142.60/19.89 | % 142.60/19.89 | COMBINE_EQS: (96), (143) imply: % 142.60/19.89 | (148) all_51_2 = all_47_2 % 142.60/19.89 | % 142.60/19.89 | SIMP: (148) implies: % 142.60/19.89 | (149) all_51_2 = all_47_2 % 142.60/19.89 | % 142.60/19.89 | COMBINE_EQS: (108), (145) imply: % 142.60/19.89 | (150) all_49_2 = all_45_2 % 142.60/19.89 | % 142.60/19.89 | SIMP: (150) implies: % 142.60/19.89 | (151) all_49_2 = all_45_2 % 142.60/19.89 | % 142.60/19.89 | COMBINE_EQS: (117), (123) imply: % 142.60/19.89 | (152) all_41_0 = all_33_0 % 142.60/19.89 | % 142.60/19.89 | SIMP: (152) implies: % 142.60/19.89 | (153) all_41_0 = all_33_0 % 142.60/19.89 | % 142.60/19.89 | COMBINE_EQS: (120), (121) imply: % 142.60/19.89 | (154) all_39_0 = all_33_0 % 142.60/19.89 | % 142.60/19.89 | COMBINE_EQS: (146), (147) imply: % 142.60/19.89 | (155) all_49_0 = all_47_1 % 142.60/19.89 | % 142.60/19.89 | COMBINE_EQS: (116), (153) imply: % 142.60/19.89 | (156) all_37_0 = all_33_0 % 142.60/19.89 | % 142.60/19.89 | SIMP: (156) implies: % 142.60/19.89 | (157) all_37_0 = all_33_0 % 142.60/19.89 | % 142.60/19.89 | COMBINE_EQS: (99), (137) imply: % 142.60/19.89 | (158) all_65_4 = all_47_2 % 142.60/19.89 | % 142.60/19.89 | COMBINE_EQS: (107), (155) imply: % 142.60/19.89 | (159) all_65_3 = all_47_1 % 142.60/19.89 | % 142.60/19.89 | COMBINE_EQS: (115), (135) imply: % 142.60/19.89 | (160) all_65_1 = all_49_1 % 142.60/19.89 | % 142.60/19.89 | REDUCE: (40), (157) imply: % 142.60/19.89 | (161) ~ (all_33_0 = sz00) % 142.60/19.89 | % 142.60/19.89 | REDUCE: (56), (151) imply: % 142.60/19.89 | (162) sdtasdt0(all_45_2, xR) = all_49_1 % 142.60/19.89 | % 142.60/19.89 | REDUCE: (89), (160) imply: % 142.60/19.89 | (163) sdtpldt0(all_65_2, all_49_1) = all_65_0 % 142.60/19.89 | % 142.60/19.89 | REDUCE: (88), (158), (159) imply: % 142.60/19.89 | (164) sdtpldt0(all_47_2, all_47_1) = all_65_2 % 142.60/19.89 | % 142.60/19.89 | REDUCE: (73), (102), (143) imply: % 142.60/19.89 | (165) sdtpldt0(all_47_2, all_47_1) = all_59_2 % 142.60/19.89 | % 142.60/19.89 | REDUCE: (63), (146), (149) imply: % 142.60/19.89 | (166) sdtpldt0(all_47_2, all_47_1) = all_51_0 % 142.60/19.89 | % 142.60/19.89 | REDUCE: (62), (101) imply: % 142.60/19.89 | (167) sdtpldt0(all_35_0, all_35_0) = all_51_3 % 142.60/19.89 | % 142.60/19.89 | REDUCE: (61), (149) imply: % 142.60/19.89 | (168) $i(all_47_2) % 142.60/19.89 | % 142.60/19.89 | GROUND_INST: instantiating (31) with all_47_0, all_59_2, all_47_1, all_47_2, % 142.60/19.89 | simplifying with (51), (165) gives: % 142.60/19.89 | (169) all_59_2 = all_47_0 % 142.60/19.89 | % 142.60/19.89 | GROUND_INST: instantiating (31) with all_59_2, all_65_2, all_47_1, all_47_2, % 142.60/19.89 | simplifying with (164), (165) gives: % 142.60/19.89 | (170) all_65_2 = all_59_2 % 142.60/19.89 | % 142.60/19.89 | GROUND_INST: instantiating (31) with all_51_0, all_65_2, all_47_1, all_47_2, % 142.60/19.89 | simplifying with (164), (166) gives: % 142.60/19.90 | (171) all_65_2 = all_51_0 % 142.60/19.90 | % 142.60/19.90 | COMBINE_EQS: (170), (171) imply: % 142.60/19.90 | (172) all_59_2 = all_51_0 % 142.60/19.90 | % 142.60/19.90 | SIMP: (172) implies: % 142.60/19.90 | (173) all_59_2 = all_51_0 % 142.60/19.90 | % 142.60/19.90 | COMBINE_EQS: (169), (173) imply: % 142.60/19.90 | (174) all_51_0 = all_47_0 % 142.60/19.90 | % 142.60/19.90 | COMBINE_EQS: (171), (174) imply: % 142.60/19.90 | (175) all_65_2 = all_47_0 % 142.60/19.90 | % 142.60/19.90 | REDUCE: (163), (175) imply: % 142.60/19.90 | (176) sdtpldt0(all_47_0, all_49_1) = all_65_0 % 142.60/19.90 | % 142.60/19.90 | REDUCE: (60), (174) imply: % 142.60/19.90 | (177) ~ sdtlseqdt0(all_51_3, all_47_0) % 142.60/19.90 | % 142.60/19.90 | GROUND_INST: instantiating (mSumSc) with xN, xN, all_47_3, simplifying with % 142.60/19.90 | (14), (23), (50) gives: % 142.60/19.90 | (178) aScalar0(all_47_3) % 142.60/19.90 | % 142.60/19.90 | GROUND_INST: instantiating (mMulSc) with xR, xR, all_47_2, simplifying with % 142.60/19.90 | (11), (25), (52) gives: % 142.60/19.90 | (179) aScalar0(all_47_2) % 142.60/19.90 | % 142.60/19.90 | GROUND_INST: instantiating (mDistr) with xR, xS, xS, xN, xN, all_47_3, % 142.60/19.90 | simplifying with (11), (13), (15), (25), (27), (50) gives: % 142.60/19.90 | (180) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v1, % 142.60/19.90 | xS) = v2 & sdtasdt0(xS, xS) = v3 & sdtasdt0(xR, v0) = all_47_3 & % 142.60/19.90 | sdtpldt0(xN, v3) = v2 & sdtpldt0(xS, xS) = v0 & sdtpldt0(xR, xS) = % 142.60/19.90 | v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_47_3)) % 142.60/19.90 | % 142.60/19.90 | GROUND_INST: instantiating (mDistr) with xP, xP, xP, all_35_0, all_35_0, % 142.60/19.90 | all_51_3, simplifying with (12), (26), (38), (167) gives: % 142.60/19.90 | (181) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v1, % 142.60/19.90 | xP) = v2 & sdtasdt0(xP, v0) = all_51_3 & sdtasdt0(xP, xP) = v3 & % 142.60/19.90 | sdtpldt0(all_35_0, v3) = v2 & sdtpldt0(xP, xP) = v1 & sdtpldt0(xP, % 142.60/19.90 | xP) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_51_3)) % 142.60/19.90 | % 142.60/19.90 | GROUND_INST: instantiating (mMulSc) with xP, xP, all_35_0, simplifying with % 142.60/19.90 | (12), (26), (38) gives: % 142.60/19.90 | (182) aScalar0(all_35_0) % 142.60/19.90 | % 142.60/19.90 | GROUND_INST: instantiating (mMulSc) with xS, xS, all_47_1, simplifying with % 142.60/19.90 | (13), (27), (53) gives: % 142.60/19.90 | (183) aScalar0(all_47_1) % 142.60/19.90 | % 142.60/19.90 | GROUND_INST: instantiating (mMNeg) with xS, xR, all_45_2, all_49_1, % 142.60/19.90 | simplifying with (11), (13), (25), (27), (47), (162) gives: % 142.60/19.90 | (184) ? [v0: $i] : ? [v1: $i] : (smndt0(v1) = all_49_1 & smndt0(xR) = v0 % 142.60/19.90 | & sdtasdt0(xS, v0) = all_49_1 & sdtasdt0(xS, xR) = v1 & $i(v1) & % 142.60/19.90 | $i(v0) & $i(all_49_1)) % 142.60/19.90 | % 142.60/19.90 | GROUND_INST: instantiating (mNegSc) with xN, all_49_1, simplifying with (14), % 142.60/19.90 | (23), (58) gives: % 142.60/19.90 | (185) aScalar0(all_49_1) % 142.60/19.90 | % 142.60/19.90 | GROUND_INST: instantiating (1) with xt, xq, simplifying with (2), (9), (69) % 142.60/19.90 | gives: % 142.60/19.91 | (186) ? [v0: $i] : (aDimensionOf0(xt) = v0 & $i(v0) & (v0 = sz00 | ( ! % 142.60/19.91 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlbdtrb0(xt, v2) % 142.60/19.91 | = v3) | ~ (aDimensionOf0(xq) = v1) | ~ $i(v2) | ~ $i(xq) % 142.60/19.91 | | ~ aNaturalNumber0(v2) | (sdtlbdtrb0(xq, v2) = v3 & % 142.60/19.91 | $i(v3))) & ! [v1: $i] : ! [v2: $i] : (v1 = xq | ~ % 142.60/19.91 | (aDimensionOf0(v1) = v2) | ~ $i(v1) | ~ aVector0(v1) | ? % 142.60/19.91 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ($i(v4) % 142.60/19.91 | & (( ~ (v6 = v5) & sdtlbdtrb0(v1, v4) = v5 & sdtlbdtrb0(xt, % 142.60/19.91 | v4) = v6 & $i(v6) & $i(v5) & aNaturalNumber0(v4)) | ( % 142.60/19.91 | ~ (v3 = v0) & szszuzczcdt0(v2) = v3 & $i(v3))))) & ! % 142.60/19.91 | [v1: $i] : ( ~ (aDimensionOf0(xq) = v1) | ~ $i(xq) | % 142.60/19.91 | szszuzczcdt0(v1) = v0) & ! [v1: $i] : ( ~ (aDimensionOf0(xq) % 142.60/19.91 | = v1) | ~ $i(xq) | aVector0(xq))))) % 142.60/19.91 | % 142.60/19.91 | DELTA: instantiating (184) with fresh symbols all_91_0, all_91_1 gives: % 142.60/19.91 | (187) smndt0(all_91_0) = all_49_1 & smndt0(xR) = all_91_1 & sdtasdt0(xS, % 142.60/19.91 | all_91_1) = all_49_1 & sdtasdt0(xS, xR) = all_91_0 & $i(all_91_0) & % 142.60/19.91 | $i(all_91_1) & $i(all_49_1) % 142.60/19.91 | % 142.60/19.91 | ALPHA: (187) implies: % 142.60/19.91 | (188) $i(all_49_1) % 142.60/19.91 | % 142.60/19.91 | DELTA: instantiating (180) with fresh symbols all_96_0, all_96_1, all_96_2, % 142.60/19.91 | all_96_3 gives: % 142.60/19.91 | (189) sdtasdt0(all_96_2, xS) = all_96_1 & sdtasdt0(xS, xS) = all_96_0 & % 142.60/19.91 | sdtasdt0(xR, all_96_3) = all_47_3 & sdtpldt0(xN, all_96_0) = all_96_1 % 142.60/19.91 | & sdtpldt0(xS, xS) = all_96_3 & sdtpldt0(xR, xS) = all_96_2 & % 142.60/19.91 | $i(all_96_0) & $i(all_96_1) & $i(all_96_2) & $i(all_96_3) & % 142.60/19.91 | $i(all_47_3) % 142.60/19.91 | % 142.60/19.91 | ALPHA: (189) implies: % 142.60/19.91 | (190) $i(all_47_3) % 142.60/19.91 | (191) $i(all_96_0) % 142.60/19.91 | (192) sdtasdt0(xS, xS) = all_96_0 % 142.60/19.91 | % 142.60/19.91 | DELTA: instantiating (181) with fresh symbols all_98_0, all_98_1, all_98_2, % 142.60/19.91 | all_98_3 gives: % 142.60/19.91 | (193) sdtasdt0(all_98_2, xP) = all_98_1 & sdtasdt0(xP, all_98_3) = all_51_3 % 142.60/19.91 | & sdtasdt0(xP, xP) = all_98_0 & sdtpldt0(all_35_0, all_98_0) = % 142.60/19.91 | all_98_1 & sdtpldt0(xP, xP) = all_98_2 & sdtpldt0(xP, xP) = all_98_3 % 142.60/19.91 | & $i(all_98_0) & $i(all_98_1) & $i(all_98_2) & $i(all_98_3) & % 142.60/19.91 | $i(all_51_3) % 142.60/19.91 | % 142.60/19.91 | ALPHA: (193) implies: % 142.60/19.91 | (194) $i(all_98_1) % 142.60/19.91 | (195) $i(all_98_0) % 142.60/19.91 | (196) sdtpldt0(all_35_0, all_98_0) = all_98_1 % 142.60/19.91 | (197) sdtasdt0(xP, xP) = all_98_0 % 142.60/19.91 | % 142.60/19.91 | DELTA: instantiating (186) with fresh symbol all_102_0 gives: % 142.60/19.91 | (198) aDimensionOf0(xt) = all_102_0 & $i(all_102_0) & (all_102_0 = sz00 | ( % 142.60/19.91 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(xt, v1) % 142.60/19.91 | = v2) | ~ (aDimensionOf0(xq) = v0) | ~ $i(v1) | ~ $i(xq) | % 142.60/19.91 | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(xq, v1) = v2 & $i(v2))) & % 142.60/19.91 | ! [v0: $i] : ! [v1: $i] : (v0 = xq | ~ (aDimensionOf0(v0) = v1) % 142.60/19.91 | | ~ $i(v0) | ~ aVector0(v0) | ? [v2: any] : ? [v3: $i] : ? % 142.60/19.91 | [v4: $i] : ? [v5: $i] : ($i(v3) & (( ~ (v5 = v4) & % 142.60/19.91 | sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xt, v3) = v5 & % 142.60/19.91 | $i(v5) & $i(v4) & aNaturalNumber0(v3)) | ( ~ (v2 = % 142.60/19.91 | all_102_0) & szszuzczcdt0(v1) = v2 & $i(v2))))) & ! % 142.60/19.91 | [v0: $i] : ( ~ (aDimensionOf0(xq) = v0) | ~ $i(xq) | % 142.60/19.91 | szszuzczcdt0(v0) = all_102_0) & ! [v0: $i] : ( ~ % 142.60/19.91 | (aDimensionOf0(xq) = v0) | ~ $i(xq) | aVector0(xq)))) % 142.60/19.91 | % 142.60/19.91 | ALPHA: (198) implies: % 142.60/19.91 | (199) aDimensionOf0(xt) = all_102_0 % 142.60/19.92 | (200) all_102_0 = sz00 | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 142.60/19.92 | (sdtlbdtrb0(xt, v1) = v2) | ~ (aDimensionOf0(xq) = v0) | ~ % 142.60/19.92 | $i(v1) | ~ $i(xq) | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(xq, v1) % 142.60/19.92 | = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : (v0 = xq | ~ % 142.60/19.92 | (aDimensionOf0(v0) = v1) | ~ $i(v0) | ~ aVector0(v0) | ? [v2: % 142.60/19.92 | any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ($i(v3) & (( ~ % 142.60/19.92 | (v5 = v4) & sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xt, v3) = % 142.60/19.92 | v5 & $i(v5) & $i(v4) & aNaturalNumber0(v3)) | ( ~ (v2 = % 142.60/19.92 | all_102_0) & szszuzczcdt0(v1) = v2 & $i(v2))))) & ! [v0: % 142.60/19.92 | $i] : ( ~ (aDimensionOf0(xq) = v0) | ~ $i(xq) | szszuzczcdt0(v0) % 142.60/19.92 | = all_102_0) & ! [v0: $i] : ( ~ (aDimensionOf0(xq) = v0) | ~ % 142.60/19.92 | $i(xq) | aVector0(xq))) % 142.60/19.92 | % 142.60/19.92 | GROUND_INST: instantiating (32) with all_35_0, all_98_0, xP, xP, simplifying % 142.60/19.92 | with (38), (197) gives: % 142.60/19.92 | (201) all_98_0 = all_35_0 % 142.60/19.92 | % 142.60/19.92 | GROUND_INST: instantiating (32) with all_47_1, all_96_0, xS, xS, simplifying % 142.60/19.92 | with (53), (192) gives: % 142.60/19.92 | (202) all_96_0 = all_47_1 % 142.60/19.92 | % 142.60/19.92 | GROUND_INST: instantiating (30) with all_33_0, all_102_0, xt, simplifying with % 142.60/19.92 | (35), (199) gives: % 142.60/19.92 | (203) all_102_0 = all_33_0 % 142.60/19.92 | % 142.60/19.92 | REDUCE: (196), (201) imply: % 142.60/19.92 | (204) sdtpldt0(all_35_0, all_35_0) = all_98_1 % 142.60/19.92 | % 142.60/19.92 | REDUCE: (195), (201) imply: % 142.60/19.92 | (205) $i(all_35_0) % 142.60/19.92 | % 142.60/19.92 | REDUCE: (191), (202) imply: % 142.60/19.92 | (206) $i(all_47_1) % 142.60/19.92 | % 142.60/19.92 | BETA: splitting (200) gives: % 142.60/19.92 | % 142.60/19.92 | Case 1: % 142.60/19.92 | | % 142.60/19.92 | | (207) all_102_0 = sz00 % 142.60/19.92 | | % 142.60/19.92 | | COMBINE_EQS: (203), (207) imply: % 142.60/19.92 | | (208) all_33_0 = sz00 % 142.60/19.92 | | % 142.60/19.92 | | REDUCE: (161), (208) imply: % 142.60/19.92 | | (209) $false % 142.60/19.92 | | % 142.60/19.92 | | CLOSE: (209) is inconsistent. % 142.60/19.92 | | % 142.60/19.92 | Case 2: % 142.60/19.92 | | % 142.60/19.92 | | % 142.60/19.92 | | GROUND_INST: instantiating (31) with all_51_3, all_98_1, all_35_0, all_35_0, % 142.60/19.92 | | simplifying with (167), (204) gives: % 142.60/19.92 | | (210) all_98_1 = all_51_3 % 142.60/19.92 | | % 142.60/19.92 | | REDUCE: (194), (210) imply: % 142.60/19.92 | | (211) $i(all_51_3) % 142.60/19.92 | | % 142.60/19.92 | | GROUND_INST: instantiating (mSumSc) with all_35_0, all_35_0, all_51_3, % 142.60/19.92 | | simplifying with (167), (182), (205) gives: % 142.60/19.92 | | (212) aScalar0(all_51_3) % 142.60/19.92 | | % 142.60/19.92 | | GROUND_INST: instantiating (mLEMon) with all_35_0, xN, all_35_0, xN, % 142.60/19.92 | | all_51_3, all_47_3, simplifying with (14), (23), (37), (50), % 142.60/19.92 | | (167), (182), (205) gives: % 142.60/19.92 | | (213) sdtlseqdt0(all_51_3, all_47_3) % 142.60/19.92 | | % 142.60/19.92 | | GROUND_INST: instantiating (mSumSc) with all_47_2, all_47_1, all_47_0, % 142.60/19.92 | | simplifying with (51), (168), (179), (183), (206) gives: % 142.60/19.92 | | (214) aScalar0(all_47_0) % 142.60/19.92 | | % 142.60/19.92 | | GROUND_INST: instantiating (mArith) with all_47_2, all_47_1, all_49_1, % 142.60/19.92 | | all_47_0, all_65_0, simplifying with (51), (168), (176), (179), % 142.60/19.92 | | (183), (185), (188), (206) gives: % 142.60/19.92 | | (215) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 142.60/19.92 | | (sdtasdt0(v1, all_49_1) = v2 & sdtasdt0(all_47_1, all_49_1) = v3 & % 142.60/19.92 | | sdtasdt0(all_47_1, all_47_2) = v1 & sdtasdt0(all_47_2, v3) = v2 & % 142.60/19.92 | | sdtasdt0(all_47_2, all_47_1) = v1 & sdtpldt0(all_47_1, all_49_1) % 142.60/19.92 | | = v0 & sdtpldt0(all_47_1, all_47_2) = all_47_0 & % 142.60/19.92 | | sdtpldt0(all_47_2, v0) = all_65_0 & $i(v3) & $i(v2) & $i(v1) & % 142.60/19.92 | | $i(v0) & $i(all_65_0) & $i(all_47_0)) % 142.60/19.92 | | % 142.60/19.92 | | DELTA: instantiating (215) with fresh symbols all_151_0, all_151_1, % 142.60/19.92 | | all_151_2, all_151_3 gives: % 142.60/19.92 | | (216) sdtasdt0(all_151_2, all_49_1) = all_151_1 & sdtasdt0(all_47_1, % 142.60/19.92 | | all_49_1) = all_151_0 & sdtasdt0(all_47_1, all_47_2) = all_151_2 % 142.60/19.92 | | & sdtasdt0(all_47_2, all_151_0) = all_151_1 & sdtasdt0(all_47_2, % 142.60/19.92 | | all_47_1) = all_151_2 & sdtpldt0(all_47_1, all_49_1) = all_151_3 % 142.60/19.92 | | & sdtpldt0(all_47_1, all_47_2) = all_47_0 & sdtpldt0(all_47_2, % 142.60/19.92 | | all_151_3) = all_65_0 & $i(all_151_0) & $i(all_151_1) & % 142.60/19.92 | | $i(all_151_2) & $i(all_151_3) & $i(all_65_0) & $i(all_47_0) % 142.60/19.92 | | % 142.60/19.92 | | ALPHA: (216) implies: % 142.60/19.93 | | (217) $i(all_47_0) % 142.60/19.93 | | % 142.60/19.93 | | GROUND_INST: instantiating (mLETrn) with all_51_3, all_47_3, all_47_0, % 142.60/19.93 | | simplifying with (49), (177), (178), (190), (211), (212), % 142.60/19.93 | | (213), (214), (217) gives: % 142.60/19.93 | | (218) $false % 142.60/19.93 | | % 142.60/19.93 | | CLOSE: (218) is inconsistent. % 142.60/19.93 | | % 142.60/19.93 | End of split % 142.60/19.93 | % 142.60/19.93 End of proof % 142.60/19.93 % SZS output end Proof for theBenchmark % 142.60/19.93 % 142.60/19.93 19304ms %------------------------------------------------------------------------------