%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG076+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 : n032.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 13:57:43 EDT 2023 % Result : Theorem 84.81s 11.91s % Output : Proof 94.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : RNG076+2 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.29 % Computer : n032.cluster.edu % 0.10/0.29 % Model : x86_64 x86_64 % 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.29 % Memory : 8042.1875MB % 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.29 % CPULimit : 300 % 0.10/0.29 % WCLimit : 300 % 0.10/0.29 % DateTime : Sun Aug 27 02:03:29 EDT 2023 % 0.10/0.29 % CPUTime : % 0.14/0.48 ________ _____ % 0.14/0.48 ___ __ \_________(_)________________________________ % 0.14/0.48 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.14/0.48 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.14/0.48 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.14/0.48 % 0.14/0.48 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.14/0.48 (2023-06-19) % 0.14/0.48 % 0.14/0.48 (c) Philipp Rümmer, 2009-2023 % 0.14/0.48 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.14/0.48 Amanda Stjerna. % 0.14/0.48 Free software under BSD-3-Clause. % 0.14/0.48 % 0.14/0.48 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.14/0.48 % 0.14/0.49 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.14/0.49 Running up to 7 provers in parallel. % 0.14/0.50 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.14/0.50 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.14/0.50 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.14/0.50 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.14/0.51 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.14/0.51 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.14/0.51 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 2.86/1.00 Prover 4: Preprocessing ... % 2.86/1.01 Prover 1: Preprocessing ... % 3.29/1.04 Prover 3: Preprocessing ... % 3.29/1.04 Prover 5: Preprocessing ... % 3.29/1.04 Prover 2: Preprocessing ... % 3.29/1.04 Prover 6: Preprocessing ... % 3.29/1.05 Prover 0: Preprocessing ... % 8.41/1.75 Prover 3: Constructing countermodel ... % 8.41/1.75 Prover 1: Constructing countermodel ... % 8.72/1.78 Prover 6: Proving ... % 9.82/1.95 Prover 5: Constructing countermodel ... % 10.62/2.10 Prover 4: Constructing countermodel ... % 10.62/2.13 Prover 2: Proving ... % 10.62/2.21 Prover 0: Proving ... % 71.32/10.22 Prover 2: stopped % 71.32/10.24 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 72.84/10.32 Prover 7: Preprocessing ... % 75.08/10.55 Prover 7: Constructing countermodel ... % 84.81/11.91 Prover 3: proved (11406ms) % 84.81/11.91 % 84.81/11.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 84.81/11.91 % 84.81/11.91 Prover 6: stopped % 84.81/11.91 Prover 5: stopped % 84.81/11.91 Prover 0: stopped % 84.81/11.91 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 84.81/11.91 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 84.81/11.91 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 84.81/11.92 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 85.77/12.03 Prover 11: Preprocessing ... % 85.77/12.04 Prover 8: Preprocessing ... % 86.28/12.06 Prover 13: Preprocessing ... % 86.44/12.07 Prover 10: Preprocessing ... % 87.03/12.16 Prover 8: Warning: ignoring some quantifiers % 87.03/12.18 Prover 8: Constructing countermodel ... % 87.03/12.22 Prover 10: Constructing countermodel ... % 87.62/12.25 Prover 13: Constructing countermodel ... % 87.99/12.35 Prover 11: Constructing countermodel ... % 93.31/13.04 Prover 10: Found proof (size 176) % 93.31/13.04 Prover 10: proved (1122ms) % 93.31/13.04 Prover 7: stopped % 93.31/13.04 Prover 13: stopped % 93.31/13.04 Prover 8: stopped % 93.31/13.04 Prover 11: stopped % 93.31/13.04 Prover 1: stopped % 93.31/13.06 Prover 4: stopped % 93.31/13.06 % 93.31/13.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 93.31/13.06 % 93.31/13.09 % SZS output start Proof for theBenchmark % 93.31/13.10 Assumptions after simplification: % 93.31/13.10 --------------------------------- % 93.31/13.10 % 93.31/13.10 (mArith) % 93.31/13.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 93.31/13.13 (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 93.31/13.13 | ~ $i(v0) | ~ aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v5: % 93.31/13.13 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(v6, v2) = v7 & % 93.31/13.13 sdtasdt0(v1, v2) = v8 & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v8) = v7 & % 93.31/13.13 sdtasdt0(v0, v1) = v6 & sdtpldt0(v1, v2) = v5 & sdtpldt0(v1, v0) = v3 & % 93.31/13.13 sdtpldt0(v0, v5) = v4 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 93.31/13.13 $i(v3))) % 93.31/13.13 % 93.31/13.13 (mDefInit) % 93.31/13.13 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sziznziztdt0(v0) = v1) | ~ $i(v0) % 93.31/13.13 | ~ aVector0(v0) | ? [v2: $i] : (aDimensionOf0(v0) = v2 & $i(v2) & (v2 = % 93.31/13.13 sz00 | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtlbdtrb0(v0, % 93.31/13.13 v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~ $i(v4) | ~ $i(v1) % 93.31/13.13 | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1, v4) = v5 & $i(v5))) & ! % 93.31/13.13 [v3: $i] : ! [v4: $i] : (v3 = v1 | ~ (aDimensionOf0(v3) = v4) | ~ % 93.31/13.13 $i(v3) | ~ aVector0(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 93.31/13.13 ? [v8: $i] : ($i(v6) & (( ~ (v8 = v7) & sdtlbdtrb0(v3, v6) = v7 & % 93.31/13.13 sdtlbdtrb0(v0, v6) = v8 & $i(v8) & $i(v7) & % 93.31/13.13 aNaturalNumber0(v6)) | ( ~ (v5 = v2) & szszuzczcdt0(v4) = v5 & % 93.31/13.13 $i(v5))))) & ! [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~ % 93.31/13.13 $i(v1) | szszuzczcdt0(v3) = v2) & ! [v3: $i] : ( ~ % 93.31/13.13 (aDimensionOf0(v1) = v3) | ~ $i(v1) | aVector0(v1)))))) % 93.31/13.13 % 93.31/13.13 (mDimNat) % 93.31/13.13 ! [v0: $i] : ! [v1: $i] : ( ~ (aDimensionOf0(v0) = v1) | ~ $i(v0) | ~ % 93.31/13.13 aVector0(v0) | aNaturalNumber0(v1)) % 93.31/13.13 % 93.31/13.13 (mDistr) % 93.31/13.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 93.31/13.13 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ % 93.31/13.13 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 93.31/13.13 aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v6: $i] : ? [v7: $i] % 93.31/13.13 : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v7, v2) = v8 & sdtasdt0(v1, v2) = v9 % 93.31/13.13 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v4, v9) = v8 & sdtpldt0(v1, v2) = v6 & % 93.31/13.13 sdtpldt0(v0, v1) = v7 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5))) % 93.31/13.13 % 93.31/13.13 (mEqInit) % 93.31/13.14 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 93.31/13.14 (sziznziztdt0(v1) = v3) | ~ (sziznziztdt0(v0) = v2) | ~ $i(v1) | ~ $i(v0) % 93.31/13.14 | ~ aVector0(v1) | ~ aVector0(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: % 93.31/13.14 $i] : ? [v7: $i] : ((v7 = v6 & aDimensionOf0(v3) = v6 & aDimensionOf0(v2) % 93.31/13.14 = v6 & $i(v6)) | (aDimensionOf0(v1) = v5 & $i(v5) & (v5 = sz00 | ( ~ (v5 % 93.31/13.14 = v4) & aDimensionOf0(v0) = v4 & $i(v4)))))) % 93.31/13.14 % 93.31/13.14 (mIH) % 93.31/13.14 ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) | ~ % 93.31/13.14 aNaturalNumber0(v0) | iLess0(v0, v1)) % 93.31/13.14 % 93.31/13.14 (mLEMon) % 93.31/13.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 93.31/13.14 $i] : ( ~ (sdtpldt0(v1, v3) = v5) | ~ (sdtpldt0(v0, v2) = v4) | ~ $i(v3) | % 93.31/13.14 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v2, v3) | ~ % 93.31/13.14 sdtlseqdt0(v0, v1) | ~ aScalar0(v3) | ~ aScalar0(v2) | ~ aScalar0(v1) | % 93.31/13.14 ~ aScalar0(v0) | sdtlseqdt0(v4, v5)) % 93.31/13.14 % 93.31/13.14 (mLETot) % 93.31/13.14 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ % 93.31/13.14 aScalar0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1)) % 93.31/13.14 % 93.31/13.14 (mMulSc) % 93.31/13.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 93.31/13.14 $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | aScalar0(v2)) % 93.31/13.14 % 93.31/13.14 (mSumSc) % 93.31/13.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 93.31/13.14 $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | aScalar0(v2)) % 93.31/13.14 % 93.31/13.14 (m__) % 93.31/13.14 $i(xS) & $i(xP) & $i(xR) & $i(xH) & $i(xE) & $i(xD) & $i(xC) & ? [v0: $i] : % 93.31/13.14 ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: % 93.31/13.14 $i] : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(xH, xH) = v2 & sdtasdt0(xE, xE) % 93.31/13.14 = v0 & sdtasdt0(xC, xD) = v5 & sdtpldt0(v6, v2) = v7 & sdtpldt0(v5, v7) = v8 % 93.31/13.14 & sdtpldt0(v1, v2) = v3 & sdtpldt0(v0, v3) = v4 & sdtpldt0(xP, xP) = v1 & % 93.31/13.14 sdtpldt0(xR, xS) = v6 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) % 93.31/13.14 & $i(v2) & $i(v1) & $i(v0) & ~ sdtlseqdt0(v4, v8)) % 93.31/13.14 % 93.31/13.14 (m__1652) % 93.31/13.14 $i(xs) & ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : ! % 93.31/13.14 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2, v2) % 93.31/13.14 = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4) = v5) | ~ % 93.31/13.14 $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1) | ? [v6: $i] : ? % 93.31/13.14 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ((sdtasasdt0(v1, v2) = v8 & % 93.31/13.14 sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8) & sdtlseqdt0(v9, v5)) | % 93.31/13.14 (aDimensionOf0(v1) = v6 & $i(v6) & ( ~ iLess0(v6, v0) | ( ~ (v7 = v6) & % 93.31/13.14 aDimensionOf0(v2) = v7 & $i(v7))))))) % 93.31/13.14 % 93.31/13.14 (m__1678) % 93.31/13.14 $i(xt) & $i(xs) & aVector0(xt) & aVector0(xs) % 93.31/13.14 % 93.31/13.14 (m__1678_01) % 93.31/13.14 $i(xt) & $i(xs) & ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) = % 93.31/13.14 v0 & $i(v0)) % 93.31/13.14 % 93.31/13.14 (m__1692) % 93.31/13.14 $i(xs) & $i(sz00) & ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 & % 93.31/13.14 $i(v0)) % 93.31/13.14 % 93.31/13.14 (m__1709) % 93.31/13.14 $i(xp) & $i(xs) & ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xs) = xp & % 93.31/13.14 aDimensionOf0(xp) = v0 & aDimensionOf0(xs) = v1 & szszuzczcdt0(v0) = v1 & % 93.31/13.14 $i(v1) & $i(v0) & aVector0(xp) & ! [v2: $i] : ! [v3: $i] : ( ~ % 93.31/13.14 (sdtlbdtrb0(xp, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) | % 93.31/13.14 (sdtlbdtrb0(xs, v2) = v3 & $i(v3)))) % 93.31/13.14 % 93.31/13.14 (m__1726) % 93.31/13.15 $i(xq) & $i(xt) & ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xt) = xq & % 93.31/13.15 aDimensionOf0(xq) = v0 & aDimensionOf0(xt) = v1 & szszuzczcdt0(v0) = v1 & % 93.31/13.15 $i(v1) & $i(v0) & aVector0(xq) & ! [v2: $i] : ! [v3: $i] : ( ~ % 93.31/13.15 (sdtlbdtrb0(xt, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) | % 93.31/13.15 (sdtlbdtrb0(xq, v2) = v3 & $i(v3)))) % 93.31/13.15 % 93.31/13.15 (m__1746) % 93.31/13.15 $i(xA) & $i(xs) & ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) = % 93.31/13.15 v0 & $i(v0) & aScalar0(xA)) % 93.31/13.15 % 93.31/13.15 (m__1766) % 93.31/13.15 $i(xB) & $i(xt) & ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) = % 93.31/13.15 v0 & $i(v0) & aScalar0(xB)) % 93.31/13.15 % 93.31/13.15 (m__1783) % 93.31/13.15 sdtasasdt0(xp, xp) = xC & $i(xC) & $i(xp) & aScalar0(xC) % 93.31/13.15 % 93.31/13.15 (m__1800) % 93.31/13.15 sdtasasdt0(xq, xq) = xD & $i(xD) & $i(xq) & aScalar0(xD) % 93.31/13.15 % 93.31/13.15 (m__1820) % 93.31/13.15 sdtasasdt0(xp, xq) = xE & $i(xE) & $i(xq) & $i(xp) & aScalar0(xE) % 93.31/13.15 % 93.31/13.15 (m__1873) % 93.31/13.15 sdtasdt0(xA, xB) = xH & $i(xH) & $i(xB) & $i(xA) & aScalar0(xH) % 93.31/13.15 % 93.31/13.15 (m__1892) % 93.31/13.15 sdtasdt0(xC, xG) = xR & $i(xR) & $i(xG) & $i(xC) & aScalar0(xR) % 93.31/13.15 % 93.31/13.15 (m__1911) % 93.31/13.15 sdtasdt0(xE, xH) = xP & $i(xP) & $i(xH) & $i(xE) & aScalar0(xP) % 93.31/13.15 % 93.31/13.15 (m__1930) % 94.08/13.15 sdtasdt0(xF, xD) = xS & $i(xS) & $i(xF) & $i(xD) & aScalar0(xS) % 94.08/13.15 % 94.08/13.15 (m__1967) % 94.08/13.15 $i(xE) & $i(xD) & $i(xC) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xE, xE) = v0 % 94.08/13.15 & sdtasdt0(xC, xD) = v1 & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1)) % 94.08/13.15 % 94.08/13.15 (m__1983) % 94.08/13.15 $i(xS) & $i(xP) & $i(xR) & ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xP, xP) = v0 % 94.08/13.15 & sdtpldt0(xR, xS) = v1 & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1)) % 94.08/13.15 % 94.08/13.15 (function-axioms) % 94.08/13.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 94.08/13.15 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 94.08/13.15 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) % 94.08/13.15 | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 94.08/13.15 ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = % 94.08/13.15 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 94.08/13.15 ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 94.08/13.15 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sziznziztdt0(v2) = v1) | ~ % 94.08/13.15 (sziznziztdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 94.08/13.15 v0 | ~ (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) & ! [v0: % 94.08/13.15 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ % 94.08/13.15 (smndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 94.08/13.15 (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0)) % 94.08/13.15 % 94.08/13.15 Further assumptions not needed in the proof: % 94.08/13.15 -------------------------------------------- % 94.08/13.15 mDefSPN, mDefSPZ, mDistr2, mElmSc, mIHOrd, mLEASm, mLEMonM, mLERef, mLETrn, % 94.08/13.15 mLess, mMDNeg, mMNeg, mNatExtr, mNatSort, mNegSc, mPosMon, mSZeroSc, mScPr, % 94.08/13.15 mScSort, mScSqPos, mScZero, mSqPos, mSqrt, mSuccEqu, mSuccNat, mVcSort, % 94.08/13.15 mZeroNat, m__1837, m__1854, m__1949 % 94.08/13.15 % 94.08/13.15 Those formulas are unsatisfiable: % 94.08/13.15 --------------------------------- % 94.08/13.15 % 94.08/13.15 Begin of proof % 94.08/13.15 | % 94.08/13.15 | ALPHA: (mDefInit) implies: % 94.08/13.16 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (sziznziztdt0(v0) = v1) | ~ $i(v0) | % 94.08/13.16 | ~ aVector0(v0) | ? [v2: $i] : (aDimensionOf0(v0) = v2 & $i(v2) & (v2 % 94.08/13.16 | = sz00 | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 94.08/13.16 | (sdtlbdtrb0(v0, v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~ % 94.08/13.16 | $i(v4) | ~ $i(v1) | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1, % 94.08/13.16 | v4) = v5 & $i(v5))) & ! [v3: $i] : ! [v4: $i] : (v3 = % 94.08/13.16 | v1 | ~ (aDimensionOf0(v3) = v4) | ~ $i(v3) | ~ % 94.08/13.16 | aVector0(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? % 94.08/13.16 | [v8: $i] : ($i(v6) & (( ~ (v8 = v7) & sdtlbdtrb0(v3, v6) = v7 % 94.08/13.16 | & sdtlbdtrb0(v0, v6) = v8 & $i(v8) & $i(v7) & % 94.08/13.16 | aNaturalNumber0(v6)) | ( ~ (v5 = v2) & szszuzczcdt0(v4) % 94.08/13.16 | = v5 & $i(v5))))) & ! [v3: $i] : ( ~ % 94.08/13.16 | (aDimensionOf0(v1) = v3) | ~ $i(v1) | szszuzczcdt0(v3) = v2) % 94.08/13.16 | & ! [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~ $i(v1) | % 94.08/13.16 | aVector0(v1)))))) % 94.08/13.16 | % 94.08/13.16 | ALPHA: (mEqInit) implies: % 94.08/13.16 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 94.08/13.16 | (sziznziztdt0(v1) = v3) | ~ (sziznziztdt0(v0) = v2) | ~ $i(v1) | ~ % 94.08/13.16 | $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) | ? [v4: $i] : ? [v5: % 94.08/13.16 | $i] : ? [v6: $i] : ? [v7: $i] : ((v7 = v6 & aDimensionOf0(v3) = % 94.08/13.16 | v6 & aDimensionOf0(v2) = v6 & $i(v6)) | (aDimensionOf0(v1) = v5 & % 94.08/13.16 | $i(v5) & (v5 = sz00 | ( ~ (v5 = v4) & aDimensionOf0(v0) = v4 & % 94.08/13.16 | $i(v4)))))) % 94.08/13.16 | % 94.08/13.16 | ALPHA: (m__1678) implies: % 94.08/13.16 | (3) aVector0(xs) % 94.08/13.16 | (4) aVector0(xt) % 94.08/13.16 | % 94.08/13.16 | ALPHA: (m__1652) implies: % 94.08/13.16 | (5) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 94.08/13.16 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2, % 94.08/13.16 | v2) = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4) % 94.08/13.16 | = v5) | ~ $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1) % 94.08/13.16 | | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 94.08/13.16 | ((sdtasasdt0(v1, v2) = v8 & sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8) % 94.08/13.16 | & sdtlseqdt0(v9, v5)) | (aDimensionOf0(v1) = v6 & $i(v6) & ( ~ % 94.08/13.16 | iLess0(v6, v0) | ( ~ (v7 = v6) & aDimensionOf0(v2) = v7 & % 94.08/13.16 | $i(v7))))))) % 94.08/13.16 | % 94.08/13.16 | ALPHA: (m__1678_01) implies: % 94.08/13.16 | (6) ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) = v0 & % 94.08/13.16 | $i(v0)) % 94.08/13.16 | % 94.08/13.16 | ALPHA: (m__1692) implies: % 94.08/13.16 | (7) ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 & $i(v0)) % 94.08/13.16 | % 94.08/13.16 | ALPHA: (m__1709) implies: % 94.08/13.16 | (8) ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xs) = xp & aDimensionOf0(xp) % 94.08/13.16 | = v0 & aDimensionOf0(xs) = v1 & szszuzczcdt0(v0) = v1 & $i(v1) & % 94.08/13.16 | $i(v0) & aVector0(xp) & ! [v2: $i] : ! [v3: $i] : ( ~ % 94.08/13.16 | (sdtlbdtrb0(xp, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) | % 94.08/13.16 | (sdtlbdtrb0(xs, v2) = v3 & $i(v3)))) % 94.08/13.16 | % 94.08/13.16 | ALPHA: (m__1726) implies: % 94.08/13.16 | (9) ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xt) = xq & aDimensionOf0(xq) % 94.08/13.16 | = v0 & aDimensionOf0(xt) = v1 & szszuzczcdt0(v0) = v1 & $i(v1) & % 94.08/13.16 | $i(v0) & aVector0(xq) & ! [v2: $i] : ! [v3: $i] : ( ~ % 94.08/13.16 | (sdtlbdtrb0(xt, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) | % 94.08/13.16 | (sdtlbdtrb0(xq, v2) = v3 & $i(v3)))) % 94.08/13.16 | % 94.08/13.16 | ALPHA: (m__1746) implies: % 94.08/13.16 | (10) $i(xs) % 94.08/13.16 | (11) ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) = v0 & % 94.08/13.16 | $i(v0) & aScalar0(xA)) % 94.08/13.16 | % 94.08/13.16 | ALPHA: (m__1766) implies: % 94.08/13.16 | (12) $i(xt) % 94.08/13.16 | % 94.08/13.16 | ALPHA: (m__1783) implies: % 94.08/13.16 | (13) aScalar0(xC) % 94.08/13.16 | (14) sdtasasdt0(xp, xp) = xC % 94.08/13.16 | % 94.08/13.16 | ALPHA: (m__1800) implies: % 94.08/13.16 | (15) aScalar0(xD) % 94.08/13.16 | (16) sdtasasdt0(xq, xq) = xD % 94.08/13.16 | % 94.08/13.16 | ALPHA: (m__1820) implies: % 94.08/13.17 | (17) aScalar0(xE) % 94.08/13.17 | (18) $i(xp) % 94.08/13.17 | (19) $i(xq) % 94.08/13.17 | (20) sdtasasdt0(xp, xq) = xE % 94.08/13.17 | % 94.08/13.17 | ALPHA: (m__1873) implies: % 94.08/13.17 | (21) aScalar0(xH) % 94.08/13.17 | % 94.08/13.17 | ALPHA: (m__1892) implies: % 94.08/13.17 | (22) aScalar0(xR) % 94.08/13.17 | % 94.08/13.17 | ALPHA: (m__1911) implies: % 94.36/13.17 | (23) aScalar0(xP) % 94.36/13.17 | (24) sdtasdt0(xE, xH) = xP % 94.36/13.17 | % 94.36/13.17 | ALPHA: (m__1930) implies: % 94.36/13.17 | (25) aScalar0(xS) % 94.36/13.17 | % 94.36/13.17 | ALPHA: (m__1967) implies: % 94.36/13.17 | (26) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xE, xE) = v0 & sdtasdt0(xC, xD) % 94.36/13.17 | = v1 & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1)) % 94.36/13.17 | % 94.36/13.17 | ALPHA: (m__1983) implies: % 94.36/13.17 | (27) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xP, xP) = v0 & sdtpldt0(xR, xS) % 94.36/13.17 | = v1 & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1)) % 94.36/13.17 | % 94.36/13.17 | ALPHA: (m__) implies: % 94.36/13.17 | (28) $i(xC) % 94.36/13.17 | (29) $i(xD) % 94.36/13.17 | (30) $i(xE) % 94.36/13.17 | (31) $i(xH) % 94.36/13.17 | (32) $i(xR) % 94.36/13.17 | (33) $i(xP) % 94.36/13.17 | (34) $i(xS) % 94.36/13.17 | (35) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 94.36/13.17 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(xH, % 94.36/13.17 | xH) = v2 & sdtasdt0(xE, xE) = v0 & sdtasdt0(xC, xD) = v5 & % 94.36/13.17 | sdtpldt0(v6, v2) = v7 & sdtpldt0(v5, v7) = v8 & sdtpldt0(v1, v2) = % 94.36/13.17 | v3 & sdtpldt0(v0, v3) = v4 & sdtpldt0(xP, xP) = v1 & sdtpldt0(xR, % 94.36/13.17 | xS) = v6 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 94.36/13.17 | $i(v2) & $i(v1) & $i(v0) & ~ sdtlseqdt0(v4, v8)) % 94.36/13.17 | % 94.36/13.17 | ALPHA: (function-axioms) implies: % 94.36/13.17 | (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 94.36/13.17 | (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) % 94.36/13.17 | (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 94.36/13.17 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 94.36/13.17 | (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 94.36/13.17 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 94.36/13.17 | (39) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 94.36/13.17 | (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) % 94.36/13.17 | % 94.36/13.17 | DELTA: instantiating (7) with fresh symbol all_33_0 gives: % 94.36/13.17 | (40) ~ (all_33_0 = sz00) & aDimensionOf0(xs) = all_33_0 & $i(all_33_0) % 94.36/13.17 | % 94.36/13.17 | ALPHA: (40) implies: % 94.36/13.17 | (41) ~ (all_33_0 = sz00) % 94.36/13.17 | (42) aDimensionOf0(xs) = all_33_0 % 94.36/13.17 | % 94.36/13.17 | DELTA: instantiating (6) with fresh symbol all_35_0 gives: % 94.36/13.17 | (43) aDimensionOf0(xt) = all_35_0 & aDimensionOf0(xs) = all_35_0 & % 94.36/13.17 | $i(all_35_0) % 94.36/13.17 | % 94.36/13.17 | ALPHA: (43) implies: % 94.36/13.17 | (44) aDimensionOf0(xs) = all_35_0 % 94.36/13.17 | (45) aDimensionOf0(xt) = all_35_0 % 94.36/13.17 | % 94.36/13.17 | DELTA: instantiating (11) with fresh symbol all_39_0 gives: % 94.36/13.17 | (46) sdtlbdtrb0(xs, all_39_0) = xA & aDimensionOf0(xs) = all_39_0 & % 94.36/13.17 | $i(all_39_0) & aScalar0(xA) % 94.36/13.17 | % 94.36/13.17 | ALPHA: (46) implies: % 94.36/13.17 | (47) aDimensionOf0(xs) = all_39_0 % 94.36/13.17 | % 94.36/13.17 | DELTA: instantiating (26) with fresh symbols all_41_0, all_41_1 gives: % 94.36/13.17 | (48) sdtasdt0(xE, xE) = all_41_1 & sdtasdt0(xC, xD) = all_41_0 & % 94.36/13.17 | $i(all_41_0) & $i(all_41_1) & sdtlseqdt0(all_41_1, all_41_0) % 94.36/13.17 | % 94.36/13.17 | ALPHA: (48) implies: % 94.36/13.17 | (49) sdtasdt0(xC, xD) = all_41_0 % 94.36/13.17 | (50) sdtasdt0(xE, xE) = all_41_1 % 94.36/13.17 | % 94.36/13.17 | DELTA: instantiating (27) with fresh symbols all_43_0, all_43_1 gives: % 94.36/13.17 | (51) sdtpldt0(xP, xP) = all_43_1 & sdtpldt0(xR, xS) = all_43_0 & % 94.36/13.17 | $i(all_43_0) & $i(all_43_1) & sdtlseqdt0(all_43_1, all_43_0) % 94.36/13.17 | % 94.36/13.17 | ALPHA: (51) implies: % 94.36/13.17 | (52) sdtlseqdt0(all_43_1, all_43_0) % 94.36/13.18 | (53) sdtpldt0(xR, xS) = all_43_0 % 94.36/13.18 | (54) sdtpldt0(xP, xP) = all_43_1 % 94.36/13.18 | % 94.36/13.18 | DELTA: instantiating (9) with fresh symbols all_45_0, all_45_1 gives: % 94.36/13.18 | (55) sziznziztdt0(xt) = xq & aDimensionOf0(xq) = all_45_1 & % 94.36/13.18 | aDimensionOf0(xt) = all_45_0 & szszuzczcdt0(all_45_1) = all_45_0 & % 94.36/13.18 | $i(all_45_0) & $i(all_45_1) & aVector0(xq) & ! [v0: $i] : ! [v1: $i] % 94.36/13.18 | : ( ~ (sdtlbdtrb0(xt, v0) = v1) | ~ $i(v0) | ~ aNaturalNumber0(v0) | % 94.36/13.18 | (sdtlbdtrb0(xq, v0) = v1 & $i(v1))) % 94.36/13.18 | % 94.36/13.18 | ALPHA: (55) implies: % 94.36/13.18 | (56) aVector0(xq) % 94.36/13.18 | (57) aDimensionOf0(xq) = all_45_1 % 94.36/13.18 | (58) sziznziztdt0(xt) = xq % 94.36/13.18 | % 94.36/13.18 | DELTA: instantiating (8) with fresh symbols all_48_0, all_48_1 gives: % 94.36/13.18 | (59) sziznziztdt0(xs) = xp & aDimensionOf0(xp) = all_48_1 & % 94.36/13.18 | aDimensionOf0(xs) = all_48_0 & szszuzczcdt0(all_48_1) = all_48_0 & % 94.36/13.18 | $i(all_48_0) & $i(all_48_1) & aVector0(xp) & ! [v0: $i] : ! [v1: $i] % 94.36/13.18 | : ( ~ (sdtlbdtrb0(xp, v0) = v1) | ~ $i(v0) | ~ aNaturalNumber0(v0) | % 94.36/13.18 | (sdtlbdtrb0(xs, v0) = v1 & $i(v1))) % 94.36/13.18 | % 94.36/13.18 | ALPHA: (59) implies: % 94.36/13.18 | (60) aVector0(xp) % 94.36/13.18 | (61) $i(all_48_1) % 94.36/13.18 | (62) szszuzczcdt0(all_48_1) = all_48_0 % 94.36/13.18 | (63) aDimensionOf0(xs) = all_48_0 % 94.36/13.18 | (64) aDimensionOf0(xp) = all_48_1 % 94.36/13.18 | (65) sziznziztdt0(xs) = xp % 94.36/13.18 | % 94.36/13.18 | DELTA: instantiating (35) with fresh symbols all_51_0, all_51_1, all_51_2, % 94.36/13.18 | all_51_3, all_51_4, all_51_5, all_51_6, all_51_7, all_51_8 gives: % 94.36/13.18 | (66) sdtasdt0(xH, xH) = all_51_6 & sdtasdt0(xE, xE) = all_51_8 & % 94.36/13.18 | sdtasdt0(xC, xD) = all_51_3 & sdtpldt0(all_51_2, all_51_6) = all_51_1 % 94.36/13.18 | & sdtpldt0(all_51_3, all_51_1) = all_51_0 & sdtpldt0(all_51_7, % 94.36/13.18 | all_51_6) = all_51_5 & sdtpldt0(all_51_8, all_51_5) = all_51_4 & % 94.36/13.18 | sdtpldt0(xP, xP) = all_51_7 & sdtpldt0(xR, xS) = all_51_2 & % 94.36/13.18 | $i(all_51_0) & $i(all_51_1) & $i(all_51_2) & $i(all_51_3) & % 94.36/13.18 | $i(all_51_4) & $i(all_51_5) & $i(all_51_6) & $i(all_51_7) & % 94.36/13.18 | $i(all_51_8) & ~ sdtlseqdt0(all_51_4, all_51_0) % 94.36/13.18 | % 94.36/13.18 | ALPHA: (66) implies: % 94.36/13.18 | (67) ~ sdtlseqdt0(all_51_4, all_51_0) % 94.36/13.18 | (68) $i(all_51_3) % 94.36/13.18 | (69) $i(all_51_2) % 94.36/13.18 | (70) sdtpldt0(xR, xS) = all_51_2 % 94.36/13.18 | (71) sdtpldt0(xP, xP) = all_51_7 % 94.36/13.18 | (72) sdtpldt0(all_51_8, all_51_5) = all_51_4 % 94.36/13.18 | (73) sdtpldt0(all_51_7, all_51_6) = all_51_5 % 94.36/13.18 | (74) sdtpldt0(all_51_3, all_51_1) = all_51_0 % 94.36/13.18 | (75) sdtpldt0(all_51_2, all_51_6) = all_51_1 % 94.36/13.18 | (76) sdtasdt0(xC, xD) = all_51_3 % 94.36/13.18 | (77) sdtasdt0(xE, xE) = all_51_8 % 94.36/13.18 | (78) sdtasdt0(xH, xH) = all_51_6 % 94.36/13.18 | % 94.36/13.18 | DELTA: instantiating (5) with fresh symbol all_53_0 gives: % 94.36/13.18 | (79) aDimensionOf0(xs) = all_53_0 & $i(all_53_0) & ! [v0: $i] : ! [v1: % 94.36/13.18 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasasdt0(v1, % 94.36/13.18 | v1) = v3) | ~ (sdtasasdt0(v0, v0) = v2) | ~ (sdtasdt0(v2, v3) % 94.36/13.18 | = v4) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) % 94.36/13.18 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 94.36/13.18 | ((sdtasasdt0(v0, v1) = v7 & sdtasdt0(v7, v7) = v8 & $i(v8) & $i(v7) % 94.36/13.18 | & sdtlseqdt0(v8, v4)) | (aDimensionOf0(v0) = v5 & $i(v5) & ( ~ % 94.36/13.18 | iLess0(v5, all_53_0) | ( ~ (v6 = v5) & aDimensionOf0(v1) = v6 % 94.36/13.18 | & $i(v6)))))) % 94.36/13.18 | % 94.36/13.18 | ALPHA: (79) implies: % 94.36/13.18 | (80) aDimensionOf0(xs) = all_53_0 % 94.36/13.18 | (81) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 94.36/13.18 | ( ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasasdt0(v0, v0) = v2) | ~ % 94.36/13.18 | (sdtasdt0(v2, v3) = v4) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | % 94.36/13.18 | ~ aVector0(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 94.36/13.18 | $i] : ((sdtasasdt0(v0, v1) = v7 & sdtasdt0(v7, v7) = v8 & $i(v8) & % 94.36/13.18 | $i(v7) & sdtlseqdt0(v8, v4)) | (aDimensionOf0(v0) = v5 & $i(v5) % 94.36/13.18 | & ( ~ iLess0(v5, all_53_0) | ( ~ (v6 = v5) & aDimensionOf0(v1) = % 94.36/13.18 | v6 & $i(v6)))))) % 94.36/13.18 | % 94.36/13.18 | GROUND_INST: instantiating (37) with all_43_0, all_51_2, xS, xR, simplifying % 94.36/13.18 | with (53), (70) gives: % 94.36/13.18 | (82) all_51_2 = all_43_0 % 94.36/13.18 | % 94.36/13.18 | GROUND_INST: instantiating (37) with all_43_1, all_51_7, xP, xP, simplifying % 94.36/13.18 | with (54), (71) gives: % 94.36/13.18 | (83) all_51_7 = all_43_1 % 94.36/13.18 | % 94.36/13.19 | GROUND_INST: instantiating (38) with all_41_0, all_51_3, xD, xC, simplifying % 94.36/13.19 | with (49), (76) gives: % 94.36/13.19 | (84) all_51_3 = all_41_0 % 94.36/13.19 | % 94.36/13.19 | GROUND_INST: instantiating (38) with all_41_1, all_51_8, xE, xE, simplifying % 94.36/13.19 | with (50), (77) gives: % 94.36/13.19 | (85) all_51_8 = all_41_1 % 94.36/13.19 | % 94.36/13.19 | GROUND_INST: instantiating (36) with all_39_0, all_48_0, xs, simplifying with % 94.36/13.19 | (47), (63) gives: % 94.36/13.19 | (86) all_48_0 = all_39_0 % 94.36/13.19 | % 94.36/13.19 | GROUND_INST: instantiating (36) with all_35_0, all_48_0, xs, simplifying with % 94.36/13.19 | (44), (63) gives: % 94.36/13.19 | (87) all_48_0 = all_35_0 % 94.36/13.19 | % 94.36/13.19 | GROUND_INST: instantiating (36) with all_48_0, all_53_0, xs, simplifying with % 94.36/13.19 | (63), (80) gives: % 94.36/13.19 | (88) all_53_0 = all_48_0 % 94.36/13.19 | % 94.36/13.19 | GROUND_INST: instantiating (36) with all_33_0, all_53_0, xs, simplifying with % 94.36/13.19 | (42), (80) gives: % 94.36/13.19 | (89) all_53_0 = all_33_0 % 94.36/13.19 | % 94.36/13.19 | COMBINE_EQS: (88), (89) imply: % 94.36/13.19 | (90) all_48_0 = all_33_0 % 94.36/13.19 | % 94.36/13.19 | SIMP: (90) implies: % 94.36/13.19 | (91) all_48_0 = all_33_0 % 94.36/13.19 | % 94.36/13.19 | COMBINE_EQS: (86), (87) imply: % 94.36/13.19 | (92) all_39_0 = all_35_0 % 94.36/13.19 | % 94.36/13.19 | COMBINE_EQS: (86), (91) imply: % 94.36/13.19 | (93) all_39_0 = all_33_0 % 94.36/13.19 | % 94.36/13.19 | COMBINE_EQS: (92), (93) imply: % 94.36/13.19 | (94) all_35_0 = all_33_0 % 94.36/13.19 | % 94.36/13.19 | REDUCE: (45), (94) imply: % 94.36/13.19 | (95) aDimensionOf0(xt) = all_33_0 % 94.36/13.19 | % 94.36/13.19 | REDUCE: (75), (82) imply: % 94.36/13.19 | (96) sdtpldt0(all_43_0, all_51_6) = all_51_1 % 94.36/13.19 | % 94.36/13.19 | REDUCE: (74), (84) imply: % 94.36/13.19 | (97) sdtpldt0(all_41_0, all_51_1) = all_51_0 % 94.36/13.19 | % 94.36/13.19 | REDUCE: (73), (83) imply: % 94.36/13.19 | (98) sdtpldt0(all_43_1, all_51_6) = all_51_5 % 94.36/13.19 | % 94.36/13.19 | REDUCE: (72), (85) imply: % 94.36/13.19 | (99) sdtpldt0(all_41_1, all_51_5) = all_51_4 % 94.36/13.19 | % 94.36/13.19 | REDUCE: (62), (91) imply: % 94.36/13.19 | (100) szszuzczcdt0(all_48_1) = all_33_0 % 94.36/13.19 | % 94.36/13.19 | REDUCE: (69), (82) imply: % 94.36/13.19 | (101) $i(all_43_0) % 94.36/13.19 | % 94.36/13.19 | REDUCE: (68), (84) imply: % 94.36/13.19 | (102) $i(all_41_0) % 94.36/13.19 | % 94.36/13.19 | GROUND_INST: instantiating (mSumSc) with xR, xS, all_43_0, simplifying with % 94.36/13.19 | (22), (25), (32), (34), (53) gives: % 94.36/13.19 | (103) aScalar0(all_43_0) % 94.36/13.19 | % 94.36/13.19 | GROUND_INST: instantiating (mSumSc) with xP, xP, all_43_1, simplifying with % 94.36/13.19 | (23), (33), (54) gives: % 94.36/13.19 | (104) aScalar0(all_43_1) % 94.36/13.19 | % 94.36/13.19 | GROUND_INST: instantiating (mMulSc) with xC, xD, all_41_0, simplifying with % 94.36/13.19 | (13), (15), (28), (29), (49) gives: % 94.36/13.19 | (105) aScalar0(all_41_0) % 94.36/13.19 | % 94.36/13.19 | GROUND_INST: instantiating (mMulSc) with xE, xE, all_41_1, simplifying with % 94.36/13.19 | (17), (30), (50) gives: % 94.36/13.19 | (106) aScalar0(all_41_1) % 94.36/13.19 | % 94.36/13.19 | GROUND_INST: instantiating (mDistr) with xE, xH, xH, xP, xP, all_43_1, % 94.36/13.19 | simplifying with (17), (21), (24), (30), (31), (54) gives: % 94.36/13.19 | (107) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v1, % 94.36/13.19 | xH) = v2 & sdtasdt0(xH, xH) = v3 & sdtasdt0(xE, v0) = all_43_1 & % 94.36/13.19 | sdtpldt0(xP, v3) = v2 & sdtpldt0(xH, xH) = v0 & sdtpldt0(xE, xH) = % 94.36/13.19 | v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_43_1)) % 94.36/13.19 | % 94.36/13.19 | GROUND_INST: instantiating (mMulSc) with xH, xH, all_51_6, simplifying with % 94.36/13.19 | (21), (31), (78) gives: % 94.36/13.19 | (108) aScalar0(all_51_6) % 94.36/13.19 | % 94.36/13.19 | GROUND_INST: instantiating (mDimNat) with xp, all_48_1, simplifying with (18), % 94.36/13.19 | (60), (64) gives: % 94.36/13.19 | (109) aNaturalNumber0(all_48_1) % 94.36/13.19 | % 94.36/13.19 | GROUND_INST: instantiating (1) with xs, xp, simplifying with (3), (10), (65) % 94.36/13.19 | gives: % 94.36/13.19 | (110) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & (v0 = sz00 | ( ! % 94.36/13.19 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlbdtrb0(xs, v2) % 94.36/13.19 | = v3) | ~ (aDimensionOf0(xp) = v1) | ~ $i(v2) | ~ $i(xp) % 94.36/13.19 | | ~ aNaturalNumber0(v2) | (sdtlbdtrb0(xp, v2) = v3 & % 94.36/13.19 | $i(v3))) & ! [v1: $i] : ! [v2: $i] : (v1 = xp | ~ % 94.36/13.19 | (aDimensionOf0(v1) = v2) | ~ $i(v1) | ~ aVector0(v1) | ? % 94.36/13.19 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ($i(v4) % 94.36/13.19 | & (( ~ (v6 = v5) & sdtlbdtrb0(v1, v4) = v5 & sdtlbdtrb0(xs, % 94.36/13.19 | v4) = v6 & $i(v6) & $i(v5) & aNaturalNumber0(v4)) | ( % 94.36/13.19 | ~ (v3 = v0) & szszuzczcdt0(v2) = v3 & $i(v3))))) & ! % 94.36/13.19 | [v1: $i] : ( ~ (aDimensionOf0(xp) = v1) | ~ $i(xp) | % 94.36/13.19 | szszuzczcdt0(v1) = v0) & ! [v1: $i] : ( ~ (aDimensionOf0(xp) % 94.36/13.19 | = v1) | ~ $i(xp) | aVector0(xp))))) % 94.36/13.19 | % 94.36/13.20 | GROUND_INST: instantiating (2) with xs, xt, xp, xq, simplifying with (3), (4), % 94.36/13.20 | (10), (12), (58), (65) gives: % 94.36/13.20 | (111) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ((v3 = v2 & % 94.36/13.20 | aDimensionOf0(xq) = v2 & aDimensionOf0(xp) = v2 & $i(v2)) | % 94.36/13.20 | (aDimensionOf0(xt) = v1 & $i(v1) & (v1 = sz00 | ( ~ (v1 = v0) & % 94.36/13.20 | aDimensionOf0(xs) = v0 & $i(v0))))) % 94.36/13.20 | % 94.36/13.20 | GROUND_INST: instantiating (2) with xt, xs, xq, xp, simplifying with (3), (4), % 94.36/13.20 | (10), (12), (58), (65) gives: % 94.36/13.20 | (112) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ((v3 = v2 & % 94.36/13.20 | aDimensionOf0(xq) = v2 & aDimensionOf0(xp) = v2 & $i(v2)) | % 94.36/13.20 | (aDimensionOf0(xs) = v1 & $i(v1) & (v1 = sz00 | ( ~ (v1 = v0) & % 94.36/13.20 | aDimensionOf0(xt) = v0 & $i(v0))))) % 94.36/13.20 | % 94.36/13.20 | GROUND_INST: instantiating (1) with xt, xq, simplifying with (4), (12), (58) % 94.36/13.20 | gives: % 94.36/13.20 | (113) ? [v0: $i] : (aDimensionOf0(xt) = v0 & $i(v0) & (v0 = sz00 | ( ! % 94.36/13.20 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlbdtrb0(xt, v2) % 94.36/13.20 | = v3) | ~ (aDimensionOf0(xq) = v1) | ~ $i(v2) | ~ $i(xq) % 94.36/13.20 | | ~ aNaturalNumber0(v2) | (sdtlbdtrb0(xq, v2) = v3 & % 94.36/13.20 | $i(v3))) & ! [v1: $i] : ! [v2: $i] : (v1 = xq | ~ % 94.36/13.20 | (aDimensionOf0(v1) = v2) | ~ $i(v1) | ~ aVector0(v1) | ? % 94.36/13.20 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ($i(v4) % 94.36/13.20 | & (( ~ (v6 = v5) & sdtlbdtrb0(v1, v4) = v5 & sdtlbdtrb0(xt, % 94.36/13.20 | v4) = v6 & $i(v6) & $i(v5) & aNaturalNumber0(v4)) | ( % 94.36/13.20 | ~ (v3 = v0) & szszuzczcdt0(v2) = v3 & $i(v3))))) & ! % 94.36/13.20 | [v1: $i] : ( ~ (aDimensionOf0(xq) = v1) | ~ $i(xq) | % 94.36/13.20 | szszuzczcdt0(v1) = v0) & ! [v1: $i] : ( ~ (aDimensionOf0(xq) % 94.36/13.20 | = v1) | ~ $i(xq) | aVector0(xq))))) % 94.36/13.20 | % 94.36/13.20 | GROUND_INST: instantiating (81) with xp, xq, xC, xD, all_41_0, simplifying % 94.36/13.20 | with (14), (16), (18), (19), (49), (56), (60) gives: % 94.36/13.20 | (114) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 94.36/13.20 | ((sdtasasdt0(xp, xq) = v2 & sdtasdt0(v2, v2) = v3 & $i(v3) & $i(v2) & % 94.36/13.20 | sdtlseqdt0(v3, all_41_0)) | (aDimensionOf0(xp) = v0 & $i(v0) & ( % 94.36/13.20 | ~ iLess0(v0, all_53_0) | ( ~ (v1 = v0) & aDimensionOf0(xq) = v1 % 94.36/13.20 | & $i(v1))))) % 94.36/13.20 | % 94.36/13.20 | DELTA: instantiating (112) with fresh symbols all_69_0, all_69_1, all_69_2, % 94.36/13.20 | all_69_3 gives: % 94.36/13.20 | (115) (all_69_0 = all_69_1 & aDimensionOf0(xq) = all_69_1 & % 94.36/13.20 | aDimensionOf0(xp) = all_69_1 & $i(all_69_1)) | (aDimensionOf0(xs) = % 94.36/13.20 | all_69_2 & $i(all_69_2) & (all_69_2 = sz00 | ( ~ (all_69_2 = % 94.36/13.20 | all_69_3) & aDimensionOf0(xt) = all_69_3 & $i(all_69_3)))) % 94.36/13.20 | % 94.36/13.20 | DELTA: instantiating (111) with fresh symbols all_70_0, all_70_1, all_70_2, % 94.36/13.20 | all_70_3 gives: % 94.36/13.20 | (116) (all_70_0 = all_70_1 & aDimensionOf0(xq) = all_70_1 & % 94.36/13.20 | aDimensionOf0(xp) = all_70_1 & $i(all_70_1)) | (aDimensionOf0(xt) = % 94.36/13.20 | all_70_2 & $i(all_70_2) & (all_70_2 = sz00 | ( ~ (all_70_2 = % 94.36/13.20 | all_70_3) & aDimensionOf0(xs) = all_70_3 & $i(all_70_3)))) % 94.36/13.20 | % 94.36/13.20 | DELTA: instantiating (107) with fresh symbols all_71_0, all_71_1, all_71_2, % 94.36/13.20 | all_71_3 gives: % 94.36/13.20 | (117) sdtasdt0(all_71_2, xH) = all_71_1 & sdtasdt0(xH, xH) = all_71_0 & % 94.36/13.20 | sdtasdt0(xE, all_71_3) = all_43_1 & sdtpldt0(xP, all_71_0) = all_71_1 % 94.36/13.20 | & sdtpldt0(xH, xH) = all_71_3 & sdtpldt0(xE, xH) = all_71_2 & % 94.36/13.20 | $i(all_71_0) & $i(all_71_1) & $i(all_71_2) & $i(all_71_3) & % 94.36/13.20 | $i(all_43_1) % 94.36/13.20 | % 94.36/13.20 | ALPHA: (117) implies: % 94.36/13.20 | (118) $i(all_43_1) % 94.36/13.20 | (119) $i(all_71_0) % 94.36/13.20 | (120) sdtasdt0(xH, xH) = all_71_0 % 94.36/13.20 | % 94.36/13.20 | DELTA: instantiating (114) with fresh symbols all_73_0, all_73_1, all_73_2, % 94.36/13.20 | all_73_3 gives: % 94.36/13.20 | (121) (sdtasasdt0(xp, xq) = all_73_1 & sdtasdt0(all_73_1, all_73_1) = % 94.36/13.20 | all_73_0 & $i(all_73_0) & $i(all_73_1) & sdtlseqdt0(all_73_0, % 94.36/13.20 | all_41_0)) | (aDimensionOf0(xp) = all_73_3 & $i(all_73_3) & ( ~ % 94.36/13.20 | iLess0(all_73_3, all_53_0) | ( ~ (all_73_2 = all_73_3) & % 94.36/13.20 | aDimensionOf0(xq) = all_73_2 & $i(all_73_2)))) % 94.36/13.20 | % 94.36/13.20 | DELTA: instantiating (113) with fresh symbol all_74_0 gives: % 94.36/13.20 | (122) aDimensionOf0(xt) = all_74_0 & $i(all_74_0) & (all_74_0 = sz00 | ( ! % 94.36/13.20 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(xt, v1) = % 94.36/13.20 | v2) | ~ (aDimensionOf0(xq) = v0) | ~ $i(v1) | ~ $i(xq) | % 94.36/13.20 | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(xq, v1) = v2 & $i(v2))) & % 94.36/13.20 | ! [v0: $i] : ! [v1: $i] : (v0 = xq | ~ (aDimensionOf0(v0) = v1) % 94.36/13.20 | | ~ $i(v0) | ~ aVector0(v0) | ? [v2: any] : ? [v3: $i] : ? % 94.36/13.20 | [v4: $i] : ? [v5: $i] : ($i(v3) & (( ~ (v5 = v4) & % 94.36/13.20 | sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xt, v3) = v5 & % 94.36/13.20 | $i(v5) & $i(v4) & aNaturalNumber0(v3)) | ( ~ (v2 = % 94.36/13.20 | all_74_0) & szszuzczcdt0(v1) = v2 & $i(v2))))) & ! % 94.36/13.20 | [v0: $i] : ( ~ (aDimensionOf0(xq) = v0) | ~ $i(xq) | % 94.36/13.20 | szszuzczcdt0(v0) = all_74_0) & ! [v0: $i] : ( ~ % 94.36/13.20 | (aDimensionOf0(xq) = v0) | ~ $i(xq) | aVector0(xq)))) % 94.36/13.20 | % 94.36/13.20 | ALPHA: (122) implies: % 94.36/13.20 | (123) aDimensionOf0(xt) = all_74_0 % 94.36/13.20 | % 94.36/13.20 | DELTA: instantiating (110) with fresh symbol all_76_0 gives: % 94.36/13.20 | (124) aDimensionOf0(xs) = all_76_0 & $i(all_76_0) & (all_76_0 = sz00 | ( ! % 94.36/13.20 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(xs, v1) = % 94.36/13.20 | v2) | ~ (aDimensionOf0(xp) = v0) | ~ $i(v1) | ~ $i(xp) | % 94.36/13.20 | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(xp, v1) = v2 & $i(v2))) & % 94.36/13.20 | ! [v0: $i] : ! [v1: $i] : (v0 = xp | ~ (aDimensionOf0(v0) = v1) % 94.36/13.20 | | ~ $i(v0) | ~ aVector0(v0) | ? [v2: any] : ? [v3: $i] : ? % 94.36/13.20 | [v4: $i] : ? [v5: $i] : ($i(v3) & (( ~ (v5 = v4) & % 94.36/13.20 | sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xs, v3) = v5 & % 94.36/13.20 | $i(v5) & $i(v4) & aNaturalNumber0(v3)) | ( ~ (v2 = % 94.36/13.20 | all_76_0) & szszuzczcdt0(v1) = v2 & $i(v2))))) & ! % 94.36/13.20 | [v0: $i] : ( ~ (aDimensionOf0(xp) = v0) | ~ $i(xp) | % 94.36/13.20 | szszuzczcdt0(v0) = all_76_0) & ! [v0: $i] : ( ~ % 94.36/13.20 | (aDimensionOf0(xp) = v0) | ~ $i(xp) | aVector0(xp)))) % 94.36/13.20 | % 94.36/13.20 | ALPHA: (124) implies: % 94.36/13.20 | (125) aDimensionOf0(xs) = all_76_0 % 94.36/13.20 | % 94.36/13.20 | GROUND_INST: instantiating (38) with all_51_6, all_71_0, xH, xH, simplifying % 94.36/13.20 | with (78), (120) gives: % 94.36/13.20 | (126) all_71_0 = all_51_6 % 94.36/13.20 | % 94.36/13.20 | GROUND_INST: instantiating (36) with all_33_0, all_76_0, xs, simplifying with % 94.36/13.20 | (42), (125) gives: % 94.36/13.20 | (127) all_76_0 = all_33_0 % 94.36/13.20 | % 94.36/13.20 | GROUND_INST: instantiating (36) with all_33_0, all_74_0, xt, simplifying with % 94.36/13.20 | (95), (123) gives: % 94.36/13.20 | (128) all_74_0 = all_33_0 % 94.36/13.20 | % 94.36/13.20 | REDUCE: (119), (126) imply: % 94.36/13.20 | (129) $i(all_51_6) % 94.36/13.20 | % 94.36/13.20 | BETA: splitting (116) gives: % 94.36/13.20 | % 94.36/13.20 | Case 1: % 94.36/13.20 | | % 94.36/13.20 | | (130) all_70_0 = all_70_1 & aDimensionOf0(xq) = all_70_1 & % 94.36/13.20 | | aDimensionOf0(xp) = all_70_1 & $i(all_70_1) % 94.36/13.21 | | % 94.36/13.21 | | ALPHA: (130) implies: % 94.36/13.21 | | (131) aDimensionOf0(xp) = all_70_1 % 94.36/13.21 | | (132) aDimensionOf0(xq) = all_70_1 % 94.36/13.21 | | % 94.36/13.21 | | BETA: splitting (115) gives: % 94.36/13.21 | | % 94.36/13.21 | | Case 1: % 94.36/13.21 | | | % 94.36/13.21 | | | (133) all_69_0 = all_69_1 & aDimensionOf0(xq) = all_69_1 & % 94.36/13.21 | | | aDimensionOf0(xp) = all_69_1 & $i(all_69_1) % 94.36/13.21 | | | % 94.36/13.21 | | | ALPHA: (133) implies: % 94.36/13.21 | | | (134) aDimensionOf0(xq) = all_69_1 % 94.36/13.21 | | | % 94.36/13.21 | | | GROUND_INST: instantiating (36) with all_48_1, all_70_1, xp, simplifying % 94.36/13.21 | | | with (64), (131) gives: % 94.36/13.21 | | | (135) all_70_1 = all_48_1 % 94.36/13.21 | | | % 94.36/13.21 | | | GROUND_INST: instantiating (36) with all_45_1, all_70_1, xq, simplifying % 94.36/13.21 | | | with (57), (132) gives: % 94.36/13.21 | | | (136) all_70_1 = all_45_1 % 94.36/13.21 | | | % 94.36/13.21 | | | GROUND_INST: instantiating (36) with all_69_1, all_70_1, xq, simplifying % 94.36/13.21 | | | with (132), (134) gives: % 94.36/13.21 | | | (137) all_70_1 = all_69_1 % 94.36/13.21 | | | % 94.36/13.21 | | | COMBINE_EQS: (135), (137) imply: % 94.36/13.21 | | | (138) all_69_1 = all_48_1 % 94.36/13.21 | | | % 94.36/13.21 | | | COMBINE_EQS: (136), (137) imply: % 94.36/13.21 | | | (139) all_69_1 = all_45_1 % 94.36/13.21 | | | % 94.36/13.21 | | | COMBINE_EQS: (138), (139) imply: % 94.36/13.21 | | | (140) all_48_1 = all_45_1 % 94.36/13.21 | | | % 94.36/13.21 | | | SIMP: (140) implies: % 94.36/13.21 | | | (141) all_48_1 = all_45_1 % 94.36/13.21 | | | % 94.36/13.21 | | | REDUCE: (64), (141) imply: % 94.36/13.21 | | | (142) aDimensionOf0(xp) = all_45_1 % 94.36/13.21 | | | % 94.36/13.21 | | | REDUCE: (100), (141) imply: % 94.36/13.21 | | | (143) szszuzczcdt0(all_45_1) = all_33_0 % 94.36/13.21 | | | % 94.36/13.21 | | | REDUCE: (61), (141) imply: % 94.36/13.21 | | | (144) $i(all_45_1) % 94.36/13.21 | | | % 94.36/13.21 | | | REDUCE: (109), (141) imply: % 94.36/13.21 | | | (145) aNaturalNumber0(all_45_1) % 94.36/13.21 | | | % 94.36/13.21 | | | GROUND_INST: instantiating (mIH) with all_45_1, all_33_0, simplifying with % 94.36/13.21 | | | (143), (144), (145) gives: % 94.36/13.21 | | | (146) iLess0(all_45_1, all_33_0) % 94.36/13.21 | | | % 94.36/13.21 | | | GROUND_INST: instantiating (mArith) with xR, xS, all_51_6, all_43_0, % 94.36/13.21 | | | all_51_1, simplifying with (22), (25), (32), (34), (53), % 94.36/13.21 | | | (96), (108), (129) gives: % 94.36/13.21 | | | (147) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 94.36/13.21 | | | (sdtasdt0(v1, all_51_6) = v2 & sdtasdt0(xS, all_51_6) = v3 & % 94.36/13.21 | | | sdtasdt0(xS, xR) = v1 & sdtasdt0(xR, v3) = v2 & sdtasdt0(xR, % 94.36/13.21 | | | xS) = v1 & sdtpldt0(xS, all_51_6) = v0 & sdtpldt0(xS, xR) = % 94.36/13.21 | | | all_43_0 & sdtpldt0(xR, v0) = all_51_1 & $i(v3) & $i(v2) & % 94.36/13.21 | | | $i(v1) & $i(v0) & $i(all_51_1) & $i(all_43_0)) % 94.36/13.21 | | | % 94.36/13.21 | | | GROUND_INST: instantiating (mSumSc) with all_43_0, all_51_6, all_51_1, % 94.36/13.21 | | | simplifying with (96), (101), (103), (108), (129) gives: % 94.36/13.21 | | | (148) aScalar0(all_51_1) % 94.36/13.21 | | | % 94.36/13.21 | | | GROUND_INST: instantiating (mArith) with xP, xP, all_51_6, all_43_1, % 94.36/13.21 | | | all_51_5, simplifying with (23), (33), (54), (98), (108), % 94.36/13.21 | | | (129) gives: % 94.36/13.21 | | | (149) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 94.36/13.21 | | | (sdtasdt0(v1, all_51_6) = v2 & sdtasdt0(xP, v3) = v2 & % 94.36/13.21 | | | sdtasdt0(xP, all_51_6) = v3 & sdtasdt0(xP, xP) = v1 & % 94.36/13.21 | | | sdtpldt0(xP, v0) = all_51_5 & sdtpldt0(xP, all_51_6) = v0 & % 94.36/13.21 | | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_51_5) & % 94.36/13.21 | | | $i(all_43_1)) % 94.36/13.21 | | | % 94.36/13.21 | | | GROUND_INST: instantiating (mSumSc) with all_43_1, all_51_6, all_51_5, % 94.36/13.21 | | | simplifying with (98), (104), (108), (118), (129) gives: % 94.36/13.21 | | | (150) aScalar0(all_51_5) % 94.36/13.21 | | | % 94.36/13.21 | | | GROUND_INST: instantiating (mLETot) with all_51_6, all_51_6, simplifying % 94.36/13.21 | | | with (108), (129) gives: % 94.36/13.21 | | | (151) sdtlseqdt0(all_51_6, all_51_6) % 94.36/13.21 | | | % 94.36/13.21 | | | DELTA: instantiating (149) with fresh symbols all_111_0, all_111_1, % 94.36/13.21 | | | all_111_2, all_111_3 gives: % 94.36/13.21 | | | (152) sdtasdt0(all_111_2, all_51_6) = all_111_1 & sdtasdt0(xP, % 94.36/13.21 | | | all_111_0) = all_111_1 & sdtasdt0(xP, all_51_6) = all_111_0 & % 94.36/13.21 | | | sdtasdt0(xP, xP) = all_111_2 & sdtpldt0(xP, all_111_3) = all_51_5 % 94.36/13.21 | | | & sdtpldt0(xP, all_51_6) = all_111_3 & $i(all_111_0) & % 94.36/13.21 | | | $i(all_111_1) & $i(all_111_2) & $i(all_111_3) & $i(all_51_5) & % 94.36/13.21 | | | $i(all_43_1) % 94.36/13.21 | | | % 94.36/13.21 | | | ALPHA: (152) implies: % 94.36/13.21 | | | (153) $i(all_51_5) % 94.36/13.21 | | | % 94.36/13.21 | | | DELTA: instantiating (147) with fresh symbols all_113_0, all_113_1, % 94.36/13.21 | | | all_113_2, all_113_3 gives: % 94.36/13.21 | | | (154) sdtasdt0(all_113_2, all_51_6) = all_113_1 & sdtasdt0(xS, % 94.36/13.21 | | | all_51_6) = all_113_0 & sdtasdt0(xS, xR) = all_113_2 & % 94.36/13.21 | | | sdtasdt0(xR, all_113_0) = all_113_1 & sdtasdt0(xR, xS) = % 94.36/13.21 | | | all_113_2 & sdtpldt0(xS, all_51_6) = all_113_3 & sdtpldt0(xS, xR) % 94.36/13.21 | | | = all_43_0 & sdtpldt0(xR, all_113_3) = all_51_1 & $i(all_113_0) & % 94.36/13.21 | | | $i(all_113_1) & $i(all_113_2) & $i(all_113_3) & $i(all_51_1) & % 94.36/13.21 | | | $i(all_43_0) % 94.36/13.21 | | | % 94.36/13.21 | | | ALPHA: (154) implies: % 94.36/13.21 | | | (155) sdtpldt0(xS, xR) = all_43_0 % 94.36/13.21 | | | % 94.36/13.21 | | | BETA: splitting (121) gives: % 94.36/13.21 | | | % 94.36/13.21 | | | Case 1: % 94.36/13.21 | | | | % 94.36/13.21 | | | | (156) sdtasasdt0(xp, xq) = all_73_1 & sdtasdt0(all_73_1, all_73_1) = % 94.36/13.21 | | | | all_73_0 & $i(all_73_0) & $i(all_73_1) & sdtlseqdt0(all_73_0, % 94.36/13.21 | | | | all_41_0) % 94.36/13.21 | | | | % 94.36/13.21 | | | | ALPHA: (156) implies: % 94.36/13.21 | | | | (157) sdtlseqdt0(all_73_0, all_41_0) % 94.36/13.21 | | | | (158) $i(all_73_0) % 94.36/13.21 | | | | (159) sdtasdt0(all_73_1, all_73_1) = all_73_0 % 94.36/13.21 | | | | (160) sdtasasdt0(xp, xq) = all_73_1 % 94.36/13.21 | | | | % 94.36/13.21 | | | | GROUND_INST: instantiating (39) with xE, all_73_1, xq, xp, simplifying % 94.36/13.21 | | | | with (20), (160) gives: % 94.36/13.21 | | | | (161) all_73_1 = xE % 94.36/13.21 | | | | % 94.36/13.21 | | | | REDUCE: (159), (161) imply: % 94.36/13.21 | | | | (162) sdtasdt0(xE, xE) = all_73_0 % 94.36/13.21 | | | | % 94.36/13.21 | | | | GROUND_INST: instantiating (38) with all_41_1, all_73_0, xE, xE, % 94.36/13.21 | | | | simplifying with (50), (162) gives: % 94.36/13.21 | | | | (163) all_73_0 = all_41_1 % 94.36/13.21 | | | | % 94.36/13.21 | | | | REDUCE: (158), (163) imply: % 94.36/13.21 | | | | (164) $i(all_41_1) % 94.36/13.21 | | | | % 94.36/13.21 | | | | REDUCE: (157), (163) imply: % 94.36/13.21 | | | | (165) sdtlseqdt0(all_41_1, all_41_0) % 94.36/13.21 | | | | % 94.36/13.21 | | | | GROUND_INST: instantiating (mLEMon) with all_43_1, all_43_0, all_51_6, % 94.36/13.21 | | | | all_51_6, all_51_5, all_51_1, simplifying with (52), (96), % 94.36/13.21 | | | | (98), (101), (103), (104), (108), (118), (129), (151) % 94.36/13.21 | | | | gives: % 94.36/13.21 | | | | (166) sdtlseqdt0(all_51_5, all_51_1) % 94.36/13.21 | | | | % 94.36/13.21 | | | | GROUND_INST: instantiating (mArith) with xS, xR, all_51_6, all_43_0, % 94.36/13.21 | | | | all_51_1, simplifying with (22), (25), (32), (34), (96), % 94.36/13.21 | | | | (108), (129), (155) gives: % 94.36/13.21 | | | | (167) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 94.36/13.21 | | | | (sdtasdt0(v1, all_51_6) = v2 & sdtasdt0(xS, v3) = v2 & % 94.36/13.21 | | | | sdtasdt0(xS, xR) = v1 & sdtasdt0(xR, all_51_6) = v3 & % 94.36/13.21 | | | | sdtasdt0(xR, xS) = v1 & sdtpldt0(xS, v0) = all_51_1 & % 94.36/13.21 | | | | sdtpldt0(xR, all_51_6) = v0 & sdtpldt0(xR, xS) = all_43_0 & % 94.36/13.21 | | | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_51_1) & % 94.36/13.21 | | | | $i(all_43_0)) % 94.36/13.21 | | | | % 94.36/13.21 | | | | DELTA: instantiating (167) with fresh symbols all_142_0, all_142_1, % 94.36/13.21 | | | | all_142_2, all_142_3 gives: % 94.36/13.22 | | | | (168) sdtasdt0(all_142_2, all_51_6) = all_142_1 & sdtasdt0(xS, % 94.36/13.22 | | | | all_142_0) = all_142_1 & sdtasdt0(xS, xR) = all_142_2 & % 94.36/13.22 | | | | sdtasdt0(xR, all_51_6) = all_142_0 & sdtasdt0(xR, xS) = % 94.36/13.22 | | | | all_142_2 & sdtpldt0(xS, all_142_3) = all_51_1 & sdtpldt0(xR, % 94.36/13.22 | | | | all_51_6) = all_142_3 & sdtpldt0(xR, xS) = all_43_0 & % 94.36/13.22 | | | | $i(all_142_0) & $i(all_142_1) & $i(all_142_2) & $i(all_142_3) & % 94.36/13.22 | | | | $i(all_51_1) & $i(all_43_0) % 94.36/13.22 | | | | % 94.36/13.22 | | | | ALPHA: (168) implies: % 94.36/13.22 | | | | (169) $i(all_51_1) % 94.36/13.22 | | | | % 94.36/13.22 | | | | GROUND_INST: instantiating (mLEMon) with all_41_1, all_41_0, all_51_5, % 94.36/13.22 | | | | all_51_1, all_51_4, all_51_0, simplifying with (67), (97), % 94.36/13.22 | | | | (99), (102), (105), (106), (148), (150), (153), (164), % 94.36/13.22 | | | | (165), (166), (169) gives: % 94.36/13.22 | | | | (170) $false % 94.36/13.22 | | | | % 94.36/13.22 | | | | CLOSE: (170) is inconsistent. % 94.36/13.22 | | | | % 94.36/13.22 | | | Case 2: % 94.36/13.22 | | | | % 94.36/13.22 | | | | (171) aDimensionOf0(xp) = all_73_3 & $i(all_73_3) & ( ~ % 94.36/13.22 | | | | iLess0(all_73_3, all_53_0) | ( ~ (all_73_2 = all_73_3) & % 94.36/13.22 | | | | aDimensionOf0(xq) = all_73_2 & $i(all_73_2))) % 94.36/13.22 | | | | % 94.36/13.22 | | | | ALPHA: (171) implies: % 94.36/13.22 | | | | (172) aDimensionOf0(xp) = all_73_3 % 94.36/13.22 | | | | (173) ~ iLess0(all_73_3, all_53_0) | ( ~ (all_73_2 = all_73_3) & % 94.36/13.22 | | | | aDimensionOf0(xq) = all_73_2 & $i(all_73_2)) % 94.36/13.22 | | | | % 94.36/13.22 | | | | GROUND_INST: instantiating (36) with all_45_1, all_73_3, xp, simplifying % 94.36/13.22 | | | | with (142), (172) gives: % 94.36/13.22 | | | | (174) all_73_3 = all_45_1 % 94.36/13.22 | | | | % 94.36/13.22 | | | | BETA: splitting (173) gives: % 94.36/13.22 | | | | % 94.36/13.22 | | | | Case 1: % 94.36/13.22 | | | | | % 94.36/13.22 | | | | | (175) ~ iLess0(all_73_3, all_53_0) % 94.36/13.22 | | | | | % 94.36/13.22 | | | | | REDUCE: (89), (174), (175) imply: % 94.36/13.22 | | | | | (176) ~ iLess0(all_45_1, all_33_0) % 94.36/13.22 | | | | | % 94.36/13.22 | | | | | PRED_UNIFY: (146), (176) imply: % 94.36/13.22 | | | | | (177) $false % 94.36/13.22 | | | | | % 94.36/13.22 | | | | | CLOSE: (177) is inconsistent. % 94.36/13.22 | | | | | % 94.36/13.22 | | | | Case 2: % 94.36/13.22 | | | | | % 94.36/13.22 | | | | | (178) ~ (all_73_2 = all_73_3) & aDimensionOf0(xq) = all_73_2 & % 94.36/13.22 | | | | | $i(all_73_2) % 94.36/13.22 | | | | | % 94.36/13.22 | | | | | ALPHA: (178) implies: % 94.36/13.22 | | | | | (179) ~ (all_73_2 = all_73_3) % 94.36/13.22 | | | | | (180) aDimensionOf0(xq) = all_73_2 % 94.36/13.22 | | | | | % 94.36/13.22 | | | | | REDUCE: (174), (179) imply: % 94.36/13.22 | | | | | (181) ~ (all_73_2 = all_45_1) % 94.36/13.22 | | | | | % 94.36/13.22 | | | | | GROUND_INST: instantiating (36) with all_45_1, all_73_2, xq, % 94.36/13.22 | | | | | simplifying with (57), (180) gives: % 94.36/13.22 | | | | | (182) all_73_2 = all_45_1 % 94.36/13.22 | | | | | % 94.36/13.22 | | | | | REDUCE: (181), (182) imply: % 94.36/13.22 | | | | | (183) $false % 94.36/13.22 | | | | | % 94.36/13.22 | | | | | CLOSE: (183) is inconsistent. % 94.36/13.22 | | | | | % 94.36/13.22 | | | | End of split % 94.36/13.22 | | | | % 94.36/13.22 | | | End of split % 94.36/13.22 | | | % 94.36/13.22 | | Case 2: % 94.36/13.22 | | | % 94.36/13.22 | | | (184) aDimensionOf0(xs) = all_69_2 & $i(all_69_2) & (all_69_2 = sz00 | % 94.36/13.22 | | | ( ~ (all_69_2 = all_69_3) & aDimensionOf0(xt) = all_69_3 & % 94.36/13.22 | | | $i(all_69_3))) % 94.36/13.22 | | | % 94.36/13.22 | | | ALPHA: (184) implies: % 94.36/13.22 | | | (185) aDimensionOf0(xs) = all_69_2 % 94.36/13.22 | | | (186) all_69_2 = sz00 | ( ~ (all_69_2 = all_69_3) & aDimensionOf0(xt) = % 94.36/13.22 | | | all_69_3 & $i(all_69_3)) % 94.36/13.22 | | | % 94.36/13.22 | | | GROUND_INST: instantiating (36) with all_33_0, all_69_2, xs, simplifying % 94.36/13.22 | | | with (42), (185) gives: % 94.36/13.22 | | | (187) all_69_2 = all_33_0 % 94.36/13.22 | | | % 94.36/13.22 | | | BETA: splitting (186) gives: % 94.36/13.22 | | | % 94.36/13.22 | | | Case 1: % 94.36/13.22 | | | | % 94.36/13.22 | | | | (188) all_69_2 = sz00 % 94.36/13.22 | | | | % 94.36/13.22 | | | | COMBINE_EQS: (187), (188) imply: % 94.36/13.22 | | | | (189) all_33_0 = sz00 % 94.36/13.22 | | | | % 94.36/13.22 | | | | SIMP: (189) implies: % 94.36/13.22 | | | | (190) all_33_0 = sz00 % 94.36/13.22 | | | | % 94.36/13.22 | | | | REDUCE: (41), (190) imply: % 94.36/13.22 | | | | (191) $false % 94.36/13.22 | | | | % 94.36/13.22 | | | | CLOSE: (191) is inconsistent. % 94.36/13.22 | | | | % 94.36/13.22 | | | Case 2: % 94.36/13.22 | | | | % 94.36/13.22 | | | | (192) ~ (all_69_2 = all_69_3) & aDimensionOf0(xt) = all_69_3 & % 94.36/13.22 | | | | $i(all_69_3) % 94.36/13.22 | | | | % 94.36/13.22 | | | | ALPHA: (192) implies: % 94.36/13.22 | | | | (193) ~ (all_69_2 = all_69_3) % 94.36/13.22 | | | | (194) aDimensionOf0(xt) = all_69_3 % 94.36/13.22 | | | | % 94.36/13.22 | | | | REDUCE: (187), (193) imply: % 94.36/13.22 | | | | (195) ~ (all_69_3 = all_33_0) % 94.36/13.22 | | | | % 94.36/13.22 | | | | SIMP: (195) implies: % 94.36/13.22 | | | | (196) ~ (all_69_3 = all_33_0) % 94.36/13.22 | | | | % 94.36/13.22 | | | | GROUND_INST: instantiating (36) with all_33_0, all_69_3, xt, simplifying % 94.36/13.22 | | | | with (95), (194) gives: % 94.36/13.22 | | | | (197) all_69_3 = all_33_0 % 94.36/13.22 | | | | % 94.36/13.22 | | | | REDUCE: (196), (197) imply: % 94.36/13.22 | | | | (198) $false % 94.36/13.22 | | | | % 94.36/13.22 | | | | CLOSE: (198) is inconsistent. % 94.36/13.22 | | | | % 94.36/13.22 | | | End of split % 94.36/13.22 | | | % 94.36/13.22 | | End of split % 94.36/13.22 | | % 94.36/13.22 | Case 2: % 94.36/13.22 | | % 94.36/13.22 | | (199) aDimensionOf0(xt) = all_70_2 & $i(all_70_2) & (all_70_2 = sz00 | ( % 94.36/13.22 | | ~ (all_70_2 = all_70_3) & aDimensionOf0(xs) = all_70_3 & % 94.36/13.22 | | $i(all_70_3))) % 94.36/13.22 | | % 94.36/13.22 | | ALPHA: (199) implies: % 94.36/13.22 | | (200) aDimensionOf0(xt) = all_70_2 % 94.36/13.22 | | (201) all_70_2 = sz00 | ( ~ (all_70_2 = all_70_3) & aDimensionOf0(xs) = % 94.36/13.22 | | all_70_3 & $i(all_70_3)) % 94.36/13.22 | | % 94.36/13.22 | | GROUND_INST: instantiating (36) with all_33_0, all_70_2, xt, simplifying % 94.36/13.22 | | with (95), (200) gives: % 94.36/13.22 | | (202) all_70_2 = all_33_0 % 94.36/13.22 | | % 94.36/13.22 | | BETA: splitting (201) gives: % 94.36/13.22 | | % 94.36/13.22 | | Case 1: % 94.36/13.22 | | | % 94.36/13.22 | | | (203) all_70_2 = sz00 % 94.36/13.22 | | | % 94.36/13.22 | | | COMBINE_EQS: (202), (203) imply: % 94.36/13.22 | | | (204) all_33_0 = sz00 % 94.36/13.22 | | | % 94.36/13.22 | | | SIMP: (204) implies: % 94.36/13.22 | | | (205) all_33_0 = sz00 % 94.36/13.22 | | | % 94.36/13.22 | | | REDUCE: (41), (205) imply: % 94.36/13.22 | | | (206) $false % 94.36/13.22 | | | % 94.36/13.22 | | | CLOSE: (206) is inconsistent. % 94.36/13.22 | | | % 94.36/13.22 | | Case 2: % 94.36/13.22 | | | % 94.36/13.22 | | | (207) ~ (all_70_2 = all_70_3) & aDimensionOf0(xs) = all_70_3 & % 94.36/13.22 | | | $i(all_70_3) % 94.36/13.22 | | | % 94.36/13.22 | | | ALPHA: (207) implies: % 94.36/13.22 | | | (208) ~ (all_70_2 = all_70_3) % 94.36/13.22 | | | (209) aDimensionOf0(xs) = all_70_3 % 94.36/13.22 | | | % 94.36/13.22 | | | REDUCE: (202), (208) imply: % 94.36/13.22 | | | (210) ~ (all_70_3 = all_33_0) % 94.36/13.22 | | | % 94.36/13.22 | | | SIMP: (210) implies: % 94.36/13.22 | | | (211) ~ (all_70_3 = all_33_0) % 94.36/13.22 | | | % 94.36/13.22 | | | GROUND_INST: instantiating (36) with all_33_0, all_70_3, xs, simplifying % 94.36/13.22 | | | with (42), (209) gives: % 94.36/13.22 | | | (212) all_70_3 = all_33_0 % 94.36/13.22 | | | % 94.36/13.22 | | | REDUCE: (211), (212) imply: % 94.36/13.22 | | | (213) $false % 94.36/13.22 | | | % 94.36/13.22 | | | CLOSE: (213) is inconsistent. % 94.36/13.22 | | | % 94.36/13.22 | | End of split % 94.36/13.22 | | % 94.36/13.22 | End of split % 94.36/13.22 | % 94.36/13.22 End of proof % 94.36/13.22 % SZS output end Proof for theBenchmark % 94.36/13.22 % 94.36/13.22 12739ms %------------------------------------------------------------------------------