%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG062+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 : n001.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 13:57:37 EDT 2023 % Result : Theorem 17.43s 3.13s % Output : Proof 38.97s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG062+2 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.32 % Computer : n001.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 300 % 0.12/0.32 % DateTime : Sun Aug 27 02:25:03 EDT 2023 % 0.12/0.32 % CPUTime : % 0.17/0.60 ________ _____ % 0.17/0.60 ___ __ \_________(_)________________________________ % 0.17/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.17/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.17/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.17/0.60 % 0.17/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.17/0.60 (2023-06-19) % 0.17/0.60 % 0.17/0.60 (c) Philipp Rümmer, 2009-2023 % 0.17/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.17/0.60 Amanda Stjerna. % 0.17/0.60 Free software under BSD-3-Clause. % 0.17/0.60 % 0.17/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.17/0.60 % 0.17/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.17/0.62 Running up to 7 provers in parallel. % 0.17/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.17/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.17/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.17/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.17/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.17/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.17/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.76/1.24 Prover 4: Preprocessing ... % 3.76/1.25 Prover 1: Preprocessing ... % 3.93/1.28 Prover 5: Preprocessing ... % 3.93/1.28 Prover 2: Preprocessing ... % 3.93/1.28 Prover 6: Preprocessing ... % 3.93/1.28 Prover 0: Preprocessing ... % 3.93/1.28 Prover 3: Preprocessing ... % 8.64/2.05 Prover 3: Constructing countermodel ... % 8.64/2.05 Prover 1: Constructing countermodel ... % 9.16/2.07 Prover 6: Proving ... % 11.15/2.27 Prover 5: Constructing countermodel ... % 11.89/2.39 Prover 2: Proving ... % 12.20/2.41 Prover 4: Constructing countermodel ... % 12.20/2.43 Prover 0: Proving ... % 17.43/3.12 Prover 3: proved (2499ms) % 17.43/3.13 % 17.43/3.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 17.43/3.13 % 17.43/3.13 Prover 5: stopped % 17.43/3.14 Prover 6: stopped % 17.43/3.15 Prover 2: stopped % 17.43/3.15 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 17.43/3.15 Prover 0: stopped % 17.43/3.15 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 17.43/3.15 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 17.43/3.15 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 17.43/3.15 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 18.38/3.26 Prover 7: Preprocessing ... % 18.38/3.28 Prover 10: Preprocessing ... % 18.38/3.29 Prover 11: Preprocessing ... % 18.38/3.31 Prover 13: Preprocessing ... % 18.38/3.31 Prover 8: Preprocessing ... % 18.38/3.43 Prover 10: Constructing countermodel ... % 18.38/3.44 Prover 8: Warning: ignoring some quantifiers % 18.38/3.46 Prover 8: Constructing countermodel ... % 18.38/3.50 Prover 7: Constructing countermodel ... % 19.54/3.51 Prover 13: Constructing countermodel ... % 21.88/3.71 Prover 11: Constructing countermodel ... % 38.02/5.81 Prover 10: Found proof (size 269) % 38.02/5.81 Prover 10: proved (2664ms) % 38.02/5.81 Prover 13: stopped % 38.02/5.81 Prover 4: stopped % 38.02/5.81 Prover 11: stopped % 38.02/5.81 Prover 7: stopped % 38.02/5.81 Prover 8: stopped % 38.02/5.81 Prover 1: stopped % 38.02/5.82 % 38.02/5.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 38.02/5.82 % 38.45/5.87 % SZS output start Proof for theBenchmark % 38.45/5.87 Assumptions after simplification: % 38.45/5.87 --------------------------------- % 38.45/5.87 % 38.45/5.87 (mArith) % 38.45/5.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 38.45/5.90 (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 38.45/5.90 | ~ $i(v0) | ~ aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v5: % 38.45/5.90 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(v6, v2) = v7 & % 38.45/5.90 sdtasdt0(v1, v2) = v8 & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v8) = v7 & % 38.45/5.90 sdtasdt0(v0, v1) = v6 & sdtpldt0(v1, v2) = v5 & sdtpldt0(v1, v0) = v3 & % 38.45/5.90 sdtpldt0(v0, v5) = v4 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 38.45/5.90 $i(v3))) % 38.45/5.90 % 38.45/5.90 (mDefInit) % 38.45/5.90 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sziznziztdt0(v0) = v1) | ~ $i(v0) % 38.45/5.90 | ~ aVector0(v0) | ? [v2: $i] : (aDimensionOf0(v0) = v2 & $i(v2) & (v2 = % 38.45/5.90 sz00 | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtlbdtrb0(v0, % 38.45/5.90 v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~ $i(v4) | ~ $i(v1) % 38.45/5.90 | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1, v4) = v5 & $i(v5))) & ! % 38.45/5.90 [v3: $i] : ! [v4: $i] : (v3 = v1 | ~ (aDimensionOf0(v3) = v4) | ~ % 38.45/5.90 $i(v3) | ~ aVector0(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 38.45/5.90 ? [v8: $i] : ($i(v6) & (( ~ (v8 = v7) & sdtlbdtrb0(v3, v6) = v7 & % 38.45/5.90 sdtlbdtrb0(v0, v6) = v8 & $i(v8) & $i(v7) & % 38.45/5.90 aNaturalNumber0(v6)) | ( ~ (v5 = v2) & szszuzczcdt0(v4) = v5 & % 38.45/5.90 $i(v5))))) & ! [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~ % 38.45/5.90 $i(v1) | szszuzczcdt0(v3) = v2) & ! [v3: $i] : ( ~ % 38.45/5.90 (aDimensionOf0(v1) = v3) | ~ $i(v1) | aVector0(v1)))))) % 38.45/5.90 % 38.45/5.90 (mDistr) % 38.45/5.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 38.45/5.91 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ % 38.45/5.91 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 38.45/5.91 aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v6: $i] : ? [v7: $i] % 38.45/5.91 : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v7, v2) = v8 & sdtasdt0(v1, v2) = v9 % 38.45/5.91 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v4, v9) = v8 & sdtpldt0(v1, v2) = v6 & % 38.45/5.91 sdtpldt0(v0, v1) = v7 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5))) % 38.45/5.91 % 38.45/5.91 (mDistr2) % 38.45/5.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 38.45/5.91 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : % 38.45/5.91 ( ~ (sdtasdt0(v1, v3) = v8) | ~ (sdtasdt0(v1, v2) = v7) | ~ (sdtasdt0(v0, % 38.45/5.91 v3) = v5) | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtpldt0(v7, v8) = v9) | ~ % 38.45/5.91 (sdtpldt0(v6, v9) = v10) | ~ (sdtpldt0(v4, v5) = v6) | ~ $i(v3) | ~ % 38.45/5.91 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aScalar0(v3) | ~ aScalar0(v2) | ~ % 38.45/5.91 aScalar0(v1) | ~ aScalar0(v0) | ? [v11: $i] : ? [v12: $i] : % 38.45/5.91 (sdtasdt0(v11, v12) = v10 & sdtpldt0(v2, v3) = v12 & sdtpldt0(v0, v1) = v11 % 38.45/5.91 & $i(v12) & $i(v11) & $i(v10))) % 38.45/5.91 % 38.45/5.91 (mMNeg) % 38.45/5.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (smndt0(v0) = v2) % 38.45/5.91 | ~ (sdtasdt0(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ % 38.45/5.91 aScalar0(v0) | ? [v4: $i] : ? [v5: $i] : (smndt0(v5) = v3 & smndt0(v1) = % 38.45/5.91 v4 & sdtasdt0(v0, v4) = v3 & sdtasdt0(v0, v1) = v5 & $i(v5) & $i(v4) & % 38.45/5.91 $i(v3))) % 38.45/5.91 % 38.45/5.91 (mMulSc) % 38.45/5.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 38.45/5.91 $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | aScalar0(v2)) % 38.45/5.91 % 38.45/5.91 (mNegSc) % 38.45/5.91 ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ~ % 38.45/5.91 aScalar0(v0) | aScalar0(v1)) % 38.45/5.91 % 38.45/5.91 (mSumSc) % 38.45/5.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 38.45/5.91 $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | aScalar0(v2)) % 38.45/5.91 % 38.45/5.91 (m__) % 38.45/5.91 $i(xN) & $i(xS) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 38.45/5.91 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 38.45/5.91 ( ~ (v8 = v2) & smndt0(xN) = v6 & smndt0(xS) = v0 & sdtasdt0(v1, v1) = v2 & % 38.45/5.91 sdtasdt0(xS, xS) = v4 & sdtasdt0(xR, xR) = v3 & sdtpldt0(v7, v6) = v8 & % 38.45/5.91 sdtpldt0(v5, v6) = v7 & sdtpldt0(v3, v4) = v5 & sdtpldt0(xR, v0) = v1 & % 38.45/5.91 $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 38.45/5.91 $i(v0)) % 38.45/5.91 % 38.45/5.91 (m__1652) % 38.74/5.92 $i(xs) & ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : ! % 38.74/5.92 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2, v2) % 38.74/5.92 = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4) = v5) | ~ % 38.74/5.92 $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1) | ? [v6: $i] : ? % 38.74/5.92 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ((sdtasasdt0(v1, v2) = v8 & % 38.74/5.92 sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8) & sdtlseqdt0(v9, v5)) | % 38.74/5.92 (aDimensionOf0(v1) = v6 & $i(v6) & ( ~ iLess0(v6, v0) | ( ~ (v7 = v6) & % 38.74/5.92 aDimensionOf0(v2) = v7 & $i(v7))))))) % 38.74/5.92 % 38.74/5.92 (m__1678) % 38.74/5.92 $i(xt) & $i(xs) & aVector0(xt) & aVector0(xs) % 38.74/5.92 % 38.74/5.92 (m__1678_01) % 38.74/5.92 $i(xt) & $i(xs) & ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) = % 38.74/5.92 v0 & $i(v0)) % 38.74/5.92 % 38.74/5.92 (m__1692) % 38.74/5.92 $i(xs) & $i(sz00) & ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 & % 38.74/5.92 $i(v0)) % 38.74/5.92 % 38.74/5.92 (m__1709) % 38.74/5.92 $i(xp) & $i(xs) & ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xs) = xp & % 38.74/5.92 aDimensionOf0(xp) = v0 & aDimensionOf0(xs) = v1 & szszuzczcdt0(v0) = v1 & % 38.74/5.92 $i(v1) & $i(v0) & aVector0(xp) & ! [v2: $i] : ! [v3: $i] : ( ~ % 38.74/5.92 (sdtlbdtrb0(xp, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) | % 38.74/5.92 (sdtlbdtrb0(xs, v2) = v3 & $i(v3)))) % 38.74/5.92 % 38.74/5.92 (m__1726) % 38.74/5.92 $i(xq) & $i(xt) & ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xt) = xq & % 38.74/5.92 aDimensionOf0(xq) = v0 & aDimensionOf0(xt) = v1 & szszuzczcdt0(v0) = v1 & % 38.74/5.92 $i(v1) & $i(v0) & aVector0(xq) & ! [v2: $i] : ! [v3: $i] : ( ~ % 38.74/5.92 (sdtlbdtrb0(xt, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) | % 38.74/5.92 (sdtlbdtrb0(xq, v2) = v3 & $i(v3)))) % 38.74/5.92 % 38.74/5.92 (m__1746) % 38.74/5.92 $i(xA) & $i(xs) & ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) = % 38.74/5.92 v0 & $i(v0) & aScalar0(xA)) % 38.74/5.92 % 38.74/5.92 (m__1766) % 38.74/5.92 $i(xB) & $i(xt) & ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) = % 38.74/5.92 v0 & $i(v0) & aScalar0(xB)) % 38.74/5.92 % 38.74/5.92 (m__1892) % 38.74/5.92 sdtasdt0(xC, xG) = xR & $i(xR) & $i(xG) & $i(xC) & aScalar0(xR) % 38.74/5.92 % 38.74/5.92 (m__1930) % 38.74/5.92 sdtasdt0(xF, xD) = xS & $i(xS) & $i(xF) & $i(xD) & aScalar0(xS) % 38.74/5.92 % 38.74/5.92 (m__1949) % 38.74/5.92 sdtasdt0(xR, xS) = xN & $i(xN) & $i(xS) & $i(xR) & aScalar0(xN) % 38.74/5.92 % 38.74/5.92 (m__2144) % 38.74/5.92 $i(xN) & $i(xS) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 38.74/5.92 (smndt0(xN) = v1 & smndt0(xS) = v0 & sdtasdt0(v0, v0) = v2 & sdtasdt0(v0, xR) % 38.74/5.92 = v1 & sdtasdt0(xS, xS) = v2 & sdtasdt0(xR, v0) = v1 & $i(v2) & $i(v1) & % 38.74/5.92 $i(v0)) % 38.74/5.92 % 38.74/5.92 (m__2180) % 38.74/5.93 $i(xN) & $i(xS) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 38.74/5.93 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (smndt0(xN) = % 38.74/5.93 v4 & smndt0(xS) = v0 & sdtasdt0(v1, v1) = v2 & sdtasdt0(xS, xS) = v6 & % 38.74/5.93 sdtasdt0(xR, xR) = v3 & sdtpldt0(v5, v7) = v2 & sdtpldt0(v4, v6) = v7 & % 38.74/5.93 sdtpldt0(v3, v4) = v5 & sdtpldt0(xR, v0) = v1 & $i(v7) & $i(v6) & $i(v5) & % 38.74/5.93 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 38.74/5.93 % 38.74/5.93 (m__2221) % 38.74/5.93 $i(xN) & $i(xS) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 38.74/5.93 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (smndt0(xN) = % 38.74/5.93 v4 & smndt0(xS) = v0 & sdtasdt0(v1, v1) = v2 & sdtasdt0(xS, xS) = v6 & % 38.74/5.93 sdtasdt0(xR, xR) = v3 & sdtpldt0(v6, v4) = v7 & sdtpldt0(v5, v7) = v2 & % 38.74/5.93 sdtpldt0(v3, v4) = v5 & sdtpldt0(xR, v0) = v1 & $i(v7) & $i(v6) & $i(v5) & % 38.74/5.93 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 38.74/5.93 % 38.74/5.93 (function-axioms) % 38.74/5.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 38.74/5.93 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 38.74/5.93 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) % 38.74/5.93 | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 38.74/5.93 ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = % 38.74/5.93 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 38.74/5.93 ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 38.74/5.93 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sziznziztdt0(v2) = v1) | ~ % 38.74/5.93 (sziznziztdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 38.74/5.93 v0 | ~ (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) & ! [v0: % 38.74/5.93 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ % 38.74/5.93 (smndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 38.74/5.93 (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0)) % 38.74/5.93 % 38.74/5.93 Further assumptions not needed in the proof: % 38.74/5.93 -------------------------------------------- % 38.74/5.93 mDefSPN, mDefSPZ, mDimNat, mElmSc, mEqInit, mIH, mIHOrd, mLEASm, mLEMon, % 38.74/5.93 mLEMonM, mLERef, mLETot, mLETrn, mLess, mMDNeg, mNatExtr, mNatSort, mPosMon, % 38.74/5.93 mSZeroSc, mScPr, mScSort, mScSqPos, mScZero, mSqPos, mSqrt, mSuccEqu, mSuccNat, % 38.74/5.93 mVcSort, mZeroNat, m__1783, m__1800, m__1820, m__1837, m__1854, m__1873, % 38.74/5.93 m__1911, m__1967, m__2004 % 38.74/5.93 % 38.74/5.93 Those formulas are unsatisfiable: % 38.74/5.93 --------------------------------- % 38.74/5.93 % 38.74/5.93 Begin of proof % 38.74/5.93 | % 38.74/5.93 | ALPHA: (mDefInit) implies: % 38.74/5.94 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (sziznziztdt0(v0) = v1) | ~ $i(v0) | % 38.74/5.94 | ~ aVector0(v0) | ? [v2: $i] : (aDimensionOf0(v0) = v2 & $i(v2) & (v2 % 38.74/5.94 | = sz00 | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 38.74/5.94 | (sdtlbdtrb0(v0, v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~ % 38.74/5.94 | $i(v4) | ~ $i(v1) | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1, % 38.74/5.94 | v4) = v5 & $i(v5))) & ! [v3: $i] : ! [v4: $i] : (v3 = % 38.74/5.94 | v1 | ~ (aDimensionOf0(v3) = v4) | ~ $i(v3) | ~ % 38.74/5.94 | aVector0(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? % 38.74/5.94 | [v8: $i] : ($i(v6) & (( ~ (v8 = v7) & sdtlbdtrb0(v3, v6) = v7 % 38.74/5.94 | & sdtlbdtrb0(v0, v6) = v8 & $i(v8) & $i(v7) & % 38.74/5.94 | aNaturalNumber0(v6)) | ( ~ (v5 = v2) & szszuzczcdt0(v4) % 38.74/5.94 | = v5 & $i(v5))))) & ! [v3: $i] : ( ~ % 38.74/5.94 | (aDimensionOf0(v1) = v3) | ~ $i(v1) | szszuzczcdt0(v3) = v2) % 38.74/5.94 | & ! [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~ $i(v1) | % 38.74/5.94 | aVector0(v1)))))) % 38.74/5.94 | % 38.74/5.94 | ALPHA: (m__1678) implies: % 38.74/5.94 | (2) aVector0(xt) % 38.74/5.94 | % 38.74/5.94 | ALPHA: (m__1652) implies: % 38.74/5.94 | (3) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 38.74/5.94 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2, % 38.74/5.94 | v2) = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4) % 38.74/5.94 | = v5) | ~ $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1) % 38.74/5.94 | | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 38.74/5.94 | ((sdtasasdt0(v1, v2) = v8 & sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8) % 38.74/5.94 | & sdtlseqdt0(v9, v5)) | (aDimensionOf0(v1) = v6 & $i(v6) & ( ~ % 38.74/5.94 | iLess0(v6, v0) | ( ~ (v7 = v6) & aDimensionOf0(v2) = v7 & % 38.74/5.94 | $i(v7))))))) % 38.74/5.94 | % 38.74/5.94 | ALPHA: (m__1678_01) implies: % 38.74/5.94 | (4) ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) = v0 & % 38.74/5.94 | $i(v0)) % 38.74/5.94 | % 38.74/5.94 | ALPHA: (m__1692) implies: % 38.74/5.94 | (5) ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 & $i(v0)) % 38.74/5.94 | % 38.74/5.94 | ALPHA: (m__1709) implies: % 38.74/5.94 | (6) ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xs) = xp & aDimensionOf0(xp) % 38.74/5.94 | = v0 & aDimensionOf0(xs) = v1 & szszuzczcdt0(v0) = v1 & $i(v1) & % 38.74/5.94 | $i(v0) & aVector0(xp) & ! [v2: $i] : ! [v3: $i] : ( ~ % 38.74/5.94 | (sdtlbdtrb0(xp, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) | % 38.74/5.94 | (sdtlbdtrb0(xs, v2) = v3 & $i(v3)))) % 38.74/5.94 | % 38.74/5.94 | ALPHA: (m__1726) implies: % 38.74/5.94 | (7) ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xt) = xq & aDimensionOf0(xq) % 38.74/5.94 | = v0 & aDimensionOf0(xt) = v1 & szszuzczcdt0(v0) = v1 & $i(v1) & % 38.74/5.94 | $i(v0) & aVector0(xq) & ! [v2: $i] : ! [v3: $i] : ( ~ % 38.74/5.94 | (sdtlbdtrb0(xt, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) | % 38.74/5.94 | (sdtlbdtrb0(xq, v2) = v3 & $i(v3)))) % 38.74/5.94 | % 38.74/5.94 | ALPHA: (m__1746) implies: % 38.74/5.94 | (8) ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) = v0 & % 38.74/5.94 | $i(v0) & aScalar0(xA)) % 38.74/5.94 | % 38.74/5.94 | ALPHA: (m__1766) implies: % 38.74/5.94 | (9) $i(xt) % 38.74/5.94 | (10) ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) = v0 & % 38.74/5.94 | $i(v0) & aScalar0(xB)) % 38.74/5.94 | % 38.74/5.94 | ALPHA: (m__1892) implies: % 38.74/5.94 | (11) aScalar0(xR) % 38.74/5.94 | % 38.74/5.94 | ALPHA: (m__1930) implies: % 38.74/5.94 | (12) aScalar0(xS) % 38.74/5.94 | % 38.74/5.94 | ALPHA: (m__1949) implies: % 38.74/5.94 | (13) aScalar0(xN) % 38.74/5.94 | % 38.74/5.94 | ALPHA: (m__2144) implies: % 38.74/5.95 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (smndt0(xN) = v1 & % 38.74/5.95 | smndt0(xS) = v0 & sdtasdt0(v0, v0) = v2 & sdtasdt0(v0, xR) = v1 & % 38.74/5.95 | sdtasdt0(xS, xS) = v2 & sdtasdt0(xR, v0) = v1 & $i(v2) & $i(v1) & % 38.74/5.95 | $i(v0)) % 38.74/5.95 | % 38.74/5.95 | ALPHA: (m__2180) implies: % 38.74/5.95 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 38.74/5.95 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (smndt0(xN) = v4 & smndt0(xS) % 38.74/5.95 | = v0 & sdtasdt0(v1, v1) = v2 & sdtasdt0(xS, xS) = v6 & sdtasdt0(xR, % 38.74/5.95 | xR) = v3 & sdtpldt0(v5, v7) = v2 & sdtpldt0(v4, v6) = v7 & % 38.74/5.95 | sdtpldt0(v3, v4) = v5 & sdtpldt0(xR, v0) = v1 & $i(v7) & $i(v6) & % 38.74/5.95 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 38.74/5.95 | % 38.74/5.95 | ALPHA: (m__2221) implies: % 38.74/5.95 | (16) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 38.74/5.95 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (smndt0(xN) = v4 & smndt0(xS) % 38.74/5.95 | = v0 & sdtasdt0(v1, v1) = v2 & sdtasdt0(xS, xS) = v6 & sdtasdt0(xR, % 38.74/5.95 | xR) = v3 & sdtpldt0(v6, v4) = v7 & sdtpldt0(v5, v7) = v2 & % 38.74/5.95 | sdtpldt0(v3, v4) = v5 & sdtpldt0(xR, v0) = v1 & $i(v7) & $i(v6) & % 38.74/5.95 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 38.74/5.95 | % 38.74/5.95 | ALPHA: (m__) implies: % 38.74/5.95 | (17) $i(xR) % 38.74/5.95 | (18) $i(xS) % 38.74/5.95 | (19) $i(xN) % 38.74/5.95 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 38.74/5.95 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ( ~ (v8 = v2) & % 38.74/5.95 | smndt0(xN) = v6 & smndt0(xS) = v0 & sdtasdt0(v1, v1) = v2 & % 38.74/5.95 | sdtasdt0(xS, xS) = v4 & sdtasdt0(xR, xR) = v3 & sdtpldt0(v7, v6) = % 38.74/5.95 | v8 & sdtpldt0(v5, v6) = v7 & sdtpldt0(v3, v4) = v5 & sdtpldt0(xR, % 38.74/5.95 | v0) = v1 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 38.74/5.95 | $i(v2) & $i(v1) & $i(v0)) % 38.74/5.95 | % 38.74/5.95 | ALPHA: (function-axioms) implies: % 38.74/5.95 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = % 38.74/5.95 | v1) | ~ (smndt0(v2) = v0)) % 38.74/5.95 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 38.74/5.95 | (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) % 38.74/5.95 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 38.74/5.95 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 38.74/5.95 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 38.74/5.95 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 38.74/5.95 | % 38.74/5.95 | DELTA: instantiating (4) with fresh symbol all_33_0 gives: % 38.74/5.95 | (25) aDimensionOf0(xt) = all_33_0 & aDimensionOf0(xs) = all_33_0 & % 38.74/5.95 | $i(all_33_0) % 38.74/5.95 | % 38.74/5.95 | ALPHA: (25) implies: % 38.74/5.95 | (26) aDimensionOf0(xs) = all_33_0 % 38.74/5.95 | (27) aDimensionOf0(xt) = all_33_0 % 38.74/5.95 | % 38.74/5.95 | DELTA: instantiating (5) with fresh symbol all_37_0 gives: % 38.74/5.95 | (28) ~ (all_37_0 = sz00) & aDimensionOf0(xs) = all_37_0 & $i(all_37_0) % 38.74/5.95 | % 38.74/5.95 | ALPHA: (28) implies: % 38.74/5.95 | (29) ~ (all_37_0 = sz00) % 38.74/5.95 | (30) aDimensionOf0(xs) = all_37_0 % 38.74/5.95 | % 38.74/5.95 | DELTA: instantiating (10) with fresh symbol all_39_0 gives: % 38.74/5.95 | (31) sdtlbdtrb0(xt, all_39_0) = xB & aDimensionOf0(xt) = all_39_0 & % 38.74/5.95 | $i(all_39_0) & aScalar0(xB) % 38.74/5.95 | % 38.74/5.95 | ALPHA: (31) implies: % 38.74/5.95 | (32) aDimensionOf0(xt) = all_39_0 % 38.74/5.95 | % 38.74/5.95 | DELTA: instantiating (8) with fresh symbol all_41_0 gives: % 38.74/5.95 | (33) sdtlbdtrb0(xs, all_41_0) = xA & aDimensionOf0(xs) = all_41_0 & % 38.74/5.96 | $i(all_41_0) & aScalar0(xA) % 38.74/5.96 | % 38.74/5.96 | ALPHA: (33) implies: % 38.74/5.96 | (34) aDimensionOf0(xs) = all_41_0 % 38.74/5.96 | % 38.74/5.96 | DELTA: instantiating (14) with fresh symbols all_45_0, all_45_1, all_45_2 % 38.74/5.96 | gives: % 38.74/5.96 | (35) smndt0(xN) = all_45_1 & smndt0(xS) = all_45_2 & sdtasdt0(all_45_2, % 38.74/5.96 | all_45_2) = all_45_0 & sdtasdt0(all_45_2, xR) = all_45_1 & % 38.74/5.96 | sdtasdt0(xS, xS) = all_45_0 & sdtasdt0(xR, all_45_2) = all_45_1 & % 38.74/5.96 | $i(all_45_0) & $i(all_45_1) & $i(all_45_2) % 38.74/5.96 | % 38.74/5.96 | ALPHA: (35) implies: % 38.74/5.96 | (36) sdtasdt0(xR, all_45_2) = all_45_1 % 38.74/5.96 | (37) sdtasdt0(xS, xS) = all_45_0 % 38.74/5.96 | (38) sdtasdt0(all_45_2, xR) = all_45_1 % 38.74/5.96 | (39) sdtasdt0(all_45_2, all_45_2) = all_45_0 % 38.74/5.96 | (40) smndt0(xS) = all_45_2 % 38.74/5.96 | (41) smndt0(xN) = all_45_1 % 38.74/5.96 | % 38.74/5.96 | DELTA: instantiating (7) with fresh symbols all_47_0, all_47_1 gives: % 38.74/5.96 | (42) sziznziztdt0(xt) = xq & aDimensionOf0(xq) = all_47_1 & % 38.74/5.96 | aDimensionOf0(xt) = all_47_0 & szszuzczcdt0(all_47_1) = all_47_0 & % 38.74/5.96 | $i(all_47_0) & $i(all_47_1) & aVector0(xq) & ! [v0: $i] : ! [v1: $i] % 38.74/5.96 | : ( ~ (sdtlbdtrb0(xt, v0) = v1) | ~ $i(v0) | ~ aNaturalNumber0(v0) | % 38.74/5.96 | (sdtlbdtrb0(xq, v0) = v1 & $i(v1))) % 38.74/5.96 | % 38.74/5.96 | ALPHA: (42) implies: % 38.74/5.96 | (43) aDimensionOf0(xt) = all_47_0 % 38.74/5.96 | (44) sziznziztdt0(xt) = xq % 38.74/5.96 | % 38.74/5.96 | DELTA: instantiating (6) with fresh symbols all_50_0, all_50_1 gives: % 38.74/5.96 | (45) sziznziztdt0(xs) = xp & aDimensionOf0(xp) = all_50_1 & % 38.74/5.96 | aDimensionOf0(xs) = all_50_0 & szszuzczcdt0(all_50_1) = all_50_0 & % 38.74/5.96 | $i(all_50_0) & $i(all_50_1) & aVector0(xp) & ! [v0: $i] : ! [v1: $i] % 38.74/5.96 | : ( ~ (sdtlbdtrb0(xp, v0) = v1) | ~ $i(v0) | ~ aNaturalNumber0(v0) | % 38.74/5.96 | (sdtlbdtrb0(xs, v0) = v1 & $i(v1))) % 38.74/5.96 | % 38.74/5.96 | ALPHA: (45) implies: % 38.74/5.96 | (46) aDimensionOf0(xs) = all_50_0 % 38.74/5.96 | % 38.74/5.96 | DELTA: instantiating (15) with fresh symbols all_53_0, all_53_1, all_53_2, % 38.74/5.96 | all_53_3, all_53_4, all_53_5, all_53_6, all_53_7 gives: % 38.74/5.96 | (47) smndt0(xN) = all_53_3 & smndt0(xS) = all_53_7 & sdtasdt0(all_53_6, % 38.74/5.96 | all_53_6) = all_53_5 & sdtasdt0(xS, xS) = all_53_1 & sdtasdt0(xR, % 38.74/5.96 | xR) = all_53_4 & sdtpldt0(all_53_2, all_53_0) = all_53_5 & % 38.74/5.96 | sdtpldt0(all_53_3, all_53_1) = all_53_0 & sdtpldt0(all_53_4, all_53_3) % 38.74/5.96 | = all_53_2 & sdtpldt0(xR, all_53_7) = all_53_6 & $i(all_53_0) & % 38.74/5.96 | $i(all_53_1) & $i(all_53_2) & $i(all_53_3) & $i(all_53_4) & % 38.74/5.96 | $i(all_53_5) & $i(all_53_6) & $i(all_53_7) % 38.74/5.96 | % 38.74/5.96 | ALPHA: (47) implies: % 38.74/5.96 | (48) $i(all_53_7) % 38.74/5.96 | (49) $i(all_53_1) % 38.74/5.96 | (50) sdtpldt0(xR, all_53_7) = all_53_6 % 38.74/5.96 | (51) sdtpldt0(all_53_4, all_53_3) = all_53_2 % 38.74/5.96 | (52) sdtpldt0(all_53_3, all_53_1) = all_53_0 % 38.74/5.96 | (53) sdtpldt0(all_53_2, all_53_0) = all_53_5 % 38.97/5.96 | (54) sdtasdt0(xR, xR) = all_53_4 % 38.97/5.96 | (55) sdtasdt0(xS, xS) = all_53_1 % 38.97/5.96 | (56) sdtasdt0(all_53_6, all_53_6) = all_53_5 % 38.97/5.96 | (57) smndt0(xS) = all_53_7 % 38.97/5.96 | (58) smndt0(xN) = all_53_3 % 38.97/5.96 | % 38.97/5.96 | DELTA: instantiating (16) with fresh symbols all_55_0, all_55_1, all_55_2, % 38.97/5.96 | all_55_3, all_55_4, all_55_5, all_55_6, all_55_7 gives: % 38.97/5.96 | (59) smndt0(xN) = all_55_3 & smndt0(xS) = all_55_7 & sdtasdt0(all_55_6, % 38.97/5.96 | all_55_6) = all_55_5 & sdtasdt0(xS, xS) = all_55_1 & sdtasdt0(xR, % 38.97/5.96 | xR) = all_55_4 & sdtpldt0(all_55_1, all_55_3) = all_55_0 & % 38.97/5.96 | sdtpldt0(all_55_2, all_55_0) = all_55_5 & sdtpldt0(all_55_4, all_55_3) % 38.97/5.96 | = all_55_2 & sdtpldt0(xR, all_55_7) = all_55_6 & $i(all_55_0) & % 38.97/5.96 | $i(all_55_1) & $i(all_55_2) & $i(all_55_3) & $i(all_55_4) & % 38.97/5.96 | $i(all_55_5) & $i(all_55_6) & $i(all_55_7) % 38.97/5.96 | % 38.97/5.96 | ALPHA: (59) implies: % 38.97/5.96 | (60) $i(all_55_4) % 38.97/5.96 | (61) sdtpldt0(xR, all_55_7) = all_55_6 % 38.97/5.96 | (62) sdtpldt0(all_55_4, all_55_3) = all_55_2 % 38.97/5.96 | (63) sdtpldt0(all_55_2, all_55_0) = all_55_5 % 38.97/5.96 | (64) sdtpldt0(all_55_1, all_55_3) = all_55_0 % 38.97/5.96 | (65) sdtasdt0(xR, xR) = all_55_4 % 38.97/5.96 | (66) sdtasdt0(xS, xS) = all_55_1 % 38.97/5.96 | (67) sdtasdt0(all_55_6, all_55_6) = all_55_5 % 38.97/5.96 | (68) smndt0(xS) = all_55_7 % 38.97/5.96 | (69) smndt0(xN) = all_55_3 % 38.97/5.96 | % 38.97/5.96 | DELTA: instantiating (20) with fresh symbols all_57_0, all_57_1, all_57_2, % 38.97/5.96 | all_57_3, all_57_4, all_57_5, all_57_6, all_57_7, all_57_8 gives: % 38.97/5.96 | (70) ~ (all_57_0 = all_57_6) & smndt0(xN) = all_57_2 & smndt0(xS) = % 38.97/5.96 | all_57_8 & sdtasdt0(all_57_7, all_57_7) = all_57_6 & sdtasdt0(xS, xS) % 38.97/5.96 | = all_57_4 & sdtasdt0(xR, xR) = all_57_5 & sdtpldt0(all_57_1, % 38.97/5.97 | all_57_2) = all_57_0 & sdtpldt0(all_57_3, all_57_2) = all_57_1 & % 38.97/5.97 | sdtpldt0(all_57_5, all_57_4) = all_57_3 & sdtpldt0(xR, all_57_8) = % 38.97/5.97 | all_57_7 & $i(all_57_0) & $i(all_57_1) & $i(all_57_2) & $i(all_57_3) & % 38.97/5.97 | $i(all_57_4) & $i(all_57_5) & $i(all_57_6) & $i(all_57_7) & % 38.97/5.97 | $i(all_57_8) % 38.97/5.97 | % 38.97/5.97 | ALPHA: (70) implies: % 38.97/5.97 | (71) ~ (all_57_0 = all_57_6) % 38.97/5.97 | (72) sdtpldt0(xR, all_57_8) = all_57_7 % 38.97/5.97 | (73) sdtpldt0(all_57_5, all_57_4) = all_57_3 % 38.97/5.97 | (74) sdtpldt0(all_57_3, all_57_2) = all_57_1 % 38.97/5.97 | (75) sdtpldt0(all_57_1, all_57_2) = all_57_0 % 38.97/5.97 | (76) sdtasdt0(xR, xR) = all_57_5 % 38.97/5.97 | (77) sdtasdt0(xS, xS) = all_57_4 % 38.97/5.97 | (78) sdtasdt0(all_57_7, all_57_7) = all_57_6 % 38.97/5.97 | (79) smndt0(xS) = all_57_8 % 38.97/5.97 | (80) smndt0(xN) = all_57_2 % 38.97/5.97 | % 38.97/5.97 | DELTA: instantiating (3) with fresh symbol all_59_0 gives: % 38.97/5.97 | (81) aDimensionOf0(xs) = all_59_0 & $i(all_59_0) & ! [v0: $i] : ! [v1: % 38.97/5.97 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasasdt0(v1, % 38.97/5.97 | v1) = v3) | ~ (sdtasasdt0(v0, v0) = v2) | ~ (sdtasdt0(v2, v3) % 38.97/5.97 | = v4) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) % 38.97/5.97 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 38.97/5.97 | ((sdtasasdt0(v0, v1) = v7 & sdtasdt0(v7, v7) = v8 & $i(v8) & $i(v7) % 38.97/5.97 | & sdtlseqdt0(v8, v4)) | (aDimensionOf0(v0) = v5 & $i(v5) & ( ~ % 38.97/5.97 | iLess0(v5, all_59_0) | ( ~ (v6 = v5) & aDimensionOf0(v1) = v6 % 38.97/5.97 | & $i(v6)))))) % 38.97/5.97 | % 38.97/5.97 | ALPHA: (81) implies: % 38.97/5.97 | (82) aDimensionOf0(xs) = all_59_0 % 38.97/5.97 | % 38.97/5.97 | GROUND_INST: instantiating (24) with all_55_4, all_57_5, xR, xR, simplifying % 38.97/5.97 | with (65), (76) gives: % 38.97/5.97 | (83) all_57_5 = all_55_4 % 38.97/5.97 | % 38.97/5.97 | GROUND_INST: instantiating (24) with all_53_4, all_57_5, xR, xR, simplifying % 38.97/5.97 | with (54), (76) gives: % 38.97/5.97 | (84) all_57_5 = all_53_4 % 38.97/5.97 | % 38.97/5.97 | GROUND_INST: instantiating (24) with all_55_1, all_57_4, xS, xS, simplifying % 38.97/5.97 | with (66), (77) gives: % 38.97/5.97 | (85) all_57_4 = all_55_1 % 38.97/5.97 | % 38.97/5.97 | GROUND_INST: instantiating (24) with all_53_1, all_57_4, xS, xS, simplifying % 38.97/5.97 | with (55), (77) gives: % 38.97/5.97 | (86) all_57_4 = all_53_1 % 38.97/5.97 | % 38.97/5.97 | GROUND_INST: instantiating (24) with all_45_0, all_57_4, xS, xS, simplifying % 38.97/5.97 | with (37), (77) gives: % 38.97/5.97 | (87) all_57_4 = all_45_0 % 38.97/5.97 | % 38.97/5.97 | GROUND_INST: instantiating (21) with all_55_7, all_57_8, xS, simplifying with % 38.97/5.97 | (68), (79) gives: % 38.97/5.97 | (88) all_57_8 = all_55_7 % 38.97/5.97 | % 38.97/5.97 | GROUND_INST: instantiating (21) with all_53_7, all_57_8, xS, simplifying with % 38.97/5.97 | (57), (79) gives: % 38.97/5.97 | (89) all_57_8 = all_53_7 % 38.97/5.97 | % 38.97/5.97 | GROUND_INST: instantiating (21) with all_45_2, all_57_8, xS, simplifying with % 38.97/5.97 | (40), (79) gives: % 38.97/5.97 | (90) all_57_8 = all_45_2 % 38.97/5.97 | % 38.97/5.97 | GROUND_INST: instantiating (21) with all_45_1, all_55_3, xN, simplifying with % 38.97/5.97 | (41), (69) gives: % 38.97/5.97 | (91) all_55_3 = all_45_1 % 38.97/5.97 | % 38.97/5.97 | GROUND_INST: instantiating (21) with all_55_3, all_57_2, xN, simplifying with % 38.97/5.97 | (69), (80) gives: % 38.97/5.97 | (92) all_57_2 = all_55_3 % 38.97/5.97 | % 38.97/5.97 | GROUND_INST: instantiating (21) with all_53_3, all_57_2, xN, simplifying with % 38.97/5.97 | (58), (80) gives: % 38.97/5.97 | (93) all_57_2 = all_53_3 % 38.97/5.97 | % 38.97/5.97 | GROUND_INST: instantiating (22) with all_41_0, all_50_0, xs, simplifying with % 38.97/5.97 | (34), (46) gives: % 38.97/5.97 | (94) all_50_0 = all_41_0 % 38.97/5.97 | % 38.97/5.97 | GROUND_INST: instantiating (22) with all_37_0, all_50_0, xs, simplifying with % 38.97/5.97 | (30), (46) gives: % 38.97/5.97 | (95) all_50_0 = all_37_0 % 38.97/5.97 | % 38.97/5.97 | GROUND_INST: instantiating (22) with all_41_0, all_59_0, xs, simplifying with % 38.97/5.97 | (34), (82) gives: % 38.97/5.97 | (96) all_59_0 = all_41_0 % 38.97/5.97 | % 38.97/5.97 | GROUND_INST: instantiating (22) with all_33_0, all_59_0, xs, simplifying with % 38.97/5.97 | (26), (82) gives: % 38.97/5.97 | (97) all_59_0 = all_33_0 % 38.97/5.97 | % 38.97/5.97 | GROUND_INST: instantiating (22) with all_39_0, all_47_0, xt, simplifying with % 38.97/5.97 | (32), (43) gives: % 38.97/5.97 | (98) all_47_0 = all_39_0 % 38.97/5.97 | % 38.97/5.97 | GROUND_INST: instantiating (22) with all_33_0, all_47_0, xt, simplifying with % 38.97/5.97 | (27), (43) gives: % 38.97/5.97 | (99) all_47_0 = all_33_0 % 38.97/5.97 | % 38.97/5.97 | COMBINE_EQS: (96), (97) imply: % 38.97/5.97 | (100) all_41_0 = all_33_0 % 38.97/5.97 | % 38.97/5.97 | SIMP: (100) implies: % 38.97/5.97 | (101) all_41_0 = all_33_0 % 38.97/5.97 | % 38.97/5.97 | COMBINE_EQS: (92), (93) imply: % 38.97/5.97 | (102) all_55_3 = all_53_3 % 38.97/5.97 | % 38.97/5.97 | SIMP: (102) implies: % 38.97/5.97 | (103) all_55_3 = all_53_3 % 38.97/5.97 | % 38.97/5.97 | COMBINE_EQS: (85), (87) imply: % 38.97/5.97 | (104) all_55_1 = all_45_0 % 38.97/5.97 | % 38.97/5.97 | COMBINE_EQS: (85), (86) imply: % 38.97/5.97 | (105) all_55_1 = all_53_1 % 38.97/5.97 | % 38.97/5.97 | COMBINE_EQS: (83), (84) imply: % 38.97/5.97 | (106) all_55_4 = all_53_4 % 38.97/5.97 | % 38.97/5.98 | SIMP: (106) implies: % 38.97/5.98 | (107) all_55_4 = all_53_4 % 38.97/5.98 | % 38.97/5.98 | COMBINE_EQS: (88), (90) imply: % 38.97/5.98 | (108) all_55_7 = all_45_2 % 38.97/5.98 | % 38.97/5.98 | COMBINE_EQS: (88), (89) imply: % 38.97/5.98 | (109) all_55_7 = all_53_7 % 38.97/5.98 | % 38.97/5.98 | COMBINE_EQS: (104), (105) imply: % 38.97/5.98 | (110) all_53_1 = all_45_0 % 38.97/5.98 | % 38.97/5.98 | COMBINE_EQS: (91), (103) imply: % 38.97/5.98 | (111) all_53_3 = all_45_1 % 38.97/5.98 | % 38.97/5.98 | COMBINE_EQS: (108), (109) imply: % 38.97/5.98 | (112) all_53_7 = all_45_2 % 38.97/5.98 | % 38.97/5.98 | COMBINE_EQS: (94), (95) imply: % 38.97/5.98 | (113) all_41_0 = all_37_0 % 38.97/5.98 | % 38.97/5.98 | SIMP: (113) implies: % 38.97/5.98 | (114) all_41_0 = all_37_0 % 38.97/5.98 | % 38.97/5.98 | COMBINE_EQS: (98), (99) imply: % 38.97/5.98 | (115) all_39_0 = all_33_0 % 38.97/5.98 | % 38.97/5.98 | COMBINE_EQS: (101), (114) imply: % 38.97/5.98 | (116) all_37_0 = all_33_0 % 38.97/5.98 | % 38.97/5.98 | SIMP: (116) implies: % 38.97/5.98 | (117) all_37_0 = all_33_0 % 38.97/5.98 | % 38.97/5.98 | COMBINE_EQS: (93), (111) imply: % 38.97/5.98 | (118) all_57_2 = all_45_1 % 38.97/5.98 | % 38.97/5.98 | REDUCE: (29), (117) imply: % 38.97/5.98 | (119) ~ (all_33_0 = sz00) % 38.97/5.98 | % 38.97/5.98 | REDUCE: (75), (118) imply: % 38.97/5.98 | (120) sdtpldt0(all_57_1, all_45_1) = all_57_0 % 38.97/5.98 | % 38.97/5.98 | REDUCE: (74), (118) imply: % 38.97/5.98 | (121) sdtpldt0(all_57_3, all_45_1) = all_57_1 % 38.97/5.98 | % 38.97/5.98 | REDUCE: (73), (84), (87) imply: % 38.97/5.98 | (122) sdtpldt0(all_53_4, all_45_0) = all_57_3 % 38.97/5.98 | % 38.97/5.98 | REDUCE: (64), (91), (104) imply: % 38.97/5.98 | (123) sdtpldt0(all_45_0, all_45_1) = all_55_0 % 38.97/5.98 | % 38.97/5.98 | REDUCE: (62), (91), (107) imply: % 38.97/5.98 | (124) sdtpldt0(all_53_4, all_45_1) = all_55_2 % 38.97/5.98 | % 38.97/5.98 | REDUCE: (52), (110), (111) imply: % 38.97/5.98 | (125) sdtpldt0(all_45_1, all_45_0) = all_53_0 % 38.97/5.98 | % 38.97/5.98 | REDUCE: (51), (111) imply: % 38.97/5.98 | (126) sdtpldt0(all_53_4, all_45_1) = all_53_2 % 38.97/5.98 | % 38.97/5.98 | REDUCE: (72), (90) imply: % 38.97/5.98 | (127) sdtpldt0(xR, all_45_2) = all_57_7 % 38.97/5.98 | % 38.97/5.98 | REDUCE: (61), (108) imply: % 38.97/5.98 | (128) sdtpldt0(xR, all_45_2) = all_55_6 % 38.97/5.98 | % 38.97/5.98 | REDUCE: (50), (112) imply: % 38.97/5.98 | (129) sdtpldt0(xR, all_45_2) = all_53_6 % 38.97/5.98 | % 38.97/5.98 | REDUCE: (60), (107) imply: % 38.97/5.98 | (130) $i(all_53_4) % 38.97/5.98 | % 38.97/5.98 | REDUCE: (49), (110) imply: % 38.97/5.98 | (131) $i(all_45_0) % 38.97/5.98 | % 38.97/5.98 | REDUCE: (48), (112) imply: % 38.97/5.98 | (132) $i(all_45_2) % 38.97/5.98 | % 38.97/5.98 | GROUND_INST: instantiating (23) with all_55_6, all_57_7, all_45_2, xR, % 38.97/5.98 | simplifying with (127), (128) gives: % 38.97/5.98 | (133) all_57_7 = all_55_6 % 38.97/5.98 | % 38.97/5.98 | GROUND_INST: instantiating (23) with all_53_6, all_57_7, all_45_2, xR, % 38.97/5.98 | simplifying with (127), (129) gives: % 38.97/5.98 | (134) all_57_7 = all_53_6 % 38.97/5.98 | % 38.97/5.98 | GROUND_INST: instantiating (23) with all_53_2, all_55_2, all_45_1, all_53_4, % 38.97/5.98 | simplifying with (124), (126) gives: % 38.97/5.98 | (135) all_55_2 = all_53_2 % 38.97/5.98 | % 38.97/5.98 | COMBINE_EQS: (133), (134) imply: % 38.97/5.98 | (136) all_55_6 = all_53_6 % 38.97/5.98 | % 38.97/5.98 | SIMP: (136) implies: % 38.97/5.98 | (137) all_55_6 = all_53_6 % 38.97/5.98 | % 38.97/5.98 | REDUCE: (78), (134) imply: % 38.97/5.98 | (138) sdtasdt0(all_53_6, all_53_6) = all_57_6 % 38.97/5.98 | % 38.97/5.98 | REDUCE: (67), (137) imply: % 38.97/5.98 | (139) sdtasdt0(all_53_6, all_53_6) = all_55_5 % 38.97/5.98 | % 38.97/5.98 | REDUCE: (63), (135) imply: % 38.97/5.98 | (140) sdtpldt0(all_53_2, all_55_0) = all_55_5 % 38.97/5.98 | % 38.97/5.98 | GROUND_INST: instantiating (24) with all_53_5, all_57_6, all_53_6, all_53_6, % 38.97/5.98 | simplifying with (56), (138) gives: % 38.97/5.98 | (141) all_57_6 = all_53_5 % 38.97/5.98 | % 38.97/5.98 | GROUND_INST: instantiating (24) with all_55_5, all_57_6, all_53_6, all_53_6, % 38.97/5.98 | simplifying with (138), (139) gives: % 38.97/5.98 | (142) all_57_6 = all_55_5 % 38.97/5.98 | % 38.97/5.98 | COMBINE_EQS: (141), (142) imply: % 38.97/5.98 | (143) all_55_5 = all_53_5 % 38.97/5.98 | % 38.97/5.98 | REDUCE: (71), (141) imply: % 38.97/5.98 | (144) ~ (all_57_0 = all_53_5) % 38.97/5.98 | % 38.97/5.98 | REDUCE: (140), (143) imply: % 38.97/5.98 | (145) sdtpldt0(all_53_2, all_55_0) = all_53_5 % 38.97/5.98 | % 38.97/5.98 | GROUND_INST: instantiating (mMulSc) with xR, xR, all_53_4, simplifying with % 38.97/5.98 | (11), (17), (54) gives: % 38.97/5.98 | (146) aScalar0(all_53_4) % 38.97/5.98 | % 38.97/5.98 | GROUND_INST: instantiating (mMulSc) with xS, xS, all_45_0, simplifying with % 38.97/5.98 | (12), (18), (37) gives: % 38.97/5.98 | (147) aScalar0(all_45_0) % 38.97/5.98 | % 38.97/5.98 | GROUND_INST: instantiating (mMNeg) with xS, xR, all_45_2, all_45_1, % 38.97/5.98 | simplifying with (11), (12), (17), (18), (38), (40) gives: % 38.97/5.98 | (148) ? [v0: $i] : ? [v1: $i] : (smndt0(v1) = all_45_1 & smndt0(xR) = v0 % 38.97/5.98 | & sdtasdt0(xS, v0) = all_45_1 & sdtasdt0(xS, xR) = v1 & $i(v1) & % 38.97/5.98 | $i(v0) & $i(all_45_1)) % 38.97/5.98 | % 38.97/5.98 | GROUND_INST: instantiating (mNegSc) with xS, all_45_2, simplifying with (12), % 38.97/5.98 | (18), (40) gives: % 38.97/5.98 | (149) aScalar0(all_45_2) % 38.97/5.98 | % 38.97/5.98 | GROUND_INST: instantiating (mNegSc) with xN, all_45_1, simplifying with (13), % 38.97/5.98 | (19), (41) gives: % 38.97/5.98 | (150) aScalar0(all_45_1) % 38.97/5.98 | % 38.97/5.98 | GROUND_INST: instantiating (1) with xt, xq, simplifying with (2), (9), (44) % 38.97/5.98 | gives: % 38.97/5.99 | (151) ? [v0: $i] : (aDimensionOf0(xt) = v0 & $i(v0) & (v0 = sz00 | ( ! % 38.97/5.99 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlbdtrb0(xt, v2) % 38.97/5.99 | = v3) | ~ (aDimensionOf0(xq) = v1) | ~ $i(v2) | ~ $i(xq) % 38.97/5.99 | | ~ aNaturalNumber0(v2) | (sdtlbdtrb0(xq, v2) = v3 & % 38.97/5.99 | $i(v3))) & ! [v1: $i] : ! [v2: $i] : (v1 = xq | ~ % 38.97/5.99 | (aDimensionOf0(v1) = v2) | ~ $i(v1) | ~ aVector0(v1) | ? % 38.97/5.99 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ($i(v4) % 38.97/5.99 | & (( ~ (v6 = v5) & sdtlbdtrb0(v1, v4) = v5 & sdtlbdtrb0(xt, % 38.97/5.99 | v4) = v6 & $i(v6) & $i(v5) & aNaturalNumber0(v4)) | ( % 38.97/5.99 | ~ (v3 = v0) & szszuzczcdt0(v2) = v3 & $i(v3))))) & ! % 38.97/5.99 | [v1: $i] : ( ~ (aDimensionOf0(xq) = v1) | ~ $i(xq) | % 38.97/5.99 | szszuzczcdt0(v1) = v0) & ! [v1: $i] : ( ~ (aDimensionOf0(xq) % 38.97/5.99 | = v1) | ~ $i(xq) | aVector0(xq))))) % 38.97/5.99 | % 38.97/5.99 | DELTA: instantiating (148) with fresh symbols all_83_0, all_83_1 gives: % 38.97/5.99 | (152) smndt0(all_83_0) = all_45_1 & smndt0(xR) = all_83_1 & sdtasdt0(xS, % 38.97/5.99 | all_83_1) = all_45_1 & sdtasdt0(xS, xR) = all_83_0 & $i(all_83_0) & % 38.97/5.99 | $i(all_83_1) & $i(all_45_1) % 38.97/5.99 | % 38.97/5.99 | ALPHA: (152) implies: % 38.97/5.99 | (153) $i(all_45_1) % 38.97/5.99 | (154) $i(all_83_1) % 38.97/5.99 | (155) sdtasdt0(xS, all_83_1) = all_45_1 % 38.97/5.99 | (156) smndt0(xR) = all_83_1 % 38.97/5.99 | % 38.97/5.99 | DELTA: instantiating (151) with fresh symbol all_90_0 gives: % 38.97/5.99 | (157) aDimensionOf0(xt) = all_90_0 & $i(all_90_0) & (all_90_0 = sz00 | ( ! % 38.97/5.99 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(xt, v1) = % 38.97/5.99 | v2) | ~ (aDimensionOf0(xq) = v0) | ~ $i(v1) | ~ $i(xq) | % 38.97/5.99 | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(xq, v1) = v2 & $i(v2))) & % 38.97/5.99 | ! [v0: $i] : ! [v1: $i] : (v0 = xq | ~ (aDimensionOf0(v0) = v1) % 38.97/5.99 | | ~ $i(v0) | ~ aVector0(v0) | ? [v2: any] : ? [v3: $i] : ? % 38.97/5.99 | [v4: $i] : ? [v5: $i] : ($i(v3) & (( ~ (v5 = v4) & % 38.97/5.99 | sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xt, v3) = v5 & % 38.97/5.99 | $i(v5) & $i(v4) & aNaturalNumber0(v3)) | ( ~ (v2 = % 38.97/5.99 | all_90_0) & szszuzczcdt0(v1) = v2 & $i(v2))))) & ! % 38.97/5.99 | [v0: $i] : ( ~ (aDimensionOf0(xq) = v0) | ~ $i(xq) | % 38.97/5.99 | szszuzczcdt0(v0) = all_90_0) & ! [v0: $i] : ( ~ % 38.97/5.99 | (aDimensionOf0(xq) = v0) | ~ $i(xq) | aVector0(xq)))) % 38.97/5.99 | % 38.97/5.99 | ALPHA: (157) implies: % 38.97/5.99 | (158) aDimensionOf0(xt) = all_90_0 % 38.97/5.99 | (159) all_90_0 = sz00 | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 38.97/5.99 | (sdtlbdtrb0(xt, v1) = v2) | ~ (aDimensionOf0(xq) = v0) | ~ % 38.97/5.99 | $i(v1) | ~ $i(xq) | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(xq, v1) % 38.97/5.99 | = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : (v0 = xq | ~ % 38.97/5.99 | (aDimensionOf0(v0) = v1) | ~ $i(v0) | ~ aVector0(v0) | ? [v2: % 38.97/5.99 | any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ($i(v3) & (( ~ % 38.97/5.99 | (v5 = v4) & sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xt, v3) = % 38.97/5.99 | v5 & $i(v5) & $i(v4) & aNaturalNumber0(v3)) | ( ~ (v2 = % 38.97/5.99 | all_90_0) & szszuzczcdt0(v1) = v2 & $i(v2))))) & ! [v0: % 38.97/5.99 | $i] : ( ~ (aDimensionOf0(xq) = v0) | ~ $i(xq) | szszuzczcdt0(v0) % 38.97/5.99 | = all_90_0) & ! [v0: $i] : ( ~ (aDimensionOf0(xq) = v0) | ~ % 38.97/5.99 | $i(xq) | aVector0(xq))) % 38.97/5.99 | % 38.97/5.99 | GROUND_INST: instantiating (22) with all_33_0, all_90_0, xt, simplifying with % 38.97/5.99 | (27), (158) gives: % 38.97/5.99 | (160) all_90_0 = all_33_0 % 38.97/5.99 | % 38.97/5.99 | BETA: splitting (159) gives: % 38.97/5.99 | % 38.97/5.99 | Case 1: % 38.97/5.99 | | % 38.97/5.99 | | (161) all_90_0 = sz00 % 38.97/5.99 | | % 38.97/5.99 | | COMBINE_EQS: (160), (161) imply: % 38.97/5.99 | | (162) all_33_0 = sz00 % 38.97/5.99 | | % 38.97/5.99 | | REDUCE: (119), (162) imply: % 38.97/5.99 | | (163) $false % 38.97/5.99 | | % 38.97/5.99 | | CLOSE: (163) is inconsistent. % 38.97/5.99 | | % 38.97/5.99 | Case 2: % 38.97/5.99 | | % 38.97/5.99 | | % 38.97/5.99 | | GROUND_INST: instantiating (mDistr) with all_45_2, xR, all_45_2, all_45_1, % 38.97/5.99 | | all_45_0, all_53_0, simplifying with (11), (17), (38), (39), % 38.97/5.99 | | (125), (132), (149) gives: % 38.97/5.99 | | (164) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 38.97/5.99 | | (sdtasdt0(v1, all_45_2) = v2 & sdtasdt0(all_45_2, v0) = all_53_0 & % 38.97/5.99 | | sdtasdt0(xR, all_45_2) = v3 & sdtpldt0(all_45_0, v3) = v2 & % 38.97/5.99 | | sdtpldt0(all_45_2, xR) = v1 & sdtpldt0(xR, all_45_2) = v0 & % 38.97/5.99 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_53_0)) % 38.97/5.99 | | % 38.97/5.99 | | GROUND_INST: instantiating (mDistr) with all_45_2, all_45_2, xR, all_45_0, % 38.97/5.99 | | all_45_1, all_55_0, simplifying with (11), (17), (38), (39), % 38.97/5.99 | | (123), (132), (149) gives: % 38.97/6.00 | | (165) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 38.97/6.00 | | (sdtasdt0(v1, xR) = v2 & sdtasdt0(all_45_2, v0) = all_55_0 & % 38.97/6.00 | | sdtasdt0(all_45_2, xR) = v3 & sdtpldt0(all_45_1, v3) = v2 & % 38.97/6.00 | | sdtpldt0(all_45_2, all_45_2) = v1 & sdtpldt0(all_45_2, xR) = v0 & % 38.97/6.00 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_55_0)) % 38.97/6.00 | | % 38.97/6.00 | | GROUND_INST: instantiating (mDistr) with xR, xR, all_45_2, all_53_4, % 38.97/6.00 | | all_45_1, all_53_2, simplifying with (11), (17), (36), (54), % 38.97/6.00 | | (126), (132), (149) gives: % 38.97/6.00 | | (166) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 38.97/6.00 | | (sdtasdt0(v1, all_45_2) = v2 & sdtasdt0(xR, v0) = all_53_2 & % 38.97/6.00 | | sdtasdt0(xR, all_45_2) = v3 & sdtpldt0(all_45_1, v3) = v2 & % 38.97/6.00 | | sdtpldt0(xR, all_45_2) = v0 & sdtpldt0(xR, xR) = v1 & $i(v3) & % 38.97/6.00 | | $i(v2) & $i(v1) & $i(v0) & $i(all_53_2)) % 38.97/6.00 | | % 38.97/6.00 | | GROUND_INST: instantiating (mSumSc) with xR, all_45_2, all_53_6, simplifying % 38.97/6.00 | | with (11), (17), (129), (132), (149) gives: % 38.97/6.00 | | (167) aScalar0(all_53_6) % 38.97/6.00 | | % 38.97/6.00 | | GROUND_INST: instantiating (mSumSc) with all_45_0, all_45_1, all_55_0, % 38.97/6.00 | | simplifying with (123), (131), (147), (150), (153) gives: % 38.97/6.00 | | (168) aScalar0(all_55_0) % 38.97/6.00 | | % 38.97/6.00 | | GROUND_INST: instantiating (mSumSc) with all_45_1, all_45_0, all_53_0, % 38.97/6.00 | | simplifying with (125), (131), (147), (150), (153) gives: % 38.97/6.00 | | (169) aScalar0(all_53_0) % 38.97/6.00 | | % 38.97/6.00 | | GROUND_INST: instantiating (mArith) with all_53_4, all_45_0, all_45_1, % 38.97/6.00 | | all_57_3, all_57_1, simplifying with (121), (122), (130), % 38.97/6.00 | | (131), (146), (147), (150), (153) gives: % 38.97/6.00 | | (170) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 38.97/6.00 | | (sdtasdt0(v1, all_45_1) = v2 & sdtasdt0(all_53_4, v3) = v2 & % 38.97/6.00 | | sdtasdt0(all_53_4, all_45_0) = v1 & sdtasdt0(all_45_0, all_53_4) % 38.97/6.00 | | = v1 & sdtasdt0(all_45_0, all_45_1) = v3 & sdtpldt0(all_53_4, v0) % 38.97/6.00 | | = all_57_1 & sdtpldt0(all_45_0, all_53_4) = all_57_3 & % 38.97/6.00 | | sdtpldt0(all_45_0, all_45_1) = v0 & $i(v3) & $i(v2) & $i(v1) & % 38.97/6.00 | | $i(v0) & $i(all_57_1) & $i(all_57_3)) % 38.97/6.00 | | % 38.97/6.00 | | GROUND_INST: instantiating (mNegSc) with xR, all_83_1, simplifying with % 38.97/6.00 | | (11), (17), (156) gives: % 38.97/6.00 | | (171) aScalar0(all_83_1) % 38.97/6.00 | | % 38.97/6.00 | | DELTA: instantiating (166) with fresh symbols all_127_0, all_127_1, % 38.97/6.00 | | all_127_2, all_127_3 gives: % 38.97/6.00 | | (172) sdtasdt0(all_127_2, all_45_2) = all_127_1 & sdtasdt0(xR, all_127_3) % 38.97/6.00 | | = all_53_2 & sdtasdt0(xR, all_45_2) = all_127_0 & % 38.97/6.00 | | sdtpldt0(all_45_1, all_127_0) = all_127_1 & sdtpldt0(xR, all_45_2) % 38.97/6.00 | | = all_127_3 & sdtpldt0(xR, xR) = all_127_2 & $i(all_127_0) & % 38.97/6.00 | | $i(all_127_1) & $i(all_127_2) & $i(all_127_3) & $i(all_53_2) % 38.97/6.00 | | % 38.97/6.00 | | ALPHA: (172) implies: % 38.97/6.00 | | (173) $i(all_127_0) % 38.97/6.00 | | (174) sdtpldt0(xR, all_45_2) = all_127_3 % 38.97/6.00 | | (175) sdtpldt0(all_45_1, all_127_0) = all_127_1 % 38.97/6.00 | | (176) sdtasdt0(xR, all_45_2) = all_127_0 % 38.97/6.00 | | (177) sdtasdt0(xR, all_127_3) = all_53_2 % 38.97/6.00 | | % 38.97/6.00 | | DELTA: instantiating (164) with fresh symbols all_129_0, all_129_1, % 38.97/6.00 | | all_129_2, all_129_3 gives: % 38.97/6.00 | | (178) sdtasdt0(all_129_2, all_45_2) = all_129_1 & sdtasdt0(all_45_2, % 38.97/6.00 | | all_129_3) = all_53_0 & sdtasdt0(xR, all_45_2) = all_129_0 & % 38.97/6.00 | | sdtpldt0(all_45_0, all_129_0) = all_129_1 & sdtpldt0(all_45_2, xR) % 38.97/6.00 | | = all_129_2 & sdtpldt0(xR, all_45_2) = all_129_3 & $i(all_129_0) & % 38.97/6.00 | | $i(all_129_1) & $i(all_129_2) & $i(all_129_3) & $i(all_53_0) % 38.97/6.00 | | % 38.97/6.00 | | ALPHA: (178) implies: % 38.97/6.00 | | (179) $i(all_53_0) % 38.97/6.00 | | (180) $i(all_129_1) % 38.97/6.00 | | (181) sdtpldt0(xR, all_45_2) = all_129_3 % 38.97/6.00 | | (182) sdtpldt0(all_45_2, xR) = all_129_2 % 38.97/6.00 | | (183) sdtpldt0(all_45_0, all_129_0) = all_129_1 % 38.97/6.00 | | (184) sdtasdt0(xR, all_45_2) = all_129_0 % 38.97/6.00 | | (185) sdtasdt0(all_45_2, all_129_3) = all_53_0 % 38.97/6.00 | | (186) sdtasdt0(all_129_2, all_45_2) = all_129_1 % 38.97/6.00 | | % 38.97/6.00 | | DELTA: instantiating (165) with fresh symbols all_131_0, all_131_1, % 38.97/6.00 | | all_131_2, all_131_3 gives: % 38.97/6.00 | | (187) sdtasdt0(all_131_2, xR) = all_131_1 & sdtasdt0(all_45_2, all_131_3) % 38.97/6.00 | | = all_55_0 & sdtasdt0(all_45_2, xR) = all_131_0 & % 38.97/6.00 | | sdtpldt0(all_45_1, all_131_0) = all_131_1 & sdtpldt0(all_45_2, % 38.97/6.00 | | all_45_2) = all_131_2 & sdtpldt0(all_45_2, xR) = all_131_3 & % 38.97/6.00 | | $i(all_131_0) & $i(all_131_1) & $i(all_131_2) & $i(all_131_3) & % 38.97/6.00 | | $i(all_55_0) % 38.97/6.00 | | % 38.97/6.00 | | ALPHA: (187) implies: % 38.97/6.00 | | (188) sdtpldt0(all_45_2, xR) = all_131_3 % 38.97/6.00 | | (189) sdtpldt0(all_45_1, all_131_0) = all_131_1 % 38.97/6.00 | | (190) sdtasdt0(all_45_2, xR) = all_131_0 % 38.97/6.00 | | (191) sdtasdt0(all_45_2, all_131_3) = all_55_0 % 38.97/6.00 | | % 38.97/6.00 | | DELTA: instantiating (170) with fresh symbols all_133_0, all_133_1, % 38.97/6.00 | | all_133_2, all_133_3 gives: % 38.97/6.00 | | (192) sdtasdt0(all_133_2, all_45_1) = all_133_1 & sdtasdt0(all_53_4, % 38.97/6.00 | | all_133_0) = all_133_1 & sdtasdt0(all_53_4, all_45_0) = all_133_2 % 38.97/6.00 | | & sdtasdt0(all_45_0, all_53_4) = all_133_2 & sdtasdt0(all_45_0, % 38.97/6.00 | | all_45_1) = all_133_0 & sdtpldt0(all_53_4, all_133_3) = all_57_1 % 38.97/6.00 | | & sdtpldt0(all_45_0, all_53_4) = all_57_3 & sdtpldt0(all_45_0, % 38.97/6.00 | | all_45_1) = all_133_3 & $i(all_133_0) & $i(all_133_1) & % 38.97/6.00 | | $i(all_133_2) & $i(all_133_3) & $i(all_57_1) & $i(all_57_3) % 38.97/6.00 | | % 38.97/6.00 | | ALPHA: (192) implies: % 38.97/6.00 | | (193) sdtpldt0(all_45_0, all_45_1) = all_133_3 % 38.97/6.00 | | (194) sdtpldt0(all_53_4, all_133_3) = all_57_1 % 38.97/6.00 | | % 38.97/6.00 | | GROUND_INST: instantiating (23) with all_53_6, all_129_3, all_45_2, xR, % 38.97/6.00 | | simplifying with (129), (181) gives: % 38.97/6.00 | | (195) all_129_3 = all_53_6 % 38.97/6.00 | | % 38.97/6.00 | | GROUND_INST: instantiating (23) with all_127_3, all_129_3, all_45_2, xR, % 38.97/6.00 | | simplifying with (174), (181) gives: % 38.97/6.00 | | (196) all_129_3 = all_127_3 % 38.97/6.00 | | % 38.97/6.00 | | GROUND_INST: instantiating (23) with all_129_2, all_131_3, xR, all_45_2, % 38.97/6.00 | | simplifying with (182), (188) gives: % 38.97/6.00 | | (197) all_131_3 = all_129_2 % 38.97/6.00 | | % 38.97/6.00 | | GROUND_INST: instantiating (23) with all_55_0, all_133_3, all_45_1, % 38.97/6.00 | | all_45_0, simplifying with (123), (193) gives: % 38.97/6.00 | | (198) all_133_3 = all_55_0 % 38.97/6.00 | | % 38.97/6.00 | | GROUND_INST: instantiating (24) with all_45_1, all_129_0, all_45_2, xR, % 38.97/6.00 | | simplifying with (36), (184) gives: % 38.97/6.00 | | (199) all_129_0 = all_45_1 % 38.97/6.00 | | % 38.97/6.00 | | GROUND_INST: instantiating (24) with all_127_0, all_129_0, all_45_2, xR, % 38.97/6.00 | | simplifying with (176), (184) gives: % 38.97/6.00 | | (200) all_129_0 = all_127_0 % 38.97/6.00 | | % 38.97/6.00 | | GROUND_INST: instantiating (24) with all_45_1, all_131_0, xR, all_45_2, % 38.97/6.00 | | simplifying with (38), (190) gives: % 38.97/6.00 | | (201) all_131_0 = all_45_1 % 38.97/6.00 | | % 38.97/6.00 | | COMBINE_EQS: (199), (200) imply: % 38.97/6.00 | | (202) all_127_0 = all_45_1 % 38.97/6.00 | | % 38.97/6.00 | | COMBINE_EQS: (195), (196) imply: % 38.97/6.01 | | (203) all_127_3 = all_53_6 % 38.97/6.01 | | % 38.97/6.01 | | REDUCE: (191), (197) imply: % 38.97/6.01 | | (204) sdtasdt0(all_45_2, all_129_2) = all_55_0 % 38.97/6.01 | | % 38.97/6.01 | | REDUCE: (185), (195) imply: % 38.97/6.01 | | (205) sdtasdt0(all_45_2, all_53_6) = all_53_0 % 38.97/6.01 | | % 38.97/6.01 | | REDUCE: (177), (203) imply: % 38.97/6.01 | | (206) sdtasdt0(xR, all_53_6) = all_53_2 % 38.97/6.01 | | % 38.97/6.01 | | REDUCE: (194), (198) imply: % 38.97/6.01 | | (207) sdtpldt0(all_53_4, all_55_0) = all_57_1 % 38.97/6.01 | | % 38.97/6.01 | | REDUCE: (183), (199) imply: % 38.97/6.01 | | (208) sdtpldt0(all_45_0, all_45_1) = all_129_1 % 38.97/6.01 | | % 38.97/6.01 | | REDUCE: (189), (201) imply: % 38.97/6.01 | | (209) sdtpldt0(all_45_1, all_45_1) = all_131_1 % 38.97/6.01 | | % 38.97/6.01 | | REDUCE: (175), (202) imply: % 38.97/6.01 | | (210) sdtpldt0(all_45_1, all_45_1) = all_127_1 % 38.97/6.01 | | % 38.97/6.01 | | GROUND_INST: instantiating (23) with all_127_1, all_131_1, all_45_1, % 38.97/6.01 | | all_45_1, simplifying with (209), (210) gives: % 38.97/6.01 | | (211) all_131_1 = all_127_1 % 38.97/6.01 | | % 38.97/6.01 | | GROUND_INST: instantiating (23) with all_55_0, all_129_1, all_45_1, % 38.97/6.01 | | all_45_0, simplifying with (123), (208) gives: % 38.97/6.01 | | (212) all_129_1 = all_55_0 % 38.97/6.01 | | % 38.97/6.01 | | REDUCE: (186), (212) imply: % 38.97/6.01 | | (213) sdtasdt0(all_129_2, all_45_2) = all_55_0 % 38.97/6.01 | | % 38.97/6.01 | | REDUCE: (180), (212) imply: % 38.97/6.01 | | (214) $i(all_55_0) % 38.97/6.01 | | % 38.97/6.01 | | GROUND_INST: instantiating (mArith) with all_53_4, all_45_1, all_53_0, % 38.97/6.01 | | all_53_2, all_53_5, simplifying with (53), (126), (130), (146), % 38.97/6.01 | | (150), (153), (169), (179) gives: % 38.97/6.01 | | (215) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 38.97/6.01 | | (sdtasdt0(v1, all_53_0) = v2 & sdtasdt0(all_53_4, v3) = v2 & % 38.97/6.01 | | sdtasdt0(all_53_4, all_45_1) = v1 & sdtasdt0(all_45_1, all_53_0) % 38.97/6.01 | | = v3 & sdtasdt0(all_45_1, all_53_4) = v1 & sdtpldt0(all_53_4, v0) % 38.97/6.01 | | = all_53_5 & sdtpldt0(all_45_1, all_53_0) = v0 & % 38.97/6.01 | | sdtpldt0(all_45_1, all_53_4) = all_53_2 & $i(v3) & $i(v2) & % 38.97/6.01 | | $i(v1) & $i(v0) & $i(all_53_2) & $i(all_53_5)) % 38.97/6.01 | | % 38.97/6.01 | | GROUND_INST: instantiating (mArith) with all_53_4, all_45_1, all_55_0, % 38.97/6.01 | | all_53_2, all_53_5, simplifying with (126), (130), (145), % 38.97/6.01 | | (146), (150), (153), (168), (214) gives: % 38.97/6.01 | | (216) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 38.97/6.01 | | (sdtasdt0(v1, all_55_0) = v2 & sdtasdt0(all_53_4, v3) = v2 & % 38.97/6.01 | | sdtasdt0(all_53_4, all_45_1) = v1 & sdtasdt0(all_45_1, all_55_0) % 38.97/6.01 | | = v3 & sdtasdt0(all_45_1, all_53_4) = v1 & sdtpldt0(all_53_4, v0) % 38.97/6.01 | | = all_53_5 & sdtpldt0(all_45_1, all_55_0) = v0 & % 38.97/6.01 | | sdtpldt0(all_45_1, all_53_4) = all_53_2 & $i(v3) & $i(v2) & % 38.97/6.01 | | $i(v1) & $i(v0) & $i(all_53_2) & $i(all_53_5)) % 38.97/6.01 | | % 38.97/6.01 | | GROUND_INST: instantiating (mDistr) with xS, xS, all_83_1, all_45_0, % 38.97/6.01 | | all_45_1, all_55_0, simplifying with (12), (18), (37), (123), % 38.97/6.01 | | (154), (155), (171) gives: % 38.97/6.01 | | (217) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 38.97/6.01 | | (sdtasdt0(v1, all_83_1) = v2 & sdtasdt0(xS, v0) = all_55_0 & % 38.97/6.01 | | sdtasdt0(xS, all_83_1) = v3 & sdtpldt0(all_45_1, v3) = v2 & % 38.97/6.01 | | sdtpldt0(xS, all_83_1) = v0 & sdtpldt0(xS, xS) = v1 & $i(v3) & % 38.97/6.01 | | $i(v2) & $i(v1) & $i(v0) & $i(all_55_0)) % 38.97/6.01 | | % 38.97/6.01 | | GROUND_INST: instantiating (mSumSc) with all_45_2, xR, all_129_2, % 38.97/6.01 | | simplifying with (11), (17), (132), (149), (182) gives: % 38.97/6.01 | | (218) aScalar0(all_129_2) % 38.97/6.01 | | % 38.97/6.01 | | GROUND_INST: instantiating (mDistr) with all_45_2, xR, xR, all_45_1, % 38.97/6.01 | | all_45_1, all_127_1, simplifying with (11), (17), (38), (132), % 38.97/6.01 | | (149), (210) gives: % 38.97/6.01 | | (219) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 38.97/6.01 | | (sdtasdt0(v1, xR) = v2 & sdtasdt0(all_45_2, v0) = all_127_1 & % 38.97/6.01 | | sdtasdt0(xR, xR) = v3 & sdtpldt0(all_45_1, v3) = v2 & % 38.97/6.01 | | sdtpldt0(all_45_2, xR) = v1 & sdtpldt0(xR, xR) = v0 & $i(v3) & % 38.97/6.01 | | $i(v2) & $i(v1) & $i(v0) & $i(all_127_1)) % 38.97/6.01 | | % 38.97/6.01 | | GROUND_INST: instantiating (mDistr) with xR, all_45_2, all_45_2, all_45_1, % 38.97/6.01 | | all_45_1, all_127_1, simplifying with (11), (17), (36), (132), % 38.97/6.01 | | (149), (210) gives: % 38.97/6.01 | | (220) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 38.97/6.01 | | (sdtasdt0(v1, all_45_2) = v2 & sdtasdt0(all_45_2, all_45_2) = v3 & % 38.97/6.01 | | sdtasdt0(xR, v0) = all_127_1 & sdtpldt0(all_45_1, v3) = v2 & % 38.97/6.01 | | sdtpldt0(all_45_2, all_45_2) = v0 & sdtpldt0(xR, all_45_2) = v1 & % 38.97/6.01 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_127_1)) % 38.97/6.01 | | % 38.97/6.01 | | GROUND_INST: instantiating (mArith) with all_53_4, all_55_0, all_45_1, % 38.97/6.01 | | all_57_1, all_57_0, simplifying with (120), (130), (146), % 38.97/6.01 | | (150), (153), (168), (207), (214) gives: % 38.97/6.01 | | (221) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 38.97/6.01 | | (sdtasdt0(v1, all_45_1) = v2 & sdtasdt0(all_55_0, all_53_4) = v1 & % 38.97/6.01 | | sdtasdt0(all_55_0, all_45_1) = v3 & sdtasdt0(all_53_4, v3) = v2 & % 38.97/6.01 | | sdtasdt0(all_53_4, all_55_0) = v1 & sdtpldt0(all_55_0, all_53_4) % 38.97/6.01 | | = all_57_1 & sdtpldt0(all_55_0, all_45_1) = v0 & % 38.97/6.01 | | sdtpldt0(all_53_4, v0) = all_57_0 & $i(v3) & $i(v2) & $i(v1) & % 38.97/6.01 | | $i(v0) & $i(all_57_0) & $i(all_57_1)) % 38.97/6.01 | | % 38.97/6.01 | | DELTA: instantiating (217) with fresh symbols all_162_0, all_162_1, % 38.97/6.01 | | all_162_2, all_162_3 gives: % 38.97/6.01 | | (222) sdtasdt0(all_162_2, all_83_1) = all_162_1 & sdtasdt0(xS, all_162_3) % 38.97/6.01 | | = all_55_0 & sdtasdt0(xS, all_83_1) = all_162_0 & % 38.97/6.01 | | sdtpldt0(all_45_1, all_162_0) = all_162_1 & sdtpldt0(xS, all_83_1) % 38.97/6.01 | | = all_162_3 & sdtpldt0(xS, xS) = all_162_2 & $i(all_162_0) & % 38.97/6.01 | | $i(all_162_1) & $i(all_162_2) & $i(all_162_3) & $i(all_55_0) % 38.97/6.01 | | % 38.97/6.01 | | ALPHA: (222) implies: % 38.97/6.01 | | (223) $i(all_162_0) % 38.97/6.01 | | (224) sdtasdt0(xS, all_83_1) = all_162_0 % 38.97/6.01 | | % 38.97/6.01 | | DELTA: instantiating (220) with fresh symbols all_164_0, all_164_1, % 38.97/6.01 | | all_164_2, all_164_3 gives: % 38.97/6.01 | | (225) sdtasdt0(all_164_2, all_45_2) = all_164_1 & sdtasdt0(all_45_2, % 38.97/6.01 | | all_45_2) = all_164_0 & sdtasdt0(xR, all_164_3) = all_127_1 & % 38.97/6.01 | | sdtpldt0(all_45_1, all_164_0) = all_164_1 & sdtpldt0(all_45_2, % 38.97/6.01 | | all_45_2) = all_164_3 & sdtpldt0(xR, all_45_2) = all_164_2 & % 38.97/6.01 | | $i(all_164_0) & $i(all_164_1) & $i(all_164_2) & $i(all_164_3) & % 38.97/6.01 | | $i(all_127_1) % 38.97/6.01 | | % 38.97/6.01 | | ALPHA: (225) implies: % 38.97/6.01 | | (226) $i(all_164_2) % 38.97/6.01 | | (227) $i(all_164_0) % 38.97/6.01 | | (228) sdtpldt0(xR, all_45_2) = all_164_2 % 38.97/6.01 | | (229) sdtpldt0(all_45_1, all_164_0) = all_164_1 % 38.97/6.01 | | (230) sdtasdt0(all_45_2, all_45_2) = all_164_0 % 38.97/6.01 | | % 38.97/6.01 | | DELTA: instantiating (219) with fresh symbols all_168_0, all_168_1, % 38.97/6.01 | | all_168_2, all_168_3 gives: % 38.97/6.01 | | (231) sdtasdt0(all_168_2, xR) = all_168_1 & sdtasdt0(all_45_2, all_168_3) % 38.97/6.01 | | = all_127_1 & sdtasdt0(xR, xR) = all_168_0 & sdtpldt0(all_45_1, % 38.97/6.01 | | all_168_0) = all_168_1 & sdtpldt0(all_45_2, xR) = all_168_2 & % 38.97/6.01 | | sdtpldt0(xR, xR) = all_168_3 & $i(all_168_0) & $i(all_168_1) & % 38.97/6.01 | | $i(all_168_2) & $i(all_168_3) & $i(all_127_1) % 38.97/6.01 | | % 38.97/6.01 | | ALPHA: (231) implies: % 38.97/6.01 | | (232) $i(all_168_2) % 38.97/6.02 | | (233) $i(all_168_0) % 38.97/6.02 | | (234) sdtpldt0(all_45_2, xR) = all_168_2 % 38.97/6.02 | | (235) sdtpldt0(all_45_1, all_168_0) = all_168_1 % 38.97/6.02 | | (236) sdtasdt0(xR, xR) = all_168_0 % 38.97/6.02 | | (237) sdtasdt0(all_168_2, xR) = all_168_1 % 38.97/6.02 | | % 38.97/6.02 | | DELTA: instantiating (215) with fresh symbols all_172_0, all_172_1, % 38.97/6.02 | | all_172_2, all_172_3 gives: % 38.97/6.02 | | (238) sdtasdt0(all_172_2, all_53_0) = all_172_1 & sdtasdt0(all_53_4, % 38.97/6.02 | | all_172_0) = all_172_1 & sdtasdt0(all_53_4, all_45_1) = all_172_2 % 38.97/6.02 | | & sdtasdt0(all_45_1, all_53_0) = all_172_0 & sdtasdt0(all_45_1, % 38.97/6.02 | | all_53_4) = all_172_2 & sdtpldt0(all_53_4, all_172_3) = all_53_5 % 38.97/6.02 | | & sdtpldt0(all_45_1, all_53_0) = all_172_3 & sdtpldt0(all_45_1, % 38.97/6.02 | | all_53_4) = all_53_2 & $i(all_172_0) & $i(all_172_1) & % 38.97/6.02 | | $i(all_172_2) & $i(all_172_3) & $i(all_53_2) & $i(all_53_5) % 38.97/6.02 | | % 38.97/6.02 | | ALPHA: (238) implies: % 38.97/6.02 | | (239) sdtpldt0(all_45_1, all_53_0) = all_172_3 % 38.97/6.02 | | % 38.97/6.02 | | DELTA: instantiating (221) with fresh symbols all_174_0, all_174_1, % 38.97/6.02 | | all_174_2, all_174_3 gives: % 38.97/6.02 | | (240) sdtasdt0(all_174_2, all_45_1) = all_174_1 & sdtasdt0(all_55_0, % 38.97/6.02 | | all_53_4) = all_174_2 & sdtasdt0(all_55_0, all_45_1) = all_174_0 % 38.97/6.02 | | & sdtasdt0(all_53_4, all_174_0) = all_174_1 & sdtasdt0(all_53_4, % 38.97/6.02 | | all_55_0) = all_174_2 & sdtpldt0(all_55_0, all_53_4) = all_57_1 & % 38.97/6.02 | | sdtpldt0(all_55_0, all_45_1) = all_174_3 & sdtpldt0(all_53_4, % 38.97/6.02 | | all_174_3) = all_57_0 & $i(all_174_0) & $i(all_174_1) & % 38.97/6.02 | | $i(all_174_2) & $i(all_174_3) & $i(all_57_0) & $i(all_57_1) % 38.97/6.02 | | % 38.97/6.02 | | ALPHA: (240) implies: % 38.97/6.02 | | (241) sdtpldt0(all_55_0, all_53_4) = all_57_1 % 38.97/6.02 | | % 38.97/6.02 | | DELTA: instantiating (216) with fresh symbols all_178_0, all_178_1, % 38.97/6.02 | | all_178_2, all_178_3 gives: % 38.97/6.02 | | (242) sdtasdt0(all_178_2, all_55_0) = all_178_1 & sdtasdt0(all_53_4, % 38.97/6.02 | | all_178_0) = all_178_1 & sdtasdt0(all_53_4, all_45_1) = all_178_2 % 38.97/6.02 | | & sdtasdt0(all_45_1, all_55_0) = all_178_0 & sdtasdt0(all_45_1, % 38.97/6.02 | | all_53_4) = all_178_2 & sdtpldt0(all_53_4, all_178_3) = all_53_5 % 38.97/6.02 | | & sdtpldt0(all_45_1, all_55_0) = all_178_3 & sdtpldt0(all_45_1, % 38.97/6.02 | | all_53_4) = all_53_2 & $i(all_178_0) & $i(all_178_1) & % 38.97/6.02 | | $i(all_178_2) & $i(all_178_3) & $i(all_53_2) & $i(all_53_5) % 38.97/6.02 | | % 38.97/6.02 | | ALPHA: (242) implies: % 38.97/6.02 | | (243) sdtpldt0(all_45_1, all_53_4) = all_53_2 % 38.97/6.02 | | (244) sdtpldt0(all_45_1, all_55_0) = all_178_3 % 38.97/6.02 | | % 38.97/6.02 | | GROUND_INST: instantiating (23) with all_53_6, all_164_2, all_45_2, xR, % 38.97/6.02 | | simplifying with (129), (228) gives: % 38.97/6.02 | | (245) all_164_2 = all_53_6 % 38.97/6.02 | | % 38.97/6.02 | | GROUND_INST: instantiating (23) with all_129_2, all_168_2, xR, all_45_2, % 38.97/6.02 | | simplifying with (182), (234) gives: % 38.97/6.02 | | (246) all_168_2 = all_129_2 % 38.97/6.02 | | % 38.97/6.02 | | GROUND_INST: instantiating (24) with all_53_4, all_168_0, xR, xR, % 38.97/6.02 | | simplifying with (54), (236) gives: % 38.97/6.02 | | (247) all_168_0 = all_53_4 % 38.97/6.02 | | % 38.97/6.02 | | GROUND_INST: instantiating (24) with all_45_1, all_162_0, all_83_1, xS, % 38.97/6.02 | | simplifying with (155), (224) gives: % 38.97/6.02 | | (248) all_162_0 = all_45_1 % 38.97/6.02 | | % 38.97/6.02 | | GROUND_INST: instantiating (24) with all_45_0, all_164_0, all_45_2, % 38.97/6.02 | | all_45_2, simplifying with (39), (230) gives: % 38.97/6.02 | | (249) all_164_0 = all_45_0 % 38.97/6.02 | | % 38.97/6.02 | | REDUCE: (237), (246) imply: % 38.97/6.02 | | (250) sdtasdt0(all_129_2, xR) = all_168_1 % 38.97/6.02 | | % 38.97/6.02 | | REDUCE: (235), (247) imply: % 38.97/6.02 | | (251) sdtpldt0(all_45_1, all_53_4) = all_168_1 % 38.97/6.02 | | % 38.97/6.02 | | REDUCE: (229), (249) imply: % 38.97/6.02 | | (252) sdtpldt0(all_45_1, all_45_0) = all_164_1 % 38.97/6.02 | | % 38.97/6.02 | | REDUCE: (232), (246) imply: % 38.97/6.02 | | (253) $i(all_129_2) % 38.97/6.02 | | % 38.97/6.02 | | REDUCE: (226), (245) imply: % 38.97/6.02 | | (254) $i(all_53_6) % 38.97/6.02 | | % 38.97/6.02 | | GROUND_INST: instantiating (23) with all_53_0, all_164_1, all_45_0, % 38.97/6.02 | | all_45_1, simplifying with (125), (252) gives: % 38.97/6.02 | | (255) all_164_1 = all_53_0 % 38.97/6.02 | | % 38.97/6.02 | | GROUND_INST: instantiating (23) with all_53_2, all_168_1, all_53_4, % 38.97/6.02 | | all_45_1, simplifying with (243), (251) gives: % 38.97/6.02 | | (256) all_168_1 = all_53_2 % 38.97/6.02 | | % 38.97/6.02 | | REDUCE: (250), (256) imply: % 38.97/6.02 | | (257) sdtasdt0(all_129_2, xR) = all_53_2 % 38.97/6.02 | | % 38.97/6.02 | | GROUND_INST: instantiating (mDistr2) with xR, all_45_2, all_45_2, xR, % 38.97/6.02 | | all_45_1, all_53_4, all_53_2, all_45_0, all_45_1, all_55_0, % 38.97/6.02 | | all_53_5, simplifying with (11), (17), (36), (38), (39), (54), % 38.97/6.02 | | (123), (132), (145), (149), (243) gives: % 38.97/6.02 | | (258) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(v0, v1) = all_53_5 & % 38.97/6.02 | | sdtpldt0(all_45_2, xR) = v1 & sdtpldt0(xR, all_45_2) = v0 & % 38.97/6.02 | | $i(v1) & $i(v0) & $i(all_53_5)) % 38.97/6.02 | | % 38.97/6.02 | | GROUND_INST: instantiating (mDistr) with xR, all_45_2, xR, all_45_1, % 38.97/6.02 | | all_53_4, all_53_2, simplifying with (11), (17), (36), (54), % 38.97/6.02 | | (132), (149), (243) gives: % 38.97/6.02 | | (259) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 38.97/6.02 | | (sdtasdt0(v1, xR) = v2 & sdtasdt0(all_45_2, xR) = v3 & sdtasdt0(xR, % 38.97/6.02 | | v0) = all_53_2 & sdtpldt0(all_53_4, v3) = v2 & % 38.97/6.02 | | sdtpldt0(all_45_2, xR) = v0 & sdtpldt0(xR, all_45_2) = v1 & % 38.97/6.02 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_53_2)) % 38.97/6.02 | | % 38.97/6.02 | | GROUND_INST: instantiating (mArith) with all_45_1, all_53_4, all_55_0, % 38.97/6.02 | | all_53_2, all_53_5, simplifying with (130), (145), (146), % 38.97/6.02 | | (150), (153), (168), (214), (243) gives: % 38.97/6.02 | | (260) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 38.97/6.02 | | (sdtasdt0(v1, all_55_0) = v2 & sdtasdt0(all_53_4, all_55_0) = v3 & % 38.97/6.02 | | sdtasdt0(all_53_4, all_45_1) = v1 & sdtasdt0(all_45_1, v3) = v2 & % 38.97/6.02 | | sdtasdt0(all_45_1, all_53_4) = v1 & sdtpldt0(all_53_4, all_55_0) % 38.97/6.02 | | = v0 & sdtpldt0(all_53_4, all_45_1) = all_53_2 & % 38.97/6.02 | | sdtpldt0(all_45_1, v0) = all_53_5 & $i(v3) & $i(v2) & $i(v1) & % 38.97/6.02 | | $i(v0) & $i(all_53_2) & $i(all_53_5)) % 38.97/6.02 | | % 38.97/6.02 | | GROUND_INST: instantiating (mDistr) with all_45_2, xR, all_53_6, all_45_1, % 38.97/6.02 | | all_53_0, all_172_3, simplifying with (11), (17), (38), (132), % 38.97/6.02 | | (149), (167), (205), (239), (254) gives: % 38.97/6.02 | | (261) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 38.97/6.02 | | (sdtasdt0(v1, all_53_6) = v2 & sdtasdt0(all_45_2, v0) = all_172_3 & % 38.97/6.02 | | sdtasdt0(xR, all_53_6) = v3 & sdtpldt0(all_53_0, v3) = v2 & % 38.97/6.02 | | sdtpldt0(all_45_2, xR) = v1 & sdtpldt0(xR, all_53_6) = v0 & % 38.97/6.02 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_172_3)) % 38.97/6.02 | | % 38.97/6.02 | | GROUND_INST: instantiating (mDistr) with all_45_2, xR, all_129_2, all_45_1, % 38.97/6.02 | | all_55_0, all_178_3, simplifying with (11), (17), (38), (132), % 38.97/6.02 | | (149), (204), (218), (244), (253) gives: % 38.97/6.02 | | (262) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 38.97/6.02 | | (sdtasdt0(v1, all_129_2) = v2 & sdtasdt0(all_45_2, v0) = all_178_3 % 38.97/6.02 | | & sdtasdt0(xR, all_129_2) = v3 & sdtpldt0(all_55_0, v3) = v2 & % 38.97/6.02 | | sdtpldt0(all_45_2, xR) = v1 & sdtpldt0(xR, all_129_2) = v0 & % 38.97/6.02 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_178_3)) % 38.97/6.02 | | % 38.97/6.02 | | GROUND_INST: instantiating (mArith) with all_55_0, all_53_4, all_45_1, % 38.97/6.02 | | all_57_1, all_57_0, simplifying with (120), (130), (146), % 38.97/6.02 | | (150), (153), (168), (214), (241) gives: % 38.97/6.02 | | (263) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 38.97/6.02 | | (sdtasdt0(v1, all_45_1) = v2 & sdtasdt0(all_55_0, v3) = v2 & % 38.97/6.02 | | sdtasdt0(all_55_0, all_53_4) = v1 & sdtasdt0(all_53_4, all_55_0) % 38.97/6.02 | | = v1 & sdtasdt0(all_53_4, all_45_1) = v3 & sdtpldt0(all_55_0, v0) % 38.97/6.02 | | = all_57_0 & sdtpldt0(all_53_4, all_55_0) = all_57_1 & % 38.97/6.02 | | sdtpldt0(all_53_4, all_45_1) = v0 & $i(v3) & $i(v2) & $i(v1) & % 38.97/6.02 | | $i(v0) & $i(all_57_0) & $i(all_57_1)) % 38.97/6.02 | | % 38.97/6.02 | | GROUND_INST: instantiating (mArith) with all_45_0, all_45_1, all_53_4, % 38.97/6.02 | | all_55_0, all_57_1, simplifying with (123), (130), (131), % 38.97/6.02 | | (146), (147), (150), (153), (241) gives: % 38.97/6.03 | | (264) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 38.97/6.03 | | (sdtasdt0(v1, all_53_4) = v2 & sdtasdt0(all_45_0, v3) = v2 & % 38.97/6.03 | | sdtasdt0(all_45_0, all_45_1) = v1 & sdtasdt0(all_45_1, all_53_4) % 38.97/6.03 | | = v3 & sdtasdt0(all_45_1, all_45_0) = v1 & sdtpldt0(all_45_0, v0) % 38.97/6.03 | | = all_57_1 & sdtpldt0(all_45_1, all_53_4) = v0 & % 38.97/6.03 | | sdtpldt0(all_45_1, all_45_0) = all_55_0 & $i(v3) & $i(v2) & % 38.97/6.03 | | $i(v1) & $i(v0) & $i(all_57_1) & $i(all_55_0)) % 38.97/6.03 | | % 38.97/6.03 | | GROUND_INST: instantiating (mDistr) with all_129_2, xR, all_45_2, all_53_2, % 38.97/6.03 | | all_55_0, all_53_5, simplifying with (11), (17), (132), (145), % 38.97/6.03 | | (149), (213), (218), (253), (257) gives: % 38.97/6.03 | | (265) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 38.97/6.03 | | (sdtasdt0(v1, all_45_2) = v2 & sdtasdt0(all_129_2, v0) = all_53_5 & % 38.97/6.03 | | sdtasdt0(xR, all_45_2) = v3 & sdtpldt0(all_129_2, xR) = v1 & % 38.97/6.03 | | sdtpldt0(all_55_0, v3) = v2 & sdtpldt0(xR, all_45_2) = v0 & % 38.97/6.03 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_53_5)) % 38.97/6.03 | | % 38.97/6.03 | | DELTA: instantiating (258) with fresh symbols all_200_0, all_200_1 gives: % 38.97/6.03 | | (266) sdtasdt0(all_200_1, all_200_0) = all_53_5 & sdtpldt0(all_45_2, xR) % 38.97/6.03 | | = all_200_0 & sdtpldt0(xR, all_45_2) = all_200_1 & $i(all_200_0) & % 38.97/6.03 | | $i(all_200_1) & $i(all_53_5) % 38.97/6.03 | | % 38.97/6.03 | | ALPHA: (266) implies: % 38.97/6.03 | | (267) sdtpldt0(all_45_2, xR) = all_200_0 % 38.97/6.03 | | % 38.97/6.03 | | DELTA: instantiating (265) with fresh symbols all_236_0, all_236_1, % 38.97/6.03 | | all_236_2, all_236_3 gives: % 38.97/6.03 | | (268) sdtasdt0(all_236_2, all_45_2) = all_236_1 & sdtasdt0(all_129_2, % 38.97/6.03 | | all_236_3) = all_53_5 & sdtasdt0(xR, all_45_2) = all_236_0 & % 38.97/6.03 | | sdtpldt0(all_129_2, xR) = all_236_2 & sdtpldt0(all_55_0, all_236_0) % 38.97/6.03 | | = all_236_1 & sdtpldt0(xR, all_45_2) = all_236_3 & $i(all_236_0) & % 38.97/6.03 | | $i(all_236_1) & $i(all_236_2) & $i(all_236_3) & $i(all_53_5) % 38.97/6.03 | | % 38.97/6.03 | | ALPHA: (268) implies: % 38.97/6.03 | | (269) sdtpldt0(xR, all_45_2) = all_236_3 % 38.97/6.03 | | (270) sdtasdt0(all_129_2, all_236_3) = all_53_5 % 38.97/6.03 | | % 38.97/6.03 | | DELTA: instantiating (262) with fresh symbols all_238_0, all_238_1, % 38.97/6.03 | | all_238_2, all_238_3 gives: % 38.97/6.03 | | (271) sdtasdt0(all_238_2, all_129_2) = all_238_1 & sdtasdt0(all_45_2, % 38.97/6.03 | | all_238_3) = all_178_3 & sdtasdt0(xR, all_129_2) = all_238_0 & % 38.97/6.03 | | sdtpldt0(all_55_0, all_238_0) = all_238_1 & sdtpldt0(all_45_2, xR) % 38.97/6.03 | | = all_238_2 & sdtpldt0(xR, all_129_2) = all_238_3 & $i(all_238_0) & % 38.97/6.03 | | $i(all_238_1) & $i(all_238_2) & $i(all_238_3) & $i(all_178_3) % 38.97/6.03 | | % 38.97/6.03 | | ALPHA: (271) implies: % 38.97/6.03 | | (272) sdtpldt0(all_45_2, xR) = all_238_2 % 38.97/6.03 | | % 38.97/6.03 | | DELTA: instantiating (261) with fresh symbols all_246_0, all_246_1, % 38.97/6.03 | | all_246_2, all_246_3 gives: % 38.97/6.03 | | (273) sdtasdt0(all_246_2, all_53_6) = all_246_1 & sdtasdt0(all_45_2, % 38.97/6.03 | | all_246_3) = all_172_3 & sdtasdt0(xR, all_53_6) = all_246_0 & % 38.97/6.03 | | sdtpldt0(all_53_0, all_246_0) = all_246_1 & sdtpldt0(all_45_2, xR) % 38.97/6.03 | | = all_246_2 & sdtpldt0(xR, all_53_6) = all_246_3 & $i(all_246_0) & % 38.97/6.03 | | $i(all_246_1) & $i(all_246_2) & $i(all_246_3) & $i(all_172_3) % 38.97/6.03 | | % 38.97/6.03 | | ALPHA: (273) implies: % 38.97/6.03 | | (274) sdtpldt0(all_45_2, xR) = all_246_2 % 38.97/6.03 | | (275) sdtpldt0(all_53_0, all_246_0) = all_246_1 % 38.97/6.03 | | (276) sdtasdt0(xR, all_53_6) = all_246_0 % 38.97/6.03 | | (277) sdtasdt0(all_246_2, all_53_6) = all_246_1 % 38.97/6.03 | | % 38.97/6.03 | | DELTA: instantiating (259) with fresh symbols all_250_0, all_250_1, % 38.97/6.03 | | all_250_2, all_250_3 gives: % 38.97/6.03 | | (278) sdtasdt0(all_250_2, xR) = all_250_1 & sdtasdt0(all_45_2, xR) = % 38.97/6.03 | | all_250_0 & sdtasdt0(xR, all_250_3) = all_53_2 & sdtpldt0(all_53_4, % 38.97/6.03 | | all_250_0) = all_250_1 & sdtpldt0(all_45_2, xR) = all_250_3 & % 38.97/6.03 | | sdtpldt0(xR, all_45_2) = all_250_2 & $i(all_250_0) & $i(all_250_1) % 38.97/6.03 | | & $i(all_250_2) & $i(all_250_3) & $i(all_53_2) % 38.97/6.03 | | % 38.97/6.03 | | ALPHA: (278) implies: % 38.97/6.03 | | (279) sdtpldt0(xR, all_45_2) = all_250_2 % 38.97/6.03 | | (280) sdtpldt0(all_45_2, xR) = all_250_3 % 38.97/6.03 | | % 38.97/6.03 | | DELTA: instantiating (264) with fresh symbols all_260_0, all_260_1, % 38.97/6.03 | | all_260_2, all_260_3 gives: % 38.97/6.03 | | (281) sdtasdt0(all_260_2, all_53_4) = all_260_1 & sdtasdt0(all_45_0, % 38.97/6.03 | | all_260_0) = all_260_1 & sdtasdt0(all_45_0, all_45_1) = all_260_2 % 38.97/6.03 | | & sdtasdt0(all_45_1, all_53_4) = all_260_0 & sdtasdt0(all_45_1, % 38.97/6.03 | | all_45_0) = all_260_2 & sdtpldt0(all_45_0, all_260_3) = all_57_1 % 38.97/6.03 | | & sdtpldt0(all_45_1, all_53_4) = all_260_3 & sdtpldt0(all_45_1, % 38.97/6.03 | | all_45_0) = all_55_0 & $i(all_260_0) & $i(all_260_1) & % 38.97/6.03 | | $i(all_260_2) & $i(all_260_3) & $i(all_57_1) & $i(all_55_0) % 38.97/6.03 | | % 38.97/6.03 | | ALPHA: (281) implies: % 38.97/6.03 | | (282) sdtpldt0(all_45_1, all_45_0) = all_55_0 % 38.97/6.03 | | % 38.97/6.03 | | DELTA: instantiating (260) with fresh symbols all_264_0, all_264_1, % 38.97/6.03 | | all_264_2, all_264_3 gives: % 38.97/6.03 | | (283) sdtasdt0(all_264_2, all_55_0) = all_264_1 & sdtasdt0(all_53_4, % 38.97/6.03 | | all_55_0) = all_264_0 & sdtasdt0(all_53_4, all_45_1) = all_264_2 % 38.97/6.03 | | & sdtasdt0(all_45_1, all_264_0) = all_264_1 & sdtasdt0(all_45_1, % 38.97/6.03 | | all_53_4) = all_264_2 & sdtpldt0(all_53_4, all_55_0) = all_264_3 % 38.97/6.03 | | & sdtpldt0(all_53_4, all_45_1) = all_53_2 & sdtpldt0(all_45_1, % 38.97/6.03 | | all_264_3) = all_53_5 & $i(all_264_0) & $i(all_264_1) & % 38.97/6.03 | | $i(all_264_2) & $i(all_264_3) & $i(all_53_2) & $i(all_53_5) % 38.97/6.03 | | % 38.97/6.03 | | DELTA: instantiating (263) with fresh symbols all_266_0, all_266_1, % 38.97/6.03 | | all_266_2, all_266_3 gives: % 38.97/6.03 | | (284) sdtasdt0(all_266_2, all_45_1) = all_266_1 & sdtasdt0(all_55_0, % 38.97/6.03 | | all_266_0) = all_266_1 & sdtasdt0(all_55_0, all_53_4) = all_266_2 % 38.97/6.03 | | & sdtasdt0(all_53_4, all_55_0) = all_266_2 & sdtasdt0(all_53_4, % 38.97/6.03 | | all_45_1) = all_266_0 & sdtpldt0(all_55_0, all_266_3) = all_57_0 % 38.97/6.03 | | & sdtpldt0(all_53_4, all_55_0) = all_57_1 & sdtpldt0(all_53_4, % 38.97/6.03 | | all_45_1) = all_266_3 & $i(all_266_0) & $i(all_266_1) & % 38.97/6.03 | | $i(all_266_2) & $i(all_266_3) & $i(all_57_0) & $i(all_57_1) % 38.97/6.03 | | % 38.97/6.03 | | ALPHA: (284) implies: % 38.97/6.03 | | (285) sdtpldt0(all_53_4, all_45_1) = all_266_3 % 38.97/6.03 | | (286) sdtpldt0(all_55_0, all_266_3) = all_57_0 % 38.97/6.03 | | % 38.97/6.03 | | GROUND_INST: instantiating (23) with all_53_6, all_250_2, all_45_2, xR, % 38.97/6.03 | | simplifying with (129), (279) gives: % 38.97/6.03 | | (287) all_250_2 = all_53_6 % 38.97/6.03 | | % 38.97/6.03 | | GROUND_INST: instantiating (23) with all_236_3, all_250_2, all_45_2, xR, % 38.97/6.03 | | simplifying with (269), (279) gives: % 38.97/6.03 | | (288) all_250_2 = all_236_3 % 38.97/6.03 | | % 38.97/6.03 | | GROUND_INST: instantiating (23) with all_129_2, all_246_2, xR, all_45_2, % 38.97/6.03 | | simplifying with (182), (274) gives: % 38.97/6.03 | | (289) all_246_2 = all_129_2 % 38.97/6.03 | | % 38.97/6.03 | | GROUND_INST: instantiating (23) with all_200_0, all_246_2, xR, all_45_2, % 38.97/6.03 | | simplifying with (267), (274) gives: % 38.97/6.03 | | (290) all_246_2 = all_200_0 % 38.97/6.03 | | % 38.97/6.03 | | GROUND_INST: instantiating (23) with all_246_2, all_250_3, xR, all_45_2, % 38.97/6.03 | | simplifying with (274), (280) gives: % 38.97/6.03 | | (291) all_250_3 = all_246_2 % 38.97/6.03 | | % 38.97/6.03 | | GROUND_INST: instantiating (23) with all_238_2, all_250_3, xR, all_45_2, % 38.97/6.03 | | simplifying with (272), (280) gives: % 38.97/6.03 | | (292) all_250_3 = all_238_2 % 38.97/6.03 | | % 38.97/6.03 | | GROUND_INST: instantiating (23) with all_53_0, all_55_0, all_45_0, all_45_1, % 38.97/6.03 | | simplifying with (125), (282) gives: % 38.97/6.03 | | (293) all_55_0 = all_53_0 % 38.97/6.03 | | % 38.97/6.03 | | GROUND_INST: instantiating (23) with all_53_2, all_266_3, all_45_1, % 38.97/6.03 | | all_53_4, simplifying with (126), (285) gives: % 38.97/6.03 | | (294) all_266_3 = all_53_2 % 38.97/6.03 | | % 38.97/6.03 | | GROUND_INST: instantiating (24) with all_53_2, all_246_0, all_53_6, xR, % 38.97/6.03 | | simplifying with (206), (276) gives: % 38.97/6.03 | | (295) all_246_0 = all_53_2 % 38.97/6.03 | | % 38.97/6.03 | | COMBINE_EQS: (287), (288) imply: % 38.97/6.03 | | (296) all_236_3 = all_53_6 % 38.97/6.03 | | % 38.97/6.03 | | COMBINE_EQS: (291), (292) imply: % 38.97/6.03 | | (297) all_246_2 = all_238_2 % 38.97/6.03 | | % 38.97/6.03 | | SIMP: (297) implies: % 38.97/6.03 | | (298) all_246_2 = all_238_2 % 38.97/6.03 | | % 38.97/6.03 | | COMBINE_EQS: (290), (298) imply: % 38.97/6.03 | | (299) all_238_2 = all_200_0 % 38.97/6.03 | | % 38.97/6.03 | | COMBINE_EQS: (289), (298) imply: % 38.97/6.03 | | (300) all_238_2 = all_129_2 % 38.97/6.03 | | % 38.97/6.03 | | COMBINE_EQS: (299), (300) imply: % 38.97/6.03 | | (301) all_200_0 = all_129_2 % 38.97/6.03 | | % 38.97/6.03 | | REDUCE: (277), (289) imply: % 38.97/6.03 | | (302) sdtasdt0(all_129_2, all_53_6) = all_246_1 % 38.97/6.03 | | % 38.97/6.03 | | REDUCE: (270), (296) imply: % 38.97/6.03 | | (303) sdtasdt0(all_129_2, all_53_6) = all_53_5 % 38.97/6.03 | | % 38.97/6.03 | | REDUCE: (286), (293), (294) imply: % 38.97/6.03 | | (304) sdtpldt0(all_53_0, all_53_2) = all_57_0 % 38.97/6.03 | | % 38.97/6.03 | | REDUCE: (275), (295) imply: % 38.97/6.03 | | (305) sdtpldt0(all_53_0, all_53_2) = all_246_1 % 38.97/6.03 | | % 38.97/6.03 | | GROUND_INST: instantiating (23) with all_57_0, all_246_1, all_53_2, % 38.97/6.03 | | all_53_0, simplifying with (304), (305) gives: % 38.97/6.03 | | (306) all_246_1 = all_57_0 % 38.97/6.03 | | % 38.97/6.03 | | GROUND_INST: instantiating (24) with all_53_5, all_246_1, all_53_6, % 38.97/6.03 | | all_129_2, simplifying with (302), (303) gives: % 38.97/6.03 | | (307) all_246_1 = all_53_5 % 38.97/6.03 | | % 38.97/6.03 | | COMBINE_EQS: (306), (307) imply: % 38.97/6.03 | | (308) all_57_0 = all_53_5 % 38.97/6.03 | | % 38.97/6.04 | | REDUCE: (144), (308) imply: % 38.97/6.04 | | (309) $false % 38.97/6.04 | | % 38.97/6.04 | | CLOSE: (309) is inconsistent. % 38.97/6.04 | | % 38.97/6.04 | End of split % 38.97/6.04 | % 38.97/6.04 End of proof % 38.97/6.04 % SZS output end Proof for theBenchmark % 38.97/6.04 % 38.97/6.04 5432ms %------------------------------------------------------------------------------