%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG069+1 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n016.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 13:57:40 EDT 2023 % Result : Theorem 14.39s 3.33s % Output : Proof 21.28s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : RNG069+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.17/0.35 % Computer : n016.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Sun Aug 27 02:18:42 EDT 2023 % 0.17/0.35 % CPUTime : % 0.22/0.55 ________ _____ % 0.22/0.55 ___ __ \_________(_)________________________________ % 0.22/0.55 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.55 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.55 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.55 % 0.22/0.55 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.55 (2023-06-19) % 0.22/0.55 % 0.22/0.55 (c) Philipp Rümmer, 2009-2023 % 0.22/0.55 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.55 Amanda Stjerna. % 0.22/0.55 Free software under BSD-3-Clause. % 0.22/0.55 % 0.22/0.55 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.55 % 0.22/0.55 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.22/0.56 Running up to 7 provers in parallel. % 0.22/0.58 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.22/0.58 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.58 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.58 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.58 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.22/0.58 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.22/0.58 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.13/1.20 Prover 4: Preprocessing ... % 3.13/1.20 Prover 1: Preprocessing ... % 3.51/1.29 Prover 0: Preprocessing ... % 3.51/1.29 Prover 2: Preprocessing ... % 3.51/1.29 Prover 6: Preprocessing ... % 3.51/1.29 Prover 5: Preprocessing ... % 3.51/1.29 Prover 3: Preprocessing ... % 7.69/2.22 Prover 1: Constructing countermodel ... % 7.69/2.22 Prover 3: Constructing countermodel ... % 7.69/2.24 Prover 6: Proving ... % 10.41/2.54 Prover 5: Constructing countermodel ... % 10.87/2.62 Prover 4: Constructing countermodel ... % 11.07/2.67 Prover 2: Proving ... % 11.76/2.83 Prover 0: Proving ... % 14.39/3.33 Prover 3: proved (2754ms) % 14.39/3.33 % 14.39/3.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.39/3.33 % 14.61/3.35 Prover 5: stopped % 14.61/3.36 Prover 0: stopped % 14.61/3.38 Prover 6: stopped % 14.61/3.38 Prover 2: stopped % 14.61/3.39 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.61/3.39 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.61/3.39 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.61/3.40 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.61/3.40 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.95/3.44 Prover 8: Preprocessing ... % 15.31/3.52 Prover 7: Preprocessing ... % 15.83/3.56 Prover 10: Preprocessing ... % 15.83/3.57 Prover 13: Preprocessing ... % 15.83/3.57 Prover 11: Preprocessing ... % 15.83/3.68 Prover 8: Warning: ignoring some quantifiers % 15.83/3.69 Prover 8: Constructing countermodel ... % 15.83/3.76 Prover 10: Constructing countermodel ... % 17.45/3.87 Prover 7: Constructing countermodel ... % 17.75/3.92 Prover 13: Constructing countermodel ... % 18.87/4.11 Prover 11: Constructing countermodel ... % 19.81/4.41 Prover 10: Found proof (size 108) % 19.81/4.41 Prover 10: proved (1037ms) % 19.81/4.41 Prover 4: stopped % 19.81/4.41 Prover 11: stopped % 19.81/4.42 Prover 13: stopped % 19.81/4.42 Prover 7: stopped % 19.81/4.42 Prover 8: stopped % 19.81/4.42 Prover 1: stopped % 19.81/4.42 % 19.81/4.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 19.81/4.42 % 19.81/4.46 % SZS output start Proof for theBenchmark % 19.81/4.46 Assumptions after simplification: % 19.81/4.46 --------------------------------- % 19.81/4.46 % 19.81/4.46 (mDistr) % 20.96/4.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 20.96/4.50 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ % 20.96/4.50 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 20.96/4.50 aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v6: $i] : ? [v7: $i] % 20.96/4.50 : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v7, v2) = v8 & sdtasdt0(v1, v2) = v9 % 20.96/4.50 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v4, v9) = v8 & sdtpldt0(v1, v2) = v6 & % 20.96/4.50 sdtpldt0(v0, v1) = v7 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5))) % 20.96/4.50 % 20.96/4.50 (mDistr2) % 20.96/4.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 20.96/4.50 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : % 20.96/4.50 ( ~ (sdtasdt0(v1, v3) = v8) | ~ (sdtasdt0(v1, v2) = v7) | ~ (sdtasdt0(v0, % 20.96/4.50 v3) = v5) | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtpldt0(v7, v8) = v9) | ~ % 20.96/4.50 (sdtpldt0(v6, v9) = v10) | ~ (sdtpldt0(v4, v5) = v6) | ~ $i(v3) | ~ % 20.96/4.50 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aScalar0(v3) | ~ aScalar0(v2) | ~ % 20.96/4.50 aScalar0(v1) | ~ aScalar0(v0) | ? [v11: $i] : ? [v12: $i] : % 20.96/4.50 (sdtasdt0(v11, v12) = v10 & sdtpldt0(v2, v3) = v12 & sdtpldt0(v0, v1) = v11 % 20.96/4.50 & $i(v12) & $i(v11) & $i(v10))) % 20.96/4.50 % 20.96/4.50 (m__) % 20.96/4.51 $i(xS) & $i(xP) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 20.96/4.51 $i] : (sdtasdt0(v2, v2) = v3 & sdtasdt0(v0, v0) = v1 & sdtpldt0(xP, xP) = v0 % 20.96/4.51 & sdtpldt0(xR, xS) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~ % 20.96/4.51 sdtlseqdt0(v1, v3)) % 20.96/4.51 % 20.96/4.51 (m__1892) % 20.96/4.51 sdtasdt0(xC, xG) = xR & $i(xR) & $i(xG) & $i(xC) & aScalar0(xR) % 20.96/4.51 % 20.96/4.51 (m__1911) % 20.96/4.51 sdtasdt0(xE, xH) = xP & $i(xP) & $i(xH) & $i(xE) & aScalar0(xP) % 20.96/4.51 % 20.96/4.51 (m__1930) % 20.96/4.51 sdtasdt0(xF, xD) = xS & $i(xS) & $i(xF) & $i(xD) & aScalar0(xS) % 20.96/4.51 % 20.96/4.51 (m__1949) % 20.96/4.51 sdtasdt0(xR, xS) = xN & $i(xN) & $i(xS) & $i(xR) & aScalar0(xN) % 20.96/4.51 % 20.96/4.51 (m__2004) % 20.96/4.51 $i(xN) & $i(xP) & ? [v0: $i] : (sdtasdt0(xP, xP) = v0 & $i(v0) & % 20.96/4.51 sdtlseqdt0(v0, xN)) % 20.96/4.51 % 20.96/4.51 (m__2104) % 20.96/4.51 $i(xS) & $i(xP) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 20.96/4.51 $i] : ? [v4: $i] : (sdtasdt0(xS, xS) = v3 & sdtasdt0(xP, xP) = v0 & % 20.96/4.51 sdtasdt0(xR, xR) = v2 & sdtpldt0(v2, v3) = v4 & sdtpldt0(v0, v0) = v1 & % 20.96/4.51 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v1, v4)) % 20.96/4.51 % 20.96/4.51 (m__2463) % 20.96/4.51 $i(xN) & $i(xS) & $i(xP) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 20.96/4.51 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 20.96/4.51 $i] : (sdtasdt0(xS, xS) = v5 & sdtasdt0(xP, xP) = v0 & sdtasdt0(xR, xR) = v4 % 20.96/4.51 & sdtpldt0(v7, xN) = v8 & sdtpldt0(v6, xN) = v7 & sdtpldt0(v4, v5) = v6 & % 20.96/4.51 sdtpldt0(v2, v0) = v3 & sdtpldt0(v1, v0) = v2 & sdtpldt0(v0, v0) = v1 & % 20.96/4.51 $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 20.96/4.51 $i(v0) & sdtlseqdt0(v3, v8)) % 20.96/4.51 % 20.96/4.51 (m__2510) % 20.96/4.51 $i(xN) & $i(xS) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 20.96/4.51 $i] : ? [v4: $i] : ? [v5: $i] : (sdtasdt0(xS, xS) = v2 & sdtasdt0(xR, xR) % 20.96/4.51 = v0 & sdtpldt0(v3, xN) = v4 & sdtpldt0(v2, xN) = v5 & sdtpldt0(v1, v5) = v4 % 20.96/4.51 & sdtpldt0(v1, v2) = v3 & sdtpldt0(v0, xN) = v1 & $i(v5) & $i(v4) & $i(v3) & % 20.96/4.51 $i(v2) & $i(v1) & $i(v0)) % 20.96/4.51 % 20.96/4.51 (m__2580) % 20.96/4.51 $i(xS) & $i(xP) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 20.96/4.52 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 20.96/4.52 ? [v9: $i] : (sdtasdt0(xS, xS) = v7 & sdtasdt0(xS, xR) = v6 & sdtasdt0(xP, xP) % 20.96/4.52 = v0 & sdtasdt0(xR, xS) = v4 & sdtasdt0(xR, xR) = v3 & sdtpldt0(v6, v7) = v8 % 20.96/4.52 & sdtpldt0(v5, v8) = v9 & sdtpldt0(v3, v4) = v5 & sdtpldt0(v1, v1) = v2 & % 20.96/4.52 sdtpldt0(v0, v0) = v1 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) % 20.96/4.52 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v2, v9)) % 20.96/4.52 % 20.96/4.52 (function-axioms) % 20.96/4.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.96/4.52 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 20.96/4.52 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) % 20.96/4.52 | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 20.96/4.52 ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = % 20.96/4.52 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 20.96/4.52 ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 20.96/4.52 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sziznziztdt0(v2) = v1) | ~ % 20.96/4.52 (sziznziztdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 20.96/4.52 v0 | ~ (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) & ! [v0: % 20.96/4.52 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ % 20.96/4.52 (smndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 20.96/4.52 (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0)) % 20.96/4.52 % 20.96/4.52 Further assumptions not needed in the proof: % 20.96/4.52 -------------------------------------------- % 20.96/4.52 mArith, mDefInit, mDefSPN, mDefSPZ, mDimNat, mElmSc, mEqInit, mIH, mIHOrd, % 20.96/4.52 mLEASm, mLEMon, mLEMonM, mLERef, mLETot, mLETrn, mLess, mMDNeg, mMNeg, mMulSc, % 20.96/4.52 mNatExtr, mNatSort, mNegSc, mPosMon, mSZeroSc, mScPr, mScSort, mScSqPos, % 20.96/4.52 mScZero, mSqPos, mSqrt, mSuccEqu, mSuccNat, mSumSc, mVcSort, mZeroNat, m__1652, % 20.96/4.52 m__1678, m__1678_01, m__1692, m__1709, m__1726, m__1746, m__1766, m__1783, % 20.96/4.52 m__1800, m__1820, m__1837, m__1854, m__1873, m__1967 % 20.96/4.52 % 20.96/4.52 Those formulas are unsatisfiable: % 20.96/4.52 --------------------------------- % 20.96/4.52 % 20.96/4.52 Begin of proof % 20.96/4.52 | % 20.96/4.52 | ALPHA: (m__1892) implies: % 20.96/4.52 | (1) aScalar0(xR) % 20.96/4.52 | % 20.96/4.52 | ALPHA: (m__1911) implies: % 20.96/4.52 | (2) aScalar0(xP) % 20.96/4.52 | % 20.96/4.52 | ALPHA: (m__1930) implies: % 20.96/4.52 | (3) aScalar0(xS) % 20.96/4.52 | % 20.96/4.52 | ALPHA: (m__1949) implies: % 20.96/4.52 | (4) sdtasdt0(xR, xS) = xN % 20.96/4.52 | % 20.96/4.52 | ALPHA: (m__2004) implies: % 20.96/4.52 | (5) ? [v0: $i] : (sdtasdt0(xP, xP) = v0 & $i(v0) & sdtlseqdt0(v0, xN)) % 20.96/4.52 | % 20.96/4.52 | ALPHA: (m__2104) implies: % 20.96/4.52 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 20.96/4.52 | (sdtasdt0(xS, xS) = v3 & sdtasdt0(xP, xP) = v0 & sdtasdt0(xR, xR) = v2 % 20.96/4.52 | & sdtpldt0(v2, v3) = v4 & sdtpldt0(v0, v0) = v1 & $i(v4) & $i(v3) & % 20.96/4.52 | $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v1, v4)) % 20.96/4.52 | % 20.96/4.52 | ALPHA: (m__2463) implies: % 20.96/4.52 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 20.96/4.52 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(xS, % 20.96/4.52 | xS) = v5 & sdtasdt0(xP, xP) = v0 & sdtasdt0(xR, xR) = v4 & % 20.96/4.52 | sdtpldt0(v7, xN) = v8 & sdtpldt0(v6, xN) = v7 & sdtpldt0(v4, v5) = v6 % 20.96/4.52 | & sdtpldt0(v2, v0) = v3 & sdtpldt0(v1, v0) = v2 & sdtpldt0(v0, v0) = % 20.96/4.52 | v1 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 20.96/4.52 | $i(v1) & $i(v0) & sdtlseqdt0(v3, v8)) % 20.96/4.52 | % 20.96/4.52 | ALPHA: (m__2510) implies: % 20.96/4.53 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 20.96/4.53 | ? [v5: $i] : (sdtasdt0(xS, xS) = v2 & sdtasdt0(xR, xR) = v0 & % 20.96/4.53 | sdtpldt0(v3, xN) = v4 & sdtpldt0(v2, xN) = v5 & sdtpldt0(v1, v5) = v4 % 20.96/4.53 | & sdtpldt0(v1, v2) = v3 & sdtpldt0(v0, xN) = v1 & $i(v5) & $i(v4) & % 20.96/4.53 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 20.96/4.53 | % 20.96/4.53 | ALPHA: (m__2580) implies: % 20.96/4.53 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 20.96/4.53 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 20.96/4.53 | (sdtasdt0(xS, xS) = v7 & sdtasdt0(xS, xR) = v6 & sdtasdt0(xP, xP) = v0 % 20.96/4.53 | & sdtasdt0(xR, xS) = v4 & sdtasdt0(xR, xR) = v3 & sdtpldt0(v6, v7) = % 20.96/4.53 | v8 & sdtpldt0(v5, v8) = v9 & sdtpldt0(v3, v4) = v5 & sdtpldt0(v1, v1) % 20.96/4.53 | = v2 & sdtpldt0(v0, v0) = v1 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 20.96/4.53 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v2, % 20.96/4.53 | v9)) % 20.96/4.53 | % 20.96/4.53 | ALPHA: (m__) implies: % 20.96/4.53 | (10) $i(xR) % 20.96/4.53 | (11) $i(xP) % 20.96/4.53 | (12) $i(xS) % 20.96/4.53 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v2, % 20.96/4.53 | v2) = v3 & sdtasdt0(v0, v0) = v1 & sdtpldt0(xP, xP) = v0 & % 20.96/4.53 | sdtpldt0(xR, xS) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~ % 20.96/4.53 | sdtlseqdt0(v1, v3)) % 20.96/4.53 | % 20.96/4.53 | ALPHA: (function-axioms) implies: % 20.96/4.53 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.96/4.53 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 20.96/4.53 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.96/4.53 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 20.96/4.53 | % 20.96/4.53 | DELTA: instantiating (5) with fresh symbol all_33_0 gives: % 20.96/4.53 | (16) sdtasdt0(xP, xP) = all_33_0 & $i(all_33_0) & sdtlseqdt0(all_33_0, xN) % 20.96/4.53 | % 20.96/4.53 | ALPHA: (16) implies: % 20.96/4.53 | (17) sdtasdt0(xP, xP) = all_33_0 % 20.96/4.53 | % 20.96/4.53 | DELTA: instantiating (13) with fresh symbols all_45_0, all_45_1, all_45_2, % 20.96/4.53 | all_45_3 gives: % 20.96/4.53 | (18) sdtasdt0(all_45_1, all_45_1) = all_45_0 & sdtasdt0(all_45_3, all_45_3) % 20.96/4.53 | = all_45_2 & sdtpldt0(xP, xP) = all_45_3 & sdtpldt0(xR, xS) = all_45_1 % 20.96/4.53 | & $i(all_45_0) & $i(all_45_1) & $i(all_45_2) & $i(all_45_3) & ~ % 20.96/4.53 | sdtlseqdt0(all_45_2, all_45_0) % 20.96/4.53 | % 20.96/4.53 | ALPHA: (18) implies: % 20.96/4.53 | (19) ~ sdtlseqdt0(all_45_2, all_45_0) % 20.96/4.53 | (20) sdtpldt0(xR, xS) = all_45_1 % 20.96/4.53 | (21) sdtpldt0(xP, xP) = all_45_3 % 20.96/4.53 | (22) sdtasdt0(all_45_3, all_45_3) = all_45_2 % 20.96/4.53 | (23) sdtasdt0(all_45_1, all_45_1) = all_45_0 % 20.96/4.53 | % 20.96/4.53 | DELTA: instantiating (6) with fresh symbols all_47_0, all_47_1, all_47_2, % 21.28/4.53 | all_47_3, all_47_4 gives: % 21.28/4.53 | (24) sdtasdt0(xS, xS) = all_47_1 & sdtasdt0(xP, xP) = all_47_4 & % 21.28/4.53 | sdtasdt0(xR, xR) = all_47_2 & sdtpldt0(all_47_2, all_47_1) = all_47_0 % 21.28/4.53 | & sdtpldt0(all_47_4, all_47_4) = all_47_3 & $i(all_47_0) & % 21.28/4.53 | $i(all_47_1) & $i(all_47_2) & $i(all_47_3) & $i(all_47_4) & % 21.28/4.53 | sdtlseqdt0(all_47_3, all_47_0) % 21.28/4.54 | % 21.28/4.54 | ALPHA: (24) implies: % 21.28/4.54 | (25) sdtpldt0(all_47_4, all_47_4) = all_47_3 % 21.28/4.54 | (26) sdtasdt0(xR, xR) = all_47_2 % 21.28/4.54 | (27) sdtasdt0(xP, xP) = all_47_4 % 21.28/4.54 | (28) sdtasdt0(xS, xS) = all_47_1 % 21.28/4.54 | % 21.28/4.54 | DELTA: instantiating (8) with fresh symbols all_49_0, all_49_1, all_49_2, % 21.28/4.54 | all_49_3, all_49_4, all_49_5 gives: % 21.28/4.54 | (29) sdtasdt0(xS, xS) = all_49_3 & sdtasdt0(xR, xR) = all_49_5 & % 21.28/4.54 | sdtpldt0(all_49_2, xN) = all_49_1 & sdtpldt0(all_49_3, xN) = all_49_0 % 21.28/4.54 | & sdtpldt0(all_49_4, all_49_0) = all_49_1 & sdtpldt0(all_49_4, % 21.28/4.54 | all_49_3) = all_49_2 & sdtpldt0(all_49_5, xN) = all_49_4 & % 21.28/4.54 | $i(all_49_0) & $i(all_49_1) & $i(all_49_2) & $i(all_49_3) & % 21.28/4.54 | $i(all_49_4) & $i(all_49_5) % 21.28/4.54 | % 21.28/4.54 | ALPHA: (29) implies: % 21.28/4.54 | (30) sdtpldt0(all_49_5, xN) = all_49_4 % 21.28/4.54 | (31) sdtasdt0(xR, xR) = all_49_5 % 21.28/4.54 | (32) sdtasdt0(xS, xS) = all_49_3 % 21.28/4.54 | % 21.28/4.54 | DELTA: instantiating (7) with fresh symbols all_51_0, all_51_1, all_51_2, % 21.28/4.54 | all_51_3, all_51_4, all_51_5, all_51_6, all_51_7, all_51_8 gives: % 21.28/4.54 | (33) sdtasdt0(xS, xS) = all_51_3 & sdtasdt0(xP, xP) = all_51_8 & % 21.28/4.54 | sdtasdt0(xR, xR) = all_51_4 & sdtpldt0(all_51_1, xN) = all_51_0 & % 21.28/4.54 | sdtpldt0(all_51_2, xN) = all_51_1 & sdtpldt0(all_51_4, all_51_3) = % 21.28/4.54 | all_51_2 & sdtpldt0(all_51_6, all_51_8) = all_51_5 & % 21.28/4.54 | sdtpldt0(all_51_7, all_51_8) = all_51_6 & sdtpldt0(all_51_8, all_51_8) % 21.28/4.54 | = all_51_7 & $i(all_51_0) & $i(all_51_1) & $i(all_51_2) & $i(all_51_3) % 21.28/4.54 | & $i(all_51_4) & $i(all_51_5) & $i(all_51_6) & $i(all_51_7) & % 21.28/4.54 | $i(all_51_8) & sdtlseqdt0(all_51_5, all_51_0) % 21.28/4.54 | % 21.28/4.54 | ALPHA: (33) implies: % 21.28/4.54 | (34) sdtpldt0(all_51_8, all_51_8) = all_51_7 % 21.28/4.54 | (35) sdtasdt0(xR, xR) = all_51_4 % 21.28/4.54 | (36) sdtasdt0(xP, xP) = all_51_8 % 21.28/4.54 | (37) sdtasdt0(xS, xS) = all_51_3 % 21.28/4.54 | % 21.28/4.54 | DELTA: instantiating (9) with fresh symbols all_56_0, all_56_1, all_56_2, % 21.28/4.54 | all_56_3, all_56_4, all_56_5, all_56_6, all_56_7, all_56_8, all_56_9 % 21.28/4.54 | gives: % 21.28/4.54 | (38) sdtasdt0(xS, xS) = all_56_2 & sdtasdt0(xS, xR) = all_56_3 & % 21.28/4.54 | sdtasdt0(xP, xP) = all_56_9 & sdtasdt0(xR, xS) = all_56_5 & % 21.28/4.54 | sdtasdt0(xR, xR) = all_56_6 & sdtpldt0(all_56_3, all_56_2) = all_56_1 % 21.28/4.54 | & sdtpldt0(all_56_4, all_56_1) = all_56_0 & sdtpldt0(all_56_6, % 21.28/4.54 | all_56_5) = all_56_4 & sdtpldt0(all_56_8, all_56_8) = all_56_7 & % 21.28/4.54 | sdtpldt0(all_56_9, all_56_9) = all_56_8 & $i(all_56_0) & $i(all_56_1) % 21.28/4.54 | & $i(all_56_2) & $i(all_56_3) & $i(all_56_4) & $i(all_56_5) & % 21.28/4.54 | $i(all_56_6) & $i(all_56_7) & $i(all_56_8) & $i(all_56_9) & % 21.28/4.54 | sdtlseqdt0(all_56_7, all_56_0) % 21.28/4.54 | % 21.28/4.54 | ALPHA: (38) implies: % 21.28/4.54 | (39) sdtlseqdt0(all_56_7, all_56_0) % 21.28/4.54 | (40) sdtpldt0(all_56_9, all_56_9) = all_56_8 % 21.28/4.54 | (41) sdtpldt0(all_56_8, all_56_8) = all_56_7 % 21.28/4.54 | (42) sdtpldt0(all_56_6, all_56_5) = all_56_4 % 21.28/4.54 | (43) sdtpldt0(all_56_4, all_56_1) = all_56_0 % 21.28/4.54 | (44) sdtpldt0(all_56_3, all_56_2) = all_56_1 % 21.28/4.54 | (45) sdtasdt0(xR, xR) = all_56_6 % 21.28/4.54 | (46) sdtasdt0(xR, xS) = all_56_5 % 21.28/4.54 | (47) sdtasdt0(xP, xP) = all_56_9 % 21.28/4.54 | (48) sdtasdt0(xS, xR) = all_56_3 % 21.28/4.54 | (49) sdtasdt0(xS, xS) = all_56_2 % 21.28/4.54 | % 21.28/4.54 | GROUND_INST: instantiating (15) with all_47_2, all_51_4, xR, xR, simplifying % 21.28/4.54 | with (26), (35) gives: % 21.28/4.54 | (50) all_51_4 = all_47_2 % 21.28/4.54 | % 21.28/4.55 | GROUND_INST: instantiating (15) with all_51_4, all_56_6, xR, xR, simplifying % 21.28/4.55 | with (35), (45) gives: % 21.28/4.55 | (51) all_56_6 = all_51_4 % 21.28/4.55 | % 21.28/4.55 | GROUND_INST: instantiating (15) with all_49_5, all_56_6, xR, xR, simplifying % 21.28/4.55 | with (31), (45) gives: % 21.28/4.55 | (52) all_56_6 = all_49_5 % 21.28/4.55 | % 21.28/4.55 | GROUND_INST: instantiating (15) with xN, all_56_5, xS, xR, simplifying with % 21.28/4.55 | (4), (46) gives: % 21.28/4.55 | (53) all_56_5 = xN % 21.28/4.55 | % 21.28/4.55 | GROUND_INST: instantiating (15) with all_47_4, all_51_8, xP, xP, simplifying % 21.28/4.55 | with (27), (36) gives: % 21.28/4.55 | (54) all_51_8 = all_47_4 % 21.28/4.55 | % 21.28/4.55 | GROUND_INST: instantiating (15) with all_51_8, all_56_9, xP, xP, simplifying % 21.28/4.55 | with (36), (47) gives: % 21.28/4.55 | (55) all_56_9 = all_51_8 % 21.28/4.55 | % 21.28/4.55 | GROUND_INST: instantiating (15) with all_33_0, all_56_9, xP, xP, simplifying % 21.28/4.55 | with (17), (47) gives: % 21.28/4.55 | (56) all_56_9 = all_33_0 % 21.28/4.55 | % 21.28/4.55 | GROUND_INST: instantiating (15) with all_49_3, all_51_3, xS, xS, simplifying % 21.28/4.55 | with (32), (37) gives: % 21.28/4.55 | (57) all_51_3 = all_49_3 % 21.28/4.55 | % 21.28/4.55 | GROUND_INST: instantiating (15) with all_51_3, all_56_2, xS, xS, simplifying % 21.28/4.55 | with (37), (49) gives: % 21.28/4.55 | (58) all_56_2 = all_51_3 % 21.28/4.55 | % 21.28/4.55 | GROUND_INST: instantiating (15) with all_47_1, all_56_2, xS, xS, simplifying % 21.28/4.55 | with (28), (49) gives: % 21.28/4.55 | (59) all_56_2 = all_47_1 % 21.28/4.55 | % 21.28/4.55 | COMBINE_EQS: (58), (59) imply: % 21.28/4.55 | (60) all_51_3 = all_47_1 % 21.28/4.55 | % 21.28/4.55 | SIMP: (60) implies: % 21.28/4.55 | (61) all_51_3 = all_47_1 % 21.28/4.55 | % 21.28/4.55 | COMBINE_EQS: (51), (52) imply: % 21.28/4.55 | (62) all_51_4 = all_49_5 % 21.28/4.55 | % 21.28/4.55 | SIMP: (62) implies: % 21.28/4.55 | (63) all_51_4 = all_49_5 % 21.28/4.55 | % 21.28/4.55 | COMBINE_EQS: (55), (56) imply: % 21.28/4.55 | (64) all_51_8 = all_33_0 % 21.28/4.55 | % 21.28/4.55 | SIMP: (64) implies: % 21.28/4.55 | (65) all_51_8 = all_33_0 % 21.28/4.55 | % 21.28/4.55 | COMBINE_EQS: (57), (61) imply: % 21.28/4.55 | (66) all_49_3 = all_47_1 % 21.28/4.55 | % 21.28/4.55 | SIMP: (66) implies: % 21.28/4.55 | (67) all_49_3 = all_47_1 % 21.28/4.55 | % 21.28/4.55 | COMBINE_EQS: (50), (63) imply: % 21.28/4.55 | (68) all_49_5 = all_47_2 % 21.28/4.55 | % 21.28/4.55 | SIMP: (68) implies: % 21.28/4.55 | (69) all_49_5 = all_47_2 % 21.28/4.55 | % 21.28/4.55 | COMBINE_EQS: (54), (65) imply: % 21.28/4.55 | (70) all_47_4 = all_33_0 % 21.28/4.55 | % 21.28/4.55 | SIMP: (70) implies: % 21.28/4.55 | (71) all_47_4 = all_33_0 % 21.28/4.55 | % 21.28/4.55 | COMBINE_EQS: (52), (69) imply: % 21.28/4.55 | (72) all_56_6 = all_47_2 % 21.28/4.55 | % 21.28/4.55 | REDUCE: (44), (59) imply: % 21.28/4.55 | (73) sdtpldt0(all_56_3, all_47_1) = all_56_1 % 21.28/4.55 | % 21.28/4.55 | REDUCE: (42), (53), (72) imply: % 21.28/4.55 | (74) sdtpldt0(all_47_2, xN) = all_56_4 % 21.28/4.55 | % 21.28/4.55 | REDUCE: (40), (56) imply: % 21.28/4.55 | (75) sdtpldt0(all_33_0, all_33_0) = all_56_8 % 21.28/4.55 | % 21.28/4.55 | REDUCE: (34), (65) imply: % 21.28/4.55 | (76) sdtpldt0(all_33_0, all_33_0) = all_51_7 % 21.28/4.55 | % 21.28/4.55 | REDUCE: (30), (69) imply: % 21.28/4.56 | (77) sdtpldt0(all_47_2, xN) = all_49_4 % 21.28/4.56 | % 21.28/4.56 | REDUCE: (25), (71) imply: % 21.28/4.56 | (78) sdtpldt0(all_33_0, all_33_0) = all_47_3 % 21.28/4.56 | % 21.28/4.56 | GROUND_INST: instantiating (14) with all_51_7, all_56_8, all_33_0, all_33_0, % 21.28/4.56 | simplifying with (75), (76) gives: % 21.28/4.56 | (79) all_56_8 = all_51_7 % 21.28/4.56 | % 21.28/4.56 | GROUND_INST: instantiating (14) with all_47_3, all_56_8, all_33_0, all_33_0, % 21.28/4.56 | simplifying with (75), (78) gives: % 21.28/4.56 | (80) all_56_8 = all_47_3 % 21.28/4.56 | % 21.28/4.56 | GROUND_INST: instantiating (14) with all_49_4, all_56_4, xN, all_47_2, % 21.28/4.56 | simplifying with (74), (77) gives: % 21.28/4.56 | (81) all_56_4 = all_49_4 % 21.28/4.56 | % 21.28/4.56 | COMBINE_EQS: (79), (80) imply: % 21.28/4.56 | (82) all_51_7 = all_47_3 % 21.28/4.56 | % 21.28/4.56 | REDUCE: (43), (81) imply: % 21.28/4.56 | (83) sdtpldt0(all_49_4, all_56_1) = all_56_0 % 21.28/4.56 | % 21.28/4.56 | REDUCE: (41), (80) imply: % 21.28/4.56 | (84) sdtpldt0(all_47_3, all_47_3) = all_56_7 % 21.28/4.56 | % 21.28/4.56 | GROUND_INST: instantiating (mDistr) with xR, xR, xS, all_47_2, xN, all_49_4, % 21.28/4.56 | simplifying with (1), (3), (4), (10), (12), (26), (77) gives: % 21.28/4.56 | (85) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v1, % 21.28/4.56 | xS) = v2 & sdtasdt0(xR, v0) = all_49_4 & sdtasdt0(xR, xS) = v3 & % 21.28/4.56 | sdtpldt0(xN, v3) = v2 & sdtpldt0(xR, xS) = v0 & sdtpldt0(xR, xR) = % 21.28/4.56 | v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_49_4)) % 21.28/4.56 | % 21.28/4.56 | GROUND_INST: instantiating (mDistr2) with xP, xP, xP, xP, all_33_0, all_33_0, % 21.28/4.56 | all_47_3, all_33_0, all_33_0, all_47_3, all_56_7, simplifying % 21.28/4.56 | with (2), (11), (17), (78), (84) gives: % 21.28/4.56 | (86) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(v0, v1) = all_56_7 & % 21.28/4.56 | sdtpldt0(xP, xP) = v1 & sdtpldt0(xP, xP) = v0 & $i(v1) & $i(v0) & % 21.28/4.56 | $i(all_56_7)) % 21.28/4.56 | % 21.28/4.56 | GROUND_INST: instantiating (mDistr) with xP, xP, xP, all_33_0, all_33_0, % 21.28/4.56 | all_47_3, simplifying with (2), (11), (17), (78) gives: % 21.28/4.56 | (87) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v1, % 21.28/4.56 | xP) = v2 & sdtasdt0(xP, v0) = all_47_3 & sdtasdt0(xP, xP) = v3 & % 21.28/4.56 | sdtpldt0(all_33_0, v3) = v2 & sdtpldt0(xP, xP) = v1 & sdtpldt0(xP, % 21.28/4.56 | xP) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_47_3)) % 21.28/4.56 | % 21.28/4.56 | GROUND_INST: instantiating (mDistr2) with xR, xS, xR, xS, all_47_2, xN, % 21.28/4.56 | all_49_4, all_56_3, all_47_1, all_56_1, all_56_0, simplifying % 21.28/4.56 | with (1), (3), (4), (10), (12), (26), (28), (48), (73), (77), % 21.28/4.56 | (83) gives: % 21.28/4.57 | (88) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(v0, v1) = all_56_0 & % 21.28/4.57 | sdtpldt0(xR, xS) = v1 & sdtpldt0(xR, xS) = v0 & $i(v1) & $i(v0) & % 21.28/4.57 | $i(all_56_0)) % 21.28/4.57 | % 21.28/4.57 | GROUND_INST: instantiating (mDistr) with xS, xR, xS, all_56_3, all_47_1, % 21.28/4.57 | all_56_1, simplifying with (1), (3), (10), (12), (28), (48), (73) % 21.28/4.57 | gives: % 21.28/4.57 | (89) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v1, % 21.28/4.57 | xS) = v2 & sdtasdt0(xS, v0) = all_56_1 & sdtasdt0(xR, xS) = v3 & % 21.28/4.57 | sdtpldt0(all_47_1, v3) = v2 & sdtpldt0(xS, xR) = v1 & sdtpldt0(xR, % 21.28/4.57 | xS) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_56_1)) % 21.28/4.57 | % 21.28/4.57 | DELTA: instantiating (86) with fresh symbols all_75_0, all_75_1 gives: % 21.28/4.57 | (90) sdtasdt0(all_75_1, all_75_0) = all_56_7 & sdtpldt0(xP, xP) = all_75_0 % 21.28/4.57 | & sdtpldt0(xP, xP) = all_75_1 & $i(all_75_0) & $i(all_75_1) & % 21.28/4.57 | $i(all_56_7) % 21.28/4.57 | % 21.28/4.57 | ALPHA: (90) implies: % 21.28/4.57 | (91) sdtpldt0(xP, xP) = all_75_1 % 21.28/4.57 | (92) sdtpldt0(xP, xP) = all_75_0 % 21.28/4.57 | (93) sdtasdt0(all_75_1, all_75_0) = all_56_7 % 21.28/4.57 | % 21.28/4.57 | DELTA: instantiating (88) with fresh symbols all_77_0, all_77_1 gives: % 21.28/4.57 | (94) sdtasdt0(all_77_1, all_77_0) = all_56_0 & sdtpldt0(xR, xS) = all_77_0 % 21.28/4.57 | & sdtpldt0(xR, xS) = all_77_1 & $i(all_77_0) & $i(all_77_1) & % 21.28/4.57 | $i(all_56_0) % 21.28/4.57 | % 21.28/4.57 | ALPHA: (94) implies: % 21.28/4.57 | (95) sdtpldt0(xR, xS) = all_77_1 % 21.28/4.57 | (96) sdtpldt0(xR, xS) = all_77_0 % 21.28/4.57 | (97) sdtasdt0(all_77_1, all_77_0) = all_56_0 % 21.28/4.57 | % 21.28/4.57 | DELTA: instantiating (87) with fresh symbols all_83_0, all_83_1, all_83_2, % 21.28/4.57 | all_83_3 gives: % 21.28/4.57 | (98) sdtasdt0(all_83_2, xP) = all_83_1 & sdtasdt0(xP, all_83_3) = all_47_3 % 21.28/4.57 | & sdtasdt0(xP, xP) = all_83_0 & sdtpldt0(all_33_0, all_83_0) = % 21.28/4.57 | all_83_1 & sdtpldt0(xP, xP) = all_83_2 & sdtpldt0(xP, xP) = all_83_3 & % 21.28/4.57 | $i(all_83_0) & $i(all_83_1) & $i(all_83_2) & $i(all_83_3) & % 21.28/4.57 | $i(all_47_3) % 21.28/4.57 | % 21.28/4.57 | ALPHA: (98) implies: % 21.28/4.57 | (99) sdtpldt0(xP, xP) = all_83_3 % 21.28/4.57 | (100) sdtpldt0(xP, xP) = all_83_2 % 21.28/4.57 | % 21.28/4.57 | DELTA: instantiating (85) with fresh symbols all_86_0, all_86_1, all_86_2, % 21.28/4.57 | all_86_3 gives: % 21.28/4.57 | (101) sdtasdt0(all_86_2, xS) = all_86_1 & sdtasdt0(xR, all_86_3) = all_49_4 % 21.28/4.57 | & sdtasdt0(xR, xS) = all_86_0 & sdtpldt0(xN, all_86_0) = all_86_1 & % 21.28/4.57 | sdtpldt0(xR, xS) = all_86_3 & sdtpldt0(xR, xR) = all_86_2 & % 21.28/4.57 | $i(all_86_0) & $i(all_86_1) & $i(all_86_2) & $i(all_86_3) & % 21.28/4.57 | $i(all_49_4) % 21.28/4.57 | % 21.28/4.57 | ALPHA: (101) implies: % 21.28/4.57 | (102) sdtpldt0(xR, xS) = all_86_3 % 21.28/4.57 | % 21.28/4.57 | DELTA: instantiating (89) with fresh symbols all_90_0, all_90_1, all_90_2, % 21.28/4.57 | all_90_3 gives: % 21.28/4.57 | (103) sdtasdt0(all_90_2, xS) = all_90_1 & sdtasdt0(xS, all_90_3) = all_56_1 % 21.28/4.57 | & sdtasdt0(xR, xS) = all_90_0 & sdtpldt0(all_47_1, all_90_0) = % 21.28/4.57 | all_90_1 & sdtpldt0(xS, xR) = all_90_2 & sdtpldt0(xR, xS) = all_90_3 % 21.28/4.57 | & $i(all_90_0) & $i(all_90_1) & $i(all_90_2) & $i(all_90_3) & % 21.28/4.57 | $i(all_56_1) % 21.28/4.57 | % 21.28/4.57 | ALPHA: (103) implies: % 21.28/4.57 | (104) sdtpldt0(xR, xS) = all_90_3 % 21.28/4.57 | % 21.28/4.57 | GROUND_INST: instantiating (14) with all_45_1, all_77_0, xS, xR, simplifying % 21.28/4.57 | with (20), (96) gives: % 21.28/4.57 | (105) all_77_0 = all_45_1 % 21.28/4.57 | % 21.28/4.57 | GROUND_INST: instantiating (14) with all_86_3, all_90_3, xS, xR, simplifying % 21.28/4.57 | with (102), (104) gives: % 21.28/4.57 | (106) all_90_3 = all_86_3 % 21.28/4.57 | % 21.28/4.57 | GROUND_INST: instantiating (14) with all_77_0, all_90_3, xS, xR, simplifying % 21.28/4.57 | with (96), (104) gives: % 21.28/4.57 | (107) all_90_3 = all_77_0 % 21.28/4.57 | % 21.28/4.57 | GROUND_INST: instantiating (14) with all_77_1, all_90_3, xS, xR, simplifying % 21.28/4.57 | with (95), (104) gives: % 21.28/4.57 | (108) all_90_3 = all_77_1 % 21.28/4.57 | % 21.28/4.57 | GROUND_INST: instantiating (14) with all_75_0, all_83_3, xP, xP, simplifying % 21.28/4.57 | with (92), (99) gives: % 21.28/4.57 | (109) all_83_3 = all_75_0 % 21.28/4.57 | % 21.28/4.57 | GROUND_INST: instantiating (14) with all_75_1, all_83_3, xP, xP, simplifying % 21.28/4.58 | with (91), (99) gives: % 21.28/4.58 | (110) all_83_3 = all_75_1 % 21.28/4.58 | % 21.28/4.58 | GROUND_INST: instantiating (14) with all_45_3, all_83_2, xP, xP, simplifying % 21.28/4.58 | with (21), (100) gives: % 21.28/4.58 | (111) all_83_2 = all_45_3 % 21.28/4.58 | % 21.28/4.58 | GROUND_INST: instantiating (14) with all_75_0, all_83_2, xP, xP, simplifying % 21.28/4.58 | with (92), (100) gives: % 21.28/4.58 | (112) all_83_2 = all_75_0 % 21.28/4.58 | % 21.28/4.58 | COMBINE_EQS: (106), (108) imply: % 21.28/4.58 | (113) all_86_3 = all_77_1 % 21.28/4.58 | % 21.28/4.58 | COMBINE_EQS: (106), (107) imply: % 21.28/4.58 | (114) all_86_3 = all_77_0 % 21.28/4.58 | % 21.28/4.58 | COMBINE_EQS: (113), (114) imply: % 21.28/4.58 | (115) all_77_0 = all_77_1 % 21.28/4.58 | % 21.28/4.58 | SIMP: (115) implies: % 21.28/4.58 | (116) all_77_0 = all_77_1 % 21.28/4.58 | % 21.28/4.58 | COMBINE_EQS: (111), (112) imply: % 21.28/4.58 | (117) all_75_0 = all_45_3 % 21.28/4.58 | % 21.28/4.58 | SIMP: (117) implies: % 21.28/4.58 | (118) all_75_0 = all_45_3 % 21.28/4.58 | % 21.28/4.58 | COMBINE_EQS: (109), (110) imply: % 21.28/4.58 | (119) all_75_0 = all_75_1 % 21.28/4.58 | % 21.28/4.58 | SIMP: (119) implies: % 21.28/4.58 | (120) all_75_0 = all_75_1 % 21.28/4.58 | % 21.28/4.58 | COMBINE_EQS: (105), (116) imply: % 21.28/4.58 | (121) all_77_1 = all_45_1 % 21.28/4.58 | % 21.28/4.58 | COMBINE_EQS: (118), (120) imply: % 21.28/4.58 | (122) all_75_1 = all_45_3 % 21.28/4.58 | % 21.28/4.58 | SIMP: (122) implies: % 21.28/4.58 | (123) all_75_1 = all_45_3 % 21.28/4.58 | % 21.28/4.58 | REDUCE: (97), (105), (121) imply: % 21.28/4.58 | (124) sdtasdt0(all_45_1, all_45_1) = all_56_0 % 21.28/4.58 | % 21.28/4.58 | REDUCE: (93), (118), (123) imply: % 21.28/4.58 | (125) sdtasdt0(all_45_3, all_45_3) = all_56_7 % 21.28/4.58 | % 21.28/4.58 | GROUND_INST: instantiating (15) with all_45_2, all_56_7, all_45_3, all_45_3, % 21.28/4.58 | simplifying with (22), (125) gives: % 21.28/4.58 | (126) all_56_7 = all_45_2 % 21.28/4.58 | % 21.28/4.58 | GROUND_INST: instantiating (15) with all_45_0, all_56_0, all_45_1, all_45_1, % 21.28/4.58 | simplifying with (23), (124) gives: % 21.28/4.58 | (127) all_56_0 = all_45_0 % 21.28/4.58 | % 21.28/4.58 | REDUCE: (39), (126), (127) imply: % 21.28/4.58 | (128) sdtlseqdt0(all_45_2, all_45_0) % 21.28/4.58 | % 21.28/4.58 | PRED_UNIFY: (19), (128) imply: % 21.28/4.58 | (129) $false % 21.28/4.58 | % 21.28/4.58 | CLOSE: (129) is inconsistent. % 21.28/4.58 | % 21.28/4.58 End of proof % 21.28/4.58 % SZS output end Proof for theBenchmark % 21.28/4.58 % 21.28/4.58 4029ms %------------------------------------------------------------------------------