%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG069+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 : n017.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 15.39s 2.82s % Output : Proof 22.98s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : RNG069+2 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n017.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Sun Aug 27 02:20:11 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.38/1.21 Prover 4: Preprocessing ... % 3.38/1.23 Prover 1: Preprocessing ... % 4.03/1.26 Prover 3: Preprocessing ... % 4.03/1.26 Prover 2: Preprocessing ... % 4.03/1.26 Prover 0: Preprocessing ... % 4.03/1.26 Prover 5: Preprocessing ... % 4.03/1.26 Prover 6: Preprocessing ... % 9.46/2.03 Prover 1: Constructing countermodel ... % 9.46/2.03 Prover 3: Constructing countermodel ... % 9.46/2.06 Prover 6: Proving ... % 9.97/2.20 Prover 5: Constructing countermodel ... % 11.99/2.36 Prover 2: Proving ... % 11.99/2.37 Prover 4: Constructing countermodel ... % 13.10/2.49 Prover 0: Proving ... % 15.39/2.81 Prover 3: proved (2186ms) % 15.39/2.82 % 15.39/2.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.39/2.82 % 15.39/2.82 Prover 5: stopped % 15.39/2.82 Prover 2: stopped % 15.39/2.82 Prover 0: stopped % 15.39/2.82 Prover 6: stopped % 15.39/2.82 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 15.39/2.82 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 15.39/2.82 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.39/2.82 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.39/2.83 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 16.58/2.96 Prover 8: Preprocessing ... % 16.89/3.00 Prover 7: Preprocessing ... % 16.89/3.00 Prover 13: Preprocessing ... % 16.89/3.00 Prover 11: Preprocessing ... % 16.89/3.01 Prover 10: Preprocessing ... % 17.67/3.15 Prover 10: Constructing countermodel ... % 18.12/3.20 Prover 8: Warning: ignoring some quantifiers % 18.12/3.21 Prover 8: Constructing countermodel ... % 18.12/3.23 Prover 7: Constructing countermodel ... % 18.89/3.27 Prover 13: Constructing countermodel ... % 19.57/3.36 Prover 11: Constructing countermodel ... % 22.23/3.74 Prover 10: Found proof (size 108) % 22.23/3.74 Prover 10: proved (918ms) % 22.23/3.74 Prover 11: stopped % 22.23/3.74 Prover 7: stopped % 22.23/3.74 Prover 8: stopped % 22.23/3.74 Prover 13: stopped % 22.23/3.74 Prover 4: stopped % 22.23/3.74 Prover 1: stopped % 22.23/3.74 % 22.23/3.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 22.23/3.74 % 22.23/3.77 % SZS output start Proof for theBenchmark % 22.76/3.77 Assumptions after simplification: % 22.76/3.77 --------------------------------- % 22.76/3.77 % 22.76/3.77 (mDistr) % 22.87/3.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 22.87/3.80 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ % 22.87/3.80 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 22.87/3.80 aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v6: $i] : ? [v7: $i] % 22.87/3.80 : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v7, v2) = v8 & sdtasdt0(v1, v2) = v9 % 22.87/3.80 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v4, v9) = v8 & sdtpldt0(v1, v2) = v6 & % 22.87/3.80 sdtpldt0(v0, v1) = v7 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5))) % 22.87/3.80 % 22.87/3.80 (mDistr2) % 22.87/3.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 22.87/3.81 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : % 22.87/3.81 ( ~ (sdtasdt0(v1, v3) = v8) | ~ (sdtasdt0(v1, v2) = v7) | ~ (sdtasdt0(v0, % 22.87/3.81 v3) = v5) | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtpldt0(v7, v8) = v9) | ~ % 22.87/3.81 (sdtpldt0(v6, v9) = v10) | ~ (sdtpldt0(v4, v5) = v6) | ~ $i(v3) | ~ % 22.87/3.81 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aScalar0(v3) | ~ aScalar0(v2) | ~ % 22.87/3.81 aScalar0(v1) | ~ aScalar0(v0) | ? [v11: $i] : ? [v12: $i] : % 22.87/3.81 (sdtasdt0(v11, v12) = v10 & sdtpldt0(v2, v3) = v12 & sdtpldt0(v0, v1) = v11 % 22.87/3.81 & $i(v12) & $i(v11) & $i(v10))) % 22.87/3.81 % 22.87/3.81 (m__) % 22.87/3.81 $i(xS) & $i(xP) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 22.87/3.81 $i] : (sdtasdt0(v2, v2) = v3 & sdtasdt0(v0, v0) = v1 & sdtpldt0(xP, xP) = v0 % 22.87/3.81 & sdtpldt0(xR, xS) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~ % 22.87/3.81 sdtlseqdt0(v1, v3)) % 22.87/3.81 % 22.87/3.81 (m__1892) % 22.87/3.81 sdtasdt0(xC, xG) = xR & $i(xR) & $i(xG) & $i(xC) & aScalar0(xR) % 22.87/3.81 % 22.87/3.81 (m__1911) % 22.87/3.81 sdtasdt0(xE, xH) = xP & $i(xP) & $i(xH) & $i(xE) & aScalar0(xP) % 22.87/3.81 % 22.87/3.81 (m__1930) % 22.87/3.81 sdtasdt0(xF, xD) = xS & $i(xS) & $i(xF) & $i(xD) & aScalar0(xS) % 22.87/3.81 % 22.87/3.81 (m__1949) % 22.87/3.81 sdtasdt0(xR, xS) = xN & $i(xN) & $i(xS) & $i(xR) & aScalar0(xN) % 22.87/3.81 % 22.87/3.81 (m__2004) % 22.87/3.81 $i(xN) & $i(xP) & ? [v0: $i] : (sdtasdt0(xP, xP) = v0 & $i(v0) & % 22.87/3.81 sdtlseqdt0(v0, xN)) % 22.87/3.81 % 22.87/3.81 (m__2104) % 22.87/3.81 $i(xS) & $i(xP) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 22.87/3.81 $i] : ? [v4: $i] : (sdtasdt0(xS, xS) = v3 & sdtasdt0(xP, xP) = v0 & % 22.87/3.81 sdtasdt0(xR, xR) = v2 & sdtpldt0(v2, v3) = v4 & sdtpldt0(v0, v0) = v1 & % 22.87/3.81 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v1, v4)) % 22.87/3.81 % 22.87/3.81 (m__2463) % 22.87/3.82 $i(xN) & $i(xS) & $i(xP) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 22.87/3.82 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 22.87/3.82 $i] : (sdtasdt0(xS, xS) = v5 & sdtasdt0(xP, xP) = v0 & sdtasdt0(xR, xR) = v4 % 22.87/3.82 & sdtpldt0(v7, xN) = v8 & sdtpldt0(v6, xN) = v7 & sdtpldt0(v4, v5) = v6 & % 22.87/3.82 sdtpldt0(v2, v0) = v3 & sdtpldt0(v1, v0) = v2 & sdtpldt0(v0, v0) = v1 & % 22.87/3.82 $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 22.87/3.82 $i(v0) & sdtlseqdt0(v3, v8)) % 22.87/3.82 % 22.87/3.82 (m__2510) % 22.87/3.82 $i(xN) & $i(xS) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 22.87/3.82 $i] : ? [v4: $i] : ? [v5: $i] : (sdtasdt0(xS, xS) = v2 & sdtasdt0(xR, xR) % 22.87/3.82 = v0 & sdtpldt0(v3, xN) = v4 & sdtpldt0(v2, xN) = v5 & sdtpldt0(v1, v5) = v4 % 22.87/3.82 & sdtpldt0(v1, v2) = v3 & sdtpldt0(v0, xN) = v1 & $i(v5) & $i(v4) & $i(v3) & % 22.87/3.82 $i(v2) & $i(v1) & $i(v0)) % 22.87/3.82 % 22.87/3.82 (m__2580) % 22.87/3.82 $i(xS) & $i(xP) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 22.87/3.82 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 22.87/3.82 ? [v9: $i] : (sdtasdt0(xS, xS) = v7 & sdtasdt0(xS, xR) = v6 & sdtasdt0(xP, xP) % 22.87/3.82 = v0 & sdtasdt0(xR, xS) = v4 & sdtasdt0(xR, xR) = v3 & sdtpldt0(v6, v7) = v8 % 22.87/3.82 & sdtpldt0(v5, v8) = v9 & sdtpldt0(v3, v4) = v5 & sdtpldt0(v1, v1) = v2 & % 22.87/3.82 sdtpldt0(v0, v0) = v1 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) % 22.87/3.82 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v2, v9)) % 22.87/3.82 % 22.87/3.82 (function-axioms) % 22.98/3.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.98/3.82 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 22.98/3.82 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) % 22.98/3.82 | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 22.98/3.82 ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = % 22.98/3.82 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 22.98/3.82 ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 22.98/3.82 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sziznziztdt0(v2) = v1) | ~ % 22.98/3.82 (sziznziztdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 22.98/3.82 v0 | ~ (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) & ! [v0: % 22.98/3.82 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ % 22.98/3.82 (smndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 22.98/3.82 (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0)) % 22.98/3.82 % 22.98/3.82 Further assumptions not needed in the proof: % 22.98/3.82 -------------------------------------------- % 22.98/3.82 mArith, mDefInit, mDefSPN, mDefSPZ, mDimNat, mElmSc, mEqInit, mIH, mIHOrd, % 22.98/3.82 mLEASm, mLEMon, mLEMonM, mLERef, mLETot, mLETrn, mLess, mMDNeg, mMNeg, mMulSc, % 22.98/3.82 mNatExtr, mNatSort, mNegSc, mPosMon, mSZeroSc, mScPr, mScSort, mScSqPos, % 22.98/3.82 mScZero, mSqPos, mSqrt, mSuccEqu, mSuccNat, mSumSc, mVcSort, mZeroNat, m__1652, % 22.98/3.82 m__1678, m__1678_01, m__1692, m__1709, m__1726, m__1746, m__1766, m__1783, % 22.98/3.82 m__1800, m__1820, m__1837, m__1854, m__1873, m__1967 % 22.98/3.82 % 22.98/3.82 Those formulas are unsatisfiable: % 22.98/3.82 --------------------------------- % 22.98/3.82 % 22.98/3.82 Begin of proof % 22.98/3.82 | % 22.98/3.82 | ALPHA: (m__1892) implies: % 22.98/3.83 | (1) aScalar0(xR) % 22.98/3.83 | % 22.98/3.83 | ALPHA: (m__1911) implies: % 22.98/3.83 | (2) aScalar0(xP) % 22.98/3.83 | % 22.98/3.83 | ALPHA: (m__1930) implies: % 22.98/3.83 | (3) aScalar0(xS) % 22.98/3.83 | % 22.98/3.83 | ALPHA: (m__1949) implies: % 22.98/3.83 | (4) sdtasdt0(xR, xS) = xN % 22.98/3.83 | % 22.98/3.83 | ALPHA: (m__2004) implies: % 22.98/3.83 | (5) ? [v0: $i] : (sdtasdt0(xP, xP) = v0 & $i(v0) & sdtlseqdt0(v0, xN)) % 22.98/3.83 | % 22.98/3.83 | ALPHA: (m__2104) implies: % 22.98/3.83 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 22.98/3.83 | (sdtasdt0(xS, xS) = v3 & sdtasdt0(xP, xP) = v0 & sdtasdt0(xR, xR) = v2 % 22.98/3.83 | & sdtpldt0(v2, v3) = v4 & sdtpldt0(v0, v0) = v1 & $i(v4) & $i(v3) & % 22.98/3.83 | $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v1, v4)) % 22.98/3.83 | % 22.98/3.83 | ALPHA: (m__2463) implies: % 22.98/3.83 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 22.98/3.83 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(xS, % 22.98/3.83 | xS) = v5 & sdtasdt0(xP, xP) = v0 & sdtasdt0(xR, xR) = v4 & % 22.98/3.83 | sdtpldt0(v7, xN) = v8 & sdtpldt0(v6, xN) = v7 & sdtpldt0(v4, v5) = v6 % 22.98/3.83 | & sdtpldt0(v2, v0) = v3 & sdtpldt0(v1, v0) = v2 & sdtpldt0(v0, v0) = % 22.98/3.83 | v1 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 22.98/3.83 | $i(v1) & $i(v0) & sdtlseqdt0(v3, v8)) % 22.98/3.83 | % 22.98/3.83 | ALPHA: (m__2510) implies: % 22.98/3.83 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 22.98/3.83 | ? [v5: $i] : (sdtasdt0(xS, xS) = v2 & sdtasdt0(xR, xR) = v0 & % 22.98/3.83 | sdtpldt0(v3, xN) = v4 & sdtpldt0(v2, xN) = v5 & sdtpldt0(v1, v5) = v4 % 22.98/3.83 | & sdtpldt0(v1, v2) = v3 & sdtpldt0(v0, xN) = v1 & $i(v5) & $i(v4) & % 22.98/3.83 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 22.98/3.83 | % 22.98/3.83 | ALPHA: (m__2580) implies: % 22.98/3.83 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 22.98/3.83 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 22.98/3.83 | (sdtasdt0(xS, xS) = v7 & sdtasdt0(xS, xR) = v6 & sdtasdt0(xP, xP) = v0 % 22.98/3.83 | & sdtasdt0(xR, xS) = v4 & sdtasdt0(xR, xR) = v3 & sdtpldt0(v6, v7) = % 22.98/3.83 | v8 & sdtpldt0(v5, v8) = v9 & sdtpldt0(v3, v4) = v5 & sdtpldt0(v1, v1) % 22.98/3.83 | = v2 & sdtpldt0(v0, v0) = v1 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 22.98/3.83 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v2, % 22.98/3.83 | v9)) % 22.98/3.83 | % 22.98/3.83 | ALPHA: (m__) implies: % 22.98/3.83 | (10) $i(xR) % 22.98/3.83 | (11) $i(xP) % 22.98/3.83 | (12) $i(xS) % 22.98/3.83 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v2, % 22.98/3.83 | v2) = v3 & sdtasdt0(v0, v0) = v1 & sdtpldt0(xP, xP) = v0 & % 22.98/3.83 | sdtpldt0(xR, xS) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~ % 22.98/3.83 | sdtlseqdt0(v1, v3)) % 22.98/3.83 | % 22.98/3.83 | ALPHA: (function-axioms) implies: % 22.98/3.83 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.98/3.83 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 22.98/3.83 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.98/3.83 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 22.98/3.83 | % 22.98/3.83 | DELTA: instantiating (5) with fresh symbol all_37_0 gives: % 22.98/3.84 | (16) sdtasdt0(xP, xP) = all_37_0 & $i(all_37_0) & sdtlseqdt0(all_37_0, xN) % 22.98/3.84 | % 22.98/3.84 | ALPHA: (16) implies: % 22.98/3.84 | (17) sdtasdt0(xP, xP) = all_37_0 % 22.98/3.84 | % 22.98/3.84 | DELTA: instantiating (13) with fresh symbols all_45_0, all_45_1, all_45_2, % 22.98/3.84 | all_45_3 gives: % 22.98/3.84 | (18) sdtasdt0(all_45_1, all_45_1) = all_45_0 & sdtasdt0(all_45_3, all_45_3) % 22.98/3.84 | = all_45_2 & sdtpldt0(xP, xP) = all_45_3 & sdtpldt0(xR, xS) = all_45_1 % 22.98/3.84 | & $i(all_45_0) & $i(all_45_1) & $i(all_45_2) & $i(all_45_3) & ~ % 22.98/3.84 | sdtlseqdt0(all_45_2, all_45_0) % 22.98/3.84 | % 22.98/3.84 | ALPHA: (18) implies: % 22.98/3.84 | (19) ~ sdtlseqdt0(all_45_2, all_45_0) % 22.98/3.84 | (20) sdtpldt0(xR, xS) = all_45_1 % 22.98/3.84 | (21) sdtpldt0(xP, xP) = all_45_3 % 22.98/3.84 | (22) sdtasdt0(all_45_3, all_45_3) = all_45_2 % 22.98/3.84 | (23) sdtasdt0(all_45_1, all_45_1) = all_45_0 % 22.98/3.84 | % 22.98/3.84 | DELTA: instantiating (6) with fresh symbols all_47_0, all_47_1, all_47_2, % 22.98/3.84 | all_47_3, all_47_4 gives: % 22.98/3.84 | (24) sdtasdt0(xS, xS) = all_47_1 & sdtasdt0(xP, xP) = all_47_4 & % 22.98/3.84 | sdtasdt0(xR, xR) = all_47_2 & sdtpldt0(all_47_2, all_47_1) = all_47_0 % 22.98/3.84 | & sdtpldt0(all_47_4, all_47_4) = all_47_3 & $i(all_47_0) & % 22.98/3.84 | $i(all_47_1) & $i(all_47_2) & $i(all_47_3) & $i(all_47_4) & % 22.98/3.84 | sdtlseqdt0(all_47_3, all_47_0) % 22.98/3.84 | % 22.98/3.84 | ALPHA: (24) implies: % 22.98/3.84 | (25) sdtpldt0(all_47_4, all_47_4) = all_47_3 % 22.98/3.84 | (26) sdtasdt0(xR, xR) = all_47_2 % 22.98/3.84 | (27) sdtasdt0(xP, xP) = all_47_4 % 22.98/3.84 | (28) sdtasdt0(xS, xS) = all_47_1 % 22.98/3.84 | % 22.98/3.84 | DELTA: instantiating (8) with fresh symbols all_55_0, all_55_1, all_55_2, % 22.98/3.84 | all_55_3, all_55_4, all_55_5 gives: % 22.98/3.84 | (29) sdtasdt0(xS, xS) = all_55_3 & sdtasdt0(xR, xR) = all_55_5 & % 22.98/3.84 | sdtpldt0(all_55_2, xN) = all_55_1 & sdtpldt0(all_55_3, xN) = all_55_0 % 22.98/3.84 | & sdtpldt0(all_55_4, all_55_0) = all_55_1 & sdtpldt0(all_55_4, % 22.98/3.84 | all_55_3) = all_55_2 & sdtpldt0(all_55_5, xN) = all_55_4 & % 22.98/3.84 | $i(all_55_0) & $i(all_55_1) & $i(all_55_2) & $i(all_55_3) & % 22.98/3.84 | $i(all_55_4) & $i(all_55_5) % 22.98/3.84 | % 22.98/3.84 | ALPHA: (29) implies: % 22.98/3.84 | (30) sdtpldt0(all_55_5, xN) = all_55_4 % 22.98/3.84 | (31) sdtasdt0(xR, xR) = all_55_5 % 22.98/3.84 | (32) sdtasdt0(xS, xS) = all_55_3 % 22.98/3.84 | % 22.98/3.84 | DELTA: instantiating (7) with fresh symbols all_57_0, all_57_1, all_57_2, % 22.98/3.84 | all_57_3, all_57_4, all_57_5, all_57_6, all_57_7, all_57_8 gives: % 22.98/3.84 | (33) sdtasdt0(xS, xS) = all_57_3 & sdtasdt0(xP, xP) = all_57_8 & % 22.98/3.84 | sdtasdt0(xR, xR) = all_57_4 & sdtpldt0(all_57_1, xN) = all_57_0 & % 22.98/3.84 | sdtpldt0(all_57_2, xN) = all_57_1 & sdtpldt0(all_57_4, all_57_3) = % 22.98/3.84 | all_57_2 & sdtpldt0(all_57_6, all_57_8) = all_57_5 & % 22.98/3.84 | sdtpldt0(all_57_7, all_57_8) = all_57_6 & sdtpldt0(all_57_8, all_57_8) % 22.98/3.84 | = all_57_7 & $i(all_57_0) & $i(all_57_1) & $i(all_57_2) & $i(all_57_3) % 22.98/3.84 | & $i(all_57_4) & $i(all_57_5) & $i(all_57_6) & $i(all_57_7) & % 22.98/3.84 | $i(all_57_8) & sdtlseqdt0(all_57_5, all_57_0) % 22.98/3.84 | % 22.98/3.84 | ALPHA: (33) implies: % 22.98/3.84 | (34) sdtpldt0(all_57_8, all_57_8) = all_57_7 % 22.98/3.84 | (35) sdtasdt0(xR, xR) = all_57_4 % 22.98/3.84 | (36) sdtasdt0(xP, xP) = all_57_8 % 22.98/3.84 | (37) sdtasdt0(xS, xS) = all_57_3 % 22.98/3.84 | % 22.98/3.84 | DELTA: instantiating (9) with fresh symbols all_62_0, all_62_1, all_62_2, % 22.98/3.84 | all_62_3, all_62_4, all_62_5, all_62_6, all_62_7, all_62_8, all_62_9 % 22.98/3.84 | gives: % 22.98/3.84 | (38) sdtasdt0(xS, xS) = all_62_2 & sdtasdt0(xS, xR) = all_62_3 & % 22.98/3.84 | sdtasdt0(xP, xP) = all_62_9 & sdtasdt0(xR, xS) = all_62_5 & % 22.98/3.84 | sdtasdt0(xR, xR) = all_62_6 & sdtpldt0(all_62_3, all_62_2) = all_62_1 % 22.98/3.84 | & sdtpldt0(all_62_4, all_62_1) = all_62_0 & sdtpldt0(all_62_6, % 22.98/3.84 | all_62_5) = all_62_4 & sdtpldt0(all_62_8, all_62_8) = all_62_7 & % 22.98/3.84 | sdtpldt0(all_62_9, all_62_9) = all_62_8 & $i(all_62_0) & $i(all_62_1) % 22.98/3.84 | & $i(all_62_2) & $i(all_62_3) & $i(all_62_4) & $i(all_62_5) & % 22.98/3.84 | $i(all_62_6) & $i(all_62_7) & $i(all_62_8) & $i(all_62_9) & % 22.98/3.84 | sdtlseqdt0(all_62_7, all_62_0) % 22.98/3.84 | % 22.98/3.84 | ALPHA: (38) implies: % 22.98/3.84 | (39) sdtlseqdt0(all_62_7, all_62_0) % 22.98/3.84 | (40) sdtpldt0(all_62_9, all_62_9) = all_62_8 % 22.98/3.84 | (41) sdtpldt0(all_62_8, all_62_8) = all_62_7 % 22.98/3.84 | (42) sdtpldt0(all_62_6, all_62_5) = all_62_4 % 22.98/3.84 | (43) sdtpldt0(all_62_4, all_62_1) = all_62_0 % 22.98/3.84 | (44) sdtpldt0(all_62_3, all_62_2) = all_62_1 % 22.98/3.84 | (45) sdtasdt0(xR, xR) = all_62_6 % 22.98/3.84 | (46) sdtasdt0(xR, xS) = all_62_5 % 22.98/3.84 | (47) sdtasdt0(xP, xP) = all_62_9 % 22.98/3.85 | (48) sdtasdt0(xS, xR) = all_62_3 % 22.98/3.85 | (49) sdtasdt0(xS, xS) = all_62_2 % 22.98/3.85 | % 22.98/3.85 | GROUND_INST: instantiating (15) with all_47_2, all_57_4, xR, xR, simplifying % 22.98/3.85 | with (26), (35) gives: % 22.98/3.85 | (50) all_57_4 = all_47_2 % 22.98/3.85 | % 22.98/3.85 | GROUND_INST: instantiating (15) with all_57_4, all_62_6, xR, xR, simplifying % 22.98/3.85 | with (35), (45) gives: % 22.98/3.85 | (51) all_62_6 = all_57_4 % 22.98/3.85 | % 22.98/3.85 | GROUND_INST: instantiating (15) with all_55_5, all_62_6, xR, xR, simplifying % 22.98/3.85 | with (31), (45) gives: % 22.98/3.85 | (52) all_62_6 = all_55_5 % 22.98/3.85 | % 22.98/3.85 | GROUND_INST: instantiating (15) with xN, all_62_5, xS, xR, simplifying with % 22.98/3.85 | (4), (46) gives: % 22.98/3.85 | (53) all_62_5 = xN % 22.98/3.85 | % 22.98/3.85 | GROUND_INST: instantiating (15) with all_47_4, all_57_8, xP, xP, simplifying % 22.98/3.85 | with (27), (36) gives: % 22.98/3.85 | (54) all_57_8 = all_47_4 % 22.98/3.85 | % 22.98/3.85 | GROUND_INST: instantiating (15) with all_57_8, all_62_9, xP, xP, simplifying % 22.98/3.85 | with (36), (47) gives: % 22.98/3.85 | (55) all_62_9 = all_57_8 % 22.98/3.85 | % 22.98/3.85 | GROUND_INST: instantiating (15) with all_37_0, all_62_9, xP, xP, simplifying % 22.98/3.85 | with (17), (47) gives: % 22.98/3.85 | (56) all_62_9 = all_37_0 % 22.98/3.85 | % 22.98/3.85 | GROUND_INST: instantiating (15) with all_55_3, all_57_3, xS, xS, simplifying % 22.98/3.85 | with (32), (37) gives: % 22.98/3.85 | (57) all_57_3 = all_55_3 % 22.98/3.85 | % 22.98/3.85 | GROUND_INST: instantiating (15) with all_57_3, all_62_2, xS, xS, simplifying % 22.98/3.85 | with (37), (49) gives: % 22.98/3.85 | (58) all_62_2 = all_57_3 % 22.98/3.85 | % 22.98/3.85 | GROUND_INST: instantiating (15) with all_47_1, all_62_2, xS, xS, simplifying % 22.98/3.85 | with (28), (49) gives: % 22.98/3.85 | (59) all_62_2 = all_47_1 % 22.98/3.85 | % 22.98/3.85 | COMBINE_EQS: (58), (59) imply: % 22.98/3.85 | (60) all_57_3 = all_47_1 % 22.98/3.85 | % 22.98/3.85 | SIMP: (60) implies: % 22.98/3.85 | (61) all_57_3 = all_47_1 % 22.98/3.85 | % 22.98/3.85 | COMBINE_EQS: (51), (52) imply: % 22.98/3.85 | (62) all_57_4 = all_55_5 % 22.98/3.85 | % 22.98/3.85 | SIMP: (62) implies: % 22.98/3.85 | (63) all_57_4 = all_55_5 % 22.98/3.85 | % 22.98/3.85 | COMBINE_EQS: (55), (56) imply: % 22.98/3.85 | (64) all_57_8 = all_37_0 % 22.98/3.85 | % 22.98/3.85 | SIMP: (64) implies: % 22.98/3.85 | (65) all_57_8 = all_37_0 % 22.98/3.85 | % 22.98/3.85 | COMBINE_EQS: (57), (61) imply: % 22.98/3.85 | (66) all_55_3 = all_47_1 % 22.98/3.85 | % 22.98/3.85 | SIMP: (66) implies: % 22.98/3.85 | (67) all_55_3 = all_47_1 % 22.98/3.85 | % 22.98/3.85 | COMBINE_EQS: (50), (63) imply: % 22.98/3.85 | (68) all_55_5 = all_47_2 % 22.98/3.85 | % 22.98/3.85 | COMBINE_EQS: (54), (65) imply: % 22.98/3.85 | (69) all_47_4 = all_37_0 % 22.98/3.85 | % 22.98/3.85 | SIMP: (69) implies: % 22.98/3.85 | (70) all_47_4 = all_37_0 % 22.98/3.85 | % 22.98/3.85 | COMBINE_EQS: (52), (68) imply: % 22.98/3.85 | (71) all_62_6 = all_47_2 % 22.98/3.85 | % 22.98/3.85 | REDUCE: (44), (59) imply: % 22.98/3.85 | (72) sdtpldt0(all_62_3, all_47_1) = all_62_1 % 22.98/3.85 | % 22.98/3.85 | REDUCE: (42), (53), (71) imply: % 22.98/3.85 | (73) sdtpldt0(all_47_2, xN) = all_62_4 % 22.98/3.85 | % 22.98/3.85 | REDUCE: (40), (56) imply: % 22.98/3.85 | (74) sdtpldt0(all_37_0, all_37_0) = all_62_8 % 22.98/3.85 | % 22.98/3.85 | REDUCE: (34), (65) imply: % 22.98/3.85 | (75) sdtpldt0(all_37_0, all_37_0) = all_57_7 % 22.98/3.85 | % 22.98/3.85 | REDUCE: (30), (68) imply: % 22.98/3.85 | (76) sdtpldt0(all_47_2, xN) = all_55_4 % 22.98/3.85 | % 22.98/3.85 | REDUCE: (25), (70) imply: % 22.98/3.85 | (77) sdtpldt0(all_37_0, all_37_0) = all_47_3 % 22.98/3.85 | % 22.98/3.85 | GROUND_INST: instantiating (14) with all_57_7, all_62_8, all_37_0, all_37_0, % 22.98/3.85 | simplifying with (74), (75) gives: % 22.98/3.85 | (78) all_62_8 = all_57_7 % 22.98/3.85 | % 22.98/3.85 | GROUND_INST: instantiating (14) with all_47_3, all_62_8, all_37_0, all_37_0, % 22.98/3.85 | simplifying with (74), (77) gives: % 22.98/3.85 | (79) all_62_8 = all_47_3 % 22.98/3.85 | % 22.98/3.85 | GROUND_INST: instantiating (14) with all_55_4, all_62_4, xN, all_47_2, % 22.98/3.85 | simplifying with (73), (76) gives: % 22.98/3.85 | (80) all_62_4 = all_55_4 % 22.98/3.85 | % 22.98/3.86 | COMBINE_EQS: (78), (79) imply: % 22.98/3.86 | (81) all_57_7 = all_47_3 % 22.98/3.86 | % 22.98/3.86 | SIMP: (81) implies: % 22.98/3.86 | (82) all_57_7 = all_47_3 % 22.98/3.86 | % 22.98/3.86 | REDUCE: (43), (80) imply: % 22.98/3.86 | (83) sdtpldt0(all_55_4, all_62_1) = all_62_0 % 22.98/3.86 | % 22.98/3.86 | REDUCE: (41), (79) imply: % 22.98/3.86 | (84) sdtpldt0(all_47_3, all_47_3) = all_62_7 % 22.98/3.86 | % 22.98/3.86 | GROUND_INST: instantiating (mDistr) with xR, xR, xS, all_47_2, xN, all_55_4, % 22.98/3.86 | simplifying with (1), (3), (4), (10), (12), (26), (76) gives: % 22.98/3.86 | (85) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v1, % 22.98/3.86 | xS) = v2 & sdtasdt0(xR, v0) = all_55_4 & sdtasdt0(xR, xS) = v3 & % 22.98/3.86 | sdtpldt0(xN, v3) = v2 & sdtpldt0(xR, xS) = v0 & sdtpldt0(xR, xR) = % 22.98/3.86 | v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_55_4)) % 22.98/3.86 | % 22.98/3.86 | GROUND_INST: instantiating (mDistr2) with xP, xP, xP, xP, all_37_0, all_37_0, % 22.98/3.86 | all_47_3, all_37_0, all_37_0, all_47_3, all_62_7, simplifying % 22.98/3.86 | with (2), (11), (17), (77), (84) gives: % 22.98/3.86 | (86) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(v0, v1) = all_62_7 & % 22.98/3.86 | sdtpldt0(xP, xP) = v1 & sdtpldt0(xP, xP) = v0 & $i(v1) & $i(v0) & % 22.98/3.86 | $i(all_62_7)) % 22.98/3.86 | % 22.98/3.86 | GROUND_INST: instantiating (mDistr) with xP, xP, xP, all_37_0, all_37_0, % 22.98/3.86 | all_47_3, simplifying with (2), (11), (17), (77) gives: % 22.98/3.86 | (87) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v1, % 22.98/3.86 | xP) = v2 & sdtasdt0(xP, v0) = all_47_3 & sdtasdt0(xP, xP) = v3 & % 22.98/3.86 | sdtpldt0(all_37_0, v3) = v2 & sdtpldt0(xP, xP) = v1 & sdtpldt0(xP, % 22.98/3.86 | xP) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_47_3)) % 22.98/3.86 | % 22.98/3.86 | GROUND_INST: instantiating (mDistr2) with xR, xS, xR, xS, all_47_2, xN, % 22.98/3.86 | all_55_4, all_62_3, all_47_1, all_62_1, all_62_0, simplifying % 22.98/3.86 | with (1), (3), (4), (10), (12), (26), (28), (48), (72), (76), % 22.98/3.86 | (83) gives: % 22.98/3.86 | (88) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(v0, v1) = all_62_0 & % 22.98/3.86 | sdtpldt0(xR, xS) = v1 & sdtpldt0(xR, xS) = v0 & $i(v1) & $i(v0) & % 22.98/3.86 | $i(all_62_0)) % 22.98/3.86 | % 22.98/3.86 | GROUND_INST: instantiating (mDistr) with xS, xR, xS, all_62_3, all_47_1, % 22.98/3.86 | all_62_1, simplifying with (1), (3), (10), (12), (28), (48), (72) % 22.98/3.86 | gives: % 22.98/3.86 | (89) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v1, % 22.98/3.87 | xS) = v2 & sdtasdt0(xS, v0) = all_62_1 & sdtasdt0(xR, xS) = v3 & % 22.98/3.87 | sdtpldt0(all_47_1, v3) = v2 & sdtpldt0(xS, xR) = v1 & sdtpldt0(xR, % 22.98/3.87 | xS) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_62_1)) % 22.98/3.87 | % 22.98/3.87 | DELTA: instantiating (88) with fresh symbols all_81_0, all_81_1 gives: % 22.98/3.87 | (90) sdtasdt0(all_81_1, all_81_0) = all_62_0 & sdtpldt0(xR, xS) = all_81_0 % 22.98/3.87 | & sdtpldt0(xR, xS) = all_81_1 & $i(all_81_0) & $i(all_81_1) & % 22.98/3.87 | $i(all_62_0) % 22.98/3.87 | % 22.98/3.87 | ALPHA: (90) implies: % 22.98/3.87 | (91) sdtpldt0(xR, xS) = all_81_1 % 22.98/3.87 | (92) sdtpldt0(xR, xS) = all_81_0 % 22.98/3.87 | (93) sdtasdt0(all_81_1, all_81_0) = all_62_0 % 22.98/3.87 | % 22.98/3.87 | DELTA: instantiating (86) with fresh symbols all_83_0, all_83_1 gives: % 22.98/3.87 | (94) sdtasdt0(all_83_1, all_83_0) = all_62_7 & sdtpldt0(xP, xP) = all_83_0 % 22.98/3.87 | & sdtpldt0(xP, xP) = all_83_1 & $i(all_83_0) & $i(all_83_1) & % 22.98/3.87 | $i(all_62_7) % 22.98/3.87 | % 22.98/3.87 | ALPHA: (94) implies: % 22.98/3.87 | (95) sdtpldt0(xP, xP) = all_83_1 % 22.98/3.87 | (96) sdtpldt0(xP, xP) = all_83_0 % 22.98/3.87 | (97) sdtasdt0(all_83_1, all_83_0) = all_62_7 % 22.98/3.87 | % 22.98/3.87 | DELTA: instantiating (85) with fresh symbols all_87_0, all_87_1, all_87_2, % 22.98/3.87 | all_87_3 gives: % 22.98/3.87 | (98) sdtasdt0(all_87_2, xS) = all_87_1 & sdtasdt0(xR, all_87_3) = all_55_4 % 22.98/3.87 | & sdtasdt0(xR, xS) = all_87_0 & sdtpldt0(xN, all_87_0) = all_87_1 & % 22.98/3.87 | sdtpldt0(xR, xS) = all_87_3 & sdtpldt0(xR, xR) = all_87_2 & % 22.98/3.87 | $i(all_87_0) & $i(all_87_1) & $i(all_87_2) & $i(all_87_3) & % 22.98/3.87 | $i(all_55_4) % 22.98/3.87 | % 22.98/3.87 | ALPHA: (98) implies: % 22.98/3.87 | (99) sdtpldt0(xR, xS) = all_87_3 % 22.98/3.87 | % 22.98/3.87 | DELTA: instantiating (87) with fresh symbols all_90_0, all_90_1, all_90_2, % 22.98/3.87 | all_90_3 gives: % 22.98/3.87 | (100) sdtasdt0(all_90_2, xP) = all_90_1 & sdtasdt0(xP, all_90_3) = all_47_3 % 22.98/3.87 | & sdtasdt0(xP, xP) = all_90_0 & sdtpldt0(all_37_0, all_90_0) = % 22.98/3.87 | all_90_1 & sdtpldt0(xP, xP) = all_90_2 & sdtpldt0(xP, xP) = all_90_3 % 22.98/3.87 | & $i(all_90_0) & $i(all_90_1) & $i(all_90_2) & $i(all_90_3) & % 22.98/3.87 | $i(all_47_3) % 22.98/3.87 | % 22.98/3.87 | ALPHA: (100) implies: % 22.98/3.87 | (101) sdtpldt0(xP, xP) = all_90_3 % 22.98/3.87 | (102) sdtpldt0(xP, xP) = all_90_2 % 22.98/3.87 | % 22.98/3.87 | DELTA: instantiating (89) with fresh symbols all_94_0, all_94_1, all_94_2, % 22.98/3.87 | all_94_3 gives: % 22.98/3.87 | (103) sdtasdt0(all_94_2, xS) = all_94_1 & sdtasdt0(xS, all_94_3) = all_62_1 % 22.98/3.87 | & sdtasdt0(xR, xS) = all_94_0 & sdtpldt0(all_47_1, all_94_0) = % 22.98/3.87 | all_94_1 & sdtpldt0(xS, xR) = all_94_2 & sdtpldt0(xR, xS) = all_94_3 % 22.98/3.87 | & $i(all_94_0) & $i(all_94_1) & $i(all_94_2) & $i(all_94_3) & % 22.98/3.87 | $i(all_62_1) % 22.98/3.87 | % 22.98/3.87 | ALPHA: (103) implies: % 22.98/3.87 | (104) sdtpldt0(xR, xS) = all_94_3 % 22.98/3.87 | % 22.98/3.87 | GROUND_INST: instantiating (14) with all_45_1, all_94_3, xS, xR, simplifying % 22.98/3.87 | with (20), (104) gives: % 22.98/3.87 | (105) all_94_3 = all_45_1 % 22.98/3.87 | % 22.98/3.87 | GROUND_INST: instantiating (14) with all_87_3, all_94_3, xS, xR, simplifying % 22.98/3.87 | with (99), (104) gives: % 22.98/3.87 | (106) all_94_3 = all_87_3 % 22.98/3.87 | % 22.98/3.87 | GROUND_INST: instantiating (14) with all_81_0, all_94_3, xS, xR, simplifying % 22.98/3.87 | with (92), (104) gives: % 22.98/3.87 | (107) all_94_3 = all_81_0 % 22.98/3.87 | % 22.98/3.87 | GROUND_INST: instantiating (14) with all_81_1, all_94_3, xS, xR, simplifying % 22.98/3.87 | with (91), (104) gives: % 22.98/3.87 | (108) all_94_3 = all_81_1 % 22.98/3.87 | % 22.98/3.87 | GROUND_INST: instantiating (14) with all_83_1, all_83_0, xP, xP, simplifying % 22.98/3.87 | with (95), (96) gives: % 22.98/3.87 | (109) all_83_0 = all_83_1 % 22.98/3.87 | % 22.98/3.87 | GROUND_INST: instantiating (14) with all_83_0, all_90_3, xP, xP, simplifying % 22.98/3.87 | with (96), (101) gives: % 22.98/3.87 | (110) all_90_3 = all_83_0 % 22.98/3.87 | % 22.98/3.87 | GROUND_INST: instantiating (14) with all_45_3, all_90_2, xP, xP, simplifying % 22.98/3.87 | with (21), (102) gives: % 22.98/3.87 | (111) all_90_2 = all_45_3 % 22.98/3.87 | % 22.98/3.87 | GROUND_INST: instantiating (14) with all_90_3, all_90_2, xP, xP, simplifying % 22.98/3.87 | with (101), (102) gives: % 22.98/3.87 | (112) all_90_2 = all_90_3 % 22.98/3.87 | % 22.98/3.87 | COMBINE_EQS: (105), (106) imply: % 22.98/3.87 | (113) all_87_3 = all_45_1 % 22.98/3.87 | % 22.98/3.87 | COMBINE_EQS: (106), (108) imply: % 22.98/3.87 | (114) all_87_3 = all_81_1 % 22.98/3.87 | % 22.98/3.87 | COMBINE_EQS: (106), (107) imply: % 22.98/3.87 | (115) all_87_3 = all_81_0 % 22.98/3.87 | % 22.98/3.87 | COMBINE_EQS: (111), (112) imply: % 22.98/3.87 | (116) all_90_3 = all_45_3 % 22.98/3.87 | % 22.98/3.87 | SIMP: (116) implies: % 22.98/3.87 | (117) all_90_3 = all_45_3 % 22.98/3.87 | % 22.98/3.87 | COMBINE_EQS: (110), (117) imply: % 22.98/3.87 | (118) all_83_0 = all_45_3 % 22.98/3.87 | % 22.98/3.87 | SIMP: (118) implies: % 22.98/3.87 | (119) all_83_0 = all_45_3 % 22.98/3.87 | % 22.98/3.87 | COMBINE_EQS: (114), (115) imply: % 22.98/3.87 | (120) all_81_0 = all_81_1 % 22.98/3.87 | % 22.98/3.87 | COMBINE_EQS: (113), (115) imply: % 22.98/3.87 | (121) all_81_0 = all_45_1 % 22.98/3.87 | % 22.98/3.87 | COMBINE_EQS: (109), (119) imply: % 22.98/3.87 | (122) all_83_1 = all_45_3 % 22.98/3.87 | % 22.98/3.87 | SIMP: (122) implies: % 22.98/3.87 | (123) all_83_1 = all_45_3 % 22.98/3.87 | % 22.98/3.87 | COMBINE_EQS: (120), (121) imply: % 22.98/3.87 | (124) all_81_1 = all_45_1 % 22.98/3.87 | % 22.98/3.87 | SIMP: (124) implies: % 22.98/3.87 | (125) all_81_1 = all_45_1 % 22.98/3.87 | % 22.98/3.87 | REDUCE: (97), (119), (123) imply: % 22.98/3.87 | (126) sdtasdt0(all_45_3, all_45_3) = all_62_7 % 22.98/3.87 | % 22.98/3.87 | REDUCE: (93), (121), (125) imply: % 22.98/3.88 | (127) sdtasdt0(all_45_1, all_45_1) = all_62_0 % 22.98/3.88 | % 22.98/3.88 | GROUND_INST: instantiating (15) with all_45_2, all_62_7, all_45_3, all_45_3, % 22.98/3.88 | simplifying with (22), (126) gives: % 22.98/3.88 | (128) all_62_7 = all_45_2 % 22.98/3.88 | % 22.98/3.88 | GROUND_INST: instantiating (15) with all_45_0, all_62_0, all_45_1, all_45_1, % 22.98/3.88 | simplifying with (23), (127) gives: % 22.98/3.88 | (129) all_62_0 = all_45_0 % 22.98/3.88 | % 22.98/3.88 | REDUCE: (39), (128), (129) imply: % 22.98/3.88 | (130) sdtlseqdt0(all_45_2, all_45_0) % 22.98/3.88 | % 22.98/3.88 | PRED_UNIFY: (19), (130) imply: % 22.98/3.88 | (131) $false % 22.98/3.88 | % 22.98/3.88 | CLOSE: (131) is inconsistent. % 22.98/3.88 | % 22.98/3.88 End of proof % 22.98/3.88 % SZS output end Proof for theBenchmark % 22.98/3.88 % 22.98/3.88 3271ms 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