%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG079+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 : n027.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 13:57:44 EDT 2023 % Result : Theorem 14.55s 2.76s % Output : Proof 21.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : RNG079+2 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.16/0.33 % Computer : n027.cluster.edu % 0.16/0.33 % Model : x86_64 x86_64 % 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.33 % Memory : 8042.1875MB % 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.33 % CPULimit : 300 % 0.16/0.33 % WCLimit : 300 % 0.16/0.33 % DateTime : Sun Aug 27 03:24:20 EDT 2023 % 0.16/0.33 % CPUTime : % 0.18/0.60 ________ _____ % 0.18/0.60 ___ __ \_________(_)________________________________ % 0.18/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.60 % 0.18/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.60 (2023-06-19) % 0.18/0.60 % 0.18/0.60 (c) Philipp Rümmer, 2009-2023 % 0.18/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.60 Amanda Stjerna. % 0.18/0.60 Free software under BSD-3-Clause. % 0.18/0.60 % 0.18/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.60 % 0.18/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.18/0.61 Running up to 7 provers in parallel. % 0.18/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.18/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.18/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.18/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.18/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.18/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.18/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.53/1.19 Prover 1: Preprocessing ... % 3.53/1.19 Prover 4: Preprocessing ... % 3.94/1.24 Prover 2: Preprocessing ... % 3.94/1.24 Prover 3: Preprocessing ... % 3.94/1.24 Prover 0: Preprocessing ... % 3.94/1.24 Prover 5: Preprocessing ... % 3.94/1.24 Prover 6: Preprocessing ... % 9.02/2.03 Prover 1: Constructing countermodel ... % 9.02/2.03 Prover 3: Constructing countermodel ... % 9.02/2.03 Prover 6: Proving ... % 10.96/2.26 Prover 5: Constructing countermodel ... % 11.49/2.33 Prover 4: Constructing countermodel ... % 11.49/2.34 Prover 2: Proving ... % 12.74/2.47 Prover 0: Proving ... % 14.55/2.76 Prover 3: proved (2134ms) % 14.55/2.76 % 14.55/2.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.55/2.76 % 14.55/2.76 Prover 5: stopped % 14.55/2.76 Prover 0: stopped % 14.55/2.76 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.55/2.76 Prover 2: stopped % 14.55/2.77 Prover 6: stopped % 15.30/2.77 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 15.30/2.77 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.30/2.77 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.30/2.77 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 15.30/2.87 Prover 11: Preprocessing ... % 15.30/2.89 Prover 10: Preprocessing ... % 15.30/2.90 Prover 8: Preprocessing ... % 15.30/2.91 Prover 13: Preprocessing ... % 16.35/2.92 Prover 7: Preprocessing ... % 17.40/3.09 Prover 10: Constructing countermodel ... % 17.77/3.10 Prover 8: Warning: ignoring some quantifiers % 17.77/3.12 Prover 8: Constructing countermodel ... % 18.12/3.16 Prover 7: Constructing countermodel ... % 18.12/3.16 Prover 13: Constructing countermodel ... % 18.90/3.26 Prover 11: Constructing countermodel ... % 21.24/3.56 Prover 10: Found proof (size 160) % 21.24/3.56 Prover 10: proved (801ms) % 21.24/3.56 Prover 11: stopped % 21.24/3.56 Prover 8: stopped % 21.24/3.56 Prover 13: stopped % 21.24/3.56 Prover 7: stopped % 21.24/3.56 Prover 4: stopped % 21.24/3.56 Prover 1: stopped % 21.24/3.56 % 21.24/3.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 21.24/3.56 % 21.24/3.60 % SZS output start Proof for theBenchmark % 21.24/3.60 Assumptions after simplification: % 21.24/3.60 --------------------------------- % 21.24/3.60 % 21.24/3.61 (mDefSPN) % 21.24/3.63 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 21.24/3.63 : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : (v2 = % 21.24/3.63 sz00 | ~ (sdtasasdt0(v3, v4) = v5) | ~ (sziznziztdt0(v1) = v4) | ~ % 21.24/3.63 (sziznziztdt0(v0) = v3) | ~ (sdtlbdtrb0(v1, v2) = v7) | ~ (sdtlbdtrb0(v0, % 21.24/3.63 v2) = v6) | ~ (aDimensionOf0(v1) = v2) | ~ (aDimensionOf0(v0) = v2) | % 21.24/3.63 ~ (sdtasdt0(v6, v7) = v8) | ~ (sdtpldt0(v5, v8) = v9) | ~ $i(v1) | ~ % 21.24/3.63 $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) | (sdtasasdt0(v0, v1) = v9 & % 21.24/3.63 $i(v9))) % 21.24/3.63 % 21.24/3.63 (mDistr) % 21.24/3.63 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 21.24/3.63 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ % 21.24/3.63 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 21.24/3.63 aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v6: $i] : ? [v7: $i] % 21.24/3.63 : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v7, v2) = v8 & sdtasdt0(v1, v2) = v9 % 21.24/3.63 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v4, v9) = v8 & sdtpldt0(v1, v2) = v6 & % 21.24/3.63 sdtpldt0(v0, v1) = v7 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5))) % 21.24/3.63 % 21.24/3.63 (mDistr2) % 21.24/3.63 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 21.24/3.63 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : % 21.24/3.63 ( ~ (sdtasdt0(v1, v3) = v8) | ~ (sdtasdt0(v1, v2) = v7) | ~ (sdtasdt0(v0, % 21.24/3.63 v3) = v5) | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtpldt0(v7, v8) = v9) | ~ % 21.24/3.63 (sdtpldt0(v6, v9) = v10) | ~ (sdtpldt0(v4, v5) = v6) | ~ $i(v3) | ~ % 21.24/3.63 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aScalar0(v3) | ~ aScalar0(v2) | ~ % 21.24/3.63 aScalar0(v1) | ~ aScalar0(v0) | ? [v11: $i] : ? [v12: $i] : % 21.24/3.63 (sdtasdt0(v11, v12) = v10 & sdtpldt0(v2, v3) = v12 & sdtpldt0(v0, v1) = v11 % 21.24/3.63 & $i(v12) & $i(v11) & $i(v10))) % 21.24/3.63 % 21.24/3.63 (m__) % 21.24/3.64 $i(xH) & $i(xG) & $i(xF) & $i(xE) & $i(xD) & $i(xC) & ? [v0: $i] : ? [v1: % 21.24/3.64 $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (sdtasdt0(v2, v3) = v4 & % 21.24/3.64 sdtasdt0(v0, v0) = v1 & sdtpldt0(xE, xH) = v0 & sdtpldt0(xD, xG) = v3 & % 21.24/3.64 sdtpldt0(xC, xF) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~ % 21.24/3.64 sdtlseqdt0(v1, v4)) % 21.24/3.64 % 21.24/3.64 (m__1652) % 21.24/3.64 $i(xs) & ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : ! % 21.24/3.64 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2, v2) % 21.24/3.64 = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4) = v5) | ~ % 21.24/3.64 $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1) | ? [v6: $i] : ? % 21.24/3.64 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ((sdtasasdt0(v1, v2) = v8 & % 21.24/3.64 sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8) & sdtlseqdt0(v9, v5)) | % 21.24/3.64 (aDimensionOf0(v1) = v6 & $i(v6) & ( ~ iLess0(v6, v0) | ( ~ (v7 = v6) & % 21.24/3.64 aDimensionOf0(v2) = v7 & $i(v7))))))) % 21.24/3.64 % 21.24/3.64 (m__1678) % 21.24/3.64 $i(xt) & $i(xs) & aVector0(xt) & aVector0(xs) % 21.24/3.64 % 21.24/3.64 (m__1678_01) % 21.24/3.64 $i(xt) & $i(xs) & ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) = % 21.24/3.64 v0 & $i(v0)) % 21.24/3.64 % 21.24/3.64 (m__1692) % 21.24/3.64 $i(xs) & $i(sz00) & ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 & % 21.24/3.64 $i(v0)) % 21.24/3.64 % 21.24/3.64 (m__1709) % 21.24/3.64 $i(xp) & $i(xs) & ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xs) = xp & % 21.24/3.64 aDimensionOf0(xp) = v0 & aDimensionOf0(xs) = v1 & szszuzczcdt0(v0) = v1 & % 21.24/3.64 $i(v1) & $i(v0) & aVector0(xp) & ! [v2: $i] : ! [v3: $i] : ( ~ % 21.24/3.64 (sdtlbdtrb0(xp, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) | % 21.24/3.64 (sdtlbdtrb0(xs, v2) = v3 & $i(v3)))) % 21.24/3.64 % 21.24/3.64 (m__1726) % 21.24/3.64 $i(xq) & $i(xt) & ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xt) = xq & % 21.24/3.64 aDimensionOf0(xq) = v0 & aDimensionOf0(xt) = v1 & szszuzczcdt0(v0) = v1 & % 21.24/3.64 $i(v1) & $i(v0) & aVector0(xq) & ! [v2: $i] : ! [v3: $i] : ( ~ % 21.24/3.64 (sdtlbdtrb0(xt, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) | % 21.24/3.64 (sdtlbdtrb0(xq, v2) = v3 & $i(v3)))) % 21.24/3.64 % 21.24/3.64 (m__1746) % 21.24/3.64 $i(xA) & $i(xs) & ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) = % 21.24/3.64 v0 & $i(v0) & aScalar0(xA)) % 21.24/3.64 % 21.24/3.64 (m__1766) % 21.24/3.64 $i(xB) & $i(xt) & ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) = % 21.24/3.64 v0 & $i(v0) & aScalar0(xB)) % 21.24/3.64 % 21.24/3.64 (m__1783) % 21.24/3.64 sdtasasdt0(xp, xp) = xC & $i(xC) & $i(xp) & aScalar0(xC) % 21.24/3.64 % 21.24/3.64 (m__1800) % 21.24/3.64 sdtasasdt0(xq, xq) = xD & $i(xD) & $i(xq) & aScalar0(xD) % 21.24/3.64 % 21.24/3.64 (m__1820) % 21.24/3.64 sdtasasdt0(xp, xq) = xE & $i(xE) & $i(xq) & $i(xp) & aScalar0(xE) % 21.24/3.64 % 21.24/3.64 (m__1837) % 21.24/3.64 sdtasdt0(xA, xA) = xF & $i(xF) & $i(xA) & aScalar0(xF) % 21.24/3.64 % 21.24/3.64 (m__1854) % 21.24/3.64 sdtasdt0(xB, xB) = xG & $i(xG) & $i(xB) & aScalar0(xG) % 21.24/3.64 % 21.24/3.64 (m__1873) % 21.24/3.64 sdtasdt0(xA, xB) = xH & $i(xH) & $i(xB) & $i(xA) & aScalar0(xH) % 21.24/3.64 % 21.24/3.64 (m__1892) % 21.24/3.64 sdtasdt0(xC, xG) = xR & $i(xR) & $i(xG) & $i(xC) & aScalar0(xR) % 21.24/3.64 % 21.24/3.64 (m__1911) % 21.24/3.64 sdtasdt0(xE, xH) = xP & $i(xP) & $i(xH) & $i(xE) & aScalar0(xP) % 21.24/3.64 % 21.24/3.64 (m__1930) % 21.24/3.64 sdtasdt0(xF, xD) = xS & $i(xS) & $i(xF) & $i(xD) & aScalar0(xS) % 21.24/3.64 % 21.24/3.64 (m__1967) % 21.24/3.65 $i(xE) & $i(xD) & $i(xC) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xE, xE) = v0 % 21.24/3.65 & sdtasdt0(xC, xD) = v1 & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1)) % 21.24/3.65 % 21.24/3.65 (m__1983) % 21.24/3.65 $i(xS) & $i(xP) & $i(xR) & ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xP, xP) = v0 % 21.24/3.65 & sdtpldt0(xR, xS) = v1 & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1)) % 21.24/3.65 % 21.24/3.65 (m__2796) % 21.24/3.65 $i(xS) & $i(xP) & $i(xR) & $i(xH) & $i(xE) & $i(xD) & $i(xC) & ? [v0: $i] : % 21.24/3.65 ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: % 21.24/3.65 $i] : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(xH, xH) = v2 & sdtasdt0(xE, xE) % 21.24/3.65 = v0 & sdtasdt0(xC, xD) = v5 & sdtpldt0(v6, v2) = v7 & sdtpldt0(v5, v7) = v8 % 21.24/3.65 & sdtpldt0(v1, v2) = v3 & sdtpldt0(v0, v3) = v4 & sdtpldt0(xP, xP) = v1 & % 21.24/3.65 sdtpldt0(xR, xS) = v6 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) % 21.24/3.65 & $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v4, v8)) % 21.24/3.65 % 21.24/3.65 (m__2835) % 21.24/3.65 $i(xP) & $i(xH) & $i(xE) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 21.24/3.65 $i] : ? [v4: $i] : ? [v5: $i] : (sdtasdt0(xH, xH) = v1 & sdtasdt0(xH, xE) % 21.24/3.65 = v4 & sdtasdt0(xE, xH) = v3 & sdtpldt0(v4, v1) = v5 & sdtpldt0(v3, v5) = v2 % 21.24/3.65 & sdtpldt0(v0, v1) = v2 & sdtpldt0(xP, xP) = v0 & $i(v5) & $i(v4) & $i(v3) & % 21.24/3.65 $i(v2) & $i(v1) & $i(v0)) % 21.24/3.65 % 21.24/3.65 (m__2905) % 21.24/3.65 $i(xH) & $i(xG) & $i(xF) & $i(xE) & $i(xD) & $i(xC) & ? [v0: $i] : ? [v1: % 21.24/3.65 $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 21.24/3.65 ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? % 21.24/3.65 [v12: $i] : ? [v13: $i] : (sdtasdt0(xH, xH) = v4 & sdtasdt0(xH, xE) = v3 & % 21.24/3.65 sdtasdt0(xF, xG) = v11 & sdtasdt0(xF, xD) = v10 & sdtasdt0(xE, xH) = v1 & % 21.24/3.65 sdtasdt0(xE, xE) = v0 & sdtasdt0(xC, xG) = v8 & sdtasdt0(xC, xD) = v7 & % 21.24/3.65 sdtpldt0(v10, v11) = v12 & sdtpldt0(v9, v12) = v13 & sdtpldt0(v7, v8) = v9 & % 21.24/3.65 sdtpldt0(v3, v4) = v5 & sdtpldt0(v2, v5) = v6 & sdtpldt0(v0, v1) = v2 & % 21.24/3.65 $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 21.24/3.65 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v6, v13)) % 21.24/3.65 % 21.24/3.65 (function-axioms) % 21.24/3.65 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.24/3.65 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 21.24/3.65 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) % 21.24/3.65 | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 21.24/3.65 ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = % 21.24/3.65 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 21.24/3.65 ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 21.24/3.65 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sziznziztdt0(v2) = v1) | ~ % 21.24/3.65 (sziznziztdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 21.24/3.65 v0 | ~ (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) & ! [v0: % 21.24/3.65 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ % 21.24/3.65 (smndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 21.24/3.65 (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0)) % 21.24/3.65 % 21.24/3.65 Further assumptions not needed in the proof: % 21.24/3.65 -------------------------------------------- % 21.24/3.65 mArith, mDefInit, mDefSPZ, mDimNat, mElmSc, mEqInit, mIH, mIHOrd, mLEASm, % 21.24/3.65 mLEMon, mLEMonM, mLERef, mLETot, mLETrn, mLess, mMDNeg, mMNeg, mMulSc, mNatExtr, % 21.24/3.65 mNatSort, mNegSc, mPosMon, mSZeroSc, mScPr, mScSort, mScSqPos, mScZero, mSqPos, % 21.24/3.65 mSqrt, mSuccEqu, mSuccNat, mSumSc, mVcSort, mZeroNat, m__1949 % 21.24/3.65 % 21.24/3.65 Those formulas are unsatisfiable: % 21.24/3.65 --------------------------------- % 21.24/3.65 % 21.24/3.65 Begin of proof % 21.24/3.65 | % 21.24/3.65 | ALPHA: (mDefSPN) implies: % 21.24/3.66 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 21.24/3.66 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : % 21.24/3.66 | (v2 = sz00 | ~ (sdtasasdt0(v3, v4) = v5) | ~ (sziznziztdt0(v1) = v4) % 21.24/3.66 | | ~ (sziznziztdt0(v0) = v3) | ~ (sdtlbdtrb0(v1, v2) = v7) | ~ % 21.24/3.66 | (sdtlbdtrb0(v0, v2) = v6) | ~ (aDimensionOf0(v1) = v2) | ~ % 21.24/3.66 | (aDimensionOf0(v0) = v2) | ~ (sdtasdt0(v6, v7) = v8) | ~ % 21.24/3.66 | (sdtpldt0(v5, v8) = v9) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | % 21.24/3.66 | ~ aVector0(v0) | (sdtasasdt0(v0, v1) = v9 & $i(v9))) % 21.24/3.66 | % 21.24/3.66 | ALPHA: (m__1678) implies: % 21.24/3.66 | (2) aVector0(xs) % 21.24/3.66 | (3) aVector0(xt) % 21.24/3.66 | % 21.24/3.66 | ALPHA: (m__1652) implies: % 21.24/3.66 | (4) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 21.24/3.66 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2, % 21.24/3.66 | v2) = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4) % 21.24/3.66 | = v5) | ~ $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1) % 21.24/3.66 | | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 21.24/3.66 | ((sdtasasdt0(v1, v2) = v8 & sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8) % 21.24/3.66 | & sdtlseqdt0(v9, v5)) | (aDimensionOf0(v1) = v6 & $i(v6) & ( ~ % 21.24/3.66 | iLess0(v6, v0) | ( ~ (v7 = v6) & aDimensionOf0(v2) = v7 & % 21.24/3.66 | $i(v7))))))) % 21.24/3.66 | % 21.24/3.66 | ALPHA: (m__1678_01) implies: % 21.24/3.66 | (5) ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) = v0 & % 21.24/3.66 | $i(v0)) % 21.24/3.66 | % 21.24/3.66 | ALPHA: (m__1692) implies: % 21.24/3.66 | (6) ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 & $i(v0)) % 21.24/3.66 | % 21.24/3.66 | ALPHA: (m__1709) implies: % 21.24/3.66 | (7) ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xs) = xp & aDimensionOf0(xp) % 21.24/3.66 | = v0 & aDimensionOf0(xs) = v1 & szszuzczcdt0(v0) = v1 & $i(v1) & % 21.24/3.66 | $i(v0) & aVector0(xp) & ! [v2: $i] : ! [v3: $i] : ( ~ % 21.24/3.66 | (sdtlbdtrb0(xp, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) | % 21.24/3.66 | (sdtlbdtrb0(xs, v2) = v3 & $i(v3)))) % 21.24/3.66 | % 21.24/3.66 | ALPHA: (m__1726) implies: % 21.24/3.66 | (8) ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xt) = xq & aDimensionOf0(xq) % 21.24/3.66 | = v0 & aDimensionOf0(xt) = v1 & szszuzczcdt0(v0) = v1 & $i(v1) & % 21.24/3.66 | $i(v0) & aVector0(xq) & ! [v2: $i] : ! [v3: $i] : ( ~ % 21.24/3.66 | (sdtlbdtrb0(xt, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) | % 21.24/3.66 | (sdtlbdtrb0(xq, v2) = v3 & $i(v3)))) % 21.24/3.66 | % 21.24/3.66 | ALPHA: (m__1746) implies: % 21.24/3.66 | (9) $i(xs) % 21.24/3.66 | (10) ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) = v0 & % 21.24/3.66 | $i(v0) & aScalar0(xA)) % 21.24/3.66 | % 21.24/3.66 | ALPHA: (m__1766) implies: % 21.24/3.66 | (11) $i(xt) % 21.24/3.67 | (12) ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) = v0 & % 21.24/3.67 | $i(v0) & aScalar0(xB)) % 21.24/3.67 | % 21.24/3.67 | ALPHA: (m__1783) implies: % 21.24/3.67 | (13) aScalar0(xC) % 21.24/3.67 | % 21.24/3.67 | ALPHA: (m__1800) implies: % 21.24/3.67 | (14) aScalar0(xD) % 21.24/3.67 | % 21.24/3.67 | ALPHA: (m__1820) implies: % 21.24/3.67 | (15) aScalar0(xE) % 21.24/3.67 | (16) sdtasasdt0(xp, xq) = xE % 21.24/3.67 | % 21.24/3.67 | ALPHA: (m__1837) implies: % 21.24/3.67 | (17) aScalar0(xF) % 21.24/3.67 | % 21.24/3.67 | ALPHA: (m__1854) implies: % 21.24/3.67 | (18) aScalar0(xG) % 21.24/3.67 | % 21.24/3.67 | ALPHA: (m__1873) implies: % 21.24/3.67 | (19) aScalar0(xH) % 21.24/3.67 | (20) sdtasdt0(xA, xB) = xH % 21.24/3.67 | % 21.24/3.67 | ALPHA: (m__1892) implies: % 21.24/3.67 | (21) sdtasdt0(xC, xG) = xR % 21.24/3.67 | % 21.24/3.67 | ALPHA: (m__1911) implies: % 21.24/3.67 | (22) sdtasdt0(xE, xH) = xP % 21.24/3.67 | % 21.24/3.67 | ALPHA: (m__1930) implies: % 21.24/3.67 | (23) sdtasdt0(xF, xD) = xS % 21.24/3.67 | % 21.24/3.67 | ALPHA: (m__1967) implies: % 21.24/3.67 | (24) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xE, xE) = v0 & sdtasdt0(xC, xD) % 21.24/3.67 | = v1 & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1)) % 21.24/3.67 | % 21.24/3.67 | ALPHA: (m__1983) implies: % 21.24/3.67 | (25) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xP, xP) = v0 & sdtpldt0(xR, xS) % 21.24/3.67 | = v1 & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1)) % 21.24/3.67 | % 21.24/3.68 | ALPHA: (m__2796) implies: % 21.24/3.68 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 21.24/3.68 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(xH, % 21.24/3.68 | xH) = v2 & sdtasdt0(xE, xE) = v0 & sdtasdt0(xC, xD) = v5 & % 21.24/3.68 | sdtpldt0(v6, v2) = v7 & sdtpldt0(v5, v7) = v8 & sdtpldt0(v1, v2) = % 21.24/3.68 | v3 & sdtpldt0(v0, v3) = v4 & sdtpldt0(xP, xP) = v1 & sdtpldt0(xR, % 21.24/3.68 | xS) = v6 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 21.24/3.68 | $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v4, v8)) % 21.24/3.68 | % 21.24/3.68 | ALPHA: (m__2835) implies: % 21.24/3.68 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 21.24/3.68 | ? [v5: $i] : (sdtasdt0(xH, xH) = v1 & sdtasdt0(xH, xE) = v4 & % 21.24/3.68 | sdtasdt0(xE, xH) = v3 & sdtpldt0(v4, v1) = v5 & sdtpldt0(v3, v5) = % 21.24/3.68 | v2 & sdtpldt0(v0, v1) = v2 & sdtpldt0(xP, xP) = v0 & $i(v5) & $i(v4) % 21.24/3.68 | & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 21.24/3.68 | % 21.24/3.68 | ALPHA: (m__2905) implies: % 21.24/3.68 | (28) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 21.24/3.68 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 21.24/3.68 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : % 21.24/3.68 | (sdtasdt0(xH, xH) = v4 & sdtasdt0(xH, xE) = v3 & sdtasdt0(xF, xG) = % 21.24/3.68 | v11 & sdtasdt0(xF, xD) = v10 & sdtasdt0(xE, xH) = v1 & sdtasdt0(xE, % 21.24/3.68 | xE) = v0 & sdtasdt0(xC, xG) = v8 & sdtasdt0(xC, xD) = v7 & % 21.24/3.68 | sdtpldt0(v10, v11) = v12 & sdtpldt0(v9, v12) = v13 & sdtpldt0(v7, % 21.24/3.68 | v8) = v9 & sdtpldt0(v3, v4) = v5 & sdtpldt0(v2, v5) = v6 & % 21.24/3.68 | sdtpldt0(v0, v1) = v2 & $i(v13) & $i(v12) & $i(v11) & $i(v10) & % 21.24/3.68 | $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 21.24/3.68 | $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v6, v13)) % 21.24/3.68 | % 21.24/3.68 | ALPHA: (m__) implies: % 21.24/3.68 | (29) $i(xC) % 21.24/3.68 | (30) $i(xD) % 21.24/3.68 | (31) $i(xE) % 21.24/3.68 | (32) $i(xF) % 21.24/3.68 | (33) $i(xG) % 21.24/3.68 | (34) $i(xH) % 21.24/3.68 | (35) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 21.24/3.68 | (sdtasdt0(v2, v3) = v4 & sdtasdt0(v0, v0) = v1 & sdtpldt0(xE, xH) = v0 % 21.24/3.68 | & sdtpldt0(xD, xG) = v3 & sdtpldt0(xC, xF) = v2 & $i(v4) & $i(v3) & % 21.24/3.68 | $i(v2) & $i(v1) & $i(v0) & ~ sdtlseqdt0(v1, v4)) % 21.24/3.68 | % 21.24/3.68 | ALPHA: (function-axioms) implies: % 21.24/3.68 | (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 21.24/3.68 | (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) % 21.24/3.68 | (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.24/3.68 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 21.24/3.68 | (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.24/3.68 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 21.24/3.68 | % 21.24/3.68 | DELTA: instantiating (5) with fresh symbol all_33_0 gives: % 21.24/3.68 | (39) aDimensionOf0(xt) = all_33_0 & aDimensionOf0(xs) = all_33_0 & % 21.24/3.68 | $i(all_33_0) % 21.24/3.68 | % 21.24/3.68 | ALPHA: (39) implies: % 21.24/3.68 | (40) aDimensionOf0(xs) = all_33_0 % 21.24/3.68 | (41) aDimensionOf0(xt) = all_33_0 % 21.24/3.68 | % 21.24/3.68 | DELTA: instantiating (6) with fresh symbol all_35_0 gives: % 21.24/3.68 | (42) ~ (all_35_0 = sz00) & aDimensionOf0(xs) = all_35_0 & $i(all_35_0) % 21.24/3.68 | % 21.24/3.68 | ALPHA: (42) implies: % 21.24/3.68 | (43) ~ (all_35_0 = sz00) % 21.24/3.68 | (44) aDimensionOf0(xs) = all_35_0 % 21.24/3.68 | % 21.24/3.68 | DELTA: instantiating (12) with fresh symbol all_37_0 gives: % 21.24/3.68 | (45) sdtlbdtrb0(xt, all_37_0) = xB & aDimensionOf0(xt) = all_37_0 & % 21.24/3.68 | $i(all_37_0) & aScalar0(xB) % 21.24/3.68 | % 21.24/3.68 | ALPHA: (45) implies: % 21.24/3.69 | (46) aDimensionOf0(xt) = all_37_0 % 21.24/3.69 | (47) sdtlbdtrb0(xt, all_37_0) = xB % 21.24/3.69 | % 21.24/3.69 | DELTA: instantiating (10) with fresh symbol all_39_0 gives: % 21.24/3.69 | (48) sdtlbdtrb0(xs, all_39_0) = xA & aDimensionOf0(xs) = all_39_0 & % 21.24/3.69 | $i(all_39_0) & aScalar0(xA) % 21.24/3.69 | % 21.24/3.69 | ALPHA: (48) implies: % 21.24/3.69 | (49) aDimensionOf0(xs) = all_39_0 % 21.24/3.69 | (50) sdtlbdtrb0(xs, all_39_0) = xA % 21.24/3.69 | % 21.24/3.69 | DELTA: instantiating (24) with fresh symbols all_41_0, all_41_1 gives: % 21.24/3.69 | (51) sdtasdt0(xE, xE) = all_41_1 & sdtasdt0(xC, xD) = all_41_0 & % 21.24/3.69 | $i(all_41_0) & $i(all_41_1) & sdtlseqdt0(all_41_1, all_41_0) % 21.24/3.69 | % 21.24/3.69 | ALPHA: (51) implies: % 21.24/3.69 | (52) sdtasdt0(xC, xD) = all_41_0 % 21.24/3.69 | (53) sdtasdt0(xE, xE) = all_41_1 % 21.24/3.69 | % 21.24/3.69 | DELTA: instantiating (25) with fresh symbols all_43_0, all_43_1 gives: % 21.24/3.69 | (54) sdtpldt0(xP, xP) = all_43_1 & sdtpldt0(xR, xS) = all_43_0 & % 21.24/3.69 | $i(all_43_0) & $i(all_43_1) & sdtlseqdt0(all_43_1, all_43_0) % 21.24/3.69 | % 21.24/3.69 | ALPHA: (54) implies: % 21.24/3.69 | (55) sdtpldt0(xP, xP) = all_43_1 % 21.24/3.69 | % 21.24/3.69 | DELTA: instantiating (35) with fresh symbols all_45_0, all_45_1, all_45_2, % 21.24/3.69 | all_45_3, all_45_4 gives: % 21.24/3.69 | (56) sdtasdt0(all_45_2, all_45_1) = all_45_0 & sdtasdt0(all_45_4, all_45_4) % 21.24/3.69 | = all_45_3 & sdtpldt0(xE, xH) = all_45_4 & sdtpldt0(xD, xG) = all_45_1 % 21.24/3.69 | & sdtpldt0(xC, xF) = all_45_2 & $i(all_45_0) & $i(all_45_1) & % 21.24/3.69 | $i(all_45_2) & $i(all_45_3) & $i(all_45_4) & ~ sdtlseqdt0(all_45_3, % 21.24/3.69 | all_45_0) % 21.24/3.69 | % 21.24/3.69 | ALPHA: (56) implies: % 21.24/3.69 | (57) ~ sdtlseqdt0(all_45_3, all_45_0) % 21.24/3.69 | (58) sdtpldt0(xC, xF) = all_45_2 % 21.24/3.69 | (59) sdtpldt0(xD, xG) = all_45_1 % 21.24/3.69 | (60) sdtpldt0(xE, xH) = all_45_4 % 21.24/3.69 | (61) sdtasdt0(all_45_4, all_45_4) = all_45_3 % 21.24/3.69 | (62) sdtasdt0(all_45_2, all_45_1) = all_45_0 % 21.24/3.69 | % 21.24/3.69 | DELTA: instantiating (8) with fresh symbols all_47_0, all_47_1 gives: % 21.24/3.69 | (63) sziznziztdt0(xt) = xq & aDimensionOf0(xq) = all_47_1 & % 21.24/3.69 | aDimensionOf0(xt) = all_47_0 & szszuzczcdt0(all_47_1) = all_47_0 & % 21.24/3.69 | $i(all_47_0) & $i(all_47_1) & aVector0(xq) & ! [v0: $i] : ! [v1: $i] % 21.24/3.69 | : ( ~ (sdtlbdtrb0(xt, v0) = v1) | ~ $i(v0) | ~ aNaturalNumber0(v0) | % 21.24/3.69 | (sdtlbdtrb0(xq, v0) = v1 & $i(v1))) % 21.24/3.69 | % 21.24/3.69 | ALPHA: (63) implies: % 21.24/3.69 | (64) aDimensionOf0(xt) = all_47_0 % 21.24/3.69 | (65) sziznziztdt0(xt) = xq % 21.24/3.69 | % 21.24/3.69 | DELTA: instantiating (7) with fresh symbols all_50_0, all_50_1 gives: % 21.24/3.69 | (66) sziznziztdt0(xs) = xp & aDimensionOf0(xp) = all_50_1 & % 21.24/3.69 | aDimensionOf0(xs) = all_50_0 & szszuzczcdt0(all_50_1) = all_50_0 & % 21.24/3.69 | $i(all_50_0) & $i(all_50_1) & aVector0(xp) & ! [v0: $i] : ! [v1: $i] % 21.24/3.69 | : ( ~ (sdtlbdtrb0(xp, v0) = v1) | ~ $i(v0) | ~ aNaturalNumber0(v0) | % 21.24/3.69 | (sdtlbdtrb0(xs, v0) = v1 & $i(v1))) % 21.24/3.69 | % 21.24/3.69 | ALPHA: (66) implies: % 21.24/3.69 | (67) aDimensionOf0(xs) = all_50_0 % 21.24/3.69 | (68) sziznziztdt0(xs) = xp % 21.24/3.69 | % 21.24/3.69 | DELTA: instantiating (27) with fresh symbols all_53_0, all_53_1, all_53_2, % 21.24/3.69 | all_53_3, all_53_4, all_53_5 gives: % 21.24/3.69 | (69) sdtasdt0(xH, xH) = all_53_4 & sdtasdt0(xH, xE) = all_53_1 & % 21.24/3.69 | sdtasdt0(xE, xH) = all_53_2 & sdtpldt0(all_53_1, all_53_4) = all_53_0 % 21.24/3.69 | & sdtpldt0(all_53_2, all_53_0) = all_53_3 & sdtpldt0(all_53_5, % 21.24/3.69 | all_53_4) = all_53_3 & sdtpldt0(xP, xP) = all_53_5 & $i(all_53_0) & % 21.24/3.69 | $i(all_53_1) & $i(all_53_2) & $i(all_53_3) & $i(all_53_4) & % 21.24/3.69 | $i(all_53_5) % 21.24/3.69 | % 21.24/3.69 | ALPHA: (69) implies: % 21.24/3.69 | (70) sdtpldt0(xP, xP) = all_53_5 % 21.24/3.69 | (71) sdtpldt0(all_53_1, all_53_4) = all_53_0 % 21.24/3.69 | (72) sdtasdt0(xE, xH) = all_53_2 % 21.24/3.69 | (73) sdtasdt0(xH, xE) = all_53_1 % 21.24/3.69 | (74) sdtasdt0(xH, xH) = all_53_4 % 21.24/3.69 | % 21.24/3.69 | DELTA: instantiating (26) with fresh symbols all_55_0, all_55_1, all_55_2, % 21.24/3.69 | all_55_3, all_55_4, all_55_5, all_55_6, all_55_7, all_55_8 gives: % 21.24/3.69 | (75) sdtasdt0(xH, xH) = all_55_6 & sdtasdt0(xE, xE) = all_55_8 & % 21.24/3.69 | sdtasdt0(xC, xD) = all_55_3 & sdtpldt0(all_55_2, all_55_6) = all_55_1 % 21.24/3.69 | & sdtpldt0(all_55_3, all_55_1) = all_55_0 & sdtpldt0(all_55_7, % 21.24/3.69 | all_55_6) = all_55_5 & sdtpldt0(all_55_8, all_55_5) = all_55_4 & % 21.24/3.69 | sdtpldt0(xP, xP) = all_55_7 & sdtpldt0(xR, xS) = all_55_2 & % 21.24/3.69 | $i(all_55_0) & $i(all_55_1) & $i(all_55_2) & $i(all_55_3) & % 21.24/3.70 | $i(all_55_4) & $i(all_55_5) & $i(all_55_6) & $i(all_55_7) & % 21.24/3.70 | $i(all_55_8) & sdtlseqdt0(all_55_4, all_55_0) % 21.24/3.70 | % 21.24/3.70 | ALPHA: (75) implies: % 21.24/3.70 | (76) sdtpldt0(xP, xP) = all_55_7 % 21.24/3.70 | (77) sdtasdt0(xC, xD) = all_55_3 % 21.24/3.70 | (78) sdtasdt0(xE, xE) = all_55_8 % 21.24/3.70 | (79) sdtasdt0(xH, xH) = all_55_6 % 21.24/3.70 | % 21.24/3.70 | DELTA: instantiating (4) with fresh symbol all_57_0 gives: % 21.24/3.70 | (80) aDimensionOf0(xs) = all_57_0 & $i(all_57_0) & ! [v0: $i] : ! [v1: % 21.24/3.70 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasasdt0(v1, % 21.24/3.70 | v1) = v3) | ~ (sdtasasdt0(v0, v0) = v2) | ~ (sdtasdt0(v2, v3) % 21.24/3.70 | = v4) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) % 21.24/3.70 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 21.24/3.70 | ((sdtasasdt0(v0, v1) = v7 & sdtasdt0(v7, v7) = v8 & $i(v8) & $i(v7) % 21.24/3.70 | & sdtlseqdt0(v8, v4)) | (aDimensionOf0(v0) = v5 & $i(v5) & ( ~ % 21.24/3.70 | iLess0(v5, all_57_0) | ( ~ (v6 = v5) & aDimensionOf0(v1) = v6 % 21.24/3.70 | & $i(v6)))))) % 21.24/3.70 | % 21.24/3.70 | ALPHA: (80) implies: % 21.24/3.70 | (81) aDimensionOf0(xs) = all_57_0 % 21.24/3.70 | % 21.24/3.70 | DELTA: instantiating (28) with fresh symbols all_63_0, all_63_1, all_63_2, % 21.24/3.70 | all_63_3, all_63_4, all_63_5, all_63_6, all_63_7, all_63_8, all_63_9, % 21.24/3.70 | all_63_10, all_63_11, all_63_12, all_63_13 gives: % 21.24/3.70 | (82) sdtasdt0(xH, xH) = all_63_9 & sdtasdt0(xH, xE) = all_63_10 & % 21.24/3.70 | sdtasdt0(xF, xG) = all_63_2 & sdtasdt0(xF, xD) = all_63_3 & % 21.24/3.70 | sdtasdt0(xE, xH) = all_63_12 & sdtasdt0(xE, xE) = all_63_13 & % 21.24/3.70 | sdtasdt0(xC, xG) = all_63_5 & sdtasdt0(xC, xD) = all_63_6 & % 21.24/3.70 | sdtpldt0(all_63_3, all_63_2) = all_63_1 & sdtpldt0(all_63_4, all_63_1) % 21.24/3.70 | = all_63_0 & sdtpldt0(all_63_6, all_63_5) = all_63_4 & % 21.24/3.70 | sdtpldt0(all_63_10, all_63_9) = all_63_8 & sdtpldt0(all_63_11, % 21.24/3.70 | all_63_8) = all_63_7 & sdtpldt0(all_63_13, all_63_12) = all_63_11 & % 21.24/3.70 | $i(all_63_0) & $i(all_63_1) & $i(all_63_2) & $i(all_63_3) & % 21.24/3.70 | $i(all_63_4) & $i(all_63_5) & $i(all_63_6) & $i(all_63_7) & % 21.24/3.70 | $i(all_63_8) & $i(all_63_9) & $i(all_63_10) & $i(all_63_11) & % 21.24/3.70 | $i(all_63_12) & $i(all_63_13) & sdtlseqdt0(all_63_7, all_63_0) % 21.24/3.70 | % 21.24/3.70 | ALPHA: (82) implies: % 21.24/3.70 | (83) sdtlseqdt0(all_63_7, all_63_0) % 21.24/3.70 | (84) sdtpldt0(all_63_13, all_63_12) = all_63_11 % 21.24/3.70 | (85) sdtpldt0(all_63_11, all_63_8) = all_63_7 % 21.24/3.70 | (86) sdtpldt0(all_63_10, all_63_9) = all_63_8 % 21.24/3.70 | (87) sdtpldt0(all_63_6, all_63_5) = all_63_4 % 21.24/3.70 | (88) sdtpldt0(all_63_4, all_63_1) = all_63_0 % 21.24/3.70 | (89) sdtpldt0(all_63_3, all_63_2) = all_63_1 % 21.24/3.70 | (90) sdtasdt0(xC, xD) = all_63_6 % 21.24/3.70 | (91) sdtasdt0(xC, xG) = all_63_5 % 21.24/3.70 | (92) sdtasdt0(xE, xE) = all_63_13 % 21.24/3.70 | (93) sdtasdt0(xE, xH) = all_63_12 % 21.24/3.70 | (94) sdtasdt0(xF, xD) = all_63_3 % 21.24/3.70 | (95) sdtasdt0(xF, xG) = all_63_2 % 21.24/3.70 | (96) sdtasdt0(xH, xE) = all_63_10 % 21.24/3.70 | (97) sdtasdt0(xH, xH) = all_63_9 % 21.24/3.70 | % 21.24/3.70 | GROUND_INST: instantiating (37) with all_53_5, all_55_7, xP, xP, simplifying % 21.24/3.70 | with (70), (76) gives: % 21.24/3.70 | (98) all_55_7 = all_53_5 % 21.24/3.70 | % 21.24/3.70 | GROUND_INST: instantiating (37) with all_43_1, all_55_7, xP, xP, simplifying % 21.24/3.70 | with (55), (76) gives: % 21.24/3.70 | (99) all_55_7 = all_43_1 % 21.24/3.70 | % 21.24/3.70 | GROUND_INST: instantiating (38) with all_55_3, all_63_6, xD, xC, simplifying % 21.24/3.70 | with (77), (90) gives: % 21.24/3.70 | (100) all_63_6 = all_55_3 % 21.24/3.70 | % 21.24/3.70 | GROUND_INST: instantiating (38) with all_41_0, all_63_6, xD, xC, simplifying % 21.24/3.70 | with (52), (90) gives: % 21.24/3.70 | (101) all_63_6 = all_41_0 % 21.24/3.70 | % 21.24/3.70 | GROUND_INST: instantiating (38) with xR, all_63_5, xG, xC, simplifying with % 21.24/3.70 | (21), (91) gives: % 21.24/3.71 | (102) all_63_5 = xR % 21.24/3.71 | % 21.24/3.71 | GROUND_INST: instantiating (38) with all_55_8, all_63_13, xE, xE, simplifying % 21.24/3.71 | with (78), (92) gives: % 21.24/3.71 | (103) all_63_13 = all_55_8 % 21.24/3.71 | % 21.24/3.71 | GROUND_INST: instantiating (38) with all_41_1, all_63_13, xE, xE, simplifying % 21.24/3.71 | with (53), (92) gives: % 21.24/3.71 | (104) all_63_13 = all_41_1 % 21.24/3.71 | % 21.24/3.71 | GROUND_INST: instantiating (38) with all_53_2, all_63_12, xH, xE, simplifying % 21.24/3.71 | with (72), (93) gives: % 21.24/3.71 | (105) all_63_12 = all_53_2 % 21.24/3.71 | % 21.24/3.71 | GROUND_INST: instantiating (38) with xP, all_63_12, xH, xE, simplifying with % 21.24/3.71 | (22), (93) gives: % 21.24/3.71 | (106) all_63_12 = xP % 21.24/3.71 | % 21.24/3.71 | GROUND_INST: instantiating (38) with xS, all_63_3, xD, xF, simplifying with % 21.24/3.71 | (23), (94) gives: % 21.24/3.71 | (107) all_63_3 = xS % 21.24/3.71 | % 21.24/3.71 | GROUND_INST: instantiating (38) with all_53_1, all_63_10, xE, xH, simplifying % 21.24/3.71 | with (73), (96) gives: % 21.24/3.71 | (108) all_63_10 = all_53_1 % 21.24/3.71 | % 21.24/3.71 | GROUND_INST: instantiating (38) with all_55_6, all_63_9, xH, xH, simplifying % 21.24/3.71 | with (79), (97) gives: % 21.24/3.71 | (109) all_63_9 = all_55_6 % 21.24/3.71 | % 21.24/3.71 | GROUND_INST: instantiating (38) with all_53_4, all_63_9, xH, xH, simplifying % 21.24/3.71 | with (74), (97) gives: % 21.24/3.71 | (110) all_63_9 = all_53_4 % 21.24/3.71 | % 21.24/3.71 | GROUND_INST: instantiating (36) with all_35_0, all_39_0, xs, simplifying with % 21.24/3.71 | (44), (49) gives: % 21.24/3.71 | (111) all_39_0 = all_35_0 % 21.24/3.71 | % 21.24/3.71 | GROUND_INST: instantiating (36) with all_50_0, all_57_0, xs, simplifying with % 21.24/3.71 | (67), (81) gives: % 21.24/3.71 | (112) all_57_0 = all_50_0 % 21.24/3.71 | % 21.24/3.71 | GROUND_INST: instantiating (36) with all_39_0, all_57_0, xs, simplifying with % 21.24/3.71 | (49), (81) gives: % 21.24/3.71 | (113) all_57_0 = all_39_0 % 21.24/3.71 | % 21.24/3.71 | GROUND_INST: instantiating (36) with all_33_0, all_57_0, xs, simplifying with % 21.24/3.71 | (40), (81) gives: % 21.24/3.71 | (114) all_57_0 = all_33_0 % 21.24/3.71 | % 21.24/3.71 | GROUND_INST: instantiating (36) with all_37_0, all_47_0, xt, simplifying with % 21.24/3.71 | (46), (64) gives: % 21.24/3.71 | (115) all_47_0 = all_37_0 % 21.24/3.71 | % 21.24/3.71 | GROUND_INST: instantiating (36) with all_33_0, all_47_0, xt, simplifying with % 21.24/3.71 | (41), (64) gives: % 21.24/3.71 | (116) all_47_0 = all_33_0 % 21.24/3.71 | % 21.24/3.71 | COMBINE_EQS: (100), (101) imply: % 21.24/3.71 | (117) all_55_3 = all_41_0 % 21.24/3.71 | % 21.24/3.71 | SIMP: (117) implies: % 21.24/3.71 | (118) all_55_3 = all_41_0 % 21.24/3.71 | % 21.24/3.71 | COMBINE_EQS: (109), (110) imply: % 21.24/3.71 | (119) all_55_6 = all_53_4 % 21.24/3.71 | % 21.24/3.71 | SIMP: (119) implies: % 21.24/3.71 | (120) all_55_6 = all_53_4 % 21.24/3.71 | % 21.24/3.71 | COMBINE_EQS: (105), (106) imply: % 21.24/3.71 | (121) all_53_2 = xP % 21.24/3.71 | % 21.24/3.71 | SIMP: (121) implies: % 21.24/3.71 | (122) all_53_2 = xP % 21.24/3.71 | % 21.24/3.71 | COMBINE_EQS: (103), (104) imply: % 21.24/3.71 | (123) all_55_8 = all_41_1 % 21.24/3.71 | % 21.24/3.71 | SIMP: (123) implies: % 21.24/3.71 | (124) all_55_8 = all_41_1 % 21.24/3.71 | % 21.24/3.71 | COMBINE_EQS: (112), (114) imply: % 21.24/3.71 | (125) all_50_0 = all_33_0 % 21.24/3.71 | % 21.24/3.71 | COMBINE_EQS: (112), (113) imply: % 21.24/3.71 | (126) all_50_0 = all_39_0 % 21.24/3.71 | % 21.24/3.71 | COMBINE_EQS: (98), (99) imply: % 21.24/3.71 | (127) all_53_5 = all_43_1 % 21.24/3.71 | % 21.24/3.71 | COMBINE_EQS: (125), (126) imply: % 21.24/3.71 | (128) all_39_0 = all_33_0 % 21.24/3.71 | % 21.24/3.71 | SIMP: (128) implies: % 21.24/3.71 | (129) all_39_0 = all_33_0 % 21.24/3.71 | % 21.24/3.71 | COMBINE_EQS: (115), (116) imply: % 21.24/3.71 | (130) all_37_0 = all_33_0 % 21.24/3.71 | % 21.24/3.71 | COMBINE_EQS: (111), (129) imply: % 21.24/3.71 | (131) all_35_0 = all_33_0 % 21.24/3.71 | % 21.24/3.71 | REDUCE: (43), (131) imply: % 21.24/3.71 | (132) ~ (all_33_0 = sz00) % 21.24/3.71 | % 21.24/3.71 | REDUCE: (47), (130) imply: % 21.24/3.71 | (133) sdtlbdtrb0(xt, all_33_0) = xB % 21.24/3.71 | % 21.24/3.71 | REDUCE: (50), (129) imply: % 21.24/3.71 | (134) sdtlbdtrb0(xs, all_33_0) = xA % 21.24/3.71 | % 21.24/3.71 | REDUCE: (89), (107) imply: % 21.24/3.71 | (135) sdtpldt0(xS, all_63_2) = all_63_1 % 21.24/3.71 | % 21.24/3.71 | REDUCE: (87), (101), (102) imply: % 21.24/3.71 | (136) sdtpldt0(all_41_0, xR) = all_63_4 % 21.24/3.71 | % 21.24/3.71 | REDUCE: (86), (108), (110) imply: % 21.24/3.71 | (137) sdtpldt0(all_53_1, all_53_4) = all_63_8 % 21.24/3.71 | % 21.24/3.71 | REDUCE: (84), (104), (106) imply: % 21.24/3.71 | (138) sdtpldt0(all_41_1, xP) = all_63_11 % 21.24/3.71 | % 21.24/3.72 | GROUND_INST: instantiating (37) with all_53_0, all_63_8, all_53_4, all_53_1, % 21.24/3.72 | simplifying with (71), (137) gives: % 21.24/3.72 | (139) all_63_8 = all_53_0 % 21.24/3.72 | % 21.24/3.72 | REDUCE: (85), (139) imply: % 21.24/3.72 | (140) sdtpldt0(all_63_11, all_53_0) = all_63_7 % 21.24/3.72 | % 21.24/3.72 | GROUND_INST: instantiating (mDistr) with xC, xD, xG, all_41_0, xR, all_63_4, % 21.24/3.72 | simplifying with (13), (14), (18), (21), (29), (30), (33), (52), % 21.24/3.72 | (136) gives: % 21.24/3.72 | (141) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v1, % 21.24/3.72 | xG) = v2 & sdtasdt0(xD, xG) = v3 & sdtasdt0(xC, v0) = all_63_4 & % 21.24/3.72 | sdtpldt0(xR, v3) = v2 & sdtpldt0(xD, xG) = v0 & sdtpldt0(xC, xD) = % 21.24/3.72 | v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_63_4)) % 21.24/3.72 | % 21.24/3.72 | GROUND_INST: instantiating (mDistr) with xE, xH, xH, xP, xP, all_43_1, % 21.24/3.72 | simplifying with (15), (19), (22), (31), (34), (55) gives: % 21.24/3.72 | (142) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v1, % 21.24/3.72 | xH) = v2 & sdtasdt0(xH, xH) = v3 & sdtasdt0(xE, v0) = all_43_1 & % 21.24/3.72 | sdtpldt0(xP, v3) = v2 & sdtpldt0(xH, xH) = v0 & sdtpldt0(xE, xH) = % 21.24/3.72 | v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_43_1)) % 21.24/3.72 | % 21.24/3.72 | GROUND_INST: instantiating (mDistr) with xE, xE, xH, all_41_1, xP, all_63_11, % 21.24/3.72 | simplifying with (15), (19), (22), (31), (34), (53), (138) gives: % 21.24/3.72 | (143) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v1, % 21.24/3.72 | xH) = v2 & sdtasdt0(xE, v0) = all_63_11 & sdtasdt0(xE, xH) = v3 & % 21.24/3.72 | sdtpldt0(xP, v3) = v2 & sdtpldt0(xE, xH) = v0 & sdtpldt0(xE, xE) = % 21.24/3.72 | v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_63_11)) % 21.24/3.72 | % 21.24/3.72 | GROUND_INST: instantiating (mDistr2) with xC, xF, xD, xG, all_41_0, xR, % 21.24/3.72 | all_63_4, xS, all_63_2, all_63_1, all_63_0, simplifying with % 21.24/3.72 | (13), (14), (17), (18), (21), (23), (29), (30), (32), (33), (52), % 21.24/3.72 | (88), (95), (135), (136) gives: % 21.24/3.72 | (144) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(v0, v1) = all_63_0 & % 21.24/3.72 | sdtpldt0(xD, xG) = v1 & sdtpldt0(xC, xF) = v0 & $i(v1) & $i(v0) & % 21.24/3.72 | $i(all_63_0)) % 21.24/3.72 | % 21.24/3.72 | GROUND_INST: instantiating (mDistr) with xF, xD, xG, xS, all_63_2, all_63_1, % 21.24/3.72 | simplifying with (14), (17), (18), (23), (30), (32), (33), (95), % 21.24/3.72 | (135) gives: % 21.24/3.72 | (145) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v1, % 21.24/3.72 | xG) = v2 & sdtasdt0(xF, v0) = all_63_1 & sdtasdt0(xD, xG) = v3 & % 21.24/3.72 | sdtpldt0(all_63_2, v3) = v2 & sdtpldt0(xF, xD) = v1 & sdtpldt0(xD, % 21.24/3.72 | xG) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_63_1)) % 21.24/3.72 | % 21.24/3.72 | GROUND_INST: instantiating (mDistr2) with xE, xH, xE, xH, all_41_1, xP, % 21.24/3.72 | all_63_11, all_53_1, all_53_4, all_53_0, all_63_7, simplifying % 21.24/3.72 | with (15), (19), (22), (31), (34), (53), (71), (73), (74), (138), % 21.24/3.72 | (140) gives: % 21.24/3.73 | (146) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(v0, v1) = all_63_7 & % 21.24/3.73 | sdtpldt0(xE, xH) = v1 & sdtpldt0(xE, xH) = v0 & $i(v1) & $i(v0) & % 21.24/3.73 | $i(all_63_7)) % 21.24/3.73 | % 21.24/3.73 | GROUND_INST: instantiating (mDistr) with xH, xE, xH, all_53_1, all_53_4, % 21.24/3.73 | all_53_0, simplifying with (15), (19), (31), (34), (71), (73), % 21.24/3.73 | (74) gives: % 21.24/3.73 | (147) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v1, % 21.24/3.73 | xH) = v2 & sdtasdt0(xH, v0) = all_53_0 & sdtasdt0(xE, xH) = v3 & % 21.24/3.73 | sdtpldt0(all_53_4, v3) = v2 & sdtpldt0(xH, xE) = v1 & sdtpldt0(xE, % 21.24/3.73 | xH) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_53_0)) % 21.24/3.73 | % 21.24/3.73 | GROUND_INST: instantiating (1) with xs, xt, all_33_0, xp, xq, xE, xA, xB, xH, % 21.24/3.73 | all_45_4, simplifying with (2), (3), (9), (11), (16), (20), (40), % 21.24/3.73 | (41), (60), (65), (68), (133), (134) gives: % 21.24/3.73 | (148) all_33_0 = sz00 | (sdtasasdt0(xs, xt) = all_45_4 & $i(all_45_4)) % 21.24/3.73 | % 21.24/3.73 | DELTA: instantiating (146) with fresh symbols all_79_0, all_79_1 gives: % 21.24/3.73 | (149) sdtasdt0(all_79_1, all_79_0) = all_63_7 & sdtpldt0(xE, xH) = all_79_0 % 21.24/3.73 | & sdtpldt0(xE, xH) = all_79_1 & $i(all_79_0) & $i(all_79_1) & % 21.24/3.73 | $i(all_63_7) % 21.24/3.73 | % 21.24/3.73 | ALPHA: (149) implies: % 21.24/3.73 | (150) sdtpldt0(xE, xH) = all_79_1 % 21.24/3.73 | (151) sdtpldt0(xE, xH) = all_79_0 % 21.24/3.73 | (152) sdtasdt0(all_79_1, all_79_0) = all_63_7 % 21.24/3.73 | % 21.24/3.73 | DELTA: instantiating (144) with fresh symbols all_81_0, all_81_1 gives: % 21.24/3.73 | (153) sdtasdt0(all_81_1, all_81_0) = all_63_0 & sdtpldt0(xD, xG) = all_81_0 % 21.24/3.73 | & sdtpldt0(xC, xF) = all_81_1 & $i(all_81_0) & $i(all_81_1) & % 21.24/3.73 | $i(all_63_0) % 21.24/3.73 | % 21.24/3.73 | ALPHA: (153) implies: % 21.24/3.73 | (154) sdtpldt0(xC, xF) = all_81_1 % 21.24/3.73 | (155) sdtpldt0(xD, xG) = all_81_0 % 21.24/3.73 | (156) sdtasdt0(all_81_1, all_81_0) = all_63_0 % 21.24/3.73 | % 21.24/3.73 | DELTA: instantiating (143) with fresh symbols all_85_0, all_85_1, all_85_2, % 21.24/3.73 | all_85_3 gives: % 21.24/3.73 | (157) sdtasdt0(all_85_2, xH) = all_85_1 & sdtasdt0(xE, all_85_3) = % 21.24/3.73 | all_63_11 & sdtasdt0(xE, xH) = all_85_0 & sdtpldt0(xP, all_85_0) = % 21.24/3.73 | all_85_1 & sdtpldt0(xE, xH) = all_85_3 & sdtpldt0(xE, xE) = all_85_2 % 21.24/3.73 | & $i(all_85_0) & $i(all_85_1) & $i(all_85_2) & $i(all_85_3) & % 21.24/3.73 | $i(all_63_11) % 21.24/3.73 | % 21.24/3.73 | ALPHA: (157) implies: % 21.24/3.73 | (158) sdtpldt0(xE, xH) = all_85_3 % 21.24/3.73 | % 21.24/3.73 | DELTA: instantiating (142) with fresh symbols all_87_0, all_87_1, all_87_2, % 21.24/3.73 | all_87_3 gives: % 21.24/3.73 | (159) sdtasdt0(all_87_2, xH) = all_87_1 & sdtasdt0(xH, xH) = all_87_0 & % 21.24/3.73 | sdtasdt0(xE, all_87_3) = all_43_1 & sdtpldt0(xP, all_87_0) = all_87_1 % 21.24/3.73 | & sdtpldt0(xH, xH) = all_87_3 & sdtpldt0(xE, xH) = all_87_2 & % 21.24/3.73 | $i(all_87_0) & $i(all_87_1) & $i(all_87_2) & $i(all_87_3) & % 21.24/3.73 | $i(all_43_1) % 21.24/3.73 | % 21.24/3.73 | ALPHA: (159) implies: % 21.24/3.73 | (160) sdtpldt0(xE, xH) = all_87_2 % 21.24/3.73 | % 21.24/3.73 | DELTA: instantiating (141) with fresh symbols all_90_0, all_90_1, all_90_2, % 21.24/3.73 | all_90_3 gives: % 21.24/3.73 | (161) sdtasdt0(all_90_2, xG) = all_90_1 & sdtasdt0(xD, xG) = all_90_0 & % 21.24/3.73 | sdtasdt0(xC, all_90_3) = all_63_4 & sdtpldt0(xR, all_90_0) = all_90_1 % 21.24/3.73 | & sdtpldt0(xD, xG) = all_90_3 & sdtpldt0(xC, xD) = all_90_2 & % 21.24/3.73 | $i(all_90_0) & $i(all_90_1) & $i(all_90_2) & $i(all_90_3) & % 21.24/3.73 | $i(all_63_4) % 21.24/3.73 | % 21.24/3.73 | ALPHA: (161) implies: % 21.24/3.73 | (162) sdtpldt0(xD, xG) = all_90_3 % 21.24/3.73 | % 21.24/3.73 | DELTA: instantiating (145) with fresh symbols all_92_0, all_92_1, all_92_2, % 21.24/3.73 | all_92_3 gives: % 21.24/3.73 | (163) sdtasdt0(all_92_2, xG) = all_92_1 & sdtasdt0(xF, all_92_3) = all_63_1 % 21.24/3.73 | & sdtasdt0(xD, xG) = all_92_0 & sdtpldt0(all_63_2, all_92_0) = % 21.24/3.73 | all_92_1 & sdtpldt0(xF, xD) = all_92_2 & sdtpldt0(xD, xG) = all_92_3 % 21.24/3.73 | & $i(all_92_0) & $i(all_92_1) & $i(all_92_2) & $i(all_92_3) & % 21.24/3.73 | $i(all_63_1) % 21.24/3.73 | % 21.24/3.73 | ALPHA: (163) implies: % 21.24/3.73 | (164) sdtpldt0(xD, xG) = all_92_3 % 21.24/3.73 | % 21.24/3.73 | DELTA: instantiating (147) with fresh symbols all_94_0, all_94_1, all_94_2, % 21.24/3.73 | all_94_3 gives: % 21.24/3.73 | (165) sdtasdt0(all_94_2, xH) = all_94_1 & sdtasdt0(xH, all_94_3) = all_53_0 % 21.24/3.73 | & sdtasdt0(xE, xH) = all_94_0 & sdtpldt0(all_53_4, all_94_0) = % 21.24/3.73 | all_94_1 & sdtpldt0(xH, xE) = all_94_2 & sdtpldt0(xE, xH) = all_94_3 % 21.24/3.73 | & $i(all_94_0) & $i(all_94_1) & $i(all_94_2) & $i(all_94_3) & % 21.24/3.73 | $i(all_53_0) % 21.24/3.73 | % 21.24/3.73 | ALPHA: (165) implies: % 21.24/3.73 | (166) sdtpldt0(xE, xH) = all_94_3 % 21.24/3.73 | % 21.24/3.73 | BETA: splitting (148) gives: % 21.24/3.73 | % 21.24/3.73 | Case 1: % 21.24/3.73 | | % 21.24/3.73 | | (167) all_33_0 = sz00 % 21.24/3.73 | | % 21.24/3.73 | | REDUCE: (132), (167) imply: % 21.24/3.73 | | (168) $false % 21.24/3.73 | | % 21.24/3.73 | | CLOSE: (168) is inconsistent. % 21.24/3.73 | | % 21.24/3.73 | Case 2: % 21.24/3.73 | | % 21.24/3.73 | | % 21.24/3.73 | | GROUND_INST: instantiating (37) with all_45_2, all_81_1, xF, xC, simplifying % 21.24/3.73 | | with (58), (154) gives: % 21.24/3.73 | | (169) all_81_1 = all_45_2 % 21.24/3.73 | | % 21.24/3.73 | | GROUND_INST: instantiating (37) with all_45_1, all_90_3, xG, xD, simplifying % 21.24/3.73 | | with (59), (162) gives: % 21.24/3.73 | | (170) all_90_3 = all_45_1 % 21.24/3.73 | | % 21.24/3.73 | | GROUND_INST: instantiating (37) with all_90_3, all_92_3, xG, xD, simplifying % 21.24/3.73 | | with (162), (164) gives: % 21.24/3.73 | | (171) all_92_3 = all_90_3 % 21.24/3.73 | | % 21.24/3.73 | | GROUND_INST: instantiating (37) with all_81_0, all_92_3, xG, xD, simplifying % 21.24/3.73 | | with (155), (164) gives: % 21.24/3.73 | | (172) all_92_3 = all_81_0 % 21.24/3.73 | | % 21.24/3.73 | | GROUND_INST: instantiating (37) with all_45_4, all_87_2, xH, xE, simplifying % 21.24/3.73 | | with (60), (160) gives: % 21.24/3.73 | | (173) all_87_2 = all_45_4 % 21.24/3.74 | | % 21.24/3.74 | | GROUND_INST: instantiating (37) with all_79_0, all_87_2, xH, xE, simplifying % 21.24/3.74 | | with (151), (160) gives: % 21.24/3.74 | | (174) all_87_2 = all_79_0 % 21.24/3.74 | | % 21.24/3.74 | | GROUND_INST: instantiating (37) with all_85_3, all_94_3, xH, xE, simplifying % 21.24/3.74 | | with (158), (166) gives: % 21.24/3.74 | | (175) all_94_3 = all_85_3 % 21.24/3.74 | | % 21.24/3.74 | | GROUND_INST: instantiating (37) with all_79_0, all_94_3, xH, xE, simplifying % 21.24/3.74 | | with (151), (166) gives: % 21.24/3.74 | | (176) all_94_3 = all_79_0 % 21.24/3.74 | | % 21.24/3.74 | | GROUND_INST: instantiating (37) with all_79_1, all_94_3, xH, xE, simplifying % 21.24/3.74 | | with (150), (166) gives: % 21.24/3.74 | | (177) all_94_3 = all_79_1 % 21.24/3.74 | | % 21.24/3.74 | | COMBINE_EQS: (175), (176) imply: % 21.24/3.74 | | (178) all_85_3 = all_79_0 % 21.24/3.74 | | % 21.24/3.74 | | COMBINE_EQS: (175), (177) imply: % 21.24/3.74 | | (179) all_85_3 = all_79_1 % 21.24/3.74 | | % 21.24/3.74 | | COMBINE_EQS: (171), (172) imply: % 21.24/3.74 | | (180) all_90_3 = all_81_0 % 21.24/3.74 | | % 21.24/3.74 | | SIMP: (180) implies: % 21.24/3.74 | | (181) all_90_3 = all_81_0 % 21.24/3.74 | | % 21.24/3.74 | | COMBINE_EQS: (170), (181) imply: % 21.24/3.74 | | (182) all_81_0 = all_45_1 % 21.24/3.74 | | % 21.24/3.74 | | COMBINE_EQS: (173), (174) imply: % 21.24/3.74 | | (183) all_79_0 = all_45_4 % 21.24/3.74 | | % 21.24/3.74 | | SIMP: (183) implies: % 21.24/3.74 | | (184) all_79_0 = all_45_4 % 21.24/3.74 | | % 21.24/3.74 | | COMBINE_EQS: (178), (179) imply: % 21.24/3.74 | | (185) all_79_0 = all_79_1 % 21.24/3.74 | | % 21.24/3.74 | | SIMP: (185) implies: % 21.24/3.74 | | (186) all_79_0 = all_79_1 % 21.24/3.74 | | % 21.24/3.74 | | COMBINE_EQS: (184), (186) imply: % 21.24/3.74 | | (187) all_79_1 = all_45_4 % 21.24/3.74 | | % 21.24/3.74 | | REDUCE: (156), (169), (182) imply: % 21.24/3.74 | | (188) sdtasdt0(all_45_2, all_45_1) = all_63_0 % 21.24/3.74 | | % 21.24/3.74 | | REDUCE: (152), (184), (187) imply: % 21.24/3.74 | | (189) sdtasdt0(all_45_4, all_45_4) = all_63_7 % 21.24/3.74 | | % 21.24/3.74 | | GROUND_INST: instantiating (38) with all_45_3, all_63_7, all_45_4, all_45_4, % 21.24/3.74 | | simplifying with (61), (189) gives: % 21.24/3.74 | | (190) all_63_7 = all_45_3 % 21.24/3.74 | | % 21.24/3.74 | | GROUND_INST: instantiating (38) with all_45_0, all_63_0, all_45_1, all_45_2, % 21.24/3.74 | | simplifying with (62), (188) gives: % 21.24/3.74 | | (191) all_63_0 = all_45_0 % 21.24/3.74 | | % 21.24/3.74 | | REDUCE: (83), (190), (191) imply: % 21.24/3.74 | | (192) sdtlseqdt0(all_45_3, all_45_0) % 21.24/3.74 | | % 21.24/3.74 | | PRED_UNIFY: (57), (192) imply: % 21.24/3.74 | | (193) $false % 21.24/3.74 | | % 21.24/3.74 | | CLOSE: (193) is inconsistent. % 21.24/3.74 | | % 21.24/3.74 | End of split % 21.24/3.74 | % 21.24/3.74 End of proof % 21.24/3.74 % SZS output end Proof for theBenchmark % 21.24/3.74 % 21.24/3.74 3137ms 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