%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG079+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 : n007.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 15.23s 2.78s % Output : Proof 23.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG079+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n007.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Sun Aug 27 01:57:42 EDT 2023 % 0.19/0.34 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.61 Running up to 7 provers in parallel. % 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.70/1.20 Prover 4: Preprocessing ... % 3.70/1.20 Prover 1: Preprocessing ... % 3.70/1.26 Prover 6: Preprocessing ... % 3.70/1.26 Prover 3: Preprocessing ... % 3.70/1.26 Prover 5: Preprocessing ... % 3.70/1.26 Prover 2: Preprocessing ... % 3.70/1.27 Prover 0: Preprocessing ... % 8.53/1.96 Prover 1: Constructing countermodel ... % 8.53/1.97 Prover 3: Constructing countermodel ... % 9.47/2.00 Prover 6: Proving ... % 11.42/2.24 Prover 5: Constructing countermodel ... % 11.42/2.27 Prover 4: Constructing countermodel ... % 12.23/2.35 Prover 0: Proving ... % 12.32/2.37 Prover 2: Proving ... % 15.23/2.77 Prover 3: proved (2156ms) % 15.23/2.78 % 15.23/2.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.23/2.78 % 15.23/2.78 Prover 5: stopped % 15.57/2.79 Prover 2: stopped % 15.57/2.79 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 15.57/2.79 Prover 6: stopped % 15.57/2.79 Prover 0: stopped % 15.57/2.80 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.57/2.80 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.57/2.80 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 15.57/2.80 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 16.05/2.86 Prover 7: Preprocessing ... % 16.47/2.91 Prover 13: Preprocessing ... % 16.47/2.92 Prover 10: Preprocessing ... % 16.47/2.92 Prover 11: Preprocessing ... % 16.47/2.93 Prover 8: Preprocessing ... % 17.88/3.11 Prover 10: Constructing countermodel ... % 17.88/3.19 Prover 8: Warning: ignoring some quantifiers % 17.88/3.19 Prover 8: Constructing countermodel ... % 17.88/3.21 Prover 7: Constructing countermodel ... % 17.88/3.22 Prover 13: Constructing countermodel ... % 19.38/3.35 Prover 11: Constructing countermodel ... % 22.34/3.70 Prover 10: Found proof (size 148) % 22.34/3.70 Prover 10: proved (910ms) % 22.34/3.70 Prover 4: stopped % 22.34/3.70 Prover 11: stopped % 22.34/3.70 Prover 7: stopped % 22.34/3.70 Prover 8: stopped % 22.34/3.71 Prover 1: stopped % 22.34/3.72 Prover 13: stopped % 22.34/3.72 % 22.34/3.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 22.34/3.72 % 22.34/3.75 % SZS output start Proof for theBenchmark % 22.34/3.76 Assumptions after simplification: % 22.34/3.76 --------------------------------- % 22.34/3.76 % 22.34/3.76 (mDefSPN) % 22.74/3.78 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 22.74/3.78 : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : (v2 = % 22.74/3.78 sz00 | ~ (sdtasasdt0(v3, v4) = v5) | ~ (sziznziztdt0(v1) = v4) | ~ % 22.74/3.78 (sziznziztdt0(v0) = v3) | ~ (sdtlbdtrb0(v1, v2) = v7) | ~ (sdtlbdtrb0(v0, % 22.74/3.78 v2) = v6) | ~ (aDimensionOf0(v1) = v2) | ~ (aDimensionOf0(v0) = v2) | % 22.74/3.78 ~ (sdtasdt0(v6, v7) = v8) | ~ (sdtpldt0(v5, v8) = v9) | ~ $i(v1) | ~ % 22.74/3.79 $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) | (sdtasasdt0(v0, v1) = v9 & % 22.74/3.79 $i(v9))) % 22.74/3.79 % 22.74/3.79 (mDistr) % 22.74/3.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 22.74/3.79 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ % 22.74/3.79 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 22.74/3.79 aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v6: $i] : ? [v7: $i] % 22.74/3.79 : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v7, v2) = v8 & sdtasdt0(v1, v2) = v9 % 22.74/3.79 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v4, v9) = v8 & sdtpldt0(v1, v2) = v6 & % 22.74/3.79 sdtpldt0(v0, v1) = v7 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5))) % 22.74/3.79 % 22.74/3.79 (mDistr2) % 22.74/3.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 22.74/3.79 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : % 22.74/3.79 ( ~ (sdtasdt0(v1, v3) = v8) | ~ (sdtasdt0(v1, v2) = v7) | ~ (sdtasdt0(v0, % 22.74/3.79 v3) = v5) | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtpldt0(v7, v8) = v9) | ~ % 22.74/3.79 (sdtpldt0(v6, v9) = v10) | ~ (sdtpldt0(v4, v5) = v6) | ~ $i(v3) | ~ % 22.74/3.79 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aScalar0(v3) | ~ aScalar0(v2) | ~ % 22.74/3.79 aScalar0(v1) | ~ aScalar0(v0) | ? [v11: $i] : ? [v12: $i] : % 22.74/3.79 (sdtasdt0(v11, v12) = v10 & sdtpldt0(v2, v3) = v12 & sdtpldt0(v0, v1) = v11 % 22.74/3.79 & $i(v12) & $i(v11) & $i(v10))) % 22.74/3.79 % 22.74/3.79 (m__) % 22.74/3.79 $i(xH) & $i(xG) & $i(xF) & $i(xE) & $i(xD) & $i(xC) & ? [v0: $i] : ? [v1: % 22.74/3.79 $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (sdtasdt0(v2, v3) = v4 & % 22.74/3.79 sdtasdt0(v0, v0) = v1 & sdtpldt0(xE, xH) = v0 & sdtpldt0(xD, xG) = v3 & % 22.74/3.79 sdtpldt0(xC, xF) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~ % 22.74/3.79 sdtlseqdt0(v1, v4)) % 22.74/3.79 % 22.74/3.79 (m__1652) % 22.74/3.80 $i(xs) & ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : ! % 22.74/3.80 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2, v2) % 22.74/3.80 = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4) = v5) | ~ % 22.74/3.80 $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1) | ? [v6: $i] : ? % 22.74/3.80 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ((sdtasasdt0(v1, v2) = v8 & % 22.74/3.80 sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8) & sdtlseqdt0(v9, v5)) | % 22.74/3.80 (aDimensionOf0(v1) = v6 & $i(v6) & ( ~ iLess0(v6, v0) | ( ~ (v7 = v6) & % 22.74/3.80 aDimensionOf0(v2) = v7 & $i(v7))))))) % 22.74/3.80 % 22.74/3.80 (m__1678) % 22.74/3.80 $i(xt) & $i(xs) & aVector0(xt) & aVector0(xs) % 22.74/3.80 % 22.74/3.80 (m__1678_01) % 22.74/3.80 $i(xt) & $i(xs) & ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) = % 22.74/3.80 v0 & $i(v0)) % 22.74/3.80 % 22.74/3.80 (m__1692) % 22.74/3.80 $i(xs) & $i(sz00) & ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 & % 22.74/3.80 $i(v0)) % 22.74/3.80 % 22.74/3.80 (m__1726) % 22.74/3.80 sziznziztdt0(xt) = xq & $i(xq) & $i(xt) & aVector0(xq) % 22.74/3.80 % 22.74/3.80 (m__1746) % 22.74/3.80 $i(xA) & $i(xs) & ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) = % 22.74/3.80 v0 & $i(v0) & aScalar0(xA)) % 22.74/3.80 % 22.74/3.80 (m__1766) % 22.74/3.80 $i(xB) & $i(xt) & ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) = % 22.74/3.80 v0 & $i(v0) & aScalar0(xB)) % 22.74/3.80 % 22.74/3.80 (m__1783) % 22.74/3.80 sdtasasdt0(xp, xp) = xC & $i(xC) & $i(xp) & aScalar0(xC) % 22.74/3.80 % 22.74/3.80 (m__1800) % 22.74/3.80 sdtasasdt0(xq, xq) = xD & $i(xD) & $i(xq) & aScalar0(xD) % 22.74/3.80 % 22.74/3.80 (m__1820) % 22.74/3.80 sdtasasdt0(xp, xq) = xE & $i(xE) & $i(xq) & $i(xp) & aScalar0(xE) % 22.74/3.80 % 22.74/3.80 (m__1837) % 22.74/3.80 sdtasdt0(xA, xA) = xF & $i(xF) & $i(xA) & aScalar0(xF) % 22.74/3.80 % 22.74/3.80 (m__1854) % 22.74/3.80 sdtasdt0(xB, xB) = xG & $i(xG) & $i(xB) & aScalar0(xG) % 22.74/3.80 % 22.74/3.80 (m__1873) % 22.74/3.80 sdtasdt0(xA, xB) = xH & $i(xH) & $i(xB) & $i(xA) & aScalar0(xH) % 22.74/3.80 % 22.74/3.80 (m__1892) % 22.74/3.80 sdtasdt0(xC, xG) = xR & $i(xR) & $i(xG) & $i(xC) & aScalar0(xR) % 22.74/3.80 % 22.74/3.80 (m__1911) % 22.74/3.80 sdtasdt0(xE, xH) = xP & $i(xP) & $i(xH) & $i(xE) & aScalar0(xP) % 22.74/3.80 % 22.74/3.80 (m__1930) % 22.74/3.80 sdtasdt0(xF, xD) = xS & $i(xS) & $i(xF) & $i(xD) & aScalar0(xS) % 22.74/3.80 % 22.74/3.80 (m__1967) % 22.74/3.80 $i(xE) & $i(xD) & $i(xC) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xE, xE) = v0 % 22.74/3.80 & sdtasdt0(xC, xD) = v1 & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1)) % 22.74/3.80 % 22.74/3.80 (m__1983) % 22.74/3.80 $i(xS) & $i(xP) & $i(xR) & ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xP, xP) = v0 % 22.74/3.80 & sdtpldt0(xR, xS) = v1 & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1)) % 22.74/3.80 % 22.74/3.80 (m__2796) % 23.13/3.81 $i(xS) & $i(xP) & $i(xR) & $i(xH) & $i(xE) & $i(xD) & $i(xC) & ? [v0: $i] : % 23.13/3.81 ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: % 23.13/3.81 $i] : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(xH, xH) = v2 & sdtasdt0(xE, xE) % 23.13/3.81 = v0 & sdtasdt0(xC, xD) = v5 & sdtpldt0(v6, v2) = v7 & sdtpldt0(v5, v7) = v8 % 23.13/3.81 & sdtpldt0(v1, v2) = v3 & sdtpldt0(v0, v3) = v4 & sdtpldt0(xP, xP) = v1 & % 23.13/3.81 sdtpldt0(xR, xS) = v6 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) % 23.13/3.81 & $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v4, v8)) % 23.13/3.81 % 23.13/3.81 (m__2835) % 23.13/3.81 $i(xP) & $i(xH) & $i(xE) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 23.13/3.81 $i] : ? [v4: $i] : ? [v5: $i] : (sdtasdt0(xH, xH) = v1 & sdtasdt0(xH, xE) % 23.13/3.81 = v4 & sdtasdt0(xE, xH) = v3 & sdtpldt0(v4, v1) = v5 & sdtpldt0(v3, v5) = v2 % 23.13/3.81 & sdtpldt0(v0, v1) = v2 & sdtpldt0(xP, xP) = v0 & $i(v5) & $i(v4) & $i(v3) & % 23.13/3.81 $i(v2) & $i(v1) & $i(v0)) % 23.13/3.81 % 23.13/3.81 (m__2905) % 23.13/3.81 $i(xH) & $i(xG) & $i(xF) & $i(xE) & $i(xD) & $i(xC) & ? [v0: $i] : ? [v1: % 23.13/3.81 $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 23.13/3.81 ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? % 23.13/3.81 [v12: $i] : ? [v13: $i] : (sdtasdt0(xH, xH) = v4 & sdtasdt0(xH, xE) = v3 & % 23.13/3.81 sdtasdt0(xF, xG) = v11 & sdtasdt0(xF, xD) = v10 & sdtasdt0(xE, xH) = v1 & % 23.13/3.81 sdtasdt0(xE, xE) = v0 & sdtasdt0(xC, xG) = v8 & sdtasdt0(xC, xD) = v7 & % 23.13/3.81 sdtpldt0(v10, v11) = v12 & sdtpldt0(v9, v12) = v13 & sdtpldt0(v7, v8) = v9 & % 23.13/3.81 sdtpldt0(v3, v4) = v5 & sdtpldt0(v2, v5) = v6 & sdtpldt0(v0, v1) = v2 & % 23.13/3.81 $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 23.13/3.81 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v6, v13)) % 23.13/3.81 % 23.13/3.81 (function-axioms) % 23.13/3.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 23.13/3.81 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 23.13/3.81 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) % 23.13/3.81 | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 23.13/3.81 ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = % 23.13/3.81 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 23.13/3.81 ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 23.13/3.81 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sziznziztdt0(v2) = v1) | ~ % 23.13/3.81 (sziznziztdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 23.13/3.81 v0 | ~ (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) & ! [v0: % 23.13/3.81 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ % 23.13/3.81 (smndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 23.13/3.81 (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0)) % 23.13/3.81 % 23.13/3.81 Further assumptions not needed in the proof: % 23.13/3.81 -------------------------------------------- % 23.13/3.81 mArith, mDefInit, mDefSPZ, mDimNat, mElmSc, mEqInit, mIH, mIHOrd, mLEASm, % 23.13/3.81 mLEMon, mLEMonM, mLERef, mLETot, mLETrn, mLess, mMDNeg, mMNeg, mMulSc, mNatExtr, % 23.13/3.81 mNatSort, mNegSc, mPosMon, mSZeroSc, mScPr, mScSort, mScSqPos, mScZero, mSqPos, % 23.13/3.81 mSqrt, mSuccEqu, mSuccNat, mSumSc, mVcSort, mZeroNat, m__1709, m__1949 % 23.13/3.81 % 23.13/3.81 Those formulas are unsatisfiable: % 23.13/3.81 --------------------------------- % 23.13/3.81 % 23.13/3.81 Begin of proof % 23.13/3.81 | % 23.13/3.81 | ALPHA: (mDefSPN) implies: % 23.13/3.82 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 23.13/3.82 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : % 23.13/3.82 | (v2 = sz00 | ~ (sdtasasdt0(v3, v4) = v5) | ~ (sziznziztdt0(v1) = v4) % 23.13/3.82 | | ~ (sziznziztdt0(v0) = v3) | ~ (sdtlbdtrb0(v1, v2) = v7) | ~ % 23.13/3.82 | (sdtlbdtrb0(v0, v2) = v6) | ~ (aDimensionOf0(v1) = v2) | ~ % 23.13/3.82 | (aDimensionOf0(v0) = v2) | ~ (sdtasdt0(v6, v7) = v8) | ~ % 23.13/3.82 | (sdtpldt0(v5, v8) = v9) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | % 23.13/3.82 | ~ aVector0(v0) | (sdtasasdt0(v0, v1) = v9 & $i(v9))) % 23.13/3.82 | % 23.13/3.82 | ALPHA: (m__1678) implies: % 23.13/3.82 | (2) aVector0(xt) % 23.13/3.82 | % 23.13/3.82 | ALPHA: (m__1652) implies: % 23.13/3.82 | (3) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 23.13/3.82 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2, % 23.13/3.82 | v2) = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4) % 23.13/3.82 | = v5) | ~ $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1) % 23.13/3.82 | | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 23.13/3.82 | ((sdtasasdt0(v1, v2) = v8 & sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8) % 23.13/3.82 | & sdtlseqdt0(v9, v5)) | (aDimensionOf0(v1) = v6 & $i(v6) & ( ~ % 23.13/3.82 | iLess0(v6, v0) | ( ~ (v7 = v6) & aDimensionOf0(v2) = v7 & % 23.13/3.82 | $i(v7))))))) % 23.13/3.82 | % 23.13/3.82 | ALPHA: (m__1678_01) implies: % 23.13/3.82 | (4) ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) = v0 & % 23.13/3.82 | $i(v0)) % 23.13/3.82 | % 23.13/3.82 | ALPHA: (m__1692) implies: % 23.13/3.82 | (5) ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 & $i(v0)) % 23.13/3.82 | % 23.13/3.82 | ALPHA: (m__1726) implies: % 23.13/3.82 | (6) sziznziztdt0(xt) = xq % 23.13/3.82 | % 23.13/3.82 | ALPHA: (m__1746) implies: % 23.13/3.82 | (7) ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) = v0 & % 23.13/3.82 | $i(v0) & aScalar0(xA)) % 23.13/3.82 | % 23.13/3.82 | ALPHA: (m__1766) implies: % 23.13/3.82 | (8) $i(xt) % 23.13/3.82 | (9) ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) = v0 & % 23.13/3.82 | $i(v0) & aScalar0(xB)) % 23.13/3.82 | % 23.13/3.82 | ALPHA: (m__1783) implies: % 23.13/3.82 | (10) aScalar0(xC) % 23.13/3.82 | % 23.13/3.82 | ALPHA: (m__1800) implies: % 23.13/3.82 | (11) aScalar0(xD) % 23.13/3.82 | (12) sdtasasdt0(xq, xq) = xD % 23.13/3.82 | % 23.13/3.82 | ALPHA: (m__1820) implies: % 23.13/3.82 | (13) aScalar0(xE) % 23.13/3.82 | % 23.13/3.82 | ALPHA: (m__1837) implies: % 23.13/3.82 | (14) aScalar0(xF) % 23.13/3.82 | % 23.13/3.82 | ALPHA: (m__1854) implies: % 23.13/3.82 | (15) aScalar0(xG) % 23.13/3.82 | (16) sdtasdt0(xB, xB) = xG % 23.13/3.82 | % 23.13/3.82 | ALPHA: (m__1873) implies: % 23.13/3.82 | (17) aScalar0(xH) % 23.13/3.82 | % 23.13/3.82 | ALPHA: (m__1892) implies: % 23.13/3.82 | (18) sdtasdt0(xC, xG) = xR % 23.13/3.82 | % 23.13/3.82 | ALPHA: (m__1911) implies: % 23.13/3.82 | (19) sdtasdt0(xE, xH) = xP % 23.13/3.82 | % 23.13/3.82 | ALPHA: (m__1930) implies: % 23.13/3.82 | (20) sdtasdt0(xF, xD) = xS % 23.13/3.82 | % 23.13/3.82 | ALPHA: (m__1967) implies: % 23.13/3.82 | (21) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xE, xE) = v0 & sdtasdt0(xC, xD) % 23.13/3.82 | = v1 & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1)) % 23.13/3.82 | % 23.13/3.82 | ALPHA: (m__1983) implies: % 23.13/3.82 | (22) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xP, xP) = v0 & sdtpldt0(xR, xS) % 23.13/3.82 | = v1 & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1)) % 23.13/3.82 | % 23.13/3.82 | ALPHA: (m__2796) implies: % 23.13/3.82 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 23.13/3.82 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(xH, % 23.13/3.82 | xH) = v2 & sdtasdt0(xE, xE) = v0 & sdtasdt0(xC, xD) = v5 & % 23.13/3.82 | sdtpldt0(v6, v2) = v7 & sdtpldt0(v5, v7) = v8 & sdtpldt0(v1, v2) = % 23.13/3.82 | v3 & sdtpldt0(v0, v3) = v4 & sdtpldt0(xP, xP) = v1 & sdtpldt0(xR, % 23.13/3.82 | xS) = v6 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 23.13/3.82 | $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v4, v8)) % 23.13/3.82 | % 23.13/3.82 | ALPHA: (m__2835) implies: % 23.13/3.83 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 23.13/3.83 | ? [v5: $i] : (sdtasdt0(xH, xH) = v1 & sdtasdt0(xH, xE) = v4 & % 23.13/3.83 | sdtasdt0(xE, xH) = v3 & sdtpldt0(v4, v1) = v5 & sdtpldt0(v3, v5) = % 23.13/3.83 | v2 & sdtpldt0(v0, v1) = v2 & sdtpldt0(xP, xP) = v0 & $i(v5) & $i(v4) % 23.13/3.83 | & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 23.13/3.83 | % 23.13/3.83 | ALPHA: (m__2905) implies: % 23.13/3.83 | (25) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 23.13/3.83 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 23.13/3.83 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : % 23.13/3.83 | (sdtasdt0(xH, xH) = v4 & sdtasdt0(xH, xE) = v3 & sdtasdt0(xF, xG) = % 23.13/3.83 | v11 & sdtasdt0(xF, xD) = v10 & sdtasdt0(xE, xH) = v1 & sdtasdt0(xE, % 23.13/3.83 | xE) = v0 & sdtasdt0(xC, xG) = v8 & sdtasdt0(xC, xD) = v7 & % 23.13/3.83 | sdtpldt0(v10, v11) = v12 & sdtpldt0(v9, v12) = v13 & sdtpldt0(v7, % 23.13/3.83 | v8) = v9 & sdtpldt0(v3, v4) = v5 & sdtpldt0(v2, v5) = v6 & % 23.13/3.83 | sdtpldt0(v0, v1) = v2 & $i(v13) & $i(v12) & $i(v11) & $i(v10) & % 23.13/3.83 | $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 23.13/3.83 | $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v6, v13)) % 23.13/3.83 | % 23.13/3.83 | ALPHA: (m__) implies: % 23.13/3.83 | (26) $i(xC) % 23.13/3.83 | (27) $i(xD) % 23.13/3.83 | (28) $i(xE) % 23.13/3.83 | (29) $i(xF) % 23.13/3.83 | (30) $i(xG) % 23.13/3.83 | (31) $i(xH) % 23.13/3.83 | (32) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 23.13/3.83 | (sdtasdt0(v2, v3) = v4 & sdtasdt0(v0, v0) = v1 & sdtpldt0(xE, xH) = v0 % 23.13/3.83 | & sdtpldt0(xD, xG) = v3 & sdtpldt0(xC, xF) = v2 & $i(v4) & $i(v3) & % 23.13/3.83 | $i(v2) & $i(v1) & $i(v0) & ~ sdtlseqdt0(v1, v4)) % 23.13/3.83 | % 23.13/3.83 | ALPHA: (function-axioms) implies: % 23.13/3.83 | (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 23.13/3.83 | (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) % 23.13/3.83 | (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 23.13/3.83 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 23.13/3.83 | (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 23.13/3.83 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 23.13/3.83 | % 23.13/3.83 | DELTA: instantiating (4) with fresh symbol all_33_0 gives: % 23.13/3.83 | (36) aDimensionOf0(xt) = all_33_0 & aDimensionOf0(xs) = all_33_0 & % 23.13/3.83 | $i(all_33_0) % 23.13/3.83 | % 23.13/3.83 | ALPHA: (36) implies: % 23.13/3.83 | (37) aDimensionOf0(xs) = all_33_0 % 23.13/3.83 | (38) aDimensionOf0(xt) = all_33_0 % 23.13/3.83 | % 23.13/3.83 | DELTA: instantiating (5) with fresh symbol all_35_0 gives: % 23.13/3.83 | (39) ~ (all_35_0 = sz00) & aDimensionOf0(xs) = all_35_0 & $i(all_35_0) % 23.13/3.83 | % 23.13/3.83 | ALPHA: (39) implies: % 23.13/3.83 | (40) ~ (all_35_0 = sz00) % 23.13/3.83 | (41) aDimensionOf0(xs) = all_35_0 % 23.13/3.83 | % 23.13/3.83 | DELTA: instantiating (7) with fresh symbol all_37_0 gives: % 23.13/3.83 | (42) sdtlbdtrb0(xs, all_37_0) = xA & aDimensionOf0(xs) = all_37_0 & % 23.13/3.83 | $i(all_37_0) & aScalar0(xA) % 23.13/3.83 | % 23.13/3.83 | ALPHA: (42) implies: % 23.13/3.83 | (43) aDimensionOf0(xs) = all_37_0 % 23.13/3.83 | % 23.13/3.83 | DELTA: instantiating (9) with fresh symbol all_39_0 gives: % 23.13/3.83 | (44) sdtlbdtrb0(xt, all_39_0) = xB & aDimensionOf0(xt) = all_39_0 & % 23.13/3.83 | $i(all_39_0) & aScalar0(xB) % 23.13/3.83 | % 23.13/3.83 | ALPHA: (44) implies: % 23.13/3.83 | (45) aDimensionOf0(xt) = all_39_0 % 23.13/3.83 | (46) sdtlbdtrb0(xt, all_39_0) = xB % 23.13/3.83 | % 23.13/3.83 | DELTA: instantiating (21) with fresh symbols all_41_0, all_41_1 gives: % 23.13/3.83 | (47) sdtasdt0(xE, xE) = all_41_1 & sdtasdt0(xC, xD) = all_41_0 & % 23.13/3.83 | $i(all_41_0) & $i(all_41_1) & sdtlseqdt0(all_41_1, all_41_0) % 23.13/3.83 | % 23.13/3.83 | ALPHA: (47) implies: % 23.13/3.83 | (48) sdtasdt0(xC, xD) = all_41_0 % 23.13/3.83 | (49) sdtasdt0(xE, xE) = all_41_1 % 23.13/3.83 | % 23.13/3.83 | DELTA: instantiating (22) with fresh symbols all_43_0, all_43_1 gives: % 23.13/3.84 | (50) sdtpldt0(xP, xP) = all_43_1 & sdtpldt0(xR, xS) = all_43_0 & % 23.13/3.84 | $i(all_43_0) & $i(all_43_1) & sdtlseqdt0(all_43_1, all_43_0) % 23.13/3.84 | % 23.13/3.84 | ALPHA: (50) implies: % 23.13/3.84 | (51) sdtpldt0(xP, xP) = all_43_1 % 23.13/3.84 | % 23.13/3.84 | DELTA: instantiating (32) with fresh symbols all_45_0, all_45_1, all_45_2, % 23.13/3.84 | all_45_3, all_45_4 gives: % 23.13/3.84 | (52) sdtasdt0(all_45_2, all_45_1) = all_45_0 & sdtasdt0(all_45_4, all_45_4) % 23.13/3.84 | = all_45_3 & sdtpldt0(xE, xH) = all_45_4 & sdtpldt0(xD, xG) = all_45_1 % 23.13/3.84 | & sdtpldt0(xC, xF) = all_45_2 & $i(all_45_0) & $i(all_45_1) & % 23.13/3.84 | $i(all_45_2) & $i(all_45_3) & $i(all_45_4) & ~ sdtlseqdt0(all_45_3, % 23.13/3.84 | all_45_0) % 23.13/3.84 | % 23.13/3.84 | ALPHA: (52) implies: % 23.13/3.84 | (53) ~ sdtlseqdt0(all_45_3, all_45_0) % 23.13/3.84 | (54) sdtpldt0(xC, xF) = all_45_2 % 23.13/3.84 | (55) sdtpldt0(xD, xG) = all_45_1 % 23.13/3.84 | (56) sdtpldt0(xE, xH) = all_45_4 % 23.13/3.84 | (57) sdtasdt0(all_45_4, all_45_4) = all_45_3 % 23.13/3.84 | (58) sdtasdt0(all_45_2, all_45_1) = all_45_0 % 23.13/3.84 | % 23.13/3.84 | DELTA: instantiating (24) with fresh symbols all_47_0, all_47_1, all_47_2, % 23.13/3.84 | all_47_3, all_47_4, all_47_5 gives: % 23.13/3.84 | (59) sdtasdt0(xH, xH) = all_47_4 & sdtasdt0(xH, xE) = all_47_1 & % 23.13/3.84 | sdtasdt0(xE, xH) = all_47_2 & sdtpldt0(all_47_1, all_47_4) = all_47_0 % 23.13/3.84 | & sdtpldt0(all_47_2, all_47_0) = all_47_3 & sdtpldt0(all_47_5, % 23.13/3.84 | all_47_4) = all_47_3 & sdtpldt0(xP, xP) = all_47_5 & $i(all_47_0) & % 23.13/3.84 | $i(all_47_1) & $i(all_47_2) & $i(all_47_3) & $i(all_47_4) & % 23.13/3.84 | $i(all_47_5) % 23.13/3.84 | % 23.13/3.84 | ALPHA: (59) implies: % 23.13/3.84 | (60) sdtpldt0(xP, xP) = all_47_5 % 23.13/3.84 | (61) sdtpldt0(all_47_1, all_47_4) = all_47_0 % 23.13/3.84 | (62) sdtasdt0(xE, xH) = all_47_2 % 23.13/3.84 | (63) sdtasdt0(xH, xE) = all_47_1 % 23.13/3.84 | (64) sdtasdt0(xH, xH) = all_47_4 % 23.13/3.84 | % 23.13/3.84 | DELTA: instantiating (23) with fresh symbols all_49_0, all_49_1, all_49_2, % 23.13/3.84 | all_49_3, all_49_4, all_49_5, all_49_6, all_49_7, all_49_8 gives: % 23.13/3.84 | (65) sdtasdt0(xH, xH) = all_49_6 & sdtasdt0(xE, xE) = all_49_8 & % 23.13/3.84 | sdtasdt0(xC, xD) = all_49_3 & sdtpldt0(all_49_2, all_49_6) = all_49_1 % 23.13/3.84 | & sdtpldt0(all_49_3, all_49_1) = all_49_0 & sdtpldt0(all_49_7, % 23.13/3.84 | all_49_6) = all_49_5 & sdtpldt0(all_49_8, all_49_5) = all_49_4 & % 23.13/3.84 | sdtpldt0(xP, xP) = all_49_7 & sdtpldt0(xR, xS) = all_49_2 & % 23.13/3.84 | $i(all_49_0) & $i(all_49_1) & $i(all_49_2) & $i(all_49_3) & % 23.13/3.84 | $i(all_49_4) & $i(all_49_5) & $i(all_49_6) & $i(all_49_7) & % 23.13/3.84 | $i(all_49_8) & sdtlseqdt0(all_49_4, all_49_0) % 23.13/3.84 | % 23.13/3.84 | ALPHA: (65) implies: % 23.13/3.84 | (66) sdtpldt0(xP, xP) = all_49_7 % 23.13/3.84 | (67) sdtasdt0(xC, xD) = all_49_3 % 23.13/3.84 | (68) sdtasdt0(xE, xE) = all_49_8 % 23.13/3.84 | (69) sdtasdt0(xH, xH) = all_49_6 % 23.13/3.84 | % 23.13/3.84 | DELTA: instantiating (3) with fresh symbol all_51_0 gives: % 23.13/3.84 | (70) aDimensionOf0(xs) = all_51_0 & $i(all_51_0) & ! [v0: $i] : ! [v1: % 23.13/3.84 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasasdt0(v1, % 23.13/3.84 | v1) = v3) | ~ (sdtasasdt0(v0, v0) = v2) | ~ (sdtasdt0(v2, v3) % 23.13/3.84 | = v4) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) % 23.13/3.84 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 23.13/3.84 | ((sdtasasdt0(v0, v1) = v7 & sdtasdt0(v7, v7) = v8 & $i(v8) & $i(v7) % 23.13/3.84 | & sdtlseqdt0(v8, v4)) | (aDimensionOf0(v0) = v5 & $i(v5) & ( ~ % 23.13/3.84 | iLess0(v5, all_51_0) | ( ~ (v6 = v5) & aDimensionOf0(v1) = v6 % 23.13/3.84 | & $i(v6)))))) % 23.13/3.84 | % 23.13/3.84 | ALPHA: (70) implies: % 23.13/3.84 | (71) aDimensionOf0(xs) = all_51_0 % 23.13/3.84 | % 23.13/3.84 | DELTA: instantiating (25) with fresh symbols all_57_0, all_57_1, all_57_2, % 23.13/3.84 | all_57_3, all_57_4, all_57_5, all_57_6, all_57_7, all_57_8, all_57_9, % 23.13/3.84 | all_57_10, all_57_11, all_57_12, all_57_13 gives: % 23.13/3.84 | (72) sdtasdt0(xH, xH) = all_57_9 & sdtasdt0(xH, xE) = all_57_10 & % 23.13/3.84 | sdtasdt0(xF, xG) = all_57_2 & sdtasdt0(xF, xD) = all_57_3 & % 23.13/3.84 | sdtasdt0(xE, xH) = all_57_12 & sdtasdt0(xE, xE) = all_57_13 & % 23.13/3.84 | sdtasdt0(xC, xG) = all_57_5 & sdtasdt0(xC, xD) = all_57_6 & % 23.13/3.84 | sdtpldt0(all_57_3, all_57_2) = all_57_1 & sdtpldt0(all_57_4, all_57_1) % 23.13/3.84 | = all_57_0 & sdtpldt0(all_57_6, all_57_5) = all_57_4 & % 23.13/3.84 | sdtpldt0(all_57_10, all_57_9) = all_57_8 & sdtpldt0(all_57_11, % 23.13/3.84 | all_57_8) = all_57_7 & sdtpldt0(all_57_13, all_57_12) = all_57_11 & % 23.13/3.84 | $i(all_57_0) & $i(all_57_1) & $i(all_57_2) & $i(all_57_3) & % 23.13/3.84 | $i(all_57_4) & $i(all_57_5) & $i(all_57_6) & $i(all_57_7) & % 23.13/3.84 | $i(all_57_8) & $i(all_57_9) & $i(all_57_10) & $i(all_57_11) & % 23.13/3.84 | $i(all_57_12) & $i(all_57_13) & sdtlseqdt0(all_57_7, all_57_0) % 23.13/3.84 | % 23.13/3.84 | ALPHA: (72) implies: % 23.13/3.85 | (73) sdtlseqdt0(all_57_7, all_57_0) % 23.13/3.85 | (74) sdtpldt0(all_57_13, all_57_12) = all_57_11 % 23.13/3.85 | (75) sdtpldt0(all_57_11, all_57_8) = all_57_7 % 23.13/3.85 | (76) sdtpldt0(all_57_10, all_57_9) = all_57_8 % 23.13/3.85 | (77) sdtpldt0(all_57_6, all_57_5) = all_57_4 % 23.13/3.85 | (78) sdtpldt0(all_57_4, all_57_1) = all_57_0 % 23.13/3.85 | (79) sdtpldt0(all_57_3, all_57_2) = all_57_1 % 23.13/3.85 | (80) sdtasdt0(xC, xD) = all_57_6 % 23.13/3.85 | (81) sdtasdt0(xC, xG) = all_57_5 % 23.13/3.85 | (82) sdtasdt0(xE, xE) = all_57_13 % 23.13/3.85 | (83) sdtasdt0(xE, xH) = all_57_12 % 23.13/3.85 | (84) sdtasdt0(xF, xD) = all_57_3 % 23.13/3.85 | (85) sdtasdt0(xF, xG) = all_57_2 % 23.13/3.85 | (86) sdtasdt0(xH, xE) = all_57_10 % 23.13/3.85 | (87) sdtasdt0(xH, xH) = all_57_9 % 23.13/3.85 | % 23.13/3.85 | GROUND_INST: instantiating (34) with all_47_5, all_49_7, xP, xP, simplifying % 23.13/3.85 | with (60), (66) gives: % 23.13/3.85 | (88) all_49_7 = all_47_5 % 23.13/3.85 | % 23.13/3.85 | GROUND_INST: instantiating (34) with all_43_1, all_49_7, xP, xP, simplifying % 23.13/3.85 | with (51), (66) gives: % 23.13/3.85 | (89) all_49_7 = all_43_1 % 23.13/3.85 | % 23.13/3.85 | GROUND_INST: instantiating (35) with all_49_3, all_57_6, xD, xC, simplifying % 23.13/3.85 | with (67), (80) gives: % 23.13/3.85 | (90) all_57_6 = all_49_3 % 23.13/3.85 | % 23.13/3.85 | GROUND_INST: instantiating (35) with all_41_0, all_57_6, xD, xC, simplifying % 23.13/3.85 | with (48), (80) gives: % 23.13/3.85 | (91) all_57_6 = all_41_0 % 23.13/3.85 | % 23.13/3.85 | GROUND_INST: instantiating (35) with xR, all_57_5, xG, xC, simplifying with % 23.13/3.85 | (18), (81) gives: % 23.13/3.85 | (92) all_57_5 = xR % 23.13/3.85 | % 23.13/3.85 | GROUND_INST: instantiating (35) with all_49_8, all_57_13, xE, xE, simplifying % 23.13/3.85 | with (68), (82) gives: % 23.13/3.85 | (93) all_57_13 = all_49_8 % 23.13/3.85 | % 23.13/3.85 | GROUND_INST: instantiating (35) with all_41_1, all_57_13, xE, xE, simplifying % 23.13/3.85 | with (49), (82) gives: % 23.13/3.85 | (94) all_57_13 = all_41_1 % 23.13/3.85 | % 23.13/3.85 | GROUND_INST: instantiating (35) with all_47_2, all_57_12, xH, xE, simplifying % 23.13/3.85 | with (62), (83) gives: % 23.13/3.85 | (95) all_57_12 = all_47_2 % 23.13/3.85 | % 23.13/3.85 | GROUND_INST: instantiating (35) with xP, all_57_12, xH, xE, simplifying with % 23.13/3.85 | (19), (83) gives: % 23.13/3.85 | (96) all_57_12 = xP % 23.13/3.85 | % 23.13/3.85 | GROUND_INST: instantiating (35) with xS, all_57_3, xD, xF, simplifying with % 23.13/3.85 | (20), (84) gives: % 23.13/3.85 | (97) all_57_3 = xS % 23.13/3.85 | % 23.13/3.85 | GROUND_INST: instantiating (35) with all_47_1, all_57_10, xE, xH, simplifying % 23.13/3.85 | with (63), (86) gives: % 23.13/3.85 | (98) all_57_10 = all_47_1 % 23.13/3.85 | % 23.13/3.85 | GROUND_INST: instantiating (35) with all_49_6, all_57_9, xH, xH, simplifying % 23.13/3.85 | with (69), (87) gives: % 23.13/3.85 | (99) all_57_9 = all_49_6 % 23.13/3.85 | % 23.13/3.85 | GROUND_INST: instantiating (35) with all_47_4, all_57_9, xH, xH, simplifying % 23.13/3.85 | with (64), (87) gives: % 23.13/3.85 | (100) all_57_9 = all_47_4 % 23.13/3.85 | % 23.13/3.85 | GROUND_INST: instantiating (33) with all_33_0, all_37_0, xs, simplifying with % 23.13/3.85 | (37), (43) gives: % 23.13/3.85 | (101) all_37_0 = all_33_0 % 23.13/3.85 | % 23.13/3.85 | GROUND_INST: instantiating (33) with all_37_0, all_51_0, xs, simplifying with % 23.13/3.85 | (43), (71) gives: % 23.13/3.85 | (102) all_51_0 = all_37_0 % 23.13/3.85 | % 23.13/3.85 | GROUND_INST: instantiating (33) with all_35_0, all_51_0, xs, simplifying with % 23.13/3.85 | (41), (71) gives: % 23.13/3.85 | (103) all_51_0 = all_35_0 % 23.13/3.85 | % 23.13/3.85 | GROUND_INST: instantiating (33) with all_33_0, all_39_0, xt, simplifying with % 23.13/3.85 | (38), (45) gives: % 23.13/3.85 | (104) all_39_0 = all_33_0 % 23.13/3.85 | % 23.13/3.85 | COMBINE_EQS: (90), (91) imply: % 23.13/3.85 | (105) all_49_3 = all_41_0 % 23.13/3.85 | % 23.13/3.85 | SIMP: (105) implies: % 23.13/3.85 | (106) all_49_3 = all_41_0 % 23.13/3.85 | % 23.13/3.85 | COMBINE_EQS: (99), (100) imply: % 23.13/3.85 | (107) all_49_6 = all_47_4 % 23.13/3.85 | % 23.13/3.85 | SIMP: (107) implies: % 23.13/3.85 | (108) all_49_6 = all_47_4 % 23.13/3.85 | % 23.13/3.85 | COMBINE_EQS: (95), (96) imply: % 23.13/3.86 | (109) all_47_2 = xP % 23.13/3.86 | % 23.13/3.86 | SIMP: (109) implies: % 23.13/3.86 | (110) all_47_2 = xP % 23.13/3.86 | % 23.13/3.86 | COMBINE_EQS: (93), (94) imply: % 23.13/3.86 | (111) all_49_8 = all_41_1 % 23.13/3.86 | % 23.13/3.86 | SIMP: (111) implies: % 23.13/3.86 | (112) all_49_8 = all_41_1 % 23.13/3.86 | % 23.13/3.86 | COMBINE_EQS: (102), (103) imply: % 23.13/3.86 | (113) all_37_0 = all_35_0 % 23.13/3.86 | % 23.13/3.86 | SIMP: (113) implies: % 23.13/3.86 | (114) all_37_0 = all_35_0 % 23.13/3.86 | % 23.13/3.86 | COMBINE_EQS: (88), (89) imply: % 23.13/3.86 | (115) all_47_5 = all_43_1 % 23.13/3.86 | % 23.13/3.86 | COMBINE_EQS: (101), (114) imply: % 23.13/3.86 | (116) all_35_0 = all_33_0 % 23.13/3.86 | % 23.13/3.86 | REDUCE: (40), (116) imply: % 23.13/3.86 | (117) ~ (all_33_0 = sz00) % 23.13/3.86 | % 23.13/3.86 | REDUCE: (46), (104) imply: % 23.13/3.86 | (118) sdtlbdtrb0(xt, all_33_0) = xB % 23.13/3.86 | % 23.13/3.86 | REDUCE: (79), (97) imply: % 23.13/3.86 | (119) sdtpldt0(xS, all_57_2) = all_57_1 % 23.13/3.86 | % 23.13/3.86 | REDUCE: (77), (91), (92) imply: % 23.13/3.86 | (120) sdtpldt0(all_41_0, xR) = all_57_4 % 23.13/3.86 | % 23.13/3.86 | REDUCE: (76), (98), (100) imply: % 23.13/3.86 | (121) sdtpldt0(all_47_1, all_47_4) = all_57_8 % 23.13/3.86 | % 23.13/3.86 | REDUCE: (74), (94), (96) imply: % 23.13/3.86 | (122) sdtpldt0(all_41_1, xP) = all_57_11 % 23.13/3.86 | % 23.13/3.86 | GROUND_INST: instantiating (34) with all_47_0, all_57_8, all_47_4, all_47_1, % 23.13/3.86 | simplifying with (61), (121) gives: % 23.13/3.86 | (123) all_57_8 = all_47_0 % 23.13/3.86 | % 23.13/3.86 | REDUCE: (75), (123) imply: % 23.13/3.86 | (124) sdtpldt0(all_57_11, all_47_0) = all_57_7 % 23.13/3.86 | % 23.13/3.86 | GROUND_INST: instantiating (mDistr) with xC, xD, xG, all_41_0, xR, all_57_4, % 23.13/3.86 | simplifying with (10), (11), (15), (18), (26), (27), (30), (48), % 23.13/3.86 | (120) gives: % 23.13/3.86 | (125) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v1, % 23.13/3.86 | xG) = v2 & sdtasdt0(xD, xG) = v3 & sdtasdt0(xC, v0) = all_57_4 & % 23.13/3.86 | sdtpldt0(xR, v3) = v2 & sdtpldt0(xD, xG) = v0 & sdtpldt0(xC, xD) = % 23.13/3.86 | v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_57_4)) % 23.13/3.86 | % 23.13/3.86 | GROUND_INST: instantiating (mDistr) with xE, xH, xH, xP, xP, all_43_1, % 23.13/3.86 | simplifying with (13), (17), (19), (28), (31), (51) gives: % 23.13/3.86 | (126) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v1, % 23.13/3.86 | xH) = v2 & sdtasdt0(xH, xH) = v3 & sdtasdt0(xE, v0) = all_43_1 & % 23.13/3.86 | sdtpldt0(xP, v3) = v2 & sdtpldt0(xH, xH) = v0 & sdtpldt0(xE, xH) = % 23.13/3.86 | v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_43_1)) % 23.13/3.86 | % 23.13/3.86 | GROUND_INST: instantiating (mDistr) with xE, xE, xH, all_41_1, xP, all_57_11, % 23.13/3.86 | simplifying with (13), (17), (19), (28), (31), (49), (122) gives: % 23.13/3.86 | (127) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v1, % 23.13/3.86 | xH) = v2 & sdtasdt0(xE, v0) = all_57_11 & sdtasdt0(xE, xH) = v3 & % 23.13/3.86 | sdtpldt0(xP, v3) = v2 & sdtpldt0(xE, xH) = v0 & sdtpldt0(xE, xE) = % 23.13/3.86 | v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_57_11)) % 23.13/3.86 | % 23.13/3.86 | GROUND_INST: instantiating (mDistr2) with xC, xF, xD, xG, all_41_0, xR, % 23.13/3.86 | all_57_4, xS, all_57_2, all_57_1, all_57_0, simplifying with % 23.13/3.86 | (10), (11), (14), (15), (18), (20), (26), (27), (29), (30), (48), % 23.13/3.86 | (78), (85), (119), (120) gives: % 23.13/3.86 | (128) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(v0, v1) = all_57_0 & % 23.13/3.86 | sdtpldt0(xD, xG) = v1 & sdtpldt0(xC, xF) = v0 & $i(v1) & $i(v0) & % 23.13/3.86 | $i(all_57_0)) % 23.13/3.86 | % 23.13/3.86 | GROUND_INST: instantiating (mDistr) with xF, xD, xG, xS, all_57_2, all_57_1, % 23.13/3.86 | simplifying with (11), (14), (15), (20), (27), (29), (30), (85), % 23.13/3.86 | (119) gives: % 23.13/3.87 | (129) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v1, % 23.13/3.87 | xG) = v2 & sdtasdt0(xF, v0) = all_57_1 & sdtasdt0(xD, xG) = v3 & % 23.13/3.87 | sdtpldt0(all_57_2, v3) = v2 & sdtpldt0(xF, xD) = v1 & sdtpldt0(xD, % 23.13/3.87 | xG) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_57_1)) % 23.13/3.87 | % 23.13/3.87 | GROUND_INST: instantiating (mDistr2) with xE, xH, xE, xH, all_41_1, xP, % 23.13/3.87 | all_57_11, all_47_1, all_47_4, all_47_0, all_57_7, simplifying % 23.13/3.87 | with (13), (17), (19), (28), (31), (49), (61), (63), (64), (122), % 23.13/3.87 | (124) gives: % 23.13/3.87 | (130) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(v0, v1) = all_57_7 & % 23.13/3.87 | sdtpldt0(xE, xH) = v1 & sdtpldt0(xE, xH) = v0 & $i(v1) & $i(v0) & % 23.13/3.87 | $i(all_57_7)) % 23.13/3.87 | % 23.13/3.87 | GROUND_INST: instantiating (mDistr) with xH, xE, xH, all_47_1, all_47_4, % 23.13/3.87 | all_47_0, simplifying with (13), (17), (28), (31), (61), (63), % 23.13/3.87 | (64) gives: % 23.13/3.87 | (131) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v1, % 23.13/3.87 | xH) = v2 & sdtasdt0(xH, v0) = all_47_0 & sdtasdt0(xE, xH) = v3 & % 23.13/3.87 | sdtpldt0(all_47_4, v3) = v2 & sdtpldt0(xH, xE) = v1 & sdtpldt0(xE, % 23.13/3.87 | xH) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_47_0)) % 23.13/3.87 | % 23.13/3.87 | GROUND_INST: instantiating (1) with xt, xt, all_33_0, xq, xq, xD, xB, xB, xG, % 23.13/3.87 | all_45_1, simplifying with (2), (6), (8), (12), (16), (38), (55), % 23.13/3.87 | (118) gives: % 23.13/3.87 | (132) all_33_0 = sz00 | (sdtasasdt0(xt, xt) = all_45_1 & $i(all_45_1)) % 23.13/3.87 | % 23.13/3.87 | DELTA: instantiating (130) with fresh symbols all_73_0, all_73_1 gives: % 23.13/3.87 | (133) sdtasdt0(all_73_1, all_73_0) = all_57_7 & sdtpldt0(xE, xH) = all_73_0 % 23.13/3.87 | & sdtpldt0(xE, xH) = all_73_1 & $i(all_73_0) & $i(all_73_1) & % 23.13/3.87 | $i(all_57_7) % 23.13/3.87 | % 23.13/3.87 | ALPHA: (133) implies: % 23.13/3.87 | (134) sdtpldt0(xE, xH) = all_73_1 % 23.13/3.87 | (135) sdtpldt0(xE, xH) = all_73_0 % 23.13/3.87 | (136) sdtasdt0(all_73_1, all_73_0) = all_57_7 % 23.13/3.87 | % 23.13/3.87 | DELTA: instantiating (128) with fresh symbols all_75_0, all_75_1 gives: % 23.13/3.87 | (137) sdtasdt0(all_75_1, all_75_0) = all_57_0 & sdtpldt0(xD, xG) = all_75_0 % 23.13/3.87 | & sdtpldt0(xC, xF) = all_75_1 & $i(all_75_0) & $i(all_75_1) & % 23.13/3.87 | $i(all_57_0) % 23.13/3.87 | % 23.13/3.87 | ALPHA: (137) implies: % 23.13/3.87 | (138) sdtpldt0(xC, xF) = all_75_1 % 23.13/3.87 | (139) sdtpldt0(xD, xG) = all_75_0 % 23.13/3.87 | (140) sdtasdt0(all_75_1, all_75_0) = all_57_0 % 23.13/3.87 | % 23.13/3.87 | DELTA: instantiating (125) with fresh symbols all_81_0, all_81_1, all_81_2, % 23.13/3.87 | all_81_3 gives: % 23.13/3.87 | (141) sdtasdt0(all_81_2, xG) = all_81_1 & sdtasdt0(xD, xG) = all_81_0 & % 23.13/3.87 | sdtasdt0(xC, all_81_3) = all_57_4 & sdtpldt0(xR, all_81_0) = all_81_1 % 23.13/3.87 | & sdtpldt0(xD, xG) = all_81_3 & sdtpldt0(xC, xD) = all_81_2 & % 23.13/3.87 | $i(all_81_0) & $i(all_81_1) & $i(all_81_2) & $i(all_81_3) & % 23.13/3.87 | $i(all_57_4) % 23.13/3.87 | % 23.13/3.87 | ALPHA: (141) implies: % 23.13/3.87 | (142) sdtpldt0(xD, xG) = all_81_3 % 23.13/3.87 | % 23.13/3.87 | DELTA: instantiating (127) with fresh symbols all_83_0, all_83_1, all_83_2, % 23.13/3.87 | all_83_3 gives: % 23.13/3.87 | (143) sdtasdt0(all_83_2, xH) = all_83_1 & sdtasdt0(xE, all_83_3) = % 23.13/3.87 | all_57_11 & sdtasdt0(xE, xH) = all_83_0 & sdtpldt0(xP, all_83_0) = % 23.13/3.87 | all_83_1 & sdtpldt0(xE, xH) = all_83_3 & sdtpldt0(xE, xE) = all_83_2 % 23.13/3.87 | & $i(all_83_0) & $i(all_83_1) & $i(all_83_2) & $i(all_83_3) & % 23.13/3.87 | $i(all_57_11) % 23.13/3.87 | % 23.13/3.87 | ALPHA: (143) implies: % 23.13/3.87 | (144) sdtpldt0(xE, xH) = all_83_3 % 23.13/3.87 | % 23.13/3.87 | DELTA: instantiating (126) with fresh symbols all_85_0, all_85_1, all_85_2, % 23.13/3.87 | all_85_3 gives: % 23.13/3.87 | (145) sdtasdt0(all_85_2, xH) = all_85_1 & sdtasdt0(xH, xH) = all_85_0 & % 23.13/3.87 | sdtasdt0(xE, all_85_3) = all_43_1 & sdtpldt0(xP, all_85_0) = all_85_1 % 23.13/3.87 | & sdtpldt0(xH, xH) = all_85_3 & sdtpldt0(xE, xH) = all_85_2 & % 23.13/3.87 | $i(all_85_0) & $i(all_85_1) & $i(all_85_2) & $i(all_85_3) & % 23.13/3.87 | $i(all_43_1) % 23.13/3.87 | % 23.13/3.87 | ALPHA: (145) implies: % 23.13/3.87 | (146) sdtpldt0(xE, xH) = all_85_2 % 23.13/3.87 | % 23.13/3.87 | DELTA: instantiating (129) with fresh symbols all_88_0, all_88_1, all_88_2, % 23.13/3.87 | all_88_3 gives: % 23.13/3.87 | (147) sdtasdt0(all_88_2, xG) = all_88_1 & sdtasdt0(xF, all_88_3) = all_57_1 % 23.13/3.87 | & sdtasdt0(xD, xG) = all_88_0 & sdtpldt0(all_57_2, all_88_0) = % 23.13/3.87 | all_88_1 & sdtpldt0(xF, xD) = all_88_2 & sdtpldt0(xD, xG) = all_88_3 % 23.13/3.87 | & $i(all_88_0) & $i(all_88_1) & $i(all_88_2) & $i(all_88_3) & % 23.13/3.87 | $i(all_57_1) % 23.13/3.87 | % 23.13/3.87 | ALPHA: (147) implies: % 23.13/3.87 | (148) sdtpldt0(xD, xG) = all_88_3 % 23.13/3.87 | % 23.13/3.87 | DELTA: instantiating (131) with fresh symbols all_90_0, all_90_1, all_90_2, % 23.13/3.87 | all_90_3 gives: % 23.13/3.87 | (149) sdtasdt0(all_90_2, xH) = all_90_1 & sdtasdt0(xH, all_90_3) = all_47_0 % 23.13/3.87 | & sdtasdt0(xE, xH) = all_90_0 & sdtpldt0(all_47_4, all_90_0) = % 23.13/3.87 | all_90_1 & sdtpldt0(xH, xE) = all_90_2 & sdtpldt0(xE, xH) = all_90_3 % 23.13/3.87 | & $i(all_90_0) & $i(all_90_1) & $i(all_90_2) & $i(all_90_3) & % 23.13/3.87 | $i(all_47_0) % 23.13/3.87 | % 23.13/3.87 | ALPHA: (149) implies: % 23.13/3.87 | (150) sdtpldt0(xE, xH) = all_90_3 % 23.13/3.87 | % 23.13/3.87 | BETA: splitting (132) gives: % 23.13/3.87 | % 23.13/3.87 | Case 1: % 23.13/3.87 | | % 23.13/3.87 | | (151) all_33_0 = sz00 % 23.13/3.87 | | % 23.13/3.87 | | REDUCE: (117), (151) imply: % 23.13/3.87 | | (152) $false % 23.13/3.87 | | % 23.13/3.87 | | CLOSE: (152) is inconsistent. % 23.13/3.87 | | % 23.13/3.87 | Case 2: % 23.13/3.87 | | % 23.13/3.87 | | % 23.13/3.87 | | GROUND_INST: instantiating (34) with all_45_2, all_75_1, xF, xC, simplifying % 23.13/3.87 | | with (54), (138) gives: % 23.13/3.87 | | (153) all_75_1 = all_45_2 % 23.13/3.87 | | % 23.13/3.87 | | GROUND_INST: instantiating (34) with all_45_1, all_81_3, xG, xD, simplifying % 23.13/3.87 | | with (55), (142) gives: % 23.13/3.87 | | (154) all_81_3 = all_45_1 % 23.13/3.87 | | % 23.13/3.87 | | GROUND_INST: instantiating (34) with all_81_3, all_88_3, xG, xD, simplifying % 23.13/3.87 | | with (142), (148) gives: % 23.13/3.87 | | (155) all_88_3 = all_81_3 % 23.13/3.87 | | % 23.13/3.87 | | GROUND_INST: instantiating (34) with all_75_0, all_88_3, xG, xD, simplifying % 23.13/3.87 | | with (139), (148) gives: % 23.13/3.87 | | (156) all_88_3 = all_75_0 % 23.13/3.87 | | % 23.13/3.87 | | GROUND_INST: instantiating (34) with all_73_1, all_73_0, xH, xE, simplifying % 23.13/3.87 | | with (134), (135) gives: % 23.13/3.88 | | (157) all_73_0 = all_73_1 % 23.13/3.88 | | % 23.13/3.88 | | GROUND_INST: instantiating (34) with all_45_4, all_85_2, xH, xE, simplifying % 23.13/3.88 | | with (56), (146) gives: % 23.13/3.88 | | (158) all_85_2 = all_45_4 % 23.13/3.88 | | % 23.13/3.88 | | GROUND_INST: instantiating (34) with all_85_2, all_90_3, xH, xE, simplifying % 23.13/3.88 | | with (146), (150) gives: % 23.13/3.88 | | (159) all_90_3 = all_85_2 % 23.13/3.88 | | % 23.13/3.88 | | GROUND_INST: instantiating (34) with all_83_3, all_90_3, xH, xE, simplifying % 23.13/3.88 | | with (144), (150) gives: % 23.13/3.88 | | (160) all_90_3 = all_83_3 % 23.13/3.88 | | % 23.13/3.88 | | GROUND_INST: instantiating (34) with all_73_0, all_90_3, xH, xE, simplifying % 23.13/3.88 | | with (135), (150) gives: % 23.13/3.88 | | (161) all_90_3 = all_73_0 % 23.13/3.88 | | % 23.13/3.88 | | COMBINE_EQS: (160), (161) imply: % 23.13/3.88 | | (162) all_83_3 = all_73_0 % 23.13/3.88 | | % 23.13/3.88 | | COMBINE_EQS: (159), (160) imply: % 23.13/3.88 | | (163) all_85_2 = all_83_3 % 23.13/3.88 | | % 23.13/3.88 | | SIMP: (163) implies: % 23.13/3.88 | | (164) all_85_2 = all_83_3 % 23.13/3.88 | | % 23.13/3.88 | | COMBINE_EQS: (155), (156) imply: % 23.13/3.88 | | (165) all_81_3 = all_75_0 % 23.13/3.88 | | % 23.13/3.88 | | SIMP: (165) implies: % 23.13/3.88 | | (166) all_81_3 = all_75_0 % 23.13/3.88 | | % 23.13/3.88 | | COMBINE_EQS: (158), (164) imply: % 23.13/3.88 | | (167) all_83_3 = all_45_4 % 23.13/3.88 | | % 23.13/3.88 | | SIMP: (167) implies: % 23.13/3.88 | | (168) all_83_3 = all_45_4 % 23.13/3.88 | | % 23.13/3.88 | | COMBINE_EQS: (162), (168) imply: % 23.13/3.88 | | (169) all_73_0 = all_45_4 % 23.13/3.88 | | % 23.13/3.88 | | SIMP: (169) implies: % 23.13/3.88 | | (170) all_73_0 = all_45_4 % 23.13/3.88 | | % 23.13/3.88 | | COMBINE_EQS: (154), (166) imply: % 23.13/3.88 | | (171) all_75_0 = all_45_1 % 23.13/3.88 | | % 23.13/3.88 | | COMBINE_EQS: (157), (170) imply: % 23.13/3.88 | | (172) all_73_1 = all_45_4 % 23.13/3.88 | | % 23.13/3.88 | | REDUCE: (140), (153), (171) imply: % 23.13/3.88 | | (173) sdtasdt0(all_45_2, all_45_1) = all_57_0 % 23.13/3.88 | | % 23.13/3.88 | | REDUCE: (136), (170), (172) imply: % 23.13/3.88 | | (174) sdtasdt0(all_45_4, all_45_4) = all_57_7 % 23.13/3.88 | | % 23.13/3.88 | | GROUND_INST: instantiating (35) with all_45_3, all_57_7, all_45_4, all_45_4, % 23.13/3.88 | | simplifying with (57), (174) gives: % 23.13/3.88 | | (175) all_57_7 = all_45_3 % 23.13/3.88 | | % 23.13/3.88 | | GROUND_INST: instantiating (35) with all_45_0, all_57_0, all_45_1, all_45_2, % 23.13/3.88 | | simplifying with (58), (173) gives: % 23.13/3.88 | | (176) all_57_0 = all_45_0 % 23.13/3.88 | | % 23.13/3.88 | | REDUCE: (73), (175), (176) imply: % 23.13/3.88 | | (177) sdtlseqdt0(all_45_3, all_45_0) % 23.13/3.88 | | % 23.13/3.88 | | PRED_UNIFY: (53), (177) imply: % 23.13/3.88 | | (178) $false % 23.13/3.88 | | % 23.13/3.88 | | CLOSE: (178) is inconsistent. % 23.13/3.88 | | % 23.13/3.88 | End of split % 23.13/3.88 | % 23.13/3.88 End of proof % 23.13/3.88 % SZS output end Proof for theBenchmark % 23.13/3.88 % 23.13/3.88 3282ms %------------------------------------------------------------------------------