%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG106+2 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n017.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 13:57:55 EDT 2023 % Result : Theorem 70.20s 9.97s % Output : Proof 88.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : RNG106+2 : TPTP v8.1.2. Released v4.0.0. % 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.32 % Computer : n017.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 300 % 0.12/0.32 % DateTime : Sun Aug 27 01:11:11 EDT 2023 % 0.12/0.32 % CPUTime : % 0.17/0.59 ________ _____ % 0.17/0.59 ___ __ \_________(_)________________________________ % 0.17/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.17/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.17/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.17/0.59 % 0.17/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.17/0.59 (2023-06-19) % 0.17/0.59 % 0.17/0.59 (c) Philipp Rümmer, 2009-2023 % 0.17/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.17/0.59 Amanda Stjerna. % 0.17/0.59 Free software under BSD-3-Clause. % 0.17/0.59 % 0.17/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.17/0.59 % 0.17/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.17/0.60 Running up to 7 provers in parallel. % 0.17/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.17/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.17/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.17/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.17/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.17/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.17/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 3.44/1.16 Prover 4: Preprocessing ... % 3.44/1.16 Prover 1: Preprocessing ... % 3.44/1.20 Prover 6: Preprocessing ... % 3.44/1.20 Prover 3: Preprocessing ... % 3.44/1.20 Prover 2: Preprocessing ... % 3.44/1.20 Prover 0: Preprocessing ... % 3.44/1.20 Prover 5: Preprocessing ... % 11.00/2.18 Prover 3: Constructing countermodel ... % 11.00/2.19 Prover 6: Proving ... % 11.00/2.19 Prover 1: Constructing countermodel ... % 11.00/2.19 Prover 5: Proving ... % 11.61/2.27 Prover 2: Proving ... % 13.77/2.63 Prover 0: Proving ... % 14.41/2.65 Prover 4: Constructing countermodel ... % 70.20/9.97 Prover 3: proved (9349ms) % 70.20/9.97 % 70.20/9.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 70.20/9.97 % 70.20/9.97 Prover 0: stopped % 70.20/9.97 Prover 2: stopped % 70.20/9.97 Prover 5: stopped % 70.20/9.97 Prover 6: stopped % 70.20/9.98 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 70.20/9.98 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 70.20/9.98 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 70.20/9.98 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 70.20/9.98 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 71.60/10.11 Prover 7: Preprocessing ... % 71.60/10.11 Prover 10: Preprocessing ... % 71.60/10.13 Prover 11: Preprocessing ... % 71.60/10.14 Prover 8: Preprocessing ... % 71.60/10.14 Prover 13: Preprocessing ... % 72.22/10.22 Prover 10: Constructing countermodel ... % 72.22/10.24 Prover 7: Constructing countermodel ... % 73.16/10.32 Prover 8: Warning: ignoring some quantifiers % 73.30/10.32 Prover 8: Constructing countermodel ... % 73.30/10.32 Prover 13: Warning: ignoring some quantifiers % 73.30/10.33 Prover 13: Constructing countermodel ... % 75.01/10.64 Prover 11: Constructing countermodel ... % 87.05/12.11 Prover 10: Found proof (size 134) % 87.05/12.11 Prover 10: proved (2141ms) % 87.05/12.11 Prover 8: stopped % 87.05/12.11 Prover 7: stopped % 87.05/12.11 Prover 13: stopped % 87.05/12.11 Prover 4: stopped % 87.05/12.11 Prover 11: stopped % 87.05/12.12 Prover 1: stopped % 87.05/12.12 % 87.05/12.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 87.05/12.12 % 87.05/12.13 % SZS output start Proof for theBenchmark % 87.05/12.13 Assumptions after simplification: % 87.05/12.13 --------------------------------- % 87.05/12.13 % 87.05/12.13 (mAMDistr) % 87.32/12.17 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 87.32/12.17 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ % 87.32/12.17 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 87.32/12.17 aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v6: $i] : ? [v7: % 87.32/12.17 $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, % 87.32/12.17 v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, % 87.32/12.17 v9) = v7 & sdtpldt0(v1, v2) = v6 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 87.32/12.17 $i(v5))) % 87.32/12.17 % 87.32/12.17 (mAddComm) % 87.32/12.17 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 87.32/12.17 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | (sdtpldt0(v1, v0) % 87.32/12.17 = v2 & $i(v2))) % 87.32/12.17 % 87.32/12.17 (mDefDiv) % 87.32/12.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ % 87.32/12.18 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v2) | ~ aElement0(v1) | ~ % 87.32/12.18 aElement0(v0) | doDivides0(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) % 87.32/12.18 | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ aElement0(v1) | ~ aElement0(v0) | % 87.32/12.18 ? [v2: $i] : (sdtasdt0(v0, v2) = v1 & $i(v2) & aElement0(v2))) % 87.32/12.18 % 87.32/12.18 (mDefPrIdeal) % 87.32/12.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (slsdtgt0(v0) = % 87.32/12.18 v1) | ~ (sdtasdt0(v0, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 87.32/12.18 $i(v0) | ~ aElement0(v3) | ~ aElement0(v0) | aElementOf0(v2, v1)) & ! % 87.32/12.18 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slsdtgt0(v0) = v1) | ~ % 87.32/12.18 $i(v2) | ~ $i(v0) | ~ aSet0(v2) | ~ aElement0(v0) | ? [v3: $i] : ? [v4: % 87.32/12.18 $i] : ? [v5: $i] : ($i(v4) & $i(v3) & ( ~ aElementOf0(v3, v2) | ! [v6: % 87.32/12.18 $i] : ( ~ (sdtasdt0(v0, v6) = v3) | ~ $i(v6) | ~ aElement0(v6))) & % 87.32/12.18 (aElementOf0(v3, v2) | (v5 = v3 & sdtasdt0(v0, v4) = v3 & % 87.32/12.18 aElement0(v4))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 87.32/12.18 (slsdtgt0(v0) = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, % 87.32/12.18 v1) | ~ aElement0(v0) | ? [v3: $i] : (sdtasdt0(v0, v3) = v2 & $i(v3) & % 87.32/12.18 aElement0(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (slsdtgt0(v0) = v1) | ~ % 87.32/12.18 $i(v1) | ~ $i(v0) | ~ aElement0(v0) | aSet0(v1)) % 87.32/12.18 % 87.32/12.18 (mEOfElem) % 87.32/12.18 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) | % 87.32/12.18 ~ aSet0(v0) | aElement0(v1)) % 87.32/12.18 % 87.32/12.18 (mMulAsso) % 87.32/12.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 87.32/12.19 (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 87.32/12.19 | ~ $i(v0) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? % 87.32/12.19 [v5: $i] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4 & $i(v5) & % 87.32/12.19 $i(v4))) % 87.32/12.19 % 87.32/12.19 (mMulComm) % 87.32/12.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 87.32/12.19 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | (sdtasdt0(v1, v0) % 87.32/12.19 = v2 & $i(v2))) % 87.32/12.19 % 87.32/12.19 (mSortsB) % 87.32/12.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 87.32/12.19 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | aElement0(v2)) % 87.32/12.19 % 87.32/12.19 (mSortsB_02) % 87.32/12.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 87.32/12.19 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | aElement0(v2)) % 87.32/12.19 % 87.32/12.19 (m__) % 87.32/12.21 $i(xc) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 87.32/12.21 ? [v5: $i] : (slsdtgt0(xc) = v0 & $i(v4) & $i(v2) & $i(v1) & $i(v0) & % 87.32/12.21 aElementOf0(v1, v0) & aSet0(v0) & ~ aIdeal0(v0) & ! [v6: $i] : ! [v7: $i] % 87.32/12.21 : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( % 87.32/12.21 ~ (sdtasdt0(v8, v6) = v10) | ~ (sdtasdt0(xc, v12) = v6) | ~ % 87.32/12.21 (sdtasdt0(xc, v11) = v7) | ~ (sdtpldt0(v6, v7) = v9) | ~ $i(v12) | ~ % 87.32/12.21 $i(v11) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ aElement0(v12) | ~ % 87.32/12.21 aElement0(v11) | ~ aElement0(v8) | ? [v13: $i] : ? [v14: $i] : ? [v15: % 87.32/12.21 $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : (sdtasdt0(v13, v8) = % 87.32/12.21 v14 & sdtasdt0(xc, v18) = v9 & sdtasdt0(xc, v17) = v10 & sdtasdt0(xc, % 87.32/12.21 v16) = v9 & sdtasdt0(xc, v15) = v7 & sdtasdt0(xc, v14) = v10 & % 87.32/12.21 sdtasdt0(xc, v13) = v6 & sdtpldt0(v13, v15) = v16 & $i(v18) & $i(v17) & % 87.32/12.21 $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v10) & $i(v9) & % 87.32/12.21 aElementOf0(v10, v0) & aElementOf0(v9, v0) & aElement0(v18) & % 87.32/12.21 aElement0(v17) & aElement0(v15) & aElement0(v13))) & ! [v6: $i] : ! % 87.32/12.21 [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 87.32/12.21 (sdtasdt0(v8, v6) = v10) | ~ (sdtasdt0(xc, v11) = v7) | ~ (sdtpldt0(v6, % 87.32/12.21 v7) = v9) | ~ $i(v11) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ % 87.32/12.21 aElementOf0(v6, v0) | ~ aElement0(v11) | ~ aElement0(v8) | ? [v12: $i] % 87.32/12.21 : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] % 87.32/12.21 : (sdtasdt0(v12, v8) = v13 & sdtasdt0(xc, v17) = v9 & sdtasdt0(xc, v16) = % 87.32/12.21 v10 & sdtasdt0(xc, v15) = v9 & sdtasdt0(xc, v14) = v7 & sdtasdt0(xc, % 87.32/12.21 v13) = v10 & sdtasdt0(xc, v12) = v6 & sdtpldt0(v12, v14) = v15 & % 87.32/12.21 $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v10) & % 87.32/12.21 $i(v9) & aElementOf0(v10, v0) & aElementOf0(v9, v0) & aElement0(v17) & % 87.32/12.21 aElement0(v16) & aElement0(v14) & aElement0(v12))) & ! [v6: $i] : ! % 87.32/12.21 [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 87.32/12.21 (sdtasdt0(v8, v6) = v10) | ~ (sdtasdt0(xc, v11) = v6) | ~ (sdtpldt0(v6, % 87.32/12.21 v7) = v9) | ~ $i(v11) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ % 87.32/12.21 aElementOf0(v7, v0) | ~ aElement0(v11) | ~ aElement0(v8) | ? [v12: $i] % 87.32/12.21 : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] % 87.32/12.21 : (sdtasdt0(v12, v8) = v13 & sdtasdt0(xc, v17) = v9 & sdtasdt0(xc, v16) = % 87.32/12.21 v10 & sdtasdt0(xc, v15) = v9 & sdtasdt0(xc, v14) = v7 & sdtasdt0(xc, % 87.32/12.21 v13) = v10 & sdtasdt0(xc, v12) = v6 & sdtpldt0(v12, v14) = v15 & % 87.32/12.21 $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v10) & % 87.32/12.21 $i(v9) & aElementOf0(v10, v0) & aElementOf0(v9, v0) & aElement0(v17) & % 87.32/12.21 aElement0(v16) & aElement0(v14) & aElement0(v12))) & ! [v6: $i] : ! % 87.32/12.21 [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~ (sdtasdt0(v8, v6) % 87.32/12.21 = v10) | ~ (sdtpldt0(v6, v7) = v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) % 87.32/12.21 | ~ aElementOf0(v7, v0) | ~ aElementOf0(v6, v0) | ~ aElement0(v8) | ? % 87.32/12.21 [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? % 87.32/12.21 [v16: $i] : (sdtasdt0(v11, v8) = v12 & sdtasdt0(xc, v16) = v9 & % 87.32/12.21 sdtasdt0(xc, v15) = v10 & sdtasdt0(xc, v14) = v9 & sdtasdt0(xc, v13) = % 87.32/12.21 v7 & sdtasdt0(xc, v12) = v10 & sdtasdt0(xc, v11) = v6 & sdtpldt0(v11, % 87.32/12.21 v13) = v14 & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) % 87.32/12.21 & $i(v10) & $i(v9) & aElementOf0(v10, v0) & aElementOf0(v9, v0) & % 87.32/12.21 aElement0(v16) & aElement0(v15) & aElement0(v13) & aElement0(v11))) & ! % 87.32/12.21 [v6: $i] : ! [v7: $i] : ( ~ (sdtasdt0(xc, v7) = v6) | ~ $i(v7) | ~ $i(v6) % 87.32/12.21 | ~ aElement0(v7) | aElementOf0(v6, v0)) & ! [v6: $i] : ( ~ $i(v6) | ~ % 87.32/12.21 aElementOf0(v6, v0) | ? [v7: $i] : (sdtasdt0(xc, v7) = v6 & $i(v7) & % 87.32/12.21 aElement0(v7))) & ((sdtasdt0(v2, v1) = v3 & $i(v3) & aElement0(v2) & ~ % 87.32/12.21 aElementOf0(v3, v0)) | (sdtpldt0(v1, v4) = v5 & $i(v5) & aElementOf0(v4, % 87.32/12.21 v0) & ~ aElementOf0(v5, v0)))) % 87.32/12.21 % 87.32/12.21 (m__1905) % 87.32/12.21 $i(xc) & aElement0(xc) % 87.32/12.21 % 87.32/12.21 (function-axioms) % 87.32/12.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 87.32/12.21 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 87.32/12.21 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) | % 87.32/12.21 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 87.32/12.21 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 87.32/12.21 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 87.32/12.21 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 87.32/12.21 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) = v1) | ~ (slsdtgt0(v2) % 87.32/12.21 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 87.32/12.21 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 87.32/12.21 ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) % 87.32/12.21 % 87.32/12.21 Further assumptions not needed in the proof: % 87.32/12.21 -------------------------------------------- % 87.32/12.21 mAddAsso, mAddInvr, mAddZero, mCancel, mChineseRemainder, mDefDvs, mDefGCD, % 87.32/12.21 mDefIdeal, mDefMod, mDefRel, mDefSInt, mDefSSum, mDivision, mElmSort, mEucSort, % 87.32/12.21 mIdeInt, mIdeSum, mMulMnOne, mMulUnit, mMulZero, mNatLess, mNatSort, mSetEq, % 87.32/12.21 mSetSort, mSortsC, mSortsC_01, mSortsU, mUnNeZr % 87.32/12.21 % 87.32/12.21 Those formulas are unsatisfiable: % 87.32/12.21 --------------------------------- % 87.32/12.21 % 87.32/12.21 Begin of proof % 87.32/12.21 | % 87.32/12.21 | ALPHA: (mDefDiv) implies: % 87.32/12.21 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, % 87.32/12.21 | v1) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v2: $i] : % 87.32/12.21 | (sdtasdt0(v0, v2) = v1 & $i(v2) & aElement0(v2))) % 87.32/12.22 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v2) = v1) | % 87.32/12.22 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v2) | ~ % 87.32/12.22 | aElement0(v1) | ~ aElement0(v0) | doDivides0(v0, v1)) % 87.32/12.22 | % 87.32/12.22 | ALPHA: (mDefPrIdeal) implies: % 87.32/12.22 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slsdtgt0(v0) = v1) | ~ % 87.32/12.22 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~ % 87.32/12.22 | aElement0(v0) | ? [v3: $i] : (sdtasdt0(v0, v3) = v2 & $i(v3) & % 87.32/12.22 | aElement0(v3))) % 87.32/12.22 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 87.32/12.22 | (slsdtgt0(v0) = v1) | ~ (sdtasdt0(v0, v3) = v2) | ~ $i(v3) | ~ % 87.32/12.22 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v3) | ~ aElement0(v0) % 87.32/12.22 | | aElementOf0(v2, v1)) % 87.32/12.22 | % 87.32/12.22 | ALPHA: (m__1905) implies: % 87.32/12.22 | (5) aElement0(xc) % 87.32/12.22 | % 87.32/12.22 | ALPHA: (m__) implies: % 87.32/12.22 | (6) $i(xc) % 87.32/12.23 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 87.32/12.23 | ? [v5: $i] : (slsdtgt0(xc) = v0 & $i(v4) & $i(v2) & $i(v1) & $i(v0) & % 87.32/12.23 | aElementOf0(v1, v0) & aSet0(v0) & ~ aIdeal0(v0) & ! [v6: $i] : ! % 87.32/12.23 | [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : % 87.32/12.23 | ! [v12: $i] : ( ~ (sdtasdt0(v8, v6) = v10) | ~ (sdtasdt0(xc, v12) = % 87.32/12.23 | v6) | ~ (sdtasdt0(xc, v11) = v7) | ~ (sdtpldt0(v6, v7) = v9) | % 87.32/12.23 | ~ $i(v12) | ~ $i(v11) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ % 87.32/12.23 | aElement0(v12) | ~ aElement0(v11) | ~ aElement0(v8) | ? [v13: % 87.32/12.23 | $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : % 87.32/12.23 | ? [v18: $i] : (sdtasdt0(v13, v8) = v14 & sdtasdt0(xc, v18) = v9 & % 87.32/12.23 | sdtasdt0(xc, v17) = v10 & sdtasdt0(xc, v16) = v9 & sdtasdt0(xc, % 87.32/12.23 | v15) = v7 & sdtasdt0(xc, v14) = v10 & sdtasdt0(xc, v13) = v6 & % 87.32/12.23 | sdtpldt0(v13, v15) = v16 & $i(v18) & $i(v17) & $i(v16) & $i(v15) % 87.32/12.23 | & $i(v14) & $i(v13) & $i(v10) & $i(v9) & aElementOf0(v10, v0) & % 87.32/12.23 | aElementOf0(v9, v0) & aElement0(v18) & aElement0(v17) & % 87.32/12.23 | aElement0(v15) & aElement0(v13))) & ! [v6: $i] : ! [v7: $i] : % 87.32/12.23 | ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 87.32/12.23 | (sdtasdt0(v8, v6) = v10) | ~ (sdtasdt0(xc, v11) = v7) | ~ % 87.32/12.23 | (sdtpldt0(v6, v7) = v9) | ~ $i(v11) | ~ $i(v8) | ~ $i(v7) | ~ % 87.32/12.23 | $i(v6) | ~ aElementOf0(v6, v0) | ~ aElement0(v11) | ~ % 87.32/12.23 | aElement0(v8) | ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? % 87.32/12.23 | [v15: $i] : ? [v16: $i] : ? [v17: $i] : (sdtasdt0(v12, v8) = v13 % 87.32/12.23 | & sdtasdt0(xc, v17) = v9 & sdtasdt0(xc, v16) = v10 & sdtasdt0(xc, % 87.32/12.23 | v15) = v9 & sdtasdt0(xc, v14) = v7 & sdtasdt0(xc, v13) = v10 & % 87.32/12.23 | sdtasdt0(xc, v12) = v6 & sdtpldt0(v12, v14) = v15 & $i(v17) & % 87.32/12.23 | $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v10) & % 87.32/12.23 | $i(v9) & aElementOf0(v10, v0) & aElementOf0(v9, v0) & % 87.32/12.23 | aElement0(v17) & aElement0(v16) & aElement0(v14) & % 87.32/12.23 | aElement0(v12))) & ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! % 87.32/12.23 | [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ (sdtasdt0(v8, v6) = v10) % 87.32/12.23 | | ~ (sdtasdt0(xc, v11) = v6) | ~ (sdtpldt0(v6, v7) = v9) | ~ % 87.32/12.23 | $i(v11) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ aElementOf0(v7, % 87.32/12.23 | v0) | ~ aElement0(v11) | ~ aElement0(v8) | ? [v12: $i] : ? % 87.32/12.23 | [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: % 87.32/12.23 | $i] : (sdtasdt0(v12, v8) = v13 & sdtasdt0(xc, v17) = v9 & % 87.32/12.23 | sdtasdt0(xc, v16) = v10 & sdtasdt0(xc, v15) = v9 & sdtasdt0(xc, % 87.32/12.23 | v14) = v7 & sdtasdt0(xc, v13) = v10 & sdtasdt0(xc, v12) = v6 & % 87.32/12.23 | sdtpldt0(v12, v14) = v15 & $i(v17) & $i(v16) & $i(v15) & $i(v14) % 87.32/12.23 | & $i(v13) & $i(v12) & $i(v10) & $i(v9) & aElementOf0(v10, v0) & % 87.32/12.23 | aElementOf0(v9, v0) & aElement0(v17) & aElement0(v16) & % 87.32/12.23 | aElement0(v14) & aElement0(v12))) & ! [v6: $i] : ! [v7: $i] : % 87.32/12.23 | ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~ (sdtasdt0(v8, v6) = % 87.32/12.23 | v10) | ~ (sdtpldt0(v6, v7) = v9) | ~ $i(v8) | ~ $i(v7) | ~ % 87.32/12.23 | $i(v6) | ~ aElementOf0(v7, v0) | ~ aElementOf0(v6, v0) | ~ % 87.32/12.23 | aElement0(v8) | ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? % 87.32/12.23 | [v14: $i] : ? [v15: $i] : ? [v16: $i] : (sdtasdt0(v11, v8) = v12 % 87.32/12.23 | & sdtasdt0(xc, v16) = v9 & sdtasdt0(xc, v15) = v10 & sdtasdt0(xc, % 87.32/12.23 | v14) = v9 & sdtasdt0(xc, v13) = v7 & sdtasdt0(xc, v12) = v10 & % 87.32/12.23 | sdtasdt0(xc, v11) = v6 & sdtpldt0(v11, v13) = v14 & $i(v16) & % 87.32/12.23 | $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & % 87.32/12.23 | $i(v9) & aElementOf0(v10, v0) & aElementOf0(v9, v0) & % 87.32/12.23 | aElement0(v16) & aElement0(v15) & aElement0(v13) & % 87.32/12.23 | aElement0(v11))) & ! [v6: $i] : ! [v7: $i] : ( ~ (sdtasdt0(xc, % 87.32/12.23 | v7) = v6) | ~ $i(v7) | ~ $i(v6) | ~ aElement0(v7) | % 87.32/12.23 | aElementOf0(v6, v0)) & ! [v6: $i] : ( ~ $i(v6) | ~ % 87.32/12.23 | aElementOf0(v6, v0) | ? [v7: $i] : (sdtasdt0(xc, v7) = v6 & $i(v7) % 87.32/12.23 | & aElement0(v7))) & ((sdtasdt0(v2, v1) = v3 & $i(v3) & % 87.32/12.23 | aElement0(v2) & ~ aElementOf0(v3, v0)) | (sdtpldt0(v1, v4) = v5 % 87.32/12.23 | & $i(v5) & aElementOf0(v4, v0) & ~ aElementOf0(v5, v0)))) % 87.32/12.23 | % 87.32/12.23 | ALPHA: (function-axioms) implies: % 87.32/12.23 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 87.32/12.23 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 87.32/12.23 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 87.32/12.23 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 87.32/12.23 | % 87.32/12.23 | DELTA: instantiating (7) with fresh symbols all_36_0, all_36_1, all_36_2, % 87.32/12.23 | all_36_3, all_36_4, all_36_5 gives: % 87.32/12.24 | (10) slsdtgt0(xc) = all_36_5 & $i(all_36_1) & $i(all_36_3) & $i(all_36_4) & % 87.32/12.24 | $i(all_36_5) & aElementOf0(all_36_4, all_36_5) & aSet0(all_36_5) & ~ % 87.32/12.24 | aIdeal0(all_36_5) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 87.32/12.24 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtasdt0(v2, % 87.32/12.24 | v0) = v4) | ~ (sdtasdt0(xc, v6) = v0) | ~ (sdtasdt0(xc, v5) = % 87.32/12.24 | v1) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v6) | ~ $i(v5) | ~ % 87.32/12.24 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v6) | ~ aElement0(v5) % 87.32/12.24 | | ~ aElement0(v2) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 87.32/12.24 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : (sdtasdt0(v7, v2) = v8 & % 87.32/12.24 | sdtasdt0(xc, v12) = v3 & sdtasdt0(xc, v11) = v4 & sdtasdt0(xc, % 87.32/12.24 | v10) = v3 & sdtasdt0(xc, v9) = v1 & sdtasdt0(xc, v8) = v4 & % 87.32/12.24 | sdtasdt0(xc, v7) = v0 & sdtpldt0(v7, v9) = v10 & $i(v12) & $i(v11) % 87.32/12.24 | & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v4) & $i(v3) & % 87.32/12.24 | aElementOf0(v4, all_36_5) & aElementOf0(v3, all_36_5) & % 87.32/12.24 | aElement0(v12) & aElement0(v11) & aElement0(v9) & aElement0(v7))) % 87.32/12.24 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 87.32/12.24 | : ! [v5: $i] : ( ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(xc, v5) = % 87.32/12.24 | v1) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v5) | ~ $i(v2) | ~ % 87.32/12.24 | $i(v1) | ~ $i(v0) | ~ aElementOf0(v0, all_36_5) | ~ aElement0(v5) % 87.32/12.24 | | ~ aElement0(v2) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? % 87.32/12.24 | [v9: $i] : ? [v10: $i] : ? [v11: $i] : (sdtasdt0(v6, v2) = v7 & % 87.32/12.24 | sdtasdt0(xc, v11) = v3 & sdtasdt0(xc, v10) = v4 & sdtasdt0(xc, v9) % 87.32/12.24 | = v3 & sdtasdt0(xc, v8) = v1 & sdtasdt0(xc, v7) = v4 & % 87.32/12.24 | sdtasdt0(xc, v6) = v0 & sdtpldt0(v6, v8) = v9 & $i(v11) & $i(v10) % 87.32/12.24 | & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v4) & $i(v3) & % 87.32/12.24 | aElementOf0(v4, all_36_5) & aElementOf0(v3, all_36_5) & % 87.32/12.24 | aElement0(v11) & aElement0(v10) & aElement0(v8) & aElement0(v6))) % 87.32/12.24 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 87.32/12.24 | : ! [v5: $i] : ( ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(xc, v5) = % 87.32/12.24 | v0) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v5) | ~ $i(v2) | ~ % 87.32/12.24 | $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, all_36_5) | ~ aElement0(v5) % 87.32/12.24 | | ~ aElement0(v2) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? % 87.32/12.24 | [v9: $i] : ? [v10: $i] : ? [v11: $i] : (sdtasdt0(v6, v2) = v7 & % 87.32/12.24 | sdtasdt0(xc, v11) = v3 & sdtasdt0(xc, v10) = v4 & sdtasdt0(xc, v9) % 87.32/12.24 | = v3 & sdtasdt0(xc, v8) = v1 & sdtasdt0(xc, v7) = v4 & % 87.32/12.24 | sdtasdt0(xc, v6) = v0 & sdtpldt0(v6, v8) = v9 & $i(v11) & $i(v10) % 87.32/12.24 | & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v4) & $i(v3) & % 87.32/12.24 | aElementOf0(v4, all_36_5) & aElementOf0(v3, all_36_5) & % 87.32/12.24 | aElement0(v11) & aElement0(v10) & aElement0(v8) & aElement0(v6))) % 87.32/12.24 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 87.32/12.24 | : ( ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) % 87.32/12.24 | | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, all_36_5) | ~ % 87.32/12.24 | aElementOf0(v0, all_36_5) | ~ aElement0(v2) | ? [v5: $i] : ? [v6: % 87.32/12.24 | $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 87.32/12.24 | (sdtasdt0(v5, v2) = v6 & sdtasdt0(xc, v10) = v3 & sdtasdt0(xc, v9) = % 87.32/12.24 | v4 & sdtasdt0(xc, v8) = v3 & sdtasdt0(xc, v7) = v1 & sdtasdt0(xc, % 87.32/12.24 | v6) = v4 & sdtasdt0(xc, v5) = v0 & sdtpldt0(v5, v7) = v8 & % 87.32/12.24 | $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 87.32/12.24 | $i(v3) & aElementOf0(v4, all_36_5) & aElementOf0(v3, all_36_5) & % 87.32/12.24 | aElement0(v10) & aElement0(v9) & aElement0(v7) & aElement0(v5))) & % 87.32/12.24 | ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(xc, v1) = v0) | ~ $i(v1) | % 87.32/12.24 | ~ $i(v0) | ~ aElement0(v1) | aElementOf0(v0, all_36_5)) & ! [v0: % 87.32/12.24 | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_36_5) | ? [v1: $i] : % 87.32/12.24 | (sdtasdt0(xc, v1) = v0 & $i(v1) & aElement0(v1))) & % 87.32/12.24 | ((sdtasdt0(all_36_3, all_36_4) = all_36_2 & $i(all_36_2) & % 87.32/12.24 | aElement0(all_36_3) & ~ aElementOf0(all_36_2, all_36_5)) | % 87.32/12.24 | (sdtpldt0(all_36_4, all_36_1) = all_36_0 & $i(all_36_0) & % 87.32/12.24 | aElementOf0(all_36_1, all_36_5) & ~ aElementOf0(all_36_0, % 87.32/12.24 | all_36_5))) % 87.32/12.24 | % 87.32/12.24 | ALPHA: (10) implies: % 87.32/12.24 | (11) aSet0(all_36_5) % 87.32/12.24 | (12) aElementOf0(all_36_4, all_36_5) % 87.32/12.24 | (13) $i(all_36_5) % 87.32/12.24 | (14) $i(all_36_4) % 87.32/12.24 | (15) $i(all_36_3) % 87.32/12.24 | (16) $i(all_36_1) % 87.32/12.24 | (17) slsdtgt0(xc) = all_36_5 % 87.32/12.24 | (18) (sdtasdt0(all_36_3, all_36_4) = all_36_2 & $i(all_36_2) & % 87.32/12.24 | aElement0(all_36_3) & ~ aElementOf0(all_36_2, all_36_5)) | % 87.32/12.24 | (sdtpldt0(all_36_4, all_36_1) = all_36_0 & $i(all_36_0) & % 87.32/12.24 | aElementOf0(all_36_1, all_36_5) & ~ aElementOf0(all_36_0, % 87.32/12.24 | all_36_5)) % 87.32/12.24 | (19) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_36_5) | ? [v1: $i] % 87.32/12.24 | : (sdtasdt0(xc, v1) = v0 & $i(v1) & aElement0(v1))) % 87.32/12.24 | % 87.32/12.24 | GROUND_INST: instantiating (mEOfElem) with all_36_5, all_36_4, simplifying % 87.32/12.24 | with (11), (12), (13), (14) gives: % 87.32/12.24 | (20) aElement0(all_36_4) % 87.32/12.24 | % 87.32/12.24 | GROUND_INST: instantiating (3) with xc, all_36_5, all_36_4, simplifying with % 87.32/12.24 | (5), (6), (12), (13), (14), (17) gives: % 87.32/12.25 | (21) ? [v0: $i] : (sdtasdt0(xc, v0) = all_36_4 & $i(v0) & aElement0(v0)) % 87.32/12.25 | % 87.32/12.25 | DELTA: instantiating (21) with fresh symbol all_45_0 gives: % 87.78/12.25 | (22) sdtasdt0(xc, all_45_0) = all_36_4 & $i(all_45_0) & aElement0(all_45_0) % 87.78/12.25 | % 87.78/12.25 | ALPHA: (22) implies: % 87.78/12.25 | (23) aElement0(all_45_0) % 87.78/12.25 | (24) $i(all_45_0) % 87.78/12.25 | (25) sdtasdt0(xc, all_45_0) = all_36_4 % 87.78/12.25 | % 87.78/12.25 | GROUND_INST: instantiating (mMulComm) with xc, all_45_0, all_36_4, simplifying % 87.78/12.25 | with (5), (6), (23), (24), (25) gives: % 87.78/12.25 | (26) sdtasdt0(all_45_0, xc) = all_36_4 & $i(all_36_4) % 87.78/12.25 | % 87.78/12.25 | ALPHA: (26) implies: % 87.78/12.25 | (27) sdtasdt0(all_45_0, xc) = all_36_4 % 87.78/12.25 | % 87.78/12.25 | GROUND_INST: instantiating (2) with xc, all_36_4, all_45_0, simplifying with % 87.78/12.25 | (5), (6), (14), (20), (23), (24), (25) gives: % 87.78/12.25 | (28) doDivides0(xc, all_36_4) % 87.78/12.25 | % 87.78/12.25 | GROUND_INST: instantiating (2) with all_45_0, all_36_4, xc, simplifying with % 87.78/12.25 | (5), (6), (14), (20), (23), (24), (27) gives: % 87.78/12.25 | (29) doDivides0(all_45_0, all_36_4) % 87.78/12.25 | % 87.78/12.25 | DELTA: instantiating (21) with fresh symbol all_63_0 gives: % 87.78/12.25 | (30) sdtasdt0(xc, all_63_0) = all_36_4 & $i(all_63_0) & aElement0(all_63_0) % 87.78/12.25 | % 87.78/12.25 | ALPHA: (30) implies: % 87.78/12.25 | (31) aElement0(all_63_0) % 87.78/12.25 | (32) $i(all_63_0) % 87.78/12.25 | (33) sdtasdt0(xc, all_63_0) = all_36_4 % 87.78/12.25 | % 87.78/12.25 | GROUND_INST: instantiating (1) with all_45_0, all_36_4, simplifying with (14), % 87.78/12.25 | (20), (23), (24), (29) gives: % 87.78/12.25 | (34) ? [v0: $i] : (sdtasdt0(all_45_0, v0) = all_36_4 & $i(v0) & % 87.78/12.25 | aElement0(v0)) % 87.78/12.25 | % 87.78/12.25 | GROUND_INST: instantiating (mMulComm) with xc, all_63_0, all_36_4, simplifying % 87.78/12.25 | with (5), (6), (31), (32), (33) gives: % 87.78/12.25 | (35) sdtasdt0(all_63_0, xc) = all_36_4 & $i(all_36_4) % 87.78/12.25 | % 87.78/12.25 | ALPHA: (35) implies: % 87.78/12.25 | (36) sdtasdt0(all_63_0, xc) = all_36_4 % 87.78/12.25 | % 87.78/12.25 | DELTA: instantiating (34) with fresh symbol all_71_0 gives: % 87.78/12.25 | (37) sdtasdt0(all_45_0, all_71_0) = all_36_4 & $i(all_71_0) & % 87.78/12.25 | aElement0(all_71_0) % 87.78/12.25 | % 87.78/12.25 | ALPHA: (37) implies: % 87.78/12.25 | (38) aElement0(all_71_0) % 87.78/12.25 | (39) $i(all_71_0) % 87.78/12.25 | (40) sdtasdt0(all_45_0, all_71_0) = all_36_4 % 87.78/12.25 | % 87.78/12.25 | GROUND_INST: instantiating (mMulComm) with all_45_0, all_71_0, all_36_4, % 87.78/12.25 | simplifying with (23), (24), (38), (39), (40) gives: % 87.78/12.25 | (41) sdtasdt0(all_71_0, all_45_0) = all_36_4 & $i(all_36_4) % 87.78/12.25 | % 87.78/12.25 | ALPHA: (41) implies: % 87.78/12.25 | (42) sdtasdt0(all_71_0, all_45_0) = all_36_4 % 87.78/12.25 | % 87.78/12.25 | GROUND_INST: instantiating (2) with all_63_0, all_36_4, xc, simplifying with % 87.78/12.25 | (5), (6), (14), (20), (31), (32), (36) gives: % 87.78/12.25 | (43) doDivides0(all_63_0, all_36_4) % 87.78/12.25 | % 87.78/12.26 | GROUND_INST: instantiating (1) with all_63_0, all_36_4, simplifying with (14), % 87.78/12.26 | (20), (31), (32), (43) gives: % 87.78/12.26 | (44) ? [v0: $i] : (sdtasdt0(all_63_0, v0) = all_36_4 & $i(v0) & % 87.78/12.26 | aElement0(v0)) % 87.78/12.26 | % 87.78/12.26 | GROUND_INST: instantiating (2) with all_71_0, all_36_4, all_45_0, simplifying % 87.78/12.26 | with (14), (20), (23), (24), (38), (39), (42) gives: % 87.78/12.26 | (45) doDivides0(all_71_0, all_36_4) % 87.78/12.26 | % 87.78/12.26 | DELTA: instantiating (44) with fresh symbol all_89_0 gives: % 87.78/12.26 | (46) sdtasdt0(all_63_0, all_89_0) = all_36_4 & $i(all_89_0) & % 87.78/12.26 | aElement0(all_89_0) % 87.78/12.26 | % 87.78/12.26 | ALPHA: (46) implies: % 87.78/12.26 | (47) aElement0(all_89_0) % 87.78/12.26 | (48) $i(all_89_0) % 87.78/12.26 | (49) sdtasdt0(all_63_0, all_89_0) = all_36_4 % 87.78/12.26 | % 87.78/12.26 | GROUND_INST: instantiating (1) with all_71_0, all_36_4, simplifying with (14), % 87.78/12.26 | (20), (38), (39), (45) gives: % 87.78/12.26 | (50) ? [v0: $i] : (sdtasdt0(all_71_0, v0) = all_36_4 & $i(v0) & % 87.78/12.26 | aElement0(v0)) % 87.78/12.26 | % 87.78/12.26 | GROUND_INST: instantiating (mMulComm) with all_63_0, all_89_0, all_36_4, % 87.78/12.26 | simplifying with (31), (32), (47), (48), (49) gives: % 87.78/12.26 | (51) sdtasdt0(all_89_0, all_63_0) = all_36_4 & $i(all_36_4) % 87.78/12.26 | % 87.78/12.26 | ALPHA: (51) implies: % 87.78/12.26 | (52) sdtasdt0(all_89_0, all_63_0) = all_36_4 % 87.78/12.26 | % 87.78/12.26 | DELTA: instantiating (50) with fresh symbol all_97_0 gives: % 87.78/12.26 | (53) sdtasdt0(all_71_0, all_97_0) = all_36_4 & $i(all_97_0) & % 87.78/12.26 | aElement0(all_97_0) % 87.78/12.26 | % 87.78/12.26 | ALPHA: (53) implies: % 87.78/12.26 | (54) aElement0(all_97_0) % 87.78/12.26 | (55) $i(all_97_0) % 87.78/12.26 | (56) sdtasdt0(all_71_0, all_97_0) = all_36_4 % 87.78/12.26 | % 87.78/12.26 | GROUND_INST: instantiating (mMulComm) with all_71_0, all_97_0, all_36_4, % 87.78/12.26 | simplifying with (38), (39), (54), (55), (56) gives: % 87.78/12.26 | (57) sdtasdt0(all_97_0, all_71_0) = all_36_4 & $i(all_36_4) % 87.78/12.26 | % 87.78/12.26 | ALPHA: (57) implies: % 87.78/12.26 | (58) sdtasdt0(all_97_0, all_71_0) = all_36_4 % 87.78/12.26 | % 87.78/12.26 | GROUND_INST: instantiating (2) with all_89_0, all_36_4, all_63_0, simplifying % 87.78/12.26 | with (14), (20), (31), (32), (47), (48), (52) gives: % 87.78/12.26 | (59) doDivides0(all_89_0, all_36_4) % 87.78/12.26 | % 87.78/12.26 | GROUND_INST: instantiating (1) with all_89_0, all_36_4, simplifying with (14), % 87.78/12.26 | (20), (47), (48), (59) gives: % 87.78/12.26 | (60) ? [v0: $i] : (sdtasdt0(all_89_0, v0) = all_36_4 & $i(v0) & % 87.78/12.26 | aElement0(v0)) % 87.78/12.26 | % 87.78/12.26 | GROUND_INST: instantiating (2) with all_97_0, all_36_4, all_71_0, simplifying % 87.78/12.26 | with (14), (20), (38), (39), (54), (55), (58) gives: % 87.78/12.26 | (61) doDivides0(all_97_0, all_36_4) % 87.78/12.26 | % 87.78/12.26 | DELTA: instantiating (60) with fresh symbol all_115_0 gives: % 87.78/12.26 | (62) sdtasdt0(all_89_0, all_115_0) = all_36_4 & $i(all_115_0) & % 87.78/12.26 | aElement0(all_115_0) % 87.78/12.26 | % 87.78/12.26 | ALPHA: (62) implies: % 87.78/12.26 | (63) aElement0(all_115_0) % 87.78/12.26 | (64) $i(all_115_0) % 87.78/12.26 | (65) sdtasdt0(all_89_0, all_115_0) = all_36_4 % 87.78/12.26 | % 87.78/12.26 | GROUND_INST: instantiating (1) with all_97_0, all_36_4, simplifying with (14), % 87.78/12.26 | (20), (54), (55), (61) gives: % 87.78/12.26 | (66) ? [v0: $i] : (sdtasdt0(all_97_0, v0) = all_36_4 & $i(v0) & % 87.78/12.26 | aElement0(v0)) % 87.78/12.26 | % 87.78/12.26 | GROUND_INST: instantiating (mMulComm) with all_89_0, all_115_0, all_36_4, % 87.78/12.26 | simplifying with (47), (48), (63), (64), (65) gives: % 87.78/12.26 | (67) sdtasdt0(all_115_0, all_89_0) = all_36_4 & $i(all_36_4) % 87.78/12.26 | % 87.78/12.26 | ALPHA: (67) implies: % 87.78/12.26 | (68) sdtasdt0(all_115_0, all_89_0) = all_36_4 % 87.78/12.26 | % 87.78/12.26 | DELTA: instantiating (66) with fresh symbol all_123_0 gives: % 87.78/12.26 | (69) sdtasdt0(all_97_0, all_123_0) = all_36_4 & $i(all_123_0) & % 87.78/12.26 | aElement0(all_123_0) % 87.78/12.26 | % 87.78/12.26 | ALPHA: (69) implies: % 87.78/12.26 | (70) aElement0(all_123_0) % 87.78/12.26 | (71) $i(all_123_0) % 87.78/12.26 | (72) sdtasdt0(all_97_0, all_123_0) = all_36_4 % 87.78/12.26 | % 87.78/12.26 | GROUND_INST: instantiating (mMulComm) with all_97_0, all_123_0, all_36_4, % 87.78/12.26 | simplifying with (54), (55), (70), (71), (72) gives: % 87.78/12.26 | (73) sdtasdt0(all_123_0, all_97_0) = all_36_4 & $i(all_36_4) % 87.78/12.26 | % 87.78/12.26 | GROUND_INST: instantiating (2) with all_115_0, all_36_4, all_89_0, simplifying % 87.78/12.26 | with (14), (20), (47), (48), (63), (64), (68) gives: % 87.78/12.26 | (74) doDivides0(all_115_0, all_36_4) % 87.78/12.26 | % 87.78/12.26 | GROUND_INST: instantiating (1) with all_115_0, all_36_4, simplifying with % 87.78/12.26 | (14), (20), (63), (64), (74) gives: % 87.78/12.26 | (75) ? [v0: $i] : (sdtasdt0(all_115_0, v0) = all_36_4 & $i(v0) & % 87.78/12.26 | aElement0(v0)) % 87.78/12.26 | % 87.78/12.26 | DELTA: instantiating (75) with fresh symbol all_141_0 gives: % 87.78/12.26 | (76) sdtasdt0(all_115_0, all_141_0) = all_36_4 & $i(all_141_0) & % 87.78/12.26 | aElement0(all_141_0) % 87.78/12.26 | % 87.78/12.26 | ALPHA: (76) implies: % 87.78/12.26 | (77) aElement0(all_141_0) % 87.78/12.26 | (78) $i(all_141_0) % 87.78/12.27 | (79) sdtasdt0(all_115_0, all_141_0) = all_36_4 % 87.78/12.27 | % 87.78/12.27 | BETA: splitting (18) gives: % 87.78/12.27 | % 87.78/12.27 | Case 1: % 87.78/12.27 | | % 87.78/12.27 | | (80) sdtasdt0(all_36_3, all_36_4) = all_36_2 & $i(all_36_2) & % 87.78/12.27 | | aElement0(all_36_3) & ~ aElementOf0(all_36_2, all_36_5) % 87.78/12.27 | | % 87.78/12.27 | | ALPHA: (80) implies: % 87.78/12.27 | | (81) ~ aElementOf0(all_36_2, all_36_5) % 87.78/12.27 | | (82) aElement0(all_36_3) % 87.78/12.27 | | (83) sdtasdt0(all_36_3, all_36_4) = all_36_2 % 87.78/12.27 | | % 87.78/12.27 | | GROUND_INST: instantiating (mMulComm) with all_36_3, all_36_4, all_36_2, % 87.78/12.27 | | simplifying with (14), (15), (20), (82), (83) gives: % 87.78/12.27 | | (84) sdtasdt0(all_36_4, all_36_3) = all_36_2 & $i(all_36_2) % 87.78/12.27 | | % 87.78/12.27 | | ALPHA: (84) implies: % 87.78/12.27 | | (85) sdtasdt0(all_36_4, all_36_3) = all_36_2 % 87.78/12.27 | | % 87.78/12.27 | | GROUND_INST: instantiating (mMulAsso) with all_89_0, all_63_0, all_36_3, % 87.78/12.27 | | all_36_4, all_36_2, simplifying with (15), (31), (32), (47), % 87.78/12.27 | | (48), (52), (82), (85) gives: % 87.78/12.27 | | (86) ? [v0: $i] : (sdtasdt0(all_89_0, v0) = all_36_2 & % 87.78/12.27 | | sdtasdt0(all_63_0, all_36_3) = v0 & $i(v0) & $i(all_36_2)) % 87.78/12.27 | | % 87.78/12.27 | | GROUND_INST: instantiating (mMulAsso) with xc, all_63_0, all_36_3, all_36_4, % 87.78/12.27 | | all_36_2, simplifying with (5), (6), (15), (31), (32), (33), % 87.78/12.27 | | (82), (85) gives: % 87.78/12.27 | | (87) ? [v0: $i] : (sdtasdt0(all_63_0, all_36_3) = v0 & sdtasdt0(xc, v0) % 87.78/12.27 | | = all_36_2 & $i(v0) & $i(all_36_2)) % 87.78/12.27 | | % 87.78/12.27 | | DELTA: instantiating (87) with fresh symbol all_193_0 gives: % 87.78/12.27 | | (88) sdtasdt0(all_63_0, all_36_3) = all_193_0 & sdtasdt0(xc, all_193_0) = % 87.78/12.27 | | all_36_2 & $i(all_193_0) & $i(all_36_2) % 87.78/12.27 | | % 87.78/12.27 | | ALPHA: (88) implies: % 87.78/12.27 | | (89) sdtasdt0(xc, all_193_0) = all_36_2 % 87.78/12.27 | | (90) sdtasdt0(all_63_0, all_36_3) = all_193_0 % 87.78/12.27 | | % 87.78/12.27 | | DELTA: instantiating (86) with fresh symbol all_197_0 gives: % 87.78/12.27 | | (91) sdtasdt0(all_89_0, all_197_0) = all_36_2 & sdtasdt0(all_63_0, % 87.78/12.27 | | all_36_3) = all_197_0 & $i(all_197_0) & $i(all_36_2) % 87.78/12.27 | | % 87.78/12.27 | | ALPHA: (91) implies: % 87.78/12.27 | | (92) sdtasdt0(all_63_0, all_36_3) = all_197_0 % 87.78/12.27 | | % 87.78/12.27 | | GROUND_INST: instantiating (9) with all_193_0, all_197_0, all_36_3, % 87.78/12.27 | | all_63_0, simplifying with (90), (92) gives: % 87.78/12.27 | | (93) all_197_0 = all_193_0 % 87.78/12.27 | | % 87.78/12.27 | | GROUND_INST: instantiating (mSortsB_02) with all_63_0, all_36_3, all_193_0, % 87.78/12.27 | | simplifying with (15), (31), (32), (82), (90) gives: % 87.78/12.27 | | (94) aElement0(all_193_0) % 87.78/12.27 | | % 87.78/12.27 | | GROUND_INST: instantiating (mMulComm) with all_63_0, all_36_3, all_193_0, % 87.78/12.27 | | simplifying with (15), (31), (32), (82), (90) gives: % 87.78/12.27 | | (95) sdtasdt0(all_36_3, all_63_0) = all_193_0 & $i(all_193_0) % 87.78/12.27 | | % 87.78/12.27 | | ALPHA: (95) implies: % 87.78/12.27 | | (96) $i(all_193_0) % 87.78/12.27 | | % 87.78/12.27 | | GROUND_INST: instantiating (mMulComm) with xc, all_193_0, all_36_2, % 87.78/12.27 | | simplifying with (5), (6), (89), (94), (96) gives: % 87.78/12.27 | | (97) sdtasdt0(all_193_0, xc) = all_36_2 & $i(all_36_2) % 87.78/12.27 | | % 87.78/12.27 | | ALPHA: (97) implies: % 87.78/12.27 | | (98) $i(all_36_2) % 87.78/12.27 | | % 87.78/12.27 | | GROUND_INST: instantiating (4) with xc, all_36_5, all_36_2, all_193_0, % 87.78/12.27 | | simplifying with (5), (6), (13), (17), (81), (89), (94), (96), % 87.78/12.27 | | (98) gives: % 87.78/12.27 | | (99) $false % 87.78/12.27 | | % 87.78/12.27 | | CLOSE: (99) is inconsistent. % 87.78/12.27 | | % 87.78/12.27 | Case 2: % 87.78/12.27 | | % 87.78/12.27 | | (100) sdtpldt0(all_36_4, all_36_1) = all_36_0 & $i(all_36_0) & % 87.78/12.27 | | aElementOf0(all_36_1, all_36_5) & ~ aElementOf0(all_36_0, % 87.78/12.27 | | all_36_5) % 87.78/12.27 | | % 87.78/12.27 | | ALPHA: (100) implies: % 87.78/12.27 | | (101) ~ aElementOf0(all_36_0, all_36_5) % 87.78/12.27 | | (102) aElementOf0(all_36_1, all_36_5) % 87.78/12.27 | | (103) sdtpldt0(all_36_4, all_36_1) = all_36_0 % 87.78/12.27 | | % 87.78/12.27 | | GROUND_INST: instantiating (mEOfElem) with all_36_5, all_36_1, simplifying % 87.78/12.27 | | with (11), (13), (16), (102) gives: % 87.78/12.27 | | (104) aElement0(all_36_1) % 87.78/12.27 | | % 87.78/12.28 | | GROUND_INST: instantiating (19) with all_36_1, simplifying with (16), (102) % 87.78/12.28 | | gives: % 87.78/12.28 | | (105) ? [v0: $i] : (sdtasdt0(xc, v0) = all_36_1 & $i(v0) & % 87.78/12.28 | | aElement0(v0)) % 87.78/12.28 | | % 87.78/12.28 | | GROUND_INST: instantiating (mMulComm) with all_115_0, all_141_0, all_36_4, % 87.78/12.28 | | simplifying with (63), (64), (77), (78), (79) gives: % 87.78/12.28 | | (106) sdtasdt0(all_141_0, all_115_0) = all_36_4 & $i(all_36_4) % 87.78/12.28 | | % 87.78/12.28 | | DELTA: instantiating (105) with fresh symbol all_157_0 gives: % 87.78/12.28 | | (107) sdtasdt0(xc, all_157_0) = all_36_1 & $i(all_157_0) & % 87.78/12.28 | | aElement0(all_157_0) % 87.78/12.28 | | % 87.78/12.28 | | ALPHA: (107) implies: % 87.78/12.28 | | (108) aElement0(all_157_0) % 87.78/12.28 | | (109) $i(all_157_0) % 87.78/12.28 | | (110) sdtasdt0(xc, all_157_0) = all_36_1 % 87.78/12.28 | | % 87.78/12.28 | | GROUND_INST: instantiating (mAddComm) with all_36_4, all_36_1, all_36_0, % 87.78/12.28 | | simplifying with (14), (16), (20), (103), (104) gives: % 87.78/12.28 | | (111) sdtpldt0(all_36_1, all_36_4) = all_36_0 & $i(all_36_0) % 87.78/12.28 | | % 87.78/12.28 | | ALPHA: (111) implies: % 87.78/12.28 | | (112) sdtpldt0(all_36_1, all_36_4) = all_36_0 % 87.78/12.28 | | % 87.78/12.28 | | GROUND_INST: instantiating (mAMDistr) with xc, all_63_0, all_157_0, % 87.78/12.28 | | all_36_4, all_36_1, all_36_0, simplifying with (5), (6), (31), % 87.78/12.28 | | (32), (33), (103), (108), (109), (110) gives: % 87.78/12.28 | | (113) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 87.78/12.28 | | (sdtasdt0(v0, xc) = v1 & sdtasdt0(all_157_0, xc) = v3 & % 87.78/12.28 | | sdtasdt0(all_63_0, xc) = v2 & sdtasdt0(xc, v0) = all_36_0 & % 87.78/12.28 | | sdtpldt0(v2, v3) = v1 & sdtpldt0(all_63_0, all_157_0) = v0 & % 87.78/12.28 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_36_0)) % 87.78/12.28 | | % 87.78/12.28 | | GROUND_INST: instantiating (mAMDistr) with xc, all_45_0, all_157_0, % 87.78/12.28 | | all_36_4, all_36_1, all_36_0, simplifying with (5), (6), (23), % 87.78/12.28 | | (24), (25), (103), (108), (109), (110) gives: % 87.78/12.28 | | (114) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 87.78/12.28 | | (sdtasdt0(v0, xc) = v1 & sdtasdt0(all_157_0, xc) = v3 & % 87.78/12.28 | | sdtasdt0(all_45_0, xc) = v2 & sdtasdt0(xc, v0) = all_36_0 & % 87.78/12.28 | | sdtpldt0(v2, v3) = v1 & sdtpldt0(all_45_0, all_157_0) = v0 & % 87.78/12.28 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_36_0)) % 87.78/12.28 | | % 87.78/12.28 | | GROUND_INST: instantiating (mMulComm) with xc, all_157_0, all_36_1, % 87.78/12.28 | | simplifying with (5), (6), (108), (109), (110) gives: % 87.78/12.28 | | (115) sdtasdt0(all_157_0, xc) = all_36_1 & $i(all_36_1) % 87.78/12.28 | | % 87.78/12.28 | | ALPHA: (115) implies: % 87.78/12.28 | | (116) sdtasdt0(all_157_0, xc) = all_36_1 % 87.78/12.28 | | % 87.78/12.28 | | DELTA: instantiating (114) with fresh symbols all_177_0, all_177_1, % 87.78/12.28 | | all_177_2, all_177_3 gives: % 87.78/12.28 | | (117) sdtasdt0(all_177_3, xc) = all_177_2 & sdtasdt0(all_157_0, xc) = % 87.78/12.28 | | all_177_0 & sdtasdt0(all_45_0, xc) = all_177_1 & sdtasdt0(xc, % 87.78/12.28 | | all_177_3) = all_36_0 & sdtpldt0(all_177_1, all_177_0) = % 87.78/12.28 | | all_177_2 & sdtpldt0(all_45_0, all_157_0) = all_177_3 & % 87.78/12.28 | | $i(all_177_0) & $i(all_177_1) & $i(all_177_2) & $i(all_177_3) & % 87.78/12.28 | | $i(all_36_0) % 87.78/12.28 | | % 87.78/12.28 | | ALPHA: (117) implies: % 87.78/12.28 | | (118) sdtpldt0(all_177_1, all_177_0) = all_177_2 % 87.78/12.28 | | (119) sdtasdt0(all_45_0, xc) = all_177_1 % 87.78/12.28 | | (120) sdtasdt0(all_157_0, xc) = all_177_0 % 87.78/12.28 | | % 87.78/12.28 | | DELTA: instantiating (113) with fresh symbols all_179_0, all_179_1, % 87.78/12.28 | | all_179_2, all_179_3 gives: % 87.78/12.28 | | (121) sdtasdt0(all_179_3, xc) = all_179_2 & sdtasdt0(all_157_0, xc) = % 87.78/12.28 | | all_179_0 & sdtasdt0(all_63_0, xc) = all_179_1 & sdtasdt0(xc, % 87.78/12.28 | | all_179_3) = all_36_0 & sdtpldt0(all_179_1, all_179_0) = % 87.78/12.28 | | all_179_2 & sdtpldt0(all_63_0, all_157_0) = all_179_3 & % 87.78/12.28 | | $i(all_179_0) & $i(all_179_1) & $i(all_179_2) & $i(all_179_3) & % 87.78/12.28 | | $i(all_36_0) % 87.78/12.28 | | % 87.78/12.28 | | ALPHA: (121) implies: % 87.78/12.28 | | (122) sdtpldt0(all_63_0, all_157_0) = all_179_3 % 87.78/12.28 | | (123) sdtpldt0(all_179_1, all_179_0) = all_179_2 % 87.78/12.28 | | (124) sdtasdt0(all_63_0, xc) = all_179_1 % 87.78/12.28 | | (125) sdtasdt0(all_157_0, xc) = all_179_0 % 87.78/12.28 | | (126) sdtasdt0(all_179_3, xc) = all_179_2 % 87.78/12.28 | | % 87.78/12.28 | | GROUND_INST: instantiating (9) with all_36_4, all_177_1, xc, all_45_0, % 87.78/12.28 | | simplifying with (27), (119) gives: % 87.78/12.28 | | (127) all_177_1 = all_36_4 % 87.78/12.28 | | % 87.78/12.28 | | GROUND_INST: instantiating (9) with all_36_4, all_179_1, xc, all_63_0, % 87.78/12.28 | | simplifying with (36), (124) gives: % 87.78/12.28 | | (128) all_179_1 = all_36_4 % 87.78/12.28 | | % 87.78/12.28 | | GROUND_INST: instantiating (9) with all_177_0, all_179_0, xc, all_157_0, % 87.78/12.28 | | simplifying with (120), (125) gives: % 87.78/12.28 | | (129) all_179_0 = all_177_0 % 87.78/12.28 | | % 87.78/12.28 | | GROUND_INST: instantiating (9) with all_36_1, all_179_0, xc, all_157_0, % 87.78/12.28 | | simplifying with (116), (125) gives: % 87.78/12.28 | | (130) all_179_0 = all_36_1 % 87.78/12.28 | | % 87.78/12.28 | | COMBINE_EQS: (129), (130) imply: % 87.78/12.28 | | (131) all_177_0 = all_36_1 % 87.78/12.28 | | % 87.78/12.28 | | SIMP: (131) implies: % 87.78/12.28 | | (132) all_177_0 = all_36_1 % 87.78/12.28 | | % 87.78/12.28 | | REDUCE: (123), (128), (130) imply: % 87.78/12.28 | | (133) sdtpldt0(all_36_4, all_36_1) = all_179_2 % 87.78/12.28 | | % 87.78/12.28 | | REDUCE: (118), (127), (132) imply: % 87.78/12.28 | | (134) sdtpldt0(all_36_4, all_36_1) = all_177_2 % 87.78/12.28 | | % 87.78/12.28 | | GROUND_INST: instantiating (8) with all_36_0, all_179_2, all_36_1, all_36_4, % 87.78/12.28 | | simplifying with (103), (133) gives: % 87.78/12.28 | | (135) all_179_2 = all_36_0 % 87.78/12.28 | | % 87.78/12.28 | | GROUND_INST: instantiating (8) with all_177_2, all_179_2, all_36_1, % 87.78/12.28 | | all_36_4, simplifying with (133), (134) gives: % 87.78/12.28 | | (136) all_179_2 = all_177_2 % 87.78/12.28 | | % 87.78/12.28 | | COMBINE_EQS: (135), (136) imply: % 87.78/12.28 | | (137) all_177_2 = all_36_0 % 87.78/12.28 | | % 87.78/12.28 | | REDUCE: (126), (135) imply: % 87.78/12.28 | | (138) sdtasdt0(all_179_3, xc) = all_36_0 % 87.78/12.28 | | % 87.78/12.28 | | GROUND_INST: instantiating (mAMDistr) with xc, all_157_0, all_63_0, % 87.78/12.28 | | all_36_1, all_36_4, all_36_0, simplifying with (5), (6), (31), % 87.78/12.28 | | (32), (33), (108), (109), (110), (112) gives: % 87.78/12.29 | | (139) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 87.78/12.29 | | (sdtasdt0(v0, xc) = v1 & sdtasdt0(all_157_0, xc) = v2 & % 87.78/12.29 | | sdtasdt0(all_63_0, xc) = v3 & sdtasdt0(xc, v0) = all_36_0 & % 87.78/12.29 | | sdtpldt0(v2, v3) = v1 & sdtpldt0(all_157_0, all_63_0) = v0 & % 87.78/12.29 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_36_0)) % 87.78/12.29 | | % 87.78/12.29 | | GROUND_INST: instantiating (mAMDistr) with xc, all_157_0, all_45_0, % 87.78/12.29 | | all_36_1, all_36_4, all_36_0, simplifying with (5), (6), (23), % 87.78/12.29 | | (24), (25), (108), (109), (110), (112) gives: % 87.78/12.29 | | (140) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 87.78/12.29 | | (sdtasdt0(v0, xc) = v1 & sdtasdt0(all_157_0, xc) = v2 & % 87.78/12.29 | | sdtasdt0(all_45_0, xc) = v3 & sdtasdt0(xc, v0) = all_36_0 & % 87.78/12.29 | | sdtpldt0(v2, v3) = v1 & sdtpldt0(all_157_0, all_45_0) = v0 & % 87.78/12.29 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_36_0)) % 87.78/12.29 | | % 87.78/12.29 | | GROUND_INST: instantiating (mSortsB) with all_63_0, all_157_0, all_179_3, % 87.78/12.29 | | simplifying with (31), (32), (108), (109), (122) gives: % 87.78/12.29 | | (141) aElement0(all_179_3) % 87.78/12.29 | | % 87.78/12.29 | | GROUND_INST: instantiating (mAddComm) with all_63_0, all_157_0, all_179_3, % 87.78/12.29 | | simplifying with (31), (32), (108), (109), (122) gives: % 87.78/12.29 | | (142) sdtpldt0(all_157_0, all_63_0) = all_179_3 & $i(all_179_3) % 87.78/12.29 | | % 87.78/12.29 | | ALPHA: (142) implies: % 87.78/12.29 | | (143) sdtpldt0(all_157_0, all_63_0) = all_179_3 % 87.78/12.29 | | % 87.78/12.29 | | DELTA: instantiating (140) with fresh symbols all_211_0, all_211_1, % 87.78/12.29 | | all_211_2, all_211_3 gives: % 87.78/12.29 | | (144) sdtasdt0(all_211_3, xc) = all_211_2 & sdtasdt0(all_157_0, xc) = % 87.78/12.29 | | all_211_1 & sdtasdt0(all_45_0, xc) = all_211_0 & sdtasdt0(xc, % 87.78/12.29 | | all_211_3) = all_36_0 & sdtpldt0(all_211_1, all_211_0) = % 87.78/12.29 | | all_211_2 & sdtpldt0(all_157_0, all_45_0) = all_211_3 & % 87.78/12.29 | | $i(all_211_0) & $i(all_211_1) & $i(all_211_2) & $i(all_211_3) & % 87.78/12.29 | | $i(all_36_0) % 87.78/12.29 | | % 87.78/12.29 | | ALPHA: (144) implies: % 87.78/12.29 | | (145) $i(all_211_2) % 87.78/12.29 | | (146) sdtpldt0(all_211_1, all_211_0) = all_211_2 % 87.78/12.29 | | (147) sdtasdt0(all_45_0, xc) = all_211_0 % 87.78/12.29 | | (148) sdtasdt0(all_157_0, xc) = all_211_1 % 87.78/12.29 | | % 87.78/12.29 | | DELTA: instantiating (139) with fresh symbols all_213_0, all_213_1, % 87.78/12.29 | | all_213_2, all_213_3 gives: % 87.78/12.29 | | (149) sdtasdt0(all_213_3, xc) = all_213_2 & sdtasdt0(all_157_0, xc) = % 87.78/12.29 | | all_213_1 & sdtasdt0(all_63_0, xc) = all_213_0 & sdtasdt0(xc, % 87.78/12.29 | | all_213_3) = all_36_0 & sdtpldt0(all_213_1, all_213_0) = % 87.78/12.29 | | all_213_2 & sdtpldt0(all_157_0, all_63_0) = all_213_3 & % 87.78/12.29 | | $i(all_213_0) & $i(all_213_1) & $i(all_213_2) & $i(all_213_3) & % 87.78/12.29 | | $i(all_36_0) % 87.78/12.29 | | % 87.78/12.29 | | ALPHA: (149) implies: % 87.78/12.29 | | (150) $i(all_213_3) % 87.78/12.29 | | (151) sdtpldt0(all_157_0, all_63_0) = all_213_3 % 87.78/12.29 | | (152) sdtpldt0(all_213_1, all_213_0) = all_213_2 % 87.78/12.29 | | (153) sdtasdt0(xc, all_213_3) = all_36_0 % 87.78/12.29 | | (154) sdtasdt0(all_63_0, xc) = all_213_0 % 87.78/12.29 | | (155) sdtasdt0(all_157_0, xc) = all_213_1 % 87.78/12.29 | | (156) sdtasdt0(all_213_3, xc) = all_213_2 % 87.78/12.29 | | % 87.78/12.29 | | GROUND_INST: instantiating (8) with all_179_3, all_213_3, all_63_0, % 87.78/12.29 | | all_157_0, simplifying with (143), (151) gives: % 87.78/12.29 | | (157) all_213_3 = all_179_3 % 87.78/12.29 | | % 87.78/12.29 | | GROUND_INST: instantiating (9) with all_36_4, all_211_0, xc, all_45_0, % 87.78/12.29 | | simplifying with (27), (147) gives: % 87.78/12.29 | | (158) all_211_0 = all_36_4 % 87.78/12.29 | | % 87.78/12.29 | | GROUND_INST: instantiating (9) with all_36_4, all_213_0, xc, all_63_0, % 87.78/12.29 | | simplifying with (36), (154) gives: % 87.78/12.29 | | (159) all_213_0 = all_36_4 % 88.00/12.29 | | % 88.00/12.29 | | GROUND_INST: instantiating (9) with all_36_1, all_213_1, xc, all_157_0, % 88.00/12.29 | | simplifying with (116), (155) gives: % 88.00/12.29 | | (160) all_213_1 = all_36_1 % 88.00/12.29 | | % 88.00/12.29 | | GROUND_INST: instantiating (9) with all_211_1, all_213_1, xc, all_157_0, % 88.00/12.29 | | simplifying with (148), (155) gives: % 88.00/12.29 | | (161) all_213_1 = all_211_1 % 88.00/12.29 | | % 88.00/12.29 | | COMBINE_EQS: (160), (161) imply: % 88.00/12.29 | | (162) all_211_1 = all_36_1 % 88.00/12.29 | | % 88.00/12.29 | | SIMP: (162) implies: % 88.00/12.29 | | (163) all_211_1 = all_36_1 % 88.00/12.29 | | % 88.00/12.29 | | REDUCE: (156), (157) imply: % 88.00/12.29 | | (164) sdtasdt0(all_179_3, xc) = all_213_2 % 88.00/12.29 | | % 88.00/12.29 | | REDUCE: (153), (157) imply: % 88.00/12.29 | | (165) sdtasdt0(xc, all_179_3) = all_36_0 % 88.00/12.29 | | % 88.00/12.29 | | REDUCE: (152), (159), (160) imply: % 88.00/12.29 | | (166) sdtpldt0(all_36_1, all_36_4) = all_213_2 % 88.00/12.29 | | % 88.00/12.29 | | REDUCE: (146), (158), (163) imply: % 88.00/12.29 | | (167) sdtpldt0(all_36_1, all_36_4) = all_211_2 % 88.00/12.29 | | % 88.00/12.29 | | REDUCE: (150), (157) imply: % 88.00/12.29 | | (168) $i(all_179_3) % 88.00/12.29 | | % 88.00/12.29 | | GROUND_INST: instantiating (8) with all_211_2, all_213_2, all_36_4, % 88.00/12.29 | | all_36_1, simplifying with (166), (167) gives: % 88.00/12.29 | | (169) all_213_2 = all_211_2 % 88.00/12.29 | | % 88.00/12.29 | | GROUND_INST: instantiating (9) with all_36_0, all_213_2, xc, all_179_3, % 88.00/12.29 | | simplifying with (138), (164) gives: % 88.00/12.29 | | (170) all_213_2 = all_36_0 % 88.00/12.29 | | % 88.00/12.29 | | COMBINE_EQS: (169), (170) imply: % 88.00/12.29 | | (171) all_211_2 = all_36_0 % 88.00/12.29 | | % 88.00/12.29 | | REDUCE: (145), (171) imply: % 88.00/12.29 | | (172) $i(all_36_0) % 88.00/12.29 | | % 88.00/12.29 | | GROUND_INST: instantiating (4) with xc, all_36_5, all_36_0, all_179_3, % 88.00/12.29 | | simplifying with (5), (6), (13), (17), (101), (141), (165), % 88.00/12.29 | | (168), (172) gives: % 88.00/12.29 | | (173) $false % 88.00/12.29 | | % 88.00/12.29 | | CLOSE: (173) is inconsistent. % 88.00/12.29 | | % 88.00/12.29 | End of split % 88.00/12.29 | % 88.00/12.29 End of proof % 88.00/12.29 % SZS output end Proof for theBenchmark % 88.00/12.29 % 88.00/12.29 11703ms %------------------------------------------------------------------------------