%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM443+4 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n012.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 11:47:47 EDT 2023 % Result : Theorem 14.12s 2.67s % Output : Proof 19.81s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM443+4 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n012.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Fri Aug 25 17:57:26 EDT 2023 % 0.13/0.33 % 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. % 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.63 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 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.03/1.23 Prover 1: Preprocessing ... % 4.03/1.23 Prover 4: Preprocessing ... % 4.03/1.27 Prover 3: Preprocessing ... % 4.03/1.27 Prover 5: Preprocessing ... % 4.03/1.27 Prover 2: Preprocessing ... % 4.03/1.27 Prover 6: Preprocessing ... % 4.03/1.27 Prover 0: Preprocessing ... % 10.53/2.14 Prover 1: Constructing countermodel ... % 10.53/2.17 Prover 5: Constructing countermodel ... % 10.53/2.17 Prover 6: Proving ... % 10.53/2.19 Prover 3: Constructing countermodel ... % 11.11/2.24 Prover 2: Proving ... % 14.12/2.66 Prover 4: Constructing countermodel ... % 14.12/2.67 Prover 3: proved (2037ms) % 14.12/2.67 Prover 0: Proving ... % 14.12/2.67 % 14.12/2.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.12/2.67 % 14.12/2.67 Prover 5: stopped % 14.12/2.68 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.12/2.68 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.12/2.68 Prover 6: stopped % 14.12/2.68 Prover 0: stopped % 14.80/2.69 Prover 2: stopped % 14.90/2.70 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.90/2.70 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.90/2.70 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 15.70/2.83 Prover 10: Preprocessing ... % 15.70/2.84 Prover 11: Preprocessing ... % 15.70/2.84 Prover 8: Preprocessing ... % 15.70/2.84 Prover 7: Preprocessing ... % 15.70/2.85 Prover 13: Preprocessing ... % 17.17/3.08 Prover 10: Constructing countermodel ... % 17.76/3.10 Prover 7: Constructing countermodel ... % 17.76/3.11 Prover 8: Warning: ignoring some quantifiers % 17.76/3.12 Prover 8: Constructing countermodel ... % 17.76/3.17 Prover 13: Constructing countermodel ... % 18.45/3.18 Prover 1: Found proof (size 132) % 18.45/3.18 Prover 1: proved (2559ms) % 18.45/3.18 Prover 10: stopped % 18.45/3.18 Prover 4: stopped % 18.45/3.18 Prover 7: stopped % 18.54/3.19 Prover 13: stopped % 18.54/3.19 Prover 8: stopped % 19.04/3.35 Prover 11: Constructing countermodel ... % 19.04/3.37 Prover 11: stopped % 19.04/3.37 % 19.04/3.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 19.04/3.37 % 19.38/3.40 % SZS output start Proof for theBenchmark % 19.38/3.41 Assumptions after simplification: % 19.38/3.41 --------------------------------- % 19.38/3.41 % 19.38/3.41 (mAddComm) % 19.38/3.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 19.38/3.44 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 19.38/3.44 (sdtpldt0(v1, v0) = v5 & aInteger0(v1) = v4 & aInteger0(v0) = v3 & $i(v5) & % 19.38/3.44 ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) % 19.38/3.44 % 19.38/3.44 (mDivisor) % 19.38/3.44 $i(sz00) & ! [v0: $i] : ( ~ (aInteger0(v0) = 0) | ~ $i(v0) | ( ! [v1: $i] : % 19.38/3.44 ! [v2: int] : (v2 = 0 | v1 = sz00 | ~ (aDivisorOf0(v1, v0) = v2) | ~ % 19.38/3.44 $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & aInteger0(v1) = v3) | ! [v3: $i] % 19.38/3.44 : ( ~ (sdtasdt0(v1, v3) = v0) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) % 19.38/3.44 & aInteger0(v3) = v4))) & ! [v1: $i] : ( ~ (aDivisorOf0(v1, v0) = % 19.38/3.44 0) | ~ $i(v1) | ( ~ (v1 = sz00) & aInteger0(v1) = 0 & ? [v2: $i] : % 19.38/3.44 (sdtasdt0(v1, v2) = v0 & aInteger0(v2) = 0 & $i(v2)))))) % 19.38/3.44 % 19.38/3.44 (mEquModSym) % 19.38/3.44 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = sz00 | ~ % 19.38/3.44 (sdteqdtlpzmzozddtrp0(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 19.38/3.44 ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: any] : % 19.38/3.44 (sdteqdtlpzmzozddtrp0(v1, v0, v2) = v6 & aInteger0(v2) = v5 & aInteger0(v1) % 19.38/3.44 = v4 & aInteger0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v6 % 19.38/3.44 = 0))) % 19.38/3.44 % 19.38/3.44 (mEquModTrn) % 19.38/3.45 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 19.38/3.45 int] : (v4 = 0 | v2 = sz00 | ~ (sdteqdtlpzmzozddtrp0(v0, v3, v2) = v4) | ~ % 19.38/3.45 (sdteqdtlpzmzozddtrp0(v0, v1, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 19.38/3.45 ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : ? % 19.38/3.45 [v9: any] : (sdteqdtlpzmzozddtrp0(v1, v3, v2) = v9 & aInteger0(v3) = v8 & % 19.38/3.45 aInteger0(v2) = v7 & aInteger0(v1) = v6 & aInteger0(v0) = v5 & ( ~ (v9 = % 19.38/3.45 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)))) % 19.38/3.45 % 19.38/3.45 (mIntMult) % 19.38/3.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 19.38/3.45 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 19.38/3.45 (aInteger0(v2) = v5 & aInteger0(v1) = v4 & aInteger0(v0) = v3 & ( ~ (v4 = 0) % 19.38/3.45 | ~ (v3 = 0) | v5 = 0))) % 19.38/3.45 % 19.38/3.45 (mIntNeg) % 19.38/3.45 ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ? [v2: any] : % 19.38/3.45 ? [v3: any] : (aInteger0(v1) = v3 & aInteger0(v0) = v2 & ( ~ (v2 = 0) | v3 % 19.38/3.45 = 0))) % 19.38/3.45 % 19.38/3.45 (mIntPlus) % 19.38/3.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 19.38/3.45 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 19.38/3.45 (aInteger0(v2) = v5 & aInteger0(v1) = v4 & aInteger0(v0) = v3 & ( ~ (v4 = 0) % 19.38/3.45 | ~ (v3 = 0) | v5 = 0))) % 19.38/3.45 % 19.38/3.45 (mMulComm) % 19.38/3.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 19.38/3.45 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 19.38/3.45 (sdtasdt0(v1, v0) = v5 & aInteger0(v1) = v4 & aInteger0(v0) = v3 & $i(v5) & % 19.38/3.45 ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) % 19.38/3.45 % 19.38/3.45 (m__) % 19.38/3.45 $i(xc) & $i(xb) & $i(xq) & $i(xa) & ? [v0: $i] : ? [v1: $i] : ? [v2: int] : % 19.38/3.45 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v2 % 19.38/3.45 = 0) & szAzrzSzezqlpdtcmdtrp0(xa, xq) = v0 & stldt0(v0) = v3 & aSet0(v0) = % 19.38/3.45 0 & aElementOf0(xc, v3) = v6 & aElementOf0(xc, v0) = 0 & aElementOf0(xb, v3) % 19.38/3.45 = 0 & aElementOf0(xb, v0) = v2 & sdteqdtlpzmzozddtrp0(xc, xb, xq) = 0 & % 19.38/3.45 aDivisorOf0(xq, v5) = 0 & sdtpldt0(xc, v4) = v5 & smndt0(xb) = v4 & % 19.38/3.45 smndt0(xa) = v1 & $i(v5) & $i(v4) & $i(v3) & $i(v1) & $i(v0) & ! [v7: $i] : % 19.38/3.45 ! [v8: int] : (v8 = 0 | ~ (aElementOf0(v7, v0) = v8) | ~ $i(v7) | ? [v9: % 19.38/3.45 any] : ? [v10: $i] : ? [v11: any] : ? [v12: any] : % 19.38/3.45 (sdteqdtlpzmzozddtrp0(v7, xa, xq) = v12 & aDivisorOf0(xq, v10) = v11 & % 19.38/3.45 sdtpldt0(v7, v1) = v10 & aInteger0(v7) = v9 & $i(v10) & ( ~ (v9 = 0) | ( % 19.38/3.45 ~ (v12 = 0) & ~ (v11 = 0) & ! [v13: $i] : ( ~ (sdtasdt0(xq, v13) = % 19.38/3.45 v10) | ~ $i(v13) | ? [v14: int] : ( ~ (v14 = 0) & % 19.38/3.45 aInteger0(v13) = v14)))))) & ! [v7: $i] : ( ~ (aElementOf0(v7, % 19.38/3.45 v0) = 0) | ~ $i(v7) | ? [v8: $i] : (sdteqdtlpzmzozddtrp0(v7, xa, xq) % 19.38/3.45 = 0 & aDivisorOf0(xq, v8) = 0 & sdtpldt0(v7, v1) = v8 & aInteger0(v7) = % 19.38/3.45 0 & $i(v8) & ? [v9: $i] : (sdtasdt0(xq, v9) = v8 & aInteger0(v9) = 0 & % 19.38/3.45 $i(v9)))) & ? [v7: $i] : (sdtasdt0(xq, v7) = v5 & aInteger0(v7) = 0 & % 19.38/3.45 $i(v7))) % 19.38/3.45 % 19.38/3.45 (m__1962) % 19.38/3.45 ~ (xq = sz00) & aInteger0(xq) = 0 & aInteger0(xa) = 0 & $i(xq) & $i(xa) & % 19.38/3.45 $i(sz00) % 19.38/3.45 % 19.38/3.45 (m__2010) % 19.38/3.46 aInteger0(xc) = 0 & aInteger0(xb) = 0 & $i(xc) & $i(xb) % 19.38/3.46 % 19.38/3.46 (function-axioms) % 19.38/3.46 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 19.38/3.46 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v1) % 19.38/3.46 | ~ (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 19.38/3.46 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (szAzrzSzezqlpdtcmdtrp0(v3, v2) = v1) % 19.38/3.46 | ~ (szAzrzSzezqlpdtcmdtrp0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.38/3.46 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtslmnbsdt0(v3, v2) = v1) | ~ % 19.38/3.46 (sdtslmnbsdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 19.38/3.46 [v3: $i] : (v1 = v0 | ~ (sdtbsmnsldt0(v3, v2) = v1) | ~ (sdtbsmnsldt0(v3, % 19.38/3.46 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 19.38/3.46 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (aSubsetOf0(v3, v2) = v1) | ~ % 19.38/3.46 (aSubsetOf0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 19.38/3.46 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 19.38/3.46 (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) & ! [v0: % 19.38/3.46 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.38/3.46 : (v1 = v0 | ~ (aDivisorOf0(v3, v2) = v1) | ~ (aDivisorOf0(v3, v2) = v0)) & % 19.38/3.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 19.38/3.46 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 19.38/3.46 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | % 19.38/3.46 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 19.38/3.46 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isFinite0(v2) = v1) | ~ % 19.38/3.46 (isFinite0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 19.38/3.46 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isClosed0(v2) = v1) | ~ % 19.38/3.46 (isClosed0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 19.38/3.46 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isOpen0(v2) = v1) | ~ % 19.38/3.46 (isOpen0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 19.38/3.46 ~ (stldt0(v2) = v1) | ~ (stldt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.38/3.46 [v2: $i] : (v1 = v0 | ~ (sbsmnsldt0(v2) = v1) | ~ (sbsmnsldt0(v2) = v0)) & % 19.38/3.46 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = % 19.38/3.46 v0 | ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) & ! [v0: MultipleValueBool] % 19.38/3.46 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isPrime0(v2) = v1) % 19.38/3.46 | ~ (isPrime0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 19.38/3.46 v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) & ! [v0: % 19.38/3.46 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 19.38/3.46 ~ (aInteger0(v2) = v1) | ~ (aInteger0(v2) = v0)) % 19.38/3.46 % 19.38/3.46 Further assumptions not needed in the proof: % 19.38/3.46 -------------------------------------------- % 19.38/3.46 mAddAsso, mAddNeg, mAddZero, mArSeq, mClosed, mComplement, mDistrib, mElements, % 19.38/3.46 mEquMod, mEquModMul, mEquModRef, mFinSet, mIntOne, mIntZero, mIntegers, % 19.38/3.46 mInterOpen, mIntersection, mMulAsso, mMulMinOne, mMulOne, mMulZero, mOpen, % 19.38/3.46 mPrime, mPrimeDivisor, mSets, mSubset, mUnion, mUnionClosed, mUnionOpen, % 19.38/3.46 mUnionSClosed, mUnionSet, mZeroDiv % 19.38/3.46 % 19.38/3.46 Those formulas are unsatisfiable: % 19.38/3.46 --------------------------------- % 19.38/3.46 % 19.38/3.46 Begin of proof % 19.38/3.46 | % 19.38/3.46 | ALPHA: (mDivisor) implies: % 19.38/3.46 | (1) ! [v0: $i] : ( ~ (aInteger0(v0) = 0) | ~ $i(v0) | ( ! [v1: $i] : ! % 19.38/3.46 | [v2: int] : (v2 = 0 | v1 = sz00 | ~ (aDivisorOf0(v1, v0) = v2) | % 19.38/3.46 | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & aInteger0(v1) = v3) | ! % 19.38/3.46 | [v3: $i] : ( ~ (sdtasdt0(v1, v3) = v0) | ~ $i(v3) | ? [v4: int] % 19.38/3.46 | : ( ~ (v4 = 0) & aInteger0(v3) = v4))) & ! [v1: $i] : ( ~ % 19.38/3.46 | (aDivisorOf0(v1, v0) = 0) | ~ $i(v1) | ( ~ (v1 = sz00) & % 19.38/3.46 | aInteger0(v1) = 0 & ? [v2: $i] : (sdtasdt0(v1, v2) = v0 & % 19.38/3.46 | aInteger0(v2) = 0 & $i(v2)))))) % 19.38/3.46 | % 19.38/3.46 | ALPHA: (mEquModSym) implies: % 19.38/3.47 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = sz00 | ~ % 19.38/3.47 | (sdteqdtlpzmzozddtrp0(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 19.38/3.47 | $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: any] : % 19.38/3.47 | (sdteqdtlpzmzozddtrp0(v1, v0, v2) = v6 & aInteger0(v2) = v5 & % 19.38/3.47 | aInteger0(v1) = v4 & aInteger0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = % 19.38/3.47 | 0) | ~ (v3 = 0) | v6 = 0))) % 19.38/3.47 | % 19.38/3.47 | ALPHA: (mEquModTrn) implies: % 19.38/3.47 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 19.38/3.47 | (v4 = 0 | v2 = sz00 | ~ (sdteqdtlpzmzozddtrp0(v0, v3, v2) = v4) | ~ % 19.38/3.47 | (sdteqdtlpzmzozddtrp0(v0, v1, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ % 19.38/3.47 | $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? % 19.38/3.47 | [v8: any] : ? [v9: any] : (sdteqdtlpzmzozddtrp0(v1, v3, v2) = v9 & % 19.38/3.47 | aInteger0(v3) = v8 & aInteger0(v2) = v7 & aInteger0(v1) = v6 & % 19.38/3.47 | aInteger0(v0) = v5 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ % 19.38/3.47 | (v6 = 0) | ~ (v5 = 0)))) % 19.38/3.47 | % 19.38/3.47 | ALPHA: (m__1962) implies: % 19.38/3.47 | (4) ~ (xq = sz00) % 19.38/3.47 | (5) aInteger0(xa) = 0 % 19.38/3.47 | (6) aInteger0(xq) = 0 % 19.38/3.47 | % 19.38/3.47 | ALPHA: (m__2010) implies: % 19.38/3.47 | (7) aInteger0(xb) = 0 % 19.38/3.47 | % 19.38/3.47 | ALPHA: (m__) implies: % 19.38/3.47 | (8) $i(xa) % 19.38/3.47 | (9) $i(xq) % 19.38/3.47 | (10) $i(xb) % 19.38/3.47 | (11) $i(xc) % 19.38/3.47 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: $i] : ? [v4: $i] : % 19.38/3.47 | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v2 = 0) & % 19.38/3.47 | szAzrzSzezqlpdtcmdtrp0(xa, xq) = v0 & stldt0(v0) = v3 & aSet0(v0) = % 19.38/3.47 | 0 & aElementOf0(xc, v3) = v6 & aElementOf0(xc, v0) = 0 & % 19.38/3.47 | aElementOf0(xb, v3) = 0 & aElementOf0(xb, v0) = v2 & % 19.38/3.47 | sdteqdtlpzmzozddtrp0(xc, xb, xq) = 0 & aDivisorOf0(xq, v5) = 0 & % 19.38/3.47 | sdtpldt0(xc, v4) = v5 & smndt0(xb) = v4 & smndt0(xa) = v1 & $i(v5) & % 19.38/3.47 | $i(v4) & $i(v3) & $i(v1) & $i(v0) & ! [v7: $i] : ! [v8: int] : (v8 % 19.38/3.47 | = 0 | ~ (aElementOf0(v7, v0) = v8) | ~ $i(v7) | ? [v9: any] : % 19.38/3.47 | ? [v10: $i] : ? [v11: any] : ? [v12: any] : % 19.38/3.47 | (sdteqdtlpzmzozddtrp0(v7, xa, xq) = v12 & aDivisorOf0(xq, v10) = % 19.38/3.47 | v11 & sdtpldt0(v7, v1) = v10 & aInteger0(v7) = v9 & $i(v10) & ( % 19.38/3.47 | ~ (v9 = 0) | ( ~ (v12 = 0) & ~ (v11 = 0) & ! [v13: $i] : ( ~ % 19.38/3.47 | (sdtasdt0(xq, v13) = v10) | ~ $i(v13) | ? [v14: int] : ( % 19.38/3.47 | ~ (v14 = 0) & aInteger0(v13) = v14)))))) & ! [v7: $i] : % 19.38/3.47 | ( ~ (aElementOf0(v7, v0) = 0) | ~ $i(v7) | ? [v8: $i] : % 19.38/3.47 | (sdteqdtlpzmzozddtrp0(v7, xa, xq) = 0 & aDivisorOf0(xq, v8) = 0 & % 19.38/3.47 | sdtpldt0(v7, v1) = v8 & aInteger0(v7) = 0 & $i(v8) & ? [v9: $i] % 19.38/3.47 | : (sdtasdt0(xq, v9) = v8 & aInteger0(v9) = 0 & $i(v9)))) & ? % 19.38/3.47 | [v7: $i] : (sdtasdt0(xq, v7) = v5 & aInteger0(v7) = 0 & $i(v7))) % 19.38/3.47 | % 19.38/3.47 | ALPHA: (function-axioms) implies: % 19.38/3.47 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 19.38/3.47 | : (v1 = v0 | ~ (aInteger0(v2) = v1) | ~ (aInteger0(v2) = v0)) % 19.38/3.47 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 19.38/3.47 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sdteqdtlpzmzozddtrp0(v4, % 19.38/3.47 | v3, v2) = v1) | ~ (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v0)) % 19.38/3.47 | % 19.38/3.47 | DELTA: instantiating (12) with fresh symbols all_41_0, all_41_1, all_41_2, % 19.38/3.47 | all_41_3, all_41_4, all_41_5, all_41_6 gives: % 19.81/3.48 | (15) ~ (all_41_0 = 0) & ~ (all_41_4 = 0) & szAzrzSzezqlpdtcmdtrp0(xa, xq) % 19.81/3.48 | = all_41_6 & stldt0(all_41_6) = all_41_3 & aSet0(all_41_6) = 0 & % 19.81/3.48 | aElementOf0(xc, all_41_3) = all_41_0 & aElementOf0(xc, all_41_6) = 0 & % 19.81/3.48 | aElementOf0(xb, all_41_3) = 0 & aElementOf0(xb, all_41_6) = all_41_4 & % 19.81/3.48 | sdteqdtlpzmzozddtrp0(xc, xb, xq) = 0 & aDivisorOf0(xq, all_41_1) = 0 & % 19.81/3.48 | sdtpldt0(xc, all_41_2) = all_41_1 & smndt0(xb) = all_41_2 & smndt0(xa) % 19.81/3.48 | = all_41_5 & $i(all_41_1) & $i(all_41_2) & $i(all_41_3) & $i(all_41_5) % 19.81/3.48 | & $i(all_41_6) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 19.81/3.48 | (aElementOf0(v0, all_41_6) = v1) | ~ $i(v0) | ? [v2: any] : ? % 19.81/3.48 | [v3: $i] : ? [v4: any] : ? [v5: any] : (sdteqdtlpzmzozddtrp0(v0, % 19.81/3.48 | xa, xq) = v5 & aDivisorOf0(xq, v3) = v4 & sdtpldt0(v0, all_41_5) % 19.81/3.48 | = v3 & aInteger0(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | ( ~ (v5 = 0) & % 19.81/3.48 | ~ (v4 = 0) & ! [v6: $i] : ( ~ (sdtasdt0(xq, v6) = v3) | ~ % 19.81/3.48 | $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & aInteger0(v6) = % 19.81/3.48 | v7)))))) & ! [v0: $i] : ( ~ (aElementOf0(v0, all_41_6) = % 19.81/3.48 | 0) | ~ $i(v0) | ? [v1: $i] : (sdteqdtlpzmzozddtrp0(v0, xa, xq) = % 19.81/3.48 | 0 & aDivisorOf0(xq, v1) = 0 & sdtpldt0(v0, all_41_5) = v1 & % 19.81/3.48 | aInteger0(v0) = 0 & $i(v1) & ? [v2: $i] : (sdtasdt0(xq, v2) = v1 % 19.81/3.48 | & aInteger0(v2) = 0 & $i(v2)))) & ? [v0: $i] : (sdtasdt0(xq, % 19.81/3.48 | v0) = all_41_1 & aInteger0(v0) = 0 & $i(v0)) % 19.81/3.48 | % 19.81/3.48 | ALPHA: (15) implies: % 19.81/3.48 | (16) ~ (all_41_4 = 0) % 19.81/3.48 | (17) $i(all_41_2) % 19.81/3.48 | (18) $i(all_41_1) % 19.81/3.48 | (19) smndt0(xa) = all_41_5 % 19.81/3.48 | (20) smndt0(xb) = all_41_2 % 19.81/3.48 | (21) sdtpldt0(xc, all_41_2) = all_41_1 % 19.81/3.48 | (22) aDivisorOf0(xq, all_41_1) = 0 % 19.81/3.48 | (23) sdteqdtlpzmzozddtrp0(xc, xb, xq) = 0 % 19.81/3.48 | (24) aElementOf0(xb, all_41_6) = all_41_4 % 19.81/3.48 | (25) aElementOf0(xc, all_41_6) = 0 % 19.81/3.48 | (26) ! [v0: $i] : ( ~ (aElementOf0(v0, all_41_6) = 0) | ~ $i(v0) | ? % 19.81/3.48 | [v1: $i] : (sdteqdtlpzmzozddtrp0(v0, xa, xq) = 0 & aDivisorOf0(xq, % 19.81/3.48 | v1) = 0 & sdtpldt0(v0, all_41_5) = v1 & aInteger0(v0) = 0 & % 19.81/3.48 | $i(v1) & ? [v2: $i] : (sdtasdt0(xq, v2) = v1 & aInteger0(v2) = 0 % 19.81/3.48 | & $i(v2)))) % 19.81/3.48 | (27) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aElementOf0(v0, all_41_6) = % 19.81/3.48 | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : ? % 19.81/3.48 | [v5: any] : (sdteqdtlpzmzozddtrp0(v0, xa, xq) = v5 & aDivisorOf0(xq, % 19.81/3.48 | v3) = v4 & sdtpldt0(v0, all_41_5) = v3 & aInteger0(v0) = v2 & % 19.81/3.48 | $i(v3) & ( ~ (v2 = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & ! [v6: $i] : % 19.81/3.48 | ( ~ (sdtasdt0(xq, v6) = v3) | ~ $i(v6) | ? [v7: int] : ( ~ % 19.81/3.48 | (v7 = 0) & aInteger0(v6) = v7)))))) % 19.81/3.48 | (28) ? [v0: $i] : (sdtasdt0(xq, v0) = all_41_1 & aInteger0(v0) = 0 & % 19.81/3.48 | $i(v0)) % 19.81/3.48 | % 19.81/3.48 | DELTA: instantiating (28) with fresh symbol all_44_0 gives: % 19.81/3.48 | (29) sdtasdt0(xq, all_44_0) = all_41_1 & aInteger0(all_44_0) = 0 & % 19.81/3.48 | $i(all_44_0) % 19.81/3.48 | % 19.81/3.48 | ALPHA: (29) implies: % 19.81/3.48 | (30) $i(all_44_0) % 19.81/3.48 | (31) aInteger0(all_44_0) = 0 % 19.81/3.48 | (32) sdtasdt0(xq, all_44_0) = all_41_1 % 19.81/3.48 | % 19.81/3.48 | GROUND_INST: instantiating (mIntNeg) with xa, all_41_5, simplifying with (8), % 19.81/3.48 | (19) gives: % 19.81/3.48 | (33) ? [v0: any] : ? [v1: any] : (aInteger0(all_41_5) = v1 & % 19.81/3.48 | aInteger0(xa) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 19.81/3.48 | % 19.81/3.48 | GROUND_INST: instantiating (mIntNeg) with xb, all_41_2, simplifying with (10), % 19.81/3.48 | (20) gives: % 19.81/3.48 | (34) ? [v0: any] : ? [v1: any] : (aInteger0(all_41_2) = v1 & % 19.81/3.48 | aInteger0(xb) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 19.81/3.48 | % 19.81/3.49 | GROUND_INST: instantiating (mAddComm) with xc, all_41_2, all_41_1, simplifying % 19.81/3.49 | with (11), (17), (21) gives: % 19.81/3.49 | (35) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(all_41_2, xc) = % 19.81/3.49 | v2 & aInteger0(all_41_2) = v1 & aInteger0(xc) = v0 & $i(v2) & ( ~ % 19.81/3.49 | (v1 = 0) | ~ (v0 = 0) | v2 = all_41_1)) % 19.81/3.49 | % 19.81/3.49 | GROUND_INST: instantiating (mIntPlus) with xc, all_41_2, all_41_1, simplifying % 19.81/3.49 | with (11), (17), (21) gives: % 19.81/3.49 | (36) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aInteger0(all_41_1) = v2 % 19.81/3.49 | & aInteger0(all_41_2) = v1 & aInteger0(xc) = v0 & ( ~ (v1 = 0) | ~ % 19.81/3.49 | (v0 = 0) | v2 = 0)) % 19.81/3.49 | % 19.81/3.49 | GROUND_INST: instantiating (mMulComm) with xq, all_44_0, all_41_1, simplifying % 19.81/3.49 | with (9), (30), (32) gives: % 19.81/3.49 | (37) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(all_44_0, xq) = % 19.81/3.49 | v2 & aInteger0(all_44_0) = v1 & aInteger0(xq) = v0 & $i(v2) & ( ~ % 19.81/3.49 | (v1 = 0) | ~ (v0 = 0) | v2 = all_41_1)) % 19.81/3.49 | % 19.81/3.49 | GROUND_INST: instantiating (mIntMult) with xq, all_44_0, all_41_1, simplifying % 19.81/3.49 | with (9), (30), (32) gives: % 19.81/3.49 | (38) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aInteger0(all_44_0) = v1 % 19.81/3.49 | & aInteger0(all_41_1) = v2 & aInteger0(xq) = v0 & ( ~ (v1 = 0) | ~ % 19.81/3.49 | (v0 = 0) | v2 = 0)) % 19.81/3.49 | % 19.81/3.49 | GROUND_INST: instantiating (2) with xc, xb, xq, simplifying with (9), (10), % 19.81/3.49 | (11), (23) gives: % 19.81/3.49 | (39) xq = sz00 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] % 19.81/3.49 | : (sdteqdtlpzmzozddtrp0(xb, xc, xq) = v3 & aInteger0(xc) = v0 & % 19.81/3.49 | aInteger0(xb) = v1 & aInteger0(xq) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) % 19.81/3.49 | | ~ (v0 = 0) | v3 = 0)) % 19.81/3.49 | % 19.81/3.49 | GROUND_INST: instantiating (27) with xb, all_41_4, simplifying with (10), (24) % 19.81/3.49 | gives: % 19.81/3.49 | (40) all_41_4 = 0 | ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: % 19.81/3.49 | any] : (sdteqdtlpzmzozddtrp0(xb, xa, xq) = v3 & aDivisorOf0(xq, v1) % 19.81/3.49 | = v2 & sdtpldt0(xb, all_41_5) = v1 & aInteger0(xb) = v0 & $i(v1) & ( % 19.81/3.49 | ~ (v0 = 0) | ( ~ (v3 = 0) & ~ (v2 = 0) & ! [v4: $i] : ( ~ % 19.81/3.49 | (sdtasdt0(xq, v4) = v1) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = % 19.81/3.49 | 0) & aInteger0(v4) = v5))))) % 19.81/3.49 | % 19.81/3.49 | GROUND_INST: instantiating (26) with xc, simplifying with (11), (25) gives: % 19.81/3.49 | (41) ? [v0: $i] : (sdteqdtlpzmzozddtrp0(xc, xa, xq) = 0 & aDivisorOf0(xq, % 19.81/3.49 | v0) = 0 & sdtpldt0(xc, all_41_5) = v0 & aInteger0(xc) = 0 & $i(v0) % 19.81/3.49 | & ? [v1: $i] : (sdtasdt0(xq, v1) = v0 & aInteger0(v1) = 0 & % 19.81/3.49 | $i(v1))) % 19.81/3.49 | % 19.81/3.49 | DELTA: instantiating (34) with fresh symbols all_64_0, all_64_1 gives: % 19.81/3.49 | (42) aInteger0(all_41_2) = all_64_0 & aInteger0(xb) = all_64_1 & ( ~ % 19.81/3.49 | (all_64_1 = 0) | all_64_0 = 0) % 19.81/3.49 | % 19.81/3.49 | ALPHA: (42) implies: % 19.81/3.49 | (43) aInteger0(xb) = all_64_1 % 19.81/3.49 | % 19.81/3.49 | DELTA: instantiating (33) with fresh symbols all_66_0, all_66_1 gives: % 19.81/3.49 | (44) aInteger0(all_41_5) = all_66_0 & aInteger0(xa) = all_66_1 & ( ~ % 19.81/3.49 | (all_66_1 = 0) | all_66_0 = 0) % 19.81/3.49 | % 19.81/3.49 | ALPHA: (44) implies: % 19.81/3.49 | (45) aInteger0(xa) = all_66_1 % 19.81/3.49 | % 19.81/3.49 | DELTA: instantiating (38) with fresh symbols all_70_0, all_70_1, all_70_2 % 19.81/3.49 | gives: % 19.81/3.49 | (46) aInteger0(all_44_0) = all_70_1 & aInteger0(all_41_1) = all_70_0 & % 19.81/3.49 | aInteger0(xq) = all_70_2 & ( ~ (all_70_1 = 0) | ~ (all_70_2 = 0) | % 19.81/3.49 | all_70_0 = 0) % 19.81/3.49 | % 19.81/3.49 | ALPHA: (46) implies: % 19.81/3.49 | (47) aInteger0(xq) = all_70_2 % 19.81/3.49 | (48) aInteger0(all_41_1) = all_70_0 % 19.81/3.49 | (49) aInteger0(all_44_0) = all_70_1 % 19.81/3.50 | (50) ~ (all_70_1 = 0) | ~ (all_70_2 = 0) | all_70_0 = 0 % 19.81/3.50 | % 19.81/3.50 | DELTA: instantiating (36) with fresh symbols all_72_0, all_72_1, all_72_2 % 19.81/3.50 | gives: % 19.81/3.50 | (51) aInteger0(all_41_1) = all_72_0 & aInteger0(all_41_2) = all_72_1 & % 19.81/3.50 | aInteger0(xc) = all_72_2 & ( ~ (all_72_1 = 0) | ~ (all_72_2 = 0) | % 19.81/3.50 | all_72_0 = 0) % 19.81/3.50 | % 19.81/3.50 | ALPHA: (51) implies: % 19.81/3.50 | (52) aInteger0(xc) = all_72_2 % 19.81/3.50 | (53) aInteger0(all_41_1) = all_72_0 % 19.81/3.50 | % 19.81/3.50 | DELTA: instantiating (37) with fresh symbols all_74_0, all_74_1, all_74_2 % 19.81/3.50 | gives: % 19.81/3.50 | (54) sdtasdt0(all_44_0, xq) = all_74_0 & aInteger0(all_44_0) = all_74_1 & % 19.81/3.50 | aInteger0(xq) = all_74_2 & $i(all_74_0) & ( ~ (all_74_1 = 0) | ~ % 19.81/3.50 | (all_74_2 = 0) | all_74_0 = all_41_1) % 19.81/3.50 | % 19.81/3.50 | ALPHA: (54) implies: % 19.81/3.50 | (55) aInteger0(xq) = all_74_2 % 19.81/3.50 | (56) aInteger0(all_44_0) = all_74_1 % 19.81/3.50 | % 19.81/3.50 | DELTA: instantiating (35) with fresh symbols all_76_0, all_76_1, all_76_2 % 19.81/3.50 | gives: % 19.81/3.50 | (57) sdtpldt0(all_41_2, xc) = all_76_0 & aInteger0(all_41_2) = all_76_1 & % 19.81/3.50 | aInteger0(xc) = all_76_2 & $i(all_76_0) & ( ~ (all_76_1 = 0) | ~ % 19.81/3.50 | (all_76_2 = 0) | all_76_0 = all_41_1) % 19.81/3.50 | % 19.81/3.50 | ALPHA: (57) implies: % 19.81/3.50 | (58) aInteger0(xc) = all_76_2 % 19.81/3.50 | % 19.81/3.50 | DELTA: instantiating (41) with fresh symbol all_78_0 gives: % 19.81/3.50 | (59) sdteqdtlpzmzozddtrp0(xc, xa, xq) = 0 & aDivisorOf0(xq, all_78_0) = 0 & % 19.81/3.50 | sdtpldt0(xc, all_41_5) = all_78_0 & aInteger0(xc) = 0 & $i(all_78_0) & % 19.81/3.50 | ? [v0: $i] : (sdtasdt0(xq, v0) = all_78_0 & aInteger0(v0) = 0 & % 19.81/3.50 | $i(v0)) % 19.81/3.50 | % 19.81/3.50 | ALPHA: (59) implies: % 19.81/3.50 | (60) aInteger0(xc) = 0 % 19.81/3.50 | (61) sdteqdtlpzmzozddtrp0(xc, xa, xq) = 0 % 19.81/3.50 | % 19.81/3.50 | BETA: splitting (39) gives: % 19.81/3.50 | % 19.81/3.50 | Case 1: % 19.81/3.50 | | % 19.81/3.50 | | (62) xq = sz00 % 19.81/3.50 | | % 19.81/3.50 | | REDUCE: (4), (62) imply: % 19.81/3.50 | | (63) $false % 19.81/3.50 | | % 19.81/3.50 | | CLOSE: (63) is inconsistent. % 19.81/3.50 | | % 19.81/3.50 | Case 2: % 19.81/3.50 | | % 19.81/3.50 | | (64) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 19.81/3.50 | | (sdteqdtlpzmzozddtrp0(xb, xc, xq) = v3 & aInteger0(xc) = v0 & % 19.81/3.50 | | aInteger0(xb) = v1 & aInteger0(xq) = v2 & ( ~ (v2 = 0) | ~ (v1 = % 19.81/3.50 | | 0) | ~ (v0 = 0) | v3 = 0)) % 19.81/3.50 | | % 19.81/3.50 | | DELTA: instantiating (64) with fresh symbols all_86_0, all_86_1, all_86_2, % 19.81/3.50 | | all_86_3 gives: % 19.81/3.50 | | (65) sdteqdtlpzmzozddtrp0(xb, xc, xq) = all_86_0 & aInteger0(xc) = % 19.81/3.50 | | all_86_3 & aInteger0(xb) = all_86_2 & aInteger0(xq) = all_86_1 & ( ~ % 19.81/3.50 | | (all_86_1 = 0) | ~ (all_86_2 = 0) | ~ (all_86_3 = 0) | all_86_0 % 19.81/3.50 | | = 0) % 19.81/3.50 | | % 19.81/3.50 | | ALPHA: (65) implies: % 19.81/3.50 | | (66) aInteger0(xq) = all_86_1 % 19.81/3.50 | | (67) aInteger0(xb) = all_86_2 % 19.81/3.50 | | (68) aInteger0(xc) = all_86_3 % 19.81/3.50 | | (69) sdteqdtlpzmzozddtrp0(xb, xc, xq) = all_86_0 % 19.81/3.50 | | (70) ~ (all_86_1 = 0) | ~ (all_86_2 = 0) | ~ (all_86_3 = 0) | all_86_0 % 19.81/3.50 | | = 0 % 19.81/3.50 | | % 19.81/3.50 | | BETA: splitting (40) gives: % 19.81/3.50 | | % 19.81/3.50 | | Case 1: % 19.81/3.50 | | | % 19.81/3.50 | | | (71) all_41_4 = 0 % 19.81/3.50 | | | % 19.81/3.50 | | | REDUCE: (16), (71) imply: % 19.81/3.50 | | | (72) $false % 19.81/3.50 | | | % 19.81/3.50 | | | CLOSE: (72) is inconsistent. % 19.81/3.50 | | | % 19.81/3.50 | | Case 2: % 19.81/3.50 | | | % 19.81/3.50 | | | (73) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : % 19.81/3.50 | | | (sdteqdtlpzmzozddtrp0(xb, xa, xq) = v3 & aDivisorOf0(xq, v1) = v2 % 19.81/3.50 | | | & sdtpldt0(xb, all_41_5) = v1 & aInteger0(xb) = v0 & $i(v1) & ( % 19.81/3.50 | | | ~ (v0 = 0) | ( ~ (v3 = 0) & ~ (v2 = 0) & ! [v4: $i] : ( ~ % 19.81/3.50 | | | (sdtasdt0(xq, v4) = v1) | ~ $i(v4) | ? [v5: int] : ( ~ % 19.81/3.50 | | | (v5 = 0) & aInteger0(v4) = v5))))) % 19.81/3.50 | | | % 19.81/3.50 | | | DELTA: instantiating (73) with fresh symbols all_91_0, all_91_1, all_91_2, % 19.81/3.50 | | | all_91_3 gives: % 19.81/3.51 | | | (74) sdteqdtlpzmzozddtrp0(xb, xa, xq) = all_91_0 & aDivisorOf0(xq, % 19.81/3.51 | | | all_91_2) = all_91_1 & sdtpldt0(xb, all_41_5) = all_91_2 & % 19.81/3.51 | | | aInteger0(xb) = all_91_3 & $i(all_91_2) & ( ~ (all_91_3 = 0) | ( ~ % 19.81/3.51 | | | (all_91_0 = 0) & ~ (all_91_1 = 0) & ! [v0: $i] : ( ~ % 19.81/3.51 | | | (sdtasdt0(xq, v0) = all_91_2) | ~ $i(v0) | ? [v1: int] : ( % 19.81/3.51 | | | ~ (v1 = 0) & aInteger0(v0) = v1)))) % 19.81/3.51 | | | % 19.81/3.51 | | | ALPHA: (74) implies: % 19.81/3.51 | | | (75) aInteger0(xb) = all_91_3 % 19.81/3.51 | | | (76) sdteqdtlpzmzozddtrp0(xb, xa, xq) = all_91_0 % 19.81/3.51 | | | (77) ~ (all_91_3 = 0) | ( ~ (all_91_0 = 0) & ~ (all_91_1 = 0) & ! % 19.81/3.51 | | | [v0: $i] : ( ~ (sdtasdt0(xq, v0) = all_91_2) | ~ $i(v0) | ? % 19.81/3.51 | | | [v1: int] : ( ~ (v1 = 0) & aInteger0(v0) = v1))) % 19.81/3.51 | | | % 19.81/3.51 | | | GROUND_INST: instantiating (13) with 0, all_66_1, xa, simplifying with % 19.81/3.51 | | | (5), (45) gives: % 19.81/3.51 | | | (78) all_66_1 = 0 % 19.81/3.51 | | | % 19.81/3.51 | | | GROUND_INST: instantiating (13) with 0, all_74_2, xq, simplifying with % 19.81/3.51 | | | (6), (55) gives: % 19.81/3.51 | | | (79) all_74_2 = 0 % 19.81/3.51 | | | % 19.81/3.51 | | | GROUND_INST: instantiating (13) with all_74_2, all_86_1, xq, simplifying % 19.81/3.51 | | | with (55), (66) gives: % 19.81/3.51 | | | (80) all_86_1 = all_74_2 % 19.81/3.51 | | | % 19.81/3.51 | | | GROUND_INST: instantiating (13) with all_70_2, all_86_1, xq, simplifying % 19.81/3.51 | | | with (47), (66) gives: % 19.81/3.51 | | | (81) all_86_1 = all_70_2 % 19.81/3.51 | | | % 19.81/3.51 | | | GROUND_INST: instantiating (13) with all_64_1, all_86_2, xb, simplifying % 19.81/3.51 | | | with (43), (67) gives: % 19.81/3.51 | | | (82) all_86_2 = all_64_1 % 19.81/3.51 | | | % 19.81/3.51 | | | GROUND_INST: instantiating (13) with 0, all_91_3, xb, simplifying with % 19.81/3.51 | | | (7), (75) gives: % 19.81/3.51 | | | (83) all_91_3 = 0 % 19.81/3.51 | | | % 19.81/3.51 | | | GROUND_INST: instantiating (13) with all_86_2, all_91_3, xb, simplifying % 19.81/3.51 | | | with (67), (75) gives: % 19.81/3.51 | | | (84) all_91_3 = all_86_2 % 19.81/3.51 | | | % 19.81/3.51 | | | GROUND_INST: instantiating (13) with 0, all_86_3, xc, simplifying with % 19.81/3.51 | | | (60), (68) gives: % 19.81/3.51 | | | (85) all_86_3 = 0 % 19.81/3.51 | | | % 19.81/3.51 | | | GROUND_INST: instantiating (13) with all_76_2, all_86_3, xc, simplifying % 19.81/3.51 | | | with (58), (68) gives: % 19.81/3.51 | | | (86) all_86_3 = all_76_2 % 19.81/3.51 | | | % 19.81/3.51 | | | GROUND_INST: instantiating (13) with all_72_2, all_86_3, xc, simplifying % 19.81/3.51 | | | with (52), (68) gives: % 19.81/3.51 | | | (87) all_86_3 = all_72_2 % 19.81/3.51 | | | % 19.81/3.51 | | | GROUND_INST: instantiating (13) with all_70_0, all_72_0, all_41_1, % 19.81/3.51 | | | simplifying with (48), (53) gives: % 19.81/3.51 | | | (88) all_72_0 = all_70_0 % 19.81/3.51 | | | % 19.81/3.51 | | | GROUND_INST: instantiating (13) with 0, all_74_1, all_44_0, simplifying % 19.81/3.51 | | | with (31), (56) gives: % 19.81/3.51 | | | (89) all_74_1 = 0 % 19.81/3.51 | | | % 19.81/3.51 | | | GROUND_INST: instantiating (13) with all_70_1, all_74_1, all_44_0, % 19.81/3.51 | | | simplifying with (49), (56) gives: % 19.81/3.51 | | | (90) all_74_1 = all_70_1 % 19.81/3.51 | | | % 19.81/3.51 | | | COMBINE_EQS: (83), (84) imply: % 19.81/3.51 | | | (91) all_86_2 = 0 % 19.81/3.51 | | | % 19.81/3.51 | | | SIMP: (91) implies: % 19.81/3.51 | | | (92) all_86_2 = 0 % 19.81/3.51 | | | % 19.81/3.51 | | | COMBINE_EQS: (80), (81) imply: % 19.81/3.51 | | | (93) all_74_2 = all_70_2 % 19.81/3.51 | | | % 19.81/3.51 | | | SIMP: (93) implies: % 19.81/3.51 | | | (94) all_74_2 = all_70_2 % 19.81/3.51 | | | % 19.81/3.51 | | | COMBINE_EQS: (82), (92) imply: % 19.81/3.51 | | | (95) all_64_1 = 0 % 19.81/3.51 | | | % 19.81/3.51 | | | SIMP: (95) implies: % 19.81/3.51 | | | (96) all_64_1 = 0 % 19.81/3.51 | | | % 19.81/3.51 | | | COMBINE_EQS: (86), (87) imply: % 19.81/3.51 | | | (97) all_76_2 = all_72_2 % 19.81/3.51 | | | % 19.81/3.51 | | | COMBINE_EQS: (85), (86) imply: % 19.81/3.51 | | | (98) all_76_2 = 0 % 19.81/3.51 | | | % 19.81/3.51 | | | COMBINE_EQS: (97), (98) imply: % 19.81/3.51 | | | (99) all_72_2 = 0 % 19.81/3.51 | | | % 19.81/3.51 | | | SIMP: (99) implies: % 19.81/3.51 | | | (100) all_72_2 = 0 % 19.81/3.51 | | | % 19.81/3.51 | | | COMBINE_EQS: (89), (90) imply: % 19.81/3.51 | | | (101) all_70_1 = 0 % 19.81/3.51 | | | % 19.81/3.51 | | | COMBINE_EQS: (79), (94) imply: % 19.81/3.51 | | | (102) all_70_2 = 0 % 19.81/3.51 | | | % 19.81/3.51 | | | COMBINE_EQS: (81), (102) imply: % 19.81/3.51 | | | (103) all_86_1 = 0 % 19.81/3.51 | | | % 19.81/3.51 | | | BETA: splitting (50) gives: % 19.81/3.51 | | | % 19.81/3.51 | | | Case 1: % 19.81/3.51 | | | | % 19.81/3.51 | | | | (104) ~ (all_70_1 = 0) % 19.81/3.51 | | | | % 19.81/3.51 | | | | REDUCE: (101), (104) imply: % 19.81/3.51 | | | | (105) $false % 19.81/3.51 | | | | % 19.81/3.51 | | | | CLOSE: (105) is inconsistent. % 19.81/3.51 | | | | % 19.81/3.51 | | | Case 2: % 19.81/3.51 | | | | % 19.81/3.51 | | | | (106) ~ (all_70_2 = 0) | all_70_0 = 0 % 19.81/3.51 | | | | % 19.81/3.51 | | | | BETA: splitting (106) gives: % 19.81/3.51 | | | | % 19.81/3.51 | | | | Case 1: % 19.81/3.51 | | | | | % 19.81/3.51 | | | | | (107) ~ (all_70_2 = 0) % 19.81/3.51 | | | | | % 19.81/3.51 | | | | | REDUCE: (102), (107) imply: % 19.81/3.51 | | | | | (108) $false % 19.81/3.51 | | | | | % 19.81/3.51 | | | | | CLOSE: (108) is inconsistent. % 19.81/3.51 | | | | | % 19.81/3.51 | | | | Case 2: % 19.81/3.51 | | | | | % 19.81/3.51 | | | | | (109) all_70_0 = 0 % 19.81/3.51 | | | | | % 19.81/3.51 | | | | | REDUCE: (48), (109) imply: % 19.81/3.51 | | | | | (110) aInteger0(all_41_1) = 0 % 19.81/3.51 | | | | | % 19.81/3.51 | | | | | BETA: splitting (77) gives: % 19.81/3.51 | | | | | % 19.81/3.51 | | | | | Case 1: % 19.81/3.51 | | | | | | % 19.81/3.51 | | | | | | (111) ~ (all_91_3 = 0) % 19.81/3.51 | | | | | | % 19.81/3.51 | | | | | | REDUCE: (83), (111) imply: % 19.81/3.51 | | | | | | (112) $false % 19.81/3.51 | | | | | | % 19.81/3.51 | | | | | | CLOSE: (112) is inconsistent. % 19.81/3.51 | | | | | | % 19.81/3.51 | | | | | Case 2: % 19.81/3.51 | | | | | | % 19.81/3.51 | | | | | | (113) ~ (all_91_0 = 0) & ~ (all_91_1 = 0) & ! [v0: $i] : ( ~ % 19.81/3.51 | | | | | | (sdtasdt0(xq, v0) = all_91_2) | ~ $i(v0) | ? [v1: int] % 19.81/3.51 | | | | | | : ( ~ (v1 = 0) & aInteger0(v0) = v1)) % 19.81/3.51 | | | | | | % 19.81/3.51 | | | | | | ALPHA: (113) implies: % 19.81/3.51 | | | | | | (114) ~ (all_91_0 = 0) % 19.81/3.51 | | | | | | % 19.81/3.51 | | | | | | BETA: splitting (70) gives: % 19.81/3.51 | | | | | | % 19.81/3.51 | | | | | | Case 1: % 19.81/3.51 | | | | | | | % 19.81/3.51 | | | | | | | (115) ~ (all_86_1 = 0) % 19.81/3.51 | | | | | | | % 19.81/3.51 | | | | | | | REDUCE: (103), (115) imply: % 19.81/3.51 | | | | | | | (116) $false % 19.81/3.51 | | | | | | | % 19.81/3.51 | | | | | | | CLOSE: (116) is inconsistent. % 19.81/3.51 | | | | | | | % 19.81/3.51 | | | | | | Case 2: % 19.81/3.51 | | | | | | | % 19.81/3.52 | | | | | | | (117) ~ (all_86_2 = 0) | ~ (all_86_3 = 0) | all_86_0 = 0 % 19.81/3.52 | | | | | | | % 19.81/3.52 | | | | | | | BETA: splitting (117) gives: % 19.81/3.52 | | | | | | | % 19.81/3.52 | | | | | | | Case 1: % 19.81/3.52 | | | | | | | | % 19.81/3.52 | | | | | | | | (118) ~ (all_86_2 = 0) % 19.81/3.52 | | | | | | | | % 19.81/3.52 | | | | | | | | REDUCE: (92), (118) imply: % 19.81/3.52 | | | | | | | | (119) $false % 19.81/3.52 | | | | | | | | % 19.81/3.52 | | | | | | | | CLOSE: (119) is inconsistent. % 19.81/3.52 | | | | | | | | % 19.81/3.52 | | | | | | | Case 2: % 19.81/3.52 | | | | | | | | % 19.81/3.52 | | | | | | | | (120) ~ (all_86_3 = 0) | all_86_0 = 0 % 19.81/3.52 | | | | | | | | % 19.81/3.52 | | | | | | | | BETA: splitting (120) gives: % 19.81/3.52 | | | | | | | | % 19.81/3.52 | | | | | | | | Case 1: % 19.81/3.52 | | | | | | | | | % 19.81/3.52 | | | | | | | | | (121) ~ (all_86_3 = 0) % 19.81/3.52 | | | | | | | | | % 19.81/3.52 | | | | | | | | | REDUCE: (85), (121) imply: % 19.81/3.52 | | | | | | | | | (122) $false % 19.81/3.52 | | | | | | | | | % 19.81/3.52 | | | | | | | | | CLOSE: (122) is inconsistent. % 19.81/3.52 | | | | | | | | | % 19.81/3.52 | | | | | | | | Case 2: % 19.81/3.52 | | | | | | | | | % 19.81/3.52 | | | | | | | | | (123) all_86_0 = 0 % 19.81/3.52 | | | | | | | | | % 19.81/3.52 | | | | | | | | | REDUCE: (69), (123) imply: % 19.81/3.52 | | | | | | | | | (124) sdteqdtlpzmzozddtrp0(xb, xc, xq) = 0 % 19.81/3.52 | | | | | | | | | % 19.81/3.52 | | | | | | | | | GROUND_INST: instantiating (1) with all_41_1, simplifying with % 19.81/3.52 | | | | | | | | | (18), (110) gives: % 19.81/3.52 | | | | | | | | | (125) ! [v0: $i] : ! [v1: int] : (v1 = 0 | v0 = sz00 | ~ % 19.81/3.52 | | | | | | | | | (aDivisorOf0(v0, all_41_1) = v1) | ~ $i(v0) | ? % 19.81/3.52 | | | | | | | | | [v2: int] : ( ~ (v2 = 0) & aInteger0(v0) = v2) | ! % 19.81/3.52 | | | | | | | | | [v2: $i] : ( ~ (sdtasdt0(v0, v2) = all_41_1) | ~ % 19.81/3.52 | | | | | | | | | $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & % 19.81/3.52 | | | | | | | | | aInteger0(v2) = v3))) & ! [v0: $i] : ( ~ % 19.81/3.52 | | | | | | | | | (aDivisorOf0(v0, all_41_1) = 0) | ~ $i(v0) | ( ~ % 19.81/3.52 | | | | | | | | | (v0 = sz00) & aInteger0(v0) = 0 & ? [v1: $i] : % 19.81/3.52 | | | | | | | | | (sdtasdt0(v0, v1) = all_41_1 & aInteger0(v1) = 0 % 19.81/3.52 | | | | | | | | | & $i(v1)))) % 19.81/3.52 | | | | | | | | | % 19.81/3.52 | | | | | | | | | ALPHA: (125) implies: % 19.81/3.52 | | | | | | | | | (126) ! [v0: $i] : ( ~ (aDivisorOf0(v0, all_41_1) = 0) | % 19.81/3.52 | | | | | | | | | ~ $i(v0) | ( ~ (v0 = sz00) & aInteger0(v0) = 0 & ? % 19.81/3.52 | | | | | | | | | [v1: $i] : (sdtasdt0(v0, v1) = all_41_1 & % 19.81/3.52 | | | | | | | | | aInteger0(v1) = 0 & $i(v1)))) % 19.81/3.52 | | | | | | | | | % 19.81/3.52 | | | | | | | | | GROUND_INST: instantiating (3) with xb, xc, xq, xa, all_91_0, % 19.81/3.52 | | | | | | | | | simplifying with (8), (9), (10), (11), (76), (124) % 19.81/3.52 | | | | | | | | | gives: % 19.81/3.52 | | | | | | | | | (127) all_91_0 = 0 | xq = sz00 | ? [v0: any] : ? [v1: % 19.81/3.52 | | | | | | | | | any] : ? [v2: any] : ? [v3: any] : ? [v4: any] : % 19.81/3.52 | | | | | | | | | (sdteqdtlpzmzozddtrp0(xc, xa, xq) = v4 & % 19.81/3.52 | | | | | | | | | aInteger0(xc) = v1 & aInteger0(xb) = v0 & % 19.81/3.52 | | | | | | | | | aInteger0(xq) = v2 & aInteger0(xa) = v3 & ( ~ (v4 = % 19.81/3.52 | | | | | | | | | 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | % 19.81/3.52 | | | | | | | | | ~ (v0 = 0))) % 19.81/3.52 | | | | | | | | | % 19.81/3.52 | | | | | | | | | GROUND_INST: instantiating (126) with xq, simplifying with (9), % 19.81/3.52 | | | | | | | | | (22) gives: % 19.81/3.52 | | | | | | | | | (128) ~ (xq = sz00) & aInteger0(xq) = 0 & ? [v0: $i] : % 19.81/3.52 | | | | | | | | | (sdtasdt0(xq, v0) = all_41_1 & aInteger0(v0) = 0 & % 19.81/3.52 | | | | | | | | | $i(v0)) % 19.81/3.52 | | | | | | | | | % 19.81/3.52 | | | | | | | | | BETA: splitting (127) gives: % 19.81/3.52 | | | | | | | | | % 19.81/3.52 | | | | | | | | | Case 1: % 19.81/3.52 | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | (129) xq = sz00 % 19.81/3.52 | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | REDUCE: (4), (129) imply: % 19.81/3.52 | | | | | | | | | | (130) $false % 19.81/3.52 | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | CLOSE: (130) is inconsistent. % 19.81/3.52 | | | | | | | | | | % 19.81/3.52 | | | | | | | | | Case 2: % 19.81/3.52 | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | (131) all_91_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 19.81/3.52 | | | | | | | | | | [v2: any] : ? [v3: any] : ? [v4: any] : % 19.81/3.52 | | | | | | | | | | (sdteqdtlpzmzozddtrp0(xc, xa, xq) = v4 & % 19.81/3.52 | | | | | | | | | | aInteger0(xc) = v1 & aInteger0(xb) = v0 & % 19.81/3.52 | | | | | | | | | | aInteger0(xq) = v2 & aInteger0(xa) = v3 & ( ~ (v4 % 19.81/3.52 | | | | | | | | | | = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = % 19.81/3.52 | | | | | | | | | | 0) | ~ (v0 = 0))) % 19.81/3.52 | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | BETA: splitting (131) gives: % 19.81/3.52 | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | Case 1: % 19.81/3.52 | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | (132) all_91_0 = 0 % 19.81/3.52 | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | REDUCE: (114), (132) imply: % 19.81/3.52 | | | | | | | | | | | (133) $false % 19.81/3.52 | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | CLOSE: (133) is inconsistent. % 19.81/3.52 | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | Case 2: % 19.81/3.52 | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | (134) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 19.81/3.52 | | | | | | | | | | | [v3: any] : ? [v4: any] : % 19.81/3.52 | | | | | | | | | | | (sdteqdtlpzmzozddtrp0(xc, xa, xq) = v4 & % 19.81/3.52 | | | | | | | | | | | aInteger0(xc) = v1 & aInteger0(xb) = v0 & % 19.81/3.52 | | | | | | | | | | | aInteger0(xq) = v2 & aInteger0(xa) = v3 & ( ~ % 19.81/3.52 | | | | | | | | | | | (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 % 19.81/3.52 | | | | | | | | | | | = 0) | ~ (v0 = 0))) % 19.81/3.52 | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | DELTA: instantiating (134) with fresh symbols all_257_0, % 19.81/3.52 | | | | | | | | | | | all_257_1, all_257_2, all_257_3, all_257_4 gives: % 19.81/3.52 | | | | | | | | | | | (135) sdteqdtlpzmzozddtrp0(xc, xa, xq) = all_257_0 & % 19.81/3.52 | | | | | | | | | | | aInteger0(xc) = all_257_3 & aInteger0(xb) = % 19.81/3.52 | | | | | | | | | | | all_257_4 & aInteger0(xq) = all_257_2 & % 19.81/3.52 | | | | | | | | | | | aInteger0(xa) = all_257_1 & ( ~ (all_257_0 = 0) | % 19.81/3.52 | | | | | | | | | | | ~ (all_257_1 = 0) | ~ (all_257_2 = 0) | ~ % 19.81/3.52 | | | | | | | | | | | (all_257_3 = 0) | ~ (all_257_4 = 0)) % 19.81/3.52 | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | ALPHA: (135) implies: % 19.81/3.52 | | | | | | | | | | | (136) aInteger0(xa) = all_257_1 % 19.81/3.52 | | | | | | | | | | | (137) aInteger0(xq) = all_257_2 % 19.81/3.52 | | | | | | | | | | | (138) aInteger0(xb) = all_257_4 % 19.81/3.52 | | | | | | | | | | | (139) aInteger0(xc) = all_257_3 % 19.81/3.52 | | | | | | | | | | | (140) sdteqdtlpzmzozddtrp0(xc, xa, xq) = all_257_0 % 19.81/3.52 | | | | | | | | | | | (141) ~ (all_257_0 = 0) | ~ (all_257_1 = 0) | ~ % 19.81/3.52 | | | | | | | | | | | (all_257_2 = 0) | ~ (all_257_3 = 0) | ~ % 19.81/3.52 | | | | | | | | | | | (all_257_4 = 0) % 19.81/3.52 | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_257_1, xa, % 19.81/3.52 | | | | | | | | | | | simplifying with (5), (136) gives: % 19.81/3.52 | | | | | | | | | | | (142) all_257_1 = 0 % 19.81/3.52 | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_257_2, xq, % 19.81/3.52 | | | | | | | | | | | simplifying with (6), (137) gives: % 19.81/3.52 | | | | | | | | | | | (143) all_257_2 = 0 % 19.81/3.52 | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_257_4, xb, % 19.81/3.52 | | | | | | | | | | | simplifying with (7), (138) gives: % 19.81/3.52 | | | | | | | | | | | (144) all_257_4 = 0 % 19.81/3.52 | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_257_3, xc, % 19.81/3.52 | | | | | | | | | | | simplifying with (60), (139) gives: % 19.81/3.52 | | | | | | | | | | | (145) all_257_3 = 0 % 19.81/3.52 | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_257_0, xq, xa, xc, % 19.81/3.52 | | | | | | | | | | | simplifying with (61), (140) gives: % 19.81/3.52 | | | | | | | | | | | (146) all_257_0 = 0 % 19.81/3.52 | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | BETA: splitting (141) gives: % 19.81/3.52 | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | Case 1: % 19.81/3.52 | | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | | (147) ~ (all_257_0 = 0) % 19.81/3.52 | | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | | REDUCE: (146), (147) imply: % 19.81/3.52 | | | | | | | | | | | | (148) $false % 19.81/3.52 | | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | | CLOSE: (148) is inconsistent. % 19.81/3.52 | | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | Case 2: % 19.81/3.52 | | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | | (149) ~ (all_257_1 = 0) | ~ (all_257_2 = 0) | ~ % 19.81/3.52 | | | | | | | | | | | | (all_257_3 = 0) | ~ (all_257_4 = 0) % 19.81/3.52 | | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | | BETA: splitting (149) gives: % 19.81/3.52 | | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | | Case 1: % 19.81/3.52 | | | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | | | (150) ~ (all_257_1 = 0) % 19.81/3.52 | | | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | | | REDUCE: (142), (150) imply: % 19.81/3.52 | | | | | | | | | | | | | (151) $false % 19.81/3.52 | | | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | | | CLOSE: (151) is inconsistent. % 19.81/3.52 | | | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | | Case 2: % 19.81/3.52 | | | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | | | (152) ~ (all_257_2 = 0) | ~ (all_257_3 = 0) | ~ % 19.81/3.52 | | | | | | | | | | | | | (all_257_4 = 0) % 19.81/3.52 | | | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | | | BETA: splitting (152) gives: % 19.81/3.52 | | | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | | | Case 1: % 19.81/3.52 | | | | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | | | | (153) ~ (all_257_2 = 0) % 19.81/3.52 | | | | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | | | | REDUCE: (143), (153) imply: % 19.81/3.52 | | | | | | | | | | | | | | (154) $false % 19.81/3.52 | | | | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | | | | CLOSE: (154) is inconsistent. % 19.81/3.52 | | | | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | | | Case 2: % 19.81/3.52 | | | | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | | | | (155) ~ (all_257_3 = 0) | ~ (all_257_4 = 0) % 19.81/3.52 | | | | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | | | | BETA: splitting (155) gives: % 19.81/3.52 | | | | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | | | | Case 1: % 19.81/3.52 | | | | | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | | | | | (156) ~ (all_257_3 = 0) % 19.81/3.52 | | | | | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | | | | | REDUCE: (145), (156) imply: % 19.81/3.52 | | | | | | | | | | | | | | | (157) $false % 19.81/3.52 | | | | | | | | | | | | | | | % 19.81/3.52 | | | | | | | | | | | | | | | CLOSE: (157) is inconsistent. % 19.81/3.52 | | | | | | | | | | | | | | | % 19.81/3.53 | | | | | | | | | | | | | | Case 2: % 19.81/3.53 | | | | | | | | | | | | | | | % 19.81/3.53 | | | | | | | | | | | | | | | (158) ~ (all_257_4 = 0) % 19.81/3.53 | | | | | | | | | | | | | | | % 19.81/3.53 | | | | | | | | | | | | | | | REDUCE: (144), (158) imply: % 19.81/3.53 | | | | | | | | | | | | | | | (159) $false % 19.81/3.53 | | | | | | | | | | | | | | | % 19.81/3.53 | | | | | | | | | | | | | | | CLOSE: (159) is inconsistent. % 19.81/3.53 | | | | | | | | | | | | | | | % 19.81/3.53 | | | | | | | | | | | | | | End of split % 19.81/3.53 | | | | | | | | | | | | | | % 19.81/3.53 | | | | | | | | | | | | | End of split % 19.81/3.53 | | | | | | | | | | | | | % 19.81/3.53 | | | | | | | | | | | | End of split % 19.81/3.53 | | | | | | | | | | | | % 19.81/3.53 | | | | | | | | | | | End of split % 19.81/3.53 | | | | | | | | | | | % 19.81/3.53 | | | | | | | | | | End of split % 19.81/3.53 | | | | | | | | | | % 19.81/3.53 | | | | | | | | | End of split % 19.81/3.53 | | | | | | | | | % 19.81/3.53 | | | | | | | | End of split % 19.81/3.53 | | | | | | | | % 19.81/3.53 | | | | | | | End of split % 19.81/3.53 | | | | | | | % 19.81/3.53 | | | | | | End of split % 19.81/3.53 | | | | | | % 19.81/3.53 | | | | | End of split % 19.81/3.53 | | | | | % 19.81/3.53 | | | | End of split % 19.81/3.53 | | | | % 19.81/3.53 | | | End of split % 19.81/3.53 | | | % 19.81/3.53 | | End of split % 19.81/3.53 | | % 19.81/3.53 | End of split % 19.81/3.53 | % 19.81/3.53 End of proof % 19.81/3.53 % SZS output end Proof for theBenchmark % 19.81/3.53 % 19.81/3.53 2925ms %------------------------------------------------------------------------------