%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM455+6 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n025.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 11:47:51 EDT 2023 % Result : Theorem 17.38s 3.08s % Output : Proof 22.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM455+6 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n025.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Fri Aug 25 13:05:22 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.62 ________ _____ % 0.19/0.62 ___ __ \_________(_)________________________________ % 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.62 % 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.62 (2023-06-19) % 0.19/0.62 % 0.19/0.62 (c) Philipp Rümmer, 2009-2023 % 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.62 Amanda Stjerna. % 0.19/0.62 Free software under BSD-3-Clause. % 0.19/0.62 % 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.62 % 0.19/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.64 Running up to 7 provers in parallel. % 0.19/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.03/1.35 Prover 1: Preprocessing ... % 4.03/1.36 Prover 4: Preprocessing ... % 4.03/1.39 Prover 5: Preprocessing ... % 4.03/1.39 Prover 6: Preprocessing ... % 4.03/1.40 Prover 0: Preprocessing ... % 4.03/1.40 Prover 2: Preprocessing ... % 4.03/1.40 Prover 3: Preprocessing ... % 12.21/2.39 Prover 1: Constructing countermodel ... % 12.21/2.39 Prover 3: Constructing countermodel ... % 12.76/2.52 Prover 5: Proving ... % 13.47/2.55 Prover 6: Proving ... % 16.29/2.94 Prover 2: Proving ... % 17.38/3.07 Prover 3: proved (2414ms) % 17.38/3.07 % 17.38/3.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 17.38/3.08 % 17.38/3.08 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 17.51/3.08 Prover 6: stopped % 17.51/3.08 Prover 5: stopped % 17.51/3.08 Prover 2: stopped % 17.51/3.09 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 17.51/3.09 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 17.51/3.09 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 18.59/3.23 Prover 7: Preprocessing ... % 18.59/3.24 Prover 8: Preprocessing ... % 18.59/3.30 Prover 10: Preprocessing ... % 18.59/3.31 Prover 11: Preprocessing ... % 18.59/3.36 Prover 1: Found proof (size 87) % 18.59/3.36 Prover 1: proved (2720ms) % 19.20/3.42 Prover 7: stopped % 19.20/3.43 Prover 10: stopped % 20.40/3.47 Prover 4: Constructing countermodel ... % 20.58/3.51 Prover 4: stopped % 20.86/3.54 Prover 11: stopped % 21.29/3.62 Prover 8: Warning: ignoring some quantifiers % 21.29/3.62 Prover 0: Proving ... % 21.29/3.63 Prover 0: stopped % 21.29/3.63 Prover 8: Constructing countermodel ... % 21.29/3.65 Prover 8: stopped % 21.29/3.65 % 21.29/3.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 21.29/3.65 % 21.29/3.67 % SZS output start Proof for theBenchmark % 21.29/3.67 Assumptions after simplification: % 21.29/3.67 --------------------------------- % 21.29/3.67 % 21.29/3.67 (mMulMinOne) % 21.63/3.70 $i(sz10) & ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 21.63/3.70 $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] % 21.63/3.70 : ? [v5: $i] : (sdtasdt0(v1, v0) = v5 & smndt0(v1) = v4 & aInteger0(v1) = % 21.63/3.70 v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | (v5 = v2 & v4 = v2))))) % 21.63/3.70 % 21.63/3.70 (mPrimeDivisor) % 21.63/3.70 $i(sz10) & ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ( ~ % 21.63/3.70 (aInteger0(v1) = 0) | ~ $i(v1) | ((v1 = v0 | v1 = sz10 | ? [v2: $i] : % 21.63/3.70 (isPrime0(v2) = 0 & aDivisorOf0(v2, v1) = 0 & $i(v2))) & ( ! [v2: $i] % 21.63/3.70 : ( ~ (isPrime0(v2) = 0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & % 21.63/3.70 aDivisorOf0(v2, v1) = v3)) | ( ~ (v1 = v0) & ~ (v1 = sz10)))))) % 21.63/3.70 % 21.63/3.70 (m__) % 21.63/3.71 $i(cS2200) & $i(xp) & $i(sz10) & ? [v0: $i] : ? [v1: $i] : % 21.63/3.71 (szAzrzSzezqlpdtcmdtrp0(sz10, xp) = v1 & smndt0(sz10) = v0 & $i(v1) & $i(v0) & % 21.63/3.71 ! [v2: $i] : ! [v3: any] : ( ~ (aElementOf0(v2, v1) = v3) | ~ $i(v2) | ? % 21.63/3.71 [v4: any] : ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? [v8: any] : % 21.63/3.71 (aElementOf0(v2, cS2200) = v8 & sdteqdtlpzmzozddtrp0(v2, sz10, xp) = v7 & % 21.63/3.71 aDivisorOf0(xp, v5) = v6 & sdtpldt0(v2, v0) = v5 & aInteger0(v2) = v4 & % 21.63/3.71 $i(v5) & ((v8 = 0 & (v2 = v0 | v2 = sz10)) | ( ~ (v3 = 0) & ( ~ (v4 = 0) % 21.63/3.71 | ( ~ (v7 = 0) & ~ (v6 = 0) & ! [v9: $i] : ( ~ (sdtasdt0(xp, v9) % 21.63/3.71 = v5) | ~ $i(v9) | ? [v10: int] : ( ~ (v10 = 0) & % 21.63/3.71 aInteger0(v9) = v10))))))))) % 21.63/3.71 % 21.63/3.71 (m__2079) % 21.63/3.71 $i(cS2076) & $i(xS) & $i(sz10) & ? [v0: $i] : ? [v1: $i] : (stldt0(v0) = % 21.63/3.71 cS2076 & sbsmnsldt0(xS) = v0 & aSet0(v0) = 0 & aSet0(cS2076) = 0 & % 21.63/3.71 smndt0(sz10) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: int] : (v3 = 0 | % 21.63/3.71 ~ (aElementOf0(v2, v0) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & % 21.63/3.71 aInteger0(v2) = v4) | ! [v4: $i] : ( ~ (aElementOf0(v4, xS) = 0) | ~ % 21.63/3.71 $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & aElementOf0(v2, v4) = v5))) & ! % 21.63/3.71 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, cS2076) = v3) | ~ % 21.63/3.71 $i(v2) | ? [v4: any] : ? [v5: any] : (aElementOf0(v2, v0) = v5 & % 21.63/3.71 aInteger0(v2) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2: $i] : ! [v3: % 21.63/3.71 int] : (v3 = 0 | ~ (aElementOf0(v2, cS2076) = v3) | ~ $i(v2) | ( ~ (v2 = % 21.63/3.71 v1) & ~ (v2 = sz10))) & ! [v2: $i] : (v2 = v1 | v2 = sz10 | ~ % 21.63/3.71 (aElementOf0(v2, cS2076) = 0) | ~ $i(v2)) & ! [v2: $i] : ( ~ % 21.63/3.71 (aElementOf0(v2, v0) = 0) | ~ $i(v2) | (aInteger0(v2) = 0 & ? [v3: $i] : % 21.63/3.71 (aElementOf0(v3, xS) = 0 & aElementOf0(v2, v3) = 0 & $i(v3)))) & ! [v2: % 21.63/3.71 $i] : ( ~ (aElementOf0(v2, cS2076) = 0) | ~ $i(v2) | ? [v3: int] : ( ~ % 21.63/3.71 (v3 = 0) & aElementOf0(v2, v0) = v3 & aInteger0(v2) = 0))) % 21.63/3.71 % 21.63/3.71 (m__2171) % 21.63/3.72 $i(xp) & $i(xS) & $i(sz10) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 21.63/3.72 $i] : ? [v3: $i] : ( ~ (xp = sz00) & szAzrzSzezqlpdtcmdtrp0(sz10, xp) = v0 % 21.63/3.72 & stldt0(v2) = v3 & sbsmnsldt0(xS) = v2 & aSubsetOf0(v0, v3) = 0 & aSet0(v2) % 21.63/3.72 = 0 & aSet0(v0) = 0 & smndt0(sz10) = v1 & aInteger0(xp) = 0 & $i(v3) & % 21.63/3.72 $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ % 21.63/3.72 (aElementOf0(v4, v3) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: any] : % 21.63/3.72 (aElementOf0(v4, v2) = v7 & aInteger0(v4) = v6 & ( ~ (v6 = 0) | v7 = 0))) % 21.63/3.72 & ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (aElementOf0(v4, v2) = v5) | ~ % 21.63/3.72 $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & aInteger0(v4) = v6) | ! [v6: $i] : % 21.63/3.72 ( ~ (aElementOf0(v6, xS) = 0) | ~ $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & % 21.63/3.72 aElementOf0(v4, v6) = v7))) & ! [v4: $i] : ! [v5: int] : (v5 = 0 | % 21.63/3.72 ~ (aElementOf0(v4, v0) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: $i] : ? % 21.63/3.72 [v8: any] : ? [v9: any] : (sdteqdtlpzmzozddtrp0(v4, sz10, xp) = v9 & % 21.63/3.72 aDivisorOf0(xp, v7) = v8 & sdtpldt0(v4, v1) = v7 & aInteger0(v4) = v6 & % 21.63/3.72 $i(v7) & ( ~ (v6 = 0) | ( ~ (v9 = 0) & ~ (v8 = 0) & ! [v10: $i] : ( ~ % 21.63/3.72 (sdtasdt0(xp, v10) = v7) | ~ $i(v10) | ? [v11: int] : ( ~ (v11 = % 21.63/3.72 0) & aInteger0(v10) = v11)))))) & ! [v4: $i] : ( ~ % 21.63/3.72 (aElementOf0(v4, v3) = 0) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & % 21.63/3.72 aElementOf0(v4, v2) = v5 & aInteger0(v4) = 0)) & ! [v4: $i] : ( ~ % 21.63/3.72 (aElementOf0(v4, v2) = 0) | ~ $i(v4) | (aInteger0(v4) = 0 & ? [v5: $i] : % 21.63/3.72 (aElementOf0(v5, xS) = 0 & aElementOf0(v4, v5) = 0 & $i(v5)))) & ! [v4: % 21.63/3.72 $i] : ( ~ (aElementOf0(v4, v0) = 0) | ~ $i(v4) | aElementOf0(v4, v3) = 0) % 21.63/3.72 & ! [v4: $i] : ( ~ (aElementOf0(v4, v0) = 0) | ~ $i(v4) | ? [v5: $i] : % 21.63/3.72 (sdteqdtlpzmzozddtrp0(v4, sz10, xp) = 0 & aDivisorOf0(xp, v5) = 0 & % 21.63/3.72 sdtpldt0(v4, v1) = v5 & aInteger0(v4) = 0 & $i(v5) & ? [v6: $i] : % 21.63/3.72 (sdtasdt0(xp, v6) = v5 & aInteger0(v6) = 0 & $i(v6))))) % 21.63/3.72 % 21.63/3.72 (m__2232) % 21.63/3.72 $i(xp) & $i(sz10) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 21.63/3.72 [v4: $i] : ? [v5: $i] : ? [v6: $i] : (szAzrzSzezqlpdtcmdtrp0(sz10, xp) = v3 % 21.63/3.72 & aElementOf0(v5, v3) = 0 & aElementOf0(v0, v3) = 0 & % 21.63/3.72 sdteqdtlpzmzozddtrp0(v5, sz10, xp) = 0 & sdteqdtlpzmzozddtrp0(v0, sz10, xp) % 21.63/3.72 = 0 & aDivisorOf0(xp, v6) = 0 & aDivisorOf0(xp, v2) = 0 & sdtpldt0(v5, v1) = % 21.63/3.72 v6 & sdtpldt0(v0, v1) = v2 & sdtpldt0(sz10, v4) = v5 & sdtpldt0(sz10, xp) = % 21.63/3.72 v0 & smndt0(xp) = v4 & smndt0(sz10) = v1 & $i(v6) & $i(v5) & $i(v4) & $i(v3) % 21.63/3.72 & $i(v2) & $i(v1) & $i(v0) & ? [v7: $i] : (sdtasdt0(xp, v7) = v6 & % 21.63/3.72 aInteger0(v7) = 0 & $i(v7)) & ? [v7: $i] : (sdtasdt0(xp, v7) = v2 & % 21.63/3.72 aInteger0(v7) = 0 & $i(v7))) % 21.63/3.72 % 21.63/3.72 (m__2258) % 21.63/3.73 $i(xp) & $i(sz10) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = sz10) % 21.63/3.73 & ~ (v0 = sz10) & sdtpldt0(sz10, v1) = v2 & sdtpldt0(sz10, xp) = v0 & % 21.63/3.73 smndt0(xp) = v1 & $i(v2) & $i(v1) & $i(v0)) % 21.63/3.73 % 21.63/3.73 (m__2286) % 21.63/3.73 $i(xp) & $i(sz10) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 21.63/3.73 (sdtpldt0(sz10, v2) = v3 & sdtpldt0(sz10, xp) = v0 & smndt0(xp) = v2 & % 21.63/3.73 smndt0(sz10) = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v3 = v0) | ~ % 21.63/3.73 (v1 = v0))) % 21.63/3.73 % 21.63/3.73 (function-axioms) % 21.63/3.73 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 21.63/3.73 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v1) % 21.63/3.73 | ~ (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 21.63/3.73 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (szAzrzSzezqlpdtcmdtrp0(v3, v2) = v1) % 21.63/3.73 | ~ (szAzrzSzezqlpdtcmdtrp0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 21.63/3.73 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtslmnbsdt0(v3, v2) = v1) | ~ % 21.63/3.73 (sdtslmnbsdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 21.63/3.73 [v3: $i] : (v1 = v0 | ~ (sdtbsmnsldt0(v3, v2) = v1) | ~ (sdtbsmnsldt0(v3, % 21.63/3.73 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 21.63/3.73 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (aSubsetOf0(v3, v2) = v1) | ~ % 21.63/3.73 (aSubsetOf0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.63/3.73 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.63/3.73 (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) & ! [v0: % 21.63/3.73 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 21.63/3.73 : (v1 = v0 | ~ (aDivisorOf0(v3, v2) = v1) | ~ (aDivisorOf0(v3, v2) = v0)) & % 21.63/3.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.63/3.73 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 21.63/3.73 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | % 21.63/3.73 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.63/3.73 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isFinite0(v2) = v1) | ~ % 21.63/3.73 (isFinite0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.63/3.73 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isClosed0(v2) = v1) | ~ % 21.63/3.73 (isClosed0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.63/3.73 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isOpen0(v2) = v1) | ~ % 21.63/3.73 (isOpen0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 21.63/3.73 ~ (stldt0(v2) = v1) | ~ (stldt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 21.63/3.73 [v2: $i] : (v1 = v0 | ~ (sbsmnsldt0(v2) = v1) | ~ (sbsmnsldt0(v2) = v0)) & % 21.63/3.73 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = % 21.63/3.73 v0 | ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) & ! [v0: MultipleValueBool] % 21.63/3.73 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isPrime0(v2) = v1) % 21.63/3.73 | ~ (isPrime0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 21.63/3.73 v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) & ! [v0: % 21.63/3.73 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 21.63/3.73 ~ (aInteger0(v2) = v1) | ~ (aInteger0(v2) = v0)) % 21.63/3.73 % 21.63/3.73 Further assumptions not needed in the proof: % 21.63/3.73 -------------------------------------------- % 21.63/3.73 mAddAsso, mAddComm, mAddNeg, mAddZero, mArSeq, mArSeqClosed, mClosed, % 21.63/3.73 mComplement, mDistrib, mDivisor, mElements, mEquMod, mEquModMul, mEquModRef, % 21.63/3.73 mEquModSym, mEquModTrn, mFinSet, mIntMult, mIntNeg, mIntOne, mIntPlus, mIntZero, % 21.63/3.73 mIntegers, mInterOpen, mIntersection, mMulAsso, mMulComm, mMulOne, mMulZero, % 21.63/3.73 mOpen, mPrime, mSets, mSubset, mUnion, mUnionClosed, mUnionOpen, mUnionSClosed, % 21.63/3.73 mUnionSet, mZeroDiv, m__2046, m__2117, m__2144 % 21.63/3.73 % 21.63/3.73 Those formulas are unsatisfiable: % 21.63/3.73 --------------------------------- % 21.63/3.73 % 21.63/3.73 Begin of proof % 21.63/3.74 | % 21.63/3.74 | ALPHA: (mMulMinOne) implies: % 21.63/3.74 | (1) ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 21.63/3.74 | ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] % 21.63/3.74 | : ? [v5: $i] : (sdtasdt0(v1, v0) = v5 & smndt0(v1) = v4 & % 21.63/3.74 | aInteger0(v1) = v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | (v5 = v2 & % 21.63/3.74 | v4 = v2))))) % 21.63/3.74 | % 21.63/3.74 | ALPHA: (mPrimeDivisor) implies: % 21.63/3.74 | (2) ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ( ~ % 21.63/3.74 | (aInteger0(v1) = 0) | ~ $i(v1) | ((v1 = v0 | v1 = sz10 | ? [v2: % 21.63/3.74 | $i] : (isPrime0(v2) = 0 & aDivisorOf0(v2, v1) = 0 & $i(v2))) % 21.63/3.74 | & ( ! [v2: $i] : ( ~ (isPrime0(v2) = 0) | ~ $i(v2) | ? [v3: % 21.63/3.74 | int] : ( ~ (v3 = 0) & aDivisorOf0(v2, v1) = v3)) | ( ~ (v1 % 21.63/3.74 | = v0) & ~ (v1 = sz10)))))) % 21.63/3.74 | % 21.63/3.74 | ALPHA: (m__2079) implies: % 21.63/3.74 | (3) ? [v0: $i] : ? [v1: $i] : (stldt0(v0) = cS2076 & sbsmnsldt0(xS) = v0 % 21.63/3.74 | & aSet0(v0) = 0 & aSet0(cS2076) = 0 & smndt0(sz10) = v1 & $i(v1) & % 21.63/3.74 | $i(v0) & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, % 21.63/3.74 | v0) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & % 21.63/3.74 | aInteger0(v2) = v4) | ! [v4: $i] : ( ~ (aElementOf0(v4, xS) = 0) % 21.63/3.74 | | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & aElementOf0(v2, v4) = % 21.63/3.74 | v5))) & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 21.63/3.74 | (aElementOf0(v2, cS2076) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: % 21.63/3.74 | any] : (aElementOf0(v2, v0) = v5 & aInteger0(v2) = v4 & ( ~ (v4 = % 21.63/3.74 | 0) | v5 = 0))) & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 21.63/3.74 | (aElementOf0(v2, cS2076) = v3) | ~ $i(v2) | ( ~ (v2 = v1) & ~ (v2 % 21.63/3.74 | = sz10))) & ! [v2: $i] : (v2 = v1 | v2 = sz10 | ~ % 21.63/3.74 | (aElementOf0(v2, cS2076) = 0) | ~ $i(v2)) & ! [v2: $i] : ( ~ % 21.63/3.74 | (aElementOf0(v2, v0) = 0) | ~ $i(v2) | (aInteger0(v2) = 0 & ? % 21.63/3.74 | [v3: $i] : (aElementOf0(v3, xS) = 0 & aElementOf0(v2, v3) = 0 & % 21.63/3.74 | $i(v3)))) & ! [v2: $i] : ( ~ (aElementOf0(v2, cS2076) = 0) | % 21.63/3.74 | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & aElementOf0(v2, v0) = v3 & % 21.63/3.74 | aInteger0(v2) = 0))) % 21.63/3.74 | % 21.63/3.74 | ALPHA: (m__2171) implies: % 21.63/3.75 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (xp = sz00) % 21.63/3.75 | & szAzrzSzezqlpdtcmdtrp0(sz10, xp) = v0 & stldt0(v2) = v3 & % 21.63/3.75 | sbsmnsldt0(xS) = v2 & aSubsetOf0(v0, v3) = 0 & aSet0(v2) = 0 & % 21.63/3.75 | aSet0(v0) = 0 & smndt0(sz10) = v1 & aInteger0(xp) = 0 & $i(v3) & % 21.63/3.75 | $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ % 21.63/3.75 | (aElementOf0(v4, v3) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: % 21.63/3.75 | any] : (aElementOf0(v4, v2) = v7 & aInteger0(v4) = v6 & ( ~ (v6 = % 21.63/3.75 | 0) | v7 = 0))) & ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ % 21.63/3.75 | (aElementOf0(v4, v2) = v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = % 21.63/3.75 | 0) & aInteger0(v4) = v6) | ! [v6: $i] : ( ~ (aElementOf0(v6, % 21.63/3.75 | xS) = 0) | ~ $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & % 21.63/3.75 | aElementOf0(v4, v6) = v7))) & ! [v4: $i] : ! [v5: int] : (v5 % 21.63/3.75 | = 0 | ~ (aElementOf0(v4, v0) = v5) | ~ $i(v4) | ? [v6: any] : ? % 21.63/3.75 | [v7: $i] : ? [v8: any] : ? [v9: any] : (sdteqdtlpzmzozddtrp0(v4, % 21.63/3.75 | sz10, xp) = v9 & aDivisorOf0(xp, v7) = v8 & sdtpldt0(v4, v1) = % 21.63/3.75 | v7 & aInteger0(v4) = v6 & $i(v7) & ( ~ (v6 = 0) | ( ~ (v9 = 0) & % 21.63/3.75 | ~ (v8 = 0) & ! [v10: $i] : ( ~ (sdtasdt0(xp, v10) = v7) | ~ % 21.63/3.75 | $i(v10) | ? [v11: int] : ( ~ (v11 = 0) & aInteger0(v10) = % 21.63/3.75 | v11)))))) & ! [v4: $i] : ( ~ (aElementOf0(v4, v3) = 0) | % 21.63/3.75 | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & aElementOf0(v4, v2) = v5 % 21.63/3.75 | & aInteger0(v4) = 0)) & ! [v4: $i] : ( ~ (aElementOf0(v4, v2) = % 21.63/3.75 | 0) | ~ $i(v4) | (aInteger0(v4) = 0 & ? [v5: $i] : % 21.63/3.75 | (aElementOf0(v5, xS) = 0 & aElementOf0(v4, v5) = 0 & $i(v5)))) & % 21.63/3.75 | ! [v4: $i] : ( ~ (aElementOf0(v4, v0) = 0) | ~ $i(v4) | % 21.63/3.75 | aElementOf0(v4, v3) = 0) & ! [v4: $i] : ( ~ (aElementOf0(v4, v0) = % 21.63/3.75 | 0) | ~ $i(v4) | ? [v5: $i] : (sdteqdtlpzmzozddtrp0(v4, sz10, % 21.63/3.75 | xp) = 0 & aDivisorOf0(xp, v5) = 0 & sdtpldt0(v4, v1) = v5 & % 21.63/3.75 | aInteger0(v4) = 0 & $i(v5) & ? [v6: $i] : (sdtasdt0(xp, v6) = v5 % 21.63/3.75 | & aInteger0(v6) = 0 & $i(v6))))) % 21.63/3.75 | % 21.63/3.75 | ALPHA: (m__2232) implies: % 21.63/3.75 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 21.63/3.75 | ? [v5: $i] : ? [v6: $i] : (szAzrzSzezqlpdtcmdtrp0(sz10, xp) = v3 & % 21.63/3.75 | aElementOf0(v5, v3) = 0 & aElementOf0(v0, v3) = 0 & % 21.63/3.75 | sdteqdtlpzmzozddtrp0(v5, sz10, xp) = 0 & sdteqdtlpzmzozddtrp0(v0, % 21.63/3.75 | sz10, xp) = 0 & aDivisorOf0(xp, v6) = 0 & aDivisorOf0(xp, v2) = 0 & % 21.63/3.75 | sdtpldt0(v5, v1) = v6 & sdtpldt0(v0, v1) = v2 & sdtpldt0(sz10, v4) = % 21.63/3.75 | v5 & sdtpldt0(sz10, xp) = v0 & smndt0(xp) = v4 & smndt0(sz10) = v1 & % 21.63/3.75 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ? % 21.63/3.75 | [v7: $i] : (sdtasdt0(xp, v7) = v6 & aInteger0(v7) = 0 & $i(v7)) & ? % 21.63/3.75 | [v7: $i] : (sdtasdt0(xp, v7) = v2 & aInteger0(v7) = 0 & $i(v7))) % 21.63/3.75 | % 21.63/3.75 | ALPHA: (m__2258) implies: % 21.63/3.76 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = sz10) & ~ (v0 = % 21.63/3.76 | sz10) & sdtpldt0(sz10, v1) = v2 & sdtpldt0(sz10, xp) = v0 & % 21.63/3.76 | smndt0(xp) = v1 & $i(v2) & $i(v1) & $i(v0)) % 21.63/3.76 | % 21.63/3.76 | ALPHA: (m__2286) implies: % 21.63/3.76 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtpldt0(sz10, % 21.63/3.76 | v2) = v3 & sdtpldt0(sz10, xp) = v0 & smndt0(xp) = v2 & smndt0(sz10) % 21.63/3.76 | = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v3 = v0) | ~ (v1 = % 21.63/3.76 | v0))) % 21.63/3.76 | % 21.63/3.76 | ALPHA: (m__) implies: % 21.63/3.76 | (8) ? [v0: $i] : ? [v1: $i] : (szAzrzSzezqlpdtcmdtrp0(sz10, xp) = v1 & % 21.63/3.76 | smndt0(sz10) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: any] : ( % 21.63/3.76 | ~ (aElementOf0(v2, v1) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: % 21.63/3.76 | $i] : ? [v6: any] : ? [v7: any] : ? [v8: any] : % 21.63/3.76 | (aElementOf0(v2, cS2200) = v8 & sdteqdtlpzmzozddtrp0(v2, sz10, xp) % 21.63/3.76 | = v7 & aDivisorOf0(xp, v5) = v6 & sdtpldt0(v2, v0) = v5 & % 21.63/3.76 | aInteger0(v2) = v4 & $i(v5) & ((v8 = 0 & (v2 = v0 | v2 = sz10)) | % 21.63/3.76 | ( ~ (v3 = 0) & ( ~ (v4 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0) & ! % 21.63/3.76 | [v9: $i] : ( ~ (sdtasdt0(xp, v9) = v5) | ~ $i(v9) | ? % 21.63/3.76 | [v10: int] : ( ~ (v10 = 0) & aInteger0(v9) = % 21.63/3.76 | v10))))))))) % 21.63/3.76 | % 21.63/3.76 | ALPHA: (function-axioms) implies: % 21.63/3.76 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = % 21.63/3.76 | v1) | ~ (smndt0(v2) = v0)) % 21.63/3.76 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.63/3.76 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 21.63/3.76 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.63/3.76 | (szAzrzSzezqlpdtcmdtrp0(v3, v2) = v1) | ~ % 21.63/3.76 | (szAzrzSzezqlpdtcmdtrp0(v3, v2) = v0)) % 21.63/3.76 | % 21.63/3.76 | DELTA: instantiating (6) with fresh symbols all_36_0, all_36_1, all_36_2 % 21.63/3.76 | gives: % 21.63/3.76 | (12) ~ (all_36_0 = sz10) & ~ (all_36_2 = sz10) & sdtpldt0(sz10, all_36_1) % 21.63/3.76 | = all_36_0 & sdtpldt0(sz10, xp) = all_36_2 & smndt0(xp) = all_36_1 & % 21.63/3.76 | $i(all_36_0) & $i(all_36_1) & $i(all_36_2) % 21.63/3.76 | % 21.63/3.76 | ALPHA: (12) implies: % 21.63/3.76 | (13) ~ (all_36_2 = sz10) % 21.63/3.76 | (14) ~ (all_36_0 = sz10) % 21.63/3.76 | (15) smndt0(xp) = all_36_1 % 21.63/3.76 | (16) sdtpldt0(sz10, xp) = all_36_2 % 21.63/3.77 | (17) sdtpldt0(sz10, all_36_1) = all_36_0 % 21.63/3.77 | % 21.63/3.77 | DELTA: instantiating (7) with fresh symbols all_38_0, all_38_1, all_38_2, % 21.63/3.77 | all_38_3 gives: % 22.06/3.77 | (18) sdtpldt0(sz10, all_38_1) = all_38_0 & sdtpldt0(sz10, xp) = all_38_3 & % 22.06/3.77 | smndt0(xp) = all_38_1 & smndt0(sz10) = all_38_2 & $i(all_38_0) & % 22.06/3.77 | $i(all_38_1) & $i(all_38_2) & $i(all_38_3) & ( ~ (all_38_0 = all_38_3) % 22.06/3.77 | | ~ (all_38_2 = all_38_3)) % 22.06/3.77 | % 22.06/3.77 | ALPHA: (18) implies: % 22.06/3.77 | (19) $i(all_38_3) % 22.06/3.77 | (20) $i(all_38_0) % 22.06/3.77 | (21) smndt0(sz10) = all_38_2 % 22.06/3.77 | (22) smndt0(xp) = all_38_1 % 22.06/3.77 | (23) sdtpldt0(sz10, xp) = all_38_3 % 22.06/3.77 | (24) sdtpldt0(sz10, all_38_1) = all_38_0 % 22.06/3.77 | (25) ~ (all_38_0 = all_38_3) | ~ (all_38_2 = all_38_3) % 22.06/3.77 | % 22.06/3.77 | DELTA: instantiating (1) with fresh symbol all_40_0 gives: % 22.06/3.77 | (26) smndt0(sz10) = all_40_0 & $i(all_40_0) & ! [v0: $i] : ! [v1: $i] : ( % 22.06/3.77 | ~ (sdtasdt0(all_40_0, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 22.06/3.77 | $i] : ? [v4: $i] : (sdtasdt0(v0, all_40_0) = v4 & smndt0(v0) = v3 % 22.06/3.77 | & aInteger0(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | (v4 = v1 & % 22.06/3.77 | v3 = v1)))) % 22.06/3.77 | % 22.06/3.77 | ALPHA: (26) implies: % 22.06/3.77 | (27) smndt0(sz10) = all_40_0 % 22.06/3.77 | % 22.06/3.77 | DELTA: instantiating (2) with fresh symbol all_43_0 gives: % 22.06/3.77 | (28) smndt0(sz10) = all_43_0 & $i(all_43_0) & ! [v0: $i] : ( ~ % 22.06/3.77 | (aInteger0(v0) = 0) | ~ $i(v0) | ((v0 = all_43_0 | v0 = sz10 | ? % 22.06/3.77 | [v1: $i] : (isPrime0(v1) = 0 & aDivisorOf0(v1, v0) = 0 & % 22.06/3.77 | $i(v1))) & ( ! [v1: $i] : ( ~ (isPrime0(v1) = 0) | ~ $i(v1) | % 22.06/3.77 | ? [v2: int] : ( ~ (v2 = 0) & aDivisorOf0(v1, v0) = v2)) | ( ~ % 22.06/3.77 | (v0 = all_43_0) & ~ (v0 = sz10))))) % 22.06/3.77 | % 22.06/3.77 | ALPHA: (28) implies: % 22.06/3.77 | (29) smndt0(sz10) = all_43_0 % 22.06/3.77 | % 22.06/3.77 | DELTA: instantiating (8) with fresh symbols all_46_0, all_46_1 gives: % 22.06/3.77 | (30) szAzrzSzezqlpdtcmdtrp0(sz10, xp) = all_46_0 & smndt0(sz10) = all_46_1 % 22.06/3.77 | & $i(all_46_0) & $i(all_46_1) & ! [v0: $i] : ! [v1: any] : ( ~ % 22.06/3.77 | (aElementOf0(v0, all_46_0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 22.06/3.77 | [v3: $i] : ? [v4: any] : ? [v5: any] : ? [v6: any] : % 22.06/3.77 | (aElementOf0(v0, cS2200) = v6 & sdteqdtlpzmzozddtrp0(v0, sz10, xp) = % 22.06/3.77 | v5 & aDivisorOf0(xp, v3) = v4 & sdtpldt0(v0, all_46_1) = v3 & % 22.06/3.77 | aInteger0(v0) = v2 & $i(v3) & ((v6 = 0 & (v0 = all_46_1 | v0 = % 22.06/3.77 | sz10)) | ( ~ (v1 = 0) & ( ~ (v2 = 0) | ( ~ (v5 = 0) & ~ (v4 % 22.06/3.77 | = 0) & ! [v7: $i] : ( ~ (sdtasdt0(xp, v7) = v3) | ~ % 22.06/3.77 | $i(v7) | ? [v8: int] : ( ~ (v8 = 0) & aInteger0(v7) = % 22.06/3.77 | v8)))))))) % 22.06/3.77 | % 22.06/3.77 | ALPHA: (30) implies: % 22.06/3.77 | (31) smndt0(sz10) = all_46_1 % 22.06/3.77 | (32) szAzrzSzezqlpdtcmdtrp0(sz10, xp) = all_46_0 % 22.06/3.77 | (33) ! [v0: $i] : ! [v1: any] : ( ~ (aElementOf0(v0, all_46_0) = v1) | ~ % 22.06/3.77 | $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : ? [v5: any] : % 22.06/3.77 | ? [v6: any] : (aElementOf0(v0, cS2200) = v6 & % 22.06/3.77 | sdteqdtlpzmzozddtrp0(v0, sz10, xp) = v5 & aDivisorOf0(xp, v3) = v4 % 22.06/3.77 | & sdtpldt0(v0, all_46_1) = v3 & aInteger0(v0) = v2 & $i(v3) & ((v6 % 22.06/3.77 | = 0 & (v0 = all_46_1 | v0 = sz10)) | ( ~ (v1 = 0) & ( ~ (v2 = % 22.06/3.77 | 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & ! [v7: $i] : ( ~ % 22.06/3.77 | (sdtasdt0(xp, v7) = v3) | ~ $i(v7) | ? [v8: int] : ( ~ % 22.06/3.77 | (v8 = 0) & aInteger0(v7) = v8)))))))) % 22.06/3.77 | % 22.06/3.77 | DELTA: instantiating (5) with fresh symbols all_49_0, all_49_1, all_49_2, % 22.06/3.78 | all_49_3, all_49_4, all_49_5, all_49_6 gives: % 22.06/3.78 | (34) szAzrzSzezqlpdtcmdtrp0(sz10, xp) = all_49_3 & aElementOf0(all_49_1, % 22.06/3.78 | all_49_3) = 0 & aElementOf0(all_49_6, all_49_3) = 0 & % 22.06/3.78 | sdteqdtlpzmzozddtrp0(all_49_1, sz10, xp) = 0 & % 22.06/3.78 | sdteqdtlpzmzozddtrp0(all_49_6, sz10, xp) = 0 & aDivisorOf0(xp, % 22.06/3.78 | all_49_0) = 0 & aDivisorOf0(xp, all_49_4) = 0 & sdtpldt0(all_49_1, % 22.06/3.78 | all_49_5) = all_49_0 & sdtpldt0(all_49_6, all_49_5) = all_49_4 & % 22.06/3.78 | sdtpldt0(sz10, all_49_2) = all_49_1 & sdtpldt0(sz10, xp) = all_49_6 & % 22.06/3.78 | smndt0(xp) = all_49_2 & smndt0(sz10) = all_49_5 & $i(all_49_0) & % 22.06/3.78 | $i(all_49_1) & $i(all_49_2) & $i(all_49_3) & $i(all_49_4) & % 22.06/3.78 | $i(all_49_5) & $i(all_49_6) & ? [v0: $i] : (sdtasdt0(xp, v0) = % 22.06/3.78 | all_49_0 & aInteger0(v0) = 0 & $i(v0)) & ? [v0: $i] : (sdtasdt0(xp, % 22.06/3.78 | v0) = all_49_4 & aInteger0(v0) = 0 & $i(v0)) % 22.06/3.78 | % 22.06/3.78 | ALPHA: (34) implies: % 22.06/3.78 | (35) smndt0(sz10) = all_49_5 % 22.06/3.78 | (36) smndt0(xp) = all_49_2 % 22.06/3.78 | (37) sdtpldt0(sz10, xp) = all_49_6 % 22.06/3.78 | (38) sdtpldt0(sz10, all_49_2) = all_49_1 % 22.06/3.78 | (39) aElementOf0(all_49_6, all_49_3) = 0 % 22.06/3.78 | (40) aElementOf0(all_49_1, all_49_3) = 0 % 22.06/3.78 | (41) szAzrzSzezqlpdtcmdtrp0(sz10, xp) = all_49_3 % 22.06/3.78 | % 22.06/3.78 | DELTA: instantiating (3) with fresh symbols all_51_0, all_51_1 gives: % 22.06/3.78 | (42) stldt0(all_51_1) = cS2076 & sbsmnsldt0(xS) = all_51_1 & % 22.06/3.78 | aSet0(all_51_1) = 0 & aSet0(cS2076) = 0 & smndt0(sz10) = all_51_0 & % 22.06/3.78 | $i(all_51_0) & $i(all_51_1) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | % 22.06/3.78 | ~ (aElementOf0(v0, all_51_1) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ % 22.06/3.78 | (v2 = 0) & aInteger0(v0) = v2) | ! [v2: $i] : ( ~ % 22.06/3.78 | (aElementOf0(v2, xS) = 0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = % 22.06/3.78 | 0) & aElementOf0(v0, v2) = v3))) & ! [v0: $i] : ! [v1: int] % 22.06/3.78 | : (v1 = 0 | ~ (aElementOf0(v0, cS2076) = v1) | ~ $i(v0) | ? [v2: % 22.06/3.78 | any] : ? [v3: any] : (aElementOf0(v0, all_51_1) = v3 & % 22.06/3.78 | aInteger0(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ! % 22.06/3.78 | [v1: int] : (v1 = 0 | ~ (aElementOf0(v0, cS2076) = v1) | ~ $i(v0) | % 22.06/3.78 | ( ~ (v0 = all_51_0) & ~ (v0 = sz10))) & ! [v0: any] : (v0 = % 22.06/3.78 | all_51_0 | v0 = sz10 | ~ (aElementOf0(v0, cS2076) = 0) | ~ $i(v0)) % 22.06/3.78 | & ! [v0: $i] : ( ~ (aElementOf0(v0, all_51_1) = 0) | ~ $i(v0) | % 22.06/3.78 | (aInteger0(v0) = 0 & ? [v1: $i] : (aElementOf0(v1, xS) = 0 & % 22.06/3.78 | aElementOf0(v0, v1) = 0 & $i(v1)))) & ! [v0: $i] : ( ~ % 22.06/3.78 | (aElementOf0(v0, cS2076) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = % 22.06/3.78 | 0) & aElementOf0(v0, all_51_1) = v1 & aInteger0(v0) = 0)) % 22.06/3.78 | % 22.06/3.78 | ALPHA: (42) implies: % 22.06/3.78 | (43) smndt0(sz10) = all_51_0 % 22.06/3.78 | % 22.06/3.78 | DELTA: instantiating (4) with fresh symbols all_58_0, all_58_1, all_58_2, % 22.06/3.78 | all_58_3 gives: % 22.06/3.78 | (44) ~ (xp = sz00) & szAzrzSzezqlpdtcmdtrp0(sz10, xp) = all_58_3 & % 22.06/3.78 | stldt0(all_58_1) = all_58_0 & sbsmnsldt0(xS) = all_58_1 & % 22.06/3.78 | aSubsetOf0(all_58_3, all_58_0) = 0 & aSet0(all_58_1) = 0 & % 22.06/3.78 | aSet0(all_58_3) = 0 & smndt0(sz10) = all_58_2 & aInteger0(xp) = 0 & % 22.06/3.78 | $i(all_58_0) & $i(all_58_1) & $i(all_58_2) & $i(all_58_3) & ! [v0: % 22.06/3.78 | $i] : ! [v1: int] : (v1 = 0 | ~ (aElementOf0(v0, all_58_0) = v1) | % 22.06/3.78 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (aElementOf0(v0, all_58_1) % 22.06/3.78 | = v3 & aInteger0(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] % 22.06/3.78 | : ! [v1: int] : (v1 = 0 | ~ (aElementOf0(v0, all_58_1) = v1) | ~ % 22.06/3.78 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & aInteger0(v0) = v2) | ! [v2: % 22.06/3.78 | $i] : ( ~ (aElementOf0(v2, xS) = 0) | ~ $i(v2) | ? [v3: int] : ( % 22.06/3.78 | ~ (v3 = 0) & aElementOf0(v0, v2) = v3))) & ! [v0: $i] : ! [v1: % 22.06/3.78 | int] : (v1 = 0 | ~ (aElementOf0(v0, all_58_3) = v1) | ~ $i(v0) | % 22.06/3.78 | ? [v2: any] : ? [v3: $i] : ? [v4: any] : ? [v5: any] : % 22.06/3.78 | (sdteqdtlpzmzozddtrp0(v0, sz10, xp) = v5 & aDivisorOf0(xp, v3) = v4 % 22.06/3.78 | & sdtpldt0(v0, all_58_2) = v3 & aInteger0(v0) = v2 & $i(v3) & ( ~ % 22.06/3.79 | (v2 = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & ! [v6: $i] : ( ~ % 22.06/3.79 | (sdtasdt0(xp, v6) = v3) | ~ $i(v6) | ? [v7: int] : ( ~ (v7 % 22.06/3.79 | = 0) & aInteger0(v6) = v7)))))) & ! [v0: $i] : ( ~ % 22.06/3.79 | (aElementOf0(v0, all_58_0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 % 22.06/3.79 | = 0) & aElementOf0(v0, all_58_1) = v1 & aInteger0(v0) = 0)) & ! % 22.06/3.79 | [v0: $i] : ( ~ (aElementOf0(v0, all_58_1) = 0) | ~ $i(v0) | % 22.06/3.79 | (aInteger0(v0) = 0 & ? [v1: $i] : (aElementOf0(v1, xS) = 0 & % 22.06/3.79 | aElementOf0(v0, v1) = 0 & $i(v1)))) & ! [v0: $i] : ( ~ % 22.06/3.79 | (aElementOf0(v0, all_58_3) = 0) | ~ $i(v0) | aElementOf0(v0, % 22.06/3.79 | all_58_0) = 0) & ! [v0: $i] : ( ~ (aElementOf0(v0, all_58_3) = 0) % 22.06/3.79 | | ~ $i(v0) | ? [v1: $i] : (sdteqdtlpzmzozddtrp0(v0, sz10, xp) = 0 % 22.06/3.79 | & aDivisorOf0(xp, v1) = 0 & sdtpldt0(v0, all_58_2) = v1 & % 22.06/3.79 | aInteger0(v0) = 0 & $i(v1) & ? [v2: $i] : (sdtasdt0(xp, v2) = v1 % 22.06/3.79 | & aInteger0(v2) = 0 & $i(v2)))) % 22.06/3.79 | % 22.06/3.79 | ALPHA: (44) implies: % 22.06/3.79 | (45) smndt0(sz10) = all_58_2 % 22.06/3.79 | (46) szAzrzSzezqlpdtcmdtrp0(sz10, xp) = all_58_3 % 22.06/3.79 | % 22.06/3.79 | GROUND_INST: instantiating (9) with all_40_0, all_46_1, sz10, simplifying with % 22.06/3.79 | (27), (31) gives: % 22.06/3.79 | (47) all_46_1 = all_40_0 % 22.06/3.79 | % 22.06/3.79 | GROUND_INST: instantiating (9) with all_46_1, all_49_5, sz10, simplifying with % 22.06/3.79 | (31), (35) gives: % 22.06/3.79 | (48) all_49_5 = all_46_1 % 22.06/3.79 | % 22.17/3.79 | GROUND_INST: instantiating (9) with all_38_2, all_49_5, sz10, simplifying with % 22.17/3.79 | (21), (35) gives: % 22.17/3.79 | (49) all_49_5 = all_38_2 % 22.17/3.79 | % 22.17/3.79 | GROUND_INST: instantiating (9) with all_49_5, all_51_0, sz10, simplifying with % 22.17/3.79 | (35), (43) gives: % 22.17/3.79 | (50) all_51_0 = all_49_5 % 22.17/3.79 | % 22.17/3.79 | GROUND_INST: instantiating (9) with all_51_0, all_58_2, sz10, simplifying with % 22.17/3.79 | (43), (45) gives: % 22.17/3.79 | (51) all_58_2 = all_51_0 % 22.17/3.79 | % 22.17/3.79 | GROUND_INST: instantiating (9) with all_43_0, all_58_2, sz10, simplifying with % 22.17/3.79 | (29), (45) gives: % 22.17/3.79 | (52) all_58_2 = all_43_0 % 22.17/3.79 | % 22.17/3.79 | GROUND_INST: instantiating (9) with all_38_1, all_49_2, xp, simplifying with % 22.17/3.79 | (22), (36) gives: % 22.17/3.79 | (53) all_49_2 = all_38_1 % 22.17/3.79 | % 22.17/3.79 | GROUND_INST: instantiating (9) with all_36_1, all_49_2, xp, simplifying with % 22.17/3.79 | (15), (36) gives: % 22.17/3.79 | (54) all_49_2 = all_36_1 % 22.17/3.79 | % 22.17/3.79 | GROUND_INST: instantiating (10) with all_38_3, all_49_6, xp, sz10, simplifying % 22.17/3.79 | with (23), (37) gives: % 22.17/3.79 | (55) all_49_6 = all_38_3 % 22.17/3.79 | % 22.17/3.79 | GROUND_INST: instantiating (10) with all_36_2, all_49_6, xp, sz10, simplifying % 22.17/3.79 | with (16), (37) gives: % 22.17/3.79 | (56) all_49_6 = all_36_2 % 22.17/3.79 | % 22.17/3.79 | GROUND_INST: instantiating (11) with all_49_3, all_58_3, xp, sz10, simplifying % 22.17/3.79 | with (41), (46) gives: % 22.17/3.79 | (57) all_58_3 = all_49_3 % 22.17/3.79 | % 22.17/3.79 | GROUND_INST: instantiating (11) with all_46_0, all_58_3, xp, sz10, simplifying % 22.17/3.79 | with (32), (46) gives: % 22.17/3.79 | (58) all_58_3 = all_46_0 % 22.17/3.79 | % 22.17/3.79 | COMBINE_EQS: (51), (52) imply: % 22.17/3.79 | (59) all_51_0 = all_43_0 % 22.17/3.79 | % 22.17/3.79 | SIMP: (59) implies: % 22.17/3.79 | (60) all_51_0 = all_43_0 % 22.17/3.79 | % 22.17/3.79 | COMBINE_EQS: (57), (58) imply: % 22.17/3.79 | (61) all_49_3 = all_46_0 % 22.17/3.79 | % 22.17/3.79 | COMBINE_EQS: (50), (60) imply: % 22.17/3.79 | (62) all_49_5 = all_43_0 % 22.17/3.79 | % 22.17/3.79 | SIMP: (62) implies: % 22.17/3.79 | (63) all_49_5 = all_43_0 % 22.17/3.79 | % 22.17/3.79 | COMBINE_EQS: (53), (54) imply: % 22.17/3.79 | (64) all_38_1 = all_36_1 % 22.17/3.79 | % 22.17/3.79 | COMBINE_EQS: (48), (63) imply: % 22.17/3.79 | (65) all_46_1 = all_43_0 % 22.17/3.79 | % 22.17/3.79 | SIMP: (65) implies: % 22.17/3.79 | (66) all_46_1 = all_43_0 % 22.17/3.79 | % 22.17/3.79 | COMBINE_EQS: (49), (63) imply: % 22.17/3.79 | (67) all_43_0 = all_38_2 % 22.17/3.79 | % 22.17/3.79 | COMBINE_EQS: (55), (56) imply: % 22.17/3.79 | (68) all_38_3 = all_36_2 % 22.17/3.79 | % 22.17/3.79 | COMBINE_EQS: (47), (66) imply: % 22.17/3.79 | (69) all_43_0 = all_40_0 % 22.17/3.79 | % 22.17/3.79 | SIMP: (69) implies: % 22.17/3.79 | (70) all_43_0 = all_40_0 % 22.17/3.79 | % 22.17/3.79 | COMBINE_EQS: (67), (70) imply: % 22.17/3.79 | (71) all_40_0 = all_38_2 % 22.17/3.79 | % 22.17/3.79 | COMBINE_EQS: (47), (71) imply: % 22.17/3.79 | (72) all_46_1 = all_38_2 % 22.17/3.79 | % 22.17/3.79 | REDUCE: (40), (61) imply: % 22.17/3.79 | (73) aElementOf0(all_49_1, all_46_0) = 0 % 22.17/3.79 | % 22.17/3.79 | REDUCE: (39), (56), (61) imply: % 22.17/3.79 | (74) aElementOf0(all_36_2, all_46_0) = 0 % 22.17/3.79 | % 22.17/3.79 | REDUCE: (38), (54) imply: % 22.17/3.79 | (75) sdtpldt0(sz10, all_36_1) = all_49_1 % 22.17/3.79 | % 22.17/3.79 | REDUCE: (24), (64) imply: % 22.17/3.79 | (76) sdtpldt0(sz10, all_36_1) = all_38_0 % 22.17/3.79 | % 22.17/3.79 | REDUCE: (19), (68) imply: % 22.17/3.79 | (77) $i(all_36_2) % 22.17/3.79 | % 22.17/3.79 | GROUND_INST: instantiating (10) with all_36_0, all_49_1, all_36_1, sz10, % 22.17/3.79 | simplifying with (17), (75) gives: % 22.17/3.79 | (78) all_49_1 = all_36_0 % 22.17/3.79 | % 22.17/3.79 | GROUND_INST: instantiating (10) with all_38_0, all_49_1, all_36_1, sz10, % 22.17/3.79 | simplifying with (75), (76) gives: % 22.17/3.79 | (79) all_49_1 = all_38_0 % 22.17/3.79 | % 22.17/3.79 | COMBINE_EQS: (78), (79) imply: % 22.17/3.79 | (80) all_38_0 = all_36_0 % 22.17/3.79 | % 22.17/3.80 | REDUCE: (73), (78) imply: % 22.17/3.80 | (81) aElementOf0(all_36_0, all_46_0) = 0 % 22.17/3.80 | % 22.17/3.80 | REDUCE: (20), (80) imply: % 22.17/3.80 | (82) $i(all_36_0) % 22.17/3.80 | % 22.17/3.80 | GROUND_INST: instantiating (33) with all_36_2, 0, simplifying with (74), (77) % 22.17/3.80 | gives: % 22.17/3.80 | (83) ? [v0: MultipleValueBool] : ? [v1: $i] : ? [v2: MultipleValueBool] % 22.17/3.80 | : ? [v3: MultipleValueBool] : (aElementOf0(all_36_2, cS2200) = 0 & % 22.17/3.80 | sdteqdtlpzmzozddtrp0(all_36_2, sz10, xp) = v3 & aDivisorOf0(xp, v1) % 22.17/3.80 | = v2 & sdtpldt0(all_36_2, all_46_1) = v1 & aInteger0(all_36_2) = v0 % 22.17/3.80 | & $i(v1) & (all_46_1 = all_36_2 | all_36_2 = sz10)) % 22.17/3.80 | % 22.17/3.80 | GROUND_INST: instantiating (33) with all_36_0, 0, simplifying with (81), (82) % 22.17/3.80 | gives: % 22.17/3.80 | (84) ? [v0: MultipleValueBool] : ? [v1: $i] : ? [v2: MultipleValueBool] % 22.17/3.80 | : ? [v3: MultipleValueBool] : (aElementOf0(all_36_0, cS2200) = 0 & % 22.17/3.80 | sdteqdtlpzmzozddtrp0(all_36_0, sz10, xp) = v3 & aDivisorOf0(xp, v1) % 22.17/3.80 | = v2 & sdtpldt0(all_36_0, all_46_1) = v1 & aInteger0(all_36_0) = v0 % 22.17/3.80 | & $i(v1) & (all_46_1 = all_36_0 | all_36_0 = sz10)) % 22.17/3.80 | % 22.17/3.80 | DELTA: instantiating (84) with fresh symbols all_122_0, all_122_1, all_122_2, % 22.17/3.80 | all_122_3 gives: % 22.17/3.80 | (85) aElementOf0(all_36_0, cS2200) = 0 & sdteqdtlpzmzozddtrp0(all_36_0, % 22.17/3.80 | sz10, xp) = all_122_0 & aDivisorOf0(xp, all_122_2) = all_122_1 & % 22.17/3.80 | sdtpldt0(all_36_0, all_46_1) = all_122_2 & aInteger0(all_36_0) = % 22.17/3.80 | all_122_3 & $i(all_122_2) & (all_46_1 = all_36_0 | all_36_0 = sz10) % 22.17/3.80 | % 22.17/3.80 | ALPHA: (85) implies: % 22.17/3.80 | (86) all_46_1 = all_36_0 | all_36_0 = sz10 % 22.17/3.80 | % 22.17/3.80 | DELTA: instantiating (83) with fresh symbols all_124_0, all_124_1, all_124_2, % 22.17/3.80 | all_124_3 gives: % 22.17/3.80 | (87) aElementOf0(all_36_2, cS2200) = 0 & sdteqdtlpzmzozddtrp0(all_36_2, % 22.17/3.80 | sz10, xp) = all_124_0 & aDivisorOf0(xp, all_124_2) = all_124_1 & % 22.17/3.80 | sdtpldt0(all_36_2, all_46_1) = all_124_2 & aInteger0(all_36_2) = % 22.17/3.80 | all_124_3 & $i(all_124_2) & (all_46_1 = all_36_2 | all_36_2 = sz10) % 22.17/3.80 | % 22.17/3.80 | ALPHA: (87) implies: % 22.17/3.80 | (88) all_46_1 = all_36_2 | all_36_2 = sz10 % 22.17/3.80 | % 22.17/3.80 | BETA: splitting (88) gives: % 22.17/3.80 | % 22.17/3.80 | Case 1: % 22.17/3.80 | | % 22.17/3.80 | | (89) all_36_2 = sz10 % 22.17/3.80 | | % 22.17/3.80 | | REDUCE: (13), (89) imply: % 22.17/3.80 | | (90) $false % 22.17/3.80 | | % 22.17/3.80 | | CLOSE: (90) is inconsistent. % 22.17/3.80 | | % 22.17/3.80 | Case 2: % 22.17/3.80 | | % 22.17/3.80 | | (91) all_46_1 = all_36_2 % 22.17/3.80 | | % 22.17/3.80 | | COMBINE_EQS: (72), (91) imply: % 22.17/3.80 | | (92) all_38_2 = all_36_2 % 22.17/3.80 | | % 22.17/3.80 | | SIMP: (92) implies: % 22.17/3.80 | | (93) all_38_2 = all_36_2 % 22.17/3.80 | | % 22.17/3.80 | | BETA: splitting (86) gives: % 22.17/3.80 | | % 22.17/3.80 | | Case 1: % 22.17/3.80 | | | % 22.17/3.80 | | | (94) all_36_0 = sz10 % 22.17/3.80 | | | % 22.17/3.80 | | | REDUCE: (14), (94) imply: % 22.17/3.80 | | | (95) $false % 22.17/3.80 | | | % 22.17/3.80 | | | CLOSE: (95) is inconsistent. % 22.17/3.80 | | | % 22.17/3.80 | | Case 2: % 22.17/3.80 | | | % 22.17/3.80 | | | (96) all_46_1 = all_36_0 % 22.17/3.80 | | | % 22.17/3.80 | | | COMBINE_EQS: (91), (96) imply: % 22.17/3.80 | | | (97) all_36_0 = all_36_2 % 22.17/3.80 | | | % 22.17/3.80 | | | COMBINE_EQS: (80), (97) imply: % 22.17/3.80 | | | (98) all_38_0 = all_36_2 % 22.17/3.80 | | | % 22.17/3.80 | | | BETA: splitting (25) gives: % 22.17/3.80 | | | % 22.17/3.80 | | | Case 1: % 22.17/3.80 | | | | % 22.17/3.80 | | | | (99) ~ (all_38_0 = all_38_3) % 22.17/3.80 | | | | % 22.17/3.80 | | | | REDUCE: (68), (98), (99) imply: % 22.17/3.80 | | | | (100) $false % 22.17/3.80 | | | | % 22.17/3.80 | | | | CLOSE: (100) is inconsistent. % 22.17/3.80 | | | | % 22.17/3.80 | | | Case 2: % 22.17/3.80 | | | | % 22.17/3.80 | | | | (101) all_38_0 = all_38_3 % 22.17/3.80 | | | | (102) ~ (all_38_2 = all_38_3) % 22.17/3.80 | | | | % 22.17/3.80 | | | | REDUCE: (68), (93), (102) imply: % 22.17/3.80 | | | | (103) $false % 22.17/3.80 | | | | % 22.17/3.80 | | | | CLOSE: (103) is inconsistent. % 22.17/3.80 | | | | % 22.17/3.80 | | | End of split % 22.17/3.80 | | | % 22.17/3.80 | | End of split % 22.17/3.80 | | % 22.17/3.80 | End of split % 22.17/3.80 | % 22.17/3.80 End of proof % 22.17/3.80 % SZS output end Proof for theBenchmark % 22.17/3.80 % 22.17/3.80 3179ms %------------------------------------------------------------------------------