%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM450+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 : n010.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 11:47:49 EDT 2023 % Result : Theorem 82.89s 11.69s % Output : Proof 83.69s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : NUM450+6 : TPTP v8.1.2. Released v4.0.0. % 0.08/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n010.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Fri Aug 25 13:24:05 EDT 2023 % 0.14/0.35 % CPUTime : % 0.22/0.63 ________ _____ % 0.22/0.63 ___ __ \_________(_)________________________________ % 0.22/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.63 % 0.22/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.63 (2023-06-19) % 0.22/0.63 % 0.22/0.63 (c) Philipp Rümmer, 2009-2023 % 0.22/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.63 Amanda Stjerna. % 0.22/0.63 Free software under BSD-3-Clause. % 0.22/0.63 % 0.22/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.63 % 0.22/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.22/0.64 Running up to 7 provers in parallel. % 0.22/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.22/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.22/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.22/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.10/1.38 Prover 1: Preprocessing ... % 4.10/1.39 Prover 4: Preprocessing ... % 4.76/1.43 Prover 0: Preprocessing ... % 4.76/1.43 Prover 3: Preprocessing ... % 4.76/1.43 Prover 6: Preprocessing ... % 4.76/1.43 Prover 2: Preprocessing ... % 4.76/1.43 Prover 5: Preprocessing ... % 12.60/2.50 Prover 3: Constructing countermodel ... % 12.60/2.52 Prover 6: Proving ... % 12.60/2.52 Prover 5: Proving ... % 13.20/2.55 Prover 1: Constructing countermodel ... % 13.90/2.70 Prover 2: Proving ... % 19.76/3.42 Prover 4: Constructing countermodel ... % 19.76/3.47 Prover 0: Proving ... % 72.60/10.31 Prover 2: stopped % 72.74/10.33 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 73.42/10.44 Prover 7: Preprocessing ... % 75.04/10.65 Prover 7: Warning: ignoring some quantifiers % 75.04/10.66 Prover 7: Constructing countermodel ... % 82.89/11.68 Prover 7: Found proof (size 57) % 82.89/11.68 Prover 7: proved (1353ms) % 82.89/11.68 Prover 0: stopped % 82.89/11.68 Prover 6: stopped % 82.89/11.68 Prover 3: stopped % 82.89/11.68 Prover 4: stopped % 82.89/11.68 Prover 5: stopped % 82.89/11.68 Prover 1: stopped % 82.89/11.68 % 82.89/11.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 82.89/11.69 % 82.89/11.69 % SZS output start Proof for theBenchmark % 82.89/11.70 Assumptions after simplification: % 82.89/11.70 --------------------------------- % 82.89/11.70 % 82.89/11.70 (mMulMinOne) % 82.89/11.72 $i(sz10) & ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 82.89/11.72 $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ~ aInteger0(v1) | % 82.89/11.72 (sdtasdt0(v0, v1) = v2 & smndt0(v1) = v2 & $i(v2))) & ! [v1: $i] : ! % 82.89/11.72 [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ aInteger0(v1) | % 82.89/11.72 (sdtasdt0(v1, v0) = v2 & smndt0(v1) = v2 & $i(v2))) & ! [v1: $i] : ! % 82.89/11.72 [v2: $i] : ( ~ (smndt0(v1) = v2) | ~ $i(v1) | ~ aInteger0(v1) | % 82.89/11.72 (sdtasdt0(v1, v0) = v2 & sdtasdt0(v0, v1) = v2 & $i(v2)))) % 82.89/11.72 % 82.89/11.72 (mPrimeDivisor) % 82.89/11.73 $i(sz10) & ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : (v1 = v0 % 82.89/11.73 | v1 = sz10 | ~ $i(v1) | ~ aInteger0(v1) | ? [v2: $i] : ($i(v2) & % 82.89/11.73 isPrime0(v2) & aDivisorOf0(v2, v1))) & ! [v1: $i] : ( ~ $i(v1) | ~ % 82.89/11.73 isPrime0(v1) | ~ aDivisorOf0(v1, v0) | ~ aInteger0(v0)) & ! [v1: $i] : % 82.89/11.73 ( ~ $i(v1) | ~ isPrime0(v1) | ~ aDivisorOf0(v1, sz10) | ~ % 82.89/11.73 aInteger0(sz10))) % 83.42/11.73 % 83.42/11.73 (m__) % 83.42/11.74 $i(xS) & $i(sz10) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 83.42/11.74 (stldt0(v1) = v2 & sbsmnsldt0(xS) = v1 & smndt0(sz10) = v0 & $i(v2) & $i(v1) & % 83.42/11.74 $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 83.42/11.74 : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ (sdtasdt0(v3, % 83.42/11.74 v7) = v6) | ~ (sdtpldt0(v5, v0) = v6) | ~ $i(v7) | ~ $i(v5) | ~ % 83.42/11.74 $i(v3) | ~ aInteger0(v7) | ~ aInteger0(v5) | ~ aInteger0(v3) | % 83.42/11.74 aElementOf0(v5, v4)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 83.42/11.74 $i] : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ % 83.42/11.74 (sdtpldt0(v5, v0) = v6) | ~ $i(v5) | ~ $i(v3) | ~ aElementOf0(v5, v4) | % 83.42/11.74 ~ aInteger0(v3) | sdteqdtlpzmzozddtrp0(v5, sz10, v3)) & ! [v3: $i] : ! % 83.42/11.74 [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = sz00 | ~ % 83.42/11.74 (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ (sdtpldt0(v5, v0) = v6) | ~ % 83.42/11.74 $i(v5) | ~ $i(v3) | ~ aElementOf0(v5, v4) | ~ aInteger0(v3) | % 83.42/11.74 aDivisorOf0(v3, v6)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 83.42/11.74 $i] : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ % 83.42/11.74 (sdtpldt0(v5, v0) = v6) | ~ $i(v5) | ~ $i(v3) | ~ aElementOf0(v5, v4) | % 83.42/11.74 ~ aInteger0(v3) | aInteger0(v5)) & ! [v3: $i] : ! [v4: $i] : ! [v5: % 83.42/11.74 $i] : ! [v6: $i] : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = % 83.42/11.74 v4) | ~ (sdtpldt0(v5, v0) = v6) | ~ $i(v5) | ~ $i(v3) | ~ % 83.42/11.74 aElementOf0(v5, v4) | ~ aInteger0(v3) | ? [v7: $i] : (sdtasdt0(v3, v7) = % 83.42/11.74 v6 & $i(v7) & $i(v6) & aInteger0(v7))) & ! [v3: $i] : ! [v4: $i] : ! % 83.42/11.74 [v5: $i] : ! [v6: $i] : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = % 83.42/11.74 v4) | ~ (sdtpldt0(v5, v0) = v6) | ~ $i(v5) | ~ $i(v3) | ~ % 83.42/11.74 sdteqdtlpzmzozddtrp0(v5, sz10, v3) | ~ aInteger0(v5) | ~ aInteger0(v3) | % 83.42/11.74 aElementOf0(v5, v4)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 83.42/11.74 $i] : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ % 83.42/11.74 (sdtpldt0(v5, v0) = v6) | ~ $i(v5) | ~ $i(v3) | ~ aDivisorOf0(v3, v6) | % 83.42/11.74 ~ aInteger0(v5) | ~ aInteger0(v3) | aElementOf0(v5, v4)) & ! [v3: $i] : % 83.42/11.74 ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = sz00 | ~ % 83.42/11.74 (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v6) | ~ $i(v5) | ~ % 83.42/11.74 $i(v3) | ~ aElementOf0(v6, xS) | ~ aElementOf0(v5, v6) | ~ % 83.42/11.74 aInteger0(v5) | ~ aInteger0(v3) | aElementOf0(v5, v1)) & ! [v3: $i] : ! % 83.42/11.74 [v4: $i] : ! [v5: $i] : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = % 83.42/11.74 v4) | ~ $i(v5) | ~ $i(v3) | ~ aElementOf0(v5, v2) | ~ % 83.42/11.74 aElementOf0(v5, v1) | ~ aInteger0(v3)) & ! [v3: $i] : ! [v4: $i] : ! % 83.42/11.74 [v5: $i] : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ % 83.42/11.74 $i(v5) | ~ $i(v3) | ~ aElementOf0(v5, v2) | ~ aInteger0(v3) | % 83.42/11.74 aInteger0(v5)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v3 = sz00 | ~ % 83.42/11.74 (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v5) | ~ $i(v3) | ~ % 83.42/11.74 aElementOf0(v5, v1) | ~ aInteger0(v3) | aInteger0(v5)) & ! [v3: $i] : ! % 83.42/11.74 [v4: $i] : ! [v5: $i] : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = % 83.42/11.74 v4) | ~ $i(v5) | ~ $i(v3) | ~ aElementOf0(v5, v1) | ~ aInteger0(v3) % 83.42/11.74 | ? [v6: $i] : ($i(v6) & aElementOf0(v6, xS) & aElementOf0(v5, v6))) & ! % 83.42/11.74 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v3 = sz00 | ~ % 83.42/11.74 (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v5) | ~ $i(v3) | ~ % 83.42/11.74 aInteger0(v5) | ~ aInteger0(v3) | aElementOf0(v5, v2) | aElementOf0(v5, % 83.42/11.74 v1)) & ! [v3: $i] : ! [v4: $i] : (v3 = sz00 | ~ % 83.42/11.74 (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v3) | ~ aSubsetOf0(v4, % 83.42/11.74 v2) | ~ aInteger0(v3)) & ! [v3: $i] : ! [v4: $i] : (v3 = sz00 | ~ % 83.42/11.74 (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v3) | ~ aInteger0(v3) | % 83.42/11.74 aSet0(v4)) & ! [v3: $i] : ! [v4: $i] : (v3 = sz00 | ~ % 83.42/11.74 (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v3) | ~ aInteger0(v3) | % 83.42/11.74 aSet0(v1)) & ! [v3: $i] : ! [v4: $i] : (v3 = sz00 | ~ % 83.42/11.74 (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v3) | ~ aInteger0(v3) | % 83.42/11.74 ? [v5: $i] : ($i(v5) & aElementOf0(v5, v4) & ~ aElementOf0(v5, v2)))) % 83.42/11.74 % 83.42/11.74 (m__2079) % 83.42/11.74 $i(cS2076) & $i(xS) & $i(sz10) & ? [v0: $i] : ? [v1: $i] : (stldt0(v0) = % 83.42/11.74 cS2076 & sbsmnsldt0(xS) = v0 & smndt0(sz10) = v1 & $i(v1) & $i(v0) & % 83.42/11.74 aElementOf0(v1, cS2076) & aElementOf0(sz10, cS2076) & aSet0(v0) & % 83.42/11.74 aSet0(cS2076) & ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ % 83.42/11.74 aElementOf0(v3, xS) | ~ aElementOf0(v2, v3) | ~ aInteger0(v2) | % 83.42/11.74 aElementOf0(v2, v0)) & ! [v2: $i] : (v2 = v1 | v2 = sz10 | ~ $i(v2) | ~ % 83.42/11.74 aElementOf0(v2, cS2076)) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, % 83.42/11.74 v0) | ~ aElementOf0(v2, cS2076)) & ! [v2: $i] : ( ~ $i(v2) | ~ % 83.42/11.74 aElementOf0(v2, v0) | aInteger0(v2)) & ! [v2: $i] : ( ~ $i(v2) | ~ % 83.42/11.74 aElementOf0(v2, v0) | ? [v3: $i] : ($i(v3) & aElementOf0(v3, xS) & % 83.42/11.74 aElementOf0(v2, v3))) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, % 83.42/11.74 cS2076) | aInteger0(v2)) & ! [v2: $i] : ( ~ $i(v2) | ~ aInteger0(v2) | % 83.42/11.74 aElementOf0(v2, v0) | aElementOf0(v2, cS2076))) % 83.42/11.74 % 83.42/11.74 (m__2144) % 83.42/11.75 $i(xS) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : (stldt0(v0) = v1 & % 83.42/11.75 sbsmnsldt0(xS) = v0 & $i(v1) & $i(v0) & isClosed0(v0) & isOpen0(v1) & % 83.42/11.75 aSet0(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (smndt0(v2) = v3) | ~ $i(v2) | % 83.42/11.75 ~ aElementOf0(v2, v1) | ? [v4: $i] : ? [v5: $i] : ( ~ (v4 = sz00) & % 83.42/11.75 szAzrzSzezqlpdtcmdtrp0(v2, v4) = v5 & $i(v5) & $i(v4) & aSubsetOf0(v5, % 83.42/11.75 v1) & aSet0(v5) & aInteger0(v4) & ! [v6: $i] : ! [v7: $i] : ! [v8: % 83.42/11.75 $i] : ( ~ (sdtasdt0(v4, v8) = v7) | ~ (sdtpldt0(v6, v3) = v7) | ~ % 83.42/11.75 $i(v8) | ~ $i(v6) | ~ aInteger0(v8) | ~ aInteger0(v6) | % 83.42/11.75 aElementOf0(v6, v5)) & ! [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, % 83.42/11.75 v3) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v5) | % 83.42/11.75 sdteqdtlpzmzozddtrp0(v6, v2, v4)) & ! [v6: $i] : ! [v7: $i] : ( ~ % 83.42/11.75 (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v5) | % 83.42/11.75 aDivisorOf0(v4, v7)) & ! [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, % 83.42/11.75 v3) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v5) | aInteger0(v6)) & % 83.42/11.75 ! [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~ % 83.42/11.75 aElementOf0(v6, v5) | ? [v8: $i] : (sdtasdt0(v4, v8) = v7 & $i(v8) & % 83.42/11.75 $i(v7) & aInteger0(v8))) & ! [v6: $i] : ! [v7: $i] : ( ~ % 83.42/11.75 (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~ sdteqdtlpzmzozddtrp0(v6, v2, % 83.42/11.75 v4) | ~ aInteger0(v6) | aElementOf0(v6, v5)) & ! [v6: $i] : ! % 83.42/11.75 [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~ aDivisorOf0(v4, % 83.42/11.75 v7) | ~ aInteger0(v6) | aElementOf0(v6, v5)) & ! [v6: $i] : ( ~ % 83.42/11.75 $i(v6) | ~ aElementOf0(v6, v5) | aElementOf0(v6, v1)))) & ! [v2: $i] % 83.42/11.75 : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ aElementOf0(v3, xS) | ~ % 83.42/11.75 aElementOf0(v2, v3) | ~ aInteger0(v2) | aElementOf0(v2, v0)) & ! [v2: % 83.42/11.75 $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | ~ aElementOf0(v2, v0)) & ! % 83.42/11.75 [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | aInteger0(v2)) & ! [v2: % 83.42/11.75 $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v0) | aInteger0(v2)) & ! [v2: $i] : % 83.42/11.75 ( ~ $i(v2) | ~ aElementOf0(v2, v0) | ? [v3: $i] : ($i(v3) & % 83.42/11.75 aElementOf0(v3, xS) & aElementOf0(v2, v3))) & ! [v2: $i] : ( ~ $i(v2) | % 83.42/11.75 ~ aInteger0(v2) | aElementOf0(v2, v1) | aElementOf0(v2, v0))) % 83.42/11.75 % 83.42/11.75 (function-axioms) % 83.42/11.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 83.42/11.75 (szAzrzSzezqlpdtcmdtrp0(v3, v2) = v1) | ~ (szAzrzSzezqlpdtcmdtrp0(v3, v2) = % 83.42/11.75 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 83.42/11.75 ~ (sdtslmnbsdt0(v3, v2) = v1) | ~ (sdtslmnbsdt0(v3, v2) = v0)) & ! [v0: % 83.42/11.75 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 83.42/11.75 (sdtbsmnsldt0(v3, v2) = v1) | ~ (sdtbsmnsldt0(v3, v2) = v0)) & ! [v0: $i] % 83.42/11.75 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = % 83.42/11.75 v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 83.42/11.75 $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, % 83.42/11.75 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 83.42/11.75 (stldt0(v2) = v1) | ~ (stldt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 83.42/11.75 [v2: $i] : (v1 = v0 | ~ (sbsmnsldt0(v2) = v1) | ~ (sbsmnsldt0(v2) = v0)) & % 83.42/11.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ % 83.42/11.75 (smndt0(v2) = v0)) % 83.42/11.75 % 83.42/11.75 Further assumptions not needed in the proof: % 83.42/11.75 -------------------------------------------- % 83.42/11.75 mAddAsso, mAddComm, mAddNeg, mAddZero, mArSeq, mArSeqClosed, mClosed, % 83.42/11.75 mComplement, mDistrib, mDivisor, mElements, mEquMod, mEquModMul, mEquModRef, % 83.42/11.75 mEquModSym, mEquModTrn, mFinSet, mIntMult, mIntNeg, mIntOne, mIntPlus, mIntZero, % 83.42/11.75 mIntegers, mInterOpen, mIntersection, mMulAsso, mMulComm, mMulOne, mMulZero, % 83.42/11.75 mOpen, mPrime, mSets, mSubset, mUnion, mUnionClosed, mUnionOpen, mUnionSClosed, % 83.42/11.75 mUnionSet, mZeroDiv, m__2046, m__2117 % 83.42/11.75 % 83.42/11.75 Those formulas are unsatisfiable: % 83.42/11.75 --------------------------------- % 83.42/11.75 % 83.42/11.75 Begin of proof % 83.42/11.76 | % 83.42/11.76 | ALPHA: (mMulMinOne) implies: % 83.42/11.76 | (1) ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 83.42/11.76 | ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ~ aInteger0(v1) | % 83.42/11.76 | (sdtasdt0(v0, v1) = v2 & smndt0(v1) = v2 & $i(v2))) & ! [v1: $i] : % 83.42/11.76 | ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ % 83.42/11.76 | aInteger0(v1) | (sdtasdt0(v1, v0) = v2 & smndt0(v1) = v2 & $i(v2))) % 83.42/11.76 | & ! [v1: $i] : ! [v2: $i] : ( ~ (smndt0(v1) = v2) | ~ $i(v1) | ~ % 83.42/11.76 | aInteger0(v1) | (sdtasdt0(v1, v0) = v2 & sdtasdt0(v0, v1) = v2 & % 83.42/11.76 | $i(v2)))) % 83.42/11.76 | % 83.42/11.76 | ALPHA: (mPrimeDivisor) implies: % 83.42/11.76 | (2) ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : (v1 = v0 | v1 % 83.42/11.76 | = sz10 | ~ $i(v1) | ~ aInteger0(v1) | ? [v2: $i] : ($i(v2) & % 83.42/11.76 | isPrime0(v2) & aDivisorOf0(v2, v1))) & ! [v1: $i] : ( ~ $i(v1) | % 83.42/11.76 | ~ isPrime0(v1) | ~ aDivisorOf0(v1, v0) | ~ aInteger0(v0)) & ! % 83.42/11.76 | [v1: $i] : ( ~ $i(v1) | ~ isPrime0(v1) | ~ aDivisorOf0(v1, sz10) | % 83.42/11.76 | ~ aInteger0(sz10))) % 83.42/11.76 | % 83.42/11.76 | ALPHA: (m__2079) implies: % 83.42/11.76 | (3) ? [v0: $i] : ? [v1: $i] : (stldt0(v0) = cS2076 & sbsmnsldt0(xS) = v0 % 83.42/11.76 | & smndt0(sz10) = v1 & $i(v1) & $i(v0) & aElementOf0(v1, cS2076) & % 83.42/11.76 | aElementOf0(sz10, cS2076) & aSet0(v0) & aSet0(cS2076) & ! [v2: $i] : % 83.42/11.76 | ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ aElementOf0(v3, xS) | ~ % 83.42/11.76 | aElementOf0(v2, v3) | ~ aInteger0(v2) | aElementOf0(v2, v0)) & ! % 83.42/11.76 | [v2: $i] : (v2 = v1 | v2 = sz10 | ~ $i(v2) | ~ aElementOf0(v2, % 83.42/11.76 | cS2076)) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v0) | ~ % 83.42/11.76 | aElementOf0(v2, cS2076)) & ! [v2: $i] : ( ~ $i(v2) | ~ % 83.42/11.76 | aElementOf0(v2, v0) | aInteger0(v2)) & ! [v2: $i] : ( ~ $i(v2) | % 83.42/11.76 | ~ aElementOf0(v2, v0) | ? [v3: $i] : ($i(v3) & aElementOf0(v3, xS) % 83.42/11.76 | & aElementOf0(v2, v3))) & ! [v2: $i] : ( ~ $i(v2) | ~ % 83.42/11.76 | aElementOf0(v2, cS2076) | aInteger0(v2)) & ! [v2: $i] : ( ~ $i(v2) % 83.42/11.76 | | ~ aInteger0(v2) | aElementOf0(v2, v0) | aElementOf0(v2, % 83.42/11.76 | cS2076))) % 83.42/11.76 | % 83.42/11.76 | ALPHA: (m__2144) implies: % 83.42/11.77 | (4) ? [v0: $i] : ? [v1: $i] : (stldt0(v0) = v1 & sbsmnsldt0(xS) = v0 & % 83.42/11.77 | $i(v1) & $i(v0) & isClosed0(v0) & isOpen0(v1) & aSet0(v0) & ! [v2: % 83.42/11.77 | $i] : ! [v3: $i] : ( ~ (smndt0(v2) = v3) | ~ $i(v2) | ~ % 83.42/11.77 | aElementOf0(v2, v1) | ? [v4: $i] : ? [v5: $i] : ( ~ (v4 = sz00) & % 83.42/11.77 | szAzrzSzezqlpdtcmdtrp0(v2, v4) = v5 & $i(v5) & $i(v4) & % 83.42/11.77 | aSubsetOf0(v5, v1) & aSet0(v5) & aInteger0(v4) & ! [v6: $i] : ! % 83.42/11.77 | [v7: $i] : ! [v8: $i] : ( ~ (sdtasdt0(v4, v8) = v7) | ~ % 83.42/11.77 | (sdtpldt0(v6, v3) = v7) | ~ $i(v8) | ~ $i(v6) | ~ % 83.42/11.77 | aInteger0(v8) | ~ aInteger0(v6) | aElementOf0(v6, v5)) & ! % 83.42/11.77 | [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6) % 83.42/11.77 | | ~ aElementOf0(v6, v5) | sdteqdtlpzmzozddtrp0(v6, v2, v4)) & % 83.42/11.77 | ! [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~ % 83.42/11.77 | $i(v6) | ~ aElementOf0(v6, v5) | aDivisorOf0(v4, v7)) & ! % 83.42/11.77 | [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6) % 83.42/11.77 | | ~ aElementOf0(v6, v5) | aInteger0(v6)) & ! [v6: $i] : ! % 83.42/11.77 | [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~ % 83.42/11.77 | aElementOf0(v6, v5) | ? [v8: $i] : (sdtasdt0(v4, v8) = v7 & % 83.42/11.77 | $i(v8) & $i(v7) & aInteger0(v8))) & ! [v6: $i] : ! [v7: $i] % 83.42/11.77 | : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~ % 83.42/11.77 | sdteqdtlpzmzozddtrp0(v6, v2, v4) | ~ aInteger0(v6) | % 83.42/11.77 | aElementOf0(v6, v5)) & ! [v6: $i] : ! [v7: $i] : ( ~ % 83.42/11.77 | (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~ aDivisorOf0(v4, v7) | % 83.42/11.77 | ~ aInteger0(v6) | aElementOf0(v6, v5)) & ! [v6: $i] : ( ~ % 83.42/11.77 | $i(v6) | ~ aElementOf0(v6, v5) | aElementOf0(v6, v1)))) & ! % 83.42/11.77 | [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ aElementOf0(v3, % 83.42/11.77 | xS) | ~ aElementOf0(v2, v3) | ~ aInteger0(v2) | aElementOf0(v2, % 83.42/11.77 | v0)) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | ~ % 83.42/11.77 | aElementOf0(v2, v0)) & ! [v2: $i] : ( ~ $i(v2) | ~ % 83.42/11.77 | aElementOf0(v2, v1) | aInteger0(v2)) & ! [v2: $i] : ( ~ $i(v2) | % 83.42/11.77 | ~ aElementOf0(v2, v0) | aInteger0(v2)) & ! [v2: $i] : ( ~ $i(v2) | % 83.42/11.77 | ~ aElementOf0(v2, v0) | ? [v3: $i] : ($i(v3) & aElementOf0(v3, % 83.42/11.77 | xS) & aElementOf0(v2, v3))) & ! [v2: $i] : ( ~ $i(v2) | ~ % 83.42/11.77 | aInteger0(v2) | aElementOf0(v2, v1) | aElementOf0(v2, v0))) % 83.42/11.77 | % 83.42/11.77 | ALPHA: (m__) implies: % 83.42/11.77 | (5) $i(sz10) % 83.42/11.78 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (stldt0(v1) = v2 & % 83.42/11.78 | sbsmnsldt0(xS) = v1 & smndt0(sz10) = v0 & $i(v2) & $i(v1) & $i(v0) & % 83.42/11.78 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : % 83.42/11.78 | (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ % 83.42/11.78 | (sdtasdt0(v3, v7) = v6) | ~ (sdtpldt0(v5, v0) = v6) | ~ $i(v7) | % 83.42/11.78 | ~ $i(v5) | ~ $i(v3) | ~ aInteger0(v7) | ~ aInteger0(v5) | ~ % 83.42/11.78 | aInteger0(v3) | aElementOf0(v5, v4)) & ! [v3: $i] : ! [v4: $i] : % 83.42/11.78 | ! [v5: $i] : ! [v6: $i] : (v3 = sz00 | ~ % 83.42/11.78 | (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ (sdtpldt0(v5, v0) = % 83.42/11.78 | v6) | ~ $i(v5) | ~ $i(v3) | ~ aElementOf0(v5, v4) | ~ % 83.42/11.78 | aInteger0(v3) | sdteqdtlpzmzozddtrp0(v5, sz10, v3)) & ! [v3: $i] : % 83.42/11.78 | ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = sz00 | ~ % 83.42/11.78 | (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ (sdtpldt0(v5, v0) = % 83.42/11.78 | v6) | ~ $i(v5) | ~ $i(v3) | ~ aElementOf0(v5, v4) | ~ % 83.42/11.78 | aInteger0(v3) | aDivisorOf0(v3, v6)) & ! [v3: $i] : ! [v4: $i] : % 83.42/11.78 | ! [v5: $i] : ! [v6: $i] : (v3 = sz00 | ~ % 83.42/11.78 | (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ (sdtpldt0(v5, v0) = % 83.42/11.78 | v6) | ~ $i(v5) | ~ $i(v3) | ~ aElementOf0(v5, v4) | ~ % 83.42/11.78 | aInteger0(v3) | aInteger0(v5)) & ! [v3: $i] : ! [v4: $i] : ! % 83.42/11.78 | [v5: $i] : ! [v6: $i] : (v3 = sz00 | ~ % 83.42/11.78 | (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ (sdtpldt0(v5, v0) = % 83.42/11.78 | v6) | ~ $i(v5) | ~ $i(v3) | ~ aElementOf0(v5, v4) | ~ % 83.42/11.78 | aInteger0(v3) | ? [v7: $i] : (sdtasdt0(v3, v7) = v6 & $i(v7) & % 83.42/11.78 | $i(v6) & aInteger0(v7))) & ! [v3: $i] : ! [v4: $i] : ! [v5: % 83.42/11.78 | $i] : ! [v6: $i] : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, % 83.42/11.78 | v3) = v4) | ~ (sdtpldt0(v5, v0) = v6) | ~ $i(v5) | ~ $i(v3) % 83.42/11.78 | | ~ sdteqdtlpzmzozddtrp0(v5, sz10, v3) | ~ aInteger0(v5) | ~ % 83.42/11.78 | aInteger0(v3) | aElementOf0(v5, v4)) & ! [v3: $i] : ! [v4: $i] : % 83.42/11.78 | ! [v5: $i] : ! [v6: $i] : (v3 = sz00 | ~ % 83.42/11.78 | (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ (sdtpldt0(v5, v0) = % 83.42/11.78 | v6) | ~ $i(v5) | ~ $i(v3) | ~ aDivisorOf0(v3, v6) | ~ % 83.42/11.78 | aInteger0(v5) | ~ aInteger0(v3) | aElementOf0(v5, v4)) & ! [v3: % 83.42/11.78 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = sz00 | ~ % 83.42/11.78 | (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v6) | ~ $i(v5) | % 83.42/11.78 | ~ $i(v3) | ~ aElementOf0(v6, xS) | ~ aElementOf0(v5, v6) | ~ % 83.42/11.78 | aInteger0(v5) | ~ aInteger0(v3) | aElementOf0(v5, v1)) & ! [v3: % 83.42/11.78 | $i] : ! [v4: $i] : ! [v5: $i] : (v3 = sz00 | ~ % 83.42/11.78 | (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v5) | ~ $i(v3) | % 83.42/11.78 | ~ aElementOf0(v5, v2) | ~ aElementOf0(v5, v1) | ~ aInteger0(v3)) % 83.42/11.78 | & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v3 = sz00 | ~ % 83.42/11.78 | (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v5) | ~ $i(v3) | % 83.42/11.78 | ~ aElementOf0(v5, v2) | ~ aInteger0(v3) | aInteger0(v5)) & ! [v3: % 83.42/11.78 | $i] : ! [v4: $i] : ! [v5: $i] : (v3 = sz00 | ~ % 83.42/11.78 | (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v5) | ~ $i(v3) | % 83.42/11.78 | ~ aElementOf0(v5, v1) | ~ aInteger0(v3) | aInteger0(v5)) & ! [v3: % 83.42/11.78 | $i] : ! [v4: $i] : ! [v5: $i] : (v3 = sz00 | ~ % 83.42/11.78 | (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v5) | ~ $i(v3) | % 83.42/11.78 | ~ aElementOf0(v5, v1) | ~ aInteger0(v3) | ? [v6: $i] : ($i(v6) & % 83.42/11.78 | aElementOf0(v6, xS) & aElementOf0(v5, v6))) & ! [v3: $i] : ! % 83.42/11.78 | [v4: $i] : ! [v5: $i] : (v3 = sz00 | ~ % 83.42/11.78 | (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v5) | ~ $i(v3) | % 83.42/11.78 | ~ aInteger0(v5) | ~ aInteger0(v3) | aElementOf0(v5, v2) | % 83.42/11.78 | aElementOf0(v5, v1)) & ! [v3: $i] : ! [v4: $i] : (v3 = sz00 | ~ % 83.42/11.78 | (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v3) | ~ % 83.42/11.78 | aSubsetOf0(v4, v2) | ~ aInteger0(v3)) & ! [v3: $i] : ! [v4: $i] % 83.69/11.78 | : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v3) % 83.69/11.78 | | ~ aInteger0(v3) | aSet0(v4)) & ! [v3: $i] : ! [v4: $i] : (v3 = % 83.69/11.78 | sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v3) | ~ % 83.69/11.78 | aInteger0(v3) | aSet0(v1)) & ! [v3: $i] : ! [v4: $i] : (v3 = sz00 % 83.69/11.78 | | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v3) | ~ % 83.69/11.78 | aInteger0(v3) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, v4) & ~ % 83.69/11.78 | aElementOf0(v5, v2)))) % 83.69/11.78 | % 83.69/11.78 | ALPHA: (function-axioms) implies: % 83.69/11.78 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = % 83.69/11.78 | v1) | ~ (smndt0(v2) = v0)) % 83.69/11.78 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sbsmnsldt0(v2) % 83.69/11.78 | = v1) | ~ (sbsmnsldt0(v2) = v0)) % 83.69/11.78 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (stldt0(v2) = % 83.69/11.78 | v1) | ~ (stldt0(v2) = v0)) % 83.69/11.78 | % 83.69/11.79 | DELTA: instantiating (2) with fresh symbol all_36_0 gives: % 83.69/11.79 | (10) smndt0(sz10) = all_36_0 & $i(all_36_0) & ! [v0: any] : (v0 = all_36_0 % 83.69/11.79 | | v0 = sz10 | ~ $i(v0) | ~ aInteger0(v0) | ? [v1: $i] : ($i(v1) & % 83.69/11.79 | isPrime0(v1) & aDivisorOf0(v1, v0))) & ! [v0: $i] : ( ~ $i(v0) | % 83.69/11.79 | ~ isPrime0(v0) | ~ aDivisorOf0(v0, all_36_0) | ~ % 83.69/11.79 | aInteger0(all_36_0)) & ! [v0: $i] : ( ~ $i(v0) | ~ isPrime0(v0) | % 83.69/11.79 | ~ aDivisorOf0(v0, sz10) | ~ aInteger0(sz10)) % 83.69/11.79 | % 83.69/11.79 | ALPHA: (10) implies: % 83.69/11.79 | (11) smndt0(sz10) = all_36_0 % 83.69/11.79 | % 83.69/11.79 | DELTA: instantiating (1) with fresh symbol all_39_0 gives: % 83.69/11.79 | (12) smndt0(sz10) = all_39_0 & $i(all_39_0) & ! [v0: $i] : ! [v1: $i] : ( % 83.69/11.79 | ~ (sdtasdt0(v0, all_39_0) = v1) | ~ $i(v0) | ~ aInteger0(v0) | % 83.69/11.79 | (sdtasdt0(all_39_0, v0) = v1 & smndt0(v0) = v1 & $i(v1))) & ! [v0: % 83.69/11.79 | $i] : ! [v1: $i] : ( ~ (sdtasdt0(all_39_0, v0) = v1) | ~ $i(v0) | % 83.69/11.79 | ~ aInteger0(v0) | (sdtasdt0(v0, all_39_0) = v1 & smndt0(v0) = v1 & % 83.69/11.79 | $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ % 83.69/11.79 | $i(v0) | ~ aInteger0(v0) | (sdtasdt0(v0, all_39_0) = v1 & % 83.69/11.79 | sdtasdt0(all_39_0, v0) = v1 & $i(v1))) % 83.69/11.79 | % 83.69/11.79 | ALPHA: (12) implies: % 83.69/11.79 | (13) smndt0(sz10) = all_39_0 % 83.69/11.79 | % 83.69/11.79 | DELTA: instantiating (3) with fresh symbols all_42_0, all_42_1 gives: % 83.69/11.79 | (14) stldt0(all_42_1) = cS2076 & sbsmnsldt0(xS) = all_42_1 & smndt0(sz10) = % 83.69/11.79 | all_42_0 & $i(all_42_0) & $i(all_42_1) & aElementOf0(all_42_0, cS2076) % 83.69/11.79 | & aElementOf0(sz10, cS2076) & aSet0(all_42_1) & aSet0(cS2076) & ! % 83.69/11.79 | [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, % 83.69/11.79 | xS) | ~ aElementOf0(v0, v1) | ~ aInteger0(v0) | aElementOf0(v0, % 83.69/11.79 | all_42_1)) & ! [v0: any] : (v0 = all_42_0 | v0 = sz10 | ~ $i(v0) % 83.69/11.79 | | ~ aElementOf0(v0, cS2076)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 83.69/11.79 | aElementOf0(v0, all_42_1) | ~ aElementOf0(v0, cS2076)) & ! [v0: % 83.69/11.79 | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_42_1) | aInteger0(v0)) & % 83.69/11.79 | ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_42_1) | ? [v1: $i] : % 83.69/11.79 | ($i(v1) & aElementOf0(v1, xS) & aElementOf0(v0, v1))) & ! [v0: $i] % 83.69/11.79 | : ( ~ $i(v0) | ~ aElementOf0(v0, cS2076) | aInteger0(v0)) & ! [v0: % 83.69/11.79 | $i] : ( ~ $i(v0) | ~ aInteger0(v0) | aElementOf0(v0, all_42_1) | % 83.69/11.79 | aElementOf0(v0, cS2076)) % 83.69/11.79 | % 83.69/11.79 | ALPHA: (14) implies: % 83.69/11.79 | (15) aElementOf0(sz10, cS2076) % 83.69/11.79 | (16) smndt0(sz10) = all_42_0 % 83.69/11.79 | (17) sbsmnsldt0(xS) = all_42_1 % 83.69/11.79 | (18) stldt0(all_42_1) = cS2076 % 83.69/11.79 | % 83.69/11.79 | DELTA: instantiating (4) with fresh symbols all_45_0, all_45_1 gives: % 83.69/11.80 | (19) stldt0(all_45_1) = all_45_0 & sbsmnsldt0(xS) = all_45_1 & $i(all_45_0) % 83.69/11.80 | & $i(all_45_1) & isClosed0(all_45_1) & isOpen0(all_45_0) & % 83.69/11.80 | aSet0(all_45_1) & ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | % 83.69/11.80 | ~ $i(v0) | ~ aElementOf0(v0, all_45_0) | ? [v2: $i] : ? [v3: $i] % 83.69/11.80 | : ( ~ (v2 = sz00) & szAzrzSzezqlpdtcmdtrp0(v0, v2) = v3 & $i(v3) & % 83.69/11.80 | $i(v2) & aSubsetOf0(v3, all_45_0) & aSet0(v3) & aInteger0(v2) & ! % 83.69/11.80 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtasdt0(v2, v6) = v5) % 83.69/11.80 | | ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v6) | ~ $i(v4) | ~ % 83.69/11.80 | aInteger0(v6) | ~ aInteger0(v4) | aElementOf0(v4, v3)) & ! % 83.69/11.80 | [v4: $i] : ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | % 83.69/11.80 | ~ aElementOf0(v4, v3) | sdteqdtlpzmzozddtrp0(v4, v0, v2)) & ! % 83.69/11.80 | [v4: $i] : ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | % 83.69/11.80 | ~ aElementOf0(v4, v3) | aDivisorOf0(v2, v5)) & ! [v4: $i] : ! % 83.69/11.80 | [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ % 83.69/11.80 | aElementOf0(v4, v3) | aInteger0(v4)) & ! [v4: $i] : ! [v5: $i] % 83.69/11.80 | : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aElementOf0(v4, v3) % 83.69/11.80 | | ? [v6: $i] : (sdtasdt0(v2, v6) = v5 & $i(v6) & $i(v5) & % 83.69/11.80 | aInteger0(v6))) & ! [v4: $i] : ! [v5: $i] : ( ~ % 83.69/11.80 | (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ % 83.69/11.80 | sdteqdtlpzmzozddtrp0(v4, v0, v2) | ~ aInteger0(v4) | % 83.69/11.80 | aElementOf0(v4, v3)) & ! [v4: $i] : ! [v5: $i] : ( ~ % 83.69/11.80 | (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aDivisorOf0(v2, v5) | % 83.69/11.80 | ~ aInteger0(v4) | aElementOf0(v4, v3)) & ! [v4: $i] : ( ~ % 83.69/11.80 | $i(v4) | ~ aElementOf0(v4, v3) | aElementOf0(v4, all_45_0)))) & % 83.69/11.80 | ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 83.69/11.80 | aElementOf0(v1, xS) | ~ aElementOf0(v0, v1) | ~ aInteger0(v0) | % 83.69/11.80 | aElementOf0(v0, all_45_1)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 83.69/11.80 | aElementOf0(v0, all_45_0) | ~ aElementOf0(v0, all_45_1)) & ! [v0: % 83.69/11.80 | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_45_0) | aInteger0(v0)) & % 83.69/11.80 | ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_45_1) | % 83.69/11.80 | aInteger0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, % 83.69/11.80 | all_45_1) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, xS) & % 83.69/11.80 | aElementOf0(v0, v1))) & ! [v0: $i] : ( ~ $i(v0) | ~ % 83.69/11.80 | aInteger0(v0) | aElementOf0(v0, all_45_0) | aElementOf0(v0, % 83.69/11.80 | all_45_1)) % 83.69/11.80 | % 83.69/11.80 | ALPHA: (19) implies: % 83.69/11.80 | (20) sbsmnsldt0(xS) = all_45_1 % 83.69/11.80 | (21) stldt0(all_45_1) = all_45_0 % 83.69/11.80 | (22) ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ~ % 83.69/11.80 | aElementOf0(v0, all_45_0) | ? [v2: $i] : ? [v3: $i] : ( ~ (v2 = % 83.69/11.80 | sz00) & szAzrzSzezqlpdtcmdtrp0(v0, v2) = v3 & $i(v3) & $i(v2) & % 83.69/11.80 | aSubsetOf0(v3, all_45_0) & aSet0(v3) & aInteger0(v2) & ! [v4: $i] % 83.69/11.80 | : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtasdt0(v2, v6) = v5) | ~ % 83.69/11.80 | (sdtpldt0(v4, v1) = v5) | ~ $i(v6) | ~ $i(v4) | ~ % 83.69/11.80 | aInteger0(v6) | ~ aInteger0(v4) | aElementOf0(v4, v3)) & ! % 83.69/11.80 | [v4: $i] : ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | % 83.69/11.80 | ~ aElementOf0(v4, v3) | sdteqdtlpzmzozddtrp0(v4, v0, v2)) & ! % 83.69/11.80 | [v4: $i] : ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | % 83.69/11.80 | ~ aElementOf0(v4, v3) | aDivisorOf0(v2, v5)) & ! [v4: $i] : ! % 83.69/11.80 | [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ % 83.69/11.80 | aElementOf0(v4, v3) | aInteger0(v4)) & ! [v4: $i] : ! [v5: $i] % 83.69/11.80 | : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aElementOf0(v4, v3) % 83.69/11.80 | | ? [v6: $i] : (sdtasdt0(v2, v6) = v5 & $i(v6) & $i(v5) & % 83.69/11.80 | aInteger0(v6))) & ! [v4: $i] : ! [v5: $i] : ( ~ % 83.69/11.80 | (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ % 83.69/11.80 | sdteqdtlpzmzozddtrp0(v4, v0, v2) | ~ aInteger0(v4) | % 83.69/11.80 | aElementOf0(v4, v3)) & ! [v4: $i] : ! [v5: $i] : ( ~ % 83.69/11.80 | (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aDivisorOf0(v2, v5) | % 83.69/11.80 | ~ aInteger0(v4) | aElementOf0(v4, v3)) & ! [v4: $i] : ( ~ % 83.69/11.80 | $i(v4) | ~ aElementOf0(v4, v3) | aElementOf0(v4, all_45_0)))) % 83.69/11.80 | % 83.69/11.80 | DELTA: instantiating (6) with fresh symbols all_48_0, all_48_1, all_48_2 % 83.69/11.80 | gives: % 83.69/11.81 | (23) stldt0(all_48_1) = all_48_0 & sbsmnsldt0(xS) = all_48_1 & smndt0(sz10) % 83.69/11.81 | = all_48_2 & $i(all_48_0) & $i(all_48_1) & $i(all_48_2) & ! [v0: $i] % 83.69/11.81 | : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v0 = sz00 | % 83.69/11.81 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~ (sdtasdt0(v0, v4) = % 83.69/11.81 | v3) | ~ (sdtpldt0(v2, all_48_2) = v3) | ~ $i(v4) | ~ $i(v2) | % 83.69/11.81 | ~ $i(v0) | ~ aInteger0(v4) | ~ aInteger0(v2) | ~ aInteger0(v0) | % 83.69/11.81 | aElementOf0(v2, v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 83.69/11.81 | [v3: $i] : (v0 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | % 83.69/11.81 | ~ (sdtpldt0(v2, all_48_2) = v3) | ~ $i(v2) | ~ $i(v0) | ~ % 83.69/11.81 | aElementOf0(v2, v1) | ~ aInteger0(v0) | sdteqdtlpzmzozddtrp0(v2, % 83.69/11.81 | sz10, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 83.69/11.81 | : (v0 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~ % 83.69/11.81 | (sdtpldt0(v2, all_48_2) = v3) | ~ $i(v2) | ~ $i(v0) | ~ % 83.69/11.81 | aElementOf0(v2, v1) | ~ aInteger0(v0) | aDivisorOf0(v0, v3)) & ! % 83.69/11.81 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v0 = sz00 | ~ % 83.69/11.81 | (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~ (sdtpldt0(v2, all_48_2) % 83.69/11.81 | = v3) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~ % 83.69/11.81 | aInteger0(v0) | aInteger0(v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 83.69/11.81 | $i] : ! [v3: $i] : (v0 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, % 83.69/11.81 | v0) = v1) | ~ (sdtpldt0(v2, all_48_2) = v3) | ~ $i(v2) | ~ % 83.69/11.81 | $i(v0) | ~ aElementOf0(v2, v1) | ~ aInteger0(v0) | ? [v4: $i] : % 83.69/11.81 | (sdtasdt0(v0, v4) = v3 & $i(v4) & $i(v3) & aInteger0(v4))) & ! [v0: % 83.69/11.81 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v0 = sz00 | ~ % 83.69/11.81 | (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~ (sdtpldt0(v2, all_48_2) % 83.69/11.81 | = v3) | ~ $i(v2) | ~ $i(v0) | ~ sdteqdtlpzmzozddtrp0(v2, sz10, % 83.69/11.81 | v0) | ~ aInteger0(v2) | ~ aInteger0(v0) | aElementOf0(v2, v1)) & % 83.69/11.81 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v0 = sz00 | % 83.69/11.81 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~ (sdtpldt0(v2, % 83.69/11.81 | all_48_2) = v3) | ~ $i(v2) | ~ $i(v0) | ~ aDivisorOf0(v0, v3) % 83.69/11.81 | | ~ aInteger0(v2) | ~ aInteger0(v0) | aElementOf0(v2, v1)) & ! % 83.69/11.81 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v0 = sz00 | ~ % 83.69/11.81 | (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~ $i(v3) | ~ $i(v2) | ~ % 83.69/11.81 | $i(v0) | ~ aElementOf0(v3, xS) | ~ aElementOf0(v2, v3) | ~ % 83.69/11.81 | aInteger0(v2) | ~ aInteger0(v0) | aElementOf0(v2, all_48_1)) & ! % 83.69/11.81 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~ % 83.69/11.81 | (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ % 83.69/11.81 | aElementOf0(v2, all_48_0) | ~ aElementOf0(v2, all_48_1) | ~ % 83.69/11.81 | aInteger0(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = % 83.69/11.81 | sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~ $i(v2) | ~ % 83.69/11.81 | $i(v0) | ~ aElementOf0(v2, all_48_0) | ~ aInteger0(v0) | % 83.69/11.81 | aInteger0(v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = % 83.69/11.81 | sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~ $i(v2) | ~ % 83.69/11.81 | $i(v0) | ~ aElementOf0(v2, all_48_1) | ~ aInteger0(v0) | % 83.69/11.81 | aInteger0(v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = % 83.69/11.81 | sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~ $i(v2) | ~ % 83.69/11.81 | $i(v0) | ~ aElementOf0(v2, all_48_1) | ~ aInteger0(v0) | ? [v3: % 83.69/11.81 | $i] : ($i(v3) & aElementOf0(v3, xS) & aElementOf0(v2, v3))) & ! % 83.69/11.81 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~ % 83.69/11.81 | (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ % 83.69/11.81 | aInteger0(v2) | ~ aInteger0(v0) | aElementOf0(v2, all_48_0) | % 83.69/11.81 | aElementOf0(v2, all_48_1)) & ! [v0: $i] : ! [v1: $i] : (v0 = sz00 % 83.69/11.81 | | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~ $i(v0) | ~ % 83.69/11.81 | aSubsetOf0(v1, all_48_0) | ~ aInteger0(v0)) & ! [v0: $i] : ! [v1: % 83.69/11.81 | $i] : (v0 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~ % 83.69/11.81 | $i(v0) | ~ aInteger0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i] : % 83.69/11.81 | (v0 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~ $i(v0) | % 83.69/11.81 | ~ aInteger0(v0) | aSet0(all_48_1)) & ! [v0: $i] : ! [v1: $i] : (v0 % 83.69/11.81 | = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~ $i(v0) | ~ % 83.69/11.81 | aInteger0(v0) | ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ % 83.69/11.81 | aElementOf0(v2, all_48_0))) % 83.69/11.81 | % 83.69/11.81 | ALPHA: (23) implies: % 83.69/11.81 | (24) smndt0(sz10) = all_48_2 % 83.69/11.81 | (25) sbsmnsldt0(xS) = all_48_1 % 83.69/11.81 | (26) stldt0(all_48_1) = all_48_0 % 83.69/11.81 | (27) ! [v0: $i] : ! [v1: $i] : (v0 = sz00 | ~ % 83.69/11.81 | (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~ $i(v0) | ~ % 83.69/11.81 | aSubsetOf0(v1, all_48_0) | ~ aInteger0(v0)) % 83.69/11.81 | % 83.69/11.81 | GROUND_INST: instantiating (7) with all_36_0, all_42_0, sz10, simplifying with % 83.69/11.81 | (11), (16) gives: % 83.69/11.81 | (28) all_42_0 = all_36_0 % 83.69/11.81 | % 83.69/11.81 | GROUND_INST: instantiating (7) with all_42_0, all_48_2, sz10, simplifying with % 83.69/11.81 | (16), (24) gives: % 83.69/11.81 | (29) all_48_2 = all_42_0 % 83.69/11.81 | % 83.69/11.81 | GROUND_INST: instantiating (7) with all_39_0, all_48_2, sz10, simplifying with % 83.69/11.81 | (13), (24) gives: % 83.69/11.81 | (30) all_48_2 = all_39_0 % 83.69/11.81 | % 83.69/11.81 | GROUND_INST: instantiating (8) with all_45_1, all_48_1, xS, simplifying with % 83.69/11.81 | (20), (25) gives: % 83.69/11.81 | (31) all_48_1 = all_45_1 % 83.69/11.81 | % 83.69/11.81 | GROUND_INST: instantiating (8) with all_42_1, all_48_1, xS, simplifying with % 83.69/11.81 | (17), (25) gives: % 83.69/11.81 | (32) all_48_1 = all_42_1 % 83.69/11.81 | % 83.69/11.81 | GROUND_INST: instantiating (9) with all_45_0, all_48_0, all_45_1, simplifying % 83.69/11.81 | with (21) gives: % 83.69/11.81 | (33) all_48_0 = all_45_0 | ~ (stldt0(all_45_1) = all_48_0) % 83.69/11.81 | % 83.69/11.81 | GROUND_INST: instantiating (9) with cS2076, all_48_0, all_42_1, simplifying % 83.69/11.81 | with (18) gives: % 83.69/11.81 | (34) all_48_0 = cS2076 | ~ (stldt0(all_42_1) = all_48_0) % 83.69/11.81 | % 83.69/11.81 | COMBINE_EQS: (31), (32) imply: % 83.69/11.81 | (35) all_45_1 = all_42_1 % 83.69/11.81 | % 83.69/11.81 | SIMP: (35) implies: % 83.69/11.81 | (36) all_45_1 = all_42_1 % 83.69/11.81 | % 83.69/11.81 | COMBINE_EQS: (29), (30) imply: % 83.69/11.81 | (37) all_42_0 = all_39_0 % 83.69/11.81 | % 83.69/11.81 | SIMP: (37) implies: % 83.69/11.81 | (38) all_42_0 = all_39_0 % 83.69/11.81 | % 83.69/11.81 | COMBINE_EQS: (28), (38) imply: % 83.69/11.81 | (39) all_39_0 = all_36_0 % 83.69/11.81 | % 83.69/11.81 | SIMP: (39) implies: % 83.69/11.81 | (40) all_39_0 = all_36_0 % 83.69/11.81 | % 83.69/11.81 | REDUCE: (26), (32) imply: % 83.69/11.81 | (41) stldt0(all_42_1) = all_48_0 % 83.69/11.81 | % 83.69/11.81 | BETA: splitting (33) gives: % 83.69/11.81 | % 83.69/11.81 | Case 1: % 83.69/11.81 | | % 83.69/11.81 | | (42) ~ (stldt0(all_45_1) = all_48_0) % 83.69/11.81 | | % 83.69/11.81 | | REDUCE: (36), (42) imply: % 83.69/11.81 | | (43) ~ (stldt0(all_42_1) = all_48_0) % 83.69/11.81 | | % 83.69/11.81 | | PRED_UNIFY: (41), (43) imply: % 83.69/11.81 | | (44) $false % 83.69/11.81 | | % 83.69/11.81 | | CLOSE: (44) is inconsistent. % 83.69/11.81 | | % 83.69/11.81 | Case 2: % 83.69/11.81 | | % 83.69/11.81 | | (45) all_48_0 = all_45_0 % 83.69/11.81 | | % 83.69/11.81 | | BETA: splitting (34) gives: % 83.69/11.81 | | % 83.69/11.81 | | Case 1: % 83.69/11.81 | | | % 83.69/11.81 | | | (46) ~ (stldt0(all_42_1) = all_48_0) % 83.69/11.81 | | | % 83.69/11.81 | | | PRED_UNIFY: (41), (46) imply: % 83.69/11.82 | | | (47) $false % 83.69/11.82 | | | % 83.69/11.82 | | | CLOSE: (47) is inconsistent. % 83.69/11.82 | | | % 83.69/11.82 | | Case 2: % 83.69/11.82 | | | % 83.69/11.82 | | | (48) all_48_0 = cS2076 % 83.69/11.82 | | | % 83.69/11.82 | | | COMBINE_EQS: (45), (48) imply: % 83.69/11.82 | | | (49) all_45_0 = cS2076 % 83.69/11.82 | | | % 83.69/11.82 | | | GROUND_INST: instantiating (22) with sz10, all_36_0, simplifying with (5), % 83.69/11.82 | | | (11) gives: % 83.69/11.82 | | | (50) ~ aElementOf0(sz10, all_45_0) | ? [v0: $i] : ? [v1: $i] : ( ~ % 83.69/11.82 | | | (v0 = sz00) & szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1 & $i(v1) & % 83.69/11.82 | | | $i(v0) & aSubsetOf0(v1, all_45_0) & aSet0(v1) & aInteger0(v0) & % 83.69/11.82 | | | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasdt0(v0, v4) = % 83.69/11.82 | | | v3) | ~ (sdtpldt0(v2, all_36_0) = v3) | ~ $i(v4) | ~ % 83.69/11.82 | | | $i(v2) | ~ aInteger0(v4) | ~ aInteger0(v2) | aElementOf0(v2, % 83.69/11.82 | | | v1)) & ! [v2: $i] : ! [v3: $i] : ( ~ (sdtpldt0(v2, % 83.69/11.82 | | | all_36_0) = v3) | ~ $i(v2) | ~ aElementOf0(v2, v1) | % 83.69/11.82 | | | sdteqdtlpzmzozddtrp0(v2, sz10, v0)) & ! [v2: $i] : ! [v3: % 83.69/11.82 | | | $i] : ( ~ (sdtpldt0(v2, all_36_0) = v3) | ~ $i(v2) | ~ % 83.69/11.82 | | | aElementOf0(v2, v1) | aDivisorOf0(v0, v3)) & ! [v2: $i] : ! % 83.69/11.82 | | | [v3: $i] : ( ~ (sdtpldt0(v2, all_36_0) = v3) | ~ $i(v2) | ~ % 83.69/11.82 | | | aElementOf0(v2, v1) | aInteger0(v2)) & ! [v2: $i] : ! [v3: % 83.69/11.82 | | | $i] : ( ~ (sdtpldt0(v2, all_36_0) = v3) | ~ $i(v2) | ~ % 83.69/11.82 | | | aElementOf0(v2, v1) | ? [v4: $i] : (sdtasdt0(v0, v4) = v3 & % 83.69/11.82 | | | $i(v4) & $i(v3) & aInteger0(v4))) & ! [v2: $i] : ! [v3: % 83.69/11.82 | | | $i] : ( ~ (sdtpldt0(v2, all_36_0) = v3) | ~ $i(v2) | ~ % 83.69/11.82 | | | sdteqdtlpzmzozddtrp0(v2, sz10, v0) | ~ aInteger0(v2) | % 83.69/11.82 | | | aElementOf0(v2, v1)) & ! [v2: $i] : ! [v3: $i] : ( ~ % 83.69/11.82 | | | (sdtpldt0(v2, all_36_0) = v3) | ~ $i(v2) | ~ aDivisorOf0(v0, % 83.69/11.82 | | | v3) | ~ aInteger0(v2) | aElementOf0(v2, v1)) & ! [v2: $i] % 83.69/11.82 | | | : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | aElementOf0(v2, % 83.69/11.82 | | | all_45_0))) % 83.69/11.82 | | | % 83.69/11.82 | | | BETA: splitting (50) gives: % 83.69/11.82 | | | % 83.69/11.82 | | | Case 1: % 83.69/11.82 | | | | % 83.69/11.82 | | | | (51) ~ aElementOf0(sz10, all_45_0) % 83.69/11.82 | | | | % 83.69/11.82 | | | | REDUCE: (49), (51) imply: % 83.69/11.82 | | | | (52) ~ aElementOf0(sz10, cS2076) % 83.69/11.82 | | | | % 83.69/11.82 | | | | PRED_UNIFY: (15), (52) imply: % 83.69/11.82 | | | | (53) $false % 83.69/11.82 | | | | % 83.69/11.82 | | | | CLOSE: (53) is inconsistent. % 83.69/11.82 | | | | % 83.69/11.82 | | | Case 2: % 83.69/11.82 | | | | % 83.69/11.82 | | | | (54) ? [v0: $i] : ? [v1: $i] : ( ~ (v0 = sz00) & % 83.69/11.82 | | | | szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1 & $i(v1) & $i(v0) & % 83.69/11.82 | | | | aSubsetOf0(v1, all_45_0) & aSet0(v1) & aInteger0(v0) & ! [v2: % 83.69/11.82 | | | | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasdt0(v0, v4) = % 83.69/11.82 | | | | v3) | ~ (sdtpldt0(v2, all_36_0) = v3) | ~ $i(v4) | ~ % 83.69/11.82 | | | | $i(v2) | ~ aInteger0(v4) | ~ aInteger0(v2) | % 83.69/11.82 | | | | aElementOf0(v2, v1)) & ! [v2: $i] : ! [v3: $i] : ( ~ % 83.69/11.82 | | | | (sdtpldt0(v2, all_36_0) = v3) | ~ $i(v2) | ~ % 83.69/11.82 | | | | aElementOf0(v2, v1) | sdteqdtlpzmzozddtrp0(v2, sz10, v0)) & % 83.69/11.82 | | | | ! [v2: $i] : ! [v3: $i] : ( ~ (sdtpldt0(v2, all_36_0) = v3) | % 83.69/11.82 | | | | ~ $i(v2) | ~ aElementOf0(v2, v1) | aDivisorOf0(v0, v3)) & % 83.69/11.82 | | | | ! [v2: $i] : ! [v3: $i] : ( ~ (sdtpldt0(v2, all_36_0) = v3) | % 83.69/11.82 | | | | ~ $i(v2) | ~ aElementOf0(v2, v1) | aInteger0(v2)) & ! % 83.69/11.82 | | | | [v2: $i] : ! [v3: $i] : ( ~ (sdtpldt0(v2, all_36_0) = v3) | % 83.69/11.82 | | | | ~ $i(v2) | ~ aElementOf0(v2, v1) | ? [v4: $i] : % 83.69/11.82 | | | | (sdtasdt0(v0, v4) = v3 & $i(v4) & $i(v3) & aInteger0(v4))) & % 83.69/11.82 | | | | ! [v2: $i] : ! [v3: $i] : ( ~ (sdtpldt0(v2, all_36_0) = v3) % 83.69/11.82 | | | | | ~ $i(v2) | ~ sdteqdtlpzmzozddtrp0(v2, sz10, v0) | ~ % 83.69/11.82 | | | | aInteger0(v2) | aElementOf0(v2, v1)) & ! [v2: $i] : ! [v3: % 83.69/11.82 | | | | $i] : ( ~ (sdtpldt0(v2, all_36_0) = v3) | ~ $i(v2) | ~ % 83.69/11.82 | | | | aDivisorOf0(v0, v3) | ~ aInteger0(v2) | aElementOf0(v2, % 83.69/11.82 | | | | v1)) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | % 83.69/11.82 | | | | aElementOf0(v2, all_45_0))) % 83.69/11.82 | | | | % 83.69/11.82 | | | | DELTA: instantiating (54) with fresh symbols all_92_0, all_92_1 gives: % 83.69/11.82 | | | | (55) ~ (all_92_1 = sz00) & szAzrzSzezqlpdtcmdtrp0(sz10, all_92_1) = % 83.69/11.82 | | | | all_92_0 & $i(all_92_0) & $i(all_92_1) & aSubsetOf0(all_92_0, % 83.69/11.82 | | | | all_45_0) & aSet0(all_92_0) & aInteger0(all_92_1) & ! [v0: % 83.69/11.82 | | | | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(all_92_1, v2) % 83.69/11.82 | | | | = v1) | ~ (sdtpldt0(v0, all_36_0) = v1) | ~ $i(v2) | ~ % 83.69/11.82 | | | | $i(v0) | ~ aInteger0(v2) | ~ aInteger0(v0) | aElementOf0(v0, % 83.69/11.82 | | | | all_92_0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(v0, % 83.69/11.82 | | | | all_36_0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_92_0) % 83.69/11.82 | | | | | sdteqdtlpzmzozddtrp0(v0, sz10, all_92_1)) & ! [v0: $i] : ! % 83.69/11.82 | | | | [v1: $i] : ( ~ (sdtpldt0(v0, all_36_0) = v1) | ~ $i(v0) | ~ % 83.69/11.82 | | | | aElementOf0(v0, all_92_0) | aDivisorOf0(all_92_1, v1)) & ! % 83.69/11.82 | | | | [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(v0, all_36_0) = v1) | ~ % 83.69/11.82 | | | | $i(v0) | ~ aElementOf0(v0, all_92_0) | aInteger0(v0)) & ! % 83.69/11.82 | | | | [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(v0, all_36_0) = v1) | ~ % 83.69/11.82 | | | | $i(v0) | ~ aElementOf0(v0, all_92_0) | ? [v2: $i] : % 83.69/11.82 | | | | (sdtasdt0(all_92_1, v2) = v1 & $i(v2) & $i(v1) & % 83.69/11.82 | | | | aInteger0(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 83.69/11.82 | | | | (sdtpldt0(v0, all_36_0) = v1) | ~ $i(v0) | ~ % 83.69/11.82 | | | | sdteqdtlpzmzozddtrp0(v0, sz10, all_92_1) | ~ aInteger0(v0) | % 83.69/11.82 | | | | aElementOf0(v0, all_92_0)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 83.69/11.82 | | | | (sdtpldt0(v0, all_36_0) = v1) | ~ $i(v0) | ~ % 83.69/11.82 | | | | aDivisorOf0(all_92_1, v1) | ~ aInteger0(v0) | aElementOf0(v0, % 83.69/11.82 | | | | all_92_0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, % 83.69/11.82 | | | | all_92_0) | aElementOf0(v0, all_45_0)) % 83.69/11.82 | | | | % 83.69/11.82 | | | | ALPHA: (55) implies: % 83.69/11.82 | | | | (56) ~ (all_92_1 = sz00) % 83.69/11.82 | | | | (57) aInteger0(all_92_1) % 83.69/11.82 | | | | (58) aSubsetOf0(all_92_0, all_45_0) % 83.69/11.82 | | | | (59) $i(all_92_1) % 83.69/11.83 | | | | (60) szAzrzSzezqlpdtcmdtrp0(sz10, all_92_1) = all_92_0 % 83.69/11.83 | | | | % 83.69/11.83 | | | | REDUCE: (49), (58) imply: % 83.69/11.83 | | | | (61) aSubsetOf0(all_92_0, cS2076) % 83.69/11.83 | | | | % 83.69/11.83 | | | | GROUND_INST: instantiating (27) with all_92_1, all_92_0, simplifying % 83.69/11.83 | | | | with (57), (59), (60) gives: % 83.69/11.83 | | | | (62) all_92_1 = sz00 | ~ aSubsetOf0(all_92_0, all_48_0) % 83.69/11.83 | | | | % 83.69/11.83 | | | | BETA: splitting (62) gives: % 83.69/11.83 | | | | % 83.69/11.83 | | | | Case 1: % 83.69/11.83 | | | | | % 83.69/11.83 | | | | | (63) ~ aSubsetOf0(all_92_0, all_48_0) % 83.69/11.83 | | | | | % 83.69/11.83 | | | | | REDUCE: (48), (63) imply: % 83.69/11.83 | | | | | (64) ~ aSubsetOf0(all_92_0, cS2076) % 83.69/11.83 | | | | | % 83.69/11.83 | | | | | PRED_UNIFY: (61), (64) imply: % 83.69/11.83 | | | | | (65) $false % 83.69/11.83 | | | | | % 83.69/11.83 | | | | | CLOSE: (65) is inconsistent. % 83.69/11.83 | | | | | % 83.69/11.83 | | | | Case 2: % 83.69/11.83 | | | | | % 83.69/11.83 | | | | | (66) all_92_1 = sz00 % 83.69/11.83 | | | | | % 83.69/11.83 | | | | | REDUCE: (56), (66) imply: % 83.69/11.83 | | | | | (67) $false % 83.69/11.83 | | | | | % 83.69/11.83 | | | | | CLOSE: (67) is inconsistent. % 83.69/11.83 | | | | | % 83.69/11.83 | | | | End of split % 83.69/11.83 | | | | % 83.69/11.83 | | | End of split % 83.69/11.83 | | | % 83.69/11.83 | | End of split % 83.69/11.83 | | % 83.69/11.83 | End of split % 83.69/11.83 | % 83.69/11.83 End of proof % 83.69/11.83 % SZS output end Proof for theBenchmark % 83.69/11.83 % 83.69/11.83 11199ms %------------------------------------------------------------------------------