%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM456+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 : n002.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 11:47:52 EDT 2023 % Result : Theorem 23.05s 3.91s % Output : Proof 37.67s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : NUM456+6 : TPTP v8.1.2. Released v4.0.0. % 0.06/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n002.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 16:34:17 EDT 2023 % 0.12/0.33 % CPUTime : % 0.18/0.62 ________ _____ % 0.18/0.62 ___ __ \_________(_)________________________________ % 0.18/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.62 % 0.18/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.62 (2023-06-19) % 0.18/0.62 % 0.18/0.62 (c) Philipp Rümmer, 2009-2023 % 0.18/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.62 Amanda Stjerna. % 0.18/0.62 Free software under BSD-3-Clause. % 0.18/0.62 % 0.18/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.62 % 0.18/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.63/0.63 Running up to 7 provers in parallel. % 0.63/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.63/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.63/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.63/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.63/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.63/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.63/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.82/1.44 Prover 1: Preprocessing ... % 4.82/1.44 Prover 4: Preprocessing ... % 5.24/1.48 Prover 5: Preprocessing ... % 5.24/1.48 Prover 6: Preprocessing ... % 5.24/1.48 Prover 0: Preprocessing ... % 5.24/1.48 Prover 3: Preprocessing ... % 5.24/1.49 Prover 2: Preprocessing ... % 16.46/3.04 Prover 1: Constructing countermodel ... % 16.95/3.08 Prover 3: Constructing countermodel ... % 17.41/3.23 Prover 5: Proving ... % 17.41/3.24 Prover 6: Proving ... % 19.80/3.47 Prover 2: Proving ... % 23.05/3.91 Prover 3: proved (3260ms) % 23.05/3.91 % 23.05/3.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 23.05/3.91 % 23.05/3.91 Prover 5: stopped % 23.05/3.91 Prover 6: stopped % 23.05/3.91 Prover 2: stopped % 23.05/3.92 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 23.05/3.92 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 23.05/3.92 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 23.05/3.93 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 24.22/4.10 Prover 0: Proving ... % 24.59/4.12 Prover 0: stopped % 24.59/4.14 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 24.91/4.20 Prover 4: Constructing countermodel ... % 25.65/4.27 Prover 8: Preprocessing ... % 26.07/4.31 Prover 10: Preprocessing ... % 26.49/4.37 Prover 11: Preprocessing ... % 26.49/4.39 Prover 7: Preprocessing ... % 26.83/4.43 Prover 13: Preprocessing ... % 27.90/4.73 Prover 10: Warning: ignoring some quantifiers % 27.90/4.75 Prover 10: Constructing countermodel ... % 27.90/4.81 Prover 7: Warning: ignoring some quantifiers % 27.90/4.83 Prover 8: Warning: ignoring some quantifiers % 27.90/4.84 Prover 8: Constructing countermodel ... % 27.90/4.84 Prover 7: Constructing countermodel ... % 30.84/4.94 Prover 13: Warning: ignoring some quantifiers % 30.84/4.97 Prover 13: Constructing countermodel ... % 34.12/5.40 Prover 10: Found proof (size 64) % 34.12/5.40 Prover 10: proved (1492ms) % 34.12/5.41 Prover 7: stopped % 34.12/5.41 Prover 8: stopped % 34.12/5.41 Prover 1: stopped % 34.12/5.41 Prover 13: stopped % 34.12/5.41 Prover 4: stopped % 36.34/5.91 Prover 11: Constructing countermodel ... % 36.58/5.94 Prover 11: stopped % 36.58/5.94 % 36.58/5.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 36.58/5.94 % 36.58/5.97 % SZS output start Proof for theBenchmark % 36.58/5.97 Assumptions after simplification: % 36.58/5.97 --------------------------------- % 36.58/5.97 % 36.58/5.97 (mArSeqClosed) % 36.58/6.01 $i(cS1395) & $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = sz00 | % 36.58/6.01 ~ (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 36.58/6.01 aInteger0(v1) | ~ aInteger0(v0) | isClosed0(v2)) & ! [v0: $i] : ! [v1: % 36.58/6.01 $i] : ! [v2: $i] : (v1 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) | % 36.58/6.01 ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) | aSubsetOf0(v2, % 36.58/6.01 cS1395)) % 36.58/6.01 % 36.58/6.01 (mIntOne) % 36.58/6.01 $i(sz10) & aInteger0(sz10) % 36.58/6.01 % 36.58/6.01 (mMulMinOne) % 36.93/6.02 $i(sz10) & ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 36.93/6.02 $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ aInteger0(v1) | % 36.93/6.02 (sdtasdt0(v1, v0) = v2 & smndt0(v1) = v2 & $i(v2)))) % 36.93/6.02 % 36.93/6.02 (mPrimeDivisor) % 36.93/6.02 $i(sz10) & ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : (v1 = v0 % 36.93/6.02 | v1 = sz10 | ~ $i(v1) | ~ aInteger0(v1) | ? [v2: $i] : ($i(v2) & % 36.93/6.02 isPrime0(v2) & aDivisorOf0(v2, v1))) & ! [v1: $i] : ( ~ $i(v1) | ~ % 36.93/6.02 isPrime0(v1) | ~ aDivisorOf0(v1, v0) | ~ aInteger0(v0)) & ! [v1: $i] : % 36.93/6.02 ( ~ $i(v1) | ~ isPrime0(v1) | ~ aDivisorOf0(v1, sz10) | ~ % 36.93/6.02 aInteger0(sz10))) % 36.93/6.02 % 36.93/6.02 (mSubset) % 36.93/6.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 36.93/6.03 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) | % 36.93/6.03 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | % 36.93/6.03 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i] % 36.93/6.03 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) | % 36.93/6.03 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0))) % 36.93/6.03 % 36.93/6.03 (m__2079) % 36.93/6.03 $i(cS2076) & $i(xS) & $i(sz10) & ? [v0: $i] : ? [v1: $i] : (stldt0(v0) = % 36.93/6.03 cS2076 & sbsmnsldt0(xS) = v0 & smndt0(sz10) = v1 & $i(v1) & $i(v0) & % 36.93/6.03 aElementOf0(v1, cS2076) & aElementOf0(sz10, cS2076) & aSet0(v0) & % 36.93/6.03 aSet0(cS2076) & ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ % 36.93/6.03 aElementOf0(v3, xS) | ~ aElementOf0(v2, v3) | ~ aInteger0(v2) | % 36.93/6.03 aElementOf0(v2, v0)) & ! [v2: $i] : (v2 = v1 | v2 = sz10 | ~ $i(v2) | ~ % 36.93/6.03 aElementOf0(v2, cS2076)) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, % 36.93/6.03 v0) | ~ aElementOf0(v2, cS2076)) & ! [v2: $i] : ( ~ $i(v2) | ~ % 36.93/6.03 aElementOf0(v2, v0) | aInteger0(v2)) & ! [v2: $i] : ( ~ $i(v2) | ~ % 36.93/6.03 aElementOf0(v2, v0) | ? [v3: $i] : ($i(v3) & aElementOf0(v3, xS) & % 36.93/6.03 aElementOf0(v2, v3))) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, % 36.93/6.03 cS2076) | aInteger0(v2)) & ! [v2: $i] : ( ~ $i(v2) | ~ aInteger0(v2) | % 36.93/6.03 aElementOf0(v2, v0) | aElementOf0(v2, cS2076))) % 36.93/6.03 % 36.93/6.03 (m__2144) % 36.93/6.04 $i(xS) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : (stldt0(v0) = v1 & % 36.93/6.04 sbsmnsldt0(xS) = v0 & $i(v1) & $i(v0) & isClosed0(v0) & isOpen0(v1) & % 36.93/6.04 aSet0(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (smndt0(v2) = v3) | ~ $i(v2) | % 36.93/6.05 ~ aElementOf0(v2, v1) | ? [v4: $i] : ? [v5: $i] : ( ~ (v4 = sz00) & % 36.93/6.05 szAzrzSzezqlpdtcmdtrp0(v2, v4) = v5 & $i(v5) & $i(v4) & aSubsetOf0(v5, % 36.93/6.05 v1) & aSet0(v5) & aInteger0(v4) & ! [v6: $i] : ! [v7: $i] : ! [v8: % 36.93/6.05 $i] : ( ~ (sdtasdt0(v4, v8) = v7) | ~ (sdtpldt0(v6, v3) = v7) | ~ % 36.93/6.05 $i(v8) | ~ $i(v6) | ~ aInteger0(v8) | ~ aInteger0(v6) | % 36.93/6.05 aElementOf0(v6, v5)) & ! [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, % 36.93/6.05 v3) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v5) | % 36.93/6.05 sdteqdtlpzmzozddtrp0(v6, v2, v4)) & ! [v6: $i] : ! [v7: $i] : ( ~ % 36.93/6.05 (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v5) | % 36.93/6.05 aDivisorOf0(v4, v7)) & ! [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, % 36.93/6.05 v3) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v5) | aInteger0(v6)) & % 36.93/6.05 ! [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~ % 36.93/6.05 aElementOf0(v6, v5) | ? [v8: $i] : (sdtasdt0(v4, v8) = v7 & $i(v8) & % 36.93/6.05 $i(v7) & aInteger0(v8))) & ! [v6: $i] : ! [v7: $i] : ( ~ % 36.93/6.05 (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~ sdteqdtlpzmzozddtrp0(v6, v2, % 36.93/6.05 v4) | ~ aInteger0(v6) | aElementOf0(v6, v5)) & ! [v6: $i] : ! % 36.93/6.05 [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~ aDivisorOf0(v4, % 36.93/6.05 v7) | ~ aInteger0(v6) | aElementOf0(v6, v5)) & ! [v6: $i] : ( ~ % 36.93/6.05 $i(v6) | ~ aElementOf0(v6, v5) | aElementOf0(v6, v1)))) & ! [v2: $i] % 36.93/6.05 : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ aElementOf0(v3, xS) | ~ % 36.93/6.05 aElementOf0(v2, v3) | ~ aInteger0(v2) | aElementOf0(v2, v0)) & ! [v2: % 36.93/6.05 $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | ~ aElementOf0(v2, v0)) & ! % 36.93/6.05 [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | aInteger0(v2)) & ! [v2: % 36.93/6.05 $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v0) | aInteger0(v2)) & ! [v2: $i] : % 36.93/6.05 ( ~ $i(v2) | ~ aElementOf0(v2, v0) | ? [v3: $i] : ($i(v3) & % 36.93/6.05 aElementOf0(v3, xS) & aElementOf0(v2, v3))) & ! [v2: $i] : ( ~ $i(v2) | % 36.93/6.05 ~ aInteger0(v2) | aElementOf0(v2, v1) | aElementOf0(v2, v0))) % 36.93/6.05 % 36.93/6.05 (m__2171) % 36.93/6.06 $i(xp) & $i(xS) & $i(sz10) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 36.93/6.06 $i] : ? [v3: $i] : ( ~ (xp = sz00) & szAzrzSzezqlpdtcmdtrp0(sz10, xp) = v0 % 36.93/6.06 & stldt0(v2) = v3 & sbsmnsldt0(xS) = v2 & smndt0(sz10) = v1 & $i(v3) & % 36.93/6.06 $i(v2) & $i(v1) & $i(v0) & aSubsetOf0(v0, v3) & aSet0(v2) & aSet0(v0) & % 36.93/6.06 aInteger0(xp) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtasdt0(xp, % 36.93/6.06 v6) = v5) | ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v6) | ~ $i(v4) | ~ % 36.93/6.06 aInteger0(v6) | ~ aInteger0(v4) | aElementOf0(v4, v0)) & ! [v4: $i] : ! % 36.93/6.06 [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aElementOf0(v4, v0) % 36.93/6.06 | sdteqdtlpzmzozddtrp0(v4, sz10, xp)) & ! [v4: $i] : ! [v5: $i] : ( ~ % 36.93/6.06 (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aElementOf0(v4, v0) | % 36.93/6.06 aDivisorOf0(xp, v5)) & ! [v4: $i] : ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) = % 36.93/6.06 v5) | ~ $i(v4) | ~ aElementOf0(v4, v0) | aInteger0(v4)) & ! [v4: $i] % 36.93/6.06 : ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aElementOf0(v4, % 36.93/6.06 v0) | ? [v6: $i] : (sdtasdt0(xp, v6) = v5 & $i(v6) & $i(v5) & % 36.93/6.06 aInteger0(v6))) & ! [v4: $i] : ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) = % 36.93/6.06 v5) | ~ $i(v4) | ~ sdteqdtlpzmzozddtrp0(v4, sz10, xp) | ~ % 36.93/6.06 aInteger0(v4) | aElementOf0(v4, v0)) & ! [v4: $i] : ! [v5: $i] : ( ~ % 36.93/6.06 (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aDivisorOf0(xp, v5) | ~ % 36.93/6.06 aInteger0(v4) | aElementOf0(v4, v0)) & ! [v4: $i] : ! [v5: $i] : ( ~ % 36.93/6.06 $i(v5) | ~ $i(v4) | ~ aElementOf0(v5, xS) | ~ aElementOf0(v4, v5) | ~ % 36.93/6.06 aInteger0(v4) | aElementOf0(v4, v2)) & ! [v4: $i] : ( ~ $i(v4) | ~ % 36.93/6.06 aElementOf0(v4, v3) | ~ aElementOf0(v4, v2)) & ! [v4: $i] : ( ~ $i(v4) | % 36.93/6.06 ~ aElementOf0(v4, v3) | aInteger0(v4)) & ! [v4: $i] : ( ~ $i(v4) | ~ % 36.93/6.06 aElementOf0(v4, v2) | aInteger0(v4)) & ! [v4: $i] : ( ~ $i(v4) | ~ % 36.93/6.06 aElementOf0(v4, v2) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, xS) & % 36.93/6.06 aElementOf0(v4, v5))) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, % 36.93/6.06 v0) | aElementOf0(v4, v3)) & ! [v4: $i] : ( ~ $i(v4) | ~ aInteger0(v4) % 36.93/6.06 | aElementOf0(v4, v3) | aElementOf0(v4, v2))) % 36.93/6.06 % 36.93/6.06 (m__2203) % 36.93/6.06 $i(cS2200) & $i(xp) & $i(sz10) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? % 36.93/6.06 [v3: $i] : ? [v4: $i] : ( ~ (v2 = v0) & ~ (v2 = sz10) & % 36.93/6.06 szAzrzSzezqlpdtcmdtrp0(sz10, xp) = v1 & sdtasdt0(xp, v4) = v3 & sdtpldt0(v2, % 36.93/6.06 v0) = v3 & smndt0(sz10) = v0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) % 36.93/6.06 & aElementOf0(v2, v1) & sdteqdtlpzmzozddtrp0(v2, sz10, xp) & aDivisorOf0(xp, % 36.93/6.06 v3) & aInteger0(v4) & aInteger0(v2) & ~ aElementOf0(v2, cS2200)) % 36.93/6.06 % 36.93/6.06 (function-axioms) % 36.93/6.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 36.93/6.07 (szAzrzSzezqlpdtcmdtrp0(v3, v2) = v1) | ~ (szAzrzSzezqlpdtcmdtrp0(v3, v2) = % 36.93/6.07 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 36.93/6.07 ~ (sdtslmnbsdt0(v3, v2) = v1) | ~ (sdtslmnbsdt0(v3, v2) = v0)) & ! [v0: % 36.93/6.07 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 36.93/6.07 (sdtbsmnsldt0(v3, v2) = v1) | ~ (sdtbsmnsldt0(v3, v2) = v0)) & ! [v0: $i] % 36.93/6.07 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = % 36.93/6.07 v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 36.93/6.07 $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, % 36.93/6.07 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 36.93/6.07 (stldt0(v2) = v1) | ~ (stldt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 36.93/6.07 [v2: $i] : (v1 = v0 | ~ (sbsmnsldt0(v2) = v1) | ~ (sbsmnsldt0(v2) = v0)) & % 36.93/6.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ % 36.93/6.07 (smndt0(v2) = v0)) % 36.93/6.07 % 36.93/6.07 Further assumptions not needed in the proof: % 36.93/6.07 -------------------------------------------- % 36.93/6.07 mAddAsso, mAddComm, mAddNeg, mAddZero, mArSeq, mClosed, mComplement, mDistrib, % 36.93/6.07 mDivisor, mElements, mEquMod, mEquModMul, mEquModRef, mEquModSym, mEquModTrn, % 36.93/6.07 mFinSet, mIntMult, mIntNeg, mIntPlus, mIntZero, mIntegers, mInterOpen, % 36.93/6.07 mIntersection, mMulAsso, mMulComm, mMulOne, mMulZero, mOpen, mPrime, mSets, % 36.93/6.07 mUnion, mUnionClosed, mUnionOpen, mUnionSClosed, mUnionSet, mZeroDiv, m__, % 36.93/6.07 m__2046, m__2117 % 36.93/6.07 % 36.93/6.07 Those formulas are unsatisfiable: % 36.93/6.07 --------------------------------- % 36.93/6.07 % 36.93/6.07 Begin of proof % 36.93/6.07 | % 36.93/6.07 | ALPHA: (mIntOne) implies: % 36.93/6.07 | (1) aInteger0(sz10) % 36.93/6.07 | % 36.93/6.07 | ALPHA: (mMulMinOne) implies: % 36.93/6.07 | (2) ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 36.93/6.07 | ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ aInteger0(v1) | % 36.93/6.07 | (sdtasdt0(v1, v0) = v2 & smndt0(v1) = v2 & $i(v2)))) % 36.93/6.07 | % 36.93/6.07 | ALPHA: (mPrimeDivisor) implies: % 36.93/6.08 | (3) ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : (v1 = v0 | v1 % 36.93/6.08 | = sz10 | ~ $i(v1) | ~ aInteger0(v1) | ? [v2: $i] : ($i(v2) & % 36.93/6.08 | isPrime0(v2) & aDivisorOf0(v2, v1))) & ! [v1: $i] : ( ~ $i(v1) | % 36.93/6.08 | ~ isPrime0(v1) | ~ aDivisorOf0(v1, v0) | ~ aInteger0(v0)) & ! % 36.93/6.08 | [v1: $i] : ( ~ $i(v1) | ~ isPrime0(v1) | ~ aDivisorOf0(v1, sz10) | % 36.93/6.08 | ~ aInteger0(sz10))) % 36.93/6.08 | % 36.93/6.08 | ALPHA: (mSubset) implies: % 36.93/6.08 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 36.93/6.08 | $i(v0) | ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ % 36.93/6.08 | aSet0(v0) | aElementOf0(v2, v0)) % 36.93/6.08 | % 36.93/6.08 | ALPHA: (mArSeqClosed) implies: % 36.93/6.08 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = sz00 | ~ % 36.93/6.08 | (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 36.93/6.08 | aInteger0(v1) | ~ aInteger0(v0) | isClosed0(v2)) % 36.93/6.08 | % 36.93/6.08 | ALPHA: (m__2079) implies: % 36.93/6.09 | (6) ? [v0: $i] : ? [v1: $i] : (stldt0(v0) = cS2076 & sbsmnsldt0(xS) = v0 % 36.93/6.09 | & smndt0(sz10) = v1 & $i(v1) & $i(v0) & aElementOf0(v1, cS2076) & % 36.93/6.09 | aElementOf0(sz10, cS2076) & aSet0(v0) & aSet0(cS2076) & ! [v2: $i] : % 36.93/6.09 | ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ aElementOf0(v3, xS) | ~ % 36.93/6.09 | aElementOf0(v2, v3) | ~ aInteger0(v2) | aElementOf0(v2, v0)) & ! % 36.93/6.09 | [v2: $i] : (v2 = v1 | v2 = sz10 | ~ $i(v2) | ~ aElementOf0(v2, % 36.93/6.09 | cS2076)) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v0) | ~ % 36.93/6.09 | aElementOf0(v2, cS2076)) & ! [v2: $i] : ( ~ $i(v2) | ~ % 36.93/6.09 | aElementOf0(v2, v0) | aInteger0(v2)) & ! [v2: $i] : ( ~ $i(v2) | % 36.93/6.09 | ~ aElementOf0(v2, v0) | ? [v3: $i] : ($i(v3) & aElementOf0(v3, xS) % 36.93/6.09 | & aElementOf0(v2, v3))) & ! [v2: $i] : ( ~ $i(v2) | ~ % 36.93/6.09 | aElementOf0(v2, cS2076) | aInteger0(v2)) & ! [v2: $i] : ( ~ $i(v2) % 36.93/6.09 | | ~ aInteger0(v2) | aElementOf0(v2, v0) | aElementOf0(v2, % 36.93/6.09 | cS2076))) % 36.93/6.09 | % 36.93/6.09 | ALPHA: (m__2144) implies: % 36.93/6.10 | (7) ? [v0: $i] : ? [v1: $i] : (stldt0(v0) = v1 & sbsmnsldt0(xS) = v0 & % 36.93/6.10 | $i(v1) & $i(v0) & isClosed0(v0) & isOpen0(v1) & aSet0(v0) & ! [v2: % 36.93/6.10 | $i] : ! [v3: $i] : ( ~ (smndt0(v2) = v3) | ~ $i(v2) | ~ % 36.93/6.10 | aElementOf0(v2, v1) | ? [v4: $i] : ? [v5: $i] : ( ~ (v4 = sz00) & % 36.93/6.10 | szAzrzSzezqlpdtcmdtrp0(v2, v4) = v5 & $i(v5) & $i(v4) & % 36.93/6.10 | aSubsetOf0(v5, v1) & aSet0(v5) & aInteger0(v4) & ! [v6: $i] : ! % 36.93/6.10 | [v7: $i] : ! [v8: $i] : ( ~ (sdtasdt0(v4, v8) = v7) | ~ % 36.93/6.10 | (sdtpldt0(v6, v3) = v7) | ~ $i(v8) | ~ $i(v6) | ~ % 36.93/6.10 | aInteger0(v8) | ~ aInteger0(v6) | aElementOf0(v6, v5)) & ! % 36.93/6.10 | [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6) % 36.93/6.10 | | ~ aElementOf0(v6, v5) | sdteqdtlpzmzozddtrp0(v6, v2, v4)) & % 36.93/6.10 | ! [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~ % 36.93/6.10 | $i(v6) | ~ aElementOf0(v6, v5) | aDivisorOf0(v4, v7)) & ! % 36.93/6.10 | [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6) % 36.93/6.10 | | ~ aElementOf0(v6, v5) | aInteger0(v6)) & ! [v6: $i] : ! % 36.93/6.10 | [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~ % 36.93/6.10 | aElementOf0(v6, v5) | ? [v8: $i] : (sdtasdt0(v4, v8) = v7 & % 36.93/6.10 | $i(v8) & $i(v7) & aInteger0(v8))) & ! [v6: $i] : ! [v7: $i] % 36.93/6.10 | : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~ % 36.93/6.10 | sdteqdtlpzmzozddtrp0(v6, v2, v4) | ~ aInteger0(v6) | % 36.93/6.10 | aElementOf0(v6, v5)) & ! [v6: $i] : ! [v7: $i] : ( ~ % 36.93/6.10 | (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~ aDivisorOf0(v4, v7) | % 36.93/6.10 | ~ aInteger0(v6) | aElementOf0(v6, v5)) & ! [v6: $i] : ( ~ % 36.93/6.10 | $i(v6) | ~ aElementOf0(v6, v5) | aElementOf0(v6, v1)))) & ! % 36.93/6.10 | [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ aElementOf0(v3, % 36.93/6.10 | xS) | ~ aElementOf0(v2, v3) | ~ aInteger0(v2) | aElementOf0(v2, % 36.93/6.10 | v0)) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | ~ % 36.93/6.10 | aElementOf0(v2, v0)) & ! [v2: $i] : ( ~ $i(v2) | ~ % 36.93/6.10 | aElementOf0(v2, v1) | aInteger0(v2)) & ! [v2: $i] : ( ~ $i(v2) | % 36.93/6.10 | ~ aElementOf0(v2, v0) | aInteger0(v2)) & ! [v2: $i] : ( ~ $i(v2) | % 36.93/6.10 | ~ aElementOf0(v2, v0) | ? [v3: $i] : ($i(v3) & aElementOf0(v3, % 36.93/6.10 | xS) & aElementOf0(v2, v3))) & ! [v2: $i] : ( ~ $i(v2) | ~ % 36.93/6.10 | aInteger0(v2) | aElementOf0(v2, v1) | aElementOf0(v2, v0))) % 36.93/6.10 | % 36.93/6.10 | ALPHA: (m__2171) implies: % 36.93/6.11 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (xp = sz00) % 36.93/6.11 | & szAzrzSzezqlpdtcmdtrp0(sz10, xp) = v0 & stldt0(v2) = v3 & % 36.93/6.11 | sbsmnsldt0(xS) = v2 & smndt0(sz10) = v1 & $i(v3) & $i(v2) & $i(v1) & % 36.93/6.11 | $i(v0) & aSubsetOf0(v0, v3) & aSet0(v2) & aSet0(v0) & aInteger0(xp) & % 36.93/6.11 | ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtasdt0(xp, v6) = v5) % 36.93/6.11 | | ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v6) | ~ $i(v4) | ~ % 36.93/6.11 | aInteger0(v6) | ~ aInteger0(v4) | aElementOf0(v4, v0)) & ! [v4: % 36.93/6.11 | $i] : ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ % 36.93/6.11 | aElementOf0(v4, v0) | sdteqdtlpzmzozddtrp0(v4, sz10, xp)) & ! [v4: % 36.93/6.11 | $i] : ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ % 36.93/6.11 | aElementOf0(v4, v0) | aDivisorOf0(xp, v5)) & ! [v4: $i] : ! [v5: % 36.93/6.11 | $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aElementOf0(v4, % 36.93/6.11 | v0) | aInteger0(v4)) & ! [v4: $i] : ! [v5: $i] : ( ~ % 36.93/6.11 | (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aElementOf0(v4, v0) | ? % 36.93/6.11 | [v6: $i] : (sdtasdt0(xp, v6) = v5 & $i(v6) & $i(v5) & % 36.93/6.11 | aInteger0(v6))) & ! [v4: $i] : ! [v5: $i] : ( ~ (sdtpldt0(v4, % 36.93/6.11 | v1) = v5) | ~ $i(v4) | ~ sdteqdtlpzmzozddtrp0(v4, sz10, xp) | % 36.93/6.11 | ~ aInteger0(v4) | aElementOf0(v4, v0)) & ! [v4: $i] : ! [v5: $i] % 36.93/6.11 | : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aDivisorOf0(xp, v5) | % 36.93/6.11 | ~ aInteger0(v4) | aElementOf0(v4, v0)) & ! [v4: $i] : ! [v5: $i] % 36.93/6.11 | : ( ~ $i(v5) | ~ $i(v4) | ~ aElementOf0(v5, xS) | ~ % 36.93/6.11 | aElementOf0(v4, v5) | ~ aInteger0(v4) | aElementOf0(v4, v2)) & ! % 36.93/6.11 | [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v3) | ~ aElementOf0(v4, % 36.93/6.11 | v2)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v3) | % 36.93/6.11 | aInteger0(v4)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v2) % 36.93/6.11 | | aInteger0(v4)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, % 36.93/6.11 | v2) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, xS) & % 36.93/6.12 | aElementOf0(v4, v5))) & ! [v4: $i] : ( ~ $i(v4) | ~ % 36.93/6.12 | aElementOf0(v4, v0) | aElementOf0(v4, v3)) & ! [v4: $i] : ( ~ % 36.93/6.12 | $i(v4) | ~ aInteger0(v4) | aElementOf0(v4, v3) | aElementOf0(v4, % 36.93/6.12 | v2))) % 36.93/6.12 | % 36.93/6.12 | ALPHA: (m__2203) implies: % 36.93/6.12 | (9) $i(sz10) % 36.93/6.12 | (10) $i(xp) % 36.93/6.12 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 36.93/6.12 | ( ~ (v2 = v0) & ~ (v2 = sz10) & szAzrzSzezqlpdtcmdtrp0(sz10, xp) = v1 % 36.93/6.12 | & sdtasdt0(xp, v4) = v3 & sdtpldt0(v2, v0) = v3 & smndt0(sz10) = v0 % 36.93/6.12 | & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v2, v1) & % 36.93/6.12 | sdteqdtlpzmzozddtrp0(v2, sz10, xp) & aDivisorOf0(xp, v3) & % 36.93/6.12 | aInteger0(v4) & aInteger0(v2) & ~ aElementOf0(v2, cS2200)) % 36.93/6.12 | % 36.93/6.12 | ALPHA: (function-axioms) implies: % 36.93/6.12 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = % 36.93/6.12 | v1) | ~ (smndt0(v2) = v0)) % 36.93/6.12 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 36.93/6.12 | (sbsmnsldt0(v2) = v1) | ~ (sbsmnsldt0(v2) = v0)) % 36.93/6.12 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (stldt0(v2) = % 36.93/6.12 | v1) | ~ (stldt0(v2) = v0)) % 36.93/6.12 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 36.93/6.12 | (szAzrzSzezqlpdtcmdtrp0(v3, v2) = v1) | ~ % 36.93/6.12 | (szAzrzSzezqlpdtcmdtrp0(v3, v2) = v0)) % 36.93/6.12 | % 36.93/6.13 | DELTA: instantiating (2) with fresh symbol all_36_0 gives: % 36.93/6.13 | (16) smndt0(sz10) = all_36_0 & $i(all_36_0) & ! [v0: $i] : ! [v1: $i] : ( % 36.93/6.13 | ~ (sdtasdt0(all_36_0, v0) = v1) | ~ $i(v0) | ~ aInteger0(v0) | % 36.93/6.13 | (sdtasdt0(v0, all_36_0) = v1 & smndt0(v0) = v1 & $i(v1))) % 36.93/6.13 | % 36.93/6.13 | ALPHA: (16) implies: % 36.93/6.13 | (17) smndt0(sz10) = all_36_0 % 36.93/6.13 | % 36.93/6.13 | DELTA: instantiating (11) with fresh symbols all_39_0, all_39_1, all_39_2, % 36.93/6.13 | all_39_3, all_39_4 gives: % 36.93/6.13 | (18) ~ (all_39_2 = all_39_4) & ~ (all_39_2 = sz10) & % 36.93/6.13 | szAzrzSzezqlpdtcmdtrp0(sz10, xp) = all_39_3 & sdtasdt0(xp, all_39_0) = % 36.93/6.13 | all_39_1 & sdtpldt0(all_39_2, all_39_4) = all_39_1 & smndt0(sz10) = % 36.93/6.13 | all_39_4 & $i(all_39_0) & $i(all_39_1) & $i(all_39_2) & $i(all_39_3) & % 36.93/6.13 | $i(all_39_4) & aElementOf0(all_39_2, all_39_3) & % 36.93/6.13 | sdteqdtlpzmzozddtrp0(all_39_2, sz10, xp) & aDivisorOf0(xp, all_39_1) & % 36.93/6.13 | aInteger0(all_39_0) & aInteger0(all_39_2) & ~ aElementOf0(all_39_2, % 36.93/6.13 | cS2200) % 36.93/6.13 | % 36.93/6.13 | ALPHA: (18) implies: % 36.93/6.13 | (19) ~ (all_39_2 = sz10) % 36.93/6.13 | (20) ~ (all_39_2 = all_39_4) % 36.93/6.13 | (21) aElementOf0(all_39_2, all_39_3) % 36.93/6.13 | (22) $i(all_39_2) % 36.93/6.13 | (23) smndt0(sz10) = all_39_4 % 36.93/6.13 | (24) szAzrzSzezqlpdtcmdtrp0(sz10, xp) = all_39_3 % 36.93/6.13 | % 36.93/6.13 | DELTA: instantiating (3) with fresh symbol all_41_0 gives: % 36.93/6.13 | (25) smndt0(sz10) = all_41_0 & $i(all_41_0) & ! [v0: any] : (v0 = all_41_0 % 36.93/6.13 | | v0 = sz10 | ~ $i(v0) | ~ aInteger0(v0) | ? [v1: $i] : ($i(v1) & % 36.93/6.13 | isPrime0(v1) & aDivisorOf0(v1, v0))) & ! [v0: $i] : ( ~ $i(v0) | % 36.93/6.13 | ~ isPrime0(v0) | ~ aDivisorOf0(v0, all_41_0) | ~ % 36.93/6.13 | aInteger0(all_41_0)) & ! [v0: $i] : ( ~ $i(v0) | ~ isPrime0(v0) | % 36.93/6.14 | ~ aDivisorOf0(v0, sz10) | ~ aInteger0(sz10)) % 36.93/6.14 | % 36.93/6.14 | ALPHA: (25) implies: % 36.93/6.14 | (26) smndt0(sz10) = all_41_0 % 36.93/6.14 | % 36.93/6.14 | DELTA: instantiating (6) with fresh symbols all_44_0, all_44_1 gives: % 36.93/6.14 | (27) stldt0(all_44_1) = cS2076 & sbsmnsldt0(xS) = all_44_1 & smndt0(sz10) = % 36.93/6.14 | all_44_0 & $i(all_44_0) & $i(all_44_1) & aElementOf0(all_44_0, cS2076) % 36.93/6.14 | & aElementOf0(sz10, cS2076) & aSet0(all_44_1) & aSet0(cS2076) & ! % 36.93/6.14 | [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, % 36.93/6.14 | xS) | ~ aElementOf0(v0, v1) | ~ aInteger0(v0) | aElementOf0(v0, % 36.93/6.14 | all_44_1)) & ! [v0: any] : (v0 = all_44_0 | v0 = sz10 | ~ $i(v0) % 36.93/6.14 | | ~ aElementOf0(v0, cS2076)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 36.93/6.14 | aElementOf0(v0, all_44_1) | ~ aElementOf0(v0, cS2076)) & ! [v0: % 36.93/6.14 | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_44_1) | aInteger0(v0)) & % 36.93/6.14 | ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_44_1) | ? [v1: $i] : % 36.93/6.14 | ($i(v1) & aElementOf0(v1, xS) & aElementOf0(v0, v1))) & ! [v0: $i] % 36.93/6.14 | : ( ~ $i(v0) | ~ aElementOf0(v0, cS2076) | aInteger0(v0)) & ! [v0: % 36.93/6.14 | $i] : ( ~ $i(v0) | ~ aInteger0(v0) | aElementOf0(v0, all_44_1) | % 36.93/6.14 | aElementOf0(v0, cS2076)) % 36.93/6.14 | % 36.93/6.14 | ALPHA: (27) implies: % 36.93/6.14 | (28) aSet0(cS2076) % 36.93/6.14 | (29) smndt0(sz10) = all_44_0 % 36.93/6.14 | (30) sbsmnsldt0(xS) = all_44_1 % 36.93/6.14 | (31) stldt0(all_44_1) = cS2076 % 36.93/6.14 | (32) ! [v0: any] : (v0 = all_44_0 | v0 = sz10 | ~ $i(v0) | ~ % 36.93/6.14 | aElementOf0(v0, cS2076)) % 36.93/6.14 | % 36.93/6.14 | DELTA: instantiating (8) with fresh symbols all_47_0, all_47_1, all_47_2, % 36.93/6.14 | all_47_3 gives: % 36.93/6.15 | (33) ~ (xp = sz00) & szAzrzSzezqlpdtcmdtrp0(sz10, xp) = all_47_3 & % 36.93/6.15 | stldt0(all_47_1) = all_47_0 & sbsmnsldt0(xS) = all_47_1 & smndt0(sz10) % 36.93/6.15 | = all_47_2 & $i(all_47_0) & $i(all_47_1) & $i(all_47_2) & $i(all_47_3) % 36.93/6.15 | & aSubsetOf0(all_47_3, all_47_0) & aSet0(all_47_1) & aSet0(all_47_3) & % 36.93/6.15 | aInteger0(xp) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 36.93/6.15 | (sdtasdt0(xp, v2) = v1) | ~ (sdtpldt0(v0, all_47_2) = v1) | ~ % 36.93/6.15 | $i(v2) | ~ $i(v0) | ~ aInteger0(v2) | ~ aInteger0(v0) | % 36.93/6.15 | aElementOf0(v0, all_47_3)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 36.93/6.15 | (sdtpldt0(v0, all_47_2) = v1) | ~ $i(v0) | ~ aElementOf0(v0, % 36.93/6.15 | all_47_3) | sdteqdtlpzmzozddtrp0(v0, sz10, xp)) & ! [v0: $i] : ! % 36.93/6.15 | [v1: $i] : ( ~ (sdtpldt0(v0, all_47_2) = v1) | ~ $i(v0) | ~ % 36.93/6.15 | aElementOf0(v0, all_47_3) | aDivisorOf0(xp, v1)) & ! [v0: $i] : ! % 36.93/6.15 | [v1: $i] : ( ~ (sdtpldt0(v0, all_47_2) = v1) | ~ $i(v0) | ~ % 36.93/6.15 | aElementOf0(v0, all_47_3) | aInteger0(v0)) & ! [v0: $i] : ! [v1: % 36.93/6.15 | $i] : ( ~ (sdtpldt0(v0, all_47_2) = v1) | ~ $i(v0) | ~ % 36.93/6.15 | aElementOf0(v0, all_47_3) | ? [v2: $i] : (sdtasdt0(xp, v2) = v1 & % 36.93/6.15 | $i(v2) & $i(v1) & aInteger0(v2))) & ! [v0: $i] : ! [v1: $i] : ( % 36.93/6.15 | ~ (sdtpldt0(v0, all_47_2) = v1) | ~ $i(v0) | ~ % 36.93/6.15 | sdteqdtlpzmzozddtrp0(v0, sz10, xp) | ~ aInteger0(v0) | % 36.93/6.15 | aElementOf0(v0, all_47_3)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 36.93/6.15 | (sdtpldt0(v0, all_47_2) = v1) | ~ $i(v0) | ~ aDivisorOf0(xp, v1) | % 36.93/6.15 | ~ aInteger0(v0) | aElementOf0(v0, all_47_3)) & ! [v0: $i] : ! % 36.93/6.15 | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, xS) | ~ % 36.93/6.15 | aElementOf0(v0, v1) | ~ aInteger0(v0) | aElementOf0(v0, all_47_1)) % 36.93/6.15 | & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_47_0) | ~ % 36.93/6.15 | aElementOf0(v0, all_47_1)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 36.93/6.15 | aElementOf0(v0, all_47_0) | aInteger0(v0)) & ! [v0: $i] : ( ~ % 36.93/6.15 | $i(v0) | ~ aElementOf0(v0, all_47_1) | aInteger0(v0)) & ! [v0: $i] % 36.93/6.15 | : ( ~ $i(v0) | ~ aElementOf0(v0, all_47_1) | ? [v1: $i] : ($i(v1) & % 36.93/6.15 | aElementOf0(v1, xS) & aElementOf0(v0, v1))) & ! [v0: $i] : ( ~ % 36.93/6.15 | $i(v0) | ~ aElementOf0(v0, all_47_3) | aElementOf0(v0, all_47_0)) & % 36.93/6.15 | ! [v0: $i] : ( ~ $i(v0) | ~ aInteger0(v0) | aElementOf0(v0, % 36.93/6.15 | all_47_0) | aElementOf0(v0, all_47_1)) % 36.93/6.15 | % 36.93/6.15 | ALPHA: (33) implies: % 36.93/6.15 | (34) ~ (xp = sz00) % 36.93/6.15 | (35) aInteger0(xp) % 36.93/6.15 | (36) aSubsetOf0(all_47_3, all_47_0) % 36.93/6.15 | (37) $i(all_47_3) % 36.93/6.15 | (38) $i(all_47_0) % 36.93/6.15 | (39) smndt0(sz10) = all_47_2 % 36.93/6.15 | (40) sbsmnsldt0(xS) = all_47_1 % 36.93/6.15 | (41) stldt0(all_47_1) = all_47_0 % 36.93/6.15 | (42) szAzrzSzezqlpdtcmdtrp0(sz10, xp) = all_47_3 % 36.93/6.15 | % 36.93/6.15 | DELTA: instantiating (7) with fresh symbols all_50_0, all_50_1 gives: % 36.93/6.16 | (43) stldt0(all_50_1) = all_50_0 & sbsmnsldt0(xS) = all_50_1 & $i(all_50_0) % 36.93/6.16 | & $i(all_50_1) & isClosed0(all_50_1) & isOpen0(all_50_0) & % 36.93/6.16 | aSet0(all_50_1) & ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | % 36.93/6.16 | ~ $i(v0) | ~ aElementOf0(v0, all_50_0) | ? [v2: $i] : ? [v3: $i] % 36.93/6.16 | : ( ~ (v2 = sz00) & szAzrzSzezqlpdtcmdtrp0(v0, v2) = v3 & $i(v3) & % 36.93/6.16 | $i(v2) & aSubsetOf0(v3, all_50_0) & aSet0(v3) & aInteger0(v2) & ! % 36.93/6.16 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtasdt0(v2, v6) = v5) % 36.93/6.16 | | ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v6) | ~ $i(v4) | ~ % 36.93/6.16 | aInteger0(v6) | ~ aInteger0(v4) | aElementOf0(v4, v3)) & ! % 36.93/6.16 | [v4: $i] : ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | % 36.93/6.16 | ~ aElementOf0(v4, v3) | sdteqdtlpzmzozddtrp0(v4, v0, v2)) & ! % 36.93/6.16 | [v4: $i] : ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | % 36.93/6.16 | ~ aElementOf0(v4, v3) | aDivisorOf0(v2, v5)) & ! [v4: $i] : ! % 36.93/6.16 | [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ % 36.93/6.16 | aElementOf0(v4, v3) | aInteger0(v4)) & ! [v4: $i] : ! [v5: $i] % 36.93/6.16 | : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aElementOf0(v4, v3) % 36.93/6.16 | | ? [v6: $i] : (sdtasdt0(v2, v6) = v5 & $i(v6) & $i(v5) & % 36.93/6.16 | aInteger0(v6))) & ! [v4: $i] : ! [v5: $i] : ( ~ % 36.93/6.16 | (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ % 36.93/6.16 | sdteqdtlpzmzozddtrp0(v4, v0, v2) | ~ aInteger0(v4) | % 36.93/6.16 | aElementOf0(v4, v3)) & ! [v4: $i] : ! [v5: $i] : ( ~ % 36.93/6.16 | (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aDivisorOf0(v2, v5) | % 36.93/6.16 | ~ aInteger0(v4) | aElementOf0(v4, v3)) & ! [v4: $i] : ( ~ % 36.93/6.16 | $i(v4) | ~ aElementOf0(v4, v3) | aElementOf0(v4, all_50_0)))) & % 36.93/6.16 | ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 36.93/6.16 | aElementOf0(v1, xS) | ~ aElementOf0(v0, v1) | ~ aInteger0(v0) | % 36.93/6.16 | aElementOf0(v0, all_50_1)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 36.93/6.16 | aElementOf0(v0, all_50_0) | ~ aElementOf0(v0, all_50_1)) & ! [v0: % 36.93/6.16 | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_50_0) | aInteger0(v0)) & % 36.93/6.16 | ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_50_1) | % 36.93/6.16 | aInteger0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, % 36.93/6.16 | all_50_1) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, xS) & % 36.93/6.16 | aElementOf0(v0, v1))) & ! [v0: $i] : ( ~ $i(v0) | ~ % 36.93/6.16 | aInteger0(v0) | aElementOf0(v0, all_50_0) | aElementOf0(v0, % 36.93/6.16 | all_50_1)) % 36.93/6.16 | % 36.93/6.16 | ALPHA: (43) implies: % 36.93/6.16 | (44) sbsmnsldt0(xS) = all_50_1 % 36.93/6.16 | (45) stldt0(all_50_1) = all_50_0 % 36.93/6.16 | % 36.93/6.17 | GROUND_INST: instantiating (12) with all_44_0, all_47_2, sz10, simplifying % 36.93/6.17 | with (29), (39) gives: % 36.93/6.17 | (46) all_47_2 = all_44_0 % 36.93/6.17 | % 36.93/6.17 | GROUND_INST: instantiating (12) with all_41_0, all_47_2, sz10, simplifying % 36.93/6.17 | with (26), (39) gives: % 36.93/6.17 | (47) all_47_2 = all_41_0 % 36.93/6.17 | % 36.93/6.17 | GROUND_INST: instantiating (12) with all_39_4, all_47_2, sz10, simplifying % 36.93/6.17 | with (23), (39) gives: % 36.93/6.17 | (48) all_47_2 = all_39_4 % 36.93/6.17 | % 36.93/6.17 | GROUND_INST: instantiating (12) with all_36_0, all_47_2, sz10, simplifying % 36.93/6.17 | with (17), (39) gives: % 36.93/6.17 | (49) all_47_2 = all_36_0 % 36.93/6.17 | % 36.93/6.17 | GROUND_INST: instantiating (13) with all_47_1, all_50_1, xS, simplifying with % 36.93/6.17 | (40), (44) gives: % 36.93/6.17 | (50) all_50_1 = all_47_1 % 36.93/6.17 | % 36.93/6.17 | GROUND_INST: instantiating (13) with all_44_1, all_50_1, xS, simplifying with % 36.93/6.17 | (30), (44) gives: % 36.93/6.17 | (51) all_50_1 = all_44_1 % 36.93/6.17 | % 36.93/6.17 | GROUND_INST: instantiating (15) with all_39_3, all_47_3, xp, sz10, simplifying % 36.93/6.17 | with (24), (42) gives: % 36.93/6.17 | (52) all_47_3 = all_39_3 % 36.93/6.17 | % 36.93/6.17 | COMBINE_EQS: (50), (51) imply: % 36.93/6.17 | (53) all_47_1 = all_44_1 % 36.93/6.17 | % 36.93/6.17 | SIMP: (53) implies: % 36.93/6.17 | (54) all_47_1 = all_44_1 % 36.93/6.17 | % 36.93/6.17 | COMBINE_EQS: (46), (49) imply: % 36.93/6.17 | (55) all_44_0 = all_36_0 % 36.93/6.17 | % 36.93/6.17 | COMBINE_EQS: (46), (48) imply: % 36.93/6.17 | (56) all_44_0 = all_39_4 % 36.93/6.17 | % 36.93/6.17 | COMBINE_EQS: (46), (47) imply: % 36.93/6.17 | (57) all_44_0 = all_41_0 % 36.93/6.17 | % 36.93/6.17 | COMBINE_EQS: (55), (57) imply: % 36.93/6.17 | (58) all_41_0 = all_36_0 % 36.93/6.17 | % 36.93/6.17 | COMBINE_EQS: (56), (57) imply: % 36.93/6.17 | (59) all_41_0 = all_39_4 % 36.93/6.17 | % 36.93/6.17 | COMBINE_EQS: (58), (59) imply: % 36.93/6.17 | (60) all_39_4 = all_36_0 % 36.93/6.17 | % 36.93/6.17 | SIMP: (60) implies: % 37.67/6.17 | (61) all_39_4 = all_36_0 % 37.67/6.17 | % 37.67/6.17 | REDUCE: (20), (61) imply: % 37.67/6.17 | (62) ~ (all_39_2 = all_36_0) % 37.67/6.17 | % 37.67/6.17 | REDUCE: (45), (51) imply: % 37.67/6.18 | (63) stldt0(all_44_1) = all_50_0 % 37.67/6.18 | % 37.67/6.18 | REDUCE: (41), (54) imply: % 37.67/6.18 | (64) stldt0(all_44_1) = all_47_0 % 37.67/6.18 | % 37.67/6.18 | REDUCE: (37), (52) imply: % 37.67/6.18 | (65) $i(all_39_3) % 37.67/6.18 | % 37.67/6.18 | REDUCE: (36), (52) imply: % 37.67/6.18 | (66) aSubsetOf0(all_39_3, all_47_0) % 37.67/6.18 | % 37.67/6.18 | GROUND_INST: instantiating (14) with cS2076, all_50_0, all_44_1, simplifying % 37.67/6.18 | with (31), (63) gives: % 37.67/6.18 | (67) all_50_0 = cS2076 % 37.67/6.18 | % 37.67/6.18 | GROUND_INST: instantiating (14) with all_47_0, all_50_0, all_44_1, simplifying % 37.67/6.18 | with (63), (64) gives: % 37.67/6.18 | (68) all_50_0 = all_47_0 % 37.67/6.18 | % 37.67/6.18 | COMBINE_EQS: (67), (68) imply: % 37.67/6.18 | (69) all_47_0 = cS2076 % 37.67/6.18 | % 37.67/6.18 | REDUCE: (38), (69) imply: % 37.67/6.18 | (70) $i(cS2076) % 37.67/6.18 | % 37.67/6.18 | REDUCE: (66), (69) imply: % 37.67/6.18 | (71) aSubsetOf0(all_39_3, cS2076) % 37.67/6.18 | % 37.67/6.18 | GROUND_INST: instantiating (4) with cS2076, all_39_3, all_39_2, simplifying % 37.67/6.18 | with (21), (22), (28), (65), (70), (71) gives: % 37.67/6.18 | (72) aElementOf0(all_39_2, cS2076) % 37.67/6.18 | % 37.67/6.18 | GROUND_INST: instantiating (5) with sz10, xp, all_39_3, simplifying with (1), % 37.67/6.18 | (9), (10), (24), (35) gives: % 37.67/6.18 | (73) xp = sz00 | isClosed0(all_39_3) % 37.67/6.18 | % 37.67/6.18 | BETA: splitting (73) gives: % 37.67/6.18 | % 37.67/6.18 | Case 1: % 37.67/6.18 | | % 37.67/6.18 | | % 37.67/6.18 | | GROUND_INST: instantiating (32) with all_39_2, simplifying with (22), (72) % 37.67/6.18 | | gives: % 37.67/6.18 | | (74) all_44_0 = all_39_2 | all_39_2 = sz10 % 37.67/6.18 | | % 37.67/6.18 | | BETA: splitting (74) gives: % 37.67/6.18 | | % 37.67/6.18 | | Case 1: % 37.67/6.18 | | | % 37.67/6.18 | | | (75) all_44_0 = all_39_2 % 37.67/6.18 | | | % 37.67/6.18 | | | COMBINE_EQS: (55), (75) imply: % 37.67/6.18 | | | (76) all_39_2 = all_36_0 % 37.67/6.18 | | | % 37.67/6.18 | | | REDUCE: (62), (76) imply: % 37.67/6.18 | | | (77) $false % 37.67/6.18 | | | % 37.67/6.18 | | | CLOSE: (77) is inconsistent. % 37.67/6.18 | | | % 37.67/6.18 | | Case 2: % 37.67/6.18 | | | % 37.67/6.19 | | | (78) all_39_2 = sz10 % 37.67/6.19 | | | % 37.67/6.19 | | | REDUCE: (19), (78) imply: % 37.67/6.19 | | | (79) $false % 37.67/6.19 | | | % 37.67/6.19 | | | CLOSE: (79) is inconsistent. % 37.67/6.19 | | | % 37.67/6.19 | | End of split % 37.67/6.19 | | % 37.67/6.19 | Case 2: % 37.67/6.19 | | % 37.67/6.19 | | (80) xp = sz00 % 37.67/6.19 | | % 37.67/6.19 | | REDUCE: (34), (80) imply: % 37.67/6.19 | | (81) $false % 37.67/6.19 | | % 37.67/6.19 | | CLOSE: (81) is inconsistent. % 37.67/6.19 | | % 37.67/6.19 | End of split % 37.67/6.19 | % 37.67/6.19 End of proof % 37.67/6.19 % SZS output end Proof for theBenchmark % 37.67/6.19 % 37.67/6.19 5569ms %------------------------------------------------------------------------------