%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM453+1 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n005.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 11:47:50 EDT 2023 % Result : Theorem 95.49s 13.16s % Output : Proof 104.75s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM453+1 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n005.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Aug 25 15:10:38 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.04/1.28 Prover 1: Preprocessing ... % 4.04/1.28 Prover 4: Preprocessing ... % 4.37/1.33 Prover 6: Preprocessing ... % 4.37/1.33 Prover 0: Preprocessing ... % 4.37/1.33 Prover 5: Preprocessing ... % 4.37/1.33 Prover 2: Preprocessing ... % 4.37/1.33 Prover 3: Preprocessing ... % 11.43/2.29 Prover 1: Constructing countermodel ... % 11.43/2.32 Prover 3: Constructing countermodel ... % 11.43/2.34 Prover 5: Constructing countermodel ... % 12.23/2.40 Prover 6: Proving ... % 12.61/2.46 Prover 2: Proving ... % 13.71/2.72 Prover 4: Constructing countermodel ... % 15.27/2.81 Prover 0: Proving ... % 72.44/10.28 Prover 2: stopped % 72.44/10.28 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 74.03/10.37 Prover 7: Preprocessing ... % 75.62/10.57 Prover 7: Constructing countermodel ... % 95.49/13.16 Prover 0: proved (12392ms) % 95.49/13.16 % 95.49/13.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 95.49/13.16 % 95.49/13.16 Prover 5: stopped % 95.49/13.17 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 95.49/13.17 Prover 6: stopped % 95.49/13.18 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 95.49/13.18 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 96.25/13.27 Prover 10: Preprocessing ... % 96.25/13.28 Prover 11: Preprocessing ... % 96.25/13.28 Prover 8: Preprocessing ... % 97.47/13.40 Prover 8: Warning: ignoring some quantifiers % 97.47/13.40 Prover 10: Constructing countermodel ... % 97.47/13.40 Prover 8: Constructing countermodel ... % 98.54/13.61 Prover 11: Constructing countermodel ... % 102.52/14.06 Prover 3: stopped % 102.52/14.07 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 102.52/14.14 Prover 13: Preprocessing ... % 103.85/14.20 Prover 7: Found proof (size 176) % 103.85/14.21 Prover 7: proved (3917ms) % 103.85/14.21 Prover 10: stopped % 103.85/14.21 Prover 8: stopped % 103.85/14.21 Prover 11: stopped % 103.85/14.21 Prover 1: stopped % 103.85/14.21 Prover 4: stopped % 103.85/14.24 Prover 13: Constructing countermodel ... % 103.85/14.24 Prover 13: stopped % 103.85/14.24 % 103.85/14.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 103.85/14.24 % 104.06/14.26 % SZS output start Proof for theBenchmark % 104.06/14.26 Assumptions after simplification: % 104.06/14.26 --------------------------------- % 104.06/14.26 % 104.06/14.26 (mAddAsso) % 104.06/14.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 104.06/14.29 (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 104.06/14.29 | ~ $i(v0) | ~ aInteger0(v2) | ~ aInteger0(v1) | ~ aInteger0(v0) | ? % 104.06/14.29 [v5: $i] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4 & $i(v5) & % 104.06/14.29 $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 104.06/14.29 $i] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ (sdtpldt0(v0, v3) = v4) | ~ $i(v2) | % 104.06/14.29 ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v2) | ~ aInteger0(v1) | ~ % 104.06/14.29 aInteger0(v0) | ? [v5: $i] : (sdtpldt0(v5, v2) = v4 & sdtpldt0(v0, v1) = v5 % 104.06/14.29 & $i(v5) & $i(v4))) % 104.06/14.29 % 104.06/14.29 (mAddComm) % 104.06/14.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ % 104.06/14.29 $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) | (sdtpldt0(v0, v1) % 104.06/14.29 = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 104.06/14.29 (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ % 104.06/14.29 aInteger0(v0) | (sdtpldt0(v1, v0) = v2 & $i(v2))) % 104.06/14.29 % 104.06/14.29 (mAddNeg) % 104.06/14.29 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ~ % 104.06/14.29 aInteger0(v0) | (sdtpldt0(v1, v0) = sz00 & sdtpldt0(v0, v1) = sz00)) % 104.06/14.29 % 104.06/14.29 (mAddZero) % 104.06/14.29 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) % 104.06/14.30 | ~ $i(v0) | ~ aInteger0(v0)) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 104.06/14.30 (sdtpldt0(sz00, v0) = v1) | ~ $i(v0) | ~ aInteger0(v0)) & ! [v0: $i] : ! % 104.06/14.30 [v1: $i] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ $i(v0) | ~ aInteger0(v0) | % 104.06/14.30 sdtpldt0(sz00, v0) = v0) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(sz00, % 104.06/14.30 v0) = v1) | ~ $i(v0) | ~ aInteger0(v0) | sdtpldt0(v0, sz00) = v0) % 104.06/14.30 % 104.06/14.30 (mArSeqClosed) % 104.06/14.30 $i(cS1395) & $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = sz00 | % 104.06/14.30 ~ (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 104.06/14.30 aInteger0(v1) | ~ aInteger0(v0) | isClosed0(v2)) & ! [v0: $i] : ! [v1: % 104.06/14.30 $i] : ! [v2: $i] : (v1 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) | % 104.06/14.30 ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) | aSubsetOf0(v2, % 104.06/14.30 cS1395)) % 104.06/14.30 % 104.06/14.30 (mDistrib) % 104.06/14.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 104.06/14.31 $i] : ( ~ (sdtasdt0(v1, v2) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ % 104.06/14.31 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 104.06/14.31 aInteger0(v2) | ~ aInteger0(v1) | ~ aInteger0(v0) | ? [v6: $i] : ? [v7: % 104.06/14.31 $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v9, v2) = v5 & sdtasdt0(v0, % 104.06/14.31 v6) = v7 & sdtasdt0(v0, v1) = v8 & sdtpldt0(v8, v3) = v7 & sdtpldt0(v1, % 104.06/14.31 v2) = v6 & sdtpldt0(v0, v1) = v9 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 104.06/14.31 $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 104.06/14.31 $i] : ! [v5: $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) % 104.06/14.31 | ~ (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 104.06/14.31 aInteger0(v2) | ~ aInteger0(v1) | ~ aInteger0(v0) | ? [v6: $i] : ? [v7: % 104.06/14.31 $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v7, v2) = v8 & sdtasdt0(v1, % 104.06/14.31 v2) = v9 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v4, v9) = v8 & sdtpldt0(v1, % 104.06/14.31 v2) = v6 & sdtpldt0(v0, v1) = v7 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 104.06/14.31 $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 104.06/14.31 $i] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | % 104.06/14.31 ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v2) | ~ aInteger0(v1) | ~ % 104.06/14.31 aInteger0(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? % 104.06/14.31 [v9: $i] : (sdtasdt0(v1, v2) = v9 & sdtasdt0(v0, v5) = v6 & sdtasdt0(v0, v2) % 104.06/14.31 = v8 & sdtasdt0(v0, v1) = v7 & sdtpldt0(v8, v9) = v4 & sdtpldt0(v7, v8) = % 104.06/14.31 v6 & sdtpldt0(v1, v2) = v5 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & % 104.06/14.31 $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 104.06/14.31 $i] : ( ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | % 104.06/14.31 ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v2) | ~ aInteger0(v1) | ~ % 104.06/14.31 aInteger0(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? % 104.06/14.31 [v9: $i] : (sdtasdt0(v7, v2) = v8 & sdtasdt0(v1, v2) = v9 & sdtasdt0(v0, v2) % 104.06/14.31 = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v6, v9) = v8 & sdtpldt0(v5, v6) = % 104.06/14.31 v4 & sdtpldt0(v0, v1) = v7 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & % 104.06/14.31 $i(v4))) % 104.06/14.31 % 104.06/14.31 (mEquModRef) % 104.06/14.31 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ $i(v1) | ~ $i(v0) | ~ % 104.06/14.31 aInteger0(v1) | ~ aInteger0(v0) | sdteqdtlpzmzozddtrp0(v0, v0, v1)) % 104.06/14.31 % 104.06/14.31 (mIntNeg) % 104.06/14.31 ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ~ % 104.06/14.31 aInteger0(v0) | aInteger0(v1)) % 104.06/14.31 % 104.06/14.31 (mIntOne) % 104.06/14.31 $i(sz10) & aInteger0(sz10) % 104.06/14.31 % 104.06/14.31 (mIntZero) % 104.06/14.31 $i(sz00) & aInteger0(sz00) % 104.06/14.31 % 104.06/14.31 (mMulAsso) % 104.06/14.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 104.06/14.31 (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 104.06/14.31 | ~ $i(v0) | ~ aInteger0(v2) | ~ aInteger0(v1) | ~ aInteger0(v0) | ? % 104.06/14.31 [v5: $i] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4 & $i(v5) & % 104.06/14.31 $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 104.06/14.31 $i] : ( ~ (sdtasdt0(v1, v2) = v3) | ~ (sdtasdt0(v0, v3) = v4) | ~ $i(v2) | % 104.06/14.31 ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v2) | ~ aInteger0(v1) | ~ % 104.06/14.31 aInteger0(v0) | ? [v5: $i] : (sdtasdt0(v5, v2) = v4 & sdtasdt0(v0, v1) = v5 % 104.06/14.31 & $i(v5) & $i(v4))) % 104.06/14.31 % 104.06/14.31 (mMulMinOne) % 104.06/14.32 $i(sz10) & ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 104.06/14.32 $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ~ aInteger0(v1) | % 104.06/14.32 (sdtasdt0(v0, v1) = v2 & smndt0(v1) = v2 & $i(v2))) & ! [v1: $i] : ! % 104.06/14.32 [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ aInteger0(v1) | % 104.06/14.32 (sdtasdt0(v1, v0) = v2 & smndt0(v1) = v2 & $i(v2))) & ! [v1: $i] : ! % 104.06/14.32 [v2: $i] : ( ~ (smndt0(v1) = v2) | ~ $i(v1) | ~ aInteger0(v1) | % 104.06/14.32 (sdtasdt0(v1, v0) = v2 & sdtasdt0(v0, v1) = v2 & $i(v2)))) % 104.06/14.32 % 104.06/14.32 (mMulZero) % 104.06/14.32 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = % 104.06/14.32 v1) | ~ $i(v0) | ~ aInteger0(v0)) & ! [v0: $i] : ! [v1: $i] : (v1 = % 104.06/14.32 sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ $i(v0) | ~ aInteger0(v0)) & ! % 104.06/14.32 [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ $i(v0) | ~ % 104.06/14.32 aInteger0(v0) | sdtasdt0(sz00, v0) = sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ % 104.06/14.32 (sdtasdt0(sz00, v0) = v1) | ~ $i(v0) | ~ aInteger0(v0) | sdtasdt0(v0, % 104.06/14.32 sz00) = sz00) % 104.06/14.32 % 104.06/14.32 (mPrimeDivisor) % 104.06/14.32 $i(sz10) & ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : (v1 = v0 % 104.06/14.32 | v1 = sz10 | ~ $i(v1) | ~ aInteger0(v1) | ? [v2: $i] : ($i(v2) & % 104.06/14.32 isPrime0(v2) & aDivisorOf0(v2, v1))) & ! [v1: $i] : ( ~ $i(v1) | ~ % 104.06/14.32 isPrime0(v1) | ~ aDivisorOf0(v1, v0) | ~ aInteger0(v0)) & ! [v1: $i] : % 104.06/14.32 ( ~ $i(v1) | ~ isPrime0(v1) | ~ aDivisorOf0(v1, sz10) | ~ % 104.06/14.32 aInteger0(sz10))) % 104.06/14.32 % 104.06/14.32 (m__) % 104.06/14.32 $i(xp) & $i(sz10) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ((v2 = sz10 & % 104.06/14.32 sdtpldt0(sz10, v1) = sz10 & smndt0(xp) = v1 & $i(v1)) | (v0 = sz10 & % 104.06/14.32 sdtpldt0(sz10, xp) = sz10)) % 104.06/14.32 % 104.06/14.32 (m__2046) % 104.06/14.32 xS = cS2043 & $i(cS2043) % 104.06/14.32 % 104.06/14.32 (m__2079) % 104.06/14.32 $i(cS2076) & $i(xS) & ? [v0: $i] : (stldt0(v0) = cS2076 & sbsmnsldt0(xS) = v0 % 104.06/14.32 & $i(v0)) % 104.06/14.32 % 104.06/14.32 (m__2144) % 104.06/14.32 $i(xS) & ? [v0: $i] : ? [v1: $i] : (stldt0(v0) = v1 & sbsmnsldt0(xS) = v0 & % 104.06/14.32 $i(v1) & $i(v0) & isClosed0(v0) & isOpen0(v1)) % 104.06/14.32 % 104.06/14.32 (m__2171) % 104.06/14.32 $i(xp) & $i(xS) & $i(sz10) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 104.06/14.32 $i] : ( ~ (xp = sz00) & szAzrzSzezqlpdtcmdtrp0(sz10, xp) = v0 & stldt0(v1) = % 104.06/14.32 v2 & sbsmnsldt0(xS) = v1 & $i(v2) & $i(v1) & $i(v0) & aSubsetOf0(v0, v2) & % 104.06/14.32 aInteger0(xp)) % 104.06/14.32 % 104.06/14.32 (m__2232) % 104.06/14.33 $i(xp) & $i(sz10) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 104.06/14.33 (szAzrzSzezqlpdtcmdtrp0(sz10, xp) = v1 & sdtpldt0(sz10, v2) = v3 & % 104.06/14.33 sdtpldt0(sz10, xp) = v0 & smndt0(xp) = v2 & $i(v3) & $i(v2) & $i(v1) & % 104.06/14.33 $i(v0) & aElementOf0(v3, v1) & aElementOf0(v0, v1)) % 104.06/14.33 % 104.06/14.33 (function-axioms) % 104.06/14.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 104.06/14.33 (szAzrzSzezqlpdtcmdtrp0(v3, v2) = v1) | ~ (szAzrzSzezqlpdtcmdtrp0(v3, v2) = % 104.06/14.33 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 104.06/14.33 ~ (sdtslmnbsdt0(v3, v2) = v1) | ~ (sdtslmnbsdt0(v3, v2) = v0)) & ! [v0: % 104.06/14.33 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 104.06/14.33 (sdtbsmnsldt0(v3, v2) = v1) | ~ (sdtbsmnsldt0(v3, v2) = v0)) & ! [v0: $i] % 104.06/14.33 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = % 104.06/14.33 v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 104.06/14.33 $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, % 104.06/14.33 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 104.06/14.33 (stldt0(v2) = v1) | ~ (stldt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 104.06/14.33 [v2: $i] : (v1 = v0 | ~ (sbsmnsldt0(v2) = v1) | ~ (sbsmnsldt0(v2) = v0)) & % 104.06/14.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ % 104.06/14.33 (smndt0(v2) = v0)) % 104.06/14.33 % 104.06/14.33 Further assumptions not needed in the proof: % 104.06/14.33 -------------------------------------------- % 104.06/14.33 mArSeq, mClosed, mComplement, mDivisor, mElements, mEquMod, mEquModMul, % 104.06/14.33 mEquModSym, mEquModTrn, mFinSet, mIntMult, mIntPlus, mIntegers, mInterOpen, % 104.06/14.33 mIntersection, mMulComm, mMulOne, mOpen, mPrime, mSets, mSubset, mUnion, % 104.06/14.33 mUnionClosed, mUnionOpen, mUnionSClosed, mUnionSet, mZeroDiv, m__2117 % 104.06/14.33 % 104.06/14.33 Those formulas are unsatisfiable: % 104.06/14.33 --------------------------------- % 104.06/14.33 % 104.06/14.33 Begin of proof % 104.06/14.33 | % 104.06/14.33 | ALPHA: (mIntZero) implies: % 104.06/14.33 | (1) aInteger0(sz00) % 104.06/14.33 | % 104.06/14.33 | ALPHA: (mIntOne) implies: % 104.06/14.33 | (2) aInteger0(sz10) % 104.06/14.33 | % 104.06/14.33 | ALPHA: (mAddAsso) implies: % 104.06/14.33 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 104.06/14.33 | ~ (sdtpldt0(v1, v2) = v3) | ~ (sdtpldt0(v0, v3) = v4) | ~ $i(v2) | % 104.06/14.33 | ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v2) | ~ aInteger0(v1) | ~ % 104.06/14.33 | aInteger0(v0) | ? [v5: $i] : (sdtpldt0(v5, v2) = v4 & sdtpldt0(v0, % 104.06/14.33 | v1) = v5 & $i(v5) & $i(v4))) % 104.06/14.33 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 104.06/14.33 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | % 104.06/14.33 | ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v2) | ~ aInteger0(v1) | ~ % 104.06/14.33 | aInteger0(v0) | ? [v5: $i] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, % 104.06/14.33 | v5) = v4 & $i(v5) & $i(v4))) % 104.06/14.33 | % 104.06/14.33 | ALPHA: (mAddComm) implies: % 104.06/14.34 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | % 104.06/14.34 | ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) | % 104.06/14.34 | (sdtpldt0(v1, v0) = v2 & $i(v2))) % 104.06/14.34 | % 104.06/14.34 | ALPHA: (mAddZero) implies: % 104.06/14.34 | (6) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | % 104.06/14.34 | ~ $i(v0) | ~ aInteger0(v0)) % 104.06/14.34 | (7) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | % 104.06/14.34 | ~ $i(v0) | ~ aInteger0(v0)) % 104.06/14.34 | % 104.06/14.34 | ALPHA: (mAddNeg) implies: % 104.06/14.34 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ~ % 104.06/14.34 | aInteger0(v0) | (sdtpldt0(v1, v0) = sz00 & sdtpldt0(v0, v1) = sz00)) % 104.06/14.34 | % 104.06/14.34 | ALPHA: (mMulAsso) implies: % 104.06/14.34 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 104.06/14.34 | ~ (sdtasdt0(v1, v2) = v3) | ~ (sdtasdt0(v0, v3) = v4) | ~ $i(v2) | % 104.06/14.34 | ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v2) | ~ aInteger0(v1) | ~ % 104.06/14.34 | aInteger0(v0) | ? [v5: $i] : (sdtasdt0(v5, v2) = v4 & sdtasdt0(v0, % 104.06/14.34 | v1) = v5 & $i(v5) & $i(v4))) % 104.06/14.34 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 104.06/14.34 | ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | % 104.06/14.34 | ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v2) | ~ aInteger0(v1) | ~ % 104.06/14.34 | aInteger0(v0) | ? [v5: $i] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, % 104.06/14.34 | v5) = v4 & $i(v5) & $i(v4))) % 104.06/14.34 | % 104.06/14.34 | ALPHA: (mDistrib) implies: % 104.06/14.34 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 104.06/14.34 | ( ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | % 104.06/14.34 | ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v2) | ~ aInteger0(v1) | ~ % 104.06/14.34 | aInteger0(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 104.06/14.34 | $i] : ? [v9: $i] : (sdtasdt0(v7, v2) = v8 & sdtasdt0(v1, v2) = v9 % 104.06/14.34 | & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v6, v9) % 104.06/14.34 | = v8 & sdtpldt0(v5, v6) = v4 & sdtpldt0(v0, v1) = v7 & $i(v9) & % 104.06/14.34 | $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4))) % 104.50/14.34 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 104.50/14.34 | ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | % 104.50/14.34 | ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v2) | ~ aInteger0(v1) | ~ % 104.50/14.34 | aInteger0(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 104.50/14.34 | $i] : ? [v9: $i] : (sdtasdt0(v1, v2) = v9 & sdtasdt0(v0, v5) = v6 % 104.50/14.34 | & sdtasdt0(v0, v2) = v8 & sdtasdt0(v0, v1) = v7 & sdtpldt0(v8, v9) % 104.50/14.34 | = v4 & sdtpldt0(v7, v8) = v6 & sdtpldt0(v1, v2) = v5 & $i(v9) & % 104.50/14.34 | $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4))) % 104.50/14.34 | % 104.50/14.34 | ALPHA: (mMulZero) implies: % 104.50/14.34 | (13) ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) % 104.50/14.34 | | ~ $i(v0) | ~ aInteger0(v0)) % 104.50/14.34 | % 104.50/14.34 | ALPHA: (mMulMinOne) implies: % 104.50/14.35 | (14) ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] % 104.50/14.35 | : ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ~ aInteger0(v1) | % 104.50/14.35 | (sdtasdt0(v0, v1) = v2 & smndt0(v1) = v2 & $i(v2))) & ! [v1: $i] % 104.50/14.35 | : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ % 104.50/14.35 | aInteger0(v1) | (sdtasdt0(v1, v0) = v2 & smndt0(v1) = v2 & % 104.50/14.35 | $i(v2))) & ! [v1: $i] : ! [v2: $i] : ( ~ (smndt0(v1) = v2) | % 104.50/14.35 | ~ $i(v1) | ~ aInteger0(v1) | (sdtasdt0(v1, v0) = v2 & % 104.50/14.35 | sdtasdt0(v0, v1) = v2 & $i(v2)))) % 104.50/14.35 | % 104.50/14.35 | ALPHA: (mEquModRef) implies: % 104.50/14.35 | (15) ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ $i(v1) | ~ $i(v0) | ~ % 104.50/14.35 | aInteger0(v1) | ~ aInteger0(v0) | sdteqdtlpzmzozddtrp0(v0, v0, v1)) % 104.50/14.35 | % 104.50/14.35 | ALPHA: (mPrimeDivisor) implies: % 104.50/14.35 | (16) ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : (v1 = v0 | % 104.50/14.35 | v1 = sz10 | ~ $i(v1) | ~ aInteger0(v1) | ? [v2: $i] : ($i(v2) & % 104.50/14.35 | isPrime0(v2) & aDivisorOf0(v2, v1))) & ! [v1: $i] : ( ~ $i(v1) % 104.50/14.35 | | ~ isPrime0(v1) | ~ aDivisorOf0(v1, v0) | ~ aInteger0(v0)) & % 104.50/14.35 | ! [v1: $i] : ( ~ $i(v1) | ~ isPrime0(v1) | ~ aDivisorOf0(v1, sz10) % 104.50/14.35 | | ~ aInteger0(sz10))) % 104.50/14.35 | % 104.50/14.35 | ALPHA: (mArSeqClosed) implies: % 104.50/14.35 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = sz00 | ~ % 104.50/14.35 | (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 104.50/14.35 | aInteger0(v1) | ~ aInteger0(v0) | isClosed0(v2)) % 104.50/14.35 | % 104.50/14.35 | ALPHA: (m__2046) implies: % 104.50/14.35 | (18) xS = cS2043 % 104.50/14.35 | % 104.50/14.35 | ALPHA: (m__2079) implies: % 104.50/14.35 | (19) ? [v0: $i] : (stldt0(v0) = cS2076 & sbsmnsldt0(xS) = v0 & $i(v0)) % 104.50/14.35 | % 104.50/14.35 | ALPHA: (m__2144) implies: % 104.50/14.35 | (20) ? [v0: $i] : ? [v1: $i] : (stldt0(v0) = v1 & sbsmnsldt0(xS) = v0 & % 104.50/14.35 | $i(v1) & $i(v0) & isClosed0(v0) & isOpen0(v1)) % 104.50/14.35 | % 104.50/14.35 | ALPHA: (m__2171) implies: % 104.50/14.35 | (21) $i(sz00) % 104.50/14.35 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (xp = sz00) & % 104.50/14.35 | szAzrzSzezqlpdtcmdtrp0(sz10, xp) = v0 & stldt0(v1) = v2 & % 104.50/14.35 | sbsmnsldt0(xS) = v1 & $i(v2) & $i(v1) & $i(v0) & aSubsetOf0(v0, v2) % 104.50/14.35 | & aInteger0(xp)) % 104.50/14.35 | % 104.50/14.35 | ALPHA: (m__2232) implies: % 104.50/14.35 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 104.50/14.35 | (szAzrzSzezqlpdtcmdtrp0(sz10, xp) = v1 & sdtpldt0(sz10, v2) = v3 & % 104.50/14.35 | sdtpldt0(sz10, xp) = v0 & smndt0(xp) = v2 & $i(v3) & $i(v2) & $i(v1) % 104.50/14.35 | & $i(v0) & aElementOf0(v3, v1) & aElementOf0(v0, v1)) % 104.50/14.35 | % 104.50/14.35 | ALPHA: (m__) implies: % 104.50/14.35 | (24) $i(sz10) % 104.50/14.35 | (25) $i(xp) % 104.50/14.35 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ((v2 = sz10 & sdtpldt0(sz10, % 104.50/14.35 | v1) = sz10 & smndt0(xp) = v1 & $i(v1)) | (v0 = sz10 & % 104.50/14.35 | sdtpldt0(sz10, xp) = sz10)) % 104.50/14.35 | % 104.50/14.35 | ALPHA: (function-axioms) implies: % 104.50/14.35 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = % 104.50/14.35 | v1) | ~ (smndt0(v2) = v0)) % 104.50/14.35 | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 104.50/14.35 | (sbsmnsldt0(v2) = v1) | ~ (sbsmnsldt0(v2) = v0)) % 104.50/14.35 | (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (stldt0(v2) = % 104.50/14.36 | v1) | ~ (stldt0(v2) = v0)) % 104.50/14.36 | (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 104.50/14.36 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 104.50/14.36 | (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 104.50/14.36 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 104.50/14.36 | (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 104.50/14.36 | (szAzrzSzezqlpdtcmdtrp0(v3, v2) = v1) | ~ % 104.50/14.36 | (szAzrzSzezqlpdtcmdtrp0(v3, v2) = v0)) % 104.50/14.36 | % 104.50/14.36 | DELTA: instantiating (19) with fresh symbol all_36_0 gives: % 104.50/14.36 | (33) stldt0(all_36_0) = cS2076 & sbsmnsldt0(xS) = all_36_0 & $i(all_36_0) % 104.50/14.36 | % 104.50/14.36 | ALPHA: (33) implies: % 104.50/14.36 | (34) sbsmnsldt0(xS) = all_36_0 % 104.50/14.36 | (35) stldt0(all_36_0) = cS2076 % 104.50/14.36 | % 104.50/14.36 | DELTA: instantiating (20) with fresh symbols all_38_0, all_38_1 gives: % 104.50/14.36 | (36) stldt0(all_38_1) = all_38_0 & sbsmnsldt0(xS) = all_38_1 & $i(all_38_0) % 104.50/14.36 | & $i(all_38_1) & isClosed0(all_38_1) & isOpen0(all_38_0) % 104.50/14.36 | % 104.50/14.36 | ALPHA: (36) implies: % 104.50/14.36 | (37) sbsmnsldt0(xS) = all_38_1 % 104.50/14.36 | (38) stldt0(all_38_1) = all_38_0 % 104.50/14.36 | % 104.50/14.36 | DELTA: instantiating (26) with fresh symbols all_40_0, all_40_1, all_40_2 % 104.50/14.36 | gives: % 104.50/14.36 | (39) (all_40_0 = sz10 & sdtpldt0(sz10, all_40_1) = sz10 & smndt0(xp) = % 104.50/14.36 | all_40_1 & $i(all_40_1)) | (all_40_2 = sz10 & sdtpldt0(sz10, xp) = % 104.50/14.36 | sz10) % 104.50/14.36 | % 104.50/14.36 | DELTA: instantiating (22) with fresh symbols all_41_0, all_41_1, all_41_2 % 104.50/14.36 | gives: % 104.50/14.36 | (40) ~ (xp = sz00) & szAzrzSzezqlpdtcmdtrp0(sz10, xp) = all_41_2 & % 104.50/14.36 | stldt0(all_41_1) = all_41_0 & sbsmnsldt0(xS) = all_41_1 & $i(all_41_0) % 104.50/14.36 | & $i(all_41_1) & $i(all_41_2) & aSubsetOf0(all_41_2, all_41_0) & % 104.50/14.36 | aInteger0(xp) % 104.50/14.36 | % 104.50/14.36 | ALPHA: (40) implies: % 104.50/14.36 | (41) ~ (xp = sz00) % 104.50/14.36 | (42) aInteger0(xp) % 104.50/14.36 | (43) sbsmnsldt0(xS) = all_41_1 % 104.50/14.36 | (44) szAzrzSzezqlpdtcmdtrp0(sz10, xp) = all_41_2 % 104.50/14.36 | % 104.50/14.36 | DELTA: instantiating (23) with fresh symbols all_43_0, all_43_1, all_43_2, % 104.50/14.36 | all_43_3 gives: % 104.50/14.36 | (45) szAzrzSzezqlpdtcmdtrp0(sz10, xp) = all_43_2 & sdtpldt0(sz10, all_43_1) % 104.50/14.36 | = all_43_0 & sdtpldt0(sz10, xp) = all_43_3 & smndt0(xp) = all_43_1 & % 104.50/14.36 | $i(all_43_0) & $i(all_43_1) & $i(all_43_2) & $i(all_43_3) & % 104.50/14.36 | aElementOf0(all_43_0, all_43_2) & aElementOf0(all_43_3, all_43_2) % 104.50/14.36 | % 104.50/14.36 | ALPHA: (45) implies: % 104.50/14.36 | (46) smndt0(xp) = all_43_1 % 104.50/14.36 | (47) sdtpldt0(sz10, xp) = all_43_3 % 104.50/14.36 | (48) szAzrzSzezqlpdtcmdtrp0(sz10, xp) = all_43_2 % 104.50/14.36 | % 104.50/14.36 | DELTA: instantiating (16) with fresh symbol all_45_0 gives: % 104.50/14.36 | (49) smndt0(sz10) = all_45_0 & $i(all_45_0) & ! [v0: any] : (v0 = all_45_0 % 104.50/14.36 | | v0 = sz10 | ~ $i(v0) | ~ aInteger0(v0) | ? [v1: $i] : ($i(v1) & % 104.50/14.36 | isPrime0(v1) & aDivisorOf0(v1, v0))) & ! [v0: $i] : ( ~ $i(v0) | % 104.50/14.36 | ~ isPrime0(v0) | ~ aDivisorOf0(v0, all_45_0) | ~ % 104.50/14.36 | aInteger0(all_45_0)) & ! [v0: $i] : ( ~ $i(v0) | ~ isPrime0(v0) | % 104.50/14.36 | ~ aDivisorOf0(v0, sz10) | ~ aInteger0(sz10)) % 104.50/14.36 | % 104.50/14.36 | ALPHA: (49) implies: % 104.50/14.36 | (50) smndt0(sz10) = all_45_0 % 104.50/14.36 | % 104.50/14.36 | DELTA: instantiating (14) with fresh symbol all_48_0 gives: % 104.50/14.37 | (51) smndt0(sz10) = all_48_0 & $i(all_48_0) & ! [v0: $i] : ! [v1: $i] : ( % 104.50/14.37 | ~ (sdtasdt0(v0, all_48_0) = v1) | ~ $i(v0) | ~ aInteger0(v0) | % 104.50/14.37 | (sdtasdt0(all_48_0, v0) = v1 & smndt0(v0) = v1 & $i(v1))) & ! [v0: % 104.50/14.37 | $i] : ! [v1: $i] : ( ~ (sdtasdt0(all_48_0, v0) = v1) | ~ $i(v0) | % 104.50/14.37 | ~ aInteger0(v0) | (sdtasdt0(v0, all_48_0) = v1 & smndt0(v0) = v1 & % 104.50/14.37 | $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ % 104.50/14.37 | $i(v0) | ~ aInteger0(v0) | (sdtasdt0(v0, all_48_0) = v1 & % 104.50/14.37 | sdtasdt0(all_48_0, v0) = v1 & $i(v1))) % 104.50/14.37 | % 104.50/14.37 | ALPHA: (51) implies: % 104.50/14.37 | (52) smndt0(sz10) = all_48_0 % 104.50/14.37 | (53) ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ~ % 104.50/14.37 | aInteger0(v0) | (sdtasdt0(v0, all_48_0) = v1 & sdtasdt0(all_48_0, % 104.50/14.37 | v0) = v1 & $i(v1))) % 104.50/14.37 | % 104.50/14.37 | REDUCE: (18), (43) imply: % 104.50/14.37 | (54) sbsmnsldt0(cS2043) = all_41_1 % 104.50/14.37 | % 104.50/14.37 | REDUCE: (18), (37) imply: % 104.50/14.37 | (55) sbsmnsldt0(cS2043) = all_38_1 % 104.50/14.37 | % 104.50/14.37 | REDUCE: (18), (34) imply: % 104.50/14.37 | (56) sbsmnsldt0(cS2043) = all_36_0 % 104.50/14.37 | % 104.50/14.37 | GROUND_INST: instantiating (27) with all_45_0, all_48_0, sz10, simplifying % 104.50/14.37 | with (50), (52) gives: % 104.50/14.37 | (57) all_48_0 = all_45_0 % 104.50/14.37 | % 104.50/14.37 | GROUND_INST: instantiating (28) with all_38_1, all_41_1, cS2043, simplifying % 104.50/14.37 | with (54), (55) gives: % 104.50/14.37 | (58) all_41_1 = all_38_1 % 104.50/14.37 | % 104.50/14.37 | GROUND_INST: instantiating (28) with all_36_0, all_41_1, cS2043, simplifying % 104.50/14.37 | with (54), (56) gives: % 104.50/14.37 | (59) all_41_1 = all_36_0 % 104.50/14.37 | % 104.50/14.37 | GROUND_INST: instantiating (29) with cS2076, all_38_0, all_36_0, simplifying % 104.50/14.37 | with (35) gives: % 104.50/14.37 | (60) all_38_0 = cS2076 | ~ (stldt0(all_36_0) = all_38_0) % 104.50/14.37 | % 104.50/14.37 | GROUND_INST: instantiating (32) with all_41_2, all_43_2, xp, sz10, simplifying % 104.50/14.37 | with (44), (48) gives: % 104.50/14.37 | (61) all_43_2 = all_41_2 % 104.50/14.37 | % 104.50/14.37 | COMBINE_EQS: (58), (59) imply: % 104.50/14.37 | (62) all_38_1 = all_36_0 % 104.50/14.37 | % 104.50/14.37 | SIMP: (62) implies: % 104.50/14.37 | (63) all_38_1 = all_36_0 % 104.50/14.37 | % 104.50/14.37 | REDUCE: (38), (63) imply: % 104.50/14.37 | (64) stldt0(all_36_0) = all_38_0 % 104.50/14.37 | % 104.50/14.37 | BETA: splitting (60) gives: % 104.50/14.37 | % 104.50/14.37 | Case 1: % 104.50/14.37 | | % 104.50/14.37 | | (65) ~ (stldt0(all_36_0) = all_38_0) % 104.50/14.37 | | % 104.50/14.37 | | PRED_UNIFY: (64), (65) imply: % 104.50/14.37 | | (66) $false % 104.50/14.37 | | % 104.50/14.37 | | CLOSE: (66) is inconsistent. % 104.50/14.37 | | % 104.50/14.37 | Case 2: % 104.50/14.37 | | % 104.50/14.37 | | % 104.50/14.37 | | GROUND_INST: instantiating (mIntNeg) with sz10, all_45_0, simplifying with % 104.50/14.37 | | (2), (24), (50) gives: % 104.50/14.37 | | (67) aInteger0(all_45_0) % 104.50/14.37 | | % 104.50/14.37 | | GROUND_INST: instantiating (53) with sz10, all_45_0, simplifying with (2), % 104.50/14.37 | | (24), (50) gives: % 104.50/14.38 | | (68) sdtasdt0(all_48_0, sz10) = all_45_0 & sdtasdt0(sz10, all_48_0) = % 104.50/14.38 | | all_45_0 & $i(all_45_0) % 104.50/14.38 | | % 104.50/14.38 | | ALPHA: (68) implies: % 104.50/14.38 | | (69) $i(all_45_0) % 104.50/14.38 | | (70) sdtasdt0(sz10, all_48_0) = all_45_0 % 104.50/14.38 | | (71) sdtasdt0(all_48_0, sz10) = all_45_0 % 104.50/14.38 | | % 104.50/14.38 | | GROUND_INST: instantiating (8) with sz10, all_45_0, simplifying with (2), % 104.50/14.38 | | (24), (50) gives: % 104.50/14.38 | | (72) sdtpldt0(all_45_0, sz10) = sz00 & sdtpldt0(sz10, all_45_0) = sz00 % 104.50/14.38 | | % 104.50/14.38 | | ALPHA: (72) implies: % 104.50/14.38 | | (73) sdtpldt0(sz10, all_45_0) = sz00 % 104.50/14.38 | | (74) sdtpldt0(all_45_0, sz10) = sz00 % 104.50/14.38 | | % 104.50/14.38 | | GROUND_INST: instantiating (mIntNeg) with xp, all_43_1, simplifying with % 104.50/14.38 | | (25), (42), (46) gives: % 104.50/14.38 | | (75) aInteger0(all_43_1) % 104.50/14.38 | | % 104.50/14.38 | | GROUND_INST: instantiating (53) with xp, all_43_1, simplifying with (25), % 104.50/14.38 | | (42), (46) gives: % 104.50/14.38 | | (76) sdtasdt0(all_48_0, xp) = all_43_1 & sdtasdt0(xp, all_48_0) = % 104.50/14.38 | | all_43_1 & $i(all_43_1) % 104.50/14.38 | | % 104.50/14.38 | | ALPHA: (76) implies: % 104.50/14.38 | | (77) sdtasdt0(xp, all_48_0) = all_43_1 % 104.50/14.38 | | (78) sdtasdt0(all_48_0, xp) = all_43_1 % 104.50/14.38 | | % 104.50/14.38 | | GROUND_INST: instantiating (8) with xp, all_43_1, simplifying with (25), % 104.50/14.38 | | (42), (46) gives: % 104.50/14.38 | | (79) sdtpldt0(all_43_1, xp) = sz00 & sdtpldt0(xp, all_43_1) = sz00 % 104.50/14.38 | | % 104.50/14.38 | | ALPHA: (79) implies: % 104.50/14.38 | | (80) sdtpldt0(all_43_1, xp) = sz00 % 104.50/14.38 | | % 104.50/14.38 | | GROUND_INST: instantiating (5) with sz10, xp, all_43_3, simplifying with % 104.50/14.38 | | (2), (24), (25), (42), (47) gives: % 104.50/14.38 | | (81) sdtpldt0(xp, sz10) = all_43_3 & $i(all_43_3) % 104.50/14.38 | | % 104.50/14.38 | | ALPHA: (81) implies: % 104.50/14.38 | | (82) sdtpldt0(xp, sz10) = all_43_3 % 104.50/14.38 | | % 104.50/14.38 | | GROUND_INST: instantiating (17) with sz10, xp, all_41_2, simplifying with % 104.50/14.38 | | (2), (24), (25), (42), (44) gives: % 104.50/14.38 | | (83) xp = sz00 | isClosed0(all_41_2) % 104.50/14.38 | | % 104.50/14.38 | | REDUCE: (57), (78) imply: % 104.50/14.38 | | (84) sdtasdt0(all_45_0, xp) = all_43_1 % 104.50/14.38 | | % 104.50/14.38 | | REDUCE: (57), (71) imply: % 104.50/14.38 | | (85) sdtasdt0(all_45_0, sz10) = all_45_0 % 104.50/14.38 | | % 104.50/14.38 | | REDUCE: (57), (77) imply: % 104.50/14.38 | | (86) sdtasdt0(xp, all_45_0) = all_43_1 % 104.50/14.38 | | % 104.50/14.38 | | REDUCE: (57), (70) imply: % 104.50/14.38 | | (87) sdtasdt0(sz10, all_45_0) = all_45_0 % 104.50/14.38 | | % 104.50/14.38 | | BETA: splitting (83) gives: % 104.50/14.38 | | % 104.50/14.38 | | Case 1: % 104.50/14.38 | | | % 104.50/14.38 | | | % 104.50/14.38 | | | GROUND_INST: instantiating (15) with xp, all_45_0, simplifying with (25), % 104.50/14.38 | | | (42), (67), (69) gives: % 104.50/14.38 | | | (88) all_45_0 = sz00 | sdteqdtlpzmzozddtrp0(xp, xp, all_45_0) % 104.50/14.38 | | | % 104.50/14.38 | | | ALPHA: (76) implies: % 104.50/14.38 | | | (89) $i(all_43_1) % 104.50/14.38 | | | % 104.50/14.38 | | | GROUND_INST: instantiating (4) with xp, sz10, all_45_0, sz10, sz00, % 104.50/14.38 | | | simplifying with (2), (24), (25), (42), (67), (69), (73) % 104.50/14.38 | | | gives: % 104.50/14.39 | | | (90) ~ (sdtpldt0(xp, sz10) = sz10) | ? [v0: $i] : (sdtpldt0(xp, v0) = % 104.50/14.39 | | | sz00 & sdtpldt0(sz10, all_45_0) = v0 & $i(v0) & $i(sz00)) % 104.50/14.39 | | | % 104.50/14.39 | | | GROUND_INST: instantiating (7) with xp, sz00, simplifying with (25), (42) % 104.50/14.39 | | | gives: % 104.50/14.39 | | | (91) xp = sz00 | ~ (sdtpldt0(xp, sz00) = sz00) % 104.50/14.39 | | | % 104.50/14.39 | | | GROUND_INST: instantiating (5) with sz00, xp, sz00, simplifying with (1), % 104.50/14.39 | | | (21), (25), (42) gives: % 104.50/14.39 | | | (92) ~ (sdtpldt0(sz00, xp) = sz00) | sdtpldt0(xp, sz00) = sz00 % 104.50/14.39 | | | % 104.50/14.39 | | | GROUND_INST: instantiating (3) with all_45_0, sz10, all_43_1, sz10, sz00, % 104.50/14.39 | | | simplifying with (2), (24), (67), (69), (74), (75), (89) % 104.50/14.39 | | | gives: % 104.50/14.39 | | | (93) ~ (sdtpldt0(sz10, all_43_1) = sz10) | ? [v0: $i] : (sdtpldt0(v0, % 104.50/14.39 | | | all_43_1) = sz00 & sdtpldt0(all_45_0, sz10) = v0 & $i(v0) & % 104.50/14.39 | | | $i(sz00)) % 104.50/14.39 | | | % 104.50/14.39 | | | GROUND_INST: instantiating (3) with all_45_0, sz10, xp, sz10, sz00, % 104.50/14.39 | | | simplifying with (2), (24), (25), (42), (67), (69), (74) % 104.50/14.39 | | | gives: % 104.50/14.39 | | | (94) ~ (sdtpldt0(sz10, xp) = sz10) | ? [v0: $i] : (sdtpldt0(v0, xp) = % 104.50/14.39 | | | sz00 & sdtpldt0(all_45_0, sz10) = v0 & $i(v0) & $i(sz00)) % 104.50/14.39 | | | % 104.50/14.39 | | | GROUND_INST: instantiating (12) with xp, sz10, all_45_0, sz10, all_45_0, % 104.50/14.39 | | | simplifying with (2), (24), (25), (42), (67), (69), (87) % 104.50/14.39 | | | gives: % 104.75/14.39 | | | (95) ~ (sdtpldt0(xp, sz10) = sz10) | ? [v0: $i] : ? [v1: $i] : ? % 104.75/14.39 | | | [v2: $i] : ? [v3: $i] : ? [v4: $i] : (sdtasdt0(xp, v0) = v1 & % 104.75/14.39 | | | sdtasdt0(xp, all_45_0) = v3 & sdtasdt0(xp, sz10) = v2 & % 104.75/14.39 | | | sdtasdt0(sz10, all_45_0) = v4 & sdtpldt0(v3, v4) = all_45_0 & % 104.75/14.39 | | | sdtpldt0(v2, v3) = v1 & sdtpldt0(sz10, all_45_0) = v0 & $i(v4) & % 104.75/14.39 | | | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 104.75/14.39 | | | % 104.75/14.39 | | | GROUND_INST: instantiating (10) with all_43_1, sz10, sz10, all_43_1, % 104.75/14.39 | | | all_43_1, simplifying with (2), (24), (75), (89) gives: % 104.75/14.39 | | | (96) ~ (sdtasdt0(all_43_1, sz10) = all_43_1) | ? [v0: $i] : % 104.75/14.39 | | | (sdtasdt0(all_43_1, v0) = all_43_1 & sdtasdt0(sz10, sz10) = v0 & % 104.75/14.39 | | | $i(v0)) % 104.75/14.39 | | | % 104.75/14.39 | | | GROUND_INST: instantiating (9) with xp, all_45_0, sz10, all_45_0, % 104.75/14.39 | | | all_43_1, simplifying with (2), (24), (25), (42), (67), (69), % 104.75/14.39 | | | (85), (86) gives: % 104.75/14.39 | | | (97) ? [v0: $i] : (sdtasdt0(v0, sz10) = all_43_1 & sdtasdt0(xp, % 104.75/14.39 | | | all_45_0) = v0 & $i(v0) & $i(all_43_1)) % 104.75/14.39 | | | % 104.75/14.39 | | | GROUND_INST: instantiating (11) with all_45_0, sz10, all_43_1, sz10, % 104.75/14.39 | | | all_45_0, simplifying with (2), (24), (67), (69), (75), (85), % 104.75/14.39 | | | (89) gives: % 104.75/14.40 | | | (98) ~ (sdtpldt0(sz10, all_43_1) = sz10) | ? [v0: $i] : ? [v1: $i] : % 104.75/14.40 | | | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (sdtasdt0(v2, all_43_1) % 104.75/14.40 | | | = v3 & sdtasdt0(all_45_0, all_43_1) = v1 & sdtasdt0(all_45_0, % 104.75/14.40 | | | sz10) = v0 & sdtasdt0(sz10, all_43_1) = v4 & sdtpldt0(v1, v4) % 104.75/14.40 | | | = v3 & sdtpldt0(v0, v1) = all_45_0 & sdtpldt0(all_45_0, sz10) = % 104.75/14.40 | | | v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 104.75/14.40 | | | % 104.75/14.40 | | | GROUND_INST: instantiating (10) with sz10, all_45_0, xp, all_45_0, % 104.75/14.40 | | | all_43_1, simplifying with (2), (24), (25), (42), (67), (69), % 104.75/14.40 | | | (84), (87) gives: % 104.75/14.40 | | | (99) ? [v0: $i] : (sdtasdt0(all_45_0, xp) = v0 & sdtasdt0(sz10, v0) = % 104.75/14.40 | | | all_43_1 & $i(v0) & $i(all_43_1)) % 104.75/14.40 | | | % 104.75/14.40 | | | GROUND_INST: instantiating (13) with xp, all_43_1, simplifying with (25), % 104.75/14.40 | | | (42) gives: % 104.75/14.40 | | | (100) all_43_1 = sz00 | ~ (sdtasdt0(sz00, xp) = all_43_1) % 104.75/14.40 | | | % 104.75/14.40 | | | DELTA: instantiating (99) with fresh symbol all_115_0 gives: % 104.75/14.40 | | | (101) sdtasdt0(all_45_0, xp) = all_115_0 & sdtasdt0(sz10, all_115_0) = % 104.75/14.40 | | | all_43_1 & $i(all_115_0) & $i(all_43_1) % 104.75/14.40 | | | % 104.75/14.40 | | | ALPHA: (101) implies: % 104.75/14.40 | | | (102) sdtasdt0(all_45_0, xp) = all_115_0 % 104.75/14.40 | | | % 104.75/14.40 | | | DELTA: instantiating (97) with fresh symbol all_119_0 gives: % 104.75/14.40 | | | (103) sdtasdt0(all_119_0, sz10) = all_43_1 & sdtasdt0(xp, all_45_0) = % 104.75/14.40 | | | all_119_0 & $i(all_119_0) & $i(all_43_1) % 104.75/14.40 | | | % 104.75/14.40 | | | ALPHA: (103) implies: % 104.75/14.40 | | | (104) sdtasdt0(xp, all_45_0) = all_119_0 % 104.75/14.40 | | | (105) sdtasdt0(all_119_0, sz10) = all_43_1 % 104.75/14.40 | | | % 104.75/14.40 | | | BETA: splitting (91) gives: % 104.75/14.40 | | | % 104.75/14.40 | | | Case 1: % 104.75/14.40 | | | | % 104.75/14.40 | | | | (106) ~ (sdtpldt0(xp, sz00) = sz00) % 104.75/14.40 | | | | % 104.75/14.40 | | | | BETA: splitting (90) gives: % 104.75/14.40 | | | | % 104.75/14.40 | | | | Case 1: % 104.75/14.40 | | | | | % 104.75/14.40 | | | | | (107) ~ (sdtpldt0(xp, sz10) = sz10) % 104.75/14.40 | | | | | % 104.75/14.40 | | | | | BETA: splitting (92) gives: % 104.75/14.40 | | | | | % 104.75/14.40 | | | | | Case 1: % 104.75/14.40 | | | | | | % 104.75/14.40 | | | | | | (108) ~ (sdtpldt0(sz00, xp) = sz00) % 104.75/14.40 | | | | | | % 104.75/14.40 | | | | | | BETA: splitting (94) gives: % 104.75/14.40 | | | | | | % 104.75/14.40 | | | | | | Case 1: % 104.75/14.40 | | | | | | | % 104.75/14.40 | | | | | | | (109) ~ (sdtpldt0(sz10, xp) = sz10) % 104.75/14.40 | | | | | | | % 104.75/14.40 | | | | | | | GROUND_INST: instantiating (31) with all_43_1, all_119_0, % 104.75/14.40 | | | | | | | all_45_0, xp, simplifying with (86), (104) gives: % 104.75/14.40 | | | | | | | (110) all_119_0 = all_43_1 % 104.75/14.40 | | | | | | | % 104.75/14.40 | | | | | | | GROUND_INST: instantiating (31) with all_43_1, all_115_0, xp, % 104.75/14.40 | | | | | | | all_45_0, simplifying with (84), (102) gives: % 104.75/14.40 | | | | | | | (111) all_115_0 = all_43_1 % 104.75/14.40 | | | | | | | % 104.75/14.40 | | | | | | | PRED_UNIFY: (80), (108) imply: % 104.75/14.40 | | | | | | | (112) ~ (all_43_1 = sz00) % 104.75/14.40 | | | | | | | % 104.75/14.40 | | | | | | | REDUCE: (105), (110) imply: % 104.75/14.40 | | | | | | | (113) sdtasdt0(all_43_1, sz10) = all_43_1 % 104.75/14.40 | | | | | | | % 104.75/14.40 | | | | | | | BETA: splitting (39) gives: % 104.75/14.40 | | | | | | | % 104.75/14.40 | | | | | | | Case 1: % 104.75/14.40 | | | | | | | | % 104.75/14.40 | | | | | | | | (114) all_40_0 = sz10 & sdtpldt0(sz10, all_40_1) = sz10 & % 104.75/14.40 | | | | | | | | smndt0(xp) = all_40_1 & $i(all_40_1) % 104.75/14.40 | | | | | | | | % 104.75/14.40 | | | | | | | | ALPHA: (114) implies: % 104.75/14.40 | | | | | | | | (115) smndt0(xp) = all_40_1 % 104.75/14.40 | | | | | | | | (116) sdtpldt0(sz10, all_40_1) = sz10 % 104.75/14.40 | | | | | | | | % 104.75/14.40 | | | | | | | | BETA: splitting (100) gives: % 104.75/14.40 | | | | | | | | % 104.75/14.40 | | | | | | | | Case 1: % 104.75/14.40 | | | | | | | | | % 104.75/14.40 | | | | | | | | | (117) ~ (sdtasdt0(sz00, xp) = all_43_1) % 104.75/14.40 | | | | | | | | | % 104.75/14.40 | | | | | | | | | BETA: splitting (96) gives: % 104.75/14.40 | | | | | | | | | % 104.75/14.40 | | | | | | | | | Case 1: % 104.75/14.40 | | | | | | | | | | % 104.75/14.40 | | | | | | | | | | (118) ~ (sdtasdt0(all_43_1, sz10) = all_43_1) % 104.75/14.40 | | | | | | | | | | % 104.75/14.40 | | | | | | | | | | PRED_UNIFY: (113), (118) imply: % 104.75/14.40 | | | | | | | | | | (119) $false % 104.75/14.40 | | | | | | | | | | % 104.75/14.40 | | | | | | | | | | CLOSE: (119) is inconsistent. % 104.75/14.40 | | | | | | | | | | % 104.75/14.40 | | | | | | | | | Case 2: % 104.75/14.40 | | | | | | | | | | % 104.75/14.40 | | | | | | | | | | % 104.75/14.40 | | | | | | | | | | GROUND_INST: instantiating (27) with all_43_1, all_40_1, xp, % 104.75/14.40 | | | | | | | | | | simplifying with (46), (115) gives: % 104.75/14.40 | | | | | | | | | | (120) all_43_1 = all_40_1 % 104.75/14.40 | | | | | | | | | | % 104.75/14.40 | | | | | | | | | | PRED_UNIFY: (84), (117) imply: % 104.75/14.40 | | | | | | | | | | (121) ~ (all_45_0 = sz00) % 104.75/14.40 | | | | | | | | | | % 104.75/14.40 | | | | | | | | | | REDUCE: (112), (120) imply: % 104.75/14.40 | | | | | | | | | | (122) ~ (all_40_1 = sz00) % 104.75/14.40 | | | | | | | | | | % 104.75/14.40 | | | | | | | | | | REDUCE: (75), (120) imply: % 104.75/14.40 | | | | | | | | | | (123) aInteger0(all_40_1) % 104.75/14.40 | | | | | | | | | | % 104.75/14.40 | | | | | | | | | | BETA: splitting (93) gives: % 104.75/14.40 | | | | | | | | | | % 104.75/14.40 | | | | | | | | | | Case 1: % 104.75/14.40 | | | | | | | | | | | % 104.75/14.40 | | | | | | | | | | | (124) ~ (sdtpldt0(sz10, all_43_1) = sz10) % 104.75/14.40 | | | | | | | | | | | % 104.75/14.40 | | | | | | | | | | | REDUCE: (120), (124) imply: % 104.75/14.40 | | | | | | | | | | | (125) ~ (sdtpldt0(sz10, all_40_1) = sz10) % 104.75/14.40 | | | | | | | | | | | % 104.75/14.40 | | | | | | | | | | | PRED_UNIFY: (116), (125) imply: % 104.75/14.40 | | | | | | | | | | | (126) $false % 104.75/14.40 | | | | | | | | | | | % 104.75/14.40 | | | | | | | | | | | CLOSE: (126) is inconsistent. % 104.75/14.40 | | | | | | | | | | | % 104.75/14.40 | | | | | | | | | | Case 2: % 104.75/14.40 | | | | | | | | | | | % 104.75/14.40 | | | | | | | | | | | (127) sdtpldt0(sz10, all_43_1) = sz10 % 104.75/14.40 | | | | | | | | | | | (128) ? [v0: $i] : (sdtpldt0(v0, all_43_1) = sz00 & % 104.75/14.40 | | | | | | | | | | | sdtpldt0(all_45_0, sz10) = v0 & $i(v0) & % 104.75/14.40 | | | | | | | | | | | $i(sz00)) % 104.75/14.40 | | | | | | | | | | | % 104.75/14.40 | | | | | | | | | | | DELTA: instantiating (128) with fresh symbol all_300_0 % 104.75/14.40 | | | | | | | | | | | gives: % 104.75/14.40 | | | | | | | | | | | (129) sdtpldt0(all_300_0, all_43_1) = sz00 & % 104.75/14.40 | | | | | | | | | | | sdtpldt0(all_45_0, sz10) = all_300_0 & % 104.75/14.40 | | | | | | | | | | | $i(all_300_0) & $i(sz00) % 104.75/14.40 | | | | | | | | | | | % 104.75/14.40 | | | | | | | | | | | ALPHA: (129) implies: % 104.75/14.40 | | | | | | | | | | | (130) sdtpldt0(all_45_0, sz10) = all_300_0 % 104.75/14.40 | | | | | | | | | | | (131) sdtpldt0(all_300_0, all_43_1) = sz00 % 104.75/14.40 | | | | | | | | | | | % 104.75/14.40 | | | | | | | | | | | REDUCE: (120), (131) imply: % 104.75/14.41 | | | | | | | | | | | (132) sdtpldt0(all_300_0, all_40_1) = sz00 % 104.75/14.41 | | | | | | | | | | | % 104.75/14.41 | | | | | | | | | | | BETA: splitting (98) gives: % 104.75/14.41 | | | | | | | | | | | % 104.75/14.41 | | | | | | | | | | | Case 1: % 104.75/14.41 | | | | | | | | | | | | % 104.75/14.41 | | | | | | | | | | | | (133) ~ (sdtpldt0(sz10, all_43_1) = sz10) % 104.75/14.41 | | | | | | | | | | | | % 104.75/14.41 | | | | | | | | | | | | REDUCE: (120), (133) imply: % 104.75/14.41 | | | | | | | | | | | | (134) ~ (sdtpldt0(sz10, all_40_1) = sz10) % 104.75/14.41 | | | | | | | | | | | | % 104.75/14.41 | | | | | | | | | | | | PRED_UNIFY: (116), (134) imply: % 104.75/14.41 | | | | | | | | | | | | (135) $false % 104.75/14.41 | | | | | | | | | | | | % 104.75/14.41 | | | | | | | | | | | | CLOSE: (135) is inconsistent. % 104.75/14.41 | | | | | | | | | | | | % 104.75/14.41 | | | | | | | | | | | Case 2: % 104.75/14.41 | | | | | | | | | | | | % 104.75/14.41 | | | | | | | | | | | | (136) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 104.75/14.41 | | | | | | | | | | | | $i] : ? [v4: $i] : (sdtasdt0(v2, all_43_1) = v3 % 104.75/14.41 | | | | | | | | | | | | & sdtasdt0(all_45_0, all_43_1) = v1 & % 104.75/14.41 | | | | | | | | | | | | sdtasdt0(all_45_0, sz10) = v0 & sdtasdt0(sz10, % 104.75/14.41 | | | | | | | | | | | | all_43_1) = v4 & sdtpldt0(v1, v4) = v3 & % 104.75/14.41 | | | | | | | | | | | | sdtpldt0(v0, v1) = all_45_0 & sdtpldt0(all_45_0, % 104.75/14.41 | | | | | | | | | | | | sz10) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) % 104.75/14.41 | | | | | | | | | | | | & $i(v0)) % 104.75/14.41 | | | | | | | | | | | | % 104.75/14.41 | | | | | | | | | | | | DELTA: instantiating (136) with fresh symbols all_310_0, % 104.75/14.41 | | | | | | | | | | | | all_310_1, all_310_2, all_310_3, all_310_4 gives: % 104.75/14.41 | | | | | | | | | | | | (137) sdtasdt0(all_310_2, all_43_1) = all_310_1 & % 104.75/14.41 | | | | | | | | | | | | sdtasdt0(all_45_0, all_43_1) = all_310_3 & % 104.75/14.41 | | | | | | | | | | | | sdtasdt0(all_45_0, sz10) = all_310_4 & % 104.75/14.41 | | | | | | | | | | | | sdtasdt0(sz10, all_43_1) = all_310_0 & % 104.75/14.41 | | | | | | | | | | | | sdtpldt0(all_310_3, all_310_0) = all_310_1 & % 104.75/14.41 | | | | | | | | | | | | sdtpldt0(all_310_4, all_310_3) = all_45_0 & % 104.75/14.41 | | | | | | | | | | | | sdtpldt0(all_45_0, sz10) = all_310_2 & % 104.75/14.41 | | | | | | | | | | | | $i(all_310_0) & $i(all_310_1) & $i(all_310_2) & % 104.75/14.41 | | | | | | | | | | | | $i(all_310_3) & $i(all_310_4) % 104.75/14.41 | | | | | | | | | | | | % 104.75/14.41 | | | | | | | | | | | | ALPHA: (137) implies: % 104.75/14.41 | | | | | | | | | | | | (138) sdtpldt0(all_45_0, sz10) = all_310_2 % 104.75/14.41 | | | | | | | | | | | | % 104.75/14.41 | | | | | | | | | | | | BETA: splitting (88) gives: % 104.75/14.41 | | | | | | | | | | | | % 104.75/14.41 | | | | | | | | | | | | Case 1: % 104.75/14.41 | | | | | | | | | | | | | % 104.75/14.41 | | | | | | | | | | | | | % 104.75/14.41 | | | | | | | | | | | | | GROUND_INST: instantiating (30) with sz00, all_310_2, sz10, % 104.75/14.41 | | | | | | | | | | | | | all_45_0, simplifying with (74), (138) gives: % 104.75/14.41 | | | | | | | | | | | | | (139) all_310_2 = sz00 % 104.75/14.41 | | | | | | | | | | | | | % 104.75/14.41 | | | | | | | | | | | | | GROUND_INST: instantiating (30) with all_300_0, all_310_2, % 104.75/14.41 | | | | | | | | | | | | | sz10, all_45_0, simplifying with (130), (138) % 104.75/14.41 | | | | | | | | | | | | | gives: % 104.75/14.41 | | | | | | | | | | | | | (140) all_310_2 = all_300_0 % 104.75/14.41 | | | | | | | | | | | | | % 104.75/14.41 | | | | | | | | | | | | | COMBINE_EQS: (139), (140) imply: % 104.75/14.41 | | | | | | | | | | | | | (141) all_300_0 = sz00 % 104.75/14.41 | | | | | | | | | | | | | % 104.75/14.41 | | | | | | | | | | | | | SIMP: (141) implies: % 104.75/14.41 | | | | | | | | | | | | | (142) all_300_0 = sz00 % 104.75/14.41 | | | | | | | | | | | | | % 104.75/14.41 | | | | | | | | | | | | | REDUCE: (132), (142) imply: % 104.75/14.41 | | | | | | | | | | | | | (143) sdtpldt0(sz00, all_40_1) = sz00 % 104.75/14.41 | | | | | | | | | | | | | % 104.75/14.41 | | | | | | | | | | | | | GROUND_INST: instantiating (53) with xp, all_40_1, simplifying % 104.75/14.41 | | | | | | | | | | | | | with (25), (42), (115) gives: % 104.75/14.41 | | | | | | | | | | | | | (144) sdtasdt0(all_48_0, xp) = all_40_1 & sdtasdt0(xp, % 104.75/14.41 | | | | | | | | | | | | | all_48_0) = all_40_1 & $i(all_40_1) % 104.75/14.41 | | | | | | | | | | | | | % 104.75/14.41 | | | | | | | | | | | | | ALPHA: (144) implies: % 104.75/14.41 | | | | | | | | | | | | | (145) $i(all_40_1) % 104.75/14.41 | | | | | | | | | | | | | % 104.75/14.41 | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_40_1, sz00, simplifying % 104.75/14.41 | | | | | | | | | | | | | with (123), (143), (145) gives: % 104.75/14.41 | | | | | | | | | | | | | (146) all_40_1 = sz00 % 104.75/14.41 | | | | | | | | | | | | | % 104.75/14.41 | | | | | | | | | | | | | REDUCE: (122), (146) imply: % 104.75/14.41 | | | | | | | | | | | | | (147) $false % 104.75/14.41 | | | | | | | | | | | | | % 104.75/14.41 | | | | | | | | | | | | | CLOSE: (147) is inconsistent. % 104.75/14.41 | | | | | | | | | | | | | % 104.75/14.41 | | | | | | | | | | | | Case 2: % 104.75/14.41 | | | | | | | | | | | | | % 104.75/14.41 | | | | | | | | | | | | | (148) all_45_0 = sz00 % 104.75/14.41 | | | | | | | | | | | | | % 104.75/14.41 | | | | | | | | | | | | | REDUCE: (121), (148) imply: % 104.75/14.41 | | | | | | | | | | | | | (149) $false % 104.75/14.41 | | | | | | | | | | | | | % 104.75/14.41 | | | | | | | | | | | | | CLOSE: (149) is inconsistent. % 104.75/14.41 | | | | | | | | | | | | | % 104.75/14.41 | | | | | | | | | | | | End of split % 104.75/14.41 | | | | | | | | | | | | % 104.75/14.41 | | | | | | | | | | | End of split % 104.75/14.41 | | | | | | | | | | | % 104.75/14.41 | | | | | | | | | | End of split % 104.75/14.41 | | | | | | | | | | % 104.75/14.41 | | | | | | | | | End of split % 104.75/14.41 | | | | | | | | | % 104.75/14.41 | | | | | | | | Case 2: % 104.75/14.41 | | | | | | | | | % 104.75/14.41 | | | | | | | | | (150) all_43_1 = sz00 % 104.75/14.41 | | | | | | | | | % 104.75/14.41 | | | | | | | | | REDUCE: (112), (150) imply: % 104.75/14.41 | | | | | | | | | (151) $false % 104.75/14.41 | | | | | | | | | % 104.75/14.41 | | | | | | | | | CLOSE: (151) is inconsistent. % 104.75/14.41 | | | | | | | | | % 104.75/14.41 | | | | | | | | End of split % 104.75/14.41 | | | | | | | | % 104.75/14.41 | | | | | | | Case 2: % 104.75/14.41 | | | | | | | | % 104.75/14.41 | | | | | | | | (152) all_40_2 = sz10 & sdtpldt0(sz10, xp) = sz10 % 104.75/14.41 | | | | | | | | % 104.75/14.41 | | | | | | | | ALPHA: (152) implies: % 104.75/14.41 | | | | | | | | (153) sdtpldt0(sz10, xp) = sz10 % 104.75/14.41 | | | | | | | | % 104.75/14.41 | | | | | | | | PRED_UNIFY: (109), (153) imply: % 104.75/14.41 | | | | | | | | (154) $false % 104.75/14.41 | | | | | | | | % 104.75/14.41 | | | | | | | | CLOSE: (154) is inconsistent. % 104.75/14.41 | | | | | | | | % 104.75/14.41 | | | | | | | End of split % 104.75/14.41 | | | | | | | % 104.75/14.41 | | | | | | Case 2: % 104.75/14.41 | | | | | | | % 104.75/14.41 | | | | | | | (155) sdtpldt0(sz10, xp) = sz10 % 104.75/14.41 | | | | | | | % 104.75/14.41 | | | | | | | GROUND_INST: instantiating (30) with all_43_3, sz10, xp, sz10, % 104.75/14.41 | | | | | | | simplifying with (47), (155) gives: % 104.75/14.41 | | | | | | | (156) all_43_3 = sz10 % 104.75/14.41 | | | | | | | % 104.75/14.41 | | | | | | | PRED_UNIFY: (82), (107) imply: % 104.75/14.41 | | | | | | | (157) ~ (all_43_3 = sz10) % 104.75/14.41 | | | | | | | % 104.75/14.41 | | | | | | | REDUCE: (156), (157) imply: % 104.75/14.41 | | | | | | | (158) $false % 104.75/14.41 | | | | | | | % 104.75/14.41 | | | | | | | CLOSE: (158) is inconsistent. % 104.75/14.41 | | | | | | | % 104.75/14.41 | | | | | | End of split % 104.75/14.41 | | | | | | % 104.75/14.41 | | | | | Case 2: % 104.75/14.41 | | | | | | % 104.75/14.41 | | | | | | (159) sdtpldt0(xp, sz00) = sz00 % 104.75/14.41 | | | | | | % 104.75/14.41 | | | | | | PRED_UNIFY: (106), (159) imply: % 104.75/14.41 | | | | | | (160) $false % 104.75/14.41 | | | | | | % 104.75/14.41 | | | | | | CLOSE: (160) is inconsistent. % 104.75/14.41 | | | | | | % 104.75/14.41 | | | | | End of split % 104.75/14.41 | | | | | % 104.75/14.41 | | | | Case 2: % 104.75/14.41 | | | | | % 104.75/14.41 | | | | | (161) sdtpldt0(xp, sz10) = sz10 % 104.75/14.41 | | | | | (162) ? [v0: $i] : (sdtpldt0(xp, v0) = sz00 & sdtpldt0(sz10, % 104.75/14.41 | | | | | all_45_0) = v0 & $i(v0) & $i(sz00)) % 104.75/14.41 | | | | | % 104.75/14.41 | | | | | DELTA: instantiating (162) with fresh symbol all_147_0 gives: % 104.75/14.41 | | | | | (163) sdtpldt0(xp, all_147_0) = sz00 & sdtpldt0(sz10, all_45_0) = % 104.75/14.41 | | | | | all_147_0 & $i(all_147_0) & $i(sz00) % 104.75/14.41 | | | | | % 104.75/14.41 | | | | | ALPHA: (163) implies: % 104.75/14.41 | | | | | (164) sdtpldt0(sz10, all_45_0) = all_147_0 % 104.75/14.41 | | | | | (165) sdtpldt0(xp, all_147_0) = sz00 % 104.75/14.41 | | | | | % 104.75/14.41 | | | | | BETA: splitting (95) gives: % 104.75/14.41 | | | | | % 104.75/14.41 | | | | | Case 1: % 104.75/14.41 | | | | | | % 104.75/14.41 | | | | | | (166) ~ (sdtpldt0(xp, sz10) = sz10) % 104.75/14.41 | | | | | | % 104.75/14.41 | | | | | | PRED_UNIFY: (161), (166) imply: % 104.75/14.41 | | | | | | (167) $false % 104.75/14.41 | | | | | | % 104.75/14.41 | | | | | | CLOSE: (167) is inconsistent. % 104.75/14.41 | | | | | | % 104.75/14.41 | | | | | Case 2: % 104.75/14.41 | | | | | | % 104.75/14.41 | | | | | | (168) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 104.75/14.41 | | | | | | [v4: $i] : (sdtasdt0(xp, v0) = v1 & sdtasdt0(xp, all_45_0) % 104.75/14.41 | | | | | | = v3 & sdtasdt0(xp, sz10) = v2 & sdtasdt0(sz10, all_45_0) % 104.75/14.41 | | | | | | = v4 & sdtpldt0(v3, v4) = all_45_0 & sdtpldt0(v2, v3) = % 104.75/14.41 | | | | | | v1 & sdtpldt0(sz10, all_45_0) = v0 & $i(v4) & $i(v3) & % 104.75/14.41 | | | | | | $i(v2) & $i(v1) & $i(v0)) % 104.75/14.41 | | | | | | % 104.75/14.41 | | | | | | DELTA: instantiating (168) with fresh symbols all_176_0, all_176_1, % 104.75/14.41 | | | | | | all_176_2, all_176_3, all_176_4 gives: % 104.75/14.41 | | | | | | (169) sdtasdt0(xp, all_176_4) = all_176_3 & sdtasdt0(xp, % 104.75/14.41 | | | | | | all_45_0) = all_176_1 & sdtasdt0(xp, sz10) = all_176_2 & % 104.75/14.41 | | | | | | sdtasdt0(sz10, all_45_0) = all_176_0 & sdtpldt0(all_176_1, % 104.75/14.41 | | | | | | all_176_0) = all_45_0 & sdtpldt0(all_176_2, all_176_1) = % 104.75/14.41 | | | | | | all_176_3 & sdtpldt0(sz10, all_45_0) = all_176_4 & % 104.75/14.41 | | | | | | $i(all_176_0) & $i(all_176_1) & $i(all_176_2) & % 104.75/14.41 | | | | | | $i(all_176_3) & $i(all_176_4) % 104.75/14.41 | | | | | | % 104.75/14.41 | | | | | | ALPHA: (169) implies: % 104.75/14.41 | | | | | | (170) sdtpldt0(sz10, all_45_0) = all_176_4 % 104.75/14.41 | | | | | | % 104.75/14.42 | | | | | | GROUND_INST: instantiating (30) with sz00, all_176_4, all_45_0, % 104.75/14.42 | | | | | | sz10, simplifying with (73), (170) gives: % 104.75/14.42 | | | | | | (171) all_176_4 = sz00 % 104.75/14.42 | | | | | | % 104.75/14.42 | | | | | | GROUND_INST: instantiating (30) with all_147_0, all_176_4, all_45_0, % 104.75/14.42 | | | | | | sz10, simplifying with (164), (170) gives: % 104.75/14.42 | | | | | | (172) all_176_4 = all_147_0 % 104.75/14.42 | | | | | | % 104.75/14.42 | | | | | | PRED_UNIFY: (106), (165) imply: % 104.75/14.42 | | | | | | (173) ~ (all_147_0 = sz00) % 104.75/14.42 | | | | | | % 104.75/14.42 | | | | | | COMBINE_EQS: (171), (172) imply: % 104.75/14.42 | | | | | | (174) all_147_0 = sz00 % 104.75/14.42 | | | | | | % 104.75/14.42 | | | | | | REDUCE: (173), (174) imply: % 104.75/14.42 | | | | | | (175) $false % 104.75/14.42 | | | | | | % 104.75/14.42 | | | | | | CLOSE: (175) is inconsistent. % 104.75/14.42 | | | | | | % 104.75/14.42 | | | | | End of split % 104.75/14.42 | | | | | % 104.75/14.42 | | | | End of split % 104.75/14.42 | | | | % 104.75/14.42 | | | Case 2: % 104.75/14.42 | | | | % 104.75/14.42 | | | | (176) xp = sz00 % 104.75/14.42 | | | | % 104.75/14.42 | | | | REDUCE: (41), (176) imply: % 104.75/14.42 | | | | (177) $false % 104.75/14.42 | | | | % 104.75/14.42 | | | | CLOSE: (177) is inconsistent. % 104.75/14.42 | | | | % 104.75/14.42 | | | End of split % 104.75/14.42 | | | % 104.75/14.42 | | Case 2: % 104.75/14.42 | | | % 104.75/14.42 | | | (178) xp = sz00 % 104.75/14.42 | | | % 104.75/14.42 | | | REDUCE: (41), (178) imply: % 104.75/14.42 | | | (179) $false % 104.75/14.42 | | | % 104.75/14.42 | | | CLOSE: (179) is inconsistent. % 104.75/14.42 | | | % 104.75/14.42 | | End of split % 104.75/14.42 | | % 104.75/14.42 | End of split % 104.75/14.42 | % 104.75/14.42 End of proof % 104.75/14.42 % SZS output end Proof for theBenchmark % 104.75/14.42 % 104.75/14.42 13811ms %------------------------------------------------------------------------------