%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM465+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 : n032.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 11:47:55 EDT 2023 % Result : Theorem 64.28s 9.30s % Output : Proof 64.28s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : NUM465+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.29 % Computer : n032.cluster.edu % 0.12/0.29 % Model : x86_64 x86_64 % 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.29 % Memory : 8042.1875MB % 0.12/0.29 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.30 % CPULimit : 300 % 0.12/0.30 % WCLimit : 300 % 0.12/0.30 % DateTime : Fri Aug 25 09:58:42 EDT 2023 % 0.12/0.30 % CPUTime : % 0.14/0.52 ________ _____ % 0.14/0.52 ___ __ \_________(_)________________________________ % 0.14/0.52 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.14/0.52 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.14/0.52 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.14/0.52 % 0.14/0.52 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.14/0.52 (2023-06-19) % 0.14/0.52 % 0.14/0.52 (c) Philipp Rümmer, 2009-2023 % 0.14/0.52 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.14/0.52 Amanda Stjerna. % 0.14/0.52 Free software under BSD-3-Clause. % 0.14/0.52 % 0.14/0.52 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.14/0.52 % 0.14/0.52 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.14/0.53 Running up to 7 provers in parallel. % 0.14/0.54 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.14/0.54 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.14/0.54 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.14/0.54 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.14/0.54 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.14/0.54 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.14/0.54 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.68/0.99 Prover 4: Preprocessing ... % 2.68/0.99 Prover 1: Preprocessing ... % 2.86/1.03 Prover 0: Preprocessing ... % 2.86/1.03 Prover 3: Preprocessing ... % 2.86/1.03 Prover 5: Preprocessing ... % 2.86/1.03 Prover 2: Preprocessing ... % 2.86/1.03 Prover 6: Preprocessing ... % 6.69/1.61 Prover 1: Constructing countermodel ... % 6.69/1.62 Prover 3: Constructing countermodel ... % 6.69/1.66 Prover 6: Proving ... % 7.76/1.78 Prover 5: Constructing countermodel ... % 8.41/1.83 Prover 2: Proving ... % 8.93/1.90 Prover 4: Constructing countermodel ... % 9.81/2.12 Prover 0: Proving ... % 10.77/2.18 Prover 3: gave up % 10.77/2.19 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.77/2.26 Prover 1: gave up % 11.63/2.27 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.63/2.29 Prover 7: Preprocessing ... % 11.63/2.32 Prover 8: Preprocessing ... % 13.06/2.47 Prover 8: Warning: ignoring some quantifiers % 13.06/2.48 Prover 8: Constructing countermodel ... % 13.61/2.56 Prover 7: Constructing countermodel ... % 18.53/3.23 Prover 8: gave up % 18.53/3.24 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 18.98/3.28 Prover 9: Preprocessing ... % 22.33/3.72 Prover 9: Constructing countermodel ... % 60.99/8.83 Prover 2: stopped % 60.99/8.84 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 61.36/8.89 Prover 10: Preprocessing ... % 62.07/8.96 Prover 10: Constructing countermodel ... % 64.28/9.29 Prover 7: Found proof (size 93) % 64.28/9.29 Prover 7: proved (7093ms) % 64.28/9.29 Prover 0: stopped % 64.28/9.29 Prover 10: stopped % 64.28/9.29 Prover 9: stopped % 64.28/9.29 Prover 6: stopped % 64.28/9.29 Prover 4: stopped % 64.28/9.29 Prover 5: stopped % 64.28/9.29 % 64.28/9.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 64.28/9.30 % 64.28/9.30 % SZS output start Proof for theBenchmark % 64.28/9.30 Assumptions after simplification: % 64.28/9.30 --------------------------------- % 64.28/9.30 % 64.28/9.30 (mAMDistr) % 64.28/9.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 64.28/9.34 $i] : ( ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ % 64.28/9.34 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 64.28/9.34 aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? % 64.28/9.34 [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v6, v0) = v5 % 64.28/9.34 & sdtasdt0(v0, v6) = v7 & sdtasdt0(v0, v2) = v9 & sdtasdt0(v0, v1) = v8 & % 64.28/9.34 sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6 & $i(v9) & $i(v8) & $i(v7) & % 64.28/9.34 $i(v6) & $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 64.28/9.34 : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, % 64.28/9.34 v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ % 64.28/9.34 $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 64.28/9.34 aNaturalNumber0(v0) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] % 64.28/9.34 : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & % 64.28/9.34 sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6 & % 64.28/9.34 $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5))) & ! [v0: $i] : ! [v1: $i] : % 64.28/9.34 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasdt0(v3, v0) = v4) | ~ % 64.28/9.34 (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 64.28/9.34 aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? % 64.28/9.34 [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 64.28/9.34 (sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v3) = v5 & % 64.28/9.34 sdtasdt0(v0, v2) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v8, v9) = v4 & % 64.28/9.34 sdtpldt0(v6, v7) = v5 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & % 64.28/9.34 $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 64.28/9.34 $i] : ( ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | % 64.28/9.34 ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 64.28/9.34 aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] % 64.28/9.34 : ? [v9: $i] : (sdtasdt0(v3, v0) = v7 & sdtasdt0(v2, v0) = v9 & % 64.28/9.34 sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & % 64.28/9.34 sdtpldt0(v8, v9) = v7 & sdtpldt0(v5, v6) = v4 & $i(v9) & $i(v8) & $i(v7) & % 64.28/9.34 $i(v6) & $i(v5) & $i(v4))) % 64.28/9.34 % 64.28/9.34 (mAddComm) % 64.28/9.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ % 64.28/9.35 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 64.28/9.35 (sdtpldt0(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 64.28/9.35 : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) % 64.28/9.35 | ~ aNaturalNumber0(v0) | (sdtpldt0(v1, v0) = v2 & $i(v2))) % 64.28/9.35 % 64.28/9.35 (mDefLE) % 64.28/9.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ % 64.28/9.35 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 64.28/9.35 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) & ! [v0: % 64.28/9.35 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ % 64.28/9.35 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] : (sdtpldt0(v0, % 64.28/9.35 v2) = v1 & $i(v2) & aNaturalNumber0(v2))) % 64.28/9.35 % 64.28/9.35 (mLETotal) % 64.28/9.35 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | % 64.28/9.35 ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1)) & ! [v0: % 64.28/9.35 $i] : ( ~ $i(v0) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0)) % 64.28/9.35 % 64.28/9.35 (mMonAdd) % 64.28/9.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 64.28/9.36 (sdtpldt0(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 64.28/9.36 sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 64.28/9.36 aNaturalNumber0(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = % 64.28/9.36 v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & % 64.28/9.36 sdtpldt0(v0, v2) = v5 & $i(v6) & $i(v5) & $i(v4) & sdtlseqdt0(v5, v6) & % 64.28/9.36 sdtlseqdt0(v4, v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 64.28/9.36 $i] : (v1 = v0 | ~ (sdtpldt0(v2, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 64.28/9.36 $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ % 64.28/9.36 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4: $i] : ? [v5: $i] : % 64.28/9.36 ? [v6: $i] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v1) = v4 & % 64.28/9.36 sdtpldt0(v1, v2) = v6 & sdtpldt0(v0, v2) = v5 & $i(v6) & $i(v5) & $i(v4) & % 64.28/9.36 sdtlseqdt0(v5, v6) & sdtlseqdt0(v3, v4))) & ! [v0: $i] : ! [v1: $i] : ! % 64.28/9.36 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | % 64.28/9.36 ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ % 64.28/9.36 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4: $i] : ? [v5: $i] : % 64.28/9.36 ? [v6: $i] : ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & % 64.28/9.36 sdtpldt0(v2, v0) = v4 & sdtpldt0(v0, v2) = v6 & $i(v6) & $i(v5) & $i(v4) & % 64.28/9.36 sdtlseqdt0(v6, v3) & sdtlseqdt0(v4, v5))) & ! [v0: $i] : ! [v1: $i] : ! % 64.28/9.36 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v0, v2) = v3) | ~ $i(v2) | % 64.28/9.36 ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ % 64.28/9.36 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4: $i] : ? [v5: $i] : % 64.28/9.36 ? [v6: $i] : ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & % 64.28/9.36 sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & $i(v6) & $i(v5) & $i(v4) & % 64.28/9.36 sdtlseqdt0(v4, v5) & sdtlseqdt0(v3, v6))) % 64.28/9.36 % 64.28/9.36 (mMonMul) % 64.28/9.37 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 64.28/9.37 : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = % 64.28/9.37 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v2) | ~ % 64.28/9.37 aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 64.28/9.37 sdtlseqdt0(v3, v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 64.28/9.37 : ! [v4: $i] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ % 64.28/9.37 (sdtasdt0(v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 64.28/9.37 sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 64.28/9.37 aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & % 64.28/9.37 sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & $i(v6) & $i(v5) & % 64.28/9.37 sdtlseqdt0(v5, v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 64.28/9.37 $i] : ! [v4: $i] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ % 64.28/9.37 (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 64.28/9.37 sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 64.28/9.37 aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v4) & ~ (v5 = % 64.28/9.37 v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5 & $i(v6) & $i(v5) & % 64.28/9.37 sdtlseqdt0(v6, v4) & sdtlseqdt0(v3, v5))) & ! [v0: $i] : ! [v1: $i] : ! % 64.28/9.37 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, % 64.28/9.37 v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 64.28/9.37 $i(v0) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ % 64.28/9.37 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: $i] : ( % 64.28/9.37 ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5 % 64.28/9.37 & $i(v6) & $i(v5) & sdtlseqdt0(v5, v3) & sdtlseqdt0(v4, v6))) & ! [v0: % 64.28/9.37 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | v0 % 64.28/9.37 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) % 64.28/9.37 | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | % 64.28/9.37 ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4)) & ! % 64.28/9.37 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | % 64.28/9.37 v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ % 64.28/9.37 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v2) | ~ % 64.28/9.37 aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? % 64.28/9.37 [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & % 64.28/9.37 sdtasdt0(v1, v0) = v5 & $i(v6) & $i(v5) & sdtlseqdt0(v5, v6))) & ! [v0: % 64.28/9.37 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | v0 = sz00 | ~ % 64.28/9.37 (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) % 64.28/9.37 | ~ $i(v0) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ % 64.28/9.37 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] : % 64.28/9.37 ! [v2: $i] : ! [v3: $i] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | % 64.28/9.37 ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 64.28/9.37 sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 64.28/9.37 aNaturalNumber0(v0)) % 64.28/9.37 % 64.28/9.37 (mMulComm) % 64.28/9.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ % 64.28/9.37 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 64.28/9.37 (sdtasdt0(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 64.28/9.37 : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) % 64.28/9.37 | ~ aNaturalNumber0(v0) | (sdtasdt0(v1, v0) = v2 & $i(v2))) % 64.28/9.37 % 64.28/9.37 (mSortsC_01) % 64.28/9.38 ~ (sz10 = sz00) & $i(sz10) & $i(sz00) & aNaturalNumber0(sz10) % 64.28/9.38 % 64.28/9.38 (m_MulUnit) % 64.28/9.38 $i(sz10) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) % 64.28/9.38 | ~ $i(v0) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 % 64.28/9.38 | ~ (sdtasdt0(sz10, v0) = v1) | ~ $i(v0) | ~ aNaturalNumber0(v0)) & ! % 64.28/9.38 [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ $i(v0) | ~ % 64.28/9.38 aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0) & ! [v0: $i] : ! [v1: $i] : % 64.28/9.38 ( ~ (sdtasdt0(sz10, v0) = v1) | ~ $i(v0) | ~ aNaturalNumber0(v0) | % 64.28/9.38 sdtasdt0(v0, sz10) = v0) % 64.28/9.38 % 64.28/9.38 (m_MulZero) % 64.28/9.38 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = % 64.28/9.38 v1) | ~ $i(v0) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] : % 64.28/9.38 (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ $i(v0) | ~ % 64.28/9.38 aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, sz00) = % 64.28/9.38 v1) | ~ $i(v0) | ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00) & ! % 64.28/9.38 [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ $i(v0) | ~ % 64.28/9.38 aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00) % 64.28/9.38 % 64.28/9.38 (m__) % 64.28/9.38 $i(xn) & $i(xm) & $i(sz00) & ? [v0: $i] : ( ~ (xm = sz00) & sdtasdt0(xn, xm) % 64.28/9.38 = v0 & $i(v0) & ~ sdtlseqdt0(xn, v0)) % 64.28/9.38 % 64.28/9.38 (m__1007) % 64.28/9.38 $i(xm) & $i(sz10) & $i(sz00) & (xm = sz00 | sdtlseqdt0(sz10, xm)) % 64.28/9.38 % 64.28/9.38 (m__987) % 64.28/9.38 $i(xn) & $i(xm) & aNaturalNumber0(xn) & aNaturalNumber0(xm) % 64.28/9.38 % 64.28/9.38 (function-axioms) % 64.28/9.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 64.28/9.38 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! % 64.28/9.38 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | % 64.28/9.38 ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 64.28/9.38 [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 64.28/9.38 % 64.28/9.38 Further assumptions not needed in the proof: % 64.28/9.38 -------------------------------------------- % 64.28/9.38 mAddAsso, mAddCanc, mDefDiff, mLEAsym, mLENTr, mLERefl, mLETran, mMulAsso, % 64.28/9.38 mMulCanc, mNatSort, mSortsB, mSortsB_02, mSortsC, mZeroAdd, mZeroMul, m_AddZero % 64.28/9.38 % 64.28/9.38 Those formulas are unsatisfiable: % 64.28/9.38 --------------------------------- % 64.28/9.38 % 64.28/9.38 Begin of proof % 64.28/9.38 | % 64.28/9.38 | ALPHA: (mSortsC_01) implies: % 64.28/9.38 | (1) aNaturalNumber0(sz10) % 64.28/9.38 | % 64.28/9.38 | ALPHA: (mAddComm) implies: % 64.28/9.38 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v1, v0) = v2) | % 64.28/9.38 | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ % 64.28/9.38 | aNaturalNumber0(v0) | (sdtpldt0(v0, v1) = v2 & $i(v2))) % 64.28/9.38 | % 64.28/9.38 | ALPHA: (mMulComm) implies: % 64.28/9.39 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | % 64.28/9.39 | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ % 64.28/9.39 | aNaturalNumber0(v0) | (sdtasdt0(v0, v1) = v2 & $i(v2))) % 64.28/9.39 | % 64.28/9.39 | ALPHA: (m_MulUnit) implies: % 64.28/9.39 | (4) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | % 64.28/9.39 | ~ $i(v0) | ~ aNaturalNumber0(v0)) % 64.28/9.39 | % 64.28/9.39 | ALPHA: (m_MulZero) implies: % 64.28/9.39 | (5) ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | % 64.28/9.39 | ~ $i(v0) | ~ aNaturalNumber0(v0)) % 64.28/9.39 | % 64.28/9.39 | ALPHA: (mAMDistr) implies: % 64.28/9.39 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 64.28/9.39 | ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | % 64.28/9.39 | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 64.28/9.39 | aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: % 64.28/9.39 | $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v3, v0) = % 64.28/9.39 | v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, % 64.28/9.39 | v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v8, v9) = v7 & % 64.28/9.39 | sdtpldt0(v5, v6) = v4 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) % 64.28/9.39 | & $i(v4))) % 64.28/9.39 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 64.28/9.39 | ~ (sdtasdt0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | % 64.28/9.39 | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 64.28/9.39 | aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: % 64.28/9.39 | $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v2, v0) = % 64.28/9.39 | v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v3) = v5 & sdtasdt0(v0, % 64.28/9.39 | v2) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v8, v9) = v4 & % 64.28/9.39 | sdtpldt0(v6, v7) = v5 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) % 64.28/9.39 | & $i(v4))) % 64.28/9.39 | % 64.28/9.39 | ALPHA: (mDefLE) implies: % 64.28/9.39 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, % 64.28/9.39 | v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] % 64.28/9.39 | : (sdtpldt0(v0, v2) = v1 & $i(v2) & aNaturalNumber0(v2))) % 64.28/9.39 | % 64.28/9.39 | ALPHA: (mLETotal) implies: % 64.28/9.39 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 64.28/9.39 | aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | % 64.28/9.39 | sdtlseqdt0(v0, v1)) % 64.28/9.39 | % 64.28/9.39 | ALPHA: (mMonAdd) implies: % 64.28/9.39 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 64.28/9.39 | (sdtpldt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 64.28/9.39 | sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) % 64.28/9.39 | | ~ aNaturalNumber0(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 64.28/9.39 | ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, % 64.28/9.39 | v0) = v4 & sdtpldt0(v1, v2) = v6 & $i(v6) & $i(v5) & $i(v4) & % 64.28/9.39 | sdtlseqdt0(v4, v5) & sdtlseqdt0(v3, v6))) % 64.28/9.39 | % 64.28/9.39 | ALPHA: (mMonMul) implies: % 64.28/9.40 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 64.28/9.40 | (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, % 64.28/9.40 | v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 64.28/9.40 | sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) % 64.28/9.40 | | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4)) % 64.28/9.40 | % 64.28/9.40 | ALPHA: (m__987) implies: % 64.28/9.40 | (12) aNaturalNumber0(xm) % 64.28/9.40 | (13) aNaturalNumber0(xn) % 64.28/9.40 | % 64.28/9.40 | ALPHA: (m__1007) implies: % 64.28/9.40 | (14) $i(sz10) % 64.28/9.40 | (15) xm = sz00 | sdtlseqdt0(sz10, xm) % 64.28/9.40 | % 64.28/9.40 | ALPHA: (m__) implies: % 64.28/9.40 | (16) $i(xm) % 64.28/9.40 | (17) $i(xn) % 64.28/9.40 | (18) ? [v0: $i] : ( ~ (xm = sz00) & sdtasdt0(xn, xm) = v0 & $i(v0) & ~ % 64.28/9.40 | sdtlseqdt0(xn, v0)) % 64.28/9.40 | % 64.28/9.40 | ALPHA: (function-axioms) implies: % 64.28/9.40 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 64.28/9.40 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 64.28/9.40 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 64.28/9.40 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 64.28/9.40 | % 64.28/9.40 | DELTA: instantiating (18) with fresh symbol all_27_0 gives: % 64.28/9.40 | (21) ~ (xm = sz00) & sdtasdt0(xn, xm) = all_27_0 & $i(all_27_0) & ~ % 64.28/9.40 | sdtlseqdt0(xn, all_27_0) % 64.28/9.40 | % 64.28/9.40 | ALPHA: (21) implies: % 64.28/9.40 | (22) ~ (xm = sz00) % 64.28/9.40 | (23) ~ sdtlseqdt0(xn, all_27_0) % 64.28/9.40 | (24) sdtasdt0(xn, xm) = all_27_0 % 64.28/9.40 | % 64.28/9.40 | BETA: splitting (15) gives: % 64.28/9.40 | % 64.28/9.40 | Case 1: % 64.28/9.40 | | % 64.28/9.40 | | (25) sdtlseqdt0(sz10, xm) % 64.28/9.40 | | % 64.28/9.40 | | GROUND_INST: instantiating (9) with sz10, sz10, simplifying with (1), (14) % 64.28/9.40 | | gives: % 64.28/9.40 | | (26) sdtlseqdt0(sz10, sz10) % 64.28/9.40 | | % 64.28/9.40 | | GROUND_INST: instantiating (9) with xn, xn, simplifying with (13), (17) % 64.28/9.40 | | gives: % 64.28/9.40 | | (27) sdtlseqdt0(xn, xn) % 64.28/9.40 | | % 64.28/9.40 | | GROUND_INST: instantiating (8) with sz10, xm, simplifying with (1), (12), % 64.28/9.40 | | (14), (16), (25) gives: % 64.28/9.40 | | (28) ? [v0: $i] : (sdtpldt0(sz10, v0) = xm & $i(v0) & % 64.28/9.40 | | aNaturalNumber0(v0)) % 64.28/9.40 | | % 64.28/9.40 | | GROUND_INST: instantiating (8) with sz10, sz10, simplifying with (1), (14) % 64.28/9.40 | | gives: % 64.28/9.40 | | (29) ~ sdtlseqdt0(sz10, sz10) | ? [v0: $i] : (sdtpldt0(sz10, v0) = sz10 % 64.28/9.40 | | & $i(v0) & aNaturalNumber0(v0)) % 64.28/9.40 | | % 64.28/9.40 | | GROUND_INST: instantiating (3) with xm, xn, all_27_0, simplifying with (12), % 64.28/9.40 | | (13), (16), (17), (24) gives: % 64.28/9.40 | | (30) sdtasdt0(xm, xn) = all_27_0 & $i(all_27_0) % 64.28/9.40 | | % 64.28/9.40 | | ALPHA: (30) implies: % 64.28/9.40 | | (31) sdtasdt0(xm, xn) = all_27_0 % 64.28/9.40 | | % 64.28/9.40 | | GROUND_INST: instantiating (4) with xn, all_27_0, simplifying with (13), % 64.28/9.40 | | (17) gives: % 64.28/9.40 | | (32) all_27_0 = xn | ~ (sdtasdt0(xn, sz10) = all_27_0) % 64.28/9.40 | | % 64.28/9.40 | | GROUND_INST: instantiating (5) with xm, all_27_0, simplifying with (12), % 64.28/9.40 | | (16) gives: % 64.28/9.41 | | (33) all_27_0 = sz00 | ~ (sdtasdt0(sz00, xm) = all_27_0) % 64.28/9.41 | | % 64.28/9.41 | | DELTA: instantiating (28) with fresh symbol all_39_0 gives: % 64.28/9.41 | | (34) sdtpldt0(sz10, all_39_0) = xm & $i(all_39_0) & % 64.28/9.41 | | aNaturalNumber0(all_39_0) % 64.28/9.41 | | % 64.28/9.41 | | ALPHA: (34) implies: % 64.28/9.41 | | (35) aNaturalNumber0(all_39_0) % 64.28/9.41 | | (36) $i(all_39_0) % 64.28/9.41 | | (37) sdtpldt0(sz10, all_39_0) = xm % 64.28/9.41 | | % 64.28/9.41 | | BETA: splitting (29) gives: % 64.28/9.41 | | % 64.28/9.41 | | Case 1: % 64.28/9.41 | | | % 64.28/9.41 | | | (38) ~ sdtlseqdt0(sz10, sz10) % 64.28/9.41 | | | % 64.28/9.41 | | | PRED_UNIFY: (26), (38) imply: % 64.28/9.41 | | | (39) $false % 64.28/9.41 | | | % 64.28/9.41 | | | CLOSE: (39) is inconsistent. % 64.28/9.41 | | | % 64.28/9.41 | | Case 2: % 64.28/9.41 | | | % 64.28/9.41 | | | (40) ? [v0: $i] : (sdtpldt0(sz10, v0) = sz10 & $i(v0) & % 64.28/9.41 | | | aNaturalNumber0(v0)) % 64.28/9.41 | | | % 64.28/9.41 | | | DELTA: instantiating (40) with fresh symbol all_45_0 gives: % 64.28/9.41 | | | (41) sdtpldt0(sz10, all_45_0) = sz10 & $i(all_45_0) & % 64.28/9.41 | | | aNaturalNumber0(all_45_0) % 64.28/9.41 | | | % 64.28/9.41 | | | ALPHA: (41) implies: % 64.28/9.41 | | | (42) aNaturalNumber0(all_45_0) % 64.28/9.41 | | | (43) $i(all_45_0) % 64.28/9.41 | | | (44) sdtpldt0(sz10, all_45_0) = sz10 % 64.28/9.41 | | | % 64.28/9.41 | | | PRED_UNIFY: (23), (27) imply: % 64.28/9.41 | | | (45) ~ (all_27_0 = xn) % 64.28/9.41 | | | % 64.28/9.41 | | | BETA: splitting (32) gives: % 64.28/9.41 | | | % 64.28/9.41 | | | Case 1: % 64.28/9.41 | | | | % 64.28/9.41 | | | | (46) ~ (sdtasdt0(xn, sz10) = all_27_0) % 64.28/9.41 | | | | % 64.28/9.41 | | | | PRED_UNIFY: (24), (46) imply: % 64.28/9.41 | | | | (47) ~ (xm = sz10) % 64.28/9.41 | | | | % 64.28/9.41 | | | | GROUND_INST: instantiating (6) with xn, sz10, all_39_0, xm, all_27_0, % 64.28/9.41 | | | | simplifying with (1), (13), (14), (17), (24), (35), (36), % 64.28/9.41 | | | | (37) gives: % 64.28/9.41 | | | | (48) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 64.28/9.41 | | | | $i] : (sdtasdt0(all_39_0, xn) = v4 & sdtasdt0(xn, all_39_0) = % 64.28/9.41 | | | | v1 & sdtasdt0(xn, sz10) = v0 & sdtasdt0(xm, xn) = v2 & % 64.28/9.41 | | | | sdtasdt0(sz10, xn) = v3 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, % 64.28/9.41 | | | | v1) = all_27_0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) % 64.28/9.41 | | | | & $i(all_27_0)) % 64.28/9.41 | | | | % 64.28/9.41 | | | | GROUND_INST: instantiating (10) with sz10, xm, all_39_0, xm, simplifying % 64.28/9.41 | | | | with (1), (12), (14), (16), (25), (35), (36), (37) gives: % 64.28/9.41 | | | | (49) xm = sz10 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = % 64.28/9.41 | | | | xm) & ~ (v1 = v0) & sdtpldt0(all_39_0, xm) = v1 & % 64.28/9.41 | | | | sdtpldt0(all_39_0, sz10) = v0 & sdtpldt0(xm, all_39_0) = v2 & % 64.28/9.41 | | | | $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1) & sdtlseqdt0(xm, % 64.28/9.41 | | | | v2)) % 64.28/9.41 | | | | % 64.28/9.41 | | | | GROUND_INST: instantiating (2) with all_39_0, sz10, xm, simplifying with % 64.28/9.41 | | | | (1), (14), (35), (36), (37) gives: % 64.28/9.42 | | | | (50) sdtpldt0(all_39_0, sz10) = xm & $i(xm) % 64.28/9.42 | | | | % 64.28/9.42 | | | | ALPHA: (50) implies: % 64.28/9.42 | | | | (51) sdtpldt0(all_39_0, sz10) = xm % 64.28/9.42 | | | | % 64.28/9.42 | | | | GROUND_INST: instantiating (10) with sz10, xm, all_45_0, sz10, % 64.28/9.42 | | | | simplifying with (1), (12), (14), (16), (25), (42), (43), % 64.28/9.42 | | | | (44) gives: % 64.28/9.42 | | | | (52) xm = sz10 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = % 64.28/9.42 | | | | sz10) & ~ (v1 = v0) & sdtpldt0(all_45_0, xm) = v1 & % 64.28/9.42 | | | | sdtpldt0(all_45_0, sz10) = v0 & sdtpldt0(xm, all_45_0) = v2 & % 64.28/9.42 | | | | $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1) & % 64.28/9.42 | | | | sdtlseqdt0(sz10, v2)) % 64.28/9.42 | | | | % 64.28/9.42 | | | | GROUND_INST: instantiating (2) with all_45_0, sz10, sz10, simplifying % 64.28/9.42 | | | | with (1), (14), (42), (43), (44) gives: % 64.28/9.42 | | | | (53) sdtpldt0(all_45_0, sz10) = sz10 % 64.28/9.42 | | | | % 64.28/9.42 | | | | GROUND_INST: instantiating (7) with xn, sz10, all_39_0, xm, all_27_0, % 64.28/9.42 | | | | simplifying with (1), (13), (14), (17), (31), (35), (36), % 64.28/9.42 | | | | (37) gives: % 64.28/9.42 | | | | (54) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 64.28/9.42 | | | | $i] : (sdtasdt0(all_39_0, xn) = v4 & sdtasdt0(xn, all_39_0) = % 64.28/9.42 | | | | v2 & sdtasdt0(xn, xm) = v0 & sdtasdt0(xn, sz10) = v1 & % 64.28/9.42 | | | | sdtasdt0(sz10, xn) = v3 & sdtpldt0(v3, v4) = all_27_0 & % 64.28/9.42 | | | | sdtpldt0(v1, v2) = v0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 64.28/9.42 | | | | $i(v0) & $i(all_27_0)) % 64.28/9.42 | | | | % 64.28/9.42 | | | | DELTA: instantiating (54) with fresh symbols all_75_0, all_75_1, % 64.28/9.42 | | | | all_75_2, all_75_3, all_75_4 gives: % 64.28/9.42 | | | | (55) sdtasdt0(all_39_0, xn) = all_75_0 & sdtasdt0(xn, all_39_0) = % 64.28/9.42 | | | | all_75_2 & sdtasdt0(xn, xm) = all_75_4 & sdtasdt0(xn, sz10) = % 64.28/9.42 | | | | all_75_3 & sdtasdt0(sz10, xn) = all_75_1 & sdtpldt0(all_75_1, % 64.28/9.42 | | | | all_75_0) = all_27_0 & sdtpldt0(all_75_3, all_75_2) = all_75_4 % 64.28/9.42 | | | | & $i(all_75_0) & $i(all_75_1) & $i(all_75_2) & $i(all_75_3) & % 64.28/9.42 | | | | $i(all_75_4) & $i(all_27_0) % 64.28/9.42 | | | | % 64.28/9.42 | | | | ALPHA: (55) implies: % 64.28/9.42 | | | | (56) sdtasdt0(xn, sz10) = all_75_3 % 64.28/9.42 | | | | (57) sdtasdt0(xn, xm) = all_75_4 % 64.28/9.42 | | | | % 64.28/9.42 | | | | DELTA: instantiating (48) with fresh symbols all_77_0, all_77_1, % 64.28/9.42 | | | | all_77_2, all_77_3, all_77_4 gives: % 64.28/9.42 | | | | (58) sdtasdt0(all_39_0, xn) = all_77_0 & sdtasdt0(xn, all_39_0) = % 64.28/9.42 | | | | all_77_3 & sdtasdt0(xn, sz10) = all_77_4 & sdtasdt0(xm, xn) = % 64.28/9.42 | | | | all_77_2 & sdtasdt0(sz10, xn) = all_77_1 & sdtpldt0(all_77_1, % 64.28/9.42 | | | | all_77_0) = all_77_2 & sdtpldt0(all_77_4, all_77_3) = all_27_0 % 64.28/9.42 | | | | & $i(all_77_0) & $i(all_77_1) & $i(all_77_2) & $i(all_77_3) & % 64.28/9.42 | | | | $i(all_77_4) & $i(all_27_0) % 64.28/9.42 | | | | % 64.28/9.42 | | | | ALPHA: (58) implies: % 64.28/9.42 | | | | (59) sdtasdt0(xn, sz10) = all_77_4 % 64.28/9.42 | | | | % 64.28/9.42 | | | | BETA: splitting (52) gives: % 64.28/9.42 | | | | % 64.28/9.42 | | | | Case 1: % 64.28/9.42 | | | | | % 64.28/9.42 | | | | | (60) xm = sz10 % 64.28/9.42 | | | | | % 64.28/9.42 | | | | | REDUCE: (47), (60) imply: % 64.28/9.42 | | | | | (61) $false % 64.28/9.42 | | | | | % 64.28/9.42 | | | | | CLOSE: (61) is inconsistent. % 64.28/9.42 | | | | | % 64.28/9.42 | | | | Case 2: % 64.28/9.42 | | | | | % 64.28/9.42 | | | | | (62) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = sz10) & ~ % 64.28/9.42 | | | | | (v1 = v0) & sdtpldt0(all_45_0, xm) = v1 & sdtpldt0(all_45_0, % 64.28/9.42 | | | | | sz10) = v0 & sdtpldt0(xm, all_45_0) = v2 & $i(v2) & $i(v1) % 64.28/9.42 | | | | | & $i(v0) & sdtlseqdt0(v0, v1) & sdtlseqdt0(sz10, v2)) % 64.28/9.42 | | | | | % 64.28/9.42 | | | | | DELTA: instantiating (62) with fresh symbols all_86_0, all_86_1, % 64.28/9.42 | | | | | all_86_2 gives: % 64.28/9.42 | | | | | (63) ~ (all_86_0 = sz10) & ~ (all_86_1 = all_86_2) & % 64.28/9.42 | | | | | sdtpldt0(all_45_0, xm) = all_86_1 & sdtpldt0(all_45_0, sz10) = % 64.28/9.42 | | | | | all_86_2 & sdtpldt0(xm, all_45_0) = all_86_0 & $i(all_86_0) & % 64.28/9.42 | | | | | $i(all_86_1) & $i(all_86_2) & sdtlseqdt0(all_86_2, all_86_1) & % 64.28/9.42 | | | | | sdtlseqdt0(sz10, all_86_0) % 64.28/9.42 | | | | | % 64.28/9.42 | | | | | ALPHA: (63) implies: % 64.28/9.42 | | | | | (64) $i(all_86_2) % 64.28/9.42 | | | | | (65) sdtpldt0(all_45_0, sz10) = all_86_2 % 64.28/9.42 | | | | | % 64.28/9.42 | | | | | BETA: splitting (49) gives: % 64.28/9.42 | | | | | % 64.28/9.42 | | | | | Case 1: % 64.28/9.42 | | | | | | % 64.28/9.42 | | | | | | (66) xm = sz10 % 64.28/9.42 | | | | | | % 64.28/9.42 | | | | | | REDUCE: (47), (66) imply: % 64.28/9.42 | | | | | | (67) $false % 64.28/9.42 | | | | | | % 64.28/9.42 | | | | | | CLOSE: (67) is inconsistent. % 64.28/9.42 | | | | | | % 64.28/9.42 | | | | | Case 2: % 64.28/9.42 | | | | | | % 64.28/9.43 | | | | | | (68) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = xm) & ~ % 64.28/9.43 | | | | | | (v1 = v0) & sdtpldt0(all_39_0, xm) = v1 & % 64.28/9.43 | | | | | | sdtpldt0(all_39_0, sz10) = v0 & sdtpldt0(xm, all_39_0) = % 64.28/9.43 | | | | | | v2 & $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1) & % 64.28/9.43 | | | | | | sdtlseqdt0(xm, v2)) % 64.28/9.43 | | | | | | % 64.28/9.43 | | | | | | DELTA: instantiating (68) with fresh symbols all_91_0, all_91_1, % 64.28/9.43 | | | | | | all_91_2 gives: % 64.28/9.43 | | | | | | (69) ~ (all_91_0 = xm) & ~ (all_91_1 = all_91_2) & % 64.28/9.43 | | | | | | sdtpldt0(all_39_0, xm) = all_91_1 & sdtpldt0(all_39_0, sz10) % 64.28/9.43 | | | | | | = all_91_2 & sdtpldt0(xm, all_39_0) = all_91_0 & % 64.28/9.43 | | | | | | $i(all_91_0) & $i(all_91_1) & $i(all_91_2) & % 64.28/9.43 | | | | | | sdtlseqdt0(all_91_2, all_91_1) & sdtlseqdt0(xm, all_91_0) % 64.28/9.43 | | | | | | % 64.28/9.43 | | | | | | ALPHA: (69) implies: % 64.28/9.43 | | | | | | (70) $i(all_91_2) % 64.28/9.43 | | | | | | (71) sdtpldt0(all_39_0, sz10) = all_91_2 % 64.28/9.43 | | | | | | % 64.28/9.43 | | | | | | GROUND_INST: instantiating (19) with xm, all_91_2, sz10, all_39_0, % 64.28/9.43 | | | | | | simplifying with (51), (71) gives: % 64.28/9.43 | | | | | | (72) all_91_2 = xm % 64.28/9.43 | | | | | | % 64.28/9.43 | | | | | | GROUND_INST: instantiating (19) with sz10, all_86_2, sz10, all_45_0, % 64.28/9.43 | | | | | | simplifying with (53), (65) gives: % 64.28/9.43 | | | | | | (73) all_86_2 = sz10 % 64.28/9.43 | | | | | | % 64.28/9.43 | | | | | | GROUND_INST: instantiating (20) with all_75_3, all_77_4, sz10, xn, % 64.28/9.43 | | | | | | simplifying with (56), (59) gives: % 64.28/9.43 | | | | | | (74) all_77_4 = all_75_3 % 64.28/9.43 | | | | | | % 64.28/9.43 | | | | | | PRED_UNIFY: (46), (59) imply: % 64.28/9.43 | | | | | | (75) ~ (all_77_4 = all_27_0) % 64.28/9.43 | | | | | | % 64.28/9.43 | | | | | | GROUND_INST: instantiating (20) with all_27_0, all_75_4, xm, xn, % 64.28/9.43 | | | | | | simplifying with (24), (57) gives: % 64.28/9.43 | | | | | | (76) all_75_4 = all_27_0 % 64.28/9.43 | | | | | | % 64.28/9.43 | | | | | | REDUCE: (74), (75) imply: % 64.28/9.43 | | | | | | (77) ~ (all_75_3 = all_27_0) % 64.28/9.43 | | | | | | % 64.28/9.43 | | | | | | GROUND_INST: instantiating (11) with xn, sz10, xm, all_75_3, % 64.28/9.43 | | | | | | all_27_0, simplifying with (1), (12), (13), (14), (16), % 64.28/9.43 | | | | | | (17), (24), (25), (56) gives: % 64.28/9.43 | | | | | | (78) xn = sz00 | xm = sz10 | sdtlseqdt0(all_75_3, all_27_0) % 64.28/9.43 | | | | | | % 64.28/9.43 | | | | | | GROUND_INST: instantiating (4) with xn, all_75_3, simplifying with % 64.28/9.43 | | | | | | (13), (17), (56) gives: % 64.28/9.43 | | | | | | (79) all_75_3 = xn % 64.28/9.43 | | | | | | % 64.28/9.43 | | | | | | REDUCE: (77), (79) imply: % 64.28/9.43 | | | | | | (80) ~ (all_27_0 = xn) % 64.28/9.43 | | | | | | % 64.28/9.43 | | | | | | BETA: splitting (78) gives: % 64.28/9.43 | | | | | | % 64.28/9.43 | | | | | | Case 1: % 64.28/9.43 | | | | | | | % 64.28/9.43 | | | | | | | (81) sdtlseqdt0(all_75_3, all_27_0) % 64.28/9.43 | | | | | | | % 64.28/9.43 | | | | | | | REDUCE: (79), (81) imply: % 64.28/9.43 | | | | | | | (82) sdtlseqdt0(xn, all_27_0) % 64.28/9.43 | | | | | | | % 64.28/9.43 | | | | | | | PRED_UNIFY: (23), (82) imply: % 64.28/9.43 | | | | | | | (83) $false % 64.28/9.43 | | | | | | | % 64.28/9.43 | | | | | | | CLOSE: (83) is inconsistent. % 64.28/9.43 | | | | | | | % 64.28/9.43 | | | | | | Case 2: % 64.28/9.43 | | | | | | | % 64.28/9.43 | | | | | | | (84) xn = sz00 | xm = sz10 % 64.28/9.43 | | | | | | | % 64.28/9.43 | | | | | | | BETA: splitting (84) gives: % 64.28/9.43 | | | | | | | % 64.28/9.43 | | | | | | | Case 1: % 64.28/9.43 | | | | | | | | % 64.28/9.43 | | | | | | | | (85) xn = sz00 % 64.28/9.43 | | | | | | | | % 64.28/9.43 | | | | | | | | REDUCE: (45), (85) imply: % 64.28/9.43 | | | | | | | | (86) ~ (all_27_0 = sz00) % 64.28/9.43 | | | | | | | | % 64.28/9.43 | | | | | | | | REDUCE: (24), (85) imply: % 64.28/9.43 | | | | | | | | (87) sdtasdt0(sz00, xm) = all_27_0 % 64.28/9.43 | | | | | | | | % 64.28/9.43 | | | | | | | | BETA: splitting (33) gives: % 64.28/9.43 | | | | | | | | % 64.28/9.43 | | | | | | | | Case 1: % 64.28/9.43 | | | | | | | | | % 64.28/9.43 | | | | | | | | | (88) ~ (sdtasdt0(sz00, xm) = all_27_0) % 64.28/9.43 | | | | | | | | | % 64.28/9.43 | | | | | | | | | PRED_UNIFY: (87), (88) imply: % 64.28/9.43 | | | | | | | | | (89) $false % 64.28/9.43 | | | | | | | | | % 64.28/9.43 | | | | | | | | | CLOSE: (89) is inconsistent. % 64.28/9.43 | | | | | | | | | % 64.28/9.43 | | | | | | | | Case 2: % 64.28/9.43 | | | | | | | | | % 64.28/9.43 | | | | | | | | | (90) all_27_0 = sz00 % 64.28/9.43 | | | | | | | | | % 64.28/9.43 | | | | | | | | | REDUCE: (86), (90) imply: % 64.28/9.43 | | | | | | | | | (91) $false % 64.28/9.43 | | | | | | | | | % 64.28/9.43 | | | | | | | | | CLOSE: (91) is inconsistent. % 64.28/9.43 | | | | | | | | | % 64.28/9.43 | | | | | | | | End of split % 64.28/9.43 | | | | | | | | % 64.28/9.43 | | | | | | | Case 2: % 64.28/9.43 | | | | | | | | % 64.28/9.43 | | | | | | | | (92) xm = sz10 % 64.28/9.43 | | | | | | | | % 64.28/9.43 | | | | | | | | REDUCE: (47), (92) imply: % 64.28/9.43 | | | | | | | | (93) $false % 64.28/9.43 | | | | | | | | % 64.28/9.43 | | | | | | | | CLOSE: (93) is inconsistent. % 64.28/9.43 | | | | | | | | % 64.28/9.43 | | | | | | | End of split % 64.28/9.43 | | | | | | | % 64.28/9.43 | | | | | | End of split % 64.28/9.43 | | | | | | % 64.28/9.43 | | | | | End of split % 64.28/9.43 | | | | | % 64.28/9.43 | | | | End of split % 64.28/9.43 | | | | % 64.28/9.43 | | | Case 2: % 64.28/9.43 | | | | % 64.28/9.43 | | | | (94) all_27_0 = xn % 64.28/9.43 | | | | % 64.28/9.43 | | | | REDUCE: (45), (94) imply: % 64.28/9.43 | | | | (95) $false % 64.28/9.43 | | | | % 64.28/9.43 | | | | CLOSE: (95) is inconsistent. % 64.28/9.43 | | | | % 64.28/9.43 | | | End of split % 64.28/9.43 | | | % 64.28/9.43 | | End of split % 64.28/9.43 | | % 64.28/9.43 | Case 2: % 64.28/9.43 | | % 64.28/9.43 | | (96) xm = sz00 % 64.28/9.43 | | % 64.28/9.43 | | REDUCE: (22), (96) imply: % 64.28/9.43 | | (97) $false % 64.28/9.43 | | % 64.28/9.43 | | CLOSE: (97) is inconsistent. % 64.28/9.43 | | % 64.28/9.43 | End of split % 64.28/9.43 | % 64.28/9.43 End of proof % 64.28/9.43 % SZS output end Proof for theBenchmark % 64.28/9.43 % 64.28/9.43 8916ms %------------------------------------------------------------------------------