%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM561+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 : n012.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 11:48:37 EDT 2023 % Result : Theorem 72.48s 10.50s % Output : Proof 74.03s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : NUM561+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n012.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Aug 25 09:59:41 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.81/1.29 Prover 4: Preprocessing ... % 3.81/1.29 Prover 1: Preprocessing ... % 3.81/1.32 Prover 0: Preprocessing ... % 3.81/1.32 Prover 2: Preprocessing ... % 3.81/1.32 Prover 6: Preprocessing ... % 3.81/1.32 Prover 3: Preprocessing ... % 3.81/1.33 Prover 5: Preprocessing ... % 11.52/2.28 Prover 1: Constructing countermodel ... % 11.62/2.29 Prover 3: Constructing countermodel ... % 11.92/2.38 Prover 5: Proving ... % 11.92/2.38 Prover 6: Proving ... % 12.55/2.47 Prover 2: Proving ... % 15.04/2.83 Prover 4: Constructing countermodel ... % 15.04/2.89 Prover 0: Proving ... % 71.35/10.33 Prover 2: stopped % 71.35/10.35 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 71.35/10.45 Prover 4: Found proof (size 126) % 71.35/10.45 Prover 4: proved (9811ms) % 71.35/10.45 Prover 5: stopped % 71.35/10.45 Prover 3: stopped % 71.35/10.46 Prover 6: stopped % 71.35/10.46 Prover 7: Preprocessing ... % 71.35/10.47 Prover 1: stopped % 72.48/10.48 Prover 0: stopped % 72.48/10.50 Prover 7: stopped % 72.48/10.50 % 72.48/10.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 72.48/10.50 % 72.48/10.51 % SZS output start Proof for theBenchmark % 72.48/10.52 Assumptions after simplification: % 72.48/10.52 --------------------------------- % 72.48/10.52 % 72.48/10.52 (mDefSImg) % 73.77/10.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 73.77/10.57 MultipleValueBool] : ! [v5: $i] : ! [v6: int] : ! [v7: $i] : (v6 = 0 | ~ % 73.77/10.57 (sdtlcdtrc0(v0, v2) = v3) | ~ (sdtlpdtrp0(v0, v7) = v5) | ~ % 73.77/10.57 (szDzozmdt0(v0) = v1) | ~ (aSet0(v3) = v4) | ~ (aElementOf0(v5, v3) = v6) % 73.77/10.57 | ~ $i(v7) | ~ $i(v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ? [v8: int] : % 73.77/10.57 (( ~ (v8 = 0) & aFunction0(v0) = v8) | ( ~ (v8 = 0) & aSubsetOf0(v2, v1) = % 73.77/10.57 v8) | ( ~ (v8 = 0) & aElementOf0(v7, v2) = v8))) & ! [v0: $i] : ! [v1: % 73.77/10.57 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: MultipleValueBool] : ! [v5: $i] : % 73.77/10.57 ! [v6: int] : ! [v7: $i] : (v6 = 0 | ~ (sdtlcdtrc0(v0, v2) = v3) | ~ % 73.77/10.57 (szDzozmdt0(v0) = v1) | ~ (aSet0(v3) = v4) | ~ (aElementOf0(v7, v2) = 0) | % 73.77/10.57 ~ (aElementOf0(v5, v3) = v6) | ~ $i(v7) | ~ $i(v5) | ~ $i(v3) | ~ % 73.77/10.57 $i(v2) | ~ $i(v0) | ? [v8: any] : (( ~ (v8 = v5) & sdtlpdtrp0(v0, v7) = v8 % 73.77/10.57 & $i(v8)) | ( ~ (v8 = 0) & aFunction0(v0) = v8) | ( ~ (v8 = 0) & % 73.77/10.57 aSubsetOf0(v2, v1) = v8))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 73.77/10.57 ! [v3: $i] : ! [v4: MultipleValueBool] : ! [v5: $i] : ( ~ (sdtlcdtrc0(v0, % 73.77/10.57 v2) = v3) | ~ (szDzozmdt0(v0) = v1) | ~ (aSet0(v3) = v4) | ~ % 73.77/10.57 (aElementOf0(v5, v3) = 0) | ~ $i(v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | % 73.77/10.57 ? [v6: int] : ? [v7: int] : ? [v8: $i] : ? [v9: int] : ? [v10: $i] : % 73.77/10.57 ($i(v8) & ((v10 = v5 & v9 = 0 & sdtlpdtrp0(v0, v8) = v5 & aElementOf0(v8, % 73.77/10.57 v2) = 0) | ( ~ (v7 = 0) & aSubsetOf0(v2, v1) = v7) | ( ~ (v6 = 0) & % 73.77/10.57 aFunction0(v0) = v6)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 73.77/10.57 [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ (sdtlcdtrc0(v0, v2) = v3) | ~ % 73.77/10.57 (szDzozmdt0(v0) = v1) | ~ (aSet0(v4) = 0) | ~ $i(v4) | ~ $i(v2) | ~ % 73.77/10.57 $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: $i] : ? [v8: any] : ? [v9: % 73.77/10.57 $i] : ? [v10: int] : ? [v11: $i] : ($i(v9) & $i(v7) & (( ~ (v6 = 0) & % 73.77/10.57 aSubsetOf0(v2, v1) = v6) | ( ~ (v5 = 0) & aFunction0(v0) = v5) | % 73.77/10.57 (aElementOf0(v7, v4) = v8 & ( ~ (v8 = 0) | ( ! [v12: $i] : ( ~ % 73.77/10.57 (sdtlpdtrp0(v0, v12) = v7) | ~ $i(v12) | ? [v13: int] : ( ~ % 73.77/10.57 (v13 = 0) & aElementOf0(v12, v2) = v13)) & ! [v12: $i] : ( ~ % 73.77/10.57 (aElementOf0(v12, v2) = 0) | ~ $i(v12) | ? [v13: $i] : ( ~ % 73.77/10.57 (v13 = v7) & sdtlpdtrp0(v0, v12) = v13 & $i(v13))))) & (v8 = 0 % 73.77/10.57 | (v11 = v7 & v10 = 0 & sdtlpdtrp0(v0, v9) = v7 & aElementOf0(v9, % 73.77/10.57 v2) = 0)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 73.77/10.57 [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (sdtlcdtrc0(v0, v2) = v3) | ~ % 73.77/10.57 (szDzozmdt0(v0) = v1) | ~ (aSet0(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 73.77/10.57 $i(v0) | ? [v5: int] : (( ~ (v5 = 0) & aFunction0(v0) = v5) | ( ~ (v5 = 0) % 73.77/10.57 & aSubsetOf0(v2, v1) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 73.77/10.57 ( ~ (szDzozmdt0(v0) = v1) | ~ (aSubsetOf0(v2, v1) = 0) | ~ $i(v2) | ~ % 73.77/10.58 $i(v0) | ? [v3: any] : (( ~ (v3 = 0) & aFunction0(v0) = v3) | % 73.77/10.58 (sdtlcdtrc0(v0, v2) = v3 & $i(v3) & ! [v4: MultipleValueBool] : ! [v5: % 73.77/10.58 $i] : ! [v6: int] : ! [v7: $i] : (v6 = 0 | ~ (sdtlpdtrp0(v0, v7) = % 73.77/10.58 v5) | ~ (aSet0(v3) = v4) | ~ (aElementOf0(v5, v3) = v6) | ~ % 73.77/10.58 $i(v7) | ~ $i(v5) | ? [v8: int] : ( ~ (v8 = 0) & aElementOf0(v7, v2) % 73.77/10.58 = v8)) & ! [v4: MultipleValueBool] : ! [v5: $i] : ! [v6: int] : % 73.77/10.58 ! [v7: $i] : (v6 = 0 | ~ (aSet0(v3) = v4) | ~ (aElementOf0(v7, v2) = % 73.77/10.58 0) | ~ (aElementOf0(v5, v3) = v6) | ~ $i(v7) | ~ $i(v5) | ? [v8: % 73.77/10.58 $i] : ( ~ (v8 = v5) & sdtlpdtrp0(v0, v7) = v8 & $i(v8))) & ! [v4: % 73.77/10.58 MultipleValueBool] : ! [v5: $i] : ( ~ (aSet0(v3) = v4) | ~ % 73.77/10.58 (aElementOf0(v5, v3) = 0) | ~ $i(v5) | ? [v6: $i] : (sdtlpdtrp0(v0, % 73.77/10.58 v6) = v5 & aElementOf0(v6, v2) = 0 & $i(v6))) & ! [v4: any] : (v4 % 73.77/10.58 = v3 | ~ (aSet0(v4) = 0) | ~ $i(v4) | ? [v5: $i] : ? [v6: any] : % 73.77/10.58 ? [v7: $i] : ? [v8: int] : ? [v9: $i] : (aElementOf0(v5, v4) = v6 & % 73.77/10.58 $i(v7) & $i(v5) & ( ~ (v6 = 0) | ( ! [v10: $i] : ( ~ (sdtlpdtrp0(v0, % 73.77/10.58 v10) = v5) | ~ $i(v10) | ? [v11: int] : ( ~ (v11 = 0) & % 73.77/10.58 aElementOf0(v10, v2) = v11)) & ! [v10: $i] : ( ~ % 73.77/10.58 (aElementOf0(v10, v2) = 0) | ~ $i(v10) | ? [v11: $i] : ( ~ % 73.77/10.58 (v11 = v5) & sdtlpdtrp0(v0, v10) = v11 & $i(v11))))) & (v6 = % 73.77/10.58 0 | (v9 = v5 & v8 = 0 & sdtlpdtrp0(v0, v7) = v5 & aElementOf0(v7, % 73.77/10.58 v2) = 0)))) & ! [v4: int] : (v4 = 0 | ~ (aSet0(v3) = v4))))) % 73.77/10.58 & ! [v0: $i] : ( ~ (aFunction0(v0) = 0) | ~ $i(v0) | ? [v1: $i] : % 73.77/10.58 (szDzozmdt0(v0) = v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] : ! [v4: % 73.77/10.58 MultipleValueBool] : ! [v5: $i] : ! [v6: int] : ! [v7: $i] : (v6 = 0 % 73.77/10.58 | ~ (sdtlcdtrc0(v0, v2) = v3) | ~ (sdtlpdtrp0(v0, v7) = v5) | ~ % 73.77/10.58 (aSet0(v3) = v4) | ~ (aElementOf0(v5, v3) = v6) | ~ $i(v7) | ~ $i(v5) % 73.77/10.58 | ~ $i(v3) | ~ $i(v2) | ? [v8: int] : (( ~ (v8 = 0) & aSubsetOf0(v2, % 73.77/10.58 v1) = v8) | ( ~ (v8 = 0) & aElementOf0(v7, v2) = v8))) & ! [v2: % 73.77/10.58 $i] : ! [v3: $i] : ! [v4: MultipleValueBool] : ! [v5: $i] : ! [v6: % 73.77/10.58 int] : ! [v7: $i] : (v6 = 0 | ~ (sdtlcdtrc0(v0, v2) = v3) | ~ % 73.77/10.58 (aSet0(v3) = v4) | ~ (aElementOf0(v7, v2) = 0) | ~ (aElementOf0(v5, % 73.77/10.58 v3) = v6) | ~ $i(v7) | ~ $i(v5) | ~ $i(v3) | ~ $i(v2) | ? [v8: % 73.77/10.58 any] : (( ~ (v8 = v5) & sdtlpdtrp0(v0, v7) = v8 & $i(v8)) | ( ~ (v8 = % 73.77/10.58 0) & aSubsetOf0(v2, v1) = v8))) & ! [v2: $i] : ! [v3: $i] : ! % 73.77/10.58 [v4: MultipleValueBool] : ! [v5: $i] : ( ~ (sdtlcdtrc0(v0, v2) = v3) | ~ % 73.77/10.58 (aSet0(v3) = v4) | ~ (aElementOf0(v5, v3) = 0) | ~ $i(v5) | ~ $i(v3) % 73.77/10.58 | ~ $i(v2) | ? [v6: int] : ? [v7: $i] : ? [v8: int] : ? [v9: $i] : % 73.77/10.58 ($i(v7) & ((v9 = v5 & v8 = 0 & sdtlpdtrp0(v0, v7) = v5 & aElementOf0(v7, % 73.77/10.58 v2) = 0) | ( ~ (v6 = 0) & aSubsetOf0(v2, v1) = v6)))) & ! [v2: % 73.77/10.58 $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ (sdtlcdtrc0(v0, v2) = % 73.77/10.58 v3) | ~ (aSet0(v4) = 0) | ~ $i(v4) | ~ $i(v2) | ? [v5: int] : ? % 73.77/10.58 [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9: int] : ? [v10: $i] : % 73.77/10.58 ($i(v8) & $i(v6) & (( ~ (v5 = 0) & aSubsetOf0(v2, v1) = v5) | % 73.77/10.58 (aElementOf0(v6, v4) = v7 & ( ~ (v7 = 0) | ( ! [v11: $i] : ( ~ % 73.77/10.58 (sdtlpdtrp0(v0, v11) = v6) | ~ $i(v11) | ? [v12: int] : ( % 73.77/10.58 ~ (v12 = 0) & aElementOf0(v11, v2) = v12)) & ! [v11: $i] % 73.77/10.58 : ( ~ (aElementOf0(v11, v2) = 0) | ~ $i(v11) | ? [v12: $i] : % 73.77/10.58 ( ~ (v12 = v6) & sdtlpdtrp0(v0, v11) = v12 & $i(v12))))) & % 73.77/10.58 (v7 = 0 | (v10 = v6 & v9 = 0 & sdtlpdtrp0(v0, v8) = v6 & % 73.77/10.58 aElementOf0(v8, v2) = 0)))))) & ! [v2: $i] : ! [v3: $i] : ! % 73.77/10.58 [v4: int] : (v4 = 0 | ~ (sdtlcdtrc0(v0, v2) = v3) | ~ (aSet0(v3) = v4) | % 73.77/10.58 ~ $i(v3) | ~ $i(v2) | ? [v5: int] : ( ~ (v5 = 0) & aSubsetOf0(v2, v1) % 73.77/10.58 = v5)) & ! [v2: $i] : ( ~ (aSubsetOf0(v2, v1) = 0) | ~ $i(v2) | ? % 73.82/10.58 [v3: $i] : (sdtlcdtrc0(v0, v2) = v3 & $i(v3) & ! [v4: % 73.82/10.58 MultipleValueBool] : ! [v5: $i] : ! [v6: int] : ! [v7: $i] : (v6 % 73.82/10.58 = 0 | ~ (sdtlpdtrp0(v0, v7) = v5) | ~ (aSet0(v3) = v4) | ~ % 73.82/10.58 (aElementOf0(v5, v3) = v6) | ~ $i(v7) | ~ $i(v5) | ? [v8: int] : % 73.82/10.58 ( ~ (v8 = 0) & aElementOf0(v7, v2) = v8)) & ! [v4: % 73.82/10.58 MultipleValueBool] : ! [v5: $i] : ! [v6: int] : ! [v7: $i] : (v6 % 73.82/10.58 = 0 | ~ (aSet0(v3) = v4) | ~ (aElementOf0(v7, v2) = 0) | ~ % 73.82/10.58 (aElementOf0(v5, v3) = v6) | ~ $i(v7) | ~ $i(v5) | ? [v8: $i] : ( % 73.82/10.58 ~ (v8 = v5) & sdtlpdtrp0(v0, v7) = v8 & $i(v8))) & ! [v4: % 73.82/10.58 MultipleValueBool] : ! [v5: $i] : ( ~ (aSet0(v3) = v4) | ~ % 73.82/10.58 (aElementOf0(v5, v3) = 0) | ~ $i(v5) | ? [v6: $i] : % 73.82/10.58 (sdtlpdtrp0(v0, v6) = v5 & aElementOf0(v6, v2) = 0 & $i(v6))) & ! % 73.82/10.58 [v4: $i] : (v4 = v3 | ~ (aSet0(v4) = 0) | ~ $i(v4) | ? [v5: $i] : % 73.82/10.58 ? [v6: any] : ? [v7: $i] : ? [v8: int] : ? [v9: $i] : % 73.82/10.58 (aElementOf0(v5, v4) = v6 & $i(v7) & $i(v5) & ( ~ (v6 = 0) | ( ! % 73.82/10.58 [v10: $i] : ( ~ (sdtlpdtrp0(v0, v10) = v5) | ~ $i(v10) | ? % 73.82/10.58 [v11: int] : ( ~ (v11 = 0) & aElementOf0(v10, v2) = v11)) & % 73.82/10.58 ! [v10: $i] : ( ~ (aElementOf0(v10, v2) = 0) | ~ $i(v10) | ? % 73.82/10.58 [v11: $i] : ( ~ (v11 = v5) & sdtlpdtrp0(v0, v10) = v11 & % 73.82/10.58 $i(v11))))) & (v6 = 0 | (v9 = v5 & v8 = 0 & sdtlpdtrp0(v0, % 73.82/10.58 v7) = v5 & aElementOf0(v7, v2) = 0)))) & ! [v4: int] : (v4 % 73.82/10.58 = 0 | ~ (aSet0(v3) = v4)))))) % 73.82/10.58 % 73.82/10.58 (mDiffCons) % 73.82/10.59 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v0, v1) = % 73.82/10.59 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 73.82/10.59 ? [v6: $i] : (sdtmndt0(v5, v0) = v6 & sdtpldt0(v1, v0) = v5 & aSet0(v1) = v4 % 73.82/10.59 & aElement0(v0) = v3 & $i(v6) & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v6 = % 73.82/10.59 v1))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v1, v0) % 73.82/10.59 = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] % 73.82/10.59 : ? [v6: $i] : (sdtmndt0(v2, v0) = v6 & aSet0(v1) = v4 & aElement0(v0) = v3 % 73.82/10.59 & aElementOf0(v0, v1) = v5 & $i(v6) & ( ~ (v4 = 0) | ~ (v3 = 0) | v6 = v1 % 73.82/10.59 | v5 = 0))) % 73.82/10.59 % 73.82/10.59 (mDomSet) % 73.82/10.59 ! [v0: $i] : ! [v1: $i] : ( ~ (szDzozmdt0(v0) = v1) | ~ $i(v0) | ? [v2: % 73.82/10.59 any] : ? [v3: any] : (aFunction0(v0) = v2 & aSet0(v1) = v3 & ( ~ (v2 = 0) % 73.82/10.59 | v3 = 0))) & ! [v0: $i] : ( ~ (aFunction0(v0) = 0) | ~ $i(v0) | ? % 73.82/10.59 [v1: $i] : (szDzozmdt0(v0) = v1 & aSet0(v1) = 0 & $i(v1))) % 73.82/10.59 % 73.82/10.59 (mImgElm) % 73.82/10.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(v0, % 73.82/10.59 v2) = v3) | ~ (szDzozmdt0(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v4: % 73.82/10.59 int] : ? [v5: any] : (( ~ (v4 = 0) & aFunction0(v0) = v4) | % 73.82/10.59 (aElement0(v3) = v5 & aElementOf0(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0)))) % 73.82/10.59 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (szDzozmdt0(v0) = v1) | ~ % 73.82/10.59 (aElementOf0(v2, v1) = 0) | ~ $i(v2) | ~ $i(v0) | ? [v3: any] : ? [v4: % 73.82/10.59 int] : ((v4 = 0 & sdtlpdtrp0(v0, v2) = v3 & aElement0(v3) = 0 & $i(v3)) | % 73.82/10.59 ( ~ (v3 = 0) & aFunction0(v0) = v3))) & ! [v0: $i] : ( ~ (aFunction0(v0) % 73.82/10.59 = 0) | ~ $i(v0) | ? [v1: $i] : (szDzozmdt0(v0) = v1 & $i(v1) & ! [v2: % 73.82/10.59 $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(v0, v2) = v3) | ~ $i(v2) | ? [v4: % 73.82/10.59 any] : ? [v5: any] : (aElement0(v3) = v5 & aElementOf0(v2, v1) = v4 & % 73.82/10.59 ( ~ (v4 = 0) | v5 = 0))) & ! [v2: $i] : ( ~ (aElementOf0(v2, v1) = 0) % 73.82/10.59 | ~ $i(v2) | ? [v3: $i] : (sdtlpdtrp0(v0, v2) = v3 & aElement0(v3) = 0 % 73.82/10.59 & $i(v3))))) % 73.82/10.59 % 73.82/10.59 (mSubRefl) % 73.82/10.59 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aSubsetOf0(v0, v0) = v1) | ~ % 73.82/10.59 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2)) & ! [v0: $i] : ( ~ % 73.82/10.59 (aSet0(v0) = 0) | ~ $i(v0) | aSubsetOf0(v0, v0) = 0) % 73.82/10.59 % 73.82/10.59 (m__) % 73.82/10.59 $i(xx) & $i(xF) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ % 73.82/10.59 (v3 = 0) & sdtlcdtrc0(xF, v1) = v2 & sdtlpdtrp0(xF, xx) = v0 & % 73.82/10.59 szDzozmdt0(xF) = v1 & aElementOf0(v0, v2) = v3 & $i(v2) & $i(v1) & $i(v0)) % 73.82/10.59 % 73.82/10.59 (m__2911) % 73.82/10.59 aFunction0(xF) = 0 & $i(xF) % 73.82/10.59 % 73.82/10.59 (m__2911_02) % 73.82/10.59 $i(xx) & $i(xF) & ? [v0: $i] : (szDzozmdt0(xF) = v0 & aElementOf0(xx, v0) = 0 % 73.82/10.59 & $i(v0)) % 73.82/10.59 % 73.82/10.59 (function-axioms) % 73.82/10.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 73.82/10.60 (sdtlcdtrc0(v3, v2) = v1) | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! % 73.82/10.60 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) % 73.82/10.60 | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 73.82/10.60 ! [v3: $i] : (v1 = v0 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) % 73.82/10.60 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 73.82/10.60 | ~ (slbdtsldtrb0(v3, v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: % 73.82/10.60 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 73.82/10.60 : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! [v0: % 73.82/10.60 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 73.82/10.60 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & ! % 73.82/10.60 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 73.82/10.60 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! % 73.82/10.60 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | % 73.82/10.60 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 73.82/10.60 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 73.82/10.60 (aSubsetOf0(v3, v2) = v1) | ~ (aSubsetOf0(v3, v2) = v0)) & ! [v0: % 73.82/10.60 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 73.82/10.60 : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) & % 73.82/10.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzozmdt0(v2) = v1) | % 73.82/10.60 ~ (szDzozmdt0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 73.82/10.60 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aFunction0(v2) = v1) | ~ % 73.82/10.60 (aFunction0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 73.82/10.60 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) = v0)) & ! [v0: $i] : ! [v1: % 73.82/10.60 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) % 73.82/10.60 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 73.82/10.60 (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 73.82/10.60 $i] : ! [v2: $i] : (v1 = v0 | ~ (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = % 73.82/10.60 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 73.82/10.60 (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0)) & ! [v0: % 73.82/10.60 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 73.82/10.60 ~ (isCountable0(v2) = v1) | ~ (isCountable0(v2) = v0)) & ! [v0: % 73.82/10.60 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 73.82/10.60 ~ (isFinite0(v2) = v1) | ~ (isFinite0(v2) = v0)) & ! [v0: % 73.82/10.60 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 73.82/10.60 ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 73.82/10.60 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) | % 73.82/10.60 ~ (aElement0(v2) = v0)) % 73.82/10.60 % 73.82/10.60 Further assumptions not needed in the proof: % 73.82/10.60 -------------------------------------------- % 73.82/10.60 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 73.82/10.60 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 73.82/10.60 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefSeg, mDefSel, % 73.82/10.60 mDefSub, mEOfElem, mElmSort, mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, % 73.82/10.60 mFunSort, mIH, mIHSort, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, % 73.82/10.60 mLessTrans, mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, % 73.82/10.60 mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, % 73.82/10.60 mSelSub, mSetSort, mSubASymm, mSubFSet, mSubTrans, mSuccEquSucc, mSuccLess, % 73.82/10.60 mSuccNum, mZeroLess, mZeroNum % 73.82/10.60 % 73.82/10.60 Those formulas are unsatisfiable: % 73.82/10.60 --------------------------------- % 73.82/10.60 % 73.82/10.60 Begin of proof % 73.82/10.60 | % 73.82/10.60 | ALPHA: (mSubRefl) implies: % 73.82/10.61 | (1) ! [v0: $i] : ( ~ (aSet0(v0) = 0) | ~ $i(v0) | aSubsetOf0(v0, v0) = 0) % 73.82/10.61 | % 73.82/10.61 | ALPHA: (mDiffCons) implies: % 73.82/10.61 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 73.95/10.61 | (aElementOf0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : % 73.95/10.61 | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : (sdtmndt0(v5, v0) = v6 & % 73.95/10.61 | sdtpldt0(v1, v0) = v5 & aSet0(v1) = v4 & aElement0(v0) = v3 & % 73.95/10.61 | $i(v6) & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v6 = v1))) % 73.95/10.61 | % 73.95/10.61 | ALPHA: (mDomSet) implies: % 73.95/10.61 | (3) ! [v0: $i] : ( ~ (aFunction0(v0) = 0) | ~ $i(v0) | ? [v1: $i] : % 73.95/10.61 | (szDzozmdt0(v0) = v1 & aSet0(v1) = 0 & $i(v1))) % 73.95/10.61 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (szDzozmdt0(v0) = v1) | ~ $i(v0) | ? % 73.95/10.61 | [v2: any] : ? [v3: any] : (aFunction0(v0) = v2 & aSet0(v1) = v3 & ( % 73.95/10.61 | ~ (v2 = 0) | v3 = 0))) % 73.95/10.61 | % 73.95/10.61 | ALPHA: (mImgElm) implies: % 73.95/10.61 | (5) ! [v0: $i] : ( ~ (aFunction0(v0) = 0) | ~ $i(v0) | ? [v1: $i] : % 73.95/10.61 | (szDzozmdt0(v0) = v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] : ( ~ % 73.95/10.61 | (sdtlpdtrp0(v0, v2) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: % 73.95/10.61 | any] : (aElement0(v3) = v5 & aElementOf0(v2, v1) = v4 & ( ~ (v4 % 73.95/10.61 | = 0) | v5 = 0))) & ! [v2: $i] : ( ~ (aElementOf0(v2, v1) = % 73.95/10.61 | 0) | ~ $i(v2) | ? [v3: $i] : (sdtlpdtrp0(v0, v2) = v3 & % 73.95/10.61 | aElement0(v3) = 0 & $i(v3))))) % 73.95/10.61 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (szDzozmdt0(v0) = v1) | % 73.95/10.61 | ~ (aElementOf0(v2, v1) = 0) | ~ $i(v2) | ~ $i(v0) | ? [v3: any] : % 73.95/10.61 | ? [v4: int] : ((v4 = 0 & sdtlpdtrp0(v0, v2) = v3 & aElement0(v3) = 0 % 73.95/10.61 | & $i(v3)) | ( ~ (v3 = 0) & aFunction0(v0) = v3))) % 73.95/10.61 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 73.95/10.61 | (sdtlpdtrp0(v0, v2) = v3) | ~ (szDzozmdt0(v0) = v1) | ~ $i(v2) | ~ % 73.95/10.61 | $i(v0) | ? [v4: int] : ? [v5: any] : (( ~ (v4 = 0) & aFunction0(v0) % 73.95/10.61 | = v4) | (aElement0(v3) = v5 & aElementOf0(v2, v1) = v4 & ( ~ (v4 % 73.95/10.61 | = 0) | v5 = 0)))) % 73.95/10.61 | % 73.95/10.61 | ALPHA: (mDefSImg) implies: % 73.95/10.62 | (8) ! [v0: $i] : ( ~ (aFunction0(v0) = 0) | ~ $i(v0) | ? [v1: $i] : % 73.95/10.62 | (szDzozmdt0(v0) = v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] : ! [v4: % 73.95/10.62 | MultipleValueBool] : ! [v5: $i] : ! [v6: int] : ! [v7: $i] : % 73.95/10.62 | (v6 = 0 | ~ (sdtlcdtrc0(v0, v2) = v3) | ~ (sdtlpdtrp0(v0, v7) = % 73.95/10.62 | v5) | ~ (aSet0(v3) = v4) | ~ (aElementOf0(v5, v3) = v6) | ~ % 73.95/10.62 | $i(v7) | ~ $i(v5) | ~ $i(v3) | ~ $i(v2) | ? [v8: int] : (( ~ % 73.95/10.62 | (v8 = 0) & aSubsetOf0(v2, v1) = v8) | ( ~ (v8 = 0) & % 73.95/10.62 | aElementOf0(v7, v2) = v8))) & ! [v2: $i] : ! [v3: $i] : ! % 73.95/10.62 | [v4: MultipleValueBool] : ! [v5: $i] : ! [v6: int] : ! [v7: $i] % 73.95/10.62 | : (v6 = 0 | ~ (sdtlcdtrc0(v0, v2) = v3) | ~ (aSet0(v3) = v4) | ~ % 73.95/10.62 | (aElementOf0(v7, v2) = 0) | ~ (aElementOf0(v5, v3) = v6) | ~ % 73.95/10.62 | $i(v7) | ~ $i(v5) | ~ $i(v3) | ~ $i(v2) | ? [v8: any] : (( ~ % 73.95/10.62 | (v8 = v5) & sdtlpdtrp0(v0, v7) = v8 & $i(v8)) | ( ~ (v8 = 0) % 73.95/10.62 | & aSubsetOf0(v2, v1) = v8))) & ! [v2: $i] : ! [v3: $i] : ! % 73.95/10.62 | [v4: MultipleValueBool] : ! [v5: $i] : ( ~ (sdtlcdtrc0(v0, v2) = % 73.95/10.62 | v3) | ~ (aSet0(v3) = v4) | ~ (aElementOf0(v5, v3) = 0) | ~ % 73.95/10.62 | $i(v5) | ~ $i(v3) | ~ $i(v2) | ? [v6: int] : ? [v7: $i] : ? % 73.95/10.62 | [v8: int] : ? [v9: $i] : ($i(v7) & ((v9 = v5 & v8 = 0 & % 73.95/10.62 | sdtlpdtrp0(v0, v7) = v5 & aElementOf0(v7, v2) = 0) | ( ~ % 73.95/10.62 | (v6 = 0) & aSubsetOf0(v2, v1) = v6)))) & ! [v2: $i] : ! % 73.95/10.62 | [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ (sdtlcdtrc0(v0, v2) = v3) | % 73.95/10.62 | ~ (aSet0(v4) = 0) | ~ $i(v4) | ~ $i(v2) | ? [v5: int] : ? % 73.95/10.62 | [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9: int] : ? [v10: % 73.95/10.62 | $i] : ($i(v8) & $i(v6) & (( ~ (v5 = 0) & aSubsetOf0(v2, v1) = % 73.95/10.62 | v5) | (aElementOf0(v6, v4) = v7 & ( ~ (v7 = 0) | ( ! [v11: % 73.95/10.62 | $i] : ( ~ (sdtlpdtrp0(v0, v11) = v6) | ~ $i(v11) | % 73.95/10.62 | ? [v12: int] : ( ~ (v12 = 0) & aElementOf0(v11, v2) = % 73.95/10.62 | v12)) & ! [v11: $i] : ( ~ (aElementOf0(v11, v2) = % 73.95/10.62 | 0) | ~ $i(v11) | ? [v12: $i] : ( ~ (v12 = v6) & % 73.95/10.62 | sdtlpdtrp0(v0, v11) = v12 & $i(v12))))) & (v7 = 0 | % 73.95/10.62 | (v10 = v6 & v9 = 0 & sdtlpdtrp0(v0, v8) = v6 & % 73.95/10.62 | aElementOf0(v8, v2) = 0)))))) & ! [v2: $i] : ! [v3: % 73.95/10.62 | $i] : ! [v4: int] : (v4 = 0 | ~ (sdtlcdtrc0(v0, v2) = v3) | ~ % 73.95/10.62 | (aSet0(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: int] : ( ~ (v5 % 73.95/10.62 | = 0) & aSubsetOf0(v2, v1) = v5)) & ! [v2: $i] : ( ~ % 73.95/10.62 | (aSubsetOf0(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : % 73.95/10.62 | (sdtlcdtrc0(v0, v2) = v3 & $i(v3) & ! [v4: MultipleValueBool] : % 73.95/10.62 | ! [v5: $i] : ! [v6: int] : ! [v7: $i] : (v6 = 0 | ~ % 73.95/10.62 | (sdtlpdtrp0(v0, v7) = v5) | ~ (aSet0(v3) = v4) | ~ % 73.95/10.62 | (aElementOf0(v5, v3) = v6) | ~ $i(v7) | ~ $i(v5) | ? [v8: % 73.95/10.62 | int] : ( ~ (v8 = 0) & aElementOf0(v7, v2) = v8)) & ! [v4: % 73.95/10.62 | MultipleValueBool] : ! [v5: $i] : ! [v6: int] : ! [v7: $i] % 73.95/10.62 | : (v6 = 0 | ~ (aSet0(v3) = v4) | ~ (aElementOf0(v7, v2) = 0) % 73.95/10.62 | | ~ (aElementOf0(v5, v3) = v6) | ~ $i(v7) | ~ $i(v5) | ? % 73.95/10.62 | [v8: $i] : ( ~ (v8 = v5) & sdtlpdtrp0(v0, v7) = v8 & $i(v8))) % 73.95/10.62 | & ! [v4: MultipleValueBool] : ! [v5: $i] : ( ~ (aSet0(v3) = % 73.95/10.62 | v4) | ~ (aElementOf0(v5, v3) = 0) | ~ $i(v5) | ? [v6: % 73.95/10.62 | $i] : (sdtlpdtrp0(v0, v6) = v5 & aElementOf0(v6, v2) = 0 & % 73.95/10.62 | $i(v6))) & ! [v4: $i] : (v4 = v3 | ~ (aSet0(v4) = 0) | ~ % 73.95/10.62 | $i(v4) | ? [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: % 73.95/10.62 | int] : ? [v9: $i] : (aElementOf0(v5, v4) = v6 & $i(v7) & % 73.95/10.62 | $i(v5) & ( ~ (v6 = 0) | ( ! [v10: $i] : ( ~ (sdtlpdtrp0(v0, % 73.95/10.62 | v10) = v5) | ~ $i(v10) | ? [v11: int] : ( ~ % 73.95/10.62 | (v11 = 0) & aElementOf0(v10, v2) = v11)) & ! [v10: % 73.95/10.62 | $i] : ( ~ (aElementOf0(v10, v2) = 0) | ~ $i(v10) | % 73.95/10.62 | ? [v11: $i] : ( ~ (v11 = v5) & sdtlpdtrp0(v0, v10) = % 73.95/10.62 | v11 & $i(v11))))) & (v6 = 0 | (v9 = v5 & v8 = 0 & % 73.95/10.62 | sdtlpdtrp0(v0, v7) = v5 & aElementOf0(v7, v2) = 0)))) & % 73.95/10.62 | ! [v4: int] : (v4 = 0 | ~ (aSet0(v3) = v4)))))) % 73.95/10.62 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 73.95/10.62 | MultipleValueBool] : ! [v5: $i] : ! [v6: int] : ! [v7: $i] : (v6 = % 73.95/10.62 | 0 | ~ (sdtlcdtrc0(v0, v2) = v3) | ~ (szDzozmdt0(v0) = v1) | ~ % 73.95/10.62 | (aSet0(v3) = v4) | ~ (aElementOf0(v7, v2) = 0) | ~ (aElementOf0(v5, % 73.95/10.62 | v3) = v6) | ~ $i(v7) | ~ $i(v5) | ~ $i(v3) | ~ $i(v2) | ~ % 73.95/10.62 | $i(v0) | ? [v8: any] : (( ~ (v8 = v5) & sdtlpdtrp0(v0, v7) = v8 & % 73.95/10.62 | $i(v8)) | ( ~ (v8 = 0) & aFunction0(v0) = v8) | ( ~ (v8 = 0) & % 73.95/10.62 | aSubsetOf0(v2, v1) = v8))) % 73.95/10.62 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 73.95/10.62 | MultipleValueBool] : ! [v5: $i] : ! [v6: int] : ! [v7: $i] : (v6 % 73.95/10.62 | = 0 | ~ (sdtlcdtrc0(v0, v2) = v3) | ~ (sdtlpdtrp0(v0, v7) = v5) | % 73.95/10.62 | ~ (szDzozmdt0(v0) = v1) | ~ (aSet0(v3) = v4) | ~ (aElementOf0(v5, % 73.95/10.62 | v3) = v6) | ~ $i(v7) | ~ $i(v5) | ~ $i(v3) | ~ $i(v2) | ~ % 73.95/10.62 | $i(v0) | ? [v8: int] : (( ~ (v8 = 0) & aFunction0(v0) = v8) | ( ~ % 73.95/10.62 | (v8 = 0) & aSubsetOf0(v2, v1) = v8) | ( ~ (v8 = 0) & % 73.95/10.62 | aElementOf0(v7, v2) = v8))) % 73.95/10.62 | % 73.95/10.62 | ALPHA: (m__2911) implies: % 73.95/10.62 | (11) aFunction0(xF) = 0 % 73.95/10.62 | % 73.95/10.62 | ALPHA: (m__2911_02) implies: % 73.95/10.62 | (12) ? [v0: $i] : (szDzozmdt0(xF) = v0 & aElementOf0(xx, v0) = 0 & $i(v0)) % 73.95/10.62 | % 73.95/10.62 | ALPHA: (m__) implies: % 73.95/10.62 | (13) $i(xF) % 73.95/10.62 | (14) $i(xx) % 73.95/10.62 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) % 73.95/10.62 | & sdtlcdtrc0(xF, v1) = v2 & sdtlpdtrp0(xF, xx) = v0 & szDzozmdt0(xF) % 73.95/10.62 | = v1 & aElementOf0(v0, v2) = v3 & $i(v2) & $i(v1) & $i(v0)) % 73.95/10.62 | % 73.95/10.62 | ALPHA: (function-axioms) implies: % 73.95/10.62 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 73.95/10.62 | : (v1 = v0 | ~ (aFunction0(v2) = v1) | ~ (aFunction0(v2) = v0)) % 73.95/10.62 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 73.95/10.62 | (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) % 73.95/10.62 | (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 73.95/10.62 | : ! [v3: $i] : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ % 73.95/10.62 | (aElementOf0(v3, v2) = v0)) % 73.95/10.62 | (19) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 73.95/10.62 | : ! [v3: $i] : (v1 = v0 | ~ (aSubsetOf0(v3, v2) = v1) | ~ % 73.95/10.62 | (aSubsetOf0(v3, v2) = v0)) % 73.95/10.62 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 73.95/10.62 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) % 73.95/10.62 | % 74.03/10.62 | DELTA: instantiating (12) with fresh symbol all_60_0 gives: % 74.03/10.62 | (21) szDzozmdt0(xF) = all_60_0 & aElementOf0(xx, all_60_0) = 0 & % 74.03/10.62 | $i(all_60_0) % 74.03/10.62 | % 74.03/10.62 | ALPHA: (21) implies: % 74.03/10.62 | (22) aElementOf0(xx, all_60_0) = 0 % 74.03/10.62 | (23) szDzozmdt0(xF) = all_60_0 % 74.03/10.62 | % 74.03/10.62 | DELTA: instantiating (15) with fresh symbols all_62_0, all_62_1, all_62_2, % 74.03/10.62 | all_62_3 gives: % 74.03/10.62 | (24) ~ (all_62_0 = 0) & sdtlcdtrc0(xF, all_62_2) = all_62_1 & % 74.03/10.62 | sdtlpdtrp0(xF, xx) = all_62_3 & szDzozmdt0(xF) = all_62_2 & % 74.03/10.62 | aElementOf0(all_62_3, all_62_1) = all_62_0 & $i(all_62_1) & % 74.03/10.62 | $i(all_62_2) & $i(all_62_3) % 74.03/10.62 | % 74.03/10.62 | ALPHA: (24) implies: % 74.03/10.62 | (25) ~ (all_62_0 = 0) % 74.03/10.63 | (26) $i(all_62_3) % 74.03/10.63 | (27) $i(all_62_1) % 74.03/10.63 | (28) aElementOf0(all_62_3, all_62_1) = all_62_0 % 74.03/10.63 | (29) szDzozmdt0(xF) = all_62_2 % 74.03/10.63 | (30) sdtlpdtrp0(xF, xx) = all_62_3 % 74.03/10.63 | (31) sdtlcdtrc0(xF, all_62_2) = all_62_1 % 74.03/10.63 | % 74.03/10.63 | GROUND_INST: instantiating (17) with all_60_0, all_62_2, xF, simplifying with % 74.03/10.63 | (23), (29) gives: % 74.03/10.63 | (32) all_62_2 = all_60_0 % 74.03/10.63 | % 74.03/10.63 | REDUCE: (31), (32) imply: % 74.03/10.63 | (33) sdtlcdtrc0(xF, all_60_0) = all_62_1 % 74.03/10.63 | % 74.03/10.63 | GROUND_INST: instantiating (2) with all_62_3, all_62_1, all_62_0, simplifying % 74.03/10.63 | with (26), (27), (28) gives: % 74.03/10.63 | (34) all_62_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] % 74.03/10.63 | : (sdtmndt0(v2, all_62_3) = v3 & sdtpldt0(all_62_1, all_62_3) = v2 & % 74.03/10.63 | aSet0(all_62_1) = v1 & aElement0(all_62_3) = v0 & $i(v3) & $i(v2) & % 74.03/10.63 | ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = all_62_1)) % 74.03/10.63 | % 74.03/10.63 | GROUND_INST: instantiating (3) with xF, simplifying with (11), (13) gives: % 74.03/10.63 | (35) ? [v0: $i] : (szDzozmdt0(xF) = v0 & aSet0(v0) = 0 & $i(v0)) % 74.03/10.63 | % 74.03/10.63 | GROUND_INST: instantiating (8) with xF, simplifying with (11), (13) gives: % 74.03/10.63 | (36) ? [v0: $i] : (szDzozmdt0(xF) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 74.03/10.63 | $i] : ! [v3: MultipleValueBool] : ! [v4: $i] : ! [v5: int] : ! % 74.03/10.63 | [v6: $i] : (v5 = 0 | ~ (sdtlcdtrc0(xF, v1) = v2) | ~ % 74.03/10.63 | (sdtlpdtrp0(xF, v6) = v4) | ~ (aSet0(v2) = v3) | ~ % 74.03/10.63 | (aElementOf0(v4, v2) = v5) | ~ $i(v6) | ~ $i(v4) | ~ $i(v2) | % 74.03/10.63 | ~ $i(v1) | ? [v7: int] : (( ~ (v7 = 0) & aSubsetOf0(v1, v0) = v7) % 74.03/10.63 | | ( ~ (v7 = 0) & aElementOf0(v6, v1) = v7))) & ! [v1: $i] : ! % 74.03/10.63 | [v2: $i] : ! [v3: MultipleValueBool] : ! [v4: $i] : ! [v5: int] : % 74.03/10.63 | ! [v6: $i] : (v5 = 0 | ~ (sdtlcdtrc0(xF, v1) = v2) | ~ (aSet0(v2) % 74.03/10.63 | = v3) | ~ (aElementOf0(v6, v1) = 0) | ~ (aElementOf0(v4, v2) = % 74.03/10.63 | v5) | ~ $i(v6) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ? [v7: % 74.03/10.63 | any] : (( ~ (v7 = v4) & sdtlpdtrp0(xF, v6) = v7 & $i(v7)) | ( ~ % 74.03/10.63 | (v7 = 0) & aSubsetOf0(v1, v0) = v7))) & ! [v1: $i] : ! [v2: % 74.03/10.63 | $i] : ! [v3: MultipleValueBool] : ! [v4: $i] : ( ~ % 74.03/10.63 | (sdtlcdtrc0(xF, v1) = v2) | ~ (aSet0(v2) = v3) | ~ % 74.03/10.63 | (aElementOf0(v4, v2) = 0) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ? % 74.03/10.63 | [v5: int] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : ($i(v6) & % 74.03/10.63 | ((v8 = v4 & v7 = 0 & sdtlpdtrp0(xF, v6) = v4 & aElementOf0(v6, % 74.03/10.63 | v1) = 0) | ( ~ (v5 = 0) & aSubsetOf0(v1, v0) = v5)))) & ! % 74.03/10.63 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ (sdtlcdtrc0(xF, % 74.03/10.63 | v1) = v2) | ~ (aSet0(v3) = 0) | ~ $i(v3) | ~ $i(v1) | ? % 74.03/10.63 | [v4: int] : ? [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: % 74.03/10.63 | int] : ? [v9: $i] : ($i(v7) & $i(v5) & (( ~ (v4 = 0) & % 74.03/10.63 | aSubsetOf0(v1, v0) = v4) | (aElementOf0(v5, v3) = v6 & ( ~ % 74.03/10.63 | (v6 = 0) | ( ! [v10: $i] : ( ~ (sdtlpdtrp0(xF, v10) = v5) % 74.03/10.63 | | ~ $i(v10) | ? [v11: int] : ( ~ (v11 = 0) & % 74.03/10.63 | aElementOf0(v10, v1) = v11)) & ! [v10: $i] : ( ~ % 74.03/10.63 | (aElementOf0(v10, v1) = 0) | ~ $i(v10) | ? [v11: $i] % 74.03/10.63 | : ( ~ (v11 = v5) & sdtlpdtrp0(xF, v10) = v11 & % 74.03/10.63 | $i(v11))))) & (v6 = 0 | (v9 = v5 & v8 = 0 & % 74.03/10.63 | sdtlpdtrp0(xF, v7) = v5 & aElementOf0(v7, v1) = 0)))))) % 74.03/10.63 | & ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 74.03/10.63 | (sdtlcdtrc0(xF, v1) = v2) | ~ (aSet0(v2) = v3) | ~ $i(v2) | ~ % 74.03/10.63 | $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & aSubsetOf0(v1, v0) = v4)) & % 74.03/10.63 | ! [v1: $i] : ( ~ (aSubsetOf0(v1, v0) = 0) | ~ $i(v1) | ? [v2: $i] % 74.03/10.63 | : (sdtlcdtrc0(xF, v1) = v2 & $i(v2) & ! [v3: MultipleValueBool] : % 74.03/10.63 | ! [v4: $i] : ! [v5: int] : ! [v6: $i] : (v5 = 0 | ~ % 74.03/10.63 | (sdtlpdtrp0(xF, v6) = v4) | ~ (aSet0(v2) = v3) | ~ % 74.03/10.63 | (aElementOf0(v4, v2) = v5) | ~ $i(v6) | ~ $i(v4) | ? [v7: % 74.03/10.63 | int] : ( ~ (v7 = 0) & aElementOf0(v6, v1) = v7)) & ! [v3: % 74.03/10.63 | MultipleValueBool] : ! [v4: $i] : ! [v5: int] : ! [v6: $i] % 74.03/10.63 | : (v5 = 0 | ~ (aSet0(v2) = v3) | ~ (aElementOf0(v6, v1) = 0) | % 74.03/10.63 | ~ (aElementOf0(v4, v2) = v5) | ~ $i(v6) | ~ $i(v4) | ? % 74.03/10.63 | [v7: $i] : ( ~ (v7 = v4) & sdtlpdtrp0(xF, v6) = v7 & $i(v7))) % 74.03/10.63 | & ! [v3: MultipleValueBool] : ! [v4: $i] : ( ~ (aSet0(v2) = % 74.03/10.63 | v3) | ~ (aElementOf0(v4, v2) = 0) | ~ $i(v4) | ? [v5: $i] % 74.03/10.63 | : (sdtlpdtrp0(xF, v5) = v4 & aElementOf0(v5, v1) = 0 & % 74.03/10.63 | $i(v5))) & ! [v3: $i] : (v3 = v2 | ~ (aSet0(v3) = 0) | ~ % 74.03/10.63 | $i(v3) | ? [v4: $i] : ? [v5: any] : ? [v6: $i] : ? [v7: % 74.03/10.63 | int] : ? [v8: $i] : (aElementOf0(v4, v3) = v5 & $i(v6) & % 74.03/10.63 | $i(v4) & ( ~ (v5 = 0) | ( ! [v9: $i] : ( ~ (sdtlpdtrp0(xF, % 74.03/10.63 | v9) = v4) | ~ $i(v9) | ? [v10: int] : ( ~ (v10 = % 74.03/10.63 | 0) & aElementOf0(v9, v1) = v10)) & ! [v9: $i] : ( % 74.03/10.63 | ~ (aElementOf0(v9, v1) = 0) | ~ $i(v9) | ? [v10: $i] % 74.03/10.63 | : ( ~ (v10 = v4) & sdtlpdtrp0(xF, v9) = v10 & % 74.03/10.63 | $i(v10))))) & (v5 = 0 | (v8 = v4 & v7 = 0 & % 74.03/10.63 | sdtlpdtrp0(xF, v6) = v4 & aElementOf0(v6, v1) = 0)))) & % 74.03/10.63 | ! [v3: int] : (v3 = 0 | ~ (aSet0(v2) = v3))))) % 74.03/10.63 | % 74.03/10.63 | GROUND_INST: instantiating (5) with xF, simplifying with (11), (13) gives: % 74.03/10.63 | (37) ? [v0: $i] : (szDzozmdt0(xF) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 74.03/10.63 | $i] : ( ~ (sdtlpdtrp0(xF, v1) = v2) | ~ $i(v1) | ? [v3: any] : % 74.03/10.63 | ? [v4: any] : (aElement0(v2) = v4 & aElementOf0(v1, v0) = v3 & ( ~ % 74.03/10.63 | (v3 = 0) | v4 = 0))) & ! [v1: $i] : ( ~ (aElementOf0(v1, v0) % 74.03/10.63 | = 0) | ~ $i(v1) | ? [v2: $i] : (sdtlpdtrp0(xF, v1) = v2 & % 74.03/10.63 | aElement0(v2) = 0 & $i(v2)))) % 74.03/10.63 | % 74.03/10.63 | GROUND_INST: instantiating (6) with xF, all_60_0, xx, simplifying with (13), % 74.03/10.63 | (14), (22), (23) gives: % 74.03/10.63 | (38) ? [v0: any] : ? [v1: int] : ((v1 = 0 & sdtlpdtrp0(xF, xx) = v0 & % 74.03/10.63 | aElement0(v0) = 0 & $i(v0)) | ( ~ (v0 = 0) & aFunction0(xF) = v0)) % 74.03/10.63 | % 74.03/10.63 | GROUND_INST: instantiating (4) with xF, all_60_0, simplifying with (13), (23) % 74.03/10.63 | gives: % 74.03/10.63 | (39) ? [v0: any] : ? [v1: any] : (aFunction0(xF) = v0 & aSet0(all_60_0) = % 74.03/10.63 | v1 & ( ~ (v0 = 0) | v1 = 0)) % 74.03/10.63 | % 74.03/10.63 | GROUND_INST: instantiating (7) with xF, all_60_0, xx, all_62_3, simplifying % 74.03/10.63 | with (13), (14), (23), (30) gives: % 74.03/10.63 | (40) ? [v0: int] : ? [v1: any] : (( ~ (v0 = 0) & aFunction0(xF) = v0) | % 74.03/10.63 | (aElement0(all_62_3) = v1 & aElementOf0(xx, all_60_0) = v0 & ( ~ (v0 % 74.03/10.63 | = 0) | v1 = 0))) % 74.03/10.63 | % 74.03/10.63 | DELTA: instantiating (35) with fresh symbol all_85_0 gives: % 74.03/10.63 | (41) szDzozmdt0(xF) = all_85_0 & aSet0(all_85_0) = 0 & $i(all_85_0) % 74.03/10.63 | % 74.03/10.63 | ALPHA: (41) implies: % 74.03/10.63 | (42) $i(all_85_0) % 74.03/10.63 | (43) aSet0(all_85_0) = 0 % 74.03/10.63 | (44) szDzozmdt0(xF) = all_85_0 % 74.03/10.63 | % 74.03/10.63 | DELTA: instantiating (39) with fresh symbols all_97_0, all_97_1 gives: % 74.03/10.64 | (45) aFunction0(xF) = all_97_1 & aSet0(all_60_0) = all_97_0 & ( ~ (all_97_1 % 74.03/10.64 | = 0) | all_97_0 = 0) % 74.03/10.64 | % 74.03/10.64 | ALPHA: (45) implies: % 74.03/10.64 | (46) aFunction0(xF) = all_97_1 % 74.03/10.64 | % 74.03/10.64 | DELTA: instantiating (40) with fresh symbols all_107_0, all_107_1 gives: % 74.03/10.64 | (47) ( ~ (all_107_1 = 0) & aFunction0(xF) = all_107_1) | % 74.03/10.64 | (aElement0(all_62_3) = all_107_0 & aElementOf0(xx, all_60_0) = % 74.03/10.64 | all_107_1 & ( ~ (all_107_1 = 0) | all_107_0 = 0)) % 74.03/10.64 | % 74.03/10.64 | DELTA: instantiating (38) with fresh symbols all_113_0, all_113_1 gives: % 74.03/10.64 | (48) (all_113_0 = 0 & sdtlpdtrp0(xF, xx) = all_113_1 & aElement0(all_113_1) % 74.03/10.64 | = 0 & $i(all_113_1)) | ( ~ (all_113_1 = 0) & aFunction0(xF) = % 74.03/10.64 | all_113_1) % 74.03/10.64 | % 74.03/10.64 | DELTA: instantiating (37) with fresh symbol all_122_0 gives: % 74.03/10.64 | (49) szDzozmdt0(xF) = all_122_0 & $i(all_122_0) & ! [v0: $i] : ! [v1: $i] % 74.03/10.64 | : ( ~ (sdtlpdtrp0(xF, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 74.03/10.64 | any] : (aElement0(v1) = v3 & aElementOf0(v0, all_122_0) = v2 & ( ~ % 74.03/10.64 | (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (aElementOf0(v0, % 74.03/10.64 | all_122_0) = 0) | ~ $i(v0) | ? [v1: $i] : (sdtlpdtrp0(xF, v0) % 74.03/10.64 | = v1 & aElement0(v1) = 0 & $i(v1))) % 74.03/10.64 | % 74.03/10.64 | ALPHA: (49) implies: % 74.03/10.64 | (50) szDzozmdt0(xF) = all_122_0 % 74.03/10.64 | (51) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xF, v0) = v1) | ~ $i(v0) % 74.03/10.64 | | ? [v2: any] : ? [v3: any] : (aElement0(v1) = v3 & % 74.03/10.64 | aElementOf0(v0, all_122_0) = v2 & ( ~ (v2 = 0) | v3 = 0))) % 74.03/10.64 | % 74.03/10.64 | GROUND_INST: instantiating (51) with xx, all_62_3, simplifying with (14), (30) % 74.03/10.64 | gives: % 74.03/10.64 | (52) ? [v0: any] : ? [v1: any] : (aElement0(all_62_3) = v1 & % 74.03/10.64 | aElementOf0(xx, all_122_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 74.03/10.64 | % 74.03/10.64 | DELTA: instantiating (52) with fresh symbols all_139_0, all_139_1 gives: % 74.03/10.64 | (53) aElement0(all_62_3) = all_139_0 & aElementOf0(xx, all_122_0) = % 74.03/10.64 | all_139_1 & ( ~ (all_139_1 = 0) | all_139_0 = 0) % 74.03/10.64 | % 74.03/10.64 | ALPHA: (53) implies: % 74.03/10.64 | (54) aElementOf0(xx, all_122_0) = all_139_1 % 74.03/10.64 | % 74.03/10.64 | DELTA: instantiating (36) with fresh symbol all_144_0 gives: % 74.03/10.64 | (55) szDzozmdt0(xF) = all_144_0 & $i(all_144_0) & ! [v0: $i] : ! [v1: $i] % 74.03/10.64 | : ! [v2: MultipleValueBool] : ! [v3: $i] : ! [v4: int] : ! [v5: % 74.03/10.64 | $i] : (v4 = 0 | ~ (sdtlcdtrc0(xF, v0) = v1) | ~ (sdtlpdtrp0(xF, % 74.03/10.64 | v5) = v3) | ~ (aSet0(v1) = v2) | ~ (aElementOf0(v3, v1) = v4) % 74.03/10.64 | | ~ $i(v5) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : (( % 74.03/10.64 | ~ (v6 = 0) & aSubsetOf0(v0, all_144_0) = v6) | ( ~ (v6 = 0) & % 74.03/10.64 | aElementOf0(v5, v0) = v6))) & ! [v0: $i] : ! [v1: $i] : ! % 74.03/10.64 | [v2: MultipleValueBool] : ! [v3: $i] : ! [v4: int] : ! [v5: $i] : % 74.03/10.64 | (v4 = 0 | ~ (sdtlcdtrc0(xF, v0) = v1) | ~ (aSet0(v1) = v2) | ~ % 74.03/10.64 | (aElementOf0(v5, v0) = 0) | ~ (aElementOf0(v3, v1) = v4) | ~ % 74.03/10.64 | $i(v5) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : (( ~ (v6 % 74.03/10.64 | = v3) & sdtlpdtrp0(xF, v5) = v6 & $i(v6)) | ( ~ (v6 = 0) & % 74.03/10.64 | aSubsetOf0(v0, all_144_0) = v6))) & ! [v0: $i] : ! [v1: $i] : % 74.03/10.64 | ! [v2: MultipleValueBool] : ! [v3: $i] : ( ~ (sdtlcdtrc0(xF, v0) = % 74.03/10.64 | v1) | ~ (aSet0(v1) = v2) | ~ (aElementOf0(v3, v1) = 0) | ~ % 74.03/10.64 | $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: $i] : ? % 74.03/10.64 | [v6: int] : ? [v7: $i] : ($i(v5) & ((v7 = v3 & v6 = 0 & % 74.03/10.64 | sdtlpdtrp0(xF, v5) = v3 & aElementOf0(v5, v0) = 0) | ( ~ (v4 = % 74.03/10.64 | 0) & aSubsetOf0(v0, all_144_0) = v4)))) & ! [v0: $i] : ! % 74.03/10.64 | [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (sdtlcdtrc0(xF, v0) = v1) | ~ % 74.03/10.64 | (aSet0(v2) = 0) | ~ $i(v2) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] % 74.03/10.64 | : ? [v5: any] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : ($i(v6) % 74.03/10.64 | & $i(v4) & (( ~ (v3 = 0) & aSubsetOf0(v0, all_144_0) = v3) | % 74.03/10.64 | (aElementOf0(v4, v2) = v5 & ( ~ (v5 = 0) | ( ! [v9: $i] : ( ~ % 74.03/10.64 | (sdtlpdtrp0(xF, v9) = v4) | ~ $i(v9) | ? [v10: int] : % 74.03/10.64 | ( ~ (v10 = 0) & aElementOf0(v9, v0) = v10)) & ! [v9: % 74.03/10.64 | $i] : ( ~ (aElementOf0(v9, v0) = 0) | ~ $i(v9) | ? % 74.03/10.64 | [v10: $i] : ( ~ (v10 = v4) & sdtlpdtrp0(xF, v9) = v10 & % 74.03/10.64 | $i(v10))))) & (v5 = 0 | (v8 = v4 & v7 = 0 & % 74.03/10.64 | sdtlpdtrp0(xF, v6) = v4 & aElementOf0(v6, v0) = 0)))))) & % 74.03/10.64 | ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (sdtlcdtrc0(xF, % 74.03/10.64 | v0) = v1) | ~ (aSet0(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 74.03/10.64 | [v3: int] : ( ~ (v3 = 0) & aSubsetOf0(v0, all_144_0) = v3)) & ! % 74.03/10.64 | [v0: $i] : ( ~ (aSubsetOf0(v0, all_144_0) = 0) | ~ $i(v0) | ? [v1: % 74.03/10.64 | $i] : (sdtlcdtrc0(xF, v0) = v1 & $i(v1) & ! [v2: % 74.03/10.64 | MultipleValueBool] : ! [v3: $i] : ! [v4: int] : ! [v5: $i] : % 74.03/10.64 | (v4 = 0 | ~ (sdtlpdtrp0(xF, v5) = v3) | ~ (aSet0(v1) = v2) | ~ % 74.03/10.64 | (aElementOf0(v3, v1) = v4) | ~ $i(v5) | ~ $i(v3) | ? [v6: % 74.03/10.64 | int] : ( ~ (v6 = 0) & aElementOf0(v5, v0) = v6)) & ! [v2: % 74.03/10.64 | MultipleValueBool] : ! [v3: $i] : ! [v4: int] : ! [v5: $i] : % 74.03/10.64 | (v4 = 0 | ~ (aSet0(v1) = v2) | ~ (aElementOf0(v5, v0) = 0) | ~ % 74.03/10.64 | (aElementOf0(v3, v1) = v4) | ~ $i(v5) | ~ $i(v3) | ? [v6: $i] % 74.03/10.64 | : ( ~ (v6 = v3) & sdtlpdtrp0(xF, v5) = v6 & $i(v6))) & ! [v2: % 74.03/10.64 | MultipleValueBool] : ! [v3: $i] : ( ~ (aSet0(v1) = v2) | ~ % 74.03/10.64 | (aElementOf0(v3, v1) = 0) | ~ $i(v3) | ? [v4: $i] : % 74.03/10.64 | (sdtlpdtrp0(xF, v4) = v3 & aElementOf0(v4, v0) = 0 & $i(v4))) & % 74.03/10.64 | ! [v2: $i] : (v2 = v1 | ~ (aSet0(v2) = 0) | ~ $i(v2) | ? [v3: % 74.03/10.64 | $i] : ? [v4: any] : ? [v5: $i] : ? [v6: int] : ? [v7: $i] % 74.03/10.64 | : (aElementOf0(v3, v2) = v4 & $i(v5) & $i(v3) & ( ~ (v4 = 0) | ( % 74.03/10.64 | ! [v8: $i] : ( ~ (sdtlpdtrp0(xF, v8) = v3) | ~ $i(v8) | % 74.03/10.64 | ? [v9: int] : ( ~ (v9 = 0) & aElementOf0(v8, v0) = v9)) % 74.03/10.64 | & ! [v8: $i] : ( ~ (aElementOf0(v8, v0) = 0) | ~ $i(v8) % 74.03/10.64 | | ? [v9: $i] : ( ~ (v9 = v3) & sdtlpdtrp0(xF, v8) = v9 % 74.03/10.64 | & $i(v9))))) & (v4 = 0 | (v7 = v3 & v6 = 0 & % 74.03/10.64 | sdtlpdtrp0(xF, v5) = v3 & aElementOf0(v5, v0) = 0)))) & ! % 74.03/10.64 | [v2: int] : (v2 = 0 | ~ (aSet0(v1) = v2)))) % 74.03/10.64 | % 74.03/10.64 | ALPHA: (55) implies: % 74.03/10.64 | (56) szDzozmdt0(xF) = all_144_0 % 74.03/10.64 | % 74.03/10.64 | BETA: splitting (34) gives: % 74.03/10.64 | % 74.03/10.64 | Case 1: % 74.03/10.64 | | % 74.03/10.64 | | (57) all_62_0 = 0 % 74.03/10.64 | | % 74.03/10.64 | | REDUCE: (25), (57) imply: % 74.03/10.64 | | (58) $false % 74.03/10.64 | | % 74.03/10.64 | | CLOSE: (58) is inconsistent. % 74.03/10.64 | | % 74.03/10.64 | Case 2: % 74.03/10.64 | | % 74.03/10.64 | | (59) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : % 74.03/10.64 | | (sdtmndt0(v2, all_62_3) = v3 & sdtpldt0(all_62_1, all_62_3) = v2 & % 74.03/10.64 | | aSet0(all_62_1) = v1 & aElement0(all_62_3) = v0 & $i(v3) & $i(v2) % 74.03/10.64 | | & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = all_62_1)) % 74.03/10.64 | | % 74.03/10.64 | | DELTA: instantiating (59) with fresh symbols all_154_0, all_154_1, % 74.03/10.64 | | all_154_2, all_154_3 gives: % 74.03/10.64 | | (60) sdtmndt0(all_154_1, all_62_3) = all_154_0 & sdtpldt0(all_62_1, % 74.03/10.64 | | all_62_3) = all_154_1 & aSet0(all_62_1) = all_154_2 & % 74.03/10.64 | | aElement0(all_62_3) = all_154_3 & $i(all_154_0) & $i(all_154_1) & ( % 74.03/10.64 | | ~ (all_154_2 = 0) | ~ (all_154_3 = 0) | all_154_0 = all_62_1) % 74.03/10.64 | | % 74.03/10.64 | | ALPHA: (60) implies: % 74.03/10.64 | | (61) aSet0(all_62_1) = all_154_2 % 74.03/10.64 | | % 74.03/10.64 | | GROUND_INST: instantiating (16) with 0, all_97_1, xF, simplifying with (11), % 74.03/10.64 | | (46) gives: % 74.03/10.64 | | (62) all_97_1 = 0 % 74.03/10.64 | | % 74.03/10.64 | | GROUND_INST: instantiating (17) with all_60_0, all_122_0, xF, simplifying % 74.03/10.64 | | with (23), (50) gives: % 74.03/10.64 | | (63) all_122_0 = all_60_0 % 74.03/10.64 | | % 74.03/10.65 | | GROUND_INST: instantiating (17) with all_122_0, all_144_0, xF, simplifying % 74.03/10.65 | | with (50), (56) gives: % 74.03/10.65 | | (64) all_144_0 = all_122_0 % 74.03/10.65 | | % 74.03/10.65 | | GROUND_INST: instantiating (17) with all_85_0, all_144_0, xF, simplifying % 74.03/10.65 | | with (44), (56) gives: % 74.03/10.65 | | (65) all_144_0 = all_85_0 % 74.03/10.65 | | % 74.03/10.65 | | COMBINE_EQS: (64), (65) imply: % 74.03/10.65 | | (66) all_122_0 = all_85_0 % 74.03/10.65 | | % 74.03/10.65 | | SIMP: (66) implies: % 74.03/10.65 | | (67) all_122_0 = all_85_0 % 74.03/10.65 | | % 74.03/10.65 | | COMBINE_EQS: (63), (67) imply: % 74.03/10.65 | | (68) all_85_0 = all_60_0 % 74.03/10.65 | | % 74.03/10.65 | | SIMP: (68) implies: % 74.03/10.65 | | (69) all_85_0 = all_60_0 % 74.03/10.65 | | % 74.03/10.65 | | REDUCE: (43), (69) imply: % 74.03/10.65 | | (70) aSet0(all_60_0) = 0 % 74.03/10.65 | | % 74.03/10.65 | | REDUCE: (54), (63) imply: % 74.03/10.65 | | (71) aElementOf0(xx, all_60_0) = all_139_1 % 74.03/10.65 | | % 74.03/10.65 | | REDUCE: (42), (69) imply: % 74.03/10.65 | | (72) $i(all_60_0) % 74.03/10.65 | | % 74.03/10.65 | | BETA: splitting (48) gives: % 74.03/10.65 | | % 74.03/10.65 | | Case 1: % 74.03/10.65 | | | % 74.03/10.65 | | | (73) all_113_0 = 0 & sdtlpdtrp0(xF, xx) = all_113_1 & % 74.03/10.65 | | | aElement0(all_113_1) = 0 & $i(all_113_1) % 74.03/10.65 | | | % 74.03/10.65 | | | ALPHA: (73) implies: % 74.03/10.65 | | | (74) $i(all_113_1) % 74.03/10.65 | | | (75) sdtlpdtrp0(xF, xx) = all_113_1 % 74.03/10.65 | | | % 74.03/10.65 | | | BETA: splitting (47) gives: % 74.03/10.65 | | | % 74.03/10.65 | | | Case 1: % 74.03/10.65 | | | | % 74.03/10.65 | | | | (76) ~ (all_107_1 = 0) & aFunction0(xF) = all_107_1 % 74.03/10.65 | | | | % 74.03/10.65 | | | | ALPHA: (76) implies: % 74.03/10.65 | | | | (77) ~ (all_107_1 = 0) % 74.03/10.65 | | | | (78) aFunction0(xF) = all_107_1 % 74.03/10.65 | | | | % 74.03/10.65 | | | | GROUND_INST: instantiating (16) with 0, all_107_1, xF, simplifying with % 74.03/10.65 | | | | (11), (78) gives: % 74.03/10.65 | | | | (79) all_107_1 = 0 % 74.03/10.65 | | | | % 74.03/10.65 | | | | REDUCE: (77), (79) imply: % 74.03/10.65 | | | | (80) $false % 74.03/10.65 | | | | % 74.03/10.65 | | | | CLOSE: (80) is inconsistent. % 74.03/10.65 | | | | % 74.03/10.65 | | | Case 2: % 74.03/10.65 | | | | % 74.03/10.65 | | | | (81) aElement0(all_62_3) = all_107_0 & aElementOf0(xx, all_60_0) = % 74.03/10.65 | | | | all_107_1 & ( ~ (all_107_1 = 0) | all_107_0 = 0) % 74.03/10.65 | | | | % 74.03/10.65 | | | | ALPHA: (81) implies: % 74.03/10.65 | | | | (82) aElementOf0(xx, all_60_0) = all_107_1 % 74.03/10.65 | | | | % 74.03/10.65 | | | | GROUND_INST: instantiating (18) with 0, all_139_1, all_60_0, xx, % 74.03/10.65 | | | | simplifying with (22), (71) gives: % 74.03/10.65 | | | | (83) all_139_1 = 0 % 74.03/10.65 | | | | % 74.03/10.65 | | | | GROUND_INST: instantiating (18) with all_107_1, all_139_1, all_60_0, xx, % 74.03/10.65 | | | | simplifying with (71), (82) gives: % 74.03/10.65 | | | | (84) all_139_1 = all_107_1 % 74.03/10.65 | | | | % 74.03/10.65 | | | | GROUND_INST: instantiating (20) with all_62_3, all_113_1, xx, xF, % 74.03/10.65 | | | | simplifying with (30), (75) gives: % 74.03/10.65 | | | | (85) all_113_1 = all_62_3 % 74.03/10.65 | | | | % 74.03/10.65 | | | | COMBINE_EQS: (83), (84) imply: % 74.03/10.65 | | | | (86) all_107_1 = 0 % 74.03/10.65 | | | | % 74.03/10.65 | | | | GROUND_INST: instantiating (1) with all_60_0, simplifying with (70), % 74.03/10.65 | | | | (72) gives: % 74.03/10.65 | | | | (87) aSubsetOf0(all_60_0, all_60_0) = 0 % 74.03/10.65 | | | | % 74.03/10.65 | | | | GROUND_INST: instantiating (10) with xF, all_60_0, all_60_0, all_62_1, % 74.03/10.65 | | | | all_154_2, all_62_3, all_62_0, xx, simplifying with (13), % 74.03/10.65 | | | | (14), (23), (26), (27), (28), (30), (33), (61), (72) gives: % 74.03/10.65 | | | | (88) all_62_0 = 0 | ? [v0: int] : (( ~ (v0 = 0) & aFunction0(xF) = % 74.03/10.65 | | | | v0) | ( ~ (v0 = 0) & aSubsetOf0(all_60_0, all_60_0) = v0) | % 74.03/10.65 | | | | ( ~ (v0 = 0) & aElementOf0(xx, all_60_0) = v0)) % 74.03/10.65 | | | | % 74.03/10.65 | | | | GROUND_INST: instantiating (9) with xF, all_60_0, all_60_0, all_62_1, % 74.03/10.65 | | | | all_154_2, all_62_3, all_62_0, xx, simplifying with (13), % 74.03/10.65 | | | | (14), (22), (23), (26), (27), (28), (33), (61), (72) gives: % 74.03/10.65 | | | | (89) all_62_0 = 0 | ? [v0: any] : (( ~ (v0 = all_62_3) & % 74.03/10.65 | | | | sdtlpdtrp0(xF, xx) = v0 & $i(v0)) | ( ~ (v0 = 0) & % 74.03/10.65 | | | | aFunction0(xF) = v0) | ( ~ (v0 = 0) & aSubsetOf0(all_60_0, % 74.03/10.65 | | | | all_60_0) = v0)) % 74.03/10.65 | | | | % 74.03/10.65 | | | | BETA: splitting (88) gives: % 74.03/10.65 | | | | % 74.03/10.65 | | | | Case 1: % 74.03/10.65 | | | | | % 74.03/10.65 | | | | | (90) all_62_0 = 0 % 74.03/10.65 | | | | | % 74.03/10.65 | | | | | REDUCE: (25), (90) imply: % 74.03/10.65 | | | | | (91) $false % 74.03/10.65 | | | | | % 74.03/10.65 | | | | | CLOSE: (91) is inconsistent. % 74.03/10.65 | | | | | % 74.03/10.65 | | | | Case 2: % 74.03/10.65 | | | | | % 74.03/10.65 | | | | | (92) ? [v0: int] : (( ~ (v0 = 0) & aFunction0(xF) = v0) | ( ~ (v0 % 74.03/10.65 | | | | | = 0) & aSubsetOf0(all_60_0, all_60_0) = v0) | ( ~ (v0 = % 74.03/10.65 | | | | | 0) & aElementOf0(xx, all_60_0) = v0)) % 74.03/10.65 | | | | | % 74.03/10.65 | | | | | DELTA: instantiating (92) with fresh symbol all_613_0 gives: % 74.03/10.65 | | | | | (93) ( ~ (all_613_0 = 0) & aFunction0(xF) = all_613_0) | ( ~ % 74.03/10.65 | | | | | (all_613_0 = 0) & aSubsetOf0(all_60_0, all_60_0) = % 74.03/10.65 | | | | | all_613_0) | ( ~ (all_613_0 = 0) & aElementOf0(xx, all_60_0) % 74.03/10.65 | | | | | = all_613_0) % 74.03/10.65 | | | | | % 74.03/10.65 | | | | | BETA: splitting (89) gives: % 74.03/10.65 | | | | | % 74.03/10.65 | | | | | Case 1: % 74.03/10.65 | | | | | | % 74.03/10.65 | | | | | | (94) all_62_0 = 0 % 74.03/10.65 | | | | | | % 74.03/10.65 | | | | | | REDUCE: (25), (94) imply: % 74.03/10.65 | | | | | | (95) $false % 74.03/10.65 | | | | | | % 74.03/10.65 | | | | | | CLOSE: (95) is inconsistent. % 74.03/10.65 | | | | | | % 74.03/10.65 | | | | | Case 2: % 74.03/10.65 | | | | | | % 74.03/10.65 | | | | | | (96) ? [v0: any] : (( ~ (v0 = all_62_3) & sdtlpdtrp0(xF, xx) = % 74.03/10.65 | | | | | | v0 & $i(v0)) | ( ~ (v0 = 0) & aFunction0(xF) = v0) | ( ~ % 74.03/10.65 | | | | | | (v0 = 0) & aSubsetOf0(all_60_0, all_60_0) = v0)) % 74.03/10.65 | | | | | | % 74.03/10.65 | | | | | | DELTA: instantiating (96) with fresh symbol all_626_0 gives: % 74.03/10.65 | | | | | | (97) ( ~ (all_626_0 = all_62_3) & sdtlpdtrp0(xF, xx) = all_626_0 % 74.03/10.65 | | | | | | & $i(all_626_0)) | ( ~ (all_626_0 = 0) & aFunction0(xF) = % 74.03/10.65 | | | | | | all_626_0) | ( ~ (all_626_0 = 0) & aSubsetOf0(all_60_0, % 74.03/10.65 | | | | | | all_60_0) = all_626_0) % 74.03/10.65 | | | | | | % 74.03/10.65 | | | | | | BETA: splitting (97) gives: % 74.03/10.65 | | | | | | % 74.03/10.65 | | | | | | Case 1: % 74.03/10.65 | | | | | | | % 74.03/10.65 | | | | | | | (98) ~ (all_626_0 = all_62_3) & sdtlpdtrp0(xF, xx) = all_626_0 % 74.03/10.65 | | | | | | | & $i(all_626_0) % 74.03/10.65 | | | | | | | % 74.03/10.65 | | | | | | | ALPHA: (98) implies: % 74.03/10.65 | | | | | | | (99) ~ (all_626_0 = all_62_3) % 74.03/10.65 | | | | | | | (100) sdtlpdtrp0(xF, xx) = all_626_0 % 74.03/10.65 | | | | | | | % 74.03/10.65 | | | | | | | GROUND_INST: instantiating (20) with all_62_3, all_626_0, xx, xF, % 74.03/10.65 | | | | | | | simplifying with (30), (100) gives: % 74.03/10.65 | | | | | | | (101) all_626_0 = all_62_3 % 74.03/10.65 | | | | | | | % 74.03/10.65 | | | | | | | REDUCE: (99), (101) imply: % 74.03/10.65 | | | | | | | (102) $false % 74.03/10.65 | | | | | | | % 74.03/10.65 | | | | | | | CLOSE: (102) is inconsistent. % 74.03/10.65 | | | | | | | % 74.03/10.65 | | | | | | Case 2: % 74.03/10.65 | | | | | | | % 74.03/10.65 | | | | | | | (103) ( ~ (all_626_0 = 0) & aFunction0(xF) = all_626_0) | ( ~ % 74.03/10.65 | | | | | | | (all_626_0 = 0) & aSubsetOf0(all_60_0, all_60_0) = % 74.03/10.65 | | | | | | | all_626_0) % 74.03/10.65 | | | | | | | % 74.03/10.65 | | | | | | | BETA: splitting (103) gives: % 74.03/10.65 | | | | | | | % 74.03/10.65 | | | | | | | Case 1: % 74.03/10.65 | | | | | | | | % 74.03/10.65 | | | | | | | | (104) ~ (all_626_0 = 0) & aFunction0(xF) = all_626_0 % 74.03/10.65 | | | | | | | | % 74.03/10.65 | | | | | | | | ALPHA: (104) implies: % 74.03/10.65 | | | | | | | | (105) ~ (all_626_0 = 0) % 74.03/10.65 | | | | | | | | (106) aFunction0(xF) = all_626_0 % 74.03/10.65 | | | | | | | | % 74.03/10.65 | | | | | | | | GROUND_INST: instantiating (16) with 0, all_626_0, xF, % 74.03/10.65 | | | | | | | | simplifying with (11), (106) gives: % 74.03/10.65 | | | | | | | | (107) all_626_0 = 0 % 74.03/10.65 | | | | | | | | % 74.03/10.65 | | | | | | | | REDUCE: (105), (107) imply: % 74.03/10.65 | | | | | | | | (108) $false % 74.03/10.65 | | | | | | | | % 74.03/10.65 | | | | | | | | CLOSE: (108) is inconsistent. % 74.03/10.65 | | | | | | | | % 74.03/10.65 | | | | | | | Case 2: % 74.03/10.65 | | | | | | | | % 74.03/10.65 | | | | | | | | (109) ~ (all_626_0 = 0) & aSubsetOf0(all_60_0, all_60_0) = % 74.03/10.65 | | | | | | | | all_626_0 % 74.03/10.65 | | | | | | | | % 74.03/10.65 | | | | | | | | ALPHA: (109) implies: % 74.03/10.65 | | | | | | | | (110) aSubsetOf0(all_60_0, all_60_0) = all_626_0 % 74.03/10.65 | | | | | | | | % 74.03/10.65 | | | | | | | | BETA: splitting (93) gives: % 74.03/10.65 | | | | | | | | % 74.03/10.65 | | | | | | | | Case 1: % 74.03/10.65 | | | | | | | | | % 74.03/10.66 | | | | | | | | | (111) ~ (all_613_0 = 0) & aFunction0(xF) = all_613_0 % 74.03/10.66 | | | | | | | | | % 74.03/10.66 | | | | | | | | | ALPHA: (111) implies: % 74.03/10.66 | | | | | | | | | (112) ~ (all_613_0 = 0) % 74.03/10.66 | | | | | | | | | (113) aFunction0(xF) = all_613_0 % 74.03/10.66 | | | | | | | | | % 74.03/10.66 | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_613_0, xF, % 74.03/10.66 | | | | | | | | | simplifying with (11), (113) gives: % 74.03/10.66 | | | | | | | | | (114) all_613_0 = 0 % 74.03/10.66 | | | | | | | | | % 74.03/10.66 | | | | | | | | | REDUCE: (112), (114) imply: % 74.03/10.66 | | | | | | | | | (115) $false % 74.03/10.66 | | | | | | | | | % 74.03/10.66 | | | | | | | | | CLOSE: (115) is inconsistent. % 74.03/10.66 | | | | | | | | | % 74.03/10.66 | | | | | | | | Case 2: % 74.03/10.66 | | | | | | | | | % 74.03/10.66 | | | | | | | | | (116) ( ~ (all_613_0 = 0) & aSubsetOf0(all_60_0, all_60_0) % 74.03/10.66 | | | | | | | | | = all_613_0) | ( ~ (all_613_0 = 0) & % 74.03/10.66 | | | | | | | | | aElementOf0(xx, all_60_0) = all_613_0) % 74.03/10.66 | | | | | | | | | % 74.03/10.66 | | | | | | | | | BETA: splitting (116) gives: % 74.03/10.66 | | | | | | | | | % 74.03/10.66 | | | | | | | | | Case 1: % 74.03/10.66 | | | | | | | | | | % 74.03/10.66 | | | | | | | | | | (117) ~ (all_613_0 = 0) & aSubsetOf0(all_60_0, all_60_0) % 74.03/10.66 | | | | | | | | | | = all_613_0 % 74.03/10.66 | | | | | | | | | | % 74.03/10.66 | | | | | | | | | | ALPHA: (117) implies: % 74.03/10.66 | | | | | | | | | | (118) ~ (all_613_0 = 0) % 74.03/10.66 | | | | | | | | | | (119) aSubsetOf0(all_60_0, all_60_0) = all_613_0 % 74.03/10.66 | | | | | | | | | | % 74.03/10.66 | | | | | | | | | | GROUND_INST: instantiating (19) with all_613_0, all_626_0, % 74.03/10.66 | | | | | | | | | | all_60_0, all_60_0, simplifying with (110), (119) % 74.03/10.66 | | | | | | | | | | gives: % 74.03/10.66 | | | | | | | | | | (120) all_626_0 = all_613_0 % 74.03/10.66 | | | | | | | | | | % 74.03/10.66 | | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_626_0, all_60_0, % 74.03/10.66 | | | | | | | | | | all_60_0, simplifying with (87), (110) gives: % 74.03/10.66 | | | | | | | | | | (121) all_626_0 = 0 % 74.03/10.66 | | | | | | | | | | % 74.03/10.66 | | | | | | | | | | COMBINE_EQS: (120), (121) imply: % 74.03/10.66 | | | | | | | | | | (122) all_613_0 = 0 % 74.03/10.66 | | | | | | | | | | % 74.03/10.66 | | | | | | | | | | SIMP: (122) implies: % 74.03/10.66 | | | | | | | | | | (123) all_613_0 = 0 % 74.03/10.66 | | | | | | | | | | % 74.03/10.66 | | | | | | | | | | REDUCE: (118), (123) imply: % 74.03/10.66 | | | | | | | | | | (124) $false % 74.03/10.66 | | | | | | | | | | % 74.03/10.66 | | | | | | | | | | CLOSE: (124) is inconsistent. % 74.03/10.66 | | | | | | | | | | % 74.03/10.66 | | | | | | | | | Case 2: % 74.03/10.66 | | | | | | | | | | % 74.03/10.66 | | | | | | | | | | (125) ~ (all_613_0 = 0) & aElementOf0(xx, all_60_0) = % 74.03/10.66 | | | | | | | | | | all_613_0 % 74.03/10.66 | | | | | | | | | | % 74.03/10.66 | | | | | | | | | | ALPHA: (125) implies: % 74.03/10.66 | | | | | | | | | | (126) ~ (all_613_0 = 0) % 74.03/10.66 | | | | | | | | | | (127) aElementOf0(xx, all_60_0) = all_613_0 % 74.03/10.66 | | | | | | | | | | % 74.03/10.66 | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_613_0, all_60_0, % 74.03/10.66 | | | | | | | | | | xx, simplifying with (22), (127) gives: % 74.03/10.66 | | | | | | | | | | (128) all_613_0 = 0 % 74.03/10.66 | | | | | | | | | | % 74.03/10.66 | | | | | | | | | | REDUCE: (126), (128) imply: % 74.03/10.66 | | | | | | | | | | (129) $false % 74.03/10.66 | | | | | | | | | | % 74.03/10.66 | | | | | | | | | | CLOSE: (129) is inconsistent. % 74.03/10.66 | | | | | | | | | | % 74.03/10.66 | | | | | | | | | End of split % 74.03/10.66 | | | | | | | | | % 74.03/10.66 | | | | | | | | End of split % 74.03/10.66 | | | | | | | | % 74.03/10.66 | | | | | | | End of split % 74.03/10.66 | | | | | | | % 74.03/10.66 | | | | | | End of split % 74.03/10.66 | | | | | | % 74.03/10.66 | | | | | End of split % 74.03/10.66 | | | | | % 74.03/10.66 | | | | End of split % 74.03/10.66 | | | | % 74.03/10.66 | | | End of split % 74.03/10.66 | | | % 74.03/10.66 | | Case 2: % 74.03/10.66 | | | % 74.03/10.66 | | | (130) ~ (all_113_1 = 0) & aFunction0(xF) = all_113_1 % 74.03/10.66 | | | % 74.03/10.66 | | | ALPHA: (130) implies: % 74.03/10.66 | | | (131) ~ (all_113_1 = 0) % 74.03/10.66 | | | (132) aFunction0(xF) = all_113_1 % 74.03/10.66 | | | % 74.03/10.66 | | | GROUND_INST: instantiating (16) with 0, all_113_1, xF, simplifying with % 74.03/10.66 | | | (11), (132) gives: % 74.03/10.66 | | | (133) all_113_1 = 0 % 74.03/10.66 | | | % 74.03/10.66 | | | REDUCE: (131), (133) imply: % 74.03/10.66 | | | (134) $false % 74.03/10.66 | | | % 74.03/10.66 | | | CLOSE: (134) is inconsistent. % 74.03/10.66 | | | % 74.03/10.66 | | End of split % 74.03/10.66 | | % 74.03/10.66 | End of split % 74.03/10.66 | % 74.03/10.66 End of proof % 74.03/10.66 % SZS output end Proof for theBenchmark % 74.03/10.66 % 74.03/10.66 10041ms %------------------------------------------------------------------------------