%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM597+3 : 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 11:48:51 EDT 2023 % Result : Theorem 41.64s 6.40s % Output : Proof 215.97s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.14/0.15 % Problem : NUM597+3 : TPTP v8.1.2. Released v4.0.0. % 0.14/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.37 % Computer : n012.cluster.edu % 0.15/0.37 % Model : x86_64 x86_64 % 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.37 % Memory : 8042.1875MB % 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.37 % CPULimit : 300 % 0.15/0.37 % WCLimit : 300 % 0.15/0.37 % DateTime : Fri Aug 25 14:46:26 EDT 2023 % 0.15/0.37 % CPUTime : % 0.23/0.64 ________ _____ % 0.23/0.64 ___ __ \_________(_)________________________________ % 0.23/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.23/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.23/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.23/0.64 % 0.23/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.23/0.64 (2023-06-19) % 0.23/0.64 % 0.23/0.64 (c) Philipp Rümmer, 2009-2023 % 0.23/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.23/0.64 Amanda Stjerna. % 0.23/0.64 Free software under BSD-3-Clause. % 0.23/0.64 % 0.23/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.23/0.64 % 0.23/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.23/0.65 Running up to 7 provers in parallel. % 0.23/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.23/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.23/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.23/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.23/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.23/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.23/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 6.20/1.66 Prover 1: Preprocessing ... % 6.20/1.66 Prover 4: Preprocessing ... % 6.20/1.68 Prover 3: Preprocessing ... % 6.20/1.68 Prover 2: Preprocessing ... % 6.20/1.68 Prover 6: Preprocessing ... % 6.20/1.68 Prover 5: Preprocessing ... % 6.89/1.71 Prover 0: Preprocessing ... % 18.35/3.25 Prover 6: Proving ... % 18.35/3.25 Prover 1: Constructing countermodel ... % 18.35/3.26 Prover 3: Constructing countermodel ... % 19.78/3.61 Prover 5: Proving ... % 41.64/6.39 Prover 3: proved (5709ms) % 41.64/6.39 % 41.64/6.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 41.64/6.40 % 41.64/6.41 Prover 6: stopped % 41.64/6.41 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 41.64/6.45 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 41.64/6.45 Prover 5: stopped % 41.64/6.46 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 43.39/6.72 Prover 7: Preprocessing ... % 44.00/6.75 Prover 8: Preprocessing ... % 44.41/6.78 Prover 10: Preprocessing ... % 46.76/7.10 Prover 4: Constructing countermodel ... % 47.33/7.26 Prover 8: Warning: ignoring some quantifiers % 47.33/7.29 Prover 8: Constructing countermodel ... % 49.98/7.54 Prover 10: Constructing countermodel ... % 50.51/7.61 Prover 7: Constructing countermodel ... % 51.73/7.82 Prover 2: Proving ... % 51.73/7.85 Prover 2: stopped % 51.73/7.85 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 53.84/8.02 Prover 11: Preprocessing ... % 53.84/8.10 Prover 0: Proving ... % 54.56/8.13 Prover 0: stopped % 54.56/8.16 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 56.20/8.35 Prover 13: Preprocessing ... % 62.29/9.15 Prover 13: Warning: ignoring some quantifiers % 62.66/9.25 Prover 13: Constructing countermodel ... % 77.02/11.13 Prover 11: Constructing countermodel ... % 87.88/12.66 Prover 13: stopped % 87.88/12.66 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 90.15/12.83 Prover 16: Preprocessing ... % 92.50/13.13 Prover 16: Warning: ignoring some quantifiers % 92.71/13.15 Prover 16: Constructing countermodel ... % 113.75/16.00 Prover 1: stopped % 113.75/16.00 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 114.97/16.16 Prover 19: Preprocessing ... % 118.07/16.63 Prover 19: Warning: ignoring some quantifiers % 118.71/16.67 Prover 19: Constructing countermodel ... % 128.28/17.95 Prover 16: stopped % 139.31/19.63 Prover 19: stopped % 188.29/28.00 Prover 4: stopped % 189.18/28.12 Prover 7: stopped % 215.36/35.48 Prover 8: Found proof (size 77) % 215.36/35.48 Prover 8: proved (28945ms) % 215.36/35.49 Prover 11: stopped % 215.36/35.49 Prover 10: stopped % 215.36/35.49 % 215.36/35.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 215.36/35.49 % 215.36/35.50 % SZS output start Proof for theBenchmark % 215.48/35.51 Assumptions after simplification: % 215.48/35.51 --------------------------------- % 215.48/35.51 % 215.48/35.51 (mCardSub) % 215.55/35.57 ! [v0: $i] : ! [v1: any] : ( ~ (isFinite0(v0) = v1) | ~ $i(v0) | ? [v2: % 215.55/35.57 any] : ? [v3: $i] : (sbrdtbr0(v0) = v3 & aSet0(v0) = v2 & $i(v3) & ( ~ % 215.55/35.57 (v2 = 0) | ! [v4: $i] : ! [v5: $i] : ! [v6: int] : ( ~ (v1 = 0) | v6 % 215.55/35.57 = 0 | ~ (sbrdtbr0(v4) = v5) | ~ (sdtlseqdt0(v5, v3) = v6) | ~ % 215.55/35.57 $i(v4) | ? [v7: int] : ( ~ (v7 = 0) & aSubsetOf0(v4, v0) = v7))))) % 215.55/35.57 % 215.55/35.57 (mDefPtt) % 215.55/35.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(v0, v1) = v2) | ~ % 215.55/35.57 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 215.55/35.57 (aFunction0(v0) = v3 & szDzozmdt0(v0) = v5 & aElement0(v1) = v4 & $i(v5) & ( % 215.55/35.57 ~ (v4 = 0) | ~ (v3 = 0) | ( ! [v6: $i] : (v6 = v2 | ~ (aSet0(v6) = 0) % 215.55/35.57 | ~ $i(v6) | ? [v7: $i] : ? [v8: any] : ? [v9: any] : ? [v10: % 215.55/35.57 $i] : (sdtlpdtrp0(v0, v7) = v10 & aElementOf0(v7, v6) = v8 & % 215.55/35.57 aElementOf0(v7, v5) = v9 & $i(v10) & $i(v7) & ( ~ (v10 = v1) | ~ % 215.55/35.57 (v9 = 0) | ~ (v8 = 0)) & (v8 = 0 | (v10 = v1 & v9 = 0)))) & ! % 215.55/35.57 [v6: any] : ( ~ (aSet0(v2) = v6) | ~ $i(v2) | (v6 = 0 & ! [v7: $i] : % 215.55/35.57 ! [v8: any] : ( ~ (aElementOf0(v7, v5) = v8) | ~ $i(v7) | ? % 215.55/35.57 [v9: any] : ? [v10: $i] : (sdtlpdtrp0(v0, v7) = v10 & % 215.55/35.57 aElementOf0(v7, v2) = v9 & $i(v10) & ( ~ (v9 = 0) | (v10 = v1 % 215.55/35.57 & v8 = 0)))) & ! [v7: $i] : ( ~ (aElementOf0(v7, v5) = 0) % 215.55/35.57 | ~ $i(v7) | ? [v8: $i] : ? [v9: any] : (sdtlpdtrp0(v0, v7) = % 215.55/35.57 v8 & aElementOf0(v7, v2) = v9 & $i(v8) & ( ~ (v8 = v1) | v9 = % 215.55/35.57 0))))))))) % 215.55/35.57 % 215.55/35.58 (mDefSub) % 215.55/35.58 ! [v0: $i] : ( ~ (aSet0(v0) = 0) | ~ $i(v0) | ( ! [v1: $i] : ! [v2: int] : % 215.55/35.58 (v2 = 0 | ~ (aSubsetOf0(v1, v0) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: % 215.55/35.58 int] : ( ~ (v4 = 0) & aElementOf0(v3, v1) = 0 & aElementOf0(v3, v0) = % 215.55/35.58 v4 & $i(v3)) | ? [v3: int] : ( ~ (v3 = 0) & aSet0(v1) = v3)) & ! % 215.55/35.58 [v1: $i] : ( ~ (aSubsetOf0(v1, v0) = 0) | ~ $i(v1) | (aSet0(v1) = 0 & ! % 215.55/35.58 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, v0) = v3) | ~ % 215.55/35.58 $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & aElementOf0(v2, v1) = % 215.55/35.58 v4)))))) % 215.55/35.58 % 215.55/35.58 (mDirichlet) % 215.55/35.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (szDzizrdt0(v0) = v1) | ~ % 215.55/35.58 (sdtlbdtrb0(v0, v1) = v2) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: % 215.55/35.58 any] : ? [v6: $i] : ? [v7: any] : ? [v8: any] : ? [v9: any] : % 215.55/35.58 (sdtlcdtrc0(v0, v4) = v6 & aFunction0(v0) = v3 & szDzozmdt0(v0) = v4 & % 215.55/35.58 isCountable0(v4) = v5 & isCountable0(v2) = v9 & isFinite0(v6) = v7 & % 215.55/35.58 aElement0(v1) = v8 & $i(v6) & $i(v4) & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v3 % 215.55/35.58 = 0) | (v9 = 0 & v8 = 0)))) % 215.55/35.58 % 215.55/35.58 (mImgRng) % 215.55/35.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlcdtrc0(v0, v1) = v2) | ~ % 215.55/35.58 (szDzozmdt0(v0) = v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 215.55/35.58 aFunction0(v0) = v3) | ! [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 % 215.55/35.58 | ~ (sdtlpdtrp0(v0, v3) = v4) | ~ (aElementOf0(v4, v2) = v5) | ~ $i(v3) % 215.55/35.59 | ? [v6: int] : ( ~ (v6 = 0) & aElementOf0(v3, v1) = v6))) % 215.55/35.59 % 215.55/35.59 (m__) % 215.55/35.59 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & szDzizrdt0(xd) = % 215.55/35.59 v0 & aElementOf0(v0, xT) = v1 & $i(v0)) % 215.55/35.59 % 215.55/35.59 (m__3291) % 215.55/35.59 isFinite0(xT) = 0 & aSet0(xT) = 0 & $i(xT) % 215.55/35.59 % 215.55/35.59 (m__4730) % 215.55/35.59 aFunction0(xd) = 0 & szDzozmdt0(xd) = szNzAzT0 & $i(xd) & $i(xC) & $i(xN) & % 215.55/35.59 $i(xk) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xC, v0) = % 215.55/35.59 v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 215.55/35.59 ? [v6: $i] : (sdtlpdtrp0(xd, v0) = v6 & sdtlpdtrp0(xN, v3) = v4 & % 215.55/35.59 slbdtsldtrb0(v4, xk) = v5 & szszuzczcdt0(v0) = v3 & aElementOf0(v0, % 215.55/35.59 szNzAzT0) = v2 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ! % 215.55/35.59 [v7: $i] : ! [v8: any] : ( ~ (aElementOf0(v7, v5) = v8) | ~ $i(v7) | % 215.55/35.59 ? [v9: any] : ? [v10: any] : ? [v11: $i] : ? [v12: $i] : % 215.55/35.59 (sdtlpdtrp0(v1, v7) = v12 & sbrdtbr0(v7) = v11 & aSubsetOf0(v7, v4) = % 215.55/35.59 v10 & aSet0(v7) = v9 & $i(v12) & $i(v11) & ( ~ (v9 = 0) | v12 = v6 | % 215.55/35.59 ( ~ (v8 = 0) & ( ~ (v11 = xk) | ( ~ (v10 = 0) & ? [v13: $i] : ? % 215.55/35.59 [v14: int] : ( ~ (v14 = 0) & aElementOf0(v13, v7) = 0 & % 215.55/35.59 aElementOf0(v13, v4) = v14 & $i(v13))))))))))) % 215.55/35.59 % 215.55/35.59 (m__4758) % 215.55/35.60 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & % 215.55/35.60 szDzozmdt0(xd) = v0 & aSubsetOf0(v1, xT) = 0 & aSet0(v1) = 0 & $i(v1) & % 215.55/35.60 $i(v0) & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, v1) = % 215.55/35.60 v3) | ~ $i(v2) | ! [v4: $i] : ( ~ (aElementOf0(v4, v0) = 0) | ~ % 215.55/35.60 $i(v4) | ? [v5: $i] : ( ~ (v5 = v2) & sdtlpdtrp0(xd, v4) = v5 & % 215.55/35.60 $i(v5)))) & ! [v2: $i] : ( ~ (aElementOf0(v2, v1) = 0) | ~ $i(v2) | % 215.55/35.60 aElementOf0(v2, xT) = 0) & ! [v2: $i] : ( ~ (aElementOf0(v2, v1) = 0) | % 215.55/35.60 ~ $i(v2) | ? [v3: $i] : (sdtlpdtrp0(xd, v3) = v2 & aElementOf0(v3, v0) = % 215.55/35.60 0 & $i(v3)))) % 215.55/35.60 % 215.55/35.60 (m__4868) % 215.55/35.60 $i(xd) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 & % 215.55/35.60 sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = v2 & aSet0(v1) = 0 & $i(v2) & % 215.55/35.60 $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (aElementOf0(v3, % 215.55/35.60 v1) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: $i] : (sdtlpdtrp0(xd, % 215.55/35.60 v3) = v6 & aElementOf0(v3, v2) = v5 & $i(v6) & ( ~ (v6 = v0) | ~ (v5 % 215.55/35.60 = 0)))) & ! [v3: $i] : ( ~ (aElementOf0(v3, v1) = 0) | ~ $i(v3) | % 215.55/35.60 (sdtlpdtrp0(xd, v3) = v0 & aElementOf0(v3, v2) = 0)) & ? [v3: $i] : % 215.55/35.60 (aElementOf0(v3, v1) = 0 & $i(v3))) % 215.55/35.60 % 215.55/35.60 (function-axioms) % 215.97/35.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 215.97/35.62 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 215.97/35.62 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 215.97/35.62 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 215.97/35.62 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 215.97/35.62 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 215.97/35.62 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 215.97/35.62 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 215.97/35.62 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: MultipleValueBool] % 215.97/35.62 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 215.97/35.62 (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! [v0: % 215.97/35.62 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 215.97/35.62 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & ! % 215.97/35.62 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 215.97/35.62 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! % 215.97/35.62 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | % 215.97/35.62 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 215.97/35.62 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 215.97/35.62 (aSubsetOf0(v3, v2) = v1) | ~ (aSubsetOf0(v3, v2) = v0)) & ! [v0: % 215.97/35.62 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 215.97/35.62 : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) & % 215.97/35.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 215.97/35.62 ~ (szDzizrdt0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 215.97/35.62 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aFunction0(v2) = v1) | ~ % 215.97/35.62 (aFunction0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 215.97/35.62 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 215.97/35.62 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 215.97/35.62 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 215.97/35.62 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 215.97/35.62 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 215.97/35.62 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 215.97/35.62 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 215.97/35.62 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 215.97/35.62 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 215.97/35.62 $i] : (v1 = v0 | ~ (isCountable0(v2) = v1) | ~ (isCountable0(v2) = v0)) & % 215.97/35.62 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = % 215.97/35.62 v0 | ~ (isFinite0(v2) = v1) | ~ (isFinite0(v2) = v0)) & ! [v0: % 215.97/35.62 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 215.97/35.62 ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 215.97/35.62 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) | % 215.97/35.62 ~ (aElement0(v2) = v0)) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 215.97/35.62 MultipleValueBool] : (iLess0(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? % 215.97/35.62 [v2: MultipleValueBool] : (sdtlseqdt0(v1, v0) = v2) & ? [v0: $i] : ? [v1: % 215.97/35.62 $i] : ? [v2: MultipleValueBool] : (aSubsetOf0(v1, v0) = v2) & ? [v0: $i] : % 215.97/35.62 ? [v1: $i] : ? [v2: MultipleValueBool] : (aElementOf0(v1, v0) = v2) & ? % 215.97/35.62 [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtexdt0(v1, v0) = v2 & $i(v2)) & ? % 215.97/35.62 [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtlcdtrc0(v1, v0) = v2 & $i(v2)) & ? % 215.97/35.62 [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtlbdtrb0(v1, v0) = v2 & $i(v2)) & ? % 215.97/35.62 [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtlpdtrp0(v1, v0) = v2 & $i(v2)) & ? % 215.97/35.62 [v0: $i] : ? [v1: $i] : ? [v2: $i] : (slbdtsldtrb0(v1, v0) = v2 & $i(v2)) & % 215.97/35.62 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtmndt0(v1, v0) = v2 & $i(v2)) & ? % 215.97/35.62 [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtpldt0(v1, v0) = v2 & $i(v2)) & ? % 215.97/35.62 [v0: $i] : ? [v1: MultipleValueBool] : (aFunction0(v0) = v1) & ? [v0: $i] : % 215.97/35.62 ? [v1: MultipleValueBool] : (isCountable0(v0) = v1) & ? [v0: $i] : ? [v1: % 215.97/35.62 MultipleValueBool] : (isFinite0(v0) = v1) & ? [v0: $i] : ? [v1: % 215.97/35.62 MultipleValueBool] : (aSet0(v0) = v1) & ? [v0: $i] : ? [v1: % 215.97/35.62 MultipleValueBool] : (aElement0(v0) = v1) & ? [v0: $i] : ? [v1: $i] : % 215.97/35.62 (szDzizrdt0(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (szDzozmdt0(v0) = % 215.97/35.62 v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (slbdtrb0(v0) = v1 & $i(v1)) & ? % 215.97/35.62 [v0: $i] : ? [v1: $i] : (szmzazxdt0(v0) = v1 & $i(v1)) & ? [v0: $i] : ? % 215.97/35.62 [v1: $i] : (szmzizndt0(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : % 215.97/35.62 (sbrdtbr0(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (szszuzczcdt0(v0) = % 215.97/35.62 v1 & $i(v1)) % 215.97/35.62 % 215.97/35.62 Further assumptions not needed in the proof: % 215.97/35.62 -------------------------------------------- % 215.97/35.62 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 215.97/35.62 mCardSeg, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, mDefCons, % 215.97/35.62 mDefDiff, mDefEmp, mDefMax, mDefMin, mDefRst, mDefSImg, mDefSeg, mDefSel, % 215.97/35.62 mDiffCons, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet, mFDiffSet, mFinRel, % 215.97/35.62 mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm, mLessASymm, mLessRefl, % 215.97/35.62 mLessRel, mLessSucc, mLessTotal, mLessTrans, mMinMin, mNATSet, mNatExtra, % 215.97/35.62 mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess, mSegSucc, mSegZero, % 215.97/35.62 mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, mSubASymm, mSubFSet, % 215.97/35.62 mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum, % 215.97/35.63 m__3398, m__3418, m__3435, m__3453, m__3462, m__3520, m__3533, m__3623, m__3671, % 215.97/35.63 m__3754, m__3821, m__3965, m__4151, m__4182, m__4331, m__4411, m__4618, m__4660 % 215.97/35.63 % 215.97/35.63 Those formulas are unsatisfiable: % 215.97/35.63 --------------------------------- % 215.97/35.63 % 215.97/35.63 Begin of proof % 215.97/35.63 | % 215.97/35.63 | ALPHA: (m__3291) implies: % 215.97/35.63 | (1) aSet0(xT) = 0 % 215.97/35.63 | (2) isFinite0(xT) = 0 % 215.97/35.63 | % 215.97/35.63 | ALPHA: (m__4730) implies: % 215.97/35.63 | (3) szDzozmdt0(xd) = szNzAzT0 % 215.97/35.63 | (4) aFunction0(xd) = 0 % 215.97/35.63 | % 215.97/35.63 | ALPHA: (m__4758) implies: % 215.97/35.63 | (5) ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & szDzozmdt0(xd) = % 215.97/35.63 | v0 & aSubsetOf0(v1, xT) = 0 & aSet0(v1) = 0 & $i(v1) & $i(v0) & ! % 215.97/35.63 | [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, v1) = v3) | % 215.97/35.63 | ~ $i(v2) | ! [v4: $i] : ( ~ (aElementOf0(v4, v0) = 0) | ~ $i(v4) % 215.97/35.63 | | ? [v5: $i] : ( ~ (v5 = v2) & sdtlpdtrp0(xd, v4) = v5 & % 215.97/35.63 | $i(v5)))) & ! [v2: $i] : ( ~ (aElementOf0(v2, v1) = 0) | ~ % 215.97/35.63 | $i(v2) | aElementOf0(v2, xT) = 0) & ! [v2: $i] : ( ~ % 215.97/35.63 | (aElementOf0(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : % 215.97/35.63 | (sdtlpdtrp0(xd, v3) = v2 & aElementOf0(v3, v0) = 0 & $i(v3)))) % 215.97/35.63 | % 215.97/35.63 | ALPHA: (m__4868) implies: % 215.97/35.63 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 & % 215.97/35.63 | sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = v2 & aSet0(v1) = 0 & % 215.97/35.63 | $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ % 215.97/35.63 | (aElementOf0(v3, v1) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: $i] % 215.97/35.63 | : (sdtlpdtrp0(xd, v3) = v6 & aElementOf0(v3, v2) = v5 & $i(v6) & ( % 215.97/35.63 | ~ (v6 = v0) | ~ (v5 = 0)))) & ! [v3: $i] : ( ~ % 215.97/35.63 | (aElementOf0(v3, v1) = 0) | ~ $i(v3) | (sdtlpdtrp0(xd, v3) = v0 & % 215.97/35.64 | aElementOf0(v3, v2) = 0)) & ? [v3: $i] : (aElementOf0(v3, v1) = % 215.97/35.64 | 0 & $i(v3))) % 215.97/35.64 | % 215.97/35.64 | ALPHA: (m__) implies: % 215.97/35.64 | (7) $i(xT) % 215.97/35.64 | (8) $i(xd) % 215.97/35.64 | (9) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & szDzizrdt0(xd) = v0 & % 215.97/35.64 | aElementOf0(v0, xT) = v1 & $i(v0)) % 215.97/35.64 | % 215.97/35.64 | ALPHA: (function-axioms) implies: % 215.97/35.64 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 215.97/35.64 | : (v1 = v0 | ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) % 215.97/35.64 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 215.97/35.64 | (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) % 215.97/35.64 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 215.97/35.64 | : (v1 = v0 | ~ (aFunction0(v2) = v1) | ~ (aFunction0(v2) = v0)) % 215.97/35.64 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 215.97/35.64 | (szDzizrdt0(v2) = v1) | ~ (szDzizrdt0(v2) = v0)) % 215.97/35.64 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 215.97/35.64 | : ! [v3: $i] : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ % 215.97/35.64 | (aElementOf0(v3, v2) = v0)) % 215.97/35.64 | % 215.97/35.64 | DELTA: instantiating (9) with fresh symbols all_123_0, all_123_1 gives: % 215.97/35.64 | (15) ~ (all_123_0 = 0) & szDzizrdt0(xd) = all_123_1 & % 215.97/35.64 | aElementOf0(all_123_1, xT) = all_123_0 & $i(all_123_1) % 215.97/35.64 | % 215.97/35.64 | ALPHA: (15) implies: % 215.97/35.64 | (16) ~ (all_123_0 = 0) % 215.97/35.64 | (17) aElementOf0(all_123_1, xT) = all_123_0 % 215.97/35.64 | (18) szDzizrdt0(xd) = all_123_1 % 215.97/35.64 | % 215.97/35.64 | DELTA: instantiating (6) with fresh symbols all_125_0, all_125_1, all_125_2 % 215.97/35.64 | gives: % 215.97/35.64 | (19) szDzizrdt0(xd) = all_125_2 & sdtlbdtrb0(xd, all_125_2) = all_125_1 & % 215.97/35.64 | szDzozmdt0(xd) = all_125_0 & aSet0(all_125_1) = 0 & $i(all_125_0) & % 215.97/35.64 | $i(all_125_1) & $i(all_125_2) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | % 215.97/35.64 | ~ (aElementOf0(v0, all_125_1) = v1) | ~ $i(v0) | ? [v2: any] : ? % 215.97/35.64 | [v3: $i] : (sdtlpdtrp0(xd, v0) = v3 & aElementOf0(v0, all_125_0) = % 215.97/35.64 | v2 & $i(v3) & ( ~ (v3 = all_125_2) | ~ (v2 = 0)))) & ! [v0: $i] % 215.97/35.64 | : ( ~ (aElementOf0(v0, all_125_1) = 0) | ~ $i(v0) | (sdtlpdtrp0(xd, % 215.97/35.64 | v0) = all_125_2 & aElementOf0(v0, all_125_0) = 0)) & ? [v0: $i] % 215.97/35.64 | : (aElementOf0(v0, all_125_1) = 0 & $i(v0)) % 215.97/35.64 | % 215.97/35.64 | ALPHA: (19) implies: % 215.97/35.64 | (20) $i(all_125_2) % 215.97/35.64 | (21) szDzozmdt0(xd) = all_125_0 % 215.97/35.64 | (22) sdtlbdtrb0(xd, all_125_2) = all_125_1 % 215.97/35.64 | (23) szDzizrdt0(xd) = all_125_2 % 215.97/35.64 | (24) ! [v0: $i] : ( ~ (aElementOf0(v0, all_125_1) = 0) | ~ $i(v0) | % 215.97/35.64 | (sdtlpdtrp0(xd, v0) = all_125_2 & aElementOf0(v0, all_125_0) = 0)) % 215.97/35.64 | (25) ? [v0: $i] : (aElementOf0(v0, all_125_1) = 0 & $i(v0)) % 215.97/35.64 | % 215.97/35.64 | DELTA: instantiating (5) with fresh symbols all_128_0, all_128_1 gives: % 215.97/35.65 | (26) sdtlcdtrc0(xd, all_128_1) = all_128_0 & szDzozmdt0(xd) = all_128_1 & % 215.97/35.65 | aSubsetOf0(all_128_0, xT) = 0 & aSet0(all_128_0) = 0 & $i(all_128_0) & % 215.97/35.65 | $i(all_128_1) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 215.97/35.65 | (aElementOf0(v0, all_128_0) = v1) | ~ $i(v0) | ! [v2: $i] : ( ~ % 215.97/35.65 | (aElementOf0(v2, all_128_1) = 0) | ~ $i(v2) | ? [v3: $i] : ( ~ % 215.97/35.65 | (v3 = v0) & sdtlpdtrp0(xd, v2) = v3 & $i(v3)))) & ! [v0: $i] : % 215.97/35.65 | ( ~ (aElementOf0(v0, all_128_0) = 0) | ~ $i(v0) | aElementOf0(v0, xT) % 215.97/35.65 | = 0) & ! [v0: $i] : ( ~ (aElementOf0(v0, all_128_0) = 0) | ~ % 215.97/35.65 | $i(v0) | ? [v1: $i] : (sdtlpdtrp0(xd, v1) = v0 & aElementOf0(v1, % 215.97/35.65 | all_128_1) = 0 & $i(v1))) % 215.97/35.65 | % 215.97/35.65 | ALPHA: (26) implies: % 215.97/35.65 | (27) $i(all_128_0) % 215.97/35.65 | (28) aSubsetOf0(all_128_0, xT) = 0 % 215.97/35.65 | (29) szDzozmdt0(xd) = all_128_1 % 215.97/35.65 | (30) sdtlcdtrc0(xd, all_128_1) = all_128_0 % 215.97/35.65 | % 215.97/35.65 | DELTA: instantiating (25) with fresh symbol all_137_0 gives: % 215.97/35.65 | (31) aElementOf0(all_137_0, all_125_1) = 0 & $i(all_137_0) % 215.97/35.65 | % 215.97/35.65 | ALPHA: (31) implies: % 215.97/35.65 | (32) $i(all_137_0) % 215.97/35.65 | (33) aElementOf0(all_137_0, all_125_1) = 0 % 215.97/35.65 | % 215.97/35.65 | GROUND_INST: instantiating (11) with all_125_0, all_128_1, xd, simplifying % 215.97/35.65 | with (21), (29) gives: % 215.97/35.65 | (34) all_128_1 = all_125_0 % 215.97/35.65 | % 215.97/35.65 | GROUND_INST: instantiating (11) with szNzAzT0, all_128_1, xd, simplifying with % 215.97/35.65 | (3), (29) gives: % 215.97/35.65 | (35) all_128_1 = szNzAzT0 % 215.97/35.65 | % 215.97/35.65 | GROUND_INST: instantiating (13) with all_123_1, all_125_2, xd, simplifying % 215.97/35.65 | with (18), (23) gives: % 215.97/35.65 | (36) all_125_2 = all_123_1 % 215.97/35.65 | % 215.97/35.65 | COMBINE_EQS: (34), (35) imply: % 215.97/35.65 | (37) all_125_0 = szNzAzT0 % 215.97/35.65 | % 215.97/35.65 | REDUCE: (30), (35) imply: % 215.97/35.65 | (38) sdtlcdtrc0(xd, szNzAzT0) = all_128_0 % 215.97/35.65 | % 215.97/35.65 | REDUCE: (22), (36) imply: % 215.97/35.65 | (39) sdtlbdtrb0(xd, all_123_1) = all_125_1 % 215.97/35.65 | % 215.97/35.65 | REDUCE: (20), (36) imply: % 215.97/35.65 | (40) $i(all_123_1) % 215.97/35.65 | % 215.97/35.65 | GROUND_INST: instantiating (24) with all_137_0, simplifying with (32), (33) % 215.97/35.65 | gives: % 215.97/35.65 | (41) sdtlpdtrp0(xd, all_137_0) = all_125_2 & aElementOf0(all_137_0, % 215.97/35.65 | all_125_0) = 0 % 215.97/35.65 | % 215.97/35.65 | ALPHA: (41) implies: % 215.97/35.65 | (42) aElementOf0(all_137_0, all_125_0) = 0 % 215.97/35.65 | (43) sdtlpdtrp0(xd, all_137_0) = all_125_2 % 215.97/35.65 | % 215.97/35.65 | GROUND_INST: instantiating (mDefSub) with xT, simplifying with (1), (7) gives: % 215.97/35.65 | (44) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aSubsetOf0(v0, xT) = v1) | % 215.97/35.65 | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 215.97/35.65 | aElementOf0(v2, v0) = 0 & aElementOf0(v2, xT) = v3 & $i(v2)) | ? % 215.97/35.65 | [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2)) & ! [v0: $i] : ( ~ % 215.97/35.65 | (aSubsetOf0(v0, xT) = 0) | ~ $i(v0) | (aSet0(v0) = 0 & ! [v1: $i] % 215.97/35.65 | : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, xT) = v2) | ~ % 215.97/35.65 | $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & aElementOf0(v1, v0) = % 215.97/35.65 | v3)))) % 215.97/35.65 | % 215.97/35.65 | ALPHA: (44) implies: % 215.97/35.66 | (45) ! [v0: $i] : ( ~ (aSubsetOf0(v0, xT) = 0) | ~ $i(v0) | (aSet0(v0) = % 215.97/35.66 | 0 & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, xT) % 215.97/35.66 | = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 215.97/35.66 | aElementOf0(v1, v0) = v3)))) % 215.97/35.66 | % 215.97/35.66 | GROUND_INST: instantiating (mCardSub) with xT, 0, simplifying with (2), (7) % 215.97/35.66 | gives: % 215.97/35.66 | (46) ? [v0: any] : ? [v1: $i] : (sbrdtbr0(xT) = v1 & aSet0(xT) = v0 & % 215.97/35.66 | $i(v1) & ( ~ (v0 = 0) | ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 215.97/35.66 | (v4 = 0 | ~ (sbrdtbr0(v2) = v3) | ~ (sdtlseqdt0(v3, v1) = v4) | % 215.97/35.66 | ~ $i(v2) | ? [v5: int] : ( ~ (v5 = 0) & aSubsetOf0(v2, xT) = % 215.97/35.66 | v5)))) % 215.97/35.66 | % 215.97/35.66 | GROUND_INST: instantiating (mDefPtt) with xd, all_123_1, all_125_1, % 215.97/35.66 | simplifying with (8), (39), (40) gives: % 215.97/35.66 | (47) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (aFunction0(xd) = v0 & % 215.97/35.66 | szDzozmdt0(xd) = v2 & aElement0(all_123_1) = v1 & $i(v2) & ( ~ (v1 = % 215.97/35.66 | 0) | ~ (v0 = 0) | ( ! [v3: any] : (v3 = all_125_1 | ~ % 215.97/35.66 | (aSet0(v3) = 0) | ~ $i(v3) | ? [v4: $i] : ? [v5: any] : ? % 215.97/35.66 | [v6: any] : ? [v7: $i] : (sdtlpdtrp0(xd, v4) = v7 & % 215.97/35.66 | aElementOf0(v4, v3) = v5 & aElementOf0(v4, v2) = v6 & $i(v7) % 215.97/35.66 | & $i(v4) & ( ~ (v7 = all_123_1) | ~ (v6 = 0) | ~ (v5 = 0)) % 215.97/35.66 | & (v5 = 0 | (v7 = all_123_1 & v6 = 0)))) & ! [v3: any] : ( % 215.97/35.66 | ~ (aSet0(all_125_1) = v3) | ~ $i(all_125_1) | (v3 = 0 & ! % 215.97/35.66 | [v4: $i] : ! [v5: any] : ( ~ (aElementOf0(v4, v2) = v5) | % 215.97/35.66 | ~ $i(v4) | ? [v6: any] : ? [v7: $i] : (sdtlpdtrp0(xd, % 215.97/35.66 | v4) = v7 & aElementOf0(v4, all_125_1) = v6 & $i(v7) & % 215.97/35.66 | ( ~ (v6 = 0) | (v7 = all_123_1 & v5 = 0)))) & ! [v4: % 215.97/35.66 | $i] : ( ~ (aElementOf0(v4, v2) = 0) | ~ $i(v4) | ? [v5: % 215.97/35.66 | $i] : ? [v6: any] : (sdtlpdtrp0(xd, v4) = v5 & % 215.97/35.66 | aElementOf0(v4, all_125_1) = v6 & $i(v5) & ( ~ (v5 = % 215.97/35.66 | all_123_1) | v6 = 0)))))))) % 215.97/35.66 | % 215.97/35.66 | GROUND_INST: instantiating (mImgRng) with xd, szNzAzT0, all_128_0, simplifying % 215.97/35.66 | with (3), (8), (38) gives: % 215.97/35.66 | (48) ? [v0: int] : ( ~ (v0 = 0) & aFunction0(xd) = v0) | ! [v0: $i] : ! % 215.97/35.66 | [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (sdtlpdtrp0(xd, v0) = v1) | ~ % 215.97/35.66 | (aElementOf0(v1, all_128_0) = v2) | ~ $i(v0) | ? [v3: int] : ( ~ % 215.97/35.66 | (v3 = 0) & aElementOf0(v0, szNzAzT0) = v3)) % 215.97/35.66 | % 215.97/35.66 | GROUND_INST: instantiating (mDirichlet) with xd, all_123_1, all_125_1, % 215.97/35.66 | simplifying with (8), (18), (39) gives: % 215.97/35.66 | (49) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any] % 215.97/35.66 | : ? [v5: any] : ? [v6: any] : (sdtlcdtrc0(xd, v1) = v3 & % 215.97/35.66 | aFunction0(xd) = v0 & szDzozmdt0(xd) = v1 & isCountable0(v1) = v2 & % 215.97/35.66 | isCountable0(all_125_1) = v6 & isFinite0(v3) = v4 & % 215.97/35.66 | aElement0(all_123_1) = v5 & $i(v3) & $i(v1) & ( ~ (v4 = 0) | ~ (v2 % 215.97/35.66 | = 0) | ~ (v0 = 0) | (v6 = 0 & v5 = 0))) % 215.97/35.66 | % 215.97/35.66 | GROUND_INST: instantiating (45) with all_128_0, simplifying with (27), (28) % 215.97/35.66 | gives: % 215.97/35.67 | (50) aSet0(all_128_0) = 0 & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 215.97/35.67 | (aElementOf0(v0, xT) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) % 215.97/35.67 | & aElementOf0(v0, all_128_0) = v2)) % 215.97/35.67 | % 215.97/35.67 | ALPHA: (50) implies: % 215.97/35.67 | (51) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aElementOf0(v0, xT) = v1) | % 215.97/35.67 | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & aElementOf0(v0, all_128_0) % 215.97/35.67 | = v2)) % 215.97/35.67 | % 215.97/35.67 | GROUND_INST: instantiating (51) with all_123_1, all_123_0, simplifying with % 215.97/35.67 | (17), (40) gives: % 215.97/35.67 | (52) all_123_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(all_123_1, % 215.97/35.67 | all_128_0) = v0) % 215.97/35.67 | % 215.97/35.67 | DELTA: instantiating (46) with fresh symbols all_290_0, all_290_1 gives: % 215.97/35.67 | (53) sbrdtbr0(xT) = all_290_0 & aSet0(xT) = all_290_1 & $i(all_290_0) & ( ~ % 215.97/35.67 | (all_290_1 = 0) | ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 % 215.97/35.67 | | ~ (sbrdtbr0(v0) = v1) | ~ (sdtlseqdt0(v1, all_290_0) = v2) | % 215.97/35.67 | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & aSubsetOf0(v0, xT) = % 215.97/35.67 | v3))) % 215.97/35.67 | % 215.97/35.67 | ALPHA: (53) implies: % 215.97/35.67 | (54) aSet0(xT) = all_290_1 % 215.97/35.67 | (55) ~ (all_290_1 = 0) | ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = % 215.97/35.67 | 0 | ~ (sbrdtbr0(v0) = v1) | ~ (sdtlseqdt0(v1, all_290_0) = v2) | % 215.97/35.67 | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & aSubsetOf0(v0, xT) = v3)) % 215.97/35.67 | % 215.97/35.67 | DELTA: instantiating (49) with fresh symbols all_350_0, all_350_1, all_350_2, % 215.97/35.67 | all_350_3, all_350_4, all_350_5, all_350_6 gives: % 215.97/35.67 | (56) sdtlcdtrc0(xd, all_350_5) = all_350_3 & aFunction0(xd) = all_350_6 & % 215.97/35.67 | szDzozmdt0(xd) = all_350_5 & isCountable0(all_350_5) = all_350_4 & % 215.97/35.67 | isCountable0(all_125_1) = all_350_0 & isFinite0(all_350_3) = all_350_2 % 215.97/35.67 | & aElement0(all_123_1) = all_350_1 & $i(all_350_3) & $i(all_350_5) & ( % 215.97/35.67 | ~ (all_350_2 = 0) | ~ (all_350_4 = 0) | ~ (all_350_6 = 0) | % 215.97/35.67 | (all_350_0 = 0 & all_350_1 = 0)) % 215.97/35.67 | % 215.97/35.67 | ALPHA: (56) implies: % 215.97/35.67 | (57) aFunction0(xd) = all_350_6 % 215.97/35.67 | % 215.97/35.67 | DELTA: instantiating (47) with fresh symbols all_464_0, all_464_1, all_464_2 % 215.97/35.67 | gives: % 215.97/35.67 | (58) aFunction0(xd) = all_464_2 & szDzozmdt0(xd) = all_464_0 & % 215.97/35.67 | aElement0(all_123_1) = all_464_1 & $i(all_464_0) & ( ~ (all_464_1 = 0) % 215.97/35.67 | | ~ (all_464_2 = 0) | ( ! [v0: any] : (v0 = all_125_1 | ~ % 215.97/35.67 | (aSet0(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : ? % 215.97/35.67 | [v3: any] : ? [v4: $i] : (sdtlpdtrp0(xd, v1) = v4 & % 215.97/35.67 | aElementOf0(v1, v0) = v2 & aElementOf0(v1, all_464_0) = v3 & % 215.97/35.67 | $i(v4) & $i(v1) & ( ~ (v4 = all_123_1) | ~ (v3 = 0) | ~ (v2 % 215.97/35.67 | = 0)) & (v2 = 0 | (v4 = all_123_1 & v3 = 0)))) & ! [v0: % 215.97/35.67 | any] : ( ~ (aSet0(all_125_1) = v0) | ~ $i(all_125_1) | (v0 = 0 % 215.97/35.67 | & ! [v1: $i] : ! [v2: any] : ( ~ (aElementOf0(v1, all_464_0) % 215.97/35.67 | = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : % 215.97/35.67 | (sdtlpdtrp0(xd, v1) = v4 & aElementOf0(v1, all_125_1) = v3 & % 215.97/35.67 | $i(v4) & ( ~ (v3 = 0) | (v4 = all_123_1 & v2 = 0)))) & ! % 215.97/35.67 | [v1: $i] : ( ~ (aElementOf0(v1, all_464_0) = 0) | ~ $i(v1) | % 215.97/35.67 | ? [v2: $i] : ? [v3: any] : (sdtlpdtrp0(xd, v1) = v2 & % 215.97/35.67 | aElementOf0(v1, all_125_1) = v3 & $i(v2) & ( ~ (v2 = % 215.97/35.67 | all_123_1) | v3 = 0))))))) % 215.97/35.67 | % 215.97/35.67 | ALPHA: (58) implies: % 215.97/35.67 | (59) aFunction0(xd) = all_464_2 % 215.97/35.67 | % 215.97/35.67 | REDUCE: (36), (43) imply: % 215.97/35.68 | (60) sdtlpdtrp0(xd, all_137_0) = all_123_1 % 215.97/35.68 | % 215.97/35.68 | REDUCE: (37), (42) imply: % 215.97/35.68 | (61) aElementOf0(all_137_0, szNzAzT0) = 0 % 215.97/35.68 | % 215.97/35.68 | BETA: splitting (52) gives: % 215.97/35.68 | % 215.97/35.68 | Case 1: % 215.97/35.68 | | % 215.97/35.68 | | (62) all_123_0 = 0 % 215.97/35.68 | | % 215.97/35.68 | | REDUCE: (16), (62) imply: % 215.97/35.68 | | (63) $false % 215.97/35.68 | | % 215.97/35.68 | | CLOSE: (63) is inconsistent. % 215.97/35.68 | | % 215.97/35.68 | Case 2: % 215.97/35.68 | | % 215.97/35.68 | | (64) ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(all_123_1, all_128_0) = % 215.97/35.68 | | v0) % 215.97/35.68 | | % 215.97/35.68 | | DELTA: instantiating (64) with fresh symbol all_488_0 gives: % 215.97/35.68 | | (65) ~ (all_488_0 = 0) & aElementOf0(all_123_1, all_128_0) = all_488_0 % 215.97/35.68 | | % 215.97/35.68 | | ALPHA: (65) implies: % 215.97/35.68 | | (66) ~ (all_488_0 = 0) % 215.97/35.68 | | (67) aElementOf0(all_123_1, all_128_0) = all_488_0 % 215.97/35.68 | | % 215.97/35.68 | | GROUND_INST: instantiating (10) with 0, all_290_1, xT, simplifying with (1), % 215.97/35.68 | | (54) gives: % 215.97/35.68 | | (68) all_290_1 = 0 % 215.97/35.68 | | % 215.97/35.68 | | GROUND_INST: instantiating (12) with 0, all_464_2, xd, simplifying with (4), % 215.97/35.68 | | (59) gives: % 215.97/35.68 | | (69) all_464_2 = 0 % 215.97/35.68 | | % 215.97/35.68 | | GROUND_INST: instantiating (12) with all_350_6, all_464_2, xd, simplifying % 215.97/35.68 | | with (57), (59) gives: % 215.97/35.68 | | (70) all_464_2 = all_350_6 % 215.97/35.68 | | % 215.97/35.68 | | COMBINE_EQS: (69), (70) imply: % 215.97/35.68 | | (71) all_350_6 = 0 % 215.97/35.68 | | % 215.97/35.68 | | BETA: splitting (48) gives: % 215.97/35.68 | | % 215.97/35.68 | | Case 1: % 215.97/35.68 | | | % 215.97/35.68 | | | (72) ? [v0: int] : ( ~ (v0 = 0) & aFunction0(xd) = v0) % 215.97/35.68 | | | % 215.97/35.68 | | | DELTA: instantiating (72) with fresh symbol all_539_0 gives: % 215.97/35.68 | | | (73) ~ (all_539_0 = 0) & aFunction0(xd) = all_539_0 % 215.97/35.68 | | | % 215.97/35.68 | | | ALPHA: (73) implies: % 215.97/35.68 | | | (74) ~ (all_539_0 = 0) % 215.97/35.68 | | | (75) aFunction0(xd) = all_539_0 % 215.97/35.68 | | | % 215.97/35.68 | | | GROUND_INST: instantiating (12) with 0, all_539_0, xd, simplifying with % 215.97/35.68 | | | (4), (75) gives: % 215.97/35.68 | | | (76) all_539_0 = 0 % 215.97/35.68 | | | % 215.97/35.68 | | | REDUCE: (74), (76) imply: % 215.97/35.68 | | | (77) $false % 215.97/35.68 | | | % 215.97/35.68 | | | CLOSE: (77) is inconsistent. % 215.97/35.68 | | | % 215.97/35.68 | | Case 2: % 215.97/35.68 | | | % 215.97/35.68 | | | (78) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 215.97/35.68 | | | (sdtlpdtrp0(xd, v0) = v1) | ~ (aElementOf0(v1, all_128_0) = v2) % 215.97/35.68 | | | | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & aElementOf0(v0, % 215.97/35.68 | | | szNzAzT0) = v3)) % 215.97/35.68 | | | % 215.97/35.68 | | | BETA: splitting (55) gives: % 215.97/35.68 | | | % 215.97/35.68 | | | Case 1: % 215.97/35.68 | | | | % 215.97/35.70 | | | | (79) ~ (all_290_1 = 0) % 215.97/35.70 | | | | % 215.97/35.70 | | | | REDUCE: (68), (79) imply: % 215.97/35.70 | | | | (80) $false % 215.97/35.70 | | | | % 215.97/35.70 | | | | CLOSE: (80) is inconsistent. % 215.97/35.70 | | | | % 215.97/35.70 | | | Case 2: % 215.97/35.70 | | | | % 215.97/35.70 | | | | % 215.97/35.70 | | | | GROUND_INST: instantiating (78) with all_137_0, all_123_1, all_488_0, % 215.97/35.70 | | | | simplifying with (32), (60), (67) gives: % 215.97/35.70 | | | | (81) all_488_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 215.97/35.70 | | | | aElementOf0(all_137_0, szNzAzT0) = v0) % 215.97/35.70 | | | | % 215.97/35.70 | | | | BETA: splitting (81) gives: % 215.97/35.70 | | | | % 215.97/35.70 | | | | Case 1: % 215.97/35.70 | | | | | % 215.97/35.70 | | | | | (82) all_488_0 = 0 % 215.97/35.70 | | | | | % 215.97/35.70 | | | | | REDUCE: (66), (82) imply: % 215.97/35.70 | | | | | (83) $false % 215.97/35.70 | | | | | % 215.97/35.70 | | | | | CLOSE: (83) is inconsistent. % 215.97/35.70 | | | | | % 215.97/35.70 | | | | Case 2: % 215.97/35.70 | | | | | % 215.97/35.70 | | | | | (84) ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(all_137_0, szNzAzT0) % 215.97/35.70 | | | | | = v0) % 215.97/35.70 | | | | | % 215.97/35.70 | | | | | DELTA: instantiating (84) with fresh symbol all_2204_0 gives: % 215.97/35.70 | | | | | (85) ~ (all_2204_0 = 0) & aElementOf0(all_137_0, szNzAzT0) = % 215.97/35.70 | | | | | all_2204_0 % 215.97/35.70 | | | | | % 215.97/35.70 | | | | | ALPHA: (85) implies: % 215.97/35.70 | | | | | (86) ~ (all_2204_0 = 0) % 215.97/35.70 | | | | | (87) aElementOf0(all_137_0, szNzAzT0) = all_2204_0 % 215.97/35.70 | | | | | % 215.97/35.70 | | | | | GROUND_INST: instantiating (14) with 0, all_2204_0, szNzAzT0, % 215.97/35.70 | | | | | all_137_0, simplifying with (61), (87) gives: % 215.97/35.70 | | | | | (88) all_2204_0 = 0 % 215.97/35.70 | | | | | % 215.97/35.70 | | | | | REDUCE: (86), (88) imply: % 215.97/35.70 | | | | | (89) $false % 215.97/35.70 | | | | | % 215.97/35.70 | | | | | CLOSE: (89) is inconsistent. % 215.97/35.70 | | | | | % 215.97/35.70 | | | | End of split % 215.97/35.70 | | | | % 215.97/35.70 | | | End of split % 215.97/35.70 | | | % 215.97/35.70 | | End of split % 215.97/35.70 | | % 215.97/35.70 | End of split % 215.97/35.70 | % 215.97/35.70 End of proof % 215.97/35.70 % SZS output end Proof for theBenchmark % 215.97/35.70 % 215.97/35.70 35058ms %------------------------------------------------------------------------------