%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM584+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 : n001.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 11:48:46 EDT 2023 % Result : Theorem 20.29s 5.17s % Output : Proof 34.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : NUM584+3 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.09/0.33 % Computer : n001.cluster.edu % 0.09/0.33 % Model : x86_64 x86_64 % 0.09/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.33 % Memory : 8042.1875MB % 0.09/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.33 % CPULimit : 300 % 0.09/0.33 % WCLimit : 300 % 0.09/0.33 % DateTime : Fri Aug 25 08:23:58 EDT 2023 % 0.09/0.34 % CPUTime : % 0.18/0.61 ________ _____ % 0.18/0.61 ___ __ \_________(_)________________________________ % 0.18/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.61 % 0.18/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.61 (2023-06-19) % 0.18/0.61 % 0.18/0.61 (c) Philipp Rümmer, 2009-2023 % 0.18/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.61 Amanda Stjerna. % 0.18/0.61 Free software under BSD-3-Clause. % 0.18/0.61 % 0.18/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.61 % 0.18/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.18/0.62 Running up to 7 provers in parallel. % 0.18/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.18/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.18/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.18/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.18/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.18/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.18/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.34/1.87 Prover 4: Preprocessing ... % 5.34/1.88 Prover 1: Preprocessing ... % 5.77/1.98 Prover 3: Preprocessing ... % 5.77/1.98 Prover 5: Preprocessing ... % 5.77/1.98 Prover 2: Preprocessing ... % 5.77/1.98 Prover 0: Preprocessing ... % 5.96/2.00 Prover 6: Preprocessing ... % 17.93/4.82 Prover 3: Constructing countermodel ... % 17.93/4.87 Prover 1: Constructing countermodel ... % 17.93/4.89 Prover 6: Proving ... % 20.29/5.16 Prover 3: proved (4507ms) % 20.29/5.16 % 20.29/5.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 20.29/5.17 % 20.29/5.17 Prover 6: proved (4498ms) % 20.29/5.17 % 20.29/5.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 20.29/5.17 % 20.29/5.19 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 20.29/5.19 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 21.14/5.34 Prover 5: Proving ... % 21.14/5.34 Prover 5: stopped % 21.14/5.38 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 21.53/5.72 Prover 8: Preprocessing ... % 21.53/5.79 Prover 7: Preprocessing ... % 22.31/5.85 Prover 10: Preprocessing ... % 24.59/6.06 Prover 1: Found proof (size 47) % 24.59/6.06 Prover 1: proved (5419ms) % 24.59/6.06 Prover 7: stopped % 24.59/6.07 Prover 10: stopped % 25.62/6.19 Prover 2: Proving ... % 25.76/6.21 Prover 2: stopped % 26.89/6.67 Prover 8: Warning: ignoring some quantifiers % 26.89/6.69 Prover 8: Constructing countermodel ... % 28.44/6.73 Prover 8: stopped % 31.01/7.36 Prover 4: Constructing countermodel ... % 31.37/7.43 Prover 4: stopped % 33.60/7.84 Prover 0: Proving ... % 33.60/7.86 Prover 0: stopped % 33.60/7.86 % 33.60/7.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 33.60/7.86 % 33.98/7.88 % SZS output start Proof for theBenchmark % 33.98/7.88 Assumptions after simplification: % 33.98/7.88 --------------------------------- % 33.98/7.88 % 33.98/7.88 (m__) % 34.15/7.93 $i(xQ) & $i(xi) & $i(xN) & $i(xS) & $i(xK) & ? [v0: $i] : ? [v1: $i] : ? % 34.15/7.93 [v2: $i] : ? [v3: any] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ( ~ (v6 = % 34.15/7.93 0) & sdtlpdtrp0(xN, xi) = v0 & slbdtsldtrb0(xS, xK) = v5 & szmzizndt0(v0) % 34.15/7.93 = v1 & sbrdtbr0(v2) = v4 & sdtpldt0(xQ, v1) = v2 & aSubsetOf0(v2, xS) = v3 & % 34.15/7.93 aSet0(v2) = 0 & aElementOf0(v2, v5) = v6 & aElementOf0(v1, v0) = 0 & $i(v5) % 34.15/7.93 & $i(v4) & $i(v2) & $i(v1) & $i(v0) & ! [v7: $i] : ! [v8: int] : (v8 = 0 | % 34.15/7.93 ~ (sdtlseqdt0(v1, v7) = v8) | ~ $i(v7) | ? [v9: int] : ( ~ (v9 = 0) & % 34.15/7.93 aElementOf0(v7, v0) = v9)) & ! [v7: $i] : ! [v8: int] : (v8 = 0 | ~ % 34.15/7.93 (aElementOf0(v7, v2) = v8) | ~ $i(v7) | ? [v9: any] : ? [v10: any] : % 34.15/7.93 (aElement0(v7) = v9 & aElementOf0(v7, xQ) = v10 & ( ~ (v9 = 0) | ( ~ (v10 % 34.15/7.93 = 0) & ~ (v7 = v1))))) & ! [v7: $i] : ( ~ (aElementOf0(v7, v2) = % 34.15/7.93 0) | ~ $i(v7) | ? [v8: any] : (aElement0(v7) = 0 & aElementOf0(v7, xQ) % 34.15/7.93 = v8 & (v8 = 0 | v7 = v1))) & ( ~ (v4 = xK) | ( ~ (v3 = 0) & ? [v7: $i] % 34.15/7.93 : ? [v8: int] : ( ~ (v8 = 0) & aElementOf0(v7, v2) = 0 & % 34.15/7.93 aElementOf0(v7, xS) = v8 & $i(v7))))) % 34.15/7.93 % 34.15/7.93 (m__3989_02) % 34.15/7.94 $i(xQ) & $i(xi) & $i(xN) & $i(xk) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 34.15/7.94 ? [v3: $i] : (sdtlpdtrp0(xN, xi) = v0 & slbdtsldtrb0(v2, xk) = v3 & % 34.15/7.94 szmzizndt0(v0) = v1 & sbrdtbr0(xQ) = xk & sdtmndt0(v0, v1) = v2 & % 34.15/7.94 aSubsetOf0(xQ, v2) = 0 & aSet0(v2) = 0 & aSet0(xQ) = 0 & aElementOf0(v1, v0) % 34.15/7.94 = 0 & aElementOf0(xQ, v3) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: % 34.15/7.94 $i] : ! [v5: int] : (v5 = 0 | v4 = v1 | ~ (aElementOf0(v4, v2) = v5) | % 34.15/7.94 ~ $i(v4) | ? [v6: any] : ? [v7: any] : (aElement0(v4) = v6 & % 34.15/7.94 aElementOf0(v4, v0) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v4: $i] : % 34.15/7.94 ! [v5: int] : (v5 = 0 | ~ (sdtlseqdt0(v1, v4) = v5) | ~ $i(v4) | ? [v6: % 34.15/7.94 int] : ( ~ (v6 = 0) & aElementOf0(v4, v0) = v6)) & ! [v4: $i] : ! [v5: % 34.15/7.94 int] : (v5 = 0 | ~ (aElementOf0(v4, v2) = v5) | ~ $i(v4) | ? [v6: int] % 34.15/7.94 : ( ~ (v6 = 0) & aElementOf0(v4, xQ) = v6)) & ! [v4: $i] : ( ~ % 34.15/7.95 (aElementOf0(v4, v2) = 0) | ~ $i(v4) | ( ~ (v4 = v1) & aElement0(v4) = 0 % 34.15/7.95 & aElementOf0(v4, v0) = 0))) % 34.15/7.95 % 34.15/7.95 (m__4007) % 34.15/7.95 $i(xQ) & $i(xi) & $i(xN) & $i(xK) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 34.15/7.95 (sdtlpdtrp0(xN, xi) = v0 & szmzizndt0(v0) = v1 & sbrdtbr0(v2) = xK & % 34.15/7.95 sdtpldt0(xQ, v1) = v2 & aSet0(v2) = 0 & aElementOf0(v1, v0) = 0 & $i(v2) & % 34.15/7.95 $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (sdtlseqdt0(v1, % 34.15/7.95 v3) = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = 0) & aElementOf0(v3, % 34.15/7.95 v0) = v5)) & ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ % 34.15/7.95 (aElementOf0(v3, v2) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: any] : % 34.15/7.95 (aElement0(v3) = v5 & aElementOf0(v3, xQ) = v6 & ( ~ (v5 = 0) | ( ~ (v6 = % 34.15/7.95 0) & ~ (v3 = v1))))) & ! [v3: $i] : ( ~ (aElementOf0(v3, v2) = % 34.15/7.95 0) | ~ $i(v3) | ? [v4: any] : (aElement0(v3) = 0 & aElementOf0(v3, xQ) % 34.15/7.95 = v4 & (v4 = 0 | v3 = v1)))) % 34.15/7.95 % 34.15/7.95 (m__4024) % 34.15/7.96 $i(xQ) & $i(xi) & $i(xN) & $i(xS) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 34.15/7.96 (sdtlpdtrp0(xN, xi) = v0 & szmzizndt0(v0) = v1 & sdtpldt0(xQ, v1) = v2 & % 34.15/7.96 aSubsetOf0(v2, xS) = 0 & aSet0(v2) = 0 & aElementOf0(v1, v0) = 0 & $i(v2) & % 34.15/7.96 $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (sdtlseqdt0(v1, % 34.15/7.96 v3) = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = 0) & aElementOf0(v3, % 34.15/7.96 v0) = v5)) & ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ % 34.15/7.96 (aElementOf0(v3, v2) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: any] : % 34.15/7.96 (aElement0(v3) = v5 & aElementOf0(v3, xQ) = v6 & ( ~ (v5 = 0) | ( ~ (v6 = % 34.15/7.96 0) & ~ (v3 = v1))))) & ! [v3: $i] : ( ~ (aElementOf0(v3, v2) = % 34.15/7.96 0) | ~ $i(v3) | aElementOf0(v3, xS) = 0) & ! [v3: $i] : ( ~ % 34.15/7.96 (aElementOf0(v3, v2) = 0) | ~ $i(v3) | ? [v4: any] : (aElement0(v3) = 0 % 34.15/7.96 & aElementOf0(v3, xQ) = v4 & (v4 = 0 | v3 = v1)))) % 34.15/7.96 % 34.15/7.96 (function-axioms) % 34.15/7.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 34.15/7.97 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 34.15/7.97 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 34.15/7.97 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 34.15/7.97 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 34.15/7.97 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 34.15/7.97 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 34.15/7.97 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 34.15/7.97 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: MultipleValueBool] % 34.15/7.97 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 34.15/7.97 (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! [v0: % 34.15/7.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 34.15/7.97 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & ! % 34.15/7.97 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 34.15/7.97 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! % 34.15/7.97 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | % 34.15/7.97 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 34.15/7.97 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 34.15/7.97 (aSubsetOf0(v3, v2) = v1) | ~ (aSubsetOf0(v3, v2) = v0)) & ! [v0: % 34.15/7.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 34.15/7.97 : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) & % 34.15/7.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 34.15/7.97 ~ (szDzizrdt0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 34.15/7.97 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aFunction0(v2) = v1) | ~ % 34.15/7.97 (aFunction0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 34.15/7.97 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 34.15/7.97 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 34.15/7.97 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 34.15/7.97 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 34.15/7.97 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 34.15/7.97 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 34.15/7.97 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 34.15/7.97 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 34.15/7.97 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 34.15/7.97 $i] : (v1 = v0 | ~ (isCountable0(v2) = v1) | ~ (isCountable0(v2) = v0)) & % 34.15/7.97 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = % 34.15/7.97 v0 | ~ (isFinite0(v2) = v1) | ~ (isFinite0(v2) = v0)) & ! [v0: % 34.15/7.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 34.15/7.97 ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 34.15/7.97 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) | % 34.15/7.97 ~ (aElement0(v2) = v0)) % 34.15/7.97 % 34.15/7.97 Further assumptions not needed in the proof: % 34.15/7.98 -------------------------------------------- % 34.15/7.98 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 34.15/7.98 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 34.15/7.98 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, % 34.15/7.98 mDefSeg, mDefSel, mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, % 34.15/7.98 mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, % 34.15/7.98 mImgCount, mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, % 34.15/7.98 mLessTotal, mLessTrans, mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, % 34.15/7.98 mPttSet, mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, % 34.15/7.98 mSelNSet, mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans, % 34.15/7.98 mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__3291, m__3398, % 34.15/7.98 m__3418, m__3435, m__3453, m__3462, m__3520, m__3533, m__3623, m__3671, m__3754, % 34.15/7.98 m__3821, m__3989 % 34.15/7.98 % 34.15/7.98 Those formulas are unsatisfiable: % 34.15/7.98 --------------------------------- % 34.15/7.98 % 34.15/7.98 Begin of proof % 34.15/7.98 | % 34.15/7.98 | ALPHA: (m__3989_02) implies: % 34.15/7.99 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtlpdtrp0(xN, % 34.15/7.99 | xi) = v0 & slbdtsldtrb0(v2, xk) = v3 & szmzizndt0(v0) = v1 & % 34.15/7.99 | sbrdtbr0(xQ) = xk & sdtmndt0(v0, v1) = v2 & aSubsetOf0(xQ, v2) = 0 & % 34.15/7.99 | aSet0(v2) = 0 & aSet0(xQ) = 0 & aElementOf0(v1, v0) = 0 & % 34.15/7.99 | aElementOf0(xQ, v3) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: % 34.15/7.99 | $i] : ! [v5: int] : (v5 = 0 | v4 = v1 | ~ (aElementOf0(v4, v2) = % 34.15/7.99 | v5) | ~ $i(v4) | ? [v6: any] : ? [v7: any] : (aElement0(v4) = % 34.15/7.99 | v6 & aElementOf0(v4, v0) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & % 34.15/7.99 | ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (sdtlseqdt0(v1, v4) = v5) | % 34.15/7.99 | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & aElementOf0(v4, v0) = v6)) % 34.15/7.99 | & ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (aElementOf0(v4, v2) = % 34.15/7.99 | v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & aElementOf0(v4, % 34.15/7.99 | xQ) = v6)) & ! [v4: $i] : ( ~ (aElementOf0(v4, v2) = 0) | ~ % 34.15/7.99 | $i(v4) | ( ~ (v4 = v1) & aElement0(v4) = 0 & aElementOf0(v4, v0) = % 34.15/7.99 | 0))) % 34.15/7.99 | % 34.15/7.99 | ALPHA: (m__4007) implies: % 34.15/7.99 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtlpdtrp0(xN, xi) = v0 & % 34.15/7.99 | szmzizndt0(v0) = v1 & sbrdtbr0(v2) = xK & sdtpldt0(xQ, v1) = v2 & % 34.15/7.99 | aSet0(v2) = 0 & aElementOf0(v1, v0) = 0 & $i(v2) & $i(v1) & $i(v0) & % 34.15/7.99 | ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (sdtlseqdt0(v1, v3) = v4) | % 34.15/7.99 | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = 0) & aElementOf0(v3, v0) = v5)) % 34.15/7.99 | & ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (aElementOf0(v3, v2) = % 34.15/7.99 | v4) | ~ $i(v3) | ? [v5: any] : ? [v6: any] : (aElement0(v3) = % 34.15/7.99 | v5 & aElementOf0(v3, xQ) = v6 & ( ~ (v5 = 0) | ( ~ (v6 = 0) & ~ % 34.15/7.99 | (v3 = v1))))) & ! [v3: $i] : ( ~ (aElementOf0(v3, v2) = 0) | % 34.15/7.99 | ~ $i(v3) | ? [v4: any] : (aElement0(v3) = 0 & aElementOf0(v3, xQ) % 34.15/7.99 | = v4 & (v4 = 0 | v3 = v1)))) % 34.15/7.99 | % 34.15/7.99 | ALPHA: (m__4024) implies: % 34.15/8.00 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtlpdtrp0(xN, xi) = v0 & % 34.15/8.00 | szmzizndt0(v0) = v1 & sdtpldt0(xQ, v1) = v2 & aSubsetOf0(v2, xS) = 0 % 34.15/8.00 | & aSet0(v2) = 0 & aElementOf0(v1, v0) = 0 & $i(v2) & $i(v1) & $i(v0) % 34.15/8.00 | & ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (sdtlseqdt0(v1, v3) = v4) % 34.15/8.00 | | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = 0) & aElementOf0(v3, v0) = % 34.15/8.00 | v5)) & ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (aElementOf0(v3, % 34.15/8.00 | v2) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: any] : % 34.15/8.00 | (aElement0(v3) = v5 & aElementOf0(v3, xQ) = v6 & ( ~ (v5 = 0) | ( ~ % 34.15/8.00 | (v6 = 0) & ~ (v3 = v1))))) & ! [v3: $i] : ( ~ % 34.15/8.00 | (aElementOf0(v3, v2) = 0) | ~ $i(v3) | aElementOf0(v3, xS) = 0) & % 34.15/8.00 | ! [v3: $i] : ( ~ (aElementOf0(v3, v2) = 0) | ~ $i(v3) | ? [v4: any] % 34.15/8.00 | : (aElement0(v3) = 0 & aElementOf0(v3, xQ) = v4 & (v4 = 0 | v3 = % 34.15/8.00 | v1)))) % 34.15/8.00 | % 34.15/8.00 | ALPHA: (m__) implies: % 34.15/8.00 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: $i] : % 34.15/8.00 | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & sdtlpdtrp0(xN, xi) = v0 & % 34.15/8.00 | slbdtsldtrb0(xS, xK) = v5 & szmzizndt0(v0) = v1 & sbrdtbr0(v2) = v4 & % 34.15/8.00 | sdtpldt0(xQ, v1) = v2 & aSubsetOf0(v2, xS) = v3 & aSet0(v2) = 0 & % 34.15/8.00 | aElementOf0(v2, v5) = v6 & aElementOf0(v1, v0) = 0 & $i(v5) & $i(v4) % 34.15/8.00 | & $i(v2) & $i(v1) & $i(v0) & ! [v7: $i] : ! [v8: int] : (v8 = 0 | % 34.15/8.00 | ~ (sdtlseqdt0(v1, v7) = v8) | ~ $i(v7) | ? [v9: int] : ( ~ (v9 = % 34.15/8.00 | 0) & aElementOf0(v7, v0) = v9)) & ! [v7: $i] : ! [v8: int] : % 34.15/8.00 | (v8 = 0 | ~ (aElementOf0(v7, v2) = v8) | ~ $i(v7) | ? [v9: any] : % 34.15/8.00 | ? [v10: any] : (aElement0(v7) = v9 & aElementOf0(v7, xQ) = v10 & ( % 34.15/8.00 | ~ (v9 = 0) | ( ~ (v10 = 0) & ~ (v7 = v1))))) & ! [v7: $i] : ( % 34.15/8.01 | ~ (aElementOf0(v7, v2) = 0) | ~ $i(v7) | ? [v8: any] : % 34.15/8.01 | (aElement0(v7) = 0 & aElementOf0(v7, xQ) = v8 & (v8 = 0 | v7 = % 34.15/8.01 | v1))) & ( ~ (v4 = xK) | ( ~ (v3 = 0) & ? [v7: $i] : ? [v8: % 34.15/8.01 | int] : ( ~ (v8 = 0) & aElementOf0(v7, v2) = 0 & aElementOf0(v7, % 34.15/8.01 | xS) = v8 & $i(v7))))) % 34.15/8.01 | % 34.15/8.01 | ALPHA: (function-axioms) implies: % 34.15/8.01 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sbrdtbr0(v2) = % 34.15/8.01 | v1) | ~ (sbrdtbr0(v2) = v0)) % 34.15/8.01 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) % 34.15/8.01 | = v1) | ~ (szmzizndt0(v2) = v0)) % 34.15/8.01 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 34.15/8.01 | ! [v3: $i] : (v1 = v0 | ~ (aSubsetOf0(v3, v2) = v1) | ~ % 34.15/8.01 | (aSubsetOf0(v3, v2) = v0)) % 34.15/8.01 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 34.15/8.01 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 34.15/8.01 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 34.15/8.01 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) % 34.15/8.01 | % 34.15/8.01 | DELTA: instantiating (2) with fresh symbols all_70_0, all_70_1, all_70_2 % 34.15/8.01 | gives: % 34.15/8.02 | (10) sdtlpdtrp0(xN, xi) = all_70_2 & szmzizndt0(all_70_2) = all_70_1 & % 34.15/8.02 | sbrdtbr0(all_70_0) = xK & sdtpldt0(xQ, all_70_1) = all_70_0 & % 34.15/8.02 | aSet0(all_70_0) = 0 & aElementOf0(all_70_1, all_70_2) = 0 & % 34.15/8.02 | $i(all_70_0) & $i(all_70_1) & $i(all_70_2) & ! [v0: $i] : ! [v1: % 34.15/8.02 | int] : (v1 = 0 | ~ (sdtlseqdt0(all_70_1, v0) = v1) | ~ $i(v0) | ? % 34.15/8.02 | [v2: int] : ( ~ (v2 = 0) & aElementOf0(v0, all_70_2) = v2)) & ! % 34.15/8.02 | [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aElementOf0(v0, all_70_0) = % 34.15/8.02 | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (aElement0(v0) = % 34.15/8.02 | v2 & aElementOf0(v0, xQ) = v3 & ( ~ (v2 = 0) | ( ~ (v3 = 0) & ~ % 34.15/8.02 | (v0 = all_70_1))))) & ! [v0: $i] : ( ~ (aElementOf0(v0, % 34.15/8.02 | all_70_0) = 0) | ~ $i(v0) | ? [v1: any] : (aElement0(v0) = 0 & % 34.15/8.02 | aElementOf0(v0, xQ) = v1 & (v1 = 0 | v0 = all_70_1))) % 34.15/8.02 | % 34.15/8.02 | ALPHA: (10) implies: % 34.15/8.02 | (11) sdtpldt0(xQ, all_70_1) = all_70_0 % 34.15/8.02 | (12) sbrdtbr0(all_70_0) = xK % 34.15/8.02 | (13) szmzizndt0(all_70_2) = all_70_1 % 34.15/8.02 | (14) sdtlpdtrp0(xN, xi) = all_70_2 % 34.15/8.02 | % 34.15/8.02 | DELTA: instantiating (3) with fresh symbols all_73_0, all_73_1, all_73_2 % 34.15/8.02 | gives: % 34.15/8.03 | (15) sdtlpdtrp0(xN, xi) = all_73_2 & szmzizndt0(all_73_2) = all_73_1 & % 34.15/8.03 | sdtpldt0(xQ, all_73_1) = all_73_0 & aSubsetOf0(all_73_0, xS) = 0 & % 34.15/8.03 | aSet0(all_73_0) = 0 & aElementOf0(all_73_1, all_73_2) = 0 & % 34.15/8.03 | $i(all_73_0) & $i(all_73_1) & $i(all_73_2) & ! [v0: $i] : ! [v1: % 34.15/8.03 | int] : (v1 = 0 | ~ (sdtlseqdt0(all_73_1, v0) = v1) | ~ $i(v0) | ? % 34.15/8.03 | [v2: int] : ( ~ (v2 = 0) & aElementOf0(v0, all_73_2) = v2)) & ! % 34.15/8.03 | [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aElementOf0(v0, all_73_0) = % 34.15/8.03 | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (aElement0(v0) = % 34.15/8.03 | v2 & aElementOf0(v0, xQ) = v3 & ( ~ (v2 = 0) | ( ~ (v3 = 0) & ~ % 34.15/8.03 | (v0 = all_73_1))))) & ! [v0: $i] : ( ~ (aElementOf0(v0, % 34.15/8.03 | all_73_0) = 0) | ~ $i(v0) | aElementOf0(v0, xS) = 0) & ! [v0: % 34.15/8.03 | $i] : ( ~ (aElementOf0(v0, all_73_0) = 0) | ~ $i(v0) | ? [v1: any] % 34.15/8.03 | : (aElement0(v0) = 0 & aElementOf0(v0, xQ) = v1 & (v1 = 0 | v0 = % 34.15/8.03 | all_73_1))) % 34.15/8.03 | % 34.15/8.03 | ALPHA: (15) implies: % 34.15/8.03 | (16) aSubsetOf0(all_73_0, xS) = 0 % 34.15/8.03 | (17) sdtpldt0(xQ, all_73_1) = all_73_0 % 34.15/8.03 | (18) szmzizndt0(all_73_2) = all_73_1 % 34.15/8.03 | (19) sdtlpdtrp0(xN, xi) = all_73_2 % 34.15/8.03 | % 34.15/8.03 | DELTA: instantiating (1) with fresh symbols all_76_0, all_76_1, all_76_2, % 34.15/8.03 | all_76_3 gives: % 34.15/8.03 | (20) sdtlpdtrp0(xN, xi) = all_76_3 & slbdtsldtrb0(all_76_1, xk) = all_76_0 % 34.15/8.03 | & szmzizndt0(all_76_3) = all_76_2 & sbrdtbr0(xQ) = xk & % 34.15/8.03 | sdtmndt0(all_76_3, all_76_2) = all_76_1 & aSubsetOf0(xQ, all_76_1) = 0 % 34.15/8.03 | & aSet0(all_76_1) = 0 & aSet0(xQ) = 0 & aElementOf0(all_76_2, % 34.15/8.03 | all_76_3) = 0 & aElementOf0(xQ, all_76_0) = 0 & $i(all_76_0) & % 34.15/8.03 | $i(all_76_1) & $i(all_76_2) & $i(all_76_3) & ! [v0: any] : ! [v1: % 34.15/8.03 | int] : (v1 = 0 | v0 = all_76_2 | ~ (aElementOf0(v0, all_76_1) = v1) % 34.15/8.04 | | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (aElement0(v0) = v2 & % 34.15/8.04 | aElementOf0(v0, all_76_3) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & % 34.15/8.04 | ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (sdtlseqdt0(all_76_2, v0) = % 34.15/8.04 | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & aElementOf0(v0, % 34.15/8.04 | all_76_3) = v2)) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 34.15/8.04 | (aElementOf0(v0, all_76_1) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ % 34.15/8.04 | (v2 = 0) & aElementOf0(v0, xQ) = v2)) & ! [v0: $i] : ( ~ % 34.15/8.04 | (aElementOf0(v0, all_76_1) = 0) | ~ $i(v0) | ( ~ (v0 = all_76_2) & % 34.15/8.04 | aElement0(v0) = 0 & aElementOf0(v0, all_76_3) = 0)) % 34.15/8.04 | % 34.15/8.04 | ALPHA: (20) implies: % 34.15/8.04 | (21) szmzizndt0(all_76_3) = all_76_2 % 34.15/8.04 | (22) sdtlpdtrp0(xN, xi) = all_76_3 % 34.15/8.04 | % 34.15/8.04 | DELTA: instantiating (4) with fresh symbols all_79_0, all_79_1, all_79_2, % 34.15/8.04 | all_79_3, all_79_4, all_79_5, all_79_6 gives: % 34.15/8.04 | (23) ~ (all_79_0 = 0) & sdtlpdtrp0(xN, xi) = all_79_6 & slbdtsldtrb0(xS, % 34.15/8.04 | xK) = all_79_1 & szmzizndt0(all_79_6) = all_79_5 & % 34.15/8.04 | sbrdtbr0(all_79_4) = all_79_2 & sdtpldt0(xQ, all_79_5) = all_79_4 & % 34.15/8.04 | aSubsetOf0(all_79_4, xS) = all_79_3 & aSet0(all_79_4) = 0 & % 34.15/8.04 | aElementOf0(all_79_4, all_79_1) = all_79_0 & aElementOf0(all_79_5, % 34.15/8.04 | all_79_6) = 0 & $i(all_79_1) & $i(all_79_2) & $i(all_79_4) & % 34.15/8.04 | $i(all_79_5) & $i(all_79_6) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | % 34.15/8.04 | ~ (sdtlseqdt0(all_79_5, v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ % 34.15/8.04 | (v2 = 0) & aElementOf0(v0, all_79_6) = v2)) & ! [v0: $i] : ! % 34.15/8.04 | [v1: int] : (v1 = 0 | ~ (aElementOf0(v0, all_79_4) = v1) | ~ $i(v0) % 34.15/8.04 | | ? [v2: any] : ? [v3: any] : (aElement0(v0) = v2 & % 34.15/8.04 | aElementOf0(v0, xQ) = v3 & ( ~ (v2 = 0) | ( ~ (v3 = 0) & ~ (v0 = % 34.15/8.04 | all_79_5))))) & ! [v0: $i] : ( ~ (aElementOf0(v0, all_79_4) % 34.15/8.04 | = 0) | ~ $i(v0) | ? [v1: any] : (aElement0(v0) = 0 & % 34.15/8.04 | aElementOf0(v0, xQ) = v1 & (v1 = 0 | v0 = all_79_5))) & ( ~ % 34.15/8.04 | (all_79_2 = xK) | ( ~ (all_79_3 = 0) & ? [v0: $i] : ? [v1: int] : % 34.15/8.04 | ( ~ (v1 = 0) & aElementOf0(v0, all_79_4) = 0 & aElementOf0(v0, xS) % 34.15/8.04 | = v1 & $i(v0)))) % 34.15/8.05 | % 34.15/8.05 | ALPHA: (23) implies: % 34.15/8.05 | (24) aSubsetOf0(all_79_4, xS) = all_79_3 % 34.15/8.05 | (25) sdtpldt0(xQ, all_79_5) = all_79_4 % 34.15/8.05 | (26) sbrdtbr0(all_79_4) = all_79_2 % 34.15/8.05 | (27) szmzizndt0(all_79_6) = all_79_5 % 34.15/8.05 | (28) sdtlpdtrp0(xN, xi) = all_79_6 % 34.15/8.05 | (29) ~ (all_79_2 = xK) | ( ~ (all_79_3 = 0) & ? [v0: $i] : ? [v1: int] : % 34.15/8.05 | ( ~ (v1 = 0) & aElementOf0(v0, all_79_4) = 0 & aElementOf0(v0, xS) = % 34.15/8.05 | v1 & $i(v0))) % 34.15/8.05 | % 34.15/8.05 | GROUND_INST: instantiating (9) with all_73_2, all_76_3, xi, xN, simplifying % 34.15/8.05 | with (19), (22) gives: % 34.15/8.05 | (30) all_76_3 = all_73_2 % 34.15/8.05 | % 34.15/8.05 | GROUND_INST: instantiating (9) with all_76_3, all_79_6, xi, xN, simplifying % 34.15/8.05 | with (22), (28) gives: % 34.15/8.05 | (31) all_79_6 = all_76_3 % 34.15/8.05 | % 34.15/8.05 | GROUND_INST: instantiating (9) with all_70_2, all_79_6, xi, xN, simplifying % 34.15/8.05 | with (14), (28) gives: % 34.15/8.05 | (32) all_79_6 = all_70_2 % 34.15/8.05 | % 34.15/8.05 | COMBINE_EQS: (31), (32) imply: % 34.15/8.05 | (33) all_76_3 = all_70_2 % 34.15/8.05 | % 34.15/8.05 | SIMP: (33) implies: % 34.15/8.05 | (34) all_76_3 = all_70_2 % 34.15/8.05 | % 34.15/8.05 | COMBINE_EQS: (30), (34) imply: % 34.15/8.05 | (35) all_73_2 = all_70_2 % 34.15/8.05 | % 34.15/8.05 | SIMP: (35) implies: % 34.15/8.05 | (36) all_73_2 = all_70_2 % 34.15/8.05 | % 34.15/8.05 | REDUCE: (27), (32) imply: % 34.15/8.05 | (37) szmzizndt0(all_70_2) = all_79_5 % 34.15/8.05 | % 34.15/8.05 | REDUCE: (21), (34) imply: % 34.15/8.06 | (38) szmzizndt0(all_70_2) = all_76_2 % 34.15/8.06 | % 34.15/8.06 | REDUCE: (18), (36) imply: % 34.15/8.06 | (39) szmzizndt0(all_70_2) = all_73_1 % 34.15/8.06 | % 34.15/8.06 | GROUND_INST: instantiating (6) with all_70_1, all_76_2, all_70_2, simplifying % 34.15/8.06 | with (13), (38) gives: % 34.15/8.06 | (40) all_76_2 = all_70_1 % 34.15/8.06 | % 34.15/8.06 | GROUND_INST: instantiating (6) with all_76_2, all_79_5, all_70_2, simplifying % 34.15/8.06 | with (37), (38) gives: % 34.15/8.06 | (41) all_79_5 = all_76_2 % 34.15/8.06 | % 34.15/8.06 | GROUND_INST: instantiating (6) with all_73_1, all_79_5, all_70_2, simplifying % 34.15/8.06 | with (37), (39) gives: % 34.15/8.06 | (42) all_79_5 = all_73_1 % 34.15/8.06 | % 34.15/8.06 | COMBINE_EQS: (41), (42) imply: % 34.15/8.06 | (43) all_76_2 = all_73_1 % 34.15/8.06 | % 34.15/8.06 | SIMP: (43) implies: % 34.15/8.06 | (44) all_76_2 = all_73_1 % 34.15/8.06 | % 34.15/8.06 | COMBINE_EQS: (40), (44) imply: % 34.15/8.06 | (45) all_73_1 = all_70_1 % 34.15/8.06 | % 34.15/8.06 | COMBINE_EQS: (42), (45) imply: % 34.15/8.06 | (46) all_79_5 = all_70_1 % 34.15/8.06 | % 34.15/8.06 | REDUCE: (25), (46) imply: % 34.15/8.06 | (47) sdtpldt0(xQ, all_70_1) = all_79_4 % 34.15/8.06 | % 34.15/8.06 | REDUCE: (17), (45) imply: % 34.15/8.06 | (48) sdtpldt0(xQ, all_70_1) = all_73_0 % 34.15/8.06 | % 34.15/8.06 | GROUND_INST: instantiating (8) with all_70_0, all_79_4, all_70_1, xQ, % 34.15/8.06 | simplifying with (11), (47) gives: % 34.15/8.06 | (49) all_79_4 = all_70_0 % 34.15/8.06 | % 34.15/8.06 | GROUND_INST: instantiating (8) with all_73_0, all_79_4, all_70_1, xQ, % 34.15/8.06 | simplifying with (47), (48) gives: % 34.15/8.06 | (50) all_79_4 = all_73_0 % 34.15/8.06 | % 34.15/8.06 | COMBINE_EQS: (49), (50) imply: % 34.15/8.06 | (51) all_73_0 = all_70_0 % 34.15/8.06 | % 34.15/8.06 | REDUCE: (26), (49) imply: % 34.15/8.06 | (52) sbrdtbr0(all_70_0) = all_79_2 % 34.15/8.06 | % 34.15/8.06 | REDUCE: (24), (49) imply: % 34.15/8.06 | (53) aSubsetOf0(all_70_0, xS) = all_79_3 % 34.15/8.06 | % 34.15/8.06 | REDUCE: (16), (51) imply: % 34.15/8.06 | (54) aSubsetOf0(all_70_0, xS) = 0 % 34.15/8.06 | % 34.15/8.07 | GROUND_INST: instantiating (7) with 0, all_79_3, xS, all_70_0, simplifying % 34.15/8.07 | with (53), (54) gives: % 34.15/8.07 | (55) all_79_3 = 0 % 34.15/8.07 | % 34.15/8.07 | GROUND_INST: instantiating (5) with xK, all_79_2, all_70_0, simplifying with % 34.15/8.07 | (12), (52) gives: % 34.15/8.07 | (56) all_79_2 = xK % 34.15/8.07 | % 34.15/8.07 | BETA: splitting (29) gives: % 34.15/8.07 | % 34.15/8.07 | Case 1: % 34.15/8.07 | | % 34.15/8.07 | | (57) ~ (all_79_2 = xK) % 34.15/8.07 | | % 34.15/8.07 | | REDUCE: (56), (57) imply: % 34.15/8.07 | | (58) $false % 34.15/8.07 | | % 34.15/8.07 | | CLOSE: (58) is inconsistent. % 34.15/8.07 | | % 34.15/8.07 | Case 2: % 34.15/8.07 | | % 34.15/8.07 | | (59) ~ (all_79_3 = 0) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 34.15/8.07 | | aElementOf0(v0, all_79_4) = 0 & aElementOf0(v0, xS) = v1 & $i(v0)) % 34.15/8.07 | | % 34.15/8.07 | | ALPHA: (59) implies: % 34.15/8.07 | | (60) ~ (all_79_3 = 0) % 34.15/8.07 | | % 34.15/8.07 | | REDUCE: (55), (60) imply: % 34.15/8.07 | | (61) $false % 34.15/8.07 | | % 34.15/8.07 | | CLOSE: (61) is inconsistent. % 34.15/8.07 | | % 34.15/8.07 | End of split % 34.15/8.07 | % 34.15/8.07 End of proof % 34.15/8.07 % SZS output end Proof for theBenchmark % 34.15/8.07 % 34.15/8.07 7462ms %------------------------------------------------------------------------------