%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM606+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 : n020.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 11:48:55 EDT 2023 % Result : Theorem 48.64s 7.42s % Output : Proof 63.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : NUM606+3 : 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 : n020.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 16:52:15 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 ... % 0.20/0.64 Running up to 7 provers in parallel. % 0.20/0.65 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 % 6.43/1.68 Prover 1: Preprocessing ... % 6.43/1.69 Prover 4: Preprocessing ... % 6.43/1.71 Prover 5: Preprocessing ... % 6.43/1.71 Prover 6: Preprocessing ... % 6.43/1.71 Prover 0: Preprocessing ... % 6.43/1.71 Prover 3: Preprocessing ... % 6.43/1.71 Prover 2: Preprocessing ... % 19.72/3.49 Prover 1: Constructing countermodel ... % 20.51/3.50 Prover 3: Constructing countermodel ... % 20.51/3.55 Prover 6: Proving ... % 24.90/4.16 Prover 5: Proving ... % 48.64/7.34 Prover 4: Constructing countermodel ... % 48.64/7.40 Prover 3: proved (6748ms) % 48.64/7.40 % 48.64/7.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 48.64/7.42 % 49.89/7.43 Prover 5: stopped % 49.89/7.44 Prover 6: stopped % 49.89/7.46 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 49.89/7.46 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 49.89/7.47 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 52.17/7.74 Prover 10: Preprocessing ... % 52.90/7.78 Prover 7: Preprocessing ... % 53.02/7.79 Prover 8: Preprocessing ... % 54.46/8.12 Prover 8: Warning: ignoring some quantifiers % 54.46/8.14 Prover 8: Constructing countermodel ... % 57.80/8.43 Prover 10: Constructing countermodel ... % 58.74/8.56 Prover 2: Proving ... % 58.93/8.58 Prover 2: stopped % 58.93/8.60 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 58.93/8.60 Prover 0: Proving ... % 59.31/8.63 Prover 0: stopped % 59.31/8.63 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 59.51/8.77 Prover 7: Constructing countermodel ... % 59.51/8.90 Prover 11: Preprocessing ... % 59.51/8.91 Prover 13: Preprocessing ... % 62.40/9.07 Prover 10: Found proof (size 38) % 62.40/9.07 Prover 10: proved (1608ms) % 62.40/9.07 Prover 4: stopped % 62.40/9.07 Prover 7: stopped % 62.40/9.07 Prover 13: stopped % 62.40/9.07 Prover 8: stopped % 62.66/9.07 Prover 1: stopped % 63.00/9.17 Prover 11: stopped % 63.00/9.17 % 63.00/9.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 63.00/9.17 % 63.00/9.17 % SZS output start Proof for theBenchmark % 63.00/9.18 Assumptions after simplification: % 63.00/9.18 --------------------------------- % 63.00/9.18 % 63.00/9.18 (mCountNFin_01) % 63.00/9.18 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)) % 63.00/9.18 % 63.00/9.18 (mDefEmp) % 63.00/9.19 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~ % 63.00/9.19 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : ( % 63.00/9.19 ~ $i(v0) | ~ aElementOf0(v0, slcrc0)) % 63.00/9.19 % 63.00/9.19 (mNATSet) % 63.00/9.19 $i(szNzAzT0) & isCountable0(szNzAzT0) & aSet0(szNzAzT0) % 63.00/9.19 % 63.00/9.19 (mSubTrans) % 63.00/9.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 63.00/9.19 ~ aSubsetOf0(v1, v2) | ~ aSubsetOf0(v0, v1) | ~ aSet0(v2) | ~ aSet0(v1) % 63.00/9.19 | ~ aSet0(v0) | aSubsetOf0(v0, v2)) % 63.00/9.19 % 63.00/9.19 (m__) % 63.00/9.19 $i(xQ) & $i(szNzAzT0) & ? [v0: $i] : ($i(v0) & aElementOf0(v0, xQ) & ~ % 63.00/9.19 aSubsetOf0(xQ, szNzAzT0) & ~ aElementOf0(v0, szNzAzT0)) % 63.00/9.19 % 63.00/9.19 (m__3435) % 63.00/9.19 $i(xS) & $i(szNzAzT0) & aSubsetOf0(xS, szNzAzT0) & isCountable0(xS) & % 63.00/9.19 aSet0(xS) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xS) | % 63.00/9.19 aElementOf0(v0, szNzAzT0)) % 63.00/9.19 % 63.00/9.19 (m__4730) % 63.00/9.21 szDzozmdt0(xd) = szNzAzT0 & $i(xd) & $i(xC) & $i(xN) & $i(xk) & $i(szNzAzT0) & % 63.00/9.21 aFunction0(xd) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xC, v0) = v1) | % 63.00/9.21 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ? % 63.00/9.21 [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xd, v0) = v5 & sdtlpdtrp0(xN, v2) = v3 % 63.00/9.21 & slbdtsldtrb0(v3, xk) = v4 & szszuzczcdt0(v0) = v2 & $i(v5) & $i(v4) & % 63.00/9.21 $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~ % 63.00/9.21 (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aSubsetOf0(v6, v3) | ~ % 63.00/9.21 aSet0(v6) | ? [v8: $i] : ( ~ (v8 = xk) & sbrdtbr0(v6) = v8 & $i(v8))) & % 63.00/9.21 ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~ (sdtlpdtrp0(v1, v6) = v7) | ~ % 63.00/9.21 $i(v6) | ~ aElementOf0(v6, v4) | ~ aSet0(v6)) & ! [v6: $i] : ! [v7: % 63.00/9.21 $i] : (v7 = v5 | ~ (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aSet0(v6) % 63.00/9.21 | ? [v8: $i] : ? [v9: $i] : ($i(v9) & (( ~ (v8 = xk) & sbrdtbr0(v6) = % 63.00/9.21 v8 & $i(v8)) | (aElementOf0(v9, v6) & ~ aElementOf0(v9, v3))))))) % 63.00/9.21 % 63.00/9.21 (m__4758) % 63.00/9.22 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & % 63.00/9.22 szDzozmdt0(xd) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT) & aSet0(v1) & ! % 63.00/9.22 [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v2) | ~ $i(v3) | ~ % 63.00/9.22 $i(v2) | ~ aElementOf0(v3, v0) | aElementOf0(v2, v1)) & ! [v2: $i] : ( ~ % 63.00/9.22 $i(v2) | ~ aElementOf0(v2, v1) | aElementOf0(v2, xT)) & ! [v2: $i] : ( ~ % 63.00/9.22 $i(v2) | ~ aElementOf0(v2, v1) | ? [v3: $i] : (sdtlpdtrp0(xd, v3) = v2 & % 63.00/9.22 $i(v3) & aElementOf0(v3, v0)))) % 63.00/9.22 % 63.00/9.22 (m__4854) % 63.00/9.22 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = % 63.00/9.22 v0 & sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) & % 63.00/9.22 $i(v0) & aElementOf0(v0, xT) & aSet0(v1) & ! [v3: $i] : ! [v4: $i] : (v4 = % 63.00/9.22 v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1)) & % 63.00/9.22 ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ % 63.00/9.22 aElementOf0(v3, v1) | aElementOf0(v3, v2)) & ! [v3: $i] : ( ~ % 63.00/9.22 (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ aElementOf0(v3, v2) | % 63.00/9.22 aElementOf0(v3, v1))) % 63.00/9.22 % 63.00/9.22 (m__4891) % 63.00/9.22 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 63.00/9.22 (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & % 63.00/9.22 szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & ! % 63.00/9.22 [v3: $i] : ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) % 63.00/9.22 | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 63.00/9.22 (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) | % 63.00/9.22 aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xe, v4) % 63.00/9.22 = v3) | ~ $i(v4) | ~ $i(v3) | ~ aElementOf0(v4, v1) | aElementOf0(v3, % 63.00/9.22 xO)) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ % 63.00/9.22 aElementOf0(v3, v2) | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~ % 63.00/9.22 aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 & $i(v4) & % 63.00/9.22 aElementOf0(v4, v1)))) % 63.00/9.22 % 63.00/9.22 (m__4998) % 63.00/9.22 $i(xO) & $i(xS) & aSubsetOf0(xO, xS) & ! [v0: $i] : ( ~ $i(v0) | ~ % 63.00/9.22 aElementOf0(v0, xO) | aElementOf0(v0, xS)) % 63.00/9.22 % 63.00/9.22 (m__5078) % 63.00/9.22 $i(xQ) & $i(xO) & $i(xK) & ? [v0: $i] : (slbdtsldtrb0(xO, xK) = v0 & % 63.00/9.22 sbrdtbr0(xQ) = xK & $i(v0) & aSubsetOf0(xQ, xO) & aElementOf0(xQ, v0) & % 63.00/9.22 aSet0(xQ) & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | % 63.00/9.22 aElementOf0(v1, xO))) % 63.00/9.22 % 63.00/9.22 (m__5093) % 63.30/9.22 $i(xQ) & $i(xO) & $i(slcrc0) & ? [v0: $i] : ( ~ (xQ = slcrc0) & $i(v0) & % 63.30/9.22 aElementOf0(v0, xQ) & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | % 63.30/9.22 aElementOf0(v1, xO))) % 63.30/9.22 % 63.30/9.22 (function-axioms) % 63.30/9.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 63.30/9.23 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 63.30/9.23 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 63.30/9.23 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 63.30/9.23 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 63.30/9.23 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 63.30/9.23 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 63.30/9.23 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 63.30/9.23 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 63.30/9.23 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 63.30/9.23 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 63.30/9.23 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 63.30/9.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 63.30/9.23 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 63.30/9.23 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 63.30/9.23 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 63.30/9.23 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 63.30/9.23 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 63.30/9.23 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 63.30/9.23 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 63.30/9.23 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 63.30/9.23 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 63.30/9.23 v0)) % 63.30/9.23 % 63.30/9.23 Further assumptions not needed in the proof: % 63.30/9.23 -------------------------------------------- % 63.30/9.23 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 63.30/9.23 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons, % 63.30/9.23 mDefDiff, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, mDefSel, % 63.30/9.23 mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet, % 63.30/9.23 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm, % 63.30/9.23 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, % 63.30/9.23 mMinMin, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess, % 63.30/9.23 mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, % 63.30/9.23 mSubASymm, mSubFSet, mSubRefl, mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, % 63.30/9.23 mZeroNum, m__3291, m__3398, m__3418, m__3453, m__3462, m__3520, m__3533, % 63.30/9.23 m__3623, m__3671, m__3754, m__3821, m__3965, m__4151, m__4182, m__4331, m__4411, % 63.30/9.23 m__4618, m__4660, m__4908, m__4982 % 63.30/9.23 % 63.30/9.23 Those formulas are unsatisfiable: % 63.30/9.23 --------------------------------- % 63.30/9.23 % 63.30/9.23 Begin of proof % 63.30/9.23 | % 63.30/9.23 | ALPHA: (mDefEmp) implies: % 63.30/9.23 | (1) aSet0(slcrc0) % 63.30/9.23 | % 63.30/9.23 | ALPHA: (mCountNFin_01) implies: % 63.30/9.23 | (2) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0) % 63.30/9.23 | % 63.30/9.23 | ALPHA: (mNATSet) implies: % 63.30/9.23 | (3) aSet0(szNzAzT0) % 63.30/9.23 | % 63.30/9.23 | ALPHA: (m__3435) implies: % 63.30/9.23 | (4) aSet0(xS) % 63.30/9.23 | (5) aSubsetOf0(xS, szNzAzT0) % 63.30/9.23 | % 63.30/9.23 | ALPHA: (m__4730) implies: % 63.30/9.23 | (6) szDzozmdt0(xd) = szNzAzT0 % 63.30/9.23 | % 63.30/9.23 | ALPHA: (m__4758) implies: % 63.30/9.23 | (7) ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & szDzozmdt0(xd) = % 63.30/9.23 | v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT) & aSet0(v1) & ! [v2: $i] : % 63.30/9.23 | ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v2) | ~ $i(v3) | ~ $i(v2) | % 63.30/9.23 | ~ aElementOf0(v3, v0) | aElementOf0(v2, v1)) & ! [v2: $i] : ( ~ % 63.30/9.23 | $i(v2) | ~ aElementOf0(v2, v1) | aElementOf0(v2, xT)) & ! [v2: % 63.30/9.23 | $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | ? [v3: $i] : % 63.30/9.23 | (sdtlpdtrp0(xd, v3) = v2 & $i(v3) & aElementOf0(v3, v0)))) % 63.30/9.23 | % 63.30/9.23 | ALPHA: (m__4854) implies: % 63.30/9.24 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 & % 63.30/9.24 | sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) & % 63.30/9.24 | $i(v0) & aElementOf0(v0, xT) & aSet0(v1) & ! [v3: $i] : ! [v4: $i] % 63.30/9.24 | : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ % 63.30/9.24 | aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 63.30/9.24 | (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) | % 63.30/9.24 | aElementOf0(v3, v2)) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v0) % 63.30/9.24 | | ~ $i(v3) | ~ aElementOf0(v3, v2) | aElementOf0(v3, v1))) % 63.30/9.24 | % 63.30/9.24 | ALPHA: (m__4891) implies: % 63.30/9.24 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 & % 63.30/9.24 | sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = % 63.30/9.24 | v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & ! [v3: $i] : % 63.30/9.24 | ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | % 63.30/9.24 | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 63.30/9.24 | (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) | % 63.30/9.24 | aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 63.30/9.24 | (sdtlpdtrp0(xe, v4) = v3) | ~ $i(v4) | ~ $i(v3) | ~ % 63.30/9.24 | aElementOf0(v4, v1) | aElementOf0(v3, xO)) & ! [v3: $i] : ( ~ % 63.30/9.24 | (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ aElementOf0(v3, v2) | % 63.30/9.24 | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~ % 63.30/9.24 | aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 & % 63.30/9.24 | $i(v4) & aElementOf0(v4, v1)))) % 63.30/9.24 | % 63.30/9.24 | ALPHA: (m__4998) implies: % 63.30/9.24 | (10) aSubsetOf0(xO, xS) % 63.30/9.24 | (11) $i(xS) % 63.30/9.24 | % 63.30/9.24 | ALPHA: (m__5078) implies: % 63.30/9.24 | (12) ? [v0: $i] : (slbdtsldtrb0(xO, xK) = v0 & sbrdtbr0(xQ) = xK & $i(v0) % 63.30/9.24 | & aSubsetOf0(xQ, xO) & aElementOf0(xQ, v0) & aSet0(xQ) & ! [v1: $i] % 63.30/9.24 | : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | aElementOf0(v1, xO))) % 63.30/9.24 | % 63.30/9.24 | ALPHA: (m__5093) implies: % 63.30/9.24 | (13) $i(xO) % 63.30/9.24 | % 63.30/9.24 | ALPHA: (m__) implies: % 63.30/9.24 | (14) $i(xQ) % 63.30/9.24 | (15) ? [v0: $i] : ($i(v0) & aElementOf0(v0, xQ) & ~ aSubsetOf0(xQ, % 63.30/9.24 | szNzAzT0) & ~ aElementOf0(v0, szNzAzT0)) % 63.30/9.24 | % 63.30/9.24 | ALPHA: (function-axioms) implies: % 63.30/9.24 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 63.30/9.24 | (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) % 63.30/9.24 | % 63.30/9.24 | DELTA: instantiating (15) with fresh symbol all_78_0 gives: % 63.30/9.24 | (17) $i(all_78_0) & aElementOf0(all_78_0, xQ) & ~ aSubsetOf0(xQ, szNzAzT0) % 63.30/9.24 | & ~ aElementOf0(all_78_0, szNzAzT0) % 63.30/9.24 | % 63.30/9.24 | ALPHA: (17) implies: % 63.30/9.24 | (18) ~ aSubsetOf0(xQ, szNzAzT0) % 63.30/9.24 | % 63.30/9.24 | DELTA: instantiating (12) with fresh symbol all_83_0 gives: % 63.30/9.24 | (19) slbdtsldtrb0(xO, xK) = all_83_0 & sbrdtbr0(xQ) = xK & $i(all_83_0) & % 63.30/9.24 | aSubsetOf0(xQ, xO) & aElementOf0(xQ, all_83_0) & aSet0(xQ) & ! [v0: % 63.30/9.24 | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xQ) | aElementOf0(v0, xO)) % 63.30/9.24 | % 63.30/9.24 | ALPHA: (19) implies: % 63.30/9.24 | (20) aSet0(xQ) % 63.30/9.24 | (21) aSubsetOf0(xQ, xO) % 63.30/9.24 | % 63.30/9.24 | DELTA: instantiating (7) with fresh symbols all_86_0, all_86_1 gives: % 63.30/9.25 | (22) sdtlcdtrc0(xd, all_86_1) = all_86_0 & szDzozmdt0(xd) = all_86_1 & % 63.30/9.25 | $i(all_86_0) & $i(all_86_1) & aSubsetOf0(all_86_0, xT) & % 63.30/9.25 | aSet0(all_86_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v1) % 63.30/9.25 | = v0) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, all_86_1) | % 63.30/9.25 | aElementOf0(v0, all_86_0)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 63.30/9.25 | aElementOf0(v0, all_86_0) | aElementOf0(v0, xT)) & ! [v0: $i] : ( ~ % 63.30/9.25 | $i(v0) | ~ aElementOf0(v0, all_86_0) | ? [v1: $i] : % 63.30/9.25 | (sdtlpdtrp0(xd, v1) = v0 & $i(v1) & aElementOf0(v1, all_86_1))) % 63.30/9.25 | % 63.30/9.25 | ALPHA: (22) implies: % 63.30/9.25 | (23) $i(all_86_1) % 63.30/9.25 | (24) szDzozmdt0(xd) = all_86_1 % 63.30/9.25 | % 63.30/9.25 | DELTA: instantiating (8) with fresh symbols all_89_0, all_89_1, all_89_2 % 63.30/9.25 | gives: % 63.30/9.25 | (25) szDzizrdt0(xd) = all_89_2 & sdtlbdtrb0(xd, all_89_2) = all_89_1 & % 63.30/9.25 | szDzozmdt0(xd) = all_89_0 & $i(all_89_0) & $i(all_89_1) & $i(all_89_2) % 63.30/9.25 | & aElementOf0(all_89_2, xT) & aSet0(all_89_1) & ! [v0: $i] : ! [v1: % 63.30/9.25 | int] : (v1 = all_89_2 | ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | % 63.30/9.25 | ~ aElementOf0(v0, all_89_1)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 63.30/9.25 | (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_89_1) % 63.30/9.25 | | aElementOf0(v0, all_89_0)) & ! [v0: $i] : ( ~ (sdtlpdtrp0(xd, v0) % 63.30/9.25 | = all_89_2) | ~ $i(v0) | ~ aElementOf0(v0, all_89_0) | % 63.30/9.25 | aElementOf0(v0, all_89_1)) % 63.30/9.25 | % 63.30/9.25 | ALPHA: (25) implies: % 63.30/9.25 | (26) szDzozmdt0(xd) = all_89_0 % 63.30/9.25 | % 63.30/9.25 | DELTA: instantiating (9) with fresh symbols all_95_0, all_95_1, all_95_2 % 63.30/9.25 | gives: % 63.30/9.25 | (27) szDzizrdt0(xd) = all_95_2 & sdtlcdtrc0(xe, all_95_1) = xO & % 63.30/9.25 | sdtlbdtrb0(xd, all_95_2) = all_95_1 & szDzozmdt0(xd) = all_95_0 & % 63.30/9.25 | $i(all_95_0) & $i(all_95_1) & $i(all_95_2) & aSet0(all_95_1) & % 63.30/9.25 | aSet0(xO) & ! [v0: $i] : ! [v1: int] : (v1 = all_95_2 | ~ % 63.30/9.25 | (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, % 63.30/9.25 | all_95_1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) = % 63.30/9.25 | v1) | ~ $i(v0) | ~ aElementOf0(v0, all_95_1) | aElementOf0(v0, % 63.30/9.25 | all_95_0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v1) = % 63.30/9.25 | v0) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, all_95_1) | % 63.30/9.25 | aElementOf0(v0, xO)) & ! [v0: $i] : ( ~ (sdtlpdtrp0(xd, v0) = % 63.30/9.25 | all_95_2) | ~ $i(v0) | ~ aElementOf0(v0, all_95_0) | % 63.30/9.25 | aElementOf0(v0, all_95_1)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 63.30/9.25 | aElementOf0(v0, xO) | ? [v1: $i] : (sdtlpdtrp0(xe, v1) = v0 & % 63.30/9.25 | $i(v1) & aElementOf0(v1, all_95_1))) % 63.30/9.25 | % 63.30/9.25 | ALPHA: (27) implies: % 63.30/9.25 | (28) aSet0(xO) % 63.30/9.25 | (29) szDzozmdt0(xd) = all_95_0 % 63.30/9.25 | % 63.30/9.25 | BETA: splitting (2) gives: % 63.30/9.25 | % 63.30/9.25 | Case 1: % 63.30/9.25 | | % 63.30/9.25 | | (30) ~ aSet0(slcrc0) % 63.30/9.25 | | % 63.30/9.25 | | PRED_UNIFY: (1), (30) imply: % 63.30/9.25 | | (31) $false % 63.30/9.25 | | % 63.30/9.25 | | CLOSE: (31) is inconsistent. % 63.30/9.25 | | % 63.30/9.25 | Case 2: % 63.30/9.25 | | % 63.30/9.25 | | % 63.30/9.25 | | GROUND_INST: instantiating (16) with all_86_1, all_89_0, xd, simplifying % 63.30/9.25 | | with (24), (26) gives: % 63.30/9.25 | | (32) all_89_0 = all_86_1 % 63.30/9.25 | | % 63.30/9.26 | | GROUND_INST: instantiating (16) with all_89_0, all_95_0, xd, simplifying % 63.30/9.26 | | with (26), (29) gives: % 63.30/9.26 | | (33) all_95_0 = all_89_0 % 63.30/9.26 | | % 63.30/9.26 | | GROUND_INST: instantiating (16) with szNzAzT0, all_95_0, xd, simplifying % 63.30/9.26 | | with (6), (29) gives: % 63.30/9.26 | | (34) all_95_0 = szNzAzT0 % 63.30/9.26 | | % 63.30/9.26 | | COMBINE_EQS: (33), (34) imply: % 63.30/9.26 | | (35) all_89_0 = szNzAzT0 % 63.30/9.26 | | % 63.30/9.26 | | SIMP: (35) implies: % 63.30/9.26 | | (36) all_89_0 = szNzAzT0 % 63.30/9.26 | | % 63.30/9.26 | | COMBINE_EQS: (32), (36) imply: % 63.30/9.26 | | (37) all_86_1 = szNzAzT0 % 63.30/9.26 | | % 63.30/9.26 | | SIMP: (37) implies: % 63.30/9.26 | | (38) all_86_1 = szNzAzT0 % 63.30/9.26 | | % 63.30/9.26 | | REDUCE: (23), (38) imply: % 63.30/9.26 | | (39) $i(szNzAzT0) % 63.30/9.26 | | % 63.30/9.26 | | GROUND_INST: instantiating (mSubTrans) with xQ, xO, xS, simplifying with % 63.30/9.26 | | (4), (10), (11), (13), (14), (20), (21), (28) gives: % 63.30/9.26 | | (40) aSubsetOf0(xQ, xS) % 63.30/9.26 | | % 63.30/9.26 | | GROUND_INST: instantiating (mSubTrans) with xQ, xS, szNzAzT0, simplifying % 63.30/9.26 | | with (3), (4), (5), (11), (14), (18), (20), (39), (40) gives: % 63.30/9.26 | | (41) $false % 63.30/9.26 | | % 63.30/9.26 | | CLOSE: (41) is inconsistent. % 63.30/9.26 | | % 63.30/9.26 | End of split % 63.30/9.26 | % 63.30/9.26 End of proof % 63.30/9.26 % SZS output end Proof for theBenchmark % 63.30/9.26 % 63.30/9.26 8634ms %------------------------------------------------------------------------------