%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM606+1 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n005.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 37.84s 5.77s % Output : Proof 52.25s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.08 % Problem : NUM606+1 : TPTP v8.1.2. Released v4.0.0. % 0.08/0.09 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.08/0.28 % Computer : n005.cluster.edu % 0.08/0.28 % Model : x86_64 x86_64 % 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.28 % Memory : 8042.1875MB % 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.28 % CPULimit : 300 % 0.08/0.28 % WCLimit : 300 % 0.08/0.28 % DateTime : Fri Aug 25 11:05:53 EDT 2023 % 0.08/0.28 % CPUTime : % 0.13/0.53 ________ _____ % 0.13/0.53 ___ __ \_________(_)________________________________ % 0.13/0.53 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.13/0.53 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.13/0.53 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.13/0.53 % 0.13/0.53 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.13/0.53 (2023-06-19) % 0.13/0.53 % 0.13/0.53 (c) Philipp Rümmer, 2009-2023 % 0.13/0.53 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.13/0.53 Amanda Stjerna. % 0.13/0.53 Free software under BSD-3-Clause. % 0.13/0.53 % 0.13/0.53 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.13/0.53 % 0.13/0.53 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.13/0.54 Running up to 7 provers in parallel. % 0.13/0.56 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.13/0.56 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.13/0.56 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.13/0.56 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.13/0.56 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.13/0.56 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.13/0.56 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.72/1.34 Prover 4: Preprocessing ... % 4.72/1.34 Prover 1: Preprocessing ... % 5.23/1.39 Prover 6: Preprocessing ... % 5.23/1.39 Prover 0: Preprocessing ... % 5.23/1.39 Prover 5: Preprocessing ... % 5.23/1.39 Prover 3: Preprocessing ... % 5.23/1.39 Prover 2: Preprocessing ... % 17.24/3.03 Prover 3: Constructing countermodel ... % 17.24/3.05 Prover 1: Constructing countermodel ... % 17.24/3.06 Prover 6: Proving ... % 18.61/3.30 Prover 5: Proving ... % 22.45/3.73 Prover 2: Proving ... % 28.26/4.58 Prover 4: Constructing countermodel ... % 29.92/4.74 Prover 0: Proving ... % 37.84/5.77 Prover 3: proved (5213ms) % 37.84/5.77 % 37.84/5.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 37.84/5.77 % 37.84/5.79 Prover 5: stopped % 37.84/5.80 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 37.84/5.80 Prover 6: stopped % 37.84/5.80 Prover 0: stopped % 37.84/5.81 Prover 2: stopped % 37.84/5.82 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 37.84/5.82 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 37.84/5.83 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 37.84/5.83 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 40.82/6.19 Prover 10: Preprocessing ... % 40.82/6.20 Prover 11: Preprocessing ... % 40.82/6.20 Prover 7: Preprocessing ... % 40.82/6.20 Prover 8: Preprocessing ... % 40.82/6.21 Prover 13: Preprocessing ... % 43.15/6.60 Prover 7: Constructing countermodel ... % 43.15/6.68 Prover 10: Constructing countermodel ... % 45.12/6.75 Prover 8: Warning: ignoring some quantifiers % 45.49/6.77 Prover 8: Constructing countermodel ... % 46.88/6.96 Prover 13: Warning: ignoring some quantifiers % 46.88/7.00 Prover 13: Constructing countermodel ... % 50.82/7.48 Prover 10: Found proof (size 62) % 50.82/7.48 Prover 10: proved (1652ms) % 50.82/7.48 Prover 7: stopped % 50.82/7.48 Prover 8: stopped % 50.82/7.48 Prover 13: stopped % 50.82/7.48 Prover 4: stopped % 51.03/7.51 Prover 1: stopped % 51.79/7.72 Prover 11: Constructing countermodel ... % 51.79/7.76 Prover 11: stopped % 51.79/7.76 % 51.79/7.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 51.79/7.76 % 52.08/7.77 % SZS output start Proof for theBenchmark % 52.11/7.77 Assumptions after simplification: % 52.11/7.77 --------------------------------- % 52.11/7.77 % 52.11/7.77 (mDefPtt) % 52.25/7.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(v0, v1) = v2) | ~ % 52.25/7.81 $i(v1) | ~ $i(v0) | ~ aFunction0(v0) | ~ aElement0(v1) | ? [v3: $i] : % 52.25/7.81 (szDzozmdt0(v0) = v3 & $i(v3) & ! [v4: $i] : ! [v5: $i] : (v5 = v1 | ~ % 52.25/7.81 (sdtlpdtrp0(v0, v4) = v5) | ~ $i(v4) | ~ $i(v2) | ~ aElementOf0(v4, % 52.25/7.81 v2)) & ! [v4: $i] : ! [v5: $i] : ( ~ (sdtlpdtrp0(v0, v4) = v5) | ~ % 52.25/7.81 $i(v4) | ~ $i(v2) | ~ aElementOf0(v4, v2) | aElementOf0(v4, v3)) & ! % 52.25/7.81 [v4: $i] : (v4 = v2 | ~ $i(v4) | ~ aSet0(v4) | ? [v5: $i] : ? [v6: $i] % 52.25/7.81 : ($i(v5) & ( ~ aElementOf0(v5, v4) | ~ aElementOf0(v5, v3) | ( ~ (v6 = % 52.25/7.81 v1) & sdtlpdtrp0(v0, v5) = v6 & $i(v6))) & (aElementOf0(v5, v4) % 52.25/7.81 | (v6 = v1 & sdtlpdtrp0(v0, v5) = v1 & aElementOf0(v5, v3))))) & ! % 52.25/7.81 [v4: $i] : ( ~ (sdtlpdtrp0(v0, v4) = v1) | ~ $i(v4) | ~ $i(v2) | ~ % 52.25/7.81 aElementOf0(v4, v3) | aElementOf0(v4, v2)) & ( ~ $i(v2) | aSet0(v2)))) % 52.25/7.81 % 52.25/7.81 (mDefSub) % 52.25/7.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 52.25/7.81 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) | % 52.25/7.81 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | % 52.25/7.81 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i] % 52.25/7.81 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) | % 52.25/7.81 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0))) % 52.25/7.81 % 52.25/7.81 (mEOfElem) % 52.25/7.81 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) | % 52.25/7.81 ~ aSet0(v0) | aElement0(v1)) % 52.25/7.81 % 52.25/7.81 (mNATSet) % 52.25/7.81 $i(szNzAzT0) & isCountable0(szNzAzT0) & aSet0(szNzAzT0) % 52.25/7.81 % 52.25/7.81 (mNatExtra) % 52.25/7.82 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ % 52.25/7.82 aElementOf0(v0, szNzAzT0) | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & % 52.25/7.82 aElementOf0(v1, szNzAzT0))) % 52.25/7.82 % 52.25/7.82 (mPttSet) % 52.25/7.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(v0, v1) = v2) | ~ % 52.25/7.82 $i(v1) | ~ $i(v0) | ~ aFunction0(v0) | ~ aElement0(v1) | ? [v3: $i] : % 52.25/7.82 (szDzozmdt0(v0) = v3 & $i(v3) & aSubsetOf0(v2, v3))) % 52.25/7.82 % 52.25/7.82 (mSubTrans) % 52.25/7.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 52.25/7.82 ~ aSubsetOf0(v1, v2) | ~ aSubsetOf0(v0, v1) | ~ aSet0(v2) | ~ aSet0(v1) % 52.25/7.82 | ~ aSet0(v0) | aSubsetOf0(v0, v2)) % 52.25/7.82 % 52.25/7.82 (m__) % 52.25/7.82 $i(xQ) & $i(szNzAzT0) & ~ aSubsetOf0(xQ, szNzAzT0) % 52.25/7.82 % 52.25/7.82 (m__3291) % 52.25/7.82 $i(xT) & isFinite0(xT) & aSet0(xT) % 52.25/7.82 % 52.25/7.82 (m__3418) % 52.25/7.82 $i(xK) & $i(szNzAzT0) & aElementOf0(xK, szNzAzT0) % 52.25/7.82 % 52.25/7.82 (m__3435) % 52.25/7.82 $i(xS) & $i(szNzAzT0) & aSubsetOf0(xS, szNzAzT0) & isCountable0(xS) % 52.25/7.82 % 52.25/7.82 (m__3462) % 52.25/7.82 ~ (xK = sz00) & $i(xK) & $i(sz00) % 52.25/7.82 % 52.25/7.82 (m__3520) % 52.25/7.82 ~ (xK = sz00) & $i(xK) & $i(sz00) % 52.25/7.82 % 52.25/7.82 (m__4730) % 52.25/7.82 szDzozmdt0(xd) = szNzAzT0 & $i(xd) & $i(xC) & $i(xN) & $i(xk) & $i(szNzAzT0) & % 52.25/7.82 aFunction0(xd) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xC, v0) = v1) | % 52.25/7.82 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ? % 52.25/7.82 [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xd, v0) = v5 & sdtlpdtrp0(xN, v2) = v3 % 52.25/7.82 & slbdtsldtrb0(v3, xk) = v4 & szszuzczcdt0(v0) = v2 & $i(v5) & $i(v4) & % 52.25/7.82 $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~ % 52.25/7.82 (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v4) | ~ % 52.25/7.82 aSet0(v6)))) % 52.25/7.82 % 52.25/7.82 (m__4758) % 52.25/7.82 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & % 52.25/7.82 szDzozmdt0(xd) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT)) % 52.25/7.82 % 52.25/7.82 (m__4854) % 52.25/7.82 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & % 52.25/7.82 sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & isCountable0(v1) & % 52.25/7.82 aElementOf0(v0, xT)) % 52.25/7.82 % 52.25/7.82 (m__4891) % 52.25/7.82 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & % 52.25/7.82 sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & % 52.25/7.82 aSet0(xO)) % 52.25/7.82 % 52.25/7.82 (m__4982) % 52.25/7.83 $i(xO) & $i(xd) & $i(xe) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] : % 52.25/7.83 (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & ! [v2: $i] % 52.25/7.83 : ( ~ $i(v2) | ~ aElementOf0(v2, xO) | ? [v3: $i] : (sdtlpdtrp0(xe, v3) = % 52.25/7.83 v2 & $i(v3) & aElementOf0(v3, v1) & aElementOf0(v3, szNzAzT0)))) % 52.25/7.83 % 52.25/7.83 (m__4998) % 52.25/7.83 $i(xO) & $i(xS) & aSubsetOf0(xO, xS) % 52.25/7.83 % 52.25/7.83 (m__5078) % 52.25/7.83 $i(xQ) & $i(xO) & $i(xK) & ? [v0: $i] : (slbdtsldtrb0(xO, xK) = v0 & $i(v0) & % 52.25/7.83 aElementOf0(xQ, v0)) % 52.25/7.83 % 52.25/7.83 (m__5093) % 52.25/7.83 ~ (xQ = slcrc0) & $i(xQ) & $i(xO) & $i(slcrc0) & aSubsetOf0(xQ, xO) % 52.25/7.83 % 52.25/7.83 (function-axioms) % 52.25/7.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 52.25/7.83 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 52.25/7.83 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 52.25/7.83 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 52.25/7.83 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 52.25/7.83 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 52.25/7.83 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 52.25/7.83 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 52.25/7.83 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 52.25/7.83 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 52.25/7.83 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 52.25/7.83 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 52.25/7.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 52.25/7.83 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 52.25/7.83 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 52.25/7.83 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 52.25/7.83 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 52.25/7.83 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 52.25/7.83 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 52.25/7.83 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 52.25/7.83 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 52.25/7.83 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 52.25/7.83 v0)) % 52.25/7.83 % 52.25/7.83 Further assumptions not needed in the proof: % 52.25/7.83 -------------------------------------------- % 52.25/7.83 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 52.25/7.83 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 52.25/7.83 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefRst, mDefSImg, mDefSeg, % 52.25/7.83 mDefSel, mDiffCons, mDirichlet, mDomSet, mElmSort, mEmpFin, mFConsSet, % 52.25/7.83 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm, % 52.25/7.83 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, % 52.25/7.83 mMinMin, mNatNSucc, mNoScLessZr, mSegFin, mSegLess, mSegSucc, mSegZero, % 52.25/7.83 mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, mSubASymm, mSubFSet, % 52.25/7.83 mSubRefl, mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__3398, % 52.25/7.83 m__3453, m__3533, m__3623, m__3671, m__3754, m__3821, m__3965, m__4151, m__4182, % 52.25/7.83 m__4331, m__4411, m__4618, m__4660, m__4908 % 52.25/7.83 % 52.25/7.83 Those formulas are unsatisfiable: % 52.25/7.83 --------------------------------- % 52.25/7.83 % 52.25/7.83 Begin of proof % 52.25/7.83 | % 52.25/7.83 | ALPHA: (mDefSub) implies: % 52.25/7.84 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, % 52.25/7.84 | v0) | ~ aSet0(v0) | aSet0(v1)) % 52.25/7.84 | % 52.25/7.84 | ALPHA: (mNATSet) implies: % 52.25/7.84 | (2) aSet0(szNzAzT0) % 52.25/7.84 | % 52.25/7.84 | ALPHA: (mNatExtra) implies: % 52.25/7.84 | (3) ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | % 52.25/7.84 | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & aElementOf0(v1, % 52.25/7.84 | szNzAzT0))) % 52.25/7.84 | % 52.25/7.84 | ALPHA: (m__3291) implies: % 52.25/7.84 | (4) aSet0(xT) % 52.25/7.84 | % 52.25/7.84 | ALPHA: (m__3418) implies: % 52.25/7.84 | (5) aElementOf0(xK, szNzAzT0) % 52.25/7.84 | % 52.25/7.84 | ALPHA: (m__3435) implies: % 52.25/7.84 | (6) aSubsetOf0(xS, szNzAzT0) % 52.25/7.84 | % 52.25/7.84 | ALPHA: (m__3520) implies: % 52.25/7.84 | (7) ~ (xK = sz00) % 52.25/7.84 | % 52.25/7.84 | ALPHA: (m__4730) implies: % 52.25/7.84 | (8) aFunction0(xd) % 52.25/7.84 | (9) szDzozmdt0(xd) = szNzAzT0 % 52.25/7.84 | % 52.25/7.84 | ALPHA: (m__4758) implies: % 52.25/7.84 | (10) ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & szDzozmdt0(xd) % 52.25/7.84 | = v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT)) % 52.25/7.84 | % 52.25/7.84 | ALPHA: (m__4854) implies: % 52.25/7.84 | (11) $i(xT) % 52.25/7.84 | (12) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) % 52.25/7.84 | = v1 & $i(v1) & $i(v0) & isCountable0(v1) & aElementOf0(v0, xT)) % 52.25/7.84 | % 52.25/7.84 | ALPHA: (m__4891) implies: % 52.25/7.84 | (13) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1) % 52.25/7.84 | = xO & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & aSet0(xO)) % 52.25/7.84 | % 52.25/7.84 | ALPHA: (m__4982) implies: % 52.25/7.84 | (14) $i(xd) % 52.25/7.84 | (15) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) % 52.25/7.84 | = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ( ~ $i(v2) | ~ % 52.25/7.84 | aElementOf0(v2, xO) | ? [v3: $i] : (sdtlpdtrp0(xe, v3) = v2 & % 52.25/7.84 | $i(v3) & aElementOf0(v3, v1) & aElementOf0(v3, szNzAzT0)))) % 52.25/7.84 | % 52.25/7.84 | ALPHA: (m__4998) implies: % 52.25/7.84 | (16) aSubsetOf0(xO, xS) % 52.25/7.84 | (17) $i(xS) % 52.25/7.84 | % 52.25/7.84 | ALPHA: (m__5078) implies: % 52.25/7.84 | (18) $i(xK) % 52.25/7.84 | % 52.25/7.84 | ALPHA: (m__5093) implies: % 52.25/7.84 | (19) aSubsetOf0(xQ, xO) % 52.25/7.84 | (20) $i(xO) % 52.25/7.84 | % 52.25/7.84 | ALPHA: (m__) implies: % 52.25/7.84 | (21) ~ aSubsetOf0(xQ, szNzAzT0) % 52.25/7.84 | (22) $i(xQ) % 52.25/7.84 | % 52.25/7.84 | ALPHA: (function-axioms) implies: % 52.25/7.84 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 52.25/7.84 | (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) % 52.25/7.84 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 52.25/7.84 | (szDzizrdt0(v2) = v1) | ~ (szDzizrdt0(v2) = v0)) % 52.25/7.84 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 52.25/7.84 | (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) = v0)) % 52.25/7.84 | % 52.25/7.84 | DELTA: instantiating (10) with fresh symbols all_78_0, all_78_1 gives: % 52.25/7.84 | (26) sdtlcdtrc0(xd, all_78_1) = all_78_0 & szDzozmdt0(xd) = all_78_1 & % 52.25/7.84 | $i(all_78_0) & $i(all_78_1) & aSubsetOf0(all_78_0, xT) % 52.25/7.84 | % 52.25/7.84 | ALPHA: (26) implies: % 52.25/7.84 | (27) $i(all_78_1) % 52.25/7.84 | (28) szDzozmdt0(xd) = all_78_1 % 52.25/7.84 | % 52.25/7.84 | DELTA: instantiating (13) with fresh symbols all_80_0, all_80_1 gives: % 52.25/7.86 | (29) szDzizrdt0(xd) = all_80_1 & sdtlcdtrc0(xe, all_80_0) = xO & % 52.25/7.86 | sdtlbdtrb0(xd, all_80_1) = all_80_0 & $i(all_80_0) & $i(all_80_1) & % 52.25/7.86 | aSet0(xO) % 52.25/7.86 | % 52.25/7.86 | ALPHA: (29) implies: % 52.25/7.86 | (30) aSet0(xO) % 52.25/7.86 | (31) sdtlbdtrb0(xd, all_80_1) = all_80_0 % 52.25/7.86 | (32) szDzizrdt0(xd) = all_80_1 % 52.25/7.86 | % 52.25/7.86 | DELTA: instantiating (12) with fresh symbols all_82_0, all_82_1 gives: % 52.25/7.86 | (33) szDzizrdt0(xd) = all_82_1 & sdtlbdtrb0(xd, all_82_1) = all_82_0 & % 52.25/7.86 | $i(all_82_0) & $i(all_82_1) & isCountable0(all_82_0) & % 52.25/7.86 | aElementOf0(all_82_1, xT) % 52.25/7.86 | % 52.25/7.86 | ALPHA: (33) implies: % 52.25/7.86 | (34) aElementOf0(all_82_1, xT) % 52.25/7.86 | (35) $i(all_82_1) % 52.25/7.86 | (36) sdtlbdtrb0(xd, all_82_1) = all_82_0 % 52.25/7.86 | (37) szDzizrdt0(xd) = all_82_1 % 52.25/7.86 | % 52.25/7.86 | DELTA: instantiating (15) with fresh symbols all_86_0, all_86_1 gives: % 52.25/7.86 | (38) szDzizrdt0(xd) = all_86_1 & sdtlbdtrb0(xd, all_86_1) = all_86_0 & % 52.25/7.86 | $i(all_86_0) & $i(all_86_1) & ! [v0: $i] : ( ~ $i(v0) | ~ % 52.25/7.86 | aElementOf0(v0, xO) | ? [v1: $i] : (sdtlpdtrp0(xe, v1) = v0 & % 52.25/7.86 | $i(v1) & aElementOf0(v1, all_86_0) & aElementOf0(v1, szNzAzT0))) % 52.25/7.86 | % 52.25/7.86 | ALPHA: (38) implies: % 52.25/7.86 | (39) sdtlbdtrb0(xd, all_86_1) = all_86_0 % 52.25/7.86 | (40) szDzizrdt0(xd) = all_86_1 % 52.25/7.86 | % 52.25/7.86 | GROUND_INST: instantiating (23) with szNzAzT0, all_78_1, xd, simplifying with % 52.25/7.86 | (9), (28) gives: % 52.25/7.86 | (41) all_78_1 = szNzAzT0 % 52.25/7.86 | % 52.25/7.86 | GROUND_INST: instantiating (24) with all_82_1, all_86_1, xd, simplifying with % 52.25/7.86 | (37), (40) gives: % 52.25/7.86 | (42) all_86_1 = all_82_1 % 52.25/7.86 | % 52.25/7.86 | GROUND_INST: instantiating (24) with all_80_1, all_86_1, xd, simplifying with % 52.25/7.86 | (32), (40) gives: % 52.25/7.86 | (43) all_86_1 = all_80_1 % 52.25/7.86 | % 52.25/7.86 | COMBINE_EQS: (42), (43) imply: % 52.25/7.86 | (44) all_82_1 = all_80_1 % 52.25/7.86 | % 52.25/7.86 | REDUCE: (39), (43) imply: % 52.25/7.86 | (45) sdtlbdtrb0(xd, all_80_1) = all_86_0 % 52.25/7.86 | % 52.25/7.86 | REDUCE: (36), (44) imply: % 52.25/7.86 | (46) sdtlbdtrb0(xd, all_80_1) = all_82_0 % 52.25/7.86 | % 52.25/7.86 | REDUCE: (35), (44) imply: % 52.25/7.86 | (47) $i(all_80_1) % 52.25/7.86 | % 52.25/7.86 | REDUCE: (27), (41) imply: % 52.25/7.86 | (48) $i(szNzAzT0) % 52.25/7.86 | % 52.25/7.86 | REDUCE: (34), (44) imply: % 52.25/7.86 | (49) aElementOf0(all_80_1, xT) % 52.25/7.86 | % 52.25/7.86 | GROUND_INST: instantiating (25) with all_80_0, all_86_0, all_80_1, xd, % 52.25/7.87 | simplifying with (31), (45) gives: % 52.25/7.87 | (50) all_86_0 = all_80_0 % 52.25/7.87 | % 52.25/7.87 | GROUND_INST: instantiating (25) with all_82_0, all_86_0, all_80_1, xd, % 52.25/7.87 | simplifying with (45), (46) gives: % 52.25/7.87 | (51) all_86_0 = all_82_0 % 52.25/7.87 | % 52.25/7.87 | COMBINE_EQS: (50), (51) imply: % 52.25/7.87 | (52) all_82_0 = all_80_0 % 52.25/7.87 | % 52.25/7.87 | GROUND_INST: instantiating (3) with xK, simplifying with (5), (18) gives: % 52.25/7.87 | (53) xK = sz00 | ? [v0: $i] : (szszuzczcdt0(v0) = xK & $i(v0) & % 52.25/7.87 | aElementOf0(v0, szNzAzT0)) % 52.25/7.87 | % 52.25/7.87 | GROUND_INST: instantiating (mEOfElem) with xT, all_80_1, simplifying with (4), % 52.25/7.87 | (11), (47), (49) gives: % 52.25/7.87 | (54) aElement0(all_80_1) % 52.25/7.87 | % 52.25/7.87 | GROUND_INST: instantiating (1) with szNzAzT0, xS, simplifying with (2), (6), % 52.25/7.87 | (17), (48) gives: % 52.25/7.87 | (55) aSet0(xS) % 52.25/7.87 | % 52.25/7.87 | GROUND_INST: instantiating (1) with xO, xQ, simplifying with (19), (20), (22), % 52.25/7.87 | (30) gives: % 52.25/7.87 | (56) aSet0(xQ) % 52.25/7.87 | % 52.25/7.87 | BETA: splitting (53) gives: % 52.25/7.87 | % 52.25/7.87 | Case 1: % 52.25/7.87 | | % 52.25/7.87 | | (57) xK = sz00 % 52.25/7.87 | | % 52.25/7.87 | | REDUCE: (7), (57) imply: % 52.25/7.87 | | (58) $false % 52.25/7.87 | | % 52.25/7.87 | | CLOSE: (58) is inconsistent. % 52.25/7.87 | | % 52.25/7.87 | Case 2: % 52.25/7.87 | | % 52.25/7.87 | | % 52.25/7.88 | | GROUND_INST: instantiating (mSubTrans) with xQ, xO, xS, simplifying with % 52.25/7.90 | | (16), (17), (19), (20), (22), (30), (55), (56) gives: % 52.25/7.90 | | (59) aSubsetOf0(xQ, xS) % 52.25/7.90 | | % 52.25/7.90 | | GROUND_INST: instantiating (mPttSet) with xd, all_80_1, all_80_0, % 52.25/7.90 | | simplifying with (8), (14), (31), (47), (54) gives: % 52.25/7.90 | | (60) ? [v0: $i] : (szDzozmdt0(xd) = v0 & $i(v0) & aSubsetOf0(all_80_0, % 52.25/7.90 | | v0)) % 52.25/7.90 | | % 52.25/7.90 | | GROUND_INST: instantiating (mDefPtt) with xd, all_80_1, all_80_0, % 52.25/7.90 | | simplifying with (8), (14), (31), (47), (54) gives: % 52.25/7.90 | | (61) ? [v0: $i] : (szDzozmdt0(xd) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 52.25/7.90 | | int] : (v2 = all_80_1 | ~ (sdtlpdtrp0(xd, v1) = v2) | ~ $i(v1) % 52.25/7.90 | | | ~ $i(all_80_0) | ~ aElementOf0(v1, all_80_0)) & ! [v1: $i] % 52.25/7.90 | | : ! [v2: $i] : ( ~ (sdtlpdtrp0(xd, v1) = v2) | ~ $i(v1) | ~ % 52.25/7.90 | | $i(all_80_0) | ~ aElementOf0(v1, all_80_0) | aElementOf0(v1, % 52.25/7.90 | | v0)) & ! [v1: any] : (v1 = all_80_0 | ~ $i(v1) | ~ % 52.25/7.90 | | aSet0(v1) | ? [v2: $i] : ? [v3: any] : ($i(v2) & ( ~ % 52.25/7.90 | | aElementOf0(v2, v1) | ~ aElementOf0(v2, v0) | ( ~ (v3 = % 52.25/7.90 | | all_80_1) & sdtlpdtrp0(xd, v2) = v3 & $i(v3))) & % 52.25/7.90 | | (aElementOf0(v2, v1) | (v3 = all_80_1 & sdtlpdtrp0(xd, v2) = % 52.25/7.90 | | all_80_1 & aElementOf0(v2, v0))))) & ! [v1: $i] : ( ~ % 52.25/7.90 | | (sdtlpdtrp0(xd, v1) = all_80_1) | ~ $i(v1) | ~ $i(all_80_0) | % 52.25/7.90 | | ~ aElementOf0(v1, v0) | aElementOf0(v1, all_80_0)) & ( ~ % 52.25/7.90 | | $i(all_80_0) | aSet0(all_80_0))) % 52.25/7.90 | | % 52.25/7.90 | | DELTA: instantiating (60) with fresh symbol all_133_0 gives: % 52.25/7.90 | | (62) szDzozmdt0(xd) = all_133_0 & $i(all_133_0) & aSubsetOf0(all_80_0, % 52.25/7.90 | | all_133_0) % 52.25/7.90 | | % 52.25/7.90 | | ALPHA: (62) implies: % 52.25/7.90 | | (63) $i(all_133_0) % 52.25/7.90 | | (64) szDzozmdt0(xd) = all_133_0 % 52.25/7.90 | | % 52.25/7.90 | | DELTA: instantiating (61) with fresh symbol all_139_0 gives: % 52.25/7.90 | | (65) szDzozmdt0(xd) = all_139_0 & $i(all_139_0) & ! [v0: $i] : ! [v1: % 52.25/7.90 | | int] : (v1 = all_80_1 | ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | % 52.25/7.90 | | ~ $i(all_80_0) | ~ aElementOf0(v0, all_80_0)) & ! [v0: $i] : ! % 52.25/7.90 | | [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ % 52.25/7.90 | | $i(all_80_0) | ~ aElementOf0(v0, all_80_0) | aElementOf0(v0, % 52.25/7.90 | | all_139_0)) & ! [v0: any] : (v0 = all_80_0 | ~ $i(v0) | ~ % 52.25/7.90 | | aSet0(v0) | ? [v1: $i] : ? [v2: any] : ($i(v1) & ( ~ % 52.25/7.90 | | aElementOf0(v1, v0) | ~ aElementOf0(v1, all_139_0) | ( ~ (v2 % 52.25/7.90 | | = all_80_1) & sdtlpdtrp0(xd, v1) = v2 & $i(v2))) & % 52.25/7.90 | | (aElementOf0(v1, v0) | (v2 = all_80_1 & sdtlpdtrp0(xd, v1) = % 52.25/7.90 | | all_80_1 & aElementOf0(v1, all_139_0))))) & ! [v0: $i] : ( % 52.25/7.90 | | ~ (sdtlpdtrp0(xd, v0) = all_80_1) | ~ $i(v0) | ~ $i(all_80_0) | % 52.25/7.90 | | ~ aElementOf0(v0, all_139_0) | aElementOf0(v0, all_80_0)) & ( ~ % 52.25/7.90 | | $i(all_80_0) | aSet0(all_80_0)) % 52.25/7.90 | | % 52.25/7.90 | | ALPHA: (65) implies: % 52.25/7.90 | | (66) szDzozmdt0(xd) = all_139_0 % 52.25/7.90 | | % 52.25/7.90 | | GROUND_INST: instantiating (23) with szNzAzT0, all_139_0, xd, simplifying % 52.25/7.90 | | with (9), (66) gives: % 52.25/7.90 | | (67) all_139_0 = szNzAzT0 % 52.25/7.90 | | % 52.25/7.90 | | GROUND_INST: instantiating (23) with all_133_0, all_139_0, xd, simplifying % 52.25/7.90 | | with (64), (66) gives: % 52.25/7.90 | | (68) all_139_0 = all_133_0 % 52.25/7.90 | | % 52.25/7.90 | | COMBINE_EQS: (67), (68) imply: % 52.25/7.90 | | (69) all_133_0 = szNzAzT0 % 52.25/7.90 | | % 52.25/7.90 | | GROUND_INST: instantiating (mSubTrans) with xQ, xS, szNzAzT0, simplifying % 52.25/7.90 | | with (2), (6), (17), (21), (22), (48), (55), (56), (59) gives: % 52.25/7.90 | | (70) $false % 52.25/7.90 | | % 52.25/7.90 | | CLOSE: (70) is inconsistent. % 52.25/7.90 | | % 52.25/7.90 | End of split % 52.25/7.90 | % 52.25/7.90 End of proof % 52.25/7.90 % SZS output end Proof for theBenchmark % 52.25/7.90 % 52.25/7.90 7373ms %------------------------------------------------------------------------------