%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM582+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 : n010.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 11:48:45 EDT 2023 % Result : Theorem 60.52s 8.93s % Output : Proof 80.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : NUM582+3 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n010.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Fri Aug 25 15:41:35 EDT 2023 % 0.12/0.33 % CPUTime : % 0.18/0.57 ________ _____ % 0.18/0.57 ___ __ \_________(_)________________________________ % 0.18/0.57 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.57 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.57 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.57 % 0.18/0.57 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.57 (2023-06-19) % 0.18/0.57 % 0.18/0.57 (c) Philipp Rümmer, 2009-2023 % 0.18/0.57 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.57 Amanda Stjerna. % 0.18/0.57 Free software under BSD-3-Clause. % 0.18/0.57 % 0.18/0.57 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.57 % 0.18/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.18/0.58 Running up to 7 provers in parallel. % 0.18/0.60 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.18/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.18/0.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.18/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.18/0.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.18/0.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.18/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 6.02/1.55 Prover 4: Preprocessing ... % 6.02/1.56 Prover 1: Preprocessing ... % 6.38/1.60 Prover 6: Preprocessing ... % 6.38/1.60 Prover 0: Preprocessing ... % 6.38/1.60 Prover 5: Preprocessing ... % 6.38/1.60 Prover 3: Preprocessing ... % 6.38/1.60 Prover 2: Preprocessing ... % 20.01/3.57 Prover 1: Constructing countermodel ... % 20.01/3.66 Prover 6: Proving ... % 20.01/3.67 Prover 3: Constructing countermodel ... % 22.62/3.80 Prover 5: Proving ... % 25.40/4.31 Prover 2: Proving ... % 36.49/5.79 Prover 4: Constructing countermodel ... % 41.05/6.28 Prover 0: Proving ... % 60.52/8.92 Prover 3: proved (8323ms) % 60.52/8.92 % 60.52/8.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 60.52/8.93 % 60.52/8.94 Prover 2: stopped % 60.52/8.94 Prover 6: stopped % 60.52/8.96 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 60.52/8.96 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 60.52/8.97 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 60.81/8.98 Prover 5: stopped % 60.81/8.99 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 60.81/9.00 Prover 0: stopped % 62.12/9.01 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 63.69/9.28 Prover 8: Preprocessing ... % 65.11/9.42 Prover 13: Preprocessing ... % 65.11/9.42 Prover 10: Preprocessing ... % 65.11/9.44 Prover 7: Preprocessing ... % 65.84/9.52 Prover 11: Preprocessing ... % 68.12/9.80 Prover 8: Warning: ignoring some quantifiers % 68.12/9.82 Prover 8: Constructing countermodel ... % 68.12/9.87 Prover 7: Constructing countermodel ... % 70.40/10.16 Prover 13: Warning: ignoring some quantifiers % 70.40/10.17 Prover 10: Constructing countermodel ... % 71.17/10.25 Prover 13: Constructing countermodel ... % 76.82/10.93 Prover 10: Found proof (size 29) % 76.82/10.93 Prover 10: proved (1962ms) % 76.82/10.93 Prover 13: stopped % 76.82/10.93 Prover 8: stopped % 76.82/10.93 Prover 7: stopped % 76.82/10.93 Prover 1: stopped % 76.82/10.94 Prover 4: stopped % 79.53/11.58 Prover 11: Constructing countermodel ... % 79.53/11.60 Prover 11: stopped % 79.53/11.60 % 79.53/11.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 79.53/11.60 % 79.53/11.61 % SZS output start Proof for theBenchmark % 79.53/11.62 Assumptions after simplification: % 79.53/11.62 --------------------------------- % 79.53/11.62 % 79.53/11.62 (mCountNFin_01) % 79.53/11.62 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)) % 79.53/11.62 % 79.53/11.62 (mDefEmp) % 79.53/11.63 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~ % 79.53/11.63 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : ( % 79.53/11.63 ~ $i(v0) | ~ aElementOf0(v0, slcrc0)) % 79.53/11.63 % 79.53/11.63 (mZeroLess) % 79.53/11.63 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, % 79.53/11.63 szNzAzT0) | sdtlseqdt0(sz00, v0)) % 79.53/11.63 % 79.53/11.63 (mZeroNum) % 79.53/11.63 $i(sz00) & $i(szNzAzT0) & aElementOf0(sz00, szNzAzT0) % 79.53/11.63 % 79.53/11.63 (m__) % 79.78/11.66 $i(xi) & $i(xN) & $i(xS) & ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xi) = % 79.78/11.66 v0 & $i(v1) & $i(v0) & aElementOf0(v1, v0) & ~ aSubsetOf0(v0, xS) & ~ % 79.78/11.66 aElementOf0(v1, xS)) % 79.78/11.66 % 79.78/11.66 (m__3623) % 79.87/11.68 sdtlpdtrp0(xN, sz00) = xS & szDzozmdt0(xN) = szNzAzT0 & $i(xN) & $i(xS) & % 79.87/11.68 $i(sz00) & $i(szNzAzT0) & aFunction0(xN) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 79.87/11.68 $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2 | ~ (sdtlpdtrp0(xN, v0) = v1) | % 79.87/11.68 ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) % 79.87/11.68 | ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v4, v1) % 79.87/11.68 | ~ aElementOf0(v0, szNzAzT0) | ~ aElement0(v4) | aElementOf0(v4, v3)) & % 79.87/11.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2 % 79.87/11.68 | ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, % 79.87/11.68 v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~ isCountable0(v1) | ~ % 79.87/11.68 aElementOf0(v4, v1) | ~ aElementOf0(v0, szNzAzT0) | ~ aElement0(v4) | ~ % 79.87/11.68 aSet0(v1) | aElementOf0(v4, v3) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, % 79.87/11.68 v1) & ~ aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! % 79.87/11.68 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ % 79.87/11.68 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | % 79.87/11.68 ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v4, v3) | % 79.87/11.68 ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v4, v1)) & ! [v0: $i] : ! [v1: % 79.87/11.68 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = % 79.87/11.68 v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | % 79.87/11.68 ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ % 79.87/11.68 aElementOf0(v4, v3) | ~ aElementOf0(v0, szNzAzT0) | aElement0(v4)) & ! % 79.87/11.68 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 79.87/11.68 (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) % 79.87/11.68 = v3) | ~ $i(v4) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~ % 79.87/11.68 isCountable0(v1) | ~ aElementOf0(v4, v1) | ~ aElementOf0(v0, szNzAzT0) | % 79.87/11.68 sdtlseqdt0(v2, v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 79.87/11.68 : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ % 79.87/11.68 (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~ isCountable0(v1) | ~ % 79.87/11.68 aElementOf0(v4, v3) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | % 79.87/11.68 aElementOf0(v4, v1) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, v1) & ~ % 79.87/11.68 aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 79.87/11.68 [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = % 79.87/11.68 v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~ % 79.87/11.68 isCountable0(v1) | ~ aElementOf0(v4, v3) | ~ aElementOf0(v0, szNzAzT0) | % 79.87/11.68 ~ aSet0(v1) | aElement0(v4) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, v1) & % 79.87/11.68 ~ aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 79.87/11.68 ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) % 79.87/11.68 = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~ % 79.87/11.68 isCountable0(v1) | ~ aElementOf0(v4, v1) | ~ aElementOf0(v0, szNzAzT0) | % 79.87/11.68 ~ aSet0(v1) | sdtlseqdt0(v2, v4) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, % 79.87/11.68 v1) & ~ aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! % 79.87/11.68 [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = % 79.87/11.68 v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ~ % 79.87/11.68 aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v2, v3) | ~ % 79.87/11.68 aElementOf0(v0, szNzAzT0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 79.87/11.68 [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ % 79.87/11.68 (sdtmndt0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ~ isCountable0(v1) | ~ % 79.87/11.68 aElementOf0(v2, v3) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | ? [v4: % 79.87/11.68 $i] : ($i(v4) & aElementOf0(v4, v1) & ~ aElementOf0(v4, szNzAzT0))) & ! % 79.87/11.68 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = % 79.87/11.68 v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | % 79.87/11.68 ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v0, % 79.87/11.68 szNzAzT0) | aElementOf0(v2, v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 79.87/11.68 : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ % 79.87/11.68 (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~ % 79.87/11.68 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | aSet0(v3)) & ! [v0: $i] : % 79.87/11.68 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ % 79.87/11.68 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ % 79.87/11.68 aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v0, % 79.87/11.68 szNzAzT0) | ? [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xN, v4) = v5 & % 79.87/11.68 szszuzczcdt0(v0) = v4 & $i(v5) & $i(v4) & aSubsetOf0(v5, v3) & % 79.87/11.68 isCountable0(v5) & aSet0(v5) & ! [v6: $i] : ( ~ $i(v6) | ~ % 79.87/11.68 aElementOf0(v6, v5) | aElementOf0(v6, v3)))) & ! [v0: $i] : ! [v1: $i] % 79.87/11.68 : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ % 79.87/11.68 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ % 79.87/11.68 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | % 79.87/11.68 aElementOf0(v2, v1) | ? [v4: $i] : ($i(v4) & aElementOf0(v4, v1) & ~ % 79.87/11.68 aElementOf0(v4, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 79.87/11.68 [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ % 79.87/11.68 (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ isCountable0(v1) | ~ % 79.87/11.68 aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | aSet0(v3) | ? [v4: $i] : ($i(v4) % 79.87/11.68 & aElementOf0(v4, v1) & ~ aElementOf0(v4, szNzAzT0))) & ! [v0: $i] : ! % 79.87/11.68 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ % 79.87/11.68 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ % 79.87/11.68 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | ? [v4: $i] % 79.87/11.68 : ? [v5: $i] : ? [v6: $i] : ($i(v6) & ((sdtlpdtrp0(xN, v4) = v5 & % 79.87/11.68 szszuzczcdt0(v0) = v4 & $i(v5) & $i(v4) & aSubsetOf0(v5, v3) & % 79.87/11.68 isCountable0(v5) & aSet0(v5) & ! [v7: $i] : ( ~ $i(v7) | ~ % 79.87/11.68 aElementOf0(v7, v5) | aElementOf0(v7, v3))) | (aElementOf0(v6, v1) & % 79.87/11.68 ~ aElementOf0(v6, szNzAzT0))))) % 79.87/11.68 % 79.87/11.68 (m__3754) % 79.87/11.68 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 79.87/11.68 : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) | % 79.87/11.68 ~ $i(v4) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v0) | ~ % 79.87/11.68 aElementOf0(v4, v2) | ~ aElementOf0(v1, szNzAzT0) | ~ aElementOf0(v0, % 79.87/11.68 szNzAzT0) | aElementOf0(v4, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 79.87/11.68 : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) | % 79.87/11.68 ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v0) | ~ aElementOf0(v1, szNzAzT0) % 79.87/11.68 | ~ aElementOf0(v0, szNzAzT0) | aSubsetOf0(v2, v3)) % 79.87/11.68 % 79.87/11.68 (m__3989) % 79.87/11.68 $i(xi) & $i(szNzAzT0) & aElementOf0(xi, szNzAzT0) % 79.87/11.68 % 79.87/11.68 (m__3989_02) % 79.87/11.69 $i(xQ) & $i(xi) & $i(xN) & $i(xk) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 79.87/11.69 ? [v3: $i] : (sdtlpdtrp0(xN, xi) = v0 & slbdtsldtrb0(v2, xk) = v3 & % 79.87/11.69 szmzizndt0(v0) = v1 & sbrdtbr0(xQ) = xk & sdtmndt0(v0, v1) = v2 & $i(v3) & % 79.87/11.69 $i(v2) & $i(v1) & $i(v0) & aSubsetOf0(xQ, v2) & aElementOf0(v1, v0) & % 79.87/11.69 aElementOf0(xQ, v3) & aSet0(v2) & aSet0(xQ) & ~ aElementOf0(v1, v2) & ! % 79.87/11.69 [v4: $i] : (v4 = v1 | ~ $i(v4) | ~ aElementOf0(v4, v0) | ~ aElement0(v4) % 79.87/11.69 | aElementOf0(v4, v2)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v2) % 79.87/11.69 | aElementOf0(v4, v0)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v2) % 79.87/11.69 | aElement0(v4)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v0) | % 79.87/11.69 sdtlseqdt0(v1, v4)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, xQ) | % 79.87/11.69 aElementOf0(v4, v2))) % 79.87/11.69 % 79.87/11.69 (m__4007) % 79.87/11.69 $i(xQ) & $i(xi) & $i(xN) & $i(xK) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 79.87/11.69 (sdtlpdtrp0(xN, xi) = v0 & szmzizndt0(v0) = v1 & sbrdtbr0(v2) = xK & % 79.87/11.69 sdtpldt0(xQ, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v1, v0) & % 79.87/11.69 aSet0(v2) & ! [v3: $i] : (v3 = v1 | ~ $i(v3) | ~ aElementOf0(v3, v2) | % 79.87/11.69 aElementOf0(v3, xQ)) & ! [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v2) | % 79.87/11.69 aElement0(v3)) & ! [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v0) | % 79.87/11.69 sdtlseqdt0(v1, v3)) & ! [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, xQ) | % 79.87/11.69 ~ aElement0(v3) | aElementOf0(v3, v2)) & ( ~ aElement0(v1) | % 79.87/11.69 aElementOf0(v1, v2))) % 79.87/11.69 % 79.87/11.69 (function-axioms) % 79.87/11.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 79.87/11.69 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 79.87/11.69 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 79.87/11.69 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 79.87/11.69 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 79.87/11.69 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 79.87/11.69 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 79.87/11.70 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 79.87/11.70 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 79.87/11.70 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 79.87/11.70 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 79.87/11.70 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 79.87/11.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 79.87/11.70 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 79.87/11.70 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 79.87/11.70 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 79.87/11.70 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 79.87/11.70 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 79.87/11.70 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 79.87/11.70 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 79.87/11.70 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 79.87/11.70 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 79.87/11.70 v0)) % 79.87/11.70 % 79.87/11.70 Further assumptions not needed in the proof: % 79.87/11.70 -------------------------------------------- % 79.87/11.70 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 79.87/11.70 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons, % 79.87/11.70 mDefDiff, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, mDefSel, % 79.87/11.70 mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet, % 79.87/11.70 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm, % 79.87/11.70 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, % 79.87/11.70 mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess, % 79.87/11.70 mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, % 79.87/11.70 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, % 79.87/11.70 m__3291, m__3398, m__3418, m__3435, m__3453, m__3462, m__3520, m__3533, m__3671, % 79.87/11.70 m__3821 % 79.87/11.70 % 79.87/11.70 Those formulas are unsatisfiable: % 79.87/11.70 --------------------------------- % 79.87/11.70 % 79.87/11.70 Begin of proof % 79.87/11.70 | % 79.87/11.70 | ALPHA: (mDefEmp) implies: % 79.87/11.70 | (1) aSet0(slcrc0) % 79.87/11.70 | % 79.87/11.70 | ALPHA: (mCountNFin_01) implies: % 79.87/11.70 | (2) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0) % 79.87/11.70 | % 79.87/11.70 | ALPHA: (mZeroNum) implies: % 79.87/11.70 | (3) aElementOf0(sz00, szNzAzT0) % 79.87/11.70 | % 79.87/11.70 | ALPHA: (mZeroLess) implies: % 79.87/11.70 | (4) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | % 79.87/11.70 | sdtlseqdt0(sz00, v0)) % 79.87/11.70 | % 79.87/11.70 | ALPHA: (m__3623) implies: % 79.87/11.70 | (5) $i(sz00) % 79.87/11.70 | (6) sdtlpdtrp0(xN, sz00) = xS % 79.87/11.70 | % 79.87/11.70 | ALPHA: (m__3754) implies: % 79.87/11.70 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 79.87/11.70 | (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) | ~ $i(v1) % 79.87/11.70 | | ~ $i(v0) | ~ sdtlseqdt0(v1, v0) | ~ aElementOf0(v1, szNzAzT0) | % 79.87/11.70 | ~ aElementOf0(v0, szNzAzT0) | aSubsetOf0(v2, v3)) % 79.87/11.70 | % 79.87/11.70 | ALPHA: (m__3989) implies: % 79.87/11.70 | (8) aElementOf0(xi, szNzAzT0) % 79.87/11.70 | % 79.87/11.70 | ALPHA: (m__3989_02) implies: % 79.87/11.71 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtlpdtrp0(xN, % 79.87/11.71 | xi) = v0 & slbdtsldtrb0(v2, xk) = v3 & szmzizndt0(v0) = v1 & % 79.87/11.71 | sbrdtbr0(xQ) = xk & sdtmndt0(v0, v1) = v2 & $i(v3) & $i(v2) & $i(v1) % 79.87/11.71 | & $i(v0) & aSubsetOf0(xQ, v2) & aElementOf0(v1, v0) & aElementOf0(xQ, % 79.87/11.71 | v3) & aSet0(v2) & aSet0(xQ) & ~ aElementOf0(v1, v2) & ! [v4: $i] % 79.87/11.71 | : (v4 = v1 | ~ $i(v4) | ~ aElementOf0(v4, v0) | ~ aElement0(v4) | % 79.87/11.71 | aElementOf0(v4, v2)) & ! [v4: $i] : ( ~ $i(v4) | ~ % 79.87/11.71 | aElementOf0(v4, v2) | aElementOf0(v4, v0)) & ! [v4: $i] : ( ~ % 79.87/11.71 | $i(v4) | ~ aElementOf0(v4, v2) | aElement0(v4)) & ! [v4: $i] : ( % 79.87/11.71 | ~ $i(v4) | ~ aElementOf0(v4, v0) | sdtlseqdt0(v1, v4)) & ! [v4: % 79.87/11.71 | $i] : ( ~ $i(v4) | ~ aElementOf0(v4, xQ) | aElementOf0(v4, v2))) % 79.87/11.71 | % 79.87/11.71 | ALPHA: (m__4007) implies: % 79.87/11.71 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtlpdtrp0(xN, xi) = v0 & % 79.87/11.71 | szmzizndt0(v0) = v1 & sbrdtbr0(v2) = xK & sdtpldt0(xQ, v1) = v2 & % 79.87/11.71 | $i(v2) & $i(v1) & $i(v0) & aElementOf0(v1, v0) & aSet0(v2) & ! [v3: % 79.87/11.71 | $i] : (v3 = v1 | ~ $i(v3) | ~ aElementOf0(v3, v2) | % 79.87/11.71 | aElementOf0(v3, xQ)) & ! [v3: $i] : ( ~ $i(v3) | ~ % 79.87/11.71 | aElementOf0(v3, v2) | aElement0(v3)) & ! [v3: $i] : ( ~ $i(v3) | % 79.87/11.71 | ~ aElementOf0(v3, v0) | sdtlseqdt0(v1, v3)) & ! [v3: $i] : ( ~ % 79.87/11.71 | $i(v3) | ~ aElementOf0(v3, xQ) | ~ aElement0(v3) | % 79.87/11.71 | aElementOf0(v3, v2)) & ( ~ aElement0(v1) | aElementOf0(v1, v2))) % 79.87/11.71 | % 79.87/11.71 | ALPHA: (m__) implies: % 79.87/11.71 | (11) $i(xi) % 79.87/11.71 | (12) ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xi) = v0 & $i(v1) & $i(v0) % 79.87/11.71 | & aElementOf0(v1, v0) & ~ aSubsetOf0(v0, xS) & ~ aElementOf0(v1, % 79.87/11.71 | xS)) % 79.87/11.71 | % 79.87/11.71 | ALPHA: (function-axioms) implies: % 79.87/11.71 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 79.87/11.71 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) % 79.87/11.71 | % 79.87/11.71 | DELTA: instantiating (12) with fresh symbols all_70_0, all_70_1 gives: % 79.87/11.71 | (14) sdtlpdtrp0(xN, xi) = all_70_1 & $i(all_70_0) & $i(all_70_1) & % 79.87/11.71 | aElementOf0(all_70_0, all_70_1) & ~ aSubsetOf0(all_70_1, xS) & ~ % 79.87/11.71 | aElementOf0(all_70_0, xS) % 79.87/11.71 | % 79.87/11.71 | ALPHA: (14) implies: % 79.87/11.71 | (15) ~ aSubsetOf0(all_70_1, xS) % 79.87/11.71 | (16) sdtlpdtrp0(xN, xi) = all_70_1 % 79.87/11.71 | % 79.87/11.71 | DELTA: instantiating (10) with fresh symbols all_72_0, all_72_1, all_72_2 % 79.87/11.71 | gives: % 79.87/11.72 | (17) sdtlpdtrp0(xN, xi) = all_72_2 & szmzizndt0(all_72_2) = all_72_1 & % 79.87/11.72 | sbrdtbr0(all_72_0) = xK & sdtpldt0(xQ, all_72_1) = all_72_0 & % 79.87/11.72 | $i(all_72_0) & $i(all_72_1) & $i(all_72_2) & aElementOf0(all_72_1, % 79.87/11.72 | all_72_2) & aSet0(all_72_0) & ! [v0: any] : (v0 = all_72_1 | ~ % 79.87/11.72 | $i(v0) | ~ aElementOf0(v0, all_72_0) | aElementOf0(v0, xQ)) & ! % 79.87/11.72 | [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_72_0) | aElement0(v0)) % 79.87/11.72 | & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_72_2) | % 79.87/11.72 | sdtlseqdt0(all_72_1, v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 79.87/11.72 | aElementOf0(v0, xQ) | ~ aElement0(v0) | aElementOf0(v0, all_72_0)) % 79.87/11.72 | & ( ~ aElement0(all_72_1) | aElementOf0(all_72_1, all_72_0)) % 79.87/11.72 | % 79.87/11.72 | ALPHA: (17) implies: % 79.87/11.72 | (18) sdtlpdtrp0(xN, xi) = all_72_2 % 79.87/11.72 | % 79.87/11.72 | DELTA: instantiating (9) with fresh symbols all_75_0, all_75_1, all_75_2, % 79.87/11.72 | all_75_3 gives: % 80.16/11.72 | (19) sdtlpdtrp0(xN, xi) = all_75_3 & slbdtsldtrb0(all_75_1, xk) = all_75_0 % 80.16/11.72 | & szmzizndt0(all_75_3) = all_75_2 & sbrdtbr0(xQ) = xk & % 80.16/11.72 | sdtmndt0(all_75_3, all_75_2) = all_75_1 & $i(all_75_0) & $i(all_75_1) % 80.16/11.72 | & $i(all_75_2) & $i(all_75_3) & aSubsetOf0(xQ, all_75_1) & % 80.16/11.72 | aElementOf0(all_75_2, all_75_3) & aElementOf0(xQ, all_75_0) & % 80.16/11.72 | aSet0(all_75_1) & aSet0(xQ) & ~ aElementOf0(all_75_2, all_75_1) & ! % 80.16/11.72 | [v0: any] : (v0 = all_75_2 | ~ $i(v0) | ~ aElementOf0(v0, all_75_3) % 80.16/11.72 | | ~ aElement0(v0) | aElementOf0(v0, all_75_1)) & ! [v0: $i] : ( ~ % 80.16/11.72 | $i(v0) | ~ aElementOf0(v0, all_75_1) | aElementOf0(v0, all_75_3)) & % 80.16/11.72 | ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_75_1) | % 80.16/11.72 | aElement0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, % 80.16/11.72 | all_75_3) | sdtlseqdt0(all_75_2, v0)) & ! [v0: $i] : ( ~ $i(v0) | % 80.16/11.72 | ~ aElementOf0(v0, xQ) | aElementOf0(v0, all_75_1)) % 80.16/11.72 | % 80.16/11.72 | ALPHA: (19) implies: % 80.16/11.72 | (20) sdtlpdtrp0(xN, xi) = all_75_3 % 80.16/11.72 | % 80.16/11.72 | BETA: splitting (2) gives: % 80.16/11.72 | % 80.16/11.72 | Case 1: % 80.16/11.72 | | % 80.16/11.72 | | (21) ~ aSet0(slcrc0) % 80.16/11.72 | | % 80.16/11.72 | | PRED_UNIFY: (1), (21) imply: % 80.16/11.72 | | (22) $false % 80.16/11.72 | | % 80.16/11.72 | | CLOSE: (22) is inconsistent. % 80.16/11.72 | | % 80.16/11.72 | Case 2: % 80.16/11.72 | | % 80.16/11.72 | | % 80.16/11.72 | | GROUND_INST: instantiating (13) with all_72_2, all_75_3, xi, xN, simplifying % 80.16/11.72 | | with (18), (20) gives: % 80.16/11.72 | | (23) all_75_3 = all_72_2 % 80.16/11.72 | | % 80.16/11.72 | | GROUND_INST: instantiating (13) with all_70_1, all_75_3, xi, xN, simplifying % 80.16/11.72 | | with (16), (20) gives: % 80.16/11.72 | | (24) all_75_3 = all_70_1 % 80.16/11.72 | | % 80.16/11.73 | | COMBINE_EQS: (23), (24) imply: % 80.16/11.73 | | (25) all_72_2 = all_70_1 % 80.16/11.73 | | % 80.16/11.73 | | SIMP: (25) implies: % 80.16/11.73 | | (26) all_72_2 = all_70_1 % 80.16/11.73 | | % 80.16/11.73 | | GROUND_INST: instantiating (4) with xi, simplifying with (8), (11) gives: % 80.16/11.73 | | (27) sdtlseqdt0(sz00, xi) % 80.16/11.73 | | % 80.16/11.73 | | GROUND_INST: instantiating (7) with xi, sz00, all_70_1, xS, simplifying with % 80.16/11.73 | | (3), (5), (6), (8), (11), (15), (16), (27) gives: % 80.16/11.73 | | (28) $false % 80.16/11.73 | | % 80.16/11.73 | | CLOSE: (28) is inconsistent. % 80.16/11.73 | | % 80.16/11.73 | End of split % 80.16/11.73 | % 80.16/11.73 End of proof % 80.16/11.73 % SZS output end Proof for theBenchmark % 80.16/11.73 % 80.16/11.73 11154ms %------------------------------------------------------------------------------