%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM603+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 : n007.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 11:48:54 EDT 2023 % Result : Theorem 54.84s 7.99s % Output : Proof 74.92s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM603+3 : TPTP v8.1.2. Released v4.0.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n007.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Aug 25 13:59:56 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 6.26/1.55 Prover 1: Preprocessing ... % 6.26/1.56 Prover 4: Preprocessing ... % 6.26/1.60 Prover 3: Preprocessing ... % 6.26/1.60 Prover 2: Preprocessing ... % 6.26/1.61 Prover 5: Preprocessing ... % 6.26/1.61 Prover 6: Preprocessing ... % 6.26/1.62 Prover 0: Preprocessing ... % 19.58/3.36 Prover 3: Constructing countermodel ... % 19.58/3.36 Prover 1: Constructing countermodel ... % 19.72/3.38 Prover 6: Proving ... % 23.57/3.91 Prover 5: Proving ... % 44.57/6.63 Prover 4: Constructing countermodel ... % 49.48/7.31 Prover 0: Proving ... % 50.10/7.35 Prover 2: Proving ... % 54.84/7.99 Prover 3: proved (7361ms) % 54.84/7.99 % 54.84/7.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 54.84/7.99 % 54.84/7.99 Prover 5: stopped % 54.84/8.00 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 54.84/8.00 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 54.84/8.00 Prover 6: stopped % 54.84/8.04 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 56.08/8.14 Prover 0: stopped % 56.08/8.15 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 56.26/8.17 Prover 2: stopped % 56.26/8.17 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 57.77/8.41 Prover 7: Preprocessing ... % 57.77/8.41 Prover 8: Preprocessing ... % 57.77/8.43 Prover 10: Preprocessing ... % 58.99/8.53 Prover 13: Preprocessing ... % 59.15/8.53 Prover 11: Preprocessing ... % 61.48/8.83 Prover 8: Warning: ignoring some quantifiers % 61.48/8.85 Prover 8: Constructing countermodel ... % 64.61/9.27 Prover 10: Constructing countermodel ... % 65.16/9.32 Prover 13: Warning: ignoring some quantifiers % 65.16/9.36 Prover 7: Constructing countermodel ... % 66.35/9.48 Prover 13: Constructing countermodel ... % 69.66/9.90 Prover 10: Found proof (size 24) % 69.66/9.90 Prover 10: proved (1867ms) % 69.66/9.90 Prover 4: stopped % 69.66/9.90 Prover 8: stopped % 69.66/9.90 Prover 13: stopped % 69.66/9.91 Prover 1: stopped % 69.66/9.91 Prover 7: stopped % 74.02/10.99 Prover 11: Constructing countermodel ... % 74.20/11.02 Prover 11: stopped % 74.20/11.02 % 74.20/11.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 74.20/11.02 % 74.20/11.02 % SZS output start Proof for theBenchmark % 74.20/11.03 Assumptions after simplification: % 74.20/11.03 --------------------------------- % 74.20/11.04 % 74.20/11.04 (mCountNFin_01) % 74.20/11.04 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)) % 74.20/11.04 % 74.20/11.04 (mDefEmp) % 74.20/11.05 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~ % 74.20/11.05 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : ( % 74.20/11.05 ~ $i(v0) | ~ aElementOf0(v0, slcrc0)) % 74.20/11.05 % 74.20/11.05 (mZeroLess) % 74.20/11.05 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, % 74.20/11.05 szNzAzT0) | sdtlseqdt0(sz00, v0)) % 74.20/11.05 % 74.20/11.05 (mZeroNum) % 74.20/11.05 $i(sz00) & $i(szNzAzT0) & aElementOf0(sz00, szNzAzT0) % 74.20/11.05 % 74.20/11.05 (m__) % 74.20/11.09 $i(xi) & $i(xN) & $i(xS) & ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xi) = % 74.20/11.09 v0 & $i(v1) & $i(v0) & aElementOf0(v1, v0) & ~ aSubsetOf0(v0, xS) & ~ % 74.20/11.09 aElementOf0(v1, xS)) % 74.20/11.09 % 74.20/11.09 (m__3623) % 74.65/11.12 sdtlpdtrp0(xN, sz00) = xS & szDzozmdt0(xN) = szNzAzT0 & $i(xN) & $i(xS) & % 74.65/11.12 $i(sz00) & $i(szNzAzT0) & aFunction0(xN) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 74.65/11.12 $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2 | ~ (sdtlpdtrp0(xN, v0) = v1) | % 74.65/11.12 ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) % 74.65/11.12 | ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v4, v1) % 74.65/11.12 | ~ aElementOf0(v0, szNzAzT0) | ~ aElement0(v4) | aElementOf0(v4, v3)) & % 74.65/11.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2 % 74.65/11.12 | ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, % 74.65/11.12 v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~ isCountable0(v1) | ~ % 74.65/11.12 aElementOf0(v4, v1) | ~ aElementOf0(v0, szNzAzT0) | ~ aElement0(v4) | ~ % 74.65/11.12 aSet0(v1) | aElementOf0(v4, v3) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, % 74.65/11.12 v1) & ~ aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! % 74.65/11.12 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ % 74.65/11.12 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | % 74.65/11.12 ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v4, v3) | % 74.65/11.12 ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v4, v1)) & ! [v0: $i] : ! [v1: % 74.65/11.12 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = % 74.65/11.12 v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | % 74.65/11.12 ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ % 74.65/11.12 aElementOf0(v4, v3) | ~ aElementOf0(v0, szNzAzT0) | aElement0(v4)) & ! % 74.65/11.12 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 74.65/11.12 (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) % 74.65/11.12 = v3) | ~ $i(v4) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~ % 74.65/11.12 isCountable0(v1) | ~ aElementOf0(v4, v1) | ~ aElementOf0(v0, szNzAzT0) | % 74.65/11.12 sdtlseqdt0(v2, v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 74.65/11.12 : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ % 74.65/11.12 (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~ isCountable0(v1) | ~ % 74.65/11.12 aElementOf0(v4, v3) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | % 74.65/11.12 aElementOf0(v4, v1) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, v1) & ~ % 74.65/11.12 aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 74.65/11.12 [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = % 74.65/11.12 v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~ % 74.65/11.12 isCountable0(v1) | ~ aElementOf0(v4, v3) | ~ aElementOf0(v0, szNzAzT0) | % 74.65/11.12 ~ aSet0(v1) | aElement0(v4) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, v1) & % 74.65/11.12 ~ aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 74.65/11.12 ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) % 74.65/11.12 = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~ % 74.65/11.12 isCountable0(v1) | ~ aElementOf0(v4, v1) | ~ aElementOf0(v0, szNzAzT0) | % 74.65/11.12 ~ aSet0(v1) | sdtlseqdt0(v2, v4) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, % 74.65/11.12 v1) & ~ aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! % 74.65/11.12 [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = % 74.65/11.12 v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ~ % 74.65/11.12 aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v2, v3) | ~ % 74.65/11.12 aElementOf0(v0, szNzAzT0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 74.65/11.12 [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ % 74.65/11.12 (sdtmndt0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ~ isCountable0(v1) | ~ % 74.65/11.12 aElementOf0(v2, v3) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | ? [v4: % 74.65/11.12 $i] : ($i(v4) & aElementOf0(v4, v1) & ~ aElementOf0(v4, szNzAzT0))) & ! % 74.65/11.12 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = % 74.65/11.12 v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | % 74.65/11.12 ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v0, % 74.65/11.12 szNzAzT0) | aElementOf0(v2, v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 74.65/11.12 : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ % 74.65/11.12 (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~ % 74.65/11.12 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | aSet0(v3)) & ! [v0: $i] : % 74.65/11.12 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ % 74.65/11.12 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ % 74.65/11.12 aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v0, % 74.65/11.12 szNzAzT0) | ? [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xN, v4) = v5 & % 74.65/11.12 szszuzczcdt0(v0) = v4 & $i(v5) & $i(v4) & aSubsetOf0(v5, v3) & % 74.65/11.12 isCountable0(v5) & aSet0(v5) & ! [v6: $i] : ( ~ $i(v6) | ~ % 74.65/11.12 aElementOf0(v6, v5) | aElementOf0(v6, v3)))) & ! [v0: $i] : ! [v1: $i] % 74.65/11.12 : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ % 74.65/11.12 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ % 74.65/11.12 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | % 74.65/11.12 aElementOf0(v2, v1) | ? [v4: $i] : ($i(v4) & aElementOf0(v4, v1) & ~ % 74.65/11.12 aElementOf0(v4, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 74.65/11.12 [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ % 74.65/11.12 (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ isCountable0(v1) | ~ % 74.65/11.12 aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | aSet0(v3) | ? [v4: $i] : ($i(v4) % 74.65/11.12 & aElementOf0(v4, v1) & ~ aElementOf0(v4, szNzAzT0))) & ! [v0: $i] : ! % 74.65/11.12 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ % 74.65/11.12 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ % 74.65/11.12 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | ? [v4: $i] % 74.65/11.12 : ? [v5: $i] : ? [v6: $i] : ($i(v6) & ((sdtlpdtrp0(xN, v4) = v5 & % 74.65/11.12 szszuzczcdt0(v0) = v4 & $i(v5) & $i(v4) & aSubsetOf0(v5, v3) & % 74.65/11.12 isCountable0(v5) & aSet0(v5) & ! [v7: $i] : ( ~ $i(v7) | ~ % 74.65/11.12 aElementOf0(v7, v5) | aElementOf0(v7, v3))) | (aElementOf0(v6, v1) & % 74.65/11.12 ~ aElementOf0(v6, szNzAzT0))))) % 74.65/11.12 % 74.65/11.12 (m__3754) % 74.65/11.13 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 74.65/11.13 : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) | % 74.65/11.13 ~ $i(v4) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v0) | ~ % 74.65/11.13 aElementOf0(v4, v2) | ~ aElementOf0(v1, szNzAzT0) | ~ aElementOf0(v0, % 74.65/11.13 szNzAzT0) | aElementOf0(v4, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 74.65/11.13 : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) | % 74.65/11.13 ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v0) | ~ aElementOf0(v1, szNzAzT0) % 74.65/11.13 | ~ aElementOf0(v0, szNzAzT0) | aSubsetOf0(v2, v3)) % 74.65/11.13 % 74.65/11.13 (m__4660) % 74.65/11.13 szDzozmdt0(xe) = szNzAzT0 & $i(xe) & $i(xN) & $i(szNzAzT0) & aFunction0(xe) & % 74.65/11.13 ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) | ~ % 74.65/11.13 aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2 & % 74.65/11.13 szmzizndt0(v2) = v1 & $i(v2) & $i(v1) & aElementOf0(v1, v2) & ! [v3: $i] % 74.65/11.13 : ( ~ $i(v3) | ~ aElementOf0(v3, v2) | sdtlseqdt0(v1, v3)))) % 74.65/11.13 % 74.65/11.13 (m__5034) % 74.65/11.13 sdtlpdtrp0(xe, xi) = xx & $i(xi) & $i(xx) & $i(xe) & $i(szNzAzT0) & % 74.65/11.13 aElementOf0(xi, szNzAzT0) % 74.65/11.13 % 74.65/11.13 (function-axioms) % 74.65/11.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.65/11.14 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 74.65/11.14 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 74.65/11.14 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 74.65/11.14 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 74.65/11.14 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 74.65/11.14 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 74.65/11.14 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 74.65/11.14 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 74.65/11.14 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 74.65/11.14 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 74.65/11.14 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 74.65/11.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 74.65/11.14 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 74.65/11.14 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 74.65/11.14 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 74.65/11.14 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 74.65/11.14 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 74.65/11.14 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 74.65/11.14 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 74.65/11.14 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 74.65/11.14 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 74.65/11.14 v0)) % 74.65/11.14 % 74.65/11.14 Further assumptions not needed in the proof: % 74.65/11.14 -------------------------------------------- % 74.65/11.14 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 74.65/11.14 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons, % 74.65/11.14 mDefDiff, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, mDefSel, % 74.65/11.14 mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet, % 74.65/11.14 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm, % 74.65/11.14 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, % 74.65/11.14 mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess, % 74.65/11.14 mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, % 74.65/11.14 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, % 74.65/11.14 m__3291, m__3398, m__3418, m__3435, m__3453, m__3462, m__3520, m__3533, m__3671, % 74.65/11.14 m__3821, m__3965, m__4151, m__4182, m__4331, m__4411, m__4618, m__4730, m__4758, % 74.65/11.14 m__4854, m__4891, m__4908, m__4982, m__5009 % 74.65/11.14 % 74.65/11.14 Those formulas are unsatisfiable: % 74.65/11.14 --------------------------------- % 74.65/11.14 % 74.65/11.14 Begin of proof % 74.65/11.14 | % 74.65/11.14 | ALPHA: (mDefEmp) implies: % 74.65/11.14 | (1) aSet0(slcrc0) % 74.65/11.14 | % 74.65/11.14 | ALPHA: (mCountNFin_01) implies: % 74.65/11.14 | (2) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0) % 74.65/11.14 | % 74.65/11.14 | ALPHA: (mZeroNum) implies: % 74.65/11.14 | (3) aElementOf0(sz00, szNzAzT0) % 74.65/11.14 | % 74.65/11.14 | ALPHA: (mZeroLess) implies: % 74.65/11.14 | (4) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | % 74.65/11.14 | sdtlseqdt0(sz00, v0)) % 74.65/11.14 | % 74.65/11.14 | ALPHA: (m__3623) implies: % 74.65/11.15 | (5) $i(sz00) % 74.65/11.15 | (6) sdtlpdtrp0(xN, sz00) = xS % 74.65/11.15 | % 74.65/11.15 | ALPHA: (m__3754) implies: % 74.65/11.15 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 74.65/11.15 | (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) | ~ $i(v1) % 74.65/11.15 | | ~ $i(v0) | ~ sdtlseqdt0(v1, v0) | ~ aElementOf0(v1, szNzAzT0) | % 74.65/11.15 | ~ aElementOf0(v0, szNzAzT0) | aSubsetOf0(v2, v3)) % 74.65/11.15 | % 74.65/11.15 | ALPHA: (m__4660) implies: % 74.65/11.15 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) | % 74.65/11.15 | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2 % 74.65/11.15 | & szmzizndt0(v2) = v1 & $i(v2) & $i(v1) & aElementOf0(v1, v2) & ! % 74.65/11.15 | [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v2) | sdtlseqdt0(v1, % 74.65/11.15 | v3)))) % 74.65/11.15 | % 74.65/11.15 | ALPHA: (m__5034) implies: % 74.65/11.15 | (9) aElementOf0(xi, szNzAzT0) % 74.65/11.15 | (10) sdtlpdtrp0(xe, xi) = xx % 74.65/11.15 | % 74.65/11.15 | ALPHA: (m__) implies: % 74.65/11.15 | (11) $i(xi) % 74.65/11.15 | (12) ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xi) = v0 & $i(v1) & $i(v0) % 74.65/11.15 | & aElementOf0(v1, v0) & ~ aSubsetOf0(v0, xS) & ~ aElementOf0(v1, % 74.65/11.15 | xS)) % 74.65/11.15 | % 74.65/11.15 | ALPHA: (function-axioms) implies: % 74.65/11.15 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.65/11.15 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) % 74.65/11.15 | % 74.65/11.15 | DELTA: instantiating (12) with fresh symbols all_77_0, all_77_1 gives: % 74.65/11.15 | (14) sdtlpdtrp0(xN, xi) = all_77_1 & $i(all_77_0) & $i(all_77_1) & % 74.65/11.15 | aElementOf0(all_77_0, all_77_1) & ~ aSubsetOf0(all_77_1, xS) & ~ % 74.65/11.15 | aElementOf0(all_77_0, xS) % 74.65/11.15 | % 74.65/11.15 | ALPHA: (14) implies: % 74.65/11.15 | (15) ~ aSubsetOf0(all_77_1, xS) % 74.65/11.15 | (16) sdtlpdtrp0(xN, xi) = all_77_1 % 74.65/11.15 | % 74.65/11.15 | BETA: splitting (2) gives: % 74.65/11.15 | % 74.65/11.15 | Case 1: % 74.65/11.15 | | % 74.65/11.15 | | (17) ~ aSet0(slcrc0) % 74.65/11.15 | | % 74.65/11.15 | | PRED_UNIFY: (1), (17) imply: % 74.65/11.15 | | (18) $false % 74.65/11.15 | | % 74.65/11.15 | | CLOSE: (18) is inconsistent. % 74.65/11.15 | | % 74.65/11.15 | Case 2: % 74.65/11.15 | | % 74.65/11.15 | | % 74.65/11.15 | | GROUND_INST: instantiating (4) with xi, simplifying with (9), (11) gives: % 74.65/11.15 | | (19) sdtlseqdt0(sz00, xi) % 74.65/11.15 | | % 74.65/11.15 | | GROUND_INST: instantiating (8) with xi, xx, simplifying with (9), (10), (11) % 74.65/11.15 | | gives: % 74.92/11.15 | | (20) ? [v0: $i] : (sdtlpdtrp0(xN, xi) = v0 & szmzizndt0(v0) = xx & % 74.92/11.15 | | $i(v0) & $i(xx) & aElementOf0(xx, v0) & ! [v1: $i] : ( ~ $i(v1) | % 74.92/11.15 | | ~ aElementOf0(v1, v0) | sdtlseqdt0(xx, v1))) % 74.92/11.15 | | % 74.92/11.15 | | DELTA: instantiating (20) with fresh symbol all_123_0 gives: % 74.92/11.16 | | (21) sdtlpdtrp0(xN, xi) = all_123_0 & szmzizndt0(all_123_0) = xx & % 74.92/11.16 | | $i(all_123_0) & $i(xx) & aElementOf0(xx, all_123_0) & ! [v0: $i] : % 74.92/11.16 | | ( ~ $i(v0) | ~ aElementOf0(v0, all_123_0) | sdtlseqdt0(xx, v0)) % 74.92/11.16 | | % 74.92/11.16 | | ALPHA: (21) implies: % 74.92/11.16 | | (22) sdtlpdtrp0(xN, xi) = all_123_0 % 74.92/11.16 | | % 74.92/11.16 | | GROUND_INST: instantiating (13) with all_77_1, all_123_0, xi, xN, % 74.92/11.16 | | simplifying with (16), (22) gives: % 74.92/11.16 | | (23) all_123_0 = all_77_1 % 74.92/11.16 | | % 74.92/11.16 | | GROUND_INST: instantiating (7) with xi, sz00, all_77_1, xS, simplifying with % 74.92/11.16 | | (3), (5), (6), (9), (11), (15), (16), (19) gives: % 74.92/11.16 | | (24) $false % 74.92/11.16 | | % 74.92/11.16 | | CLOSE: (24) is inconsistent. % 74.92/11.16 | | % 74.92/11.16 | End of split % 74.92/11.16 | % 74.92/11.16 End of proof % 74.92/11.16 % SZS output end Proof for theBenchmark % 74.92/11.16 % 74.92/11.16 10550ms %------------------------------------------------------------------------------