%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM581+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 : n019.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 118.50s 16.69s % Output : Proof 118.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : NUM581+3 : TPTP v8.1.2. Released v4.0.0. % 0.13/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n019.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Aug 25 12:01:28 EDT 2023 % 0.20/0.34 % CPUTime : % 0.20/0.59 ________ _____ % 0.20/0.59 ___ __ \_________(_)________________________________ % 0.20/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.59 % 0.20/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.59 (2023-06-19) % 0.20/0.59 % 0.20/0.59 (c) Philipp Rümmer, 2009-2023 % 0.20/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.59 Amanda Stjerna. % 0.20/0.59 Free software under BSD-3-Clause. % 0.20/0.59 % 0.20/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.59 % 0.20/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.61 Running up to 7 provers in parallel. % 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.56/1.46 Prover 4: Preprocessing ... % 4.56/1.47 Prover 1: Preprocessing ... % 4.56/1.50 Prover 0: Preprocessing ... % 4.56/1.50 Prover 5: Preprocessing ... % 4.56/1.50 Prover 2: Preprocessing ... % 4.56/1.50 Prover 3: Preprocessing ... % 4.56/1.50 Prover 6: Preprocessing ... % 14.83/2.82 Prover 3: Constructing countermodel ... % 14.83/2.83 Prover 6: Proving ... % 14.83/2.84 Prover 1: Constructing countermodel ... % 17.06/3.09 Prover 5: Proving ... % 20.03/3.62 Prover 2: Proving ... % 28.58/4.65 Prover 4: Constructing countermodel ... % 32.62/5.16 Prover 0: Proving ... % 83.42/11.87 Prover 2: stopped % 83.42/11.87 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 84.47/12.02 Prover 7: Preprocessing ... % 86.86/12.29 Prover 7: Constructing countermodel ... % 99.89/13.95 Prover 5: stopped % 99.89/13.96 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 100.85/14.14 Prover 8: Preprocessing ... % 103.18/14.40 Prover 8: Warning: ignoring some quantifiers % 103.18/14.42 Prover 8: Constructing countermodel ... % 114.86/15.96 Prover 1: stopped % 114.86/15.96 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 115.92/16.07 Prover 9: Preprocessing ... % 115.92/16.12 Prover 7: Found proof (size 76) % 115.92/16.13 Prover 7: proved (4239ms) % 115.92/16.13 Prover 8: stopped % 115.92/16.13 Prover 4: stopped % 115.92/16.13 Prover 6: stopped % 115.92/16.14 Prover 3: stopped % 115.92/16.14 Prover 0: stopped % 118.50/16.69 Prover 9: Constructing countermodel ... % 118.50/16.69 Prover 9: stopped % 118.50/16.69 % 118.50/16.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 118.50/16.69 % 118.50/16.72 % SZS output start Proof for theBenchmark % 118.50/16.72 Assumptions after simplification: % 118.50/16.72 --------------------------------- % 118.50/16.72 % 118.50/16.72 (mDefCons) % 118.96/16.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 118.96/16.79 (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ % 118.96/16.79 aElement0(v1) | ~ aSet0(v3) | ~ aSet0(v0) | ? [v4: $i] : ($i(v4) & ( ~ % 118.96/16.79 aElementOf0(v4, v3) | ~ aElement0(v4) | ( ~ (v4 = v1) & ~ % 118.96/16.79 aElementOf0(v4, v0))) & (aElementOf0(v4, v3) | (aElement0(v4) & (v4 = % 118.96/16.79 v1 | aElementOf0(v4, v0)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 118.96/16.79 $i] : ! [v3: $i] : (v3 = v1 | ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ % 118.96/16.79 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | % 118.96/16.79 ~ aSet0(v0) | aElementOf0(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 118.96/16.79 $i] : ! [v3: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 118.96/16.79 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ % 118.96/16.79 aSet0(v0) | aElement0(v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 118.96/16.79 [v3: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 118.96/16.79 ~ $i(v0) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ aElement0(v1) | ~ % 118.96/16.79 aSet0(v0) | aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 118.96/16.79 ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 118.96/16.79 aElement0(v1) | ~ aSet0(v0) | aElementOf0(v1, v2)) & ! [v0: $i] : ! [v1: % 118.96/16.79 $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ % 118.96/16.79 $i(v0) | ~ aElement0(v1) | ~ aSet0(v0) | aSet0(v2)) % 118.96/16.79 % 118.96/16.79 (mDefSub) % 118.96/16.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 118.96/16.80 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) | % 118.96/16.80 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | % 118.96/16.80 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i] % 118.96/16.80 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) | % 118.96/16.80 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0))) % 118.96/16.80 % 118.96/16.80 (mEOfElem) % 118.96/16.80 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) | % 118.96/16.80 ~ aSet0(v0) | aElement0(v1)) % 118.96/16.80 % 118.96/16.80 (mNATSet) % 118.96/16.80 $i(szNzAzT0) & isCountable0(szNzAzT0) & aSet0(szNzAzT0) % 118.96/16.80 % 118.96/16.80 (mZeroLess) % 118.96/16.80 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, % 118.96/16.80 szNzAzT0) | sdtlseqdt0(sz00, v0)) % 118.96/16.80 % 118.96/16.80 (mZeroNum) % 118.96/16.80 $i(sz00) & $i(szNzAzT0) & aElementOf0(sz00, szNzAzT0) % 118.96/16.80 % 118.96/16.80 (m__) % 118.96/16.81 $i(xQ) & $i(xi) & $i(xN) & $i(xS) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 118.96/16.81 ? [v3: $i] : (sdtlpdtrp0(xN, xi) = v0 & szmzizndt0(v0) = v1 & sdtpldt0(xQ, v1) % 118.96/16.81 = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v3, v2) & % 118.96/16.81 aElementOf0(v1, v0) & aSet0(v2) & ~ aSubsetOf0(v2, xS) & ~ aElementOf0(v3, % 118.96/16.81 xS) & ! [v4: $i] : (v4 = v1 | ~ $i(v4) | ~ aElementOf0(v4, v2) | % 118.96/16.81 aElementOf0(v4, xQ)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v2) | % 118.96/16.81 aElement0(v4)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v0) | % 118.96/16.81 sdtlseqdt0(v1, v4)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, xQ) | % 118.96/16.81 ~ aElement0(v4) | aElementOf0(v4, v2)) & ( ~ aElement0(v1) | % 118.96/16.81 aElementOf0(v1, v2))) % 118.96/16.81 % 118.96/16.81 (m__3623) % 118.96/16.83 sdtlpdtrp0(xN, sz00) = xS & szDzozmdt0(xN) = szNzAzT0 & $i(xN) & $i(xS) & % 118.96/16.83 $i(sz00) & $i(szNzAzT0) & aFunction0(xN) & ! [v0: $i] : ! [v1: $i] : ( ~ % 118.96/16.83 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~ % 118.96/16.83 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] % 118.96/16.83 : ? [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xN, v4) = v5 & szmzizndt0(v1) = v2 % 118.96/16.83 & szszuzczcdt0(v0) = v4 & sdtmndt0(v1, v2) = v3 & $i(v5) & $i(v4) & $i(v3) % 118.96/16.83 & $i(v2) & aSubsetOf0(v5, v3) & isCountable0(v5) & aElementOf0(v2, v1) & % 118.96/16.83 aSet0(v5) & aSet0(v3) & ~ aElementOf0(v2, v3) & ! [v6: $i] : (v6 = v2 | % 118.96/16.83 ~ $i(v6) | ~ aElementOf0(v6, v1) | ~ aElement0(v6) | aElementOf0(v6, % 118.96/16.83 v3)) & ! [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6, v5) | % 118.96/16.83 aElementOf0(v6, v3)) & ! [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6, v3) % 118.96/16.83 | aElementOf0(v6, v1)) & ! [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6, % 118.96/16.83 v3) | aElement0(v6)) & ! [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6, % 118.96/16.83 v1) | sdtlseqdt0(v2, v6)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 118.96/16.83 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ isCountable0(v1) | ~ % 118.96/16.83 aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | ? [v2: $i] : ? [v3: $i] : ? % 118.96/16.83 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ($i(v6) & ((sdtlpdtrp0(xN, v4) = v5 & % 118.96/16.83 szmzizndt0(v1) = v2 & szszuzczcdt0(v0) = v4 & sdtmndt0(v1, v2) = v3 & % 118.96/16.83 $i(v5) & $i(v4) & $i(v3) & $i(v2) & aSubsetOf0(v5, v3) & % 118.96/16.83 isCountable0(v5) & aElementOf0(v2, v1) & aSet0(v5) & aSet0(v3) & ~ % 118.96/16.83 aElementOf0(v2, v3) & ! [v7: $i] : (v7 = v2 | ~ $i(v7) | ~ % 118.96/16.83 aElementOf0(v7, v1) | ~ aElement0(v7) | aElementOf0(v7, v3)) & ! % 118.96/16.83 [v7: $i] : ( ~ $i(v7) | ~ aElementOf0(v7, v5) | aElementOf0(v7, v3)) % 118.96/16.83 & ! [v7: $i] : ( ~ $i(v7) | ~ aElementOf0(v7, v3) | aElementOf0(v7, % 118.96/16.83 v1)) & ! [v7: $i] : ( ~ $i(v7) | ~ aElementOf0(v7, v3) | % 118.96/16.83 aElement0(v7)) & ! [v7: $i] : ( ~ $i(v7) | ~ aElementOf0(v7, v1) | % 118.96/16.83 sdtlseqdt0(v2, v7))) | (aElementOf0(v6, v1) & ~ aElementOf0(v6, % 118.96/16.83 szNzAzT0))))) & ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = % 118.96/16.83 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] % 118.96/16.83 : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (sdtlpdtrp0(xN, v0) = v2 & % 118.96/16.83 $i(v6) & $i(v2) & ( ~ isCountable0(v2) | (sdtlpdtrp0(xN, v1) = v5 & % 118.96/16.83 szmzizndt0(v2) = v3 & sdtmndt0(v2, v3) = v4 & $i(v5) & $i(v4) & $i(v3) % 118.96/16.83 & aSubsetOf0(v5, v4) & isCountable0(v5) & aElementOf0(v3, v2) & % 118.96/16.83 aSet0(v5) & aSet0(v4) & ~ aElementOf0(v3, v4) & ! [v7: $i] : (v7 = % 118.96/16.83 v3 | ~ $i(v7) | ~ aElementOf0(v7, v2) | ~ aElement0(v7) | % 118.96/16.83 aElementOf0(v7, v4)) & ! [v7: $i] : ( ~ $i(v7) | ~ aElementOf0(v7, % 118.96/16.83 v5) | aElementOf0(v7, v4)) & ! [v7: $i] : ( ~ $i(v7) | ~ % 118.96/16.83 aElementOf0(v7, v4) | aElementOf0(v7, v2)) & ! [v7: $i] : ( ~ % 118.96/16.83 $i(v7) | ~ aElementOf0(v7, v4) | aElement0(v7)) & ! [v7: $i] : ( ~ % 118.96/16.83 $i(v7) | ~ aElementOf0(v7, v2) | sdtlseqdt0(v3, v7))) | ( ~ % 118.96/16.83 aSubsetOf0(v2, szNzAzT0) & ( ~ aSet0(v2) | (aElementOf0(v6, v2) & ~ % 118.96/16.83 aElementOf0(v6, szNzAzT0))))))) % 118.96/16.83 % 118.96/16.83 (m__3671) % 118.96/16.83 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 118.96/16.83 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v2, v1) | % 118.96/16.83 ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v2, szNzAzT0)) & ! [v0: $i] : ! % 118.96/16.83 [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, % 118.96/16.83 szNzAzT0) | aSubsetOf0(v1, szNzAzT0)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 118.96/16.83 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | % 118.96/16.83 isCountable0(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = % 118.96/16.83 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | aSet0(v1)) % 118.96/16.83 % 118.96/16.84 (m__3754) % 118.96/16.84 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 118.96/16.84 : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) | % 118.96/16.84 ~ $i(v4) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v0) | ~ % 118.96/16.84 aElementOf0(v4, v2) | ~ aElementOf0(v1, szNzAzT0) | ~ aElementOf0(v0, % 118.96/16.84 szNzAzT0) | aElementOf0(v4, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 118.96/16.84 : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) | % 118.96/16.84 ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v0) | ~ aElementOf0(v1, szNzAzT0) % 118.96/16.84 | ~ aElementOf0(v0, szNzAzT0) | aSubsetOf0(v2, v3)) % 118.96/16.84 % 118.96/16.84 (m__3989) % 118.96/16.84 $i(xi) & $i(szNzAzT0) & aElementOf0(xi, szNzAzT0) % 118.96/16.84 % 118.96/16.84 (m__3989_02) % 118.96/16.84 $i(xQ) & $i(xi) & $i(xN) & $i(xk) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 118.96/16.84 ? [v3: $i] : (sdtlpdtrp0(xN, xi) = v0 & slbdtsldtrb0(v2, xk) = v3 & % 118.96/16.84 szmzizndt0(v0) = v1 & sbrdtbr0(xQ) = xk & sdtmndt0(v0, v1) = v2 & $i(v3) & % 118.96/16.84 $i(v2) & $i(v1) & $i(v0) & aSubsetOf0(xQ, v2) & aElementOf0(v1, v0) & % 118.96/16.84 aElementOf0(xQ, v3) & aSet0(v2) & aSet0(xQ) & ~ aElementOf0(v1, v2) & ! % 118.96/16.84 [v4: $i] : (v4 = v1 | ~ $i(v4) | ~ aElementOf0(v4, v0) | ~ aElement0(v4) % 118.96/16.84 | aElementOf0(v4, v2)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v2) % 118.96/16.84 | aElementOf0(v4, v0)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v2) % 118.96/16.84 | aElement0(v4)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v0) | % 118.96/16.84 sdtlseqdt0(v1, v4)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, xQ) | % 118.96/16.84 aElementOf0(v4, v2))) % 118.96/16.84 % 118.96/16.84 (m__4007) % 118.96/16.84 $i(xQ) & $i(xi) & $i(xN) & $i(xK) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 118.96/16.84 (sdtlpdtrp0(xN, xi) = v0 & szmzizndt0(v0) = v1 & sbrdtbr0(v2) = xK & % 118.96/16.84 sdtpldt0(xQ, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v1, v0) & % 118.96/16.84 aSet0(v2) & ! [v3: $i] : (v3 = v1 | ~ $i(v3) | ~ aElementOf0(v3, v2) | % 118.96/16.84 aElementOf0(v3, xQ)) & ! [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v2) | % 118.96/16.84 aElement0(v3)) & ! [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v0) | % 118.96/16.84 sdtlseqdt0(v1, v3)) & ! [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, xQ) | % 118.96/16.84 ~ aElement0(v3) | aElementOf0(v3, v2)) & ( ~ aElement0(v1) | % 118.96/16.84 aElementOf0(v1, v2))) % 118.96/16.84 % 118.96/16.84 (function-axioms) % 118.96/16.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 118.96/16.85 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 118.96/16.85 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 118.96/16.85 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 118.96/16.85 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 118.96/16.85 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 118.96/16.85 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 118.96/16.85 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 118.96/16.85 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 118.96/16.85 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 118.96/16.85 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 118.96/16.85 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 118.96/16.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 118.96/16.85 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 118.96/16.85 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 118.96/16.85 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 118.96/16.85 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 118.96/16.85 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 118.96/16.85 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 118.96/16.85 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 118.96/16.85 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 118.96/16.85 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 118.96/16.85 v0)) % 118.96/16.85 % 118.96/16.85 Further assumptions not needed in the proof: % 118.96/16.85 -------------------------------------------- % 118.96/16.85 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 118.96/16.85 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 118.96/16.85 mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, % 118.96/16.85 mDefSel, mDiffCons, mDirichlet, mDomSet, mElmSort, mEmpFin, mFConsSet, % 118.96/16.85 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm, % 118.96/16.85 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, % 118.96/16.85 mMinMin, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess, % 118.96/16.85 mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, % 118.96/16.85 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, % 118.96/16.85 m__3291, m__3398, m__3418, m__3435, m__3453, m__3462, m__3520, m__3533, m__3821 % 118.96/16.85 % 118.96/16.85 Those formulas are unsatisfiable: % 118.96/16.85 --------------------------------- % 118.96/16.85 % 118.96/16.85 Begin of proof % 118.96/16.85 | % 118.96/16.85 | ALPHA: (mDefSub) implies: % 118.96/16.85 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 118.96/16.85 | $i(v0) | ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ % 118.96/16.85 | aSet0(v0) | aElementOf0(v2, v0)) % 118.96/16.85 | % 118.96/16.85 | ALPHA: (mDefCons) implies: % 118.96/16.85 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ % 118.96/16.85 | (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 118.96/16.85 | $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | % 118.96/16.85 | aElementOf0(v3, v0)) % 118.96/16.85 | % 118.96/16.85 | ALPHA: (mNATSet) implies: % 118.96/16.85 | (3) aSet0(szNzAzT0) % 118.96/16.85 | % 118.96/16.85 | ALPHA: (mZeroNum) implies: % 118.96/16.85 | (4) aElementOf0(sz00, szNzAzT0) % 118.96/16.85 | % 118.96/16.85 | ALPHA: (mZeroLess) implies: % 118.96/16.85 | (5) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | % 118.96/16.85 | sdtlseqdt0(sz00, v0)) % 118.96/16.85 | % 118.96/16.85 | ALPHA: (m__3623) implies: % 118.96/16.85 | (6) $i(sz00) % 118.96/16.85 | (7) sdtlpdtrp0(xN, sz00) = xS % 118.96/16.85 | % 118.96/16.85 | ALPHA: (m__3671) implies: % 118.96/16.86 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) % 118.96/16.86 | | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~ aElementOf0(v0, % 118.96/16.86 | szNzAzT0) | aElementOf0(v2, szNzAzT0)) % 118.96/16.86 | % 118.96/16.86 | ALPHA: (m__3754) implies: % 118.96/16.86 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 118.96/16.86 | ~ (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) | ~ % 118.96/16.86 | $i(v4) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v0) | ~ % 118.96/16.86 | aElementOf0(v4, v2) | ~ aElementOf0(v1, szNzAzT0) | ~ % 118.96/16.86 | aElementOf0(v0, szNzAzT0) | aElementOf0(v4, v3)) % 118.96/16.86 | % 118.96/16.86 | ALPHA: (m__3989) implies: % 118.96/16.86 | (10) aElementOf0(xi, szNzAzT0) % 118.96/16.86 | (11) $i(szNzAzT0) % 118.96/16.86 | % 118.96/16.86 | ALPHA: (m__3989_02) implies: % 118.96/16.86 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 118.96/16.86 | (sdtlpdtrp0(xN, xi) = v0 & slbdtsldtrb0(v2, xk) = v3 & szmzizndt0(v0) % 118.96/16.86 | = v1 & sbrdtbr0(xQ) = xk & sdtmndt0(v0, v1) = v2 & $i(v3) & $i(v2) & % 118.96/16.86 | $i(v1) & $i(v0) & aSubsetOf0(xQ, v2) & aElementOf0(v1, v0) & % 118.96/16.86 | aElementOf0(xQ, v3) & aSet0(v2) & aSet0(xQ) & ~ aElementOf0(v1, v2) % 118.96/16.86 | & ! [v4: $i] : (v4 = v1 | ~ $i(v4) | ~ aElementOf0(v4, v0) | ~ % 118.96/16.86 | aElement0(v4) | aElementOf0(v4, v2)) & ! [v4: $i] : ( ~ $i(v4) | % 118.96/16.86 | ~ aElementOf0(v4, v2) | aElementOf0(v4, v0)) & ! [v4: $i] : ( ~ % 118.96/16.86 | $i(v4) | ~ aElementOf0(v4, v2) | aElement0(v4)) & ! [v4: $i] : ( % 118.96/16.86 | ~ $i(v4) | ~ aElementOf0(v4, v0) | sdtlseqdt0(v1, v4)) & ! [v4: % 118.96/16.86 | $i] : ( ~ $i(v4) | ~ aElementOf0(v4, xQ) | aElementOf0(v4, v2))) % 118.96/16.86 | % 118.96/16.86 | ALPHA: (m__4007) implies: % 118.96/16.86 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtlpdtrp0(xN, xi) = v0 & % 118.96/16.86 | szmzizndt0(v0) = v1 & sbrdtbr0(v2) = xK & sdtpldt0(xQ, v1) = v2 & % 118.96/16.86 | $i(v2) & $i(v1) & $i(v0) & aElementOf0(v1, v0) & aSet0(v2) & ! [v3: % 118.96/16.86 | $i] : (v3 = v1 | ~ $i(v3) | ~ aElementOf0(v3, v2) | % 118.96/16.86 | aElementOf0(v3, xQ)) & ! [v3: $i] : ( ~ $i(v3) | ~ % 118.96/16.86 | aElementOf0(v3, v2) | aElement0(v3)) & ! [v3: $i] : ( ~ $i(v3) | % 118.96/16.86 | ~ aElementOf0(v3, v0) | sdtlseqdt0(v1, v3)) & ! [v3: $i] : ( ~ % 118.96/16.86 | $i(v3) | ~ aElementOf0(v3, xQ) | ~ aElement0(v3) | % 118.96/16.86 | aElementOf0(v3, v2)) & ( ~ aElement0(v1) | aElementOf0(v1, v2))) % 118.96/16.86 | % 118.96/16.86 | ALPHA: (m__) implies: % 118.96/16.86 | (14) $i(xi) % 118.96/16.86 | (15) $i(xQ) % 118.96/16.86 | (16) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 118.96/16.86 | (sdtlpdtrp0(xN, xi) = v0 & szmzizndt0(v0) = v1 & sdtpldt0(xQ, v1) = v2 % 118.96/16.86 | & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v3, v2) & % 118.96/16.86 | aElementOf0(v1, v0) & aSet0(v2) & ~ aSubsetOf0(v2, xS) & ~ % 118.96/16.86 | aElementOf0(v3, xS) & ! [v4: $i] : (v4 = v1 | ~ $i(v4) | ~ % 118.96/16.86 | aElementOf0(v4, v2) | aElementOf0(v4, xQ)) & ! [v4: $i] : ( ~ % 118.96/16.86 | $i(v4) | ~ aElementOf0(v4, v2) | aElement0(v4)) & ! [v4: $i] : ( % 118.96/16.86 | ~ $i(v4) | ~ aElementOf0(v4, v0) | sdtlseqdt0(v1, v4)) & ! [v4: % 118.96/16.86 | $i] : ( ~ $i(v4) | ~ aElementOf0(v4, xQ) | ~ aElement0(v4) | % 118.96/16.86 | aElementOf0(v4, v2)) & ( ~ aElement0(v1) | aElementOf0(v1, v2))) % 118.96/16.86 | % 118.96/16.86 | ALPHA: (function-axioms) implies: % 118.96/16.87 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 118.96/16.87 | (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) = v0)) % 118.96/16.87 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 118.96/16.87 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 118.96/16.87 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 118.96/16.87 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) % 118.96/16.87 | % 118.96/16.87 | DELTA: instantiating (13) with fresh symbols all_70_0, all_70_1, all_70_2 % 118.96/16.87 | gives: % 118.96/16.87 | (20) sdtlpdtrp0(xN, xi) = all_70_2 & szmzizndt0(all_70_2) = all_70_1 & % 118.96/16.87 | sbrdtbr0(all_70_0) = xK & sdtpldt0(xQ, all_70_1) = all_70_0 & % 118.96/16.87 | $i(all_70_0) & $i(all_70_1) & $i(all_70_2) & aElementOf0(all_70_1, % 118.96/16.87 | all_70_2) & aSet0(all_70_0) & ! [v0: any] : (v0 = all_70_1 | ~ % 118.96/16.87 | $i(v0) | ~ aElementOf0(v0, all_70_0) | aElementOf0(v0, xQ)) & ! % 118.96/16.87 | [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_70_0) | aElement0(v0)) % 118.96/16.87 | & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_70_2) | % 118.96/16.87 | sdtlseqdt0(all_70_1, v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 118.96/16.87 | aElementOf0(v0, xQ) | ~ aElement0(v0) | aElementOf0(v0, all_70_0)) % 118.96/16.87 | & ( ~ aElement0(all_70_1) | aElementOf0(all_70_1, all_70_0)) % 118.96/16.87 | % 118.96/16.87 | ALPHA: (20) implies: % 118.96/16.87 | (21) sdtpldt0(xQ, all_70_1) = all_70_0 % 118.96/16.87 | (22) szmzizndt0(all_70_2) = all_70_1 % 118.96/16.87 | (23) sdtlpdtrp0(xN, xi) = all_70_2 % 118.96/16.87 | % 118.96/16.87 | DELTA: instantiating (16) with fresh symbols all_73_0, all_73_1, all_73_2, % 118.96/16.87 | all_73_3 gives: % 118.96/16.87 | (24) sdtlpdtrp0(xN, xi) = all_73_3 & szmzizndt0(all_73_3) = all_73_2 & % 118.96/16.87 | sdtpldt0(xQ, all_73_2) = all_73_1 & $i(all_73_0) & $i(all_73_1) & % 118.96/16.87 | $i(all_73_2) & $i(all_73_3) & aElementOf0(all_73_0, all_73_1) & % 118.96/16.87 | aElementOf0(all_73_2, all_73_3) & aSet0(all_73_1) & ~ % 118.96/16.87 | aSubsetOf0(all_73_1, xS) & ~ aElementOf0(all_73_0, xS) & ! [v0: any] % 118.96/16.87 | : (v0 = all_73_2 | ~ $i(v0) | ~ aElementOf0(v0, all_73_1) | % 118.96/16.87 | aElementOf0(v0, xQ)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, % 118.96/16.87 | all_73_1) | aElement0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 118.96/16.87 | aElementOf0(v0, all_73_3) | sdtlseqdt0(all_73_2, v0)) & ! [v0: $i] % 118.96/16.87 | : ( ~ $i(v0) | ~ aElementOf0(v0, xQ) | ~ aElement0(v0) | % 118.96/16.87 | aElementOf0(v0, all_73_1)) & ( ~ aElement0(all_73_2) | % 118.96/16.87 | aElementOf0(all_73_2, all_73_1)) % 118.96/16.87 | % 118.96/16.87 | ALPHA: (24) implies: % 118.96/16.87 | (25) ~ aElementOf0(all_73_0, xS) % 118.96/16.87 | (26) aElementOf0(all_73_2, all_73_3) % 118.96/16.87 | (27) aElementOf0(all_73_0, all_73_1) % 118.96/16.87 | (28) $i(all_73_2) % 118.96/16.87 | (29) $i(all_73_1) % 118.96/16.87 | (30) $i(all_73_0) % 118.96/16.87 | (31) sdtpldt0(xQ, all_73_2) = all_73_1 % 118.96/16.88 | (32) szmzizndt0(all_73_3) = all_73_2 % 118.96/16.88 | (33) sdtlpdtrp0(xN, xi) = all_73_3 % 118.96/16.88 | % 118.96/16.88 | DELTA: instantiating (12) with fresh symbols all_76_0, all_76_1, all_76_2, % 118.96/16.88 | all_76_3 gives: % 118.96/16.88 | (34) sdtlpdtrp0(xN, xi) = all_76_3 & slbdtsldtrb0(all_76_1, xk) = all_76_0 % 118.96/16.88 | & szmzizndt0(all_76_3) = all_76_2 & sbrdtbr0(xQ) = xk & % 118.96/16.88 | sdtmndt0(all_76_3, all_76_2) = all_76_1 & $i(all_76_0) & $i(all_76_1) % 118.96/16.88 | & $i(all_76_2) & $i(all_76_3) & aSubsetOf0(xQ, all_76_1) & % 118.96/16.88 | aElementOf0(all_76_2, all_76_3) & aElementOf0(xQ, all_76_0) & % 118.96/16.88 | aSet0(all_76_1) & aSet0(xQ) & ~ aElementOf0(all_76_2, all_76_1) & ! % 118.96/16.88 | [v0: any] : (v0 = all_76_2 | ~ $i(v0) | ~ aElementOf0(v0, all_76_3) % 118.96/16.88 | | ~ aElement0(v0) | aElementOf0(v0, all_76_1)) & ! [v0: $i] : ( ~ % 118.96/16.88 | $i(v0) | ~ aElementOf0(v0, all_76_1) | aElementOf0(v0, all_76_3)) & % 118.96/16.88 | ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_76_1) | % 118.96/16.88 | aElement0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, % 118.96/16.88 | all_76_3) | sdtlseqdt0(all_76_2, v0)) & ! [v0: $i] : ( ~ $i(v0) | % 118.96/16.88 | ~ aElementOf0(v0, xQ) | aElementOf0(v0, all_76_1)) % 118.96/16.88 | % 118.96/16.88 | ALPHA: (34) implies: % 118.96/16.88 | (35) aSet0(xQ) % 118.96/16.88 | (36) aSet0(all_76_1) % 118.96/16.88 | (37) aSubsetOf0(xQ, all_76_1) % 118.96/16.88 | (38) $i(all_76_1) % 118.96/16.88 | (39) szmzizndt0(all_76_3) = all_76_2 % 118.96/16.88 | (40) sdtlpdtrp0(xN, xi) = all_76_3 % 118.96/16.88 | (41) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_76_1) | % 118.96/16.88 | aElementOf0(v0, all_76_3)) % 118.96/16.88 | % 118.96/16.88 | GROUND_INST: instantiating (18) with all_70_0, all_73_1, all_70_1, xQ, % 118.96/16.88 | simplifying with (21) gives: % 118.96/16.88 | (42) all_73_1 = all_70_0 | ~ (sdtpldt0(xQ, all_70_1) = all_73_1) % 118.96/16.88 | % 118.96/16.88 | GROUND_INST: instantiating (17) with all_73_2, all_76_2, all_73_3, simplifying % 118.96/16.88 | with (32) gives: % 118.96/16.88 | (43) all_76_2 = all_73_2 | ~ (szmzizndt0(all_73_3) = all_76_2) % 118.96/16.88 | % 118.96/16.88 | GROUND_INST: instantiating (17) with all_70_1, all_76_2, all_70_2, simplifying % 118.96/16.88 | with (22) gives: % 118.96/16.88 | (44) all_76_2 = all_70_1 | ~ (szmzizndt0(all_70_2) = all_76_2) % 118.96/16.88 | % 118.96/16.88 | GROUND_INST: instantiating (19) with all_73_3, all_76_3, xi, xN, simplifying % 118.96/16.88 | with (33), (40) gives: % 118.96/16.88 | (45) all_76_3 = all_73_3 % 118.96/16.88 | % 118.96/16.88 | GROUND_INST: instantiating (19) with all_70_2, all_76_3, xi, xN, simplifying % 118.96/16.88 | with (23), (40) gives: % 118.96/16.88 | (46) all_76_3 = all_70_2 % 118.96/16.88 | % 118.96/16.88 | COMBINE_EQS: (45), (46) imply: % 118.96/16.88 | (47) all_73_3 = all_70_2 % 118.96/16.88 | % 118.96/16.88 | SIMP: (47) implies: % 118.96/16.88 | (48) all_73_3 = all_70_2 % 118.96/16.88 | % 118.96/16.88 | REDUCE: (39), (46) imply: % 118.96/16.88 | (49) szmzizndt0(all_70_2) = all_76_2 % 118.96/16.88 | % 118.96/16.88 | REDUCE: (26), (48) imply: % 118.96/16.88 | (50) aElementOf0(all_73_2, all_70_2) % 118.96/16.88 | % 118.96/16.88 | BETA: splitting (44) gives: % 118.96/16.88 | % 118.96/16.88 | Case 1: % 118.96/16.88 | | % 118.96/16.88 | | (51) ~ (szmzizndt0(all_70_2) = all_76_2) % 118.96/16.88 | | % 118.96/16.88 | | PRED_UNIFY: (49), (51) imply: % 118.96/16.88 | | (52) $false % 118.96/16.89 | | % 118.96/16.89 | | CLOSE: (52) is inconsistent. % 118.96/16.89 | | % 118.96/16.89 | Case 2: % 118.96/16.89 | | % 118.96/16.89 | | (53) all_76_2 = all_70_1 % 118.96/16.89 | | % 118.96/16.89 | | BETA: splitting (43) gives: % 118.96/16.89 | | % 118.96/16.89 | | Case 1: % 118.96/16.89 | | | % 118.96/16.89 | | | (54) ~ (szmzizndt0(all_73_3) = all_76_2) % 118.96/16.89 | | | % 118.96/16.89 | | | REDUCE: (48), (53), (54) imply: % 118.96/16.89 | | | (55) ~ (szmzizndt0(all_70_2) = all_70_1) % 118.96/16.89 | | | % 118.96/16.89 | | | PRED_UNIFY: (22), (55) imply: % 118.96/16.89 | | | (56) $false % 118.96/16.89 | | | % 118.96/16.89 | | | CLOSE: (56) is inconsistent. % 118.96/16.89 | | | % 118.96/16.89 | | Case 2: % 118.96/16.89 | | | % 118.96/16.89 | | | (57) all_76_2 = all_73_2 % 118.96/16.89 | | | % 118.96/16.89 | | | COMBINE_EQS: (53), (57) imply: % 118.96/16.89 | | | (58) all_73_2 = all_70_1 % 118.96/16.89 | | | % 118.96/16.89 | | | SIMP: (58) implies: % 118.96/16.89 | | | (59) all_73_2 = all_70_1 % 118.96/16.89 | | | % 118.96/16.89 | | | REDUCE: (31), (59) imply: % 118.96/16.89 | | | (60) sdtpldt0(xQ, all_70_1) = all_73_1 % 118.96/16.89 | | | % 118.96/16.89 | | | REDUCE: (28), (59) imply: % 118.96/16.89 | | | (61) $i(all_70_1) % 118.96/16.89 | | | % 118.96/16.89 | | | REDUCE: (50), (59) imply: % 118.96/16.89 | | | (62) aElementOf0(all_70_1, all_70_2) % 118.96/16.89 | | | % 118.96/16.89 | | | BETA: splitting (42) gives: % 118.96/16.89 | | | % 118.96/16.89 | | | Case 1: % 118.96/16.89 | | | | % 118.96/16.89 | | | | (63) ~ (sdtpldt0(xQ, all_70_1) = all_73_1) % 118.96/16.89 | | | | % 118.96/16.89 | | | | PRED_UNIFY: (60), (63) imply: % 118.96/16.89 | | | | (64) $false % 118.96/16.89 | | | | % 118.96/16.89 | | | | CLOSE: (64) is inconsistent. % 118.96/16.89 | | | | % 118.96/16.89 | | | Case 2: % 118.96/16.89 | | | | % 118.96/16.89 | | | | (65) all_73_1 = all_70_0 % 118.96/16.89 | | | | % 118.96/16.89 | | | | REDUCE: (29), (65) imply: % 118.96/16.89 | | | | (66) $i(all_70_0) % 118.96/16.89 | | | | % 118.96/16.89 | | | | REDUCE: (27), (65) imply: % 118.96/16.89 | | | | (67) aElementOf0(all_73_0, all_70_0) % 118.96/16.89 | | | | % 118.96/16.89 | | | | GROUND_INST: instantiating (5) with xi, simplifying with (10), (14) % 118.96/16.89 | | | | gives: % 118.96/16.89 | | | | (68) sdtlseqdt0(sz00, xi) % 118.96/16.89 | | | | % 118.96/16.89 | | | | GROUND_INST: instantiating (mEOfElem) with szNzAzT0, all_70_1, % 118.96/16.89 | | | | simplifying with (3), (11), (61) gives: % 118.96/16.89 | | | | (69) ~ aElementOf0(all_70_1, szNzAzT0) | aElement0(all_70_1) % 118.96/16.89 | | | | % 118.96/16.89 | | | | GROUND_INST: instantiating (41) with all_73_0, simplifying with (30) % 118.96/16.89 | | | | gives: % 118.96/16.89 | | | | (70) ~ aElementOf0(all_73_0, all_76_1) | aElementOf0(all_73_0, % 118.96/16.89 | | | | all_76_3) % 118.96/16.89 | | | | % 118.96/16.89 | | | | GROUND_INST: instantiating (1) with all_76_1, xQ, all_73_0, simplifying % 118.96/16.89 | | | | with (15), (30), (36), (37), (38) gives: % 118.96/16.89 | | | | (71) ~ aElementOf0(all_73_0, xQ) | aElementOf0(all_73_0, all_76_1) % 118.96/16.89 | | | | % 118.96/16.89 | | | | GROUND_INST: instantiating (8) with xi, all_70_2, all_70_1, simplifying % 118.96/16.89 | | | | with (10), (14), (23), (61), (62) gives: % 118.96/16.89 | | | | (72) aElementOf0(all_70_1, szNzAzT0) % 118.96/16.89 | | | | % 118.96/16.89 | | | | BETA: splitting (69) gives: % 118.96/16.89 | | | | % 118.96/16.89 | | | | Case 1: % 118.96/16.89 | | | | | % 118.96/16.89 | | | | | (73) ~ aElementOf0(all_70_1, szNzAzT0) % 118.96/16.89 | | | | | % 118.96/16.89 | | | | | PRED_UNIFY: (72), (73) imply: % 118.96/16.89 | | | | | (74) $false % 118.96/16.89 | | | | | % 118.96/16.89 | | | | | CLOSE: (74) is inconsistent. % 118.96/16.89 | | | | | % 118.96/16.89 | | | | Case 2: % 118.96/16.89 | | | | | % 118.96/16.89 | | | | | (75) aElement0(all_70_1) % 118.96/16.89 | | | | | % 118.96/16.89 | | | | | GROUND_INST: instantiating (2) with xQ, all_70_1, all_70_0, all_73_0, % 118.96/16.89 | | | | | simplifying with (15), (21), (30), (35), (61), (66), % 118.96/16.89 | | | | | (67), (75) gives: % 118.96/16.89 | | | | | (76) all_73_0 = all_70_1 | aElementOf0(all_73_0, xQ) % 118.96/16.89 | | | | | % 118.96/16.89 | | | | | GROUND_INST: instantiating (9) with xi, sz00, all_70_2, xS, all_73_0, % 118.96/16.89 | | | | | simplifying with (4), (6), (7), (10), (14), (23), (25), % 118.96/16.89 | | | | | (30), (68) gives: % 118.96/16.89 | | | | | (77) ~ aElementOf0(all_73_0, all_70_2) % 118.96/16.89 | | | | | % 118.96/16.89 | | | | | BETA: splitting (70) gives: % 118.96/16.89 | | | | | % 118.96/16.89 | | | | | Case 1: % 118.96/16.89 | | | | | | % 118.96/16.89 | | | | | | (78) ~ aElementOf0(all_73_0, all_76_1) % 118.96/16.89 | | | | | | % 118.96/16.89 | | | | | | BETA: splitting (71) gives: % 118.96/16.89 | | | | | | % 118.96/16.89 | | | | | | Case 1: % 118.96/16.89 | | | | | | | % 118.96/16.89 | | | | | | | (79) ~ aElementOf0(all_73_0, xQ) % 118.96/16.89 | | | | | | | % 118.96/16.89 | | | | | | | BETA: splitting (76) gives: % 118.96/16.89 | | | | | | | % 118.96/16.89 | | | | | | | Case 1: % 118.96/16.89 | | | | | | | | % 118.96/16.89 | | | | | | | | (80) aElementOf0(all_73_0, xQ) % 118.96/16.89 | | | | | | | | % 118.96/16.89 | | | | | | | | PRED_UNIFY: (79), (80) imply: % 118.96/16.89 | | | | | | | | (81) $false % 118.96/16.89 | | | | | | | | % 118.96/16.89 | | | | | | | | CLOSE: (81) is inconsistent. % 118.96/16.89 | | | | | | | | % 118.96/16.89 | | | | | | | Case 2: % 118.96/16.89 | | | | | | | | % 118.96/16.89 | | | | | | | | (82) all_73_0 = all_70_1 % 118.96/16.89 | | | | | | | | % 118.96/16.89 | | | | | | | | REDUCE: (77), (82) imply: % 118.96/16.89 | | | | | | | | (83) ~ aElementOf0(all_70_1, all_70_2) % 118.96/16.89 | | | | | | | | % 118.96/16.89 | | | | | | | | PRED_UNIFY: (62), (83) imply: % 118.96/16.89 | | | | | | | | (84) $false % 118.96/16.89 | | | | | | | | % 118.96/16.89 | | | | | | | | CLOSE: (84) is inconsistent. % 118.96/16.89 | | | | | | | | % 118.96/16.89 | | | | | | | End of split % 118.96/16.89 | | | | | | | % 118.96/16.89 | | | | | | Case 2: % 118.96/16.89 | | | | | | | % 118.96/16.89 | | | | | | | (85) aElementOf0(all_73_0, all_76_1) % 118.96/16.89 | | | | | | | % 118.96/16.89 | | | | | | | PRED_UNIFY: (78), (85) imply: % 118.96/16.89 | | | | | | | (86) $false % 118.96/16.89 | | | | | | | % 118.96/16.89 | | | | | | | CLOSE: (86) is inconsistent. % 118.96/16.89 | | | | | | | % 118.96/16.89 | | | | | | End of split % 118.96/16.89 | | | | | | % 118.96/16.89 | | | | | Case 2: % 118.96/16.89 | | | | | | % 118.96/16.89 | | | | | | (87) aElementOf0(all_73_0, all_76_3) % 118.96/16.89 | | | | | | % 118.96/16.89 | | | | | | REDUCE: (46), (87) imply: % 118.96/16.89 | | | | | | (88) aElementOf0(all_73_0, all_70_2) % 118.96/16.89 | | | | | | % 118.96/16.89 | | | | | | PRED_UNIFY: (77), (88) imply: % 118.96/16.89 | | | | | | (89) $false % 118.96/16.89 | | | | | | % 118.96/16.89 | | | | | | CLOSE: (89) is inconsistent. % 118.96/16.89 | | | | | | % 118.96/16.89 | | | | | End of split % 118.96/16.89 | | | | | % 118.96/16.89 | | | | End of split % 118.96/16.89 | | | | % 118.96/16.89 | | | End of split % 118.96/16.89 | | | % 118.96/16.89 | | End of split % 118.96/16.89 | | % 118.96/16.89 | End of split % 118.96/16.89 | % 118.96/16.89 End of proof % 118.96/16.90 % SZS output end Proof for theBenchmark % 118.96/16.90 % 118.96/16.90 16301ms %------------------------------------------------------------------------------