%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM574+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 : n031.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 11:48:42 EDT 2023 % Result : Theorem 167.85s 22.96s % Output : Proof 168.69s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : NUM574+3 : TPTP v8.1.2. Released v4.0.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n031.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Aug 25 12:08:22 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 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 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 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 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 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 % 5.23/1.46 Prover 1: Preprocessing ... % 5.23/1.46 Prover 4: Preprocessing ... % 5.23/1.50 Prover 5: Preprocessing ... % 5.23/1.50 Prover 0: Preprocessing ... % 5.23/1.50 Prover 3: Preprocessing ... % 5.23/1.50 Prover 2: Preprocessing ... % 5.23/1.50 Prover 6: Preprocessing ... % 15.07/2.82 Prover 3: Constructing countermodel ... % 15.07/2.82 Prover 1: Constructing countermodel ... % 15.75/2.88 Prover 6: Proving ... % 16.33/2.98 Prover 5: Proving ... % 19.36/3.35 Prover 2: Proving ... % 24.86/4.08 Prover 4: Constructing countermodel ... % 27.90/4.47 Prover 0: Proving ... % 72.78/10.29 Prover 2: stopped % 72.78/10.29 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 73.62/10.41 Prover 7: Preprocessing ... % 75.53/10.70 Prover 7: Constructing countermodel ... % 100.78/13.96 Prover 5: stopped % 100.78/13.96 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 101.54/14.10 Prover 8: Preprocessing ... % 103.19/14.28 Prover 8: Warning: ignoring some quantifiers % 103.19/14.28 Prover 8: Constructing countermodel ... % 116.42/15.98 Prover 1: stopped % 116.42/15.99 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 117.24/16.09 Prover 9: Preprocessing ... % 123.30/16.96 Prover 9: Constructing countermodel ... % 130.88/17.87 Prover 6: stopped % 130.88/17.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 131.76/18.00 Prover 10: Preprocessing ... % 133.19/18.18 Prover 10: Constructing countermodel ... % 167.85/22.92 Prover 10: Found proof (size 71) % 167.85/22.92 Prover 10: proved (5032ms) % 167.85/22.93 Prover 9: stopped % 167.85/22.93 Prover 3: stopped % 167.85/22.93 Prover 4: stopped % 167.85/22.93 Prover 8: stopped % 167.85/22.94 Prover 0: stopped % 167.85/22.96 Prover 7: stopped % 167.85/22.96 % 167.85/22.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 167.85/22.96 % 167.85/22.96 % SZS output start Proof for theBenchmark % 167.85/22.97 Assumptions after simplification: % 167.85/22.97 --------------------------------- % 167.85/22.97 % 167.85/22.97 (mDefSub) % 167.85/22.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 167.85/22.98 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) | % 167.85/22.98 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | % 167.85/22.98 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i] % 167.85/22.98 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) | % 167.85/22.98 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0))) % 167.85/22.98 % 167.85/22.98 (mNatExtra) % 167.85/23.00 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ % 167.85/23.00 aElementOf0(v0, szNzAzT0) | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & % 167.85/23.00 aElementOf0(v1, szNzAzT0))) % 167.85/23.00 % 167.85/23.00 (mNoScLessZr) % 167.85/23.00 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = % 167.85/23.00 v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, sz00) | ~ aElementOf0(v0, szNzAzT0)) % 167.85/23.00 % 167.85/23.00 (mSegSucc) % 168.36/23.01 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slbdtrb0(v1) = % 168.36/23.01 v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ % 168.36/23.01 aElementOf0(v0, szNzAzT0) | ? [v3: $i] : ? [v4: $i] : ((v1 = v0 | % 168.36/23.01 aElementOf0(v0, v2) | (slbdtrb0(v3) = v4 & szszuzczcdt0(v1) = v3 & % 168.36/23.01 $i(v4) & $i(v3) & ~ aElementOf0(v0, v4))) & (( ~ (v1 = v0) & ~ % 168.36/23.01 aElementOf0(v0, v2)) | (slbdtrb0(v3) = v4 & szszuzczcdt0(v1) = v3 & % 168.36/23.01 $i(v4) & $i(v3) & aElementOf0(v0, v4))))) % 168.36/23.01 % 168.36/23.01 (mSegZero) % 168.36/23.01 slbdtrb0(sz00) = slcrc0 & $i(sz00) & $i(slcrc0) % 168.36/23.01 % 168.36/23.01 (mZeroNum) % 168.36/23.01 $i(sz00) & $i(szNzAzT0) & aElementOf0(sz00, szNzAzT0) % 168.36/23.01 % 168.36/23.01 (m__) % 168.36/23.01 $i(xi) & $i(xj) & $i(xN) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 168.36/23.01 (sdtlpdtrp0(xN, xi) = v0 & sdtlpdtrp0(xN, xj) = v1 & $i(v2) & $i(v1) & $i(v0) % 168.36/23.01 & sdtlseqdt0(xj, xi) & aElementOf0(v2, v0) & ~ aSubsetOf0(v0, v1) & ~ % 168.36/23.01 aElementOf0(v2, v1)) % 168.36/23.01 % 168.36/23.01 (m__3623) % 168.36/23.03 sdtlpdtrp0(xN, sz00) = xS & szDzozmdt0(xN) = szNzAzT0 & $i(xN) & $i(xS) & % 168.36/23.03 $i(sz00) & $i(szNzAzT0) & aFunction0(xN) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 168.36/23.03 $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2 | ~ (sdtlpdtrp0(xN, v0) = v1) | % 168.36/23.03 ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) % 168.36/23.03 | ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v4, v1) % 168.36/23.03 | ~ aElementOf0(v0, szNzAzT0) | ~ aElement0(v4) | aElementOf0(v4, v3)) & % 168.36/23.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2 % 168.36/23.03 | ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, % 168.36/23.03 v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~ isCountable0(v1) | ~ % 168.36/23.03 aElementOf0(v4, v1) | ~ aElementOf0(v0, szNzAzT0) | ~ aElement0(v4) | ~ % 168.36/23.03 aSet0(v1) | aElementOf0(v4, v3) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, % 168.36/23.03 v1) & ~ aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! % 168.36/23.03 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ % 168.36/23.03 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | % 168.36/23.03 ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v4, v3) | % 168.36/23.03 ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v4, v1)) & ! [v0: $i] : ! [v1: % 168.36/23.03 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = % 168.36/23.03 v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | % 168.36/23.03 ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ % 168.36/23.03 aElementOf0(v4, v3) | ~ aElementOf0(v0, szNzAzT0) | aElement0(v4)) & ! % 168.36/23.03 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 168.36/23.03 (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) % 168.36/23.03 = v3) | ~ $i(v4) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~ % 168.36/23.03 isCountable0(v1) | ~ aElementOf0(v4, v1) | ~ aElementOf0(v0, szNzAzT0) | % 168.36/23.03 sdtlseqdt0(v2, v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 168.36/23.03 : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ % 168.36/23.03 (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~ isCountable0(v1) | ~ % 168.36/23.03 aElementOf0(v4, v3) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | % 168.36/23.03 aElementOf0(v4, v1) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, v1) & ~ % 168.36/23.03 aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 168.36/23.03 [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = % 168.36/23.03 v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~ % 168.36/23.03 isCountable0(v1) | ~ aElementOf0(v4, v3) | ~ aElementOf0(v0, szNzAzT0) | % 168.36/23.03 ~ aSet0(v1) | aElement0(v4) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, v1) & % 168.36/23.03 ~ aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 168.36/23.03 ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) % 168.36/23.03 = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~ % 168.36/23.03 isCountable0(v1) | ~ aElementOf0(v4, v1) | ~ aElementOf0(v0, szNzAzT0) | % 168.36/23.03 ~ aSet0(v1) | sdtlseqdt0(v2, v4) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, % 168.36/23.03 v1) & ~ aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! % 168.36/23.03 [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = % 168.36/23.03 v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ~ % 168.36/23.03 aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v2, v3) | ~ % 168.36/23.03 aElementOf0(v0, szNzAzT0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 168.36/23.03 [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ % 168.36/23.03 (sdtmndt0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ~ isCountable0(v1) | ~ % 168.36/23.03 aElementOf0(v2, v3) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | ? [v4: % 168.36/23.03 $i] : ($i(v4) & aElementOf0(v4, v1) & ~ aElementOf0(v4, szNzAzT0))) & ! % 168.36/23.03 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = % 168.36/23.03 v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | % 168.36/23.03 ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v0, % 168.36/23.03 szNzAzT0) | aElementOf0(v2, v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 168.36/23.03 : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ % 168.36/23.03 (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~ % 168.36/23.03 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | aSet0(v3)) & ! [v0: $i] : % 168.36/23.03 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ % 168.36/23.03 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ % 168.36/23.03 aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v0, % 168.36/23.03 szNzAzT0) | ? [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xN, v4) = v5 & % 168.36/23.03 szszuzczcdt0(v0) = v4 & $i(v5) & $i(v4) & aSubsetOf0(v5, v3) & % 168.36/23.03 isCountable0(v5) & aSet0(v5) & ! [v6: $i] : ( ~ $i(v6) | ~ % 168.36/23.03 aElementOf0(v6, v5) | aElementOf0(v6, v3)))) & ! [v0: $i] : ! [v1: $i] % 168.36/23.03 : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ % 168.36/23.03 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ % 168.36/23.03 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | % 168.36/23.03 aElementOf0(v2, v1) | ? [v4: $i] : ($i(v4) & aElementOf0(v4, v1) & ~ % 168.36/23.03 aElementOf0(v4, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 168.36/23.03 [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ % 168.36/23.03 (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ isCountable0(v1) | ~ % 168.36/23.03 aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | aSet0(v3) | ? [v4: $i] : ($i(v4) % 168.36/23.03 & aElementOf0(v4, v1) & ~ aElementOf0(v4, szNzAzT0))) & ! [v0: $i] : ! % 168.36/23.03 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ % 168.36/23.03 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ % 168.36/23.03 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | ? [v4: $i] % 168.36/23.03 : ? [v5: $i] : ? [v6: $i] : ($i(v6) & ((sdtlpdtrp0(xN, v4) = v5 & % 168.36/23.03 szszuzczcdt0(v0) = v4 & $i(v5) & $i(v4) & aSubsetOf0(v5, v3) & % 168.36/23.03 isCountable0(v5) & aSet0(v5) & ! [v7: $i] : ( ~ $i(v7) | ~ % 168.36/23.03 aElementOf0(v7, v5) | aElementOf0(v7, v3))) | (aElementOf0(v6, v1) & % 168.36/23.03 ~ aElementOf0(v6, szNzAzT0))))) % 168.36/23.03 % 168.36/23.03 (m__3671) % 168.36/23.03 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 168.36/23.03 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v2, v1) | % 168.36/23.03 ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v2, szNzAzT0)) & ! [v0: $i] : ! % 168.36/23.03 [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, % 168.36/23.03 szNzAzT0) | aSubsetOf0(v1, szNzAzT0)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 168.36/23.03 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | % 168.36/23.03 isCountable0(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = % 168.36/23.03 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | aSet0(v1)) % 168.36/23.03 % 168.36/23.03 (m__3786) % 168.36/23.04 $i(xi) & $i(xj) & $i(szNzAzT0) & aElementOf0(xi, szNzAzT0) & aElementOf0(xj, % 168.36/23.04 szNzAzT0) % 168.36/23.04 % 168.36/23.04 (m__3786_02) % 168.36/23.04 $i(xi) & $i(xj) & $i(xN) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] : ( ~ % 168.36/23.04 sdtlseqdt0(xj, xi) | ! [v2: $i] : ( ~ (szszuzczcdt0(v2) = xi) | ~ $i(v2) | % 168.36/23.04 ~ aElementOf0(v2, szNzAzT0)) | (sdtlpdtrp0(xN, xi) = v0 & sdtlpdtrp0(xN, % 168.36/23.04 xj) = v1 & $i(v1) & $i(v0) & aSubsetOf0(v0, v1) & ! [v2: $i] : ( ~ % 168.36/23.04 $i(v2) | ~ aElementOf0(v2, v0) | aElementOf0(v2, v1)))) % 168.36/23.04 % 168.36/23.04 (function-axioms) % 168.36/23.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 168.36/23.04 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 168.36/23.04 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 168.36/23.04 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 168.36/23.04 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 168.36/23.04 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 168.36/23.04 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 168.36/23.04 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 168.36/23.04 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 168.36/23.04 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 168.36/23.04 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 168.36/23.04 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 168.36/23.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 168.36/23.04 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 168.36/23.04 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 168.36/23.04 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 168.36/23.04 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 168.36/23.04 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 168.36/23.04 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 168.36/23.04 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 168.36/23.04 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 168.36/23.04 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 168.36/23.04 v0)) % 168.36/23.04 % 168.36/23.04 Further assumptions not needed in the proof: % 168.36/23.04 -------------------------------------------- % 168.36/23.04 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 168.36/23.04 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 168.36/23.04 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, % 168.36/23.04 mDefSeg, mDefSel, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, % 168.36/23.04 mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, % 168.36/23.04 mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, % 168.36/23.04 mLessTrans, mMinMin, mNATSet, mNatNSucc, mPttSet, mSegFin, mSegLess, mSelCSet, % 168.36/23.04 mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl, % 168.36/23.04 mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, m__3291, m__3398, % 168.36/23.04 m__3418, m__3435, m__3453, m__3462, m__3520, m__3533, m__3754 % 168.36/23.04 % 168.36/23.04 Those formulas are unsatisfiable: % 168.36/23.04 --------------------------------- % 168.36/23.04 % 168.36/23.04 Begin of proof % 168.36/23.04 | % 168.36/23.04 | ALPHA: (mDefSub) implies: % 168.36/23.05 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ % 168.36/23.05 | aSet0(v0) | aSubsetOf0(v1, v0) | ? [v2: $i] : ($i(v2) & % 168.36/23.05 | aElementOf0(v2, v1) & ~ aElementOf0(v2, v0))) % 168.36/23.05 | % 168.36/23.05 | ALPHA: (mZeroNum) implies: % 168.36/23.05 | (2) aElementOf0(sz00, szNzAzT0) % 168.36/23.05 | % 168.36/23.05 | ALPHA: (mNatExtra) implies: % 168.36/23.05 | (3) ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | % 168.36/23.05 | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & aElementOf0(v1, % 168.36/23.05 | szNzAzT0))) % 168.36/23.05 | % 168.36/23.05 | ALPHA: (mNoScLessZr) implies: % 168.36/23.05 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) | % 168.36/23.05 | ~ sdtlseqdt0(v1, sz00) | ~ aElementOf0(v0, szNzAzT0)) % 168.36/23.05 | % 168.36/23.05 | ALPHA: (mSegZero) implies: % 168.36/23.05 | (5) slbdtrb0(sz00) = slcrc0 % 168.36/23.05 | % 168.36/23.05 | ALPHA: (mSegSucc) implies: % 168.36/23.05 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slbdtrb0(v1) = v2) | ~ % 168.36/23.05 | $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ % 168.36/23.05 | aElementOf0(v0, szNzAzT0) | ? [v3: $i] : ? [v4: $i] : ((v1 = v0 | % 168.36/23.05 | aElementOf0(v0, v2) | (slbdtrb0(v3) = v4 & szszuzczcdt0(v1) = v3 % 168.36/23.05 | & $i(v4) & $i(v3) & ~ aElementOf0(v0, v4))) & (( ~ (v1 = v0) & % 168.36/23.05 | ~ aElementOf0(v0, v2)) | (slbdtrb0(v3) = v4 & szszuzczcdt0(v1) % 168.36/23.05 | = v3 & $i(v4) & $i(v3) & aElementOf0(v0, v4))))) % 168.36/23.05 | % 168.36/23.05 | ALPHA: (m__3623) implies: % 168.36/23.05 | (7) $i(sz00) % 168.36/23.05 | (8) sdtlpdtrp0(xN, sz00) = xS % 168.36/23.05 | % 168.36/23.05 | ALPHA: (m__3671) implies: % 168.36/23.05 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | % 168.36/23.05 | ~ aElementOf0(v0, szNzAzT0) | aSet0(v1)) % 168.36/23.05 | % 168.36/23.05 | ALPHA: (m__3786) implies: % 168.36/23.05 | (10) aElementOf0(xj, szNzAzT0) % 168.36/23.05 | (11) aElementOf0(xi, szNzAzT0) % 168.36/23.05 | % 168.36/23.05 | ALPHA: (m__3786_02) implies: % 168.36/23.05 | (12) ? [v0: $i] : ? [v1: $i] : ( ~ sdtlseqdt0(xj, xi) | ! [v2: $i] : ( ~ % 168.36/23.05 | (szszuzczcdt0(v2) = xi) | ~ $i(v2) | ~ aElementOf0(v2, % 168.36/23.05 | szNzAzT0)) | (sdtlpdtrp0(xN, xi) = v0 & sdtlpdtrp0(xN, xj) = v1 % 168.36/23.05 | & $i(v1) & $i(v0) & aSubsetOf0(v0, v1) & ! [v2: $i] : ( ~ $i(v2) % 168.36/23.05 | | ~ aElementOf0(v2, v0) | aElementOf0(v2, v1)))) % 168.36/23.05 | % 168.36/23.05 | ALPHA: (m__) implies: % 168.36/23.05 | (13) $i(xj) % 168.36/23.05 | (14) $i(xi) % 168.36/23.05 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtlpdtrp0(xN, xi) = v0 & % 168.36/23.05 | sdtlpdtrp0(xN, xj) = v1 & $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(xj, % 168.36/23.05 | xi) & aElementOf0(v2, v0) & ~ aSubsetOf0(v0, v1) & ~ % 168.36/23.05 | aElementOf0(v2, v1)) % 168.36/23.05 | % 168.36/23.05 | ALPHA: (function-axioms) implies: % 168.36/23.06 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 168.36/23.06 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) % 168.36/23.06 | % 168.36/23.06 | DELTA: instantiating (15) with fresh symbols all_69_0, all_69_1, all_69_2 % 168.36/23.06 | gives: % 168.36/23.06 | (17) sdtlpdtrp0(xN, xi) = all_69_2 & sdtlpdtrp0(xN, xj) = all_69_1 & % 168.36/23.06 | $i(all_69_0) & $i(all_69_1) & $i(all_69_2) & sdtlseqdt0(xj, xi) & % 168.36/23.06 | aElementOf0(all_69_0, all_69_2) & ~ aSubsetOf0(all_69_2, all_69_1) & % 168.36/23.06 | ~ aElementOf0(all_69_0, all_69_1) % 168.36/23.06 | % 168.36/23.06 | ALPHA: (17) implies: % 168.36/23.06 | (18) ~ aSubsetOf0(all_69_2, all_69_1) % 168.36/23.06 | (19) sdtlseqdt0(xj, xi) % 168.36/23.06 | (20) $i(all_69_2) % 168.36/23.06 | (21) sdtlpdtrp0(xN, xj) = all_69_1 % 168.36/23.06 | (22) sdtlpdtrp0(xN, xi) = all_69_2 % 168.36/23.06 | % 168.36/23.06 | DELTA: instantiating (12) with fresh symbols all_71_0, all_71_1 gives: % 168.36/23.06 | (23) ~ sdtlseqdt0(xj, xi) | ! [v0: $i] : ( ~ (szszuzczcdt0(v0) = xi) | ~ % 168.36/23.06 | $i(v0) | ~ aElementOf0(v0, szNzAzT0)) | (sdtlpdtrp0(xN, xi) = % 168.36/23.06 | all_71_1 & sdtlpdtrp0(xN, xj) = all_71_0 & $i(all_71_0) & % 168.36/23.06 | $i(all_71_1) & aSubsetOf0(all_71_1, all_71_0) & ! [v0: $i] : ( ~ % 168.36/23.06 | $i(v0) | ~ aElementOf0(v0, all_71_1) | aElementOf0(v0, % 168.36/23.06 | all_71_0))) % 168.36/23.06 | % 168.36/23.06 | BETA: splitting (23) gives: % 168.36/23.06 | % 168.36/23.06 | Case 1: % 168.36/23.06 | | % 168.36/23.06 | | (24) ~ sdtlseqdt0(xj, xi) % 168.36/23.06 | | % 168.36/23.06 | | PRED_UNIFY: (19), (24) imply: % 168.36/23.06 | | (25) $false % 168.36/23.06 | | % 168.36/23.06 | | CLOSE: (25) is inconsistent. % 168.36/23.06 | | % 168.36/23.06 | Case 2: % 168.36/23.06 | | % 168.36/23.06 | | (26) ! [v0: $i] : ( ~ (szszuzczcdt0(v0) = xi) | ~ $i(v0) | ~ % 168.36/23.06 | | aElementOf0(v0, szNzAzT0)) | (sdtlpdtrp0(xN, xi) = all_71_1 & % 168.36/23.06 | | sdtlpdtrp0(xN, xj) = all_71_0 & $i(all_71_0) & $i(all_71_1) & % 168.36/23.06 | | aSubsetOf0(all_71_1, all_71_0) & ! [v0: $i] : ( ~ $i(v0) | ~ % 168.36/23.06 | | aElementOf0(v0, all_71_1) | aElementOf0(v0, all_71_0))) % 168.36/23.06 | | % 168.36/23.06 | | BETA: splitting (26) gives: % 168.36/23.06 | | % 168.36/23.06 | | Case 1: % 168.36/23.06 | | | % 168.36/23.06 | | | (27) ! [v0: $i] : ( ~ (szszuzczcdt0(v0) = xi) | ~ $i(v0) | ~ % 168.36/23.06 | | | aElementOf0(v0, szNzAzT0)) % 168.36/23.06 | | | % 168.36/23.06 | | | GROUND_INST: instantiating (3) with xj, simplifying with (10), (13) gives: % 168.36/23.06 | | | (28) xj = sz00 | ? [v0: $i] : (szszuzczcdt0(v0) = xj & $i(v0) & % 168.36/23.06 | | | aElementOf0(v0, szNzAzT0)) % 168.36/23.06 | | | % 168.36/23.06 | | | GROUND_INST: instantiating (3) with xi, simplifying with (11), (14) gives: % 168.36/23.06 | | | (29) xi = sz00 | ? [v0: $i] : (szszuzczcdt0(v0) = xi & $i(v0) & % 168.36/23.06 | | | aElementOf0(v0, szNzAzT0)) % 168.36/23.06 | | | % 168.36/23.07 | | | GROUND_INST: instantiating (6) with xj, sz00, slcrc0, simplifying with % 168.36/23.07 | | | (2), (5), (7), (10), (13) gives: % 168.36/23.07 | | | (30) ? [v0: $i] : ? [v1: $i] : ((xj = sz00 | aElementOf0(xj, slcrc0) % 168.36/23.07 | | | | (slbdtrb0(v0) = v1 & szszuzczcdt0(sz00) = v0 & $i(v1) & % 168.36/23.07 | | | $i(v0) & ~ aElementOf0(xj, v1))) & (( ~ (xj = sz00) & ~ % 168.36/23.07 | | | aElementOf0(xj, slcrc0)) | (slbdtrb0(v0) = v1 & % 168.36/23.07 | | | szszuzczcdt0(sz00) = v0 & $i(v1) & $i(v0) & aElementOf0(xj, % 168.36/23.07 | | | v1)))) % 168.36/23.07 | | | % 168.36/23.07 | | | GROUND_INST: instantiating (9) with xi, all_69_2, simplifying with (11), % 168.36/23.07 | | | (14), (22) gives: % 168.36/23.07 | | | (31) aSet0(all_69_2) % 168.36/23.07 | | | % 168.36/23.07 | | | DELTA: instantiating (30) with fresh symbols all_96_0, all_96_1 gives: % 168.36/23.07 | | | (32) (xj = sz00 | aElementOf0(xj, slcrc0) | (slbdtrb0(all_96_1) = % 168.36/23.07 | | | all_96_0 & szszuzczcdt0(sz00) = all_96_1 & $i(all_96_0) & % 168.36/23.07 | | | $i(all_96_1) & ~ aElementOf0(xj, all_96_0))) & (( ~ (xj = % 168.36/23.07 | | | sz00) & ~ aElementOf0(xj, slcrc0)) | (slbdtrb0(all_96_1) = % 168.36/23.07 | | | all_96_0 & szszuzczcdt0(sz00) = all_96_1 & $i(all_96_0) & % 168.36/23.07 | | | $i(all_96_1) & aElementOf0(xj, all_96_0))) % 168.36/23.07 | | | % 168.36/23.07 | | | ALPHA: (32) implies: % 168.36/23.07 | | | (33) ( ~ (xj = sz00) & ~ aElementOf0(xj, slcrc0)) | % 168.36/23.07 | | | (slbdtrb0(all_96_1) = all_96_0 & szszuzczcdt0(sz00) = all_96_1 & % 168.36/23.07 | | | $i(all_96_0) & $i(all_96_1) & aElementOf0(xj, all_96_0)) % 168.36/23.07 | | | % 168.36/23.07 | | | GROUND_INST: instantiating (1) with all_69_2, all_69_2, simplifying with % 168.36/23.07 | | | (20), (31) gives: % 168.36/23.07 | | | (34) aSubsetOf0(all_69_2, all_69_2) % 168.36/23.07 | | | % 168.36/23.07 | | | BETA: splitting (28) gives: % 168.36/23.07 | | | % 168.36/23.07 | | | Case 1: % 168.36/23.07 | | | | % 168.36/23.07 | | | | (35) xj = sz00 % 168.36/23.07 | | | | % 168.36/23.07 | | | | REDUCE: (21), (35) imply: % 168.36/23.07 | | | | (36) sdtlpdtrp0(xN, sz00) = all_69_1 % 168.36/23.07 | | | | % 168.36/23.07 | | | | BETA: splitting (33) gives: % 168.36/23.07 | | | | % 168.36/23.07 | | | | Case 1: % 168.36/23.07 | | | | | % 168.69/23.07 | | | | | (37) ~ (xj = sz00) & ~ aElementOf0(xj, slcrc0) % 168.69/23.07 | | | | | % 168.69/23.07 | | | | | ALPHA: (37) implies: % 168.69/23.07 | | | | | (38) ~ (xj = sz00) % 168.69/23.07 | | | | | % 168.69/23.07 | | | | | REDUCE: (35), (38) imply: % 168.69/23.07 | | | | | (39) $false % 168.69/23.07 | | | | | % 168.69/23.07 | | | | | CLOSE: (39) is inconsistent. % 168.69/23.07 | | | | | % 168.69/23.07 | | | | Case 2: % 168.69/23.07 | | | | | % 168.69/23.07 | | | | | % 168.69/23.07 | | | | | GROUND_INST: instantiating (16) with xS, all_69_1, sz00, xN, % 168.69/23.07 | | | | | simplifying with (8), (36) gives: % 168.69/23.07 | | | | | (40) all_69_1 = xS % 168.69/23.07 | | | | | % 168.69/23.07 | | | | | REDUCE: (18), (40) imply: % 168.69/23.07 | | | | | (41) ~ aSubsetOf0(all_69_2, xS) % 168.69/23.07 | | | | | % 168.69/23.07 | | | | | BETA: splitting (29) gives: % 168.69/23.07 | | | | | % 168.69/23.07 | | | | | Case 1: % 168.69/23.07 | | | | | | % 168.69/23.07 | | | | | | (42) xi = sz00 % 168.69/23.07 | | | | | | % 168.69/23.07 | | | | | | REDUCE: (22), (42) imply: % 168.69/23.07 | | | | | | (43) sdtlpdtrp0(xN, sz00) = all_69_2 % 168.69/23.07 | | | | | | % 168.69/23.07 | | | | | | GROUND_INST: instantiating (16) with xS, all_69_2, sz00, xN, % 168.69/23.07 | | | | | | simplifying with (8), (43) gives: % 168.69/23.07 | | | | | | (44) all_69_2 = xS % 168.69/23.07 | | | | | | % 168.69/23.07 | | | | | | REDUCE: (34), (44) imply: % 168.69/23.07 | | | | | | (45) aSubsetOf0(xS, xS) % 168.69/23.07 | | | | | | % 168.69/23.07 | | | | | | REDUCE: (41), (44) imply: % 168.69/23.07 | | | | | | (46) ~ aSubsetOf0(xS, xS) % 168.69/23.07 | | | | | | % 168.69/23.07 | | | | | | PRED_UNIFY: (45), (46) imply: % 168.69/23.07 | | | | | | (47) $false % 168.69/23.07 | | | | | | % 168.69/23.07 | | | | | | CLOSE: (47) is inconsistent. % 168.69/23.07 | | | | | | % 168.69/23.07 | | | | | Case 2: % 168.69/23.07 | | | | | | % 168.69/23.07 | | | | | | (48) ? [v0: $i] : (szszuzczcdt0(v0) = xi & $i(v0) & % 168.69/23.07 | | | | | | aElementOf0(v0, szNzAzT0)) % 168.69/23.07 | | | | | | % 168.69/23.07 | | | | | | DELTA: instantiating (48) with fresh symbol all_731_0 gives: % 168.69/23.07 | | | | | | (49) szszuzczcdt0(all_731_0) = xi & $i(all_731_0) & % 168.69/23.07 | | | | | | aElementOf0(all_731_0, szNzAzT0) % 168.69/23.07 | | | | | | % 168.69/23.07 | | | | | | ALPHA: (49) implies: % 168.69/23.07 | | | | | | (50) aElementOf0(all_731_0, szNzAzT0) % 168.69/23.07 | | | | | | (51) $i(all_731_0) % 168.69/23.07 | | | | | | (52) szszuzczcdt0(all_731_0) = xi % 168.69/23.07 | | | | | | % 168.69/23.07 | | | | | | GROUND_INST: instantiating (27) with all_731_0, simplifying with % 168.69/23.07 | | | | | | (50), (51), (52) gives: % 168.69/23.08 | | | | | | (53) $false % 168.69/23.08 | | | | | | % 168.69/23.08 | | | | | | CLOSE: (53) is inconsistent. % 168.69/23.08 | | | | | | % 168.69/23.08 | | | | | End of split % 168.69/23.08 | | | | | % 168.69/23.08 | | | | End of split % 168.69/23.08 | | | | % 168.69/23.08 | | | Case 2: % 168.69/23.08 | | | | % 168.69/23.08 | | | | (54) ? [v0: $i] : (szszuzczcdt0(v0) = xj & $i(v0) & aElementOf0(v0, % 168.69/23.08 | | | | szNzAzT0)) % 168.69/23.08 | | | | % 168.69/23.08 | | | | DELTA: instantiating (54) with fresh symbol all_621_0 gives: % 168.69/23.08 | | | | (55) szszuzczcdt0(all_621_0) = xj & $i(all_621_0) & % 168.69/23.08 | | | | aElementOf0(all_621_0, szNzAzT0) % 168.69/23.08 | | | | % 168.69/23.08 | | | | ALPHA: (55) implies: % 168.69/23.08 | | | | (56) aElementOf0(all_621_0, szNzAzT0) % 168.69/23.08 | | | | (57) $i(all_621_0) % 168.69/23.08 | | | | (58) szszuzczcdt0(all_621_0) = xj % 168.69/23.08 | | | | % 168.69/23.08 | | | | BETA: splitting (29) gives: % 168.69/23.08 | | | | % 168.69/23.08 | | | | Case 1: % 168.69/23.08 | | | | | % 168.69/23.08 | | | | | (59) xi = sz00 % 168.69/23.08 | | | | | % 168.69/23.08 | | | | | REDUCE: (19), (59) imply: % 168.69/23.08 | | | | | (60) sdtlseqdt0(xj, sz00) % 168.69/23.08 | | | | | % 168.69/23.08 | | | | | GROUND_INST: instantiating (4) with all_621_0, xj, simplifying with % 168.69/23.08 | | | | | (56), (57), (58), (60) gives: % 168.69/23.08 | | | | | (61) $false % 168.69/23.08 | | | | | % 168.69/23.08 | | | | | CLOSE: (61) is inconsistent. % 168.69/23.08 | | | | | % 168.69/23.08 | | | | Case 2: % 168.69/23.08 | | | | | % 168.69/23.08 | | | | | (62) ? [v0: $i] : (szszuzczcdt0(v0) = xi & $i(v0) & % 168.69/23.08 | | | | | aElementOf0(v0, szNzAzT0)) % 168.69/23.08 | | | | | % 168.69/23.08 | | | | | DELTA: instantiating (62) with fresh symbol all_643_0 gives: % 168.69/23.08 | | | | | (63) szszuzczcdt0(all_643_0) = xi & $i(all_643_0) & % 168.69/23.08 | | | | | aElementOf0(all_643_0, szNzAzT0) % 168.69/23.08 | | | | | % 168.69/23.08 | | | | | ALPHA: (63) implies: % 168.69/23.08 | | | | | (64) aElementOf0(all_643_0, szNzAzT0) % 168.69/23.08 | | | | | (65) $i(all_643_0) % 168.69/23.08 | | | | | (66) szszuzczcdt0(all_643_0) = xi % 168.69/23.08 | | | | | % 168.69/23.08 | | | | | GROUND_INST: instantiating (27) with all_643_0, simplifying with (64), % 168.69/23.08 | | | | | (65), (66) gives: % 168.69/23.08 | | | | | (67) $false % 168.69/23.08 | | | | | % 168.69/23.08 | | | | | CLOSE: (67) is inconsistent. % 168.69/23.08 | | | | | % 168.69/23.08 | | | | End of split % 168.69/23.08 | | | | % 168.69/23.08 | | | End of split % 168.69/23.08 | | | % 168.69/23.08 | | Case 2: % 168.69/23.08 | | | % 168.69/23.08 | | | (68) sdtlpdtrp0(xN, xi) = all_71_1 & sdtlpdtrp0(xN, xj) = all_71_0 & % 168.69/23.08 | | | $i(all_71_0) & $i(all_71_1) & aSubsetOf0(all_71_1, all_71_0) & ! % 168.69/23.08 | | | [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_71_1) | % 168.69/23.08 | | | aElementOf0(v0, all_71_0)) % 168.69/23.08 | | | % 168.69/23.08 | | | ALPHA: (68) implies: % 168.69/23.08 | | | (69) aSubsetOf0(all_71_1, all_71_0) % 168.69/23.08 | | | (70) sdtlpdtrp0(xN, xj) = all_71_0 % 168.69/23.08 | | | (71) sdtlpdtrp0(xN, xi) = all_71_1 % 168.69/23.08 | | | % 168.69/23.08 | | | GROUND_INST: instantiating (16) with all_69_1, all_71_0, xj, xN, % 168.69/23.08 | | | simplifying with (21), (70) gives: % 168.69/23.08 | | | (72) all_71_0 = all_69_1 % 168.69/23.08 | | | % 168.69/23.08 | | | GROUND_INST: instantiating (16) with all_69_2, all_71_1, xi, xN, % 168.69/23.08 | | | simplifying with (22), (71) gives: % 168.69/23.08 | | | (73) all_71_1 = all_69_2 % 168.69/23.08 | | | % 168.69/23.08 | | | REDUCE: (69), (72), (73) imply: % 168.69/23.08 | | | (74) aSubsetOf0(all_69_2, all_69_1) % 168.69/23.08 | | | % 168.69/23.08 | | | PRED_UNIFY: (18), (74) imply: % 168.69/23.08 | | | (75) $false % 168.69/23.08 | | | % 168.69/23.08 | | | CLOSE: (75) is inconsistent. % 168.69/23.08 | | | % 168.69/23.08 | | End of split % 168.69/23.08 | | % 168.69/23.08 | End of split % 168.69/23.08 | % 168.69/23.08 End of proof % 168.69/23.08 % SZS output end Proof for theBenchmark % 168.69/23.08 % 168.69/23.08 22480ms %------------------------------------------------------------------------------