%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM630+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 11:49:06 EDT 2023 % Result : Theorem 35.34s 5.47s % Output : Proof 58.27s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : NUM630+3 : TPTP v8.1.2. Released v4.0.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % 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 11:52:07 EDT 2023 % 0.13/0.34 % 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/sandbox2/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 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 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 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 % 6.95/1.67 Prover 4: Preprocessing ... % 6.95/1.67 Prover 1: Preprocessing ... % 7.37/1.72 Prover 2: Preprocessing ... % 7.37/1.72 Prover 0: Preprocessing ... % 7.37/1.72 Prover 6: Preprocessing ... % 7.37/1.72 Prover 5: Preprocessing ... % 7.37/1.72 Prover 3: Preprocessing ... % 19.09/3.26 Prover 3: Constructing countermodel ... % 19.09/3.27 Prover 1: Constructing countermodel ... % 19.09/3.33 Prover 6: Proving ... % 25.52/4.13 Prover 5: Proving ... % 35.34/5.47 Prover 3: proved (4848ms) % 35.34/5.47 % 35.34/5.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 35.34/5.47 % 35.34/5.48 Prover 5: stopped % 35.34/5.49 Prover 6: stopped % 35.93/5.51 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 35.93/5.51 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 35.93/5.51 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 37.67/5.74 Prover 10: Preprocessing ... % 38.33/5.78 Prover 7: Preprocessing ... % 38.51/5.79 Prover 8: Preprocessing ... % 41.93/6.31 Prover 8: Warning: ignoring some quantifiers % 42.41/6.34 Prover 8: Constructing countermodel ... % 45.12/6.67 Prover 10: Constructing countermodel ... % 45.95/6.87 Prover 7: Constructing countermodel ... % 49.60/7.25 Prover 4: Constructing countermodel ... % 52.62/7.65 Prover 2: Proving ... % 52.80/7.68 Prover 2: stopped % 52.80/7.68 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 55.13/8.00 Prover 11: Preprocessing ... % 55.13/8.12 Prover 10: Found proof (size 77) % 55.13/8.12 Prover 10: proved (2617ms) % 55.13/8.12 Prover 4: stopped % 55.13/8.12 Prover 7: stopped % 55.13/8.12 Prover 8: stopped % 55.13/8.12 Prover 1: stopped % 57.06/8.30 Prover 11: stopped % 57.06/8.32 Prover 0: Proving ... % 57.32/8.35 Prover 0: stopped % 57.32/8.35 % 57.32/8.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 57.32/8.35 % 57.41/8.36 % SZS output start Proof for theBenchmark % 57.41/8.37 Assumptions after simplification: % 57.41/8.37 --------------------------------- % 57.41/8.37 % 57.41/8.37 (mCountNFin_01) % 57.41/8.37 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)) % 57.41/8.37 % 57.41/8.37 (mDefEmp) % 57.41/8.38 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~ % 57.41/8.38 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : ( % 57.41/8.38 ~ $i(v0) | ~ aElementOf0(v0, slcrc0)) % 57.41/8.38 % 57.41/8.38 (m__) % 57.41/8.41 $i(xn) & $i(xP) & $i(xC) & $i(xN) & $i(xc) & ? [v0: $i] : ? [v1: $i] : ? % 57.41/8.41 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ( ~ (v5 = v3) & % 57.41/8.41 sdtlpdtrp0(v4, xP) = v5 & sdtlpdtrp0(xC, xn) = v4 & sdtlpdtrp0(xN, xn) = v0 % 57.41/8.41 & sdtlpdtrp0(xc, v2) = v3 & szmzizndt0(v0) = v1 & sdtpldt0(xP, v1) = v2 & % 57.41/8.41 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aSet0(v2) & ! [v6: % 57.41/8.41 $i] : (v6 = v1 | ~ $i(v6) | ~ aElementOf0(v6, v2) | aElementOf0(v6, xP)) % 57.41/8.41 & ! [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6, v2) | aElement0(v6)) & ! % 57.41/8.41 [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6, v0) | sdtlseqdt0(v1, v6)) & ! % 57.41/8.41 [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6, xP) | ~ aElement0(v6) | % 57.41/8.41 aElementOf0(v6, v2)) & ( ~ aElement0(v1) | aElementOf0(v1, v2))) % 57.41/8.41 % 57.41/8.41 (m__4151) % 57.70/8.43 szDzozmdt0(xC) = szNzAzT0 & $i(xC) & $i(xN) & $i(xk) & $i(xc) & $i(szNzAzT0) & % 57.70/8.43 aFunction0(xC) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 57.70/8.43 [v4: $i] : (v4 = v2 | ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) % 57.70/8.43 | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~ aElementOf0(v4, % 57.70/8.43 v1) | ~ aElementOf0(v0, szNzAzT0) | ~ aElement0(v4) | aElementOf0(v4, % 57.70/8.43 v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 57.70/8.43 : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, % 57.70/8.43 v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~ aElementOf0(v4, v3) | ~ % 57.70/8.43 aElementOf0(v0, szNzAzT0) | aElementOf0(v4, v1)) & ! [v0: $i] : ! [v1: $i] % 57.70/8.43 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ % 57.70/8.43 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | % 57.70/8.43 ~ aElementOf0(v4, v3) | ~ aElementOf0(v0, szNzAzT0) | aElement0(v4)) & ! % 57.70/8.43 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 57.70/8.43 (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) % 57.70/8.43 = v3) | ~ $i(v4) | ~ $i(v0) | ~ aElementOf0(v4, v1) | ~ % 57.70/8.43 aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v2, v4)) & ! [v0: $i] : ! [v1: $i] % 57.70/8.43 : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ % 57.70/8.43 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v0) | % 57.70/8.43 ~ aElementOf0(v2, v3) | ~ aElementOf0(v0, szNzAzT0)) & ! [v0: $i] : ! % 57.70/8.43 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ % 57.70/8.43 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ % 57.70/8.43 aElementOf0(v0, szNzAzT0) | aElementOf0(v2, v1)) & ! [v0: $i] : ! [v1: $i] % 57.70/8.43 : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ % 57.70/8.43 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ % 57.70/8.43 aElementOf0(v0, szNzAzT0) | aSet0(v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 57.70/8.43 $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) % 57.70/8.43 | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? % 57.70/8.43 [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xC, v0) = v4 & szDzozmdt0(v4) = v5 & % 57.70/8.43 slbdtsldtrb0(v3, xk) = v5 & $i(v5) & $i(v4) & aFunction0(v4) & ! [v6: $i] % 57.70/8.43 : ! [v7: $i] : ! [v8: $i] : ( ~ (sbrdtbr0(v6) = v7) | ~ $i(v8) | ~ % 57.70/8.43 $i(v6) | ~ aElementOf0(v8, v6) | ~ aElementOf0(v6, v5) | % 57.70/8.43 aElementOf0(v8, v3)) & ! [v6: $i] : ! [v7: $i] : (v7 = xk | ~ % 57.70/8.43 (sbrdtbr0(v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v5)) & ! [v6: $i] % 57.70/8.43 : ! [v7: $i] : ( ~ (sbrdtbr0(v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, % 57.70/8.43 v5) | aSubsetOf0(v6, v3)) & ! [v6: $i] : ! [v7: $i] : ( ~ % 57.70/8.43 (sbrdtbr0(v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v5) | aSet0(v6)) & % 57.70/8.43 ! [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, v2) = v7) | ~ $i(v6) | ~ % 57.70/8.43 aSet0(v6) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : % 57.70/8.43 ($i(v11) & aElementOf0(v2, v1) & ! [v12: $i] : ( ~ $i(v12) | ~ % 57.70/8.43 aElementOf0(v12, v1) | sdtlseqdt0(v2, v12)) & ((v10 = v9 & % 57.70/8.43 sdtlpdtrp0(v4, v6) = v9 & sdtlpdtrp0(xc, v7) = v9 & $i(v9) & ! % 57.70/8.43 [v12: $i] : (v12 = v2 | ~ $i(v12) | ~ aElementOf0(v12, v7) | % 57.70/8.43 aElementOf0(v12, v6)) & ! [v12: $i] : ( ~ $i(v12) | ~ % 57.70/8.43 aElementOf0(v12, v7) | aElement0(v12)) & ! [v12: $i] : ( ~ % 57.70/8.43 $i(v12) | ~ aElementOf0(v12, v6) | ~ aElement0(v12) | % 57.70/8.43 aElementOf0(v12, v7)) & ( ~ $i(v2) | ~ aElement0(v2) | % 57.70/8.43 aElementOf0(v2, v7))) | (aSet0(v3) & ~ aElementOf0(v6, v5) & ! % 57.70/8.43 [v12: $i] : (v12 = v2 | ~ $i(v12) | ~ aElementOf0(v12, v1) | ~ % 57.70/8.43 aElement0(v12) | aElementOf0(v12, v3)) & ! [v12: $i] : ( ~ % 57.70/8.43 $i(v12) | ~ aElementOf0(v12, v3) | aElementOf0(v12, v1)) & ! % 57.70/8.43 [v12: $i] : ( ~ $i(v12) | ~ aElementOf0(v12, v3) | % 57.70/8.43 aElement0(v12)) & ( ~ $i(v2) | ~ aElementOf0(v2, v3)) & (( ~ % 57.70/8.43 (v8 = xk) & sbrdtbr0(v6) = v8 & $i(v8)) | (aElementOf0(v11, % 57.70/8.43 v6) & ~ aSubsetOf0(v6, v3) & ~ aElementOf0(v11, v3))))))) % 57.70/8.43 & ! [v6: $i] : ( ~ (sbrdtbr0(v6) = xk) | ~ $i(v6) | ~ aSubsetOf0(v6, % 57.70/8.43 v3) | aElementOf0(v6, v5)) & ! [v6: $i] : ( ~ (sbrdtbr0(v6) = xk) | % 57.70/8.44 ~ $i(v6) | ~ aSet0(v6) | aElementOf0(v6, v5) | ? [v7: $i] : ($i(v7) & % 57.70/8.44 aElementOf0(v7, v6) & ~ aElementOf0(v7, v3))))) % 57.70/8.44 % 57.70/8.44 (m__4411) % 57.70/8.44 $i(xC) & $i(xN) & $i(xk) & $i(xT) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : % 57.70/8.44 ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) % 57.70/8.44 = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ aElementOf0(v0, % 57.70/8.44 szNzAzT0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 57.70/8.44 (sdtlpdtrp0(xC, v0) = v4 & slbdtsldtrb0(v6, xk) = v7 & $i(v7) & $i(v6) & % 57.70/8.44 $i(v5) & $i(v4) & aSubsetOf0(v6, v3) & isCountable0(v6) & aElementOf0(v5, % 57.70/8.44 xT) & aElementOf0(v2, v1) & aSet0(v6) & aSet0(v3) & ! [v8: $i] : ! % 57.70/8.44 [v9: $i] : (v9 = v5 | ~ (sdtlpdtrp0(v4, v8) = v9) | ~ $i(v8) | ~ % 57.70/8.44 aSubsetOf0(v8, v6) | ~ aSet0(v8) | ? [v10: $i] : ( ~ (v10 = xk) & % 57.70/8.44 sbrdtbr0(v8) = v10 & $i(v10))) & ! [v8: $i] : ! [v9: $i] : (v9 = v5 % 57.70/8.44 | ~ (sdtlpdtrp0(v4, v8) = v9) | ~ $i(v8) | ~ aElementOf0(v8, v7) | ~ % 57.70/8.44 aSet0(v8)) & ! [v8: $i] : ! [v9: $i] : (v9 = v5 | ~ (sdtlpdtrp0(v4, % 57.70/8.44 v8) = v9) | ~ $i(v8) | ~ aSet0(v8) | ? [v10: $i] : ? [v11: $i] : % 57.70/8.44 ($i(v11) & (( ~ (v10 = xk) & sbrdtbr0(v8) = v10 & $i(v10)) | % 57.70/8.44 (aElementOf0(v11, v8) & ~ aElementOf0(v11, v6))))) & ! [v8: $i] : % 57.70/8.44 (v8 = v2 | ~ $i(v8) | ~ aElementOf0(v8, v1) | ~ aElement0(v8) | % 57.70/8.44 aElementOf0(v8, v3)) & ! [v8: $i] : ( ~ $i(v8) | ~ aElementOf0(v8, v6) % 57.70/8.44 | aElementOf0(v8, v3)) & ! [v8: $i] : ( ~ $i(v8) | ~ aElementOf0(v8, % 57.70/8.44 v3) | aElementOf0(v8, v1)) & ! [v8: $i] : ( ~ $i(v8) | ~ % 57.70/8.44 aElementOf0(v8, v3) | aElement0(v8)) & ! [v8: $i] : ( ~ $i(v8) | ~ % 57.70/8.44 aElementOf0(v8, v1) | sdtlseqdt0(v2, v8)) & ( ~ $i(v2) | ~ % 57.70/8.44 aElementOf0(v2, v3)))) % 57.70/8.44 % 57.70/8.44 (m__4730) % 57.70/8.45 szDzozmdt0(xd) = szNzAzT0 & $i(xd) & $i(xC) & $i(xN) & $i(xk) & $i(szNzAzT0) & % 57.70/8.45 aFunction0(xd) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xC, v0) = v1) | % 57.70/8.45 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ? % 57.70/8.45 [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xd, v0) = v5 & sdtlpdtrp0(xN, v2) = v3 % 57.70/8.45 & slbdtsldtrb0(v3, xk) = v4 & szszuzczcdt0(v0) = v2 & $i(v5) & $i(v4) & % 57.70/8.45 $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~ % 57.70/8.45 (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aSubsetOf0(v6, v3) | ~ % 57.70/8.45 aSet0(v6) | ? [v8: $i] : ( ~ (v8 = xk) & sbrdtbr0(v6) = v8 & $i(v8))) & % 57.70/8.45 ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~ (sdtlpdtrp0(v1, v6) = v7) | ~ % 57.70/8.45 $i(v6) | ~ aElementOf0(v6, v4) | ~ aSet0(v6)) & ! [v6: $i] : ! [v7: % 57.70/8.45 $i] : (v7 = v5 | ~ (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aSet0(v6) % 57.70/8.45 | ? [v8: $i] : ? [v9: $i] : ($i(v9) & (( ~ (v8 = xk) & sbrdtbr0(v6) = % 57.70/8.45 v8 & $i(v8)) | (aElementOf0(v9, v6) & ~ aElementOf0(v9, v3))))))) % 57.70/8.45 % 57.70/8.45 (m__4758) % 57.70/8.45 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & % 57.70/8.45 szDzozmdt0(xd) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT) & aSet0(v1) & ! % 57.70/8.45 [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v2) | ~ $i(v3) | ~ % 57.70/8.45 $i(v2) | ~ aElementOf0(v3, v0) | aElementOf0(v2, v1)) & ! [v2: $i] : ( ~ % 57.70/8.45 $i(v2) | ~ aElementOf0(v2, v1) | aElementOf0(v2, xT)) & ! [v2: $i] : ( ~ % 57.70/8.45 $i(v2) | ~ aElementOf0(v2, v1) | ? [v3: $i] : (sdtlpdtrp0(xd, v3) = v2 & % 57.70/8.45 $i(v3) & aElementOf0(v3, v0)))) % 57.70/8.45 % 57.70/8.45 (m__4854) % 57.70/8.45 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = % 57.70/8.45 v0 & sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) & % 57.70/8.45 $i(v0) & aElementOf0(v0, xT) & aSet0(v1) & ! [v3: $i] : ! [v4: $i] : (v4 = % 57.70/8.45 v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1)) & % 57.70/8.45 ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ % 57.70/8.45 aElementOf0(v3, v1) | aElementOf0(v3, v2)) & ! [v3: $i] : ( ~ % 57.70/8.45 (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ aElementOf0(v3, v2) | % 57.70/8.45 aElementOf0(v3, v1))) % 57.70/8.45 % 57.70/8.45 (m__4891) % 57.70/8.46 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 57.70/8.46 (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & % 57.70/8.46 szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & ! % 57.70/8.46 [v3: $i] : ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) % 57.70/8.46 | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 57.70/8.46 (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) | % 57.70/8.46 aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xe, v4) % 57.70/8.46 = v3) | ~ $i(v4) | ~ $i(v3) | ~ aElementOf0(v4, v1) | aElementOf0(v3, % 57.70/8.46 xO)) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ % 57.70/8.46 aElementOf0(v3, v2) | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~ % 57.70/8.46 aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 & $i(v4) & % 57.70/8.46 aElementOf0(v4, v1)))) % 57.70/8.46 % 57.70/8.46 (m__5164) % 57.91/8.46 $i(xP) & $i(xQ) & ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & % 57.91/8.46 $i(v0) & aSet0(xP) & ~ aElementOf0(v0, xP) & ! [v1: $i] : (v1 = v0 | ~ % 57.91/8.46 $i(v1) | ~ aElementOf0(v1, xQ) | ~ aElement0(v1) | aElementOf0(v1, xP)) % 57.91/8.46 & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xP) | aElementOf0(v1, xQ)) & % 57.91/8.46 ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xP) | aElement0(v1)) & ! [v1: % 57.91/8.46 $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | sdtlseqdt0(v0, v1))) % 57.91/8.46 % 57.91/8.46 (m__5217) % 57.91/8.46 sbrdtbr0(xP) = xk & $i(xP) & $i(xk) % 57.91/8.46 % 57.91/8.46 (m__5309) % 57.91/8.46 $i(xn) & $i(xp) & $i(xd) & $i(xe) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] : % 57.91/8.46 ? [v2: $i] : (szDzizrdt0(xd) = v1 & sdtlbdtrb0(xd, v1) = v2 & sdtlpdtrp0(xd, % 57.91/8.46 xn) = v1 & sdtlpdtrp0(xe, xn) = xp & szDzozmdt0(xd) = v0 & $i(v2) & $i(v1) % 57.91/8.46 & $i(v0) & aElementOf0(xn, v2) & aElementOf0(xn, v0) & aElementOf0(xn, % 57.91/8.46 szNzAzT0)) % 57.91/8.46 % 57.91/8.46 (m__5585) % 57.91/8.47 $i(xD) & $i(xn) & $i(xN) & ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xn) = % 57.91/8.47 v0 & szmzizndt0(v0) = v1 & sdtmndt0(v0, v1) = xD & $i(v1) & $i(v0) & % 57.91/8.47 aSet0(xD) & ~ aElementOf0(v1, xD) & ! [v2: $i] : (v2 = v1 | ~ $i(v2) | ~ % 57.91/8.47 aElementOf0(v2, v0) | ~ aElement0(v2) | aElementOf0(v2, xD)) & ! [v2: % 57.91/8.47 $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v0) | sdtlseqdt0(v1, v2)) & ! [v2: % 57.91/8.47 $i] : ( ~ $i(v2) | ~ aElementOf0(v2, xD) | aElementOf0(v2, v0)) & ! [v2: % 57.91/8.47 $i] : ( ~ $i(v2) | ~ aElementOf0(v2, xD) | aElement0(v2))) % 57.91/8.47 % 57.91/8.47 (m__5599) % 57.91/8.47 $i(xD) & $i(xP) & $i(xk) & ? [v0: $i] : (slbdtsldtrb0(xD, xk) = v0 & $i(v0) & % 57.91/8.47 aSubsetOf0(xP, xD) & aElementOf0(xP, v0) & ! [v1: $i] : ( ~ $i(v1) | ~ % 57.91/8.47 aElementOf0(v1, xP) | aElementOf0(v1, xD))) % 57.91/8.47 % 57.91/8.47 (function-axioms) % 57.91/8.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 57.91/8.48 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 57.91/8.48 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 57.91/8.48 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 57.91/8.48 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 57.91/8.48 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 57.91/8.48 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 57.91/8.48 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 57.91/8.48 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 57.91/8.48 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 57.91/8.48 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 57.91/8.48 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 57.91/8.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 57.91/8.48 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 57.91/8.48 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 57.91/8.48 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 57.91/8.48 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 57.91/8.48 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 57.91/8.48 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 57.91/8.48 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 57.91/8.48 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 57.91/8.48 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 57.91/8.48 v0)) % 57.91/8.48 % 57.91/8.48 Further assumptions not needed in the proof: % 57.91/8.48 -------------------------------------------- % 57.91/8.48 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 57.91/8.48 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons, % 57.91/8.48 mDefDiff, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, mDefSel, % 57.91/8.48 mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet, % 57.91/8.48 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm, % 57.91/8.48 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, % 57.91/8.48 mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess, % 57.91/8.48 mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, % 57.91/8.48 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, % 57.91/8.48 mZeroLess, mZeroNum, m__3291, m__3398, m__3418, m__3435, m__3453, m__3462, % 57.91/8.48 m__3520, m__3533, m__3623, m__3671, m__3754, m__3821, m__3965, m__4182, m__4331, % 57.91/8.48 m__4618, m__4660, m__4908, m__4982, m__4998, m__5078, m__5093, m__5106, m__5116, % 57.91/8.48 m__5147, m__5173, m__5182, m__5195, m__5208, m__5270, m__5321, m__5334 % 57.91/8.48 % 57.91/8.48 Those formulas are unsatisfiable: % 57.91/8.48 --------------------------------- % 57.91/8.48 % 57.91/8.48 Begin of proof % 57.91/8.48 | % 57.91/8.48 | ALPHA: (mDefEmp) implies: % 57.91/8.48 | (1) aSet0(slcrc0) % 57.91/8.48 | % 57.91/8.48 | ALPHA: (mCountNFin_01) implies: % 57.91/8.48 | (2) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0) % 57.91/8.48 | % 57.91/8.48 | ALPHA: (m__4151) implies: % 57.91/8.49 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 57.91/8.49 | (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ % 57.91/8.49 | (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | % 57.91/8.49 | ? [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xC, v0) = v4 & szDzozmdt0(v4) % 57.91/8.49 | = v5 & slbdtsldtrb0(v3, xk) = v5 & $i(v5) & $i(v4) & aFunction0(v4) % 57.91/8.49 | & ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (sbrdtbr0(v6) = v7) % 57.91/8.49 | | ~ $i(v8) | ~ $i(v6) | ~ aElementOf0(v8, v6) | ~ % 57.91/8.49 | aElementOf0(v6, v5) | aElementOf0(v8, v3)) & ! [v6: $i] : ! % 57.91/8.49 | [v7: $i] : (v7 = xk | ~ (sbrdtbr0(v6) = v7) | ~ $i(v6) | ~ % 57.91/8.49 | aElementOf0(v6, v5)) & ! [v6: $i] : ! [v7: $i] : ( ~ % 57.91/8.49 | (sbrdtbr0(v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v5) | % 57.91/8.49 | aSubsetOf0(v6, v3)) & ! [v6: $i] : ! [v7: $i] : ( ~ % 57.91/8.49 | (sbrdtbr0(v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v5) | % 57.91/8.49 | aSet0(v6)) & ! [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, v2) = % 57.91/8.49 | v7) | ~ $i(v6) | ~ aSet0(v6) | ? [v8: $i] : ? [v9: $i] : ? % 57.91/8.49 | [v10: $i] : ? [v11: $i] : ($i(v11) & aElementOf0(v2, v1) & ! % 57.91/8.49 | [v12: $i] : ( ~ $i(v12) | ~ aElementOf0(v12, v1) | % 57.91/8.49 | sdtlseqdt0(v2, v12)) & ((v10 = v9 & sdtlpdtrp0(v4, v6) = v9 & % 57.91/8.49 | sdtlpdtrp0(xc, v7) = v9 & $i(v9) & ! [v12: $i] : (v12 = v2 % 57.91/8.49 | | ~ $i(v12) | ~ aElementOf0(v12, v7) | aElementOf0(v12, % 57.91/8.49 | v6)) & ! [v12: $i] : ( ~ $i(v12) | ~ aElementOf0(v12, % 57.91/8.49 | v7) | aElement0(v12)) & ! [v12: $i] : ( ~ $i(v12) | ~ % 57.91/8.49 | aElementOf0(v12, v6) | ~ aElement0(v12) | % 57.91/8.49 | aElementOf0(v12, v7)) & ( ~ $i(v2) | ~ aElement0(v2) | % 57.91/8.49 | aElementOf0(v2, v7))) | (aSet0(v3) & ~ aElementOf0(v6, % 57.91/8.49 | v5) & ! [v12: $i] : (v12 = v2 | ~ $i(v12) | ~ % 57.91/8.49 | aElementOf0(v12, v1) | ~ aElement0(v12) | % 57.91/8.49 | aElementOf0(v12, v3)) & ! [v12: $i] : ( ~ $i(v12) | ~ % 57.91/8.49 | aElementOf0(v12, v3) | aElementOf0(v12, v1)) & ! [v12: % 57.91/8.49 | $i] : ( ~ $i(v12) | ~ aElementOf0(v12, v3) | % 57.91/8.49 | aElement0(v12)) & ( ~ $i(v2) | ~ aElementOf0(v2, v3)) & % 57.91/8.49 | (( ~ (v8 = xk) & sbrdtbr0(v6) = v8 & $i(v8)) | % 57.91/8.49 | (aElementOf0(v11, v6) & ~ aSubsetOf0(v6, v3) & ~ % 57.91/8.49 | aElementOf0(v11, v3))))))) & ! [v6: $i] : ( ~ % 57.91/8.49 | (sbrdtbr0(v6) = xk) | ~ $i(v6) | ~ aSubsetOf0(v6, v3) | % 57.91/8.49 | aElementOf0(v6, v5)) & ! [v6: $i] : ( ~ (sbrdtbr0(v6) = xk) | ~ % 57.91/8.49 | $i(v6) | ~ aSet0(v6) | aElementOf0(v6, v5) | ? [v7: $i] : % 57.91/8.49 | ($i(v7) & aElementOf0(v7, v6) & ~ aElementOf0(v7, v3))))) % 57.91/8.49 | % 57.91/8.49 | ALPHA: (m__4411) implies: % 57.91/8.50 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 57.91/8.50 | (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ % 57.91/8.50 | (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | % 57.91/8.50 | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 57.91/8.50 | (sdtlpdtrp0(xC, v0) = v4 & slbdtsldtrb0(v6, xk) = v7 & $i(v7) & % 57.91/8.50 | $i(v6) & $i(v5) & $i(v4) & aSubsetOf0(v6, v3) & isCountable0(v6) & % 57.91/8.50 | aElementOf0(v5, xT) & aElementOf0(v2, v1) & aSet0(v6) & aSet0(v3) & % 57.91/8.50 | ! [v8: $i] : ! [v9: $i] : (v9 = v5 | ~ (sdtlpdtrp0(v4, v8) = v9) % 57.91/8.50 | | ~ $i(v8) | ~ aSubsetOf0(v8, v6) | ~ aSet0(v8) | ? [v10: $i] % 57.91/8.50 | : ( ~ (v10 = xk) & sbrdtbr0(v8) = v10 & $i(v10))) & ! [v8: $i] : % 57.91/8.50 | ! [v9: $i] : (v9 = v5 | ~ (sdtlpdtrp0(v4, v8) = v9) | ~ $i(v8) | % 57.91/8.50 | ~ aElementOf0(v8, v7) | ~ aSet0(v8)) & ! [v8: $i] : ! [v9: % 57.91/8.50 | $i] : (v9 = v5 | ~ (sdtlpdtrp0(v4, v8) = v9) | ~ $i(v8) | ~ % 57.91/8.50 | aSet0(v8) | ? [v10: $i] : ? [v11: $i] : ($i(v11) & (( ~ (v10 = % 57.91/8.50 | xk) & sbrdtbr0(v8) = v10 & $i(v10)) | (aElementOf0(v11, % 57.91/8.50 | v8) & ~ aElementOf0(v11, v6))))) & ! [v8: $i] : (v8 = % 57.91/8.50 | v2 | ~ $i(v8) | ~ aElementOf0(v8, v1) | ~ aElement0(v8) | % 57.91/8.50 | aElementOf0(v8, v3)) & ! [v8: $i] : ( ~ $i(v8) | ~ % 57.91/8.50 | aElementOf0(v8, v6) | aElementOf0(v8, v3)) & ! [v8: $i] : ( ~ % 57.91/8.50 | $i(v8) | ~ aElementOf0(v8, v3) | aElementOf0(v8, v1)) & ! [v8: % 57.91/8.50 | $i] : ( ~ $i(v8) | ~ aElementOf0(v8, v3) | aElement0(v8)) & ! % 57.91/8.50 | [v8: $i] : ( ~ $i(v8) | ~ aElementOf0(v8, v1) | sdtlseqdt0(v2, % 57.91/8.50 | v8)) & ( ~ $i(v2) | ~ aElementOf0(v2, v3)))) % 57.91/8.50 | % 57.91/8.50 | ALPHA: (m__4730) implies: % 57.91/8.50 | (5) szDzozmdt0(xd) = szNzAzT0 % 57.91/8.50 | % 57.91/8.50 | ALPHA: (m__4758) implies: % 57.91/8.50 | (6) ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & szDzozmdt0(xd) = % 57.91/8.50 | v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT) & aSet0(v1) & ! [v2: $i] : % 57.91/8.50 | ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v2) | ~ $i(v3) | ~ $i(v2) | % 57.91/8.50 | ~ aElementOf0(v3, v0) | aElementOf0(v2, v1)) & ! [v2: $i] : ( ~ % 57.91/8.50 | $i(v2) | ~ aElementOf0(v2, v1) | aElementOf0(v2, xT)) & ! [v2: % 57.91/8.50 | $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | ? [v3: $i] : % 57.91/8.50 | (sdtlpdtrp0(xd, v3) = v2 & $i(v3) & aElementOf0(v3, v0)))) % 57.91/8.50 | % 57.91/8.50 | ALPHA: (m__4854) implies: % 57.91/8.50 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 & % 57.91/8.50 | sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) & % 57.91/8.50 | $i(v0) & aElementOf0(v0, xT) & aSet0(v1) & ! [v3: $i] : ! [v4: $i] % 57.91/8.50 | : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ % 57.91/8.50 | aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 57.91/8.50 | (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) | % 57.91/8.50 | aElementOf0(v3, v2)) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v0) % 57.91/8.50 | | ~ $i(v3) | ~ aElementOf0(v3, v2) | aElementOf0(v3, v1))) % 57.91/8.50 | % 57.91/8.50 | ALPHA: (m__4891) implies: % 57.91/8.50 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 & % 57.91/8.50 | sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = % 57.91/8.50 | v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & ! [v3: $i] : % 57.91/8.50 | ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | % 57.91/8.50 | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 57.91/8.50 | (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) | % 57.91/8.50 | aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 57.91/8.50 | (sdtlpdtrp0(xe, v4) = v3) | ~ $i(v4) | ~ $i(v3) | ~ % 57.91/8.50 | aElementOf0(v4, v1) | aElementOf0(v3, xO)) & ! [v3: $i] : ( ~ % 57.91/8.50 | (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ aElementOf0(v3, v2) | % 57.91/8.50 | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~ % 57.91/8.50 | aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 & % 57.91/8.50 | $i(v4) & aElementOf0(v4, v1)))) % 57.91/8.50 | % 57.91/8.50 | ALPHA: (m__5164) implies: % 57.91/8.51 | (9) ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & $i(v0) & % 57.91/8.51 | aSet0(xP) & ~ aElementOf0(v0, xP) & ! [v1: $i] : (v1 = v0 | ~ % 57.91/8.51 | $i(v1) | ~ aElementOf0(v1, xQ) | ~ aElement0(v1) | % 57.91/8.51 | aElementOf0(v1, xP)) & ! [v1: $i] : ( ~ $i(v1) | ~ % 57.91/8.51 | aElementOf0(v1, xP) | aElementOf0(v1, xQ)) & ! [v1: $i] : ( ~ % 57.91/8.51 | $i(v1) | ~ aElementOf0(v1, xP) | aElement0(v1)) & ! [v1: $i] : ( % 57.91/8.51 | ~ $i(v1) | ~ aElementOf0(v1, xQ) | sdtlseqdt0(v0, v1))) % 57.91/8.51 | % 57.91/8.51 | ALPHA: (m__5217) implies: % 57.91/8.51 | (10) sbrdtbr0(xP) = xk % 57.91/8.51 | % 57.91/8.51 | ALPHA: (m__5309) implies: % 57.91/8.51 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v1 & % 57.91/8.51 | sdtlbdtrb0(xd, v1) = v2 & sdtlpdtrp0(xd, xn) = v1 & sdtlpdtrp0(xe, % 57.91/8.51 | xn) = xp & szDzozmdt0(xd) = v0 & $i(v2) & $i(v1) & $i(v0) & % 57.91/8.51 | aElementOf0(xn, v2) & aElementOf0(xn, v0) & aElementOf0(xn, % 57.91/8.51 | szNzAzT0)) % 57.91/8.51 | % 57.91/8.51 | ALPHA: (m__5585) implies: % 57.91/8.51 | (12) ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xn) = v0 & szmzizndt0(v0) % 57.91/8.51 | = v1 & sdtmndt0(v0, v1) = xD & $i(v1) & $i(v0) & aSet0(xD) & ~ % 57.91/8.51 | aElementOf0(v1, xD) & ! [v2: $i] : (v2 = v1 | ~ $i(v2) | ~ % 57.91/8.51 | aElementOf0(v2, v0) | ~ aElement0(v2) | aElementOf0(v2, xD)) & ! % 57.91/8.51 | [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v0) | sdtlseqdt0(v1, v2)) % 57.91/8.51 | & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, xD) | % 57.91/8.51 | aElementOf0(v2, v0)) & ! [v2: $i] : ( ~ $i(v2) | ~ % 57.91/8.51 | aElementOf0(v2, xD) | aElement0(v2))) % 57.91/8.51 | % 57.91/8.51 | ALPHA: (m__5599) implies: % 57.91/8.51 | (13) ? [v0: $i] : (slbdtsldtrb0(xD, xk) = v0 & $i(v0) & aSubsetOf0(xP, xD) % 57.91/8.51 | & aElementOf0(xP, v0) & ! [v1: $i] : ( ~ $i(v1) | ~ % 57.91/8.51 | aElementOf0(v1, xP) | aElementOf0(v1, xD))) % 57.91/8.51 | % 57.91/8.51 | ALPHA: (m__) implies: % 57.91/8.51 | (14) $i(xP) % 57.91/8.51 | (15) $i(xn) % 57.91/8.51 | (16) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 57.91/8.51 | ? [v5: $i] : ( ~ (v5 = v3) & sdtlpdtrp0(v4, xP) = v5 & sdtlpdtrp0(xC, % 57.91/8.51 | xn) = v4 & sdtlpdtrp0(xN, xn) = v0 & sdtlpdtrp0(xc, v2) = v3 & % 57.91/8.51 | szmzizndt0(v0) = v1 & sdtpldt0(xP, v1) = v2 & $i(v5) & $i(v4) & % 57.91/8.51 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & aSet0(v2) & ! [v6: $i] : (v6 = % 57.91/8.51 | v1 | ~ $i(v6) | ~ aElementOf0(v6, v2) | aElementOf0(v6, xP)) & % 57.91/8.51 | ! [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6, v2) | aElement0(v6)) & % 57.91/8.51 | ! [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6, v0) | sdtlseqdt0(v1, % 57.91/8.51 | v6)) & ! [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6, xP) | ~ % 57.91/8.51 | aElement0(v6) | aElementOf0(v6, v2)) & ( ~ aElement0(v1) | % 57.91/8.51 | aElementOf0(v1, v2))) % 57.91/8.51 | % 57.91/8.51 | ALPHA: (function-axioms) implies: % 57.91/8.51 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 57.91/8.51 | (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) = v0)) % 57.91/8.51 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 57.91/8.51 | (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) % 57.91/8.51 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 57.91/8.51 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) % 57.91/8.51 | % 57.91/8.51 | DELTA: instantiating (13) with fresh symbol all_91_0 gives: % 57.91/8.51 | (20) slbdtsldtrb0(xD, xk) = all_91_0 & $i(all_91_0) & aSubsetOf0(xP, xD) & % 57.91/8.51 | aElementOf0(xP, all_91_0) & ! [v0: $i] : ( ~ $i(v0) | ~ % 57.91/8.51 | aElementOf0(v0, xP) | aElementOf0(v0, xD)) % 57.91/8.51 | % 57.91/8.51 | ALPHA: (20) implies: % 57.91/8.51 | (21) aSubsetOf0(xP, xD) % 57.91/8.51 | % 57.91/8.51 | DELTA: instantiating (11) with fresh symbols all_103_0, all_103_1, all_103_2 % 57.91/8.51 | gives: % 57.91/8.51 | (22) szDzizrdt0(xd) = all_103_1 & sdtlbdtrb0(xd, all_103_1) = all_103_0 & % 57.91/8.51 | sdtlpdtrp0(xd, xn) = all_103_1 & sdtlpdtrp0(xe, xn) = xp & % 57.91/8.51 | szDzozmdt0(xd) = all_103_2 & $i(all_103_0) & $i(all_103_1) & % 57.91/8.51 | $i(all_103_2) & aElementOf0(xn, all_103_0) & aElementOf0(xn, % 57.91/8.51 | all_103_2) & aElementOf0(xn, szNzAzT0) % 57.91/8.51 | % 57.91/8.51 | ALPHA: (22) implies: % 57.91/8.51 | (23) aElementOf0(xn, all_103_2) % 57.91/8.51 | (24) szDzozmdt0(xd) = all_103_2 % 57.91/8.51 | % 57.91/8.51 | DELTA: instantiating (6) with fresh symbols all_105_0, all_105_1 gives: % 57.91/8.51 | (25) sdtlcdtrc0(xd, all_105_1) = all_105_0 & szDzozmdt0(xd) = all_105_1 & % 57.91/8.51 | $i(all_105_0) & $i(all_105_1) & aSubsetOf0(all_105_0, xT) & % 57.91/8.51 | aSet0(all_105_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v1) % 57.91/8.51 | = v0) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, all_105_1) | % 57.91/8.51 | aElementOf0(v0, all_105_0)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 57.91/8.51 | aElementOf0(v0, all_105_0) | aElementOf0(v0, xT)) & ! [v0: $i] : ( % 57.91/8.51 | ~ $i(v0) | ~ aElementOf0(v0, all_105_0) | ? [v1: $i] : % 57.91/8.51 | (sdtlpdtrp0(xd, v1) = v0 & $i(v1) & aElementOf0(v1, all_105_1))) % 57.91/8.51 | % 57.91/8.51 | ALPHA: (25) implies: % 57.91/8.51 | (26) szDzozmdt0(xd) = all_105_1 % 57.91/8.51 | % 57.91/8.51 | DELTA: instantiating (9) with fresh symbol all_108_0 gives: % 57.91/8.52 | (27) szmzizndt0(xQ) = all_108_0 & sdtmndt0(xQ, all_108_0) = xP & % 57.91/8.52 | $i(all_108_0) & aSet0(xP) & ~ aElementOf0(all_108_0, xP) & ! [v0: % 57.91/8.52 | any] : (v0 = all_108_0 | ~ $i(v0) | ~ aElementOf0(v0, xQ) | ~ % 57.91/8.52 | aElement0(v0) | aElementOf0(v0, xP)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 57.91/8.52 | aElementOf0(v0, xP) | aElementOf0(v0, xQ)) & ! [v0: $i] : ( ~ % 57.91/8.52 | $i(v0) | ~ aElementOf0(v0, xP) | aElement0(v0)) & ! [v0: $i] : ( ~ % 57.91/8.52 | $i(v0) | ~ aElementOf0(v0, xQ) | sdtlseqdt0(all_108_0, v0)) % 57.91/8.52 | % 57.91/8.52 | ALPHA: (27) implies: % 57.91/8.52 | (28) aSet0(xP) % 57.91/8.52 | % 57.91/8.52 | DELTA: instantiating (7) with fresh symbols all_111_0, all_111_1, all_111_2 % 57.91/8.52 | gives: % 57.91/8.52 | (29) szDzizrdt0(xd) = all_111_2 & sdtlbdtrb0(xd, all_111_2) = all_111_1 & % 57.91/8.52 | szDzozmdt0(xd) = all_111_0 & $i(all_111_0) & $i(all_111_1) & % 57.91/8.52 | $i(all_111_2) & aElementOf0(all_111_2, xT) & aSet0(all_111_1) & ! % 57.91/8.52 | [v0: $i] : ! [v1: int] : (v1 = all_111_2 | ~ (sdtlpdtrp0(xd, v0) = % 57.91/8.52 | v1) | ~ $i(v0) | ~ aElementOf0(v0, all_111_1)) & ! [v0: $i] : % 57.91/8.52 | ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ % 57.91/8.52 | aElementOf0(v0, all_111_1) | aElementOf0(v0, all_111_0)) & ! [v0: % 57.91/8.52 | $i] : ( ~ (sdtlpdtrp0(xd, v0) = all_111_2) | ~ $i(v0) | ~ % 57.91/8.52 | aElementOf0(v0, all_111_0) | aElementOf0(v0, all_111_1)) % 57.91/8.52 | % 57.91/8.52 | ALPHA: (29) implies: % 57.91/8.52 | (30) szDzozmdt0(xd) = all_111_0 % 57.91/8.52 | % 57.91/8.52 | DELTA: instantiating (12) with fresh symbols all_117_0, all_117_1 gives: % 57.91/8.52 | (31) sdtlpdtrp0(xN, xn) = all_117_1 & szmzizndt0(all_117_1) = all_117_0 & % 57.91/8.52 | sdtmndt0(all_117_1, all_117_0) = xD & $i(all_117_0) & $i(all_117_1) & % 57.91/8.52 | aSet0(xD) & ~ aElementOf0(all_117_0, xD) & ! [v0: any] : (v0 = % 57.91/8.52 | all_117_0 | ~ $i(v0) | ~ aElementOf0(v0, all_117_1) | ~ % 57.91/8.52 | aElement0(v0) | aElementOf0(v0, xD)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 57.91/8.52 | aElementOf0(v0, all_117_1) | sdtlseqdt0(all_117_0, v0)) & ! [v0: % 57.91/8.52 | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xD) | aElementOf0(v0, % 57.91/8.52 | all_117_1)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xD) | % 57.91/8.52 | aElement0(v0)) % 57.91/8.52 | % 57.91/8.52 | ALPHA: (31) implies: % 57.91/8.52 | (32) sdtmndt0(all_117_1, all_117_0) = xD % 57.91/8.52 | (33) szmzizndt0(all_117_1) = all_117_0 % 57.91/8.52 | (34) sdtlpdtrp0(xN, xn) = all_117_1 % 57.91/8.52 | % 57.91/8.52 | DELTA: instantiating (16) with fresh symbols all_120_0, all_120_1, all_120_2, % 57.91/8.52 | all_120_3, all_120_4, all_120_5 gives: % 57.91/8.52 | (35) ~ (all_120_0 = all_120_2) & sdtlpdtrp0(all_120_1, xP) = all_120_0 & % 57.91/8.52 | sdtlpdtrp0(xC, xn) = all_120_1 & sdtlpdtrp0(xN, xn) = all_120_5 & % 57.91/8.52 | sdtlpdtrp0(xc, all_120_3) = all_120_2 & szmzizndt0(all_120_5) = % 57.91/8.52 | all_120_4 & sdtpldt0(xP, all_120_4) = all_120_3 & $i(all_120_0) & % 57.91/8.52 | $i(all_120_1) & $i(all_120_2) & $i(all_120_3) & $i(all_120_4) & % 57.91/8.52 | $i(all_120_5) & aSet0(all_120_3) & ! [v0: any] : (v0 = all_120_4 | ~ % 57.91/8.52 | $i(v0) | ~ aElementOf0(v0, all_120_3) | aElementOf0(v0, xP)) & ! % 57.91/8.52 | [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_120_3) | aElement0(v0)) % 57.91/8.52 | & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_120_5) | % 57.91/8.52 | sdtlseqdt0(all_120_4, v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 57.91/8.52 | aElementOf0(v0, xP) | ~ aElement0(v0) | aElementOf0(v0, all_120_3)) % 57.91/8.52 | & ( ~ aElement0(all_120_4) | aElementOf0(all_120_4, all_120_3)) % 57.91/8.52 | % 57.91/8.52 | ALPHA: (35) implies: % 57.91/8.52 | (36) ~ (all_120_0 = all_120_2) % 57.91/8.52 | (37) sdtpldt0(xP, all_120_4) = all_120_3 % 57.91/8.52 | (38) szmzizndt0(all_120_5) = all_120_4 % 57.91/8.52 | (39) sdtlpdtrp0(xc, all_120_3) = all_120_2 % 57.91/8.52 | (40) sdtlpdtrp0(xN, xn) = all_120_5 % 57.91/8.52 | (41) sdtlpdtrp0(xC, xn) = all_120_1 % 57.91/8.52 | (42) sdtlpdtrp0(all_120_1, xP) = all_120_0 % 57.91/8.52 | % 57.91/8.52 | DELTA: instantiating (8) with fresh symbols all_123_0, all_123_1, all_123_2 % 57.91/8.52 | gives: % 57.91/8.52 | (43) szDzizrdt0(xd) = all_123_2 & sdtlcdtrc0(xe, all_123_1) = xO & % 57.91/8.52 | sdtlbdtrb0(xd, all_123_2) = all_123_1 & szDzozmdt0(xd) = all_123_0 & % 57.91/8.52 | $i(all_123_0) & $i(all_123_1) & $i(all_123_2) & aSet0(all_123_1) & % 57.91/8.52 | aSet0(xO) & ! [v0: $i] : ! [v1: int] : (v1 = all_123_2 | ~ % 57.91/8.52 | (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, % 57.91/8.52 | all_123_1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) % 57.91/8.52 | = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_123_1) | % 57.91/8.52 | aElementOf0(v0, all_123_0)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 57.91/8.52 | (sdtlpdtrp0(xe, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~ % 57.91/8.52 | aElementOf0(v1, all_123_1) | aElementOf0(v0, xO)) & ! [v0: $i] : ( % 57.91/8.52 | ~ (sdtlpdtrp0(xd, v0) = all_123_2) | ~ $i(v0) | ~ aElementOf0(v0, % 57.91/8.52 | all_123_0) | aElementOf0(v0, all_123_1)) & ! [v0: $i] : ( ~ % 57.91/8.52 | $i(v0) | ~ aElementOf0(v0, xO) | ? [v1: $i] : (sdtlpdtrp0(xe, v1) % 57.91/8.52 | = v0 & $i(v1) & aElementOf0(v1, all_123_1))) % 57.91/8.52 | % 57.91/8.52 | ALPHA: (43) implies: % 57.91/8.52 | (44) szDzozmdt0(xd) = all_123_0 % 57.91/8.52 | % 57.91/8.52 | BETA: splitting (2) gives: % 57.91/8.52 | % 57.91/8.52 | Case 1: % 57.91/8.52 | | % 57.91/8.52 | | (45) ~ aSet0(slcrc0) % 57.91/8.52 | | % 57.91/8.52 | | PRED_UNIFY: (1), (45) imply: % 57.91/8.53 | | (46) $false % 57.91/8.53 | | % 57.91/8.53 | | CLOSE: (46) is inconsistent. % 57.91/8.53 | | % 57.91/8.53 | Case 2: % 57.91/8.53 | | % 57.91/8.53 | | % 57.91/8.53 | | GROUND_INST: instantiating (18) with all_105_1, all_111_0, xd, simplifying % 57.91/8.53 | | with (26), (30) gives: % 57.91/8.53 | | (47) all_111_0 = all_105_1 % 57.91/8.53 | | % 57.91/8.53 | | GROUND_INST: instantiating (18) with szNzAzT0, all_111_0, xd, simplifying % 57.91/8.53 | | with (5), (30) gives: % 57.91/8.53 | | (48) all_111_0 = szNzAzT0 % 57.91/8.53 | | % 57.91/8.53 | | GROUND_INST: instantiating (18) with all_105_1, all_123_0, xd, simplifying % 57.91/8.53 | | with (26), (44) gives: % 57.91/8.53 | | (49) all_123_0 = all_105_1 % 57.91/8.53 | | % 57.91/8.53 | | GROUND_INST: instantiating (18) with all_103_2, all_123_0, xd, simplifying % 57.91/8.53 | | with (24), (44) gives: % 57.91/8.53 | | (50) all_123_0 = all_103_2 % 57.91/8.53 | | % 57.91/8.53 | | GROUND_INST: instantiating (19) with all_117_1, all_120_5, xn, xN, % 57.91/8.53 | | simplifying with (34), (40) gives: % 57.91/8.53 | | (51) all_120_5 = all_117_1 % 57.91/8.53 | | % 57.91/8.53 | | COMBINE_EQS: (49), (50) imply: % 57.91/8.53 | | (52) all_105_1 = all_103_2 % 57.91/8.53 | | % 57.91/8.53 | | SIMP: (52) implies: % 57.91/8.53 | | (53) all_105_1 = all_103_2 % 57.91/8.53 | | % 57.91/8.53 | | COMBINE_EQS: (47), (48) imply: % 57.91/8.53 | | (54) all_105_1 = szNzAzT0 % 57.91/8.53 | | % 57.91/8.53 | | SIMP: (54) implies: % 57.91/8.53 | | (55) all_105_1 = szNzAzT0 % 57.91/8.53 | | % 57.91/8.53 | | COMBINE_EQS: (53), (55) imply: % 57.91/8.53 | | (56) all_103_2 = szNzAzT0 % 57.91/8.53 | | % 57.91/8.53 | | SIMP: (56) implies: % 57.91/8.53 | | (57) all_103_2 = szNzAzT0 % 57.91/8.53 | | % 57.91/8.53 | | REDUCE: (38), (51) imply: % 57.91/8.53 | | (58) szmzizndt0(all_117_1) = all_120_4 % 57.91/8.53 | | % 57.91/8.53 | | REDUCE: (23), (57) imply: % 57.91/8.53 | | (59) aElementOf0(xn, szNzAzT0) % 57.91/8.53 | | % 57.91/8.53 | | GROUND_INST: instantiating (17) with all_117_0, all_120_4, all_117_1, % 57.91/8.53 | | simplifying with (33), (58) gives: % 57.91/8.53 | | (60) all_120_4 = all_117_0 % 57.91/8.53 | | % 57.91/8.53 | | REDUCE: (37), (60) imply: % 57.91/8.53 | | (61) sdtpldt0(xP, all_117_0) = all_120_3 % 57.91/8.53 | | % 57.91/8.53 | | GROUND_INST: instantiating (4) with xn, all_117_1, all_117_0, xD, % 57.91/8.53 | | simplifying with (15), (32), (33), (34), (59) gives: % 57.91/8.53 | | (62) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 57.91/8.53 | | (sdtlpdtrp0(xC, xn) = v0 & slbdtsldtrb0(v2, xk) = v3 & $i(v3) & % 57.91/8.53 | | $i(v2) & $i(v1) & $i(v0) & aSubsetOf0(v2, xD) & isCountable0(v2) & % 57.91/8.53 | | aElementOf0(v1, xT) & aElementOf0(all_117_0, all_117_1) & % 57.91/8.53 | | aSet0(v2) & aSet0(xD) & ! [v4: $i] : ! [v5: $i] : (v5 = v1 | ~ % 57.91/8.53 | | (sdtlpdtrp0(v0, v4) = v5) | ~ $i(v4) | ~ aSubsetOf0(v4, v2) | % 57.91/8.53 | | ~ aSet0(v4) | ? [v6: $i] : ( ~ (v6 = xk) & sbrdtbr0(v4) = v6 & % 57.91/8.53 | | $i(v6))) & ! [v4: $i] : ! [v5: $i] : (v5 = v1 | ~ % 57.91/8.53 | | (sdtlpdtrp0(v0, v4) = v5) | ~ $i(v4) | ~ aElementOf0(v4, v3) | % 57.91/8.53 | | ~ aSet0(v4)) & ! [v4: $i] : ! [v5: $i] : (v5 = v1 | ~ % 57.91/8.53 | | (sdtlpdtrp0(v0, v4) = v5) | ~ $i(v4) | ~ aSet0(v4) | ? [v6: % 57.91/8.53 | | $i] : ? [v7: $i] : ($i(v7) & (( ~ (v6 = xk) & sbrdtbr0(v4) = % 57.91/8.53 | | v6 & $i(v6)) | (aElementOf0(v7, v4) & ~ aElementOf0(v7, % 57.91/8.53 | | v2))))) & ! [v4: any] : (v4 = all_117_0 | ~ $i(v4) | % 57.91/8.53 | | ~ aElementOf0(v4, all_117_1) | ~ aElement0(v4) | % 57.91/8.53 | | aElementOf0(v4, xD)) & ! [v4: $i] : ( ~ $i(v4) | ~ % 57.91/8.53 | | aElementOf0(v4, v2) | aElementOf0(v4, xD)) & ! [v4: $i] : ( ~ % 57.91/8.53 | | $i(v4) | ~ aElementOf0(v4, all_117_1) | sdtlseqdt0(all_117_0, % 57.91/8.53 | | v4)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, xD) | % 57.91/8.53 | | aElementOf0(v4, all_117_1)) & ! [v4: $i] : ( ~ $i(v4) | ~ % 57.91/8.53 | | aElementOf0(v4, xD) | aElement0(v4)) & ( ~ $i(all_117_0) | ~ % 57.91/8.53 | | aElementOf0(all_117_0, xD))) % 57.91/8.53 | | % 57.91/8.53 | | GROUND_INST: instantiating (3) with xn, all_117_1, all_117_0, xD, % 57.91/8.53 | | simplifying with (15), (32), (33), (34), (59) gives: % 57.91/8.54 | | (63) ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xC, xn) = v0 & % 57.91/8.54 | | szDzozmdt0(v0) = v1 & slbdtsldtrb0(xD, xk) = v1 & $i(v1) & $i(v0) % 57.91/8.54 | | & aFunction0(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 57.91/8.54 | | (sbrdtbr0(v2) = v3) | ~ $i(v4) | ~ $i(v2) | ~ aElementOf0(v4, % 57.91/8.54 | | v2) | ~ aElementOf0(v2, v1) | aElementOf0(v4, xD)) & ! [v2: % 57.91/8.54 | | $i] : ! [v3: $i] : (v3 = xk | ~ (sbrdtbr0(v2) = v3) | ~ % 57.91/8.54 | | $i(v2) | ~ aElementOf0(v2, v1)) & ! [v2: $i] : ! [v3: $i] : ( % 57.91/8.54 | | ~ (sbrdtbr0(v2) = v3) | ~ $i(v2) | ~ aElementOf0(v2, v1) | % 57.91/8.54 | | aSubsetOf0(v2, xD)) & ! [v2: $i] : ! [v3: $i] : ( ~ % 57.91/8.54 | | (sbrdtbr0(v2) = v3) | ~ $i(v2) | ~ aElementOf0(v2, v1) | % 57.91/8.54 | | aSet0(v2)) & ! [v2: $i] : ! [v3: $i] : ( ~ (sdtpldt0(v2, % 57.91/8.54 | | all_117_0) = v3) | ~ $i(v2) | ~ aSet0(v2) | ? [v4: $i] : % 57.91/8.54 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ($i(v7) & % 57.91/8.54 | | aElementOf0(all_117_0, all_117_1) & ! [v8: $i] : ( ~ $i(v8) | % 57.91/8.54 | | ~ aElementOf0(v8, all_117_1) | sdtlseqdt0(all_117_0, v8)) & % 57.91/8.54 | | ((v6 = v5 & sdtlpdtrp0(v0, v2) = v5 & sdtlpdtrp0(xc, v3) = v5 % 57.91/8.54 | | & $i(v5) & ! [v8: any] : (v8 = all_117_0 | ~ $i(v8) | ~ % 57.91/8.54 | | aElementOf0(v8, v3) | aElementOf0(v8, v2)) & ! [v8: $i] % 57.91/8.54 | | : ( ~ $i(v8) | ~ aElementOf0(v8, v3) | aElement0(v8)) & % 57.91/8.54 | | ! [v8: $i] : ( ~ $i(v8) | ~ aElementOf0(v8, v2) | ~ % 57.91/8.54 | | aElement0(v8) | aElementOf0(v8, v3)) & ( ~ $i(all_117_0) % 57.91/8.54 | | | ~ aElement0(all_117_0) | aElementOf0(all_117_0, v3))) % 57.91/8.54 | | | (aSet0(xD) & ~ aElementOf0(v2, v1) & ! [v8: any] : (v8 = % 57.91/8.54 | | all_117_0 | ~ $i(v8) | ~ aElementOf0(v8, all_117_1) | % 57.91/8.54 | | ~ aElement0(v8) | aElementOf0(v8, xD)) & ! [v8: $i] : ( % 57.91/8.54 | | ~ $i(v8) | ~ aElementOf0(v8, xD) | aElementOf0(v8, % 57.91/8.54 | | all_117_1)) & ! [v8: $i] : ( ~ $i(v8) | ~ % 57.91/8.54 | | aElementOf0(v8, xD) | aElement0(v8)) & ( ~ $i(all_117_0) % 57.91/8.54 | | | ~ aElementOf0(all_117_0, xD)) & (( ~ (v4 = xk) & % 57.91/8.54 | | sbrdtbr0(v2) = v4 & $i(v4)) | (aElementOf0(v7, v2) & % 57.91/8.54 | | ~ aSubsetOf0(v2, xD) & ~ aElementOf0(v7, xD))))))) & % 57.91/8.54 | | ! [v2: $i] : ( ~ (sbrdtbr0(v2) = xk) | ~ $i(v2) | ~ % 57.91/8.54 | | aSubsetOf0(v2, xD) | aElementOf0(v2, v1)) & ! [v2: $i] : ( ~ % 57.91/8.54 | | (sbrdtbr0(v2) = xk) | ~ $i(v2) | ~ aSet0(v2) | aElementOf0(v2, % 57.91/8.54 | | v1) | ? [v3: $i] : ($i(v3) & aElementOf0(v3, v2) & ~ % 57.91/8.54 | | aElementOf0(v3, xD)))) % 57.91/8.54 | | % 57.91/8.54 | | DELTA: instantiating (62) with fresh symbols all_167_0, all_167_1, % 57.91/8.54 | | all_167_2, all_167_3 gives: % 58.27/8.54 | | (64) sdtlpdtrp0(xC, xn) = all_167_3 & slbdtsldtrb0(all_167_1, xk) = % 58.27/8.54 | | all_167_0 & $i(all_167_0) & $i(all_167_1) & $i(all_167_2) & % 58.27/8.54 | | $i(all_167_3) & aSubsetOf0(all_167_1, xD) & isCountable0(all_167_1) % 58.27/8.54 | | & aElementOf0(all_167_2, xT) & aElementOf0(all_117_0, all_117_1) & % 58.27/8.54 | | aSet0(all_167_1) & aSet0(xD) & ! [v0: $i] : ! [v1: int] : (v1 = % 58.27/8.54 | | all_167_2 | ~ (sdtlpdtrp0(all_167_3, v0) = v1) | ~ $i(v0) | ~ % 58.27/8.54 | | aSubsetOf0(v0, all_167_1) | ~ aSet0(v0) | ? [v2: $i] : ( ~ (v2 = % 58.27/8.54 | | xk) & sbrdtbr0(v0) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: % 58.27/8.54 | | int] : (v1 = all_167_2 | ~ (sdtlpdtrp0(all_167_3, v0) = v1) | ~ % 58.27/8.54 | | $i(v0) | ~ aElementOf0(v0, all_167_0) | ~ aSet0(v0)) & ! [v0: % 58.27/8.54 | | $i] : ! [v1: int] : (v1 = all_167_2 | ~ (sdtlpdtrp0(all_167_3, % 58.27/8.54 | | v0) = v1) | ~ $i(v0) | ~ aSet0(v0) | ? [v2: $i] : ? [v3: % 58.27/8.54 | | $i] : ($i(v3) & (( ~ (v2 = xk) & sbrdtbr0(v0) = v2 & $i(v2)) | % 58.27/8.54 | | (aElementOf0(v3, v0) & ~ aElementOf0(v3, all_167_1))))) & ! % 58.27/8.54 | | [v0: any] : (v0 = all_117_0 | ~ $i(v0) | ~ aElementOf0(v0, % 58.27/8.54 | | all_117_1) | ~ aElement0(v0) | aElementOf0(v0, xD)) & ! [v0: % 58.27/8.54 | | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_167_1) | aElementOf0(v0, % 58.27/8.54 | | xD)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_117_1) % 58.27/8.54 | | | sdtlseqdt0(all_117_0, v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 58.27/8.54 | | aElementOf0(v0, xD) | aElementOf0(v0, all_117_1)) & ! [v0: $i] : % 58.27/8.54 | | ( ~ $i(v0) | ~ aElementOf0(v0, xD) | aElement0(v0)) & ( ~ % 58.27/8.54 | | $i(all_117_0) | ~ aElementOf0(all_117_0, xD)) % 58.27/8.54 | | % 58.27/8.54 | | ALPHA: (64) implies: % 58.27/8.54 | | (65) sdtlpdtrp0(xC, xn) = all_167_3 % 58.27/8.54 | | % 58.27/8.54 | | DELTA: instantiating (63) with fresh symbols all_173_0, all_173_1 gives: % 58.27/8.54 | | (66) sdtlpdtrp0(xC, xn) = all_173_1 & szDzozmdt0(all_173_1) = all_173_0 & % 58.27/8.54 | | slbdtsldtrb0(xD, xk) = all_173_0 & $i(all_173_0) & $i(all_173_1) & % 58.27/8.54 | | aFunction0(all_173_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( % 58.27/8.54 | | ~ (sbrdtbr0(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v2, % 58.27/8.54 | | v0) | ~ aElementOf0(v0, all_173_0) | aElementOf0(v2, xD)) & ! % 58.27/8.54 | | [v0: $i] : ! [v1: $i] : (v1 = xk | ~ (sbrdtbr0(v0) = v1) | ~ % 58.27/8.54 | | $i(v0) | ~ aElementOf0(v0, all_173_0)) & ! [v0: $i] : ! [v1: % 58.27/8.54 | | $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, % 58.27/8.54 | | all_173_0) | aSubsetOf0(v0, xD)) & ! [v0: $i] : ! [v1: $i] : ( % 58.27/8.54 | | ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_173_0) % 58.27/8.54 | | | aSet0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(v0, % 58.27/8.54 | | all_117_0) = v1) | ~ $i(v0) | ~ aSet0(v0) | ? [v2: $i] : ? % 58.27/8.54 | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ($i(v5) & % 58.27/8.54 | | aElementOf0(all_117_0, all_117_1) & ! [v6: $i] : ( ~ $i(v6) | % 58.27/8.54 | | ~ aElementOf0(v6, all_117_1) | sdtlseqdt0(all_117_0, v6)) & % 58.27/8.54 | | ((v4 = v3 & sdtlpdtrp0(all_173_1, v0) = v3 & sdtlpdtrp0(xc, v1) % 58.27/8.54 | | = v3 & $i(v3) & ! [v6: any] : (v6 = all_117_0 | ~ $i(v6) | % 58.27/8.54 | | ~ aElementOf0(v6, v1) | aElementOf0(v6, v0)) & ! [v6: % 58.27/8.54 | | $i] : ( ~ $i(v6) | ~ aElementOf0(v6, v1) | aElement0(v6)) % 58.27/8.54 | | & ! [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6, v0) | ~ % 58.27/8.54 | | aElement0(v6) | aElementOf0(v6, v1)) & ( ~ $i(all_117_0) | % 58.27/8.54 | | ~ aElement0(all_117_0) | aElementOf0(all_117_0, v1))) | % 58.27/8.54 | | (aSet0(xD) & ~ aElementOf0(v0, all_173_0) & ! [v6: any] : % 58.27/8.54 | | (v6 = all_117_0 | ~ $i(v6) | ~ aElementOf0(v6, all_117_1) % 58.27/8.54 | | | ~ aElement0(v6) | aElementOf0(v6, xD)) & ! [v6: $i] : % 58.27/8.54 | | ( ~ $i(v6) | ~ aElementOf0(v6, xD) | aElementOf0(v6, % 58.27/8.54 | | all_117_1)) & ! [v6: $i] : ( ~ $i(v6) | ~ % 58.27/8.54 | | aElementOf0(v6, xD) | aElement0(v6)) & ( ~ $i(all_117_0) | % 58.27/8.54 | | ~ aElementOf0(all_117_0, xD)) & (( ~ (v2 = xk) & % 58.27/8.54 | | sbrdtbr0(v0) = v2 & $i(v2)) | (aElementOf0(v5, v0) & ~ % 58.27/8.54 | | aSubsetOf0(v0, xD) & ~ aElementOf0(v5, xD))))))) & ! % 58.27/8.54 | | [v0: $i] : ( ~ (sbrdtbr0(v0) = xk) | ~ $i(v0) | ~ aSubsetOf0(v0, % 58.27/8.54 | | xD) | aElementOf0(v0, all_173_0)) & ! [v0: $i] : ( ~ % 58.27/8.54 | | (sbrdtbr0(v0) = xk) | ~ $i(v0) | ~ aSet0(v0) | aElementOf0(v0, % 58.27/8.54 | | all_173_0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0) & ~ % 58.27/8.54 | | aElementOf0(v1, xD))) % 58.27/8.54 | | % 58.27/8.54 | | ALPHA: (66) implies: % 58.27/8.54 | | (67) sdtlpdtrp0(xC, xn) = all_173_1 % 58.27/8.54 | | (68) ! [v0: $i] : ( ~ (sbrdtbr0(v0) = xk) | ~ $i(v0) | ~ % 58.27/8.54 | | aSubsetOf0(v0, xD) | aElementOf0(v0, all_173_0)) % 58.27/8.55 | | (69) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(v0, all_117_0) = v1) | ~ % 58.27/8.55 | | $i(v0) | ~ aSet0(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 58.27/8.55 | | ? [v5: $i] : ($i(v5) & aElementOf0(all_117_0, all_117_1) & ! [v6: % 58.27/8.55 | | $i] : ( ~ $i(v6) | ~ aElementOf0(v6, all_117_1) | % 58.27/8.55 | | sdtlseqdt0(all_117_0, v6)) & ((v4 = v3 & sdtlpdtrp0(all_173_1, % 58.27/8.55 | | v0) = v3 & sdtlpdtrp0(xc, v1) = v3 & $i(v3) & ! [v6: any] % 58.27/8.55 | | : (v6 = all_117_0 | ~ $i(v6) | ~ aElementOf0(v6, v1) | % 58.27/8.55 | | aElementOf0(v6, v0)) & ! [v6: $i] : ( ~ $i(v6) | ~ % 58.27/8.55 | | aElementOf0(v6, v1) | aElement0(v6)) & ! [v6: $i] : ( ~ % 58.27/8.55 | | $i(v6) | ~ aElementOf0(v6, v0) | ~ aElement0(v6) | % 58.27/8.55 | | aElementOf0(v6, v1)) & ( ~ $i(all_117_0) | ~ % 58.27/8.55 | | aElement0(all_117_0) | aElementOf0(all_117_0, v1))) | % 58.27/8.55 | | (aSet0(xD) & ~ aElementOf0(v0, all_173_0) & ! [v6: any] : % 58.27/8.55 | | (v6 = all_117_0 | ~ $i(v6) | ~ aElementOf0(v6, all_117_1) % 58.27/8.55 | | | ~ aElement0(v6) | aElementOf0(v6, xD)) & ! [v6: $i] : % 58.27/8.55 | | ( ~ $i(v6) | ~ aElementOf0(v6, xD) | aElementOf0(v6, % 58.27/8.55 | | all_117_1)) & ! [v6: $i] : ( ~ $i(v6) | ~ % 58.27/8.55 | | aElementOf0(v6, xD) | aElement0(v6)) & ( ~ $i(all_117_0) | % 58.27/8.55 | | ~ aElementOf0(all_117_0, xD)) & (( ~ (v2 = xk) & % 58.27/8.55 | | sbrdtbr0(v0) = v2 & $i(v2)) | (aElementOf0(v5, v0) & ~ % 58.27/8.55 | | aSubsetOf0(v0, xD) & ~ aElementOf0(v5, xD))))))) % 58.27/8.55 | | % 58.27/8.55 | | GROUND_INST: instantiating (69) with xP, all_120_3, simplifying with (14), % 58.27/8.55 | | (28), (61) gives: % 58.27/8.55 | | (70) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v3) & % 58.27/8.55 | | aElementOf0(all_117_0, all_117_1) & ! [v4: $i] : ( ~ $i(v4) | ~ % 58.27/8.55 | | aElementOf0(v4, all_117_1) | sdtlseqdt0(all_117_0, v4)) & ((v2 = % 58.27/8.55 | | v1 & sdtlpdtrp0(all_173_1, xP) = v1 & sdtlpdtrp0(xc, % 58.27/8.55 | | all_120_3) = v1 & $i(v1) & ! [v4: any] : (v4 = all_117_0 | % 58.27/8.55 | | ~ $i(v4) | ~ aElementOf0(v4, all_120_3) | aElementOf0(v4, % 58.27/8.55 | | xP)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, % 58.27/8.55 | | all_120_3) | aElement0(v4)) & ! [v4: $i] : ( ~ $i(v4) | % 58.27/8.55 | | ~ aElementOf0(v4, xP) | ~ aElement0(v4) | aElementOf0(v4, % 58.27/8.55 | | all_120_3)) & ( ~ $i(all_117_0) | ~ aElement0(all_117_0) % 58.27/8.55 | | | aElementOf0(all_117_0, all_120_3))) | (aSet0(xD) & ~ % 58.27/8.55 | | aElementOf0(xP, all_173_0) & ! [v4: any] : (v4 = all_117_0 | % 58.27/8.55 | | ~ $i(v4) | ~ aElementOf0(v4, all_117_1) | ~ aElement0(v4) % 58.27/8.55 | | | aElementOf0(v4, xD)) & ! [v4: $i] : ( ~ $i(v4) | ~ % 58.27/8.55 | | aElementOf0(v4, xD) | aElementOf0(v4, all_117_1)) & ! [v4: % 58.27/8.55 | | $i] : ( ~ $i(v4) | ~ aElementOf0(v4, xD) | aElement0(v4)) & % 58.27/8.55 | | ( ~ $i(all_117_0) | ~ aElementOf0(all_117_0, xD)) & (( ~ (v0 % 58.27/8.55 | | = xk) & sbrdtbr0(xP) = v0 & $i(v0)) | (aElementOf0(v3, % 58.27/8.55 | | xP) & ~ aSubsetOf0(xP, xD) & ~ aElementOf0(v3, % 58.27/8.55 | | xD)))))) % 58.27/8.55 | | % 58.27/8.55 | | GROUND_INST: instantiating (68) with xP, simplifying with (10), (14), (21) % 58.27/8.55 | | gives: % 58.27/8.55 | | (71) aElementOf0(xP, all_173_0) % 58.27/8.55 | | % 58.27/8.55 | | DELTA: instantiating (70) with fresh symbols all_177_0, all_177_1, % 58.27/8.55 | | all_177_2, all_177_3 gives: % 58.27/8.55 | | (72) $i(all_177_0) & aElementOf0(all_117_0, all_117_1) & ! [v0: $i] : ( % 58.27/8.55 | | ~ $i(v0) | ~ aElementOf0(v0, all_117_1) | sdtlseqdt0(all_117_0, % 58.27/8.55 | | v0)) & ((all_177_1 = all_177_2 & sdtlpdtrp0(all_173_1, xP) = % 58.27/8.55 | | all_177_2 & sdtlpdtrp0(xc, all_120_3) = all_177_2 & % 58.27/8.55 | | $i(all_177_2) & ! [v0: any] : (v0 = all_117_0 | ~ $i(v0) | ~ % 58.27/8.55 | | aElementOf0(v0, all_120_3) | aElementOf0(v0, xP)) & ! [v0: % 58.27/8.55 | | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_120_3) | % 58.27/8.55 | | aElement0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, % 58.27/8.55 | | xP) | ~ aElement0(v0) | aElementOf0(v0, all_120_3)) & ( ~ % 58.27/8.55 | | $i(all_117_0) | ~ aElement0(all_117_0) | % 58.27/8.55 | | aElementOf0(all_117_0, all_120_3))) | (aSet0(xD) & ~ % 58.27/8.55 | | aElementOf0(xP, all_173_0) & ! [v0: any] : (v0 = all_117_0 | ~ % 58.27/8.55 | | $i(v0) | ~ aElementOf0(v0, all_117_1) | ~ aElement0(v0) | % 58.27/8.55 | | aElementOf0(v0, xD)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 58.27/8.55 | | aElementOf0(v0, xD) | aElementOf0(v0, all_117_1)) & ! [v0: % 58.27/8.55 | | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xD) | aElement0(v0)) & ( % 58.27/8.55 | | ~ $i(all_117_0) | ~ aElementOf0(all_117_0, xD)) & (( ~ % 58.27/8.55 | | (all_177_3 = xk) & sbrdtbr0(xP) = all_177_3 & $i(all_177_3)) % 58.27/8.55 | | | (aElementOf0(all_177_0, xP) & ~ aSubsetOf0(xP, xD) & ~ % 58.27/8.55 | | aElementOf0(all_177_0, xD))))) % 58.27/8.55 | | % 58.27/8.55 | | ALPHA: (72) implies: % 58.27/8.55 | | (73) (all_177_1 = all_177_2 & sdtlpdtrp0(all_173_1, xP) = all_177_2 & % 58.27/8.55 | | sdtlpdtrp0(xc, all_120_3) = all_177_2 & $i(all_177_2) & ! [v0: % 58.27/8.55 | | any] : (v0 = all_117_0 | ~ $i(v0) | ~ aElementOf0(v0, % 58.27/8.55 | | all_120_3) | aElementOf0(v0, xP)) & ! [v0: $i] : ( ~ $i(v0) | % 58.27/8.55 | | ~ aElementOf0(v0, all_120_3) | aElement0(v0)) & ! [v0: $i] : ( % 58.27/8.55 | | ~ $i(v0) | ~ aElementOf0(v0, xP) | ~ aElement0(v0) | % 58.27/8.55 | | aElementOf0(v0, all_120_3)) & ( ~ $i(all_117_0) | ~ % 58.27/8.55 | | aElement0(all_117_0) | aElementOf0(all_117_0, all_120_3))) | % 58.27/8.55 | | (aSet0(xD) & ~ aElementOf0(xP, all_173_0) & ! [v0: any] : (v0 = % 58.27/8.55 | | all_117_0 | ~ $i(v0) | ~ aElementOf0(v0, all_117_1) | ~ % 58.27/8.55 | | aElement0(v0) | aElementOf0(v0, xD)) & ! [v0: $i] : ( ~ $i(v0) % 58.27/8.55 | | | ~ aElementOf0(v0, xD) | aElementOf0(v0, all_117_1)) & ! [v0: % 58.27/8.55 | | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xD) | aElement0(v0)) & ( ~ % 58.27/8.55 | | $i(all_117_0) | ~ aElementOf0(all_117_0, xD)) & (( ~ (all_177_3 % 58.27/8.55 | | = xk) & sbrdtbr0(xP) = all_177_3 & $i(all_177_3)) | % 58.27/8.55 | | (aElementOf0(all_177_0, xP) & ~ aSubsetOf0(xP, xD) & ~ % 58.27/8.55 | | aElementOf0(all_177_0, xD)))) % 58.27/8.55 | | % 58.27/8.55 | | BETA: splitting (73) gives: % 58.27/8.55 | | % 58.27/8.55 | | Case 1: % 58.27/8.55 | | | % 58.27/8.56 | | | (74) all_177_1 = all_177_2 & sdtlpdtrp0(all_173_1, xP) = all_177_2 & % 58.27/8.56 | | | sdtlpdtrp0(xc, all_120_3) = all_177_2 & $i(all_177_2) & ! [v0: % 58.27/8.56 | | | any] : (v0 = all_117_0 | ~ $i(v0) | ~ aElementOf0(v0, % 58.27/8.56 | | | all_120_3) | aElementOf0(v0, xP)) & ! [v0: $i] : ( ~ $i(v0) | % 58.27/8.56 | | | ~ aElementOf0(v0, all_120_3) | aElement0(v0)) & ! [v0: $i] : ( % 58.27/8.56 | | | ~ $i(v0) | ~ aElementOf0(v0, xP) | ~ aElement0(v0) | % 58.27/8.56 | | | aElementOf0(v0, all_120_3)) & ( ~ $i(all_117_0) | ~ % 58.27/8.56 | | | aElement0(all_117_0) | aElementOf0(all_117_0, all_120_3)) % 58.27/8.56 | | | % 58.27/8.56 | | | ALPHA: (74) implies: % 58.27/8.56 | | | (75) sdtlpdtrp0(xc, all_120_3) = all_177_2 % 58.27/8.56 | | | (76) sdtlpdtrp0(all_173_1, xP) = all_177_2 % 58.27/8.56 | | | % 58.27/8.56 | | | GROUND_INST: instantiating (19) with all_120_2, all_177_2, all_120_3, xc, % 58.27/8.56 | | | simplifying with (39), (75) gives: % 58.27/8.56 | | | (77) all_177_2 = all_120_2 % 58.27/8.56 | | | % 58.27/8.56 | | | GROUND_INST: instantiating (19) with all_120_1, all_173_1, xn, xC, % 58.27/8.56 | | | simplifying with (41), (67) gives: % 58.27/8.56 | | | (78) all_173_1 = all_120_1 % 58.27/8.56 | | | % 58.27/8.56 | | | GROUND_INST: instantiating (19) with all_167_3, all_173_1, xn, xC, % 58.27/8.56 | | | simplifying with (65), (67) gives: % 58.27/8.56 | | | (79) all_173_1 = all_167_3 % 58.27/8.56 | | | % 58.27/8.56 | | | COMBINE_EQS: (78), (79) imply: % 58.27/8.56 | | | (80) all_167_3 = all_120_1 % 58.27/8.56 | | | % 58.27/8.56 | | | REDUCE: (76), (77), (78) imply: % 58.27/8.56 | | | (81) sdtlpdtrp0(all_120_1, xP) = all_120_2 % 58.27/8.56 | | | % 58.27/8.56 | | | GROUND_INST: instantiating (19) with all_120_0, all_120_2, xP, all_120_1, % 58.27/8.56 | | | simplifying with (42), (81) gives: % 58.27/8.56 | | | (82) all_120_0 = all_120_2 % 58.27/8.56 | | | % 58.27/8.56 | | | REDUCE: (36), (82) imply: % 58.27/8.56 | | | (83) $false % 58.27/8.56 | | | % 58.27/8.56 | | | CLOSE: (83) is inconsistent. % 58.27/8.56 | | | % 58.27/8.56 | | Case 2: % 58.27/8.56 | | | % 58.27/8.56 | | | (84) aSet0(xD) & ~ aElementOf0(xP, all_173_0) & ! [v0: any] : (v0 = % 58.27/8.56 | | | all_117_0 | ~ $i(v0) | ~ aElementOf0(v0, all_117_1) | ~ % 58.27/8.56 | | | aElement0(v0) | aElementOf0(v0, xD)) & ! [v0: $i] : ( ~ $i(v0) % 58.27/8.56 | | | | ~ aElementOf0(v0, xD) | aElementOf0(v0, all_117_1)) & ! [v0: % 58.27/8.56 | | | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xD) | aElement0(v0)) & ( ~ % 58.27/8.56 | | | $i(all_117_0) | ~ aElementOf0(all_117_0, xD)) & (( ~ (all_177_3 % 58.27/8.56 | | | = xk) & sbrdtbr0(xP) = all_177_3 & $i(all_177_3)) | % 58.27/8.56 | | | (aElementOf0(all_177_0, xP) & ~ aSubsetOf0(xP, xD) & ~ % 58.27/8.56 | | | aElementOf0(all_177_0, xD))) % 58.27/8.56 | | | % 58.27/8.56 | | | ALPHA: (84) implies: % 58.27/8.56 | | | (85) ~ aElementOf0(xP, all_173_0) % 58.27/8.56 | | | % 58.27/8.56 | | | PRED_UNIFY: (71), (85) imply: % 58.27/8.56 | | | (86) $false % 58.27/8.56 | | | % 58.27/8.56 | | | CLOSE: (86) is inconsistent. % 58.27/8.56 | | | % 58.27/8.56 | | End of split % 58.27/8.56 | | % 58.27/8.56 | End of split % 58.27/8.56 | % 58.27/8.56 End of proof % 58.27/8.56 % SZS output end Proof for theBenchmark % 58.27/8.56 % 58.27/8.56 7965ms %------------------------------------------------------------------------------