%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM631+3 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n019.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 11:49:06 EDT 2023 % Result : Theorem 153.82s 21.24s % Output : Proof 155.26s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM631+3 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n019.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Fri Aug 25 16:23:13 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 6.61/1.64 Prover 1: Preprocessing ... % 6.61/1.64 Prover 4: Preprocessing ... % 6.83/1.71 Prover 6: Preprocessing ... % 6.83/1.71 Prover 3: Preprocessing ... % 6.83/1.71 Prover 0: Preprocessing ... % 6.83/1.71 Prover 2: Preprocessing ... % 6.83/1.72 Prover 5: Preprocessing ... % 20.18/3.60 Prover 1: Constructing countermodel ... % 20.18/3.61 Prover 3: Constructing countermodel ... % 21.91/3.69 Prover 6: Proving ... % 24.47/4.09 Prover 5: Proving ... % 50.92/7.48 Prover 4: Constructing countermodel ... % 54.65/7.99 Prover 2: Proving ... % 60.03/8.70 Prover 0: Proving ... % 100.27/14.04 Prover 5: stopped % 100.27/14.05 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 102.38/14.30 Prover 7: Preprocessing ... % 108.00/15.06 Prover 7: Constructing countermodel ... % 110.11/15.44 Prover 2: stopped % 110.11/15.46 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 112.79/15.71 Prover 8: Preprocessing ... % 115.12/16.02 Prover 1: stopped % 115.12/16.04 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 115.99/16.09 Prover 8: Warning: ignoring some quantifiers % 115.99/16.12 Prover 8: Constructing countermodel ... % 115.99/16.25 Prover 9: Preprocessing ... % 129.48/17.88 Prover 6: stopped % 129.48/17.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 131.05/18.12 Prover 10: Preprocessing ... % 134.63/18.57 Prover 10: Constructing countermodel ... % 136.43/18.80 Prover 9: Constructing countermodel ... % 153.06/21.19 Prover 10: Found proof (size 164) % 153.06/21.19 Prover 10: proved (3299ms) % 153.06/21.20 Prover 0: stopped % 153.06/21.20 Prover 7: stopped % 153.06/21.20 Prover 8: stopped % 153.06/21.20 Prover 4: stopped % 153.06/21.20 Prover 9: stopped % 153.82/21.24 Prover 3: stopped % 153.82/21.24 % 153.82/21.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 153.82/21.24 % 153.82/21.26 % SZS output start Proof for theBenchmark % 153.82/21.27 Assumptions after simplification: % 153.82/21.27 --------------------------------- % 153.82/21.27 % 153.82/21.27 (mConsDiff) % 153.82/21.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 153.82/21.30 (sdtmndt0(v0, v1) = v2) | ~ (sdtpldt0(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) % 153.82/21.30 | ~ aElementOf0(v1, v0) | ~ aSet0(v0)) % 153.82/21.30 % 153.82/21.30 (mCountNFin_01) % 153.82/21.30 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)) % 153.82/21.30 % 153.82/21.30 (mDefEmp) % 153.82/21.30 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~ % 153.82/21.30 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : ( % 153.82/21.30 ~ $i(v0) | ~ aElementOf0(v0, slcrc0)) % 153.82/21.30 % 153.82/21.30 (mImgElm) % 154.61/21.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(v0, % 154.61/21.30 v2) = v3) | ~ (szDzozmdt0(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ % 154.61/21.30 aFunction0(v0) | ~ aElementOf0(v2, v1) | aElement0(v3)) % 154.61/21.30 % 154.61/21.30 (m__) % 154.61/21.30 $i(xn) & $i(xQ) & $i(xd) & $i(xc) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) % 154.61/21.30 & sdtlpdtrp0(xd, xn) = v1 & sdtlpdtrp0(xc, xQ) = v0 & $i(v1) & $i(v0)) % 154.61/21.30 % 154.61/21.30 (m__4151) % 154.61/21.33 szDzozmdt0(xC) = szNzAzT0 & $i(xC) & $i(xN) & $i(xk) & $i(xc) & $i(szNzAzT0) & % 154.61/21.33 aFunction0(xC) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 154.61/21.33 [v4: $i] : (v4 = v2 | ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) % 154.61/21.33 | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~ aElementOf0(v4, % 154.61/21.33 v1) | ~ aElementOf0(v0, szNzAzT0) | ~ aElement0(v4) | aElementOf0(v4, % 154.61/21.33 v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 154.61/21.33 : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, % 154.61/21.33 v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~ aElementOf0(v4, v3) | ~ % 154.61/21.33 aElementOf0(v0, szNzAzT0) | aElementOf0(v4, v1)) & ! [v0: $i] : ! [v1: $i] % 154.61/21.33 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ % 154.61/21.33 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | % 154.61/21.33 ~ aElementOf0(v4, v3) | ~ aElementOf0(v0, szNzAzT0) | aElement0(v4)) & ! % 154.61/21.33 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 154.61/21.33 (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) % 154.61/21.33 = v3) | ~ $i(v4) | ~ $i(v0) | ~ aElementOf0(v4, v1) | ~ % 154.61/21.33 aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v2, v4)) & ! [v0: $i] : ! [v1: $i] % 154.61/21.33 : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ % 154.61/21.33 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v0) | % 154.61/21.33 ~ aElementOf0(v2, v3) | ~ aElementOf0(v0, szNzAzT0)) & ! [v0: $i] : ! % 154.61/21.33 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ % 154.61/21.33 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ % 154.61/21.33 aElementOf0(v0, szNzAzT0) | aElementOf0(v2, v1)) & ! [v0: $i] : ! [v1: $i] % 154.61/21.33 : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ % 154.61/21.33 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ % 154.61/21.33 aElementOf0(v0, szNzAzT0) | aSet0(v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 154.61/21.33 $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) % 154.61/21.33 | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? % 154.61/21.33 [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xC, v0) = v4 & szDzozmdt0(v4) = v5 & % 154.61/21.33 slbdtsldtrb0(v3, xk) = v5 & $i(v5) & $i(v4) & aFunction0(v4) & ! [v6: $i] % 154.61/21.33 : ! [v7: $i] : ! [v8: $i] : ( ~ (sbrdtbr0(v6) = v7) | ~ $i(v8) | ~ % 154.61/21.33 $i(v6) | ~ aElementOf0(v8, v6) | ~ aElementOf0(v6, v5) | % 154.61/21.33 aElementOf0(v8, v3)) & ! [v6: $i] : ! [v7: $i] : (v7 = xk | ~ % 154.61/21.33 (sbrdtbr0(v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v5)) & ! [v6: $i] % 154.61/21.33 : ! [v7: $i] : ( ~ (sbrdtbr0(v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, % 154.61/21.33 v5) | aSubsetOf0(v6, v3)) & ! [v6: $i] : ! [v7: $i] : ( ~ % 154.61/21.33 (sbrdtbr0(v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v5) | aSet0(v6)) & % 154.61/21.33 ! [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, v2) = v7) | ~ $i(v6) | ~ % 154.61/21.33 aSet0(v6) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : % 154.61/21.33 ($i(v11) & aElementOf0(v2, v1) & ! [v12: $i] : ( ~ $i(v12) | ~ % 154.61/21.33 aElementOf0(v12, v1) | sdtlseqdt0(v2, v12)) & ((v10 = v9 & % 154.61/21.33 sdtlpdtrp0(v4, v6) = v9 & sdtlpdtrp0(xc, v7) = v9 & $i(v9) & ! % 154.61/21.33 [v12: $i] : (v12 = v2 | ~ $i(v12) | ~ aElementOf0(v12, v7) | % 154.61/21.33 aElementOf0(v12, v6)) & ! [v12: $i] : ( ~ $i(v12) | ~ % 154.61/21.33 aElementOf0(v12, v7) | aElement0(v12)) & ! [v12: $i] : ( ~ % 154.61/21.33 $i(v12) | ~ aElementOf0(v12, v6) | ~ aElement0(v12) | % 154.61/21.33 aElementOf0(v12, v7)) & ( ~ $i(v2) | ~ aElement0(v2) | % 154.61/21.33 aElementOf0(v2, v7))) | (aSet0(v3) & ~ aElementOf0(v6, v5) & ! % 154.61/21.33 [v12: $i] : (v12 = v2 | ~ $i(v12) | ~ aElementOf0(v12, v1) | ~ % 154.61/21.33 aElement0(v12) | aElementOf0(v12, v3)) & ! [v12: $i] : ( ~ % 154.61/21.33 $i(v12) | ~ aElementOf0(v12, v3) | aElementOf0(v12, v1)) & ! % 154.61/21.33 [v12: $i] : ( ~ $i(v12) | ~ aElementOf0(v12, v3) | % 154.61/21.33 aElement0(v12)) & ( ~ $i(v2) | ~ aElementOf0(v2, v3)) & (( ~ % 154.61/21.33 (v8 = xk) & sbrdtbr0(v6) = v8 & $i(v8)) | (aElementOf0(v11, % 154.61/21.33 v6) & ~ aSubsetOf0(v6, v3) & ~ aElementOf0(v11, v3))))))) % 154.61/21.33 & ! [v6: $i] : ( ~ (sbrdtbr0(v6) = xk) | ~ $i(v6) | ~ aSubsetOf0(v6, % 154.61/21.33 v3) | aElementOf0(v6, v5)) & ! [v6: $i] : ( ~ (sbrdtbr0(v6) = xk) | % 154.61/21.33 ~ $i(v6) | ~ aSet0(v6) | aElementOf0(v6, v5) | ? [v7: $i] : ($i(v7) & % 154.61/21.33 aElementOf0(v7, v6) & ~ aElementOf0(v7, v3))))) % 154.61/21.33 % 154.61/21.33 (m__4618) % 154.61/21.33 $i(xC) & $i(xN) & $i(xk) & $i(xT) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : % 154.61/21.33 ( ~ (sdtlpdtrp0(xC, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? % 154.61/21.33 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xN, v2) = % 154.61/21.33 v3 & slbdtsldtrb0(v3, xk) = v4 & szszuzczcdt0(v0) = v2 & $i(v5) & $i(v4) & % 154.61/21.33 $i(v3) & $i(v2) & aElementOf0(v5, xT) & ! [v6: $i] : ! [v7: $i] : (v7 = % 154.61/21.33 v5 | ~ (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aSubsetOf0(v6, v3) | % 154.61/21.33 ~ aSet0(v6) | ? [v8: $i] : ( ~ (v8 = xk) & sbrdtbr0(v6) = v8 & $i(v8))) % 154.61/21.33 & ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~ (sdtlpdtrp0(v1, v6) = v7) | ~ % 154.61/21.33 $i(v6) | ~ aElementOf0(v6, v4) | ~ aSet0(v6)) & ! [v6: $i] : ! [v7: % 154.61/21.33 $i] : (v7 = v5 | ~ (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aSet0(v6) % 154.61/21.33 | ? [v8: $i] : ? [v9: $i] : ($i(v9) & (( ~ (v8 = xk) & sbrdtbr0(v6) = % 154.61/21.33 v8 & $i(v8)) | (aElementOf0(v9, v6) & ~ aElementOf0(v9, v3))))))) % 154.61/21.33 % 154.61/21.33 (m__4660) % 154.61/21.33 szDzozmdt0(xe) = szNzAzT0 & $i(xe) & $i(xN) & $i(szNzAzT0) & aFunction0(xe) & % 154.61/21.33 ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) | ~ % 154.61/21.33 aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2 & % 154.61/21.33 szmzizndt0(v2) = v1 & $i(v2) & $i(v1) & aElementOf0(v1, v2) & ! [v3: $i] % 154.61/21.33 : ( ~ $i(v3) | ~ aElementOf0(v3, v2) | sdtlseqdt0(v1, v3)))) % 154.61/21.33 % 154.61/21.33 (m__4730) % 154.61/21.34 szDzozmdt0(xd) = szNzAzT0 & $i(xd) & $i(xC) & $i(xN) & $i(xk) & $i(szNzAzT0) & % 154.61/21.34 aFunction0(xd) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xC, v0) = v1) | % 154.61/21.34 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ? % 154.61/21.34 [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xd, v0) = v5 & sdtlpdtrp0(xN, v2) = v3 % 154.61/21.34 & slbdtsldtrb0(v3, xk) = v4 & szszuzczcdt0(v0) = v2 & $i(v5) & $i(v4) & % 154.61/21.34 $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~ % 154.61/21.34 (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aSubsetOf0(v6, v3) | ~ % 154.61/21.34 aSet0(v6) | ? [v8: $i] : ( ~ (v8 = xk) & sbrdtbr0(v6) = v8 & $i(v8))) & % 154.61/21.34 ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~ (sdtlpdtrp0(v1, v6) = v7) | ~ % 154.61/21.34 $i(v6) | ~ aElementOf0(v6, v4) | ~ aSet0(v6)) & ! [v6: $i] : ! [v7: % 154.61/21.34 $i] : (v7 = v5 | ~ (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aSet0(v6) % 154.61/21.34 | ? [v8: $i] : ? [v9: $i] : ($i(v9) & (( ~ (v8 = xk) & sbrdtbr0(v6) = % 154.61/21.34 v8 & $i(v8)) | (aElementOf0(v9, v6) & ~ aElementOf0(v9, v3))))))) % 154.61/21.34 % 154.61/21.34 (m__4758) % 154.79/21.34 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & % 154.79/21.34 szDzozmdt0(xd) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT) & aSet0(v1) & ! % 154.79/21.34 [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v2) | ~ $i(v3) | ~ % 154.79/21.34 $i(v2) | ~ aElementOf0(v3, v0) | aElementOf0(v2, v1)) & ! [v2: $i] : ( ~ % 154.79/21.34 $i(v2) | ~ aElementOf0(v2, v1) | aElementOf0(v2, xT)) & ! [v2: $i] : ( ~ % 154.79/21.34 $i(v2) | ~ aElementOf0(v2, v1) | ? [v3: $i] : (sdtlpdtrp0(xd, v3) = v2 & % 154.79/21.34 $i(v3) & aElementOf0(v3, v0)))) % 154.79/21.34 % 154.79/21.34 (m__4854) % 154.79/21.34 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = % 154.79/21.34 v0 & sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) & % 154.79/21.34 $i(v0) & aElementOf0(v0, xT) & aSet0(v1) & ! [v3: $i] : ! [v4: $i] : (v4 = % 154.79/21.34 v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1)) & % 154.79/21.34 ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ % 154.79/21.34 aElementOf0(v3, v1) | aElementOf0(v3, v2)) & ! [v3: $i] : ( ~ % 154.79/21.34 (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ aElementOf0(v3, v2) | % 154.79/21.34 aElementOf0(v3, v1))) % 154.79/21.34 % 154.79/21.34 (m__4891) % 154.79/21.34 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 154.79/21.34 (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & % 154.79/21.34 szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & ! % 154.79/21.34 [v3: $i] : ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) % 154.79/21.34 | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 154.79/21.34 (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) | % 154.79/21.34 aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xe, v4) % 154.79/21.34 = v3) | ~ $i(v4) | ~ $i(v3) | ~ aElementOf0(v4, v1) | aElementOf0(v3, % 154.79/21.34 xO)) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ % 154.79/21.34 aElementOf0(v3, v2) | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~ % 154.79/21.34 aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 & $i(v4) & % 154.79/21.34 aElementOf0(v4, v1)))) % 154.79/21.34 % 154.79/21.34 (m__4982) % 154.79/21.35 $i(xO) & $i(xd) & $i(xe) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] : % 154.79/21.35 (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & ! [v2: $i] % 154.79/21.35 : ! [v3: $i] : ( ~ (sdtlpdtrp0(xe, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 154.79/21.35 aElementOf0(v3, v1) | ? [v4: $i] : (sdtlpdtrp0(xd, v4) = v0 & % 154.79/21.35 sdtlpdtrp0(xe, v4) = v2 & $i(v4) & aElementOf0(v4, v1) & aElementOf0(v4, % 154.79/21.35 szNzAzT0))) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, xO) | ? % 154.79/21.35 [v3: $i] : (sdtlpdtrp0(xd, v3) = v0 & sdtlpdtrp0(xe, v3) = v2 & $i(v3) & % 154.79/21.35 aElementOf0(v3, v1) & aElementOf0(v3, szNzAzT0)))) % 154.79/21.35 % 154.79/21.35 (m__5078) % 154.79/21.35 $i(xQ) & $i(xO) & $i(xK) & ? [v0: $i] : (slbdtsldtrb0(xO, xK) = v0 & % 154.79/21.35 sbrdtbr0(xQ) = xK & $i(v0) & aSubsetOf0(xQ, xO) & aElementOf0(xQ, v0) & % 154.79/21.35 aSet0(xQ) & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | % 154.79/21.35 aElementOf0(v1, xO))) % 154.79/21.35 % 154.79/21.35 (m__5147) % 154.79/21.35 szmzizndt0(xQ) = xp & $i(xp) & $i(xQ) & aElementOf0(xp, xQ) & ! [v0: $i] : ( % 154.79/21.35 ~ $i(v0) | ~ aElementOf0(v0, xQ) | sdtlseqdt0(xp, v0)) % 154.79/21.35 % 154.79/21.35 (m__5164) % 154.79/21.35 $i(xP) & $i(xQ) & ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & % 154.79/21.35 $i(v0) & aSet0(xP) & ~ aElementOf0(v0, xP) & ! [v1: $i] : (v1 = v0 | ~ % 154.79/21.35 $i(v1) | ~ aElementOf0(v1, xQ) | ~ aElement0(v1) | aElementOf0(v1, xP)) % 154.79/21.35 & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xP) | aElementOf0(v1, xQ)) & % 154.79/21.35 ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xP) | aElement0(v1)) & ! [v1: % 154.79/21.35 $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | sdtlseqdt0(v0, v1))) % 154.79/21.35 % 154.79/21.35 (m__5173) % 154.79/21.35 $i(xp) & $i(xQ) & aElementOf0(xp, xQ) % 154.79/21.35 % 154.79/21.35 (m__5182) % 154.79/21.35 $i(xp) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 154.79/21.35 (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = v1 & sdtlpdtrp0(xe, v2) = xp & % 154.79/21.35 $i(v2) & $i(v1) & $i(v0) & aElementOf0(v2, v1)) % 154.79/21.35 % 154.79/21.35 (m__5217) % 154.79/21.35 sbrdtbr0(xP) = xk & $i(xP) & $i(xk) % 154.79/21.35 % 154.79/21.35 (m__5309) % 154.79/21.35 $i(xn) & $i(xp) & $i(xd) & $i(xe) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] : % 154.79/21.35 ? [v2: $i] : (szDzizrdt0(xd) = v1 & sdtlbdtrb0(xd, v1) = v2 & sdtlpdtrp0(xd, % 154.79/21.35 xn) = v1 & sdtlpdtrp0(xe, xn) = xp & szDzozmdt0(xd) = v0 & $i(v2) & $i(v1) % 154.79/21.35 & $i(v0) & aElementOf0(xn, v2) & aElementOf0(xn, v0) & aElementOf0(xn, % 154.79/21.35 szNzAzT0)) % 154.79/21.35 % 154.79/21.35 (m__5321) % 154.79/21.35 $i(xn) & $i(xd) & ? [v0: $i] : (szDzizrdt0(xd) = v0 & sdtlpdtrp0(xd, xn) = v0 % 154.79/21.35 & $i(v0)) % 154.79/21.35 % 154.79/21.35 (m__5334) % 154.79/21.36 $i(xn) & $i(xP) & $i(xN) & ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, v0) = % 154.79/21.36 v1 & szszuzczcdt0(xn) = v0 & $i(v1) & $i(v0) & aSubsetOf0(xP, v1) & ! [v2: % 154.79/21.36 $i] : ( ~ $i(v2) | ~ aElementOf0(v2, xP) | aElementOf0(v2, v1))) % 154.79/21.36 % 154.79/21.36 (m__5585) % 154.79/21.36 $i(xD) & $i(xn) & $i(xN) & ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xn) = % 154.79/21.36 v0 & szmzizndt0(v0) = v1 & sdtmndt0(v0, v1) = xD & $i(v1) & $i(v0) & % 154.79/21.36 aSet0(xD) & ~ aElementOf0(v1, xD) & ! [v2: $i] : (v2 = v1 | ~ $i(v2) | ~ % 154.79/21.36 aElementOf0(v2, v0) | ~ aElement0(v2) | aElementOf0(v2, xD)) & ! [v2: % 154.79/21.36 $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v0) | sdtlseqdt0(v1, v2)) & ! [v2: % 154.79/21.36 $i] : ( ~ $i(v2) | ~ aElementOf0(v2, xD) | aElementOf0(v2, v0)) & ! [v2: % 154.79/21.36 $i] : ( ~ $i(v2) | ~ aElementOf0(v2, xD) | aElement0(v2))) % 154.79/21.36 % 154.79/21.36 (m__5599) % 154.79/21.36 $i(xD) & $i(xP) & $i(xk) & ? [v0: $i] : (slbdtsldtrb0(xD, xk) = v0 & $i(v0) & % 154.79/21.36 aSubsetOf0(xP, xD) & aElementOf0(xP, v0) & ! [v1: $i] : ( ~ $i(v1) | ~ % 154.79/21.36 aElementOf0(v1, xP) | aElementOf0(v1, xD))) % 154.79/21.36 % 154.79/21.36 (m__5632) % 154.79/21.36 $i(xn) & $i(xP) & $i(xC) & $i(xN) & $i(xc) & ? [v0: $i] : ? [v1: $i] : ? % 154.79/21.36 [v2: $i] : ? [v3: $i] : ? [v4: $i] : (sdtlpdtrp0(v4, xP) = v3 & % 154.79/21.36 sdtlpdtrp0(xC, xn) = v4 & sdtlpdtrp0(xN, xn) = v0 & sdtlpdtrp0(xc, v2) = v3 % 154.79/21.36 & szmzizndt0(v0) = v1 & sdtpldt0(xP, v1) = v2 & $i(v4) & $i(v3) & $i(v2) & % 154.79/21.36 $i(v1) & $i(v0) & aSet0(v2) & ! [v5: $i] : (v5 = v1 | ~ $i(v5) | ~ % 154.79/21.36 aElementOf0(v5, v2) | aElementOf0(v5, xP)) & ! [v5: $i] : ( ~ $i(v5) | ~ % 154.79/21.36 aElementOf0(v5, v2) | aElement0(v5)) & ! [v5: $i] : ( ~ $i(v5) | ~ % 154.79/21.36 aElementOf0(v5, v0) | sdtlseqdt0(v1, v5)) & ! [v5: $i] : ( ~ $i(v5) | ~ % 154.79/21.36 aElementOf0(v5, xP) | ~ aElement0(v5) | aElementOf0(v5, v2)) & ( ~ % 154.79/21.36 aElement0(v1) | aElementOf0(v1, v2))) % 154.79/21.36 % 154.79/21.36 (function-axioms) % 154.79/21.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.79/21.37 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 154.79/21.37 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 154.79/21.37 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 154.79/21.37 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 154.79/21.37 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 154.79/21.37 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 154.79/21.37 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 154.79/21.37 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 154.79/21.37 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 154.79/21.37 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 154.79/21.37 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 154.79/21.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 154.79/21.37 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 154.79/21.37 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 154.79/21.37 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 154.79/21.37 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 154.79/21.37 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 154.79/21.37 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 154.79/21.37 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 154.79/21.37 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 154.79/21.37 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 154.79/21.37 v0)) % 154.79/21.37 % 154.79/21.37 Further assumptions not needed in the proof: % 154.79/21.37 -------------------------------------------- % 154.79/21.37 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 154.79/21.37 mCardSeg, mCardSub, mCardSubEx, mCntRel, mCountNFin, mDefCons, mDefDiff, % 154.79/21.37 mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, mDefSel, mDefSub, % 154.79/21.37 mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet, % 154.79/21.37 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgRng, % 154.79/21.37 mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, mMinMin, % 154.79/21.37 mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess, % 154.79/21.37 mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, % 154.79/21.37 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, % 154.79/21.37 mZeroLess, mZeroNum, m__3291, m__3398, m__3418, m__3435, m__3453, m__3462, % 154.79/21.37 m__3520, m__3533, m__3623, m__3671, m__3754, m__3821, m__3965, m__4182, m__4331, % 154.79/21.37 m__4411, m__4908, m__4998, m__5093, m__5106, m__5116, m__5195, m__5208, m__5270 % 154.79/21.37 % 154.79/21.37 Those formulas are unsatisfiable: % 154.79/21.37 --------------------------------- % 154.79/21.37 % 154.79/21.37 Begin of proof % 154.79/21.37 | % 154.79/21.37 | ALPHA: (mDefEmp) implies: % 154.79/21.37 | (1) aSet0(slcrc0) % 154.79/21.37 | % 154.79/21.37 | ALPHA: (mCountNFin_01) implies: % 154.79/21.37 | (2) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0) % 154.79/21.37 | % 154.79/21.37 | ALPHA: (m__4151) implies: % 154.79/21.38 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 154.79/21.38 | (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ % 154.79/21.38 | (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | % 154.79/21.38 | ? [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xC, v0) = v4 & szDzozmdt0(v4) % 154.79/21.38 | = v5 & slbdtsldtrb0(v3, xk) = v5 & $i(v5) & $i(v4) & aFunction0(v4) % 154.79/21.38 | & ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (sbrdtbr0(v6) = v7) % 154.79/21.38 | | ~ $i(v8) | ~ $i(v6) | ~ aElementOf0(v8, v6) | ~ % 154.79/21.38 | aElementOf0(v6, v5) | aElementOf0(v8, v3)) & ! [v6: $i] : ! % 154.79/21.38 | [v7: $i] : (v7 = xk | ~ (sbrdtbr0(v6) = v7) | ~ $i(v6) | ~ % 154.79/21.38 | aElementOf0(v6, v5)) & ! [v6: $i] : ! [v7: $i] : ( ~ % 154.79/21.38 | (sbrdtbr0(v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v5) | % 154.79/21.38 | aSubsetOf0(v6, v3)) & ! [v6: $i] : ! [v7: $i] : ( ~ % 154.79/21.38 | (sbrdtbr0(v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v5) | % 154.79/21.38 | aSet0(v6)) & ! [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, v2) = % 154.79/21.38 | v7) | ~ $i(v6) | ~ aSet0(v6) | ? [v8: $i] : ? [v9: $i] : ? % 154.79/21.38 | [v10: $i] : ? [v11: $i] : ($i(v11) & aElementOf0(v2, v1) & ! % 154.79/21.38 | [v12: $i] : ( ~ $i(v12) | ~ aElementOf0(v12, v1) | % 154.79/21.38 | sdtlseqdt0(v2, v12)) & ((v10 = v9 & sdtlpdtrp0(v4, v6) = v9 & % 154.79/21.38 | sdtlpdtrp0(xc, v7) = v9 & $i(v9) & ! [v12: $i] : (v12 = v2 % 154.79/21.38 | | ~ $i(v12) | ~ aElementOf0(v12, v7) | aElementOf0(v12, % 154.79/21.38 | v6)) & ! [v12: $i] : ( ~ $i(v12) | ~ aElementOf0(v12, % 154.79/21.38 | v7) | aElement0(v12)) & ! [v12: $i] : ( ~ $i(v12) | ~ % 154.79/21.38 | aElementOf0(v12, v6) | ~ aElement0(v12) | % 154.79/21.38 | aElementOf0(v12, v7)) & ( ~ $i(v2) | ~ aElement0(v2) | % 154.79/21.38 | aElementOf0(v2, v7))) | (aSet0(v3) & ~ aElementOf0(v6, % 154.79/21.38 | v5) & ! [v12: $i] : (v12 = v2 | ~ $i(v12) | ~ % 154.79/21.38 | aElementOf0(v12, v1) | ~ aElement0(v12) | % 154.79/21.38 | aElementOf0(v12, v3)) & ! [v12: $i] : ( ~ $i(v12) | ~ % 154.79/21.38 | aElementOf0(v12, v3) | aElementOf0(v12, v1)) & ! [v12: % 154.79/21.38 | $i] : ( ~ $i(v12) | ~ aElementOf0(v12, v3) | % 154.79/21.38 | aElement0(v12)) & ( ~ $i(v2) | ~ aElementOf0(v2, v3)) & % 154.79/21.38 | (( ~ (v8 = xk) & sbrdtbr0(v6) = v8 & $i(v8)) | % 154.79/21.38 | (aElementOf0(v11, v6) & ~ aSubsetOf0(v6, v3) & ~ % 154.79/21.38 | aElementOf0(v11, v3))))))) & ! [v6: $i] : ( ~ % 154.79/21.38 | (sbrdtbr0(v6) = xk) | ~ $i(v6) | ~ aSubsetOf0(v6, v3) | % 154.79/21.38 | aElementOf0(v6, v5)) & ! [v6: $i] : ( ~ (sbrdtbr0(v6) = xk) | ~ % 154.79/21.38 | $i(v6) | ~ aSet0(v6) | aElementOf0(v6, v5) | ? [v7: $i] : % 154.79/21.38 | ($i(v7) & aElementOf0(v7, v6) & ~ aElementOf0(v7, v3))))) % 154.79/21.38 | % 154.79/21.38 | ALPHA: (m__4618) implies: % 154.79/21.38 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xC, v0) = v1) | ~ $i(v0) | % 154.79/21.38 | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ? [v4: % 154.79/21.38 | $i] : ? [v5: $i] : (sdtlpdtrp0(xN, v2) = v3 & slbdtsldtrb0(v3, xk) % 154.79/21.38 | = v4 & szszuzczcdt0(v0) = v2 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 154.79/21.38 | aElementOf0(v5, xT) & ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~ % 154.79/21.38 | (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aSubsetOf0(v6, v3) | % 154.79/21.38 | ~ aSet0(v6) | ? [v8: $i] : ( ~ (v8 = xk) & sbrdtbr0(v6) = v8 & % 154.79/21.38 | $i(v8))) & ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~ % 154.79/21.38 | (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v4) | % 154.79/21.38 | ~ aSet0(v6)) & ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~ % 154.79/21.38 | (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aSet0(v6) | ? [v8: % 154.79/21.38 | $i] : ? [v9: $i] : ($i(v9) & (( ~ (v8 = xk) & sbrdtbr0(v6) = % 154.79/21.38 | v8 & $i(v8)) | (aElementOf0(v9, v6) & ~ aElementOf0(v9, % 154.79/21.38 | v3))))))) % 154.79/21.38 | % 154.79/21.38 | ALPHA: (m__4660) implies: % 154.79/21.38 | (5) aFunction0(xe) % 154.79/21.38 | (6) szDzozmdt0(xe) = szNzAzT0 % 154.79/21.38 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) | % 154.79/21.38 | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2 % 154.79/21.38 | & szmzizndt0(v2) = v1 & $i(v2) & $i(v1) & aElementOf0(v1, v2) & ! % 154.79/21.38 | [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v2) | sdtlseqdt0(v1, % 154.79/21.38 | v3)))) % 154.79/21.39 | % 154.79/21.39 | ALPHA: (m__4730) implies: % 154.79/21.39 | (8) szDzozmdt0(xd) = szNzAzT0 % 154.79/21.39 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xC, v0) = v1) | ~ $i(v0) | % 154.79/21.39 | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ? [v4: % 154.79/21.39 | $i] : ? [v5: $i] : (sdtlpdtrp0(xd, v0) = v5 & sdtlpdtrp0(xN, v2) = % 154.79/21.39 | v3 & slbdtsldtrb0(v3, xk) = v4 & szszuzczcdt0(v0) = v2 & $i(v5) & % 154.79/21.39 | $i(v4) & $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] : (v7 = v5 | % 154.79/21.39 | ~ (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aSubsetOf0(v6, v3) | % 154.79/21.39 | ~ aSet0(v6) | ? [v8: $i] : ( ~ (v8 = xk) & sbrdtbr0(v6) = v8 & % 154.79/21.39 | $i(v8))) & ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~ % 154.79/21.39 | (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v4) | % 154.79/21.39 | ~ aSet0(v6)) & ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~ % 154.79/21.39 | (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aSet0(v6) | ? [v8: % 154.79/21.39 | $i] : ? [v9: $i] : ($i(v9) & (( ~ (v8 = xk) & sbrdtbr0(v6) = % 154.79/21.39 | v8 & $i(v8)) | (aElementOf0(v9, v6) & ~ aElementOf0(v9, % 154.79/21.39 | v3))))))) % 154.79/21.39 | % 154.79/21.39 | ALPHA: (m__4758) implies: % 154.79/21.39 | (10) ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & szDzozmdt0(xd) % 154.79/21.39 | = v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT) & aSet0(v1) & ! [v2: % 154.79/21.39 | $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v2) | ~ $i(v3) | ~ % 154.79/21.39 | $i(v2) | ~ aElementOf0(v3, v0) | aElementOf0(v2, v1)) & ! [v2: % 154.79/21.39 | $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | aElementOf0(v2, xT)) & % 154.79/21.39 | ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | ? [v3: $i] : % 154.79/21.39 | (sdtlpdtrp0(xd, v3) = v2 & $i(v3) & aElementOf0(v3, v0)))) % 154.79/21.39 | % 154.79/21.39 | ALPHA: (m__4854) implies: % 154.79/21.39 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 & % 154.79/21.39 | sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) & % 154.79/21.39 | $i(v0) & aElementOf0(v0, xT) & aSet0(v1) & ! [v3: $i] : ! [v4: $i] % 154.79/21.39 | : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ % 154.79/21.39 | aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 154.79/21.39 | (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) | % 154.79/21.39 | aElementOf0(v3, v2)) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v0) % 154.79/21.39 | | ~ $i(v3) | ~ aElementOf0(v3, v2) | aElementOf0(v3, v1))) % 154.79/21.39 | % 154.79/21.39 | ALPHA: (m__4891) implies: % 154.79/21.40 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 & % 154.79/21.40 | sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = % 154.79/21.40 | v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & ! [v3: $i] % 154.79/21.40 | : ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) % 154.79/21.40 | | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 154.79/21.40 | (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) | % 154.79/21.40 | aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 154.79/21.40 | (sdtlpdtrp0(xe, v4) = v3) | ~ $i(v4) | ~ $i(v3) | ~ % 154.79/21.40 | aElementOf0(v4, v1) | aElementOf0(v3, xO)) & ! [v3: $i] : ( ~ % 154.79/21.40 | (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ aElementOf0(v3, v2) | % 154.79/21.40 | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~ % 154.79/21.40 | aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 & % 154.79/21.40 | $i(v4) & aElementOf0(v4, v1)))) % 154.79/21.40 | % 154.79/21.40 | ALPHA: (m__4982) implies: % 154.79/21.40 | (13) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) % 154.79/21.40 | = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ % 154.79/21.40 | (sdtlpdtrp0(xe, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 154.79/21.40 | aElementOf0(v3, v1) | ? [v4: $i] : (sdtlpdtrp0(xd, v4) = v0 & % 154.79/21.40 | sdtlpdtrp0(xe, v4) = v2 & $i(v4) & aElementOf0(v4, v1) & % 154.79/21.40 | aElementOf0(v4, szNzAzT0))) & ! [v2: $i] : ( ~ $i(v2) | ~ % 154.79/21.40 | aElementOf0(v2, xO) | ? [v3: $i] : (sdtlpdtrp0(xd, v3) = v0 & % 154.79/21.40 | sdtlpdtrp0(xe, v3) = v2 & $i(v3) & aElementOf0(v3, v1) & % 154.79/21.40 | aElementOf0(v3, szNzAzT0)))) % 154.79/21.40 | % 154.79/21.40 | ALPHA: (m__5078) implies: % 154.79/21.40 | (14) ? [v0: $i] : (slbdtsldtrb0(xO, xK) = v0 & sbrdtbr0(xQ) = xK & $i(v0) % 154.79/21.40 | & aSubsetOf0(xQ, xO) & aElementOf0(xQ, v0) & aSet0(xQ) & ! [v1: $i] % 154.79/21.40 | : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | aElementOf0(v1, xO))) % 154.79/21.40 | % 154.79/21.40 | ALPHA: (m__5147) implies: % 154.79/21.40 | (15) szmzizndt0(xQ) = xp % 154.79/21.40 | % 154.79/21.40 | ALPHA: (m__5164) implies: % 154.79/21.40 | (16) ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & $i(v0) & % 154.79/21.40 | aSet0(xP) & ~ aElementOf0(v0, xP) & ! [v1: $i] : (v1 = v0 | ~ % 154.79/21.40 | $i(v1) | ~ aElementOf0(v1, xQ) | ~ aElement0(v1) | % 154.79/21.40 | aElementOf0(v1, xP)) & ! [v1: $i] : ( ~ $i(v1) | ~ % 154.79/21.40 | aElementOf0(v1, xP) | aElementOf0(v1, xQ)) & ! [v1: $i] : ( ~ % 154.79/21.40 | $i(v1) | ~ aElementOf0(v1, xP) | aElement0(v1)) & ! [v1: $i] : ( % 154.79/21.40 | ~ $i(v1) | ~ aElementOf0(v1, xQ) | sdtlseqdt0(v0, v1))) % 154.79/21.40 | % 154.79/21.40 | ALPHA: (m__5173) implies: % 154.79/21.40 | (17) aElementOf0(xp, xQ) % 154.79/21.40 | % 154.79/21.40 | ALPHA: (m__5182) implies: % 154.79/21.40 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 & % 154.79/21.40 | sdtlbdtrb0(xd, v0) = v1 & sdtlpdtrp0(xe, v2) = xp & $i(v2) & $i(v1) % 154.79/21.40 | & $i(v0) & aElementOf0(v2, v1)) % 154.79/21.40 | % 154.79/21.40 | ALPHA: (m__5217) implies: % 154.79/21.40 | (19) sbrdtbr0(xP) = xk % 154.79/21.40 | % 154.79/21.40 | ALPHA: (m__5309) implies: % 154.79/21.40 | (20) $i(xe) % 154.79/21.40 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v1 & % 154.79/21.40 | sdtlbdtrb0(xd, v1) = v2 & sdtlpdtrp0(xd, xn) = v1 & sdtlpdtrp0(xe, % 154.79/21.40 | xn) = xp & szDzozmdt0(xd) = v0 & $i(v2) & $i(v1) & $i(v0) & % 154.79/21.40 | aElementOf0(xn, v2) & aElementOf0(xn, v0) & aElementOf0(xn, % 154.79/21.40 | szNzAzT0)) % 154.79/21.40 | % 154.79/21.40 | ALPHA: (m__5321) implies: % 154.79/21.40 | (22) ? [v0: $i] : (szDzizrdt0(xd) = v0 & sdtlpdtrp0(xd, xn) = v0 & $i(v0)) % 154.79/21.40 | % 154.79/21.40 | ALPHA: (m__5334) implies: % 154.79/21.41 | (23) ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, v0) = v1 & % 154.79/21.41 | szszuzczcdt0(xn) = v0 & $i(v1) & $i(v0) & aSubsetOf0(xP, v1) & ! % 154.79/21.41 | [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, xP) | aElementOf0(v2, % 154.79/21.41 | v1))) % 154.79/21.41 | % 154.79/21.41 | ALPHA: (m__5585) implies: % 154.79/21.41 | (24) ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xn) = v0 & szmzizndt0(v0) % 154.79/21.41 | = v1 & sdtmndt0(v0, v1) = xD & $i(v1) & $i(v0) & aSet0(xD) & ~ % 154.79/21.41 | aElementOf0(v1, xD) & ! [v2: $i] : (v2 = v1 | ~ $i(v2) | ~ % 154.79/21.41 | aElementOf0(v2, v0) | ~ aElement0(v2) | aElementOf0(v2, xD)) & ! % 154.79/21.41 | [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v0) | sdtlseqdt0(v1, v2)) % 154.79/21.41 | & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, xD) | % 154.79/21.41 | aElementOf0(v2, v0)) & ! [v2: $i] : ( ~ $i(v2) | ~ % 154.79/21.41 | aElementOf0(v2, xD) | aElement0(v2))) % 154.79/21.41 | % 154.79/21.41 | ALPHA: (m__5599) implies: % 154.79/21.41 | (25) ? [v0: $i] : (slbdtsldtrb0(xD, xk) = v0 & $i(v0) & aSubsetOf0(xP, xD) % 154.79/21.41 | & aElementOf0(xP, v0) & ! [v1: $i] : ( ~ $i(v1) | ~ % 154.79/21.41 | aElementOf0(v1, xP) | aElementOf0(v1, xD))) % 154.79/21.41 | % 154.79/21.41 | ALPHA: (m__5632) implies: % 154.79/21.41 | (26) $i(xP) % 154.79/21.41 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 154.79/21.41 | (sdtlpdtrp0(v4, xP) = v3 & sdtlpdtrp0(xC, xn) = v4 & sdtlpdtrp0(xN, % 154.79/21.41 | xn) = v0 & sdtlpdtrp0(xc, v2) = v3 & szmzizndt0(v0) = v1 & % 154.79/21.41 | sdtpldt0(xP, v1) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 154.79/21.41 | aSet0(v2) & ! [v5: $i] : (v5 = v1 | ~ $i(v5) | ~ aElementOf0(v5, % 154.79/21.41 | v2) | aElementOf0(v5, xP)) & ! [v5: $i] : ( ~ $i(v5) | ~ % 154.79/21.41 | aElementOf0(v5, v2) | aElement0(v5)) & ! [v5: $i] : ( ~ $i(v5) | % 154.79/21.41 | ~ aElementOf0(v5, v0) | sdtlseqdt0(v1, v5)) & ! [v5: $i] : ( ~ % 154.79/21.41 | $i(v5) | ~ aElementOf0(v5, xP) | ~ aElement0(v5) | % 154.79/21.41 | aElementOf0(v5, v2)) & ( ~ aElement0(v1) | aElementOf0(v1, v2))) % 154.79/21.41 | % 154.79/21.41 | ALPHA: (m__) implies: % 154.79/21.41 | (28) $i(xQ) % 154.79/21.41 | (29) $i(xn) % 154.79/21.41 | (30) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & sdtlpdtrp0(xd, xn) = v1 & % 154.79/21.41 | sdtlpdtrp0(xc, xQ) = v0 & $i(v1) & $i(v0)) % 154.79/21.41 | % 154.79/21.41 | ALPHA: (function-axioms) implies: % 154.79/21.41 | (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 154.79/21.41 | (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0)) % 154.79/21.41 | (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sbrdtbr0(v2) % 154.79/21.41 | = v1) | ~ (sbrdtbr0(v2) = v0)) % 154.79/21.41 | (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 154.79/21.41 | (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) = v0)) % 154.79/21.41 | (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 154.79/21.41 | (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) % 154.79/21.41 | (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 154.79/21.41 | (szDzizrdt0(v2) = v1) | ~ (szDzizrdt0(v2) = v0)) % 154.79/21.41 | (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.79/21.41 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) % 154.79/21.41 | % 154.79/21.41 | DELTA: instantiating (22) with fresh symbol all_82_0 gives: % 154.79/21.41 | (37) szDzizrdt0(xd) = all_82_0 & sdtlpdtrp0(xd, xn) = all_82_0 & % 154.79/21.41 | $i(all_82_0) % 154.79/21.41 | % 154.79/21.41 | ALPHA: (37) implies: % 154.79/21.42 | (38) szDzizrdt0(xd) = all_82_0 % 154.79/21.42 | % 154.79/21.42 | DELTA: instantiating (30) with fresh symbols all_86_0, all_86_1 gives: % 154.79/21.42 | (39) ~ (all_86_0 = all_86_1) & sdtlpdtrp0(xd, xn) = all_86_0 & % 154.79/21.42 | sdtlpdtrp0(xc, xQ) = all_86_1 & $i(all_86_0) & $i(all_86_1) % 154.79/21.42 | % 154.79/21.42 | ALPHA: (39) implies: % 154.79/21.42 | (40) ~ (all_86_0 = all_86_1) % 154.79/21.42 | (41) sdtlpdtrp0(xc, xQ) = all_86_1 % 154.79/21.42 | (42) sdtlpdtrp0(xd, xn) = all_86_0 % 154.79/21.42 | % 154.79/21.42 | DELTA: instantiating (25) with fresh symbol all_94_0 gives: % 154.79/21.42 | (43) slbdtsldtrb0(xD, xk) = all_94_0 & $i(all_94_0) & aSubsetOf0(xP, xD) & % 154.79/21.42 | aElementOf0(xP, all_94_0) & ! [v0: $i] : ( ~ $i(v0) | ~ % 154.79/21.42 | aElementOf0(v0, xP) | aElementOf0(v0, xD)) % 154.79/21.42 | % 154.79/21.42 | ALPHA: (43) implies: % 154.79/21.42 | (44) aSubsetOf0(xP, xD) % 154.79/21.42 | % 154.79/21.42 | DELTA: instantiating (18) with fresh symbols all_97_0, all_97_1, all_97_2 % 154.79/21.42 | gives: % 154.79/21.42 | (45) szDzizrdt0(xd) = all_97_2 & sdtlbdtrb0(xd, all_97_2) = all_97_1 & % 154.79/21.42 | sdtlpdtrp0(xe, all_97_0) = xp & $i(all_97_0) & $i(all_97_1) & % 154.79/21.42 | $i(all_97_2) & aElementOf0(all_97_0, all_97_1) % 154.79/21.42 | % 154.79/21.42 | ALPHA: (45) implies: % 154.79/21.42 | (46) szDzizrdt0(xd) = all_97_2 % 154.79/21.42 | % 154.79/21.42 | DELTA: instantiating (23) with fresh symbols all_99_0, all_99_1 gives: % 154.79/21.42 | (47) sdtlpdtrp0(xN, all_99_1) = all_99_0 & szszuzczcdt0(xn) = all_99_1 & % 154.79/21.42 | $i(all_99_0) & $i(all_99_1) & aSubsetOf0(xP, all_99_0) & ! [v0: $i] : % 154.79/21.42 | ( ~ $i(v0) | ~ aElementOf0(v0, xP) | aElementOf0(v0, all_99_0)) % 154.79/21.42 | % 154.79/21.42 | ALPHA: (47) implies: % 154.79/21.42 | (48) szszuzczcdt0(xn) = all_99_1 % 154.79/21.42 | (49) sdtlpdtrp0(xN, all_99_1) = all_99_0 % 154.79/21.42 | (50) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xP) | aElementOf0(v0, % 154.79/21.42 | all_99_0)) % 154.79/21.42 | % 154.79/21.42 | DELTA: instantiating (14) with fresh symbol all_102_0 gives: % 154.79/21.42 | (51) slbdtsldtrb0(xO, xK) = all_102_0 & sbrdtbr0(xQ) = xK & $i(all_102_0) & % 154.79/21.42 | aSubsetOf0(xQ, xO) & aElementOf0(xQ, all_102_0) & aSet0(xQ) & ! [v0: % 154.79/21.42 | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xQ) | aElementOf0(v0, xO)) % 154.79/21.42 | % 154.79/21.42 | ALPHA: (51) implies: % 154.79/21.42 | (52) aSet0(xQ) % 154.79/21.42 | % 154.79/21.42 | DELTA: instantiating (21) with fresh symbols all_105_0, all_105_1, all_105_2 % 154.79/21.42 | gives: % 154.79/21.42 | (53) szDzizrdt0(xd) = all_105_1 & sdtlbdtrb0(xd, all_105_1) = all_105_0 & % 154.79/21.42 | sdtlpdtrp0(xd, xn) = all_105_1 & sdtlpdtrp0(xe, xn) = xp & % 154.79/21.42 | szDzozmdt0(xd) = all_105_2 & $i(all_105_0) & $i(all_105_1) & % 154.79/21.42 | $i(all_105_2) & aElementOf0(xn, all_105_0) & aElementOf0(xn, % 154.79/21.42 | all_105_2) & aElementOf0(xn, szNzAzT0) % 154.79/21.42 | % 154.79/21.42 | ALPHA: (53) implies: % 154.79/21.42 | (54) aElementOf0(xn, all_105_2) % 154.79/21.42 | (55) szDzozmdt0(xd) = all_105_2 % 154.79/21.42 | (56) sdtlpdtrp0(xe, xn) = xp % 154.79/21.42 | (57) sdtlpdtrp0(xd, xn) = all_105_1 % 154.79/21.42 | (58) szDzizrdt0(xd) = all_105_1 % 154.79/21.42 | % 154.79/21.42 | DELTA: instantiating (10) with fresh symbols all_107_0, all_107_1 gives: % 154.79/21.42 | (59) sdtlcdtrc0(xd, all_107_1) = all_107_0 & szDzozmdt0(xd) = all_107_1 & % 154.79/21.42 | $i(all_107_0) & $i(all_107_1) & aSubsetOf0(all_107_0, xT) & % 154.79/21.42 | aSet0(all_107_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v1) % 154.79/21.42 | = v0) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, all_107_1) | % 154.79/21.42 | aElementOf0(v0, all_107_0)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 154.79/21.42 | aElementOf0(v0, all_107_0) | aElementOf0(v0, xT)) & ! [v0: $i] : ( % 154.79/21.42 | ~ $i(v0) | ~ aElementOf0(v0, all_107_0) | ? [v1: $i] : % 154.79/21.42 | (sdtlpdtrp0(xd, v1) = v0 & $i(v1) & aElementOf0(v1, all_107_1))) % 154.79/21.42 | % 154.79/21.42 | ALPHA: (59) implies: % 154.79/21.42 | (60) szDzozmdt0(xd) = all_107_1 % 154.79/21.42 | % 154.79/21.42 | DELTA: instantiating (16) with fresh symbol all_110_0 gives: % 154.79/21.42 | (61) szmzizndt0(xQ) = all_110_0 & sdtmndt0(xQ, all_110_0) = xP & % 154.79/21.42 | $i(all_110_0) & aSet0(xP) & ~ aElementOf0(all_110_0, xP) & ! [v0: % 154.79/21.42 | any] : (v0 = all_110_0 | ~ $i(v0) | ~ aElementOf0(v0, xQ) | ~ % 154.79/21.42 | aElement0(v0) | aElementOf0(v0, xP)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 154.79/21.42 | aElementOf0(v0, xP) | aElementOf0(v0, xQ)) & ! [v0: $i] : ( ~ % 154.79/21.43 | $i(v0) | ~ aElementOf0(v0, xP) | aElement0(v0)) & ! [v0: $i] : ( ~ % 154.79/21.43 | $i(v0) | ~ aElementOf0(v0, xQ) | sdtlseqdt0(all_110_0, v0)) % 154.79/21.43 | % 154.79/21.43 | ALPHA: (61) implies: % 154.79/21.43 | (62) aSet0(xP) % 154.79/21.43 | (63) sdtmndt0(xQ, all_110_0) = xP % 154.79/21.43 | (64) szmzizndt0(xQ) = all_110_0 % 154.79/21.43 | % 154.79/21.43 | DELTA: instantiating (11) with fresh symbols all_113_0, all_113_1, all_113_2 % 154.79/21.43 | gives: % 154.79/21.43 | (65) szDzizrdt0(xd) = all_113_2 & sdtlbdtrb0(xd, all_113_2) = all_113_1 & % 154.79/21.43 | szDzozmdt0(xd) = all_113_0 & $i(all_113_0) & $i(all_113_1) & % 154.79/21.43 | $i(all_113_2) & aElementOf0(all_113_2, xT) & aSet0(all_113_1) & ! % 154.79/21.43 | [v0: $i] : ! [v1: int] : (v1 = all_113_2 | ~ (sdtlpdtrp0(xd, v0) = % 154.79/21.43 | v1) | ~ $i(v0) | ~ aElementOf0(v0, all_113_1)) & ! [v0: $i] : % 154.79/21.43 | ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ % 154.79/21.43 | aElementOf0(v0, all_113_1) | aElementOf0(v0, all_113_0)) & ! [v0: % 154.79/21.43 | $i] : ( ~ (sdtlpdtrp0(xd, v0) = all_113_2) | ~ $i(v0) | ~ % 154.79/21.43 | aElementOf0(v0, all_113_0) | aElementOf0(v0, all_113_1)) % 154.79/21.43 | % 154.79/21.43 | ALPHA: (65) implies: % 154.79/21.43 | (66) szDzozmdt0(xd) = all_113_0 % 154.79/21.43 | (67) szDzizrdt0(xd) = all_113_2 % 154.79/21.43 | % 154.79/21.43 | DELTA: instantiating (13) with fresh symbols all_116_0, all_116_1 gives: % 154.79/21.43 | (68) szDzizrdt0(xd) = all_116_1 & sdtlbdtrb0(xd, all_116_1) = all_116_0 & % 154.79/21.43 | $i(all_116_0) & $i(all_116_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 154.79/21.43 | (sdtlpdtrp0(xe, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~ % 154.79/21.43 | aElementOf0(v1, all_116_0) | ? [v2: $i] : (sdtlpdtrp0(xd, v2) = % 154.79/21.43 | all_116_1 & sdtlpdtrp0(xe, v2) = v0 & $i(v2) & aElementOf0(v2, % 154.79/21.43 | all_116_0) & aElementOf0(v2, szNzAzT0))) & ! [v0: $i] : ( ~ % 154.79/21.43 | $i(v0) | ~ aElementOf0(v0, xO) | ? [v1: $i] : (sdtlpdtrp0(xd, v1) % 154.79/21.43 | = all_116_1 & sdtlpdtrp0(xe, v1) = v0 & $i(v1) & aElementOf0(v1, % 154.79/21.43 | all_116_0) & aElementOf0(v1, szNzAzT0))) % 154.79/21.43 | % 154.79/21.43 | ALPHA: (68) implies: % 154.79/21.43 | (69) szDzizrdt0(xd) = all_116_1 % 154.79/21.43 | % 154.79/21.43 | DELTA: instantiating (24) with fresh symbols all_119_0, all_119_1 gives: % 154.79/21.43 | (70) sdtlpdtrp0(xN, xn) = all_119_1 & szmzizndt0(all_119_1) = all_119_0 & % 154.79/21.43 | sdtmndt0(all_119_1, all_119_0) = xD & $i(all_119_0) & $i(all_119_1) & % 154.79/21.43 | aSet0(xD) & ~ aElementOf0(all_119_0, xD) & ! [v0: any] : (v0 = % 154.79/21.43 | all_119_0 | ~ $i(v0) | ~ aElementOf0(v0, all_119_1) | ~ % 154.79/21.43 | aElement0(v0) | aElementOf0(v0, xD)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 154.79/21.43 | aElementOf0(v0, all_119_1) | sdtlseqdt0(all_119_0, v0)) & ! [v0: % 154.79/21.43 | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xD) | aElementOf0(v0, % 154.79/21.43 | all_119_1)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xD) | % 154.79/21.43 | aElement0(v0)) % 154.79/21.43 | % 154.79/21.43 | ALPHA: (70) implies: % 154.79/21.43 | (71) sdtmndt0(all_119_1, all_119_0) = xD % 154.79/21.43 | (72) szmzizndt0(all_119_1) = all_119_0 % 154.79/21.43 | (73) sdtlpdtrp0(xN, xn) = all_119_1 % 154.79/21.43 | % 154.79/21.43 | DELTA: instantiating (27) with fresh symbols all_122_0, all_122_1, all_122_2, % 154.79/21.43 | all_122_3, all_122_4 gives: % 154.79/21.43 | (74) sdtlpdtrp0(all_122_0, xP) = all_122_1 & sdtlpdtrp0(xC, xn) = all_122_0 % 154.79/21.43 | & sdtlpdtrp0(xN, xn) = all_122_4 & sdtlpdtrp0(xc, all_122_2) = % 154.79/21.43 | all_122_1 & szmzizndt0(all_122_4) = all_122_3 & sdtpldt0(xP, % 154.79/21.43 | all_122_3) = all_122_2 & $i(all_122_0) & $i(all_122_1) & % 154.79/21.43 | $i(all_122_2) & $i(all_122_3) & $i(all_122_4) & aSet0(all_122_2) & ! % 154.79/21.43 | [v0: any] : (v0 = all_122_3 | ~ $i(v0) | ~ aElementOf0(v0, % 154.79/21.43 | all_122_2) | aElementOf0(v0, xP)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 154.79/21.43 | aElementOf0(v0, all_122_2) | aElement0(v0)) & ! [v0: $i] : ( ~ % 154.79/21.43 | $i(v0) | ~ aElementOf0(v0, all_122_4) | sdtlseqdt0(all_122_3, v0)) % 154.79/21.43 | & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xP) | ~ aElement0(v0) % 154.79/21.43 | | aElementOf0(v0, all_122_2)) & ( ~ aElement0(all_122_3) | % 154.79/21.43 | aElementOf0(all_122_3, all_122_2)) % 154.79/21.43 | % 154.79/21.43 | ALPHA: (74) implies: % 154.79/21.43 | (75) $i(all_122_3) % 154.79/21.43 | (76) sdtpldt0(xP, all_122_3) = all_122_2 % 154.79/21.43 | (77) szmzizndt0(all_122_4) = all_122_3 % 155.26/21.43 | (78) sdtlpdtrp0(xc, all_122_2) = all_122_1 % 155.26/21.43 | (79) sdtlpdtrp0(xN, xn) = all_122_4 % 155.26/21.43 | (80) sdtlpdtrp0(xC, xn) = all_122_0 % 155.26/21.43 | (81) sdtlpdtrp0(all_122_0, xP) = all_122_1 % 155.26/21.43 | (82) ~ aElement0(all_122_3) | aElementOf0(all_122_3, all_122_2) % 155.26/21.43 | % 155.26/21.43 | DELTA: instantiating (12) with fresh symbols all_125_0, all_125_1, all_125_2 % 155.26/21.43 | gives: % 155.26/21.44 | (83) szDzizrdt0(xd) = all_125_2 & sdtlcdtrc0(xe, all_125_1) = xO & % 155.26/21.44 | sdtlbdtrb0(xd, all_125_2) = all_125_1 & szDzozmdt0(xd) = all_125_0 & % 155.26/21.44 | $i(all_125_0) & $i(all_125_1) & $i(all_125_2) & aSet0(all_125_1) & % 155.26/21.44 | aSet0(xO) & ! [v0: $i] : ! [v1: int] : (v1 = all_125_2 | ~ % 155.26/21.44 | (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, % 155.26/21.44 | all_125_1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) % 155.26/21.44 | = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_125_1) | % 155.26/21.44 | aElementOf0(v0, all_125_0)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 155.26/21.44 | (sdtlpdtrp0(xe, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~ % 155.26/21.44 | aElementOf0(v1, all_125_1) | aElementOf0(v0, xO)) & ! [v0: $i] : ( % 155.26/21.44 | ~ (sdtlpdtrp0(xd, v0) = all_125_2) | ~ $i(v0) | ~ aElementOf0(v0, % 155.26/21.44 | all_125_0) | aElementOf0(v0, all_125_1)) & ! [v0: $i] : ( ~ % 155.26/21.44 | $i(v0) | ~ aElementOf0(v0, xO) | ? [v1: $i] : (sdtlpdtrp0(xe, v1) % 155.26/21.44 | = v0 & $i(v1) & aElementOf0(v1, all_125_1))) % 155.26/21.44 | % 155.26/21.44 | ALPHA: (83) implies: % 155.26/21.44 | (84) szDzozmdt0(xd) = all_125_0 % 155.26/21.44 | (85) szDzizrdt0(xd) = all_125_2 % 155.26/21.44 | % 155.26/21.44 | BETA: splitting (2) gives: % 155.26/21.44 | % 155.26/21.44 | Case 1: % 155.26/21.44 | | % 155.26/21.44 | | (86) ~ aSet0(slcrc0) % 155.26/21.44 | | % 155.26/21.44 | | PRED_UNIFY: (1), (86) imply: % 155.26/21.44 | | (87) $false % 155.26/21.44 | | % 155.26/21.44 | | CLOSE: (87) is inconsistent. % 155.26/21.44 | | % 155.26/21.44 | Case 2: % 155.26/21.44 | | % 155.26/21.44 | | % 155.26/21.44 | | GROUND_INST: instantiating (33) with xp, all_110_0, xQ, simplifying with % 155.26/21.44 | | (15), (64) gives: % 155.26/21.44 | | (88) all_110_0 = xp % 155.26/21.44 | | % 155.26/21.44 | | GROUND_INST: instantiating (34) with all_113_0, all_125_0, xd, simplifying % 155.26/21.44 | | with (66), (84) gives: % 155.26/21.44 | | (89) all_125_0 = all_113_0 % 155.26/21.44 | | % 155.26/21.44 | | GROUND_INST: instantiating (34) with all_107_1, all_125_0, xd, simplifying % 155.26/21.44 | | with (60), (84) gives: % 155.26/21.44 | | (90) all_125_0 = all_107_1 % 155.26/21.44 | | % 155.26/21.44 | | GROUND_INST: instantiating (34) with all_105_2, all_125_0, xd, simplifying % 155.26/21.44 | | with (55), (84) gives: % 155.26/21.44 | | (91) all_125_0 = all_105_2 % 155.26/21.44 | | % 155.26/21.44 | | GROUND_INST: instantiating (34) with szNzAzT0, all_125_0, xd, simplifying % 155.26/21.44 | | with (8), (84) gives: % 155.26/21.44 | | (92) all_125_0 = szNzAzT0 % 155.26/21.44 | | % 155.26/21.44 | | GROUND_INST: instantiating (36) with all_119_1, all_122_4, xn, xN, % 155.26/21.44 | | simplifying with (73), (79) gives: % 155.26/21.44 | | (93) all_122_4 = all_119_1 % 155.26/21.44 | | % 155.26/21.44 | | GROUND_INST: instantiating (36) with all_86_0, all_105_1, xn, xd, % 155.26/21.44 | | simplifying with (42), (57) gives: % 155.26/21.44 | | (94) all_105_1 = all_86_0 % 155.26/21.44 | | % 155.26/21.44 | | GROUND_INST: instantiating (35) with all_82_0, all_105_1, xd, simplifying % 155.26/21.44 | | with (38), (58) gives: % 155.26/21.44 | | (95) all_105_1 = all_82_0 % 155.26/21.44 | | % 155.26/21.44 | | GROUND_INST: instantiating (35) with all_113_2, all_116_1, xd, simplifying % 155.26/21.44 | | with (67), (69) gives: % 155.26/21.44 | | (96) all_116_1 = all_113_2 % 155.26/21.44 | | % 155.26/21.44 | | GROUND_INST: instantiating (35) with all_105_1, all_116_1, xd, simplifying % 155.26/21.44 | | with (58), (69) gives: % 155.26/21.44 | | (97) all_116_1 = all_105_1 % 155.26/21.44 | | % 155.26/21.44 | | GROUND_INST: instantiating (35) with all_116_1, all_125_2, xd, simplifying % 155.26/21.44 | | with (69), (85) gives: % 155.26/21.44 | | (98) all_125_2 = all_116_1 % 155.26/21.44 | | % 155.26/21.44 | | GROUND_INST: instantiating (35) with all_97_2, all_125_2, xd, simplifying % 155.26/21.44 | | with (46), (85) gives: % 155.26/21.44 | | (99) all_125_2 = all_97_2 % 155.26/21.44 | | % 155.26/21.44 | | COMBINE_EQS: (89), (91) imply: % 155.26/21.44 | | (100) all_113_0 = all_105_2 % 155.26/21.44 | | % 155.26/21.44 | | COMBINE_EQS: (89), (90) imply: % 155.26/21.44 | | (101) all_113_0 = all_107_1 % 155.26/21.44 | | % 155.26/21.44 | | COMBINE_EQS: (89), (92) imply: % 155.26/21.44 | | (102) all_113_0 = szNzAzT0 % 155.26/21.44 | | % 155.26/21.44 | | COMBINE_EQS: (98), (99) imply: % 155.26/21.44 | | (103) all_116_1 = all_97_2 % 155.26/21.44 | | % 155.26/21.44 | | SIMP: (103) implies: % 155.26/21.44 | | (104) all_116_1 = all_97_2 % 155.26/21.44 | | % 155.26/21.44 | | COMBINE_EQS: (96), (97) imply: % 155.26/21.44 | | (105) all_113_2 = all_105_1 % 155.26/21.44 | | % 155.26/21.44 | | COMBINE_EQS: (96), (104) imply: % 155.26/21.44 | | (106) all_113_2 = all_97_2 % 155.26/21.44 | | % 155.26/21.44 | | COMBINE_EQS: (100), (101) imply: % 155.26/21.44 | | (107) all_107_1 = all_105_2 % 155.26/21.44 | | % 155.26/21.44 | | COMBINE_EQS: (101), (102) imply: % 155.26/21.44 | | (108) all_107_1 = szNzAzT0 % 155.26/21.44 | | % 155.26/21.44 | | COMBINE_EQS: (105), (106) imply: % 155.26/21.44 | | (109) all_105_1 = all_97_2 % 155.26/21.44 | | % 155.26/21.44 | | SIMP: (109) implies: % 155.26/21.44 | | (110) all_105_1 = all_97_2 % 155.26/21.44 | | % 155.26/21.44 | | COMBINE_EQS: (107), (108) imply: % 155.26/21.44 | | (111) all_105_2 = szNzAzT0 % 155.26/21.44 | | % 155.26/21.44 | | SIMP: (111) implies: % 155.26/21.44 | | (112) all_105_2 = szNzAzT0 % 155.26/21.44 | | % 155.26/21.44 | | COMBINE_EQS: (94), (110) imply: % 155.26/21.44 | | (113) all_97_2 = all_86_0 % 155.26/21.44 | | % 155.26/21.44 | | COMBINE_EQS: (95), (110) imply: % 155.26/21.44 | | (114) all_97_2 = all_82_0 % 155.26/21.44 | | % 155.26/21.44 | | COMBINE_EQS: (113), (114) imply: % 155.26/21.44 | | (115) all_86_0 = all_82_0 % 155.26/21.44 | | % 155.26/21.44 | | SIMP: (115) implies: % 155.26/21.44 | | (116) all_86_0 = all_82_0 % 155.26/21.44 | | % 155.26/21.44 | | REDUCE: (40), (116) imply: % 155.26/21.44 | | (117) ~ (all_86_1 = all_82_0) % 155.26/21.44 | | % 155.26/21.44 | | SIMP: (117) implies: % 155.26/21.44 | | (118) ~ (all_86_1 = all_82_0) % 155.26/21.45 | | % 155.26/21.45 | | REDUCE: (42), (116) imply: % 155.26/21.45 | | (119) sdtlpdtrp0(xd, xn) = all_82_0 % 155.26/21.45 | | % 155.26/21.45 | | REDUCE: (77), (93) imply: % 155.26/21.45 | | (120) szmzizndt0(all_119_1) = all_122_3 % 155.26/21.45 | | % 155.26/21.45 | | REDUCE: (63), (88) imply: % 155.26/21.45 | | (121) sdtmndt0(xQ, xp) = xP % 155.26/21.45 | | % 155.26/21.45 | | REDUCE: (54), (112) imply: % 155.26/21.45 | | (122) aElementOf0(xn, szNzAzT0) % 155.26/21.45 | | % 155.26/21.45 | | GROUND_INST: instantiating (33) with all_119_0, all_122_3, all_119_1, % 155.26/21.45 | | simplifying with (72), (120) gives: % 155.26/21.45 | | (123) all_122_3 = all_119_0 % 155.26/21.45 | | % 155.26/21.45 | | REDUCE: (76), (123) imply: % 155.26/21.45 | | (124) sdtpldt0(xP, all_119_0) = all_122_2 % 155.26/21.45 | | % 155.26/21.45 | | REDUCE: (75), (123) imply: % 155.26/21.45 | | (125) $i(all_119_0) % 155.26/21.45 | | % 155.26/21.45 | | GROUND_INST: instantiating (3) with xn, all_119_1, all_119_0, xD, % 155.26/21.45 | | simplifying with (29), (71), (72), (73), (122) gives: % 155.26/21.45 | | (126) ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xC, xn) = v0 & % 155.26/21.45 | | szDzozmdt0(v0) = v1 & slbdtsldtrb0(xD, xk) = v1 & $i(v1) & $i(v0) % 155.26/21.45 | | & aFunction0(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 155.26/21.45 | | (sbrdtbr0(v2) = v3) | ~ $i(v4) | ~ $i(v2) | ~ % 155.26/21.45 | | aElementOf0(v4, v2) | ~ aElementOf0(v2, v1) | aElementOf0(v4, % 155.26/21.45 | | xD)) & ! [v2: $i] : ! [v3: $i] : (v3 = xk | ~ % 155.26/21.45 | | (sbrdtbr0(v2) = v3) | ~ $i(v2) | ~ aElementOf0(v2, v1)) & ! % 155.26/21.45 | | [v2: $i] : ! [v3: $i] : ( ~ (sbrdtbr0(v2) = v3) | ~ $i(v2) | ~ % 155.26/21.45 | | aElementOf0(v2, v1) | aSubsetOf0(v2, xD)) & ! [v2: $i] : ! % 155.26/21.45 | | [v3: $i] : ( ~ (sbrdtbr0(v2) = v3) | ~ $i(v2) | ~ % 155.26/21.45 | | aElementOf0(v2, v1) | aSet0(v2)) & ! [v2: $i] : ! [v3: $i] : % 155.26/21.45 | | ( ~ (sdtpldt0(v2, all_119_0) = v3) | ~ $i(v2) | ~ aSet0(v2) | % 155.26/21.45 | | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ($i(v7) % 155.26/21.45 | | & aElementOf0(all_119_0, all_119_1) & ! [v8: $i] : ( ~ % 155.26/21.45 | | $i(v8) | ~ aElementOf0(v8, all_119_1) | % 155.26/21.45 | | sdtlseqdt0(all_119_0, v8)) & ((v6 = v5 & sdtlpdtrp0(v0, v2) % 155.26/21.45 | | = v5 & sdtlpdtrp0(xc, v3) = v5 & $i(v5) & ! [v8: any] : % 155.26/21.45 | | (v8 = all_119_0 | ~ $i(v8) | ~ aElementOf0(v8, v3) | % 155.26/21.45 | | aElementOf0(v8, v2)) & ! [v8: $i] : ( ~ $i(v8) | ~ % 155.26/21.45 | | aElementOf0(v8, v3) | aElement0(v8)) & ! [v8: $i] : ( % 155.26/21.45 | | ~ $i(v8) | ~ aElementOf0(v8, v2) | ~ aElement0(v8) | % 155.26/21.45 | | aElementOf0(v8, v3)) & ( ~ $i(all_119_0) | ~ % 155.26/21.45 | | aElement0(all_119_0) | aElementOf0(all_119_0, v3))) | % 155.26/21.45 | | (aSet0(xD) & ~ aElementOf0(v2, v1) & ! [v8: any] : (v8 = % 155.26/21.45 | | all_119_0 | ~ $i(v8) | ~ aElementOf0(v8, all_119_1) | % 155.26/21.45 | | ~ aElement0(v8) | aElementOf0(v8, xD)) & ! [v8: $i] : % 155.26/21.45 | | ( ~ $i(v8) | ~ aElementOf0(v8, xD) | aElementOf0(v8, % 155.26/21.45 | | all_119_1)) & ! [v8: $i] : ( ~ $i(v8) | ~ % 155.26/21.45 | | aElementOf0(v8, xD) | aElement0(v8)) & ( ~ % 155.26/21.45 | | $i(all_119_0) | ~ aElementOf0(all_119_0, xD)) & (( ~ % 155.26/21.45 | | (v4 = xk) & sbrdtbr0(v2) = v4 & $i(v4)) | % 155.26/21.45 | | (aElementOf0(v7, v2) & ~ aSubsetOf0(v2, xD) & ~ % 155.26/21.45 | | aElementOf0(v7, xD))))))) & ! [v2: $i] : ( ~ % 155.26/21.45 | | (sbrdtbr0(v2) = xk) | ~ $i(v2) | ~ aSubsetOf0(v2, xD) | % 155.26/21.45 | | aElementOf0(v2, v1)) & ! [v2: $i] : ( ~ (sbrdtbr0(v2) = xk) | % 155.26/21.45 | | ~ $i(v2) | ~ aSet0(v2) | aElementOf0(v2, v1) | ? [v3: $i] : % 155.26/21.45 | | ($i(v3) & aElementOf0(v3, v2) & ~ aElementOf0(v3, xD)))) % 155.26/21.45 | | % 155.26/21.45 | | GROUND_INST: instantiating (9) with xn, all_122_0, simplifying with (29), % 155.26/21.45 | | (80), (122) gives: % 155.26/21.45 | | (127) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 155.26/21.45 | | (sdtlpdtrp0(xd, xn) = v3 & sdtlpdtrp0(xN, v0) = v1 & % 155.26/21.45 | | slbdtsldtrb0(v1, xk) = v2 & szszuzczcdt0(xn) = v0 & $i(v3) & % 155.26/21.45 | | $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : (v5 = v3 | % 155.26/21.45 | | ~ (sdtlpdtrp0(all_122_0, v4) = v5) | ~ $i(v4) | ~ % 155.26/21.45 | | aSubsetOf0(v4, v1) | ~ aSet0(v4) | ? [v6: $i] : ( ~ (v6 = xk) % 155.26/21.45 | | & sbrdtbr0(v4) = v6 & $i(v6))) & ! [v4: $i] : ! [v5: $i] : % 155.26/21.45 | | (v5 = v3 | ~ (sdtlpdtrp0(all_122_0, v4) = v5) | ~ $i(v4) | ~ % 155.26/21.45 | | aElementOf0(v4, v2) | ~ aSet0(v4)) & ! [v4: $i] : ! [v5: $i] % 155.26/21.45 | | : (v5 = v3 | ~ (sdtlpdtrp0(all_122_0, v4) = v5) | ~ $i(v4) | ~ % 155.26/21.45 | | aSet0(v4) | ? [v6: $i] : ? [v7: $i] : ($i(v7) & (( ~ (v6 = % 155.26/21.45 | | xk) & sbrdtbr0(v4) = v6 & $i(v6)) | (aElementOf0(v7, % 155.26/21.45 | | v4) & ~ aElementOf0(v7, v1)))))) % 155.26/21.45 | | % 155.26/21.45 | | GROUND_INST: instantiating (4) with xn, all_122_0, simplifying with (29), % 155.26/21.45 | | (80), (122) gives: % 155.26/21.46 | | (128) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 155.26/21.46 | | (sdtlpdtrp0(xN, v0) = v1 & slbdtsldtrb0(v1, xk) = v2 & % 155.26/21.46 | | szszuzczcdt0(xn) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 155.26/21.46 | | aElementOf0(v3, xT) & ! [v4: $i] : ! [v5: $i] : (v5 = v3 | ~ % 155.26/21.46 | | (sdtlpdtrp0(all_122_0, v4) = v5) | ~ $i(v4) | ~ % 155.26/21.46 | | aSubsetOf0(v4, v1) | ~ aSet0(v4) | ? [v6: $i] : ( ~ (v6 = xk) % 155.26/21.46 | | & sbrdtbr0(v4) = v6 & $i(v6))) & ! [v4: $i] : ! [v5: $i] : % 155.26/21.46 | | (v5 = v3 | ~ (sdtlpdtrp0(all_122_0, v4) = v5) | ~ $i(v4) | ~ % 155.26/21.46 | | aElementOf0(v4, v2) | ~ aSet0(v4)) & ! [v4: $i] : ! [v5: $i] % 155.26/21.46 | | : (v5 = v3 | ~ (sdtlpdtrp0(all_122_0, v4) = v5) | ~ $i(v4) | ~ % 155.26/21.46 | | aSet0(v4) | ? [v6: $i] : ? [v7: $i] : ($i(v7) & (( ~ (v6 = % 155.26/21.46 | | xk) & sbrdtbr0(v4) = v6 & $i(v6)) | (aElementOf0(v7, % 155.26/21.46 | | v4) & ~ aElementOf0(v7, v1)))))) % 155.26/21.46 | | % 155.26/21.46 | | GROUND_INST: instantiating (mImgElm) with xe, szNzAzT0, xn, xp, simplifying % 155.26/21.46 | | with (5), (6), (20), (29), (56), (122) gives: % 155.26/21.46 | | (129) aElement0(xp) % 155.26/21.46 | | % 155.26/21.46 | | GROUND_INST: instantiating (7) with xn, xp, simplifying with (29), (56), % 155.26/21.46 | | (122) gives: % 155.26/21.46 | | (130) ? [v0: $i] : (sdtlpdtrp0(xN, xn) = v0 & szmzizndt0(v0) = xp & % 155.26/21.46 | | $i(v0) & $i(xp) & aElementOf0(xp, v0) & ! [v1: $i] : ( ~ $i(v1) % 155.26/21.46 | | | ~ aElementOf0(v1, v0) | sdtlseqdt0(xp, v1))) % 155.26/21.46 | | % 155.26/21.46 | | DELTA: instantiating (130) with fresh symbol all_154_0 gives: % 155.26/21.46 | | (131) sdtlpdtrp0(xN, xn) = all_154_0 & szmzizndt0(all_154_0) = xp & % 155.26/21.46 | | $i(all_154_0) & $i(xp) & aElementOf0(xp, all_154_0) & ! [v0: $i] : % 155.26/21.46 | | ( ~ $i(v0) | ~ aElementOf0(v0, all_154_0) | sdtlseqdt0(xp, v0)) % 155.26/21.46 | | % 155.26/21.46 | | ALPHA: (131) implies: % 155.26/21.46 | | (132) szmzizndt0(all_154_0) = xp % 155.26/21.46 | | (133) sdtlpdtrp0(xN, xn) = all_154_0 % 155.26/21.46 | | % 155.26/21.46 | | DELTA: instantiating (128) with fresh symbols all_160_0, all_160_1, % 155.26/21.46 | | all_160_2, all_160_3 gives: % 155.26/21.46 | | (134) sdtlpdtrp0(xN, all_160_3) = all_160_2 & slbdtsldtrb0(all_160_2, xk) % 155.26/21.46 | | = all_160_1 & szszuzczcdt0(xn) = all_160_3 & $i(all_160_0) & % 155.26/21.46 | | $i(all_160_1) & $i(all_160_2) & $i(all_160_3) & % 155.26/21.46 | | aElementOf0(all_160_0, xT) & ! [v0: $i] : ! [v1: int] : (v1 = % 155.26/21.46 | | all_160_0 | ~ (sdtlpdtrp0(all_122_0, v0) = v1) | ~ $i(v0) | ~ % 155.26/21.46 | | aSubsetOf0(v0, all_160_2) | ~ aSet0(v0) | ? [v2: $i] : ( ~ (v2 % 155.26/21.46 | | = xk) & sbrdtbr0(v0) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: % 155.26/21.46 | | int] : (v1 = all_160_0 | ~ (sdtlpdtrp0(all_122_0, v0) = v1) | ~ % 155.26/21.46 | | $i(v0) | ~ aElementOf0(v0, all_160_1) | ~ aSet0(v0)) & ! [v0: % 155.26/21.46 | | $i] : ! [v1: int] : (v1 = all_160_0 | ~ (sdtlpdtrp0(all_122_0, % 155.26/21.46 | | v0) = v1) | ~ $i(v0) | ~ aSet0(v0) | ? [v2: $i] : ? [v3: % 155.26/21.46 | | $i] : ($i(v3) & (( ~ (v2 = xk) & sbrdtbr0(v0) = v2 & $i(v2)) | % 155.26/21.46 | | (aElementOf0(v3, v0) & ~ aElementOf0(v3, all_160_2))))) % 155.26/21.46 | | % 155.26/21.46 | | ALPHA: (134) implies: % 155.26/21.46 | | (135) szszuzczcdt0(xn) = all_160_3 % 155.26/21.46 | | (136) sdtlpdtrp0(xN, all_160_3) = all_160_2 % 155.26/21.46 | | % 155.26/21.46 | | DELTA: instantiating (127) with fresh symbols all_163_0, all_163_1, % 155.26/21.46 | | all_163_2, all_163_3 gives: % 155.26/21.46 | | (137) sdtlpdtrp0(xd, xn) = all_163_0 & sdtlpdtrp0(xN, all_163_3) = % 155.26/21.46 | | all_163_2 & slbdtsldtrb0(all_163_2, xk) = all_163_1 & % 155.26/21.46 | | szszuzczcdt0(xn) = all_163_3 & $i(all_163_0) & $i(all_163_1) & % 155.26/21.46 | | $i(all_163_2) & $i(all_163_3) & ! [v0: $i] : ! [v1: int] : (v1 = % 155.26/21.46 | | all_163_0 | ~ (sdtlpdtrp0(all_122_0, v0) = v1) | ~ $i(v0) | ~ % 155.26/21.46 | | aSubsetOf0(v0, all_163_2) | ~ aSet0(v0) | ? [v2: $i] : ( ~ (v2 % 155.26/21.46 | | = xk) & sbrdtbr0(v0) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: % 155.26/21.46 | | int] : (v1 = all_163_0 | ~ (sdtlpdtrp0(all_122_0, v0) = v1) | ~ % 155.26/21.46 | | $i(v0) | ~ aElementOf0(v0, all_163_1) | ~ aSet0(v0)) & ! [v0: % 155.26/21.46 | | $i] : ! [v1: int] : (v1 = all_163_0 | ~ (sdtlpdtrp0(all_122_0, % 155.26/21.46 | | v0) = v1) | ~ $i(v0) | ~ aSet0(v0) | ? [v2: $i] : ? [v3: % 155.26/21.46 | | $i] : ($i(v3) & (( ~ (v2 = xk) & sbrdtbr0(v0) = v2 & $i(v2)) | % 155.26/21.46 | | (aElementOf0(v3, v0) & ~ aElementOf0(v3, all_163_2))))) % 155.26/21.46 | | % 155.26/21.46 | | ALPHA: (137) implies: % 155.26/21.46 | | (138) szszuzczcdt0(xn) = all_163_3 % 155.26/21.46 | | (139) sdtlpdtrp0(xN, all_163_3) = all_163_2 % 155.26/21.46 | | (140) sdtlpdtrp0(xd, xn) = all_163_0 % 155.26/21.46 | | (141) ! [v0: $i] : ! [v1: int] : (v1 = all_163_0 | ~ % 155.26/21.46 | | (sdtlpdtrp0(all_122_0, v0) = v1) | ~ $i(v0) | ~ aSet0(v0) | ? % 155.26/21.46 | | [v2: $i] : ? [v3: $i] : ($i(v3) & (( ~ (v2 = xk) & sbrdtbr0(v0) % 155.26/21.46 | | = v2 & $i(v2)) | (aElementOf0(v3, v0) & ~ aElementOf0(v3, % 155.26/21.46 | | all_163_2))))) % 155.26/21.46 | | % 155.26/21.46 | | GROUND_INST: instantiating (141) with xP, all_122_1, simplifying with (26), % 155.26/21.46 | | (62), (81) gives: % 155.26/21.46 | | (142) all_163_0 = all_122_1 | ? [v0: $i] : ? [v1: $i] : ($i(v1) & (( ~ % 155.26/21.46 | | (v0 = xk) & sbrdtbr0(xP) = v0 & $i(v0)) | (aElementOf0(v1, % 155.26/21.46 | | xP) & ~ aElementOf0(v1, all_163_2)))) % 155.26/21.46 | | % 155.26/21.46 | | DELTA: instantiating (126) with fresh symbols all_175_0, all_175_1 gives: % 155.26/21.47 | | (143) sdtlpdtrp0(xC, xn) = all_175_1 & szDzozmdt0(all_175_1) = all_175_0 % 155.26/21.47 | | & slbdtsldtrb0(xD, xk) = all_175_0 & $i(all_175_0) & $i(all_175_1) % 155.26/21.47 | | & aFunction0(all_175_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 155.26/21.47 | | ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ % 155.26/21.47 | | aElementOf0(v2, v0) | ~ aElementOf0(v0, all_175_0) | % 155.26/21.47 | | aElementOf0(v2, xD)) & ! [v0: $i] : ! [v1: $i] : (v1 = xk | ~ % 155.26/21.47 | | (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_175_0)) % 155.26/21.47 | | & ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | % 155.26/21.47 | | ~ aElementOf0(v0, all_175_0) | aSubsetOf0(v0, xD)) & ! [v0: $i] % 155.26/21.47 | | : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ % 155.26/21.47 | | aElementOf0(v0, all_175_0) | aSet0(v0)) & ! [v0: $i] : ! [v1: % 155.26/21.47 | | $i] : ( ~ (sdtpldt0(v0, all_119_0) = v1) | ~ $i(v0) | ~ % 155.26/21.47 | | aSet0(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] % 155.26/21.47 | | : ($i(v5) & aElementOf0(all_119_0, all_119_1) & ! [v6: $i] : ( ~ % 155.26/21.47 | | $i(v6) | ~ aElementOf0(v6, all_119_1) | % 155.26/21.47 | | sdtlseqdt0(all_119_0, v6)) & ((v4 = v3 & % 155.26/21.47 | | sdtlpdtrp0(all_175_1, v0) = v3 & sdtlpdtrp0(xc, v1) = v3 & % 155.26/21.47 | | $i(v3) & ! [v6: any] : (v6 = all_119_0 | ~ $i(v6) | ~ % 155.26/21.47 | | aElementOf0(v6, v1) | aElementOf0(v6, v0)) & ! [v6: $i] % 155.26/21.47 | | : ( ~ $i(v6) | ~ aElementOf0(v6, v1) | aElement0(v6)) & ! % 155.26/21.47 | | [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6, v0) | ~ % 155.26/21.47 | | aElement0(v6) | aElementOf0(v6, v1)) & ( ~ $i(all_119_0) % 155.26/21.47 | | | ~ aElement0(all_119_0) | aElementOf0(all_119_0, v1))) % 155.26/21.47 | | | (aSet0(xD) & ~ aElementOf0(v0, all_175_0) & ! [v6: any] : % 155.26/21.47 | | (v6 = all_119_0 | ~ $i(v6) | ~ aElementOf0(v6, all_119_1) % 155.26/21.47 | | | ~ aElement0(v6) | aElementOf0(v6, xD)) & ! [v6: $i] : % 155.26/21.47 | | ( ~ $i(v6) | ~ aElementOf0(v6, xD) | aElementOf0(v6, % 155.26/21.47 | | all_119_1)) & ! [v6: $i] : ( ~ $i(v6) | ~ % 155.26/21.47 | | aElementOf0(v6, xD) | aElement0(v6)) & ( ~ $i(all_119_0) % 155.26/21.47 | | | ~ aElementOf0(all_119_0, xD)) & (( ~ (v2 = xk) & % 155.26/21.47 | | sbrdtbr0(v0) = v2 & $i(v2)) | (aElementOf0(v5, v0) & ~ % 155.26/21.47 | | aSubsetOf0(v0, xD) & ~ aElementOf0(v5, xD))))))) & ! % 155.26/21.47 | | [v0: $i] : ( ~ (sbrdtbr0(v0) = xk) | ~ $i(v0) | ~ aSubsetOf0(v0, % 155.26/21.47 | | xD) | aElementOf0(v0, all_175_0)) & ! [v0: $i] : ( ~ % 155.26/21.47 | | (sbrdtbr0(v0) = xk) | ~ $i(v0) | ~ aSet0(v0) | aElementOf0(v0, % 155.26/21.47 | | all_175_0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0) & ~ % 155.26/21.47 | | aElementOf0(v1, xD))) % 155.26/21.47 | | % 155.26/21.47 | | ALPHA: (143) implies: % 155.26/21.47 | | (144) ! [v0: $i] : ( ~ (sbrdtbr0(v0) = xk) | ~ $i(v0) | ~ % 155.26/21.47 | | aSubsetOf0(v0, xD) | aElementOf0(v0, all_175_0)) % 155.26/21.47 | | (145) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(v0, all_119_0) = v1) | ~ % 155.26/21.47 | | $i(v0) | ~ aSet0(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 155.26/21.47 | | ? [v5: $i] : ($i(v5) & aElementOf0(all_119_0, all_119_1) & ! % 155.26/21.47 | | [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6, all_119_1) | % 155.26/21.47 | | sdtlseqdt0(all_119_0, v6)) & ((v4 = v3 & % 155.26/21.47 | | sdtlpdtrp0(all_175_1, v0) = v3 & sdtlpdtrp0(xc, v1) = v3 & % 155.26/21.47 | | $i(v3) & ! [v6: any] : (v6 = all_119_0 | ~ $i(v6) | ~ % 155.26/21.47 | | aElementOf0(v6, v1) | aElementOf0(v6, v0)) & ! [v6: $i] % 155.26/21.47 | | : ( ~ $i(v6) | ~ aElementOf0(v6, v1) | aElement0(v6)) & ! % 155.26/21.47 | | [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6, v0) | ~ % 155.26/21.47 | | aElement0(v6) | aElementOf0(v6, v1)) & ( ~ $i(all_119_0) % 155.26/21.47 | | | ~ aElement0(all_119_0) | aElementOf0(all_119_0, v1))) % 155.26/21.47 | | | (aSet0(xD) & ~ aElementOf0(v0, all_175_0) & ! [v6: any] : % 155.26/21.47 | | (v6 = all_119_0 | ~ $i(v6) | ~ aElementOf0(v6, all_119_1) % 155.26/21.47 | | | ~ aElement0(v6) | aElementOf0(v6, xD)) & ! [v6: $i] : % 155.26/21.47 | | ( ~ $i(v6) | ~ aElementOf0(v6, xD) | aElementOf0(v6, % 155.26/21.47 | | all_119_1)) & ! [v6: $i] : ( ~ $i(v6) | ~ % 155.26/21.47 | | aElementOf0(v6, xD) | aElement0(v6)) & ( ~ $i(all_119_0) % 155.26/21.47 | | | ~ aElementOf0(all_119_0, xD)) & (( ~ (v2 = xk) & % 155.26/21.47 | | sbrdtbr0(v0) = v2 & $i(v2)) | (aElementOf0(v5, v0) & ~ % 155.26/21.47 | | aSubsetOf0(v0, xD) & ~ aElementOf0(v5, xD))))))) % 155.26/21.47 | | % 155.26/21.47 | | GROUND_INST: instantiating (145) with xP, all_122_2, simplifying with (26), % 155.26/21.47 | | (62), (124) gives: % 155.26/21.47 | | (146) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v3) & % 155.26/21.47 | | aElementOf0(all_119_0, all_119_1) & ! [v4: $i] : ( ~ $i(v4) | ~ % 155.26/21.47 | | aElementOf0(v4, all_119_1) | sdtlseqdt0(all_119_0, v4)) & ((v2 % 155.26/21.47 | | = v1 & sdtlpdtrp0(all_175_1, xP) = v1 & sdtlpdtrp0(xc, % 155.26/21.47 | | all_122_2) = v1 & $i(v1) & ! [v4: any] : (v4 = all_119_0 | % 155.26/21.47 | | ~ $i(v4) | ~ aElementOf0(v4, all_122_2) | aElementOf0(v4, % 155.26/21.47 | | xP)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, % 155.26/21.47 | | all_122_2) | aElement0(v4)) & ! [v4: $i] : ( ~ $i(v4) | % 155.26/21.47 | | ~ aElementOf0(v4, xP) | ~ aElement0(v4) | aElementOf0(v4, % 155.26/21.47 | | all_122_2)) & ( ~ $i(all_119_0) | ~ aElement0(all_119_0) % 155.26/21.47 | | | aElementOf0(all_119_0, all_122_2))) | (aSet0(xD) & ~ % 155.26/21.47 | | aElementOf0(xP, all_175_0) & ! [v4: any] : (v4 = all_119_0 | % 155.26/21.47 | | ~ $i(v4) | ~ aElementOf0(v4, all_119_1) | ~ % 155.26/21.47 | | aElement0(v4) | aElementOf0(v4, xD)) & ! [v4: $i] : ( ~ % 155.26/21.47 | | $i(v4) | ~ aElementOf0(v4, xD) | aElementOf0(v4, % 155.26/21.47 | | all_119_1)) & ! [v4: $i] : ( ~ $i(v4) | ~ % 155.26/21.47 | | aElementOf0(v4, xD) | aElement0(v4)) & ( ~ $i(all_119_0) | % 155.26/21.47 | | ~ aElementOf0(all_119_0, xD)) & (( ~ (v0 = xk) & % 155.26/21.47 | | sbrdtbr0(xP) = v0 & $i(v0)) | (aElementOf0(v3, xP) & ~ % 155.26/21.47 | | aSubsetOf0(xP, xD) & ~ aElementOf0(v3, xD)))))) % 155.26/21.47 | | % 155.26/21.47 | | GROUND_INST: instantiating (144) with xP, simplifying with (19), (26), (44) % 155.26/21.47 | | gives: % 155.26/21.47 | | (147) aElementOf0(xP, all_175_0) % 155.26/21.47 | | % 155.26/21.47 | | DELTA: instantiating (146) with fresh symbols all_179_0, all_179_1, % 155.26/21.47 | | all_179_2, all_179_3 gives: % 155.26/21.48 | | (148) $i(all_179_0) & aElementOf0(all_119_0, all_119_1) & ! [v0: $i] : ( % 155.26/21.48 | | ~ $i(v0) | ~ aElementOf0(v0, all_119_1) | sdtlseqdt0(all_119_0, % 155.26/21.48 | | v0)) & ((all_179_1 = all_179_2 & sdtlpdtrp0(all_175_1, xP) = % 155.26/21.48 | | all_179_2 & sdtlpdtrp0(xc, all_122_2) = all_179_2 & % 155.26/21.48 | | $i(all_179_2) & ! [v0: any] : (v0 = all_119_0 | ~ $i(v0) | ~ % 155.26/21.48 | | aElementOf0(v0, all_122_2) | aElementOf0(v0, xP)) & ! [v0: % 155.26/21.48 | | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_122_2) | % 155.26/21.48 | | aElement0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 155.26/21.48 | | aElementOf0(v0, xP) | ~ aElement0(v0) | aElementOf0(v0, % 155.26/21.48 | | all_122_2)) & ( ~ $i(all_119_0) | ~ aElement0(all_119_0) | % 155.26/21.48 | | aElementOf0(all_119_0, all_122_2))) | (aSet0(xD) & ~ % 155.26/21.48 | | aElementOf0(xP, all_175_0) & ! [v0: any] : (v0 = all_119_0 | % 155.26/21.48 | | ~ $i(v0) | ~ aElementOf0(v0, all_119_1) | ~ aElement0(v0) | % 155.26/21.48 | | aElementOf0(v0, xD)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 155.26/21.48 | | aElementOf0(v0, xD) | aElementOf0(v0, all_119_1)) & ! [v0: % 155.26/21.48 | | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xD) | aElement0(v0)) & % 155.26/21.48 | | ( ~ $i(all_119_0) | ~ aElementOf0(all_119_0, xD)) & (( ~ % 155.26/21.48 | | (all_179_3 = xk) & sbrdtbr0(xP) = all_179_3 & % 155.26/21.48 | | $i(all_179_3)) | (aElementOf0(all_179_0, xP) & ~ % 155.26/21.48 | | aSubsetOf0(xP, xD) & ~ aElementOf0(all_179_0, xD))))) % 155.26/21.48 | | % 155.26/21.48 | | ALPHA: (148) implies: % 155.26/21.48 | | (149) (all_179_1 = all_179_2 & sdtlpdtrp0(all_175_1, xP) = all_179_2 & % 155.26/21.48 | | sdtlpdtrp0(xc, all_122_2) = all_179_2 & $i(all_179_2) & ! [v0: % 155.26/21.48 | | any] : (v0 = all_119_0 | ~ $i(v0) | ~ aElementOf0(v0, % 155.26/21.48 | | all_122_2) | aElementOf0(v0, xP)) & ! [v0: $i] : ( ~ $i(v0) % 155.26/21.48 | | | ~ aElementOf0(v0, all_122_2) | aElement0(v0)) & ! [v0: $i] % 155.26/21.48 | | : ( ~ $i(v0) | ~ aElementOf0(v0, xP) | ~ aElement0(v0) | % 155.26/21.48 | | aElementOf0(v0, all_122_2)) & ( ~ $i(all_119_0) | ~ % 155.26/21.48 | | aElement0(all_119_0) | aElementOf0(all_119_0, all_122_2))) | % 155.26/21.48 | | (aSet0(xD) & ~ aElementOf0(xP, all_175_0) & ! [v0: any] : (v0 = % 155.26/21.48 | | all_119_0 | ~ $i(v0) | ~ aElementOf0(v0, all_119_1) | ~ % 155.26/21.48 | | aElement0(v0) | aElementOf0(v0, xD)) & ! [v0: $i] : ( ~ $i(v0) % 155.26/21.48 | | | ~ aElementOf0(v0, xD) | aElementOf0(v0, all_119_1)) & ! % 155.26/21.48 | | [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xD) | aElement0(v0)) & % 155.26/21.48 | | ( ~ $i(all_119_0) | ~ aElementOf0(all_119_0, xD)) & (( ~ % 155.26/21.48 | | (all_179_3 = xk) & sbrdtbr0(xP) = all_179_3 & $i(all_179_3)) % 155.26/21.48 | | | (aElementOf0(all_179_0, xP) & ~ aSubsetOf0(xP, xD) & ~ % 155.26/21.48 | | aElementOf0(all_179_0, xD)))) % 155.26/21.48 | | % 155.26/21.48 | | BETA: splitting (149) gives: % 155.26/21.48 | | % 155.26/21.48 | | Case 1: % 155.26/21.48 | | | % 155.26/21.48 | | | (150) all_179_1 = all_179_2 & sdtlpdtrp0(all_175_1, xP) = all_179_2 & % 155.26/21.48 | | | sdtlpdtrp0(xc, all_122_2) = all_179_2 & $i(all_179_2) & ! [v0: % 155.26/21.48 | | | any] : (v0 = all_119_0 | ~ $i(v0) | ~ aElementOf0(v0, % 155.26/21.48 | | | all_122_2) | aElementOf0(v0, xP)) & ! [v0: $i] : ( ~ $i(v0) % 155.26/21.48 | | | | ~ aElementOf0(v0, all_122_2) | aElement0(v0)) & ! [v0: $i] % 155.26/21.48 | | | : ( ~ $i(v0) | ~ aElementOf0(v0, xP) | ~ aElement0(v0) | % 155.26/21.48 | | | aElementOf0(v0, all_122_2)) & ( ~ $i(all_119_0) | ~ % 155.26/21.48 | | | aElement0(all_119_0) | aElementOf0(all_119_0, all_122_2)) % 155.26/21.48 | | | % 155.26/21.48 | | | ALPHA: (150) implies: % 155.26/21.48 | | | (151) sdtlpdtrp0(xc, all_122_2) = all_179_2 % 155.26/21.48 | | | % 155.26/21.48 | | | GROUND_INST: instantiating (31) with all_99_1, all_163_3, xn, simplifying % 155.26/21.48 | | | with (48), (138) gives: % 155.26/21.48 | | | (152) all_163_3 = all_99_1 % 155.26/21.48 | | | % 155.26/21.48 | | | GROUND_INST: instantiating (31) with all_160_3, all_163_3, xn, simplifying % 155.26/21.48 | | | with (135), (138) gives: % 155.26/21.48 | | | (153) all_163_3 = all_160_3 % 155.26/21.48 | | | % 155.26/21.48 | | | GROUND_INST: instantiating (36) with all_122_1, all_179_2, all_122_2, xc, % 155.26/21.48 | | | simplifying with (78), (151) gives: % 155.26/21.48 | | | (154) all_179_2 = all_122_1 % 155.26/21.48 | | | % 155.26/21.48 | | | GROUND_INST: instantiating (36) with all_119_1, all_154_0, xn, xN, % 155.26/21.48 | | | simplifying with (73), (133) gives: % 155.26/21.48 | | | (155) all_154_0 = all_119_1 % 155.26/21.48 | | | % 155.26/21.48 | | | GROUND_INST: instantiating (36) with all_82_0, all_163_0, xn, xd, % 155.26/21.48 | | | simplifying with (119), (140) gives: % 155.26/21.48 | | | (156) all_163_0 = all_82_0 % 155.26/21.48 | | | % 155.26/21.48 | | | COMBINE_EQS: (152), (153) imply: % 155.26/21.48 | | | (157) all_160_3 = all_99_1 % 155.26/21.48 | | | % 155.26/21.48 | | | REDUCE: (139), (152) imply: % 155.26/21.48 | | | (158) sdtlpdtrp0(xN, all_99_1) = all_163_2 % 155.26/21.48 | | | % 155.26/21.48 | | | REDUCE: (136), (157) imply: % 155.26/21.48 | | | (159) sdtlpdtrp0(xN, all_99_1) = all_160_2 % 155.26/21.48 | | | % 155.26/21.48 | | | REDUCE: (132), (155) imply: % 155.26/21.48 | | | (160) szmzizndt0(all_119_1) = xp % 155.26/21.48 | | | % 155.26/21.48 | | | GROUND_INST: instantiating (33) with all_119_0, xp, all_119_1, simplifying % 155.26/21.48 | | | with (72), (160) gives: % 155.26/21.48 | | | (161) all_119_0 = xp % 155.26/21.48 | | | % 155.26/21.48 | | | GROUND_INST: instantiating (36) with all_99_0, all_163_2, all_99_1, xN, % 155.26/21.48 | | | simplifying with (49), (158) gives: % 155.26/21.48 | | | (162) all_163_2 = all_99_0 % 155.26/21.48 | | | % 155.26/21.48 | | | GROUND_INST: instantiating (36) with all_160_2, all_163_2, all_99_1, xN, % 155.26/21.48 | | | simplifying with (158), (159) gives: % 155.26/21.48 | | | (163) all_163_2 = all_160_2 % 155.26/21.48 | | | % 155.26/21.48 | | | COMBINE_EQS: (162), (163) imply: % 155.26/21.48 | | | (164) all_160_2 = all_99_0 % 155.26/21.48 | | | % 155.26/21.48 | | | COMBINE_EQS: (123), (161) imply: % 155.26/21.48 | | | (165) all_122_3 = xp % 155.26/21.48 | | | % 155.26/21.48 | | | REDUCE: (124), (161) imply: % 155.26/21.48 | | | (166) sdtpldt0(xP, xp) = all_122_2 % 155.26/21.48 | | | % 155.26/21.48 | | | REDUCE: (125), (161) imply: % 155.26/21.48 | | | (167) $i(xp) % 155.26/21.48 | | | % 155.26/21.48 | | | BETA: splitting (82) gives: % 155.26/21.48 | | | % 155.26/21.48 | | | Case 1: % 155.26/21.48 | | | | % 155.26/21.48 | | | | % 155.26/21.48 | | | | GROUND_INST: instantiating (mConsDiff) with xQ, xp, xP, all_122_2, % 155.26/21.48 | | | | simplifying with (17), (28), (52), (121), (166), (167) % 155.26/21.48 | | | | gives: % 155.26/21.48 | | | | (168) all_122_2 = xQ % 155.26/21.48 | | | | % 155.26/21.48 | | | | REDUCE: (78), (168) imply: % 155.26/21.48 | | | | (169) sdtlpdtrp0(xc, xQ) = all_122_1 % 155.26/21.48 | | | | % 155.26/21.48 | | | | GROUND_INST: instantiating (36) with all_86_1, all_122_1, xQ, xc, % 155.26/21.48 | | | | simplifying with (41), (169) gives: % 155.26/21.48 | | | | (170) all_122_1 = all_86_1 % 155.26/21.48 | | | | % 155.26/21.48 | | | | BETA: splitting (142) gives: % 155.26/21.48 | | | | % 155.26/21.48 | | | | Case 1: % 155.26/21.48 | | | | | % 155.26/21.48 | | | | | (171) all_163_0 = all_122_1 % 155.26/21.48 | | | | | % 155.26/21.48 | | | | | COMBINE_EQS: (156), (171) imply: % 155.26/21.48 | | | | | (172) all_122_1 = all_82_0 % 155.26/21.48 | | | | | % 155.26/21.48 | | | | | COMBINE_EQS: (170), (172) imply: % 155.26/21.48 | | | | | (173) all_86_1 = all_82_0 % 155.26/21.48 | | | | | % 155.26/21.48 | | | | | SIMP: (173) implies: % 155.26/21.48 | | | | | (174) all_86_1 = all_82_0 % 155.26/21.48 | | | | | % 155.26/21.48 | | | | | REDUCE: (118), (174) imply: % 155.26/21.48 | | | | | (175) $false % 155.26/21.48 | | | | | % 155.26/21.48 | | | | | CLOSE: (175) is inconsistent. % 155.26/21.48 | | | | | % 155.26/21.48 | | | | Case 2: % 155.26/21.48 | | | | | % 155.26/21.49 | | | | | (176) ? [v0: $i] : ? [v1: $i] : ($i(v1) & (( ~ (v0 = xk) & % 155.26/21.49 | | | | | sbrdtbr0(xP) = v0 & $i(v0)) | (aElementOf0(v1, xP) & ~ % 155.26/21.49 | | | | | aElementOf0(v1, all_163_2)))) % 155.26/21.49 | | | | | % 155.26/21.49 | | | | | DELTA: instantiating (176) with fresh symbols all_370_0, all_370_1 % 155.26/21.49 | | | | | gives: % 155.26/21.49 | | | | | (177) $i(all_370_0) & (( ~ (all_370_1 = xk) & sbrdtbr0(xP) = % 155.26/21.49 | | | | | all_370_1 & $i(all_370_1)) | (aElementOf0(all_370_0, xP) % 155.26/21.49 | | | | | & ~ aElementOf0(all_370_0, all_163_2))) % 155.26/21.49 | | | | | % 155.26/21.49 | | | | | ALPHA: (177) implies: % 155.26/21.49 | | | | | (178) $i(all_370_0) % 155.26/21.49 | | | | | (179) ( ~ (all_370_1 = xk) & sbrdtbr0(xP) = all_370_1 & % 155.26/21.49 | | | | | $i(all_370_1)) | (aElementOf0(all_370_0, xP) & ~ % 155.26/21.49 | | | | | aElementOf0(all_370_0, all_163_2)) % 155.26/21.49 | | | | | % 155.26/21.49 | | | | | BETA: splitting (179) gives: % 155.26/21.49 | | | | | % 155.26/21.49 | | | | | Case 1: % 155.26/21.49 | | | | | | % 155.26/21.49 | | | | | | (180) ~ (all_370_1 = xk) & sbrdtbr0(xP) = all_370_1 & % 155.26/21.49 | | | | | | $i(all_370_1) % 155.26/21.49 | | | | | | % 155.26/21.49 | | | | | | ALPHA: (180) implies: % 155.26/21.49 | | | | | | (181) ~ (all_370_1 = xk) % 155.26/21.49 | | | | | | (182) sbrdtbr0(xP) = all_370_1 % 155.26/21.49 | | | | | | % 155.26/21.49 | | | | | | GROUND_INST: instantiating (32) with xk, all_370_1, xP, simplifying % 155.26/21.49 | | | | | | with (19), (182) gives: % 155.26/21.49 | | | | | | (183) all_370_1 = xk % 155.26/21.49 | | | | | | % 155.26/21.49 | | | | | | REDUCE: (181), (183) imply: % 155.26/21.49 | | | | | | (184) $false % 155.26/21.49 | | | | | | % 155.26/21.49 | | | | | | CLOSE: (184) is inconsistent. % 155.26/21.49 | | | | | | % 155.26/21.49 | | | | | Case 2: % 155.26/21.49 | | | | | | % 155.26/21.49 | | | | | | (185) aElementOf0(all_370_0, xP) & ~ aElementOf0(all_370_0, % 155.26/21.49 | | | | | | all_163_2) % 155.26/21.49 | | | | | | % 155.26/21.49 | | | | | | ALPHA: (185) implies: % 155.26/21.49 | | | | | | (186) ~ aElementOf0(all_370_0, all_163_2) % 155.26/21.49 | | | | | | (187) aElementOf0(all_370_0, xP) % 155.26/21.49 | | | | | | % 155.26/21.49 | | | | | | REDUCE: (162), (186) imply: % 155.26/21.49 | | | | | | (188) ~ aElementOf0(all_370_0, all_99_0) % 155.26/21.49 | | | | | | % 155.26/21.49 | | | | | | GROUND_INST: instantiating (50) with all_370_0, simplifying with % 155.26/21.49 | | | | | | (178), (187), (188) gives: % 155.26/21.49 | | | | | | (189) $false % 155.26/21.49 | | | | | | % 155.26/21.49 | | | | | | CLOSE: (189) is inconsistent. % 155.26/21.49 | | | | | | % 155.26/21.49 | | | | | End of split % 155.26/21.49 | | | | | % 155.26/21.49 | | | | End of split % 155.26/21.49 | | | | % 155.26/21.49 | | | Case 2: % 155.26/21.49 | | | | % 155.26/21.49 | | | | (190) ~ aElement0(all_122_3) % 155.26/21.49 | | | | % 155.26/21.49 | | | | REDUCE: (165), (190) imply: % 155.26/21.49 | | | | (191) ~ aElement0(xp) % 155.26/21.49 | | | | % 155.26/21.49 | | | | PRED_UNIFY: (129), (191) imply: % 155.26/21.49 | | | | (192) $false % 155.26/21.49 | | | | % 155.26/21.49 | | | | CLOSE: (192) is inconsistent. % 155.26/21.49 | | | | % 155.26/21.49 | | | End of split % 155.26/21.49 | | | % 155.26/21.49 | | Case 2: % 155.26/21.49 | | | % 155.26/21.49 | | | (193) aSet0(xD) & ~ aElementOf0(xP, all_175_0) & ! [v0: any] : (v0 = % 155.26/21.49 | | | all_119_0 | ~ $i(v0) | ~ aElementOf0(v0, all_119_1) | ~ % 155.26/21.49 | | | aElement0(v0) | aElementOf0(v0, xD)) & ! [v0: $i] : ( ~ $i(v0) % 155.26/21.49 | | | | ~ aElementOf0(v0, xD) | aElementOf0(v0, all_119_1)) & ! % 155.26/21.49 | | | [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xD) | aElement0(v0)) & % 155.26/21.49 | | | ( ~ $i(all_119_0) | ~ aElementOf0(all_119_0, xD)) & (( ~ % 155.26/21.49 | | | (all_179_3 = xk) & sbrdtbr0(xP) = all_179_3 & $i(all_179_3)) % 155.26/21.49 | | | | (aElementOf0(all_179_0, xP) & ~ aSubsetOf0(xP, xD) & ~ % 155.26/21.49 | | | aElementOf0(all_179_0, xD))) % 155.26/21.49 | | | % 155.26/21.49 | | | ALPHA: (193) implies: % 155.26/21.49 | | | (194) ~ aElementOf0(xP, all_175_0) % 155.26/21.49 | | | % 155.26/21.49 | | | PRED_UNIFY: (147), (194) imply: % 155.26/21.49 | | | (195) $false % 155.26/21.49 | | | % 155.26/21.49 | | | CLOSE: (195) is inconsistent. % 155.26/21.49 | | | % 155.26/21.49 | | End of split % 155.26/21.49 | | % 155.26/21.49 | End of split % 155.26/21.49 | % 155.26/21.49 End of proof % 155.26/21.49 % SZS output end Proof for theBenchmark % 155.26/21.49 % 155.26/21.49 20879ms %------------------------------------------------------------------------------