TSTP Solution File: NUM631+3 by Princess---230619
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%------------------------------------------------------------------------------
% 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
%------------------------------------------------------------------------------