TSTP Solution File: NUM566+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM566+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 : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 11:48:39 EDT 2023
% Result : Theorem 91.63s 13.00s
% Output : Proof 92.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM566+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 16:31:48 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 4.56/1.39 Prover 4: Preprocessing ...
% 4.56/1.40 Prover 1: Preprocessing ...
% 4.56/1.44 Prover 5: Preprocessing ...
% 4.56/1.44 Prover 3: Preprocessing ...
% 4.56/1.44 Prover 2: Preprocessing ...
% 4.56/1.44 Prover 6: Preprocessing ...
% 4.56/1.44 Prover 0: Preprocessing ...
% 13.81/2.68 Prover 1: Constructing countermodel ...
% 13.81/2.71 Prover 3: Constructing countermodel ...
% 14.75/2.79 Prover 6: Proving ...
% 15.56/2.90 Prover 5: Proving ...
% 18.51/3.26 Prover 2: Proving ...
% 23.64/3.95 Prover 4: Constructing countermodel ...
% 27.71/4.50 Prover 0: Proving ...
% 71.53/10.28 Prover 2: stopped
% 71.53/10.30 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 72.23/10.39 Prover 7: Preprocessing ...
% 72.46/10.54 Prover 7: Constructing countermodel ...
% 91.63/12.95 Prover 7: Found proof (size 105)
% 91.63/12.96 Prover 7: proved (2659ms)
% 91.63/12.97 Prover 5: stopped
% 91.63/12.97 Prover 0: stopped
% 91.63/12.98 Prover 1: stopped
% 91.63/12.98 Prover 3: stopped
% 91.63/13.00 Prover 4: stopped
% 91.63/13.00 Prover 6: stopped
% 91.63/13.00
% 91.63/13.00 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 91.63/13.00
% 91.63/13.02 % SZS output start Proof for theBenchmark
% 91.63/13.02 Assumptions after simplification:
% 91.63/13.02 ---------------------------------
% 91.63/13.02
% 91.63/13.02 (mCardEmpty)
% 91.63/13.05 $i(sz00) & $i(slcrc0) & ! [v0: $i] : (v0 = sz00 | ~ (sbrdtbr0(slcrc0) = v0)
% 91.63/13.05 | ~ aSet0(slcrc0)) & ! [v0: $i] : (v0 = slcrc0 | ~ (sbrdtbr0(v0) = sz00)
% 91.63/13.05 | ~ $i(v0) | ~ aSet0(v0))
% 91.63/13.05
% 91.63/13.05 (mCardSeg)
% 91.63/13.05 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ $i(v0)
% 91.63/13.05 | ~ aElementOf0(v0, szNzAzT0) | sbrdtbr0(v1) = v0)
% 91.63/13.05
% 92.12/13.05 (mCountNFin_01)
% 92.12/13.05 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0))
% 92.12/13.05
% 92.12/13.05 (mDefSeg)
% 92.12/13.06 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 92.12/13.06 (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 92.12/13.06 ~ $i(v0) | ~ sdtlseqdt0(v3, v0) | ~ aElementOf0(v2, szNzAzT0) | ~
% 92.12/13.06 aElementOf0(v0, szNzAzT0) | aElementOf0(v2, v1)) & ! [v0: $i] : ! [v1: $i]
% 92.12/13.06 : ! [v2: $i] : ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) =
% 92.12/13.06 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~
% 92.12/13.06 aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v3, v0)) & ! [v0: $i] : ! [v1: $i]
% 92.12/13.06 : ! [v2: $i] : ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) =
% 92.12/13.06 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~
% 92.12/13.06 aElementOf0(v0, szNzAzT0) | aElementOf0(v2, szNzAzT0)) & ! [v0: $i] : !
% 92.12/13.06 [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slbdtrb0(v0) = v1) | ~ $i(v2) | ~
% 92.12/13.06 $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v2) | ? [v3: $i] : ? [v4:
% 92.12/13.06 $i] : ($i(v3) & ( ~ aElementOf0(v3, v2) | ~ aElementOf0(v3, szNzAzT0) |
% 92.12/13.06 (szszuzczcdt0(v3) = v4 & $i(v4) & ~ sdtlseqdt0(v4, v0))) &
% 92.12/13.06 (aElementOf0(v3, v2) | (szszuzczcdt0(v3) = v4 & $i(v4) & sdtlseqdt0(v4,
% 92.12/13.06 v0) & aElementOf0(v3, szNzAzT0))))) & ! [v0: $i] : ! [v1: $i] : (
% 92.12/13.06 ~ (slbdtrb0(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0)
% 92.12/13.06 | aSet0(v1))
% 92.12/13.06
% 92.12/13.06 (mDefSel)
% 92.12/13.07 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 92.12/13.07 $i] : (v4 = v1 | ~ (slbdtsldtrb0(v0, v1) = v2) | ~ (sbrdtbr0(v3) = v4) |
% 92.12/13.07 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~
% 92.12/13.07 aElementOf0(v1, szNzAzT0) | ~ aSet0(v0)) & ! [v0: $i] : ! [v1: $i] : !
% 92.12/13.07 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (slbdtsldtrb0(v0, v1) = v2) | ~
% 92.12/13.07 (sbrdtbr0(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 92.12/13.07 aElementOf0(v3, v2) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) |
% 92.12/13.07 aSubsetOf0(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 92.12/13.07 : (v3 = v2 | ~ (slbdtsldtrb0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~
% 92.12/13.07 $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v3) | ~ aSet0(v0) | ?
% 92.12/13.07 [v4: $i] : ? [v5: $i] : ($i(v4) & ( ~ aSubsetOf0(v4, v0) | ~
% 92.12/13.07 aElementOf0(v4, v3) | ( ~ (v5 = v1) & sbrdtbr0(v4) = v5 & $i(v5))) &
% 92.12/13.07 (aElementOf0(v4, v3) | (v5 = v1 & sbrdtbr0(v4) = v1 & aSubsetOf0(v4,
% 92.12/13.07 v0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (
% 92.12/13.07 ~ (slbdtsldtrb0(v0, v1) = v2) | ~ (sbrdtbr0(v3) = v1) | ~ $i(v3) | ~
% 92.12/13.07 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v3, v0) | ~ aElementOf0(v1,
% 92.12/13.07 szNzAzT0) | ~ aSet0(v0) | aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1:
% 92.12/13.07 $i] : ! [v2: $i] : ( ~ (slbdtsldtrb0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1)
% 92.12/13.07 | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) | aSet0(v2))
% 92.12/13.07
% 92.12/13.07 (mDefSub)
% 92.12/13.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 92.12/13.07 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) |
% 92.12/13.07 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) |
% 92.12/13.07 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i]
% 92.12/13.07 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) |
% 92.12/13.07 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)))
% 92.12/13.07
% 92.12/13.07 (mImgRng)
% 92.12/13.07 ! [v0: $i] : ! [v1: $i] : ( ~ (szDzozmdt0(v0) = v1) | ~ $i(v0) | ~
% 92.12/13.07 aFunction0(v0) | ? [v2: $i] : (sdtlcdtrc0(v0, v1) = v2 & $i(v2) & ! [v3:
% 92.12/13.07 $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(v0, v3) = v4) | ~ $i(v3) | ~
% 92.12/13.07 aElementOf0(v3, v1) | aElementOf0(v4, v2))))
% 92.12/13.07
% 92.12/13.07 (mNATSet)
% 92.12/13.07 $i(szNzAzT0) & isCountable0(szNzAzT0) & aSet0(szNzAzT0)
% 92.12/13.07
% 92.12/13.07 (mSegSucc)
% 92.12/13.08 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 92.12/13.08 (slbdtrb0(v2) = v3) | ~ (szszuzczcdt0(v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 92.12/13.08 ~ aElementOf0(v1, szNzAzT0) | ~ aElementOf0(v0, szNzAzT0) | ? [v4: $i] :
% 92.12/13.08 ((v1 = v0 | ~ aElementOf0(v0, v3) | (slbdtrb0(v1) = v4 & $i(v4) &
% 92.12/13.08 aElementOf0(v0, v4))) & (aElementOf0(v0, v3) | ( ~ (v1 = v0) &
% 92.12/13.08 slbdtrb0(v1) = v4 & $i(v4) & ~ aElementOf0(v0, v4))))) & ! [v0: $i]
% 92.12/13.08 : ! [v1: $i] : ! [v2: $i] : ( ~ (slbdtrb0(v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 92.12/13.08 | ~ aElementOf0(v1, szNzAzT0) | ~ aElementOf0(v0, szNzAzT0) | ? [v3: $i]
% 92.12/13.08 : ? [v4: $i] : ((v1 = v0 | aElementOf0(v0, v2) | (slbdtrb0(v3) = v4 &
% 92.12/13.08 szszuzczcdt0(v1) = v3 & $i(v4) & $i(v3) & ~ aElementOf0(v0, v4))) &
% 92.12/13.08 (( ~ (v1 = v0) & ~ aElementOf0(v0, v2)) | (slbdtrb0(v3) = v4 &
% 92.12/13.08 szszuzczcdt0(v1) = v3 & $i(v4) & $i(v3) & aElementOf0(v0, v4)))))
% 92.12/13.08
% 92.12/13.08 (mSegZero)
% 92.12/13.08 slbdtrb0(sz00) = slcrc0 & $i(sz00) & $i(slcrc0)
% 92.12/13.08
% 92.12/13.08 (mSuccNum)
% 92.12/13.08 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) =
% 92.12/13.08 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v1,
% 92.12/13.08 szNzAzT0)) & ! [v0: $i] : ( ~ (szszuzczcdt0(v0) = sz00) | ~ $i(v0) | ~
% 92.12/13.08 aElementOf0(v0, szNzAzT0))
% 92.12/13.08
% 92.12/13.08 (m__)
% 92.12/13.08 $i(xc) & $i(xS) & $i(xK) & $i(xT) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 92.12/13.08 ( ~ (slbdtsldtrb0(v1, xK) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1,
% 92.12/13.08 xS) | ~ isCountable0(v1) | ~ aElementOf0(v0, xT) | ? [v3: $i] : ? [v4:
% 92.12/13.08 $i] : ( ~ (v4 = v0) & sdtlpdtrp0(xc, v3) = v4 & sbrdtbr0(v3) = xK & $i(v4)
% 92.12/13.08 & $i(v3) & aSubsetOf0(v3, v1) & aElementOf0(v3, v2) & aSet0(v3) & ! [v5:
% 92.12/13.08 $i] : ( ~ $i(v5) | ~ aElementOf0(v5, v3) | aElementOf0(v5, v1)))) & !
% 92.12/13.08 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slbdtsldtrb0(v1, xK) = v2) | ~
% 92.12/13.08 $i(v1) | ~ $i(v0) | ~ isCountable0(v1) | ~ aElementOf0(v0, xT) | ~
% 92.12/13.08 aSet0(v1) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ($i(v6)
% 92.12/13.08 & $i(v3) & ((v4 = xK & ~ (v5 = v0) & sdtlpdtrp0(xc, v3) = v5 &
% 92.12/13.08 sbrdtbr0(v3) = xK & $i(v5) & aSubsetOf0(v3, v1) & aElementOf0(v3, v2)
% 92.12/13.08 & aSet0(v3) & ! [v7: $i] : ( ~ $i(v7) | ~ aElementOf0(v7, v3) |
% 92.12/13.08 aElementOf0(v7, v1))) | (aElementOf0(v6, v1) & ~ aElementOf0(v6,
% 92.12/13.08 xS)))))
% 92.12/13.08
% 92.12/13.08 (m__3398)
% 92.33/13.10 $i(xK) & $i(xT) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 92.33/13.10 [v3: $i] : ! [v4: $i] : ( ~ (szDzozmdt0(v3) = v4) | ~ (slbdtsldtrb0(v1, v0)
% 92.33/13.10 = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ aFunction0(v3) | ~
% 92.33/13.10 iLess0(v0, xK) | ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~
% 92.33/13.10 aElementOf0(v0, szNzAzT0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 92.33/13.10 [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] :
% 92.33/13.10 ($i(v12) & $i(v10) & $i(v8) & $i(v7) & $i(v6) & ((v11 = v0 & sbrdtbr0(v10) =
% 92.33/13.10 v0 & aSubsetOf0(v10, v1) & aSet0(v10) & ~ aElementOf0(v10, v4) & !
% 92.33/13.10 [v13: $i] : ( ~ $i(v13) | ~ aElementOf0(v13, v10) | aElementOf0(v13,
% 92.33/13.10 v1))) | (sdtlcdtrc0(v3, v4) = v5 & $i(v5) & aElementOf0(v6, v5) &
% 92.33/13.10 aSet0(v5) & ~ aSubsetOf0(v5, xT) & ~ aElementOf0(v6, xT) & ! [v13:
% 92.33/13.10 $i] : ! [v14: $i] : ( ~ (sdtlpdtrp0(v3, v14) = v13) | ~ $i(v14) |
% 92.33/13.10 ~ $i(v13) | ~ aElementOf0(v14, v4) | aElementOf0(v13, v5)) & !
% 92.33/13.10 [v13: $i] : ( ~ $i(v13) | ~ aElementOf0(v13, v5) | ? [v14: $i] :
% 92.33/13.10 (sdtlpdtrp0(v3, v14) = v13 & $i(v14) & aElementOf0(v14, v4)))) |
% 92.33/13.10 (slbdtsldtrb0(v8, v0) = v9 & $i(v9) & aSubsetOf0(v8, v1) &
% 92.33/13.10 isCountable0(v8) & aElementOf0(v7, xT) & aSet0(v8) & ! [v13: $i] : !
% 92.33/13.10 [v14: $i] : (v14 = v7 | ~ (sdtlpdtrp0(v3, v13) = v14) | ~ $i(v13) |
% 92.33/13.10 ~ aSubsetOf0(v13, v8) | ? [v15: $i] : ( ~ (v15 = v0) &
% 92.33/13.10 sbrdtbr0(v13) = v15 & $i(v15))) & ! [v13: $i] : ! [v14: $i] :
% 92.33/13.10 (v14 = v7 | ~ (sdtlpdtrp0(v3, v13) = v14) | ~ $i(v13) | ~
% 92.33/13.10 aElementOf0(v13, v9)) & ! [v13: $i] : ! [v14: $i] : (v14 = v7 | ~
% 92.33/13.10 (sdtlpdtrp0(v3, v13) = v14) | ~ $i(v13) | ~ aSet0(v13) | ? [v15:
% 92.33/13.10 $i] : ? [v16: $i] : ($i(v16) & (( ~ (v15 = v0) & sbrdtbr0(v13) =
% 92.33/13.10 v15 & $i(v15)) | (aElementOf0(v16, v13) & ~ aElementOf0(v16,
% 92.33/13.10 v8))))) & ! [v13: $i] : ! [v14: $i] : ( ~ (sbrdtbr0(v13) =
% 92.33/13.10 v14) | ~ $i(v13) | ~ aElementOf0(v13, v9) | sdtlpdtrp0(v3, v13)
% 92.33/13.10 = v7) & ! [v13: $i] : ( ~ (sbrdtbr0(v13) = v0) | ~ $i(v13) | ~
% 92.33/13.10 aSubsetOf0(v13, v8) | sdtlpdtrp0(v3, v13) = v7) & ! [v13: $i] : ( ~
% 92.33/13.10 (sbrdtbr0(v13) = v0) | ~ $i(v13) | ~ aSet0(v13) | ? [v14: $i] :
% 92.33/13.10 ? [v15: $i] : ($i(v15) & ((v14 = v7 & sdtlpdtrp0(v3, v13) = v7) |
% 92.33/13.10 (aElementOf0(v15, v13) & ~ aElementOf0(v15, v8))))) & ! [v13:
% 92.33/13.10 $i] : ( ~ $i(v13) | ~ aElementOf0(v13, v8) | aElementOf0(v13, v1)))
% 92.33/13.10 | (aElementOf0(v10, v4) & (( ~ (v11 = v0) & sbrdtbr0(v10) = v11 &
% 92.33/13.10 $i(v11)) | ( ~ aSubsetOf0(v10, v1) & ( ~ aSet0(v10) |
% 92.33/13.10 (aElementOf0(v12, v10) & ~ aElementOf0(v12, v1))))))))) & !
% 92.33/13.10 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 92.33/13.10 (szDzozmdt0(v3) = v4) | ~ (slbdtsldtrb0(v1, v0) = v2) | ~ $i(v3) | ~
% 92.33/13.10 $i(v1) | ~ $i(v0) | ~ aFunction0(v3) | ~ iLess0(v0, xK) | ~
% 92.33/13.10 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | ? [v5: $i]
% 92.33/13.10 : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ?
% 92.33/13.10 [v11: $i] : ? [v12: $i] : ? [v13: $i] : ($i(v13) & $i(v12) & $i(v10) &
% 92.33/13.10 $i(v8) & $i(v7) & $i(v6) & ((v11 = v0 & sbrdtbr0(v10) = v0 &
% 92.33/13.10 aSubsetOf0(v10, v1) & aSet0(v10) & ~ aElementOf0(v10, v4) & ! [v14:
% 92.33/13.10 $i] : ( ~ $i(v14) | ~ aElementOf0(v14, v10) | aElementOf0(v14,
% 92.33/13.10 v1))) | (sdtlcdtrc0(v3, v4) = v5 & $i(v5) & aElementOf0(v6, v5) &
% 92.33/13.10 aSet0(v5) & ~ aSubsetOf0(v5, xT) & ~ aElementOf0(v6, xT) & ! [v14:
% 92.33/13.10 $i] : ! [v15: $i] : ( ~ (sdtlpdtrp0(v3, v15) = v14) | ~ $i(v15) |
% 92.33/13.10 ~ $i(v14) | ~ aElementOf0(v15, v4) | aElementOf0(v14, v5)) & !
% 92.33/13.10 [v14: $i] : ( ~ $i(v14) | ~ aElementOf0(v14, v5) | ? [v15: $i] :
% 92.33/13.10 (sdtlpdtrp0(v3, v15) = v14 & $i(v15) & aElementOf0(v15, v4)))) |
% 92.33/13.10 (slbdtsldtrb0(v8, v0) = v9 & $i(v9) & aSubsetOf0(v8, v1) &
% 92.33/13.10 isCountable0(v8) & aElementOf0(v7, xT) & aSet0(v8) & ! [v14: $i] : !
% 92.33/13.10 [v15: $i] : (v15 = v7 | ~ (sdtlpdtrp0(v3, v14) = v15) | ~ $i(v14) |
% 92.33/13.10 ~ aSubsetOf0(v14, v8) | ? [v16: $i] : ( ~ (v16 = v0) &
% 92.33/13.10 sbrdtbr0(v14) = v16 & $i(v16))) & ! [v14: $i] : ! [v15: $i] :
% 92.33/13.10 (v15 = v7 | ~ (sdtlpdtrp0(v3, v14) = v15) | ~ $i(v14) | ~
% 92.33/13.10 aElementOf0(v14, v9)) & ! [v14: $i] : ! [v15: $i] : (v15 = v7 | ~
% 92.33/13.10 (sdtlpdtrp0(v3, v14) = v15) | ~ $i(v14) | ~ aSet0(v14) | ? [v16:
% 92.33/13.10 $i] : ? [v17: $i] : ($i(v17) & (( ~ (v16 = v0) & sbrdtbr0(v14) =
% 92.33/13.10 v16 & $i(v16)) | (aElementOf0(v17, v14) & ~ aElementOf0(v17,
% 92.33/13.10 v8))))) & ! [v14: $i] : ! [v15: $i] : ( ~ (sbrdtbr0(v14) =
% 92.33/13.10 v15) | ~ $i(v14) | ~ aElementOf0(v14, v9) | sdtlpdtrp0(v3, v14)
% 92.33/13.10 = v7) & ! [v14: $i] : ( ~ (sbrdtbr0(v14) = v0) | ~ $i(v14) | ~
% 92.33/13.10 aSubsetOf0(v14, v8) | sdtlpdtrp0(v3, v14) = v7) & ! [v14: $i] : ( ~
% 92.33/13.10 (sbrdtbr0(v14) = v0) | ~ $i(v14) | ~ aSet0(v14) | ? [v15: $i] :
% 92.33/13.10 ? [v16: $i] : ($i(v16) & ((v15 = v7 & sdtlpdtrp0(v3, v14) = v7) |
% 92.33/13.10 (aElementOf0(v16, v14) & ~ aElementOf0(v16, v8))))) & ! [v14:
% 92.33/13.10 $i] : ( ~ $i(v14) | ~ aElementOf0(v14, v8) | aElementOf0(v14, v1)))
% 92.33/13.10 | (aElementOf0(v13, v1) & ~ aElementOf0(v13, szNzAzT0)) |
% 92.33/13.10 (aElementOf0(v10, v4) & (( ~ (v11 = v0) & sbrdtbr0(v10) = v11 & $i(v11))
% 92.33/13.10 | ( ~ aSubsetOf0(v10, v1) & ( ~ aSet0(v10) | (aElementOf0(v12, v10)
% 92.33/13.10 & ~ aElementOf0(v12, v1))))))))) & ! [v0: $i] : ! [v1: $i]
% 92.33/13.10 : ! [v2: $i] : ! [v3: $i] : ( ~ (szDzozmdt0(v3) = v2) | ~ (slbdtsldtrb0(v1,
% 92.33/13.10 v0) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ aFunction0(v3) | ~
% 92.33/13.10 iLess0(v0, xK) | ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~
% 92.33/13.10 aElementOf0(v0, szNzAzT0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ?
% 92.33/13.10 [v7: $i] : ? [v8: $i] : ($i(v7) & $i(v6) & $i(v5) & ((sdtlcdtrc0(v3, v2) =
% 92.33/13.10 v4 & $i(v4) & aElementOf0(v5, v4) & aSet0(v4) & ~ aSubsetOf0(v4, xT)
% 92.33/13.10 & ~ aElementOf0(v5, xT) & ! [v9: $i] : ! [v10: $i] : ( ~
% 92.33/13.10 (sdtlpdtrp0(v3, v10) = v9) | ~ $i(v10) | ~ $i(v9) | ~
% 92.33/13.10 aElementOf0(v10, v2) | aElementOf0(v9, v4)) & ! [v9: $i] : ( ~
% 92.33/13.10 $i(v9) | ~ aElementOf0(v9, v4) | ? [v10: $i] : (sdtlpdtrp0(v3,
% 92.33/13.10 v10) = v9 & $i(v10) & aElementOf0(v10, v2)))) |
% 92.33/13.10 (slbdtsldtrb0(v7, v0) = v8 & $i(v8) & aSubsetOf0(v7, v1) &
% 92.33/13.10 isCountable0(v7) & aElementOf0(v6, xT) & aSet0(v7) & ! [v9: $i] : !
% 92.33/13.10 [v10: $i] : (v10 = v6 | ~ (sdtlpdtrp0(v3, v9) = v10) | ~ $i(v9) | ~
% 92.33/13.10 aSubsetOf0(v9, v7) | ? [v11: $i] : ( ~ (v11 = v0) & sbrdtbr0(v9) =
% 92.33/13.10 v11 & $i(v11))) & ! [v9: $i] : ! [v10: $i] : (v10 = v6 | ~
% 92.33/13.10 (sdtlpdtrp0(v3, v9) = v10) | ~ $i(v9) | ~ aElementOf0(v9, v8)) &
% 92.33/13.10 ! [v9: $i] : ! [v10: $i] : (v10 = v6 | ~ (sdtlpdtrp0(v3, v9) = v10)
% 92.33/13.10 | ~ $i(v9) | ~ aSet0(v9) | ? [v11: $i] : ? [v12: $i] : ($i(v12)
% 92.33/13.10 & (( ~ (v11 = v0) & sbrdtbr0(v9) = v11 & $i(v11)) |
% 92.33/13.10 (aElementOf0(v12, v9) & ~ aElementOf0(v12, v7))))) & ! [v9:
% 92.33/13.10 $i] : ! [v10: $i] : ( ~ (sbrdtbr0(v9) = v10) | ~ $i(v9) | ~
% 92.33/13.10 aElementOf0(v9, v8) | sdtlpdtrp0(v3, v9) = v6) & ! [v9: $i] : ( ~
% 92.33/13.10 (sbrdtbr0(v9) = v0) | ~ $i(v9) | ~ aSubsetOf0(v9, v7) |
% 92.33/13.10 sdtlpdtrp0(v3, v9) = v6) & ! [v9: $i] : ( ~ (sbrdtbr0(v9) = v0) |
% 92.33/13.10 ~ $i(v9) | ~ aSet0(v9) | ? [v10: $i] : ? [v11: $i] : ($i(v11) &
% 92.33/13.10 ((v10 = v6 & sdtlpdtrp0(v3, v9) = v6) | (aElementOf0(v11, v9) & ~
% 92.33/13.10 aElementOf0(v11, v7))))) & ! [v9: $i] : ( ~ $i(v9) | ~
% 92.33/13.10 aElementOf0(v9, v7) | aElementOf0(v9, v1)))))) & ! [v0: $i] : !
% 92.33/13.10 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (szDzozmdt0(v3) = v2) | ~
% 92.33/13.10 (slbdtsldtrb0(v1, v0) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~
% 92.33/13.10 aFunction0(v3) | ~ iLess0(v0, xK) | ~ isCountable0(v1) | ~
% 92.33/13.10 aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | ? [v4: $i] : ? [v5: $i] : ?
% 92.33/13.10 [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v9) & $i(v7) &
% 92.33/13.10 $i(v6) & $i(v5) & ((sdtlcdtrc0(v3, v2) = v4 & $i(v4) & aElementOf0(v5, v4)
% 92.33/13.10 & aSet0(v4) & ~ aSubsetOf0(v4, xT) & ~ aElementOf0(v5, xT) & !
% 92.33/13.10 [v10: $i] : ! [v11: $i] : ( ~ (sdtlpdtrp0(v3, v11) = v10) | ~
% 92.33/13.10 $i(v11) | ~ $i(v10) | ~ aElementOf0(v11, v2) | aElementOf0(v10,
% 92.33/13.10 v4)) & ! [v10: $i] : ( ~ $i(v10) | ~ aElementOf0(v10, v4) | ?
% 92.33/13.10 [v11: $i] : (sdtlpdtrp0(v3, v11) = v10 & $i(v11) & aElementOf0(v11,
% 92.33/13.10 v2)))) | (slbdtsldtrb0(v7, v0) = v8 & $i(v8) & aSubsetOf0(v7,
% 92.33/13.10 v1) & isCountable0(v7) & aElementOf0(v6, xT) & aSet0(v7) & ! [v10:
% 92.33/13.10 $i] : ! [v11: $i] : (v11 = v6 | ~ (sdtlpdtrp0(v3, v10) = v11) | ~
% 92.33/13.10 $i(v10) | ~ aSubsetOf0(v10, v7) | ? [v12: $i] : ( ~ (v12 = v0) &
% 92.33/13.10 sbrdtbr0(v10) = v12 & $i(v12))) & ! [v10: $i] : ! [v11: $i] :
% 92.33/13.10 (v11 = v6 | ~ (sdtlpdtrp0(v3, v10) = v11) | ~ $i(v10) | ~
% 92.33/13.10 aElementOf0(v10, v8)) & ! [v10: $i] : ! [v11: $i] : (v11 = v6 | ~
% 92.33/13.10 (sdtlpdtrp0(v3, v10) = v11) | ~ $i(v10) | ~ aSet0(v10) | ? [v12:
% 92.33/13.10 $i] : ? [v13: $i] : ($i(v13) & (( ~ (v12 = v0) & sbrdtbr0(v10) =
% 92.33/13.10 v12 & $i(v12)) | (aElementOf0(v13, v10) & ~ aElementOf0(v13,
% 92.33/13.10 v7))))) & ! [v10: $i] : ! [v11: $i] : ( ~ (sbrdtbr0(v10) =
% 92.33/13.10 v11) | ~ $i(v10) | ~ aElementOf0(v10, v8) | sdtlpdtrp0(v3, v10)
% 92.33/13.10 = v6) & ! [v10: $i] : ( ~ (sbrdtbr0(v10) = v0) | ~ $i(v10) | ~
% 92.33/13.10 aSubsetOf0(v10, v7) | sdtlpdtrp0(v3, v10) = v6) & ! [v10: $i] : ( ~
% 92.33/13.10 (sbrdtbr0(v10) = v0) | ~ $i(v10) | ~ aSet0(v10) | ? [v11: $i] :
% 92.33/13.10 ? [v12: $i] : ($i(v12) & ((v11 = v6 & sdtlpdtrp0(v3, v10) = v6) |
% 92.33/13.10 (aElementOf0(v12, v10) & ~ aElementOf0(v12, v7))))) & ! [v10:
% 92.33/13.10 $i] : ( ~ $i(v10) | ~ aElementOf0(v10, v7) | aElementOf0(v10, v1)))
% 92.33/13.10 | (aElementOf0(v9, v1) & ~ aElementOf0(v9, szNzAzT0)))))
% 92.33/13.10
% 92.33/13.10 (m__3418)
% 92.33/13.10 $i(xK) & $i(szNzAzT0) & aElementOf0(xK, szNzAzT0)
% 92.33/13.10
% 92.33/13.10 (m__3435)
% 92.33/13.10 $i(xS) & $i(szNzAzT0) & aSubsetOf0(xS, szNzAzT0) & isCountable0(xS) &
% 92.33/13.10 aSet0(xS) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xS) |
% 92.33/13.10 aElementOf0(v0, szNzAzT0))
% 92.33/13.10
% 92.33/13.10 (m__3453)
% 92.33/13.11 $i(xc) & $i(xS) & $i(xK) & $i(xT) & ? [v0: $i] : ? [v1: $i] :
% 92.33/13.11 (sdtlcdtrc0(xc, v0) = v1 & szDzozmdt0(xc) = v0 & slbdtsldtrb0(xS, xK) = v0 &
% 92.33/13.11 $i(v1) & $i(v0) & aFunction0(xc) & aSubsetOf0(v1, xT) & aSet0(v1) & ! [v2:
% 92.33/13.11 $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sbrdtbr0(v2) = v3) | ~ $i(v4) | ~
% 92.33/13.11 $i(v2) | ~ aElementOf0(v4, v2) | ~ aElementOf0(v2, v0) | aElementOf0(v4,
% 92.33/13.11 xS)) & ! [v2: $i] : ! [v3: $i] : (v3 = xK | ~ (sbrdtbr0(v2) = v3) |
% 92.33/13.11 ~ $i(v2) | ~ aElementOf0(v2, v0)) & ! [v2: $i] : ! [v3: $i] : ( ~
% 92.33/13.11 (sdtlpdtrp0(xc, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~ aElementOf0(v3, v0)
% 92.33/13.11 | aElementOf0(v2, v1)) & ! [v2: $i] : ! [v3: $i] : ( ~ (sbrdtbr0(v2) =
% 92.33/13.11 v3) | ~ $i(v2) | ~ aElementOf0(v2, v0) | aSubsetOf0(v2, xS)) & ! [v2:
% 92.33/13.11 $i] : ! [v3: $i] : ( ~ (sbrdtbr0(v2) = v3) | ~ $i(v2) | ~
% 92.33/13.11 aElementOf0(v2, v0) | aSet0(v2)) & ! [v2: $i] : ( ~ (sbrdtbr0(v2) = xK) |
% 92.33/13.11 ~ $i(v2) | ~ aSubsetOf0(v2, xS) | aElementOf0(v2, v0)) & ! [v2: $i] : (
% 92.33/13.11 ~ (sbrdtbr0(v2) = xK) | ~ $i(v2) | ~ aSet0(v2) | aElementOf0(v2, v0) |
% 92.33/13.11 ? [v3: $i] : ($i(v3) & aElementOf0(v3, v2) & ~ aElementOf0(v3, xS))) & !
% 92.33/13.11 [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | aElementOf0(v2, xT)) & !
% 92.33/13.11 [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | ? [v3: $i] :
% 92.33/13.11 (sdtlpdtrp0(xc, v3) = v2 & $i(v3) & aElementOf0(v3, v0))))
% 92.33/13.11
% 92.33/13.11 (m__3462)
% 92.33/13.11 xK = sz00 & $i(sz00)
% 92.33/13.11
% 92.33/13.11 (m__3476)
% 92.33/13.11 $i(xS) & $i(sz00) & $i(slcrc0) & ? [v0: $i] : (slbdtsldtrb0(xS, sz00) = v0 &
% 92.33/13.11 $i(v0) & aSubsetOf0(slcrc0, xS) & aElementOf0(slcrc0, v0) & aSet0(slcrc0) &
% 92.33/13.11 ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, slcrc0) | aElementOf0(v1, xS))
% 92.33/13.11 & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, slcrc0)))
% 92.33/13.11
% 92.33/13.11 (m__3507)
% 92.33/13.12 $i(xc) & $i(xS) & $i(sz00) & $i(slcrc0) & ? [v0: $i] : ? [v1: $i] :
% 92.33/13.12 (sdtlpdtrp0(xc, slcrc0) = v1 & slbdtsldtrb0(xS, sz00) = v0 & $i(v1) & $i(v0) &
% 92.33/13.12 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xc, v2) = v3) | ~
% 92.33/13.12 $i(v4) | ~ $i(v2) | ~ aSubsetOf0(v2, xS) | ~ aElementOf0(v4, slcrc0) |
% 92.33/13.12 ? [v5: $i] : ( ~ (v5 = sz00) & sbrdtbr0(v2) = v5 & $i(v5))) & ! [v2: $i]
% 92.33/13.12 : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xc, v2) = v3) | ~ $i(v4) | ~
% 92.33/13.12 $i(v2) | ~ aElementOf0(v4, slcrc0) | ~ aElementOf0(v2, v0)) & ! [v2:
% 92.33/13.12 $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xc, v2) = v3) | ~
% 92.33/13.12 $i(v4) | ~ $i(v2) | ~ aElementOf0(v4, slcrc0) | ~ aSet0(v2) | ? [v5:
% 92.33/13.12 $i] : ? [v6: $i] : ($i(v6) & (( ~ (v5 = sz00) & sbrdtbr0(v2) = v5 &
% 92.33/13.12 $i(v5)) | (aElementOf0(v6, v2) & ~ aElementOf0(v6, xS))))) & !
% 92.33/13.12 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sbrdtbr0(v2) = v3) | ~ $i(v4) |
% 92.33/13.12 ~ $i(v2) | ~ aElementOf0(v4, slcrc0) | ~ aElementOf0(v2, v0)) & ! [v2:
% 92.33/13.12 $i] : ! [v3: $i] : (v3 = v1 | ~ (sdtlpdtrp0(xc, v2) = v3) | ~ $i(v2) |
% 92.33/13.12 ~ aSubsetOf0(v2, xS) | ? [v4: $i] : ( ~ (v4 = sz00) & sbrdtbr0(v2) = v4 &
% 92.33/13.12 $i(v4))) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (sdtlpdtrp0(xc, v2)
% 92.33/13.12 = v3) | ~ $i(v2) | ~ aElementOf0(v2, v0)) & ! [v2: $i] : ! [v3: $i]
% 92.33/13.12 : (v3 = v1 | ~ (sdtlpdtrp0(xc, v2) = v3) | ~ $i(v2) | ~ aSet0(v2) | ?
% 92.33/13.12 [v4: $i] : ? [v5: $i] : ($i(v5) & (( ~ (v4 = sz00) & sbrdtbr0(v2) = v4 &
% 92.33/13.12 $i(v4)) | (aElementOf0(v5, v2) & ~ aElementOf0(v5, xS))))) & !
% 92.33/13.12 [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xc, v2) = v3) | ~ $i(v2) | ~
% 92.33/13.12 aSubsetOf0(v2, xS) | aSet0(slcrc0) | ? [v4: $i] : ( ~ (v4 = sz00) &
% 92.33/13.12 sbrdtbr0(v2) = v4 & $i(v4))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 92.33/13.12 (sdtlpdtrp0(xc, v2) = v3) | ~ $i(v2) | ~ aElementOf0(v2, v0) |
% 92.33/13.12 aSet0(slcrc0)) & ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xc, v2) = v3)
% 92.33/13.12 | ~ $i(v2) | ~ aSet0(v2) | aSet0(slcrc0) | ? [v4: $i] : ? [v5: $i] :
% 92.33/13.12 ($i(v5) & (( ~ (v4 = sz00) & sbrdtbr0(v2) = v4 & $i(v4)) |
% 92.33/13.12 (aElementOf0(v5, v2) & ~ aElementOf0(v5, xS))))) & ! [v2: $i] : !
% 92.33/13.12 [v3: $i] : ( ~ (sbrdtbr0(v2) = v3) | ~ $i(v2) | ~ aElementOf0(v2, v0) |
% 92.33/13.12 sdtlpdtrp0(xc, v2) = v1) & ! [v2: $i] : ! [v3: $i] : ( ~ (sbrdtbr0(v2) =
% 92.33/13.12 v3) | ~ $i(v2) | ~ aElementOf0(v2, v0) | aSet0(slcrc0)) & ! [v2: $i]
% 92.33/13.12 : ! [v3: $i] : ( ~ (sbrdtbr0(v2) = sz00) | ~ $i(v3) | ~ $i(v2) | ~
% 92.33/13.12 aSubsetOf0(v2, xS) | ~ aElementOf0(v3, slcrc0)) & ! [v2: $i] : ! [v3:
% 92.33/13.12 $i] : ( ~ (sbrdtbr0(v2) = sz00) | ~ $i(v3) | ~ $i(v2) | ~
% 92.33/13.12 aElementOf0(v3, slcrc0) | ~ aSet0(v2) | ? [v4: $i] : ($i(v4) &
% 92.33/13.12 aElementOf0(v4, v2) & ~ aElementOf0(v4, xS))) & ! [v2: $i] : ( ~
% 92.33/13.12 (sbrdtbr0(v2) = sz00) | ~ $i(v2) | ~ aSubsetOf0(v2, xS) | sdtlpdtrp0(xc,
% 92.33/13.12 v2) = v1) & ! [v2: $i] : ( ~ (sbrdtbr0(v2) = sz00) | ~ $i(v2) | ~
% 92.33/13.12 aSubsetOf0(v2, xS) | aSet0(slcrc0)) & ! [v2: $i] : ( ~ (sbrdtbr0(v2) =
% 92.33/13.12 sz00) | ~ $i(v2) | ~ aSet0(v2) | aSet0(slcrc0) | ? [v3: $i] : ($i(v3)
% 92.33/13.12 & aElementOf0(v3, v2) & ~ aElementOf0(v3, xS))) & ! [v2: $i] : ( ~
% 92.33/13.12 (sbrdtbr0(v2) = sz00) | ~ $i(v2) | ~ aSet0(v2) | ? [v3: $i] : ? [v4:
% 92.33/13.12 $i] : ($i(v4) & ((v3 = v1 & sdtlpdtrp0(xc, v2) = v1) | (aElementOf0(v4,
% 92.33/13.12 v2) & ~ aElementOf0(v4, xS))))))
% 92.33/13.12
% 92.33/13.12 (function-axioms)
% 92.33/13.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 92.33/13.12 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 92.33/13.12 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 92.33/13.12 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 92.33/13.12 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 92.33/13.12 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 92.33/13.12 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 92.33/13.12 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 92.33/13.12 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 92.33/13.12 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~
% 92.33/13.12 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 92.33/13.12 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) &
% 92.33/13.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 92.33/13.12 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 92.33/13.12 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 92.33/13.12 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 92.33/13.12 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 92.33/13.12 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 92.33/13.12 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 92.33/13.12 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 92.33/13.12 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 92.33/13.12 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 92.33/13.12 v0))
% 92.33/13.12
% 92.33/13.12 Further assumptions not needed in the proof:
% 92.33/13.12 --------------------------------------------
% 92.33/13.12 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardNum, mCardS, mCardSub,
% 92.33/13.12 mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons, mDefDiff, mDefEmp,
% 92.33/13.12 mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDiffCons, mDirichlet, mDomSet,
% 92.33/13.12 mEOfElem, mElmSort, mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg,
% 92.33/13.12 mFunSort, mIH, mIHSort, mImgCount, mImgElm, mLessASymm, mLessRefl, mLessRel,
% 92.33/13.12 mLessSucc, mLessTotal, mLessTrans, mMinMin, mNatExtra, mNatNSucc, mNoScLessZr,
% 92.33/13.12 mPttSet, mSegFin, mSegLess, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub,
% 92.33/13.12 mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess,
% 92.33/13.12 mZeroLess, mZeroNum, m__3291
% 92.33/13.12
% 92.33/13.12 Those formulas are unsatisfiable:
% 92.33/13.12 ---------------------------------
% 92.33/13.12
% 92.33/13.12 Begin of proof
% 92.33/13.12 |
% 92.33/13.12 | ALPHA: (mCountNFin_01) implies:
% 92.33/13.12 | (1) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)
% 92.33/13.12 |
% 92.33/13.12 | ALPHA: (mDefSub) implies:
% 92.33/13.13 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~
% 92.33/13.13 | aSet0(v0) | aSubsetOf0(v1, v0) | ? [v2: $i] : ($i(v2) &
% 92.33/13.13 | aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)))
% 92.33/13.13 |
% 92.33/13.13 | ALPHA: (mNATSet) implies:
% 92.33/13.13 | (3) aSet0(szNzAzT0)
% 92.33/13.13 | (4) isCountable0(szNzAzT0)
% 92.33/13.13 |
% 92.33/13.13 | ALPHA: (mSuccNum) implies:
% 92.33/13.13 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) |
% 92.33/13.13 | ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v1, szNzAzT0))
% 92.33/13.13 |
% 92.33/13.13 | ALPHA: (mCardEmpty) implies:
% 92.33/13.13 | (6) ! [v0: $i] : (v0 = slcrc0 | ~ (sbrdtbr0(v0) = sz00) | ~ $i(v0) | ~
% 92.33/13.13 | aSet0(v0))
% 92.33/13.13 |
% 92.33/13.13 | ALPHA: (mDefSeg) implies:
% 92.33/13.13 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slbdtrb0(v0) =
% 92.33/13.13 | v1) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ~
% 92.33/13.13 | aSet0(v2) | ? [v3: $i] : ? [v4: $i] : ($i(v3) & ( ~ aElementOf0(v3,
% 92.33/13.13 | v2) | ~ aElementOf0(v3, szNzAzT0) | (szszuzczcdt0(v3) = v4 &
% 92.33/13.13 | $i(v4) & ~ sdtlseqdt0(v4, v0))) & (aElementOf0(v3, v2) |
% 92.33/13.13 | (szszuzczcdt0(v3) = v4 & $i(v4) & sdtlseqdt0(v4, v0) &
% 92.33/13.13 | aElementOf0(v3, szNzAzT0)))))
% 92.33/13.13 |
% 92.33/13.13 | ALPHA: (mSegZero) implies:
% 92.33/13.13 | (8) slbdtrb0(sz00) = slcrc0
% 92.33/13.13 |
% 92.33/13.13 | ALPHA: (mSegSucc) implies:
% 92.33/13.13 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slbdtrb0(v1) = v2) | ~
% 92.33/13.13 | $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~
% 92.33/13.13 | aElementOf0(v0, szNzAzT0) | ? [v3: $i] : ? [v4: $i] : ((v1 = v0 |
% 92.33/13.13 | aElementOf0(v0, v2) | (slbdtrb0(v3) = v4 & szszuzczcdt0(v1) = v3
% 92.33/13.13 | & $i(v4) & $i(v3) & ~ aElementOf0(v0, v4))) & (( ~ (v1 = v0) &
% 92.33/13.13 | ~ aElementOf0(v0, v2)) | (slbdtrb0(v3) = v4 & szszuzczcdt0(v1)
% 92.33/13.13 | = v3 & $i(v4) & $i(v3) & aElementOf0(v0, v4)))))
% 92.33/13.13 |
% 92.33/13.13 | ALPHA: (mCardSeg) implies:
% 92.33/13.13 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ $i(v0) | ~
% 92.33/13.13 | aElementOf0(v0, szNzAzT0) | sbrdtbr0(v1) = v0)
% 92.33/13.13 |
% 92.33/13.13 | ALPHA: (mDefSel) implies:
% 92.33/13.13 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 92.33/13.13 | (slbdtsldtrb0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~
% 92.33/13.13 | aElementOf0(v1, szNzAzT0) | ~ aSet0(v3) | ~ aSet0(v0) | ? [v4:
% 92.33/13.13 | $i] : ? [v5: $i] : ($i(v4) & ( ~ aSubsetOf0(v4, v0) | ~
% 92.33/13.13 | aElementOf0(v4, v3) | ( ~ (v5 = v1) & sbrdtbr0(v4) = v5 &
% 92.33/13.13 | $i(v5))) & (aElementOf0(v4, v3) | (v5 = v1 & sbrdtbr0(v4) = v1
% 92.33/13.13 | & aSubsetOf0(v4, v0)))))
% 92.33/13.13 |
% 92.33/13.13 | ALPHA: (m__3418) implies:
% 92.33/13.13 | (12) aElementOf0(xK, szNzAzT0)
% 92.33/13.13 |
% 92.33/13.13 | ALPHA: (m__3435) implies:
% 92.33/13.13 | (13) aSet0(xS)
% 92.33/13.13 | (14) isCountable0(xS)
% 92.33/13.13 |
% 92.33/13.13 | ALPHA: (m__3453) implies:
% 92.33/13.14 | (15) ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xc, v0) = v1 & szDzozmdt0(xc)
% 92.33/13.14 | = v0 & slbdtsldtrb0(xS, xK) = v0 & $i(v1) & $i(v0) & aFunction0(xc)
% 92.33/13.14 | & aSubsetOf0(v1, xT) & aSet0(v1) & ! [v2: $i] : ! [v3: $i] : !
% 92.33/13.14 | [v4: $i] : ( ~ (sbrdtbr0(v2) = v3) | ~ $i(v4) | ~ $i(v2) | ~
% 92.33/13.14 | aElementOf0(v4, v2) | ~ aElementOf0(v2, v0) | aElementOf0(v4,
% 92.33/13.14 | xS)) & ! [v2: $i] : ! [v3: $i] : (v3 = xK | ~ (sbrdtbr0(v2) =
% 92.33/13.14 | v3) | ~ $i(v2) | ~ aElementOf0(v2, v0)) & ! [v2: $i] : !
% 92.33/13.14 | [v3: $i] : ( ~ (sdtlpdtrp0(xc, v3) = v2) | ~ $i(v3) | ~ $i(v2) |
% 92.33/13.14 | ~ aElementOf0(v3, v0) | aElementOf0(v2, v1)) & ! [v2: $i] : !
% 92.33/13.14 | [v3: $i] : ( ~ (sbrdtbr0(v2) = v3) | ~ $i(v2) | ~ aElementOf0(v2,
% 92.33/13.14 | v0) | aSubsetOf0(v2, xS)) & ! [v2: $i] : ! [v3: $i] : ( ~
% 92.33/13.14 | (sbrdtbr0(v2) = v3) | ~ $i(v2) | ~ aElementOf0(v2, v0) |
% 92.33/13.14 | aSet0(v2)) & ! [v2: $i] : ( ~ (sbrdtbr0(v2) = xK) | ~ $i(v2) |
% 92.33/13.14 | ~ aSubsetOf0(v2, xS) | aElementOf0(v2, v0)) & ! [v2: $i] : ( ~
% 92.33/13.14 | (sbrdtbr0(v2) = xK) | ~ $i(v2) | ~ aSet0(v2) | aElementOf0(v2,
% 92.33/13.14 | v0) | ? [v3: $i] : ($i(v3) & aElementOf0(v3, v2) & ~
% 92.33/13.14 | aElementOf0(v3, xS))) & ! [v2: $i] : ( ~ $i(v2) | ~
% 92.33/13.14 | aElementOf0(v2, v1) | aElementOf0(v2, xT)) & ! [v2: $i] : ( ~
% 92.33/13.14 | $i(v2) | ~ aElementOf0(v2, v1) | ? [v3: $i] : (sdtlpdtrp0(xc,
% 92.33/13.14 | v3) = v2 & $i(v3) & aElementOf0(v3, v0))))
% 92.33/13.14 |
% 92.33/13.14 | ALPHA: (m__3398) implies:
% 92.33/13.14 | (16) $i(szNzAzT0)
% 92.33/13.14 |
% 92.33/13.14 | ALPHA: (m__3462) implies:
% 92.33/13.14 | (17) xK = sz00
% 92.33/13.14 |
% 92.33/13.14 | ALPHA: (m__3476) implies:
% 92.33/13.14 | (18) ? [v0: $i] : (slbdtsldtrb0(xS, sz00) = v0 & $i(v0) &
% 92.33/13.14 | aSubsetOf0(slcrc0, xS) & aElementOf0(slcrc0, v0) & aSet0(slcrc0) &
% 92.33/13.14 | ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, slcrc0) |
% 92.33/13.14 | aElementOf0(v1, xS)) & ! [v1: $i] : ( ~ $i(v1) | ~
% 92.33/13.14 | aElementOf0(v1, slcrc0)))
% 92.33/13.14 |
% 92.33/13.14 | ALPHA: (m__3507) implies:
% 92.33/13.14 | (19) $i(slcrc0)
% 92.56/13.14 | (20) ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xc, slcrc0) = v1 &
% 92.56/13.14 | slbdtsldtrb0(xS, sz00) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : !
% 92.56/13.14 | [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xc, v2) = v3) | ~ $i(v4) |
% 92.56/13.14 | ~ $i(v2) | ~ aSubsetOf0(v2, xS) | ~ aElementOf0(v4, slcrc0) |
% 92.56/13.14 | ? [v5: $i] : ( ~ (v5 = sz00) & sbrdtbr0(v2) = v5 & $i(v5))) & !
% 92.56/13.14 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xc, v2) = v3)
% 92.56/13.14 | | ~ $i(v4) | ~ $i(v2) | ~ aElementOf0(v4, slcrc0) | ~
% 92.56/13.14 | aElementOf0(v2, v0)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 92.56/13.14 | ~ (sdtlpdtrp0(xc, v2) = v3) | ~ $i(v4) | ~ $i(v2) | ~
% 92.56/13.14 | aElementOf0(v4, slcrc0) | ~ aSet0(v2) | ? [v5: $i] : ? [v6: $i]
% 92.56/13.14 | : ($i(v6) & (( ~ (v5 = sz00) & sbrdtbr0(v2) = v5 & $i(v5)) |
% 92.56/13.14 | (aElementOf0(v6, v2) & ~ aElementOf0(v6, xS))))) & ! [v2:
% 92.56/13.14 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sbrdtbr0(v2) = v3) | ~
% 92.56/13.14 | $i(v4) | ~ $i(v2) | ~ aElementOf0(v4, slcrc0) | ~
% 92.56/13.14 | aElementOf0(v2, v0)) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 92.56/13.14 | (sdtlpdtrp0(xc, v2) = v3) | ~ $i(v2) | ~ aSubsetOf0(v2, xS) | ?
% 92.56/13.14 | [v4: $i] : ( ~ (v4 = sz00) & sbrdtbr0(v2) = v4 & $i(v4))) & !
% 92.56/13.14 | [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (sdtlpdtrp0(xc, v2) = v3) |
% 92.56/13.14 | ~ $i(v2) | ~ aElementOf0(v2, v0)) & ! [v2: $i] : ! [v3: $i] :
% 92.56/13.14 | (v3 = v1 | ~ (sdtlpdtrp0(xc, v2) = v3) | ~ $i(v2) | ~ aSet0(v2) |
% 92.56/13.14 | ? [v4: $i] : ? [v5: $i] : ($i(v5) & (( ~ (v4 = sz00) &
% 92.56/13.14 | sbrdtbr0(v2) = v4 & $i(v4)) | (aElementOf0(v5, v2) & ~
% 92.56/13.14 | aElementOf0(v5, xS))))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 92.56/13.14 | (sdtlpdtrp0(xc, v2) = v3) | ~ $i(v2) | ~ aSubsetOf0(v2, xS) |
% 92.56/13.14 | aSet0(slcrc0) | ? [v4: $i] : ( ~ (v4 = sz00) & sbrdtbr0(v2) = v4
% 92.56/13.14 | & $i(v4))) & ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xc, v2)
% 92.56/13.14 | = v3) | ~ $i(v2) | ~ aElementOf0(v2, v0) | aSet0(slcrc0)) & !
% 92.56/13.14 | [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xc, v2) = v3) | ~ $i(v2) |
% 92.56/13.14 | ~ aSet0(v2) | aSet0(slcrc0) | ? [v4: $i] : ? [v5: $i] : ($i(v5)
% 92.56/13.14 | & (( ~ (v4 = sz00) & sbrdtbr0(v2) = v4 & $i(v4)) |
% 92.56/13.14 | (aElementOf0(v5, v2) & ~ aElementOf0(v5, xS))))) & ! [v2:
% 92.56/13.14 | $i] : ! [v3: $i] : ( ~ (sbrdtbr0(v2) = v3) | ~ $i(v2) | ~
% 92.56/13.14 | aElementOf0(v2, v0) | sdtlpdtrp0(xc, v2) = v1) & ! [v2: $i] : !
% 92.56/13.14 | [v3: $i] : ( ~ (sbrdtbr0(v2) = v3) | ~ $i(v2) | ~ aElementOf0(v2,
% 92.56/13.14 | v0) | aSet0(slcrc0)) & ! [v2: $i] : ! [v3: $i] : ( ~
% 92.56/13.14 | (sbrdtbr0(v2) = sz00) | ~ $i(v3) | ~ $i(v2) | ~ aSubsetOf0(v2,
% 92.56/13.14 | xS) | ~ aElementOf0(v3, slcrc0)) & ! [v2: $i] : ! [v3: $i] :
% 92.56/13.14 | ( ~ (sbrdtbr0(v2) = sz00) | ~ $i(v3) | ~ $i(v2) | ~
% 92.56/13.14 | aElementOf0(v3, slcrc0) | ~ aSet0(v2) | ? [v4: $i] : ($i(v4) &
% 92.56/13.14 | aElementOf0(v4, v2) & ~ aElementOf0(v4, xS))) & ! [v2: $i] : (
% 92.56/13.14 | ~ (sbrdtbr0(v2) = sz00) | ~ $i(v2) | ~ aSubsetOf0(v2, xS) |
% 92.56/13.14 | sdtlpdtrp0(xc, v2) = v1) & ! [v2: $i] : ( ~ (sbrdtbr0(v2) = sz00)
% 92.56/13.14 | | ~ $i(v2) | ~ aSubsetOf0(v2, xS) | aSet0(slcrc0)) & ! [v2: $i]
% 92.56/13.14 | : ( ~ (sbrdtbr0(v2) = sz00) | ~ $i(v2) | ~ aSet0(v2) |
% 92.56/13.14 | aSet0(slcrc0) | ? [v3: $i] : ($i(v3) & aElementOf0(v3, v2) & ~
% 92.56/13.14 | aElementOf0(v3, xS))) & ! [v2: $i] : ( ~ (sbrdtbr0(v2) = sz00)
% 92.56/13.14 | | ~ $i(v2) | ~ aSet0(v2) | ? [v3: $i] : ? [v4: $i] : ($i(v4) &
% 92.56/13.14 | ((v3 = v1 & sdtlpdtrp0(xc, v2) = v1) | (aElementOf0(v4, v2) & ~
% 92.56/13.14 | aElementOf0(v4, xS))))))
% 92.56/13.14 |
% 92.56/13.14 | ALPHA: (m__) implies:
% 92.56/13.14 | (21) $i(xK)
% 92.56/13.14 | (22) $i(xS)
% 92.56/13.14 | (23) $i(xc)
% 92.58/13.14 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slbdtsldtrb0(v1, xK) =
% 92.58/13.14 | v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, xS) | ~
% 92.58/13.14 | isCountable0(v1) | ~ aElementOf0(v0, xT) | ? [v3: $i] : ? [v4:
% 92.58/13.14 | $i] : ( ~ (v4 = v0) & sdtlpdtrp0(xc, v3) = v4 & sbrdtbr0(v3) = xK
% 92.58/13.14 | & $i(v4) & $i(v3) & aSubsetOf0(v3, v1) & aElementOf0(v3, v2) &
% 92.58/13.14 | aSet0(v3) & ! [v5: $i] : ( ~ $i(v5) | ~ aElementOf0(v5, v3) |
% 92.58/13.14 | aElementOf0(v5, v1))))
% 92.58/13.14 |
% 92.58/13.14 | ALPHA: (function-axioms) implies:
% 92.58/13.14 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 92.58/13.14 | (slbdtsldtrb0(v3, v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0))
% 92.58/13.14 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 92.58/13.14 | (sdtlcdtrc0(v3, v2) = v1) | ~ (sdtlcdtrc0(v3, v2) = v0))
% 92.58/13.14 |
% 92.58/13.15 | DELTA: instantiating (18) with fresh symbol all_67_0 gives:
% 92.58/13.15 | (27) slbdtsldtrb0(xS, sz00) = all_67_0 & $i(all_67_0) & aSubsetOf0(slcrc0,
% 92.58/13.15 | xS) & aElementOf0(slcrc0, all_67_0) & aSet0(slcrc0) & ! [v0: $i] :
% 92.58/13.15 | ( ~ $i(v0) | ~ aElementOf0(v0, slcrc0) | aElementOf0(v0, xS)) & !
% 92.58/13.15 | [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, slcrc0))
% 92.58/13.15 |
% 92.58/13.15 | ALPHA: (27) implies:
% 92.58/13.15 | (28) aSet0(slcrc0)
% 92.58/13.15 | (29) aElementOf0(slcrc0, all_67_0)
% 92.58/13.15 | (30) aSubsetOf0(slcrc0, xS)
% 92.58/13.15 | (31) slbdtsldtrb0(xS, sz00) = all_67_0
% 92.58/13.15 | (32) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, slcrc0))
% 92.58/13.15 |
% 92.58/13.15 | DELTA: instantiating (15) with fresh symbols all_70_0, all_70_1 gives:
% 92.58/13.15 | (33) sdtlcdtrc0(xc, all_70_1) = all_70_0 & szDzozmdt0(xc) = all_70_1 &
% 92.58/13.15 | slbdtsldtrb0(xS, xK) = all_70_1 & $i(all_70_0) & $i(all_70_1) &
% 92.58/13.15 | aFunction0(xc) & aSubsetOf0(all_70_0, xT) & aSet0(all_70_0) & ! [v0:
% 92.58/13.15 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~
% 92.58/13.15 | $i(v2) | ~ $i(v0) | ~ aElementOf0(v2, v0) | ~ aElementOf0(v0,
% 92.58/13.15 | all_70_1) | aElementOf0(v2, xS)) & ! [v0: $i] : ! [v1: $i] : (v1
% 92.58/13.15 | = xK | ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0,
% 92.58/13.15 | all_70_1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xc, v1) =
% 92.58/13.15 | v0) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, all_70_1) |
% 92.58/13.15 | aElementOf0(v0, all_70_0)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 92.58/13.15 | (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_70_1) |
% 92.58/13.15 | aSubsetOf0(v0, xS)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0)
% 92.58/13.15 | = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_70_1) | aSet0(v0)) & !
% 92.58/13.15 | [v0: $i] : ( ~ (sbrdtbr0(v0) = xK) | ~ $i(v0) | ~ aSubsetOf0(v0, xS)
% 92.58/13.15 | | aElementOf0(v0, all_70_1)) & ! [v0: $i] : ( ~ (sbrdtbr0(v0) = xK)
% 92.58/13.15 | | ~ $i(v0) | ~ aSet0(v0) | aElementOf0(v0, all_70_1) | ? [v1: $i]
% 92.58/13.15 | : ($i(v1) & aElementOf0(v1, v0) & ~ aElementOf0(v1, xS))) & ! [v0:
% 92.58/13.15 | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_70_0) | aElementOf0(v0,
% 92.58/13.15 | xT)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_70_0) |
% 92.58/13.15 | ? [v1: $i] : (sdtlpdtrp0(xc, v1) = v0 & $i(v1) & aElementOf0(v1,
% 92.58/13.15 | all_70_1)))
% 92.58/13.15 |
% 92.58/13.15 | ALPHA: (33) implies:
% 92.58/13.15 | (34) aFunction0(xc)
% 92.58/13.15 | (35) slbdtsldtrb0(xS, xK) = all_70_1
% 92.58/13.15 | (36) szDzozmdt0(xc) = all_70_1
% 92.58/13.15 | (37) sdtlcdtrc0(xc, all_70_1) = all_70_0
% 92.58/13.15 | (38) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_70_0) |
% 92.58/13.15 | aElementOf0(v0, xT))
% 92.58/13.15 |
% 92.58/13.15 | DELTA: instantiating (20) with fresh symbols all_73_0, all_73_1 gives:
% 92.58/13.15 | (39) sdtlpdtrp0(xc, slcrc0) = all_73_0 & slbdtsldtrb0(xS, sz00) = all_73_1
% 92.58/13.15 | & $i(all_73_0) & $i(all_73_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 92.58/13.15 | $i] : ( ~ (sdtlpdtrp0(xc, v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~
% 92.58/13.15 | aSubsetOf0(v0, xS) | ~ aElementOf0(v2, slcrc0) | ? [v3: $i] : ( ~
% 92.58/13.15 | (v3 = sz00) & sbrdtbr0(v0) = v3 & $i(v3))) & ! [v0: $i] : ! [v1:
% 92.58/13.15 | $i] : ! [v2: $i] : ( ~ (sdtlpdtrp0(xc, v0) = v1) | ~ $i(v2) | ~
% 92.58/13.15 | $i(v0) | ~ aElementOf0(v2, slcrc0) | ~ aElementOf0(v0, all_73_1))
% 92.58/13.15 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlpdtrp0(xc, v0) =
% 92.58/13.15 | v1) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v2, slcrc0) | ~
% 92.58/13.15 | aSet0(v0) | ? [v3: $i] : ? [v4: $i] : ($i(v4) & (( ~ (v3 = sz00) &
% 92.58/13.15 | sbrdtbr0(v0) = v3 & $i(v3)) | (aElementOf0(v4, v0) & ~
% 92.58/13.15 | aElementOf0(v4, xS))))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 92.58/13.15 | $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~
% 92.58/13.15 | aElementOf0(v2, slcrc0) | ~ aElementOf0(v0, all_73_1)) & ! [v0:
% 92.58/13.15 | $i] : ! [v1: int] : (v1 = all_73_0 | ~ (sdtlpdtrp0(xc, v0) = v1) |
% 92.58/13.15 | ~ $i(v0) | ~ aSubsetOf0(v0, xS) | ? [v2: $i] : ( ~ (v2 = sz00) &
% 92.58/13.15 | sbrdtbr0(v0) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: int] : (v1 =
% 92.58/13.15 | all_73_0 | ~ (sdtlpdtrp0(xc, v0) = v1) | ~ $i(v0) | ~
% 92.58/13.15 | aElementOf0(v0, all_73_1)) & ! [v0: $i] : ! [v1: int] : (v1 =
% 92.58/13.15 | all_73_0 | ~ (sdtlpdtrp0(xc, v0) = v1) | ~ $i(v0) | ~ aSet0(v0) |
% 92.58/13.15 | ? [v2: $i] : ? [v3: $i] : ($i(v3) & (( ~ (v2 = sz00) &
% 92.58/13.15 | sbrdtbr0(v0) = v2 & $i(v2)) | (aElementOf0(v3, v0) & ~
% 92.58/13.15 | aElementOf0(v3, xS))))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 92.58/13.15 | (sdtlpdtrp0(xc, v0) = v1) | ~ $i(v0) | ~ aSubsetOf0(v0, xS) |
% 92.58/13.15 | aSet0(slcrc0) | ? [v2: $i] : ( ~ (v2 = sz00) & sbrdtbr0(v0) = v2 &
% 92.58/13.15 | $i(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xc, v0) =
% 92.58/13.15 | v1) | ~ $i(v0) | ~ aElementOf0(v0, all_73_1) | aSet0(slcrc0)) &
% 92.58/13.15 | ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xc, v0) = v1) | ~ $i(v0) |
% 92.58/13.15 | ~ aSet0(v0) | aSet0(slcrc0) | ? [v2: $i] : ? [v3: $i] : ($i(v3) &
% 92.58/13.15 | (( ~ (v2 = sz00) & sbrdtbr0(v0) = v2 & $i(v2)) | (aElementOf0(v3,
% 92.58/13.15 | v0) & ~ aElementOf0(v3, xS))))) & ! [v0: $i] : ! [v1: $i]
% 92.58/13.15 | : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_73_1) |
% 92.58/13.15 | sdtlpdtrp0(xc, v0) = all_73_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 92.58/13.15 | (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_73_1) |
% 92.58/13.15 | aSet0(slcrc0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) =
% 92.58/13.15 | sz00) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v0, xS) | ~
% 92.58/13.15 | aElementOf0(v1, slcrc0)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 92.58/13.15 | (sbrdtbr0(v0) = sz00) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1,
% 92.58/13.15 | slcrc0) | ~ aSet0(v0) | ? [v2: $i] : ($i(v2) & aElementOf0(v2,
% 92.58/13.15 | v0) & ~ aElementOf0(v2, xS))) & ! [v0: $i] : ( ~ (sbrdtbr0(v0)
% 92.58/13.15 | = sz00) | ~ $i(v0) | ~ aSubsetOf0(v0, xS) | sdtlpdtrp0(xc, v0) =
% 92.58/13.15 | all_73_0) & ! [v0: $i] : ( ~ (sbrdtbr0(v0) = sz00) | ~ $i(v0) | ~
% 92.58/13.15 | aSubsetOf0(v0, xS) | aSet0(slcrc0)) & ! [v0: $i] : ( ~
% 92.58/13.15 | (sbrdtbr0(v0) = sz00) | ~ $i(v0) | ~ aSet0(v0) | aSet0(slcrc0) |
% 92.58/13.15 | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0) & ~ aElementOf0(v1,
% 92.58/13.15 | xS))) & ! [v0: $i] : ( ~ (sbrdtbr0(v0) = sz00) | ~ $i(v0) | ~
% 92.58/13.16 | aSet0(v0) | ? [v1: int] : ? [v2: $i] : ($i(v2) & ((v1 = all_73_0 &
% 92.58/13.16 | sdtlpdtrp0(xc, v0) = all_73_0) | (aElementOf0(v2, v0) & ~
% 92.58/13.16 | aElementOf0(v2, xS)))))
% 92.58/13.16 |
% 92.58/13.16 | ALPHA: (39) implies:
% 92.58/13.16 | (40) $i(all_73_0)
% 92.58/13.16 | (41) slbdtsldtrb0(xS, sz00) = all_73_1
% 92.58/13.16 | (42) sdtlpdtrp0(xc, slcrc0) = all_73_0
% 92.58/13.16 | (43) ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = sz00) | ~ $i(v1) | ~
% 92.58/13.16 | $i(v0) | ~ aSubsetOf0(v0, xS) | ~ aElementOf0(v1, slcrc0))
% 92.58/13.16 | (44) ! [v0: $i] : ! [v1: int] : (v1 = all_73_0 | ~ (sdtlpdtrp0(xc, v0) =
% 92.58/13.16 | v1) | ~ $i(v0) | ~ aElementOf0(v0, all_73_1))
% 92.58/13.16 |
% 92.58/13.16 | REDUCE: (17), (35) imply:
% 92.58/13.16 | (45) slbdtsldtrb0(xS, sz00) = all_70_1
% 92.58/13.16 |
% 92.58/13.16 | REDUCE: (17), (21) imply:
% 92.58/13.16 | (46) $i(sz00)
% 92.58/13.16 |
% 92.58/13.16 | REDUCE: (12), (17) imply:
% 92.58/13.16 | (47) aElementOf0(sz00, szNzAzT0)
% 92.58/13.16 |
% 92.58/13.16 | BETA: splitting (1) gives:
% 92.58/13.16 |
% 92.58/13.16 | Case 1:
% 92.58/13.16 | |
% 92.58/13.16 | | (48) ~ isCountable0(slcrc0)
% 92.58/13.16 | |
% 92.58/13.16 | | GROUND_INST: instantiating (25) with all_70_1, all_73_1, sz00, xS,
% 92.58/13.16 | | simplifying with (41), (45) gives:
% 92.58/13.16 | | (49) all_73_1 = all_70_1
% 92.58/13.16 | |
% 92.58/13.16 | | GROUND_INST: instantiating (25) with all_67_0, all_73_1, sz00, xS,
% 92.58/13.16 | | simplifying with (31), (41) gives:
% 92.58/13.16 | | (50) all_73_1 = all_67_0
% 92.58/13.16 | |
% 92.58/13.16 | | PRED_UNIFY: (4), (48) imply:
% 92.58/13.16 | | (51) ~ (szNzAzT0 = slcrc0)
% 92.58/13.16 | |
% 92.58/13.16 | | COMBINE_EQS: (49), (50) imply:
% 92.58/13.16 | | (52) all_70_1 = all_67_0
% 92.58/13.16 | |
% 92.58/13.16 | | SIMP: (52) implies:
% 92.58/13.16 | | (53) all_70_1 = all_67_0
% 92.58/13.16 | |
% 92.58/13.16 | | REDUCE: (37), (53) imply:
% 92.58/13.16 | | (54) sdtlcdtrc0(xc, all_67_0) = all_70_0
% 92.58/13.16 | |
% 92.58/13.16 | | REDUCE: (36), (53) imply:
% 92.58/13.16 | | (55) szDzozmdt0(xc) = all_67_0
% 92.58/13.16 | |
% 92.58/13.16 | | GROUND_INST: instantiating (2) with xS, xS, simplifying with (13), (22)
% 92.58/13.16 | | gives:
% 92.58/13.16 | | (56) aSubsetOf0(xS, xS)
% 92.58/13.16 | |
% 92.58/13.16 | | GROUND_INST: instantiating (32) with slcrc0, simplifying with (19) gives:
% 92.58/13.16 | | (57) ~ aElementOf0(slcrc0, slcrc0)
% 92.58/13.16 | |
% 92.58/13.16 | | GROUND_INST: instantiating (7) with sz00, slcrc0, szNzAzT0, simplifying with
% 92.58/13.16 | | (3), (8), (16), (46), (47) gives:
% 92.58/13.16 | | (58) szNzAzT0 = slcrc0 | ? [v0: $i] : ? [v1: $i] : (szszuzczcdt0(v0) =
% 92.58/13.16 | | v1 & $i(v1) & $i(v0) & aElementOf0(v0, szNzAzT0) & ~
% 92.58/13.16 | | sdtlseqdt0(v1, sz00))
% 92.58/13.16 | |
% 92.58/13.16 | | GROUND_INST: instantiating (9) with sz00, sz00, slcrc0, simplifying with
% 92.58/13.16 | | (8), (46), (47) gives:
% 92.58/13.16 | | (59) ? [v0: $i] : ? [v1: $i] : (slbdtrb0(v0) = v1 & szszuzczcdt0(sz00)
% 92.58/13.16 | | = v0 & $i(v1) & $i(v0) & aElementOf0(sz00, v1))
% 92.58/13.16 | |
% 92.58/13.16 | | GROUND_INST: instantiating (10) with sz00, slcrc0, simplifying with (8),
% 92.58/13.16 | | (46), (47) gives:
% 92.58/13.16 | | (60) sbrdtbr0(slcrc0) = sz00
% 92.58/13.16 | |
% 92.58/13.16 | | GROUND_INST: instantiating (11) with xS, sz00, all_67_0, slcrc0, simplifying
% 92.58/13.16 | | with (13), (19), (22), (28), (31), (46), (47) gives:
% 92.58/13.16 | | (61) all_67_0 = slcrc0 | ? [v0: $i] : ? [v1: $i] : ($i(v0) & ( ~
% 92.58/13.16 | | aSubsetOf0(v0, xS) | ~ aElementOf0(v0, slcrc0) | ( ~ (v1 =
% 92.58/13.16 | | sz00) & sbrdtbr0(v0) = v1 & $i(v1))) & (aElementOf0(v0,
% 92.58/13.16 | | slcrc0) | (v1 = sz00 & sbrdtbr0(v0) = sz00 & aSubsetOf0(v0,
% 92.58/13.16 | | xS))))
% 92.58/13.16 | |
% 92.58/13.16 | | GROUND_INST: instantiating (mImgRng) with xc, all_67_0, simplifying with
% 92.58/13.16 | | (23), (34), (55) gives:
% 92.58/13.16 | | (62) ? [v0: $i] : (sdtlcdtrc0(xc, all_67_0) = v0 & $i(v0) & ! [v1: $i]
% 92.58/13.16 | | : ! [v2: $i] : ( ~ (sdtlpdtrp0(xc, v1) = v2) | ~ $i(v1) | ~
% 92.58/13.16 | | aElementOf0(v1, all_67_0) | aElementOf0(v2, v0)))
% 92.58/13.16 | |
% 92.58/13.16 | | DELTA: instantiating (59) with fresh symbols all_90_0, all_90_1 gives:
% 92.58/13.16 | | (63) slbdtrb0(all_90_1) = all_90_0 & szszuzczcdt0(sz00) = all_90_1 &
% 92.58/13.16 | | $i(all_90_0) & $i(all_90_1) & aElementOf0(sz00, all_90_0)
% 92.58/13.16 | |
% 92.58/13.16 | | ALPHA: (63) implies:
% 92.58/13.16 | | (64) aElementOf0(sz00, all_90_0)
% 92.58/13.16 | | (65) $i(all_90_1)
% 92.58/13.16 | | (66) szszuzczcdt0(sz00) = all_90_1
% 92.58/13.16 | | (67) slbdtrb0(all_90_1) = all_90_0
% 92.58/13.16 | |
% 92.58/13.16 | | DELTA: instantiating (62) with fresh symbol all_92_0 gives:
% 92.58/13.17 | | (68) sdtlcdtrc0(xc, all_67_0) = all_92_0 & $i(all_92_0) & ! [v0: $i] :
% 92.58/13.17 | | ! [v1: $i] : ( ~ (sdtlpdtrp0(xc, v0) = v1) | ~ $i(v0) | ~
% 92.58/13.17 | | aElementOf0(v0, all_67_0) | aElementOf0(v1, all_92_0))
% 92.58/13.17 | |
% 92.58/13.17 | | ALPHA: (68) implies:
% 92.58/13.17 | | (69) sdtlcdtrc0(xc, all_67_0) = all_92_0
% 92.58/13.17 | | (70) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xc, v0) = v1) | ~
% 92.58/13.17 | | $i(v0) | ~ aElementOf0(v0, all_67_0) | aElementOf0(v1, all_92_0))
% 92.58/13.17 | |
% 92.58/13.17 | | GROUND_INST: instantiating (70) with slcrc0, all_73_0, simplifying with
% 92.58/13.17 | | (19), (29), (42) gives:
% 92.58/13.17 | | (71) aElementOf0(all_73_0, all_92_0)
% 92.58/13.17 | |
% 92.58/13.17 | | BETA: splitting (58) gives:
% 92.58/13.17 | |
% 92.58/13.17 | | Case 1:
% 92.58/13.17 | | |
% 92.58/13.17 | | | (72) szNzAzT0 = slcrc0
% 92.58/13.17 | | |
% 92.58/13.17 | | | REDUCE: (51), (72) imply:
% 92.58/13.17 | | | (73) $false
% 92.58/13.17 | | |
% 92.58/13.17 | | | CLOSE: (73) is inconsistent.
% 92.58/13.17 | | |
% 92.58/13.17 | | Case 2:
% 92.58/13.17 | | |
% 92.58/13.17 | | | (74) ? [v0: $i] : ? [v1: $i] : (szszuzczcdt0(v0) = v1 & $i(v1) &
% 92.58/13.17 | | | $i(v0) & aElementOf0(v0, szNzAzT0) & ~ sdtlseqdt0(v1, sz00))
% 92.58/13.17 | | |
% 92.58/13.17 | | | DELTA: instantiating (74) with fresh symbols all_128_0, all_128_1 gives:
% 92.58/13.17 | | | (75) szszuzczcdt0(all_128_1) = all_128_0 & $i(all_128_0) &
% 92.58/13.17 | | | $i(all_128_1) & aElementOf0(all_128_1, szNzAzT0) & ~
% 92.58/13.17 | | | sdtlseqdt0(all_128_0, sz00)
% 92.58/13.17 | | |
% 92.58/13.17 | | | ALPHA: (75) implies:
% 92.58/13.17 | | | (76) aElementOf0(all_128_1, szNzAzT0)
% 92.58/13.17 | | | (77) $i(all_128_1)
% 92.58/13.17 | | |
% 92.58/13.17 | | | GROUND_INST: instantiating (26) with all_70_0, all_92_0, all_67_0, xc,
% 92.58/13.17 | | | simplifying with (54), (69) gives:
% 92.58/13.17 | | | (78) all_92_0 = all_70_0
% 92.58/13.17 | | |
% 92.58/13.17 | | | PRED_UNIFY: (29), (57) imply:
% 92.58/13.17 | | | (79) ~ (all_67_0 = slcrc0)
% 92.58/13.17 | | |
% 92.58/13.17 | | | REDUCE: (71), (78) imply:
% 92.58/13.17 | | | (80) aElementOf0(all_73_0, all_70_0)
% 92.58/13.17 | | |
% 92.58/13.17 | | | BETA: splitting (61) gives:
% 92.58/13.17 | | |
% 92.58/13.17 | | | Case 1:
% 92.58/13.17 | | | |
% 92.58/13.17 | | | | (81) all_67_0 = slcrc0
% 92.58/13.17 | | | |
% 92.58/13.17 | | | | REDUCE: (79), (81) imply:
% 92.58/13.17 | | | | (82) $false
% 92.58/13.17 | | | |
% 92.58/13.17 | | | | CLOSE: (82) is inconsistent.
% 92.58/13.17 | | | |
% 92.58/13.17 | | | Case 2:
% 92.58/13.17 | | | |
% 92.58/13.17 | | | |
% 92.58/13.17 | | | | GROUND_INST: instantiating (38) with all_73_0, simplifying with (40),
% 92.58/13.17 | | | | (80) gives:
% 92.58/13.17 | | | | (83) aElementOf0(all_73_0, xT)
% 92.58/13.17 | | | |
% 92.58/13.17 | | | | GROUND_INST: instantiating (24) with all_73_0, xS, all_67_0, simplifying
% 92.58/13.17 | | | | with (14), (22), (40), (56) gives:
% 92.58/13.17 | | | | (84) ~ (slbdtsldtrb0(xS, xK) = all_67_0) | ~ aElementOf0(all_73_0,
% 92.58/13.17 | | | | xT) | ? [v0: $i] : ? [v1: any] : ( ~ (v1 = all_73_0) &
% 92.58/13.17 | | | | sdtlpdtrp0(xc, v0) = v1 & sbrdtbr0(v0) = xK & $i(v1) & $i(v0)
% 92.58/13.17 | | | | & aSubsetOf0(v0, xS) & aElementOf0(v0, all_67_0) & aSet0(v0) &
% 92.58/13.17 | | | | ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v0) |
% 92.58/13.17 | | | | aElementOf0(v2, xS)))
% 92.58/13.17 | | | |
% 92.58/13.17 | | | | GROUND_INST: instantiating (5) with sz00, all_90_1, simplifying with
% 92.58/13.17 | | | | (46), (47), (66) gives:
% 92.58/13.17 | | | | (85) aElementOf0(all_90_1, szNzAzT0)
% 92.58/13.17 | | | |
% 92.58/13.17 | | | | GROUND_INST: instantiating (43) with slcrc0, sz00, simplifying with
% 92.58/13.17 | | | | (19), (30), (46), (60) gives:
% 92.58/13.17 | | | | (86) ~ aElementOf0(sz00, slcrc0)
% 92.58/13.17 | | | |
% 92.58/13.17 | | | | GROUND_INST: instantiating (7) with all_90_1, all_90_0, slcrc0,
% 92.58/13.17 | | | | simplifying with (19), (28), (65), (67) gives:
% 92.58/13.17 | | | | (87) all_90_0 = slcrc0 | ~ aElementOf0(all_90_1, szNzAzT0) | ? [v0:
% 92.58/13.17 | | | | $i] : ? [v1: $i] : ($i(v0) & ( ~ aElementOf0(v0, szNzAzT0) |
% 92.58/13.17 | | | | ~ aElementOf0(v0, slcrc0) | (szszuzczcdt0(v0) = v1 & $i(v1)
% 92.58/13.17 | | | | & ~ sdtlseqdt0(v1, all_90_1))) & (aElementOf0(v0, slcrc0)
% 92.58/13.17 | | | | | (szszuzczcdt0(v0) = v1 & $i(v1) & sdtlseqdt0(v1, all_90_1)
% 92.58/13.17 | | | | & aElementOf0(v0, szNzAzT0))))
% 92.58/13.17 | | | |
% 92.58/13.17 | | | | GROUND_INST: instantiating (9) with all_128_1, all_90_1, all_90_0,
% 92.58/13.17 | | | | simplifying with (65), (67), (76), (77) gives:
% 92.58/13.17 | | | | (88) ~ aElementOf0(all_90_1, szNzAzT0) | ? [v0: $i] : ? [v1: $i] :
% 92.58/13.17 | | | | ((all_128_1 = all_90_1 | aElementOf0(all_128_1, all_90_0) |
% 92.58/13.17 | | | | (slbdtrb0(v0) = v1 & szszuzczcdt0(all_90_1) = v0 & $i(v1) &
% 92.58/13.17 | | | | $i(v0) & ~ aElementOf0(all_128_1, v1))) & (( ~ (all_128_1
% 92.58/13.17 | | | | = all_90_1) & ~ aElementOf0(all_128_1, all_90_0)) |
% 92.58/13.17 | | | | (slbdtrb0(v0) = v1 & szszuzczcdt0(all_90_1) = v0 & $i(v1) &
% 92.58/13.17 | | | | $i(v0) & aElementOf0(all_128_1, v1))))
% 92.58/13.17 | | | |
% 92.58/13.17 | | | | BETA: splitting (84) gives:
% 92.58/13.17 | | | |
% 92.58/13.17 | | | | Case 1:
% 92.58/13.17 | | | | |
% 92.58/13.17 | | | | | (89) ~ aElementOf0(all_73_0, xT)
% 92.58/13.17 | | | | |
% 92.58/13.17 | | | | | PRED_UNIFY: (83), (89) imply:
% 92.58/13.17 | | | | | (90) $false
% 92.58/13.17 | | | | |
% 92.58/13.17 | | | | | CLOSE: (90) is inconsistent.
% 92.58/13.17 | | | | |
% 92.58/13.17 | | | | Case 2:
% 92.58/13.17 | | | | |
% 92.58/13.17 | | | | | (91) ~ (slbdtsldtrb0(xS, xK) = all_67_0) | ? [v0: $i] : ? [v1:
% 92.58/13.17 | | | | | any] : ( ~ (v1 = all_73_0) & sdtlpdtrp0(xc, v0) = v1 &
% 92.58/13.17 | | | | | sbrdtbr0(v0) = xK & $i(v1) & $i(v0) & aSubsetOf0(v0, xS) &
% 92.58/13.17 | | | | | aElementOf0(v0, all_67_0) & aSet0(v0) & ! [v2: $i] : ( ~
% 92.58/13.17 | | | | | $i(v2) | ~ aElementOf0(v2, v0) | aElementOf0(v2, xS)))
% 92.58/13.17 | | | | |
% 92.58/13.17 | | | | | BETA: splitting (91) gives:
% 92.58/13.17 | | | | |
% 92.58/13.17 | | | | | Case 1:
% 92.58/13.17 | | | | | |
% 92.58/13.17 | | | | | | (92) ~ (slbdtsldtrb0(xS, xK) = all_67_0)
% 92.58/13.17 | | | | | |
% 92.58/13.18 | | | | | | REDUCE: (17), (92) imply:
% 92.58/13.18 | | | | | | (93) ~ (slbdtsldtrb0(xS, sz00) = all_67_0)
% 92.58/13.18 | | | | | |
% 92.58/13.18 | | | | | | PRED_UNIFY: (31), (93) imply:
% 92.58/13.18 | | | | | | (94) $false
% 92.58/13.18 | | | | | |
% 92.58/13.18 | | | | | | CLOSE: (94) is inconsistent.
% 92.58/13.18 | | | | | |
% 92.58/13.18 | | | | | Case 2:
% 92.58/13.18 | | | | | |
% 92.58/13.18 | | | | | | (95) ? [v0: $i] : ? [v1: any] : ( ~ (v1 = all_73_0) &
% 92.58/13.18 | | | | | | sdtlpdtrp0(xc, v0) = v1 & sbrdtbr0(v0) = xK & $i(v1) &
% 92.58/13.18 | | | | | | $i(v0) & aSubsetOf0(v0, xS) & aElementOf0(v0, all_67_0) &
% 92.58/13.18 | | | | | | aSet0(v0) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2,
% 92.58/13.18 | | | | | | v0) | aElementOf0(v2, xS)))
% 92.58/13.18 | | | | | |
% 92.58/13.18 | | | | | | DELTA: instantiating (95) with fresh symbols all_219_0, all_219_1
% 92.58/13.18 | | | | | | gives:
% 92.58/13.18 | | | | | | (96) ~ (all_219_0 = all_73_0) & sdtlpdtrp0(xc, all_219_1) =
% 92.58/13.18 | | | | | | all_219_0 & sbrdtbr0(all_219_1) = xK & $i(all_219_0) &
% 92.58/13.18 | | | | | | $i(all_219_1) & aSubsetOf0(all_219_1, xS) &
% 92.58/13.18 | | | | | | aElementOf0(all_219_1, all_67_0) & aSet0(all_219_1) & !
% 92.58/13.18 | | | | | | [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_219_1) |
% 92.58/13.18 | | | | | | aElementOf0(v0, xS))
% 92.58/13.18 | | | | | |
% 92.58/13.18 | | | | | | ALPHA: (96) implies:
% 92.58/13.18 | | | | | | (97) ~ (all_219_0 = all_73_0)
% 92.58/13.18 | | | | | | (98) aSet0(all_219_1)
% 92.58/13.18 | | | | | | (99) aElementOf0(all_219_1, all_67_0)
% 92.58/13.18 | | | | | | (100) $i(all_219_1)
% 92.58/13.18 | | | | | | (101) sbrdtbr0(all_219_1) = xK
% 92.58/13.18 | | | | | | (102) sdtlpdtrp0(xc, all_219_1) = all_219_0
% 92.58/13.18 | | | | | |
% 92.58/13.18 | | | | | | REDUCE: (17), (101) imply:
% 92.58/13.18 | | | | | | (103) sbrdtbr0(all_219_1) = sz00
% 92.58/13.18 | | | | | |
% 92.58/13.18 | | | | | | BETA: splitting (88) gives:
% 92.58/13.18 | | | | | |
% 92.58/13.18 | | | | | | Case 1:
% 92.58/13.18 | | | | | | |
% 92.58/13.18 | | | | | | | (104) ~ aElementOf0(all_90_1, szNzAzT0)
% 92.58/13.18 | | | | | | |
% 92.58/13.18 | | | | | | | PRED_UNIFY: (85), (104) imply:
% 92.58/13.18 | | | | | | | (105) $false
% 92.58/13.18 | | | | | | |
% 92.58/13.18 | | | | | | | CLOSE: (105) is inconsistent.
% 92.58/13.18 | | | | | | |
% 92.58/13.18 | | | | | | Case 2:
% 92.58/13.18 | | | | | | |
% 92.58/13.18 | | | | | | |
% 92.58/13.18 | | | | | | | PRED_UNIFY: (64), (86) imply:
% 92.58/13.18 | | | | | | | (106) ~ (all_90_0 = slcrc0)
% 92.58/13.18 | | | | | | |
% 92.58/13.18 | | | | | | | BETA: splitting (87) gives:
% 92.58/13.18 | | | | | | |
% 92.58/13.18 | | | | | | | Case 1:
% 92.58/13.18 | | | | | | | |
% 92.58/13.18 | | | | | | | | (107) ~ aElementOf0(all_90_1, szNzAzT0)
% 92.58/13.18 | | | | | | | |
% 92.58/13.18 | | | | | | | | PRED_UNIFY: (85), (107) imply:
% 92.58/13.18 | | | | | | | | (108) $false
% 92.58/13.18 | | | | | | | |
% 92.58/13.18 | | | | | | | | CLOSE: (108) is inconsistent.
% 92.58/13.18 | | | | | | | |
% 92.58/13.18 | | | | | | | Case 2:
% 92.58/13.18 | | | | | | | |
% 92.58/13.18 | | | | | | | | (109) all_90_0 = slcrc0 | ? [v0: $i] : ? [v1: $i] : ($i(v0)
% 92.58/13.18 | | | | | | | | & ( ~ aElementOf0(v0, szNzAzT0) | ~ aElementOf0(v0,
% 92.58/13.18 | | | | | | | | slcrc0) | (szszuzczcdt0(v0) = v1 & $i(v1) & ~
% 92.58/13.18 | | | | | | | | sdtlseqdt0(v1, all_90_1))) & (aElementOf0(v0,
% 92.58/13.18 | | | | | | | | slcrc0) | (szszuzczcdt0(v0) = v1 & $i(v1) &
% 92.58/13.18 | | | | | | | | sdtlseqdt0(v1, all_90_1) & aElementOf0(v0,
% 92.58/13.18 | | | | | | | | szNzAzT0))))
% 92.58/13.18 | | | | | | | |
% 92.58/13.18 | | | | | | | | BETA: splitting (109) gives:
% 92.58/13.18 | | | | | | | |
% 92.58/13.18 | | | | | | | | Case 1:
% 92.58/13.18 | | | | | | | | |
% 92.58/13.18 | | | | | | | | | (110) all_90_0 = slcrc0
% 92.58/13.18 | | | | | | | | |
% 92.58/13.18 | | | | | | | | | REDUCE: (106), (110) imply:
% 92.58/13.18 | | | | | | | | | (111) $false
% 92.58/13.18 | | | | | | | | |
% 92.58/13.18 | | | | | | | | | CLOSE: (111) is inconsistent.
% 92.58/13.18 | | | | | | | | |
% 92.58/13.18 | | | | | | | | Case 2:
% 92.58/13.18 | | | | | | | | |
% 92.58/13.18 | | | | | | | | |
% 92.58/13.18 | | | | | | | | | GROUND_INST: instantiating (6) with all_219_1, simplifying with
% 92.58/13.18 | | | | | | | | | (98), (100), (103) gives:
% 92.58/13.18 | | | | | | | | | (112) all_219_1 = slcrc0
% 92.58/13.18 | | | | | | | | |
% 92.58/13.18 | | | | | | | | | GROUND_INST: instantiating (44) with all_219_1, all_219_0,
% 92.58/13.18 | | | | | | | | | simplifying with (100), (102) gives:
% 92.58/13.18 | | | | | | | | | (113) all_219_0 = all_73_0 | ~ aElementOf0(all_219_1,
% 92.58/13.18 | | | | | | | | | all_73_1)
% 92.58/13.18 | | | | | | | | |
% 92.58/13.18 | | | | | | | | | BETA: splitting (113) gives:
% 92.58/13.18 | | | | | | | | |
% 92.58/13.18 | | | | | | | | | Case 1:
% 92.58/13.18 | | | | | | | | | |
% 92.58/13.18 | | | | | | | | | | (114) ~ aElementOf0(all_219_1, all_73_1)
% 92.58/13.18 | | | | | | | | | |
% 92.58/13.18 | | | | | | | | | | REDUCE: (50), (112), (114) imply:
% 92.58/13.18 | | | | | | | | | | (115) ~ aElementOf0(slcrc0, all_67_0)
% 92.58/13.18 | | | | | | | | | |
% 92.58/13.18 | | | | | | | | | | PRED_UNIFY: (29), (115) imply:
% 92.58/13.18 | | | | | | | | | | (116) $false
% 92.58/13.18 | | | | | | | | | |
% 92.58/13.18 | | | | | | | | | | CLOSE: (116) is inconsistent.
% 92.58/13.18 | | | | | | | | | |
% 92.58/13.18 | | | | | | | | | Case 2:
% 92.58/13.18 | | | | | | | | | |
% 92.58/13.18 | | | | | | | | | | (117) all_219_0 = all_73_0
% 92.58/13.18 | | | | | | | | | |
% 92.58/13.18 | | | | | | | | | | REDUCE: (97), (117) imply:
% 92.58/13.18 | | | | | | | | | | (118) $false
% 92.58/13.18 | | | | | | | | | |
% 92.58/13.18 | | | | | | | | | | CLOSE: (118) is inconsistent.
% 92.58/13.18 | | | | | | | | | |
% 92.58/13.18 | | | | | | | | | End of split
% 92.58/13.18 | | | | | | | | |
% 92.58/13.18 | | | | | | | | End of split
% 92.58/13.18 | | | | | | | |
% 92.58/13.18 | | | | | | | End of split
% 92.58/13.18 | | | | | | |
% 92.58/13.18 | | | | | | End of split
% 92.58/13.18 | | | | | |
% 92.58/13.18 | | | | | End of split
% 92.58/13.18 | | | | |
% 92.58/13.18 | | | | End of split
% 92.58/13.18 | | | |
% 92.58/13.18 | | | End of split
% 92.58/13.18 | | |
% 92.58/13.18 | | End of split
% 92.58/13.18 | |
% 92.58/13.18 | Case 2:
% 92.58/13.18 | |
% 92.58/13.18 | | (119) ~ aSet0(slcrc0)
% 92.58/13.18 | |
% 92.58/13.18 | | PRED_UNIFY: (28), (119) imply:
% 92.58/13.18 | | (120) $false
% 92.58/13.18 | |
% 92.58/13.18 | | CLOSE: (120) is inconsistent.
% 92.58/13.18 | |
% 92.58/13.18 | End of split
% 92.58/13.18 |
% 92.58/13.18 End of proof
% 92.58/13.18 % SZS output end Proof for theBenchmark
% 92.58/13.18
% 92.58/13.18 12578ms
%------------------------------------------------------------------------------