TSTP Solution File: NUM630+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM630+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 11:49:06 EDT 2023
% Result : Theorem 22.55s 3.78s
% Output : Proof 55.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM630+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n031.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 12:37:37 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (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.
% 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.51/1.38 Prover 1: Preprocessing ...
% 4.51/1.38 Prover 4: Preprocessing ...
% 4.51/1.42 Prover 0: Preprocessing ...
% 4.51/1.42 Prover 2: Preprocessing ...
% 4.51/1.42 Prover 6: Preprocessing ...
% 4.51/1.42 Prover 3: Preprocessing ...
% 4.51/1.43 Prover 5: Preprocessing ...
% 14.30/2.67 Prover 1: Constructing countermodel ...
% 14.30/2.68 Prover 6: Proving ...
% 14.30/2.69 Prover 3: Constructing countermodel ...
% 15.41/2.80 Prover 5: Proving ...
% 16.32/2.92 Prover 2: Proving ...
% 18.61/3.34 Prover 4: Constructing countermodel ...
% 21.03/3.61 Prover 0: Proving ...
% 22.55/3.78 Prover 3: proved (3161ms)
% 22.55/3.78
% 22.55/3.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.55/3.78
% 22.55/3.78 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 22.55/3.79 Prover 5: stopped
% 22.55/3.79 Prover 2: stopped
% 22.55/3.79 Prover 6: stopped
% 22.96/3.82 Prover 0: stopped
% 22.96/3.82 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 22.96/3.82 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 22.96/3.83 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 22.96/3.84 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 24.05/4.04 Prover 7: Preprocessing ...
% 24.05/4.06 Prover 8: Preprocessing ...
% 25.12/4.12 Prover 13: Preprocessing ...
% 25.12/4.15 Prover 10: Preprocessing ...
% 25.12/4.16 Prover 11: Preprocessing ...
% 26.87/4.34 Prover 10: Constructing countermodel ...
% 26.87/4.38 Prover 7: Constructing countermodel ...
% 27.41/4.44 Prover 8: Warning: ignoring some quantifiers
% 27.41/4.46 Prover 8: Constructing countermodel ...
% 28.44/4.53 Prover 13: Warning: ignoring some quantifiers
% 28.44/4.56 Prover 13: Constructing countermodel ...
% 33.77/5.23 Prover 11: Constructing countermodel ...
% 54.20/7.96 Prover 7: Found proof (size 201)
% 54.20/7.96 Prover 7: proved (4174ms)
% 54.20/7.96 Prover 8: stopped
% 54.20/7.96 Prover 1: stopped
% 54.20/7.96 Prover 11: stopped
% 54.20/7.96 Prover 13: stopped
% 54.20/7.96 Prover 4: stopped
% 54.20/7.96 Prover 10: stopped
% 54.20/7.96
% 54.20/7.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 54.20/7.96
% 54.20/7.98 % SZS output start Proof for theBenchmark
% 54.20/7.99 Assumptions after simplification:
% 54.20/7.99 ---------------------------------
% 54.20/7.99
% 54.20/7.99 (mCountNFin_01)
% 54.20/7.99 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0))
% 54.20/7.99
% 54.20/7.99 (mDefEmp)
% 54.20/8.00 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~
% 54.20/8.00 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : (
% 54.20/8.00 ~ $i(v0) | ~ aElementOf0(v0, slcrc0))
% 54.20/8.00
% 54.20/8.00 (mDefSeg)
% 54.20/8.02 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 54.20/8.02 (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 54.20/8.02 ~ $i(v0) | ~ sdtlseqdt0(v3, v0) | ~ aElementOf0(v2, szNzAzT0) | ~
% 54.20/8.02 aElementOf0(v0, szNzAzT0) | aElementOf0(v2, v1)) & ! [v0: $i] : ! [v1: $i]
% 54.20/8.02 : ! [v2: $i] : ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) =
% 54.20/8.02 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~
% 54.20/8.02 aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v3, v0)) & ! [v0: $i] : ! [v1: $i]
% 54.20/8.02 : ! [v2: $i] : ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) =
% 54.20/8.02 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~
% 54.20/8.02 aElementOf0(v0, szNzAzT0) | aElementOf0(v2, szNzAzT0)) & ! [v0: $i] : !
% 54.20/8.02 [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slbdtrb0(v0) = v1) | ~ $i(v2) | ~
% 54.20/8.02 $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v2) | ? [v3: $i] : ? [v4:
% 54.20/8.02 $i] : ($i(v3) & ( ~ aElementOf0(v3, v2) | ~ aElementOf0(v3, szNzAzT0) |
% 54.20/8.02 (szszuzczcdt0(v3) = v4 & $i(v4) & ~ sdtlseqdt0(v4, v0))) &
% 54.20/8.02 (aElementOf0(v3, v2) | (szszuzczcdt0(v3) = v4 & $i(v4) & sdtlseqdt0(v4,
% 54.20/8.02 v0) & aElementOf0(v3, szNzAzT0))))) & ! [v0: $i] : ! [v1: $i] : (
% 54.20/8.02 ~ (slbdtrb0(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0)
% 54.20/8.02 | aSet0(v1))
% 54.20/8.02
% 54.20/8.02 (mSegZero)
% 54.20/8.02 slbdtrb0(sz00) = slcrc0 & $i(sz00) & $i(slcrc0)
% 54.20/8.02
% 54.20/8.02 (mZeroNum)
% 54.20/8.02 $i(sz00) & $i(szNzAzT0) & aElementOf0(sz00, szNzAzT0)
% 54.20/8.02
% 54.20/8.03 (m__)
% 54.20/8.03 $i(xn) & $i(xP) & $i(xC) & $i(xN) & $i(xc) & ? [v0: $i] : ? [v1: $i] : ?
% 54.20/8.03 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ( ~ (v5 = v3) &
% 54.20/8.03 sdtlpdtrp0(v4, xP) = v5 & sdtlpdtrp0(xC, xn) = v4 & sdtlpdtrp0(xN, xn) = v0
% 54.20/8.03 & sdtlpdtrp0(xc, v2) = v3 & szmzizndt0(v0) = v1 & sdtpldt0(xP, v1) = v2 &
% 54.20/8.03 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 54.20/8.03
% 54.20/8.03 (m__3623)
% 54.20/8.03 sdtlpdtrp0(xN, sz00) = xS & szDzozmdt0(xN) = szNzAzT0 & $i(xN) & $i(xS) &
% 54.20/8.03 $i(sz00) & $i(szNzAzT0) & aFunction0(xN) & ! [v0: $i] : ! [v1: $i] : ( ~
% 54.20/8.03 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~
% 54.20/8.03 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i]
% 54.20/8.03 : ? [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xN, v2) = v3 & szmzizndt0(v1) = v4
% 54.20/8.03 & szszuzczcdt0(v0) = v2 & sdtmndt0(v1, v4) = v5 & $i(v5) & $i(v4) & $i(v3)
% 54.20/8.03 & $i(v2) & aSubsetOf0(v3, v5) & isCountable0(v3))) & ! [v0: $i] : ! [v1:
% 54.20/8.03 $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0)
% 54.20/8.03 | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xN,
% 54.20/8.03 v0) = v2 & $i(v2) & ( ~ aSubsetOf0(v2, szNzAzT0) | ~ isCountable0(v2) |
% 54.20/8.03 (sdtlpdtrp0(xN, v1) = v3 & szmzizndt0(v2) = v4 & sdtmndt0(v2, v4) = v5 &
% 54.20/8.03 $i(v5) & $i(v4) & $i(v3) & aSubsetOf0(v3, v5) & isCountable0(v3)))))
% 54.20/8.03
% 54.20/8.03 (m__3965)
% 54.20/8.03 $i(xN) & $i(xk) & $i(xS) & $i(xK) & $i(szNzAzT0) & ? [v0: $i] :
% 54.20/8.03 (slbdtsldtrb0(xS, xK) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 54.20/8.03 (sdtlpdtrp0(xN, v1) = v2) | ~ $i(v1) | ~ aElementOf0(v1, szNzAzT0) | ?
% 54.20/8.03 [v3: $i] : ? [v4: $i] : ? [v5: $i] : (slbdtsldtrb0(v4, xk) = v5 &
% 54.20/8.03 szmzizndt0(v2) = v3 & sdtmndt0(v2, v3) = v4 & $i(v5) & $i(v4) & $i(v3) &
% 54.20/8.03 ! [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~
% 54.20/8.03 aElementOf0(v6, v5) | ~ aSet0(v6) | aElementOf0(v7, v0)))))
% 54.20/8.03
% 54.20/8.03 (m__4151)
% 55.25/8.04 szDzozmdt0(xC) = szNzAzT0 & $i(xC) & $i(xN) & $i(xk) & $i(xc) & $i(szNzAzT0) &
% 55.25/8.04 aFunction0(xC) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xC, v0) = v1) |
% 55.25/8.04 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | aFunction0(v1)) & ! [v0: $i] : !
% 55.25/8.04 [v1: $i] : ( ~ (sdtlpdtrp0(xC, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0,
% 55.25/8.04 szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 55.25/8.04 (sdtlpdtrp0(xN, v0) = v3 & szDzozmdt0(v1) = v2 & slbdtsldtrb0(v5, xk) = v2 &
% 55.25/8.04 szmzizndt0(v3) = v4 & sdtmndt0(v3, v4) = v5 & $i(v5) & $i(v4) & $i(v3) &
% 55.25/8.04 $i(v2) & ! [v6: $i] : ! [v7: $i] : ( ~ (sdtlpdtrp0(v1, v6) = v7) | ~
% 55.25/8.04 $i(v6) | ~ aElementOf0(v6, v2) | ~ aSet0(v6) | ? [v8: $i] :
% 55.25/8.04 (sdtlpdtrp0(xc, v8) = v7 & sdtpldt0(v6, v4) = v8 & $i(v8) & $i(v7))) &
% 55.25/8.04 ! [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, v4) = v7) | ~ $i(v6) | ~
% 55.25/8.04 aElementOf0(v6, v2) | ~ aSet0(v6) | ? [v8: $i] : (sdtlpdtrp0(v1, v6) =
% 55.25/8.04 v8 & sdtlpdtrp0(xc, v7) = v8 & $i(v8))))) & ! [v0: $i] : ! [v1: $i]
% 55.25/8.04 : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) |
% 55.25/8.04 ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xC, v0) =
% 55.25/8.04 v2 & szDzozmdt0(v2) = v3 & slbdtsldtrb0(v5, xk) = v3 & szmzizndt0(v1) = v4
% 55.25/8.04 & sdtmndt0(v1, v4) = v5 & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 55.25/8.04 aFunction0(v2) & ! [v6: $i] : ! [v7: $i] : ( ~ (sdtlpdtrp0(v2, v6) = v7)
% 55.25/8.04 | ~ $i(v6) | ~ aElementOf0(v6, v3) | ~ aSet0(v6) | ? [v8: $i] :
% 55.25/8.04 (sdtlpdtrp0(xc, v8) = v7 & sdtpldt0(v6, v4) = v8 & $i(v8) & $i(v7))) &
% 55.25/8.04 ! [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, v4) = v7) | ~ $i(v6) | ~
% 55.25/8.04 aElementOf0(v6, v3) | ~ aSet0(v6) | ? [v8: $i] : (sdtlpdtrp0(v2, v6) =
% 55.25/8.04 v8 & sdtlpdtrp0(xc, v7) = v8 & $i(v8)))))
% 55.25/8.04
% 55.25/8.04 (m__4182)
% 55.25/8.04 $i(xC) & $i(xT) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 55.25/8.04 (sdtlpdtrp0(xC, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ?
% 55.25/8.04 [v2: $i] : ? [v3: $i] : (sdtlcdtrc0(v1, v2) = v3 & szDzozmdt0(v1) = v2 &
% 55.25/8.04 $i(v3) & $i(v2) & aSubsetOf0(v3, xT)))
% 55.25/8.04
% 55.25/8.04 (m__4331)
% 55.25/8.05 $i(xN) & $i(xk) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 55.25/8.05 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ?
% 55.25/8.05 [v2: $i] : ? [v3: $i] : ? [v4: $i] : (slbdtsldtrb0(v3, xk) = v4 &
% 55.25/8.05 szmzizndt0(v1) = v2 & sdtmndt0(v1, v2) = v3 & $i(v4) & $i(v3) & $i(v2) &
% 55.25/8.05 ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (slbdtsldtrb0(v5, xk) = v6) |
% 55.25/8.05 ~ $i(v7) | ~ $i(v5) | ~ aSubsetOf0(v5, v3) | ~ isCountable0(v5) | ~
% 55.25/8.05 aElementOf0(v7, v6) | ~ aSet0(v7) | aElementOf0(v7, v4))))
% 55.25/8.05
% 55.25/8.05 (m__4411)
% 55.25/8.05 $i(xC) & $i(xN) & $i(xk) & $i(xT) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] :
% 55.25/8.05 ( ~ (sdtlpdtrp0(xC, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ?
% 55.25/8.05 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7:
% 55.25/8.05 $i] : (sdtlpdtrp0(xN, v0) = v2 & slbdtsldtrb0(v6, xk) = v7 &
% 55.25/8.05 szmzizndt0(v2) = v3 & sdtmndt0(v2, v3) = v4 & $i(v7) & $i(v6) & $i(v5) &
% 55.25/8.05 $i(v4) & $i(v3) & $i(v2) & aSubsetOf0(v6, v4) & isCountable0(v6) &
% 55.25/8.05 aElementOf0(v5, xT) & ! [v8: $i] : ! [v9: $i] : (v9 = v5 | ~
% 55.25/8.05 (sdtlpdtrp0(v1, v8) = v9) | ~ $i(v8) | ~ aElementOf0(v8, v7) | ~
% 55.25/8.05 aSet0(v8)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1)
% 55.25/8.05 | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ?
% 55.25/8.05 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (sdtlpdtrp0(xC, v0) =
% 55.25/8.05 v4 & slbdtsldtrb0(v6, xk) = v7 & szmzizndt0(v1) = v2 & sdtmndt0(v1, v2) =
% 55.25/8.05 v3 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & aSubsetOf0(v6,
% 55.25/8.05 v3) & isCountable0(v6) & aElementOf0(v5, xT) & ! [v8: $i] : ! [v9: $i]
% 55.25/8.05 : (v9 = v5 | ~ (sdtlpdtrp0(v4, v8) = v9) | ~ $i(v8) | ~ aElementOf0(v8,
% 55.25/8.05 v7) | ~ aSet0(v8))))
% 55.25/8.05
% 55.25/8.05 (m__4618)
% 55.25/8.05 $i(xC) & $i(xN) & $i(xk) & $i(xT) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] :
% 55.25/8.05 ( ~ (sdtlpdtrp0(xC, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ?
% 55.25/8.05 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xN, v2) =
% 55.25/8.05 v3 & slbdtsldtrb0(v3, xk) = v4 & szszuzczcdt0(v0) = v2 & $i(v5) & $i(v4) &
% 55.25/8.05 $i(v3) & $i(v2) & aElementOf0(v5, xT) & ! [v6: $i] : ! [v7: $i] : (v7 =
% 55.25/8.05 v5 | ~ (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v4) |
% 55.25/8.05 ~ aSet0(v6)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) =
% 55.25/8.05 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i]
% 55.25/8.05 : ? [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xC, v0) = v4 & sdtlpdtrp0(xN, v1)
% 55.25/8.05 = v2 & slbdtsldtrb0(v2, xk) = v3 & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 55.25/8.06 aElementOf0(v5, xT) & ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~
% 55.25/8.06 (sdtlpdtrp0(v4, v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v3) | ~
% 55.25/8.06 aSet0(v6))))
% 55.25/8.06
% 55.25/8.06 (m__4660)
% 55.25/8.06 szDzozmdt0(xe) = szNzAzT0 & $i(xe) & $i(xN) & $i(szNzAzT0) & aFunction0(xe) &
% 55.25/8.06 ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) | ~
% 55.25/8.06 aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2 &
% 55.25/8.06 szmzizndt0(v2) = v1 & $i(v2) & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 55.25/8.06 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ?
% 55.25/8.06 [v2: $i] : (sdtlpdtrp0(xe, v0) = v2 & szmzizndt0(v1) = v2 & $i(v2)))
% 55.25/8.06
% 55.25/8.06 (m__4730)
% 55.25/8.06 szDzozmdt0(xd) = szNzAzT0 & $i(xd) & $i(xC) & $i(xN) & $i(xk) & $i(szNzAzT0) &
% 55.25/8.06 aFunction0(xd) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) = v1) |
% 55.25/8.06 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ?
% 55.25/8.06 [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xC, v0) = v5 & sdtlpdtrp0(xN, v2) = v3
% 55.25/8.06 & slbdtsldtrb0(v3, xk) = v4 & szszuzczcdt0(v0) = v2 & $i(v5) & $i(v4) &
% 55.25/8.06 $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] : (v7 = v1 | ~
% 55.25/8.06 (sdtlpdtrp0(v5, v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v4) | ~
% 55.25/8.06 aSet0(v6)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xC, v0) = v1)
% 55.25/8.06 | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ?
% 55.25/8.06 [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xd, v0) = v5 & sdtlpdtrp0(xN, v2) = v3
% 55.25/8.06 & slbdtsldtrb0(v3, xk) = v4 & szszuzczcdt0(v0) = v2 & $i(v5) & $i(v4) &
% 55.25/8.06 $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~
% 55.25/8.06 (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v4) | ~
% 55.25/8.06 aSet0(v6)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) |
% 55.25/8.06 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ?
% 55.25/8.06 [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xd, v0) = v4 & sdtlpdtrp0(xC, v0) = v5
% 55.25/8.06 & sdtlpdtrp0(xN, v1) = v2 & slbdtsldtrb0(v2, xk) = v3 & $i(v5) & $i(v4) &
% 55.25/8.06 $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] : (v7 = v4 | ~
% 55.25/8.06 (sdtlpdtrp0(v5, v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v3) | ~
% 55.25/8.06 aSet0(v6))))
% 55.25/8.06
% 55.25/8.06 (m__4891)
% 55.25/8.06 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 &
% 55.25/8.06 sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) &
% 55.25/8.06 aSet0(xO))
% 55.25/8.06
% 55.25/8.06 (m__4908)
% 55.25/8.06 $i(xO) & isCountable0(xO) & aSet0(xO)
% 55.25/8.06
% 55.25/8.06 (m__5164)
% 55.25/8.06 $i(xP) & $i(xQ) & ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP &
% 55.25/8.06 $i(v0) & aSet0(xP))
% 55.25/8.06
% 55.25/8.06 (m__5270)
% 55.25/8.06 $i(xP) & $i(xO) & $i(xk) & ? [v0: $i] : (slbdtsldtrb0(xO, xk) = v0 & $i(v0) &
% 55.25/8.06 aElementOf0(xP, v0))
% 55.25/8.06
% 55.25/8.06 (m__5309)
% 55.25/8.06 $i(xn) & $i(xp) & $i(xd) & $i(xe) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] :
% 55.25/8.07 (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = v1 & sdtlpdtrp0(xe, xn) = xp &
% 55.25/8.07 $i(v1) & $i(v0) & aElementOf0(xn, v1) & aElementOf0(xn, szNzAzT0))
% 55.25/8.07
% 55.25/8.07 (m__5321)
% 55.25/8.07 $i(xn) & $i(xd) & ? [v0: $i] : (szDzizrdt0(xd) = v0 & sdtlpdtrp0(xd, xn) = v0
% 55.25/8.07 & $i(v0))
% 55.25/8.07
% 55.43/8.07 (m__5334)
% 55.43/8.07 $i(xn) & $i(xP) & $i(xN) & ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, v0) =
% 55.43/8.07 v1 & szszuzczcdt0(xn) = v0 & $i(v1) & $i(v0) & aSubsetOf0(xP, v1))
% 55.43/8.07
% 55.43/8.07 (m__5585)
% 55.43/8.07 $i(xD) & $i(xn) & $i(xN) & ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xn) =
% 55.43/8.07 v0 & szmzizndt0(v0) = v1 & sdtmndt0(v0, v1) = xD & $i(v1) & $i(v0))
% 55.43/8.07
% 55.43/8.07 (m__5599)
% 55.43/8.07 $i(xD) & $i(xP) & $i(xk) & ? [v0: $i] : (slbdtsldtrb0(xD, xk) = v0 & $i(v0) &
% 55.43/8.07 aElementOf0(xP, v0))
% 55.43/8.07
% 55.43/8.07 (function-axioms)
% 55.43/8.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 55.43/8.07 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 55.43/8.07 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 55.43/8.07 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 55.43/8.07 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 55.43/8.07 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 55.43/8.07 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 55.43/8.07 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 55.43/8.07 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 55.43/8.07 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~
% 55.43/8.07 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 55.43/8.07 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) &
% 55.43/8.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 55.43/8.07 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 55.43/8.07 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 55.43/8.07 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 55.43/8.07 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 55.43/8.07 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 55.43/8.07 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 55.43/8.07 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 55.43/8.07 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 55.43/8.07 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 55.43/8.07 v0))
% 55.43/8.07
% 55.43/8.07 Further assumptions not needed in the proof:
% 55.43/8.07 --------------------------------------------
% 55.43/8.07 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 55.43/8.07 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons,
% 55.43/8.07 mDefDiff, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSel, mDefSub,
% 55.43/8.07 mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet,
% 55.43/8.07 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm,
% 55.43/8.07 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans,
% 55.43/8.07 mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess,
% 55.43/8.07 mSegSucc, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, mSubASymm,
% 55.43/8.07 mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess,
% 55.43/8.07 m__3291, m__3398, m__3418, m__3435, m__3453, m__3462, m__3520, m__3533, m__3671,
% 55.43/8.07 m__3754, m__3821, m__4758, m__4854, m__4982, m__4998, m__5078, m__5093, m__5106,
% 55.43/8.07 m__5116, m__5147, m__5173, m__5182, m__5195, m__5208, m__5217
% 55.43/8.07
% 55.43/8.07 Those formulas are unsatisfiable:
% 55.43/8.07 ---------------------------------
% 55.43/8.07
% 55.43/8.07 Begin of proof
% 55.43/8.07 |
% 55.43/8.07 | ALPHA: (mDefEmp) implies:
% 55.43/8.07 | (1) aSet0(slcrc0)
% 55.43/8.07 |
% 55.43/8.07 | ALPHA: (mCountNFin_01) implies:
% 55.43/8.07 | (2) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)
% 55.43/8.07 |
% 55.43/8.07 | ALPHA: (mZeroNum) implies:
% 55.43/8.07 | (3) aElementOf0(sz00, szNzAzT0)
% 55.43/8.07 |
% 55.43/8.07 | ALPHA: (mDefSeg) implies:
% 55.43/8.08 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slbdtrb0(v0) =
% 55.43/8.08 | v1) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ~
% 55.43/8.08 | aSet0(v2) | ? [v3: $i] : ? [v4: $i] : ($i(v3) & ( ~ aElementOf0(v3,
% 55.43/8.08 | v2) | ~ aElementOf0(v3, szNzAzT0) | (szszuzczcdt0(v3) = v4 &
% 55.43/8.08 | $i(v4) & ~ sdtlseqdt0(v4, v0))) & (aElementOf0(v3, v2) |
% 55.43/8.08 | (szszuzczcdt0(v3) = v4 & $i(v4) & sdtlseqdt0(v4, v0) &
% 55.43/8.08 | aElementOf0(v3, szNzAzT0)))))
% 55.43/8.08 |
% 55.43/8.08 | ALPHA: (mSegZero) implies:
% 55.43/8.08 | (5) slbdtrb0(sz00) = slcrc0
% 55.43/8.08 |
% 55.43/8.08 | ALPHA: (m__3623) implies:
% 55.43/8.08 | (6) $i(sz00)
% 55.43/8.08 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) |
% 55.43/8.08 | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 55.43/8.08 | : ? [v5: $i] : (sdtlpdtrp0(xN, v0) = v2 & $i(v2) & ( ~
% 55.43/8.08 | aSubsetOf0(v2, szNzAzT0) | ~ isCountable0(v2) | (sdtlpdtrp0(xN,
% 55.43/8.08 | v1) = v3 & szmzizndt0(v2) = v4 & sdtmndt0(v2, v4) = v5 &
% 55.43/8.08 | $i(v5) & $i(v4) & $i(v3) & aSubsetOf0(v3, v5) &
% 55.43/8.08 | isCountable0(v3)))))
% 55.43/8.08 |
% 55.43/8.08 | ALPHA: (m__3965) implies:
% 55.43/8.08 | (8) ? [v0: $i] : (slbdtsldtrb0(xS, xK) = v0 & $i(v0) & ! [v1: $i] : !
% 55.43/8.08 | [v2: $i] : ( ~ (sdtlpdtrp0(xN, v1) = v2) | ~ $i(v1) | ~
% 55.43/8.08 | aElementOf0(v1, szNzAzT0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i]
% 55.43/8.08 | : (slbdtsldtrb0(v4, xk) = v5 & szmzizndt0(v2) = v3 & sdtmndt0(v2,
% 55.43/8.08 | v3) = v4 & $i(v5) & $i(v4) & $i(v3) & ! [v6: $i] : ! [v7: $i]
% 55.43/8.08 | : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~ aElementOf0(v6,
% 55.43/8.08 | v5) | ~ aSet0(v6) | aElementOf0(v7, v0)))))
% 55.43/8.08 |
% 55.43/8.08 | ALPHA: (m__4151) implies:
% 55.43/8.08 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) |
% 55.43/8.08 | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ? [v4:
% 55.43/8.08 | $i] : ? [v5: $i] : (sdtlpdtrp0(xC, v0) = v2 & szDzozmdt0(v2) = v3
% 55.43/8.08 | & slbdtsldtrb0(v5, xk) = v3 & szmzizndt0(v1) = v4 & sdtmndt0(v1,
% 55.43/8.08 | v4) = v5 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & aFunction0(v2) &
% 55.43/8.08 | ! [v6: $i] : ! [v7: $i] : ( ~ (sdtlpdtrp0(v2, v6) = v7) | ~
% 55.43/8.08 | $i(v6) | ~ aElementOf0(v6, v3) | ~ aSet0(v6) | ? [v8: $i] :
% 55.43/8.08 | (sdtlpdtrp0(xc, v8) = v7 & sdtpldt0(v6, v4) = v8 & $i(v8) &
% 55.43/8.08 | $i(v7))) & ! [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, v4) =
% 55.43/8.08 | v7) | ~ $i(v6) | ~ aElementOf0(v6, v3) | ~ aSet0(v6) | ?
% 55.43/8.08 | [v8: $i] : (sdtlpdtrp0(v2, v6) = v8 & sdtlpdtrp0(xc, v7) = v8 &
% 55.43/8.08 | $i(v8)))))
% 55.43/8.08 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xC, v0) = v1) | ~ $i(v0)
% 55.43/8.08 | | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ? [v4:
% 55.43/8.08 | $i] : ? [v5: $i] : (sdtlpdtrp0(xN, v0) = v3 & szDzozmdt0(v1) = v2
% 55.43/8.08 | & slbdtsldtrb0(v5, xk) = v2 & szmzizndt0(v3) = v4 & sdtmndt0(v3,
% 55.43/8.08 | v4) = v5 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & ! [v6: $i] : !
% 55.43/8.08 | [v7: $i] : ( ~ (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~
% 55.43/8.08 | aElementOf0(v6, v2) | ~ aSet0(v6) | ? [v8: $i] :
% 55.43/8.08 | (sdtlpdtrp0(xc, v8) = v7 & sdtpldt0(v6, v4) = v8 & $i(v8) &
% 55.43/8.08 | $i(v7))) & ! [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, v4) =
% 55.43/8.08 | v7) | ~ $i(v6) | ~ aElementOf0(v6, v2) | ~ aSet0(v6) | ?
% 55.43/8.08 | [v8: $i] : (sdtlpdtrp0(v1, v6) = v8 & sdtlpdtrp0(xc, v7) = v8 &
% 55.43/8.08 | $i(v8)))))
% 55.43/8.08 |
% 55.43/8.08 | ALPHA: (m__4182) implies:
% 55.43/8.08 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xC, v0) = v1) | ~ $i(v0)
% 55.43/8.08 | | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] :
% 55.43/8.08 | (sdtlcdtrc0(v1, v2) = v3 & szDzozmdt0(v1) = v2 & $i(v3) & $i(v2) &
% 55.43/8.08 | aSubsetOf0(v3, xT)))
% 55.43/8.08 |
% 55.43/8.08 | ALPHA: (m__4331) implies:
% 55.43/8.08 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0)
% 55.43/8.08 | | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ? [v4:
% 55.43/8.08 | $i] : (slbdtsldtrb0(v3, xk) = v4 & szmzizndt0(v1) = v2 &
% 55.43/8.08 | sdtmndt0(v1, v2) = v3 & $i(v4) & $i(v3) & $i(v2) & ! [v5: $i] :
% 55.43/8.08 | ! [v6: $i] : ! [v7: $i] : ( ~ (slbdtsldtrb0(v5, xk) = v6) | ~
% 55.43/8.08 | $i(v7) | ~ $i(v5) | ~ aSubsetOf0(v5, v3) | ~ isCountable0(v5)
% 55.43/8.08 | | ~ aElementOf0(v7, v6) | ~ aSet0(v7) | aElementOf0(v7, v4))))
% 55.43/8.08 |
% 55.43/8.08 | ALPHA: (m__4411) implies:
% 55.43/8.09 | (13) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0)
% 55.43/8.09 | | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ? [v4:
% 55.43/8.09 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (sdtlpdtrp0(xC,
% 55.43/8.09 | v0) = v4 & slbdtsldtrb0(v6, xk) = v7 & szmzizndt0(v1) = v2 &
% 55.43/8.09 | sdtmndt0(v1, v2) = v3 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3)
% 55.43/8.09 | & $i(v2) & aSubsetOf0(v6, v3) & isCountable0(v6) & aElementOf0(v5,
% 55.43/8.09 | xT) & ! [v8: $i] : ! [v9: $i] : (v9 = v5 | ~ (sdtlpdtrp0(v4,
% 55.43/8.09 | v8) = v9) | ~ $i(v8) | ~ aElementOf0(v8, v7) | ~
% 55.43/8.09 | aSet0(v8))))
% 55.43/8.09 | (14) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xC, v0) = v1) | ~ $i(v0)
% 55.43/8.09 | | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ? [v4:
% 55.43/8.09 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (sdtlpdtrp0(xN,
% 55.43/8.09 | v0) = v2 & slbdtsldtrb0(v6, xk) = v7 & szmzizndt0(v2) = v3 &
% 55.43/8.09 | sdtmndt0(v2, v3) = v4 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3)
% 55.43/8.09 | & $i(v2) & aSubsetOf0(v6, v4) & isCountable0(v6) & aElementOf0(v5,
% 55.43/8.09 | xT) & ! [v8: $i] : ! [v9: $i] : (v9 = v5 | ~ (sdtlpdtrp0(v1,
% 55.43/8.09 | v8) = v9) | ~ $i(v8) | ~ aElementOf0(v8, v7) | ~
% 55.43/8.09 | aSet0(v8))))
% 55.43/8.09 |
% 55.43/8.09 | ALPHA: (m__4618) implies:
% 55.43/8.09 | (15) ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) |
% 55.43/8.09 | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ? [v4:
% 55.43/8.09 | $i] : ? [v5: $i] : (sdtlpdtrp0(xC, v0) = v4 & sdtlpdtrp0(xN, v1)
% 55.43/8.09 | = v2 & slbdtsldtrb0(v2, xk) = v3 & $i(v5) & $i(v4) & $i(v3) &
% 55.43/8.09 | $i(v2) & aElementOf0(v5, xT) & ! [v6: $i] : ! [v7: $i] : (v7 =
% 55.43/8.09 | v5 | ~ (sdtlpdtrp0(v4, v6) = v7) | ~ $i(v6) | ~
% 55.43/8.09 | aElementOf0(v6, v3) | ~ aSet0(v6))))
% 55.43/8.09 |
% 55.43/8.09 | ALPHA: (m__4660) implies:
% 55.43/8.09 | (16) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0)
% 55.43/8.09 | | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xe, v0) =
% 55.43/8.09 | v2 & szmzizndt0(v1) = v2 & $i(v2)))
% 55.43/8.09 | (17) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0)
% 55.43/8.09 | | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) =
% 55.43/8.09 | v2 & szmzizndt0(v2) = v1 & $i(v2) & $i(v1)))
% 55.43/8.09 |
% 55.43/8.09 | ALPHA: (m__4730) implies:
% 55.43/8.09 | (18) ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) |
% 55.43/8.09 | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ? [v4:
% 55.43/8.09 | $i] : ? [v5: $i] : (sdtlpdtrp0(xd, v0) = v4 & sdtlpdtrp0(xC, v0)
% 55.43/8.09 | = v5 & sdtlpdtrp0(xN, v1) = v2 & slbdtsldtrb0(v2, xk) = v3 &
% 55.43/8.09 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] :
% 55.43/8.09 | (v7 = v4 | ~ (sdtlpdtrp0(v5, v6) = v7) | ~ $i(v6) | ~
% 55.43/8.09 | aElementOf0(v6, v3) | ~ aSet0(v6))))
% 55.43/8.09 | (19) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0)
% 55.43/8.09 | | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ? [v4:
% 55.43/8.09 | $i] : ? [v5: $i] : (sdtlpdtrp0(xC, v0) = v5 & sdtlpdtrp0(xN, v2)
% 55.43/8.09 | = v3 & slbdtsldtrb0(v3, xk) = v4 & szszuzczcdt0(v0) = v2 & $i(v5)
% 55.43/8.09 | & $i(v4) & $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] : (v7 = v1
% 55.43/8.09 | | ~ (sdtlpdtrp0(v5, v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6,
% 55.43/8.09 | v4) | ~ aSet0(v6))))
% 55.43/8.09 |
% 55.43/8.09 | ALPHA: (m__4891) implies:
% 55.43/8.09 | (20) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1)
% 55.43/8.09 | = xO & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & aSet0(xO))
% 55.43/8.09 |
% 55.43/8.09 | ALPHA: (m__4908) implies:
% 55.43/8.09 | (21) isCountable0(xO)
% 55.43/8.09 |
% 55.43/8.09 | ALPHA: (m__5164) implies:
% 55.43/8.09 | (22) ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & $i(v0) &
% 55.43/8.09 | aSet0(xP))
% 55.43/8.09 |
% 55.43/8.09 | ALPHA: (m__5270) implies:
% 55.43/8.09 | (23) $i(xO)
% 55.43/8.09 |
% 55.43/8.09 | ALPHA: (m__5309) implies:
% 55.43/8.09 | (24) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0)
% 55.43/8.09 | = v1 & sdtlpdtrp0(xe, xn) = xp & $i(v1) & $i(v0) & aElementOf0(xn,
% 55.43/8.09 | v1) & aElementOf0(xn, szNzAzT0))
% 55.43/8.09 |
% 55.43/8.09 | ALPHA: (m__5321) implies:
% 55.43/8.10 | (25) ? [v0: $i] : (szDzizrdt0(xd) = v0 & sdtlpdtrp0(xd, xn) = v0 & $i(v0))
% 55.43/8.10 |
% 55.43/8.10 | ALPHA: (m__5334) implies:
% 55.43/8.10 | (26) ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, v0) = v1 &
% 55.43/8.10 | szszuzczcdt0(xn) = v0 & $i(v1) & $i(v0) & aSubsetOf0(xP, v1))
% 55.43/8.10 |
% 55.43/8.10 | ALPHA: (m__5585) implies:
% 55.43/8.10 | (27) ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xn) = v0 & szmzizndt0(v0)
% 55.58/8.10 | = v1 & sdtmndt0(v0, v1) = xD & $i(v1) & $i(v0))
% 55.58/8.10 |
% 55.58/8.10 | ALPHA: (m__5599) implies:
% 55.58/8.10 | (28) ? [v0: $i] : (slbdtsldtrb0(xD, xk) = v0 & $i(v0) & aElementOf0(xP,
% 55.58/8.10 | v0))
% 55.58/8.10 |
% 55.58/8.10 | ALPHA: (m__) implies:
% 55.58/8.10 | (29) $i(xP)
% 55.58/8.10 | (30) $i(xn)
% 55.58/8.10 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 55.58/8.10 | ? [v5: $i] : ( ~ (v5 = v3) & sdtlpdtrp0(v4, xP) = v5 & sdtlpdtrp0(xC,
% 55.58/8.10 | xn) = v4 & sdtlpdtrp0(xN, xn) = v0 & sdtlpdtrp0(xc, v2) = v3 &
% 55.58/8.10 | szmzizndt0(v0) = v1 & sdtpldt0(xP, v1) = v2 & $i(v5) & $i(v4) &
% 55.58/8.10 | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 55.58/8.10 |
% 55.58/8.10 | ALPHA: (function-axioms) implies:
% 55.58/8.10 | (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 55.58/8.10 | (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) = v0))
% 55.58/8.10 | (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 55.58/8.10 | (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0))
% 55.58/8.10 | (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 55.58/8.10 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 55.58/8.10 | (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 55.58/8.10 | (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 55.58/8.10 | (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 55.58/8.10 | (slbdtsldtrb0(v3, v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0))
% 55.58/8.10 | (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 55.58/8.10 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0))
% 55.58/8.10 |
% 55.58/8.10 | DELTA: instantiating (28) with fresh symbol all_80_0 gives:
% 55.58/8.10 | (38) slbdtsldtrb0(xD, xk) = all_80_0 & $i(all_80_0) & aElementOf0(xP,
% 55.58/8.10 | all_80_0)
% 55.58/8.10 |
% 55.58/8.10 | ALPHA: (38) implies:
% 55.58/8.10 | (39) aElementOf0(xP, all_80_0)
% 55.58/8.10 | (40) slbdtsldtrb0(xD, xk) = all_80_0
% 55.58/8.10 |
% 55.58/8.10 | DELTA: instantiating (25) with fresh symbol all_84_0 gives:
% 55.58/8.10 | (41) szDzizrdt0(xd) = all_84_0 & sdtlpdtrp0(xd, xn) = all_84_0 &
% 55.58/8.10 | $i(all_84_0)
% 55.58/8.10 |
% 55.58/8.10 | ALPHA: (41) implies:
% 55.58/8.10 | (42) sdtlpdtrp0(xd, xn) = all_84_0
% 55.58/8.10 |
% 55.58/8.10 | DELTA: instantiating (22) with fresh symbol all_86_0 gives:
% 55.58/8.10 | (43) szmzizndt0(xQ) = all_86_0 & sdtmndt0(xQ, all_86_0) = xP & $i(all_86_0)
% 55.58/8.10 | & aSet0(xP)
% 55.58/8.10 |
% 55.58/8.10 | ALPHA: (43) implies:
% 55.58/8.10 | (44) aSet0(xP)
% 55.58/8.10 |
% 55.58/8.10 | DELTA: instantiating (26) with fresh symbols all_90_0, all_90_1 gives:
% 55.58/8.10 | (45) sdtlpdtrp0(xN, all_90_1) = all_90_0 & szszuzczcdt0(xn) = all_90_1 &
% 55.58/8.10 | $i(all_90_0) & $i(all_90_1) & aSubsetOf0(xP, all_90_0)
% 55.58/8.10 |
% 55.58/8.10 | ALPHA: (45) implies:
% 55.58/8.10 | (46) szszuzczcdt0(xn) = all_90_1
% 55.58/8.10 |
% 55.58/8.10 | DELTA: instantiating (27) with fresh symbols all_92_0, all_92_1 gives:
% 55.58/8.10 | (47) sdtlpdtrp0(xN, xn) = all_92_1 & szmzizndt0(all_92_1) = all_92_0 &
% 55.58/8.10 | sdtmndt0(all_92_1, all_92_0) = xD & $i(all_92_0) & $i(all_92_1)
% 55.58/8.10 |
% 55.58/8.10 | ALPHA: (47) implies:
% 55.58/8.10 | (48) sdtmndt0(all_92_1, all_92_0) = xD
% 55.58/8.10 | (49) szmzizndt0(all_92_1) = all_92_0
% 55.58/8.10 | (50) sdtlpdtrp0(xN, xn) = all_92_1
% 55.58/8.10 |
% 55.58/8.10 | DELTA: instantiating (20) with fresh symbols all_96_0, all_96_1 gives:
% 55.58/8.10 | (51) szDzizrdt0(xd) = all_96_1 & sdtlcdtrc0(xe, all_96_0) = xO &
% 55.58/8.10 | sdtlbdtrb0(xd, all_96_1) = all_96_0 & $i(all_96_0) & $i(all_96_1) &
% 55.58/8.10 | aSet0(xO)
% 55.58/8.10 |
% 55.58/8.10 | ALPHA: (51) implies:
% 55.58/8.10 | (52) aSet0(xO)
% 55.58/8.10 |
% 55.58/8.10 | DELTA: instantiating (24) with fresh symbols all_98_0, all_98_1 gives:
% 55.58/8.11 | (53) szDzizrdt0(xd) = all_98_1 & sdtlbdtrb0(xd, all_98_1) = all_98_0 &
% 55.58/8.11 | sdtlpdtrp0(xe, xn) = xp & $i(all_98_0) & $i(all_98_1) &
% 55.58/8.11 | aElementOf0(xn, all_98_0) & aElementOf0(xn, szNzAzT0)
% 55.58/8.11 |
% 55.58/8.11 | ALPHA: (53) implies:
% 55.58/8.11 | (54) aElementOf0(xn, szNzAzT0)
% 55.58/8.11 | (55) sdtlpdtrp0(xe, xn) = xp
% 55.58/8.11 |
% 55.58/8.11 | DELTA: instantiating (31) with fresh symbols all_105_0, all_105_1, all_105_2,
% 55.58/8.11 | all_105_3, all_105_4, all_105_5 gives:
% 55.58/8.11 | (56) ~ (all_105_0 = all_105_2) & sdtlpdtrp0(all_105_1, xP) = all_105_0 &
% 55.58/8.11 | sdtlpdtrp0(xC, xn) = all_105_1 & sdtlpdtrp0(xN, xn) = all_105_5 &
% 55.58/8.11 | sdtlpdtrp0(xc, all_105_3) = all_105_2 & szmzizndt0(all_105_5) =
% 55.58/8.11 | all_105_4 & sdtpldt0(xP, all_105_4) = all_105_3 & $i(all_105_0) &
% 55.58/8.11 | $i(all_105_1) & $i(all_105_2) & $i(all_105_3) & $i(all_105_4) &
% 55.58/8.11 | $i(all_105_5)
% 55.58/8.11 |
% 55.58/8.11 | ALPHA: (56) implies:
% 55.58/8.11 | (57) ~ (all_105_0 = all_105_2)
% 55.58/8.11 | (58) sdtpldt0(xP, all_105_4) = all_105_3
% 55.58/8.11 | (59) szmzizndt0(all_105_5) = all_105_4
% 55.58/8.11 | (60) sdtlpdtrp0(xc, all_105_3) = all_105_2
% 55.58/8.11 | (61) sdtlpdtrp0(xN, xn) = all_105_5
% 55.58/8.11 | (62) sdtlpdtrp0(xC, xn) = all_105_1
% 55.58/8.11 | (63) sdtlpdtrp0(all_105_1, xP) = all_105_0
% 55.58/8.11 |
% 55.58/8.11 | DELTA: instantiating (8) with fresh symbol all_107_0 gives:
% 55.58/8.11 | (64) slbdtsldtrb0(xS, xK) = all_107_0 & $i(all_107_0) & ! [v0: $i] : !
% 55.58/8.11 | [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~
% 55.58/8.11 | aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 55.58/8.11 | : (slbdtsldtrb0(v3, xk) = v4 & szmzizndt0(v1) = v2 & sdtmndt0(v1,
% 55.58/8.11 | v2) = v3 & $i(v4) & $i(v3) & $i(v2) & ! [v5: $i] : ! [v6: $i]
% 55.58/8.11 | : ( ~ (sdtpldt0(v5, v2) = v6) | ~ $i(v5) | ~ aElementOf0(v5, v4)
% 55.58/8.11 | | ~ aSet0(v5) | aElementOf0(v6, all_107_0))))
% 55.58/8.11 |
% 55.58/8.11 | ALPHA: (64) implies:
% 55.58/8.11 | (65) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0)
% 55.58/8.11 | | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ? [v4:
% 55.58/8.11 | $i] : (slbdtsldtrb0(v3, xk) = v4 & szmzizndt0(v1) = v2 &
% 55.58/8.11 | sdtmndt0(v1, v2) = v3 & $i(v4) & $i(v3) & $i(v2) & ! [v5: $i] :
% 55.58/8.11 | ! [v6: $i] : ( ~ (sdtpldt0(v5, v2) = v6) | ~ $i(v5) | ~
% 55.58/8.11 | aElementOf0(v5, v4) | ~ aSet0(v5) | aElementOf0(v6,
% 55.58/8.11 | all_107_0))))
% 55.58/8.11 |
% 55.58/8.11 | BETA: splitting (2) gives:
% 55.58/8.11 |
% 55.58/8.11 | Case 1:
% 55.58/8.11 | |
% 55.58/8.11 | | (66) ~ isCountable0(slcrc0)
% 55.58/8.11 | |
% 55.58/8.11 | | GROUND_INST: instantiating (32) with all_92_0, all_105_4, all_92_1,
% 55.58/8.11 | | simplifying with (49) gives:
% 55.58/8.11 | | (67) all_105_4 = all_92_0 | ~ (szmzizndt0(all_92_1) = all_105_4)
% 55.58/8.11 | |
% 55.58/8.11 | | GROUND_INST: instantiating (37) with all_92_1, all_105_5, xn, xN,
% 55.58/8.11 | | simplifying with (50), (61) gives:
% 55.58/8.11 | | (68) all_105_5 = all_92_1
% 55.58/8.11 | |
% 55.58/8.11 | | PRED_UNIFY: (21), (66) imply:
% 55.58/8.11 | | (69) ~ (xO = slcrc0)
% 55.58/8.11 | |
% 55.58/8.11 | | REDUCE: (59), (68) imply:
% 55.58/8.11 | | (70) szmzizndt0(all_92_1) = all_105_4
% 55.58/8.11 | |
% 55.58/8.11 | | BETA: splitting (67) gives:
% 55.58/8.11 | |
% 55.58/8.11 | | Case 1:
% 55.58/8.11 | | |
% 55.58/8.11 | | | (71) ~ (szmzizndt0(all_92_1) = all_105_4)
% 55.58/8.11 | | |
% 55.58/8.11 | | | PRED_UNIFY: (70), (71) imply:
% 55.58/8.11 | | | (72) $false
% 55.58/8.11 | | |
% 55.58/8.11 | | | CLOSE: (72) is inconsistent.
% 55.58/8.11 | | |
% 55.58/8.11 | | Case 2:
% 55.58/8.11 | | |
% 55.58/8.11 | | | (73) all_105_4 = all_92_0
% 55.58/8.11 | | |
% 55.58/8.11 | | | REDUCE: (58), (73) imply:
% 55.58/8.11 | | | (74) sdtpldt0(xP, all_92_0) = all_105_3
% 55.58/8.11 | | |
% 55.58/8.11 | | | GROUND_INST: instantiating (18) with xn, all_90_1, simplifying with (30),
% 55.58/8.11 | | | (46), (54) gives:
% 55.58/8.12 | | | (75) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 55.58/8.12 | | | (sdtlpdtrp0(xd, xn) = v2 & sdtlpdtrp0(xC, xn) = v3 &
% 55.58/8.12 | | | sdtlpdtrp0(xN, all_90_1) = v0 & slbdtsldtrb0(v0, xk) = v1 &
% 55.58/8.12 | | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] :
% 55.58/8.12 | | | (v5 = v2 | ~ (sdtlpdtrp0(v3, v4) = v5) | ~ $i(v4) | ~
% 55.58/8.12 | | | aElementOf0(v4, v1) | ~ aSet0(v4)))
% 55.58/8.12 | | |
% 55.58/8.12 | | | GROUND_INST: instantiating (15) with xn, all_90_1, simplifying with (30),
% 55.58/8.12 | | | (46), (54) gives:
% 55.58/8.12 | | | (76) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 55.58/8.12 | | | (sdtlpdtrp0(xC, xn) = v2 & sdtlpdtrp0(xN, all_90_1) = v0 &
% 55.58/8.12 | | | slbdtsldtrb0(v0, xk) = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 55.58/8.12 | | | aElementOf0(v3, xT) & ! [v4: $i] : ! [v5: $i] : (v5 = v3 | ~
% 55.58/8.12 | | | (sdtlpdtrp0(v2, v4) = v5) | ~ $i(v4) | ~ aElementOf0(v4, v1)
% 55.58/8.12 | | | | ~ aSet0(v4)))
% 55.58/8.12 | | |
% 55.58/8.12 | | | GROUND_INST: instantiating (7) with xn, all_90_1, simplifying with (30),
% 55.58/8.12 | | | (46), (54) gives:
% 55.58/8.12 | | | (77) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 55.58/8.12 | | | (sdtlpdtrp0(xN, xn) = v0 & $i(v0) & ( ~ aSubsetOf0(v0, szNzAzT0) |
% 55.58/8.12 | | | ~ isCountable0(v0) | (sdtlpdtrp0(xN, all_90_1) = v1 &
% 55.58/8.12 | | | szmzizndt0(v0) = v2 & sdtmndt0(v0, v2) = v3 & $i(v3) &
% 55.58/8.12 | | | $i(v2) & $i(v1) & aSubsetOf0(v1, v3) & isCountable0(v1))))
% 55.58/8.12 | | |
% 55.58/8.12 | | | GROUND_INST: instantiating (4) with sz00, slcrc0, xO, simplifying with
% 55.58/8.12 | | | (3), (5), (6), (23), (52) gives:
% 55.58/8.12 | | | (78) xO = slcrc0 | ? [v0: $i] : ? [v1: $i] : ($i(v0) & ( ~
% 55.58/8.12 | | | aElementOf0(v0, xO) | ~ aElementOf0(v0, szNzAzT0) |
% 55.58/8.12 | | | (szszuzczcdt0(v0) = v1 & $i(v1) & ~ sdtlseqdt0(v1, sz00))) &
% 55.58/8.12 | | | (aElementOf0(v0, xO) | (szszuzczcdt0(v0) = v1 & $i(v1) &
% 55.58/8.12 | | | sdtlseqdt0(v1, sz00) & aElementOf0(v0, szNzAzT0))))
% 55.58/8.12 | | |
% 55.58/8.12 | | | GROUND_INST: instantiating (13) with xn, all_92_1, simplifying with (30),
% 55.58/8.12 | | | (50), (54) gives:
% 55.58/8.12 | | | (79) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 55.58/8.12 | | | $i] : ? [v5: $i] : (sdtlpdtrp0(xC, xn) = v2 & slbdtsldtrb0(v4,
% 55.58/8.12 | | | xk) = v5 & szmzizndt0(all_92_1) = v0 & sdtmndt0(all_92_1, v0)
% 55.58/8.12 | | | = v1 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 55.58/8.12 | | | aSubsetOf0(v4, v1) & isCountable0(v4) & aElementOf0(v3, xT) & !
% 55.58/8.12 | | | [v6: $i] : ! [v7: $i] : (v7 = v3 | ~ (sdtlpdtrp0(v2, v6) = v7)
% 55.58/8.12 | | | | ~ $i(v6) | ~ aElementOf0(v6, v5) | ~ aSet0(v6)))
% 55.58/8.12 | | |
% 55.58/8.12 | | | GROUND_INST: instantiating (9) with xn, all_92_1, simplifying with (30),
% 55.58/8.12 | | | (50), (54) gives:
% 55.58/8.12 | | | (80) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 55.58/8.12 | | | (sdtlpdtrp0(xC, xn) = v0 & szDzozmdt0(v0) = v1 & slbdtsldtrb0(v3,
% 55.58/8.12 | | | xk) = v1 & szmzizndt0(all_92_1) = v2 & sdtmndt0(all_92_1, v2)
% 55.58/8.12 | | | = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aFunction0(v0) & !
% 55.58/8.12 | | | [v4: $i] : ! [v5: $i] : ( ~ (sdtlpdtrp0(v0, v4) = v5) | ~
% 55.58/8.12 | | | $i(v4) | ~ aElementOf0(v4, v1) | ~ aSet0(v4) | ? [v6: $i] :
% 55.58/8.12 | | | (sdtlpdtrp0(xc, v6) = v5 & sdtpldt0(v4, v2) = v6 & $i(v6) &
% 55.58/8.12 | | | $i(v5))) & ! [v4: $i] : ! [v5: $i] : ( ~ (sdtpldt0(v4, v2)
% 55.58/8.12 | | | = v5) | ~ $i(v4) | ~ aElementOf0(v4, v1) | ~ aSet0(v4) |
% 55.58/8.12 | | | ? [v6: $i] : (sdtlpdtrp0(v0, v4) = v6 & sdtlpdtrp0(xc, v5) =
% 55.58/8.12 | | | v6 & $i(v6))))
% 55.58/8.12 | | |
% 55.58/8.12 | | | GROUND_INST: instantiating (12) with xn, all_92_1, simplifying with (30),
% 55.58/8.12 | | | (50), (54) gives:
% 55.58/8.12 | | | (81) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (slbdtsldtrb0(v1, xk) =
% 55.58/8.12 | | | v2 & szmzizndt0(all_92_1) = v0 & sdtmndt0(all_92_1, v0) = v1 &
% 55.58/8.12 | | | $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5:
% 55.58/8.12 | | | $i] : ( ~ (slbdtsldtrb0(v3, xk) = v4) | ~ $i(v5) | ~ $i(v3)
% 55.58/8.12 | | | | ~ aSubsetOf0(v3, v1) | ~ isCountable0(v3) | ~
% 55.58/8.12 | | | aElementOf0(v5, v4) | ~ aSet0(v5) | aElementOf0(v5, v2)))
% 55.58/8.12 | | |
% 55.58/8.12 | | | GROUND_INST: instantiating (65) with xn, all_92_1, simplifying with (30),
% 55.58/8.12 | | | (50), (54) gives:
% 55.58/8.12 | | | (82) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (slbdtsldtrb0(v1, xk) =
% 55.58/8.12 | | | v2 & szmzizndt0(all_92_1) = v0 & sdtmndt0(all_92_1, v0) = v1 &
% 55.58/8.12 | | | $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~
% 55.58/8.12 | | | (sdtpldt0(v3, v0) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v2) |
% 55.58/8.12 | | | ~ aSet0(v3) | aElementOf0(v4, all_107_0)))
% 55.58/8.12 | | |
% 55.58/8.12 | | | GROUND_INST: instantiating (16) with xn, all_92_1, simplifying with (30),
% 55.58/8.12 | | | (50), (54) gives:
% 55.58/8.12 | | | (83) ? [v0: $i] : (sdtlpdtrp0(xe, xn) = v0 & szmzizndt0(all_92_1) = v0
% 55.58/8.12 | | | & $i(v0))
% 55.58/8.12 | | |
% 55.58/8.12 | | | GROUND_INST: instantiating (14) with xn, all_105_1, simplifying with (30),
% 55.58/8.12 | | | (54), (62) gives:
% 55.58/8.12 | | | (84) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 55.58/8.12 | | | $i] : ? [v5: $i] : (sdtlpdtrp0(xN, xn) = v0 & slbdtsldtrb0(v4,
% 55.58/8.12 | | | xk) = v5 & szmzizndt0(v0) = v1 & sdtmndt0(v0, v1) = v2 &
% 55.58/8.12 | | | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 55.58/8.12 | | | aSubsetOf0(v4, v2) & isCountable0(v4) & aElementOf0(v3, xT) & !
% 55.58/8.12 | | | [v6: $i] : ! [v7: $i] : (v7 = v3 | ~ (sdtlpdtrp0(all_105_1,
% 55.58/8.12 | | | v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v5) | ~
% 55.58/8.12 | | | aSet0(v6)))
% 55.58/8.12 | | |
% 55.58/8.12 | | | GROUND_INST: instantiating (10) with xn, all_105_1, simplifying with (30),
% 55.58/8.12 | | | (54), (62) gives:
% 55.58/8.12 | | | (85) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 55.58/8.12 | | | (sdtlpdtrp0(xN, xn) = v1 & szDzozmdt0(all_105_1) = v0 &
% 55.58/8.12 | | | slbdtsldtrb0(v3, xk) = v0 & szmzizndt0(v1) = v2 & sdtmndt0(v1,
% 55.58/8.12 | | | v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] :
% 55.58/8.12 | | | ! [v5: $i] : ( ~ (sdtlpdtrp0(all_105_1, v4) = v5) | ~ $i(v4) |
% 55.58/8.12 | | | ~ aElementOf0(v4, v0) | ~ aSet0(v4) | ? [v6: $i] :
% 55.58/8.12 | | | (sdtlpdtrp0(xc, v6) = v5 & sdtpldt0(v4, v2) = v6 & $i(v6) &
% 55.58/8.12 | | | $i(v5))) & ! [v4: $i] : ! [v5: $i] : ( ~ (sdtpldt0(v4, v2)
% 55.58/8.12 | | | = v5) | ~ $i(v4) | ~ aElementOf0(v4, v0) | ~ aSet0(v4) |
% 55.58/8.12 | | | ? [v6: $i] : (sdtlpdtrp0(all_105_1, v4) = v6 & sdtlpdtrp0(xc,
% 55.58/8.12 | | | v5) = v6 & $i(v6))))
% 55.58/8.12 | | |
% 55.58/8.12 | | | GROUND_INST: instantiating (11) with xn, all_105_1, simplifying with (30),
% 55.58/8.12 | | | (54), (62) gives:
% 55.58/8.12 | | | (86) ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(all_105_1, v0) = v1 &
% 55.58/8.12 | | | szDzozmdt0(all_105_1) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v1,
% 55.58/8.13 | | | xT))
% 55.58/8.13 | | |
% 55.58/8.13 | | | GROUND_INST: instantiating (17) with xn, xp, simplifying with (30), (54),
% 55.58/8.13 | | | (55) gives:
% 55.58/8.13 | | | (87) ? [v0: $i] : (sdtlpdtrp0(xN, xn) = v0 & szmzizndt0(v0) = xp &
% 55.58/8.13 | | | $i(v0) & $i(xp))
% 55.58/8.13 | | |
% 55.58/8.13 | | | GROUND_INST: instantiating (19) with xn, all_84_0, simplifying with (30),
% 55.58/8.13 | | | (42), (54) gives:
% 55.58/8.13 | | | (88) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 55.58/8.13 | | | (sdtlpdtrp0(xC, xn) = v3 & sdtlpdtrp0(xN, v0) = v1 &
% 55.58/8.13 | | | slbdtsldtrb0(v1, xk) = v2 & szszuzczcdt0(xn) = v0 & $i(v3) &
% 55.58/8.13 | | | $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: int] : (v5 =
% 55.58/8.13 | | | all_84_0 | ~ (sdtlpdtrp0(v3, v4) = v5) | ~ $i(v4) | ~
% 55.58/8.13 | | | aElementOf0(v4, v2) | ~ aSet0(v4)))
% 55.58/8.13 | | |
% 55.58/8.13 | | | DELTA: instantiating (83) with fresh symbol all_140_0 gives:
% 55.58/8.13 | | | (89) sdtlpdtrp0(xe, xn) = all_140_0 & szmzizndt0(all_92_1) = all_140_0
% 55.58/8.13 | | | & $i(all_140_0)
% 55.73/8.13 | | |
% 55.73/8.13 | | | ALPHA: (89) implies:
% 55.73/8.13 | | | (90) szmzizndt0(all_92_1) = all_140_0
% 55.73/8.13 | | | (91) sdtlpdtrp0(xe, xn) = all_140_0
% 55.73/8.13 | | |
% 55.73/8.13 | | | DELTA: instantiating (87) with fresh symbol all_144_0 gives:
% 55.73/8.13 | | | (92) sdtlpdtrp0(xN, xn) = all_144_0 & szmzizndt0(all_144_0) = xp &
% 55.73/8.13 | | | $i(all_144_0) & $i(xp)
% 55.73/8.13 | | |
% 55.73/8.13 | | | ALPHA: (92) implies:
% 55.73/8.13 | | | (93) szmzizndt0(all_144_0) = xp
% 55.73/8.13 | | | (94) sdtlpdtrp0(xN, xn) = all_144_0
% 55.73/8.13 | | |
% 55.73/8.13 | | | DELTA: instantiating (86) with fresh symbols all_150_0, all_150_1 gives:
% 55.73/8.13 | | | (95) sdtlcdtrc0(all_105_1, all_150_1) = all_150_0 &
% 55.73/8.13 | | | szDzozmdt0(all_105_1) = all_150_1 & $i(all_150_0) & $i(all_150_1)
% 55.73/8.13 | | | & aSubsetOf0(all_150_0, xT)
% 55.73/8.13 | | |
% 55.73/8.13 | | | ALPHA: (95) implies:
% 55.73/8.13 | | | (96) szDzozmdt0(all_105_1) = all_150_1
% 55.73/8.13 | | |
% 55.73/8.13 | | | DELTA: instantiating (82) with fresh symbols all_178_0, all_178_1,
% 55.73/8.13 | | | all_178_2 gives:
% 55.73/8.13 | | | (97) slbdtsldtrb0(all_178_1, xk) = all_178_0 & szmzizndt0(all_92_1) =
% 55.73/8.13 | | | all_178_2 & sdtmndt0(all_92_1, all_178_2) = all_178_1 &
% 55.73/8.13 | | | $i(all_178_0) & $i(all_178_1) & $i(all_178_2) & ! [v0: $i] : !
% 55.73/8.13 | | | [v1: $i] : ( ~ (sdtpldt0(v0, all_178_2) = v1) | ~ $i(v0) | ~
% 55.73/8.13 | | | aElementOf0(v0, all_178_0) | ~ aSet0(v0) | aElementOf0(v1,
% 55.73/8.13 | | | all_107_0))
% 55.73/8.13 | | |
% 55.73/8.13 | | | ALPHA: (97) implies:
% 55.73/8.13 | | | (98) sdtmndt0(all_92_1, all_178_2) = all_178_1
% 55.73/8.13 | | | (99) szmzizndt0(all_92_1) = all_178_2
% 55.73/8.13 | | |
% 55.73/8.13 | | | DELTA: instantiating (77) with fresh symbols all_186_0, all_186_1,
% 55.73/8.13 | | | all_186_2, all_186_3 gives:
% 55.73/8.13 | | | (100) sdtlpdtrp0(xN, xn) = all_186_3 & $i(all_186_3) & ( ~
% 55.73/8.13 | | | aSubsetOf0(all_186_3, szNzAzT0) | ~ isCountable0(all_186_3) |
% 55.73/8.13 | | | (sdtlpdtrp0(xN, all_90_1) = all_186_2 & szmzizndt0(all_186_3) =
% 55.73/8.13 | | | all_186_1 & sdtmndt0(all_186_3, all_186_1) = all_186_0 &
% 55.73/8.13 | | | $i(all_186_0) & $i(all_186_1) & $i(all_186_2) &
% 55.73/8.13 | | | aSubsetOf0(all_186_2, all_186_0) & isCountable0(all_186_2)))
% 55.73/8.13 | | |
% 55.73/8.13 | | | ALPHA: (100) implies:
% 55.73/8.13 | | | (101) sdtlpdtrp0(xN, xn) = all_186_3
% 55.73/8.13 | | |
% 55.73/8.13 | | | DELTA: instantiating (76) with fresh symbols all_194_0, all_194_1,
% 55.73/8.13 | | | all_194_2, all_194_3 gives:
% 55.73/8.13 | | | (102) sdtlpdtrp0(xC, xn) = all_194_1 & sdtlpdtrp0(xN, all_90_1) =
% 55.73/8.13 | | | all_194_3 & slbdtsldtrb0(all_194_3, xk) = all_194_2 &
% 55.73/8.13 | | | $i(all_194_0) & $i(all_194_1) & $i(all_194_2) & $i(all_194_3) &
% 55.73/8.13 | | | aElementOf0(all_194_0, xT) & ! [v0: $i] : ! [v1: int] : (v1 =
% 55.73/8.13 | | | all_194_0 | ~ (sdtlpdtrp0(all_194_1, v0) = v1) | ~ $i(v0) |
% 55.73/8.13 | | | ~ aElementOf0(v0, all_194_2) | ~ aSet0(v0))
% 55.73/8.13 | | |
% 55.73/8.13 | | | ALPHA: (102) implies:
% 55.73/8.13 | | | (103) sdtlpdtrp0(xC, xn) = all_194_1
% 55.73/8.13 | | |
% 55.73/8.13 | | | DELTA: instantiating (88) with fresh symbols all_203_0, all_203_1,
% 55.73/8.13 | | | all_203_2, all_203_3 gives:
% 55.73/8.13 | | | (104) sdtlpdtrp0(xC, xn) = all_203_0 & sdtlpdtrp0(xN, all_203_3) =
% 55.73/8.13 | | | all_203_2 & slbdtsldtrb0(all_203_2, xk) = all_203_1 &
% 55.73/8.13 | | | szszuzczcdt0(xn) = all_203_3 & $i(all_203_0) & $i(all_203_1) &
% 55.73/8.13 | | | $i(all_203_2) & $i(all_203_3) & ! [v0: $i] : ! [v1: int] : (v1
% 55.73/8.13 | | | = all_84_0 | ~ (sdtlpdtrp0(all_203_0, v0) = v1) | ~ $i(v0) |
% 55.73/8.13 | | | ~ aElementOf0(v0, all_203_1) | ~ aSet0(v0))
% 55.73/8.13 | | |
% 55.73/8.13 | | | ALPHA: (104) implies:
% 55.73/8.13 | | | (105) sdtlpdtrp0(xC, xn) = all_203_0
% 55.73/8.13 | | |
% 55.73/8.13 | | | DELTA: instantiating (75) with fresh symbols all_206_0, all_206_1,
% 55.73/8.13 | | | all_206_2, all_206_3 gives:
% 55.73/8.13 | | | (106) sdtlpdtrp0(xd, xn) = all_206_1 & sdtlpdtrp0(xC, xn) = all_206_0 &
% 55.73/8.13 | | | sdtlpdtrp0(xN, all_90_1) = all_206_3 & slbdtsldtrb0(all_206_3,
% 55.73/8.13 | | | xk) = all_206_2 & $i(all_206_0) & $i(all_206_1) & $i(all_206_2)
% 55.73/8.13 | | | & $i(all_206_3) & ! [v0: $i] : ! [v1: int] : (v1 = all_206_1 |
% 55.73/8.13 | | | ~ (sdtlpdtrp0(all_206_0, v0) = v1) | ~ $i(v0) | ~
% 55.73/8.13 | | | aElementOf0(v0, all_206_2) | ~ aSet0(v0))
% 55.73/8.13 | | |
% 55.73/8.13 | | | ALPHA: (106) implies:
% 55.73/8.13 | | | (107) sdtlpdtrp0(xC, xn) = all_206_0
% 55.73/8.13 | | |
% 55.73/8.13 | | | DELTA: instantiating (81) with fresh symbols all_211_0, all_211_1,
% 55.73/8.13 | | | all_211_2 gives:
% 55.73/8.13 | | | (108) slbdtsldtrb0(all_211_1, xk) = all_211_0 & szmzizndt0(all_92_1) =
% 55.73/8.13 | | | all_211_2 & sdtmndt0(all_92_1, all_211_2) = all_211_1 &
% 55.73/8.13 | | | $i(all_211_0) & $i(all_211_1) & $i(all_211_2) & ! [v0: $i] : !
% 55.73/8.13 | | | [v1: $i] : ! [v2: $i] : ( ~ (slbdtsldtrb0(v0, xk) = v1) | ~
% 55.73/8.13 | | | $i(v2) | ~ $i(v0) | ~ aSubsetOf0(v0, all_211_1) | ~
% 55.73/8.13 | | | isCountable0(v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v2) |
% 55.73/8.13 | | | aElementOf0(v2, all_211_0))
% 55.73/8.13 | | |
% 55.73/8.13 | | | ALPHA: (108) implies:
% 55.73/8.13 | | | (109) szmzizndt0(all_92_1) = all_211_2
% 55.73/8.13 | | |
% 55.73/8.13 | | | DELTA: instantiating (79) with fresh symbols all_218_0, all_218_1,
% 55.73/8.13 | | | all_218_2, all_218_3, all_218_4, all_218_5 gives:
% 55.73/8.13 | | | (110) sdtlpdtrp0(xC, xn) = all_218_3 & slbdtsldtrb0(all_218_1, xk) =
% 55.73/8.13 | | | all_218_0 & szmzizndt0(all_92_1) = all_218_5 & sdtmndt0(all_92_1,
% 55.73/8.13 | | | all_218_5) = all_218_4 & $i(all_218_0) & $i(all_218_1) &
% 55.73/8.13 | | | $i(all_218_2) & $i(all_218_3) & $i(all_218_4) & $i(all_218_5) &
% 55.73/8.13 | | | aSubsetOf0(all_218_1, all_218_4) & isCountable0(all_218_1) &
% 55.73/8.13 | | | aElementOf0(all_218_2, xT) & ! [v0: $i] : ! [v1: int] : (v1 =
% 55.73/8.13 | | | all_218_2 | ~ (sdtlpdtrp0(all_218_3, v0) = v1) | ~ $i(v0) |
% 55.73/8.13 | | | ~ aElementOf0(v0, all_218_0) | ~ aSet0(v0))
% 55.73/8.13 | | |
% 55.73/8.13 | | | ALPHA: (110) implies:
% 55.73/8.13 | | | (111) szmzizndt0(all_92_1) = all_218_5
% 55.73/8.13 | | | (112) sdtlpdtrp0(xC, xn) = all_218_3
% 55.73/8.13 | | |
% 55.73/8.13 | | | DELTA: instantiating (84) with fresh symbols all_221_0, all_221_1,
% 55.73/8.13 | | | all_221_2, all_221_3, all_221_4, all_221_5 gives:
% 55.73/8.13 | | | (113) sdtlpdtrp0(xN, xn) = all_221_5 & slbdtsldtrb0(all_221_1, xk) =
% 55.73/8.13 | | | all_221_0 & szmzizndt0(all_221_5) = all_221_4 &
% 55.73/8.13 | | | sdtmndt0(all_221_5, all_221_4) = all_221_3 & $i(all_221_0) &
% 55.73/8.13 | | | $i(all_221_1) & $i(all_221_2) & $i(all_221_3) & $i(all_221_4) &
% 55.73/8.13 | | | $i(all_221_5) & aSubsetOf0(all_221_1, all_221_3) &
% 55.73/8.13 | | | isCountable0(all_221_1) & aElementOf0(all_221_2, xT) & ! [v0:
% 55.73/8.13 | | | $i] : ! [v1: int] : (v1 = all_221_2 | ~
% 55.73/8.13 | | | (sdtlpdtrp0(all_105_1, v0) = v1) | ~ $i(v0) | ~
% 55.73/8.13 | | | aElementOf0(v0, all_221_0) | ~ aSet0(v0))
% 55.73/8.13 | | |
% 55.73/8.13 | | | ALPHA: (113) implies:
% 55.73/8.13 | | | (114) sdtlpdtrp0(xN, xn) = all_221_5
% 55.73/8.13 | | |
% 55.73/8.13 | | | DELTA: instantiating (85) with fresh symbols all_227_0, all_227_1,
% 55.73/8.13 | | | all_227_2, all_227_3 gives:
% 55.73/8.13 | | | (115) sdtlpdtrp0(xN, xn) = all_227_2 & szDzozmdt0(all_105_1) =
% 55.73/8.13 | | | all_227_3 & slbdtsldtrb0(all_227_0, xk) = all_227_3 &
% 55.73/8.13 | | | szmzizndt0(all_227_2) = all_227_1 & sdtmndt0(all_227_2,
% 55.73/8.13 | | | all_227_1) = all_227_0 & $i(all_227_0) & $i(all_227_1) &
% 55.73/8.13 | | | $i(all_227_2) & $i(all_227_3) & ! [v0: $i] : ! [v1: $i] : ( ~
% 55.73/8.13 | | | (sdtlpdtrp0(all_105_1, v0) = v1) | ~ $i(v0) | ~
% 55.73/8.13 | | | aElementOf0(v0, all_227_3) | ~ aSet0(v0) | ? [v2: $i] :
% 55.73/8.13 | | | (sdtlpdtrp0(xc, v2) = v1 & sdtpldt0(v0, all_227_1) = v2 &
% 55.73/8.13 | | | $i(v2) & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 55.73/8.13 | | | (sdtpldt0(v0, all_227_1) = v1) | ~ $i(v0) | ~ aElementOf0(v0,
% 55.73/8.13 | | | all_227_3) | ~ aSet0(v0) | ? [v2: $i] :
% 55.73/8.13 | | | (sdtlpdtrp0(all_105_1, v0) = v2 & sdtlpdtrp0(xc, v1) = v2 &
% 55.73/8.13 | | | $i(v2)))
% 55.73/8.13 | | |
% 55.73/8.13 | | | ALPHA: (115) implies:
% 55.73/8.14 | | | (116) szmzizndt0(all_227_2) = all_227_1
% 55.73/8.14 | | | (117) szDzozmdt0(all_105_1) = all_227_3
% 55.73/8.14 | | | (118) sdtlpdtrp0(xN, xn) = all_227_2
% 55.73/8.14 | | | (119) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(all_105_1, v0) = v1)
% 55.73/8.14 | | | | ~ $i(v0) | ~ aElementOf0(v0, all_227_3) | ~ aSet0(v0) | ?
% 55.73/8.14 | | | [v2: $i] : (sdtlpdtrp0(xc, v2) = v1 & sdtpldt0(v0, all_227_1) =
% 55.73/8.14 | | | v2 & $i(v2) & $i(v1)))
% 55.73/8.14 | | |
% 55.73/8.14 | | | GROUND_INST: instantiating (119) with xP, all_105_0, simplifying with
% 55.73/8.14 | | | (29), (44), (63) gives:
% 55.73/8.14 | | | (120) ~ aElementOf0(xP, all_227_3) | ? [v0: $i] : (sdtlpdtrp0(xc, v0)
% 55.73/8.14 | | | = all_105_0 & sdtpldt0(xP, all_227_1) = v0 & $i(v0) &
% 55.73/8.14 | | | $i(all_105_0))
% 55.73/8.14 | | |
% 55.73/8.14 | | | DELTA: instantiating (80) with fresh symbols all_230_0, all_230_1,
% 55.73/8.14 | | | all_230_2, all_230_3 gives:
% 55.73/8.14 | | | (121) sdtlpdtrp0(xC, xn) = all_230_3 & szDzozmdt0(all_230_3) =
% 55.73/8.14 | | | all_230_2 & slbdtsldtrb0(all_230_0, xk) = all_230_2 &
% 55.73/8.14 | | | szmzizndt0(all_92_1) = all_230_1 & sdtmndt0(all_92_1, all_230_1)
% 55.73/8.14 | | | = all_230_0 & $i(all_230_0) & $i(all_230_1) & $i(all_230_2) &
% 55.73/8.14 | | | $i(all_230_3) & aFunction0(all_230_3) & ! [v0: $i] : ! [v1: $i]
% 55.73/8.14 | | | : ( ~ (sdtlpdtrp0(all_230_3, v0) = v1) | ~ $i(v0) | ~
% 55.73/8.14 | | | aElementOf0(v0, all_230_2) | ~ aSet0(v0) | ? [v2: $i] :
% 55.73/8.14 | | | (sdtlpdtrp0(xc, v2) = v1 & sdtpldt0(v0, all_230_1) = v2 &
% 55.73/8.14 | | | $i(v2) & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 55.73/8.14 | | | (sdtpldt0(v0, all_230_1) = v1) | ~ $i(v0) | ~ aElementOf0(v0,
% 55.73/8.14 | | | all_230_2) | ~ aSet0(v0) | ? [v2: $i] :
% 55.73/8.14 | | | (sdtlpdtrp0(all_230_3, v0) = v2 & sdtlpdtrp0(xc, v1) = v2 &
% 55.73/8.14 | | | $i(v2)))
% 55.73/8.14 | | |
% 55.73/8.14 | | | ALPHA: (121) implies:
% 55.73/8.14 | | | (122) sdtmndt0(all_92_1, all_230_1) = all_230_0
% 55.73/8.14 | | | (123) szmzizndt0(all_92_1) = all_230_1
% 55.73/8.14 | | | (124) slbdtsldtrb0(all_230_0, xk) = all_230_2
% 55.73/8.14 | | | (125) szDzozmdt0(all_230_3) = all_230_2
% 55.73/8.14 | | | (126) sdtlpdtrp0(xC, xn) = all_230_3
% 55.73/8.14 | | |
% 55.73/8.14 | | | BETA: splitting (78) gives:
% 55.73/8.14 | | |
% 55.73/8.14 | | | Case 1:
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | (127) xO = slcrc0
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | REDUCE: (69), (127) imply:
% 55.73/8.14 | | | | (128) $false
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | CLOSE: (128) is inconsistent.
% 55.73/8.14 | | | |
% 55.73/8.14 | | | Case 2:
% 55.73/8.14 | | | |
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | GROUND_INST: instantiating (35) with xD, all_230_0, all_92_0, all_92_1,
% 55.73/8.14 | | | | simplifying with (48) gives:
% 55.73/8.14 | | | | (129) all_230_0 = xD | ~ (sdtmndt0(all_92_1, all_92_0) = all_230_0)
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | GROUND_INST: instantiating (35) with all_178_1, all_230_0, all_178_2,
% 55.73/8.14 | | | | all_92_1, simplifying with (98) gives:
% 55.73/8.14 | | | | (130) all_230_0 = all_178_1 | ~ (sdtmndt0(all_92_1, all_178_2) =
% 55.73/8.14 | | | | all_230_0)
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | GROUND_INST: instantiating (32) with all_178_2, all_211_2, all_92_1,
% 55.73/8.14 | | | | simplifying with (99), (109) gives:
% 55.73/8.14 | | | | (131) all_211_2 = all_178_2
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | GROUND_INST: instantiating (32) with all_140_0, all_211_2, all_92_1,
% 55.73/8.14 | | | | simplifying with (90), (109) gives:
% 55.73/8.14 | | | | (132) all_211_2 = all_140_0
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | GROUND_INST: instantiating (32) with all_92_0, all_230_1, all_92_1,
% 55.73/8.14 | | | | simplifying with (49), (123) gives:
% 55.73/8.14 | | | | (133) all_230_1 = all_92_0
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | GROUND_INST: instantiating (32) with all_218_5, all_230_1, all_92_1,
% 55.73/8.14 | | | | simplifying with (111), (123) gives:
% 55.73/8.14 | | | | (134) all_230_1 = all_218_5
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | GROUND_INST: instantiating (32) with all_178_2, all_230_1, all_92_1,
% 55.73/8.14 | | | | simplifying with (99), (123) gives:
% 55.73/8.14 | | | | (135) all_230_1 = all_178_2
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | GROUND_INST: instantiating (32) with xp, all_227_1, all_144_0,
% 55.73/8.14 | | | | simplifying with (93) gives:
% 55.73/8.14 | | | | (136) all_227_1 = xp | ~ (szmzizndt0(all_144_0) = all_227_1)
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | GROUND_INST: instantiating (36) with all_80_0, all_230_2, xk, xD,
% 55.73/8.14 | | | | simplifying with (40) gives:
% 55.73/8.14 | | | | (137) all_230_2 = all_80_0 | ~ (slbdtsldtrb0(xD, xk) = all_230_2)
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | GROUND_INST: instantiating (33) with all_150_1, all_227_3, all_105_1,
% 55.73/8.14 | | | | simplifying with (96), (117) gives:
% 55.73/8.14 | | | | (138) all_227_3 = all_150_1
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | GROUND_INST: instantiating (33) with all_150_1, all_230_2, all_105_1,
% 55.73/8.14 | | | | simplifying with (96) gives:
% 55.73/8.14 | | | | (139) all_230_2 = all_150_1 | ~ (szDzozmdt0(all_105_1) = all_230_2)
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | GROUND_INST: instantiating (37) with all_92_1, all_221_5, xn, xN,
% 55.73/8.14 | | | | simplifying with (50), (114) gives:
% 55.73/8.14 | | | | (140) all_221_5 = all_92_1
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | GROUND_INST: instantiating (37) with all_144_0, all_221_5, xn, xN,
% 55.73/8.14 | | | | simplifying with (94), (114) gives:
% 55.73/8.14 | | | | (141) all_221_5 = all_144_0
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | GROUND_INST: instantiating (37) with all_221_5, all_227_2, xn, xN,
% 55.73/8.14 | | | | simplifying with (114), (118) gives:
% 55.73/8.14 | | | | (142) all_227_2 = all_221_5
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | GROUND_INST: instantiating (37) with all_186_3, all_227_2, xn, xN,
% 55.73/8.14 | | | | simplifying with (101), (118) gives:
% 55.73/8.14 | | | | (143) all_227_2 = all_186_3
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | GROUND_INST: instantiating (37) with all_105_1, all_206_0, xn, xC,
% 55.73/8.14 | | | | simplifying with (62), (107) gives:
% 55.73/8.14 | | | | (144) all_206_0 = all_105_1
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | GROUND_INST: instantiating (37) with all_194_1, all_206_0, xn, xC,
% 55.73/8.14 | | | | simplifying with (103), (107) gives:
% 55.73/8.14 | | | | (145) all_206_0 = all_194_1
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | GROUND_INST: instantiating (37) with all_206_0, all_218_3, xn, xC,
% 55.73/8.14 | | | | simplifying with (107), (112) gives:
% 55.73/8.14 | | | | (146) all_218_3 = all_206_0
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | GROUND_INST: instantiating (37) with all_218_3, all_230_3, xn, xC,
% 55.73/8.14 | | | | simplifying with (112), (126) gives:
% 55.73/8.14 | | | | (147) all_230_3 = all_218_3
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | GROUND_INST: instantiating (37) with all_203_0, all_230_3, xn, xC,
% 55.73/8.14 | | | | simplifying with (105), (126) gives:
% 55.73/8.14 | | | | (148) all_230_3 = all_203_0
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | GROUND_INST: instantiating (37) with xp, all_140_0, xn, xe, simplifying
% 55.73/8.14 | | | | with (55), (91) gives:
% 55.73/8.14 | | | | (149) all_140_0 = xp
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | COMBINE_EQS: (133), (134) imply:
% 55.73/8.14 | | | | (150) all_218_5 = all_92_0
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | COMBINE_EQS: (134), (135) imply:
% 55.73/8.14 | | | | (151) all_218_5 = all_178_2
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | COMBINE_EQS: (147), (148) imply:
% 55.73/8.14 | | | | (152) all_218_3 = all_203_0
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | SIMP: (152) implies:
% 55.73/8.14 | | | | (153) all_218_3 = all_203_0
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | COMBINE_EQS: (142), (143) imply:
% 55.73/8.14 | | | | (154) all_221_5 = all_186_3
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | SIMP: (154) implies:
% 55.73/8.14 | | | | (155) all_221_5 = all_186_3
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | COMBINE_EQS: (141), (155) imply:
% 55.73/8.14 | | | | (156) all_186_3 = all_144_0
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | COMBINE_EQS: (140), (155) imply:
% 55.73/8.14 | | | | (157) all_186_3 = all_92_1
% 55.73/8.14 | | | |
% 55.73/8.14 | | | | COMBINE_EQS: (146), (153) imply:
% 55.73/8.14 | | | | (158) all_206_0 = all_203_0
% 55.73/8.15 | | | |
% 55.73/8.15 | | | | SIMP: (158) implies:
% 55.73/8.15 | | | | (159) all_206_0 = all_203_0
% 55.73/8.15 | | | |
% 55.73/8.15 | | | | COMBINE_EQS: (150), (151) imply:
% 55.73/8.15 | | | | (160) all_178_2 = all_92_0
% 55.73/8.15 | | | |
% 55.73/8.15 | | | | SIMP: (160) implies:
% 55.73/8.15 | | | | (161) all_178_2 = all_92_0
% 55.73/8.15 | | | |
% 55.73/8.15 | | | | COMBINE_EQS: (131), (132) imply:
% 55.73/8.15 | | | | (162) all_178_2 = all_140_0
% 55.73/8.15 | | | |
% 55.73/8.15 | | | | SIMP: (162) implies:
% 55.73/8.15 | | | | (163) all_178_2 = all_140_0
% 55.73/8.15 | | | |
% 55.73/8.15 | | | | COMBINE_EQS: (144), (159) imply:
% 55.73/8.15 | | | | (164) all_203_0 = all_105_1
% 55.73/8.15 | | | |
% 55.73/8.15 | | | | COMBINE_EQS: (145), (159) imply:
% 55.73/8.15 | | | | (165) all_203_0 = all_194_1
% 55.73/8.15 | | | |
% 55.73/8.15 | | | | COMBINE_EQS: (164), (165) imply:
% 55.73/8.15 | | | | (166) all_194_1 = all_105_1
% 55.73/8.15 | | | |
% 55.73/8.15 | | | | COMBINE_EQS: (156), (157) imply:
% 55.73/8.15 | | | | (167) all_144_0 = all_92_1
% 55.73/8.15 | | | |
% 55.73/8.15 | | | | COMBINE_EQS: (161), (163) imply:
% 55.73/8.15 | | | | (168) all_140_0 = all_92_0
% 55.73/8.15 | | | |
% 55.73/8.15 | | | | SIMP: (168) implies:
% 55.73/8.15 | | | | (169) all_140_0 = all_92_0
% 55.73/8.15 | | | |
% 55.73/8.15 | | | | COMBINE_EQS: (149), (169) imply:
% 55.73/8.15 | | | | (170) all_92_0 = xp
% 55.73/8.15 | | | |
% 55.73/8.15 | | | | COMBINE_EQS: (161), (170) imply:
% 55.73/8.15 | | | | (171) all_178_2 = xp
% 55.73/8.15 | | | |
% 55.73/8.15 | | | | COMBINE_EQS: (150), (170) imply:
% 55.73/8.15 | | | | (172) all_218_5 = xp
% 55.73/8.15 | | | |
% 55.73/8.15 | | | | COMBINE_EQS: (143), (157) imply:
% 55.73/8.15 | | | | (173) all_227_2 = all_92_1
% 55.73/8.15 | | | |
% 55.73/8.15 | | | | COMBINE_EQS: (148), (164) imply:
% 55.73/8.15 | | | | (174) all_230_3 = all_105_1
% 55.73/8.15 | | | |
% 55.73/8.15 | | | | COMBINE_EQS: (134), (172) imply:
% 55.73/8.15 | | | | (175) all_230_1 = xp
% 55.73/8.15 | | | |
% 55.73/8.15 | | | | REDUCE: (125), (174) imply:
% 55.73/8.15 | | | | (176) szDzozmdt0(all_105_1) = all_230_2
% 55.73/8.15 | | | |
% 55.73/8.15 | | | | REDUCE: (116), (173) imply:
% 55.73/8.15 | | | | (177) szmzizndt0(all_92_1) = all_227_1
% 55.73/8.15 | | | |
% 55.73/8.15 | | | | REDUCE: (122), (175) imply:
% 55.73/8.15 | | | | (178) sdtmndt0(all_92_1, xp) = all_230_0
% 55.73/8.15 | | | |
% 55.73/8.15 | | | | REDUCE: (74), (170) imply:
% 55.73/8.15 | | | | (179) sdtpldt0(xP, xp) = all_105_3
% 55.73/8.15 | | | |
% 55.73/8.15 | | | | BETA: splitting (139) gives:
% 55.73/8.15 | | | |
% 55.73/8.15 | | | | Case 1:
% 55.73/8.15 | | | | |
% 55.73/8.15 | | | | | (180) ~ (szDzozmdt0(all_105_1) = all_230_2)
% 55.73/8.15 | | | | |
% 55.73/8.15 | | | | | PRED_UNIFY: (176), (180) imply:
% 55.73/8.15 | | | | | (181) $false
% 55.73/8.15 | | | | |
% 55.73/8.15 | | | | | CLOSE: (181) is inconsistent.
% 55.73/8.15 | | | | |
% 55.73/8.15 | | | | Case 2:
% 55.73/8.15 | | | | |
% 55.73/8.15 | | | | | (182) all_230_2 = all_150_1
% 55.73/8.15 | | | | |
% 55.73/8.15 | | | | | REDUCE: (124), (182) imply:
% 55.73/8.15 | | | | | (183) slbdtsldtrb0(all_230_0, xk) = all_150_1
% 55.73/8.15 | | | | |
% 55.73/8.15 | | | | | BETA: splitting (130) gives:
% 55.73/8.15 | | | | |
% 55.73/8.15 | | | | | Case 1:
% 55.73/8.15 | | | | | |
% 55.73/8.15 | | | | | | (184) ~ (sdtmndt0(all_92_1, all_178_2) = all_230_0)
% 55.73/8.15 | | | | | |
% 55.73/8.15 | | | | | | REDUCE: (171), (184) imply:
% 55.73/8.15 | | | | | | (185) ~ (sdtmndt0(all_92_1, xp) = all_230_0)
% 55.73/8.15 | | | | | |
% 55.73/8.15 | | | | | | PRED_UNIFY: (178), (185) imply:
% 55.73/8.15 | | | | | | (186) $false
% 55.73/8.15 | | | | | |
% 55.73/8.15 | | | | | | CLOSE: (186) is inconsistent.
% 55.73/8.15 | | | | | |
% 55.73/8.15 | | | | | Case 2:
% 55.73/8.15 | | | | | |
% 55.73/8.15 | | | | | | (187) all_230_0 = all_178_1
% 55.73/8.15 | | | | | |
% 55.73/8.15 | | | | | | REDUCE: (183), (187) imply:
% 55.73/8.15 | | | | | | (188) slbdtsldtrb0(all_178_1, xk) = all_150_1
% 55.73/8.15 | | | | | |
% 55.73/8.15 | | | | | | REDUCE: (178), (187) imply:
% 55.73/8.15 | | | | | | (189) sdtmndt0(all_92_1, xp) = all_178_1
% 55.73/8.15 | | | | | |
% 55.73/8.15 | | | | | | BETA: splitting (136) gives:
% 55.73/8.15 | | | | | |
% 55.73/8.15 | | | | | | Case 1:
% 55.73/8.15 | | | | | | |
% 55.73/8.15 | | | | | | | (190) ~ (szmzizndt0(all_144_0) = all_227_1)
% 55.73/8.15 | | | | | | |
% 55.73/8.15 | | | | | | | REDUCE: (167), (190) imply:
% 55.73/8.15 | | | | | | | (191) ~ (szmzizndt0(all_92_1) = all_227_1)
% 55.73/8.15 | | | | | | |
% 55.73/8.15 | | | | | | | PRED_UNIFY: (177), (191) imply:
% 55.73/8.15 | | | | | | | (192) $false
% 55.73/8.15 | | | | | | |
% 55.73/8.15 | | | | | | | CLOSE: (192) is inconsistent.
% 55.73/8.15 | | | | | | |
% 55.73/8.15 | | | | | | Case 2:
% 55.73/8.15 | | | | | | |
% 55.73/8.15 | | | | | | | (193) all_227_1 = xp
% 55.73/8.15 | | | | | | |
% 55.73/8.15 | | | | | | | BETA: splitting (120) gives:
% 55.73/8.15 | | | | | | |
% 55.73/8.15 | | | | | | | Case 1:
% 55.73/8.15 | | | | | | | |
% 55.73/8.15 | | | | | | | | (194) ~ aElementOf0(xP, all_227_3)
% 55.73/8.15 | | | | | | | |
% 55.73/8.15 | | | | | | | | REDUCE: (138), (194) imply:
% 55.73/8.15 | | | | | | | | (195) ~ aElementOf0(xP, all_150_1)
% 55.73/8.15 | | | | | | | |
% 55.73/8.15 | | | | | | | | BETA: splitting (129) gives:
% 55.73/8.15 | | | | | | | |
% 55.73/8.15 | | | | | | | | Case 1:
% 55.73/8.15 | | | | | | | | |
% 55.73/8.15 | | | | | | | | | (196) ~ (sdtmndt0(all_92_1, all_92_0) = all_230_0)
% 55.73/8.15 | | | | | | | | |
% 55.73/8.15 | | | | | | | | | REDUCE: (170), (187), (196) imply:
% 55.73/8.15 | | | | | | | | | (197) ~ (sdtmndt0(all_92_1, xp) = all_178_1)
% 55.73/8.15 | | | | | | | | |
% 55.73/8.15 | | | | | | | | | PRED_UNIFY: (189), (197) imply:
% 55.73/8.15 | | | | | | | | | (198) $false
% 55.73/8.15 | | | | | | | | |
% 55.73/8.15 | | | | | | | | | CLOSE: (198) is inconsistent.
% 55.73/8.15 | | | | | | | | |
% 55.73/8.15 | | | | | | | | Case 2:
% 55.73/8.15 | | | | | | | | |
% 55.73/8.15 | | | | | | | | | (199) all_230_0 = xD
% 55.73/8.15 | | | | | | | | |
% 55.73/8.15 | | | | | | | | | COMBINE_EQS: (187), (199) imply:
% 55.73/8.15 | | | | | | | | | (200) all_178_1 = xD
% 55.73/8.15 | | | | | | | | |
% 55.73/8.15 | | | | | | | | | REDUCE: (188), (200) imply:
% 55.73/8.15 | | | | | | | | | (201) slbdtsldtrb0(xD, xk) = all_150_1
% 55.73/8.15 | | | | | | | | |
% 55.73/8.15 | | | | | | | | | BETA: splitting (137) gives:
% 55.73/8.15 | | | | | | | | |
% 55.73/8.15 | | | | | | | | | Case 1:
% 55.73/8.15 | | | | | | | | | |
% 55.73/8.15 | | | | | | | | | | (202) ~ (slbdtsldtrb0(xD, xk) = all_230_2)
% 55.73/8.15 | | | | | | | | | |
% 55.73/8.15 | | | | | | | | | | REDUCE: (182), (202) imply:
% 55.73/8.15 | | | | | | | | | | (203) ~ (slbdtsldtrb0(xD, xk) = all_150_1)
% 55.73/8.15 | | | | | | | | | |
% 55.73/8.15 | | | | | | | | | | PRED_UNIFY: (201), (203) imply:
% 55.73/8.15 | | | | | | | | | | (204) $false
% 55.73/8.15 | | | | | | | | | |
% 55.73/8.15 | | | | | | | | | | CLOSE: (204) is inconsistent.
% 55.73/8.15 | | | | | | | | | |
% 55.73/8.15 | | | | | | | | | Case 2:
% 55.73/8.15 | | | | | | | | | |
% 55.73/8.15 | | | | | | | | | | (205) all_230_2 = all_80_0
% 55.73/8.15 | | | | | | | | | |
% 55.73/8.15 | | | | | | | | | | COMBINE_EQS: (182), (205) imply:
% 55.73/8.15 | | | | | | | | | | (206) all_150_1 = all_80_0
% 55.73/8.15 | | | | | | | | | |
% 55.73/8.15 | | | | | | | | | | REDUCE: (195), (206) imply:
% 55.73/8.15 | | | | | | | | | | (207) ~ aElementOf0(xP, all_80_0)
% 55.73/8.15 | | | | | | | | | |
% 55.73/8.15 | | | | | | | | | | PRED_UNIFY: (39), (207) imply:
% 55.73/8.15 | | | | | | | | | | (208) $false
% 55.73/8.15 | | | | | | | | | |
% 55.73/8.15 | | | | | | | | | | CLOSE: (208) is inconsistent.
% 55.73/8.15 | | | | | | | | | |
% 55.73/8.15 | | | | | | | | | End of split
% 55.73/8.15 | | | | | | | | |
% 55.73/8.15 | | | | | | | | End of split
% 55.73/8.15 | | | | | | | |
% 55.73/8.15 | | | | | | | Case 2:
% 55.73/8.15 | | | | | | | |
% 55.73/8.15 | | | | | | | | (209) ? [v0: $i] : (sdtlpdtrp0(xc, v0) = all_105_0 &
% 55.73/8.15 | | | | | | | | sdtpldt0(xP, all_227_1) = v0 & $i(v0) &
% 55.73/8.15 | | | | | | | | $i(all_105_0))
% 55.73/8.15 | | | | | | | |
% 55.73/8.15 | | | | | | | | DELTA: instantiating (209) with fresh symbol all_361_0 gives:
% 55.73/8.15 | | | | | | | | (210) sdtlpdtrp0(xc, all_361_0) = all_105_0 & sdtpldt0(xP,
% 55.73/8.15 | | | | | | | | all_227_1) = all_361_0 & $i(all_361_0) &
% 55.73/8.15 | | | | | | | | $i(all_105_0)
% 55.73/8.15 | | | | | | | |
% 55.73/8.15 | | | | | | | | ALPHA: (210) implies:
% 55.73/8.15 | | | | | | | | (211) sdtpldt0(xP, all_227_1) = all_361_0
% 55.73/8.15 | | | | | | | | (212) sdtlpdtrp0(xc, all_361_0) = all_105_0
% 55.73/8.15 | | | | | | | |
% 55.73/8.15 | | | | | | | | REDUCE: (193), (211) imply:
% 55.73/8.15 | | | | | | | | (213) sdtpldt0(xP, xp) = all_361_0
% 55.73/8.15 | | | | | | | |
% 55.73/8.15 | | | | | | | | GROUND_INST: instantiating (34) with all_105_3, all_361_0, xp,
% 55.73/8.15 | | | | | | | | xP, simplifying with (179), (213) gives:
% 55.73/8.15 | | | | | | | | (214) all_361_0 = all_105_3
% 55.73/8.15 | | | | | | | |
% 55.73/8.15 | | | | | | | | GROUND_INST: instantiating (37) with all_105_2, all_105_0,
% 55.73/8.15 | | | | | | | | all_105_3, xc, simplifying with (60) gives:
% 55.73/8.15 | | | | | | | | (215) all_105_0 = all_105_2 | ~ (sdtlpdtrp0(xc, all_105_3) =
% 55.73/8.15 | | | | | | | | all_105_0)
% 55.73/8.15 | | | | | | | |
% 55.73/8.15 | | | | | | | | REDUCE: (212), (214) imply:
% 55.73/8.15 | | | | | | | | (216) sdtlpdtrp0(xc, all_105_3) = all_105_0
% 55.73/8.15 | | | | | | | |
% 55.73/8.15 | | | | | | | | BETA: splitting (215) gives:
% 55.73/8.15 | | | | | | | |
% 55.73/8.15 | | | | | | | | Case 1:
% 55.73/8.15 | | | | | | | | |
% 55.73/8.15 | | | | | | | | | (217) ~ (sdtlpdtrp0(xc, all_105_3) = all_105_0)
% 55.73/8.15 | | | | | | | | |
% 55.73/8.15 | | | | | | | | | PRED_UNIFY: (216), (217) imply:
% 55.73/8.15 | | | | | | | | | (218) $false
% 55.73/8.15 | | | | | | | | |
% 55.73/8.15 | | | | | | | | | CLOSE: (218) is inconsistent.
% 55.73/8.15 | | | | | | | | |
% 55.73/8.15 | | | | | | | | Case 2:
% 55.73/8.15 | | | | | | | | |
% 55.73/8.15 | | | | | | | | | (219) all_105_0 = all_105_2
% 55.73/8.15 | | | | | | | | |
% 55.73/8.15 | | | | | | | | | REDUCE: (57), (219) imply:
% 55.73/8.15 | | | | | | | | | (220) $false
% 55.73/8.15 | | | | | | | | |
% 55.73/8.15 | | | | | | | | | CLOSE: (220) is inconsistent.
% 55.73/8.15 | | | | | | | | |
% 55.73/8.15 | | | | | | | | End of split
% 55.73/8.15 | | | | | | | |
% 55.73/8.16 | | | | | | | End of split
% 55.73/8.16 | | | | | | |
% 55.73/8.16 | | | | | | End of split
% 55.73/8.16 | | | | | |
% 55.73/8.16 | | | | | End of split
% 55.73/8.16 | | | | |
% 55.73/8.16 | | | | End of split
% 55.73/8.16 | | | |
% 55.73/8.16 | | | End of split
% 55.73/8.16 | | |
% 55.73/8.16 | | End of split
% 55.73/8.16 | |
% 55.73/8.16 | Case 2:
% 55.73/8.16 | |
% 55.73/8.16 | | (221) ~ aSet0(slcrc0)
% 55.73/8.16 | |
% 55.73/8.16 | | PRED_UNIFY: (1), (221) imply:
% 55.73/8.16 | | (222) $false
% 55.73/8.16 | |
% 55.73/8.16 | | CLOSE: (222) is inconsistent.
% 55.73/8.16 | |
% 55.73/8.16 | End of split
% 55.73/8.16 |
% 55.73/8.16 End of proof
% 55.73/8.16 % SZS output end Proof for theBenchmark
% 55.73/8.16
% 55.73/8.16 7560ms
%------------------------------------------------------------------------------