TSTP Solution File: NUM599+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM599+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 : n003.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 11:48:52 EDT 2023
% Result : Theorem 142.61s 19.40s
% Output : Proof 143.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM599+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 : n003.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 16:54:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 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 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 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 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 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
% 6.64/1.62 Prover 6: Preprocessing ...
% 6.64/1.63 Prover 0: Preprocessing ...
% 6.64/1.64 Prover 2: Preprocessing ...
% 6.64/1.65 Prover 4: Preprocessing ...
% 6.64/1.66 Prover 3: Preprocessing ...
% 6.64/1.67 Prover 1: Preprocessing ...
% 6.64/1.68 Prover 5: Preprocessing ...
% 18.69/3.24 Prover 3: Constructing countermodel ...
% 19.37/3.31 Prover 1: Constructing countermodel ...
% 20.03/3.40 Prover 6: Proving ...
% 22.36/3.76 Prover 5: Proving ...
% 54.79/7.94 Prover 4: Constructing countermodel ...
% 55.10/8.02 Prover 2: Proving ...
% 57.99/8.36 Prover 0: Proving ...
% 100.95/13.96 Prover 5: stopped
% 100.95/13.96 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 102.13/14.13 Prover 7: Preprocessing ...
% 109.39/15.02 Prover 7: Constructing countermodel ...
% 111.93/15.49 Prover 2: stopped
% 111.93/15.49 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 113.63/15.63 Prover 8: Preprocessing ...
% 116.02/15.93 Prover 8: Warning: ignoring some quantifiers
% 116.61/15.95 Prover 8: Constructing countermodel ...
% 116.85/15.99 Prover 1: stopped
% 116.85/16.00 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 117.82/16.16 Prover 9: Preprocessing ...
% 131.46/17.88 Prover 6: stopped
% 131.46/17.90 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 132.06/18.14 Prover 10: Preprocessing ...
% 135.63/18.47 Prover 9: Constructing countermodel ...
% 137.58/18.71 Prover 10: Constructing countermodel ...
% 142.61/19.38 Prover 10: Found proof (size 114)
% 142.61/19.38 Prover 10: proved (1483ms)
% 142.61/19.38 Prover 9: stopped
% 142.61/19.38 Prover 3: stopped
% 142.61/19.38 Prover 7: stopped
% 142.61/19.39 Prover 4: stopped
% 142.61/19.39 Prover 8: stopped
% 142.61/19.40 Prover 0: stopped
% 142.61/19.40
% 142.61/19.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 142.61/19.40
% 143.13/19.42 % SZS output start Proof for theBenchmark
% 143.13/19.42 Assumptions after simplification:
% 143.13/19.42 ---------------------------------
% 143.13/19.42
% 143.13/19.42 (mDefPtt)
% 143.13/19.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(v0, v1) = v2) | ~
% 143.13/19.46 $i(v1) | ~ $i(v0) | ~ aFunction0(v0) | ~ aElement0(v1) | ? [v3: $i] :
% 143.13/19.46 (szDzozmdt0(v0) = v3 & $i(v3) & ! [v4: $i] : ! [v5: $i] : (v5 = v1 | ~
% 143.13/19.46 (sdtlpdtrp0(v0, v4) = v5) | ~ $i(v4) | ~ $i(v2) | ~ aElementOf0(v4,
% 143.13/19.46 v2)) & ! [v4: $i] : ! [v5: $i] : ( ~ (sdtlpdtrp0(v0, v4) = v5) | ~
% 143.13/19.46 $i(v4) | ~ $i(v2) | ~ aElementOf0(v4, v2) | aElementOf0(v4, v3)) & !
% 143.13/19.46 [v4: $i] : (v4 = v2 | ~ $i(v4) | ~ aSet0(v4) | ? [v5: $i] : ? [v6: $i]
% 143.13/19.46 : ($i(v5) & ( ~ aElementOf0(v5, v4) | ~ aElementOf0(v5, v3) | ( ~ (v6 =
% 143.13/19.46 v1) & sdtlpdtrp0(v0, v5) = v6 & $i(v6))) & (aElementOf0(v5, v4)
% 143.13/19.46 | (v6 = v1 & sdtlpdtrp0(v0, v5) = v1 & aElementOf0(v5, v3))))) & !
% 143.13/19.46 [v4: $i] : ( ~ (sdtlpdtrp0(v0, v4) = v1) | ~ $i(v4) | ~ $i(v2) | ~
% 143.13/19.46 aElementOf0(v4, v3) | aElementOf0(v4, v2)) & ( ~ $i(v2) | aSet0(v2))))
% 143.13/19.46
% 143.13/19.46 (mDirichlet)
% 143.13/19.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (szDzizrdt0(v0) = v1) | ~
% 143.13/19.46 (sdtlbdtrb0(v0, v1) = v2) | ~ $i(v0) | ~ aFunction0(v0) | isCountable0(v2)
% 143.13/19.46 | ? [v3: $i] : ? [v4: $i] : (szDzozmdt0(v0) = v3 & $i(v3) & ( ~
% 143.13/19.46 isCountable0(v3) | (sdtlcdtrc0(v0, v3) = v4 & $i(v4) & ~
% 143.13/19.46 isFinite0(v4))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 143.13/19.46 (szDzizrdt0(v0) = v1) | ~ (sdtlbdtrb0(v0, v1) = v2) | ~ $i(v0) | ~
% 143.13/19.46 aFunction0(v0) | aElement0(v1) | ? [v3: $i] : ? [v4: $i] : (szDzozmdt0(v0)
% 143.13/19.46 = v3 & $i(v3) & ( ~ isCountable0(v3) | (sdtlcdtrc0(v0, v3) = v4 & $i(v4) &
% 143.13/19.46 ~ isFinite0(v4)))))
% 143.13/19.46
% 143.13/19.46 (mEOfElem)
% 143.13/19.46 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) |
% 143.13/19.46 ~ aSet0(v0) | aElement0(v1))
% 143.13/19.46
% 143.13/19.46 (mImgCount)
% 143.13/19.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlcdtrc0(v0,
% 143.13/19.46 v2) = v3) | ~ (szDzozmdt0(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~
% 143.13/19.46 aFunction0(v0) | ~ aSubsetOf0(v2, v1) | ~ isCountable0(v2) |
% 143.13/19.46 isCountable0(v3) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v5 = v4) &
% 143.13/19.46 sdtlpdtrp0(v0, v5) = v6 & sdtlpdtrp0(v0, v4) = v6 & $i(v6) & $i(v5) &
% 143.13/19.46 $i(v4) & aElementOf0(v5, v1) & aElementOf0(v4, v1)))
% 143.13/19.46
% 143.13/19.46 (mNATSet)
% 143.13/19.46 $i(szNzAzT0) & isCountable0(szNzAzT0) & aSet0(szNzAzT0)
% 143.13/19.46
% 143.13/19.46 (mNatExtra)
% 143.13/19.47 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~
% 143.13/19.47 aElementOf0(v0, szNzAzT0) | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) &
% 143.13/19.47 aElementOf0(v1, szNzAzT0)))
% 143.13/19.47
% 143.13/19.47 (mPttSet)
% 143.13/19.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(v0, v1) = v2) | ~
% 143.13/19.47 $i(v1) | ~ $i(v0) | ~ aFunction0(v0) | ~ aElement0(v1) | ? [v3: $i] :
% 143.13/19.47 (szDzozmdt0(v0) = v3 & $i(v3) & aSubsetOf0(v2, v3)))
% 143.13/19.47
% 143.13/19.47 (mSubFSet)
% 143.13/19.47 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, v0) |
% 143.13/19.47 ~ isFinite0(v0) | ~ aSet0(v0) | isFinite0(v1))
% 143.13/19.47
% 143.13/19.47 (m__)
% 143.13/19.47 $i(xO) & ~ isCountable0(xO)
% 143.13/19.47
% 143.13/19.47 (m__3291)
% 143.13/19.47 $i(xT) & isFinite0(xT) & aSet0(xT)
% 143.13/19.47
% 143.13/19.47 (m__3418)
% 143.13/19.47 $i(xK) & $i(szNzAzT0) & aElementOf0(xK, szNzAzT0)
% 143.13/19.47
% 143.13/19.47 (m__3462)
% 143.13/19.47 ~ (xK = sz00) & $i(xK) & $i(sz00)
% 143.13/19.47
% 143.13/19.47 (m__3520)
% 143.13/19.47 ~ (xK = sz00) & $i(xK) & $i(sz00)
% 143.13/19.47
% 143.13/19.47 (m__3821)
% 143.42/19.47 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 143.42/19.47 : (v1 = v0 | ~ (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) | ~
% 143.42/19.47 $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aElementOf0(v0,
% 143.42/19.47 szNzAzT0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v5 = v4) &
% 143.42/19.47 szmzizndt0(v3) = v5 & szmzizndt0(v2) = v4 & $i(v6) & $i(v5) & $i(v4) &
% 143.42/19.47 aElementOf0(v4, v2) & ! [v7: $i] : ( ~ $i(v7) | ~ aElementOf0(v7, v2) |
% 143.42/19.47 sdtlseqdt0(v4, v7)) & ( ~ aElementOf0(v4, v3) | (aElementOf0(v6, v3) &
% 143.42/19.47 ~ sdtlseqdt0(v4, v6)))))
% 143.42/19.47
% 143.42/19.47 (m__3965)
% 143.42/19.48 $i(xN) & $i(xk) & $i(xS) & $i(xK) & $i(szNzAzT0) & ? [v0: $i] :
% 143.42/19.48 (slbdtsldtrb0(xS, xK) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 143.42/19.48 : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v1) = v2) | ~ (szmzizndt0(v2) = v3) |
% 143.42/19.48 ~ (sdtmndt0(v2, v3) = v4) | ~ $i(v1) | ~ aElementOf0(v1, szNzAzT0) | ?
% 143.42/19.48 [v5: $i] : (slbdtsldtrb0(v4, xk) = v5 & $i(v5) & ! [v6: $i] : ! [v7: $i]
% 143.42/19.48 : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~ aSet0(v6) | ? [v8: $i] :
% 143.42/19.48 ? [v9: $i] : ? [v10: $i] : ($i(v10) & aElementOf0(v3, v2) & ! [v11:
% 143.42/19.48 $i] : ( ~ $i(v11) | ~ aElementOf0(v11, v2) | sdtlseqdt0(v3, v11))
% 143.42/19.48 & ((v9 = xK & sbrdtbr0(v7) = xK & aSubsetOf0(v7, xS) &
% 143.42/19.48 aElementOf0(v7, v0) & aSet0(v7) & ! [v11: $i] : (v11 = v3 | ~
% 143.42/19.48 $i(v11) | ~ aElementOf0(v11, v7) | aElementOf0(v11, v6)) & !
% 143.42/19.48 [v11: $i] : ( ~ $i(v11) | ~ aElementOf0(v11, v7) |
% 143.42/19.48 aElementOf0(v11, xS)) & ! [v11: $i] : ( ~ $i(v11) | ~
% 143.42/19.48 aElementOf0(v11, v7) | aElement0(v11)) & ! [v11: $i] : ( ~
% 143.42/19.48 $i(v11) | ~ aElementOf0(v11, v6) | ~ aElement0(v11) |
% 143.42/19.48 aElementOf0(v11, v7)) & ( ~ $i(v3) | ~ aElement0(v3) |
% 143.42/19.48 aElementOf0(v3, v7))) | (aSet0(v4) & ~ aElementOf0(v6, v5) &
% 143.42/19.48 ! [v11: $i] : (v11 = v3 | ~ $i(v11) | ~ aElementOf0(v11, v2) |
% 143.42/19.48 ~ aElement0(v11) | aElementOf0(v11, v4)) & ! [v11: $i] : ( ~
% 143.42/19.48 $i(v11) | ~ aElementOf0(v11, v4) | aElementOf0(v11, v2)) & !
% 143.42/19.48 [v11: $i] : ( ~ $i(v11) | ~ aElementOf0(v11, v4) |
% 143.42/19.48 aElement0(v11)) & ( ~ $i(v3) | ~ aElementOf0(v3, v4)) & (( ~
% 143.42/19.48 (v8 = xk) & sbrdtbr0(v6) = v8 & $i(v8)) | (aElementOf0(v10,
% 143.42/19.48 v6) & ~ aSubsetOf0(v6, v4) & ~ aElementOf0(v10,
% 143.42/19.48 v4))))))))))
% 143.42/19.48
% 143.42/19.48 (m__4660)
% 143.42/19.48 szDzozmdt0(xe) = szNzAzT0 & $i(xe) & $i(xN) & $i(szNzAzT0) & aFunction0(xe) &
% 143.42/19.48 ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) | ~
% 143.42/19.48 aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2 &
% 143.42/19.48 szmzizndt0(v2) = v1 & $i(v2) & $i(v1) & aElementOf0(v1, v2) & ! [v3: $i]
% 143.42/19.48 : ( ~ $i(v3) | ~ aElementOf0(v3, v2) | sdtlseqdt0(v1, v3))))
% 143.42/19.48
% 143.42/19.48 (m__4730)
% 143.42/19.48 szDzozmdt0(xd) = szNzAzT0 & $i(xd) & $i(xC) & $i(xN) & $i(xk) & $i(szNzAzT0) &
% 143.42/19.48 aFunction0(xd) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xC, v0) = v1) |
% 143.42/19.48 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ?
% 143.42/19.48 [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xd, v0) = v5 & sdtlpdtrp0(xN, v2) = v3
% 143.42/19.48 & slbdtsldtrb0(v3, xk) = v4 & szszuzczcdt0(v0) = v2 & $i(v5) & $i(v4) &
% 143.42/19.48 $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~
% 143.42/19.48 (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aSubsetOf0(v6, v3) | ~
% 143.42/19.48 aSet0(v6) | ? [v8: $i] : ( ~ (v8 = xk) & sbrdtbr0(v6) = v8 & $i(v8))) &
% 143.42/19.48 ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~ (sdtlpdtrp0(v1, v6) = v7) | ~
% 143.42/19.48 $i(v6) | ~ aElementOf0(v6, v4) | ~ aSet0(v6)) & ! [v6: $i] : ! [v7:
% 143.42/19.48 $i] : (v7 = v5 | ~ (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aSet0(v6)
% 143.42/19.48 | ? [v8: $i] : ? [v9: $i] : ($i(v9) & (( ~ (v8 = xk) & sbrdtbr0(v6) =
% 143.42/19.48 v8 & $i(v8)) | (aElementOf0(v9, v6) & ~ aElementOf0(v9, v3)))))))
% 143.42/19.48
% 143.42/19.48 (m__4758)
% 143.42/19.48 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 &
% 143.42/19.48 szDzozmdt0(xd) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT) & aSet0(v1) & !
% 143.42/19.48 [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v2) | ~ $i(v3) | ~
% 143.42/19.48 $i(v2) | ~ aElementOf0(v3, v0) | aElementOf0(v2, v1)) & ! [v2: $i] : ( ~
% 143.42/19.48 $i(v2) | ~ aElementOf0(v2, v1) | aElementOf0(v2, xT)) & ! [v2: $i] : ( ~
% 143.42/19.48 $i(v2) | ~ aElementOf0(v2, v1) | ? [v3: $i] : (sdtlpdtrp0(xd, v3) = v2 &
% 143.42/19.48 $i(v3) & aElementOf0(v3, v0))))
% 143.42/19.48
% 143.42/19.48 (m__4854)
% 143.42/19.48 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) =
% 143.42/19.48 v0 & sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) &
% 143.42/19.48 $i(v0) & aElementOf0(v0, xT) & aSet0(v1) & ! [v3: $i] : ! [v4: $i] : (v4 =
% 143.42/19.48 v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1)) &
% 143.42/19.48 ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~
% 143.42/19.48 aElementOf0(v3, v1) | aElementOf0(v3, v2)) & ! [v3: $i] : ( ~
% 143.42/19.48 (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ aElementOf0(v3, v2) |
% 143.42/19.48 aElementOf0(v3, v1)))
% 143.42/19.48
% 143.42/19.48 (m__4891)
% 143.42/19.49 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 143.42/19.49 (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 &
% 143.42/19.49 szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & !
% 143.42/19.49 [v3: $i] : ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3)
% 143.42/19.49 | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 143.42/19.49 (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) |
% 143.42/19.49 aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xe, v4)
% 143.42/19.49 = v3) | ~ $i(v4) | ~ $i(v3) | ~ aElementOf0(v4, v1) | aElementOf0(v3,
% 143.42/19.49 xO)) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~
% 143.42/19.49 aElementOf0(v3, v2) | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~
% 143.42/19.49 aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 & $i(v4) &
% 143.42/19.49 aElementOf0(v4, v1))))
% 143.42/19.49
% 143.42/19.49 (m__4930)
% 143.42/19.49 $i(xd) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 143.42/19.49 (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = v2 & $i(v2)
% 143.42/19.49 & $i(v1) & $i(v0) & aSet0(v1) & ! [v3: $i] : ! [v4: $i] : (v4 = v0 | ~
% 143.42/19.49 (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1)) & ! [v3:
% 143.42/19.49 $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~
% 143.42/19.49 aElementOf0(v3, v1) | aElementOf0(v3, v2)) & ! [v3: $i] : ( ~
% 143.42/19.49 (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ aElementOf0(v3, v2) |
% 143.42/19.49 aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v1) |
% 143.42/19.49 aElementOf0(v3, szNzAzT0)))
% 143.42/19.49
% 143.42/19.49 (function-axioms)
% 143.42/19.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 143.42/19.49 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 143.42/19.49 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 143.42/19.49 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 143.42/19.49 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 143.42/19.49 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 143.42/19.49 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 143.42/19.49 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 143.42/19.49 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 143.42/19.49 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~
% 143.42/19.49 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 143.42/19.49 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) &
% 143.42/19.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 143.42/19.49 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 143.42/19.49 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 143.42/19.49 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 143.42/19.49 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 143.42/19.49 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 143.42/19.49 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 143.42/19.49 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 143.42/19.49 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 143.42/19.49 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 143.42/19.49 v0))
% 143.42/19.49
% 143.42/19.49 Further assumptions not needed in the proof:
% 143.42/19.49 --------------------------------------------
% 143.42/19.49 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 143.42/19.49 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01,
% 143.42/19.49 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefRst, mDefSImg, mDefSeg,
% 143.42/19.49 mDefSel, mDefSub, mDiffCons, mDomSet, mElmSort, mEmpFin, mFConsSet, mFDiffSet,
% 143.42/19.49 mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgElm, mImgRng, mLessASymm,
% 143.42/19.49 mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, mMinMin, mNatNSucc,
% 143.42/19.49 mNoScLessZr, mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra,
% 143.42/19.49 mSelFSet, mSelNSet, mSelSub, mSetSort, mSubASymm, mSubRefl, mSubTrans,
% 143.42/19.49 mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__3398, m__3435,
% 143.42/19.49 m__3453, m__3533, m__3623, m__3671, m__3754, m__4151, m__4182, m__4331, m__4411,
% 143.42/19.49 m__4618
% 143.42/19.49
% 143.42/19.49 Those formulas are unsatisfiable:
% 143.42/19.49 ---------------------------------
% 143.42/19.49
% 143.42/19.49 Begin of proof
% 143.42/19.49 |
% 143.42/19.49 | ALPHA: (mNATSet) implies:
% 143.42/19.49 | (1) isCountable0(szNzAzT0)
% 143.42/19.50 |
% 143.42/19.50 | ALPHA: (mNatExtra) implies:
% 143.42/19.50 | (2) ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) |
% 143.42/19.50 | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & aElementOf0(v1,
% 143.42/19.50 | szNzAzT0)))
% 143.42/19.50 |
% 143.42/19.50 | ALPHA: (mDirichlet) implies:
% 143.42/19.50 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (szDzizrdt0(v0) = v1) |
% 143.42/19.50 | ~ (sdtlbdtrb0(v0, v1) = v2) | ~ $i(v0) | ~ aFunction0(v0) |
% 143.42/19.50 | isCountable0(v2) | ? [v3: $i] : ? [v4: $i] : (szDzozmdt0(v0) = v3 &
% 143.42/19.50 | $i(v3) & ( ~ isCountable0(v3) | (sdtlcdtrc0(v0, v3) = v4 & $i(v4) &
% 143.42/19.50 | ~ isFinite0(v4)))))
% 143.42/19.50 |
% 143.42/19.50 | ALPHA: (m__3291) implies:
% 143.42/19.50 | (4) aSet0(xT)
% 143.42/19.50 | (5) isFinite0(xT)
% 143.42/19.50 |
% 143.42/19.50 | ALPHA: (m__3418) implies:
% 143.42/19.50 | (6) aElementOf0(xK, szNzAzT0)
% 143.42/19.50 |
% 143.42/19.50 | ALPHA: (m__3520) implies:
% 143.42/19.50 | (7) ~ (xK = sz00)
% 143.42/19.50 |
% 143.42/19.50 | ALPHA: (m__3821) implies:
% 143.42/19.50 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 143.42/19.50 | (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) | ~ $i(v1)
% 143.42/19.50 | | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aElementOf0(v0,
% 143.42/19.50 | szNzAzT0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v5 = v4)
% 143.42/19.50 | & szmzizndt0(v3) = v5 & szmzizndt0(v2) = v4 & $i(v6) & $i(v5) &
% 143.42/19.50 | $i(v4) & aElementOf0(v4, v2) & ! [v7: $i] : ( ~ $i(v7) | ~
% 143.42/19.50 | aElementOf0(v7, v2) | sdtlseqdt0(v4, v7)) & ( ~ aElementOf0(v4,
% 143.42/19.50 | v3) | (aElementOf0(v6, v3) & ~ sdtlseqdt0(v4, v6)))))
% 143.42/19.50 |
% 143.42/19.50 | ALPHA: (m__3965) implies:
% 143.42/19.50 | (9) $i(xK)
% 143.42/19.50 |
% 143.42/19.50 | ALPHA: (m__4660) implies:
% 143.42/19.50 | (10) aFunction0(xe)
% 143.42/19.50 | (11) szDzozmdt0(xe) = szNzAzT0
% 143.42/19.50 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0)
% 143.42/19.50 | | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) =
% 143.42/19.50 | v2 & szmzizndt0(v2) = v1 & $i(v2) & $i(v1) & aElementOf0(v1, v2) &
% 143.42/19.50 | ! [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v2) | sdtlseqdt0(v1,
% 143.42/19.50 | v3))))
% 143.42/19.50 |
% 143.42/19.50 | ALPHA: (m__4730) implies:
% 143.42/19.50 | (13) aFunction0(xd)
% 143.42/19.50 | (14) szDzozmdt0(xd) = szNzAzT0
% 143.42/19.50 |
% 143.42/19.50 | ALPHA: (m__4758) implies:
% 143.42/19.50 | (15) ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & szDzozmdt0(xd)
% 143.42/19.50 | = v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT) & aSet0(v1) & ! [v2:
% 143.42/19.50 | $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v2) | ~ $i(v3) | ~
% 143.42/19.50 | $i(v2) | ~ aElementOf0(v3, v0) | aElementOf0(v2, v1)) & ! [v2:
% 143.42/19.50 | $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | aElementOf0(v2, xT)) &
% 143.42/19.50 | ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | ? [v3: $i] :
% 143.42/19.50 | (sdtlpdtrp0(xd, v3) = v2 & $i(v3) & aElementOf0(v3, v0))))
% 143.42/19.50 |
% 143.42/19.50 | ALPHA: (m__4854) implies:
% 143.42/19.50 | (16) $i(xT)
% 143.42/19.50 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 &
% 143.42/19.50 | sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) &
% 143.42/19.50 | $i(v0) & aElementOf0(v0, xT) & aSet0(v1) & ! [v3: $i] : ! [v4: $i]
% 143.42/19.50 | : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~
% 143.42/19.50 | aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 143.42/19.50 | (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) |
% 143.42/19.50 | aElementOf0(v3, v2)) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v0)
% 143.42/19.50 | | ~ $i(v3) | ~ aElementOf0(v3, v2) | aElementOf0(v3, v1)))
% 143.42/19.50 |
% 143.42/19.50 | ALPHA: (m__4891) implies:
% 143.42/19.50 | (18) $i(xe)
% 143.42/19.51 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 &
% 143.42/19.51 | sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) =
% 143.42/19.51 | v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & ! [v3: $i]
% 143.42/19.51 | : ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3)
% 143.42/19.51 | | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 143.42/19.51 | (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) |
% 143.42/19.51 | aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 143.42/19.51 | (sdtlpdtrp0(xe, v4) = v3) | ~ $i(v4) | ~ $i(v3) | ~
% 143.42/19.51 | aElementOf0(v4, v1) | aElementOf0(v3, xO)) & ! [v3: $i] : ( ~
% 143.42/19.51 | (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ aElementOf0(v3, v2) |
% 143.42/19.51 | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~
% 143.42/19.51 | aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 &
% 143.42/19.51 | $i(v4) & aElementOf0(v4, v1))))
% 143.42/19.51 |
% 143.42/19.51 | ALPHA: (m__4930) implies:
% 143.42/19.51 | (20) $i(xd)
% 143.42/19.51 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 &
% 143.42/19.51 | sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) &
% 143.42/19.51 | $i(v0) & aSet0(v1) & ! [v3: $i] : ! [v4: $i] : (v4 = v0 | ~
% 143.42/19.51 | (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1)) &
% 143.42/19.51 | ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3)
% 143.42/19.51 | | ~ aElementOf0(v3, v1) | aElementOf0(v3, v2)) & ! [v3: $i] : (
% 143.42/19.51 | ~ (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ aElementOf0(v3, v2) |
% 143.42/19.51 | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~
% 143.42/19.51 | aElementOf0(v3, v1) | aElementOf0(v3, szNzAzT0)))
% 143.42/19.51 |
% 143.42/19.51 | ALPHA: (m__) implies:
% 143.42/19.51 | (22) ~ isCountable0(xO)
% 143.42/19.51 |
% 143.42/19.51 | ALPHA: (function-axioms) implies:
% 143.42/19.51 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 143.42/19.51 | (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) = v0))
% 143.42/19.51 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 143.42/19.51 | (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0))
% 143.42/19.51 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 143.42/19.51 | (szDzizrdt0(v2) = v1) | ~ (szDzizrdt0(v2) = v0))
% 143.42/19.51 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 143.42/19.51 | (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) = v0))
% 143.42/19.51 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 143.42/19.51 | (sdtlcdtrc0(v3, v2) = v1) | ~ (sdtlcdtrc0(v3, v2) = v0))
% 143.42/19.51 |
% 143.42/19.51 | DELTA: instantiating (15) with fresh symbols all_77_0, all_77_1 gives:
% 143.42/19.51 | (28) sdtlcdtrc0(xd, all_77_1) = all_77_0 & szDzozmdt0(xd) = all_77_1 &
% 143.42/19.51 | $i(all_77_0) & $i(all_77_1) & aSubsetOf0(all_77_0, xT) &
% 143.42/19.51 | aSet0(all_77_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v1)
% 143.42/19.51 | = v0) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, all_77_1) |
% 143.42/19.51 | aElementOf0(v0, all_77_0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 143.42/19.51 | aElementOf0(v0, all_77_0) | aElementOf0(v0, xT)) & ! [v0: $i] : ( ~
% 143.42/19.51 | $i(v0) | ~ aElementOf0(v0, all_77_0) | ? [v1: $i] :
% 143.42/19.51 | (sdtlpdtrp0(xd, v1) = v0 & $i(v1) & aElementOf0(v1, all_77_1)))
% 143.42/19.51 |
% 143.42/19.51 | ALPHA: (28) implies:
% 143.42/19.51 | (29) aSubsetOf0(all_77_0, xT)
% 143.42/19.51 | (30) $i(all_77_0)
% 143.42/19.51 | (31) szDzozmdt0(xd) = all_77_1
% 143.42/19.51 | (32) sdtlcdtrc0(xd, all_77_1) = all_77_0
% 143.42/19.51 |
% 143.42/19.51 | DELTA: instantiating (17) with fresh symbols all_80_0, all_80_1, all_80_2
% 143.42/19.51 | gives:
% 143.42/19.52 | (33) szDzizrdt0(xd) = all_80_2 & sdtlbdtrb0(xd, all_80_2) = all_80_1 &
% 143.42/19.52 | szDzozmdt0(xd) = all_80_0 & $i(all_80_0) & $i(all_80_1) & $i(all_80_2)
% 143.42/19.52 | & aElementOf0(all_80_2, xT) & aSet0(all_80_1) & ! [v0: $i] : ! [v1:
% 143.42/19.52 | int] : (v1 = all_80_2 | ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) |
% 143.42/19.52 | ~ aElementOf0(v0, all_80_1)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 143.42/19.52 | (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_80_1)
% 143.42/19.52 | | aElementOf0(v0, all_80_0)) & ! [v0: $i] : ( ~ (sdtlpdtrp0(xd, v0)
% 143.42/19.52 | = all_80_2) | ~ $i(v0) | ~ aElementOf0(v0, all_80_0) |
% 143.42/19.52 | aElementOf0(v0, all_80_1))
% 143.42/19.52 |
% 143.42/19.52 | ALPHA: (33) implies:
% 143.42/19.52 | (34) aElementOf0(all_80_2, xT)
% 143.42/19.52 | (35) szDzozmdt0(xd) = all_80_0
% 143.42/19.52 | (36) sdtlbdtrb0(xd, all_80_2) = all_80_1
% 143.42/19.52 | (37) szDzizrdt0(xd) = all_80_2
% 143.42/19.52 |
% 143.42/19.52 | DELTA: instantiating (21) with fresh symbols all_83_0, all_83_1, all_83_2
% 143.42/19.52 | gives:
% 143.42/19.52 | (38) szDzizrdt0(xd) = all_83_2 & sdtlbdtrb0(xd, all_83_2) = all_83_1 &
% 143.42/19.52 | szDzozmdt0(xd) = all_83_0 & $i(all_83_0) & $i(all_83_1) & $i(all_83_2)
% 143.42/19.52 | & aSet0(all_83_1) & ! [v0: $i] : ! [v1: int] : (v1 = all_83_2 | ~
% 143.42/19.52 | (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0,
% 143.42/19.52 | all_83_1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) =
% 143.42/19.52 | v1) | ~ $i(v0) | ~ aElementOf0(v0, all_83_1) | aElementOf0(v0,
% 143.42/19.52 | all_83_0)) & ! [v0: $i] : ( ~ (sdtlpdtrp0(xd, v0) = all_83_2) |
% 143.42/19.52 | ~ $i(v0) | ~ aElementOf0(v0, all_83_0) | aElementOf0(v0, all_83_1))
% 143.42/19.52 | & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_83_1) |
% 143.42/19.52 | aElementOf0(v0, szNzAzT0))
% 143.42/19.52 |
% 143.42/19.52 | ALPHA: (38) implies:
% 143.42/19.52 | (39) $i(all_83_2)
% 143.42/19.52 | (40) $i(all_83_1)
% 143.42/19.52 | (41) szDzozmdt0(xd) = all_83_0
% 143.42/19.52 | (42) sdtlbdtrb0(xd, all_83_2) = all_83_1
% 143.42/19.52 | (43) szDzizrdt0(xd) = all_83_2
% 143.42/19.52 |
% 143.42/19.52 | DELTA: instantiating (19) with fresh symbols all_86_0, all_86_1, all_86_2
% 143.42/19.52 | gives:
% 143.42/19.52 | (44) szDzizrdt0(xd) = all_86_2 & sdtlcdtrc0(xe, all_86_1) = xO &
% 143.42/19.52 | sdtlbdtrb0(xd, all_86_2) = all_86_1 & szDzozmdt0(xd) = all_86_0 &
% 143.42/19.52 | $i(all_86_0) & $i(all_86_1) & $i(all_86_2) & aSet0(all_86_1) &
% 143.42/19.52 | aSet0(xO) & ! [v0: $i] : ! [v1: int] : (v1 = all_86_2 | ~
% 143.42/19.52 | (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0,
% 143.42/19.52 | all_86_1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) =
% 143.42/19.52 | v1) | ~ $i(v0) | ~ aElementOf0(v0, all_86_1) | aElementOf0(v0,
% 143.42/19.52 | all_86_0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v1) =
% 143.42/19.52 | v0) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, all_86_1) |
% 143.42/19.52 | aElementOf0(v0, xO)) & ! [v0: $i] : ( ~ (sdtlpdtrp0(xd, v0) =
% 143.42/19.52 | all_86_2) | ~ $i(v0) | ~ aElementOf0(v0, all_86_0) |
% 143.42/19.52 | aElementOf0(v0, all_86_1)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 143.42/19.52 | aElementOf0(v0, xO) | ? [v1: $i] : (sdtlpdtrp0(xe, v1) = v0 &
% 143.42/19.52 | $i(v1) & aElementOf0(v1, all_86_1)))
% 143.42/19.52 |
% 143.42/19.52 | ALPHA: (44) implies:
% 143.42/19.52 | (45) szDzozmdt0(xd) = all_86_0
% 143.42/19.52 | (46) sdtlbdtrb0(xd, all_86_2) = all_86_1
% 143.42/19.52 | (47) sdtlcdtrc0(xe, all_86_1) = xO
% 143.42/19.52 | (48) szDzizrdt0(xd) = all_86_2
% 143.42/19.52 |
% 143.42/19.52 | GROUND_INST: instantiating (24) with all_80_0, all_83_0, xd, simplifying with
% 143.42/19.52 | (35), (41) gives:
% 143.42/19.52 | (49) all_83_0 = all_80_0
% 143.42/19.52 |
% 143.42/19.52 | GROUND_INST: instantiating (24) with szNzAzT0, all_83_0, xd, simplifying with
% 143.42/19.52 | (14), (41) gives:
% 143.42/19.52 | (50) all_83_0 = szNzAzT0
% 143.42/19.52 |
% 143.42/19.52 | GROUND_INST: instantiating (24) with all_83_0, all_86_0, xd, simplifying with
% 143.42/19.52 | (41), (45) gives:
% 143.42/19.52 | (51) all_86_0 = all_83_0
% 143.42/19.52 |
% 143.42/19.52 | GROUND_INST: instantiating (24) with all_77_1, all_86_0, xd, simplifying with
% 143.42/19.52 | (31), (45) gives:
% 143.42/19.52 | (52) all_86_0 = all_77_1
% 143.42/19.52 |
% 143.42/19.52 | GROUND_INST: instantiating (25) with all_83_2, all_86_2, xd, simplifying with
% 143.42/19.52 | (43), (48) gives:
% 143.42/19.52 | (53) all_86_2 = all_83_2
% 143.42/19.52 |
% 143.42/19.52 | GROUND_INST: instantiating (25) with all_80_2, all_86_2, xd, simplifying with
% 143.42/19.52 | (37), (48) gives:
% 143.42/19.52 | (54) all_86_2 = all_80_2
% 143.42/19.52 |
% 143.42/19.52 | COMBINE_EQS: (51), (52) imply:
% 143.42/19.52 | (55) all_83_0 = all_77_1
% 143.42/19.52 |
% 143.42/19.52 | SIMP: (55) implies:
% 143.42/19.52 | (56) all_83_0 = all_77_1
% 143.42/19.52 |
% 143.42/19.52 | COMBINE_EQS: (53), (54) imply:
% 143.42/19.53 | (57) all_83_2 = all_80_2
% 143.42/19.53 |
% 143.42/19.53 | COMBINE_EQS: (49), (50) imply:
% 143.42/19.53 | (58) all_80_0 = szNzAzT0
% 143.42/19.53 |
% 143.42/19.53 | COMBINE_EQS: (49), (56) imply:
% 143.42/19.53 | (59) all_80_0 = all_77_1
% 143.42/19.53 |
% 143.42/19.53 | COMBINE_EQS: (58), (59) imply:
% 143.42/19.53 | (60) all_77_1 = szNzAzT0
% 143.42/19.53 |
% 143.42/19.53 | REDUCE: (32), (60) imply:
% 143.42/19.53 | (61) sdtlcdtrc0(xd, szNzAzT0) = all_77_0
% 143.42/19.53 |
% 143.42/19.53 | REDUCE: (46), (54) imply:
% 143.42/19.53 | (62) sdtlbdtrb0(xd, all_80_2) = all_86_1
% 143.42/19.53 |
% 143.42/19.53 | REDUCE: (42), (57) imply:
% 143.42/19.53 | (63) sdtlbdtrb0(xd, all_80_2) = all_83_1
% 143.42/19.53 |
% 143.42/19.53 | REDUCE: (39), (57) imply:
% 143.42/19.53 | (64) $i(all_80_2)
% 143.42/19.53 |
% 143.42/19.53 | GROUND_INST: instantiating (26) with all_80_1, all_86_1, all_80_2, xd,
% 143.42/19.53 | simplifying with (36), (62) gives:
% 143.42/19.53 | (65) all_86_1 = all_80_1
% 143.42/19.53 |
% 143.42/19.53 | GROUND_INST: instantiating (26) with all_83_1, all_86_1, all_80_2, xd,
% 143.42/19.53 | simplifying with (62), (63) gives:
% 143.42/19.53 | (66) all_86_1 = all_83_1
% 143.42/19.53 |
% 143.42/19.53 | COMBINE_EQS: (65), (66) imply:
% 143.42/19.53 | (67) all_83_1 = all_80_1
% 143.42/19.53 |
% 143.42/19.53 | REDUCE: (47), (65) imply:
% 143.42/19.53 | (68) sdtlcdtrc0(xe, all_80_1) = xO
% 143.42/19.53 |
% 143.42/19.53 | REDUCE: (40), (67) imply:
% 143.42/19.53 | (69) $i(all_80_1)
% 143.42/19.53 |
% 143.42/19.53 | GROUND_INST: instantiating (2) with xK, simplifying with (6), (9) gives:
% 143.42/19.53 | (70) xK = sz00 | ? [v0: $i] : (szszuzczcdt0(v0) = xK & $i(v0) &
% 143.42/19.53 | aElementOf0(v0, szNzAzT0))
% 143.42/19.53 |
% 143.42/19.53 | GROUND_INST: instantiating (mEOfElem) with xT, all_80_2, simplifying with (4),
% 143.42/19.53 | (16), (34), (64) gives:
% 143.42/19.53 | (71) aElement0(all_80_2)
% 143.42/19.53 |
% 143.42/19.53 | GROUND_INST: instantiating (mSubFSet) with xT, all_77_0, simplifying with (4),
% 143.42/19.53 | (5), (16), (29), (30) gives:
% 143.42/19.53 | (72) isFinite0(all_77_0)
% 143.42/19.53 |
% 143.42/19.53 | GROUND_INST: instantiating (3) with xd, all_80_2, all_80_1, simplifying with
% 143.42/19.53 | (13), (20), (36), (37) gives:
% 143.42/19.53 | (73) isCountable0(all_80_1) | ? [v0: $i] : ? [v1: $i] : (szDzozmdt0(xd) =
% 143.42/19.53 | v0 & $i(v0) & ( ~ isCountable0(v0) | (sdtlcdtrc0(xd, v0) = v1 &
% 143.42/19.53 | $i(v1) & ~ isFinite0(v1))))
% 143.42/19.53 |
% 143.42/19.53 | BETA: splitting (73) gives:
% 143.42/19.53 |
% 143.42/19.53 | Case 1:
% 143.42/19.53 | |
% 143.42/19.53 | | (74) isCountable0(all_80_1)
% 143.42/19.53 | |
% 143.42/19.53 | | BETA: splitting (70) gives:
% 143.42/19.53 | |
% 143.42/19.53 | | Case 1:
% 143.42/19.53 | | |
% 143.42/19.53 | | | (75) xK = sz00
% 143.42/19.53 | | |
% 143.42/19.53 | | | REDUCE: (7), (75) imply:
% 143.42/19.53 | | | (76) $false
% 143.42/19.53 | | |
% 143.42/19.53 | | | CLOSE: (76) is inconsistent.
% 143.42/19.53 | | |
% 143.42/19.53 | | Case 2:
% 143.42/19.53 | | |
% 143.42/19.53 | | |
% 143.42/19.53 | | | GROUND_INST: instantiating (mPttSet) with xd, all_80_2, all_80_1,
% 143.42/19.53 | | | simplifying with (13), (20), (36), (64), (71) gives:
% 143.42/19.53 | | | (77) ? [v0: $i] : (szDzozmdt0(xd) = v0 & $i(v0) & aSubsetOf0(all_80_1,
% 143.42/19.53 | | | v0))
% 143.42/19.53 | | |
% 143.42/19.53 | | | GROUND_INST: instantiating (mDefPtt) with xd, all_80_2, all_80_1,
% 143.42/19.53 | | | simplifying with (13), (20), (36), (64), (71) gives:
% 143.42/19.54 | | | (78) ? [v0: $i] : (szDzozmdt0(xd) = v0 & $i(v0) & ! [v1: $i] : !
% 143.42/19.54 | | | [v2: int] : (v2 = all_80_2 | ~ (sdtlpdtrp0(xd, v1) = v2) | ~
% 143.42/19.54 | | | $i(v1) | ~ $i(all_80_1) | ~ aElementOf0(v1, all_80_1)) & !
% 143.42/19.54 | | | [v1: $i] : ! [v2: $i] : ( ~ (sdtlpdtrp0(xd, v1) = v2) | ~
% 143.42/19.54 | | | $i(v1) | ~ $i(all_80_1) | ~ aElementOf0(v1, all_80_1) |
% 143.42/19.54 | | | aElementOf0(v1, v0)) & ! [v1: any] : (v1 = all_80_1 | ~
% 143.42/19.54 | | | $i(v1) | ~ aSet0(v1) | ? [v2: $i] : ? [v3: any] : ($i(v2) &
% 143.42/19.54 | | | ( ~ aElementOf0(v2, v1) | ~ aElementOf0(v2, v0) | ( ~ (v3 =
% 143.42/19.54 | | | all_80_2) & sdtlpdtrp0(xd, v2) = v3 & $i(v3))) &
% 143.42/19.54 | | | (aElementOf0(v2, v1) | (v3 = all_80_2 & sdtlpdtrp0(xd, v2) =
% 143.42/19.54 | | | all_80_2 & aElementOf0(v2, v0))))) & ! [v1: $i] : ( ~
% 143.42/19.54 | | | (sdtlpdtrp0(xd, v1) = all_80_2) | ~ $i(v1) | ~ $i(all_80_1)
% 143.42/19.54 | | | | ~ aElementOf0(v1, v0) | aElementOf0(v1, all_80_1)) & ( ~
% 143.42/19.54 | | | $i(all_80_1) | aSet0(all_80_1)))
% 143.42/19.54 | | |
% 143.42/19.54 | | | DELTA: instantiating (77) with fresh symbol all_136_0 gives:
% 143.42/19.54 | | | (79) szDzozmdt0(xd) = all_136_0 & $i(all_136_0) & aSubsetOf0(all_80_1,
% 143.42/19.54 | | | all_136_0)
% 143.42/19.54 | | |
% 143.42/19.54 | | | ALPHA: (79) implies:
% 143.42/19.54 | | | (80) aSubsetOf0(all_80_1, all_136_0)
% 143.42/19.54 | | | (81) szDzozmdt0(xd) = all_136_0
% 143.42/19.54 | | |
% 143.42/19.54 | | | DELTA: instantiating (78) with fresh symbol all_144_0 gives:
% 143.42/19.54 | | | (82) szDzozmdt0(xd) = all_144_0 & $i(all_144_0) & ! [v0: $i] : ! [v1:
% 143.42/19.54 | | | int] : (v1 = all_80_2 | ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0)
% 143.42/19.54 | | | | ~ $i(all_80_1) | ~ aElementOf0(v0, all_80_1)) & ! [v0: $i]
% 143.42/19.54 | | | : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~
% 143.42/19.54 | | | $i(all_80_1) | ~ aElementOf0(v0, all_80_1) | aElementOf0(v0,
% 143.42/19.54 | | | all_144_0)) & ! [v0: any] : (v0 = all_80_1 | ~ $i(v0) | ~
% 143.42/19.54 | | | aSet0(v0) | ? [v1: $i] : ? [v2: any] : ($i(v1) & ( ~
% 143.42/19.54 | | | aElementOf0(v1, v0) | ~ aElementOf0(v1, all_144_0) | ( ~
% 143.42/19.54 | | | (v2 = all_80_2) & sdtlpdtrp0(xd, v1) = v2 & $i(v2))) &
% 143.42/19.54 | | | (aElementOf0(v1, v0) | (v2 = all_80_2 & sdtlpdtrp0(xd, v1) =
% 143.42/19.54 | | | all_80_2 & aElementOf0(v1, all_144_0))))) & ! [v0: $i] :
% 143.42/19.54 | | | ( ~ (sdtlpdtrp0(xd, v0) = all_80_2) | ~ $i(v0) | ~ $i(all_80_1)
% 143.42/19.54 | | | | ~ aElementOf0(v0, all_144_0) | aElementOf0(v0, all_80_1)) & (
% 143.42/19.54 | | | ~ $i(all_80_1) | aSet0(all_80_1))
% 143.42/19.54 | | |
% 143.42/19.54 | | | ALPHA: (82) implies:
% 143.42/19.54 | | | (83) szDzozmdt0(xd) = all_144_0
% 143.42/19.54 | | |
% 143.42/19.54 | | | GROUND_INST: instantiating (24) with szNzAzT0, all_144_0, xd, simplifying
% 143.42/19.54 | | | with (14), (83) gives:
% 143.42/19.54 | | | (84) all_144_0 = szNzAzT0
% 143.42/19.54 | | |
% 143.42/19.54 | | | GROUND_INST: instantiating (24) with all_136_0, all_144_0, xd, simplifying
% 143.42/19.54 | | | with (81), (83) gives:
% 143.42/19.54 | | | (85) all_144_0 = all_136_0
% 143.42/19.54 | | |
% 143.42/19.54 | | | COMBINE_EQS: (84), (85) imply:
% 143.42/19.54 | | | (86) all_136_0 = szNzAzT0
% 143.42/19.54 | | |
% 143.42/19.54 | | | REDUCE: (80), (86) imply:
% 143.42/19.54 | | | (87) aSubsetOf0(all_80_1, szNzAzT0)
% 143.42/19.54 | | |
% 143.42/19.54 | | | GROUND_INST: instantiating (mImgCount) with xe, szNzAzT0, all_80_1, xO,
% 143.42/19.54 | | | simplifying with (10), (11), (18), (22), (68), (69), (74),
% 143.42/19.54 | | | (87) gives:
% 143.42/19.54 | | | (88) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = v0) &
% 143.42/19.54 | | | sdtlpdtrp0(xe, v1) = v2 & sdtlpdtrp0(xe, v0) = v2 & $i(v2) &
% 143.42/19.54 | | | $i(v1) & $i(v0) & aElementOf0(v1, szNzAzT0) & aElementOf0(v0,
% 143.42/19.54 | | | szNzAzT0))
% 143.42/19.54 | | |
% 143.42/19.54 | | | DELTA: instantiating (88) with fresh symbols all_159_0, all_159_1,
% 143.42/19.54 | | | all_159_2 gives:
% 143.42/19.54 | | | (89) ~ (all_159_1 = all_159_2) & sdtlpdtrp0(xe, all_159_1) = all_159_0
% 143.42/19.54 | | | & sdtlpdtrp0(xe, all_159_2) = all_159_0 & $i(all_159_0) &
% 143.42/19.54 | | | $i(all_159_1) & $i(all_159_2) & aElementOf0(all_159_1, szNzAzT0) &
% 143.42/19.54 | | | aElementOf0(all_159_2, szNzAzT0)
% 143.42/19.54 | | |
% 143.42/19.54 | | | ALPHA: (89) implies:
% 143.42/19.54 | | | (90) ~ (all_159_1 = all_159_2)
% 143.42/19.54 | | | (91) aElementOf0(all_159_2, szNzAzT0)
% 143.42/19.54 | | | (92) aElementOf0(all_159_1, szNzAzT0)
% 143.42/19.55 | | | (93) $i(all_159_2)
% 143.42/19.55 | | | (94) $i(all_159_1)
% 143.42/19.55 | | | (95) sdtlpdtrp0(xe, all_159_2) = all_159_0
% 143.42/19.55 | | | (96) sdtlpdtrp0(xe, all_159_1) = all_159_0
% 143.42/19.55 | | |
% 143.42/19.55 | | | GROUND_INST: instantiating (12) with all_159_2, all_159_0, simplifying
% 143.42/19.55 | | | with (91), (93), (95) gives:
% 143.42/19.55 | | | (97) ? [v0: $i] : (sdtlpdtrp0(xN, all_159_2) = v0 & szmzizndt0(v0) =
% 143.42/19.55 | | | all_159_0 & $i(v0) & $i(all_159_0) & aElementOf0(all_159_0, v0)
% 143.42/19.55 | | | & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, v0) |
% 143.42/19.55 | | | sdtlseqdt0(all_159_0, v1)))
% 143.42/19.55 | | |
% 143.42/19.55 | | | GROUND_INST: instantiating (12) with all_159_1, all_159_0, simplifying
% 143.42/19.55 | | | with (92), (94), (96) gives:
% 143.42/19.55 | | | (98) ? [v0: $i] : (sdtlpdtrp0(xN, all_159_1) = v0 & szmzizndt0(v0) =
% 143.42/19.55 | | | all_159_0 & $i(v0) & $i(all_159_0) & aElementOf0(all_159_0, v0)
% 143.42/19.55 | | | & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, v0) |
% 143.42/19.55 | | | sdtlseqdt0(all_159_0, v1)))
% 143.42/19.55 | | |
% 143.42/19.55 | | | DELTA: instantiating (98) with fresh symbol all_195_0 gives:
% 143.42/19.55 | | | (99) sdtlpdtrp0(xN, all_159_1) = all_195_0 & szmzizndt0(all_195_0) =
% 143.42/19.55 | | | all_159_0 & $i(all_195_0) & $i(all_159_0) & aElementOf0(all_159_0,
% 143.42/19.55 | | | all_195_0) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0,
% 143.42/19.55 | | | all_195_0) | sdtlseqdt0(all_159_0, v0))
% 143.42/19.55 | | |
% 143.42/19.55 | | | ALPHA: (99) implies:
% 143.42/19.55 | | | (100) szmzizndt0(all_195_0) = all_159_0
% 143.42/19.55 | | | (101) sdtlpdtrp0(xN, all_159_1) = all_195_0
% 143.42/19.55 | | |
% 143.42/19.55 | | | DELTA: instantiating (97) with fresh symbol all_198_0 gives:
% 143.42/19.55 | | | (102) sdtlpdtrp0(xN, all_159_2) = all_198_0 & szmzizndt0(all_198_0) =
% 143.42/19.55 | | | all_159_0 & $i(all_198_0) & $i(all_159_0) &
% 143.42/19.55 | | | aElementOf0(all_159_0, all_198_0) & ! [v0: $i] : ( ~ $i(v0) | ~
% 143.42/19.55 | | | aElementOf0(v0, all_198_0) | sdtlseqdt0(all_159_0, v0))
% 143.42/19.55 | | |
% 143.42/19.55 | | | ALPHA: (102) implies:
% 143.42/19.55 | | | (103) szmzizndt0(all_198_0) = all_159_0
% 143.42/19.55 | | | (104) sdtlpdtrp0(xN, all_159_2) = all_198_0
% 143.42/19.55 | | |
% 143.42/19.55 | | | GROUND_INST: instantiating (8) with all_159_2, all_159_1, all_198_0,
% 143.42/19.55 | | | all_195_0, simplifying with (91), (92), (93), (94), (101),
% 143.42/19.55 | | | (104) gives:
% 143.42/19.55 | | | (105) all_159_1 = all_159_2 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 143.42/19.55 | | | ( ~ (v1 = v0) & szmzizndt0(all_198_0) = v0 &
% 143.42/19.55 | | | szmzizndt0(all_195_0) = v1 & $i(v2) & $i(v1) & $i(v0) &
% 143.42/19.55 | | | aElementOf0(v0, all_198_0) & ! [v3: $i] : ( ~ $i(v3) | ~
% 143.42/19.55 | | | aElementOf0(v3, all_198_0) | sdtlseqdt0(v0, v3)) & ( ~
% 143.42/19.55 | | | aElementOf0(v0, all_195_0) | (aElementOf0(v2, all_195_0) & ~
% 143.42/19.55 | | | sdtlseqdt0(v0, v2))))
% 143.42/19.55 | | |
% 143.42/19.55 | | | GROUND_INST: instantiating (8) with all_159_1, all_159_2, all_195_0,
% 143.42/19.55 | | | all_198_0, simplifying with (91), (92), (93), (94), (101),
% 143.42/19.55 | | | (104) gives:
% 143.42/19.55 | | | (106) all_159_1 = all_159_2 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 143.42/19.55 | | | ( ~ (v1 = v0) & szmzizndt0(all_198_0) = v1 &
% 143.42/19.55 | | | szmzizndt0(all_195_0) = v0 & $i(v2) & $i(v1) & $i(v0) &
% 143.42/19.55 | | | aElementOf0(v0, all_195_0) & ! [v3: $i] : ( ~ $i(v3) | ~
% 143.42/19.55 | | | aElementOf0(v3, all_195_0) | sdtlseqdt0(v0, v3)) & ( ~
% 143.42/19.55 | | | aElementOf0(v0, all_198_0) | (aElementOf0(v2, all_198_0) & ~
% 143.42/19.55 | | | sdtlseqdt0(v0, v2))))
% 143.42/19.55 | | |
% 143.42/19.55 | | | BETA: splitting (106) gives:
% 143.42/19.55 | | |
% 143.42/19.55 | | | Case 1:
% 143.42/19.55 | | | |
% 143.42/19.55 | | | | (107) all_159_1 = all_159_2
% 143.42/19.55 | | | |
% 143.42/19.55 | | | | REDUCE: (90), (107) imply:
% 143.42/19.55 | | | | (108) $false
% 143.42/19.55 | | | |
% 143.42/19.55 | | | | CLOSE: (108) is inconsistent.
% 143.42/19.55 | | | |
% 143.42/19.55 | | | Case 2:
% 143.42/19.55 | | | |
% 143.42/19.55 | | | | (109) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = v0) &
% 143.42/19.55 | | | | szmzizndt0(all_198_0) = v1 & szmzizndt0(all_195_0) = v0 &
% 143.42/19.55 | | | | $i(v2) & $i(v1) & $i(v0) & aElementOf0(v0, all_195_0) & !
% 143.42/19.55 | | | | [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, all_195_0) |
% 143.42/19.55 | | | | sdtlseqdt0(v0, v3)) & ( ~ aElementOf0(v0, all_198_0) |
% 143.42/19.55 | | | | (aElementOf0(v2, all_198_0) & ~ sdtlseqdt0(v0, v2))))
% 143.42/19.55 | | | |
% 143.42/19.55 | | | | DELTA: instantiating (109) with fresh symbols all_233_0, all_233_1,
% 143.42/19.55 | | | | all_233_2 gives:
% 143.42/19.55 | | | | (110) ~ (all_233_1 = all_233_2) & szmzizndt0(all_198_0) = all_233_1
% 143.42/19.55 | | | | & szmzizndt0(all_195_0) = all_233_2 & $i(all_233_0) &
% 143.42/19.55 | | | | $i(all_233_1) & $i(all_233_2) & aElementOf0(all_233_2,
% 143.42/19.55 | | | | all_195_0) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0,
% 143.42/19.55 | | | | all_195_0) | sdtlseqdt0(all_233_2, v0)) & ( ~
% 143.42/19.55 | | | | aElementOf0(all_233_2, all_198_0) | (aElementOf0(all_233_0,
% 143.42/19.55 | | | | all_198_0) & ~ sdtlseqdt0(all_233_2, all_233_0)))
% 143.42/19.55 | | | |
% 143.42/19.55 | | | | ALPHA: (110) implies:
% 143.42/19.55 | | | | (111) ~ (all_233_1 = all_233_2)
% 143.42/19.55 | | | | (112) szmzizndt0(all_195_0) = all_233_2
% 143.42/19.55 | | | | (113) szmzizndt0(all_198_0) = all_233_1
% 143.42/19.55 | | | |
% 143.42/19.55 | | | | BETA: splitting (105) gives:
% 143.42/19.56 | | | |
% 143.42/19.56 | | | | Case 1:
% 143.42/19.56 | | | | |
% 143.42/19.56 | | | | | (114) all_159_1 = all_159_2
% 143.42/19.56 | | | | |
% 143.42/19.56 | | | | | REDUCE: (90), (114) imply:
% 143.42/19.56 | | | | | (115) $false
% 143.42/19.56 | | | | |
% 143.42/19.56 | | | | | CLOSE: (115) is inconsistent.
% 143.42/19.56 | | | | |
% 143.42/19.56 | | | | Case 2:
% 143.42/19.56 | | | | |
% 143.42/19.56 | | | | | (116) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = v0) &
% 143.42/19.56 | | | | | szmzizndt0(all_198_0) = v0 & szmzizndt0(all_195_0) = v1 &
% 143.42/19.56 | | | | | $i(v2) & $i(v1) & $i(v0) & aElementOf0(v0, all_198_0) & !
% 143.42/19.56 | | | | | [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, all_198_0) |
% 143.42/19.56 | | | | | sdtlseqdt0(v0, v3)) & ( ~ aElementOf0(v0, all_195_0) |
% 143.42/19.56 | | | | | (aElementOf0(v2, all_195_0) & ~ sdtlseqdt0(v0, v2))))
% 143.42/19.56 | | | | |
% 143.42/19.56 | | | | | DELTA: instantiating (116) with fresh symbols all_245_0, all_245_1,
% 143.42/19.56 | | | | | all_245_2 gives:
% 143.42/19.56 | | | | | (117) ~ (all_245_1 = all_245_2) & szmzizndt0(all_198_0) =
% 143.42/19.56 | | | | | all_245_2 & szmzizndt0(all_195_0) = all_245_1 & $i(all_245_0)
% 143.42/19.56 | | | | | & $i(all_245_1) & $i(all_245_2) & aElementOf0(all_245_2,
% 143.42/19.56 | | | | | all_198_0) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0,
% 143.42/19.56 | | | | | all_198_0) | sdtlseqdt0(all_245_2, v0)) & ( ~
% 143.42/19.56 | | | | | aElementOf0(all_245_2, all_195_0) | (aElementOf0(all_245_0,
% 143.42/19.56 | | | | | all_195_0) & ~ sdtlseqdt0(all_245_2, all_245_0)))
% 143.42/19.56 | | | | |
% 143.42/19.56 | | | | | ALPHA: (117) implies:
% 143.42/19.56 | | | | | (118) szmzizndt0(all_195_0) = all_245_1
% 143.42/19.56 | | | | | (119) szmzizndt0(all_198_0) = all_245_2
% 143.42/19.56 | | | | |
% 143.42/19.56 | | | | | GROUND_INST: instantiating (23) with all_159_0, all_245_1, all_195_0,
% 143.42/19.56 | | | | | simplifying with (100), (118) gives:
% 143.42/19.56 | | | | | (120) all_245_1 = all_159_0
% 143.42/19.56 | | | | |
% 143.42/19.56 | | | | | GROUND_INST: instantiating (23) with all_233_2, all_245_1, all_195_0,
% 143.42/19.56 | | | | | simplifying with (112), (118) gives:
% 143.42/19.56 | | | | | (121) all_245_1 = all_233_2
% 143.42/19.56 | | | | |
% 143.42/19.56 | | | | | GROUND_INST: instantiating (23) with all_159_0, all_245_2, all_198_0,
% 143.42/19.56 | | | | | simplifying with (103), (119) gives:
% 143.84/19.56 | | | | | (122) all_245_2 = all_159_0
% 143.84/19.56 | | | | |
% 143.84/19.56 | | | | | GROUND_INST: instantiating (23) with all_233_1, all_245_2, all_198_0,
% 143.84/19.56 | | | | | simplifying with (113), (119) gives:
% 143.84/19.56 | | | | | (123) all_245_2 = all_233_1
% 143.84/19.56 | | | | |
% 143.84/19.56 | | | | | COMBINE_EQS: (120), (121) imply:
% 143.84/19.56 | | | | | (124) all_233_2 = all_159_0
% 143.84/19.56 | | | | |
% 143.84/19.56 | | | | | COMBINE_EQS: (122), (123) imply:
% 143.84/19.56 | | | | | (125) all_233_1 = all_159_0
% 143.84/19.56 | | | | |
% 143.84/19.56 | | | | | REDUCE: (111), (124), (125) imply:
% 143.84/19.56 | | | | | (126) $false
% 143.84/19.56 | | | | |
% 143.84/19.56 | | | | | CLOSE: (126) is inconsistent.
% 143.84/19.56 | | | | |
% 143.84/19.56 | | | | End of split
% 143.84/19.56 | | | |
% 143.84/19.56 | | | End of split
% 143.84/19.56 | | |
% 143.84/19.56 | | End of split
% 143.84/19.56 | |
% 143.84/19.56 | Case 2:
% 143.84/19.56 | |
% 143.84/19.56 | | (127) ? [v0: $i] : ? [v1: $i] : (szDzozmdt0(xd) = v0 & $i(v0) & ( ~
% 143.84/19.56 | | isCountable0(v0) | (sdtlcdtrc0(xd, v0) = v1 & $i(v1) & ~
% 143.84/19.56 | | isFinite0(v1))))
% 143.84/19.56 | |
% 143.84/19.56 | | DELTA: instantiating (127) with fresh symbols all_121_0, all_121_1 gives:
% 143.84/19.56 | | (128) szDzozmdt0(xd) = all_121_1 & $i(all_121_1) & ( ~
% 143.84/19.56 | | isCountable0(all_121_1) | (sdtlcdtrc0(xd, all_121_1) = all_121_0
% 143.84/19.56 | | & $i(all_121_0) & ~ isFinite0(all_121_0)))
% 143.84/19.56 | |
% 143.84/19.56 | | ALPHA: (128) implies:
% 143.84/19.56 | | (129) szDzozmdt0(xd) = all_121_1
% 143.84/19.56 | | (130) ~ isCountable0(all_121_1) | (sdtlcdtrc0(xd, all_121_1) = all_121_0
% 143.84/19.56 | | & $i(all_121_0) & ~ isFinite0(all_121_0))
% 143.84/19.56 | |
% 143.84/19.56 | | GROUND_INST: instantiating (24) with szNzAzT0, all_121_1, xd, simplifying
% 143.84/19.56 | | with (14), (129) gives:
% 143.84/19.56 | | (131) all_121_1 = szNzAzT0
% 143.84/19.56 | |
% 143.84/19.56 | | BETA: splitting (130) gives:
% 143.84/19.56 | |
% 143.84/19.56 | | Case 1:
% 143.84/19.56 | | |
% 143.84/19.56 | | | (132) ~ isCountable0(all_121_1)
% 143.84/19.56 | | |
% 143.84/19.56 | | | REDUCE: (131), (132) imply:
% 143.84/19.56 | | | (133) ~ isCountable0(szNzAzT0)
% 143.84/19.56 | | |
% 143.84/19.56 | | | PRED_UNIFY: (1), (133) imply:
% 143.84/19.56 | | | (134) $false
% 143.84/19.56 | | |
% 143.84/19.56 | | | CLOSE: (134) is inconsistent.
% 143.84/19.56 | | |
% 143.84/19.56 | | Case 2:
% 143.84/19.56 | | |
% 143.84/19.56 | | | (135) sdtlcdtrc0(xd, all_121_1) = all_121_0 & $i(all_121_0) & ~
% 143.84/19.56 | | | isFinite0(all_121_0)
% 143.84/19.56 | | |
% 143.84/19.56 | | | ALPHA: (135) implies:
% 143.84/19.56 | | | (136) ~ isFinite0(all_121_0)
% 143.84/19.56 | | | (137) sdtlcdtrc0(xd, all_121_1) = all_121_0
% 143.84/19.56 | | |
% 143.84/19.56 | | | REDUCE: (131), (137) imply:
% 143.84/19.56 | | | (138) sdtlcdtrc0(xd, szNzAzT0) = all_121_0
% 143.84/19.56 | | |
% 143.84/19.56 | | | GROUND_INST: instantiating (27) with all_77_0, all_121_0, szNzAzT0, xd,
% 143.84/19.56 | | | simplifying with (61), (138) gives:
% 143.84/19.56 | | | (139) all_121_0 = all_77_0
% 143.84/19.56 | | |
% 143.84/19.56 | | | REDUCE: (136), (139) imply:
% 143.84/19.56 | | | (140) ~ isFinite0(all_77_0)
% 143.84/19.56 | | |
% 143.84/19.56 | | | PRED_UNIFY: (72), (140) imply:
% 143.84/19.56 | | | (141) $false
% 143.84/19.56 | | |
% 143.84/19.56 | | | CLOSE: (141) is inconsistent.
% 143.84/19.56 | | |
% 143.84/19.56 | | End of split
% 143.84/19.56 | |
% 143.84/19.56 | End of split
% 143.84/19.56 |
% 143.84/19.56 End of proof
% 143.84/19.56 % SZS output end Proof for theBenchmark
% 143.84/19.56
% 143.84/19.56 18956ms
%------------------------------------------------------------------------------