TSTP Solution File: NUM598+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM598+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 11:48:52 EDT 2023
% Result : Theorem 141.02s 19.46s
% Output : Proof 141.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM598+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 16:20:13 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 5.09/1.69 Prover 1: Preprocessing ...
% 5.77/1.70 Prover 4: Preprocessing ...
% 5.77/1.71 Prover 0: Preprocessing ...
% 5.77/1.71 Prover 5: Preprocessing ...
% 5.77/1.71 Prover 2: Preprocessing ...
% 5.77/1.71 Prover 6: Preprocessing ...
% 5.77/1.71 Prover 3: Preprocessing ...
% 18.62/3.36 Prover 6: Proving ...
% 18.62/3.36 Prover 3: Constructing countermodel ...
% 19.12/3.42 Prover 1: Constructing countermodel ...
% 20.45/3.75 Prover 5: Proving ...
% 52.90/7.93 Prover 2: Proving ...
% 52.90/7.93 Prover 4: Constructing countermodel ...
% 52.90/7.94 Prover 0: Proving ...
% 98.22/13.97 Prover 5: stopped
% 98.22/13.99 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 101.73/14.29 Prover 7: Preprocessing ...
% 107.16/15.04 Prover 7: Constructing countermodel ...
% 108.82/15.30 Prover 2: stopped
% 108.82/15.30 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 108.82/15.44 Prover 8: Preprocessing ...
% 112.74/15.74 Prover 8: Warning: ignoring some quantifiers
% 112.74/15.78 Prover 8: Constructing countermodel ...
% 114.36/15.98 Prover 1: stopped
% 114.36/15.98 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 114.36/16.09 Prover 9: Preprocessing ...
% 129.07/17.89 Prover 6: stopped
% 129.07/17.90 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 130.99/18.17 Prover 10: Preprocessing ...
% 131.40/18.20 Prover 9: Constructing countermodel ...
% 134.27/18.57 Prover 10: Constructing countermodel ...
% 140.92/19.45 Prover 10: Found proof (size 101)
% 140.92/19.45 Prover 10: proved (1542ms)
% 140.92/19.45 Prover 9: stopped
% 140.92/19.45 Prover 3: stopped
% 140.92/19.45 Prover 7: stopped
% 141.02/19.45 Prover 4: stopped
% 141.02/19.46 Prover 0: stopped
% 141.02/19.46 Prover 8: stopped
% 141.02/19.46
% 141.02/19.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 141.02/19.46
% 141.02/19.47 % SZS output start Proof for theBenchmark
% 141.02/19.48 Assumptions after simplification:
% 141.02/19.48 ---------------------------------
% 141.02/19.48
% 141.02/19.48 (mDefPtt)
% 141.27/19.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(v0, v1) = v2) | ~
% 141.27/19.51 $i(v1) | ~ $i(v0) | ~ aFunction0(v0) | ~ aElement0(v1) | ? [v3: $i] :
% 141.27/19.51 (szDzozmdt0(v0) = v3 & $i(v3) & ! [v4: $i] : ! [v5: $i] : (v5 = v1 | ~
% 141.27/19.51 (sdtlpdtrp0(v0, v4) = v5) | ~ $i(v4) | ~ $i(v2) | ~ aElementOf0(v4,
% 141.27/19.51 v2)) & ! [v4: $i] : ! [v5: $i] : ( ~ (sdtlpdtrp0(v0, v4) = v5) | ~
% 141.27/19.51 $i(v4) | ~ $i(v2) | ~ aElementOf0(v4, v2) | aElementOf0(v4, v3)) & !
% 141.27/19.51 [v4: $i] : (v4 = v2 | ~ $i(v4) | ~ aSet0(v4) | ? [v5: $i] : ? [v6: $i]
% 141.27/19.51 : ($i(v5) & ( ~ aElementOf0(v5, v4) | ~ aElementOf0(v5, v3) | ( ~ (v6 =
% 141.27/19.51 v1) & sdtlpdtrp0(v0, v5) = v6 & $i(v6))) & (aElementOf0(v5, v4)
% 141.27/19.51 | (v6 = v1 & sdtlpdtrp0(v0, v5) = v1 & aElementOf0(v5, v3))))) & !
% 141.27/19.51 [v4: $i] : ( ~ (sdtlpdtrp0(v0, v4) = v1) | ~ $i(v4) | ~ $i(v2) | ~
% 141.27/19.51 aElementOf0(v4, v3) | aElementOf0(v4, v2)) & ( ~ $i(v2) | aSet0(v2))))
% 141.27/19.51
% 141.27/19.51 (mDirichlet)
% 141.27/19.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (szDzizrdt0(v0) = v1) | ~
% 141.27/19.52 (sdtlbdtrb0(v0, v1) = v2) | ~ $i(v0) | ~ aFunction0(v0) | isCountable0(v2)
% 141.27/19.52 | ? [v3: $i] : ? [v4: $i] : (szDzozmdt0(v0) = v3 & $i(v3) & ( ~
% 141.27/19.52 isCountable0(v3) | (sdtlcdtrc0(v0, v3) = v4 & $i(v4) & ~
% 141.27/19.52 isFinite0(v4))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 141.27/19.52 (szDzizrdt0(v0) = v1) | ~ (sdtlbdtrb0(v0, v1) = v2) | ~ $i(v0) | ~
% 141.27/19.52 aFunction0(v0) | aElement0(v1) | ? [v3: $i] : ? [v4: $i] : (szDzozmdt0(v0)
% 141.27/19.52 = v3 & $i(v3) & ( ~ isCountable0(v3) | (sdtlcdtrc0(v0, v3) = v4 & $i(v4) &
% 141.27/19.52 ~ isFinite0(v4)))))
% 141.27/19.52
% 141.27/19.52 (mEOfElem)
% 141.27/19.52 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) |
% 141.27/19.52 ~ aSet0(v0) | aElement0(v1))
% 141.27/19.52
% 141.27/19.52 (mImgCount)
% 141.27/19.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlcdtrc0(v0,
% 141.27/19.52 v2) = v3) | ~ (szDzozmdt0(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~
% 141.27/19.52 aFunction0(v0) | ~ aSubsetOf0(v2, v1) | ~ isCountable0(v2) |
% 141.27/19.52 isCountable0(v3) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v5 = v4) &
% 141.27/19.52 sdtlpdtrp0(v0, v5) = v6 & sdtlpdtrp0(v0, v4) = v6 & $i(v6) & $i(v5) &
% 141.27/19.52 $i(v4) & aElementOf0(v5, v1) & aElementOf0(v4, v1)))
% 141.27/19.52
% 141.27/19.52 (mNATSet)
% 141.27/19.52 $i(szNzAzT0) & isCountable0(szNzAzT0) & aSet0(szNzAzT0)
% 141.27/19.52
% 141.27/19.52 (mNatExtra)
% 141.27/19.52 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~
% 141.27/19.52 aElementOf0(v0, szNzAzT0) | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) &
% 141.27/19.52 aElementOf0(v1, szNzAzT0)))
% 141.27/19.52
% 141.27/19.52 (mPttSet)
% 141.27/19.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(v0, v1) = v2) | ~
% 141.27/19.52 $i(v1) | ~ $i(v0) | ~ aFunction0(v0) | ~ aElement0(v1) | ? [v3: $i] :
% 141.27/19.52 (szDzozmdt0(v0) = v3 & $i(v3) & aSubsetOf0(v2, v3)))
% 141.27/19.52
% 141.27/19.52 (mSubFSet)
% 141.27/19.52 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, v0) |
% 141.27/19.53 ~ isFinite0(v0) | ~ aSet0(v0) | isFinite0(v1))
% 141.27/19.53
% 141.27/19.53 (m__)
% 141.27/19.53 $i(xO) & ~ isCountable0(xO)
% 141.27/19.53
% 141.27/19.53 (m__3291)
% 141.27/19.53 $i(xT) & isFinite0(xT) & aSet0(xT)
% 141.27/19.53
% 141.27/19.53 (m__3418)
% 141.27/19.53 $i(xK) & $i(szNzAzT0) & aElementOf0(xK, szNzAzT0)
% 141.27/19.53
% 141.27/19.53 (m__3462)
% 141.27/19.53 ~ (xK = sz00) & $i(xK) & $i(sz00)
% 141.27/19.53
% 141.27/19.53 (m__3520)
% 141.27/19.53 ~ (xK = sz00) & $i(xK) & $i(sz00)
% 141.27/19.53
% 141.27/19.53 (m__3821)
% 141.27/19.53 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 141.27/19.53 : (v1 = v0 | ~ (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) | ~
% 141.27/19.53 $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aElementOf0(v0,
% 141.27/19.53 szNzAzT0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v5 = v4) &
% 141.27/19.53 szmzizndt0(v3) = v5 & szmzizndt0(v2) = v4 & $i(v6) & $i(v5) & $i(v4) &
% 141.27/19.53 aElementOf0(v4, v2) & ! [v7: $i] : ( ~ $i(v7) | ~ aElementOf0(v7, v2) |
% 141.27/19.53 sdtlseqdt0(v4, v7)) & ( ~ aElementOf0(v4, v3) | (aElementOf0(v6, v3) &
% 141.27/19.53 ~ sdtlseqdt0(v4, v6)))))
% 141.27/19.53
% 141.27/19.53 (m__3965)
% 141.27/19.53 $i(xN) & $i(xk) & $i(xS) & $i(xK) & $i(szNzAzT0) & ? [v0: $i] :
% 141.27/19.53 (slbdtsldtrb0(xS, xK) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 141.27/19.53 : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v1) = v2) | ~ (szmzizndt0(v2) = v3) |
% 141.27/19.53 ~ (sdtmndt0(v2, v3) = v4) | ~ $i(v1) | ~ aElementOf0(v1, szNzAzT0) | ?
% 141.27/19.53 [v5: $i] : (slbdtsldtrb0(v4, xk) = v5 & $i(v5) & ! [v6: $i] : ! [v7: $i]
% 141.27/19.53 : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~ aSet0(v6) | ? [v8: $i] :
% 141.27/19.53 ? [v9: $i] : ? [v10: $i] : ($i(v10) & aElementOf0(v3, v2) & ! [v11:
% 141.27/19.53 $i] : ( ~ $i(v11) | ~ aElementOf0(v11, v2) | sdtlseqdt0(v3, v11))
% 141.27/19.53 & ((v9 = xK & sbrdtbr0(v7) = xK & aSubsetOf0(v7, xS) &
% 141.27/19.53 aElementOf0(v7, v0) & aSet0(v7) & ! [v11: $i] : (v11 = v3 | ~
% 141.27/19.53 $i(v11) | ~ aElementOf0(v11, v7) | aElementOf0(v11, v6)) & !
% 141.27/19.53 [v11: $i] : ( ~ $i(v11) | ~ aElementOf0(v11, v7) |
% 141.27/19.53 aElementOf0(v11, xS)) & ! [v11: $i] : ( ~ $i(v11) | ~
% 141.27/19.53 aElementOf0(v11, v7) | aElement0(v11)) & ! [v11: $i] : ( ~
% 141.27/19.53 $i(v11) | ~ aElementOf0(v11, v6) | ~ aElement0(v11) |
% 141.27/19.53 aElementOf0(v11, v7)) & ( ~ $i(v3) | ~ aElement0(v3) |
% 141.27/19.53 aElementOf0(v3, v7))) | (aSet0(v4) & ~ aElementOf0(v6, v5) &
% 141.27/19.53 ! [v11: $i] : (v11 = v3 | ~ $i(v11) | ~ aElementOf0(v11, v2) |
% 141.27/19.53 ~ aElement0(v11) | aElementOf0(v11, v4)) & ! [v11: $i] : ( ~
% 141.27/19.53 $i(v11) | ~ aElementOf0(v11, v4) | aElementOf0(v11, v2)) & !
% 141.27/19.53 [v11: $i] : ( ~ $i(v11) | ~ aElementOf0(v11, v4) |
% 141.27/19.53 aElement0(v11)) & ( ~ $i(v3) | ~ aElementOf0(v3, v4)) & (( ~
% 141.27/19.53 (v8 = xk) & sbrdtbr0(v6) = v8 & $i(v8)) | (aElementOf0(v10,
% 141.27/19.53 v6) & ~ aSubsetOf0(v6, v4) & ~ aElementOf0(v10,
% 141.27/19.53 v4))))))))))
% 141.27/19.53
% 141.27/19.54 (m__4660)
% 141.27/19.54 szDzozmdt0(xe) = szNzAzT0 & $i(xe) & $i(xN) & $i(szNzAzT0) & aFunction0(xe) &
% 141.27/19.54 ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) | ~
% 141.27/19.54 aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2 &
% 141.27/19.54 szmzizndt0(v2) = v1 & $i(v2) & $i(v1) & aElementOf0(v1, v2) & ! [v3: $i]
% 141.27/19.54 : ( ~ $i(v3) | ~ aElementOf0(v3, v2) | sdtlseqdt0(v1, v3))))
% 141.27/19.54
% 141.27/19.54 (m__4730)
% 141.27/19.54 szDzozmdt0(xd) = szNzAzT0 & $i(xd) & $i(xC) & $i(xN) & $i(xk) & $i(szNzAzT0) &
% 141.27/19.54 aFunction0(xd) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xC, v0) = v1) |
% 141.27/19.54 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ?
% 141.27/19.54 [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xd, v0) = v5 & sdtlpdtrp0(xN, v2) = v3
% 141.27/19.54 & slbdtsldtrb0(v3, xk) = v4 & szszuzczcdt0(v0) = v2 & $i(v5) & $i(v4) &
% 141.27/19.54 $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~
% 141.27/19.54 (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aSubsetOf0(v6, v3) | ~
% 141.27/19.54 aSet0(v6) | ? [v8: $i] : ( ~ (v8 = xk) & sbrdtbr0(v6) = v8 & $i(v8))) &
% 141.27/19.54 ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~ (sdtlpdtrp0(v1, v6) = v7) | ~
% 141.27/19.54 $i(v6) | ~ aElementOf0(v6, v4) | ~ aSet0(v6)) & ! [v6: $i] : ! [v7:
% 141.27/19.54 $i] : (v7 = v5 | ~ (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aSet0(v6)
% 141.27/19.54 | ? [v8: $i] : ? [v9: $i] : ($i(v9) & (( ~ (v8 = xk) & sbrdtbr0(v6) =
% 141.27/19.54 v8 & $i(v8)) | (aElementOf0(v9, v6) & ~ aElementOf0(v9, v3)))))))
% 141.27/19.54
% 141.27/19.54 (m__4758)
% 141.27/19.54 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 &
% 141.27/19.54 szDzozmdt0(xd) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT) & aSet0(v1) & !
% 141.27/19.54 [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v2) | ~ $i(v3) | ~
% 141.27/19.54 $i(v2) | ~ aElementOf0(v3, v0) | aElementOf0(v2, v1)) & ! [v2: $i] : ( ~
% 141.27/19.54 $i(v2) | ~ aElementOf0(v2, v1) | aElementOf0(v2, xT)) & ! [v2: $i] : ( ~
% 141.27/19.54 $i(v2) | ~ aElementOf0(v2, v1) | ? [v3: $i] : (sdtlpdtrp0(xd, v3) = v2 &
% 141.27/19.54 $i(v3) & aElementOf0(v3, v0))))
% 141.27/19.54
% 141.27/19.54 (m__4854)
% 141.27/19.54 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) =
% 141.27/19.54 v0 & sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) &
% 141.27/19.54 $i(v0) & aElementOf0(v0, xT) & aSet0(v1) & ! [v3: $i] : ! [v4: $i] : (v4 =
% 141.27/19.54 v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1)) &
% 141.27/19.54 ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~
% 141.27/19.54 aElementOf0(v3, v1) | aElementOf0(v3, v2)) & ! [v3: $i] : ( ~
% 141.27/19.54 (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ aElementOf0(v3, v2) |
% 141.27/19.54 aElementOf0(v3, v1)))
% 141.27/19.54
% 141.27/19.54 (m__4891)
% 141.27/19.55 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 141.27/19.55 (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 &
% 141.27/19.55 szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & !
% 141.27/19.55 [v3: $i] : ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3)
% 141.27/19.55 | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 141.27/19.55 (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) |
% 141.27/19.55 aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xe, v4)
% 141.27/19.55 = v3) | ~ $i(v4) | ~ $i(v3) | ~ aElementOf0(v4, v1) | aElementOf0(v3,
% 141.27/19.55 xO)) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~
% 141.27/19.55 aElementOf0(v3, v2) | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~
% 141.27/19.55 aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 & $i(v4) &
% 141.27/19.55 aElementOf0(v4, v1))))
% 141.27/19.55
% 141.27/19.55 (function-axioms)
% 141.27/19.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.27/19.55 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 141.27/19.55 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 141.27/19.55 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 141.27/19.55 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 141.27/19.55 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 141.27/19.55 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 141.27/19.55 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 141.27/19.55 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 141.27/19.55 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~
% 141.27/19.55 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 141.27/19.55 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) &
% 141.27/19.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 141.27/19.55 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 141.27/19.55 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 141.27/19.55 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 141.27/19.55 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 141.27/19.55 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 141.27/19.55 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 141.27/19.55 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 141.27/19.55 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 141.27/19.55 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 141.27/19.55 v0))
% 141.27/19.55
% 141.27/19.55 Further assumptions not needed in the proof:
% 141.27/19.55 --------------------------------------------
% 141.27/19.55 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 141.27/19.55 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01,
% 141.27/19.55 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefRst, mDefSImg, mDefSeg,
% 141.27/19.55 mDefSel, mDefSub, mDiffCons, mDomSet, mElmSort, mEmpFin, mFConsSet, mFDiffSet,
% 141.27/19.55 mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgElm, mImgRng, mLessASymm,
% 141.27/19.55 mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, mMinMin, mNatNSucc,
% 141.27/19.55 mNoScLessZr, mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra,
% 141.27/19.55 mSelFSet, mSelNSet, mSelSub, mSetSort, mSubASymm, mSubRefl, mSubTrans,
% 141.27/19.55 mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__3398, m__3435,
% 141.27/19.55 m__3453, m__3533, m__3623, m__3671, m__3754, m__4151, m__4182, m__4331, m__4411,
% 141.27/19.55 m__4618
% 141.27/19.55
% 141.27/19.55 Those formulas are unsatisfiable:
% 141.27/19.55 ---------------------------------
% 141.27/19.55
% 141.27/19.55 Begin of proof
% 141.27/19.56 |
% 141.49/19.56 | ALPHA: (mNATSet) implies:
% 141.49/19.56 | (1) isCountable0(szNzAzT0)
% 141.49/19.56 |
% 141.49/19.56 | ALPHA: (mNatExtra) implies:
% 141.49/19.56 | (2) ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) |
% 141.49/19.56 | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & aElementOf0(v1,
% 141.49/19.56 | szNzAzT0)))
% 141.49/19.56 |
% 141.49/19.56 | ALPHA: (mDirichlet) implies:
% 141.49/19.56 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (szDzizrdt0(v0) = v1) |
% 141.49/19.56 | ~ (sdtlbdtrb0(v0, v1) = v2) | ~ $i(v0) | ~ aFunction0(v0) |
% 141.49/19.56 | isCountable0(v2) | ? [v3: $i] : ? [v4: $i] : (szDzozmdt0(v0) = v3 &
% 141.49/19.56 | $i(v3) & ( ~ isCountable0(v3) | (sdtlcdtrc0(v0, v3) = v4 & $i(v4) &
% 141.49/19.56 | ~ isFinite0(v4)))))
% 141.49/19.56 |
% 141.49/19.56 | ALPHA: (m__3291) implies:
% 141.49/19.56 | (4) aSet0(xT)
% 141.49/19.56 | (5) isFinite0(xT)
% 141.49/19.56 |
% 141.49/19.56 | ALPHA: (m__3418) implies:
% 141.49/19.56 | (6) aElementOf0(xK, szNzAzT0)
% 141.49/19.56 |
% 141.49/19.56 | ALPHA: (m__3520) implies:
% 141.49/19.56 | (7) ~ (xK = sz00)
% 141.49/19.56 |
% 141.49/19.56 | ALPHA: (m__3821) implies:
% 141.49/19.56 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.49/19.56 | (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) | ~ $i(v1)
% 141.49/19.56 | | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aElementOf0(v0,
% 141.49/19.56 | szNzAzT0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v5 = v4)
% 141.49/19.56 | & szmzizndt0(v3) = v5 & szmzizndt0(v2) = v4 & $i(v6) & $i(v5) &
% 141.49/19.56 | $i(v4) & aElementOf0(v4, v2) & ! [v7: $i] : ( ~ $i(v7) | ~
% 141.49/19.56 | aElementOf0(v7, v2) | sdtlseqdt0(v4, v7)) & ( ~ aElementOf0(v4,
% 141.49/19.56 | v3) | (aElementOf0(v6, v3) & ~ sdtlseqdt0(v4, v6)))))
% 141.49/19.56 |
% 141.49/19.56 | ALPHA: (m__3965) implies:
% 141.49/19.56 | (9) $i(xK)
% 141.49/19.56 |
% 141.49/19.56 | ALPHA: (m__4660) implies:
% 141.49/19.56 | (10) aFunction0(xe)
% 141.49/19.56 | (11) szDzozmdt0(xe) = szNzAzT0
% 141.49/19.56 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0)
% 141.49/19.56 | | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) =
% 141.49/19.56 | v2 & szmzizndt0(v2) = v1 & $i(v2) & $i(v1) & aElementOf0(v1, v2) &
% 141.49/19.56 | ! [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v2) | sdtlseqdt0(v1,
% 141.49/19.56 | v3))))
% 141.49/19.56 |
% 141.49/19.56 | ALPHA: (m__4730) implies:
% 141.49/19.56 | (13) aFunction0(xd)
% 141.49/19.56 | (14) szDzozmdt0(xd) = szNzAzT0
% 141.49/19.56 |
% 141.49/19.57 | ALPHA: (m__4758) implies:
% 141.49/19.57 | (15) ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & szDzozmdt0(xd)
% 141.49/19.57 | = v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT) & aSet0(v1) & ! [v2:
% 141.49/19.57 | $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v2) | ~ $i(v3) | ~
% 141.49/19.57 | $i(v2) | ~ aElementOf0(v3, v0) | aElementOf0(v2, v1)) & ! [v2:
% 141.49/19.57 | $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | aElementOf0(v2, xT)) &
% 141.49/19.57 | ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | ? [v3: $i] :
% 141.49/19.57 | (sdtlpdtrp0(xd, v3) = v2 & $i(v3) & aElementOf0(v3, v0))))
% 141.49/19.57 |
% 141.49/19.57 | ALPHA: (m__4854) implies:
% 141.49/19.57 | (16) $i(xT)
% 141.49/19.57 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 &
% 141.49/19.57 | sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) &
% 141.49/19.57 | $i(v0) & aElementOf0(v0, xT) & aSet0(v1) & ! [v3: $i] : ! [v4: $i]
% 141.49/19.57 | : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~
% 141.49/19.57 | aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 141.49/19.57 | (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) |
% 141.49/19.57 | aElementOf0(v3, v2)) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v0)
% 141.49/19.57 | | ~ $i(v3) | ~ aElementOf0(v3, v2) | aElementOf0(v3, v1)))
% 141.49/19.57 |
% 141.49/19.57 | ALPHA: (m__4891) implies:
% 141.49/19.57 | (18) $i(xe)
% 141.49/19.57 | (19) $i(xd)
% 141.49/19.57 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 &
% 141.49/19.57 | sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) =
% 141.49/19.57 | v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & ! [v3: $i]
% 141.49/19.57 | : ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3)
% 141.49/19.57 | | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 141.49/19.57 | (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) |
% 141.49/19.57 | aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 141.49/19.57 | (sdtlpdtrp0(xe, v4) = v3) | ~ $i(v4) | ~ $i(v3) | ~
% 141.49/19.57 | aElementOf0(v4, v1) | aElementOf0(v3, xO)) & ! [v3: $i] : ( ~
% 141.49/19.57 | (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ aElementOf0(v3, v2) |
% 141.49/19.57 | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~
% 141.49/19.57 | aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 &
% 141.49/19.57 | $i(v4) & aElementOf0(v4, v1))))
% 141.49/19.57 |
% 141.49/19.57 | ALPHA: (m__) implies:
% 141.49/19.57 | (21) ~ isCountable0(xO)
% 141.49/19.57 |
% 141.49/19.57 | ALPHA: (function-axioms) implies:
% 141.49/19.57 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 141.49/19.57 | (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) = v0))
% 141.49/19.57 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 141.49/19.57 | (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0))
% 141.49/19.57 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 141.49/19.57 | (szDzizrdt0(v2) = v1) | ~ (szDzizrdt0(v2) = v0))
% 141.49/19.58 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.49/19.58 | (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) = v0))
% 141.49/19.58 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.49/19.58 | (sdtlcdtrc0(v3, v2) = v1) | ~ (sdtlcdtrc0(v3, v2) = v0))
% 141.49/19.58 |
% 141.49/19.58 | DELTA: instantiating (15) with fresh symbols all_77_0, all_77_1 gives:
% 141.49/19.58 | (27) sdtlcdtrc0(xd, all_77_1) = all_77_0 & szDzozmdt0(xd) = all_77_1 &
% 141.49/19.58 | $i(all_77_0) & $i(all_77_1) & aSubsetOf0(all_77_0, xT) &
% 141.49/19.58 | aSet0(all_77_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v1)
% 141.49/19.58 | = v0) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, all_77_1) |
% 141.49/19.58 | aElementOf0(v0, all_77_0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 141.49/19.58 | aElementOf0(v0, all_77_0) | aElementOf0(v0, xT)) & ! [v0: $i] : ( ~
% 141.49/19.58 | $i(v0) | ~ aElementOf0(v0, all_77_0) | ? [v1: $i] :
% 141.49/19.58 | (sdtlpdtrp0(xd, v1) = v0 & $i(v1) & aElementOf0(v1, all_77_1)))
% 141.49/19.58 |
% 141.49/19.58 | ALPHA: (27) implies:
% 141.49/19.58 | (28) aSubsetOf0(all_77_0, xT)
% 141.49/19.58 | (29) $i(all_77_0)
% 141.49/19.58 | (30) szDzozmdt0(xd) = all_77_1
% 141.49/19.58 | (31) sdtlcdtrc0(xd, all_77_1) = all_77_0
% 141.49/19.58 |
% 141.49/19.58 | DELTA: instantiating (17) with fresh symbols all_80_0, all_80_1, all_80_2
% 141.49/19.58 | gives:
% 141.49/19.58 | (32) szDzizrdt0(xd) = all_80_2 & sdtlbdtrb0(xd, all_80_2) = all_80_1 &
% 141.49/19.58 | szDzozmdt0(xd) = all_80_0 & $i(all_80_0) & $i(all_80_1) & $i(all_80_2)
% 141.49/19.58 | & aElementOf0(all_80_2, xT) & aSet0(all_80_1) & ! [v0: $i] : ! [v1:
% 141.49/19.58 | int] : (v1 = all_80_2 | ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) |
% 141.49/19.58 | ~ aElementOf0(v0, all_80_1)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 141.49/19.58 | (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_80_1)
% 141.49/19.58 | | aElementOf0(v0, all_80_0)) & ! [v0: $i] : ( ~ (sdtlpdtrp0(xd, v0)
% 141.49/19.58 | = all_80_2) | ~ $i(v0) | ~ aElementOf0(v0, all_80_0) |
% 141.49/19.58 | aElementOf0(v0, all_80_1))
% 141.49/19.58 |
% 141.49/19.58 | ALPHA: (32) implies:
% 141.49/19.58 | (33) aElementOf0(all_80_2, xT)
% 141.49/19.58 | (34) szDzozmdt0(xd) = all_80_0
% 141.49/19.58 | (35) sdtlbdtrb0(xd, all_80_2) = all_80_1
% 141.49/19.58 | (36) szDzizrdt0(xd) = all_80_2
% 141.49/19.58 |
% 141.49/19.58 | DELTA: instantiating (20) with fresh symbols all_83_0, all_83_1, all_83_2
% 141.49/19.58 | gives:
% 141.49/19.59 | (37) szDzizrdt0(xd) = all_83_2 & sdtlcdtrc0(xe, all_83_1) = xO &
% 141.49/19.59 | sdtlbdtrb0(xd, all_83_2) = all_83_1 & szDzozmdt0(xd) = all_83_0 &
% 141.49/19.59 | $i(all_83_0) & $i(all_83_1) & $i(all_83_2) & aSet0(all_83_1) &
% 141.49/19.59 | aSet0(xO) & ! [v0: $i] : ! [v1: int] : (v1 = all_83_2 | ~
% 141.49/19.59 | (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0,
% 141.49/19.59 | all_83_1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) =
% 141.49/19.59 | v1) | ~ $i(v0) | ~ aElementOf0(v0, all_83_1) | aElementOf0(v0,
% 141.49/19.59 | all_83_0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v1) =
% 141.49/19.59 | v0) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, all_83_1) |
% 141.49/19.59 | aElementOf0(v0, xO)) & ! [v0: $i] : ( ~ (sdtlpdtrp0(xd, v0) =
% 141.49/19.59 | all_83_2) | ~ $i(v0) | ~ aElementOf0(v0, all_83_0) |
% 141.49/19.59 | aElementOf0(v0, all_83_1)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 141.49/19.59 | aElementOf0(v0, xO) | ? [v1: $i] : (sdtlpdtrp0(xe, v1) = v0 &
% 141.49/19.59 | $i(v1) & aElementOf0(v1, all_83_1)))
% 141.49/19.59 |
% 141.49/19.59 | ALPHA: (37) implies:
% 141.49/19.59 | (38) $i(all_83_2)
% 141.49/19.59 | (39) $i(all_83_1)
% 141.49/19.59 | (40) szDzozmdt0(xd) = all_83_0
% 141.49/19.59 | (41) sdtlbdtrb0(xd, all_83_2) = all_83_1
% 141.49/19.59 | (42) sdtlcdtrc0(xe, all_83_1) = xO
% 141.49/19.59 | (43) szDzizrdt0(xd) = all_83_2
% 141.49/19.59 |
% 141.49/19.59 | GROUND_INST: instantiating (23) with all_77_1, all_80_0, xd, simplifying with
% 141.49/19.59 | (30), (34) gives:
% 141.49/19.59 | (44) all_80_0 = all_77_1
% 141.49/19.59 |
% 141.49/19.59 | GROUND_INST: instantiating (23) with all_80_0, all_83_0, xd, simplifying with
% 141.49/19.59 | (34), (40) gives:
% 141.49/19.59 | (45) all_83_0 = all_80_0
% 141.49/19.59 |
% 141.49/19.59 | GROUND_INST: instantiating (23) with szNzAzT0, all_83_0, xd, simplifying with
% 141.49/19.59 | (14), (40) gives:
% 141.49/19.59 | (46) all_83_0 = szNzAzT0
% 141.49/19.59 |
% 141.49/19.59 | GROUND_INST: instantiating (24) with all_80_2, all_83_2, xd, simplifying with
% 141.49/19.59 | (36), (43) gives:
% 141.49/19.59 | (47) all_83_2 = all_80_2
% 141.49/19.59 |
% 141.49/19.59 | COMBINE_EQS: (45), (46) imply:
% 141.49/19.59 | (48) all_80_0 = szNzAzT0
% 141.49/19.59 |
% 141.49/19.59 | SIMP: (48) implies:
% 141.49/19.59 | (49) all_80_0 = szNzAzT0
% 141.49/19.59 |
% 141.49/19.59 | COMBINE_EQS: (44), (49) imply:
% 141.49/19.59 | (50) all_77_1 = szNzAzT0
% 141.49/19.59 |
% 141.49/19.59 | REDUCE: (31), (50) imply:
% 141.49/19.59 | (51) sdtlcdtrc0(xd, szNzAzT0) = all_77_0
% 141.49/19.59 |
% 141.49/19.59 | REDUCE: (41), (47) imply:
% 141.49/19.59 | (52) sdtlbdtrb0(xd, all_80_2) = all_83_1
% 141.49/19.59 |
% 141.49/19.59 | REDUCE: (38), (47) imply:
% 141.49/19.59 | (53) $i(all_80_2)
% 141.49/19.59 |
% 141.49/19.59 | GROUND_INST: instantiating (25) with all_80_1, all_83_1, all_80_2, xd,
% 141.49/19.59 | simplifying with (35), (52) gives:
% 141.49/19.59 | (54) all_83_1 = all_80_1
% 141.49/19.59 |
% 141.49/19.59 | REDUCE: (42), (54) imply:
% 141.49/19.59 | (55) sdtlcdtrc0(xe, all_80_1) = xO
% 141.49/19.59 |
% 141.49/19.59 | REDUCE: (39), (54) imply:
% 141.49/19.59 | (56) $i(all_80_1)
% 141.49/19.59 |
% 141.49/19.59 | GROUND_INST: instantiating (2) with xK, simplifying with (6), (9) gives:
% 141.49/19.59 | (57) xK = sz00 | ? [v0: $i] : (szszuzczcdt0(v0) = xK & $i(v0) &
% 141.49/19.59 | aElementOf0(v0, szNzAzT0))
% 141.49/19.59 |
% 141.49/19.60 | GROUND_INST: instantiating (mEOfElem) with xT, all_80_2, simplifying with (4),
% 141.49/19.60 | (16), (33), (53) gives:
% 141.49/19.60 | (58) aElement0(all_80_2)
% 141.49/19.60 |
% 141.49/19.60 | GROUND_INST: instantiating (mSubFSet) with xT, all_77_0, simplifying with (4),
% 141.49/19.60 | (5), (16), (28), (29) gives:
% 141.49/19.60 | (59) isFinite0(all_77_0)
% 141.49/19.60 |
% 141.49/19.60 | GROUND_INST: instantiating (3) with xd, all_80_2, all_80_1, simplifying with
% 141.49/19.60 | (13), (19), (35), (36) gives:
% 141.49/19.60 | (60) isCountable0(all_80_1) | ? [v0: $i] : ? [v1: $i] : (szDzozmdt0(xd) =
% 141.49/19.60 | v0 & $i(v0) & ( ~ isCountable0(v0) | (sdtlcdtrc0(xd, v0) = v1 &
% 141.49/19.60 | $i(v1) & ~ isFinite0(v1))))
% 141.49/19.60 |
% 141.49/19.60 | BETA: splitting (60) gives:
% 141.49/19.60 |
% 141.49/19.60 | Case 1:
% 141.49/19.60 | |
% 141.49/19.60 | | (61) isCountable0(all_80_1)
% 141.49/19.60 | |
% 141.49/19.60 | | BETA: splitting (57) gives:
% 141.49/19.60 | |
% 141.49/19.60 | | Case 1:
% 141.49/19.60 | | |
% 141.49/19.60 | | | (62) xK = sz00
% 141.49/19.60 | | |
% 141.49/19.60 | | | REDUCE: (7), (62) imply:
% 141.49/19.60 | | | (63) $false
% 141.49/19.60 | | |
% 141.49/19.60 | | | CLOSE: (63) is inconsistent.
% 141.49/19.60 | | |
% 141.49/19.60 | | Case 2:
% 141.49/19.60 | | |
% 141.49/19.60 | | |
% 141.49/19.60 | | | GROUND_INST: instantiating (mPttSet) with xd, all_80_2, all_80_1,
% 141.49/19.60 | | | simplifying with (13), (19), (35), (53), (58) gives:
% 141.49/19.60 | | | (64) ? [v0: $i] : (szDzozmdt0(xd) = v0 & $i(v0) & aSubsetOf0(all_80_1,
% 141.49/19.60 | | | v0))
% 141.49/19.60 | | |
% 141.49/19.60 | | | GROUND_INST: instantiating (mDefPtt) with xd, all_80_2, all_80_1,
% 141.49/19.60 | | | simplifying with (13), (19), (35), (53), (58) gives:
% 141.49/19.60 | | | (65) ? [v0: $i] : (szDzozmdt0(xd) = v0 & $i(v0) & ! [v1: $i] : !
% 141.49/19.60 | | | [v2: int] : (v2 = all_80_2 | ~ (sdtlpdtrp0(xd, v1) = v2) | ~
% 141.49/19.60 | | | $i(v1) | ~ $i(all_80_1) | ~ aElementOf0(v1, all_80_1)) & !
% 141.49/19.60 | | | [v1: $i] : ! [v2: $i] : ( ~ (sdtlpdtrp0(xd, v1) = v2) | ~
% 141.49/19.60 | | | $i(v1) | ~ $i(all_80_1) | ~ aElementOf0(v1, all_80_1) |
% 141.49/19.60 | | | aElementOf0(v1, v0)) & ! [v1: any] : (v1 = all_80_1 | ~
% 141.49/19.60 | | | $i(v1) | ~ aSet0(v1) | ? [v2: $i] : ? [v3: any] : ($i(v2) &
% 141.49/19.60 | | | ( ~ aElementOf0(v2, v1) | ~ aElementOf0(v2, v0) | ( ~ (v3 =
% 141.49/19.60 | | | all_80_2) & sdtlpdtrp0(xd, v2) = v3 & $i(v3))) &
% 141.49/19.60 | | | (aElementOf0(v2, v1) | (v3 = all_80_2 & sdtlpdtrp0(xd, v2) =
% 141.49/19.60 | | | all_80_2 & aElementOf0(v2, v0))))) & ! [v1: $i] : ( ~
% 141.49/19.60 | | | (sdtlpdtrp0(xd, v1) = all_80_2) | ~ $i(v1) | ~ $i(all_80_1)
% 141.49/19.60 | | | | ~ aElementOf0(v1, v0) | aElementOf0(v1, all_80_1)) & ( ~
% 141.49/19.60 | | | $i(all_80_1) | aSet0(all_80_1)))
% 141.49/19.60 | | |
% 141.49/19.60 | | | DELTA: instantiating (64) with fresh symbol all_133_0 gives:
% 141.49/19.60 | | | (66) szDzozmdt0(xd) = all_133_0 & $i(all_133_0) & aSubsetOf0(all_80_1,
% 141.49/19.60 | | | all_133_0)
% 141.49/19.60 | | |
% 141.49/19.60 | | | ALPHA: (66) implies:
% 141.49/19.60 | | | (67) aSubsetOf0(all_80_1, all_133_0)
% 141.49/19.60 | | | (68) szDzozmdt0(xd) = all_133_0
% 141.49/19.60 | | |
% 141.49/19.60 | | | DELTA: instantiating (65) with fresh symbol all_141_0 gives:
% 141.49/19.61 | | | (69) szDzozmdt0(xd) = all_141_0 & $i(all_141_0) & ! [v0: $i] : ! [v1:
% 141.49/19.61 | | | int] : (v1 = all_80_2 | ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0)
% 141.49/19.61 | | | | ~ $i(all_80_1) | ~ aElementOf0(v0, all_80_1)) & ! [v0: $i]
% 141.49/19.61 | | | : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~
% 141.49/19.61 | | | $i(all_80_1) | ~ aElementOf0(v0, all_80_1) | aElementOf0(v0,
% 141.49/19.61 | | | all_141_0)) & ! [v0: any] : (v0 = all_80_1 | ~ $i(v0) | ~
% 141.49/19.61 | | | aSet0(v0) | ? [v1: $i] : ? [v2: any] : ($i(v1) & ( ~
% 141.49/19.61 | | | aElementOf0(v1, v0) | ~ aElementOf0(v1, all_141_0) | ( ~
% 141.49/19.61 | | | (v2 = all_80_2) & sdtlpdtrp0(xd, v1) = v2 & $i(v2))) &
% 141.49/19.61 | | | (aElementOf0(v1, v0) | (v2 = all_80_2 & sdtlpdtrp0(xd, v1) =
% 141.49/19.61 | | | all_80_2 & aElementOf0(v1, all_141_0))))) & ! [v0: $i] :
% 141.49/19.61 | | | ( ~ (sdtlpdtrp0(xd, v0) = all_80_2) | ~ $i(v0) | ~ $i(all_80_1)
% 141.49/19.61 | | | | ~ aElementOf0(v0, all_141_0) | aElementOf0(v0, all_80_1)) & (
% 141.49/19.61 | | | ~ $i(all_80_1) | aSet0(all_80_1))
% 141.49/19.61 | | |
% 141.49/19.61 | | | ALPHA: (69) implies:
% 141.49/19.61 | | | (70) szDzozmdt0(xd) = all_141_0
% 141.49/19.61 | | |
% 141.49/19.61 | | | GROUND_INST: instantiating (23) with szNzAzT0, all_141_0, xd, simplifying
% 141.49/19.61 | | | with (14), (70) gives:
% 141.49/19.61 | | | (71) all_141_0 = szNzAzT0
% 141.49/19.61 | | |
% 141.49/19.61 | | | GROUND_INST: instantiating (23) with all_133_0, all_141_0, xd, simplifying
% 141.49/19.61 | | | with (68), (70) gives:
% 141.49/19.61 | | | (72) all_141_0 = all_133_0
% 141.49/19.61 | | |
% 141.49/19.61 | | | COMBINE_EQS: (71), (72) imply:
% 141.49/19.61 | | | (73) all_133_0 = szNzAzT0
% 141.49/19.61 | | |
% 141.49/19.61 | | | REDUCE: (67), (73) imply:
% 141.49/19.61 | | | (74) aSubsetOf0(all_80_1, szNzAzT0)
% 141.49/19.61 | | |
% 141.49/19.61 | | | GROUND_INST: instantiating (mImgCount) with xe, szNzAzT0, all_80_1, xO,
% 141.49/19.61 | | | simplifying with (10), (11), (18), (21), (55), (56), (61),
% 141.49/19.61 | | | (74) gives:
% 141.49/19.61 | | | (75) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = v0) &
% 141.49/19.61 | | | sdtlpdtrp0(xe, v1) = v2 & sdtlpdtrp0(xe, v0) = v2 & $i(v2) &
% 141.49/19.61 | | | $i(v1) & $i(v0) & aElementOf0(v1, szNzAzT0) & aElementOf0(v0,
% 141.49/19.61 | | | szNzAzT0))
% 141.49/19.61 | | |
% 141.49/19.61 | | | DELTA: instantiating (75) with fresh symbols all_156_0, all_156_1,
% 141.49/19.61 | | | all_156_2 gives:
% 141.49/19.61 | | | (76) ~ (all_156_1 = all_156_2) & sdtlpdtrp0(xe, all_156_1) = all_156_0
% 141.49/19.61 | | | & sdtlpdtrp0(xe, all_156_2) = all_156_0 & $i(all_156_0) &
% 141.49/19.61 | | | $i(all_156_1) & $i(all_156_2) & aElementOf0(all_156_1, szNzAzT0) &
% 141.49/19.61 | | | aElementOf0(all_156_2, szNzAzT0)
% 141.49/19.61 | | |
% 141.49/19.61 | | | ALPHA: (76) implies:
% 141.49/19.61 | | | (77) ~ (all_156_1 = all_156_2)
% 141.49/19.61 | | | (78) aElementOf0(all_156_2, szNzAzT0)
% 141.49/19.61 | | | (79) aElementOf0(all_156_1, szNzAzT0)
% 141.49/19.61 | | | (80) $i(all_156_2)
% 141.49/19.61 | | | (81) $i(all_156_1)
% 141.49/19.61 | | | (82) sdtlpdtrp0(xe, all_156_2) = all_156_0
% 141.49/19.61 | | | (83) sdtlpdtrp0(xe, all_156_1) = all_156_0
% 141.49/19.61 | | |
% 141.49/19.61 | | | GROUND_INST: instantiating (12) with all_156_2, all_156_0, simplifying
% 141.49/19.61 | | | with (78), (80), (82) gives:
% 141.49/19.61 | | | (84) ? [v0: $i] : (sdtlpdtrp0(xN, all_156_2) = v0 & szmzizndt0(v0) =
% 141.49/19.61 | | | all_156_0 & $i(v0) & $i(all_156_0) & aElementOf0(all_156_0, v0)
% 141.49/19.61 | | | & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, v0) |
% 141.49/19.61 | | | sdtlseqdt0(all_156_0, v1)))
% 141.49/19.61 | | |
% 141.49/19.61 | | | GROUND_INST: instantiating (12) with all_156_1, all_156_0, simplifying
% 141.49/19.61 | | | with (79), (81), (83) gives:
% 141.49/19.61 | | | (85) ? [v0: $i] : (sdtlpdtrp0(xN, all_156_1) = v0 & szmzizndt0(v0) =
% 141.49/19.61 | | | all_156_0 & $i(v0) & $i(all_156_0) & aElementOf0(all_156_0, v0)
% 141.49/19.61 | | | & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, v0) |
% 141.49/19.61 | | | sdtlseqdt0(all_156_0, v1)))
% 141.49/19.61 | | |
% 141.49/19.61 | | | DELTA: instantiating (85) with fresh symbol all_192_0 gives:
% 141.49/19.61 | | | (86) sdtlpdtrp0(xN, all_156_1) = all_192_0 & szmzizndt0(all_192_0) =
% 141.49/19.61 | | | all_156_0 & $i(all_192_0) & $i(all_156_0) & aElementOf0(all_156_0,
% 141.49/19.61 | | | all_192_0) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0,
% 141.49/19.61 | | | all_192_0) | sdtlseqdt0(all_156_0, v0))
% 141.49/19.61 | | |
% 141.49/19.61 | | | ALPHA: (86) implies:
% 141.49/19.61 | | | (87) szmzizndt0(all_192_0) = all_156_0
% 141.49/19.61 | | | (88) sdtlpdtrp0(xN, all_156_1) = all_192_0
% 141.49/19.61 | | |
% 141.49/19.61 | | | DELTA: instantiating (84) with fresh symbol all_195_0 gives:
% 141.49/19.62 | | | (89) sdtlpdtrp0(xN, all_156_2) = all_195_0 & szmzizndt0(all_195_0) =
% 141.49/19.62 | | | all_156_0 & $i(all_195_0) & $i(all_156_0) & aElementOf0(all_156_0,
% 141.49/19.62 | | | all_195_0) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0,
% 141.49/19.62 | | | all_195_0) | sdtlseqdt0(all_156_0, v0))
% 141.49/19.62 | | |
% 141.49/19.62 | | | ALPHA: (89) implies:
% 141.49/19.62 | | | (90) szmzizndt0(all_195_0) = all_156_0
% 141.49/19.62 | | | (91) sdtlpdtrp0(xN, all_156_2) = all_195_0
% 141.49/19.62 | | |
% 141.49/19.62 | | | GROUND_INST: instantiating (8) with all_156_2, all_156_1, all_195_0,
% 141.49/19.62 | | | all_192_0, simplifying with (78), (79), (80), (81), (88),
% 141.49/19.62 | | | (91) gives:
% 141.49/19.62 | | | (92) all_156_1 = all_156_2 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 141.49/19.62 | | | ( ~ (v1 = v0) & szmzizndt0(all_195_0) = v0 & szmzizndt0(all_192_0)
% 141.49/19.62 | | | = v1 & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v0, all_195_0) &
% 141.49/19.62 | | | ! [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, all_195_0) |
% 141.49/19.62 | | | sdtlseqdt0(v0, v3)) & ( ~ aElementOf0(v0, all_192_0) |
% 141.49/19.62 | | | (aElementOf0(v2, all_192_0) & ~ sdtlseqdt0(v0, v2))))
% 141.49/19.62 | | |
% 141.49/19.62 | | | GROUND_INST: instantiating (8) with all_156_1, all_156_2, all_192_0,
% 141.49/19.62 | | | all_195_0, simplifying with (78), (79), (80), (81), (88),
% 141.49/19.62 | | | (91) gives:
% 141.49/19.62 | | | (93) all_156_1 = all_156_2 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 141.49/19.62 | | | ( ~ (v1 = v0) & szmzizndt0(all_195_0) = v1 & szmzizndt0(all_192_0)
% 141.49/19.62 | | | = v0 & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v0, all_192_0) &
% 141.49/19.62 | | | ! [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, all_192_0) |
% 141.49/19.62 | | | sdtlseqdt0(v0, v3)) & ( ~ aElementOf0(v0, all_195_0) |
% 141.49/19.62 | | | (aElementOf0(v2, all_195_0) & ~ sdtlseqdt0(v0, v2))))
% 141.49/19.62 | | |
% 141.49/19.62 | | | BETA: splitting (93) gives:
% 141.49/19.62 | | |
% 141.49/19.62 | | | Case 1:
% 141.49/19.62 | | | |
% 141.49/19.62 | | | | (94) all_156_1 = all_156_2
% 141.49/19.62 | | | |
% 141.49/19.62 | | | | REDUCE: (77), (94) imply:
% 141.49/19.62 | | | | (95) $false
% 141.49/19.62 | | | |
% 141.49/19.62 | | | | CLOSE: (95) is inconsistent.
% 141.49/19.62 | | | |
% 141.49/19.62 | | | Case 2:
% 141.49/19.62 | | | |
% 141.49/19.62 | | | | (96) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = v0) &
% 141.49/19.62 | | | | szmzizndt0(all_195_0) = v1 & szmzizndt0(all_192_0) = v0 &
% 141.49/19.62 | | | | $i(v2) & $i(v1) & $i(v0) & aElementOf0(v0, all_192_0) & !
% 141.49/19.62 | | | | [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, all_192_0) |
% 141.49/19.62 | | | | sdtlseqdt0(v0, v3)) & ( ~ aElementOf0(v0, all_195_0) |
% 141.49/19.62 | | | | (aElementOf0(v2, all_195_0) & ~ sdtlseqdt0(v0, v2))))
% 141.49/19.62 | | | |
% 141.49/19.62 | | | | DELTA: instantiating (96) with fresh symbols all_230_0, all_230_1,
% 141.49/19.62 | | | | all_230_2 gives:
% 141.49/19.62 | | | | (97) ~ (all_230_1 = all_230_2) & szmzizndt0(all_195_0) = all_230_1 &
% 141.49/19.62 | | | | szmzizndt0(all_192_0) = all_230_2 & $i(all_230_0) &
% 141.49/19.62 | | | | $i(all_230_1) & $i(all_230_2) & aElementOf0(all_230_2,
% 141.49/19.62 | | | | all_192_0) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0,
% 141.49/19.62 | | | | all_192_0) | sdtlseqdt0(all_230_2, v0)) & ( ~
% 141.49/19.62 | | | | aElementOf0(all_230_2, all_195_0) | (aElementOf0(all_230_0,
% 141.49/19.62 | | | | all_195_0) & ~ sdtlseqdt0(all_230_2, all_230_0)))
% 141.49/19.62 | | | |
% 141.49/19.62 | | | | ALPHA: (97) implies:
% 141.49/19.62 | | | | (98) ~ (all_230_1 = all_230_2)
% 141.49/19.62 | | | | (99) szmzizndt0(all_192_0) = all_230_2
% 141.49/19.62 | | | | (100) szmzizndt0(all_195_0) = all_230_1
% 141.49/19.62 | | | |
% 141.49/19.62 | | | | BETA: splitting (92) gives:
% 141.49/19.62 | | | |
% 141.49/19.62 | | | | Case 1:
% 141.49/19.62 | | | | |
% 141.49/19.62 | | | | | (101) all_156_1 = all_156_2
% 141.49/19.62 | | | | |
% 141.49/19.62 | | | | | REDUCE: (77), (101) imply:
% 141.49/19.62 | | | | | (102) $false
% 141.49/19.62 | | | | |
% 141.49/19.62 | | | | | CLOSE: (102) is inconsistent.
% 141.49/19.62 | | | | |
% 141.49/19.62 | | | | Case 2:
% 141.49/19.62 | | | | |
% 141.49/19.62 | | | | | (103) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = v0) &
% 141.49/19.62 | | | | | szmzizndt0(all_195_0) = v0 & szmzizndt0(all_192_0) = v1 &
% 141.49/19.62 | | | | | $i(v2) & $i(v1) & $i(v0) & aElementOf0(v0, all_195_0) & !
% 141.49/19.62 | | | | | [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, all_195_0) |
% 141.49/19.62 | | | | | sdtlseqdt0(v0, v3)) & ( ~ aElementOf0(v0, all_192_0) |
% 141.49/19.62 | | | | | (aElementOf0(v2, all_192_0) & ~ sdtlseqdt0(v0, v2))))
% 141.49/19.62 | | | | |
% 141.49/19.62 | | | | | DELTA: instantiating (103) with fresh symbols all_242_0, all_242_1,
% 141.49/19.62 | | | | | all_242_2 gives:
% 141.49/19.62 | | | | | (104) ~ (all_242_1 = all_242_2) & szmzizndt0(all_195_0) =
% 141.49/19.62 | | | | | all_242_2 & szmzizndt0(all_192_0) = all_242_1 & $i(all_242_0)
% 141.49/19.62 | | | | | & $i(all_242_1) & $i(all_242_2) & aElementOf0(all_242_2,
% 141.49/19.62 | | | | | all_195_0) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0,
% 141.49/19.62 | | | | | all_195_0) | sdtlseqdt0(all_242_2, v0)) & ( ~
% 141.49/19.62 | | | | | aElementOf0(all_242_2, all_192_0) | (aElementOf0(all_242_0,
% 141.49/19.62 | | | | | all_192_0) & ~ sdtlseqdt0(all_242_2, all_242_0)))
% 141.49/19.62 | | | | |
% 141.49/19.62 | | | | | ALPHA: (104) implies:
% 141.49/19.62 | | | | | (105) szmzizndt0(all_192_0) = all_242_1
% 141.49/19.62 | | | | | (106) szmzizndt0(all_195_0) = all_242_2
% 141.49/19.62 | | | | |
% 141.49/19.62 | | | | | GROUND_INST: instantiating (22) with all_156_0, all_242_1, all_192_0,
% 141.49/19.62 | | | | | simplifying with (87), (105) gives:
% 141.49/19.62 | | | | | (107) all_242_1 = all_156_0
% 141.49/19.62 | | | | |
% 141.49/19.62 | | | | | GROUND_INST: instantiating (22) with all_230_2, all_242_1, all_192_0,
% 141.49/19.62 | | | | | simplifying with (99), (105) gives:
% 141.49/19.62 | | | | | (108) all_242_1 = all_230_2
% 141.49/19.62 | | | | |
% 141.49/19.62 | | | | | GROUND_INST: instantiating (22) with all_156_0, all_242_2, all_195_0,
% 141.49/19.62 | | | | | simplifying with (90), (106) gives:
% 141.49/19.62 | | | | | (109) all_242_2 = all_156_0
% 141.49/19.62 | | | | |
% 141.49/19.62 | | | | | GROUND_INST: instantiating (22) with all_230_1, all_242_2, all_195_0,
% 141.49/19.62 | | | | | simplifying with (100), (106) gives:
% 141.49/19.62 | | | | | (110) all_242_2 = all_230_1
% 141.49/19.62 | | | | |
% 141.49/19.62 | | | | | COMBINE_EQS: (107), (108) imply:
% 141.49/19.62 | | | | | (111) all_230_2 = all_156_0
% 141.49/19.62 | | | | |
% 141.49/19.62 | | | | | COMBINE_EQS: (109), (110) imply:
% 141.49/19.63 | | | | | (112) all_230_1 = all_156_0
% 141.49/19.63 | | | | |
% 141.49/19.63 | | | | | REDUCE: (98), (111), (112) imply:
% 141.49/19.63 | | | | | (113) $false
% 141.49/19.63 | | | | |
% 141.49/19.63 | | | | | CLOSE: (113) is inconsistent.
% 141.49/19.63 | | | | |
% 141.49/19.63 | | | | End of split
% 141.49/19.63 | | | |
% 141.49/19.63 | | | End of split
% 141.49/19.63 | | |
% 141.49/19.63 | | End of split
% 141.49/19.63 | |
% 141.49/19.63 | Case 2:
% 141.49/19.63 | |
% 141.49/19.63 | | (114) ? [v0: $i] : ? [v1: $i] : (szDzozmdt0(xd) = v0 & $i(v0) & ( ~
% 141.49/19.63 | | isCountable0(v0) | (sdtlcdtrc0(xd, v0) = v1 & $i(v1) & ~
% 141.49/19.63 | | isFinite0(v1))))
% 141.49/19.63 | |
% 141.49/19.63 | | DELTA: instantiating (114) with fresh symbols all_118_0, all_118_1 gives:
% 141.49/19.63 | | (115) szDzozmdt0(xd) = all_118_1 & $i(all_118_1) & ( ~
% 141.49/19.63 | | isCountable0(all_118_1) | (sdtlcdtrc0(xd, all_118_1) = all_118_0
% 141.49/19.63 | | & $i(all_118_0) & ~ isFinite0(all_118_0)))
% 141.49/19.63 | |
% 141.49/19.63 | | ALPHA: (115) implies:
% 141.49/19.63 | | (116) szDzozmdt0(xd) = all_118_1
% 141.49/19.63 | | (117) ~ isCountable0(all_118_1) | (sdtlcdtrc0(xd, all_118_1) = all_118_0
% 141.49/19.63 | | & $i(all_118_0) & ~ isFinite0(all_118_0))
% 141.49/19.63 | |
% 141.49/19.63 | | GROUND_INST: instantiating (23) with szNzAzT0, all_118_1, xd, simplifying
% 141.49/19.63 | | with (14), (116) gives:
% 141.49/19.63 | | (118) all_118_1 = szNzAzT0
% 141.49/19.63 | |
% 141.49/19.63 | | BETA: splitting (117) gives:
% 141.49/19.63 | |
% 141.49/19.63 | | Case 1:
% 141.49/19.63 | | |
% 141.49/19.63 | | | (119) ~ isCountable0(all_118_1)
% 141.49/19.63 | | |
% 141.49/19.63 | | | REDUCE: (118), (119) imply:
% 141.49/19.63 | | | (120) ~ isCountable0(szNzAzT0)
% 141.49/19.63 | | |
% 141.49/19.63 | | | PRED_UNIFY: (1), (120) imply:
% 141.49/19.63 | | | (121) $false
% 141.49/19.63 | | |
% 141.49/19.63 | | | CLOSE: (121) is inconsistent.
% 141.49/19.63 | | |
% 141.49/19.63 | | Case 2:
% 141.49/19.63 | | |
% 141.49/19.63 | | | (122) sdtlcdtrc0(xd, all_118_1) = all_118_0 & $i(all_118_0) & ~
% 141.49/19.63 | | | isFinite0(all_118_0)
% 141.49/19.63 | | |
% 141.49/19.63 | | | ALPHA: (122) implies:
% 141.49/19.63 | | | (123) ~ isFinite0(all_118_0)
% 141.49/19.63 | | | (124) sdtlcdtrc0(xd, all_118_1) = all_118_0
% 141.49/19.63 | | |
% 141.49/19.63 | | | REDUCE: (118), (124) imply:
% 141.49/19.63 | | | (125) sdtlcdtrc0(xd, szNzAzT0) = all_118_0
% 141.49/19.63 | | |
% 141.49/19.63 | | | GROUND_INST: instantiating (26) with all_77_0, all_118_0, szNzAzT0, xd,
% 141.49/19.63 | | | simplifying with (51), (125) gives:
% 141.49/19.63 | | | (126) all_118_0 = all_77_0
% 141.49/19.63 | | |
% 141.49/19.63 | | | REDUCE: (123), (126) imply:
% 141.49/19.63 | | | (127) ~ isFinite0(all_77_0)
% 141.49/19.63 | | |
% 141.49/19.63 | | | PRED_UNIFY: (59), (127) imply:
% 141.49/19.63 | | | (128) $false
% 141.49/19.63 | | |
% 141.49/19.63 | | | CLOSE: (128) is inconsistent.
% 141.49/19.63 | | |
% 141.49/19.63 | | End of split
% 141.49/19.63 | |
% 141.49/19.63 | End of split
% 141.49/19.63 |
% 141.49/19.63 End of proof
% 141.49/19.63 % SZS output end Proof for theBenchmark
% 141.49/19.63
% 141.49/19.63 19011ms
%------------------------------------------------------------------------------