TSTP Solution File: NUM574+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM574+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n012.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 11:48:42 EDT 2023
% Result : Theorem 155.46s 21.54s
% Output : Proof 156.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM574+1 : 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 : n012.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 15:11:41 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 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 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 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
% 4.72/1.38 Prover 4: Preprocessing ...
% 4.72/1.38 Prover 1: Preprocessing ...
% 4.77/1.41 Prover 0: Preprocessing ...
% 4.77/1.41 Prover 5: Preprocessing ...
% 4.77/1.41 Prover 2: Preprocessing ...
% 4.77/1.42 Prover 6: Preprocessing ...
% 4.77/1.42 Prover 3: Preprocessing ...
% 13.27/2.60 Prover 3: Constructing countermodel ...
% 13.27/2.61 Prover 1: Constructing countermodel ...
% 13.90/2.67 Prover 6: Proving ...
% 13.90/2.68 Prover 5: Proving ...
% 14.18/2.86 Prover 2: Proving ...
% 17.66/3.17 Prover 4: Constructing countermodel ...
% 19.06/3.37 Prover 0: Proving ...
% 72.21/10.39 Prover 2: stopped
% 72.21/10.40 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 72.73/10.50 Prover 7: Preprocessing ...
% 74.90/10.75 Prover 7: Constructing countermodel ...
% 99.57/13.97 Prover 5: stopped
% 99.57/13.97 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 100.35/14.12 Prover 8: Preprocessing ...
% 102.55/14.37 Prover 8: Warning: ignoring some quantifiers
% 102.55/14.37 Prover 8: Constructing countermodel ...
% 114.86/16.01 Prover 1: stopped
% 114.86/16.02 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 115.73/16.11 Prover 9: Preprocessing ...
% 119.36/16.64 Prover 9: Constructing countermodel ...
% 129.07/17.90 Prover 6: stopped
% 129.07/17.92 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 130.13/18.03 Prover 10: Preprocessing ...
% 131.24/18.14 Prover 10: Constructing countermodel ...
% 155.46/21.51 Prover 10: Found proof (size 96)
% 155.46/21.52 Prover 10: proved (3592ms)
% 155.46/21.52 Prover 9: stopped
% 155.46/21.52 Prover 3: stopped
% 155.46/21.52 Prover 4: stopped
% 155.46/21.53 Prover 8: stopped
% 155.46/21.53 Prover 7: stopped
% 155.46/21.54 Prover 0: stopped
% 155.46/21.54
% 155.46/21.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 155.46/21.54
% 155.99/21.55 % SZS output start Proof for theBenchmark
% 155.99/21.56 Assumptions after simplification:
% 155.99/21.56 ---------------------------------
% 155.99/21.56
% 155.99/21.56 (mCardCons)
% 155.99/21.58 ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~
% 155.99/21.58 isFinite0(v0) | ~ aSet0(v0) | ? [v2: $i] : (szszuzczcdt0(v1) = v2 & $i(v2)
% 155.99/21.58 & ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v0, v3) = v4) | ~ $i(v3) | ~
% 155.99/21.58 aElement0(v3) | sbrdtbr0(v4) = v2 | aElementOf0(v3, v0))))
% 155.99/21.58
% 155.99/21.58 (mCardSeg)
% 155.99/21.59 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ $i(v0)
% 155.99/21.59 | ~ aElementOf0(v0, szNzAzT0) | sbrdtbr0(v1) = v0)
% 155.99/21.59
% 155.99/21.59 (mDefEmp)
% 155.99/21.59 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~
% 155.99/21.59 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : (
% 155.99/21.59 ~ $i(v0) | ~ aElementOf0(v0, slcrc0))
% 155.99/21.59
% 155.99/21.59 (mDefSub)
% 156.14/21.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 156.14/21.59 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) |
% 156.14/21.59 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) |
% 156.14/21.59 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i]
% 156.14/21.59 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) |
% 156.14/21.59 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)))
% 156.14/21.59
% 156.14/21.59 (mEmpFin)
% 156.14/21.59 $i(slcrc0) & isFinite0(slcrc0)
% 156.14/21.59
% 156.14/21.59 (mNATSet)
% 156.14/21.59 $i(szNzAzT0) & isCountable0(szNzAzT0) & aSet0(szNzAzT0)
% 156.14/21.59
% 156.14/21.59 (mNatExtra)
% 156.14/21.59 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~
% 156.14/21.59 aElementOf0(v0, szNzAzT0) | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) &
% 156.14/21.59 aElementOf0(v1, szNzAzT0)))
% 156.14/21.59
% 156.14/21.59 (mNoScLessZr)
% 156.14/21.59 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) =
% 156.14/21.59 v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, sz00) | ~ aElementOf0(v0, szNzAzT0))
% 156.14/21.59
% 156.14/21.59 (mSegSucc)
% 156.14/21.60 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slbdtrb0(v1) =
% 156.14/21.60 v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~
% 156.14/21.60 aElementOf0(v0, szNzAzT0) | ? [v3: $i] : ? [v4: $i] : ((v1 = v0 |
% 156.14/21.60 aElementOf0(v0, v2) | (slbdtrb0(v3) = v4 & szszuzczcdt0(v1) = v3 &
% 156.14/21.60 $i(v4) & $i(v3) & ~ aElementOf0(v0, v4))) & (( ~ (v1 = v0) & ~
% 156.14/21.60 aElementOf0(v0, v2)) | (slbdtrb0(v3) = v4 & szszuzczcdt0(v1) = v3 &
% 156.14/21.60 $i(v4) & $i(v3) & aElementOf0(v0, v4)))))
% 156.14/21.60
% 156.14/21.60 (mSegZero)
% 156.14/21.60 slbdtrb0(sz00) = slcrc0 & $i(sz00) & $i(slcrc0)
% 156.14/21.60
% 156.14/21.60 (mSelCSet)
% 156.14/21.60 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = sz00
% 156.14/21.60 | ~ (slbdtsldtrb0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 156.14/21.60 isCountable0(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) |
% 156.14/21.60 isCountable0(v2))
% 156.14/21.60
% 156.14/21.60 (mSelSub)
% 156.14/21.60 $i(sz00) & $i(szNzAzT0) & $i(slcrc0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 156.14/21.60 : ! [v3: $i] : ! [v4: $i] : (v3 = slcrc0 | v0 = sz00 | ~ (slbdtsldtrb0(v2,
% 156.14/21.60 v0) = v4) | ~ (slbdtsldtrb0(v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 156.14/21.60 $i(v0) | ~ aSubsetOf0(v3, v4) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v2)
% 156.14/21.60 | ~ aSet0(v1) | aSubsetOf0(v1, v2))
% 156.14/21.60
% 156.14/21.60 (mSuccNum)
% 156.14/21.60 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) =
% 156.14/21.60 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v1,
% 156.14/21.60 szNzAzT0)) & ! [v0: $i] : ( ~ (szszuzczcdt0(v0) = sz00) | ~ $i(v0) | ~
% 156.14/21.60 aElementOf0(v0, szNzAzT0))
% 156.14/21.60
% 156.14/21.60 (mZeroNum)
% 156.14/21.60 $i(sz00) & $i(szNzAzT0) & aElementOf0(sz00, szNzAzT0)
% 156.14/21.60
% 156.14/21.60 (m__)
% 156.14/21.61 $i(xi) & $i(xj) & $i(xN) & ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xi) =
% 156.14/21.61 v0 & sdtlpdtrp0(xN, xj) = v1 & $i(v1) & $i(v0) & sdtlseqdt0(xj, xi) & ~
% 156.14/21.61 aSubsetOf0(v0, v1))
% 156.14/21.61
% 156.14/21.61 (m__3418)
% 156.14/21.61 $i(xK) & $i(szNzAzT0) & aElementOf0(xK, szNzAzT0)
% 156.14/21.61
% 156.14/21.61 (m__3435)
% 156.14/21.61 $i(xS) & $i(szNzAzT0) & aSubsetOf0(xS, szNzAzT0) & isCountable0(xS)
% 156.14/21.61
% 156.14/21.61 (m__3453)
% 156.14/21.61 $i(xc) & $i(xS) & $i(xK) & $i(xT) & ? [v0: $i] : ? [v1: $i] :
% 156.14/21.61 (sdtlcdtrc0(xc, v0) = v1 & szDzozmdt0(xc) = v0 & slbdtsldtrb0(xS, xK) = v0 &
% 156.14/21.61 $i(v1) & $i(v0) & aFunction0(xc) & aSubsetOf0(v1, xT))
% 156.14/21.61
% 156.14/21.61 (m__3462)
% 156.14/21.61 ~ (xK = sz00) & $i(xK) & $i(sz00)
% 156.14/21.61
% 156.14/21.61 (m__3520)
% 156.14/21.61 ~ (xK = sz00) & $i(xK) & $i(sz00)
% 156.14/21.61
% 156.14/21.61 (m__3533)
% 156.14/21.61 szszuzczcdt0(xk) = xK & $i(xk) & $i(xK) & $i(szNzAzT0) & aElementOf0(xk,
% 156.14/21.61 szNzAzT0)
% 156.14/21.61
% 156.14/21.61 (m__3623)
% 156.14/21.61 sdtlpdtrp0(xN, sz00) = xS & szDzozmdt0(xN) = szNzAzT0 & $i(xN) & $i(xS) &
% 156.14/21.61 $i(sz00) & $i(szNzAzT0) & aFunction0(xN) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 156.14/21.61 $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2)
% 156.14/21.61 | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~
% 156.14/21.61 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | ? [v4: $i] : ? [v5: $i]
% 156.14/21.61 : (sdtlpdtrp0(xN, v4) = v5 & szszuzczcdt0(v0) = v4 & $i(v5) & $i(v4) &
% 156.14/21.61 aSubsetOf0(v5, v3) & isCountable0(v5)))
% 156.14/21.61
% 156.14/21.61 (m__3671)
% 156.14/21.61 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) =
% 156.14/21.61 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | aSubsetOf0(v1, szNzAzT0))
% 156.14/21.61 & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~
% 156.14/21.61 aElementOf0(v0, szNzAzT0) | isCountable0(v1))
% 156.14/21.61
% 156.14/21.61 (m__3786)
% 156.14/21.61 $i(xi) & $i(xj) & $i(szNzAzT0) & aElementOf0(xi, szNzAzT0) & aElementOf0(xj,
% 156.14/21.61 szNzAzT0)
% 156.14/21.61
% 156.14/21.61 (m__3786_02)
% 156.14/21.61 $i(xi) & $i(xj) & $i(xN) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] : ( ~
% 156.14/21.61 sdtlseqdt0(xj, xi) | ! [v2: $i] : ( ~ (szszuzczcdt0(v2) = xi) | ~ $i(v2) |
% 156.14/21.61 ~ aElementOf0(v2, szNzAzT0)) | (sdtlpdtrp0(xN, xi) = v0 & sdtlpdtrp0(xN,
% 156.14/21.61 xj) = v1 & $i(v1) & $i(v0) & aSubsetOf0(v0, v1)))
% 156.14/21.61
% 156.14/21.61 (function-axioms)
% 156.14/21.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.14/21.62 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 156.14/21.62 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 156.14/21.62 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 156.14/21.62 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 156.14/21.62 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 156.14/21.62 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 156.14/21.62 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 156.14/21.62 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 156.14/21.62 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~
% 156.14/21.62 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 156.14/21.62 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) &
% 156.14/21.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 156.14/21.62 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 156.14/21.62 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 156.14/21.62 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 156.14/21.62 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 156.14/21.62 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 156.14/21.62 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 156.14/21.62 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 156.14/21.62 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 156.14/21.62 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 156.14/21.62 v0))
% 156.14/21.62
% 156.14/21.62 Further assumptions not needed in the proof:
% 156.14/21.62 --------------------------------------------
% 156.14/21.62 mCConsSet, mCDiffSet, mCardDiff, mCardEmpty, mCardNum, mCardS, mCardSub,
% 156.14/21.62 mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, mDefCons, mDefDiff,
% 156.14/21.62 mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, mDefSel, mDiffCons,
% 156.14/21.62 mDirichlet, mDomSet, mEOfElem, mElmSort, mFConsSet, mFDiffSet, mFinRel,
% 156.14/21.62 mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm, mImgRng, mLessASymm,
% 156.14/21.62 mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, mMinMin, mNatNSucc,
% 156.14/21.62 mPttSet, mSegFin, mSegLess, mSelExtra, mSelFSet, mSelNSet, mSetSort, mSubASymm,
% 156.14/21.62 mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mZeroLess, m__3291,
% 156.14/21.62 m__3398, m__3754
% 156.14/21.62
% 156.14/21.62 Those formulas are unsatisfiable:
% 156.14/21.62 ---------------------------------
% 156.14/21.62
% 156.14/21.62 Begin of proof
% 156.14/21.62 |
% 156.14/21.62 | ALPHA: (mDefEmp) implies:
% 156.14/21.62 | (1) aSet0(slcrc0)
% 156.14/21.62 |
% 156.14/21.62 | ALPHA: (mEmpFin) implies:
% 156.14/21.62 | (2) isFinite0(slcrc0)
% 156.14/21.62 |
% 156.14/21.62 | ALPHA: (mDefSub) implies:
% 156.14/21.62 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~
% 156.14/21.62 | aSet0(v0) | aSubsetOf0(v1, v0) | ? [v2: $i] : ($i(v2) &
% 156.14/21.62 | aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)))
% 156.14/21.62 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1,
% 156.14/21.62 | v0) | ~ aSet0(v0) | aSet0(v1))
% 156.14/21.62 |
% 156.14/21.62 | ALPHA: (mNATSet) implies:
% 156.14/21.62 | (5) aSet0(szNzAzT0)
% 156.14/21.62 |
% 156.14/21.62 | ALPHA: (mZeroNum) implies:
% 156.14/21.63 | (6) aElementOf0(sz00, szNzAzT0)
% 156.14/21.63 |
% 156.14/21.63 | ALPHA: (mSuccNum) implies:
% 156.14/21.63 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) |
% 156.14/21.63 | ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v1, szNzAzT0))
% 156.14/21.63 |
% 156.14/21.63 | ALPHA: (mNatExtra) implies:
% 156.14/21.63 | (8) ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) |
% 156.14/21.63 | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & aElementOf0(v1,
% 156.14/21.63 | szNzAzT0)))
% 156.14/21.63 |
% 156.14/21.63 | ALPHA: (mNoScLessZr) implies:
% 156.14/21.63 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) |
% 156.14/21.63 | ~ sdtlseqdt0(v1, sz00) | ~ aElementOf0(v0, szNzAzT0))
% 156.14/21.63 |
% 156.14/21.63 | ALPHA: (mSegZero) implies:
% 156.14/21.63 | (10) slbdtrb0(sz00) = slcrc0
% 156.14/21.63 |
% 156.14/21.63 | ALPHA: (mSegSucc) implies:
% 156.14/21.63 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slbdtrb0(v1) = v2) | ~
% 156.14/21.63 | $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~
% 156.14/21.63 | aElementOf0(v0, szNzAzT0) | ? [v3: $i] : ? [v4: $i] : ((v1 = v0 |
% 156.14/21.63 | aElementOf0(v0, v2) | (slbdtrb0(v3) = v4 & szszuzczcdt0(v1) = v3
% 156.14/21.63 | & $i(v4) & $i(v3) & ~ aElementOf0(v0, v4))) & (( ~ (v1 = v0)
% 156.14/21.63 | & ~ aElementOf0(v0, v2)) | (slbdtrb0(v3) = v4 &
% 156.14/21.63 | szszuzczcdt0(v1) = v3 & $i(v4) & $i(v3) & aElementOf0(v0,
% 156.14/21.63 | v4)))))
% 156.14/21.63 |
% 156.14/21.63 | ALPHA: (mCardSeg) implies:
% 156.14/21.63 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ $i(v0) | ~
% 156.14/21.63 | aElementOf0(v0, szNzAzT0) | sbrdtbr0(v1) = v0)
% 156.14/21.63 |
% 156.14/21.63 | ALPHA: (mSelCSet) implies:
% 156.14/21.63 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = sz00 | ~
% 156.14/21.63 | (slbdtsldtrb0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 156.14/21.63 | isCountable0(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) |
% 156.14/21.63 | isCountable0(v2))
% 156.14/21.63 |
% 156.14/21.63 | ALPHA: (mSelSub) implies:
% 156.14/21.63 | (14) $i(slcrc0)
% 156.14/21.63 |
% 156.14/21.63 | ALPHA: (m__3418) implies:
% 156.14/21.63 | (15) aElementOf0(xK, szNzAzT0)
% 156.14/21.63 |
% 156.14/21.63 | ALPHA: (m__3435) implies:
% 156.14/21.63 | (16) isCountable0(xS)
% 156.14/21.63 | (17) aSubsetOf0(xS, szNzAzT0)
% 156.14/21.63 |
% 156.14/21.63 | ALPHA: (m__3453) implies:
% 156.14/21.63 | (18) ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xc, v0) = v1 & szDzozmdt0(xc)
% 156.14/21.63 | = v0 & slbdtsldtrb0(xS, xK) = v0 & $i(v1) & $i(v0) & aFunction0(xc)
% 156.14/21.63 | & aSubsetOf0(v1, xT))
% 156.14/21.63 |
% 156.14/21.63 | ALPHA: (m__3520) implies:
% 156.14/21.63 | (19) ~ (xK = sz00)
% 156.14/21.63 |
% 156.14/21.63 | ALPHA: (m__3533) implies:
% 156.14/21.63 | (20) $i(xK)
% 156.14/21.63 |
% 156.14/21.63 | ALPHA: (m__3623) implies:
% 156.14/21.63 | (21) $i(sz00)
% 156.14/21.63 | (22) $i(xS)
% 156.14/21.63 | (23) sdtlpdtrp0(xN, sz00) = xS
% 156.14/21.63 |
% 156.14/21.63 | ALPHA: (m__3671) implies:
% 156.14/21.63 | (24) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0)
% 156.14/21.63 | | ~ aElementOf0(v0, szNzAzT0) | aSubsetOf0(v1, szNzAzT0))
% 156.14/21.63 |
% 156.14/21.63 | ALPHA: (m__3786) implies:
% 156.14/21.63 | (25) aElementOf0(xj, szNzAzT0)
% 156.14/21.63 | (26) aElementOf0(xi, szNzAzT0)
% 156.14/21.63 |
% 156.14/21.63 | ALPHA: (m__3786_02) implies:
% 156.14/21.63 | (27) $i(szNzAzT0)
% 156.14/21.64 | (28) ? [v0: $i] : ? [v1: $i] : ( ~ sdtlseqdt0(xj, xi) | ! [v2: $i] : ( ~
% 156.14/21.64 | (szszuzczcdt0(v2) = xi) | ~ $i(v2) | ~ aElementOf0(v2,
% 156.14/21.64 | szNzAzT0)) | (sdtlpdtrp0(xN, xi) = v0 & sdtlpdtrp0(xN, xj) = v1
% 156.14/21.64 | & $i(v1) & $i(v0) & aSubsetOf0(v0, v1)))
% 156.14/21.64 |
% 156.14/21.64 | ALPHA: (m__) implies:
% 156.14/21.64 | (29) $i(xj)
% 156.38/21.64 | (30) $i(xi)
% 156.38/21.64 | (31) ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xi) = v0 & sdtlpdtrp0(xN,
% 156.38/21.64 | xj) = v1 & $i(v1) & $i(v0) & sdtlseqdt0(xj, xi) & ~
% 156.38/21.64 | aSubsetOf0(v0, v1))
% 156.38/21.64 |
% 156.38/21.64 | ALPHA: (function-axioms) implies:
% 156.38/21.64 | (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 156.38/21.64 | (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0))
% 156.38/21.64 | (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.38/21.64 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0))
% 156.38/21.64 |
% 156.38/21.64 | DELTA: instantiating (31) with fresh symbols all_68_0, all_68_1 gives:
% 156.38/21.64 | (34) sdtlpdtrp0(xN, xi) = all_68_1 & sdtlpdtrp0(xN, xj) = all_68_0 &
% 156.38/21.64 | $i(all_68_0) & $i(all_68_1) & sdtlseqdt0(xj, xi) & ~
% 156.38/21.64 | aSubsetOf0(all_68_1, all_68_0)
% 156.38/21.64 |
% 156.38/21.64 | ALPHA: (34) implies:
% 156.38/21.64 | (35) ~ aSubsetOf0(all_68_1, all_68_0)
% 156.38/21.64 | (36) sdtlseqdt0(xj, xi)
% 156.38/21.64 | (37) $i(all_68_0)
% 156.38/21.64 | (38) sdtlpdtrp0(xN, xj) = all_68_0
% 156.38/21.64 | (39) sdtlpdtrp0(xN, xi) = all_68_1
% 156.38/21.64 |
% 156.38/21.64 | DELTA: instantiating (18) with fresh symbols all_70_0, all_70_1 gives:
% 156.38/21.64 | (40) sdtlcdtrc0(xc, all_70_1) = all_70_0 & szDzozmdt0(xc) = all_70_1 &
% 156.38/21.64 | slbdtsldtrb0(xS, xK) = all_70_1 & $i(all_70_0) & $i(all_70_1) &
% 156.38/21.64 | aFunction0(xc) & aSubsetOf0(all_70_0, xT)
% 156.38/21.64 |
% 156.38/21.64 | ALPHA: (40) implies:
% 156.38/21.64 | (41) slbdtsldtrb0(xS, xK) = all_70_1
% 156.38/21.64 |
% 156.38/21.64 | DELTA: instantiating (28) with fresh symbols all_72_0, all_72_1 gives:
% 156.38/21.64 | (42) ~ sdtlseqdt0(xj, xi) | ! [v0: $i] : ( ~ (szszuzczcdt0(v0) = xi) | ~
% 156.38/21.64 | $i(v0) | ~ aElementOf0(v0, szNzAzT0)) | (sdtlpdtrp0(xN, xi) =
% 156.38/21.64 | all_72_1 & sdtlpdtrp0(xN, xj) = all_72_0 & $i(all_72_0) &
% 156.38/21.64 | $i(all_72_1) & aSubsetOf0(all_72_1, all_72_0))
% 156.38/21.64 |
% 156.38/21.64 | BETA: splitting (42) gives:
% 156.38/21.64 |
% 156.38/21.64 | Case 1:
% 156.38/21.64 | |
% 156.38/21.64 | | (43) ~ sdtlseqdt0(xj, xi)
% 156.38/21.64 | |
% 156.38/21.64 | | PRED_UNIFY: (36), (43) imply:
% 156.38/21.64 | | (44) $false
% 156.38/21.64 | |
% 156.38/21.64 | | CLOSE: (44) is inconsistent.
% 156.38/21.64 | |
% 156.38/21.64 | Case 2:
% 156.38/21.64 | |
% 156.38/21.65 | | (45) ! [v0: $i] : ( ~ (szszuzczcdt0(v0) = xi) | ~ $i(v0) | ~
% 156.38/21.65 | | aElementOf0(v0, szNzAzT0)) | (sdtlpdtrp0(xN, xi) = all_72_1 &
% 156.38/21.65 | | sdtlpdtrp0(xN, xj) = all_72_0 & $i(all_72_0) & $i(all_72_1) &
% 156.38/21.65 | | aSubsetOf0(all_72_1, all_72_0))
% 156.38/21.65 | |
% 156.38/21.65 | | BETA: splitting (45) gives:
% 156.38/21.65 | |
% 156.38/21.65 | | Case 1:
% 156.38/21.65 | | |
% 156.38/21.65 | | | (46) ! [v0: $i] : ( ~ (szszuzczcdt0(v0) = xi) | ~ $i(v0) | ~
% 156.38/21.65 | | | aElementOf0(v0, szNzAzT0))
% 156.38/21.65 | | |
% 156.38/21.65 | | | GROUND_INST: instantiating (8) with xj, simplifying with (25), (29) gives:
% 156.38/21.65 | | | (47) xj = sz00 | ? [v0: $i] : (szszuzczcdt0(v0) = xj & $i(v0) &
% 156.38/21.65 | | | aElementOf0(v0, szNzAzT0))
% 156.38/21.65 | | |
% 156.38/21.65 | | | GROUND_INST: instantiating (8) with xi, simplifying with (26), (30) gives:
% 156.38/21.65 | | | (48) xi = sz00 | ? [v0: $i] : (szszuzczcdt0(v0) = xi & $i(v0) &
% 156.38/21.65 | | | aElementOf0(v0, szNzAzT0))
% 156.38/21.65 | | |
% 156.38/21.65 | | | GROUND_INST: instantiating (4) with szNzAzT0, xS, simplifying with (5),
% 156.38/21.65 | | | (17), (22), (27) gives:
% 156.38/21.65 | | | (49) aSet0(xS)
% 156.38/21.65 | | |
% 156.38/21.65 | | | GROUND_INST: instantiating (11) with sz00, sz00, slcrc0, simplifying with
% 156.38/21.65 | | | (6), (10), (21) gives:
% 156.38/21.65 | | | (50) ? [v0: $i] : ? [v1: $i] : (slbdtrb0(v0) = v1 &
% 156.38/21.65 | | | szszuzczcdt0(sz00) = v0 & $i(v1) & $i(v0) & aElementOf0(sz00,
% 156.38/21.65 | | | v1))
% 156.38/21.65 | | |
% 156.38/21.65 | | | GROUND_INST: instantiating (12) with sz00, slcrc0, simplifying with (6),
% 156.38/21.65 | | | (10), (21) gives:
% 156.38/21.65 | | | (51) sbrdtbr0(slcrc0) = sz00
% 156.38/21.65 | | |
% 156.38/21.65 | | | GROUND_INST: instantiating (24) with xj, all_68_0, simplifying with (25),
% 156.38/21.65 | | | (29), (38) gives:
% 156.38/21.65 | | | (52) aSubsetOf0(all_68_0, szNzAzT0)
% 156.38/21.65 | | |
% 156.38/21.65 | | | DELTA: instantiating (50) with fresh symbols all_89_0, all_89_1 gives:
% 156.38/21.65 | | | (53) slbdtrb0(all_89_1) = all_89_0 & szszuzczcdt0(sz00) = all_89_1 &
% 156.38/21.65 | | | $i(all_89_0) & $i(all_89_1) & aElementOf0(sz00, all_89_0)
% 156.38/21.65 | | |
% 156.38/21.65 | | | ALPHA: (53) implies:
% 156.38/21.65 | | | (54) aElementOf0(sz00, all_89_0)
% 156.38/21.65 | | | (55) szszuzczcdt0(sz00) = all_89_1
% 156.38/21.65 | | | (56) slbdtrb0(all_89_1) = all_89_0
% 156.38/21.65 | | |
% 156.38/21.65 | | | GROUND_INST: instantiating (13) with xS, xK, all_70_1, simplifying with
% 156.38/21.65 | | | (15), (16), (20), (22), (41), (49) gives:
% 156.38/21.65 | | | (57) xK = sz00 | isCountable0(all_70_1)
% 156.38/21.65 | | |
% 156.38/21.65 | | | GROUND_INST: instantiating (4) with szNzAzT0, all_68_0, simplifying with
% 156.38/21.65 | | | (5), (27), (37), (52) gives:
% 156.38/21.65 | | | (58) aSet0(all_68_0)
% 156.38/21.65 | | |
% 156.38/21.65 | | | GROUND_INST: instantiating (7) with sz00, all_89_1, simplifying with (6),
% 156.38/21.65 | | | (21), (55) gives:
% 156.38/21.65 | | | (59) aElementOf0(all_89_1, szNzAzT0)
% 156.38/21.65 | | |
% 156.38/21.65 | | | GROUND_INST: instantiating (mCardCons) with slcrc0, sz00, simplifying with
% 156.38/21.65 | | | (1), (2), (14), (51) gives:
% 156.38/21.66 | | | (60) ? [v0: $i] : (szszuzczcdt0(sz00) = v0 & $i(v0) & ! [v1: $i] : !
% 156.38/21.66 | | | [v2: $i] : ( ~ (sdtpldt0(slcrc0, v1) = v2) | ~ $i(v1) | ~
% 156.38/21.66 | | | aElement0(v1) | sbrdtbr0(v2) = v0 | aElementOf0(v1, slcrc0)))
% 156.38/21.66 | | |
% 156.38/21.66 | | | DELTA: instantiating (60) with fresh symbol all_109_0 gives:
% 156.38/21.66 | | | (61) szszuzczcdt0(sz00) = all_109_0 & $i(all_109_0) & ! [v0: $i] : !
% 156.38/21.66 | | | [v1: $i] : ( ~ (sdtpldt0(slcrc0, v0) = v1) | ~ $i(v0) | ~
% 156.38/21.66 | | | aElement0(v0) | sbrdtbr0(v1) = all_109_0 | aElementOf0(v0,
% 156.38/21.66 | | | slcrc0))
% 156.38/21.66 | | |
% 156.38/21.66 | | | ALPHA: (61) implies:
% 156.38/21.66 | | | (62) $i(all_109_0)
% 156.38/21.66 | | | (63) szszuzczcdt0(sz00) = all_109_0
% 156.38/21.66 | | |
% 156.38/21.66 | | | BETA: splitting (57) gives:
% 156.38/21.66 | | |
% 156.38/21.66 | | | Case 1:
% 156.38/21.66 | | | |
% 156.38/21.66 | | | |
% 156.38/21.66 | | | | GROUND_INST: instantiating (32) with all_89_1, all_109_0, sz00,
% 156.38/21.66 | | | | simplifying with (55), (63) gives:
% 156.38/21.66 | | | | (64) all_109_0 = all_89_1
% 156.38/21.66 | | | |
% 156.38/21.66 | | | | REDUCE: (62), (64) imply:
% 156.38/21.66 | | | | (65) $i(all_89_1)
% 156.38/21.66 | | | |
% 156.38/21.66 | | | | GROUND_INST: instantiating (3) with all_68_0, all_68_0, simplifying with
% 156.38/21.66 | | | | (37), (58) gives:
% 156.38/21.66 | | | | (66) aSubsetOf0(all_68_0, all_68_0)
% 156.38/21.66 | | | |
% 156.38/21.66 | | | | GROUND_INST: instantiating (11) with xi, all_89_1, all_89_0, simplifying
% 156.38/21.66 | | | | with (26), (30), (56), (59), (65) gives:
% 156.38/21.66 | | | | (67) ? [v0: $i] : ? [v1: $i] : ((all_89_1 = xi | aElementOf0(xi,
% 156.38/21.66 | | | | all_89_0) | (slbdtrb0(v0) = v1 & szszuzczcdt0(all_89_1) =
% 156.38/21.66 | | | | v0 & $i(v1) & $i(v0) & ~ aElementOf0(xi, v1))) & (( ~
% 156.38/21.66 | | | | (all_89_1 = xi) & ~ aElementOf0(xi, all_89_0)) |
% 156.38/21.66 | | | | (slbdtrb0(v0) = v1 & szszuzczcdt0(all_89_1) = v0 & $i(v1) &
% 156.38/21.66 | | | | $i(v0) & aElementOf0(xi, v1))))
% 156.38/21.66 | | | |
% 156.38/21.66 | | | | DELTA: instantiating (67) with fresh symbols all_136_0, all_136_1 gives:
% 156.38/21.66 | | | | (68) (all_89_1 = xi | aElementOf0(xi, all_89_0) |
% 156.38/21.66 | | | | (slbdtrb0(all_136_1) = all_136_0 & szszuzczcdt0(all_89_1) =
% 156.38/21.66 | | | | all_136_1 & $i(all_136_0) & $i(all_136_1) & ~
% 156.38/21.66 | | | | aElementOf0(xi, all_136_0))) & (( ~ (all_89_1 = xi) & ~
% 156.38/21.66 | | | | aElementOf0(xi, all_89_0)) | (slbdtrb0(all_136_1) =
% 156.38/21.66 | | | | all_136_0 & szszuzczcdt0(all_89_1) = all_136_1 &
% 156.38/21.66 | | | | $i(all_136_0) & $i(all_136_1) & aElementOf0(xi, all_136_0)))
% 156.38/21.66 | | | |
% 156.38/21.66 | | | | ALPHA: (68) implies:
% 156.38/21.66 | | | | (69) ( ~ (all_89_1 = xi) & ~ aElementOf0(xi, all_89_0)) |
% 156.38/21.66 | | | | (slbdtrb0(all_136_1) = all_136_0 & szszuzczcdt0(all_89_1) =
% 156.38/21.66 | | | | all_136_1 & $i(all_136_0) & $i(all_136_1) & aElementOf0(xi,
% 156.38/21.66 | | | | all_136_0))
% 156.38/21.66 | | | |
% 156.38/21.66 | | | | BETA: splitting (48) gives:
% 156.38/21.66 | | | |
% 156.38/21.66 | | | | Case 1:
% 156.38/21.66 | | | | |
% 156.38/21.66 | | | | | (70) xi = sz00
% 156.38/21.66 | | | | |
% 156.38/21.66 | | | | | REDUCE: (39), (70) imply:
% 156.38/21.66 | | | | | (71) sdtlpdtrp0(xN, sz00) = all_68_1
% 156.38/21.66 | | | | |
% 156.38/21.66 | | | | | REDUCE: (36), (70) imply:
% 156.38/21.66 | | | | | (72) sdtlseqdt0(xj, sz00)
% 156.38/21.66 | | | | |
% 156.38/21.66 | | | | | BETA: splitting (69) gives:
% 156.38/21.66 | | | | |
% 156.38/21.66 | | | | | Case 1:
% 156.38/21.66 | | | | | |
% 156.38/21.66 | | | | | | (73) ~ (all_89_1 = xi) & ~ aElementOf0(xi, all_89_0)
% 156.38/21.66 | | | | | |
% 156.38/21.66 | | | | | | ALPHA: (73) implies:
% 156.38/21.66 | | | | | | (74) ~ aElementOf0(xi, all_89_0)
% 156.38/21.66 | | | | | |
% 156.38/21.66 | | | | | | REDUCE: (70), (74) imply:
% 156.38/21.66 | | | | | | (75) ~ aElementOf0(sz00, all_89_0)
% 156.38/21.66 | | | | | |
% 156.38/21.66 | | | | | | PRED_UNIFY: (54), (75) imply:
% 156.38/21.66 | | | | | | (76) $false
% 156.38/21.66 | | | | | |
% 156.38/21.66 | | | | | | CLOSE: (76) is inconsistent.
% 156.38/21.66 | | | | | |
% 156.38/21.66 | | | | | Case 2:
% 156.38/21.66 | | | | | |
% 156.38/21.66 | | | | | |
% 156.38/21.66 | | | | | | GROUND_INST: instantiating (33) with xS, all_68_1, sz00, xN,
% 156.38/21.66 | | | | | | simplifying with (23), (71) gives:
% 156.38/21.66 | | | | | | (77) all_68_1 = xS
% 156.38/21.66 | | | | | |
% 156.38/21.66 | | | | | | REDUCE: (35), (77) imply:
% 156.38/21.67 | | | | | | (78) ~ aSubsetOf0(xS, all_68_0)
% 156.38/21.67 | | | | | |
% 156.38/21.67 | | | | | | BETA: splitting (47) gives:
% 156.38/21.67 | | | | | |
% 156.38/21.67 | | | | | | Case 1:
% 156.38/21.67 | | | | | | |
% 156.38/21.67 | | | | | | | (79) xj = sz00
% 156.38/21.67 | | | | | | |
% 156.38/21.67 | | | | | | | REDUCE: (38), (79) imply:
% 156.38/21.67 | | | | | | | (80) sdtlpdtrp0(xN, sz00) = all_68_0
% 156.38/21.67 | | | | | | |
% 156.38/21.67 | | | | | | | GROUND_INST: instantiating (33) with xS, all_68_0, sz00, xN,
% 156.38/21.67 | | | | | | | simplifying with (23), (80) gives:
% 156.38/21.67 | | | | | | | (81) all_68_0 = xS
% 156.38/21.67 | | | | | | |
% 156.38/21.67 | | | | | | | REDUCE: (66), (81) imply:
% 156.38/21.67 | | | | | | | (82) aSubsetOf0(xS, xS)
% 156.38/21.67 | | | | | | |
% 156.38/21.67 | | | | | | | REDUCE: (78), (81) imply:
% 156.38/21.67 | | | | | | | (83) ~ aSubsetOf0(xS, xS)
% 156.38/21.67 | | | | | | |
% 156.38/21.67 | | | | | | | PRED_UNIFY: (82), (83) imply:
% 156.38/21.67 | | | | | | | (84) $false
% 156.38/21.67 | | | | | | |
% 156.38/21.67 | | | | | | | CLOSE: (84) is inconsistent.
% 156.38/21.67 | | | | | | |
% 156.38/21.67 | | | | | | Case 2:
% 156.38/21.67 | | | | | | |
% 156.38/21.67 | | | | | | | (85) ? [v0: $i] : (szszuzczcdt0(v0) = xj & $i(v0) &
% 156.38/21.67 | | | | | | | aElementOf0(v0, szNzAzT0))
% 156.38/21.67 | | | | | | |
% 156.38/21.67 | | | | | | | DELTA: instantiating (85) with fresh symbol all_336_0 gives:
% 156.38/21.67 | | | | | | | (86) szszuzczcdt0(all_336_0) = xj & $i(all_336_0) &
% 156.38/21.67 | | | | | | | aElementOf0(all_336_0, szNzAzT0)
% 156.38/21.67 | | | | | | |
% 156.38/21.67 | | | | | | | ALPHA: (86) implies:
% 156.38/21.67 | | | | | | | (87) aElementOf0(all_336_0, szNzAzT0)
% 156.38/21.67 | | | | | | | (88) $i(all_336_0)
% 156.38/21.67 | | | | | | | (89) szszuzczcdt0(all_336_0) = xj
% 156.38/21.67 | | | | | | |
% 156.38/21.67 | | | | | | | GROUND_INST: instantiating (9) with all_336_0, xj, simplifying
% 156.38/21.67 | | | | | | | with (72), (87), (88), (89) gives:
% 156.38/21.67 | | | | | | | (90) $false
% 156.38/21.67 | | | | | | |
% 156.38/21.67 | | | | | | | CLOSE: (90) is inconsistent.
% 156.38/21.67 | | | | | | |
% 156.38/21.67 | | | | | | End of split
% 156.38/21.67 | | | | | |
% 156.38/21.67 | | | | | End of split
% 156.38/21.67 | | | | |
% 156.38/21.67 | | | | Case 2:
% 156.38/21.67 | | | | |
% 156.38/21.67 | | | | | (91) ? [v0: $i] : (szszuzczcdt0(v0) = xi & $i(v0) &
% 156.38/21.67 | | | | | aElementOf0(v0, szNzAzT0))
% 156.38/21.67 | | | | |
% 156.38/21.67 | | | | | DELTA: instantiating (91) with fresh symbol all_304_0 gives:
% 156.38/21.67 | | | | | (92) szszuzczcdt0(all_304_0) = xi & $i(all_304_0) &
% 156.38/21.67 | | | | | aElementOf0(all_304_0, szNzAzT0)
% 156.38/21.67 | | | | |
% 156.38/21.67 | | | | | ALPHA: (92) implies:
% 156.38/21.67 | | | | | (93) aElementOf0(all_304_0, szNzAzT0)
% 156.38/21.67 | | | | | (94) $i(all_304_0)
% 156.38/21.67 | | | | | (95) szszuzczcdt0(all_304_0) = xi
% 156.38/21.67 | | | | |
% 156.38/21.67 | | | | | GROUND_INST: instantiating (46) with all_304_0, simplifying with (93),
% 156.38/21.67 | | | | | (94), (95) gives:
% 156.38/21.67 | | | | | (96) $false
% 156.38/21.67 | | | | |
% 156.38/21.67 | | | | | CLOSE: (96) is inconsistent.
% 156.38/21.67 | | | | |
% 156.38/21.67 | | | | End of split
% 156.38/21.67 | | | |
% 156.38/21.67 | | | Case 2:
% 156.38/21.67 | | | |
% 156.38/21.67 | | | | (97) xK = sz00
% 156.38/21.67 | | | |
% 156.38/21.67 | | | | REDUCE: (19), (97) imply:
% 156.38/21.67 | | | | (98) $false
% 156.38/21.67 | | | |
% 156.38/21.67 | | | | CLOSE: (98) is inconsistent.
% 156.38/21.67 | | | |
% 156.38/21.67 | | | End of split
% 156.38/21.67 | | |
% 156.38/21.67 | | Case 2:
% 156.38/21.67 | | |
% 156.38/21.67 | | | (99) sdtlpdtrp0(xN, xi) = all_72_1 & sdtlpdtrp0(xN, xj) = all_72_0 &
% 156.38/21.67 | | | $i(all_72_0) & $i(all_72_1) & aSubsetOf0(all_72_1, all_72_0)
% 156.38/21.67 | | |
% 156.38/21.67 | | | ALPHA: (99) implies:
% 156.38/21.67 | | | (100) aSubsetOf0(all_72_1, all_72_0)
% 156.38/21.67 | | | (101) sdtlpdtrp0(xN, xj) = all_72_0
% 156.38/21.67 | | | (102) sdtlpdtrp0(xN, xi) = all_72_1
% 156.38/21.67 | | |
% 156.38/21.67 | | | GROUND_INST: instantiating (33) with all_68_0, all_72_0, xj, xN,
% 156.38/21.67 | | | simplifying with (38), (101) gives:
% 156.38/21.67 | | | (103) all_72_0 = all_68_0
% 156.38/21.67 | | |
% 156.38/21.67 | | | GROUND_INST: instantiating (33) with all_68_1, all_72_1, xi, xN,
% 156.38/21.67 | | | simplifying with (39), (102) gives:
% 156.38/21.67 | | | (104) all_72_1 = all_68_1
% 156.38/21.67 | | |
% 156.38/21.67 | | | REDUCE: (100), (103), (104) imply:
% 156.38/21.67 | | | (105) aSubsetOf0(all_68_1, all_68_0)
% 156.38/21.67 | | |
% 156.38/21.67 | | | PRED_UNIFY: (35), (105) imply:
% 156.38/21.67 | | | (106) $false
% 156.38/21.67 | | |
% 156.38/21.67 | | | CLOSE: (106) is inconsistent.
% 156.38/21.67 | | |
% 156.38/21.67 | | End of split
% 156.38/21.67 | |
% 156.38/21.67 | End of split
% 156.38/21.67 |
% 156.38/21.67 End of proof
% 156.38/21.68 % SZS output end Proof for theBenchmark
% 156.38/21.68
% 156.38/21.68 21061ms
%------------------------------------------------------------------------------