TSTP Solution File: NUM600+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM600+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 : n022.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 11:48:53 EDT 2023
% Result : Theorem 26.66s 4.44s
% Output : Proof 49.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM600+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 12:19:25 EDT 2023
% 0.13/0.35 % 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
% 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 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
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 6.09/1.61 Prover 1: Preprocessing ...
% 6.22/1.62 Prover 4: Preprocessing ...
% 6.22/1.65 Prover 5: Preprocessing ...
% 6.22/1.65 Prover 0: Preprocessing ...
% 6.22/1.65 Prover 2: Preprocessing ...
% 6.22/1.65 Prover 3: Preprocessing ...
% 6.22/1.65 Prover 6: Preprocessing ...
% 19.20/3.38 Prover 1: Constructing countermodel ...
% 19.42/3.42 Prover 3: Constructing countermodel ...
% 19.67/3.48 Prover 6: Proving ...
% 21.88/3.83 Prover 5: Proving ...
% 26.66/4.43 Prover 3: proved (3794ms)
% 26.66/4.43
% 26.66/4.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.66/4.44
% 26.66/4.45 Prover 5: stopped
% 26.66/4.46 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 26.66/4.46 Prover 6: stopped
% 26.66/4.47 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 26.66/4.47 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 28.41/4.68 Prover 8: Preprocessing ...
% 28.93/4.72 Prover 10: Preprocessing ...
% 28.93/4.72 Prover 7: Preprocessing ...
% 31.86/5.13 Prover 8: Warning: ignoring some quantifiers
% 31.86/5.14 Prover 8: Constructing countermodel ...
% 34.86/5.54 Prover 10: Constructing countermodel ...
% 37.98/5.90 Prover 7: Constructing countermodel ...
% 45.11/6.88 Prover 10: Found proof (size 73)
% 45.11/6.88 Prover 10: proved (2411ms)
% 45.59/6.89 Prover 8: stopped
% 45.59/6.89 Prover 1: stopped
% 45.59/6.89 Prover 7: stopped
% 46.32/7.04 Prover 4: Constructing countermodel ...
% 46.32/7.07 Prover 4: stopped
% 47.81/7.33 Prover 2: Proving ...
% 47.81/7.36 Prover 2: stopped
% 49.19/7.59 Prover 0: Proving ...
% 49.19/7.62 Prover 0: stopped
% 49.19/7.62
% 49.19/7.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 49.19/7.62
% 49.19/7.63 % SZS output start Proof for theBenchmark
% 49.19/7.64 Assumptions after simplification:
% 49.19/7.64 ---------------------------------
% 49.19/7.65
% 49.19/7.65 (mCountNFin_01)
% 49.19/7.65 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0))
% 49.19/7.65
% 49.19/7.65 (mDefEmp)
% 49.19/7.66 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~
% 49.19/7.66 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : (
% 49.19/7.66 ~ $i(v0) | ~ aElementOf0(v0, slcrc0))
% 49.19/7.66
% 49.19/7.66 (mDefPtt)
% 49.54/7.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(v0, v1) = v2) | ~
% 49.54/7.70 $i(v1) | ~ $i(v0) | ~ aFunction0(v0) | ~ aElement0(v1) | ? [v3: $i] :
% 49.54/7.70 (szDzozmdt0(v0) = v3 & $i(v3) & ! [v4: $i] : ! [v5: $i] : (v5 = v1 | ~
% 49.54/7.70 (sdtlpdtrp0(v0, v4) = v5) | ~ $i(v4) | ~ $i(v2) | ~ aElementOf0(v4,
% 49.54/7.70 v2)) & ! [v4: $i] : ! [v5: $i] : ( ~ (sdtlpdtrp0(v0, v4) = v5) | ~
% 49.54/7.70 $i(v4) | ~ $i(v2) | ~ aElementOf0(v4, v2) | aElementOf0(v4, v3)) & !
% 49.54/7.70 [v4: $i] : (v4 = v2 | ~ $i(v4) | ~ aSet0(v4) | ? [v5: $i] : ? [v6: $i]
% 49.54/7.70 : ($i(v5) & ( ~ aElementOf0(v5, v4) | ~ aElementOf0(v5, v3) | ( ~ (v6 =
% 49.54/7.70 v1) & sdtlpdtrp0(v0, v5) = v6 & $i(v6))) & (aElementOf0(v5, v4)
% 49.54/7.70 | (v6 = v1 & sdtlpdtrp0(v0, v5) = v1 & aElementOf0(v5, v3))))) & !
% 49.54/7.70 [v4: $i] : ( ~ (sdtlpdtrp0(v0, v4) = v1) | ~ $i(v4) | ~ $i(v2) | ~
% 49.54/7.70 aElementOf0(v4, v3) | aElementOf0(v4, v2)) & ( ~ $i(v2) | aSet0(v2))))
% 49.54/7.70
% 49.54/7.71 (mDefSub)
% 49.54/7.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 49.54/7.71 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) |
% 49.54/7.71 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) |
% 49.54/7.71 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i]
% 49.54/7.71 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) |
% 49.54/7.71 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)))
% 49.54/7.71
% 49.54/7.71 (mEOfElem)
% 49.54/7.71 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) |
% 49.54/7.71 ~ aSet0(v0) | aElement0(v1))
% 49.54/7.71
% 49.54/7.71 (mNATSet)
% 49.54/7.71 $i(szNzAzT0) & isCountable0(szNzAzT0) & aSet0(szNzAzT0)
% 49.54/7.71
% 49.54/7.71 (mNatExtra)
% 49.54/7.71 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~
% 49.54/7.71 aElementOf0(v0, szNzAzT0) | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) &
% 49.54/7.71 aElementOf0(v1, szNzAzT0)))
% 49.54/7.71
% 49.54/7.71 (mPttSet)
% 49.54/7.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(v0, v1) = v2) | ~
% 49.54/7.71 $i(v1) | ~ $i(v0) | ~ aFunction0(v0) | ~ aElement0(v1) | ? [v3: $i] :
% 49.54/7.71 (szDzozmdt0(v0) = v3 & $i(v3) & aSubsetOf0(v2, v3)))
% 49.54/7.71
% 49.54/7.71 (m__)
% 49.54/7.71 $i(xO) & $i(xd) & $i(xe) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 49.54/7.71 $i] : ? [v3: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = v1 &
% 49.54/7.71 sdtlpdtrp0(xe, v3) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 49.54/7.71 aElementOf0(v3, v1) & aElementOf0(v2, xO) & ! [v4: $i] : ( ~
% 49.54/7.71 (sdtlpdtrp0(xe, v4) = v2) | ~ $i(v4) | ~ aElementOf0(v4, v1) | ~
% 49.54/7.71 aElementOf0(v4, szNzAzT0)) & ! [v4: $i] : ( ~ (sdtlpdtrp0(xe, v4) = v2) |
% 49.54/7.71 ~ $i(v4) | ~ aElementOf0(v4, szNzAzT0) | ? [v5: $i] : ( ~ (v5 = v0) &
% 49.54/7.71 sdtlpdtrp0(xd, v4) = v5 & $i(v5))))
% 49.54/7.71
% 49.54/7.71 (m__3291)
% 49.54/7.71 $i(xT) & isFinite0(xT) & aSet0(xT)
% 49.54/7.71
% 49.54/7.71 (m__3418)
% 49.54/7.71 $i(xK) & $i(szNzAzT0) & aElementOf0(xK, szNzAzT0)
% 49.54/7.71
% 49.54/7.71 (m__3462)
% 49.54/7.71 ~ (xK = sz00) & $i(xK) & $i(sz00)
% 49.54/7.71
% 49.54/7.71 (m__3520)
% 49.54/7.72 ~ (xK = sz00) & $i(xK) & $i(sz00)
% 49.54/7.72
% 49.54/7.72 (m__3965)
% 49.54/7.72 $i(xN) & $i(xk) & $i(xS) & $i(xK) & $i(szNzAzT0) & ? [v0: $i] :
% 49.54/7.72 (slbdtsldtrb0(xS, xK) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 49.54/7.72 : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v1) = v2) | ~ (szmzizndt0(v2) = v3) |
% 49.54/7.72 ~ (sdtmndt0(v2, v3) = v4) | ~ $i(v1) | ~ aElementOf0(v1, szNzAzT0) | ?
% 49.54/7.72 [v5: $i] : (slbdtsldtrb0(v4, xk) = v5 & $i(v5) & ! [v6: $i] : ! [v7: $i]
% 49.54/7.72 : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~ aSet0(v6) | ? [v8: $i] :
% 49.54/7.72 ? [v9: $i] : ? [v10: $i] : ($i(v10) & aElementOf0(v3, v2) & ! [v11:
% 49.54/7.72 $i] : ( ~ $i(v11) | ~ aElementOf0(v11, v2) | sdtlseqdt0(v3, v11))
% 49.54/7.72 & ((v9 = xK & sbrdtbr0(v7) = xK & aSubsetOf0(v7, xS) &
% 49.54/7.72 aElementOf0(v7, v0) & aSet0(v7) & ! [v11: $i] : (v11 = v3 | ~
% 49.54/7.72 $i(v11) | ~ aElementOf0(v11, v7) | aElementOf0(v11, v6)) & !
% 49.54/7.72 [v11: $i] : ( ~ $i(v11) | ~ aElementOf0(v11, v7) |
% 49.54/7.72 aElementOf0(v11, xS)) & ! [v11: $i] : ( ~ $i(v11) | ~
% 49.54/7.72 aElementOf0(v11, v7) | aElement0(v11)) & ! [v11: $i] : ( ~
% 49.54/7.72 $i(v11) | ~ aElementOf0(v11, v6) | ~ aElement0(v11) |
% 49.54/7.72 aElementOf0(v11, v7)) & ( ~ $i(v3) | ~ aElement0(v3) |
% 49.54/7.72 aElementOf0(v3, v7))) | (aSet0(v4) & ~ aElementOf0(v6, v5) &
% 49.54/7.72 ! [v11: $i] : (v11 = v3 | ~ $i(v11) | ~ aElementOf0(v11, v2) |
% 49.54/7.72 ~ aElement0(v11) | aElementOf0(v11, v4)) & ! [v11: $i] : ( ~
% 49.54/7.72 $i(v11) | ~ aElementOf0(v11, v4) | aElementOf0(v11, v2)) & !
% 49.54/7.72 [v11: $i] : ( ~ $i(v11) | ~ aElementOf0(v11, v4) |
% 49.54/7.72 aElement0(v11)) & ( ~ $i(v3) | ~ aElementOf0(v3, v4)) & (( ~
% 49.54/7.72 (v8 = xk) & sbrdtbr0(v6) = v8 & $i(v8)) | (aElementOf0(v10,
% 49.54/7.72 v6) & ~ aSubsetOf0(v6, v4) & ~ aElementOf0(v10,
% 49.54/7.72 v4))))))))))
% 49.54/7.72
% 49.54/7.72 (m__4730)
% 49.54/7.72 szDzozmdt0(xd) = szNzAzT0 & $i(xd) & $i(xC) & $i(xN) & $i(xk) & $i(szNzAzT0) &
% 49.54/7.72 aFunction0(xd) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xC, v0) = v1) |
% 49.54/7.72 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ?
% 49.54/7.72 [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xd, v0) = v5 & sdtlpdtrp0(xN, v2) = v3
% 49.54/7.72 & slbdtsldtrb0(v3, xk) = v4 & szszuzczcdt0(v0) = v2 & $i(v5) & $i(v4) &
% 49.54/7.72 $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~
% 49.54/7.72 (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aSubsetOf0(v6, v3) | ~
% 49.54/7.72 aSet0(v6) | ? [v8: $i] : ( ~ (v8 = xk) & sbrdtbr0(v6) = v8 & $i(v8))) &
% 49.54/7.72 ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~ (sdtlpdtrp0(v1, v6) = v7) | ~
% 49.54/7.72 $i(v6) | ~ aElementOf0(v6, v4) | ~ aSet0(v6)) & ! [v6: $i] : ! [v7:
% 49.54/7.72 $i] : (v7 = v5 | ~ (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aSet0(v6)
% 49.54/7.72 | ? [v8: $i] : ? [v9: $i] : ($i(v9) & (( ~ (v8 = xk) & sbrdtbr0(v6) =
% 49.54/7.72 v8 & $i(v8)) | (aElementOf0(v9, v6) & ~ aElementOf0(v9, v3)))))))
% 49.54/7.72
% 49.54/7.72 (m__4758)
% 49.54/7.73 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 &
% 49.54/7.73 szDzozmdt0(xd) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT) & aSet0(v1) & !
% 49.54/7.73 [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v2) | ~ $i(v3) | ~
% 49.54/7.73 $i(v2) | ~ aElementOf0(v3, v0) | aElementOf0(v2, v1)) & ! [v2: $i] : ( ~
% 49.54/7.73 $i(v2) | ~ aElementOf0(v2, v1) | aElementOf0(v2, xT)) & ! [v2: $i] : ( ~
% 49.54/7.73 $i(v2) | ~ aElementOf0(v2, v1) | ? [v3: $i] : (sdtlpdtrp0(xd, v3) = v2 &
% 49.54/7.73 $i(v3) & aElementOf0(v3, v0))))
% 49.54/7.73
% 49.54/7.73 (m__4854)
% 49.54/7.73 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) =
% 49.54/7.73 v0 & sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) &
% 49.54/7.73 $i(v0) & aElementOf0(v0, xT) & aSet0(v1) & ! [v3: $i] : ! [v4: $i] : (v4 =
% 49.54/7.73 v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1)) &
% 49.54/7.73 ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~
% 49.54/7.73 aElementOf0(v3, v1) | aElementOf0(v3, v2)) & ! [v3: $i] : ( ~
% 49.54/7.73 (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ aElementOf0(v3, v2) |
% 49.54/7.73 aElementOf0(v3, v1)))
% 49.54/7.73
% 49.54/7.73 (m__4891)
% 49.54/7.73 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 49.54/7.73 (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 &
% 49.54/7.73 szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & !
% 49.54/7.73 [v3: $i] : ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3)
% 49.54/7.73 | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 49.54/7.73 (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) |
% 49.54/7.73 aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xe, v4)
% 49.54/7.73 = v3) | ~ $i(v4) | ~ $i(v3) | ~ aElementOf0(v4, v1) | aElementOf0(v3,
% 49.54/7.73 xO)) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~
% 49.54/7.74 aElementOf0(v3, v2) | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~
% 49.54/7.74 aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 & $i(v4) &
% 49.54/7.74 aElementOf0(v4, v1))))
% 49.54/7.74
% 49.54/7.74 (function-axioms)
% 49.54/7.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 49.54/7.74 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 49.54/7.74 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 49.54/7.74 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 49.54/7.74 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 49.54/7.74 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 49.54/7.74 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 49.54/7.74 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 49.54/7.74 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 49.54/7.74 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~
% 49.54/7.74 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 49.54/7.74 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) &
% 49.54/7.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 49.54/7.74 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 49.54/7.74 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 49.54/7.74 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 49.54/7.74 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 49.54/7.74 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 49.54/7.74 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 49.54/7.74 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 49.54/7.74 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 49.54/7.74 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 49.54/7.74 v0))
% 49.54/7.74
% 49.54/7.74 Further assumptions not needed in the proof:
% 49.54/7.74 --------------------------------------------
% 49.54/7.74 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 49.54/7.74 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons,
% 49.54/7.74 mDefDiff, mDefMax, mDefMin, mDefRst, mDefSImg, mDefSeg, mDefSel, mDiffCons,
% 49.54/7.74 mDirichlet, mDomSet, mElmSort, mEmpFin, mFConsSet, mFDiffSet, mFinRel,
% 49.54/7.74 mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm, mImgRng, mLessASymm,
% 49.54/7.74 mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, mMinMin, mNatNSucc,
% 49.54/7.74 mNoScLessZr, mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra,
% 49.54/7.74 mSelFSet, mSelNSet, mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans,
% 49.54/7.74 mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__3398, m__3435,
% 49.54/7.74 m__3453, m__3533, m__3623, m__3671, m__3754, m__3821, m__4151, m__4182, m__4331,
% 49.54/7.74 m__4411, m__4618, m__4660, m__4908
% 49.54/7.74
% 49.54/7.74 Those formulas are unsatisfiable:
% 49.54/7.74 ---------------------------------
% 49.54/7.74
% 49.54/7.74 Begin of proof
% 49.54/7.75 |
% 49.54/7.75 | ALPHA: (mDefEmp) implies:
% 49.54/7.75 | (1) aSet0(slcrc0)
% 49.54/7.75 |
% 49.54/7.75 | ALPHA: (mCountNFin_01) implies:
% 49.54/7.75 | (2) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)
% 49.54/7.75 |
% 49.54/7.75 | ALPHA: (mDefSub) implies:
% 49.54/7.75 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 49.54/7.75 | $i(v0) | ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~
% 49.54/7.75 | aSet0(v0) | aElementOf0(v2, v0))
% 49.54/7.75 |
% 49.54/7.75 | ALPHA: (mNATSet) implies:
% 49.54/7.75 | (4) aSet0(szNzAzT0)
% 49.54/7.75 |
% 49.54/7.75 | ALPHA: (mNatExtra) implies:
% 49.54/7.75 | (5) ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) |
% 49.54/7.75 | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & aElementOf0(v1,
% 49.54/7.75 | szNzAzT0)))
% 49.54/7.75 |
% 49.54/7.75 | ALPHA: (m__3291) implies:
% 49.54/7.75 | (6) aSet0(xT)
% 49.54/7.75 |
% 49.54/7.75 | ALPHA: (m__3418) implies:
% 49.54/7.75 | (7) aElementOf0(xK, szNzAzT0)
% 49.54/7.75 |
% 49.54/7.75 | ALPHA: (m__3520) implies:
% 49.54/7.75 | (8) ~ (xK = sz00)
% 49.54/7.75 |
% 49.54/7.75 | ALPHA: (m__3965) implies:
% 49.54/7.75 | (9) $i(xK)
% 49.54/7.75 |
% 49.54/7.75 | ALPHA: (m__4730) implies:
% 49.54/7.75 | (10) aFunction0(xd)
% 49.54/7.75 | (11) szDzozmdt0(xd) = szNzAzT0
% 49.54/7.75 |
% 49.54/7.75 | ALPHA: (m__4758) implies:
% 49.54/7.75 | (12) ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & szDzozmdt0(xd)
% 49.54/7.75 | = v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT) & aSet0(v1) & ! [v2:
% 49.54/7.75 | $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v2) | ~ $i(v3) | ~
% 49.54/7.75 | $i(v2) | ~ aElementOf0(v3, v0) | aElementOf0(v2, v1)) & ! [v2:
% 49.54/7.75 | $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | aElementOf0(v2, xT)) &
% 49.54/7.75 | ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | ? [v3: $i] :
% 49.54/7.75 | (sdtlpdtrp0(xd, v3) = v2 & $i(v3) & aElementOf0(v3, v0))))
% 49.54/7.75 |
% 49.54/7.75 | ALPHA: (m__4854) implies:
% 49.54/7.75 | (13) $i(xT)
% 49.54/7.75 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 &
% 49.54/7.75 | sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) &
% 49.54/7.75 | $i(v0) & aElementOf0(v0, xT) & aSet0(v1) & ! [v3: $i] : ! [v4: $i]
% 49.54/7.76 | : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~
% 49.54/7.76 | aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 49.54/7.76 | (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) |
% 49.54/7.76 | aElementOf0(v3, v2)) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v0)
% 49.54/7.76 | | ~ $i(v3) | ~ aElementOf0(v3, v2) | aElementOf0(v3, v1)))
% 49.54/7.76 |
% 49.54/7.76 | ALPHA: (m__4891) implies:
% 49.54/7.76 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 &
% 49.54/7.76 | sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) =
% 49.54/7.76 | v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & ! [v3: $i]
% 49.54/7.76 | : ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3)
% 49.54/7.76 | | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 49.54/7.76 | (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) |
% 49.54/7.76 | aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 49.54/7.76 | (sdtlpdtrp0(xe, v4) = v3) | ~ $i(v4) | ~ $i(v3) | ~
% 49.54/7.76 | aElementOf0(v4, v1) | aElementOf0(v3, xO)) & ! [v3: $i] : ( ~
% 49.54/7.76 | (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ aElementOf0(v3, v2) |
% 49.54/7.76 | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~
% 49.54/7.76 | aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 &
% 49.54/7.76 | $i(v4) & aElementOf0(v4, v1))))
% 49.54/7.76 |
% 49.54/7.76 | ALPHA: (m__) implies:
% 49.54/7.76 | (16) $i(xd)
% 49.54/7.76 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 49.54/7.76 | (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = v1 & sdtlpdtrp0(xe, v3) =
% 49.54/7.76 | v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v3, v1) &
% 49.54/7.76 | aElementOf0(v2, xO) & ! [v4: $i] : ( ~ (sdtlpdtrp0(xe, v4) = v2) |
% 49.54/7.76 | ~ $i(v4) | ~ aElementOf0(v4, v1) | ~ aElementOf0(v4, szNzAzT0))
% 49.54/7.76 | & ! [v4: $i] : ( ~ (sdtlpdtrp0(xe, v4) = v2) | ~ $i(v4) | ~
% 49.54/7.76 | aElementOf0(v4, szNzAzT0) | ? [v5: $i] : ( ~ (v5 = v0) &
% 49.54/7.76 | sdtlpdtrp0(xd, v4) = v5 & $i(v5))))
% 49.54/7.76 |
% 49.54/7.76 | ALPHA: (function-axioms) implies:
% 49.54/7.76 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 49.54/7.76 | (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0))
% 49.54/7.76 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 49.54/7.76 | (szDzizrdt0(v2) = v1) | ~ (szDzizrdt0(v2) = v0))
% 49.54/7.76 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 49.54/7.76 | (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) = v0))
% 49.54/7.76 |
% 49.54/7.76 | DELTA: instantiating (12) with fresh symbols all_77_0, all_77_1 gives:
% 49.54/7.76 | (21) sdtlcdtrc0(xd, all_77_1) = all_77_0 & szDzozmdt0(xd) = all_77_1 &
% 49.54/7.76 | $i(all_77_0) & $i(all_77_1) & aSubsetOf0(all_77_0, xT) &
% 49.54/7.77 | aSet0(all_77_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v1)
% 49.54/7.77 | = v0) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, all_77_1) |
% 49.54/7.77 | aElementOf0(v0, all_77_0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 49.54/7.77 | aElementOf0(v0, all_77_0) | aElementOf0(v0, xT)) & ! [v0: $i] : ( ~
% 49.54/7.77 | $i(v0) | ~ aElementOf0(v0, all_77_0) | ? [v1: $i] :
% 49.54/7.77 | (sdtlpdtrp0(xd, v1) = v0 & $i(v1) & aElementOf0(v1, all_77_1)))
% 49.54/7.77 |
% 49.54/7.77 | ALPHA: (21) implies:
% 49.54/7.77 | (22) szDzozmdt0(xd) = all_77_1
% 49.54/7.77 |
% 49.54/7.77 | DELTA: instantiating (17) with fresh symbols all_80_0, all_80_1, all_80_2,
% 49.54/7.77 | all_80_3 gives:
% 49.54/7.77 | (23) szDzizrdt0(xd) = all_80_3 & sdtlbdtrb0(xd, all_80_3) = all_80_2 &
% 49.54/7.77 | sdtlpdtrp0(xe, all_80_0) = all_80_1 & $i(all_80_0) & $i(all_80_1) &
% 49.54/7.77 | $i(all_80_2) & $i(all_80_3) & aElementOf0(all_80_0, all_80_2) &
% 49.54/7.77 | aElementOf0(all_80_1, xO) & ! [v0: $i] : ( ~ (sdtlpdtrp0(xe, v0) =
% 49.54/7.77 | all_80_1) | ~ $i(v0) | ~ aElementOf0(v0, all_80_2) | ~
% 49.54/7.77 | aElementOf0(v0, szNzAzT0)) & ! [v0: $i] : ( ~ (sdtlpdtrp0(xe, v0) =
% 49.54/7.77 | all_80_1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v1:
% 49.54/7.77 | any] : ( ~ (v1 = all_80_3) & sdtlpdtrp0(xd, v0) = v1 & $i(v1)))
% 49.54/7.77 |
% 49.54/7.77 | ALPHA: (23) implies:
% 49.54/7.77 | (24) aElementOf0(all_80_1, xO)
% 49.54/7.77 | (25) $i(all_80_1)
% 49.54/7.77 | (26) sdtlbdtrb0(xd, all_80_3) = all_80_2
% 49.54/7.77 | (27) szDzizrdt0(xd) = all_80_3
% 49.54/7.77 | (28) ! [v0: $i] : ( ~ (sdtlpdtrp0(xe, v0) = all_80_1) | ~ $i(v0) | ~
% 49.54/7.77 | aElementOf0(v0, all_80_2) | ~ aElementOf0(v0, szNzAzT0))
% 49.54/7.77 |
% 49.54/7.77 | DELTA: instantiating (14) with fresh symbols all_83_0, all_83_1, all_83_2
% 49.54/7.77 | gives:
% 49.54/7.77 | (29) szDzizrdt0(xd) = all_83_2 & sdtlbdtrb0(xd, all_83_2) = all_83_1 &
% 49.54/7.77 | szDzozmdt0(xd) = all_83_0 & $i(all_83_0) & $i(all_83_1) & $i(all_83_2)
% 49.54/7.77 | & aElementOf0(all_83_2, xT) & aSet0(all_83_1) & ! [v0: $i] : ! [v1:
% 49.54/7.77 | int] : (v1 = all_83_2 | ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) |
% 49.54/7.77 | ~ aElementOf0(v0, all_83_1)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 49.54/7.77 | (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_83_1)
% 49.54/7.77 | | aElementOf0(v0, all_83_0)) & ! [v0: $i] : ( ~ (sdtlpdtrp0(xd, v0)
% 49.54/7.77 | = all_83_2) | ~ $i(v0) | ~ aElementOf0(v0, all_83_0) |
% 49.54/7.77 | aElementOf0(v0, all_83_1))
% 49.54/7.77 |
% 49.54/7.77 | ALPHA: (29) implies:
% 49.54/7.77 | (30) aElementOf0(all_83_2, xT)
% 49.54/7.77 | (31) $i(all_83_2)
% 49.54/7.77 | (32) $i(all_83_1)
% 49.54/7.77 | (33) szDzozmdt0(xd) = all_83_0
% 49.54/7.77 | (34) sdtlbdtrb0(xd, all_83_2) = all_83_1
% 49.54/7.77 | (35) szDzizrdt0(xd) = all_83_2
% 49.54/7.77 |
% 49.54/7.77 | DELTA: instantiating (15) with fresh symbols all_86_0, all_86_1, all_86_2
% 49.54/7.77 | gives:
% 49.54/7.78 | (36) szDzizrdt0(xd) = all_86_2 & sdtlcdtrc0(xe, all_86_1) = xO &
% 49.54/7.78 | sdtlbdtrb0(xd, all_86_2) = all_86_1 & szDzozmdt0(xd) = all_86_0 &
% 49.54/7.78 | $i(all_86_0) & $i(all_86_1) & $i(all_86_2) & aSet0(all_86_1) &
% 49.54/7.78 | aSet0(xO) & ! [v0: $i] : ! [v1: int] : (v1 = all_86_2 | ~
% 49.54/7.78 | (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0,
% 49.54/7.78 | all_86_1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) =
% 49.54/7.78 | v1) | ~ $i(v0) | ~ aElementOf0(v0, all_86_1) | aElementOf0(v0,
% 49.54/7.78 | all_86_0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v1) =
% 49.54/7.78 | v0) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, all_86_1) |
% 49.54/7.78 | aElementOf0(v0, xO)) & ! [v0: $i] : ( ~ (sdtlpdtrp0(xd, v0) =
% 49.54/7.78 | all_86_2) | ~ $i(v0) | ~ aElementOf0(v0, all_86_0) |
% 49.54/7.78 | aElementOf0(v0, all_86_1)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 49.54/7.78 | aElementOf0(v0, xO) | ? [v1: $i] : (sdtlpdtrp0(xe, v1) = v0 &
% 49.54/7.78 | $i(v1) & aElementOf0(v1, all_86_1)))
% 49.54/7.78 |
% 49.54/7.78 | ALPHA: (36) implies:
% 49.54/7.78 | (37) szDzozmdt0(xd) = all_86_0
% 49.54/7.78 | (38) sdtlbdtrb0(xd, all_86_2) = all_86_1
% 49.54/7.78 | (39) szDzizrdt0(xd) = all_86_2
% 49.54/7.78 | (40) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xO) | ? [v1: $i] :
% 49.54/7.78 | (sdtlpdtrp0(xe, v1) = v0 & $i(v1) & aElementOf0(v1, all_86_1)))
% 49.54/7.78 |
% 49.54/7.78 | BETA: splitting (2) gives:
% 49.54/7.78 |
% 49.54/7.78 | Case 1:
% 49.54/7.78 | |
% 49.54/7.78 | | (41) ~ aSet0(slcrc0)
% 49.54/7.78 | |
% 49.54/7.78 | | PRED_UNIFY: (1), (41) imply:
% 49.54/7.78 | | (42) $false
% 49.54/7.78 | |
% 49.54/7.78 | | CLOSE: (42) is inconsistent.
% 49.54/7.78 | |
% 49.54/7.78 | Case 2:
% 49.54/7.78 | |
% 49.54/7.78 | |
% 49.54/7.78 | | GROUND_INST: instantiating (18) with all_77_1, all_83_0, xd, simplifying
% 49.54/7.78 | | with (22), (33) gives:
% 49.54/7.78 | | (43) all_83_0 = all_77_1
% 49.54/7.78 | |
% 49.54/7.78 | | GROUND_INST: instantiating (18) with all_83_0, all_86_0, xd, simplifying
% 49.54/7.78 | | with (33), (37) gives:
% 49.54/7.78 | | (44) all_86_0 = all_83_0
% 49.54/7.78 | |
% 49.54/7.78 | | GROUND_INST: instantiating (18) with szNzAzT0, all_86_0, xd, simplifying
% 49.54/7.78 | | with (11), (37) gives:
% 49.54/7.78 | | (45) all_86_0 = szNzAzT0
% 49.54/7.78 | |
% 49.54/7.78 | | GROUND_INST: instantiating (19) with all_83_2, all_86_2, xd, simplifying
% 49.54/7.78 | | with (35), (39) gives:
% 49.54/7.78 | | (46) all_86_2 = all_83_2
% 49.54/7.78 | |
% 49.54/7.78 | | GROUND_INST: instantiating (19) with all_80_3, all_86_2, xd, simplifying
% 49.54/7.78 | | with (27), (39) gives:
% 49.54/7.78 | | (47) all_86_2 = all_80_3
% 49.54/7.78 | |
% 49.54/7.78 | | COMBINE_EQS: (44), (45) imply:
% 49.54/7.78 | | (48) all_83_0 = szNzAzT0
% 49.54/7.78 | |
% 49.54/7.78 | | SIMP: (48) implies:
% 49.54/7.78 | | (49) all_83_0 = szNzAzT0
% 49.54/7.78 | |
% 49.54/7.78 | | COMBINE_EQS: (46), (47) imply:
% 49.54/7.78 | | (50) all_83_2 = all_80_3
% 49.54/7.79 | |
% 49.54/7.79 | | SIMP: (50) implies:
% 49.54/7.79 | | (51) all_83_2 = all_80_3
% 49.54/7.79 | |
% 49.54/7.79 | | COMBINE_EQS: (43), (49) imply:
% 49.54/7.79 | | (52) all_77_1 = szNzAzT0
% 49.54/7.79 | |
% 49.54/7.79 | | SIMP: (52) implies:
% 49.54/7.79 | | (53) all_77_1 = szNzAzT0
% 49.54/7.79 | |
% 49.54/7.79 | | REDUCE: (38), (47) imply:
% 49.54/7.79 | | (54) sdtlbdtrb0(xd, all_80_3) = all_86_1
% 49.54/7.79 | |
% 49.54/7.79 | | REDUCE: (34), (51) imply:
% 49.54/7.79 | | (55) sdtlbdtrb0(xd, all_80_3) = all_83_1
% 49.54/7.79 | |
% 49.54/7.79 | | REDUCE: (31), (51) imply:
% 49.54/7.79 | | (56) $i(all_80_3)
% 49.54/7.79 | |
% 49.54/7.79 | | REDUCE: (30), (51) imply:
% 49.54/7.79 | | (57) aElementOf0(all_80_3, xT)
% 49.54/7.79 | |
% 49.54/7.79 | | GROUND_INST: instantiating (20) with all_80_2, all_86_1, all_80_3, xd,
% 49.54/7.79 | | simplifying with (26), (54) gives:
% 49.54/7.79 | | (58) all_86_1 = all_80_2
% 49.54/7.79 | |
% 49.54/7.79 | | GROUND_INST: instantiating (20) with all_83_1, all_86_1, all_80_3, xd,
% 49.54/7.79 | | simplifying with (54), (55) gives:
% 49.54/7.79 | | (59) all_86_1 = all_83_1
% 49.54/7.79 | |
% 49.54/7.79 | | COMBINE_EQS: (58), (59) imply:
% 49.54/7.79 | | (60) all_83_1 = all_80_2
% 49.54/7.79 | |
% 49.54/7.79 | | SIMP: (60) implies:
% 49.54/7.79 | | (61) all_83_1 = all_80_2
% 49.54/7.79 | |
% 49.54/7.79 | | REDUCE: (32), (61) imply:
% 49.54/7.79 | | (62) $i(all_80_2)
% 49.54/7.79 | |
% 49.54/7.79 | | GROUND_INST: instantiating (5) with xK, simplifying with (7), (9) gives:
% 49.54/7.79 | | (63) xK = sz00 | ? [v0: $i] : (szszuzczcdt0(v0) = xK & $i(v0) &
% 49.54/7.79 | | aElementOf0(v0, szNzAzT0))
% 49.54/7.79 | |
% 49.54/7.79 | | GROUND_INST: instantiating (mEOfElem) with xT, all_80_3, simplifying with
% 49.54/7.79 | | (6), (13), (56), (57) gives:
% 49.54/7.79 | | (64) aElement0(all_80_3)
% 49.54/7.79 | |
% 49.54/7.79 | | GROUND_INST: instantiating (40) with all_80_1, simplifying with (24), (25)
% 49.54/7.79 | | gives:
% 49.54/7.79 | | (65) ? [v0: $i] : (sdtlpdtrp0(xe, v0) = all_80_1 & $i(v0) &
% 49.54/7.79 | | aElementOf0(v0, all_86_1))
% 49.54/7.79 | |
% 49.54/7.79 | | DELTA: instantiating (65) with fresh symbol all_113_0 gives:
% 49.54/7.79 | | (66) sdtlpdtrp0(xe, all_113_0) = all_80_1 & $i(all_113_0) &
% 49.54/7.79 | | aElementOf0(all_113_0, all_86_1)
% 49.54/7.79 | |
% 49.54/7.79 | | ALPHA: (66) implies:
% 49.54/7.80 | | (67) aElementOf0(all_113_0, all_86_1)
% 49.54/7.80 | | (68) $i(all_113_0)
% 49.54/7.80 | | (69) sdtlpdtrp0(xe, all_113_0) = all_80_1
% 49.54/7.80 | |
% 49.54/7.80 | | REDUCE: (58), (67) imply:
% 49.54/7.80 | | (70) aElementOf0(all_113_0, all_80_2)
% 49.54/7.80 | |
% 49.54/7.80 | | BETA: splitting (63) gives:
% 49.54/7.80 | |
% 49.54/7.80 | | Case 1:
% 49.54/7.80 | | |
% 49.54/7.80 | | | (71) xK = sz00
% 49.54/7.80 | | |
% 49.54/7.80 | | | REDUCE: (8), (71) imply:
% 49.54/7.80 | | | (72) $false
% 49.54/7.80 | | |
% 49.54/7.80 | | | CLOSE: (72) is inconsistent.
% 49.54/7.80 | | |
% 49.54/7.80 | | Case 2:
% 49.54/7.80 | | |
% 49.54/7.80 | | |
% 49.54/7.80 | | | GROUND_INST: instantiating (mPttSet) with xd, all_80_3, all_80_2,
% 49.54/7.80 | | | simplifying with (10), (16), (26), (56), (64) gives:
% 49.54/7.80 | | | (73) ? [v0: $i] : (szDzozmdt0(xd) = v0 & $i(v0) & aSubsetOf0(all_80_2,
% 49.54/7.80 | | | v0))
% 49.54/7.80 | | |
% 49.54/7.80 | | | GROUND_INST: instantiating (mDefPtt) with xd, all_80_3, all_80_2,
% 49.54/7.80 | | | simplifying with (10), (16), (26), (56), (64) gives:
% 49.54/7.80 | | | (74) ? [v0: $i] : (szDzozmdt0(xd) = v0 & $i(v0) & ! [v1: $i] : !
% 49.54/7.80 | | | [v2: int] : (v2 = all_80_3 | ~ (sdtlpdtrp0(xd, v1) = v2) | ~
% 49.54/7.80 | | | $i(v1) | ~ $i(all_80_2) | ~ aElementOf0(v1, all_80_2)) & !
% 49.54/7.80 | | | [v1: $i] : ! [v2: $i] : ( ~ (sdtlpdtrp0(xd, v1) = v2) | ~
% 49.54/7.80 | | | $i(v1) | ~ $i(all_80_2) | ~ aElementOf0(v1, all_80_2) |
% 49.54/7.80 | | | aElementOf0(v1, v0)) & ! [v1: any] : (v1 = all_80_2 | ~
% 49.54/7.80 | | | $i(v1) | ~ aSet0(v1) | ? [v2: $i] : ? [v3: any] : ($i(v2) &
% 49.54/7.80 | | | ( ~ aElementOf0(v2, v1) | ~ aElementOf0(v2, v0) | ( ~ (v3 =
% 49.54/7.80 | | | all_80_3) & sdtlpdtrp0(xd, v2) = v3 & $i(v3))) &
% 49.54/7.80 | | | (aElementOf0(v2, v1) | (v3 = all_80_3 & sdtlpdtrp0(xd, v2) =
% 49.54/7.81 | | | all_80_3 & aElementOf0(v2, v0))))) & ! [v1: $i] : ( ~
% 49.54/7.81 | | | (sdtlpdtrp0(xd, v1) = all_80_3) | ~ $i(v1) | ~ $i(all_80_2)
% 49.54/7.81 | | | | ~ aElementOf0(v1, v0) | aElementOf0(v1, all_80_2)) & ( ~
% 49.54/7.81 | | | $i(all_80_2) | aSet0(all_80_2)))
% 49.54/7.81 | | |
% 49.54/7.81 | | | DELTA: instantiating (73) with fresh symbol all_140_0 gives:
% 49.54/7.81 | | | (75) szDzozmdt0(xd) = all_140_0 & $i(all_140_0) & aSubsetOf0(all_80_2,
% 49.54/7.81 | | | all_140_0)
% 49.54/7.81 | | |
% 49.54/7.81 | | | ALPHA: (75) implies:
% 49.54/7.81 | | | (76) aSubsetOf0(all_80_2, all_140_0)
% 49.54/7.81 | | | (77) $i(all_140_0)
% 49.54/7.81 | | | (78) szDzozmdt0(xd) = all_140_0
% 49.54/7.81 | | |
% 49.54/7.81 | | | DELTA: instantiating (74) with fresh symbol all_146_0 gives:
% 49.54/7.81 | | | (79) szDzozmdt0(xd) = all_146_0 & $i(all_146_0) & ! [v0: $i] : ! [v1:
% 49.54/7.81 | | | int] : (v1 = all_80_3 | ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0)
% 49.54/7.81 | | | | ~ $i(all_80_2) | ~ aElementOf0(v0, all_80_2)) & ! [v0: $i]
% 49.54/7.81 | | | : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~
% 49.54/7.81 | | | $i(all_80_2) | ~ aElementOf0(v0, all_80_2) | aElementOf0(v0,
% 49.54/7.81 | | | all_146_0)) & ! [v0: any] : (v0 = all_80_2 | ~ $i(v0) | ~
% 49.54/7.81 | | | aSet0(v0) | ? [v1: $i] : ? [v2: any] : ($i(v1) & ( ~
% 49.54/7.81 | | | aElementOf0(v1, v0) | ~ aElementOf0(v1, all_146_0) | ( ~
% 49.54/7.81 | | | (v2 = all_80_3) & sdtlpdtrp0(xd, v1) = v2 & $i(v2))) &
% 49.54/7.81 | | | (aElementOf0(v1, v0) | (v2 = all_80_3 & sdtlpdtrp0(xd, v1) =
% 49.54/7.81 | | | all_80_3 & aElementOf0(v1, all_146_0))))) & ! [v0: $i] :
% 49.54/7.81 | | | ( ~ (sdtlpdtrp0(xd, v0) = all_80_3) | ~ $i(v0) | ~ $i(all_80_2)
% 49.54/7.81 | | | | ~ aElementOf0(v0, all_146_0) | aElementOf0(v0, all_80_2)) & (
% 49.54/7.81 | | | ~ $i(all_80_2) | aSet0(all_80_2))
% 49.54/7.81 | | |
% 49.54/7.81 | | | ALPHA: (79) implies:
% 49.54/7.81 | | | (80) szDzozmdt0(xd) = all_146_0
% 49.54/7.81 | | |
% 49.54/7.81 | | | GROUND_INST: instantiating (18) with szNzAzT0, all_146_0, xd, simplifying
% 49.54/7.81 | | | with (11), (80) gives:
% 49.54/7.81 | | | (81) all_146_0 = szNzAzT0
% 49.54/7.81 | | |
% 49.54/7.81 | | | GROUND_INST: instantiating (18) with all_140_0, all_146_0, xd, simplifying
% 49.54/7.81 | | | with (78), (80) gives:
% 49.54/7.81 | | | (82) all_146_0 = all_140_0
% 49.54/7.81 | | |
% 49.54/7.81 | | | COMBINE_EQS: (81), (82) imply:
% 49.54/7.81 | | | (83) all_140_0 = szNzAzT0
% 49.54/7.81 | | |
% 49.54/7.81 | | | REDUCE: (77), (83) imply:
% 49.54/7.81 | | | (84) $i(szNzAzT0)
% 49.54/7.81 | | |
% 49.54/7.81 | | | REDUCE: (76), (83) imply:
% 49.54/7.82 | | | (85) aSubsetOf0(all_80_2, szNzAzT0)
% 49.54/7.82 | | |
% 49.54/7.82 | | | GROUND_INST: instantiating (3) with szNzAzT0, all_80_2, all_113_0,
% 49.54/7.82 | | | simplifying with (4), (62), (68), (70), (84), (85) gives:
% 49.54/7.82 | | | (86) aElementOf0(all_113_0, szNzAzT0)
% 49.54/7.82 | | |
% 49.54/7.82 | | | GROUND_INST: instantiating (28) with all_113_0, simplifying with (68),
% 49.54/7.82 | | | (69), (70), (86) gives:
% 49.54/7.82 | | | (87) $false
% 49.54/7.82 | | |
% 49.54/7.82 | | | CLOSE: (87) is inconsistent.
% 49.54/7.82 | | |
% 49.54/7.82 | | End of split
% 49.54/7.82 | |
% 49.54/7.82 | End of split
% 49.54/7.82 |
% 49.54/7.82 End of proof
% 49.54/7.82 % SZS output end Proof for theBenchmark
% 49.54/7.82
% 49.54/7.82 7203ms
%------------------------------------------------------------------------------