TSTP Solution File: NUM601+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM601+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 : n018.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 139.96s 19.09s
% Output : Proof 140.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM601+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.33 % Computer : n018.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Fri Aug 25 08:14:28 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 6.59/1.64 Prover 4: Preprocessing ...
% 6.59/1.67 Prover 0: Preprocessing ...
% 6.59/1.67 Prover 3: Preprocessing ...
% 6.59/1.67 Prover 6: Preprocessing ...
% 6.59/1.67 Prover 5: Preprocessing ...
% 6.59/1.67 Prover 2: Preprocessing ...
% 6.59/1.68 Prover 1: Preprocessing ...
% 17.72/3.14 Prover 1: Constructing countermodel ...
% 17.72/3.15 Prover 3: Constructing countermodel ...
% 17.72/3.16 Prover 6: Proving ...
% 19.77/3.43 Prover 5: Proving ...
% 40.56/6.21 Prover 4: Constructing countermodel ...
% 48.38/7.12 Prover 2: Proving ...
% 49.03/7.27 Prover 0: Proving ...
% 99.40/13.73 Prover 2: stopped
% 99.40/13.75 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 100.50/13.96 Prover 5: stopped
% 100.50/13.97 Prover 7: Preprocessing ...
% 100.50/13.97 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 103.00/14.26 Prover 8: Preprocessing ...
% 105.33/14.57 Prover 8: Warning: ignoring some quantifiers
% 105.89/14.58 Prover 8: Constructing countermodel ...
% 105.89/14.62 Prover 7: Constructing countermodel ...
% 116.51/15.97 Prover 1: stopped
% 116.51/15.98 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 116.51/16.15 Prover 9: Preprocessing ...
% 131.13/17.88 Prover 6: stopped
% 131.13/17.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 131.84/18.08 Prover 10: Preprocessing ...
% 134.94/18.43 Prover 9: Constructing countermodel ...
% 136.24/18.58 Prover 10: Constructing countermodel ...
% 139.96/19.08 Prover 10: Found proof (size 74)
% 139.96/19.08 Prover 10: proved (1186ms)
% 139.96/19.08 Prover 9: stopped
% 139.96/19.08 Prover 3: stopped
% 139.96/19.08 Prover 7: stopped
% 139.96/19.09 Prover 4: stopped
% 139.96/19.09 Prover 0: stopped
% 139.96/19.09 Prover 8: stopped
% 139.96/19.09
% 139.96/19.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 139.96/19.09
% 139.96/19.10 % SZS output start Proof for theBenchmark
% 140.49/19.11 Assumptions after simplification:
% 140.49/19.11 ---------------------------------
% 140.49/19.11
% 140.49/19.11 (mCountNFin_01)
% 140.49/19.11 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0))
% 140.49/19.11
% 140.49/19.11 (mDefEmp)
% 140.49/19.11 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~
% 140.49/19.11 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : (
% 140.49/19.11 ~ $i(v0) | ~ aElementOf0(v0, slcrc0))
% 140.49/19.11
% 140.49/19.11 (mDefPtt)
% 140.49/19.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(v0, v1) = v2) | ~
% 140.49/19.14 $i(v1) | ~ $i(v0) | ~ aFunction0(v0) | ~ aElement0(v1) | ? [v3: $i] :
% 140.49/19.14 (szDzozmdt0(v0) = v3 & $i(v3) & ! [v4: $i] : ! [v5: $i] : (v5 = v1 | ~
% 140.49/19.14 (sdtlpdtrp0(v0, v4) = v5) | ~ $i(v4) | ~ $i(v2) | ~ aElementOf0(v4,
% 140.49/19.14 v2)) & ! [v4: $i] : ! [v5: $i] : ( ~ (sdtlpdtrp0(v0, v4) = v5) | ~
% 140.49/19.14 $i(v4) | ~ $i(v2) | ~ aElementOf0(v4, v2) | aElementOf0(v4, v3)) & !
% 140.49/19.14 [v4: $i] : (v4 = v2 | ~ $i(v4) | ~ aSet0(v4) | ? [v5: $i] : ? [v6: $i]
% 140.49/19.14 : ($i(v5) & ( ~ aElementOf0(v5, v4) | ~ aElementOf0(v5, v3) | ( ~ (v6 =
% 140.49/19.14 v1) & sdtlpdtrp0(v0, v5) = v6 & $i(v6))) & (aElementOf0(v5, v4)
% 140.49/19.14 | (v6 = v1 & sdtlpdtrp0(v0, v5) = v1 & aElementOf0(v5, v3))))) & !
% 140.49/19.14 [v4: $i] : ( ~ (sdtlpdtrp0(v0, v4) = v1) | ~ $i(v4) | ~ $i(v2) | ~
% 140.49/19.14 aElementOf0(v4, v3) | aElementOf0(v4, v2)) & ( ~ $i(v2) | aSet0(v2))))
% 140.49/19.14
% 140.49/19.14 (mEOfElem)
% 140.49/19.14 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) |
% 140.49/19.14 ~ aSet0(v0) | aElement0(v1))
% 140.49/19.14
% 140.49/19.14 (mPttSet)
% 140.49/19.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(v0, v1) = v2) | ~
% 140.49/19.14 $i(v1) | ~ $i(v0) | ~ aFunction0(v0) | ~ aElement0(v1) | ? [v3: $i] :
% 140.49/19.14 (szDzozmdt0(v0) = v3 & $i(v3) & aSubsetOf0(v2, v3)))
% 140.49/19.14
% 140.49/19.14 (mZeroLess)
% 140.49/19.14 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0,
% 140.49/19.14 szNzAzT0) | sdtlseqdt0(sz00, v0))
% 140.49/19.14
% 140.49/19.14 (mZeroNum)
% 140.49/19.14 $i(sz00) & $i(szNzAzT0) & aElementOf0(sz00, szNzAzT0)
% 140.49/19.14
% 140.49/19.14 (m__)
% 140.49/19.15 $i(xO) & $i(xS) & ? [v0: $i] : ($i(v0) & aElementOf0(v0, xO) & ~
% 140.49/19.15 aSubsetOf0(xO, xS) & ~ aElementOf0(v0, xS))
% 140.49/19.15
% 140.49/19.15 (m__3291)
% 140.49/19.15 $i(xT) & isFinite0(xT) & aSet0(xT)
% 140.49/19.15
% 140.49/19.15 (m__3623)
% 140.49/19.16 sdtlpdtrp0(xN, sz00) = xS & szDzozmdt0(xN) = szNzAzT0 & $i(xN) & $i(xS) &
% 140.49/19.16 $i(sz00) & $i(szNzAzT0) & aFunction0(xN) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 140.49/19.16 $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2 | ~ (sdtlpdtrp0(xN, v0) = v1) |
% 140.49/19.16 ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0)
% 140.49/19.16 | ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v4, v1)
% 140.49/19.16 | ~ aElementOf0(v0, szNzAzT0) | ~ aElement0(v4) | aElementOf0(v4, v3)) &
% 140.49/19.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2
% 140.49/19.16 | ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1,
% 140.49/19.16 v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~ isCountable0(v1) | ~
% 140.49/19.16 aElementOf0(v4, v1) | ~ aElementOf0(v0, szNzAzT0) | ~ aElement0(v4) | ~
% 140.49/19.16 aSet0(v1) | aElementOf0(v4, v3) | ? [v5: $i] : ($i(v5) & aElementOf0(v5,
% 140.49/19.16 v1) & ~ aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : !
% 140.49/19.16 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~
% 140.49/19.16 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) |
% 140.49/19.16 ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v4, v3) |
% 140.49/19.16 ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v4, v1)) & ! [v0: $i] : ! [v1:
% 140.49/19.16 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) =
% 140.49/19.16 v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) |
% 140.49/19.16 ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~
% 140.49/19.16 aElementOf0(v4, v3) | ~ aElementOf0(v0, szNzAzT0) | aElement0(v4)) & !
% 140.49/19.16 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 140.49/19.16 (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2)
% 140.49/19.16 = v3) | ~ $i(v4) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~
% 140.49/19.16 isCountable0(v1) | ~ aElementOf0(v4, v1) | ~ aElementOf0(v0, szNzAzT0) |
% 140.49/19.16 sdtlseqdt0(v2, v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 140.49/19.16 : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~
% 140.49/19.16 (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~ isCountable0(v1) | ~
% 140.49/19.16 aElementOf0(v4, v3) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) |
% 140.49/19.16 aElementOf0(v4, v1) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, v1) & ~
% 140.49/19.16 aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 140.49/19.16 [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) =
% 140.49/19.16 v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~
% 140.49/19.16 isCountable0(v1) | ~ aElementOf0(v4, v3) | ~ aElementOf0(v0, szNzAzT0) |
% 140.49/19.16 ~ aSet0(v1) | aElement0(v4) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, v1) &
% 140.49/19.16 ~ aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 140.49/19.16 ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1)
% 140.49/19.16 = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~
% 140.49/19.16 isCountable0(v1) | ~ aElementOf0(v4, v1) | ~ aElementOf0(v0, szNzAzT0) |
% 140.49/19.16 ~ aSet0(v1) | sdtlseqdt0(v2, v4) | ? [v5: $i] : ($i(v5) & aElementOf0(v5,
% 140.49/19.16 v1) & ~ aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : !
% 140.49/19.16 [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) =
% 140.49/19.16 v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ~
% 140.49/19.16 aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v2, v3) | ~
% 140.49/19.16 aElementOf0(v0, szNzAzT0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 140.49/19.16 [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~
% 140.49/19.16 (sdtmndt0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ~ isCountable0(v1) | ~
% 140.49/19.16 aElementOf0(v2, v3) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | ? [v4:
% 140.49/19.16 $i] : ($i(v4) & aElementOf0(v4, v1) & ~ aElementOf0(v4, szNzAzT0))) & !
% 140.49/19.16 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) =
% 140.49/19.16 v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) |
% 140.49/19.17 ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v0,
% 140.49/19.17 szNzAzT0) | aElementOf0(v2, v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 140.49/19.17 : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~
% 140.49/19.17 (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~
% 140.49/19.17 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | aSet0(v3)) & ! [v0: $i] :
% 140.49/19.17 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~
% 140.49/19.17 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~
% 140.49/19.17 aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v0,
% 140.49/19.17 szNzAzT0) | ? [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xN, v4) = v5 &
% 140.49/19.17 szszuzczcdt0(v0) = v4 & $i(v5) & $i(v4) & aSubsetOf0(v5, v3) &
% 140.49/19.17 isCountable0(v5) & aSet0(v5) & ! [v6: $i] : ( ~ $i(v6) | ~
% 140.49/19.17 aElementOf0(v6, v5) | aElementOf0(v6, v3)))) & ! [v0: $i] : ! [v1: $i]
% 140.49/19.17 : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~
% 140.49/19.17 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~
% 140.49/19.17 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) |
% 140.49/19.17 aElementOf0(v2, v1) | ? [v4: $i] : ($i(v4) & aElementOf0(v4, v1) & ~
% 140.49/19.17 aElementOf0(v4, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 140.49/19.17 [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~
% 140.49/19.17 (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ isCountable0(v1) | ~
% 140.49/19.17 aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | aSet0(v3) | ? [v4: $i] : ($i(v4)
% 140.49/19.17 & aElementOf0(v4, v1) & ~ aElementOf0(v4, szNzAzT0))) & ! [v0: $i] : !
% 140.49/19.17 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~
% 140.49/19.17 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~
% 140.49/19.17 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | ? [v4: $i]
% 140.49/19.17 : ? [v5: $i] : ? [v6: $i] : ($i(v6) & ((sdtlpdtrp0(xN, v4) = v5 &
% 140.49/19.17 szszuzczcdt0(v0) = v4 & $i(v5) & $i(v4) & aSubsetOf0(v5, v3) &
% 140.49/19.17 isCountable0(v5) & aSet0(v5) & ! [v7: $i] : ( ~ $i(v7) | ~
% 140.49/19.17 aElementOf0(v7, v5) | aElementOf0(v7, v3))) | (aElementOf0(v6, v1) &
% 140.49/19.17 ~ aElementOf0(v6, szNzAzT0)))))
% 140.49/19.17
% 140.49/19.17 (m__3754)
% 140.49/19.17 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 140.49/19.17 : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) |
% 140.49/19.17 ~ $i(v4) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v0) | ~
% 140.49/19.17 aElementOf0(v4, v2) | ~ aElementOf0(v1, szNzAzT0) | ~ aElementOf0(v0,
% 140.49/19.17 szNzAzT0) | aElementOf0(v4, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 140.49/19.17 : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) |
% 140.49/19.17 ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v0) | ~ aElementOf0(v1, szNzAzT0)
% 140.49/19.17 | ~ aElementOf0(v0, szNzAzT0) | aSubsetOf0(v2, v3))
% 140.49/19.17
% 140.49/19.17 (m__4660)
% 140.49/19.17 szDzozmdt0(xe) = szNzAzT0 & $i(xe) & $i(xN) & $i(szNzAzT0) & aFunction0(xe) &
% 140.49/19.17 ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) | ~
% 140.49/19.17 aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2 &
% 140.49/19.17 szmzizndt0(v2) = v1 & $i(v2) & $i(v1) & aElementOf0(v1, v2) & ! [v3: $i]
% 140.49/19.17 : ( ~ $i(v3) | ~ aElementOf0(v3, v2) | sdtlseqdt0(v1, v3))))
% 140.49/19.17
% 140.49/19.17 (m__4730)
% 140.49/19.17 szDzozmdt0(xd) = szNzAzT0 & $i(xd) & $i(xC) & $i(xN) & $i(xk) & $i(szNzAzT0) &
% 140.49/19.17 aFunction0(xd) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xC, v0) = v1) |
% 140.49/19.17 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ?
% 140.49/19.17 [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xd, v0) = v5 & sdtlpdtrp0(xN, v2) = v3
% 140.49/19.17 & slbdtsldtrb0(v3, xk) = v4 & szszuzczcdt0(v0) = v2 & $i(v5) & $i(v4) &
% 140.49/19.17 $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~
% 140.49/19.17 (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aSubsetOf0(v6, v3) | ~
% 140.49/19.17 aSet0(v6) | ? [v8: $i] : ( ~ (v8 = xk) & sbrdtbr0(v6) = v8 & $i(v8))) &
% 140.49/19.17 ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~ (sdtlpdtrp0(v1, v6) = v7) | ~
% 140.49/19.17 $i(v6) | ~ aElementOf0(v6, v4) | ~ aSet0(v6)) & ! [v6: $i] : ! [v7:
% 140.49/19.17 $i] : (v7 = v5 | ~ (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aSet0(v6)
% 140.49/19.17 | ? [v8: $i] : ? [v9: $i] : ($i(v9) & (( ~ (v8 = xk) & sbrdtbr0(v6) =
% 140.49/19.17 v8 & $i(v8)) | (aElementOf0(v9, v6) & ~ aElementOf0(v9, v3)))))))
% 140.49/19.17
% 140.49/19.17 (m__4758)
% 140.82/19.17 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 &
% 140.82/19.17 szDzozmdt0(xd) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT) & aSet0(v1) & !
% 140.82/19.17 [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v2) | ~ $i(v3) | ~
% 140.82/19.17 $i(v2) | ~ aElementOf0(v3, v0) | aElementOf0(v2, v1)) & ! [v2: $i] : ( ~
% 140.82/19.17 $i(v2) | ~ aElementOf0(v2, v1) | aElementOf0(v2, xT)) & ! [v2: $i] : ( ~
% 140.82/19.17 $i(v2) | ~ aElementOf0(v2, v1) | ? [v3: $i] : (sdtlpdtrp0(xd, v3) = v2 &
% 140.82/19.17 $i(v3) & aElementOf0(v3, v0))))
% 140.82/19.17
% 140.82/19.17 (m__4854)
% 140.82/19.18 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) =
% 140.82/19.18 v0 & sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) &
% 140.82/19.18 $i(v0) & aElementOf0(v0, xT) & aSet0(v1) & ! [v3: $i] : ! [v4: $i] : (v4 =
% 140.82/19.18 v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1)) &
% 140.82/19.18 ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~
% 140.82/19.18 aElementOf0(v3, v1) | aElementOf0(v3, v2)) & ! [v3: $i] : ( ~
% 140.82/19.18 (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ aElementOf0(v3, v2) |
% 140.82/19.18 aElementOf0(v3, v1)))
% 140.82/19.18
% 140.82/19.18 (m__4891)
% 140.82/19.18 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 140.82/19.18 (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 &
% 140.82/19.18 szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & !
% 140.82/19.18 [v3: $i] : ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3)
% 140.82/19.18 | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 140.82/19.18 (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) |
% 140.82/19.18 aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xe, v4)
% 140.82/19.18 = v3) | ~ $i(v4) | ~ $i(v3) | ~ aElementOf0(v4, v1) | aElementOf0(v3,
% 140.82/19.18 xO)) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~
% 140.82/19.18 aElementOf0(v3, v2) | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~
% 140.82/19.18 aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 & $i(v4) &
% 140.82/19.18 aElementOf0(v4, v1))))
% 140.82/19.18
% 140.82/19.18 (m__4982)
% 140.82/19.18 $i(xO) & $i(xd) & $i(xe) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] :
% 140.82/19.18 (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & ! [v2: $i]
% 140.82/19.18 : ! [v3: $i] : ( ~ (sdtlpdtrp0(xe, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 140.82/19.18 aElementOf0(v3, v1) | ? [v4: $i] : (sdtlpdtrp0(xd, v4) = v0 &
% 140.82/19.18 sdtlpdtrp0(xe, v4) = v2 & $i(v4) & aElementOf0(v4, v1) & aElementOf0(v4,
% 140.82/19.18 szNzAzT0))) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, xO) | ?
% 140.82/19.18 [v3: $i] : (sdtlpdtrp0(xd, v3) = v0 & sdtlpdtrp0(xe, v3) = v2 & $i(v3) &
% 140.82/19.18 aElementOf0(v3, v1) & aElementOf0(v3, szNzAzT0))))
% 140.82/19.18
% 140.82/19.18 (function-axioms)
% 140.82/19.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.82/19.19 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 140.82/19.19 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 140.82/19.19 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 140.82/19.19 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 140.82/19.19 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 140.82/19.19 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 140.82/19.19 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 140.82/19.19 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 140.82/19.19 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~
% 140.82/19.19 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 140.82/19.19 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) &
% 140.82/19.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 140.82/19.19 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 140.82/19.19 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 140.82/19.19 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 140.82/19.19 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 140.82/19.19 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 140.82/19.19 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 140.82/19.19 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 140.82/19.19 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 140.82/19.19 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 140.82/19.19 v0))
% 140.82/19.19
% 140.82/19.19 Further assumptions not needed in the proof:
% 140.82/19.19 --------------------------------------------
% 140.82/19.19 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 140.82/19.19 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons,
% 140.82/19.19 mDefDiff, mDefMax, mDefMin, mDefRst, mDefSImg, mDefSeg, mDefSel, mDefSub,
% 140.82/19.19 mDiffCons, mDirichlet, mDomSet, mElmSort, mEmpFin, mFConsSet, mFDiffSet,
% 140.82/19.19 mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm, mImgRng,
% 140.82/19.19 mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, mMinMin,
% 140.82/19.19 mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mSegFin, mSegLess, mSegSucc,
% 140.82/19.19 mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, mSubASymm,
% 140.82/19.19 mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, m__3398,
% 140.82/19.19 m__3418, m__3435, m__3453, m__3462, m__3520, m__3533, m__3671, m__3821, m__3965,
% 140.82/19.19 m__4151, m__4182, m__4331, m__4411, m__4618, m__4908
% 140.82/19.19
% 140.82/19.19 Those formulas are unsatisfiable:
% 140.82/19.19 ---------------------------------
% 140.82/19.19
% 140.82/19.19 Begin of proof
% 140.82/19.19 |
% 140.82/19.19 | ALPHA: (mDefEmp) implies:
% 140.82/19.19 | (1) aSet0(slcrc0)
% 140.82/19.19 |
% 140.82/19.19 | ALPHA: (mCountNFin_01) implies:
% 140.82/19.19 | (2) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)
% 140.82/19.19 |
% 140.82/19.19 | ALPHA: (mZeroNum) implies:
% 140.82/19.19 | (3) aElementOf0(sz00, szNzAzT0)
% 140.82/19.19 |
% 140.82/19.19 | ALPHA: (mZeroLess) implies:
% 140.82/19.19 | (4) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) |
% 140.82/19.19 | sdtlseqdt0(sz00, v0))
% 140.82/19.19 |
% 140.82/19.19 | ALPHA: (m__3291) implies:
% 140.82/19.19 | (5) aSet0(xT)
% 140.82/19.19 |
% 140.82/19.19 | ALPHA: (m__3623) implies:
% 140.82/19.19 | (6) $i(sz00)
% 140.82/19.19 | (7) sdtlpdtrp0(xN, sz00) = xS
% 140.82/19.19 |
% 140.82/19.19 | ALPHA: (m__3754) implies:
% 140.82/19.19 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 140.82/19.19 | ~ (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) | ~
% 140.82/19.19 | $i(v4) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v0) | ~
% 140.82/19.19 | aElementOf0(v4, v2) | ~ aElementOf0(v1, szNzAzT0) | ~
% 140.82/19.19 | aElementOf0(v0, szNzAzT0) | aElementOf0(v4, v3))
% 140.82/19.19 |
% 140.82/19.19 | ALPHA: (m__4660) implies:
% 140.82/19.20 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) |
% 140.82/19.20 | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2
% 140.82/19.20 | & szmzizndt0(v2) = v1 & $i(v2) & $i(v1) & aElementOf0(v1, v2) & !
% 140.82/19.20 | [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v2) | sdtlseqdt0(v1,
% 140.82/19.20 | v3))))
% 140.82/19.20 |
% 140.82/19.20 | ALPHA: (m__4730) implies:
% 140.82/19.20 | (10) aFunction0(xd)
% 140.82/19.20 | (11) szDzozmdt0(xd) = szNzAzT0
% 140.82/19.20 |
% 140.82/19.20 | ALPHA: (m__4758) implies:
% 140.82/19.20 | (12) ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & szDzozmdt0(xd)
% 140.82/19.20 | = v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT) & aSet0(v1) & ! [v2:
% 140.82/19.20 | $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v2) | ~ $i(v3) | ~
% 140.82/19.20 | $i(v2) | ~ aElementOf0(v3, v0) | aElementOf0(v2, v1)) & ! [v2:
% 140.82/19.20 | $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | aElementOf0(v2, xT)) &
% 140.82/19.20 | ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | ? [v3: $i] :
% 140.82/19.20 | (sdtlpdtrp0(xd, v3) = v2 & $i(v3) & aElementOf0(v3, v0))))
% 140.82/19.20 |
% 140.82/19.20 | ALPHA: (m__4854) implies:
% 140.82/19.20 | (13) $i(xT)
% 140.82/19.20 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 &
% 140.82/19.20 | sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) &
% 140.82/19.20 | $i(v0) & aElementOf0(v0, xT) & aSet0(v1) & ! [v3: $i] : ! [v4: $i]
% 140.82/19.20 | : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~
% 140.82/19.20 | aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 140.82/19.20 | (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) |
% 140.82/19.20 | aElementOf0(v3, v2)) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v0)
% 140.82/19.20 | | ~ $i(v3) | ~ aElementOf0(v3, v2) | aElementOf0(v3, v1)))
% 140.82/19.20 |
% 140.82/19.20 | ALPHA: (m__4891) implies:
% 140.82/19.20 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 &
% 140.82/19.20 | sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) =
% 140.82/19.20 | v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & ! [v3: $i]
% 140.82/19.20 | : ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3)
% 140.82/19.20 | | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 140.82/19.20 | (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) |
% 140.82/19.20 | aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 140.82/19.20 | (sdtlpdtrp0(xe, v4) = v3) | ~ $i(v4) | ~ $i(v3) | ~
% 140.82/19.20 | aElementOf0(v4, v1) | aElementOf0(v3, xO)) & ! [v3: $i] : ( ~
% 140.82/19.20 | (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ aElementOf0(v3, v2) |
% 140.82/19.20 | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~
% 140.82/19.20 | aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 &
% 140.82/19.20 | $i(v4) & aElementOf0(v4, v1))))
% 140.82/19.20 |
% 140.82/19.20 | ALPHA: (m__4982) implies:
% 140.82/19.20 | (16) $i(xd)
% 140.82/19.20 | (17) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0)
% 140.82/19.20 | = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~
% 140.82/19.20 | (sdtlpdtrp0(xe, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 140.82/19.21 | aElementOf0(v3, v1) | ? [v4: $i] : (sdtlpdtrp0(xd, v4) = v0 &
% 140.82/19.21 | sdtlpdtrp0(xe, v4) = v2 & $i(v4) & aElementOf0(v4, v1) &
% 140.82/19.21 | aElementOf0(v4, szNzAzT0))) & ! [v2: $i] : ( ~ $i(v2) | ~
% 140.82/19.21 | aElementOf0(v2, xO) | ? [v3: $i] : (sdtlpdtrp0(xd, v3) = v0 &
% 140.82/19.21 | sdtlpdtrp0(xe, v3) = v2 & $i(v3) & aElementOf0(v3, v1) &
% 140.82/19.21 | aElementOf0(v3, szNzAzT0))))
% 140.82/19.21 |
% 140.82/19.21 | ALPHA: (m__) implies:
% 140.82/19.21 | (18) ? [v0: $i] : ($i(v0) & aElementOf0(v0, xO) & ~ aSubsetOf0(xO, xS) &
% 140.82/19.21 | ~ aElementOf0(v0, xS))
% 140.82/19.21 |
% 140.82/19.21 | ALPHA: (function-axioms) implies:
% 140.82/19.21 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 140.82/19.21 | (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0))
% 140.82/19.21 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 140.82/19.21 | (szDzizrdt0(v2) = v1) | ~ (szDzizrdt0(v2) = v0))
% 140.82/19.21 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.82/19.21 | (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) = v0))
% 140.82/19.21 |
% 140.82/19.21 | DELTA: instantiating (18) with fresh symbol all_77_0 gives:
% 140.82/19.21 | (22) $i(all_77_0) & aElementOf0(all_77_0, xO) & ~ aSubsetOf0(xO, xS) & ~
% 140.82/19.21 | aElementOf0(all_77_0, xS)
% 140.82/19.21 |
% 140.82/19.21 | ALPHA: (22) implies:
% 140.82/19.21 | (23) ~ aElementOf0(all_77_0, xS)
% 140.82/19.21 | (24) aElementOf0(all_77_0, xO)
% 140.82/19.21 | (25) $i(all_77_0)
% 140.82/19.21 |
% 140.82/19.21 | DELTA: instantiating (12) with fresh symbols all_79_0, all_79_1 gives:
% 140.82/19.21 | (26) sdtlcdtrc0(xd, all_79_1) = all_79_0 & szDzozmdt0(xd) = all_79_1 &
% 140.82/19.21 | $i(all_79_0) & $i(all_79_1) & aSubsetOf0(all_79_0, xT) &
% 140.82/19.21 | aSet0(all_79_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v1)
% 140.82/19.21 | = v0) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, all_79_1) |
% 140.82/19.21 | aElementOf0(v0, all_79_0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 140.82/19.21 | aElementOf0(v0, all_79_0) | aElementOf0(v0, xT)) & ! [v0: $i] : ( ~
% 140.82/19.21 | $i(v0) | ~ aElementOf0(v0, all_79_0) | ? [v1: $i] :
% 140.82/19.21 | (sdtlpdtrp0(xd, v1) = v0 & $i(v1) & aElementOf0(v1, all_79_1)))
% 140.82/19.21 |
% 140.82/19.21 | ALPHA: (26) implies:
% 140.82/19.21 | (27) szDzozmdt0(xd) = all_79_1
% 140.82/19.21 |
% 140.82/19.21 | DELTA: instantiating (14) with fresh symbols all_82_0, all_82_1, all_82_2
% 140.82/19.21 | gives:
% 140.82/19.21 | (28) szDzizrdt0(xd) = all_82_2 & sdtlbdtrb0(xd, all_82_2) = all_82_1 &
% 140.82/19.21 | szDzozmdt0(xd) = all_82_0 & $i(all_82_0) & $i(all_82_1) & $i(all_82_2)
% 140.82/19.21 | & aElementOf0(all_82_2, xT) & aSet0(all_82_1) & ! [v0: $i] : ! [v1:
% 140.82/19.21 | int] : (v1 = all_82_2 | ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) |
% 140.82/19.21 | ~ aElementOf0(v0, all_82_1)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 140.82/19.21 | (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_82_1)
% 140.82/19.21 | | aElementOf0(v0, all_82_0)) & ! [v0: $i] : ( ~ (sdtlpdtrp0(xd, v0)
% 140.82/19.21 | = all_82_2) | ~ $i(v0) | ~ aElementOf0(v0, all_82_0) |
% 140.82/19.21 | aElementOf0(v0, all_82_1))
% 140.82/19.21 |
% 140.82/19.21 | ALPHA: (28) implies:
% 140.82/19.21 | (29) aElementOf0(all_82_2, xT)
% 140.82/19.21 | (30) szDzozmdt0(xd) = all_82_0
% 140.82/19.21 | (31) sdtlbdtrb0(xd, all_82_2) = all_82_1
% 140.82/19.21 | (32) szDzizrdt0(xd) = all_82_2
% 140.82/19.21 |
% 140.82/19.21 | DELTA: instantiating (17) with fresh symbols all_85_0, all_85_1 gives:
% 140.82/19.22 | (33) szDzizrdt0(xd) = all_85_1 & sdtlbdtrb0(xd, all_85_1) = all_85_0 &
% 140.82/19.22 | $i(all_85_0) & $i(all_85_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 140.82/19.22 | (sdtlpdtrp0(xe, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~
% 140.82/19.22 | aElementOf0(v1, all_85_0) | ? [v2: $i] : (sdtlpdtrp0(xd, v2) =
% 140.82/19.22 | all_85_1 & sdtlpdtrp0(xe, v2) = v0 & $i(v2) & aElementOf0(v2,
% 140.82/19.22 | all_85_0) & aElementOf0(v2, szNzAzT0))) & ! [v0: $i] : ( ~
% 140.82/19.22 | $i(v0) | ~ aElementOf0(v0, xO) | ? [v1: $i] : (sdtlpdtrp0(xd, v1)
% 140.82/19.22 | = all_85_1 & sdtlpdtrp0(xe, v1) = v0 & $i(v1) & aElementOf0(v1,
% 140.82/19.22 | all_85_0) & aElementOf0(v1, szNzAzT0)))
% 140.82/19.22 |
% 140.82/19.22 | ALPHA: (33) implies:
% 140.82/19.22 | (34) $i(all_85_1)
% 140.82/19.22 | (35) $i(all_85_0)
% 140.82/19.22 | (36) sdtlbdtrb0(xd, all_85_1) = all_85_0
% 140.82/19.22 | (37) szDzizrdt0(xd) = all_85_1
% 140.82/19.22 | (38) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xO) | ? [v1: $i] :
% 140.82/19.22 | (sdtlpdtrp0(xd, v1) = all_85_1 & sdtlpdtrp0(xe, v1) = v0 & $i(v1) &
% 140.82/19.22 | aElementOf0(v1, all_85_0) & aElementOf0(v1, szNzAzT0)))
% 140.82/19.22 |
% 140.82/19.22 | DELTA: instantiating (15) with fresh symbols all_88_0, all_88_1, all_88_2
% 140.82/19.22 | gives:
% 140.82/19.22 | (39) szDzizrdt0(xd) = all_88_2 & sdtlcdtrc0(xe, all_88_1) = xO &
% 140.82/19.22 | sdtlbdtrb0(xd, all_88_2) = all_88_1 & szDzozmdt0(xd) = all_88_0 &
% 140.82/19.22 | $i(all_88_0) & $i(all_88_1) & $i(all_88_2) & aSet0(all_88_1) &
% 140.82/19.22 | aSet0(xO) & ! [v0: $i] : ! [v1: int] : (v1 = all_88_2 | ~
% 140.82/19.22 | (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0,
% 140.82/19.22 | all_88_1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) =
% 140.82/19.22 | v1) | ~ $i(v0) | ~ aElementOf0(v0, all_88_1) | aElementOf0(v0,
% 140.82/19.22 | all_88_0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v1) =
% 140.82/19.22 | v0) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, all_88_1) |
% 140.82/19.22 | aElementOf0(v0, xO)) & ! [v0: $i] : ( ~ (sdtlpdtrp0(xd, v0) =
% 140.82/19.22 | all_88_2) | ~ $i(v0) | ~ aElementOf0(v0, all_88_0) |
% 140.82/19.22 | aElementOf0(v0, all_88_1)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 140.82/19.22 | aElementOf0(v0, xO) | ? [v1: $i] : (sdtlpdtrp0(xe, v1) = v0 &
% 140.82/19.22 | $i(v1) & aElementOf0(v1, all_88_1)))
% 140.82/19.22 |
% 140.82/19.22 | ALPHA: (39) implies:
% 140.82/19.22 | (40) szDzozmdt0(xd) = all_88_0
% 140.82/19.22 | (41) sdtlbdtrb0(xd, all_88_2) = all_88_1
% 140.82/19.22 | (42) szDzizrdt0(xd) = all_88_2
% 140.82/19.22 |
% 140.82/19.22 | BETA: splitting (2) gives:
% 140.82/19.22 |
% 140.82/19.22 | Case 1:
% 140.82/19.22 | |
% 140.82/19.22 | | (43) ~ aSet0(slcrc0)
% 140.82/19.22 | |
% 140.82/19.22 | | PRED_UNIFY: (1), (43) imply:
% 140.82/19.22 | | (44) $false
% 140.82/19.22 | |
% 140.82/19.22 | | CLOSE: (44) is inconsistent.
% 140.82/19.22 | |
% 140.82/19.22 | Case 2:
% 140.82/19.22 | |
% 140.82/19.22 | |
% 140.82/19.22 | | GROUND_INST: instantiating (19) with all_79_1, all_82_0, xd, simplifying
% 140.82/19.23 | | with (27), (30) gives:
% 140.82/19.23 | | (45) all_82_0 = all_79_1
% 140.82/19.23 | |
% 140.82/19.23 | | GROUND_INST: instantiating (19) with all_82_0, all_88_0, xd, simplifying
% 140.82/19.23 | | with (30), (40) gives:
% 140.82/19.23 | | (46) all_88_0 = all_82_0
% 140.82/19.23 | |
% 140.82/19.23 | | GROUND_INST: instantiating (19) with szNzAzT0, all_88_0, xd, simplifying
% 140.82/19.23 | | with (11), (40) gives:
% 140.82/19.23 | | (47) all_88_0 = szNzAzT0
% 140.82/19.23 | |
% 140.82/19.23 | | GROUND_INST: instantiating (20) with all_85_1, all_88_2, xd, simplifying
% 140.82/19.23 | | with (37), (42) gives:
% 140.82/19.23 | | (48) all_88_2 = all_85_1
% 140.82/19.23 | |
% 140.82/19.23 | | GROUND_INST: instantiating (20) with all_82_2, all_88_2, xd, simplifying
% 140.82/19.23 | | with (32), (42) gives:
% 140.82/19.23 | | (49) all_88_2 = all_82_2
% 140.82/19.23 | |
% 140.82/19.23 | | COMBINE_EQS: (46), (47) imply:
% 140.82/19.23 | | (50) all_82_0 = szNzAzT0
% 140.82/19.23 | |
% 140.82/19.23 | | SIMP: (50) implies:
% 140.82/19.23 | | (51) all_82_0 = szNzAzT0
% 140.82/19.23 | |
% 140.82/19.23 | | COMBINE_EQS: (48), (49) imply:
% 140.82/19.23 | | (52) all_85_1 = all_82_2
% 140.82/19.23 | |
% 140.82/19.23 | | SIMP: (52) implies:
% 140.82/19.23 | | (53) all_85_1 = all_82_2
% 140.82/19.23 | |
% 140.82/19.23 | | COMBINE_EQS: (45), (51) imply:
% 140.82/19.23 | | (54) all_79_1 = szNzAzT0
% 140.82/19.23 | |
% 140.82/19.23 | | SIMP: (54) implies:
% 140.82/19.23 | | (55) all_79_1 = szNzAzT0
% 140.82/19.23 | |
% 140.82/19.23 | | REDUCE: (41), (49) imply:
% 140.82/19.23 | | (56) sdtlbdtrb0(xd, all_82_2) = all_88_1
% 140.82/19.23 | |
% 140.82/19.23 | | REDUCE: (36), (53) imply:
% 140.82/19.23 | | (57) sdtlbdtrb0(xd, all_82_2) = all_85_0
% 140.82/19.23 | |
% 140.82/19.23 | | REDUCE: (34), (53) imply:
% 140.82/19.23 | | (58) $i(all_82_2)
% 140.82/19.23 | |
% 140.82/19.23 | | GROUND_INST: instantiating (21) with all_82_1, all_88_1, all_82_2, xd,
% 140.82/19.23 | | simplifying with (31), (56) gives:
% 140.82/19.23 | | (59) all_88_1 = all_82_1
% 140.82/19.23 | |
% 140.82/19.23 | | GROUND_INST: instantiating (21) with all_85_0, all_88_1, all_82_2, xd,
% 140.82/19.23 | | simplifying with (56), (57) gives:
% 140.82/19.23 | | (60) all_88_1 = all_85_0
% 140.82/19.23 | |
% 140.82/19.23 | | COMBINE_EQS: (59), (60) imply:
% 140.82/19.23 | | (61) all_85_0 = all_82_1
% 140.82/19.23 | |
% 140.82/19.23 | | SIMP: (61) implies:
% 140.82/19.23 | | (62) all_85_0 = all_82_1
% 140.82/19.23 | |
% 140.82/19.23 | | REDUCE: (35), (62) imply:
% 140.82/19.23 | | (63) $i(all_82_1)
% 140.82/19.23 | |
% 140.82/19.23 | | GROUND_INST: instantiating (38) with all_77_0, simplifying with (24), (25)
% 140.82/19.23 | | gives:
% 140.82/19.23 | | (64) ? [v0: $i] : (sdtlpdtrp0(xd, v0) = all_85_1 & sdtlpdtrp0(xe, v0) =
% 140.82/19.23 | | all_77_0 & $i(v0) & aElementOf0(v0, all_85_0) & aElementOf0(v0,
% 140.82/19.23 | | szNzAzT0))
% 140.82/19.23 | |
% 140.82/19.23 | | GROUND_INST: instantiating (mEOfElem) with xT, all_82_2, simplifying with
% 140.82/19.23 | | (5), (13), (29), (58) gives:
% 140.82/19.23 | | (65) aElement0(all_82_2)
% 140.82/19.23 | |
% 140.82/19.23 | | DELTA: instantiating (64) with fresh symbol all_121_0 gives:
% 140.82/19.23 | | (66) sdtlpdtrp0(xd, all_121_0) = all_85_1 & sdtlpdtrp0(xe, all_121_0) =
% 140.82/19.23 | | all_77_0 & $i(all_121_0) & aElementOf0(all_121_0, all_85_0) &
% 140.82/19.23 | | aElementOf0(all_121_0, szNzAzT0)
% 140.82/19.23 | |
% 140.82/19.23 | | ALPHA: (66) implies:
% 140.82/19.23 | | (67) aElementOf0(all_121_0, szNzAzT0)
% 140.82/19.23 | | (68) aElementOf0(all_121_0, all_85_0)
% 140.82/19.23 | | (69) $i(all_121_0)
% 140.82/19.23 | | (70) sdtlpdtrp0(xe, all_121_0) = all_77_0
% 140.82/19.23 | | (71) sdtlpdtrp0(xd, all_121_0) = all_85_1
% 140.82/19.23 | |
% 140.82/19.23 | | REDUCE: (53), (71) imply:
% 140.82/19.23 | | (72) sdtlpdtrp0(xd, all_121_0) = all_82_2
% 140.82/19.23 | |
% 140.82/19.23 | | REDUCE: (62), (68) imply:
% 140.82/19.23 | | (73) aElementOf0(all_121_0, all_82_1)
% 140.82/19.23 | |
% 140.82/19.23 | | GROUND_INST: instantiating (mPttSet) with xd, all_82_2, all_82_1,
% 140.82/19.23 | | simplifying with (10), (16), (31), (58), (65) gives:
% 140.82/19.23 | | (74) ? [v0: $i] : (szDzozmdt0(xd) = v0 & $i(v0) & aSubsetOf0(all_82_1,
% 140.82/19.23 | | v0))
% 140.82/19.23 | |
% 140.82/19.23 | | GROUND_INST: instantiating (mDefPtt) with xd, all_82_2, all_82_1,
% 140.82/19.23 | | simplifying with (10), (16), (31), (58), (65) gives:
% 140.82/19.24 | | (75) ? [v0: $i] : (szDzozmdt0(xd) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 140.82/19.24 | | int] : (v2 = all_82_2 | ~ (sdtlpdtrp0(xd, v1) = v2) | ~ $i(v1)
% 140.82/19.24 | | | ~ $i(all_82_1) | ~ aElementOf0(v1, all_82_1)) & ! [v1: $i]
% 140.82/19.24 | | : ! [v2: $i] : ( ~ (sdtlpdtrp0(xd, v1) = v2) | ~ $i(v1) | ~
% 140.82/19.24 | | $i(all_82_1) | ~ aElementOf0(v1, all_82_1) | aElementOf0(v1,
% 140.82/19.24 | | v0)) & ! [v1: any] : (v1 = all_82_1 | ~ $i(v1) | ~
% 140.82/19.24 | | aSet0(v1) | ? [v2: $i] : ? [v3: any] : ($i(v2) & ( ~
% 140.82/19.24 | | aElementOf0(v2, v1) | ~ aElementOf0(v2, v0) | ( ~ (v3 =
% 140.82/19.24 | | all_82_2) & sdtlpdtrp0(xd, v2) = v3 & $i(v3))) &
% 140.82/19.24 | | (aElementOf0(v2, v1) | (v3 = all_82_2 & sdtlpdtrp0(xd, v2) =
% 140.82/19.24 | | all_82_2 & aElementOf0(v2, v0))))) & ! [v1: $i] : ( ~
% 140.82/19.24 | | (sdtlpdtrp0(xd, v1) = all_82_2) | ~ $i(v1) | ~ $i(all_82_1) |
% 140.82/19.24 | | ~ aElementOf0(v1, v0) | aElementOf0(v1, all_82_1)) & ( ~
% 140.82/19.24 | | $i(all_82_1) | aSet0(all_82_1)))
% 140.82/19.24 | |
% 140.82/19.24 | | GROUND_INST: instantiating (4) with all_121_0, simplifying with (67), (69)
% 140.82/19.24 | | gives:
% 140.82/19.24 | | (76) sdtlseqdt0(sz00, all_121_0)
% 140.82/19.24 | |
% 140.82/19.24 | | GROUND_INST: instantiating (9) with all_121_0, all_77_0, simplifying with
% 140.82/19.24 | | (67), (69), (70) gives:
% 140.82/19.24 | | (77) ? [v0: $i] : (sdtlpdtrp0(xN, all_121_0) = v0 & szmzizndt0(v0) =
% 140.82/19.24 | | all_77_0 & $i(v0) & $i(all_77_0) & aElementOf0(all_77_0, v0) & !
% 140.82/19.24 | | [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, v0) |
% 140.82/19.24 | | sdtlseqdt0(all_77_0, v1)))
% 140.82/19.24 | |
% 140.82/19.24 | | DELTA: instantiating (74) with fresh symbol all_148_0 gives:
% 140.82/19.24 | | (78) szDzozmdt0(xd) = all_148_0 & $i(all_148_0) & aSubsetOf0(all_82_1,
% 140.82/19.24 | | all_148_0)
% 140.82/19.24 | |
% 140.82/19.24 | | ALPHA: (78) implies:
% 140.82/19.24 | | (79) szDzozmdt0(xd) = all_148_0
% 140.82/19.24 | |
% 140.82/19.24 | | DELTA: instantiating (77) with fresh symbol all_155_0 gives:
% 140.82/19.24 | | (80) sdtlpdtrp0(xN, all_121_0) = all_155_0 & szmzizndt0(all_155_0) =
% 140.82/19.24 | | all_77_0 & $i(all_155_0) & $i(all_77_0) & aElementOf0(all_77_0,
% 140.82/19.24 | | all_155_0) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0,
% 140.82/19.24 | | all_155_0) | sdtlseqdt0(all_77_0, v0))
% 140.82/19.24 | |
% 140.82/19.24 | | ALPHA: (80) implies:
% 140.82/19.24 | | (81) aElementOf0(all_77_0, all_155_0)
% 140.82/19.24 | | (82) sdtlpdtrp0(xN, all_121_0) = all_155_0
% 140.82/19.24 | |
% 140.82/19.24 | | DELTA: instantiating (75) with fresh symbol all_160_0 gives:
% 140.82/19.24 | | (83) szDzozmdt0(xd) = all_160_0 & $i(all_160_0) & ! [v0: $i] : ! [v1:
% 140.82/19.24 | | int] : (v1 = all_82_2 | ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) |
% 140.82/19.24 | | ~ $i(all_82_1) | ~ aElementOf0(v0, all_82_1)) & ! [v0: $i] : !
% 140.82/19.24 | | [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~
% 140.82/19.24 | | $i(all_82_1) | ~ aElementOf0(v0, all_82_1) | aElementOf0(v0,
% 140.82/19.24 | | all_160_0)) & ! [v0: any] : (v0 = all_82_1 | ~ $i(v0) | ~
% 140.82/19.24 | | aSet0(v0) | ? [v1: $i] : ? [v2: any] : ($i(v1) & ( ~
% 140.82/19.24 | | aElementOf0(v1, v0) | ~ aElementOf0(v1, all_160_0) | ( ~ (v2
% 140.82/19.24 | | = all_82_2) & sdtlpdtrp0(xd, v1) = v2 & $i(v2))) &
% 140.82/19.24 | | (aElementOf0(v1, v0) | (v2 = all_82_2 & sdtlpdtrp0(xd, v1) =
% 140.82/19.24 | | all_82_2 & aElementOf0(v1, all_160_0))))) & ! [v0: $i] : (
% 140.82/19.24 | | ~ (sdtlpdtrp0(xd, v0) = all_82_2) | ~ $i(v0) | ~ $i(all_82_1) |
% 140.82/19.24 | | ~ aElementOf0(v0, all_160_0) | aElementOf0(v0, all_82_1)) & ( ~
% 140.82/19.24 | | $i(all_82_1) | aSet0(all_82_1))
% 140.82/19.24 | |
% 140.82/19.24 | | ALPHA: (83) implies:
% 140.82/19.24 | | (84) szDzozmdt0(xd) = all_160_0
% 140.82/19.24 | | (85) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) = v1) | ~
% 140.82/19.24 | | $i(v0) | ~ $i(all_82_1) | ~ aElementOf0(v0, all_82_1) |
% 140.82/19.24 | | aElementOf0(v0, all_160_0))
% 140.82/19.24 | |
% 140.82/19.24 | | GROUND_INST: instantiating (85) with all_121_0, all_82_2, simplifying with
% 140.82/19.24 | | (63), (69), (72), (73) gives:
% 140.82/19.24 | | (86) aElementOf0(all_121_0, all_160_0)
% 140.82/19.24 | |
% 140.82/19.24 | | GROUND_INST: instantiating (19) with szNzAzT0, all_160_0, xd, simplifying
% 140.82/19.24 | | with (11), (84) gives:
% 140.82/19.24 | | (87) all_160_0 = szNzAzT0
% 140.82/19.24 | |
% 140.82/19.24 | | GROUND_INST: instantiating (19) with all_148_0, all_160_0, xd, simplifying
% 140.82/19.24 | | with (79), (84) gives:
% 140.82/19.24 | | (88) all_160_0 = all_148_0
% 140.82/19.24 | |
% 140.82/19.24 | | COMBINE_EQS: (87), (88) imply:
% 140.82/19.24 | | (89) all_148_0 = szNzAzT0
% 140.82/19.24 | |
% 140.82/19.24 | | GROUND_INST: instantiating (8) with all_121_0, sz00, all_155_0, xS,
% 140.82/19.24 | | all_77_0, simplifying with (3), (6), (7), (23), (25), (67),
% 140.82/19.24 | | (69), (76), (81), (82) gives:
% 140.82/19.24 | | (90) $false
% 140.82/19.24 | |
% 140.82/19.24 | | CLOSE: (90) is inconsistent.
% 140.82/19.24 | |
% 140.82/19.25 | End of split
% 140.82/19.25 |
% 140.82/19.25 End of proof
% 140.82/19.25 % SZS output end Proof for theBenchmark
% 140.82/19.25
% 140.82/19.25 18638ms
%------------------------------------------------------------------------------