TSTP Solution File: NUM574+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM574+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 : n031.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 167.85s 22.96s
% Output : Proof 168.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM574+3 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n031.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 12:08:22 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 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 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 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
% 5.23/1.46 Prover 1: Preprocessing ...
% 5.23/1.46 Prover 4: Preprocessing ...
% 5.23/1.50 Prover 5: Preprocessing ...
% 5.23/1.50 Prover 0: Preprocessing ...
% 5.23/1.50 Prover 3: Preprocessing ...
% 5.23/1.50 Prover 2: Preprocessing ...
% 5.23/1.50 Prover 6: Preprocessing ...
% 15.07/2.82 Prover 3: Constructing countermodel ...
% 15.07/2.82 Prover 1: Constructing countermodel ...
% 15.75/2.88 Prover 6: Proving ...
% 16.33/2.98 Prover 5: Proving ...
% 19.36/3.35 Prover 2: Proving ...
% 24.86/4.08 Prover 4: Constructing countermodel ...
% 27.90/4.47 Prover 0: Proving ...
% 72.78/10.29 Prover 2: stopped
% 72.78/10.29 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 73.62/10.41 Prover 7: Preprocessing ...
% 75.53/10.70 Prover 7: Constructing countermodel ...
% 100.78/13.96 Prover 5: stopped
% 100.78/13.96 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 101.54/14.10 Prover 8: Preprocessing ...
% 103.19/14.28 Prover 8: Warning: ignoring some quantifiers
% 103.19/14.28 Prover 8: Constructing countermodel ...
% 116.42/15.98 Prover 1: stopped
% 116.42/15.99 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 117.24/16.09 Prover 9: Preprocessing ...
% 123.30/16.96 Prover 9: Constructing countermodel ...
% 130.88/17.87 Prover 6: stopped
% 130.88/17.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 131.76/18.00 Prover 10: Preprocessing ...
% 133.19/18.18 Prover 10: Constructing countermodel ...
% 167.85/22.92 Prover 10: Found proof (size 71)
% 167.85/22.92 Prover 10: proved (5032ms)
% 167.85/22.93 Prover 9: stopped
% 167.85/22.93 Prover 3: stopped
% 167.85/22.93 Prover 4: stopped
% 167.85/22.93 Prover 8: stopped
% 167.85/22.94 Prover 0: stopped
% 167.85/22.96 Prover 7: stopped
% 167.85/22.96
% 167.85/22.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 167.85/22.96
% 167.85/22.96 % SZS output start Proof for theBenchmark
% 167.85/22.97 Assumptions after simplification:
% 167.85/22.97 ---------------------------------
% 167.85/22.97
% 167.85/22.97 (mDefSub)
% 167.85/22.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 167.85/22.98 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) |
% 167.85/22.98 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) |
% 167.85/22.98 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i]
% 167.85/22.98 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) |
% 167.85/22.98 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)))
% 167.85/22.98
% 167.85/22.98 (mNatExtra)
% 167.85/23.00 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~
% 167.85/23.00 aElementOf0(v0, szNzAzT0) | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) &
% 167.85/23.00 aElementOf0(v1, szNzAzT0)))
% 167.85/23.00
% 167.85/23.00 (mNoScLessZr)
% 167.85/23.00 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) =
% 167.85/23.00 v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, sz00) | ~ aElementOf0(v0, szNzAzT0))
% 167.85/23.00
% 167.85/23.00 (mSegSucc)
% 168.36/23.01 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slbdtrb0(v1) =
% 168.36/23.01 v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~
% 168.36/23.01 aElementOf0(v0, szNzAzT0) | ? [v3: $i] : ? [v4: $i] : ((v1 = v0 |
% 168.36/23.01 aElementOf0(v0, v2) | (slbdtrb0(v3) = v4 & szszuzczcdt0(v1) = v3 &
% 168.36/23.01 $i(v4) & $i(v3) & ~ aElementOf0(v0, v4))) & (( ~ (v1 = v0) & ~
% 168.36/23.01 aElementOf0(v0, v2)) | (slbdtrb0(v3) = v4 & szszuzczcdt0(v1) = v3 &
% 168.36/23.01 $i(v4) & $i(v3) & aElementOf0(v0, v4)))))
% 168.36/23.01
% 168.36/23.01 (mSegZero)
% 168.36/23.01 slbdtrb0(sz00) = slcrc0 & $i(sz00) & $i(slcrc0)
% 168.36/23.01
% 168.36/23.01 (mZeroNum)
% 168.36/23.01 $i(sz00) & $i(szNzAzT0) & aElementOf0(sz00, szNzAzT0)
% 168.36/23.01
% 168.36/23.01 (m__)
% 168.36/23.01 $i(xi) & $i(xj) & $i(xN) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 168.36/23.01 (sdtlpdtrp0(xN, xi) = v0 & sdtlpdtrp0(xN, xj) = v1 & $i(v2) & $i(v1) & $i(v0)
% 168.36/23.01 & sdtlseqdt0(xj, xi) & aElementOf0(v2, v0) & ~ aSubsetOf0(v0, v1) & ~
% 168.36/23.01 aElementOf0(v2, v1))
% 168.36/23.01
% 168.36/23.01 (m__3623)
% 168.36/23.03 sdtlpdtrp0(xN, sz00) = xS & szDzozmdt0(xN) = szNzAzT0 & $i(xN) & $i(xS) &
% 168.36/23.03 $i(sz00) & $i(szNzAzT0) & aFunction0(xN) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 168.36/23.03 $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2 | ~ (sdtlpdtrp0(xN, v0) = v1) |
% 168.36/23.03 ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0)
% 168.36/23.03 | ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v4, v1)
% 168.36/23.03 | ~ aElementOf0(v0, szNzAzT0) | ~ aElement0(v4) | aElementOf0(v4, v3)) &
% 168.36/23.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2
% 168.36/23.03 | ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1,
% 168.36/23.03 v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~ isCountable0(v1) | ~
% 168.36/23.03 aElementOf0(v4, v1) | ~ aElementOf0(v0, szNzAzT0) | ~ aElement0(v4) | ~
% 168.36/23.03 aSet0(v1) | aElementOf0(v4, v3) | ? [v5: $i] : ($i(v5) & aElementOf0(v5,
% 168.36/23.03 v1) & ~ aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : !
% 168.36/23.03 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~
% 168.36/23.03 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) |
% 168.36/23.03 ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v4, v3) |
% 168.36/23.03 ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v4, v1)) & ! [v0: $i] : ! [v1:
% 168.36/23.03 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) =
% 168.36/23.03 v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) |
% 168.36/23.03 ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~
% 168.36/23.03 aElementOf0(v4, v3) | ~ aElementOf0(v0, szNzAzT0) | aElement0(v4)) & !
% 168.36/23.03 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 168.36/23.03 (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2)
% 168.36/23.03 = v3) | ~ $i(v4) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~
% 168.36/23.03 isCountable0(v1) | ~ aElementOf0(v4, v1) | ~ aElementOf0(v0, szNzAzT0) |
% 168.36/23.03 sdtlseqdt0(v2, v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 168.36/23.03 : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~
% 168.36/23.03 (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~ isCountable0(v1) | ~
% 168.36/23.03 aElementOf0(v4, v3) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) |
% 168.36/23.03 aElementOf0(v4, v1) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, v1) & ~
% 168.36/23.03 aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 168.36/23.03 [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) =
% 168.36/23.03 v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~
% 168.36/23.03 isCountable0(v1) | ~ aElementOf0(v4, v3) | ~ aElementOf0(v0, szNzAzT0) |
% 168.36/23.03 ~ aSet0(v1) | aElement0(v4) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, v1) &
% 168.36/23.03 ~ aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 168.36/23.03 ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1)
% 168.36/23.03 = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~
% 168.36/23.03 isCountable0(v1) | ~ aElementOf0(v4, v1) | ~ aElementOf0(v0, szNzAzT0) |
% 168.36/23.03 ~ aSet0(v1) | sdtlseqdt0(v2, v4) | ? [v5: $i] : ($i(v5) & aElementOf0(v5,
% 168.36/23.03 v1) & ~ aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : !
% 168.36/23.03 [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) =
% 168.36/23.03 v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ~
% 168.36/23.03 aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v2, v3) | ~
% 168.36/23.03 aElementOf0(v0, szNzAzT0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 168.36/23.03 [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~
% 168.36/23.03 (sdtmndt0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ~ isCountable0(v1) | ~
% 168.36/23.03 aElementOf0(v2, v3) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | ? [v4:
% 168.36/23.03 $i] : ($i(v4) & aElementOf0(v4, v1) & ~ aElementOf0(v4, szNzAzT0))) & !
% 168.36/23.03 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) =
% 168.36/23.03 v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) |
% 168.36/23.03 ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v0,
% 168.36/23.03 szNzAzT0) | aElementOf0(v2, v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 168.36/23.03 : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~
% 168.36/23.03 (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~
% 168.36/23.03 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | aSet0(v3)) & ! [v0: $i] :
% 168.36/23.03 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~
% 168.36/23.03 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~
% 168.36/23.03 aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v0,
% 168.36/23.03 szNzAzT0) | ? [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xN, v4) = v5 &
% 168.36/23.03 szszuzczcdt0(v0) = v4 & $i(v5) & $i(v4) & aSubsetOf0(v5, v3) &
% 168.36/23.03 isCountable0(v5) & aSet0(v5) & ! [v6: $i] : ( ~ $i(v6) | ~
% 168.36/23.03 aElementOf0(v6, v5) | aElementOf0(v6, v3)))) & ! [v0: $i] : ! [v1: $i]
% 168.36/23.03 : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~
% 168.36/23.03 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~
% 168.36/23.03 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) |
% 168.36/23.03 aElementOf0(v2, v1) | ? [v4: $i] : ($i(v4) & aElementOf0(v4, v1) & ~
% 168.36/23.03 aElementOf0(v4, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 168.36/23.03 [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~
% 168.36/23.03 (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ isCountable0(v1) | ~
% 168.36/23.03 aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | aSet0(v3) | ? [v4: $i] : ($i(v4)
% 168.36/23.03 & aElementOf0(v4, v1) & ~ aElementOf0(v4, szNzAzT0))) & ! [v0: $i] : !
% 168.36/23.03 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~
% 168.36/23.03 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~
% 168.36/23.03 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | ? [v4: $i]
% 168.36/23.03 : ? [v5: $i] : ? [v6: $i] : ($i(v6) & ((sdtlpdtrp0(xN, v4) = v5 &
% 168.36/23.03 szszuzczcdt0(v0) = v4 & $i(v5) & $i(v4) & aSubsetOf0(v5, v3) &
% 168.36/23.03 isCountable0(v5) & aSet0(v5) & ! [v7: $i] : ( ~ $i(v7) | ~
% 168.36/23.03 aElementOf0(v7, v5) | aElementOf0(v7, v3))) | (aElementOf0(v6, v1) &
% 168.36/23.03 ~ aElementOf0(v6, szNzAzT0)))))
% 168.36/23.03
% 168.36/23.03 (m__3671)
% 168.36/23.03 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 168.36/23.03 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v2, v1) |
% 168.36/23.03 ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v2, szNzAzT0)) & ! [v0: $i] : !
% 168.36/23.03 [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0,
% 168.36/23.03 szNzAzT0) | aSubsetOf0(v1, szNzAzT0)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 168.36/23.03 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) |
% 168.36/23.03 isCountable0(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) =
% 168.36/23.03 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | aSet0(v1))
% 168.36/23.03
% 168.36/23.03 (m__3786)
% 168.36/23.04 $i(xi) & $i(xj) & $i(szNzAzT0) & aElementOf0(xi, szNzAzT0) & aElementOf0(xj,
% 168.36/23.04 szNzAzT0)
% 168.36/23.04
% 168.36/23.04 (m__3786_02)
% 168.36/23.04 $i(xi) & $i(xj) & $i(xN) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] : ( ~
% 168.36/23.04 sdtlseqdt0(xj, xi) | ! [v2: $i] : ( ~ (szszuzczcdt0(v2) = xi) | ~ $i(v2) |
% 168.36/23.04 ~ aElementOf0(v2, szNzAzT0)) | (sdtlpdtrp0(xN, xi) = v0 & sdtlpdtrp0(xN,
% 168.36/23.04 xj) = v1 & $i(v1) & $i(v0) & aSubsetOf0(v0, v1) & ! [v2: $i] : ( ~
% 168.36/23.04 $i(v2) | ~ aElementOf0(v2, v0) | aElementOf0(v2, v1))))
% 168.36/23.04
% 168.36/23.04 (function-axioms)
% 168.36/23.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.36/23.04 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 168.36/23.04 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 168.36/23.04 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 168.36/23.04 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 168.36/23.04 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 168.36/23.04 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 168.36/23.04 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 168.36/23.04 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 168.36/23.04 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~
% 168.36/23.04 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 168.36/23.04 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) &
% 168.36/23.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 168.36/23.04 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 168.36/23.04 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 168.36/23.04 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 168.36/23.04 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 168.36/23.04 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 168.36/23.04 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 168.36/23.04 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 168.36/23.04 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 168.36/23.04 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 168.36/23.04 v0))
% 168.36/23.04
% 168.36/23.04 Further assumptions not needed in the proof:
% 168.36/23.04 --------------------------------------------
% 168.36/23.04 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 168.36/23.04 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01,
% 168.36/23.04 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg,
% 168.36/23.04 mDefSeg, mDefSel, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin,
% 168.36/23.04 mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount,
% 168.36/23.04 mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal,
% 168.36/23.04 mLessTrans, mMinMin, mNATSet, mNatNSucc, mPttSet, mSegFin, mSegLess, mSelCSet,
% 168.36/23.04 mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl,
% 168.36/23.04 mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, m__3291, m__3398,
% 168.36/23.04 m__3418, m__3435, m__3453, m__3462, m__3520, m__3533, m__3754
% 168.36/23.04
% 168.36/23.04 Those formulas are unsatisfiable:
% 168.36/23.04 ---------------------------------
% 168.36/23.04
% 168.36/23.04 Begin of proof
% 168.36/23.04 |
% 168.36/23.04 | ALPHA: (mDefSub) implies:
% 168.36/23.05 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~
% 168.36/23.05 | aSet0(v0) | aSubsetOf0(v1, v0) | ? [v2: $i] : ($i(v2) &
% 168.36/23.05 | aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)))
% 168.36/23.05 |
% 168.36/23.05 | ALPHA: (mZeroNum) implies:
% 168.36/23.05 | (2) aElementOf0(sz00, szNzAzT0)
% 168.36/23.05 |
% 168.36/23.05 | ALPHA: (mNatExtra) implies:
% 168.36/23.05 | (3) ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) |
% 168.36/23.05 | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & aElementOf0(v1,
% 168.36/23.05 | szNzAzT0)))
% 168.36/23.05 |
% 168.36/23.05 | ALPHA: (mNoScLessZr) implies:
% 168.36/23.05 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) |
% 168.36/23.05 | ~ sdtlseqdt0(v1, sz00) | ~ aElementOf0(v0, szNzAzT0))
% 168.36/23.05 |
% 168.36/23.05 | ALPHA: (mSegZero) implies:
% 168.36/23.05 | (5) slbdtrb0(sz00) = slcrc0
% 168.36/23.05 |
% 168.36/23.05 | ALPHA: (mSegSucc) implies:
% 168.36/23.05 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slbdtrb0(v1) = v2) | ~
% 168.36/23.05 | $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~
% 168.36/23.05 | aElementOf0(v0, szNzAzT0) | ? [v3: $i] : ? [v4: $i] : ((v1 = v0 |
% 168.36/23.05 | aElementOf0(v0, v2) | (slbdtrb0(v3) = v4 & szszuzczcdt0(v1) = v3
% 168.36/23.05 | & $i(v4) & $i(v3) & ~ aElementOf0(v0, v4))) & (( ~ (v1 = v0) &
% 168.36/23.05 | ~ aElementOf0(v0, v2)) | (slbdtrb0(v3) = v4 & szszuzczcdt0(v1)
% 168.36/23.05 | = v3 & $i(v4) & $i(v3) & aElementOf0(v0, v4)))))
% 168.36/23.05 |
% 168.36/23.05 | ALPHA: (m__3623) implies:
% 168.36/23.05 | (7) $i(sz00)
% 168.36/23.05 | (8) sdtlpdtrp0(xN, sz00) = xS
% 168.36/23.05 |
% 168.36/23.05 | ALPHA: (m__3671) implies:
% 168.36/23.05 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) |
% 168.36/23.05 | ~ aElementOf0(v0, szNzAzT0) | aSet0(v1))
% 168.36/23.05 |
% 168.36/23.05 | ALPHA: (m__3786) implies:
% 168.36/23.05 | (10) aElementOf0(xj, szNzAzT0)
% 168.36/23.05 | (11) aElementOf0(xi, szNzAzT0)
% 168.36/23.05 |
% 168.36/23.05 | ALPHA: (m__3786_02) implies:
% 168.36/23.05 | (12) ? [v0: $i] : ? [v1: $i] : ( ~ sdtlseqdt0(xj, xi) | ! [v2: $i] : ( ~
% 168.36/23.05 | (szszuzczcdt0(v2) = xi) | ~ $i(v2) | ~ aElementOf0(v2,
% 168.36/23.05 | szNzAzT0)) | (sdtlpdtrp0(xN, xi) = v0 & sdtlpdtrp0(xN, xj) = v1
% 168.36/23.05 | & $i(v1) & $i(v0) & aSubsetOf0(v0, v1) & ! [v2: $i] : ( ~ $i(v2)
% 168.36/23.05 | | ~ aElementOf0(v2, v0) | aElementOf0(v2, v1))))
% 168.36/23.05 |
% 168.36/23.05 | ALPHA: (m__) implies:
% 168.36/23.05 | (13) $i(xj)
% 168.36/23.05 | (14) $i(xi)
% 168.36/23.05 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtlpdtrp0(xN, xi) = v0 &
% 168.36/23.05 | sdtlpdtrp0(xN, xj) = v1 & $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(xj,
% 168.36/23.05 | xi) & aElementOf0(v2, v0) & ~ aSubsetOf0(v0, v1) & ~
% 168.36/23.05 | aElementOf0(v2, v1))
% 168.36/23.05 |
% 168.36/23.05 | ALPHA: (function-axioms) implies:
% 168.36/23.06 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.36/23.06 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0))
% 168.36/23.06 |
% 168.36/23.06 | DELTA: instantiating (15) with fresh symbols all_69_0, all_69_1, all_69_2
% 168.36/23.06 | gives:
% 168.36/23.06 | (17) sdtlpdtrp0(xN, xi) = all_69_2 & sdtlpdtrp0(xN, xj) = all_69_1 &
% 168.36/23.06 | $i(all_69_0) & $i(all_69_1) & $i(all_69_2) & sdtlseqdt0(xj, xi) &
% 168.36/23.06 | aElementOf0(all_69_0, all_69_2) & ~ aSubsetOf0(all_69_2, all_69_1) &
% 168.36/23.06 | ~ aElementOf0(all_69_0, all_69_1)
% 168.36/23.06 |
% 168.36/23.06 | ALPHA: (17) implies:
% 168.36/23.06 | (18) ~ aSubsetOf0(all_69_2, all_69_1)
% 168.36/23.06 | (19) sdtlseqdt0(xj, xi)
% 168.36/23.06 | (20) $i(all_69_2)
% 168.36/23.06 | (21) sdtlpdtrp0(xN, xj) = all_69_1
% 168.36/23.06 | (22) sdtlpdtrp0(xN, xi) = all_69_2
% 168.36/23.06 |
% 168.36/23.06 | DELTA: instantiating (12) with fresh symbols all_71_0, all_71_1 gives:
% 168.36/23.06 | (23) ~ sdtlseqdt0(xj, xi) | ! [v0: $i] : ( ~ (szszuzczcdt0(v0) = xi) | ~
% 168.36/23.06 | $i(v0) | ~ aElementOf0(v0, szNzAzT0)) | (sdtlpdtrp0(xN, xi) =
% 168.36/23.06 | all_71_1 & sdtlpdtrp0(xN, xj) = all_71_0 & $i(all_71_0) &
% 168.36/23.06 | $i(all_71_1) & aSubsetOf0(all_71_1, all_71_0) & ! [v0: $i] : ( ~
% 168.36/23.06 | $i(v0) | ~ aElementOf0(v0, all_71_1) | aElementOf0(v0,
% 168.36/23.06 | all_71_0)))
% 168.36/23.06 |
% 168.36/23.06 | BETA: splitting (23) gives:
% 168.36/23.06 |
% 168.36/23.06 | Case 1:
% 168.36/23.06 | |
% 168.36/23.06 | | (24) ~ sdtlseqdt0(xj, xi)
% 168.36/23.06 | |
% 168.36/23.06 | | PRED_UNIFY: (19), (24) imply:
% 168.36/23.06 | | (25) $false
% 168.36/23.06 | |
% 168.36/23.06 | | CLOSE: (25) is inconsistent.
% 168.36/23.06 | |
% 168.36/23.06 | Case 2:
% 168.36/23.06 | |
% 168.36/23.06 | | (26) ! [v0: $i] : ( ~ (szszuzczcdt0(v0) = xi) | ~ $i(v0) | ~
% 168.36/23.06 | | aElementOf0(v0, szNzAzT0)) | (sdtlpdtrp0(xN, xi) = all_71_1 &
% 168.36/23.06 | | sdtlpdtrp0(xN, xj) = all_71_0 & $i(all_71_0) & $i(all_71_1) &
% 168.36/23.06 | | aSubsetOf0(all_71_1, all_71_0) & ! [v0: $i] : ( ~ $i(v0) | ~
% 168.36/23.06 | | aElementOf0(v0, all_71_1) | aElementOf0(v0, all_71_0)))
% 168.36/23.06 | |
% 168.36/23.06 | | BETA: splitting (26) gives:
% 168.36/23.06 | |
% 168.36/23.06 | | Case 1:
% 168.36/23.06 | | |
% 168.36/23.06 | | | (27) ! [v0: $i] : ( ~ (szszuzczcdt0(v0) = xi) | ~ $i(v0) | ~
% 168.36/23.06 | | | aElementOf0(v0, szNzAzT0))
% 168.36/23.06 | | |
% 168.36/23.06 | | | GROUND_INST: instantiating (3) with xj, simplifying with (10), (13) gives:
% 168.36/23.06 | | | (28) xj = sz00 | ? [v0: $i] : (szszuzczcdt0(v0) = xj & $i(v0) &
% 168.36/23.06 | | | aElementOf0(v0, szNzAzT0))
% 168.36/23.06 | | |
% 168.36/23.06 | | | GROUND_INST: instantiating (3) with xi, simplifying with (11), (14) gives:
% 168.36/23.06 | | | (29) xi = sz00 | ? [v0: $i] : (szszuzczcdt0(v0) = xi & $i(v0) &
% 168.36/23.06 | | | aElementOf0(v0, szNzAzT0))
% 168.36/23.06 | | |
% 168.36/23.07 | | | GROUND_INST: instantiating (6) with xj, sz00, slcrc0, simplifying with
% 168.36/23.07 | | | (2), (5), (7), (10), (13) gives:
% 168.36/23.07 | | | (30) ? [v0: $i] : ? [v1: $i] : ((xj = sz00 | aElementOf0(xj, slcrc0)
% 168.36/23.07 | | | | (slbdtrb0(v0) = v1 & szszuzczcdt0(sz00) = v0 & $i(v1) &
% 168.36/23.07 | | | $i(v0) & ~ aElementOf0(xj, v1))) & (( ~ (xj = sz00) & ~
% 168.36/23.07 | | | aElementOf0(xj, slcrc0)) | (slbdtrb0(v0) = v1 &
% 168.36/23.07 | | | szszuzczcdt0(sz00) = v0 & $i(v1) & $i(v0) & aElementOf0(xj,
% 168.36/23.07 | | | v1))))
% 168.36/23.07 | | |
% 168.36/23.07 | | | GROUND_INST: instantiating (9) with xi, all_69_2, simplifying with (11),
% 168.36/23.07 | | | (14), (22) gives:
% 168.36/23.07 | | | (31) aSet0(all_69_2)
% 168.36/23.07 | | |
% 168.36/23.07 | | | DELTA: instantiating (30) with fresh symbols all_96_0, all_96_1 gives:
% 168.36/23.07 | | | (32) (xj = sz00 | aElementOf0(xj, slcrc0) | (slbdtrb0(all_96_1) =
% 168.36/23.07 | | | all_96_0 & szszuzczcdt0(sz00) = all_96_1 & $i(all_96_0) &
% 168.36/23.07 | | | $i(all_96_1) & ~ aElementOf0(xj, all_96_0))) & (( ~ (xj =
% 168.36/23.07 | | | sz00) & ~ aElementOf0(xj, slcrc0)) | (slbdtrb0(all_96_1) =
% 168.36/23.07 | | | all_96_0 & szszuzczcdt0(sz00) = all_96_1 & $i(all_96_0) &
% 168.36/23.07 | | | $i(all_96_1) & aElementOf0(xj, all_96_0)))
% 168.36/23.07 | | |
% 168.36/23.07 | | | ALPHA: (32) implies:
% 168.36/23.07 | | | (33) ( ~ (xj = sz00) & ~ aElementOf0(xj, slcrc0)) |
% 168.36/23.07 | | | (slbdtrb0(all_96_1) = all_96_0 & szszuzczcdt0(sz00) = all_96_1 &
% 168.36/23.07 | | | $i(all_96_0) & $i(all_96_1) & aElementOf0(xj, all_96_0))
% 168.36/23.07 | | |
% 168.36/23.07 | | | GROUND_INST: instantiating (1) with all_69_2, all_69_2, simplifying with
% 168.36/23.07 | | | (20), (31) gives:
% 168.36/23.07 | | | (34) aSubsetOf0(all_69_2, all_69_2)
% 168.36/23.07 | | |
% 168.36/23.07 | | | BETA: splitting (28) gives:
% 168.36/23.07 | | |
% 168.36/23.07 | | | Case 1:
% 168.36/23.07 | | | |
% 168.36/23.07 | | | | (35) xj = sz00
% 168.36/23.07 | | | |
% 168.36/23.07 | | | | REDUCE: (21), (35) imply:
% 168.36/23.07 | | | | (36) sdtlpdtrp0(xN, sz00) = all_69_1
% 168.36/23.07 | | | |
% 168.36/23.07 | | | | BETA: splitting (33) gives:
% 168.36/23.07 | | | |
% 168.36/23.07 | | | | Case 1:
% 168.36/23.07 | | | | |
% 168.69/23.07 | | | | | (37) ~ (xj = sz00) & ~ aElementOf0(xj, slcrc0)
% 168.69/23.07 | | | | |
% 168.69/23.07 | | | | | ALPHA: (37) implies:
% 168.69/23.07 | | | | | (38) ~ (xj = sz00)
% 168.69/23.07 | | | | |
% 168.69/23.07 | | | | | REDUCE: (35), (38) imply:
% 168.69/23.07 | | | | | (39) $false
% 168.69/23.07 | | | | |
% 168.69/23.07 | | | | | CLOSE: (39) is inconsistent.
% 168.69/23.07 | | | | |
% 168.69/23.07 | | | | Case 2:
% 168.69/23.07 | | | | |
% 168.69/23.07 | | | | |
% 168.69/23.07 | | | | | GROUND_INST: instantiating (16) with xS, all_69_1, sz00, xN,
% 168.69/23.07 | | | | | simplifying with (8), (36) gives:
% 168.69/23.07 | | | | | (40) all_69_1 = xS
% 168.69/23.07 | | | | |
% 168.69/23.07 | | | | | REDUCE: (18), (40) imply:
% 168.69/23.07 | | | | | (41) ~ aSubsetOf0(all_69_2, xS)
% 168.69/23.07 | | | | |
% 168.69/23.07 | | | | | BETA: splitting (29) gives:
% 168.69/23.07 | | | | |
% 168.69/23.07 | | | | | Case 1:
% 168.69/23.07 | | | | | |
% 168.69/23.07 | | | | | | (42) xi = sz00
% 168.69/23.07 | | | | | |
% 168.69/23.07 | | | | | | REDUCE: (22), (42) imply:
% 168.69/23.07 | | | | | | (43) sdtlpdtrp0(xN, sz00) = all_69_2
% 168.69/23.07 | | | | | |
% 168.69/23.07 | | | | | | GROUND_INST: instantiating (16) with xS, all_69_2, sz00, xN,
% 168.69/23.07 | | | | | | simplifying with (8), (43) gives:
% 168.69/23.07 | | | | | | (44) all_69_2 = xS
% 168.69/23.07 | | | | | |
% 168.69/23.07 | | | | | | REDUCE: (34), (44) imply:
% 168.69/23.07 | | | | | | (45) aSubsetOf0(xS, xS)
% 168.69/23.07 | | | | | |
% 168.69/23.07 | | | | | | REDUCE: (41), (44) imply:
% 168.69/23.07 | | | | | | (46) ~ aSubsetOf0(xS, xS)
% 168.69/23.07 | | | | | |
% 168.69/23.07 | | | | | | PRED_UNIFY: (45), (46) imply:
% 168.69/23.07 | | | | | | (47) $false
% 168.69/23.07 | | | | | |
% 168.69/23.07 | | | | | | CLOSE: (47) is inconsistent.
% 168.69/23.07 | | | | | |
% 168.69/23.07 | | | | | Case 2:
% 168.69/23.07 | | | | | |
% 168.69/23.07 | | | | | | (48) ? [v0: $i] : (szszuzczcdt0(v0) = xi & $i(v0) &
% 168.69/23.07 | | | | | | aElementOf0(v0, szNzAzT0))
% 168.69/23.07 | | | | | |
% 168.69/23.07 | | | | | | DELTA: instantiating (48) with fresh symbol all_731_0 gives:
% 168.69/23.07 | | | | | | (49) szszuzczcdt0(all_731_0) = xi & $i(all_731_0) &
% 168.69/23.07 | | | | | | aElementOf0(all_731_0, szNzAzT0)
% 168.69/23.07 | | | | | |
% 168.69/23.07 | | | | | | ALPHA: (49) implies:
% 168.69/23.07 | | | | | | (50) aElementOf0(all_731_0, szNzAzT0)
% 168.69/23.07 | | | | | | (51) $i(all_731_0)
% 168.69/23.07 | | | | | | (52) szszuzczcdt0(all_731_0) = xi
% 168.69/23.07 | | | | | |
% 168.69/23.07 | | | | | | GROUND_INST: instantiating (27) with all_731_0, simplifying with
% 168.69/23.07 | | | | | | (50), (51), (52) gives:
% 168.69/23.08 | | | | | | (53) $false
% 168.69/23.08 | | | | | |
% 168.69/23.08 | | | | | | CLOSE: (53) is inconsistent.
% 168.69/23.08 | | | | | |
% 168.69/23.08 | | | | | End of split
% 168.69/23.08 | | | | |
% 168.69/23.08 | | | | End of split
% 168.69/23.08 | | | |
% 168.69/23.08 | | | Case 2:
% 168.69/23.08 | | | |
% 168.69/23.08 | | | | (54) ? [v0: $i] : (szszuzczcdt0(v0) = xj & $i(v0) & aElementOf0(v0,
% 168.69/23.08 | | | | szNzAzT0))
% 168.69/23.08 | | | |
% 168.69/23.08 | | | | DELTA: instantiating (54) with fresh symbol all_621_0 gives:
% 168.69/23.08 | | | | (55) szszuzczcdt0(all_621_0) = xj & $i(all_621_0) &
% 168.69/23.08 | | | | aElementOf0(all_621_0, szNzAzT0)
% 168.69/23.08 | | | |
% 168.69/23.08 | | | | ALPHA: (55) implies:
% 168.69/23.08 | | | | (56) aElementOf0(all_621_0, szNzAzT0)
% 168.69/23.08 | | | | (57) $i(all_621_0)
% 168.69/23.08 | | | | (58) szszuzczcdt0(all_621_0) = xj
% 168.69/23.08 | | | |
% 168.69/23.08 | | | | BETA: splitting (29) gives:
% 168.69/23.08 | | | |
% 168.69/23.08 | | | | Case 1:
% 168.69/23.08 | | | | |
% 168.69/23.08 | | | | | (59) xi = sz00
% 168.69/23.08 | | | | |
% 168.69/23.08 | | | | | REDUCE: (19), (59) imply:
% 168.69/23.08 | | | | | (60) sdtlseqdt0(xj, sz00)
% 168.69/23.08 | | | | |
% 168.69/23.08 | | | | | GROUND_INST: instantiating (4) with all_621_0, xj, simplifying with
% 168.69/23.08 | | | | | (56), (57), (58), (60) gives:
% 168.69/23.08 | | | | | (61) $false
% 168.69/23.08 | | | | |
% 168.69/23.08 | | | | | CLOSE: (61) is inconsistent.
% 168.69/23.08 | | | | |
% 168.69/23.08 | | | | Case 2:
% 168.69/23.08 | | | | |
% 168.69/23.08 | | | | | (62) ? [v0: $i] : (szszuzczcdt0(v0) = xi & $i(v0) &
% 168.69/23.08 | | | | | aElementOf0(v0, szNzAzT0))
% 168.69/23.08 | | | | |
% 168.69/23.08 | | | | | DELTA: instantiating (62) with fresh symbol all_643_0 gives:
% 168.69/23.08 | | | | | (63) szszuzczcdt0(all_643_0) = xi & $i(all_643_0) &
% 168.69/23.08 | | | | | aElementOf0(all_643_0, szNzAzT0)
% 168.69/23.08 | | | | |
% 168.69/23.08 | | | | | ALPHA: (63) implies:
% 168.69/23.08 | | | | | (64) aElementOf0(all_643_0, szNzAzT0)
% 168.69/23.08 | | | | | (65) $i(all_643_0)
% 168.69/23.08 | | | | | (66) szszuzczcdt0(all_643_0) = xi
% 168.69/23.08 | | | | |
% 168.69/23.08 | | | | | GROUND_INST: instantiating (27) with all_643_0, simplifying with (64),
% 168.69/23.08 | | | | | (65), (66) gives:
% 168.69/23.08 | | | | | (67) $false
% 168.69/23.08 | | | | |
% 168.69/23.08 | | | | | CLOSE: (67) is inconsistent.
% 168.69/23.08 | | | | |
% 168.69/23.08 | | | | End of split
% 168.69/23.08 | | | |
% 168.69/23.08 | | | End of split
% 168.69/23.08 | | |
% 168.69/23.08 | | Case 2:
% 168.69/23.08 | | |
% 168.69/23.08 | | | (68) sdtlpdtrp0(xN, xi) = all_71_1 & sdtlpdtrp0(xN, xj) = all_71_0 &
% 168.69/23.08 | | | $i(all_71_0) & $i(all_71_1) & aSubsetOf0(all_71_1, all_71_0) & !
% 168.69/23.08 | | | [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_71_1) |
% 168.69/23.08 | | | aElementOf0(v0, all_71_0))
% 168.69/23.08 | | |
% 168.69/23.08 | | | ALPHA: (68) implies:
% 168.69/23.08 | | | (69) aSubsetOf0(all_71_1, all_71_0)
% 168.69/23.08 | | | (70) sdtlpdtrp0(xN, xj) = all_71_0
% 168.69/23.08 | | | (71) sdtlpdtrp0(xN, xi) = all_71_1
% 168.69/23.08 | | |
% 168.69/23.08 | | | GROUND_INST: instantiating (16) with all_69_1, all_71_0, xj, xN,
% 168.69/23.08 | | | simplifying with (21), (70) gives:
% 168.69/23.08 | | | (72) all_71_0 = all_69_1
% 168.69/23.08 | | |
% 168.69/23.08 | | | GROUND_INST: instantiating (16) with all_69_2, all_71_1, xi, xN,
% 168.69/23.08 | | | simplifying with (22), (71) gives:
% 168.69/23.08 | | | (73) all_71_1 = all_69_2
% 168.69/23.08 | | |
% 168.69/23.08 | | | REDUCE: (69), (72), (73) imply:
% 168.69/23.08 | | | (74) aSubsetOf0(all_69_2, all_69_1)
% 168.69/23.08 | | |
% 168.69/23.08 | | | PRED_UNIFY: (18), (74) imply:
% 168.69/23.08 | | | (75) $false
% 168.69/23.08 | | |
% 168.69/23.08 | | | CLOSE: (75) is inconsistent.
% 168.69/23.08 | | |
% 168.69/23.08 | | End of split
% 168.69/23.08 | |
% 168.69/23.08 | End of split
% 168.69/23.08 |
% 168.69/23.08 End of proof
% 168.69/23.08 % SZS output end Proof for theBenchmark
% 168.69/23.08
% 168.69/23.08 22480ms
%------------------------------------------------------------------------------