TSTP Solution File: NUM564+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM564+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n028.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 11:48:38 EDT 2023
% Result : Theorem 29.87s 4.90s
% Output : Proof 247.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM564+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n028.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 09:28:35 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,
% 0.19/0.61 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.
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.23/1.32 Prover 1: Preprocessing ...
% 4.23/1.32 Prover 4: Preprocessing ...
% 4.23/1.37 Prover 5: Preprocessing ...
% 4.23/1.37 Prover 3: Preprocessing ...
% 4.23/1.38 Prover 0: Preprocessing ...
% 4.23/1.38 Prover 6: Preprocessing ...
% 4.23/1.39 Prover 2: Preprocessing ...
% 12.95/2.49 Prover 1: Constructing countermodel ...
% 13.32/2.64 Prover 6: Proving ...
% 13.32/2.66 Prover 3: Constructing countermodel ...
% 13.32/2.71 Prover 5: Proving ...
% 15.78/2.90 Prover 2: Proving ...
% 19.98/3.48 Prover 4: Constructing countermodel ...
% 20.94/3.60 Prover 0: Proving ...
% 29.87/4.89 Prover 3: proved (4259ms)
% 29.87/4.89
% 29.87/4.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.87/4.90
% 29.87/4.90 Prover 2: stopped
% 29.87/4.90 Prover 6: stopped
% 29.87/4.90 Prover 5: stopped
% 30.93/4.93 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 30.93/4.93 Prover 0: stopped
% 30.93/4.93 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 30.93/4.93 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 30.93/4.93 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 30.93/4.94 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 32.18/5.09 Prover 8: Preprocessing ...
% 32.18/5.09 Prover 7: Preprocessing ...
% 32.18/5.11 Prover 11: Preprocessing ...
% 32.18/5.11 Prover 10: Preprocessing ...
% 32.18/5.15 Prover 13: Preprocessing ...
% 33.95/5.31 Prover 10: Constructing countermodel ...
% 33.95/5.34 Prover 7: Constructing countermodel ...
% 33.95/5.35 Prover 8: Warning: ignoring some quantifiers
% 33.95/5.36 Prover 8: Constructing countermodel ...
% 34.52/5.48 Prover 13: Warning: ignoring some quantifiers
% 34.52/5.50 Prover 13: Constructing countermodel ...
% 39.54/6.09 Prover 11: Constructing countermodel ...
% 69.74/10.07 Prover 13: stopped
% 70.29/10.07 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 70.29/10.14 Prover 16: Preprocessing ...
% 71.28/10.27 Prover 16: Warning: ignoring some quantifiers
% 71.28/10.28 Prover 16: Constructing countermodel ...
% 111.60/15.61 Prover 16: stopped
% 111.60/15.63 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 112.14/15.75 Prover 19: Preprocessing ...
% 114.82/15.99 Prover 1: stopped
% 114.82/16.00 Prover 19: Warning: ignoring some quantifiers
% 114.82/16.01 Prover 19: Constructing countermodel ...
% 137.24/19.36 Prover 19: stopped
% 186.50/27.70 Prover 7: stopped
% 187.34/27.96 Prover 4: stopped
% 228.99/38.94 Prover 11: stopped
% 230.58/39.68 Prover 8: stopped
% 247.02/54.12 Prover 10: Found proof (size 117)
% 247.02/54.12 Prover 10: proved (49204ms)
% 247.02/54.12
% 247.02/54.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 247.02/54.12
% 247.15/54.13 % SZS output start Proof for theBenchmark
% 247.15/54.13 Assumptions after simplification:
% 247.15/54.13 ---------------------------------
% 247.15/54.13
% 247.15/54.13 (mCardCons)
% 247.15/54.16 ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~
% 247.15/54.16 isFinite0(v0) | ~ aSet0(v0) | ? [v2: $i] : (szszuzczcdt0(v1) = v2 & $i(v2)
% 247.15/54.16 & ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v0, v3) = v4) | ~ $i(v3) | ~
% 247.15/54.16 aElement0(v3) | sbrdtbr0(v4) = v2 | aElementOf0(v3, v0))))
% 247.15/54.16
% 247.15/54.16 (mCardEmpty)
% 247.15/54.17 $i(sz00) & $i(slcrc0) & ! [v0: $i] : (v0 = sz00 | ~ (sbrdtbr0(slcrc0) = v0)
% 247.15/54.17 | ~ aSet0(slcrc0)) & ! [v0: $i] : (v0 = slcrc0 | ~ (sbrdtbr0(v0) = sz00)
% 247.15/54.17 | ~ $i(v0) | ~ aSet0(v0))
% 247.15/54.17
% 247.15/54.17 (mCardSeg)
% 247.15/54.17 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ $i(v0)
% 247.15/54.17 | ~ aElementOf0(v0, szNzAzT0) | sbrdtbr0(v1) = v0)
% 247.15/54.17
% 247.15/54.17 (mCardSubEx)
% 247.15/54.17 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sbrdtbr0(v0) =
% 247.15/54.17 v2) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v2) | ~ isFinite0(v0) |
% 247.15/54.17 ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) | ? [v3: $i] : (sbrdtbr0(v3) =
% 247.15/54.17 v1 & $i(v3) & aSubsetOf0(v3, v0)))
% 247.15/54.17
% 247.15/54.17 (mDefEmp)
% 247.15/54.17 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~
% 247.15/54.17 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : (
% 247.15/54.17 ~ $i(v0) | ~ aElementOf0(v0, slcrc0))
% 247.15/54.17
% 247.15/54.17 (mDefSeg)
% 247.15/54.18 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 247.15/54.18 (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 247.15/54.18 ~ $i(v0) | ~ sdtlseqdt0(v3, v0) | ~ aElementOf0(v2, szNzAzT0) | ~
% 247.15/54.18 aElementOf0(v0, szNzAzT0) | aElementOf0(v2, v1)) & ! [v0: $i] : ! [v1: $i]
% 247.15/54.18 : ! [v2: $i] : ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) =
% 247.15/54.18 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~
% 247.15/54.18 aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v3, v0)) & ! [v0: $i] : ! [v1: $i]
% 247.15/54.18 : ! [v2: $i] : ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) =
% 247.15/54.18 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~
% 247.15/54.18 aElementOf0(v0, szNzAzT0) | aElementOf0(v2, szNzAzT0)) & ! [v0: $i] : !
% 247.15/54.18 [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slbdtrb0(v0) = v1) | ~ $i(v2) | ~
% 247.15/54.18 $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v2) | ? [v3: $i] : ? [v4:
% 247.15/54.18 $i] : ($i(v3) & ( ~ aElementOf0(v3, v2) | ~ aElementOf0(v3, szNzAzT0) |
% 247.15/54.18 (szszuzczcdt0(v3) = v4 & $i(v4) & ~ sdtlseqdt0(v4, v0))) &
% 247.15/54.18 (aElementOf0(v3, v2) | (szszuzczcdt0(v3) = v4 & $i(v4) & sdtlseqdt0(v4,
% 247.15/54.18 v0) & aElementOf0(v3, szNzAzT0))))) & ! [v0: $i] : ! [v1: $i] : (
% 247.15/54.18 ~ (slbdtrb0(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0)
% 247.15/54.18 | aSet0(v1))
% 247.15/54.18
% 247.15/54.18 (mDefSel)
% 247.15/54.19 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 247.15/54.19 $i] : (v4 = v1 | ~ (slbdtsldtrb0(v0, v1) = v2) | ~ (sbrdtbr0(v3) = v4) |
% 247.15/54.19 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~
% 247.15/54.19 aElementOf0(v1, szNzAzT0) | ~ aSet0(v0)) & ! [v0: $i] : ! [v1: $i] : !
% 247.15/54.19 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (slbdtsldtrb0(v0, v1) = v2) | ~
% 247.15/54.19 (sbrdtbr0(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 247.15/54.19 aElementOf0(v3, v2) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) |
% 247.15/54.19 aSubsetOf0(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 247.15/54.19 : (v3 = v2 | ~ (slbdtsldtrb0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~
% 247.15/54.19 $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v3) | ~ aSet0(v0) | ?
% 247.15/54.19 [v4: $i] : ? [v5: $i] : ($i(v4) & ( ~ aSubsetOf0(v4, v0) | ~
% 247.15/54.19 aElementOf0(v4, v3) | ( ~ (v5 = v1) & sbrdtbr0(v4) = v5 & $i(v5))) &
% 247.15/54.19 (aElementOf0(v4, v3) | (v5 = v1 & sbrdtbr0(v4) = v1 & aSubsetOf0(v4,
% 247.15/54.19 v0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (
% 247.15/54.19 ~ (slbdtsldtrb0(v0, v1) = v2) | ~ (sbrdtbr0(v3) = v1) | ~ $i(v3) | ~
% 247.15/54.19 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v3, v0) | ~ aElementOf0(v1,
% 247.15/54.19 szNzAzT0) | ~ aSet0(v0) | aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1:
% 247.45/54.19 $i] : ! [v2: $i] : ( ~ (slbdtsldtrb0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1)
% 247.45/54.19 | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) | aSet0(v2))
% 247.45/54.19
% 247.45/54.19 (mDefSub)
% 247.45/54.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 247.45/54.19 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) |
% 247.45/54.19 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) |
% 247.45/54.19 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i]
% 247.45/54.19 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) |
% 247.45/54.19 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)))
% 247.45/54.19
% 247.45/54.19 (mEmpFin)
% 247.45/54.19 $i(slcrc0) & isFinite0(slcrc0)
% 247.45/54.19
% 247.45/54.19 (mLessRefl)
% 247.45/54.19 $i(szNzAzT0) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) |
% 247.45/54.19 sdtlseqdt0(v0, v0))
% 247.45/54.19
% 247.45/54.19 (mNATSet)
% 247.45/54.19 $i(szNzAzT0) & isCountable0(szNzAzT0) & aSet0(szNzAzT0)
% 247.45/54.19
% 247.45/54.19 (mSegFin)
% 247.45/54.20 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ $i(v0)
% 247.45/54.20 | ~ aElementOf0(v0, szNzAzT0) | isFinite0(v1))
% 247.45/54.20
% 247.45/54.20 (mSegSucc)
% 247.45/54.20 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slbdtrb0(v1) =
% 247.45/54.20 v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~
% 247.45/54.20 aElementOf0(v0, szNzAzT0) | ? [v3: $i] : ? [v4: $i] : ((v1 = v0 |
% 247.45/54.20 aElementOf0(v0, v2) | (slbdtrb0(v3) = v4 & szszuzczcdt0(v1) = v3 &
% 247.45/54.20 $i(v4) & $i(v3) & ~ aElementOf0(v0, v4))) & (( ~ (v1 = v0) & ~
% 247.45/54.20 aElementOf0(v0, v2)) | (slbdtrb0(v3) = v4 & szszuzczcdt0(v1) = v3 &
% 247.45/54.20 $i(v4) & $i(v3) & aElementOf0(v0, v4)))))
% 247.45/54.20
% 247.45/54.20 (mSegZero)
% 247.45/54.20 slbdtrb0(sz00) = slcrc0 & $i(sz00) & $i(slcrc0)
% 247.45/54.20
% 247.45/54.20 (mSubFSet)
% 247.45/54.20 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, v0) |
% 247.45/54.20 ~ isFinite0(v0) | ~ aSet0(v0) | isFinite0(v1))
% 247.45/54.20
% 247.45/54.20 (mSuccNum)
% 247.45/54.20 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) =
% 247.45/54.20 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v1,
% 247.45/54.20 szNzAzT0)) & ! [v0: $i] : ( ~ (szszuzczcdt0(v0) = sz00) | ~ $i(v0) | ~
% 247.45/54.20 aElementOf0(v0, szNzAzT0))
% 247.45/54.20
% 247.45/54.20 (m__)
% 247.45/54.20 $i(xS) & $i(sz00) & $i(slcrc0) & ? [v0: $i] : (slbdtsldtrb0(xS, sz00) = v0 &
% 247.45/54.20 $i(v0) & ~ aElementOf0(slcrc0, v0))
% 247.45/54.20
% 247.45/54.20 (m__3398)
% 247.45/54.21 $i(xK) & $i(xT) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 247.45/54.21 [v3: $i] : ! [v4: $i] : ( ~ (sdtlcdtrc0(v3, v2) = v4) | ~ (szDzozmdt0(v3) =
% 247.45/54.21 v2) | ~ (slbdtsldtrb0(v1, v0) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) |
% 247.45/54.21 ~ aFunction0(v3) | ~ iLess0(v0, xK) | ~ aSubsetOf0(v4, xT) | ~
% 247.45/54.21 aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v0,
% 247.45/54.21 szNzAzT0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (slbdtsldtrb0(v6,
% 247.45/54.21 v0) = v7 & $i(v7) & $i(v6) & $i(v5) & aSubsetOf0(v6, v1) &
% 247.45/54.21 isCountable0(v6) & aElementOf0(v5, xT) & ! [v8: $i] : ! [v9: $i] : (v9 =
% 247.45/54.21 v5 | ~ (sdtlpdtrp0(v3, v8) = v9) | ~ $i(v8) | ~ aElementOf0(v8,
% 247.45/54.21 v7))))
% 247.45/54.21
% 247.45/54.21 (m__3418)
% 247.45/54.21 $i(xK) & $i(szNzAzT0) & aElementOf0(xK, szNzAzT0)
% 247.45/54.21
% 247.45/54.21 (m__3435)
% 247.45/54.21 $i(xS) & $i(szNzAzT0) & aSubsetOf0(xS, szNzAzT0) & isCountable0(xS)
% 247.45/54.21
% 247.45/54.21 (m__3453)
% 247.45/54.21 $i(xc) & $i(xS) & $i(xK) & $i(xT) & ? [v0: $i] : ? [v1: $i] :
% 247.45/54.21 (sdtlcdtrc0(xc, v0) = v1 & szDzozmdt0(xc) = v0 & slbdtsldtrb0(xS, xK) = v0 &
% 247.45/54.21 $i(v1) & $i(v0) & aFunction0(xc) & aSubsetOf0(v1, xT))
% 247.45/54.21
% 247.45/54.21 (m__3462)
% 247.45/54.21 xK = sz00 & $i(sz00)
% 247.45/54.21
% 247.45/54.21 (function-axioms)
% 247.45/54.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.45/54.22 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 247.45/54.22 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 247.45/54.22 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 247.45/54.22 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 247.45/54.22 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 247.45/54.22 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 247.45/54.22 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 247.45/54.22 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 247.45/54.22 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~
% 247.45/54.22 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 247.45/54.22 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) &
% 247.45/54.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 247.45/54.22 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 247.45/54.22 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 247.45/54.22 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 247.45/54.22 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 247.45/54.22 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 247.45/54.22 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 247.45/54.22 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 247.45/54.22 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 247.45/54.22 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 247.45/54.22 v0))
% 247.45/54.22
% 247.45/54.22 Further assumptions not needed in the proof:
% 247.45/54.22 --------------------------------------------
% 247.45/54.22 mCConsSet, mCDiffSet, mCardDiff, mCardNum, mCardS, mCardSub, mCntRel, mConsDiff,
% 247.45/54.22 mCountNFin, mCountNFin_01, mDefCons, mDefDiff, mDefMax, mDefMin, mDefPtt,
% 247.45/54.22 mDefRst, mDefSImg, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort,
% 247.45/54.22 mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount,
% 247.45/54.22 mImgElm, mImgRng, mLessASymm, mLessRel, mLessSucc, mLessTotal, mLessTrans,
% 247.45/54.22 mMinMin, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegLess, mSelCSet,
% 247.45/54.22 mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, mSubASymm, mSubRefl,
% 247.45/54.22 mSubTrans, mSuccEquSucc, mSuccLess, mZeroLess, mZeroNum, m__3291
% 247.45/54.22
% 247.45/54.22 Those formulas are unsatisfiable:
% 247.45/54.22 ---------------------------------
% 247.45/54.22
% 247.45/54.22 Begin of proof
% 247.45/54.22 |
% 247.45/54.22 | ALPHA: (mDefEmp) implies:
% 247.45/54.22 | (1) aSet0(slcrc0)
% 247.45/54.22 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, slcrc0))
% 247.45/54.22 |
% 247.45/54.22 | ALPHA: (mEmpFin) implies:
% 247.45/54.22 | (3) isFinite0(slcrc0)
% 247.45/54.22 |
% 247.45/54.22 | ALPHA: (mDefSub) implies:
% 247.45/54.22 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~
% 247.45/54.22 | aSet0(v0) | aSubsetOf0(v1, v0) | ? [v2: $i] : ($i(v2) &
% 247.45/54.22 | aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)))
% 247.45/54.22 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1,
% 247.45/54.22 | v0) | ~ aSet0(v0) | aSet0(v1))
% 247.45/54.22 |
% 247.45/54.22 | ALPHA: (mNATSet) implies:
% 247.45/54.22 | (6) aSet0(szNzAzT0)
% 247.45/54.22 |
% 247.45/54.22 | ALPHA: (mSuccNum) implies:
% 247.45/54.22 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) |
% 247.45/54.22 | ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v1, szNzAzT0))
% 247.45/54.22 |
% 247.45/54.22 | ALPHA: (mLessRefl) implies:
% 247.45/54.22 | (8) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) |
% 247.45/54.22 | sdtlseqdt0(v0, v0))
% 247.45/54.22 |
% 247.45/54.22 | ALPHA: (mCardEmpty) implies:
% 247.45/54.22 | (9) ! [v0: $i] : (v0 = slcrc0 | ~ (sbrdtbr0(v0) = sz00) | ~ $i(v0) | ~
% 247.45/54.22 | aSet0(v0))
% 247.45/54.22 |
% 247.45/54.22 | ALPHA: (mCardSubEx) implies:
% 247.45/54.23 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sbrdtbr0(v0) = v2) | ~
% 247.45/54.23 | $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v2) | ~ isFinite0(v0) | ~
% 247.45/54.23 | aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) | ? [v3: $i] :
% 247.45/54.23 | (sbrdtbr0(v3) = v1 & $i(v3) & aSubsetOf0(v3, v0)))
% 247.45/54.23 |
% 247.45/54.23 | ALPHA: (mDefSeg) implies:
% 247.45/54.23 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ $i(v1) | ~
% 247.45/54.23 | $i(v0) | ~ aElementOf0(v0, szNzAzT0) | aSet0(v1))
% 247.45/54.23 |
% 247.45/54.23 | ALPHA: (mSegFin) implies:
% 247.45/54.23 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ $i(v0) | ~
% 247.45/54.23 | aElementOf0(v0, szNzAzT0) | isFinite0(v1))
% 247.45/54.23 |
% 247.45/54.23 | ALPHA: (mSegZero) implies:
% 247.45/54.23 | (13) slbdtrb0(sz00) = slcrc0
% 247.45/54.23 |
% 247.45/54.23 | ALPHA: (mSegSucc) implies:
% 247.45/54.23 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slbdtrb0(v1) = v2) | ~
% 247.45/54.23 | $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~
% 247.45/54.23 | aElementOf0(v0, szNzAzT0) | ? [v3: $i] : ? [v4: $i] : ((v1 = v0 |
% 247.45/54.23 | aElementOf0(v0, v2) | (slbdtrb0(v3) = v4 & szszuzczcdt0(v1) = v3
% 247.45/54.23 | & $i(v4) & $i(v3) & ~ aElementOf0(v0, v4))) & (( ~ (v1 = v0)
% 247.45/54.23 | & ~ aElementOf0(v0, v2)) | (slbdtrb0(v3) = v4 &
% 247.45/54.23 | szszuzczcdt0(v1) = v3 & $i(v4) & $i(v3) & aElementOf0(v0,
% 247.45/54.23 | v4)))))
% 247.45/54.23 |
% 247.45/54.23 | ALPHA: (mCardSeg) implies:
% 247.45/54.23 | (15) ! [v0: $i] : ! [v1: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ $i(v0) | ~
% 247.45/54.23 | aElementOf0(v0, szNzAzT0) | sbrdtbr0(v1) = v0)
% 247.45/54.23 |
% 247.45/54.23 | ALPHA: (mDefSel) implies:
% 247.45/54.23 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 247.45/54.23 | (slbdtsldtrb0(v0, v1) = v2) | ~ (sbrdtbr0(v3) = v1) | ~ $i(v3) |
% 247.45/54.23 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v3, v0) | ~
% 247.45/54.23 | aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) | aElementOf0(v3, v2))
% 247.45/54.23 |
% 247.45/54.23 | ALPHA: (m__3418) implies:
% 247.45/54.23 | (17) aElementOf0(xK, szNzAzT0)
% 247.45/54.23 |
% 247.45/54.23 | ALPHA: (m__3435) implies:
% 247.45/54.23 | (18) aSubsetOf0(xS, szNzAzT0)
% 247.45/54.23 |
% 247.45/54.23 | ALPHA: (m__3453) implies:
% 247.45/54.23 | (19) ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xc, v0) = v1 & szDzozmdt0(xc)
% 247.45/54.23 | = v0 & slbdtsldtrb0(xS, xK) = v0 & $i(v1) & $i(v0) & aFunction0(xc)
% 247.45/54.23 | & aSubsetOf0(v1, xT))
% 247.45/54.23 |
% 247.45/54.23 | ALPHA: (m__3398) implies:
% 247.45/54.23 | (20) $i(szNzAzT0)
% 247.45/54.23 | (21) $i(xK)
% 247.45/54.23 |
% 247.45/54.23 | ALPHA: (m__3462) implies:
% 247.45/54.23 | (22) xK = sz00
% 247.45/54.23 |
% 247.45/54.23 | ALPHA: (m__) implies:
% 247.45/54.23 | (23) $i(slcrc0)
% 247.45/54.23 | (24) $i(xS)
% 247.45/54.23 | (25) ? [v0: $i] : (slbdtsldtrb0(xS, sz00) = v0 & $i(v0) & ~
% 247.45/54.23 | aElementOf0(slcrc0, v0))
% 247.45/54.23 |
% 247.45/54.23 | ALPHA: (function-axioms) implies:
% 247.45/54.24 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 247.45/54.24 | (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0))
% 247.45/54.24 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2)
% 247.45/54.24 | = v1) | ~ (slbdtrb0(v2) = v0))
% 247.45/54.24 | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.45/54.24 | (slbdtsldtrb0(v3, v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0))
% 247.45/54.24 |
% 247.45/54.24 | DELTA: instantiating (25) with fresh symbol all_65_0 gives:
% 247.45/54.24 | (29) slbdtsldtrb0(xS, sz00) = all_65_0 & $i(all_65_0) & ~
% 247.45/54.24 | aElementOf0(slcrc0, all_65_0)
% 247.45/54.24 |
% 247.45/54.24 | ALPHA: (29) implies:
% 247.45/54.24 | (30) ~ aElementOf0(slcrc0, all_65_0)
% 247.45/54.24 | (31) slbdtsldtrb0(xS, sz00) = all_65_0
% 247.45/54.24 |
% 247.45/54.24 | DELTA: instantiating (19) with fresh symbols all_67_0, all_67_1 gives:
% 247.45/54.24 | (32) sdtlcdtrc0(xc, all_67_1) = all_67_0 & szDzozmdt0(xc) = all_67_1 &
% 247.45/54.24 | slbdtsldtrb0(xS, xK) = all_67_1 & $i(all_67_0) & $i(all_67_1) &
% 247.45/54.24 | aFunction0(xc) & aSubsetOf0(all_67_0, xT)
% 247.45/54.24 |
% 247.45/54.24 | ALPHA: (32) implies:
% 247.45/54.24 | (33) $i(all_67_1)
% 247.45/54.24 | (34) slbdtsldtrb0(xS, xK) = all_67_1
% 247.45/54.24 |
% 247.45/54.24 | REDUCE: (22), (34) imply:
% 247.45/54.24 | (35) slbdtsldtrb0(xS, sz00) = all_67_1
% 247.45/54.24 |
% 247.45/54.24 | REDUCE: (21), (22) imply:
% 247.45/54.24 | (36) $i(sz00)
% 247.45/54.24 |
% 247.45/54.24 | REDUCE: (17), (22) imply:
% 247.45/54.24 | (37) aElementOf0(sz00, szNzAzT0)
% 247.45/54.24 |
% 247.45/54.24 | GROUND_INST: instantiating (28) with all_65_0, all_67_1, sz00, xS, simplifying
% 247.45/54.24 | with (31), (35) gives:
% 247.45/54.24 | (38) all_67_1 = all_65_0
% 247.45/54.24 |
% 247.45/54.24 | REDUCE: (33), (38) imply:
% 247.45/54.24 | (39) $i(all_65_0)
% 247.45/54.24 |
% 247.45/54.24 | GROUND_INST: instantiating (8) with sz00, simplifying with (36), (37) gives:
% 247.45/54.24 | (40) sdtlseqdt0(sz00, sz00)
% 247.45/54.24 |
% 247.45/54.24 | GROUND_INST: instantiating (5) with szNzAzT0, xS, simplifying with (6), (18),
% 247.45/54.24 | (20), (24) gives:
% 247.45/54.24 | (41) aSet0(xS)
% 247.45/54.24 |
% 247.45/54.24 | GROUND_INST: instantiating (14) with sz00, sz00, slcrc0, simplifying with
% 247.45/54.24 | (13), (36), (37) gives:
% 247.45/54.24 | (42) ? [v0: $i] : ? [v1: $i] : (slbdtrb0(v0) = v1 & szszuzczcdt0(sz00) =
% 247.45/54.24 | v0 & $i(v1) & $i(v0) & aElementOf0(sz00, v1))
% 247.45/54.24 |
% 247.45/54.24 | GROUND_INST: instantiating (15) with sz00, slcrc0, simplifying with (13),
% 247.45/54.24 | (36), (37) gives:
% 247.45/54.24 | (43) sbrdtbr0(slcrc0) = sz00
% 247.45/54.24 |
% 247.45/54.24 | DELTA: instantiating (42) with fresh symbols all_83_0, all_83_1 gives:
% 247.45/54.24 | (44) slbdtrb0(all_83_1) = all_83_0 & szszuzczcdt0(sz00) = all_83_1 &
% 247.45/54.24 | $i(all_83_0) & $i(all_83_1) & aElementOf0(sz00, all_83_0)
% 247.45/54.24 |
% 247.45/54.24 | ALPHA: (44) implies:
% 247.45/54.24 | (45) aElementOf0(sz00, all_83_0)
% 247.45/54.24 | (46) $i(all_83_0)
% 247.45/54.24 | (47) szszuzczcdt0(sz00) = all_83_1
% 247.45/54.24 | (48) slbdtrb0(all_83_1) = all_83_0
% 247.45/54.24 |
% 247.45/54.25 | GROUND_INST: instantiating (4) with xS, slcrc0, simplifying with (1), (23),
% 247.45/54.25 | (24), (41) gives:
% 247.45/54.25 | (49) aSubsetOf0(slcrc0, xS) | ? [v0: $i] : ($i(v0) & aElementOf0(v0,
% 247.45/54.25 | slcrc0) & ~ aElementOf0(v0, xS))
% 247.45/54.25 |
% 247.45/54.25 | GROUND_INST: instantiating (7) with sz00, all_83_1, simplifying with (36),
% 247.45/54.25 | (37), (47) gives:
% 247.45/54.25 | (50) aElementOf0(all_83_1, szNzAzT0)
% 247.45/54.25 |
% 247.45/54.25 | GROUND_INST: instantiating (10) with slcrc0, sz00, sz00, simplifying with (1),
% 247.45/54.25 | (3), (23), (36), (37), (40), (43) gives:
% 247.45/54.25 | (51) ? [v0: $i] : (sbrdtbr0(v0) = sz00 & $i(v0) & aSubsetOf0(v0, slcrc0))
% 247.45/54.25 |
% 247.45/54.25 | GROUND_INST: instantiating (mCardCons) with slcrc0, sz00, simplifying with
% 247.45/54.25 | (1), (3), (23), (43) gives:
% 247.45/54.25 | (52) ? [v0: $i] : (szszuzczcdt0(sz00) = v0 & $i(v0) & ! [v1: $i] : !
% 247.45/54.25 | [v2: $i] : ( ~ (sdtpldt0(slcrc0, v1) = v2) | ~ $i(v1) | ~
% 247.45/54.25 | aElement0(v1) | sbrdtbr0(v2) = v0 | aElementOf0(v1, slcrc0)))
% 247.45/54.25 |
% 247.45/54.25 | DELTA: instantiating (51) with fresh symbol all_91_0 gives:
% 247.45/54.25 | (53) sbrdtbr0(all_91_0) = sz00 & $i(all_91_0) & aSubsetOf0(all_91_0,
% 247.45/54.25 | slcrc0)
% 247.45/54.25 |
% 247.45/54.25 | ALPHA: (53) implies:
% 247.45/54.25 | (54) aSubsetOf0(all_91_0, slcrc0)
% 247.45/54.25 | (55) $i(all_91_0)
% 247.45/54.25 | (56) sbrdtbr0(all_91_0) = sz00
% 247.45/54.25 |
% 247.45/54.25 | DELTA: instantiating (52) with fresh symbol all_93_0 gives:
% 247.45/54.25 | (57) szszuzczcdt0(sz00) = all_93_0 & $i(all_93_0) & ! [v0: $i] : ! [v1:
% 247.45/54.25 | $i] : ( ~ (sdtpldt0(slcrc0, v0) = v1) | ~ $i(v0) | ~ aElement0(v0)
% 247.45/54.25 | | sbrdtbr0(v1) = all_93_0 | aElementOf0(v0, slcrc0))
% 247.45/54.25 |
% 247.45/54.25 | ALPHA: (57) implies:
% 247.45/54.25 | (58) $i(all_93_0)
% 247.45/54.25 | (59) szszuzczcdt0(sz00) = all_93_0
% 247.45/54.25 |
% 247.45/54.25 | GROUND_INST: instantiating (26) with all_83_1, all_93_0, sz00, simplifying
% 247.45/54.25 | with (47), (59) gives:
% 247.45/54.25 | (60) all_93_0 = all_83_1
% 247.45/54.25 |
% 247.45/54.25 | REDUCE: (58), (60) imply:
% 247.45/54.25 | (61) $i(all_83_1)
% 247.45/54.25 |
% 247.45/54.25 | GROUND_INST: instantiating (14) with all_83_1, all_83_1, all_83_0, simplifying
% 247.45/54.25 | with (48), (50), (61) gives:
% 247.45/54.25 | (62) ? [v0: $i] : ? [v1: $i] : (slbdtrb0(v0) = v1 &
% 247.45/54.25 | szszuzczcdt0(all_83_1) = v0 & $i(v1) & $i(v0) &
% 247.45/54.25 | aElementOf0(all_83_1, v1))
% 247.45/54.25 |
% 247.45/54.25 | GROUND_INST: instantiating (14) with sz00, all_83_1, all_83_0, simplifying
% 247.45/54.25 | with (36), (37), (48), (50), (61) gives:
% 247.45/54.26 | (63) ? [v0: $i] : ? [v1: $i] : ((all_83_1 = sz00 | aElementOf0(sz00,
% 247.45/54.26 | all_83_0) | (slbdtrb0(v0) = v1 & szszuzczcdt0(all_83_1) = v0 &
% 247.45/54.26 | $i(v1) & $i(v0) & ~ aElementOf0(sz00, v1))) & (( ~ (all_83_1 =
% 247.45/54.26 | sz00) & ~ aElementOf0(sz00, all_83_0)) | (slbdtrb0(v0) = v1 &
% 247.45/54.26 | szszuzczcdt0(all_83_1) = v0 & $i(v1) & $i(v0) &
% 247.45/54.26 | aElementOf0(sz00, v1))))
% 247.45/54.26 |
% 247.45/54.26 | GROUND_INST: instantiating (11) with all_83_1, all_83_0, simplifying with
% 247.45/54.26 | (46), (48), (50), (61) gives:
% 247.45/54.26 | (64) aSet0(all_83_0)
% 247.45/54.26 |
% 247.45/54.26 | GROUND_INST: instantiating (15) with all_83_1, all_83_0, simplifying with
% 247.45/54.26 | (48), (50), (61) gives:
% 247.45/54.26 | (65) sbrdtbr0(all_83_0) = all_83_1
% 247.45/54.26 |
% 247.45/54.26 | GROUND_INST: instantiating (12) with all_83_1, all_83_0, simplifying with
% 247.45/54.26 | (48), (50), (61) gives:
% 247.45/54.26 | (66) isFinite0(all_83_0)
% 247.45/54.26 |
% 247.45/54.26 | GROUND_INST: instantiating (mSubFSet) with slcrc0, all_91_0, simplifying with
% 247.45/54.26 | (1), (3), (23), (54), (55) gives:
% 247.45/54.26 | (67) isFinite0(all_91_0)
% 247.45/54.26 |
% 247.45/54.26 | GROUND_INST: instantiating (5) with slcrc0, all_91_0, simplifying with (1),
% 247.45/54.26 | (23), (54), (55) gives:
% 247.45/54.26 | (68) aSet0(all_91_0)
% 247.45/54.26 |
% 247.45/54.26 | DELTA: instantiating (62) with fresh symbols all_106_0, all_106_1 gives:
% 247.45/54.26 | (69) slbdtrb0(all_106_1) = all_106_0 & szszuzczcdt0(all_83_1) = all_106_1 &
% 247.45/54.26 | $i(all_106_0) & $i(all_106_1) & aElementOf0(all_83_1, all_106_0)
% 247.45/54.26 |
% 247.45/54.26 | ALPHA: (69) implies:
% 247.45/54.26 | (70) aElementOf0(all_83_1, all_106_0)
% 247.45/54.26 | (71) szszuzczcdt0(all_83_1) = all_106_1
% 247.45/54.26 | (72) slbdtrb0(all_106_1) = all_106_0
% 247.45/54.26 |
% 247.45/54.26 | DELTA: instantiating (63) with fresh symbols all_108_0, all_108_1 gives:
% 247.45/54.26 | (73) (all_83_1 = sz00 | aElementOf0(sz00, all_83_0) | (slbdtrb0(all_108_1)
% 247.45/54.26 | = all_108_0 & szszuzczcdt0(all_83_1) = all_108_1 & $i(all_108_0) &
% 247.45/54.26 | $i(all_108_1) & ~ aElementOf0(sz00, all_108_0))) & (( ~ (all_83_1
% 247.45/54.26 | = sz00) & ~ aElementOf0(sz00, all_83_0)) | (slbdtrb0(all_108_1)
% 247.45/54.26 | = all_108_0 & szszuzczcdt0(all_83_1) = all_108_1 & $i(all_108_0) &
% 247.45/54.26 | $i(all_108_1) & aElementOf0(sz00, all_108_0)))
% 247.45/54.26 |
% 247.45/54.26 | ALPHA: (73) implies:
% 247.45/54.26 | (74) ( ~ (all_83_1 = sz00) & ~ aElementOf0(sz00, all_83_0)) |
% 247.45/54.26 | (slbdtrb0(all_108_1) = all_108_0 & szszuzczcdt0(all_83_1) = all_108_1
% 247.45/54.26 | & $i(all_108_0) & $i(all_108_1) & aElementOf0(sz00, all_108_0))
% 247.45/54.26 |
% 247.45/54.26 | BETA: splitting (74) gives:
% 247.45/54.26 |
% 247.45/54.26 | Case 1:
% 247.45/54.26 | |
% 247.45/54.26 | | (75) ~ (all_83_1 = sz00) & ~ aElementOf0(sz00, all_83_0)
% 247.45/54.26 | |
% 247.45/54.26 | | ALPHA: (75) implies:
% 247.45/54.26 | | (76) ~ aElementOf0(sz00, all_83_0)
% 247.45/54.26 | |
% 247.45/54.26 | | PRED_UNIFY: (45), (76) imply:
% 247.45/54.26 | | (77) $false
% 247.45/54.27 | |
% 247.45/54.27 | | CLOSE: (77) is inconsistent.
% 247.45/54.27 | |
% 247.45/54.27 | Case 2:
% 247.45/54.27 | |
% 247.45/54.27 | | (78) slbdtrb0(all_108_1) = all_108_0 & szszuzczcdt0(all_83_1) = all_108_1
% 247.45/54.27 | | & $i(all_108_0) & $i(all_108_1) & aElementOf0(sz00, all_108_0)
% 247.45/54.27 | |
% 247.45/54.27 | | ALPHA: (78) implies:
% 247.45/54.27 | | (79) szszuzczcdt0(all_83_1) = all_108_1
% 247.45/54.27 | | (80) slbdtrb0(all_108_1) = all_108_0
% 247.45/54.27 | |
% 247.45/54.27 | | GROUND_INST: instantiating (26) with all_106_1, all_108_1, all_83_1,
% 247.45/54.27 | | simplifying with (71), (79) gives:
% 247.45/54.27 | | (81) all_108_1 = all_106_1
% 247.45/54.27 | |
% 247.45/54.27 | | REDUCE: (80), (81) imply:
% 247.45/54.27 | | (82) slbdtrb0(all_106_1) = all_108_0
% 247.45/54.27 | |
% 247.45/54.27 | | GROUND_INST: instantiating (27) with all_106_0, all_108_0, all_106_1,
% 247.45/54.27 | | simplifying with (72), (82) gives:
% 247.45/54.27 | | (83) all_108_0 = all_106_0
% 247.45/54.27 | |
% 247.45/54.27 | | GROUND_INST: instantiating (9) with all_91_0, simplifying with (55), (56),
% 247.45/54.27 | | (68) gives:
% 247.45/54.27 | | (84) all_91_0 = slcrc0
% 247.45/54.27 | |
% 247.45/54.27 | | GROUND_INST: instantiating (10) with all_91_0, sz00, sz00, simplifying with
% 247.45/54.27 | | (36), (37), (40), (55), (56), (67), (68) gives:
% 247.45/54.27 | | (85) ? [v0: $i] : (sbrdtbr0(v0) = sz00 & $i(v0) & aSubsetOf0(v0,
% 247.45/54.27 | | all_91_0))
% 247.45/54.28 | |
% 247.45/54.28 | | GROUND_INST: instantiating (mCardCons) with all_91_0, sz00, simplifying with
% 247.45/54.28 | | (55), (56), (67), (68) gives:
% 247.45/54.28 | | (86) ? [v0: $i] : (szszuzczcdt0(sz00) = v0 & $i(v0) & ! [v1: $i] : !
% 247.45/54.28 | | [v2: $i] : ( ~ (sdtpldt0(all_91_0, v1) = v2) | ~ $i(v1) | ~
% 247.45/54.28 | | aElement0(v1) | sbrdtbr0(v2) = v0 | aElementOf0(v1, all_91_0)))
% 247.45/54.28 | |
% 247.45/54.28 | | GROUND_INST: instantiating (7) with all_83_1, all_106_1, simplifying with
% 247.45/54.28 | | (50), (61), (71) gives:
% 247.45/54.28 | | (87) aElementOf0(all_106_1, szNzAzT0)
% 247.45/54.28 | |
% 247.45/54.28 | | GROUND_INST: instantiating (mCardCons) with all_83_0, all_83_1, simplifying
% 247.45/54.28 | | with (46), (64), (65), (66) gives:
% 247.45/54.28 | | (88) ? [v0: $i] : (szszuzczcdt0(all_83_1) = v0 & $i(v0) & ! [v1: $i] :
% 247.45/54.28 | | ! [v2: $i] : ( ~ (sdtpldt0(all_83_0, v1) = v2) | ~ $i(v1) | ~
% 247.45/54.28 | | aElement0(v1) | sbrdtbr0(v2) = v0 | aElementOf0(v1, all_83_0)))
% 247.45/54.28 | |
% 247.45/54.28 | | DELTA: instantiating (85) with fresh symbol all_128_0 gives:
% 247.45/54.28 | | (89) sbrdtbr0(all_128_0) = sz00 & $i(all_128_0) & aSubsetOf0(all_128_0,
% 247.45/54.28 | | all_91_0)
% 247.45/54.28 | |
% 247.45/54.28 | | ALPHA: (89) implies:
% 247.45/54.28 | | (90) aSubsetOf0(all_128_0, all_91_0)
% 247.45/54.28 | | (91) $i(all_128_0)
% 247.45/54.28 | | (92) sbrdtbr0(all_128_0) = sz00
% 247.45/54.28 | |
% 247.45/54.28 | | DELTA: instantiating (86) with fresh symbol all_134_0 gives:
% 247.45/54.28 | | (93) szszuzczcdt0(sz00) = all_134_0 & $i(all_134_0) & ! [v0: $i] : !
% 247.45/54.28 | | [v1: $i] : ( ~ (sdtpldt0(all_91_0, v0) = v1) | ~ $i(v0) | ~
% 247.45/54.28 | | aElement0(v0) | sbrdtbr0(v1) = all_134_0 | aElementOf0(v0,
% 247.45/54.28 | | all_91_0))
% 247.45/54.28 | |
% 247.45/54.28 | | ALPHA: (93) implies:
% 247.45/54.28 | | (94) $i(all_134_0)
% 247.45/54.28 | | (95) szszuzczcdt0(sz00) = all_134_0
% 247.45/54.28 | |
% 247.45/54.28 | | DELTA: instantiating (88) with fresh symbol all_137_0 gives:
% 247.45/54.28 | | (96) szszuzczcdt0(all_83_1) = all_137_0 & $i(all_137_0) & ! [v0: $i] :
% 247.45/54.28 | | ! [v1: $i] : ( ~ (sdtpldt0(all_83_0, v0) = v1) | ~ $i(v0) | ~
% 247.45/54.28 | | aElement0(v0) | sbrdtbr0(v1) = all_137_0 | aElementOf0(v0,
% 247.45/54.28 | | all_83_0))
% 247.45/54.28 | |
% 247.45/54.28 | | ALPHA: (96) implies:
% 247.45/54.28 | | (97) $i(all_137_0)
% 247.45/54.28 | | (98) szszuzczcdt0(all_83_1) = all_137_0
% 247.45/54.28 | |
% 247.45/54.28 | | REDUCE: (84), (90) imply:
% 247.45/54.28 | | (99) aSubsetOf0(all_128_0, slcrc0)
% 247.45/54.28 | |
% 247.45/54.28 | | GROUND_INST: instantiating (26) with all_83_1, all_134_0, sz00, simplifying
% 247.45/54.28 | | with (47), (95) gives:
% 247.45/54.28 | | (100) all_134_0 = all_83_1
% 247.45/54.28 | |
% 247.45/54.28 | | GROUND_INST: instantiating (26) with all_106_1, all_137_0, all_83_1,
% 247.45/54.28 | | simplifying with (71), (98) gives:
% 247.45/54.28 | | (101) all_137_0 = all_106_1
% 247.45/54.28 | |
% 247.45/54.28 | | REDUCE: (97), (101) imply:
% 247.45/54.28 | | (102) $i(all_106_1)
% 247.45/54.28 | |
% 247.45/54.28 | | GROUND_INST: instantiating (14) with all_83_1, all_106_1, all_106_0,
% 247.45/54.28 | | simplifying with (50), (61), (72), (87), (102) gives:
% 247.45/54.28 | | (103) ? [v0: $i] : ? [v1: $i] : ((all_106_1 = all_83_1 |
% 247.45/54.28 | | aElementOf0(all_83_1, all_106_0) | (slbdtrb0(v0) = v1 &
% 247.45/54.28 | | szszuzczcdt0(all_106_1) = v0 & $i(v1) & $i(v0) & ~
% 247.45/54.28 | | aElementOf0(all_83_1, v1))) & (( ~ (all_106_1 = all_83_1) &
% 247.45/54.28 | | ~ aElementOf0(all_83_1, all_106_0)) | (slbdtrb0(v0) = v1 &
% 247.45/54.28 | | szszuzczcdt0(all_106_1) = v0 & $i(v1) & $i(v0) &
% 247.45/54.28 | | aElementOf0(all_83_1, v1))))
% 247.45/54.28 | |
% 247.45/54.28 | | GROUND_INST: instantiating (5) with slcrc0, all_128_0, simplifying with (1),
% 247.45/54.28 | | (23), (91), (99) gives:
% 247.45/54.28 | | (104) aSet0(all_128_0)
% 247.45/54.28 | |
% 247.45/54.28 | | DELTA: instantiating (103) with fresh symbols all_153_0, all_153_1 gives:
% 247.45/54.28 | | (105) (all_106_1 = all_83_1 | aElementOf0(all_83_1, all_106_0) |
% 247.45/54.28 | | (slbdtrb0(all_153_1) = all_153_0 & szszuzczcdt0(all_106_1) =
% 247.45/54.28 | | all_153_1 & $i(all_153_0) & $i(all_153_1) & ~
% 247.45/54.28 | | aElementOf0(all_83_1, all_153_0))) & (( ~ (all_106_1 =
% 247.45/54.28 | | all_83_1) & ~ aElementOf0(all_83_1, all_106_0)) |
% 247.45/54.28 | | (slbdtrb0(all_153_1) = all_153_0 & szszuzczcdt0(all_106_1) =
% 247.45/54.28 | | all_153_1 & $i(all_153_0) & $i(all_153_1) &
% 247.45/54.28 | | aElementOf0(all_83_1, all_153_0)))
% 247.45/54.28 | |
% 247.45/54.28 | | ALPHA: (105) implies:
% 247.45/54.28 | | (106) ( ~ (all_106_1 = all_83_1) & ~ aElementOf0(all_83_1, all_106_0)) |
% 247.45/54.28 | | (slbdtrb0(all_153_1) = all_153_0 & szszuzczcdt0(all_106_1) =
% 247.45/54.28 | | all_153_1 & $i(all_153_0) & $i(all_153_1) & aElementOf0(all_83_1,
% 247.45/54.28 | | all_153_0))
% 247.45/54.28 | |
% 247.45/54.28 | | BETA: splitting (106) gives:
% 247.45/54.28 | |
% 247.45/54.28 | | Case 1:
% 247.45/54.28 | | |
% 247.45/54.28 | | | (107) ~ (all_106_1 = all_83_1) & ~ aElementOf0(all_83_1, all_106_0)
% 247.45/54.28 | | |
% 247.45/54.28 | | | ALPHA: (107) implies:
% 247.45/54.28 | | | (108) ~ aElementOf0(all_83_1, all_106_0)
% 247.45/54.28 | | |
% 247.45/54.28 | | | PRED_UNIFY: (70), (108) imply:
% 247.45/54.29 | | | (109) $false
% 247.45/54.29 | | |
% 247.45/54.29 | | | CLOSE: (109) is inconsistent.
% 247.45/54.29 | | |
% 247.45/54.29 | | Case 2:
% 247.45/54.29 | | |
% 247.45/54.29 | | |
% 247.45/54.29 | | | GROUND_INST: instantiating (9) with all_128_0, simplifying with (91),
% 247.45/54.29 | | | (92), (104) gives:
% 247.45/54.29 | | | (110) all_128_0 = slcrc0
% 247.45/54.29 | | |
% 247.45/54.29 | | | GROUND_INST: instantiating (4) with xS, all_128_0, simplifying with (24),
% 247.45/54.29 | | | (41), (91), (104) gives:
% 247.45/54.29 | | | (111) aSubsetOf0(all_128_0, xS) | ? [v0: $i] : ($i(v0) &
% 247.45/54.29 | | | aElementOf0(v0, all_128_0) & ~ aElementOf0(v0, xS))
% 247.45/54.29 | | |
% 247.45/54.29 | | | BETA: splitting (49) gives:
% 247.45/54.29 | | |
% 247.45/54.29 | | | Case 1:
% 247.45/54.29 | | | |
% 247.45/54.29 | | | | (112) aSubsetOf0(slcrc0, xS)
% 247.45/54.29 | | | |
% 247.45/54.29 | | | | GROUND_INST: instantiating (16) with xS, sz00, all_65_0, slcrc0,
% 247.45/54.29 | | | | simplifying with (23), (24), (30), (31), (36), (37), (39),
% 247.45/54.29 | | | | (41), (43), (112) gives:
% 247.45/54.29 | | | | (113) $false
% 247.45/54.29 | | | |
% 247.45/54.29 | | | | CLOSE: (113) is inconsistent.
% 247.45/54.29 | | | |
% 247.45/54.29 | | | Case 2:
% 247.45/54.29 | | | |
% 247.45/54.29 | | | | (114) ~ aSubsetOf0(slcrc0, xS)
% 247.45/54.29 | | | |
% 247.45/54.29 | | | | BETA: splitting (111) gives:
% 247.45/54.29 | | | |
% 247.45/54.29 | | | | Case 1:
% 247.45/54.29 | | | | |
% 247.45/54.29 | | | | | (115) aSubsetOf0(all_128_0, xS)
% 247.45/54.29 | | | | |
% 247.45/54.29 | | | | | REDUCE: (110), (115) imply:
% 247.45/54.29 | | | | | (116) aSubsetOf0(slcrc0, xS)
% 247.45/54.29 | | | | |
% 247.45/54.29 | | | | | PRED_UNIFY: (114), (116) imply:
% 247.45/54.29 | | | | | (117) $false
% 247.45/54.29 | | | | |
% 247.45/54.29 | | | | | CLOSE: (117) is inconsistent.
% 247.45/54.29 | | | | |
% 247.45/54.29 | | | | Case 2:
% 247.45/54.29 | | | | |
% 247.45/54.29 | | | | | (118) ? [v0: $i] : ($i(v0) & aElementOf0(v0, all_128_0) & ~
% 247.45/54.29 | | | | | aElementOf0(v0, xS))
% 247.45/54.29 | | | | |
% 247.45/54.29 | | | | | DELTA: instantiating (118) with fresh symbol all_402_0 gives:
% 247.45/54.29 | | | | | (119) $i(all_402_0) & aElementOf0(all_402_0, all_128_0) & ~
% 247.45/54.29 | | | | | aElementOf0(all_402_0, xS)
% 247.45/54.29 | | | | |
% 247.45/54.29 | | | | | ALPHA: (119) implies:
% 247.45/54.29 | | | | | (120) aElementOf0(all_402_0, all_128_0)
% 247.45/54.29 | | | | | (121) $i(all_402_0)
% 247.45/54.29 | | | | |
% 247.45/54.29 | | | | | REDUCE: (110), (120) imply:
% 247.45/54.29 | | | | | (122) aElementOf0(all_402_0, slcrc0)
% 247.45/54.29 | | | | |
% 247.45/54.29 | | | | | GROUND_INST: instantiating (2) with all_402_0, simplifying with (121),
% 247.45/54.29 | | | | | (122) gives:
% 247.45/54.29 | | | | | (123) $false
% 247.45/54.29 | | | | |
% 247.45/54.29 | | | | | CLOSE: (123) is inconsistent.
% 247.45/54.29 | | | | |
% 247.45/54.29 | | | | End of split
% 247.45/54.29 | | | |
% 247.45/54.29 | | | End of split
% 247.45/54.29 | | |
% 247.45/54.29 | | End of split
% 247.45/54.29 | |
% 247.45/54.29 | End of split
% 247.45/54.29 |
% 247.45/54.29 End of proof
% 247.45/54.29 % SZS output end Proof for theBenchmark
% 247.45/54.29
% 247.45/54.29 53685ms
%------------------------------------------------------------------------------