TSTP Solution File: NUM580+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM580+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 : n013.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 11:48:44 EDT 2023
% Result : Theorem 119.43s 16.83s
% Output : Proof 120.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM580+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.35 % Computer : n013.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Fri Aug 25 12:54:02 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.86/1.46 Prover 4: Preprocessing ...
% 4.86/1.46 Prover 1: Preprocessing ...
% 4.86/1.50 Prover 3: Preprocessing ...
% 4.86/1.50 Prover 0: Preprocessing ...
% 4.86/1.50 Prover 5: Preprocessing ...
% 4.86/1.50 Prover 6: Preprocessing ...
% 4.86/1.50 Prover 2: Preprocessing ...
% 13.98/2.71 Prover 1: Constructing countermodel ...
% 13.98/2.78 Prover 3: Constructing countermodel ...
% 13.98/2.80 Prover 6: Proving ...
% 16.08/2.93 Prover 5: Proving ...
% 21.54/3.67 Prover 2: Proving ...
% 31.30/5.02 Prover 4: Constructing countermodel ...
% 37.30/5.73 Prover 0: Proving ...
% 84.24/11.93 Prover 2: stopped
% 84.24/11.93 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 84.24/12.11 Prover 7: Preprocessing ...
% 87.68/12.46 Prover 7: Constructing countermodel ...
% 99.52/13.97 Prover 5: stopped
% 99.52/13.99 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 100.70/14.08 Prover 8: Preprocessing ...
% 101.05/14.31 Prover 8: Warning: ignoring some quantifiers
% 101.05/14.32 Prover 8: Constructing countermodel ...
% 114.28/15.99 Prover 1: stopped
% 114.28/15.99 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 115.20/16.09 Prover 9: Preprocessing ...
% 118.31/16.46 Prover 7: Found proof (size 82)
% 118.31/16.46 Prover 7: proved (4510ms)
% 118.31/16.46 Prover 0: stopped
% 118.31/16.46 Prover 8: stopped
% 118.31/16.46 Prover 6: stopped
% 118.31/16.47 Prover 4: stopped
% 118.31/16.47 Prover 3: stopped
% 119.43/16.82 Prover 9: Constructing countermodel ...
% 119.43/16.83 Prover 9: stopped
% 119.43/16.83
% 119.43/16.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 119.43/16.83
% 119.43/16.85 % SZS output start Proof for theBenchmark
% 119.43/16.85 Assumptions after simplification:
% 119.43/16.85 ---------------------------------
% 119.43/16.85
% 119.43/16.85 (mCardCons)
% 119.80/16.90 ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~
% 119.80/16.90 isFinite0(v0) | ~ aSet0(v0) | ? [v2: $i] : (szszuzczcdt0(v1) = v2 & $i(v2)
% 119.80/16.90 & ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v0, v3) = v4) | ~ $i(v3) | ~
% 119.80/16.90 aElement0(v3) | sbrdtbr0(v4) = v2 | aElementOf0(v3, v0))))
% 119.80/16.90
% 119.80/16.90 (mCardNum)
% 119.80/16.91 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0)
% 119.80/16.91 | ~ isFinite0(v0) | ~ aSet0(v0) | aElementOf0(v1, szNzAzT0)) & ! [v0: $i]
% 119.80/16.91 : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ aElementOf0(v1,
% 119.80/16.91 szNzAzT0) | ~ aSet0(v0) | isFinite0(v0))
% 119.80/16.91
% 119.80/16.91 (mCountNFin_01)
% 119.80/16.91 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0))
% 119.80/16.91
% 119.80/16.91 (mDefEmp)
% 119.80/16.91 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~
% 119.80/16.91 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : (
% 119.80/16.91 ~ $i(v0) | ~ aElementOf0(v0, slcrc0))
% 119.80/16.91
% 119.80/16.91 (mDefSeg)
% 119.80/16.92 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 119.80/16.92 (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 119.80/16.92 ~ $i(v0) | ~ sdtlseqdt0(v3, v0) | ~ aElementOf0(v2, szNzAzT0) | ~
% 119.80/16.92 aElementOf0(v0, szNzAzT0) | aElementOf0(v2, v1)) & ! [v0: $i] : ! [v1: $i]
% 119.80/16.92 : ! [v2: $i] : ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) =
% 119.80/16.92 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~
% 119.80/16.92 aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v3, v0)) & ! [v0: $i] : ! [v1: $i]
% 119.80/16.92 : ! [v2: $i] : ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) =
% 119.80/16.92 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~
% 119.80/16.92 aElementOf0(v0, szNzAzT0) | aElementOf0(v2, szNzAzT0)) & ! [v0: $i] : !
% 119.80/16.92 [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slbdtrb0(v0) = v1) | ~ $i(v2) | ~
% 119.80/16.92 $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v2) | ? [v3: $i] : ? [v4:
% 119.80/16.92 $i] : ($i(v3) & ( ~ aElementOf0(v3, v2) | ~ aElementOf0(v3, szNzAzT0) |
% 119.80/16.92 (szszuzczcdt0(v3) = v4 & $i(v4) & ~ sdtlseqdt0(v4, v0))) &
% 119.80/16.92 (aElementOf0(v3, v2) | (szszuzczcdt0(v3) = v4 & $i(v4) & sdtlseqdt0(v4,
% 119.80/16.92 v0) & aElementOf0(v3, szNzAzT0))))) & ! [v0: $i] : ! [v1: $i] : (
% 119.80/16.92 ~ (slbdtrb0(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0)
% 119.80/16.92 | aSet0(v1))
% 119.80/16.92
% 119.80/16.92 (mDefSub)
% 119.80/16.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 119.80/16.92 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) |
% 119.80/16.92 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) |
% 119.80/16.92 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i]
% 119.80/16.92 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) |
% 119.80/16.92 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)))
% 119.80/16.92
% 119.80/16.92 (mEOfElem)
% 119.80/16.92 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) |
% 119.80/16.92 ~ aSet0(v0) | aElement0(v1))
% 119.80/16.92
% 119.80/16.92 (mNATSet)
% 119.80/16.92 $i(szNzAzT0) & isCountable0(szNzAzT0) & aSet0(szNzAzT0)
% 119.80/16.92
% 119.80/16.92 (mNatExtra)
% 119.80/16.93 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~
% 119.80/16.93 aElementOf0(v0, szNzAzT0) | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) &
% 119.80/16.93 aElementOf0(v1, szNzAzT0)))
% 119.80/16.93
% 119.80/16.93 (mSegZero)
% 119.80/16.93 slbdtrb0(sz00) = slcrc0 & $i(sz00) & $i(slcrc0)
% 119.80/16.93
% 119.80/16.93 (mSuccEquSucc)
% 119.80/16.93 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 119.80/16.93 (szszuzczcdt0(v1) = v2) | ~ (szszuzczcdt0(v0) = v2) | ~ $i(v1) | ~ $i(v0)
% 119.80/16.93 | ~ aElementOf0(v1, szNzAzT0) | ~ aElementOf0(v0, szNzAzT0))
% 119.80/16.93
% 119.80/16.93 (mZeroNum)
% 119.80/16.93 $i(sz00) & $i(szNzAzT0) & aElementOf0(sz00, szNzAzT0)
% 119.80/16.93
% 119.80/16.93 (m__)
% 119.80/16.93 $i(xQ) & $i(xi) & $i(xN) & $i(xK) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 119.80/16.93 ? [v3: $i] : ( ~ (v3 = xK) & sdtlpdtrp0(xN, xi) = v0 & szmzizndt0(v0) = v1 &
% 119.80/16.93 sbrdtbr0(v2) = v3 & sdtpldt0(xQ, v1) = v2 & $i(v3) & $i(v2) & $i(v1) &
% 119.80/16.93 $i(v0) & aElementOf0(v1, v0) & aSet0(v2) & ! [v4: $i] : (v4 = v1 | ~
% 119.80/16.93 $i(v4) | ~ aElementOf0(v4, v2) | aElementOf0(v4, xQ)) & ! [v4: $i] : ( ~
% 119.80/16.93 $i(v4) | ~ aElementOf0(v4, v2) | aElement0(v4)) & ! [v4: $i] : ( ~
% 119.80/16.93 $i(v4) | ~ aElementOf0(v4, v0) | sdtlseqdt0(v1, v4)) & ! [v4: $i] : ( ~
% 119.80/16.93 $i(v4) | ~ aElementOf0(v4, xQ) | ~ aElement0(v4) | aElementOf0(v4, v2))
% 119.80/16.93 & ( ~ aElement0(v1) | aElementOf0(v1, v2)))
% 119.80/16.93
% 119.80/16.93 (m__3418)
% 119.80/16.93 $i(xK) & $i(szNzAzT0) & aElementOf0(xK, szNzAzT0)
% 119.80/16.93
% 119.80/16.93 (m__3462)
% 119.80/16.93 ~ (xK = sz00) & $i(xK) & $i(sz00)
% 119.80/16.93
% 119.80/16.93 (m__3520)
% 119.80/16.93 ~ (xK = sz00) & $i(xK) & $i(sz00)
% 119.80/16.93
% 119.80/16.93 (m__3533)
% 119.80/16.93 szszuzczcdt0(xk) = xK & $i(xk) & $i(xK) & $i(szNzAzT0) & aElementOf0(xk,
% 119.80/16.93 szNzAzT0)
% 119.80/16.93
% 119.80/16.93 (m__3623)
% 119.80/16.94 sdtlpdtrp0(xN, sz00) = xS & szDzozmdt0(xN) = szNzAzT0 & $i(xN) & $i(xS) &
% 119.80/16.94 $i(sz00) & $i(szNzAzT0) & aFunction0(xN) & ! [v0: $i] : ! [v1: $i] : ( ~
% 119.80/16.94 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~
% 119.80/16.94 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i]
% 119.80/16.94 : ? [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xN, v4) = v5 & szmzizndt0(v1) = v2
% 119.80/16.94 & szszuzczcdt0(v0) = v4 & sdtmndt0(v1, v2) = v3 & $i(v5) & $i(v4) & $i(v3)
% 119.80/16.94 & $i(v2) & aSubsetOf0(v5, v3) & isCountable0(v5) & aElementOf0(v2, v1) &
% 119.80/16.94 aSet0(v5) & aSet0(v3) & ~ aElementOf0(v2, v3) & ! [v6: $i] : (v6 = v2 |
% 119.80/16.94 ~ $i(v6) | ~ aElementOf0(v6, v1) | ~ aElement0(v6) | aElementOf0(v6,
% 119.80/16.94 v3)) & ! [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6, v5) |
% 119.80/16.94 aElementOf0(v6, v3)) & ! [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6, v3)
% 119.80/16.94 | aElementOf0(v6, v1)) & ! [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6,
% 119.80/16.94 v3) | aElement0(v6)) & ! [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6,
% 119.80/16.94 v1) | sdtlseqdt0(v2, v6)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 119.80/16.94 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ isCountable0(v1) | ~
% 119.80/16.94 aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | ? [v2: $i] : ? [v3: $i] : ?
% 119.80/16.94 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ($i(v6) & ((sdtlpdtrp0(xN, v4) = v5 &
% 119.80/16.94 szmzizndt0(v1) = v2 & szszuzczcdt0(v0) = v4 & sdtmndt0(v1, v2) = v3 &
% 119.80/16.94 $i(v5) & $i(v4) & $i(v3) & $i(v2) & aSubsetOf0(v5, v3) &
% 119.80/16.94 isCountable0(v5) & aElementOf0(v2, v1) & aSet0(v5) & aSet0(v3) & ~
% 119.80/16.94 aElementOf0(v2, v3) & ! [v7: $i] : (v7 = v2 | ~ $i(v7) | ~
% 119.80/16.94 aElementOf0(v7, v1) | ~ aElement0(v7) | aElementOf0(v7, v3)) & !
% 119.80/16.94 [v7: $i] : ( ~ $i(v7) | ~ aElementOf0(v7, v5) | aElementOf0(v7, v3))
% 119.80/16.94 & ! [v7: $i] : ( ~ $i(v7) | ~ aElementOf0(v7, v3) | aElementOf0(v7,
% 119.80/16.94 v1)) & ! [v7: $i] : ( ~ $i(v7) | ~ aElementOf0(v7, v3) |
% 119.80/16.94 aElement0(v7)) & ! [v7: $i] : ( ~ $i(v7) | ~ aElementOf0(v7, v1) |
% 119.80/16.94 sdtlseqdt0(v2, v7))) | (aElementOf0(v6, v1) & ~ aElementOf0(v6,
% 119.80/16.94 szNzAzT0))))) & ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) =
% 119.80/16.94 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i]
% 119.80/16.94 : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (sdtlpdtrp0(xN, v0) = v2 &
% 119.80/16.94 $i(v6) & $i(v2) & ( ~ isCountable0(v2) | (sdtlpdtrp0(xN, v1) = v5 &
% 119.80/16.94 szmzizndt0(v2) = v3 & sdtmndt0(v2, v3) = v4 & $i(v5) & $i(v4) & $i(v3)
% 119.80/16.94 & aSubsetOf0(v5, v4) & isCountable0(v5) & aElementOf0(v3, v2) &
% 119.80/16.94 aSet0(v5) & aSet0(v4) & ~ aElementOf0(v3, v4) & ! [v7: $i] : (v7 =
% 119.80/16.94 v3 | ~ $i(v7) | ~ aElementOf0(v7, v2) | ~ aElement0(v7) |
% 119.80/16.94 aElementOf0(v7, v4)) & ! [v7: $i] : ( ~ $i(v7) | ~ aElementOf0(v7,
% 119.80/16.94 v5) | aElementOf0(v7, v4)) & ! [v7: $i] : ( ~ $i(v7) | ~
% 119.80/16.94 aElementOf0(v7, v4) | aElementOf0(v7, v2)) & ! [v7: $i] : ( ~
% 119.80/16.94 $i(v7) | ~ aElementOf0(v7, v4) | aElement0(v7)) & ! [v7: $i] : ( ~
% 119.80/16.94 $i(v7) | ~ aElementOf0(v7, v2) | sdtlseqdt0(v3, v7))) | ( ~
% 119.80/16.94 aSubsetOf0(v2, szNzAzT0) & ( ~ aSet0(v2) | (aElementOf0(v6, v2) & ~
% 119.80/16.94 aElementOf0(v6, szNzAzT0)))))))
% 119.80/16.94
% 119.80/16.94 (m__3671)
% 119.80/16.95 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 119.80/16.95 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v2, v1) |
% 119.80/16.95 ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v2, szNzAzT0)) & ! [v0: $i] : !
% 119.80/16.95 [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0,
% 119.80/16.95 szNzAzT0) | aSubsetOf0(v1, szNzAzT0)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 119.80/16.95 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) |
% 119.80/16.95 isCountable0(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) =
% 119.80/16.95 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | aSet0(v1))
% 119.80/16.95
% 119.80/16.95 (m__3989)
% 119.80/16.95 $i(xi) & $i(szNzAzT0) & aElementOf0(xi, szNzAzT0)
% 119.80/16.95
% 119.80/16.95 (m__3989_02)
% 119.80/16.95 $i(xQ) & $i(xi) & $i(xN) & $i(xk) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 119.80/16.95 ? [v3: $i] : (sdtlpdtrp0(xN, xi) = v0 & slbdtsldtrb0(v2, xk) = v3 &
% 119.80/16.95 szmzizndt0(v0) = v1 & sbrdtbr0(xQ) = xk & sdtmndt0(v0, v1) = v2 & $i(v3) &
% 119.80/16.95 $i(v2) & $i(v1) & $i(v0) & aSubsetOf0(xQ, v2) & aElementOf0(v1, v0) &
% 119.80/16.95 aElementOf0(xQ, v3) & aSet0(v2) & aSet0(xQ) & ~ aElementOf0(v1, v2) & !
% 119.80/16.95 [v4: $i] : (v4 = v1 | ~ $i(v4) | ~ aElementOf0(v4, v0) | ~ aElement0(v4)
% 119.80/16.95 | aElementOf0(v4, v2)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v2)
% 119.80/16.95 | aElementOf0(v4, v0)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v2)
% 119.80/16.95 | aElement0(v4)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v0) |
% 119.80/16.95 sdtlseqdt0(v1, v4)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, xQ) |
% 119.80/16.95 aElementOf0(v4, v2)))
% 119.80/16.95
% 119.80/16.95 (function-axioms)
% 119.80/16.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 119.80/16.96 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 119.80/16.96 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 119.80/16.96 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 119.80/16.96 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 119.80/16.96 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 119.80/16.96 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 119.80/16.96 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 119.80/16.96 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 119.80/16.96 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~
% 119.80/16.96 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 119.80/16.96 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) &
% 119.80/16.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 119.80/16.96 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 119.80/16.96 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 119.80/16.96 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 119.80/16.96 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 119.80/16.96 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 119.80/16.96 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 119.80/16.96 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 119.80/16.96 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 119.80/16.96 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 119.80/16.96 v0))
% 119.80/16.96
% 119.80/16.96 Further assumptions not needed in the proof:
% 119.80/16.96 --------------------------------------------
% 119.80/16.96 mCConsSet, mCDiffSet, mCardDiff, mCardEmpty, mCardS, mCardSeg, mCardSub,
% 119.80/16.96 mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons, mDefDiff, mDefMax,
% 119.80/16.96 mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSel, mDiffCons, mDirichlet, mDomSet,
% 119.80/16.96 mElmSort, mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH,
% 119.80/16.96 mIHSort, mImgCount, mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel,
% 119.80/16.96 mLessSucc, mLessTotal, mLessTrans, mMinMin, mNatNSucc, mNoScLessZr, mPttSet,
% 119.80/16.96 mSegFin, mSegLess, mSegSucc, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub,
% 119.80/16.96 mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccLess, mSuccNum,
% 119.80/16.96 mZeroLess, m__3291, m__3398, m__3435, m__3453, m__3754, m__3821
% 119.80/16.96
% 119.80/16.96 Those formulas are unsatisfiable:
% 119.80/16.96 ---------------------------------
% 119.80/16.96
% 119.80/16.96 Begin of proof
% 119.80/16.96 |
% 119.80/16.96 | ALPHA: (mDefEmp) implies:
% 119.80/16.96 | (1) aSet0(slcrc0)
% 119.80/16.96 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, slcrc0))
% 119.80/16.96 |
% 119.80/16.96 | ALPHA: (mCountNFin_01) implies:
% 119.80/16.96 | (3) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)
% 119.80/16.96 |
% 119.80/16.96 | ALPHA: (mDefSub) implies:
% 119.80/16.96 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 119.80/16.96 | $i(v0) | ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~
% 119.80/16.96 | aSet0(v0) | aElementOf0(v2, v0))
% 119.80/16.96 |
% 119.80/16.96 | ALPHA: (mNATSet) implies:
% 119.80/16.96 | (5) aSet0(szNzAzT0)
% 119.80/16.96 | (6) isCountable0(szNzAzT0)
% 119.80/16.96 |
% 119.80/16.96 | ALPHA: (mZeroNum) implies:
% 119.80/16.96 | (7) aElementOf0(sz00, szNzAzT0)
% 119.80/16.96 |
% 119.80/16.96 | ALPHA: (mSuccEquSucc) implies:
% 119.80/16.96 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 119.80/16.96 | (szszuzczcdt0(v1) = v2) | ~ (szszuzczcdt0(v0) = v2) | ~ $i(v1) | ~
% 119.80/16.96 | $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aElementOf0(v0, szNzAzT0))
% 119.80/16.96 |
% 119.80/16.96 | ALPHA: (mNatExtra) implies:
% 119.80/16.96 | (9) ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) |
% 119.80/16.96 | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & aElementOf0(v1,
% 119.80/16.96 | szNzAzT0)))
% 119.80/16.96 |
% 119.80/16.96 | ALPHA: (mCardNum) implies:
% 119.80/16.96 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~
% 119.80/16.96 | aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) | isFinite0(v0))
% 119.80/16.96 |
% 119.80/16.96 | ALPHA: (mDefSeg) implies:
% 119.80/16.96 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slbdtrb0(v0)
% 119.80/16.96 | = v1) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ~
% 119.80/16.96 | aSet0(v2) | ? [v3: $i] : ? [v4: $i] : ($i(v3) & ( ~
% 119.80/16.96 | aElementOf0(v3, v2) | ~ aElementOf0(v3, szNzAzT0) |
% 119.80/16.97 | (szszuzczcdt0(v3) = v4 & $i(v4) & ~ sdtlseqdt0(v4, v0))) &
% 119.80/16.97 | (aElementOf0(v3, v2) | (szszuzczcdt0(v3) = v4 & $i(v4) &
% 119.80/16.97 | sdtlseqdt0(v4, v0) & aElementOf0(v3, szNzAzT0)))))
% 119.80/16.97 |
% 119.80/16.97 | ALPHA: (mSegZero) implies:
% 119.80/16.97 | (12) slbdtrb0(sz00) = slcrc0
% 119.80/16.97 |
% 119.80/16.97 | ALPHA: (m__3418) implies:
% 119.80/16.97 | (13) aElementOf0(xK, szNzAzT0)
% 119.80/16.97 |
% 119.80/16.97 | ALPHA: (m__3520) implies:
% 119.80/16.97 | (14) ~ (xK = sz00)
% 119.80/16.97 |
% 119.80/16.97 | ALPHA: (m__3533) implies:
% 119.80/16.97 | (15) aElementOf0(xk, szNzAzT0)
% 119.80/16.97 | (16) szszuzczcdt0(xk) = xK
% 119.80/16.97 |
% 119.80/16.97 | ALPHA: (m__3623) implies:
% 119.80/16.97 | (17) $i(sz00)
% 119.80/16.97 |
% 119.80/16.97 | ALPHA: (m__3671) implies:
% 119.80/16.97 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlpdtrp0(xN, v0) =
% 119.80/16.97 | v1) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~
% 119.80/16.97 | aElementOf0(v0, szNzAzT0) | aElementOf0(v2, szNzAzT0))
% 119.80/16.97 |
% 119.80/16.97 | ALPHA: (m__3989) implies:
% 119.80/16.97 | (19) aElementOf0(xi, szNzAzT0)
% 119.80/16.97 | (20) $i(szNzAzT0)
% 119.80/16.97 |
% 119.80/16.97 | ALPHA: (m__3989_02) implies:
% 119.80/16.97 | (21) $i(xk)
% 119.80/16.97 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 119.80/16.97 | (sdtlpdtrp0(xN, xi) = v0 & slbdtsldtrb0(v2, xk) = v3 & szmzizndt0(v0)
% 119.80/16.97 | = v1 & sbrdtbr0(xQ) = xk & sdtmndt0(v0, v1) = v2 & $i(v3) & $i(v2) &
% 119.80/16.97 | $i(v1) & $i(v0) & aSubsetOf0(xQ, v2) & aElementOf0(v1, v0) &
% 119.80/16.97 | aElementOf0(xQ, v3) & aSet0(v2) & aSet0(xQ) & ~ aElementOf0(v1, v2)
% 119.80/16.97 | & ! [v4: $i] : (v4 = v1 | ~ $i(v4) | ~ aElementOf0(v4, v0) | ~
% 119.80/16.97 | aElement0(v4) | aElementOf0(v4, v2)) & ! [v4: $i] : ( ~ $i(v4) |
% 119.80/16.97 | ~ aElementOf0(v4, v2) | aElementOf0(v4, v0)) & ! [v4: $i] : ( ~
% 119.80/16.97 | $i(v4) | ~ aElementOf0(v4, v2) | aElement0(v4)) & ! [v4: $i] : (
% 119.80/16.97 | ~ $i(v4) | ~ aElementOf0(v4, v0) | sdtlseqdt0(v1, v4)) & ! [v4:
% 119.80/16.97 | $i] : ( ~ $i(v4) | ~ aElementOf0(v4, xQ) | aElementOf0(v4, v2)))
% 119.80/16.97 |
% 119.80/16.97 | ALPHA: (m__) implies:
% 119.80/16.97 | (23) $i(xK)
% 119.80/16.97 | (24) $i(xi)
% 119.80/16.97 | (25) $i(xQ)
% 119.80/16.97 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = xK)
% 119.80/16.97 | & sdtlpdtrp0(xN, xi) = v0 & szmzizndt0(v0) = v1 & sbrdtbr0(v2) = v3
% 119.80/16.97 | & sdtpldt0(xQ, v1) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 119.80/16.97 | aElementOf0(v1, v0) & aSet0(v2) & ! [v4: $i] : (v4 = v1 | ~ $i(v4)
% 119.80/16.97 | | ~ aElementOf0(v4, v2) | aElementOf0(v4, xQ)) & ! [v4: $i] : (
% 119.80/16.97 | ~ $i(v4) | ~ aElementOf0(v4, v2) | aElement0(v4)) & ! [v4: $i] :
% 119.80/16.97 | ( ~ $i(v4) | ~ aElementOf0(v4, v0) | sdtlseqdt0(v1, v4)) & ! [v4:
% 119.80/16.97 | $i] : ( ~ $i(v4) | ~ aElementOf0(v4, xQ) | ~ aElement0(v4) |
% 119.80/16.97 | aElementOf0(v4, v2)) & ( ~ aElement0(v1) | aElementOf0(v1, v2)))
% 119.80/16.97 |
% 119.80/16.97 | ALPHA: (function-axioms) implies:
% 119.80/16.97 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 119.80/16.97 | (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0))
% 119.80/16.97 | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sbrdtbr0(v2)
% 119.80/16.97 | = v1) | ~ (sbrdtbr0(v2) = v0))
% 119.80/16.98 | (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 119.80/16.98 | (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) = v0))
% 119.80/16.98 | (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 119.80/16.98 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0))
% 119.80/16.98 |
% 119.80/16.98 | DELTA: instantiating (26) with fresh symbols all_70_0, all_70_1, all_70_2,
% 119.80/16.98 | all_70_3 gives:
% 119.80/16.98 | (31) ~ (all_70_0 = xK) & sdtlpdtrp0(xN, xi) = all_70_3 &
% 119.80/16.98 | szmzizndt0(all_70_3) = all_70_2 & sbrdtbr0(all_70_1) = all_70_0 &
% 119.80/16.98 | sdtpldt0(xQ, all_70_2) = all_70_1 & $i(all_70_0) & $i(all_70_1) &
% 119.80/16.98 | $i(all_70_2) & $i(all_70_3) & aElementOf0(all_70_2, all_70_3) &
% 119.80/16.98 | aSet0(all_70_1) & ! [v0: any] : (v0 = all_70_2 | ~ $i(v0) | ~
% 119.80/16.98 | aElementOf0(v0, all_70_1) | aElementOf0(v0, xQ)) & ! [v0: $i] : ( ~
% 119.80/16.98 | $i(v0) | ~ aElementOf0(v0, all_70_1) | aElement0(v0)) & ! [v0: $i]
% 119.80/16.98 | : ( ~ $i(v0) | ~ aElementOf0(v0, all_70_3) | sdtlseqdt0(all_70_2,
% 119.80/16.98 | v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xQ) | ~
% 119.80/16.98 | aElement0(v0) | aElementOf0(v0, all_70_1)) & ( ~ aElement0(all_70_2)
% 119.80/16.98 | | aElementOf0(all_70_2, all_70_1))
% 119.80/16.98 |
% 119.80/16.98 | ALPHA: (31) implies:
% 119.80/16.98 | (32) ~ (all_70_0 = xK)
% 119.80/16.98 | (33) aSet0(all_70_1)
% 119.80/16.98 | (34) $i(all_70_1)
% 119.80/16.98 | (35) sdtpldt0(xQ, all_70_2) = all_70_1
% 119.80/16.98 | (36) sbrdtbr0(all_70_1) = all_70_0
% 119.80/16.98 | (37) szmzizndt0(all_70_3) = all_70_2
% 119.80/16.98 | (38) sdtlpdtrp0(xN, xi) = all_70_3
% 119.80/16.98 | (39) ~ aElement0(all_70_2) | aElementOf0(all_70_2, all_70_1)
% 119.80/16.98 |
% 119.80/16.98 | DELTA: instantiating (22) with fresh symbols all_73_0, all_73_1, all_73_2,
% 119.80/16.98 | all_73_3 gives:
% 119.80/16.98 | (40) sdtlpdtrp0(xN, xi) = all_73_3 & slbdtsldtrb0(all_73_1, xk) = all_73_0
% 119.80/16.98 | & szmzizndt0(all_73_3) = all_73_2 & sbrdtbr0(xQ) = xk &
% 119.80/16.98 | sdtmndt0(all_73_3, all_73_2) = all_73_1 & $i(all_73_0) & $i(all_73_1)
% 119.80/16.98 | & $i(all_73_2) & $i(all_73_3) & aSubsetOf0(xQ, all_73_1) &
% 119.80/16.98 | aElementOf0(all_73_2, all_73_3) & aElementOf0(xQ, all_73_0) &
% 119.80/16.98 | aSet0(all_73_1) & aSet0(xQ) & ~ aElementOf0(all_73_2, all_73_1) & !
% 119.80/16.98 | [v0: any] : (v0 = all_73_2 | ~ $i(v0) | ~ aElementOf0(v0, all_73_3)
% 119.80/16.98 | | ~ aElement0(v0) | aElementOf0(v0, all_73_1)) & ! [v0: $i] : ( ~
% 119.80/16.98 | $i(v0) | ~ aElementOf0(v0, all_73_1) | aElementOf0(v0, all_73_3)) &
% 119.80/16.98 | ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_73_1) |
% 119.80/16.98 | aElement0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0,
% 119.80/16.98 | all_73_3) | sdtlseqdt0(all_73_2, v0)) & ! [v0: $i] : ( ~ $i(v0) |
% 119.80/16.98 | ~ aElementOf0(v0, xQ) | aElementOf0(v0, all_73_1))
% 119.80/16.98 |
% 119.80/16.98 | ALPHA: (40) implies:
% 119.80/16.98 | (41) ~ aElementOf0(all_73_2, all_73_1)
% 119.80/16.98 | (42) aSet0(xQ)
% 119.80/16.98 | (43) aSet0(all_73_1)
% 119.80/16.98 | (44) aElementOf0(all_73_2, all_73_3)
% 119.80/16.98 | (45) aSubsetOf0(xQ, all_73_1)
% 119.80/16.99 | (46) $i(all_73_2)
% 119.80/16.99 | (47) $i(all_73_1)
% 119.80/16.99 | (48) sbrdtbr0(xQ) = xk
% 119.80/16.99 | (49) szmzizndt0(all_73_3) = all_73_2
% 119.80/16.99 | (50) sdtlpdtrp0(xN, xi) = all_73_3
% 119.80/16.99 |
% 119.80/16.99 | BETA: splitting (3) gives:
% 119.80/16.99 |
% 119.80/16.99 | Case 1:
% 119.80/16.99 | |
% 119.80/16.99 | | (51) ~ isCountable0(slcrc0)
% 119.80/16.99 | |
% 119.80/16.99 | | GROUND_INST: instantiating (29) with all_70_2, all_73_2, all_70_3,
% 119.80/16.99 | | simplifying with (37) gives:
% 119.80/16.99 | | (52) all_73_2 = all_70_2 | ~ (szmzizndt0(all_70_3) = all_73_2)
% 119.80/16.99 | |
% 119.80/16.99 | | GROUND_INST: instantiating (30) with all_70_3, all_73_3, xi, xN, simplifying
% 119.80/16.99 | | with (38), (50) gives:
% 119.80/16.99 | | (53) all_73_3 = all_70_3
% 119.80/16.99 | |
% 119.80/16.99 | | PRED_UNIFY: (6), (51) imply:
% 119.80/16.99 | | (54) ~ (szNzAzT0 = slcrc0)
% 119.80/16.99 | |
% 119.80/16.99 | | REDUCE: (49), (53) imply:
% 119.80/16.99 | | (55) szmzizndt0(all_70_3) = all_73_2
% 119.80/16.99 | |
% 119.80/16.99 | | REDUCE: (44), (53) imply:
% 119.80/16.99 | | (56) aElementOf0(all_73_2, all_70_3)
% 119.80/16.99 | |
% 119.80/16.99 | | BETA: splitting (52) gives:
% 119.80/16.99 | |
% 119.80/16.99 | | Case 1:
% 119.80/16.99 | | |
% 120.23/16.99 | | | (57) ~ (szmzizndt0(all_70_3) = all_73_2)
% 120.23/16.99 | | |
% 120.23/16.99 | | | PRED_UNIFY: (55), (57) imply:
% 120.23/16.99 | | | (58) $false
% 120.23/16.99 | | |
% 120.23/16.99 | | | CLOSE: (58) is inconsistent.
% 120.23/16.99 | | |
% 120.23/16.99 | | Case 2:
% 120.23/16.99 | | |
% 120.23/16.99 | | | (59) all_73_2 = all_70_2
% 120.23/16.99 | | |
% 120.23/16.99 | | | REDUCE: (46), (59) imply:
% 120.23/16.99 | | | (60) $i(all_70_2)
% 120.23/16.99 | | |
% 120.23/16.99 | | | REDUCE: (56), (59) imply:
% 120.23/16.99 | | | (61) aElementOf0(all_70_2, all_70_3)
% 120.23/16.99 | | |
% 120.23/16.99 | | | REDUCE: (41), (59) imply:
% 120.23/16.99 | | | (62) ~ aElementOf0(all_70_2, all_73_1)
% 120.23/16.99 | | |
% 120.23/16.99 | | | GROUND_INST: instantiating (9) with xK, simplifying with (13), (23) gives:
% 120.23/17.00 | | | (63) xK = sz00 | ? [v0: $i] : (szszuzczcdt0(v0) = xK & $i(v0) &
% 120.23/17.00 | | | aElementOf0(v0, szNzAzT0))
% 120.23/17.00 | | |
% 120.23/17.00 | | | GROUND_INST: instantiating (mEOfElem) with szNzAzT0, all_70_2, simplifying
% 120.23/17.00 | | | with (5), (20), (60) gives:
% 120.23/17.00 | | | (64) ~ aElementOf0(all_70_2, szNzAzT0) | aElement0(all_70_2)
% 120.23/17.00 | | |
% 120.23/17.00 | | | GROUND_INST: instantiating (2) with all_70_2, simplifying with (60) gives:
% 120.23/17.00 | | | (65) ~ aElementOf0(all_70_2, slcrc0)
% 120.23/17.00 | | |
% 120.23/17.00 | | | GROUND_INST: instantiating (4) with all_73_1, xQ, all_70_2, simplifying
% 120.23/17.00 | | | with (25), (43), (45), (47), (60), (62) gives:
% 120.23/17.00 | | | (66) ~ aElementOf0(all_70_2, xQ)
% 120.23/17.00 | | |
% 120.23/17.00 | | | GROUND_INST: instantiating (10) with xQ, xk, simplifying with (15), (25),
% 120.23/17.00 | | | (42), (48) gives:
% 120.23/17.00 | | | (67) isFinite0(xQ)
% 120.23/17.00 | | |
% 120.23/17.00 | | | GROUND_INST: instantiating (11) with sz00, slcrc0, all_70_1, simplifying
% 120.23/17.00 | | | with (7), (12), (17), (33), (34) gives:
% 120.23/17.00 | | | (68) all_70_1 = slcrc0 | ? [v0: $i] : ? [v1: $i] : ($i(v0) & ( ~
% 120.23/17.00 | | | aElementOf0(v0, all_70_1) | ~ aElementOf0(v0, szNzAzT0) |
% 120.23/17.00 | | | (szszuzczcdt0(v0) = v1 & $i(v1) & ~ sdtlseqdt0(v1, sz00))) &
% 120.23/17.00 | | | (aElementOf0(v0, all_70_1) | (szszuzczcdt0(v0) = v1 & $i(v1) &
% 120.23/17.00 | | | sdtlseqdt0(v1, sz00) & aElementOf0(v0, szNzAzT0))))
% 120.23/17.00 | | |
% 120.23/17.00 | | | GROUND_INST: instantiating (11) with sz00, slcrc0, szNzAzT0, simplifying
% 120.23/17.00 | | | with (5), (7), (12), (17), (20) gives:
% 120.23/17.00 | | | (69) szNzAzT0 = slcrc0 | ? [v0: $i] : ? [v1: $i] : (szszuzczcdt0(v0)
% 120.23/17.00 | | | = v1 & $i(v1) & $i(v0) & aElementOf0(v0, szNzAzT0) & ~
% 120.23/17.00 | | | sdtlseqdt0(v1, sz00))
% 120.23/17.00 | | |
% 120.23/17.00 | | | GROUND_INST: instantiating (18) with xi, all_70_3, all_70_2, simplifying
% 120.23/17.00 | | | with (19), (24), (38), (60), (61) gives:
% 120.23/17.00 | | | (70) aElementOf0(all_70_2, szNzAzT0)
% 120.23/17.00 | | |
% 120.23/17.00 | | | BETA: splitting (64) gives:
% 120.23/17.00 | | |
% 120.23/17.00 | | | Case 1:
% 120.23/17.00 | | | |
% 120.23/17.00 | | | | (71) ~ aElementOf0(all_70_2, szNzAzT0)
% 120.23/17.00 | | | |
% 120.23/17.00 | | | | PRED_UNIFY: (70), (71) imply:
% 120.23/17.00 | | | | (72) $false
% 120.23/17.00 | | | |
% 120.23/17.00 | | | | CLOSE: (72) is inconsistent.
% 120.23/17.00 | | | |
% 120.23/17.00 | | | Case 2:
% 120.23/17.00 | | | |
% 120.23/17.00 | | | | (73) aElement0(all_70_2)
% 120.23/17.00 | | | |
% 120.23/17.00 | | | | BETA: splitting (63) gives:
% 120.23/17.00 | | | |
% 120.23/17.00 | | | | Case 1:
% 120.23/17.00 | | | | |
% 120.23/17.00 | | | | | (74) xK = sz00
% 120.23/17.00 | | | | |
% 120.23/17.00 | | | | | REDUCE: (14), (74) imply:
% 120.23/17.00 | | | | | (75) $false
% 120.23/17.00 | | | | |
% 120.23/17.00 | | | | | CLOSE: (75) is inconsistent.
% 120.23/17.00 | | | | |
% 120.23/17.00 | | | | Case 2:
% 120.23/17.00 | | | | |
% 120.23/17.00 | | | | | (76) ? [v0: $i] : (szszuzczcdt0(v0) = xK & $i(v0) &
% 120.23/17.00 | | | | | aElementOf0(v0, szNzAzT0))
% 120.23/17.00 | | | | |
% 120.23/17.00 | | | | | DELTA: instantiating (76) with fresh symbol all_137_0 gives:
% 120.23/17.00 | | | | | (77) szszuzczcdt0(all_137_0) = xK & $i(all_137_0) &
% 120.23/17.00 | | | | | aElementOf0(all_137_0, szNzAzT0)
% 120.23/17.00 | | | | |
% 120.23/17.00 | | | | | ALPHA: (77) implies:
% 120.23/17.00 | | | | | (78) aElementOf0(all_137_0, szNzAzT0)
% 120.23/17.00 | | | | | (79) $i(all_137_0)
% 120.23/17.00 | | | | | (80) szszuzczcdt0(all_137_0) = xK
% 120.23/17.00 | | | | |
% 120.23/17.00 | | | | | BETA: splitting (39) gives:
% 120.23/17.00 | | | | |
% 120.23/17.00 | | | | | Case 1:
% 120.23/17.00 | | | | | |
% 120.23/17.00 | | | | | | (81) aElementOf0(all_70_2, all_70_1)
% 120.23/17.00 | | | | | |
% 120.23/17.00 | | | | | | BETA: splitting (69) gives:
% 120.23/17.00 | | | | | |
% 120.23/17.00 | | | | | | Case 1:
% 120.23/17.00 | | | | | | |
% 120.23/17.00 | | | | | | | (82) szNzAzT0 = slcrc0
% 120.23/17.00 | | | | | | |
% 120.23/17.00 | | | | | | | REDUCE: (54), (82) imply:
% 120.23/17.00 | | | | | | | (83) $false
% 120.23/17.00 | | | | | | |
% 120.23/17.00 | | | | | | | CLOSE: (83) is inconsistent.
% 120.23/17.00 | | | | | | |
% 120.23/17.00 | | | | | | Case 2:
% 120.23/17.00 | | | | | | |
% 120.23/17.00 | | | | | | |
% 120.23/17.01 | | | | | | | PRED_UNIFY: (65), (81) imply:
% 120.23/17.01 | | | | | | | (84) ~ (all_70_1 = slcrc0)
% 120.23/17.01 | | | | | | |
% 120.23/17.01 | | | | | | | BETA: splitting (68) gives:
% 120.23/17.01 | | | | | | |
% 120.23/17.01 | | | | | | | Case 1:
% 120.23/17.01 | | | | | | | |
% 120.23/17.01 | | | | | | | | (85) all_70_1 = slcrc0
% 120.23/17.01 | | | | | | | |
% 120.23/17.01 | | | | | | | | REDUCE: (84), (85) imply:
% 120.23/17.01 | | | | | | | | (86) $false
% 120.23/17.01 | | | | | | | |
% 120.23/17.01 | | | | | | | | CLOSE: (86) is inconsistent.
% 120.23/17.01 | | | | | | | |
% 120.23/17.01 | | | | | | | Case 2:
% 120.23/17.01 | | | | | | | |
% 120.23/17.01 | | | | | | | |
% 120.23/17.01 | | | | | | | | GROUND_INST: instantiating (mCardCons) with xQ, xk, simplifying
% 120.23/17.01 | | | | | | | | with (25), (42), (48), (67) gives:
% 120.23/17.01 | | | | | | | | (87) ? [v0: $i] : (szszuzczcdt0(xk) = v0 & $i(v0) & ! [v1:
% 120.23/17.01 | | | | | | | | $i] : ! [v2: $i] : ( ~ (sdtpldt0(xQ, v1) = v2) | ~
% 120.23/17.01 | | | | | | | | $i(v1) | ~ aElement0(v1) | sbrdtbr0(v2) = v0 |
% 120.23/17.01 | | | | | | | | aElementOf0(v1, xQ)))
% 120.23/17.01 | | | | | | | |
% 120.23/17.01 | | | | | | | | GROUND_INST: instantiating (8) with all_137_0, xk, xK,
% 120.23/17.01 | | | | | | | | simplifying with (15), (16), (21), (78), (79), (80)
% 120.23/17.01 | | | | | | | | gives:
% 120.23/17.01 | | | | | | | | (88) all_137_0 = xk
% 120.23/17.01 | | | | | | | |
% 120.23/17.01 | | | | | | | | DELTA: instantiating (87) with fresh symbol all_211_0 gives:
% 120.23/17.01 | | | | | | | | (89) szszuzczcdt0(xk) = all_211_0 & $i(all_211_0) & ! [v0:
% 120.23/17.01 | | | | | | | | $i] : ! [v1: $i] : ( ~ (sdtpldt0(xQ, v0) = v1) | ~
% 120.23/17.01 | | | | | | | | $i(v0) | ~ aElement0(v0) | sbrdtbr0(v1) = all_211_0 |
% 120.23/17.01 | | | | | | | | aElementOf0(v0, xQ))
% 120.23/17.01 | | | | | | | |
% 120.23/17.01 | | | | | | | | ALPHA: (89) implies:
% 120.23/17.01 | | | | | | | | (90) szszuzczcdt0(xk) = all_211_0
% 120.23/17.01 | | | | | | | | (91) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(xQ, v0) = v1)
% 120.23/17.01 | | | | | | | | | ~ $i(v0) | ~ aElement0(v0) | sbrdtbr0(v1) =
% 120.23/17.01 | | | | | | | | all_211_0 | aElementOf0(v0, xQ))
% 120.23/17.01 | | | | | | | |
% 120.23/17.01 | | | | | | | | GROUND_INST: instantiating (91) with all_70_2, all_70_1,
% 120.23/17.01 | | | | | | | | simplifying with (35), (60), (66), (73) gives:
% 120.23/17.01 | | | | | | | | (92) sbrdtbr0(all_70_1) = all_211_0
% 120.23/17.01 | | | | | | | |
% 120.23/17.01 | | | | | | | | GROUND_INST: instantiating (27) with xK, all_211_0, xk,
% 120.23/17.01 | | | | | | | | simplifying with (16), (90) gives:
% 120.23/17.01 | | | | | | | | (93) all_211_0 = xK
% 120.23/17.01 | | | | | | | |
% 120.23/17.01 | | | | | | | | GROUND_INST: instantiating (28) with all_70_0, all_211_0,
% 120.23/17.01 | | | | | | | | all_70_1, simplifying with (36), (92) gives:
% 120.23/17.01 | | | | | | | | (94) all_211_0 = all_70_0
% 120.23/17.01 | | | | | | | |
% 120.23/17.01 | | | | | | | | COMBINE_EQS: (93), (94) imply:
% 120.23/17.01 | | | | | | | | (95) all_70_0 = xK
% 120.23/17.01 | | | | | | | |
% 120.23/17.01 | | | | | | | | SIMP: (95) implies:
% 120.23/17.01 | | | | | | | | (96) all_70_0 = xK
% 120.23/17.01 | | | | | | | |
% 120.23/17.01 | | | | | | | | REDUCE: (32), (96) imply:
% 120.23/17.01 | | | | | | | | (97) $false
% 120.23/17.01 | | | | | | | |
% 120.23/17.01 | | | | | | | | CLOSE: (97) is inconsistent.
% 120.23/17.01 | | | | | | | |
% 120.23/17.01 | | | | | | | End of split
% 120.23/17.01 | | | | | | |
% 120.23/17.01 | | | | | | End of split
% 120.23/17.01 | | | | | |
% 120.23/17.01 | | | | | Case 2:
% 120.23/17.01 | | | | | |
% 120.23/17.01 | | | | | | (98) ~ aElement0(all_70_2)
% 120.23/17.01 | | | | | |
% 120.23/17.01 | | | | | | PRED_UNIFY: (73), (98) imply:
% 120.23/17.01 | | | | | | (99) $false
% 120.23/17.01 | | | | | |
% 120.23/17.01 | | | | | | CLOSE: (99) is inconsistent.
% 120.23/17.01 | | | | | |
% 120.23/17.01 | | | | | End of split
% 120.23/17.01 | | | | |
% 120.23/17.01 | | | | End of split
% 120.23/17.01 | | | |
% 120.23/17.01 | | | End of split
% 120.23/17.01 | | |
% 120.23/17.01 | | End of split
% 120.23/17.01 | |
% 120.23/17.01 | Case 2:
% 120.23/17.01 | |
% 120.23/17.01 | | (100) ~ aSet0(slcrc0)
% 120.23/17.01 | |
% 120.23/17.01 | | PRED_UNIFY: (1), (100) imply:
% 120.23/17.01 | | (101) $false
% 120.23/17.01 | |
% 120.23/17.01 | | CLOSE: (101) is inconsistent.
% 120.23/17.01 | |
% 120.23/17.01 | End of split
% 120.23/17.01 |
% 120.23/17.01 End of proof
% 120.23/17.01 % SZS output end Proof for theBenchmark
% 120.23/17.01
% 120.23/17.01 16396ms
%------------------------------------------------------------------------------