TSTP Solution File: NUM581+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM581+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 : n019.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 11:48:45 EDT 2023
% Result : Theorem 118.50s 16.69s
% Output : Proof 118.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM581+3 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n019.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 12:01:28 EDT 2023
% 0.20/0.34 % CPUTime :
% 0.20/0.59 ________ _____
% 0.20/0.59 ___ __ \_________(_)________________________________
% 0.20/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.59
% 0.20/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.59 (2023-06-19)
% 0.20/0.59
% 0.20/0.59 (c) Philipp Rümmer, 2009-2023
% 0.20/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.59 Amanda Stjerna.
% 0.20/0.59 Free software under BSD-3-Clause.
% 0.20/0.59
% 0.20/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.59
% 0.20/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.56/1.46 Prover 4: Preprocessing ...
% 4.56/1.47 Prover 1: Preprocessing ...
% 4.56/1.50 Prover 0: Preprocessing ...
% 4.56/1.50 Prover 5: Preprocessing ...
% 4.56/1.50 Prover 2: Preprocessing ...
% 4.56/1.50 Prover 3: Preprocessing ...
% 4.56/1.50 Prover 6: Preprocessing ...
% 14.83/2.82 Prover 3: Constructing countermodel ...
% 14.83/2.83 Prover 6: Proving ...
% 14.83/2.84 Prover 1: Constructing countermodel ...
% 17.06/3.09 Prover 5: Proving ...
% 20.03/3.62 Prover 2: Proving ...
% 28.58/4.65 Prover 4: Constructing countermodel ...
% 32.62/5.16 Prover 0: Proving ...
% 83.42/11.87 Prover 2: stopped
% 83.42/11.87 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 84.47/12.02 Prover 7: Preprocessing ...
% 86.86/12.29 Prover 7: Constructing countermodel ...
% 99.89/13.95 Prover 5: stopped
% 99.89/13.96 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 100.85/14.14 Prover 8: Preprocessing ...
% 103.18/14.40 Prover 8: Warning: ignoring some quantifiers
% 103.18/14.42 Prover 8: Constructing countermodel ...
% 114.86/15.96 Prover 1: stopped
% 114.86/15.96 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 115.92/16.07 Prover 9: Preprocessing ...
% 115.92/16.12 Prover 7: Found proof (size 76)
% 115.92/16.13 Prover 7: proved (4239ms)
% 115.92/16.13 Prover 8: stopped
% 115.92/16.13 Prover 4: stopped
% 115.92/16.13 Prover 6: stopped
% 115.92/16.14 Prover 3: stopped
% 115.92/16.14 Prover 0: stopped
% 118.50/16.69 Prover 9: Constructing countermodel ...
% 118.50/16.69 Prover 9: stopped
% 118.50/16.69
% 118.50/16.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 118.50/16.69
% 118.50/16.72 % SZS output start Proof for theBenchmark
% 118.50/16.72 Assumptions after simplification:
% 118.50/16.72 ---------------------------------
% 118.50/16.72
% 118.50/16.72 (mDefCons)
% 118.96/16.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 118.96/16.79 (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~
% 118.96/16.79 aElement0(v1) | ~ aSet0(v3) | ~ aSet0(v0) | ? [v4: $i] : ($i(v4) & ( ~
% 118.96/16.79 aElementOf0(v4, v3) | ~ aElement0(v4) | ( ~ (v4 = v1) & ~
% 118.96/16.79 aElementOf0(v4, v0))) & (aElementOf0(v4, v3) | (aElement0(v4) & (v4 =
% 118.96/16.79 v1 | aElementOf0(v4, v0)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 118.96/16.79 $i] : ! [v3: $i] : (v3 = v1 | ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~
% 118.96/16.79 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) |
% 118.96/16.79 ~ aSet0(v0) | aElementOf0(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 118.96/16.79 $i] : ! [v3: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 118.96/16.79 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~
% 118.96/16.79 aSet0(v0) | aElement0(v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 118.96/16.79 [v3: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 118.96/16.79 ~ $i(v0) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ aElement0(v1) | ~
% 118.96/16.79 aSet0(v0) | aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 118.96/16.79 ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 118.96/16.79 aElement0(v1) | ~ aSet0(v0) | aElementOf0(v1, v2)) & ! [v0: $i] : ! [v1:
% 118.96/16.79 $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~
% 118.96/16.79 $i(v0) | ~ aElement0(v1) | ~ aSet0(v0) | aSet0(v2))
% 118.96/16.79
% 118.96/16.79 (mDefSub)
% 118.96/16.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 118.96/16.80 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) |
% 118.96/16.80 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) |
% 118.96/16.80 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i]
% 118.96/16.80 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) |
% 118.96/16.80 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)))
% 118.96/16.80
% 118.96/16.80 (mEOfElem)
% 118.96/16.80 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) |
% 118.96/16.80 ~ aSet0(v0) | aElement0(v1))
% 118.96/16.80
% 118.96/16.80 (mNATSet)
% 118.96/16.80 $i(szNzAzT0) & isCountable0(szNzAzT0) & aSet0(szNzAzT0)
% 118.96/16.80
% 118.96/16.80 (mZeroLess)
% 118.96/16.80 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0,
% 118.96/16.80 szNzAzT0) | sdtlseqdt0(sz00, v0))
% 118.96/16.80
% 118.96/16.80 (mZeroNum)
% 118.96/16.80 $i(sz00) & $i(szNzAzT0) & aElementOf0(sz00, szNzAzT0)
% 118.96/16.80
% 118.96/16.80 (m__)
% 118.96/16.81 $i(xQ) & $i(xi) & $i(xN) & $i(xS) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 118.96/16.81 ? [v3: $i] : (sdtlpdtrp0(xN, xi) = v0 & szmzizndt0(v0) = v1 & sdtpldt0(xQ, v1)
% 118.96/16.81 = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v3, v2) &
% 118.96/16.81 aElementOf0(v1, v0) & aSet0(v2) & ~ aSubsetOf0(v2, xS) & ~ aElementOf0(v3,
% 118.96/16.81 xS) & ! [v4: $i] : (v4 = v1 | ~ $i(v4) | ~ aElementOf0(v4, v2) |
% 118.96/16.81 aElementOf0(v4, xQ)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v2) |
% 118.96/16.81 aElement0(v4)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v0) |
% 118.96/16.81 sdtlseqdt0(v1, v4)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, xQ) |
% 118.96/16.81 ~ aElement0(v4) | aElementOf0(v4, v2)) & ( ~ aElement0(v1) |
% 118.96/16.81 aElementOf0(v1, v2)))
% 118.96/16.81
% 118.96/16.81 (m__3623)
% 118.96/16.83 sdtlpdtrp0(xN, sz00) = xS & szDzozmdt0(xN) = szNzAzT0 & $i(xN) & $i(xS) &
% 118.96/16.83 $i(sz00) & $i(szNzAzT0) & aFunction0(xN) & ! [v0: $i] : ! [v1: $i] : ( ~
% 118.96/16.83 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~
% 118.96/16.83 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i]
% 118.96/16.83 : ? [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xN, v4) = v5 & szmzizndt0(v1) = v2
% 118.96/16.83 & szszuzczcdt0(v0) = v4 & sdtmndt0(v1, v2) = v3 & $i(v5) & $i(v4) & $i(v3)
% 118.96/16.83 & $i(v2) & aSubsetOf0(v5, v3) & isCountable0(v5) & aElementOf0(v2, v1) &
% 118.96/16.83 aSet0(v5) & aSet0(v3) & ~ aElementOf0(v2, v3) & ! [v6: $i] : (v6 = v2 |
% 118.96/16.83 ~ $i(v6) | ~ aElementOf0(v6, v1) | ~ aElement0(v6) | aElementOf0(v6,
% 118.96/16.83 v3)) & ! [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6, v5) |
% 118.96/16.83 aElementOf0(v6, v3)) & ! [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6, v3)
% 118.96/16.83 | aElementOf0(v6, v1)) & ! [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6,
% 118.96/16.83 v3) | aElement0(v6)) & ! [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6,
% 118.96/16.83 v1) | sdtlseqdt0(v2, v6)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 118.96/16.83 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ isCountable0(v1) | ~
% 118.96/16.83 aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | ? [v2: $i] : ? [v3: $i] : ?
% 118.96/16.83 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ($i(v6) & ((sdtlpdtrp0(xN, v4) = v5 &
% 118.96/16.83 szmzizndt0(v1) = v2 & szszuzczcdt0(v0) = v4 & sdtmndt0(v1, v2) = v3 &
% 118.96/16.83 $i(v5) & $i(v4) & $i(v3) & $i(v2) & aSubsetOf0(v5, v3) &
% 118.96/16.83 isCountable0(v5) & aElementOf0(v2, v1) & aSet0(v5) & aSet0(v3) & ~
% 118.96/16.83 aElementOf0(v2, v3) & ! [v7: $i] : (v7 = v2 | ~ $i(v7) | ~
% 118.96/16.83 aElementOf0(v7, v1) | ~ aElement0(v7) | aElementOf0(v7, v3)) & !
% 118.96/16.83 [v7: $i] : ( ~ $i(v7) | ~ aElementOf0(v7, v5) | aElementOf0(v7, v3))
% 118.96/16.83 & ! [v7: $i] : ( ~ $i(v7) | ~ aElementOf0(v7, v3) | aElementOf0(v7,
% 118.96/16.83 v1)) & ! [v7: $i] : ( ~ $i(v7) | ~ aElementOf0(v7, v3) |
% 118.96/16.83 aElement0(v7)) & ! [v7: $i] : ( ~ $i(v7) | ~ aElementOf0(v7, v1) |
% 118.96/16.83 sdtlseqdt0(v2, v7))) | (aElementOf0(v6, v1) & ~ aElementOf0(v6,
% 118.96/16.83 szNzAzT0))))) & ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) =
% 118.96/16.83 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i]
% 118.96/16.83 : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (sdtlpdtrp0(xN, v0) = v2 &
% 118.96/16.83 $i(v6) & $i(v2) & ( ~ isCountable0(v2) | (sdtlpdtrp0(xN, v1) = v5 &
% 118.96/16.83 szmzizndt0(v2) = v3 & sdtmndt0(v2, v3) = v4 & $i(v5) & $i(v4) & $i(v3)
% 118.96/16.83 & aSubsetOf0(v5, v4) & isCountable0(v5) & aElementOf0(v3, v2) &
% 118.96/16.83 aSet0(v5) & aSet0(v4) & ~ aElementOf0(v3, v4) & ! [v7: $i] : (v7 =
% 118.96/16.83 v3 | ~ $i(v7) | ~ aElementOf0(v7, v2) | ~ aElement0(v7) |
% 118.96/16.83 aElementOf0(v7, v4)) & ! [v7: $i] : ( ~ $i(v7) | ~ aElementOf0(v7,
% 118.96/16.83 v5) | aElementOf0(v7, v4)) & ! [v7: $i] : ( ~ $i(v7) | ~
% 118.96/16.83 aElementOf0(v7, v4) | aElementOf0(v7, v2)) & ! [v7: $i] : ( ~
% 118.96/16.83 $i(v7) | ~ aElementOf0(v7, v4) | aElement0(v7)) & ! [v7: $i] : ( ~
% 118.96/16.83 $i(v7) | ~ aElementOf0(v7, v2) | sdtlseqdt0(v3, v7))) | ( ~
% 118.96/16.83 aSubsetOf0(v2, szNzAzT0) & ( ~ aSet0(v2) | (aElementOf0(v6, v2) & ~
% 118.96/16.83 aElementOf0(v6, szNzAzT0)))))))
% 118.96/16.83
% 118.96/16.83 (m__3671)
% 118.96/16.83 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 118.96/16.83 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v2, v1) |
% 118.96/16.83 ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v2, szNzAzT0)) & ! [v0: $i] : !
% 118.96/16.83 [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0,
% 118.96/16.83 szNzAzT0) | aSubsetOf0(v1, szNzAzT0)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 118.96/16.83 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) |
% 118.96/16.83 isCountable0(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) =
% 118.96/16.83 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | aSet0(v1))
% 118.96/16.83
% 118.96/16.84 (m__3754)
% 118.96/16.84 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 118.96/16.84 : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) |
% 118.96/16.84 ~ $i(v4) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v0) | ~
% 118.96/16.84 aElementOf0(v4, v2) | ~ aElementOf0(v1, szNzAzT0) | ~ aElementOf0(v0,
% 118.96/16.84 szNzAzT0) | aElementOf0(v4, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 118.96/16.84 : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) |
% 118.96/16.84 ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v0) | ~ aElementOf0(v1, szNzAzT0)
% 118.96/16.84 | ~ aElementOf0(v0, szNzAzT0) | aSubsetOf0(v2, v3))
% 118.96/16.84
% 118.96/16.84 (m__3989)
% 118.96/16.84 $i(xi) & $i(szNzAzT0) & aElementOf0(xi, szNzAzT0)
% 118.96/16.84
% 118.96/16.84 (m__3989_02)
% 118.96/16.84 $i(xQ) & $i(xi) & $i(xN) & $i(xk) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 118.96/16.84 ? [v3: $i] : (sdtlpdtrp0(xN, xi) = v0 & slbdtsldtrb0(v2, xk) = v3 &
% 118.96/16.84 szmzizndt0(v0) = v1 & sbrdtbr0(xQ) = xk & sdtmndt0(v0, v1) = v2 & $i(v3) &
% 118.96/16.84 $i(v2) & $i(v1) & $i(v0) & aSubsetOf0(xQ, v2) & aElementOf0(v1, v0) &
% 118.96/16.84 aElementOf0(xQ, v3) & aSet0(v2) & aSet0(xQ) & ~ aElementOf0(v1, v2) & !
% 118.96/16.84 [v4: $i] : (v4 = v1 | ~ $i(v4) | ~ aElementOf0(v4, v0) | ~ aElement0(v4)
% 118.96/16.84 | aElementOf0(v4, v2)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v2)
% 118.96/16.84 | aElementOf0(v4, v0)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v2)
% 118.96/16.84 | aElement0(v4)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v0) |
% 118.96/16.84 sdtlseqdt0(v1, v4)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, xQ) |
% 118.96/16.84 aElementOf0(v4, v2)))
% 118.96/16.84
% 118.96/16.84 (m__4007)
% 118.96/16.84 $i(xQ) & $i(xi) & $i(xN) & $i(xK) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 118.96/16.84 (sdtlpdtrp0(xN, xi) = v0 & szmzizndt0(v0) = v1 & sbrdtbr0(v2) = xK &
% 118.96/16.84 sdtpldt0(xQ, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v1, v0) &
% 118.96/16.84 aSet0(v2) & ! [v3: $i] : (v3 = v1 | ~ $i(v3) | ~ aElementOf0(v3, v2) |
% 118.96/16.84 aElementOf0(v3, xQ)) & ! [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v2) |
% 118.96/16.84 aElement0(v3)) & ! [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v0) |
% 118.96/16.84 sdtlseqdt0(v1, v3)) & ! [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, xQ) |
% 118.96/16.84 ~ aElement0(v3) | aElementOf0(v3, v2)) & ( ~ aElement0(v1) |
% 118.96/16.84 aElementOf0(v1, v2)))
% 118.96/16.84
% 118.96/16.84 (function-axioms)
% 118.96/16.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 118.96/16.85 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 118.96/16.85 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 118.96/16.85 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 118.96/16.85 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 118.96/16.85 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 118.96/16.85 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 118.96/16.85 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 118.96/16.85 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 118.96/16.85 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~
% 118.96/16.85 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 118.96/16.85 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) &
% 118.96/16.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 118.96/16.85 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 118.96/16.85 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 118.96/16.85 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 118.96/16.85 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 118.96/16.85 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 118.96/16.85 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 118.96/16.85 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 118.96/16.85 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 118.96/16.85 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 118.96/16.85 v0))
% 118.96/16.85
% 118.96/16.85 Further assumptions not needed in the proof:
% 118.96/16.85 --------------------------------------------
% 118.96/16.85 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 118.96/16.85 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01,
% 118.96/16.85 mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg,
% 118.96/16.85 mDefSel, mDiffCons, mDirichlet, mDomSet, mElmSort, mEmpFin, mFConsSet,
% 118.96/16.85 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm,
% 118.96/16.85 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans,
% 118.96/16.85 mMinMin, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess,
% 118.96/16.85 mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort,
% 118.96/16.85 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum,
% 118.96/16.85 m__3291, m__3398, m__3418, m__3435, m__3453, m__3462, m__3520, m__3533, m__3821
% 118.96/16.85
% 118.96/16.85 Those formulas are unsatisfiable:
% 118.96/16.85 ---------------------------------
% 118.96/16.85
% 118.96/16.85 Begin of proof
% 118.96/16.85 |
% 118.96/16.85 | ALPHA: (mDefSub) implies:
% 118.96/16.85 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 118.96/16.85 | $i(v0) | ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~
% 118.96/16.85 | aSet0(v0) | aElementOf0(v2, v0))
% 118.96/16.85 |
% 118.96/16.85 | ALPHA: (mDefCons) implies:
% 118.96/16.85 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 118.96/16.85 | (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 118.96/16.85 | $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) |
% 118.96/16.85 | aElementOf0(v3, v0))
% 118.96/16.85 |
% 118.96/16.85 | ALPHA: (mNATSet) implies:
% 118.96/16.85 | (3) aSet0(szNzAzT0)
% 118.96/16.85 |
% 118.96/16.85 | ALPHA: (mZeroNum) implies:
% 118.96/16.85 | (4) aElementOf0(sz00, szNzAzT0)
% 118.96/16.85 |
% 118.96/16.85 | ALPHA: (mZeroLess) implies:
% 118.96/16.85 | (5) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) |
% 118.96/16.85 | sdtlseqdt0(sz00, v0))
% 118.96/16.85 |
% 118.96/16.85 | ALPHA: (m__3623) implies:
% 118.96/16.85 | (6) $i(sz00)
% 118.96/16.85 | (7) sdtlpdtrp0(xN, sz00) = xS
% 118.96/16.85 |
% 118.96/16.85 | ALPHA: (m__3671) implies:
% 118.96/16.86 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1)
% 118.96/16.86 | | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~ aElementOf0(v0,
% 118.96/16.86 | szNzAzT0) | aElementOf0(v2, szNzAzT0))
% 118.96/16.86 |
% 118.96/16.86 | ALPHA: (m__3754) implies:
% 118.96/16.86 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 118.96/16.86 | ~ (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) | ~
% 118.96/16.86 | $i(v4) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v0) | ~
% 118.96/16.86 | aElementOf0(v4, v2) | ~ aElementOf0(v1, szNzAzT0) | ~
% 118.96/16.86 | aElementOf0(v0, szNzAzT0) | aElementOf0(v4, v3))
% 118.96/16.86 |
% 118.96/16.86 | ALPHA: (m__3989) implies:
% 118.96/16.86 | (10) aElementOf0(xi, szNzAzT0)
% 118.96/16.86 | (11) $i(szNzAzT0)
% 118.96/16.86 |
% 118.96/16.86 | ALPHA: (m__3989_02) implies:
% 118.96/16.86 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 118.96/16.86 | (sdtlpdtrp0(xN, xi) = v0 & slbdtsldtrb0(v2, xk) = v3 & szmzizndt0(v0)
% 118.96/16.86 | = v1 & sbrdtbr0(xQ) = xk & sdtmndt0(v0, v1) = v2 & $i(v3) & $i(v2) &
% 118.96/16.86 | $i(v1) & $i(v0) & aSubsetOf0(xQ, v2) & aElementOf0(v1, v0) &
% 118.96/16.86 | aElementOf0(xQ, v3) & aSet0(v2) & aSet0(xQ) & ~ aElementOf0(v1, v2)
% 118.96/16.86 | & ! [v4: $i] : (v4 = v1 | ~ $i(v4) | ~ aElementOf0(v4, v0) | ~
% 118.96/16.86 | aElement0(v4) | aElementOf0(v4, v2)) & ! [v4: $i] : ( ~ $i(v4) |
% 118.96/16.86 | ~ aElementOf0(v4, v2) | aElementOf0(v4, v0)) & ! [v4: $i] : ( ~
% 118.96/16.86 | $i(v4) | ~ aElementOf0(v4, v2) | aElement0(v4)) & ! [v4: $i] : (
% 118.96/16.86 | ~ $i(v4) | ~ aElementOf0(v4, v0) | sdtlseqdt0(v1, v4)) & ! [v4:
% 118.96/16.86 | $i] : ( ~ $i(v4) | ~ aElementOf0(v4, xQ) | aElementOf0(v4, v2)))
% 118.96/16.86 |
% 118.96/16.86 | ALPHA: (m__4007) implies:
% 118.96/16.86 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtlpdtrp0(xN, xi) = v0 &
% 118.96/16.86 | szmzizndt0(v0) = v1 & sbrdtbr0(v2) = xK & sdtpldt0(xQ, v1) = v2 &
% 118.96/16.86 | $i(v2) & $i(v1) & $i(v0) & aElementOf0(v1, v0) & aSet0(v2) & ! [v3:
% 118.96/16.86 | $i] : (v3 = v1 | ~ $i(v3) | ~ aElementOf0(v3, v2) |
% 118.96/16.86 | aElementOf0(v3, xQ)) & ! [v3: $i] : ( ~ $i(v3) | ~
% 118.96/16.86 | aElementOf0(v3, v2) | aElement0(v3)) & ! [v3: $i] : ( ~ $i(v3) |
% 118.96/16.86 | ~ aElementOf0(v3, v0) | sdtlseqdt0(v1, v3)) & ! [v3: $i] : ( ~
% 118.96/16.86 | $i(v3) | ~ aElementOf0(v3, xQ) | ~ aElement0(v3) |
% 118.96/16.86 | aElementOf0(v3, v2)) & ( ~ aElement0(v1) | aElementOf0(v1, v2)))
% 118.96/16.86 |
% 118.96/16.86 | ALPHA: (m__) implies:
% 118.96/16.86 | (14) $i(xi)
% 118.96/16.86 | (15) $i(xQ)
% 118.96/16.86 | (16) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 118.96/16.86 | (sdtlpdtrp0(xN, xi) = v0 & szmzizndt0(v0) = v1 & sdtpldt0(xQ, v1) = v2
% 118.96/16.86 | & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v3, v2) &
% 118.96/16.86 | aElementOf0(v1, v0) & aSet0(v2) & ~ aSubsetOf0(v2, xS) & ~
% 118.96/16.86 | aElementOf0(v3, xS) & ! [v4: $i] : (v4 = v1 | ~ $i(v4) | ~
% 118.96/16.86 | aElementOf0(v4, v2) | aElementOf0(v4, xQ)) & ! [v4: $i] : ( ~
% 118.96/16.86 | $i(v4) | ~ aElementOf0(v4, v2) | aElement0(v4)) & ! [v4: $i] : (
% 118.96/16.86 | ~ $i(v4) | ~ aElementOf0(v4, v0) | sdtlseqdt0(v1, v4)) & ! [v4:
% 118.96/16.86 | $i] : ( ~ $i(v4) | ~ aElementOf0(v4, xQ) | ~ aElement0(v4) |
% 118.96/16.86 | aElementOf0(v4, v2)) & ( ~ aElement0(v1) | aElementOf0(v1, v2)))
% 118.96/16.86 |
% 118.96/16.86 | ALPHA: (function-axioms) implies:
% 118.96/16.87 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 118.96/16.87 | (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) = v0))
% 118.96/16.87 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 118.96/16.87 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 118.96/16.87 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 118.96/16.87 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0))
% 118.96/16.87 |
% 118.96/16.87 | DELTA: instantiating (13) with fresh symbols all_70_0, all_70_1, all_70_2
% 118.96/16.87 | gives:
% 118.96/16.87 | (20) sdtlpdtrp0(xN, xi) = all_70_2 & szmzizndt0(all_70_2) = all_70_1 &
% 118.96/16.87 | sbrdtbr0(all_70_0) = xK & sdtpldt0(xQ, all_70_1) = all_70_0 &
% 118.96/16.87 | $i(all_70_0) & $i(all_70_1) & $i(all_70_2) & aElementOf0(all_70_1,
% 118.96/16.87 | all_70_2) & aSet0(all_70_0) & ! [v0: any] : (v0 = all_70_1 | ~
% 118.96/16.87 | $i(v0) | ~ aElementOf0(v0, all_70_0) | aElementOf0(v0, xQ)) & !
% 118.96/16.87 | [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_70_0) | aElement0(v0))
% 118.96/16.87 | & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_70_2) |
% 118.96/16.87 | sdtlseqdt0(all_70_1, v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 118.96/16.87 | aElementOf0(v0, xQ) | ~ aElement0(v0) | aElementOf0(v0, all_70_0))
% 118.96/16.87 | & ( ~ aElement0(all_70_1) | aElementOf0(all_70_1, all_70_0))
% 118.96/16.87 |
% 118.96/16.87 | ALPHA: (20) implies:
% 118.96/16.87 | (21) sdtpldt0(xQ, all_70_1) = all_70_0
% 118.96/16.87 | (22) szmzizndt0(all_70_2) = all_70_1
% 118.96/16.87 | (23) sdtlpdtrp0(xN, xi) = all_70_2
% 118.96/16.87 |
% 118.96/16.87 | DELTA: instantiating (16) with fresh symbols all_73_0, all_73_1, all_73_2,
% 118.96/16.87 | all_73_3 gives:
% 118.96/16.87 | (24) sdtlpdtrp0(xN, xi) = all_73_3 & szmzizndt0(all_73_3) = all_73_2 &
% 118.96/16.87 | sdtpldt0(xQ, all_73_2) = all_73_1 & $i(all_73_0) & $i(all_73_1) &
% 118.96/16.87 | $i(all_73_2) & $i(all_73_3) & aElementOf0(all_73_0, all_73_1) &
% 118.96/16.87 | aElementOf0(all_73_2, all_73_3) & aSet0(all_73_1) & ~
% 118.96/16.87 | aSubsetOf0(all_73_1, xS) & ~ aElementOf0(all_73_0, xS) & ! [v0: any]
% 118.96/16.87 | : (v0 = all_73_2 | ~ $i(v0) | ~ aElementOf0(v0, all_73_1) |
% 118.96/16.87 | aElementOf0(v0, xQ)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0,
% 118.96/16.87 | all_73_1) | aElement0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 118.96/16.87 | aElementOf0(v0, all_73_3) | sdtlseqdt0(all_73_2, v0)) & ! [v0: $i]
% 118.96/16.87 | : ( ~ $i(v0) | ~ aElementOf0(v0, xQ) | ~ aElement0(v0) |
% 118.96/16.87 | aElementOf0(v0, all_73_1)) & ( ~ aElement0(all_73_2) |
% 118.96/16.87 | aElementOf0(all_73_2, all_73_1))
% 118.96/16.87 |
% 118.96/16.87 | ALPHA: (24) implies:
% 118.96/16.87 | (25) ~ aElementOf0(all_73_0, xS)
% 118.96/16.87 | (26) aElementOf0(all_73_2, all_73_3)
% 118.96/16.87 | (27) aElementOf0(all_73_0, all_73_1)
% 118.96/16.87 | (28) $i(all_73_2)
% 118.96/16.87 | (29) $i(all_73_1)
% 118.96/16.87 | (30) $i(all_73_0)
% 118.96/16.87 | (31) sdtpldt0(xQ, all_73_2) = all_73_1
% 118.96/16.88 | (32) szmzizndt0(all_73_3) = all_73_2
% 118.96/16.88 | (33) sdtlpdtrp0(xN, xi) = all_73_3
% 118.96/16.88 |
% 118.96/16.88 | DELTA: instantiating (12) with fresh symbols all_76_0, all_76_1, all_76_2,
% 118.96/16.88 | all_76_3 gives:
% 118.96/16.88 | (34) sdtlpdtrp0(xN, xi) = all_76_3 & slbdtsldtrb0(all_76_1, xk) = all_76_0
% 118.96/16.88 | & szmzizndt0(all_76_3) = all_76_2 & sbrdtbr0(xQ) = xk &
% 118.96/16.88 | sdtmndt0(all_76_3, all_76_2) = all_76_1 & $i(all_76_0) & $i(all_76_1)
% 118.96/16.88 | & $i(all_76_2) & $i(all_76_3) & aSubsetOf0(xQ, all_76_1) &
% 118.96/16.88 | aElementOf0(all_76_2, all_76_3) & aElementOf0(xQ, all_76_0) &
% 118.96/16.88 | aSet0(all_76_1) & aSet0(xQ) & ~ aElementOf0(all_76_2, all_76_1) & !
% 118.96/16.88 | [v0: any] : (v0 = all_76_2 | ~ $i(v0) | ~ aElementOf0(v0, all_76_3)
% 118.96/16.88 | | ~ aElement0(v0) | aElementOf0(v0, all_76_1)) & ! [v0: $i] : ( ~
% 118.96/16.88 | $i(v0) | ~ aElementOf0(v0, all_76_1) | aElementOf0(v0, all_76_3)) &
% 118.96/16.88 | ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_76_1) |
% 118.96/16.88 | aElement0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0,
% 118.96/16.88 | all_76_3) | sdtlseqdt0(all_76_2, v0)) & ! [v0: $i] : ( ~ $i(v0) |
% 118.96/16.88 | ~ aElementOf0(v0, xQ) | aElementOf0(v0, all_76_1))
% 118.96/16.88 |
% 118.96/16.88 | ALPHA: (34) implies:
% 118.96/16.88 | (35) aSet0(xQ)
% 118.96/16.88 | (36) aSet0(all_76_1)
% 118.96/16.88 | (37) aSubsetOf0(xQ, all_76_1)
% 118.96/16.88 | (38) $i(all_76_1)
% 118.96/16.88 | (39) szmzizndt0(all_76_3) = all_76_2
% 118.96/16.88 | (40) sdtlpdtrp0(xN, xi) = all_76_3
% 118.96/16.88 | (41) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_76_1) |
% 118.96/16.88 | aElementOf0(v0, all_76_3))
% 118.96/16.88 |
% 118.96/16.88 | GROUND_INST: instantiating (18) with all_70_0, all_73_1, all_70_1, xQ,
% 118.96/16.88 | simplifying with (21) gives:
% 118.96/16.88 | (42) all_73_1 = all_70_0 | ~ (sdtpldt0(xQ, all_70_1) = all_73_1)
% 118.96/16.88 |
% 118.96/16.88 | GROUND_INST: instantiating (17) with all_73_2, all_76_2, all_73_3, simplifying
% 118.96/16.88 | with (32) gives:
% 118.96/16.88 | (43) all_76_2 = all_73_2 | ~ (szmzizndt0(all_73_3) = all_76_2)
% 118.96/16.88 |
% 118.96/16.88 | GROUND_INST: instantiating (17) with all_70_1, all_76_2, all_70_2, simplifying
% 118.96/16.88 | with (22) gives:
% 118.96/16.88 | (44) all_76_2 = all_70_1 | ~ (szmzizndt0(all_70_2) = all_76_2)
% 118.96/16.88 |
% 118.96/16.88 | GROUND_INST: instantiating (19) with all_73_3, all_76_3, xi, xN, simplifying
% 118.96/16.88 | with (33), (40) gives:
% 118.96/16.88 | (45) all_76_3 = all_73_3
% 118.96/16.88 |
% 118.96/16.88 | GROUND_INST: instantiating (19) with all_70_2, all_76_3, xi, xN, simplifying
% 118.96/16.88 | with (23), (40) gives:
% 118.96/16.88 | (46) all_76_3 = all_70_2
% 118.96/16.88 |
% 118.96/16.88 | COMBINE_EQS: (45), (46) imply:
% 118.96/16.88 | (47) all_73_3 = all_70_2
% 118.96/16.88 |
% 118.96/16.88 | SIMP: (47) implies:
% 118.96/16.88 | (48) all_73_3 = all_70_2
% 118.96/16.88 |
% 118.96/16.88 | REDUCE: (39), (46) imply:
% 118.96/16.88 | (49) szmzizndt0(all_70_2) = all_76_2
% 118.96/16.88 |
% 118.96/16.88 | REDUCE: (26), (48) imply:
% 118.96/16.88 | (50) aElementOf0(all_73_2, all_70_2)
% 118.96/16.88 |
% 118.96/16.88 | BETA: splitting (44) gives:
% 118.96/16.88 |
% 118.96/16.88 | Case 1:
% 118.96/16.88 | |
% 118.96/16.88 | | (51) ~ (szmzizndt0(all_70_2) = all_76_2)
% 118.96/16.88 | |
% 118.96/16.88 | | PRED_UNIFY: (49), (51) imply:
% 118.96/16.88 | | (52) $false
% 118.96/16.89 | |
% 118.96/16.89 | | CLOSE: (52) is inconsistent.
% 118.96/16.89 | |
% 118.96/16.89 | Case 2:
% 118.96/16.89 | |
% 118.96/16.89 | | (53) all_76_2 = all_70_1
% 118.96/16.89 | |
% 118.96/16.89 | | BETA: splitting (43) gives:
% 118.96/16.89 | |
% 118.96/16.89 | | Case 1:
% 118.96/16.89 | | |
% 118.96/16.89 | | | (54) ~ (szmzizndt0(all_73_3) = all_76_2)
% 118.96/16.89 | | |
% 118.96/16.89 | | | REDUCE: (48), (53), (54) imply:
% 118.96/16.89 | | | (55) ~ (szmzizndt0(all_70_2) = all_70_1)
% 118.96/16.89 | | |
% 118.96/16.89 | | | PRED_UNIFY: (22), (55) imply:
% 118.96/16.89 | | | (56) $false
% 118.96/16.89 | | |
% 118.96/16.89 | | | CLOSE: (56) is inconsistent.
% 118.96/16.89 | | |
% 118.96/16.89 | | Case 2:
% 118.96/16.89 | | |
% 118.96/16.89 | | | (57) all_76_2 = all_73_2
% 118.96/16.89 | | |
% 118.96/16.89 | | | COMBINE_EQS: (53), (57) imply:
% 118.96/16.89 | | | (58) all_73_2 = all_70_1
% 118.96/16.89 | | |
% 118.96/16.89 | | | SIMP: (58) implies:
% 118.96/16.89 | | | (59) all_73_2 = all_70_1
% 118.96/16.89 | | |
% 118.96/16.89 | | | REDUCE: (31), (59) imply:
% 118.96/16.89 | | | (60) sdtpldt0(xQ, all_70_1) = all_73_1
% 118.96/16.89 | | |
% 118.96/16.89 | | | REDUCE: (28), (59) imply:
% 118.96/16.89 | | | (61) $i(all_70_1)
% 118.96/16.89 | | |
% 118.96/16.89 | | | REDUCE: (50), (59) imply:
% 118.96/16.89 | | | (62) aElementOf0(all_70_1, all_70_2)
% 118.96/16.89 | | |
% 118.96/16.89 | | | BETA: splitting (42) gives:
% 118.96/16.89 | | |
% 118.96/16.89 | | | Case 1:
% 118.96/16.89 | | | |
% 118.96/16.89 | | | | (63) ~ (sdtpldt0(xQ, all_70_1) = all_73_1)
% 118.96/16.89 | | | |
% 118.96/16.89 | | | | PRED_UNIFY: (60), (63) imply:
% 118.96/16.89 | | | | (64) $false
% 118.96/16.89 | | | |
% 118.96/16.89 | | | | CLOSE: (64) is inconsistent.
% 118.96/16.89 | | | |
% 118.96/16.89 | | | Case 2:
% 118.96/16.89 | | | |
% 118.96/16.89 | | | | (65) all_73_1 = all_70_0
% 118.96/16.89 | | | |
% 118.96/16.89 | | | | REDUCE: (29), (65) imply:
% 118.96/16.89 | | | | (66) $i(all_70_0)
% 118.96/16.89 | | | |
% 118.96/16.89 | | | | REDUCE: (27), (65) imply:
% 118.96/16.89 | | | | (67) aElementOf0(all_73_0, all_70_0)
% 118.96/16.89 | | | |
% 118.96/16.89 | | | | GROUND_INST: instantiating (5) with xi, simplifying with (10), (14)
% 118.96/16.89 | | | | gives:
% 118.96/16.89 | | | | (68) sdtlseqdt0(sz00, xi)
% 118.96/16.89 | | | |
% 118.96/16.89 | | | | GROUND_INST: instantiating (mEOfElem) with szNzAzT0, all_70_1,
% 118.96/16.89 | | | | simplifying with (3), (11), (61) gives:
% 118.96/16.89 | | | | (69) ~ aElementOf0(all_70_1, szNzAzT0) | aElement0(all_70_1)
% 118.96/16.89 | | | |
% 118.96/16.89 | | | | GROUND_INST: instantiating (41) with all_73_0, simplifying with (30)
% 118.96/16.89 | | | | gives:
% 118.96/16.89 | | | | (70) ~ aElementOf0(all_73_0, all_76_1) | aElementOf0(all_73_0,
% 118.96/16.89 | | | | all_76_3)
% 118.96/16.89 | | | |
% 118.96/16.89 | | | | GROUND_INST: instantiating (1) with all_76_1, xQ, all_73_0, simplifying
% 118.96/16.89 | | | | with (15), (30), (36), (37), (38) gives:
% 118.96/16.89 | | | | (71) ~ aElementOf0(all_73_0, xQ) | aElementOf0(all_73_0, all_76_1)
% 118.96/16.89 | | | |
% 118.96/16.89 | | | | GROUND_INST: instantiating (8) with xi, all_70_2, all_70_1, simplifying
% 118.96/16.89 | | | | with (10), (14), (23), (61), (62) gives:
% 118.96/16.89 | | | | (72) aElementOf0(all_70_1, szNzAzT0)
% 118.96/16.89 | | | |
% 118.96/16.89 | | | | BETA: splitting (69) gives:
% 118.96/16.89 | | | |
% 118.96/16.89 | | | | Case 1:
% 118.96/16.89 | | | | |
% 118.96/16.89 | | | | | (73) ~ aElementOf0(all_70_1, szNzAzT0)
% 118.96/16.89 | | | | |
% 118.96/16.89 | | | | | PRED_UNIFY: (72), (73) imply:
% 118.96/16.89 | | | | | (74) $false
% 118.96/16.89 | | | | |
% 118.96/16.89 | | | | | CLOSE: (74) is inconsistent.
% 118.96/16.89 | | | | |
% 118.96/16.89 | | | | Case 2:
% 118.96/16.89 | | | | |
% 118.96/16.89 | | | | | (75) aElement0(all_70_1)
% 118.96/16.89 | | | | |
% 118.96/16.89 | | | | | GROUND_INST: instantiating (2) with xQ, all_70_1, all_70_0, all_73_0,
% 118.96/16.89 | | | | | simplifying with (15), (21), (30), (35), (61), (66),
% 118.96/16.89 | | | | | (67), (75) gives:
% 118.96/16.89 | | | | | (76) all_73_0 = all_70_1 | aElementOf0(all_73_0, xQ)
% 118.96/16.89 | | | | |
% 118.96/16.89 | | | | | GROUND_INST: instantiating (9) with xi, sz00, all_70_2, xS, all_73_0,
% 118.96/16.89 | | | | | simplifying with (4), (6), (7), (10), (14), (23), (25),
% 118.96/16.89 | | | | | (30), (68) gives:
% 118.96/16.89 | | | | | (77) ~ aElementOf0(all_73_0, all_70_2)
% 118.96/16.89 | | | | |
% 118.96/16.89 | | | | | BETA: splitting (70) gives:
% 118.96/16.89 | | | | |
% 118.96/16.89 | | | | | Case 1:
% 118.96/16.89 | | | | | |
% 118.96/16.89 | | | | | | (78) ~ aElementOf0(all_73_0, all_76_1)
% 118.96/16.89 | | | | | |
% 118.96/16.89 | | | | | | BETA: splitting (71) gives:
% 118.96/16.89 | | | | | |
% 118.96/16.89 | | | | | | Case 1:
% 118.96/16.89 | | | | | | |
% 118.96/16.89 | | | | | | | (79) ~ aElementOf0(all_73_0, xQ)
% 118.96/16.89 | | | | | | |
% 118.96/16.89 | | | | | | | BETA: splitting (76) gives:
% 118.96/16.89 | | | | | | |
% 118.96/16.89 | | | | | | | Case 1:
% 118.96/16.89 | | | | | | | |
% 118.96/16.89 | | | | | | | | (80) aElementOf0(all_73_0, xQ)
% 118.96/16.89 | | | | | | | |
% 118.96/16.89 | | | | | | | | PRED_UNIFY: (79), (80) imply:
% 118.96/16.89 | | | | | | | | (81) $false
% 118.96/16.89 | | | | | | | |
% 118.96/16.89 | | | | | | | | CLOSE: (81) is inconsistent.
% 118.96/16.89 | | | | | | | |
% 118.96/16.89 | | | | | | | Case 2:
% 118.96/16.89 | | | | | | | |
% 118.96/16.89 | | | | | | | | (82) all_73_0 = all_70_1
% 118.96/16.89 | | | | | | | |
% 118.96/16.89 | | | | | | | | REDUCE: (77), (82) imply:
% 118.96/16.89 | | | | | | | | (83) ~ aElementOf0(all_70_1, all_70_2)
% 118.96/16.89 | | | | | | | |
% 118.96/16.89 | | | | | | | | PRED_UNIFY: (62), (83) imply:
% 118.96/16.89 | | | | | | | | (84) $false
% 118.96/16.89 | | | | | | | |
% 118.96/16.89 | | | | | | | | CLOSE: (84) is inconsistent.
% 118.96/16.89 | | | | | | | |
% 118.96/16.89 | | | | | | | End of split
% 118.96/16.89 | | | | | | |
% 118.96/16.89 | | | | | | Case 2:
% 118.96/16.89 | | | | | | |
% 118.96/16.89 | | | | | | | (85) aElementOf0(all_73_0, all_76_1)
% 118.96/16.89 | | | | | | |
% 118.96/16.89 | | | | | | | PRED_UNIFY: (78), (85) imply:
% 118.96/16.89 | | | | | | | (86) $false
% 118.96/16.89 | | | | | | |
% 118.96/16.89 | | | | | | | CLOSE: (86) is inconsistent.
% 118.96/16.89 | | | | | | |
% 118.96/16.89 | | | | | | End of split
% 118.96/16.89 | | | | | |
% 118.96/16.89 | | | | | Case 2:
% 118.96/16.89 | | | | | |
% 118.96/16.89 | | | | | | (87) aElementOf0(all_73_0, all_76_3)
% 118.96/16.89 | | | | | |
% 118.96/16.89 | | | | | | REDUCE: (46), (87) imply:
% 118.96/16.89 | | | | | | (88) aElementOf0(all_73_0, all_70_2)
% 118.96/16.89 | | | | | |
% 118.96/16.89 | | | | | | PRED_UNIFY: (77), (88) imply:
% 118.96/16.89 | | | | | | (89) $false
% 118.96/16.89 | | | | | |
% 118.96/16.89 | | | | | | CLOSE: (89) is inconsistent.
% 118.96/16.89 | | | | | |
% 118.96/16.89 | | | | | End of split
% 118.96/16.89 | | | | |
% 118.96/16.89 | | | | End of split
% 118.96/16.89 | | | |
% 118.96/16.89 | | | End of split
% 118.96/16.89 | | |
% 118.96/16.89 | | End of split
% 118.96/16.89 | |
% 118.96/16.89 | End of split
% 118.96/16.89 |
% 118.96/16.89 End of proof
% 118.96/16.90 % SZS output end Proof for theBenchmark
% 118.96/16.90
% 118.96/16.90 16301ms
%------------------------------------------------------------------------------