TSTP Solution File: NUM582+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM582+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 : n010.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 60.52s 8.93s
% Output : Proof 80.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM582+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Aug 25 15:41:35 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.57 ________ _____
% 0.18/0.57 ___ __ \_________(_)________________________________
% 0.18/0.57 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.57 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.57 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.57
% 0.18/0.57 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.57 (2023-06-19)
% 0.18/0.57
% 0.18/0.57 (c) Philipp Rümmer, 2009-2023
% 0.18/0.57 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.57 Amanda Stjerna.
% 0.18/0.57 Free software under BSD-3-Clause.
% 0.18/0.57
% 0.18/0.57 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.57
% 0.18/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.58 Running up to 7 provers in parallel.
% 0.18/0.60 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.18/0.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 6.02/1.55 Prover 4: Preprocessing ...
% 6.02/1.56 Prover 1: Preprocessing ...
% 6.38/1.60 Prover 6: Preprocessing ...
% 6.38/1.60 Prover 0: Preprocessing ...
% 6.38/1.60 Prover 5: Preprocessing ...
% 6.38/1.60 Prover 3: Preprocessing ...
% 6.38/1.60 Prover 2: Preprocessing ...
% 20.01/3.57 Prover 1: Constructing countermodel ...
% 20.01/3.66 Prover 6: Proving ...
% 20.01/3.67 Prover 3: Constructing countermodel ...
% 22.62/3.80 Prover 5: Proving ...
% 25.40/4.31 Prover 2: Proving ...
% 36.49/5.79 Prover 4: Constructing countermodel ...
% 41.05/6.28 Prover 0: Proving ...
% 60.52/8.92 Prover 3: proved (8323ms)
% 60.52/8.92
% 60.52/8.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 60.52/8.93
% 60.52/8.94 Prover 2: stopped
% 60.52/8.94 Prover 6: stopped
% 60.52/8.96 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 60.52/8.96 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 60.52/8.97 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 60.81/8.98 Prover 5: stopped
% 60.81/8.99 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 60.81/9.00 Prover 0: stopped
% 62.12/9.01 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 63.69/9.28 Prover 8: Preprocessing ...
% 65.11/9.42 Prover 13: Preprocessing ...
% 65.11/9.42 Prover 10: Preprocessing ...
% 65.11/9.44 Prover 7: Preprocessing ...
% 65.84/9.52 Prover 11: Preprocessing ...
% 68.12/9.80 Prover 8: Warning: ignoring some quantifiers
% 68.12/9.82 Prover 8: Constructing countermodel ...
% 68.12/9.87 Prover 7: Constructing countermodel ...
% 70.40/10.16 Prover 13: Warning: ignoring some quantifiers
% 70.40/10.17 Prover 10: Constructing countermodel ...
% 71.17/10.25 Prover 13: Constructing countermodel ...
% 76.82/10.93 Prover 10: Found proof (size 29)
% 76.82/10.93 Prover 10: proved (1962ms)
% 76.82/10.93 Prover 13: stopped
% 76.82/10.93 Prover 8: stopped
% 76.82/10.93 Prover 7: stopped
% 76.82/10.93 Prover 1: stopped
% 76.82/10.94 Prover 4: stopped
% 79.53/11.58 Prover 11: Constructing countermodel ...
% 79.53/11.60 Prover 11: stopped
% 79.53/11.60
% 79.53/11.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 79.53/11.60
% 79.53/11.61 % SZS output start Proof for theBenchmark
% 79.53/11.62 Assumptions after simplification:
% 79.53/11.62 ---------------------------------
% 79.53/11.62
% 79.53/11.62 (mCountNFin_01)
% 79.53/11.62 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0))
% 79.53/11.62
% 79.53/11.62 (mDefEmp)
% 79.53/11.63 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~
% 79.53/11.63 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : (
% 79.53/11.63 ~ $i(v0) | ~ aElementOf0(v0, slcrc0))
% 79.53/11.63
% 79.53/11.63 (mZeroLess)
% 79.53/11.63 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0,
% 79.53/11.63 szNzAzT0) | sdtlseqdt0(sz00, v0))
% 79.53/11.63
% 79.53/11.63 (mZeroNum)
% 79.53/11.63 $i(sz00) & $i(szNzAzT0) & aElementOf0(sz00, szNzAzT0)
% 79.53/11.63
% 79.53/11.63 (m__)
% 79.78/11.66 $i(xi) & $i(xN) & $i(xS) & ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xi) =
% 79.78/11.66 v0 & $i(v1) & $i(v0) & aElementOf0(v1, v0) & ~ aSubsetOf0(v0, xS) & ~
% 79.78/11.66 aElementOf0(v1, xS))
% 79.78/11.66
% 79.78/11.66 (m__3623)
% 79.87/11.68 sdtlpdtrp0(xN, sz00) = xS & szDzozmdt0(xN) = szNzAzT0 & $i(xN) & $i(xS) &
% 79.87/11.68 $i(sz00) & $i(szNzAzT0) & aFunction0(xN) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 79.87/11.68 $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2 | ~ (sdtlpdtrp0(xN, v0) = v1) |
% 79.87/11.68 ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0)
% 79.87/11.68 | ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v4, v1)
% 79.87/11.68 | ~ aElementOf0(v0, szNzAzT0) | ~ aElement0(v4) | aElementOf0(v4, v3)) &
% 79.87/11.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2
% 79.87/11.68 | ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1,
% 79.87/11.68 v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~ isCountable0(v1) | ~
% 79.87/11.68 aElementOf0(v4, v1) | ~ aElementOf0(v0, szNzAzT0) | ~ aElement0(v4) | ~
% 79.87/11.68 aSet0(v1) | aElementOf0(v4, v3) | ? [v5: $i] : ($i(v5) & aElementOf0(v5,
% 79.87/11.68 v1) & ~ aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : !
% 79.87/11.68 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~
% 79.87/11.68 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) |
% 79.87/11.68 ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v4, v3) |
% 79.87/11.68 ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v4, v1)) & ! [v0: $i] : ! [v1:
% 79.87/11.68 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) =
% 79.87/11.68 v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) |
% 79.87/11.68 ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~
% 79.87/11.68 aElementOf0(v4, v3) | ~ aElementOf0(v0, szNzAzT0) | aElement0(v4)) & !
% 79.87/11.68 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 79.87/11.68 (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2)
% 79.87/11.68 = v3) | ~ $i(v4) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~
% 79.87/11.68 isCountable0(v1) | ~ aElementOf0(v4, v1) | ~ aElementOf0(v0, szNzAzT0) |
% 79.87/11.68 sdtlseqdt0(v2, v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 79.87/11.68 : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~
% 79.87/11.68 (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~ isCountable0(v1) | ~
% 79.87/11.68 aElementOf0(v4, v3) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) |
% 79.87/11.68 aElementOf0(v4, v1) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, v1) & ~
% 79.87/11.68 aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 79.87/11.68 [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) =
% 79.87/11.68 v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~
% 79.87/11.68 isCountable0(v1) | ~ aElementOf0(v4, v3) | ~ aElementOf0(v0, szNzAzT0) |
% 79.87/11.68 ~ aSet0(v1) | aElement0(v4) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, v1) &
% 79.87/11.68 ~ aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 79.87/11.68 ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1)
% 79.87/11.68 = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~
% 79.87/11.68 isCountable0(v1) | ~ aElementOf0(v4, v1) | ~ aElementOf0(v0, szNzAzT0) |
% 79.87/11.68 ~ aSet0(v1) | sdtlseqdt0(v2, v4) | ? [v5: $i] : ($i(v5) & aElementOf0(v5,
% 79.87/11.68 v1) & ~ aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : !
% 79.87/11.68 [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) =
% 79.87/11.68 v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ~
% 79.87/11.68 aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v2, v3) | ~
% 79.87/11.68 aElementOf0(v0, szNzAzT0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 79.87/11.68 [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~
% 79.87/11.68 (sdtmndt0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ~ isCountable0(v1) | ~
% 79.87/11.68 aElementOf0(v2, v3) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | ? [v4:
% 79.87/11.68 $i] : ($i(v4) & aElementOf0(v4, v1) & ~ aElementOf0(v4, szNzAzT0))) & !
% 79.87/11.68 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) =
% 79.87/11.68 v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) |
% 79.87/11.68 ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v0,
% 79.87/11.68 szNzAzT0) | aElementOf0(v2, v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 79.87/11.68 : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~
% 79.87/11.68 (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~
% 79.87/11.68 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | aSet0(v3)) & ! [v0: $i] :
% 79.87/11.68 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~
% 79.87/11.68 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~
% 79.87/11.68 aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v0,
% 79.87/11.68 szNzAzT0) | ? [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xN, v4) = v5 &
% 79.87/11.68 szszuzczcdt0(v0) = v4 & $i(v5) & $i(v4) & aSubsetOf0(v5, v3) &
% 79.87/11.68 isCountable0(v5) & aSet0(v5) & ! [v6: $i] : ( ~ $i(v6) | ~
% 79.87/11.68 aElementOf0(v6, v5) | aElementOf0(v6, v3)))) & ! [v0: $i] : ! [v1: $i]
% 79.87/11.68 : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~
% 79.87/11.68 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~
% 79.87/11.68 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) |
% 79.87/11.68 aElementOf0(v2, v1) | ? [v4: $i] : ($i(v4) & aElementOf0(v4, v1) & ~
% 79.87/11.68 aElementOf0(v4, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 79.87/11.68 [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~
% 79.87/11.68 (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ isCountable0(v1) | ~
% 79.87/11.68 aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | aSet0(v3) | ? [v4: $i] : ($i(v4)
% 79.87/11.68 & aElementOf0(v4, v1) & ~ aElementOf0(v4, szNzAzT0))) & ! [v0: $i] : !
% 79.87/11.68 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~
% 79.87/11.68 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~
% 79.87/11.68 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | ? [v4: $i]
% 79.87/11.68 : ? [v5: $i] : ? [v6: $i] : ($i(v6) & ((sdtlpdtrp0(xN, v4) = v5 &
% 79.87/11.68 szszuzczcdt0(v0) = v4 & $i(v5) & $i(v4) & aSubsetOf0(v5, v3) &
% 79.87/11.68 isCountable0(v5) & aSet0(v5) & ! [v7: $i] : ( ~ $i(v7) | ~
% 79.87/11.68 aElementOf0(v7, v5) | aElementOf0(v7, v3))) | (aElementOf0(v6, v1) &
% 79.87/11.68 ~ aElementOf0(v6, szNzAzT0)))))
% 79.87/11.68
% 79.87/11.68 (m__3754)
% 79.87/11.68 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 79.87/11.68 : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) |
% 79.87/11.68 ~ $i(v4) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v0) | ~
% 79.87/11.68 aElementOf0(v4, v2) | ~ aElementOf0(v1, szNzAzT0) | ~ aElementOf0(v0,
% 79.87/11.68 szNzAzT0) | aElementOf0(v4, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 79.87/11.68 : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) |
% 79.87/11.68 ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v0) | ~ aElementOf0(v1, szNzAzT0)
% 79.87/11.68 | ~ aElementOf0(v0, szNzAzT0) | aSubsetOf0(v2, v3))
% 79.87/11.68
% 79.87/11.68 (m__3989)
% 79.87/11.68 $i(xi) & $i(szNzAzT0) & aElementOf0(xi, szNzAzT0)
% 79.87/11.68
% 79.87/11.68 (m__3989_02)
% 79.87/11.69 $i(xQ) & $i(xi) & $i(xN) & $i(xk) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 79.87/11.69 ? [v3: $i] : (sdtlpdtrp0(xN, xi) = v0 & slbdtsldtrb0(v2, xk) = v3 &
% 79.87/11.69 szmzizndt0(v0) = v1 & sbrdtbr0(xQ) = xk & sdtmndt0(v0, v1) = v2 & $i(v3) &
% 79.87/11.69 $i(v2) & $i(v1) & $i(v0) & aSubsetOf0(xQ, v2) & aElementOf0(v1, v0) &
% 79.87/11.69 aElementOf0(xQ, v3) & aSet0(v2) & aSet0(xQ) & ~ aElementOf0(v1, v2) & !
% 79.87/11.69 [v4: $i] : (v4 = v1 | ~ $i(v4) | ~ aElementOf0(v4, v0) | ~ aElement0(v4)
% 79.87/11.69 | aElementOf0(v4, v2)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v2)
% 79.87/11.69 | aElementOf0(v4, v0)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v2)
% 79.87/11.69 | aElement0(v4)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v0) |
% 79.87/11.69 sdtlseqdt0(v1, v4)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, xQ) |
% 79.87/11.69 aElementOf0(v4, v2)))
% 79.87/11.69
% 79.87/11.69 (m__4007)
% 79.87/11.69 $i(xQ) & $i(xi) & $i(xN) & $i(xK) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 79.87/11.69 (sdtlpdtrp0(xN, xi) = v0 & szmzizndt0(v0) = v1 & sbrdtbr0(v2) = xK &
% 79.87/11.69 sdtpldt0(xQ, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v1, v0) &
% 79.87/11.69 aSet0(v2) & ! [v3: $i] : (v3 = v1 | ~ $i(v3) | ~ aElementOf0(v3, v2) |
% 79.87/11.69 aElementOf0(v3, xQ)) & ! [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v2) |
% 79.87/11.69 aElement0(v3)) & ! [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v0) |
% 79.87/11.69 sdtlseqdt0(v1, v3)) & ! [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, xQ) |
% 79.87/11.69 ~ aElement0(v3) | aElementOf0(v3, v2)) & ( ~ aElement0(v1) |
% 79.87/11.69 aElementOf0(v1, v2)))
% 79.87/11.69
% 79.87/11.69 (function-axioms)
% 79.87/11.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 79.87/11.69 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 79.87/11.69 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 79.87/11.69 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 79.87/11.69 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 79.87/11.69 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 79.87/11.69 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 79.87/11.70 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 79.87/11.70 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 79.87/11.70 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~
% 79.87/11.70 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 79.87/11.70 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) &
% 79.87/11.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 79.87/11.70 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 79.87/11.70 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 79.87/11.70 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 79.87/11.70 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 79.87/11.70 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 79.87/11.70 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 79.87/11.70 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 79.87/11.70 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 79.87/11.70 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 79.87/11.70 v0))
% 79.87/11.70
% 79.87/11.70 Further assumptions not needed in the proof:
% 79.87/11.70 --------------------------------------------
% 79.87/11.70 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 79.87/11.70 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons,
% 79.87/11.70 mDefDiff, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, mDefSel,
% 79.87/11.70 mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet,
% 79.87/11.70 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm,
% 79.87/11.70 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans,
% 79.87/11.70 mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess,
% 79.87/11.70 mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort,
% 79.87/11.70 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum,
% 79.87/11.70 m__3291, m__3398, m__3418, m__3435, m__3453, m__3462, m__3520, m__3533, m__3671,
% 79.87/11.70 m__3821
% 79.87/11.70
% 79.87/11.70 Those formulas are unsatisfiable:
% 79.87/11.70 ---------------------------------
% 79.87/11.70
% 79.87/11.70 Begin of proof
% 79.87/11.70 |
% 79.87/11.70 | ALPHA: (mDefEmp) implies:
% 79.87/11.70 | (1) aSet0(slcrc0)
% 79.87/11.70 |
% 79.87/11.70 | ALPHA: (mCountNFin_01) implies:
% 79.87/11.70 | (2) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)
% 79.87/11.70 |
% 79.87/11.70 | ALPHA: (mZeroNum) implies:
% 79.87/11.70 | (3) aElementOf0(sz00, szNzAzT0)
% 79.87/11.70 |
% 79.87/11.70 | ALPHA: (mZeroLess) implies:
% 79.87/11.70 | (4) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) |
% 79.87/11.70 | sdtlseqdt0(sz00, v0))
% 79.87/11.70 |
% 79.87/11.70 | ALPHA: (m__3623) implies:
% 79.87/11.70 | (5) $i(sz00)
% 79.87/11.70 | (6) sdtlpdtrp0(xN, sz00) = xS
% 79.87/11.70 |
% 79.87/11.70 | ALPHA: (m__3754) implies:
% 79.87/11.70 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 79.87/11.70 | (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) | ~ $i(v1)
% 79.87/11.70 | | ~ $i(v0) | ~ sdtlseqdt0(v1, v0) | ~ aElementOf0(v1, szNzAzT0) |
% 79.87/11.70 | ~ aElementOf0(v0, szNzAzT0) | aSubsetOf0(v2, v3))
% 79.87/11.70 |
% 79.87/11.70 | ALPHA: (m__3989) implies:
% 79.87/11.70 | (8) aElementOf0(xi, szNzAzT0)
% 79.87/11.70 |
% 79.87/11.70 | ALPHA: (m__3989_02) implies:
% 79.87/11.71 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtlpdtrp0(xN,
% 79.87/11.71 | xi) = v0 & slbdtsldtrb0(v2, xk) = v3 & szmzizndt0(v0) = v1 &
% 79.87/11.71 | sbrdtbr0(xQ) = xk & sdtmndt0(v0, v1) = v2 & $i(v3) & $i(v2) & $i(v1)
% 79.87/11.71 | & $i(v0) & aSubsetOf0(xQ, v2) & aElementOf0(v1, v0) & aElementOf0(xQ,
% 79.87/11.71 | v3) & aSet0(v2) & aSet0(xQ) & ~ aElementOf0(v1, v2) & ! [v4: $i]
% 79.87/11.71 | : (v4 = v1 | ~ $i(v4) | ~ aElementOf0(v4, v0) | ~ aElement0(v4) |
% 79.87/11.71 | aElementOf0(v4, v2)) & ! [v4: $i] : ( ~ $i(v4) | ~
% 79.87/11.71 | aElementOf0(v4, v2) | aElementOf0(v4, v0)) & ! [v4: $i] : ( ~
% 79.87/11.71 | $i(v4) | ~ aElementOf0(v4, v2) | aElement0(v4)) & ! [v4: $i] : (
% 79.87/11.71 | ~ $i(v4) | ~ aElementOf0(v4, v0) | sdtlseqdt0(v1, v4)) & ! [v4:
% 79.87/11.71 | $i] : ( ~ $i(v4) | ~ aElementOf0(v4, xQ) | aElementOf0(v4, v2)))
% 79.87/11.71 |
% 79.87/11.71 | ALPHA: (m__4007) implies:
% 79.87/11.71 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtlpdtrp0(xN, xi) = v0 &
% 79.87/11.71 | szmzizndt0(v0) = v1 & sbrdtbr0(v2) = xK & sdtpldt0(xQ, v1) = v2 &
% 79.87/11.71 | $i(v2) & $i(v1) & $i(v0) & aElementOf0(v1, v0) & aSet0(v2) & ! [v3:
% 79.87/11.71 | $i] : (v3 = v1 | ~ $i(v3) | ~ aElementOf0(v3, v2) |
% 79.87/11.71 | aElementOf0(v3, xQ)) & ! [v3: $i] : ( ~ $i(v3) | ~
% 79.87/11.71 | aElementOf0(v3, v2) | aElement0(v3)) & ! [v3: $i] : ( ~ $i(v3) |
% 79.87/11.71 | ~ aElementOf0(v3, v0) | sdtlseqdt0(v1, v3)) & ! [v3: $i] : ( ~
% 79.87/11.71 | $i(v3) | ~ aElementOf0(v3, xQ) | ~ aElement0(v3) |
% 79.87/11.71 | aElementOf0(v3, v2)) & ( ~ aElement0(v1) | aElementOf0(v1, v2)))
% 79.87/11.71 |
% 79.87/11.71 | ALPHA: (m__) implies:
% 79.87/11.71 | (11) $i(xi)
% 79.87/11.71 | (12) ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xi) = v0 & $i(v1) & $i(v0)
% 79.87/11.71 | & aElementOf0(v1, v0) & ~ aSubsetOf0(v0, xS) & ~ aElementOf0(v1,
% 79.87/11.71 | xS))
% 79.87/11.71 |
% 79.87/11.71 | ALPHA: (function-axioms) implies:
% 79.87/11.71 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 79.87/11.71 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0))
% 79.87/11.71 |
% 79.87/11.71 | DELTA: instantiating (12) with fresh symbols all_70_0, all_70_1 gives:
% 79.87/11.71 | (14) sdtlpdtrp0(xN, xi) = all_70_1 & $i(all_70_0) & $i(all_70_1) &
% 79.87/11.71 | aElementOf0(all_70_0, all_70_1) & ~ aSubsetOf0(all_70_1, xS) & ~
% 79.87/11.71 | aElementOf0(all_70_0, xS)
% 79.87/11.71 |
% 79.87/11.71 | ALPHA: (14) implies:
% 79.87/11.71 | (15) ~ aSubsetOf0(all_70_1, xS)
% 79.87/11.71 | (16) sdtlpdtrp0(xN, xi) = all_70_1
% 79.87/11.71 |
% 79.87/11.71 | DELTA: instantiating (10) with fresh symbols all_72_0, all_72_1, all_72_2
% 79.87/11.71 | gives:
% 79.87/11.72 | (17) sdtlpdtrp0(xN, xi) = all_72_2 & szmzizndt0(all_72_2) = all_72_1 &
% 79.87/11.72 | sbrdtbr0(all_72_0) = xK & sdtpldt0(xQ, all_72_1) = all_72_0 &
% 79.87/11.72 | $i(all_72_0) & $i(all_72_1) & $i(all_72_2) & aElementOf0(all_72_1,
% 79.87/11.72 | all_72_2) & aSet0(all_72_0) & ! [v0: any] : (v0 = all_72_1 | ~
% 79.87/11.72 | $i(v0) | ~ aElementOf0(v0, all_72_0) | aElementOf0(v0, xQ)) & !
% 79.87/11.72 | [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_72_0) | aElement0(v0))
% 79.87/11.72 | & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_72_2) |
% 79.87/11.72 | sdtlseqdt0(all_72_1, v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 79.87/11.72 | aElementOf0(v0, xQ) | ~ aElement0(v0) | aElementOf0(v0, all_72_0))
% 79.87/11.72 | & ( ~ aElement0(all_72_1) | aElementOf0(all_72_1, all_72_0))
% 79.87/11.72 |
% 79.87/11.72 | ALPHA: (17) implies:
% 79.87/11.72 | (18) sdtlpdtrp0(xN, xi) = all_72_2
% 79.87/11.72 |
% 79.87/11.72 | DELTA: instantiating (9) with fresh symbols all_75_0, all_75_1, all_75_2,
% 79.87/11.72 | all_75_3 gives:
% 80.16/11.72 | (19) sdtlpdtrp0(xN, xi) = all_75_3 & slbdtsldtrb0(all_75_1, xk) = all_75_0
% 80.16/11.72 | & szmzizndt0(all_75_3) = all_75_2 & sbrdtbr0(xQ) = xk &
% 80.16/11.72 | sdtmndt0(all_75_3, all_75_2) = all_75_1 & $i(all_75_0) & $i(all_75_1)
% 80.16/11.72 | & $i(all_75_2) & $i(all_75_3) & aSubsetOf0(xQ, all_75_1) &
% 80.16/11.72 | aElementOf0(all_75_2, all_75_3) & aElementOf0(xQ, all_75_0) &
% 80.16/11.72 | aSet0(all_75_1) & aSet0(xQ) & ~ aElementOf0(all_75_2, all_75_1) & !
% 80.16/11.72 | [v0: any] : (v0 = all_75_2 | ~ $i(v0) | ~ aElementOf0(v0, all_75_3)
% 80.16/11.72 | | ~ aElement0(v0) | aElementOf0(v0, all_75_1)) & ! [v0: $i] : ( ~
% 80.16/11.72 | $i(v0) | ~ aElementOf0(v0, all_75_1) | aElementOf0(v0, all_75_3)) &
% 80.16/11.72 | ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_75_1) |
% 80.16/11.72 | aElement0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0,
% 80.16/11.72 | all_75_3) | sdtlseqdt0(all_75_2, v0)) & ! [v0: $i] : ( ~ $i(v0) |
% 80.16/11.72 | ~ aElementOf0(v0, xQ) | aElementOf0(v0, all_75_1))
% 80.16/11.72 |
% 80.16/11.72 | ALPHA: (19) implies:
% 80.16/11.72 | (20) sdtlpdtrp0(xN, xi) = all_75_3
% 80.16/11.72 |
% 80.16/11.72 | BETA: splitting (2) gives:
% 80.16/11.72 |
% 80.16/11.72 | Case 1:
% 80.16/11.72 | |
% 80.16/11.72 | | (21) ~ aSet0(slcrc0)
% 80.16/11.72 | |
% 80.16/11.72 | | PRED_UNIFY: (1), (21) imply:
% 80.16/11.72 | | (22) $false
% 80.16/11.72 | |
% 80.16/11.72 | | CLOSE: (22) is inconsistent.
% 80.16/11.72 | |
% 80.16/11.72 | Case 2:
% 80.16/11.72 | |
% 80.16/11.72 | |
% 80.16/11.72 | | GROUND_INST: instantiating (13) with all_72_2, all_75_3, xi, xN, simplifying
% 80.16/11.72 | | with (18), (20) gives:
% 80.16/11.72 | | (23) all_75_3 = all_72_2
% 80.16/11.72 | |
% 80.16/11.72 | | GROUND_INST: instantiating (13) with all_70_1, all_75_3, xi, xN, simplifying
% 80.16/11.72 | | with (16), (20) gives:
% 80.16/11.72 | | (24) all_75_3 = all_70_1
% 80.16/11.72 | |
% 80.16/11.73 | | COMBINE_EQS: (23), (24) imply:
% 80.16/11.73 | | (25) all_72_2 = all_70_1
% 80.16/11.73 | |
% 80.16/11.73 | | SIMP: (25) implies:
% 80.16/11.73 | | (26) all_72_2 = all_70_1
% 80.16/11.73 | |
% 80.16/11.73 | | GROUND_INST: instantiating (4) with xi, simplifying with (8), (11) gives:
% 80.16/11.73 | | (27) sdtlseqdt0(sz00, xi)
% 80.16/11.73 | |
% 80.16/11.73 | | GROUND_INST: instantiating (7) with xi, sz00, all_70_1, xS, simplifying with
% 80.16/11.73 | | (3), (5), (6), (8), (11), (15), (16), (27) gives:
% 80.16/11.73 | | (28) $false
% 80.16/11.73 | |
% 80.16/11.73 | | CLOSE: (28) is inconsistent.
% 80.16/11.73 | |
% 80.16/11.73 | End of split
% 80.16/11.73 |
% 80.16/11.73 End of proof
% 80.16/11.73 % SZS output end Proof for theBenchmark
% 80.16/11.73
% 80.16/11.73 11154ms
%------------------------------------------------------------------------------