TSTP Solution File: NUM604+3 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM604+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 11:48:54 EDT 2023
% Result : Theorem 50.54s 7.52s
% Output : Proof 71.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM604+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 13:33:28 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 6.17/1.61 Prover 0: Preprocessing ...
% 6.17/1.61 Prover 3: Preprocessing ...
% 6.17/1.62 Prover 2: Preprocessing ...
% 6.17/1.63 Prover 1: Preprocessing ...
% 6.17/1.64 Prover 4: Preprocessing ...
% 6.17/1.64 Prover 6: Preprocessing ...
% 6.17/1.64 Prover 5: Preprocessing ...
% 18.52/3.32 Prover 1: Constructing countermodel ...
% 19.22/3.33 Prover 3: Constructing countermodel ...
% 19.22/3.34 Prover 6: Proving ...
% 21.65/3.68 Prover 5: Proving ...
% 43.35/6.58 Prover 4: Constructing countermodel ...
% 46.86/7.00 Prover 2: Proving ...
% 49.83/7.42 Prover 0: Proving ...
% 50.54/7.51 Prover 3: proved (6888ms)
% 50.54/7.51
% 50.54/7.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 50.54/7.52
% 50.54/7.52 Prover 5: stopped
% 50.54/7.52 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 50.54/7.52 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 50.54/7.52 Prover 6: stopped
% 51.13/7.54 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 51.47/7.59 Prover 0: stopped
% 51.47/7.59 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 51.98/7.66 Prover 2: stopped
% 51.98/7.66 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 52.58/7.75 Prover 7: Preprocessing ...
% 53.46/7.89 Prover 11: Preprocessing ...
% 53.46/7.92 Prover 10: Preprocessing ...
% 53.46/7.96 Prover 8: Preprocessing ...
% 53.46/7.99 Prover 13: Preprocessing ...
% 56.82/8.29 Prover 8: Warning: ignoring some quantifiers
% 56.82/8.30 Prover 8: Constructing countermodel ...
% 59.20/8.74 Prover 10: Constructing countermodel ...
% 59.20/8.77 Prover 7: Constructing countermodel ...
% 62.03/9.00 Prover 13: Warning: ignoring some quantifiers
% 62.88/9.12 Prover 13: Constructing countermodel ...
% 64.37/9.28 Prover 10: Found proof (size 26)
% 64.37/9.28 Prover 10: proved (1745ms)
% 64.37/9.28 Prover 7: stopped
% 64.37/9.28 Prover 1: stopped
% 64.37/9.28 Prover 8: stopped
% 64.37/9.29 Prover 4: stopped
% 64.37/9.31 Prover 13: stopped
% 69.91/10.66 Prover 11: Constructing countermodel ...
% 69.91/10.69 Prover 11: stopped
% 69.91/10.69
% 69.91/10.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 69.91/10.69
% 69.91/10.70 % SZS output start Proof for theBenchmark
% 69.91/10.71 Assumptions after simplification:
% 69.91/10.71 ---------------------------------
% 69.91/10.71
% 69.91/10.71 (mCountNFin_01)
% 70.42/10.72 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0))
% 70.42/10.72
% 70.42/10.72 (mDefEmp)
% 70.42/10.72 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~
% 70.42/10.72 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : (
% 70.42/10.72 ~ $i(v0) | ~ aElementOf0(v0, slcrc0))
% 70.42/10.72
% 70.42/10.72 (mZeroLess)
% 70.42/10.72 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0,
% 70.42/10.72 szNzAzT0) | sdtlseqdt0(sz00, v0))
% 70.42/10.72
% 70.42/10.72 (mZeroNum)
% 70.42/10.72 $i(sz00) & $i(szNzAzT0) & aElementOf0(sz00, szNzAzT0)
% 70.42/10.72
% 70.42/10.72 (m__)
% 70.42/10.73 $i(xx) & $i(xS) & ~ aElementOf0(xx, xS)
% 70.42/10.73
% 70.42/10.73 (m__3623)
% 70.80/10.80 sdtlpdtrp0(xN, sz00) = xS & szDzozmdt0(xN) = szNzAzT0 & $i(xN) & $i(xS) &
% 70.80/10.80 $i(sz00) & $i(szNzAzT0) & aFunction0(xN) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 70.80/10.80 $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2 | ~ (sdtlpdtrp0(xN, v0) = v1) |
% 70.80/10.80 ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0)
% 70.80/10.80 | ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v4, v1)
% 70.80/10.80 | ~ aElementOf0(v0, szNzAzT0) | ~ aElement0(v4) | aElementOf0(v4, v3)) &
% 70.80/10.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2
% 70.80/10.80 | ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1,
% 70.80/10.80 v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~ isCountable0(v1) | ~
% 70.80/10.80 aElementOf0(v4, v1) | ~ aElementOf0(v0, szNzAzT0) | ~ aElement0(v4) | ~
% 70.80/10.80 aSet0(v1) | aElementOf0(v4, v3) | ? [v5: $i] : ($i(v5) & aElementOf0(v5,
% 70.80/10.80 v1) & ~ aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : !
% 70.80/10.80 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~
% 70.80/10.80 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) |
% 70.80/10.80 ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v4, v3) |
% 70.80/10.80 ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v4, v1)) & ! [v0: $i] : ! [v1:
% 70.80/10.80 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) =
% 70.80/10.80 v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) |
% 70.80/10.80 ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~
% 70.80/10.80 aElementOf0(v4, v3) | ~ aElementOf0(v0, szNzAzT0) | aElement0(v4)) & !
% 70.80/10.80 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 70.80/10.80 (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2)
% 70.80/10.80 = v3) | ~ $i(v4) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~
% 70.80/10.80 isCountable0(v1) | ~ aElementOf0(v4, v1) | ~ aElementOf0(v0, szNzAzT0) |
% 70.80/10.80 sdtlseqdt0(v2, v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 70.80/10.80 : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~
% 70.80/10.80 (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~ isCountable0(v1) | ~
% 70.80/10.80 aElementOf0(v4, v3) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) |
% 70.80/10.80 aElementOf0(v4, v1) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, v1) & ~
% 70.80/10.80 aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 70.80/10.80 [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) =
% 70.80/10.80 v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~
% 70.80/10.80 isCountable0(v1) | ~ aElementOf0(v4, v3) | ~ aElementOf0(v0, szNzAzT0) |
% 70.80/10.80 ~ aSet0(v1) | aElement0(v4) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, v1) &
% 70.80/10.80 ~ aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 70.80/10.80 ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1)
% 70.80/10.80 = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~
% 70.80/10.80 isCountable0(v1) | ~ aElementOf0(v4, v1) | ~ aElementOf0(v0, szNzAzT0) |
% 70.80/10.80 ~ aSet0(v1) | sdtlseqdt0(v2, v4) | ? [v5: $i] : ($i(v5) & aElementOf0(v5,
% 70.80/10.80 v1) & ~ aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : !
% 70.80/10.80 [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) =
% 70.80/10.80 v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ~
% 70.80/10.80 aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v2, v3) | ~
% 70.80/10.80 aElementOf0(v0, szNzAzT0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 70.80/10.80 [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~
% 70.80/10.80 (sdtmndt0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ~ isCountable0(v1) | ~
% 70.80/10.80 aElementOf0(v2, v3) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | ? [v4:
% 70.80/10.80 $i] : ($i(v4) & aElementOf0(v4, v1) & ~ aElementOf0(v4, szNzAzT0))) & !
% 70.80/10.80 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) =
% 70.80/10.80 v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) |
% 70.80/10.80 ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v0,
% 70.80/10.80 szNzAzT0) | aElementOf0(v2, v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 70.80/10.80 : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~
% 70.80/10.80 (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~
% 70.80/10.80 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | aSet0(v3)) & ! [v0: $i] :
% 70.80/10.80 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~
% 70.80/10.80 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~
% 70.80/10.80 aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v0,
% 70.80/10.80 szNzAzT0) | ? [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xN, v4) = v5 &
% 70.80/10.80 szszuzczcdt0(v0) = v4 & $i(v5) & $i(v4) & aSubsetOf0(v5, v3) &
% 70.80/10.80 isCountable0(v5) & aSet0(v5) & ! [v6: $i] : ( ~ $i(v6) | ~
% 70.80/10.80 aElementOf0(v6, v5) | aElementOf0(v6, v3)))) & ! [v0: $i] : ! [v1: $i]
% 70.80/10.80 : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~
% 70.80/10.80 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~
% 70.80/10.80 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) |
% 70.80/10.80 aElementOf0(v2, v1) | ? [v4: $i] : ($i(v4) & aElementOf0(v4, v1) & ~
% 70.80/10.80 aElementOf0(v4, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 70.80/10.80 [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~
% 70.80/10.80 (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ isCountable0(v1) | ~
% 70.80/10.80 aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | aSet0(v3) | ? [v4: $i] : ($i(v4)
% 70.80/10.80 & aElementOf0(v4, v1) & ~ aElementOf0(v4, szNzAzT0))) & ! [v0: $i] : !
% 70.80/10.80 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~
% 70.80/10.80 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~
% 70.80/10.80 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | ? [v4: $i]
% 70.80/10.80 : ? [v5: $i] : ? [v6: $i] : ($i(v6) & ((sdtlpdtrp0(xN, v4) = v5 &
% 70.80/10.80 szszuzczcdt0(v0) = v4 & $i(v5) & $i(v4) & aSubsetOf0(v5, v3) &
% 70.80/10.80 isCountable0(v5) & aSet0(v5) & ! [v7: $i] : ( ~ $i(v7) | ~
% 70.80/10.80 aElementOf0(v7, v5) | aElementOf0(v7, v3))) | (aElementOf0(v6, v1) &
% 70.80/10.80 ~ aElementOf0(v6, szNzAzT0)))))
% 70.80/10.80
% 70.80/10.80 (m__3754)
% 70.80/10.81 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 70.80/10.81 : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) |
% 70.80/10.81 ~ $i(v4) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v0) | ~
% 70.80/10.81 aElementOf0(v4, v2) | ~ aElementOf0(v1, szNzAzT0) | ~ aElementOf0(v0,
% 70.80/10.81 szNzAzT0) | aElementOf0(v4, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 70.80/10.81 : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) |
% 70.80/10.81 ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v0) | ~ aElementOf0(v1, szNzAzT0)
% 70.80/10.81 | ~ aElementOf0(v0, szNzAzT0) | aSubsetOf0(v2, v3))
% 70.80/10.81
% 70.80/10.81 (m__4660)
% 70.80/10.81 szDzozmdt0(xe) = szNzAzT0 & $i(xe) & $i(xN) & $i(szNzAzT0) & aFunction0(xe) &
% 70.80/10.81 ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) | ~
% 70.80/10.81 aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2 &
% 70.80/10.81 szmzizndt0(v2) = v1 & $i(v2) & $i(v1) & aElementOf0(v1, v2) & ! [v3: $i]
% 70.80/10.81 : ( ~ $i(v3) | ~ aElementOf0(v3, v2) | sdtlseqdt0(v1, v3))))
% 70.80/10.81
% 70.80/10.81 (m__5034)
% 70.80/10.81 sdtlpdtrp0(xe, xi) = xx & $i(xi) & $i(xx) & $i(xe) & $i(szNzAzT0) &
% 70.80/10.81 aElementOf0(xi, szNzAzT0)
% 70.80/10.81
% 70.80/10.81 (m__5045)
% 70.80/10.81 $i(xi) & $i(xN) & $i(xS) & ? [v0: $i] : (sdtlpdtrp0(xN, xi) = v0 & $i(v0) &
% 70.80/10.81 aSubsetOf0(v0, xS) & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, v0) |
% 70.80/10.81 aElementOf0(v1, xS)))
% 70.80/10.81
% 70.80/10.81 (function-axioms)
% 70.80/10.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 70.80/10.82 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 70.80/10.82 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 70.80/10.82 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 70.80/10.82 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 70.80/10.82 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 70.80/10.82 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 70.80/10.82 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 70.80/10.82 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 70.80/10.82 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~
% 70.80/10.82 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 70.80/10.82 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) &
% 70.80/10.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 70.80/10.82 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 70.80/10.82 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 70.80/10.82 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 70.80/10.82 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 70.80/10.82 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 70.80/10.82 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 70.80/10.82 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 70.80/10.82 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 70.80/10.82 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 70.80/10.82 v0))
% 70.80/10.82
% 70.80/10.82 Further assumptions not needed in the proof:
% 70.80/10.82 --------------------------------------------
% 70.80/10.83 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 70.80/10.83 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons,
% 70.80/10.83 mDefDiff, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, mDefSel,
% 70.80/10.83 mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet,
% 70.80/10.83 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm,
% 70.80/10.83 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans,
% 70.80/10.83 mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess,
% 70.80/10.83 mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort,
% 70.80/10.83 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum,
% 70.80/10.83 m__3291, m__3398, m__3418, m__3435, m__3453, m__3462, m__3520, m__3533, m__3671,
% 70.80/10.83 m__3821, m__3965, m__4151, m__4182, m__4331, m__4411, m__4618, m__4730, m__4758,
% 70.80/10.83 m__4854, m__4891, m__4908, m__4982, m__5009
% 70.80/10.83
% 70.80/10.83 Those formulas are unsatisfiable:
% 70.80/10.83 ---------------------------------
% 70.80/10.83
% 70.80/10.83 Begin of proof
% 70.80/10.83 |
% 70.80/10.83 | ALPHA: (mDefEmp) implies:
% 70.80/10.83 | (1) aSet0(slcrc0)
% 70.80/10.83 |
% 70.80/10.83 | ALPHA: (mCountNFin_01) implies:
% 70.80/10.83 | (2) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)
% 70.80/10.83 |
% 70.80/10.83 | ALPHA: (mZeroNum) implies:
% 70.80/10.83 | (3) aElementOf0(sz00, szNzAzT0)
% 70.80/10.83 |
% 70.80/10.83 | ALPHA: (mZeroLess) implies:
% 70.80/10.83 | (4) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) |
% 70.80/10.83 | sdtlseqdt0(sz00, v0))
% 70.80/10.83 |
% 70.80/10.83 | ALPHA: (m__3623) implies:
% 70.80/10.83 | (5) $i(sz00)
% 70.80/10.83 | (6) sdtlpdtrp0(xN, sz00) = xS
% 70.80/10.83 |
% 70.80/10.83 | ALPHA: (m__3754) implies:
% 70.80/10.83 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 70.80/10.83 | ~ (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) | ~
% 70.80/10.83 | $i(v4) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v0) | ~
% 70.80/10.83 | aElementOf0(v4, v2) | ~ aElementOf0(v1, szNzAzT0) | ~
% 70.80/10.83 | aElementOf0(v0, szNzAzT0) | aElementOf0(v4, v3))
% 70.80/10.83 |
% 70.80/10.83 | ALPHA: (m__4660) implies:
% 70.80/10.83 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) |
% 70.80/10.83 | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2
% 70.80/10.83 | & szmzizndt0(v2) = v1 & $i(v2) & $i(v1) & aElementOf0(v1, v2) & !
% 70.80/10.83 | [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v2) | sdtlseqdt0(v1,
% 70.80/10.83 | v3))))
% 70.80/10.83 |
% 70.80/10.83 | ALPHA: (m__5034) implies:
% 70.80/10.84 | (9) aElementOf0(xi, szNzAzT0)
% 70.80/10.84 | (10) sdtlpdtrp0(xe, xi) = xx
% 70.80/10.84 |
% 70.80/10.84 | ALPHA: (m__5045) implies:
% 70.80/10.84 | (11) $i(xi)
% 70.80/10.84 | (12) ? [v0: $i] : (sdtlpdtrp0(xN, xi) = v0 & $i(v0) & aSubsetOf0(v0, xS) &
% 70.80/10.84 | ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, v0) | aElementOf0(v1,
% 70.80/10.84 | xS)))
% 70.80/10.84 |
% 70.80/10.84 | ALPHA: (m__) implies:
% 70.80/10.84 | (13) ~ aElementOf0(xx, xS)
% 70.80/10.84 |
% 70.80/10.84 | ALPHA: (function-axioms) implies:
% 70.80/10.84 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 70.80/10.84 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0))
% 70.80/10.84 |
% 70.80/10.84 | DELTA: instantiating (12) with fresh symbol all_77_0 gives:
% 70.80/10.84 | (15) sdtlpdtrp0(xN, xi) = all_77_0 & $i(all_77_0) & aSubsetOf0(all_77_0,
% 70.80/10.84 | xS) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_77_0) |
% 70.80/10.84 | aElementOf0(v0, xS))
% 70.80/10.84 |
% 70.80/10.84 | ALPHA: (15) implies:
% 70.80/10.84 | (16) sdtlpdtrp0(xN, xi) = all_77_0
% 70.80/10.84 |
% 70.80/10.84 | BETA: splitting (2) gives:
% 70.80/10.84 |
% 70.80/10.84 | Case 1:
% 70.80/10.84 | |
% 70.80/10.84 | | (17) ~ aSet0(slcrc0)
% 70.80/10.84 | |
% 70.80/10.84 | | PRED_UNIFY: (1), (17) imply:
% 70.80/10.84 | | (18) $false
% 70.80/10.84 | |
% 70.80/10.84 | | CLOSE: (18) is inconsistent.
% 70.80/10.84 | |
% 70.80/10.84 | Case 2:
% 70.80/10.84 | |
% 70.80/10.84 | |
% 70.80/10.84 | | GROUND_INST: instantiating (4) with xi, simplifying with (9), (11) gives:
% 70.80/10.84 | | (19) sdtlseqdt0(sz00, xi)
% 70.80/10.84 | |
% 70.80/10.84 | | GROUND_INST: instantiating (8) with xi, xx, simplifying with (9), (10), (11)
% 70.80/10.84 | | gives:
% 70.80/10.85 | | (20) ? [v0: $i] : (sdtlpdtrp0(xN, xi) = v0 & szmzizndt0(v0) = xx &
% 70.80/10.85 | | $i(v0) & $i(xx) & aElementOf0(xx, v0) & ! [v1: $i] : ( ~ $i(v1) |
% 70.80/10.85 | | ~ aElementOf0(v1, v0) | sdtlseqdt0(xx, v1)))
% 70.80/10.85 | |
% 70.80/10.85 | | DELTA: instantiating (20) with fresh symbol all_124_0 gives:
% 70.80/10.85 | | (21) sdtlpdtrp0(xN, xi) = all_124_0 & szmzizndt0(all_124_0) = xx &
% 70.80/10.85 | | $i(all_124_0) & $i(xx) & aElementOf0(xx, all_124_0) & ! [v0: $i] :
% 70.80/10.85 | | ( ~ $i(v0) | ~ aElementOf0(v0, all_124_0) | sdtlseqdt0(xx, v0))
% 70.80/10.85 | |
% 70.80/10.85 | | ALPHA: (21) implies:
% 70.80/10.85 | | (22) aElementOf0(xx, all_124_0)
% 70.80/10.85 | | (23) $i(xx)
% 70.80/10.85 | | (24) sdtlpdtrp0(xN, xi) = all_124_0
% 70.80/10.85 | |
% 70.80/10.85 | | GROUND_INST: instantiating (14) with all_77_0, all_124_0, xi, xN,
% 70.80/10.85 | | simplifying with (16), (24) gives:
% 70.80/10.85 | | (25) all_124_0 = all_77_0
% 70.80/10.85 | |
% 70.80/10.85 | | REDUCE: (22), (25) imply:
% 70.80/10.85 | | (26) aElementOf0(xx, all_77_0)
% 70.80/10.85 | |
% 70.80/10.85 | | GROUND_INST: instantiating (7) with xi, sz00, all_77_0, xS, xx, simplifying
% 70.80/10.85 | | with (3), (5), (6), (9), (11), (13), (16), (19), (23), (26)
% 70.80/10.85 | | gives:
% 70.80/10.85 | | (27) $false
% 70.80/10.85 | |
% 70.80/10.85 | | CLOSE: (27) is inconsistent.
% 70.80/10.85 | |
% 70.80/10.85 | End of split
% 70.80/10.85 |
% 71.24/10.85 End of proof
% 71.24/10.85 % SZS output end Proof for theBenchmark
% 71.24/10.85
% 71.24/10.85 10250ms
%------------------------------------------------------------------------------