TSTP Solution File: PUZ075+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : PUZ075+1 : TPTP v8.1.2. Released v3.5.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n005.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 13:23:03 EDT 2023
% Result : Theorem 11.20s 2.24s
% Output : Proof 13.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : PUZ075+1 : TPTP v8.1.2. Released v3.5.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n005.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 21:58:23 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.62 ___ __ \_________(_)________________________________
% 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62
% 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62 (2023-06-19)
% 0.21/0.62
% 0.21/0.62 (c) Philipp Rümmer, 2009-2023
% 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62 Amanda Stjerna.
% 0.21/0.62 Free software under BSD-3-Clause.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.64 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.42/1.20 Prover 1: Preprocessing ...
% 3.42/1.20 Prover 4: Preprocessing ...
% 3.91/1.24 Prover 6: Preprocessing ...
% 3.91/1.24 Prover 3: Preprocessing ...
% 3.91/1.24 Prover 5: Preprocessing ...
% 3.91/1.24 Prover 0: Preprocessing ...
% 3.91/1.24 Prover 2: Preprocessing ...
% 7.58/1.80 Prover 5: Proving ...
% 7.58/1.80 Prover 1: Constructing countermodel ...
% 7.58/1.81 Prover 3: Constructing countermodel ...
% 7.58/1.82 Prover 6: Constructing countermodel ...
% 11.20/2.24 Prover 6: proved (1586ms)
% 11.20/2.24
% 11.20/2.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.20/2.24
% 11.20/2.24 Prover 3: stopped
% 11.20/2.24 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.20/2.24 Prover 5: stopped
% 11.20/2.25 Prover 0: stopped
% 11.40/2.26 Prover 2: stopped
% 11.40/2.26 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.40/2.26 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.40/2.26 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.40/2.26 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.40/2.29 Prover 1: Found proof (size 14)
% 11.40/2.29 Prover 1: proved (1652ms)
% 11.40/2.29 Prover 4: stopped
% 11.98/2.35 Prover 7: Preprocessing ...
% 11.98/2.36 Prover 8: Preprocessing ...
% 11.98/2.36 Prover 10: Preprocessing ...
% 12.33/2.38 Prover 13: Preprocessing ...
% 12.33/2.38 Prover 11: Preprocessing ...
% 12.33/2.41 Prover 7: stopped
% 12.33/2.44 Prover 10: stopped
% 12.89/2.46 Prover 11: stopped
% 12.89/2.46 Prover 13: stopped
% 13.04/2.49 Prover 8: Warning: ignoring some quantifiers
% 13.04/2.49 Prover 8: Constructing countermodel ...
% 13.04/2.49 Prover 8: stopped
% 13.04/2.49
% 13.04/2.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.04/2.49
% 13.04/2.50 % SZS output start Proof for theBenchmark
% 13.04/2.50 Assumptions after simplification:
% 13.04/2.50 ---------------------------------
% 13.04/2.50
% 13.04/2.50 (tlhfof24987)
% 13.43/2.57 $i(cell100) & $i(cell99) & $i(cell98) & $i(cell97) & $i(cell96) & $i(cell95) &
% 13.43/2.57 $i(cell94) & $i(cell93) & $i(cell92) & $i(cell91) & $i(cell90) & $i(cell89) &
% 13.43/2.57 $i(cell88) & $i(cell87) & $i(cell86) & $i(cell85) & $i(cell84) & $i(cell83) &
% 13.43/2.57 $i(cell82) & $i(cell81) & $i(cell80) & $i(cell79) & $i(cell78) & $i(cell77) &
% 13.43/2.57 $i(cell76) & $i(cell75) & $i(cell74) & $i(cell73) & $i(cell72) & $i(cell71) &
% 13.43/2.57 $i(cell70) & $i(cell69) & $i(cell68) & $i(cell67) & $i(cell66) & $i(cell65) &
% 13.43/2.57 $i(cell64) & $i(cell63) & $i(cell62) & $i(cell61) & $i(cell60) & $i(cell59) &
% 13.43/2.57 $i(cell58) & $i(cell57) & $i(cell56) & $i(cell55) & $i(cell54) & $i(cell53) &
% 13.43/2.57 $i(cell52) & $i(cell51) & $i(cell50) & $i(cell49) & $i(cell48) & $i(cell47) &
% 13.43/2.57 $i(cell46) & $i(cell45) & $i(cell44) & $i(cell43) & $i(cell42) & $i(cell41) &
% 13.43/2.57 $i(cell40) & $i(cell39) & $i(cell38) & $i(cell37) & $i(cell36) & $i(cell35) &
% 13.43/2.57 $i(cell34) & $i(cell33) & $i(cell32) & $i(cell31) & $i(cell30) & $i(cell29) &
% 13.43/2.57 $i(cell28) & $i(cell27) & $i(cell26) & $i(cell25) & $i(cell24) & $i(cell23) &
% 13.43/2.57 $i(cell22) & $i(cell21) & $i(cell20) & $i(cell19) & $i(cell18) & $i(cell17) &
% 13.43/2.57 $i(cell16) & $i(cell15) & $i(cell14) & $i(cell13) & $i(cell12) & $i(cell11) &
% 13.43/2.57 $i(cell10) & $i(cell9) & $i(cell8) & $i(cell7) & $i(cell6) & $i(cell5) &
% 13.43/2.57 $i(cell4) & $i(cell3) & $i(cell2) & $i(cell1) & ! [v0: $i] : ! [v1: $i] : !
% 13.43/2.57 [v2: int] : (v2 = 0 | ~ (edge(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | (( ~
% 13.43/2.57 (v1 = cell99) | ~ (v0 = cell100)) & ( ~ (v1 = cell98) | ~ (v0 =
% 13.43/2.57 cell99)) & ( ~ (v1 = cell97) | ~ (v0 = cell98)) & ( ~ (v1 = cell96) |
% 13.43/2.57 ~ (v0 = cell97)) & ( ~ (v1 = cell95) | ~ (v0 = cell96)) & ( ~ (v1 =
% 13.43/2.57 cell94) | ~ (v0 = cell95)) & ( ~ (v1 = cell93) | ~ (v0 = cell94)) &
% 13.43/2.57 ( ~ (v1 = cell92) | ~ (v0 = cell93)) & ( ~ (v1 = cell91) | ~ (v0 =
% 13.43/2.57 cell92)) & ( ~ (v1 = cell90) | ~ (v0 = cell100)) & ( ~ (v1 = cell89)
% 13.43/2.57 | ~ (v0 = cell99)) & ( ~ (v1 = cell89) | ~ (v0 = cell90)) & ( ~ (v1 =
% 13.43/2.57 cell88) | ~ (v0 = cell98)) & ( ~ (v1 = cell88) | ~ (v0 = cell89)) &
% 13.43/2.57 ( ~ (v1 = cell87) | ~ (v0 = cell97)) & ( ~ (v1 = cell87) | ~ (v0 =
% 13.43/2.57 cell88)) & ( ~ (v1 = cell86) | ~ (v0 = cell96)) & ( ~ (v1 = cell86) |
% 13.43/2.57 ~ (v0 = cell87)) & ( ~ (v1 = cell85) | ~ (v0 = cell95)) & ( ~ (v1 =
% 13.43/2.57 cell85) | ~ (v0 = cell86)) & ( ~ (v1 = cell84) | ~ (v0 = cell94)) &
% 13.43/2.57 ( ~ (v1 = cell84) | ~ (v0 = cell85)) & ( ~ (v1 = cell83) | ~ (v0 =
% 13.43/2.57 cell93)) & ( ~ (v1 = cell83) | ~ (v0 = cell84)) & ( ~ (v1 = cell82) |
% 13.43/2.57 ~ (v0 = cell92)) & ( ~ (v1 = cell82) | ~ (v0 = cell83)) & ( ~ (v1 =
% 13.43/2.57 cell81) | ~ (v0 = cell91)) & ( ~ (v1 = cell81) | ~ (v0 = cell82)) &
% 13.43/2.57 ( ~ (v1 = cell80) | ~ (v0 = cell90)) & ( ~ (v1 = cell79) | ~ (v0 =
% 13.43/2.57 cell89)) & ( ~ (v1 = cell79) | ~ (v0 = cell80)) & ( ~ (v1 = cell78) |
% 13.43/2.57 ~ (v0 = cell88)) & ( ~ (v1 = cell78) | ~ (v0 = cell79)) & ( ~ (v1 =
% 13.43/2.57 cell77) | ~ (v0 = cell87)) & ( ~ (v1 = cell77) | ~ (v0 = cell78)) &
% 13.43/2.57 ( ~ (v1 = cell76) | ~ (v0 = cell86)) & ( ~ (v1 = cell76) | ~ (v0 =
% 13.43/2.57 cell77)) & ( ~ (v1 = cell75) | ~ (v0 = cell85)) & ( ~ (v1 = cell75) |
% 13.43/2.57 ~ (v0 = cell76)) & ( ~ (v1 = cell74) | ~ (v0 = cell84)) & ( ~ (v1 =
% 13.43/2.57 cell74) | ~ (v0 = cell75)) & ( ~ (v1 = cell73) | ~ (v0 = cell83)) &
% 13.43/2.57 ( ~ (v1 = cell73) | ~ (v0 = cell74)) & ( ~ (v1 = cell72) | ~ (v0 =
% 13.43/2.57 cell82)) & ( ~ (v1 = cell72) | ~ (v0 = cell73)) & ( ~ (v1 = cell71) |
% 13.43/2.57 ~ (v0 = cell81)) & ( ~ (v1 = cell71) | ~ (v0 = cell72)) & ( ~ (v1 =
% 13.43/2.57 cell70) | ~ (v0 = cell80)) & ( ~ (v1 = cell69) | ~ (v0 = cell79)) &
% 13.43/2.57 ( ~ (v1 = cell69) | ~ (v0 = cell70)) & ( ~ (v1 = cell68) | ~ (v0 =
% 13.43/2.57 cell78)) & ( ~ (v1 = cell68) | ~ (v0 = cell69)) & ( ~ (v1 = cell67) |
% 13.43/2.57 ~ (v0 = cell77)) & ( ~ (v1 = cell67) | ~ (v0 = cell68)) & ( ~ (v1 =
% 13.43/2.57 cell66) | ~ (v0 = cell76)) & ( ~ (v1 = cell66) | ~ (v0 = cell67)) &
% 13.43/2.57 ( ~ (v1 = cell65) | ~ (v0 = cell75)) & ( ~ (v1 = cell65) | ~ (v0 =
% 13.43/2.57 cell66)) & ( ~ (v1 = cell64) | ~ (v0 = cell74)) & ( ~ (v1 = cell64) |
% 13.43/2.57 ~ (v0 = cell65)) & ( ~ (v1 = cell63) | ~ (v0 = cell73)) & ( ~ (v1 =
% 13.43/2.57 cell63) | ~ (v0 = cell64)) & ( ~ (v1 = cell62) | ~ (v0 = cell72)) &
% 13.43/2.57 ( ~ (v1 = cell62) | ~ (v0 = cell63)) & ( ~ (v1 = cell61) | ~ (v0 =
% 13.43/2.57 cell71)) & ( ~ (v1 = cell61) | ~ (v0 = cell62)) & ( ~ (v1 = cell60) |
% 13.43/2.57 ~ (v0 = cell70)) & ( ~ (v1 = cell59) | ~ (v0 = cell69)) & ( ~ (v1 =
% 13.43/2.57 cell59) | ~ (v0 = cell60)) & ( ~ (v1 = cell58) | ~ (v0 = cell68)) &
% 13.43/2.57 ( ~ (v1 = cell58) | ~ (v0 = cell59)) & ( ~ (v1 = cell57) | ~ (v0 =
% 13.43/2.57 cell67)) & ( ~ (v1 = cell57) | ~ (v0 = cell58)) & ( ~ (v1 = cell56) |
% 13.43/2.57 ~ (v0 = cell66)) & ( ~ (v1 = cell56) | ~ (v0 = cell57)) & ( ~ (v1 =
% 13.43/2.57 cell55) | ~ (v0 = cell65)) & ( ~ (v1 = cell55) | ~ (v0 = cell56)) &
% 13.43/2.57 ( ~ (v1 = cell54) | ~ (v0 = cell64)) & ( ~ (v1 = cell54) | ~ (v0 =
% 13.43/2.57 cell55)) & ( ~ (v1 = cell53) | ~ (v0 = cell63)) & ( ~ (v1 = cell53) |
% 13.43/2.57 ~ (v0 = cell54)) & ( ~ (v1 = cell52) | ~ (v0 = cell62)) & ( ~ (v1 =
% 13.43/2.57 cell52) | ~ (v0 = cell53)) & ( ~ (v1 = cell51) | ~ (v0 = cell61)) &
% 13.43/2.57 ( ~ (v1 = cell51) | ~ (v0 = cell52)) & ( ~ (v1 = cell50) | ~ (v0 =
% 13.43/2.57 cell60)) & ( ~ (v1 = cell49) | ~ (v0 = cell59)) & ( ~ (v1 = cell49) |
% 13.43/2.57 ~ (v0 = cell50)) & ( ~ (v1 = cell48) | ~ (v0 = cell58)) & ( ~ (v1 =
% 13.43/2.57 cell48) | ~ (v0 = cell49)) & ( ~ (v1 = cell47) | ~ (v0 = cell57)) &
% 13.43/2.57 ( ~ (v1 = cell47) | ~ (v0 = cell48)) & ( ~ (v1 = cell46) | ~ (v0 =
% 13.43/2.57 cell56)) & ( ~ (v1 = cell46) | ~ (v0 = cell47)) & ( ~ (v1 = cell45) |
% 13.43/2.57 ~ (v0 = cell55)) & ( ~ (v1 = cell45) | ~ (v0 = cell46)) & ( ~ (v1 =
% 13.43/2.57 cell44) | ~ (v0 = cell54)) & ( ~ (v1 = cell44) | ~ (v0 = cell45)) &
% 13.43/2.57 ( ~ (v1 = cell43) | ~ (v0 = cell53)) & ( ~ (v1 = cell43) | ~ (v0 =
% 13.43/2.57 cell44)) & ( ~ (v1 = cell42) | ~ (v0 = cell52)) & ( ~ (v1 = cell42) |
% 13.43/2.57 ~ (v0 = cell43)) & ( ~ (v1 = cell41) | ~ (v0 = cell51)) & ( ~ (v1 =
% 13.43/2.57 cell41) | ~ (v0 = cell42)) & ( ~ (v1 = cell40) | ~ (v0 = cell50)) &
% 13.43/2.57 ( ~ (v1 = cell39) | ~ (v0 = cell49)) & ( ~ (v1 = cell39) | ~ (v0 =
% 13.43/2.57 cell40)) & ( ~ (v1 = cell38) | ~ (v0 = cell48)) & ( ~ (v1 = cell38) |
% 13.43/2.57 ~ (v0 = cell39)) & ( ~ (v1 = cell37) | ~ (v0 = cell47)) & ( ~ (v1 =
% 13.43/2.57 cell37) | ~ (v0 = cell38)) & ( ~ (v1 = cell36) | ~ (v0 = cell46)) &
% 13.43/2.57 ( ~ (v1 = cell36) | ~ (v0 = cell37)) & ( ~ (v1 = cell35) | ~ (v0 =
% 13.43/2.57 cell45)) & ( ~ (v1 = cell35) | ~ (v0 = cell36)) & ( ~ (v1 = cell34) |
% 13.43/2.57 ~ (v0 = cell44)) & ( ~ (v1 = cell34) | ~ (v0 = cell35)) & ( ~ (v1 =
% 13.43/2.57 cell33) | ~ (v0 = cell43)) & ( ~ (v1 = cell33) | ~ (v0 = cell34)) &
% 13.43/2.57 ( ~ (v1 = cell32) | ~ (v0 = cell42)) & ( ~ (v1 = cell32) | ~ (v0 =
% 13.43/2.57 cell33)) & ( ~ (v1 = cell31) | ~ (v0 = cell41)) & ( ~ (v1 = cell31) |
% 13.43/2.57 ~ (v0 = cell32)) & ( ~ (v1 = cell30) | ~ (v0 = cell40)) & ( ~ (v1 =
% 13.43/2.57 cell29) | ~ (v0 = cell39)) & ( ~ (v1 = cell29) | ~ (v0 = cell30)) &
% 13.43/2.57 ( ~ (v1 = cell28) | ~ (v0 = cell38)) & ( ~ (v1 = cell28) | ~ (v0 =
% 13.43/2.57 cell29)) & ( ~ (v1 = cell27) | ~ (v0 = cell37)) & ( ~ (v1 = cell27) |
% 13.43/2.57 ~ (v0 = cell28)) & ( ~ (v1 = cell26) | ~ (v0 = cell36)) & ( ~ (v1 =
% 13.43/2.57 cell26) | ~ (v0 = cell27)) & ( ~ (v1 = cell25) | ~ (v0 = cell35)) &
% 13.43/2.57 ( ~ (v1 = cell25) | ~ (v0 = cell26)) & ( ~ (v1 = cell24) | ~ (v0 =
% 13.43/2.57 cell34)) & ( ~ (v1 = cell24) | ~ (v0 = cell25)) & ( ~ (v1 = cell23) |
% 13.43/2.57 ~ (v0 = cell33)) & ( ~ (v1 = cell23) | ~ (v0 = cell24)) & ( ~ (v1 =
% 13.43/2.57 cell22) | ~ (v0 = cell32)) & ( ~ (v1 = cell22) | ~ (v0 = cell23)) &
% 13.43/2.57 ( ~ (v1 = cell21) | ~ (v0 = cell31)) & ( ~ (v1 = cell21) | ~ (v0 =
% 13.43/2.57 cell22)) & ( ~ (v1 = cell20) | ~ (v0 = cell30)) & ( ~ (v1 = cell19) |
% 13.43/2.57 ~ (v0 = cell29)) & ( ~ (v1 = cell19) | ~ (v0 = cell20)) & ( ~ (v1 =
% 13.43/2.57 cell18) | ~ (v0 = cell28)) & ( ~ (v1 = cell18) | ~ (v0 = cell19)) &
% 13.43/2.57 ( ~ (v1 = cell17) | ~ (v0 = cell27)) & ( ~ (v1 = cell17) | ~ (v0 =
% 13.43/2.57 cell18)) & ( ~ (v1 = cell16) | ~ (v0 = cell26)) & ( ~ (v1 = cell16) |
% 13.43/2.57 ~ (v0 = cell17)) & ( ~ (v1 = cell15) | ~ (v0 = cell25)) & ( ~ (v1 =
% 13.43/2.57 cell15) | ~ (v0 = cell16)) & ( ~ (v1 = cell14) | ~ (v0 = cell24)) &
% 13.43/2.57 ( ~ (v1 = cell14) | ~ (v0 = cell15)) & ( ~ (v1 = cell13) | ~ (v0 =
% 13.43/2.57 cell23)) & ( ~ (v1 = cell13) | ~ (v0 = cell14)) & ( ~ (v1 = cell12) |
% 13.43/2.57 ~ (v0 = cell22)) & ( ~ (v1 = cell12) | ~ (v0 = cell13)) & ( ~ (v1 =
% 13.43/2.57 cell11) | ~ (v0 = cell21)) & ( ~ (v1 = cell11) | ~ (v0 = cell12)) &
% 13.43/2.57 ( ~ (v1 = cell10) | ~ (v0 = cell20)) & ( ~ (v1 = cell9) | ~ (v0 =
% 13.43/2.57 cell19)) & ( ~ (v1 = cell9) | ~ (v0 = cell10)) & ( ~ (v1 = cell8) |
% 13.43/2.57 ~ (v0 = cell18)) & ( ~ (v1 = cell8) | ~ (v0 = cell9)) & ( ~ (v1 =
% 13.43/2.57 cell7) | ~ (v0 = cell17)) & ( ~ (v1 = cell7) | ~ (v0 = cell8)) & ( ~
% 13.43/2.57 (v1 = cell6) | ~ (v0 = cell16)) & ( ~ (v1 = cell6) | ~ (v0 = cell7)) &
% 13.43/2.57 ( ~ (v1 = cell5) | ~ (v0 = cell15)) & ( ~ (v1 = cell5) | ~ (v0 = cell6))
% 13.43/2.57 & ( ~ (v1 = cell4) | ~ (v0 = cell14)) & ( ~ (v1 = cell4) | ~ (v0 =
% 13.43/2.57 cell5)) & ( ~ (v1 = cell3) | ~ (v0 = cell13)) & ( ~ (v1 = cell3) | ~
% 13.43/2.58 (v0 = cell4)) & ( ~ (v1 = cell2) | ~ (v0 = cell12)) & ( ~ (v1 = cell2)
% 13.43/2.58 | ~ (v0 = cell3)) & ( ~ (v1 = cell1) | ~ (v0 = cell11)) & ( ~ (v1 =
% 13.43/2.58 cell1) | ~ (v0 = cell2)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 13.43/2.58 (edge(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | (v1 = cell99 & v0 = cell100) |
% 13.43/2.58 (v1 = cell98 & v0 = cell99) | (v1 = cell97 & v0 = cell98) | (v1 = cell96 &
% 13.43/2.58 v0 = cell97) | (v1 = cell95 & v0 = cell96) | (v1 = cell94 & v0 = cell95) |
% 13.43/2.58 (v1 = cell93 & v0 = cell94) | (v1 = cell92 & v0 = cell93) | (v1 = cell91 &
% 13.43/2.58 v0 = cell92) | (v1 = cell90 & v0 = cell100) | (v1 = cell89 & v0 = cell99)
% 13.43/2.58 | (v1 = cell89 & v0 = cell90) | (v1 = cell88 & v0 = cell98) | (v1 = cell88 &
% 13.43/2.58 v0 = cell89) | (v1 = cell87 & v0 = cell97) | (v1 = cell87 & v0 = cell88) |
% 13.43/2.58 (v1 = cell86 & v0 = cell96) | (v1 = cell86 & v0 = cell87) | (v1 = cell85 &
% 13.43/2.58 v0 = cell95) | (v1 = cell85 & v0 = cell86) | (v1 = cell84 & v0 = cell94) |
% 13.43/2.58 (v1 = cell84 & v0 = cell85) | (v1 = cell83 & v0 = cell93) | (v1 = cell83 &
% 13.43/2.58 v0 = cell84) | (v1 = cell82 & v0 = cell92) | (v1 = cell82 & v0 = cell83) |
% 13.43/2.58 (v1 = cell81 & v0 = cell91) | (v1 = cell81 & v0 = cell82) | (v1 = cell80 &
% 13.43/2.58 v0 = cell90) | (v1 = cell79 & v0 = cell89) | (v1 = cell79 & v0 = cell80) |
% 13.43/2.58 (v1 = cell78 & v0 = cell88) | (v1 = cell78 & v0 = cell79) | (v1 = cell77 &
% 13.43/2.58 v0 = cell87) | (v1 = cell77 & v0 = cell78) | (v1 = cell76 & v0 = cell86) |
% 13.43/2.58 (v1 = cell76 & v0 = cell77) | (v1 = cell75 & v0 = cell85) | (v1 = cell75 &
% 13.43/2.58 v0 = cell76) | (v1 = cell74 & v0 = cell84) | (v1 = cell74 & v0 = cell75) |
% 13.43/2.58 (v1 = cell73 & v0 = cell83) | (v1 = cell73 & v0 = cell74) | (v1 = cell72 &
% 13.43/2.58 v0 = cell82) | (v1 = cell72 & v0 = cell73) | (v1 = cell71 & v0 = cell81) |
% 13.43/2.58 (v1 = cell71 & v0 = cell72) | (v1 = cell70 & v0 = cell80) | (v1 = cell69 &
% 13.43/2.58 v0 = cell79) | (v1 = cell69 & v0 = cell70) | (v1 = cell68 & v0 = cell78) |
% 13.43/2.58 (v1 = cell68 & v0 = cell69) | (v1 = cell67 & v0 = cell77) | (v1 = cell67 &
% 13.43/2.58 v0 = cell68) | (v1 = cell66 & v0 = cell76) | (v1 = cell66 & v0 = cell67) |
% 13.43/2.58 (v1 = cell65 & v0 = cell75) | (v1 = cell65 & v0 = cell66) | (v1 = cell64 &
% 13.43/2.58 v0 = cell74) | (v1 = cell64 & v0 = cell65) | (v1 = cell63 & v0 = cell73) |
% 13.43/2.58 (v1 = cell63 & v0 = cell64) | (v1 = cell62 & v0 = cell72) | (v1 = cell62 &
% 13.43/2.58 v0 = cell63) | (v1 = cell61 & v0 = cell71) | (v1 = cell61 & v0 = cell62) |
% 13.43/2.58 (v1 = cell60 & v0 = cell70) | (v1 = cell59 & v0 = cell69) | (v1 = cell59 &
% 13.43/2.58 v0 = cell60) | (v1 = cell58 & v0 = cell68) | (v1 = cell58 & v0 = cell59) |
% 13.43/2.58 (v1 = cell57 & v0 = cell67) | (v1 = cell57 & v0 = cell58) | (v1 = cell56 &
% 13.43/2.58 v0 = cell66) | (v1 = cell56 & v0 = cell57) | (v1 = cell55 & v0 = cell65) |
% 13.43/2.58 (v1 = cell55 & v0 = cell56) | (v1 = cell54 & v0 = cell64) | (v1 = cell54 &
% 13.43/2.58 v0 = cell55) | (v1 = cell53 & v0 = cell63) | (v1 = cell53 & v0 = cell54) |
% 13.43/2.58 (v1 = cell52 & v0 = cell62) | (v1 = cell52 & v0 = cell53) | (v1 = cell51 &
% 13.43/2.58 v0 = cell61) | (v1 = cell51 & v0 = cell52) | (v1 = cell50 & v0 = cell60) |
% 13.43/2.58 (v1 = cell49 & v0 = cell59) | (v1 = cell49 & v0 = cell50) | (v1 = cell48 &
% 13.43/2.58 v0 = cell58) | (v1 = cell48 & v0 = cell49) | (v1 = cell47 & v0 = cell57) |
% 13.43/2.58 (v1 = cell47 & v0 = cell48) | (v1 = cell46 & v0 = cell56) | (v1 = cell46 &
% 13.43/2.58 v0 = cell47) | (v1 = cell45 & v0 = cell55) | (v1 = cell45 & v0 = cell46) |
% 13.43/2.58 (v1 = cell44 & v0 = cell54) | (v1 = cell44 & v0 = cell45) | (v1 = cell43 &
% 13.43/2.58 v0 = cell53) | (v1 = cell43 & v0 = cell44) | (v1 = cell42 & v0 = cell52) |
% 13.43/2.58 (v1 = cell42 & v0 = cell43) | (v1 = cell41 & v0 = cell51) | (v1 = cell41 &
% 13.43/2.58 v0 = cell42) | (v1 = cell40 & v0 = cell50) | (v1 = cell39 & v0 = cell49) |
% 13.43/2.58 (v1 = cell39 & v0 = cell40) | (v1 = cell38 & v0 = cell48) | (v1 = cell38 &
% 13.43/2.58 v0 = cell39) | (v1 = cell37 & v0 = cell47) | (v1 = cell37 & v0 = cell38) |
% 13.43/2.58 (v1 = cell36 & v0 = cell46) | (v1 = cell36 & v0 = cell37) | (v1 = cell35 &
% 13.43/2.58 v0 = cell45) | (v1 = cell35 & v0 = cell36) | (v1 = cell34 & v0 = cell44) |
% 13.43/2.58 (v1 = cell34 & v0 = cell35) | (v1 = cell33 & v0 = cell43) | (v1 = cell33 &
% 13.43/2.58 v0 = cell34) | (v1 = cell32 & v0 = cell42) | (v1 = cell32 & v0 = cell33) |
% 13.43/2.58 (v1 = cell31 & v0 = cell41) | (v1 = cell31 & v0 = cell32) | (v1 = cell30 &
% 13.43/2.58 v0 = cell40) | (v1 = cell29 & v0 = cell39) | (v1 = cell29 & v0 = cell30) |
% 13.43/2.58 (v1 = cell28 & v0 = cell38) | (v1 = cell28 & v0 = cell29) | (v1 = cell27 &
% 13.43/2.58 v0 = cell37) | (v1 = cell27 & v0 = cell28) | (v1 = cell26 & v0 = cell36) |
% 13.43/2.58 (v1 = cell26 & v0 = cell27) | (v1 = cell25 & v0 = cell35) | (v1 = cell25 &
% 13.43/2.58 v0 = cell26) | (v1 = cell24 & v0 = cell34) | (v1 = cell24 & v0 = cell25) |
% 13.43/2.58 (v1 = cell23 & v0 = cell33) | (v1 = cell23 & v0 = cell24) | (v1 = cell22 &
% 13.43/2.58 v0 = cell32) | (v1 = cell22 & v0 = cell23) | (v1 = cell21 & v0 = cell31) |
% 13.43/2.58 (v1 = cell21 & v0 = cell22) | (v1 = cell20 & v0 = cell30) | (v1 = cell19 &
% 13.43/2.58 v0 = cell29) | (v1 = cell19 & v0 = cell20) | (v1 = cell18 & v0 = cell28) |
% 13.43/2.58 (v1 = cell18 & v0 = cell19) | (v1 = cell17 & v0 = cell27) | (v1 = cell17 &
% 13.43/2.58 v0 = cell18) | (v1 = cell16 & v0 = cell26) | (v1 = cell16 & v0 = cell17) |
% 13.43/2.58 (v1 = cell15 & v0 = cell25) | (v1 = cell15 & v0 = cell16) | (v1 = cell14 &
% 13.43/2.58 v0 = cell24) | (v1 = cell14 & v0 = cell15) | (v1 = cell13 & v0 = cell23) |
% 13.43/2.58 (v1 = cell13 & v0 = cell14) | (v1 = cell12 & v0 = cell22) | (v1 = cell12 &
% 13.43/2.58 v0 = cell13) | (v1 = cell11 & v0 = cell21) | (v1 = cell11 & v0 = cell12) |
% 13.43/2.58 (v1 = cell10 & v0 = cell20) | (v1 = cell9 & v0 = cell19) | (v1 = cell9 & v0
% 13.43/2.58 = cell10) | (v1 = cell8 & v0 = cell18) | (v1 = cell8 & v0 = cell9) | (v1 =
% 13.43/2.58 cell7 & v0 = cell17) | (v1 = cell7 & v0 = cell8) | (v1 = cell6 & v0 =
% 13.43/2.58 cell16) | (v1 = cell6 & v0 = cell7) | (v1 = cell5 & v0 = cell15) | (v1 =
% 13.43/2.58 cell5 & v0 = cell6) | (v1 = cell4 & v0 = cell14) | (v1 = cell4 & v0 =
% 13.43/2.58 cell5) | (v1 = cell3 & v0 = cell13) | (v1 = cell3 & v0 = cell4) | (v1 =
% 13.43/2.58 cell2 & v0 = cell12) | (v1 = cell2 & v0 = cell3) | (v1 = cell1 & v0 =
% 13.43/2.58 cell11) | (v1 = cell1 & v0 = cell2))
% 13.43/2.58
% 13.43/2.58 (tlhfof24988)
% 13.43/2.58 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (adj(v1, v0) = v2) |
% 13.43/2.58 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ( ~ (v4 = 0) & ~ (v3 =
% 13.43/2.58 0) & edge(v1, v0) = v3 & edge(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i]
% 13.43/2.58 : ( ~ (adj(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any]
% 13.43/2.58 : (edge(v1, v0) = v2 & edge(v0, v1) = v3 & (v3 = 0 | v2 = 0)))
% 13.43/2.58
% 13.43/2.58 (tlhfof24989)
% 13.43/2.58 $i(cell13) & $i(cell12) & ? [v0: int] : ( ~ (v0 = 0) & adj(cell12, cell13) =
% 13.43/2.58 v0)
% 13.43/2.58
% 13.43/2.58 Those formulas are unsatisfiable:
% 13.43/2.58 ---------------------------------
% 13.43/2.58
% 13.43/2.58 Begin of proof
% 13.43/2.58 |
% 13.43/2.58 | ALPHA: (tlhfof24987) implies:
% 13.43/2.60 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (edge(v1, v0) =
% 13.43/2.60 | v2) | ~ $i(v1) | ~ $i(v0) | (( ~ (v1 = cell99) | ~ (v0 =
% 13.43/2.60 | cell100)) & ( ~ (v1 = cell98) | ~ (v0 = cell99)) & ( ~ (v1 =
% 13.43/2.60 | cell97) | ~ (v0 = cell98)) & ( ~ (v1 = cell96) | ~ (v0 =
% 13.43/2.60 | cell97)) & ( ~ (v1 = cell95) | ~ (v0 = cell96)) & ( ~ (v1 =
% 13.43/2.60 | cell94) | ~ (v0 = cell95)) & ( ~ (v1 = cell93) | ~ (v0 =
% 13.43/2.60 | cell94)) & ( ~ (v1 = cell92) | ~ (v0 = cell93)) & ( ~ (v1 =
% 13.43/2.60 | cell91) | ~ (v0 = cell92)) & ( ~ (v1 = cell90) | ~ (v0 =
% 13.43/2.60 | cell100)) & ( ~ (v1 = cell89) | ~ (v0 = cell99)) & ( ~ (v1 =
% 13.43/2.60 | cell89) | ~ (v0 = cell90)) & ( ~ (v1 = cell88) | ~ (v0 =
% 13.43/2.60 | cell98)) & ( ~ (v1 = cell88) | ~ (v0 = cell89)) & ( ~ (v1 =
% 13.43/2.60 | cell87) | ~ (v0 = cell97)) & ( ~ (v1 = cell87) | ~ (v0 =
% 13.43/2.60 | cell88)) & ( ~ (v1 = cell86) | ~ (v0 = cell96)) & ( ~ (v1 =
% 13.43/2.60 | cell86) | ~ (v0 = cell87)) & ( ~ (v1 = cell85) | ~ (v0 =
% 13.43/2.60 | cell95)) & ( ~ (v1 = cell85) | ~ (v0 = cell86)) & ( ~ (v1 =
% 13.43/2.60 | cell84) | ~ (v0 = cell94)) & ( ~ (v1 = cell84) | ~ (v0 =
% 13.43/2.60 | cell85)) & ( ~ (v1 = cell83) | ~ (v0 = cell93)) & ( ~ (v1 =
% 13.43/2.60 | cell83) | ~ (v0 = cell84)) & ( ~ (v1 = cell82) | ~ (v0 =
% 13.43/2.60 | cell92)) & ( ~ (v1 = cell82) | ~ (v0 = cell83)) & ( ~ (v1 =
% 13.43/2.60 | cell81) | ~ (v0 = cell91)) & ( ~ (v1 = cell81) | ~ (v0 =
% 13.43/2.60 | cell82)) & ( ~ (v1 = cell80) | ~ (v0 = cell90)) & ( ~ (v1 =
% 13.43/2.60 | cell79) | ~ (v0 = cell89)) & ( ~ (v1 = cell79) | ~ (v0 =
% 13.43/2.60 | cell80)) & ( ~ (v1 = cell78) | ~ (v0 = cell88)) & ( ~ (v1 =
% 13.43/2.60 | cell78) | ~ (v0 = cell79)) & ( ~ (v1 = cell77) | ~ (v0 =
% 13.43/2.60 | cell87)) & ( ~ (v1 = cell77) | ~ (v0 = cell78)) & ( ~ (v1 =
% 13.43/2.60 | cell76) | ~ (v0 = cell86)) & ( ~ (v1 = cell76) | ~ (v0 =
% 13.43/2.60 | cell77)) & ( ~ (v1 = cell75) | ~ (v0 = cell85)) & ( ~ (v1 =
% 13.43/2.60 | cell75) | ~ (v0 = cell76)) & ( ~ (v1 = cell74) | ~ (v0 =
% 13.43/2.60 | cell84)) & ( ~ (v1 = cell74) | ~ (v0 = cell75)) & ( ~ (v1 =
% 13.43/2.60 | cell73) | ~ (v0 = cell83)) & ( ~ (v1 = cell73) | ~ (v0 =
% 13.43/2.60 | cell74)) & ( ~ (v1 = cell72) | ~ (v0 = cell82)) & ( ~ (v1 =
% 13.43/2.60 | cell72) | ~ (v0 = cell73)) & ( ~ (v1 = cell71) | ~ (v0 =
% 13.43/2.60 | cell81)) & ( ~ (v1 = cell71) | ~ (v0 = cell72)) & ( ~ (v1 =
% 13.43/2.60 | cell70) | ~ (v0 = cell80)) & ( ~ (v1 = cell69) | ~ (v0 =
% 13.43/2.60 | cell79)) & ( ~ (v1 = cell69) | ~ (v0 = cell70)) & ( ~ (v1 =
% 13.43/2.60 | cell68) | ~ (v0 = cell78)) & ( ~ (v1 = cell68) | ~ (v0 =
% 13.43/2.60 | cell69)) & ( ~ (v1 = cell67) | ~ (v0 = cell77)) & ( ~ (v1 =
% 13.43/2.60 | cell67) | ~ (v0 = cell68)) & ( ~ (v1 = cell66) | ~ (v0 =
% 13.43/2.60 | cell76)) & ( ~ (v1 = cell66) | ~ (v0 = cell67)) & ( ~ (v1 =
% 13.43/2.60 | cell65) | ~ (v0 = cell75)) & ( ~ (v1 = cell65) | ~ (v0 =
% 13.43/2.60 | cell66)) & ( ~ (v1 = cell64) | ~ (v0 = cell74)) & ( ~ (v1 =
% 13.43/2.60 | cell64) | ~ (v0 = cell65)) & ( ~ (v1 = cell63) | ~ (v0 =
% 13.43/2.60 | cell73)) & ( ~ (v1 = cell63) | ~ (v0 = cell64)) & ( ~ (v1 =
% 13.43/2.60 | cell62) | ~ (v0 = cell72)) & ( ~ (v1 = cell62) | ~ (v0 =
% 13.43/2.60 | cell63)) & ( ~ (v1 = cell61) | ~ (v0 = cell71)) & ( ~ (v1 =
% 13.43/2.60 | cell61) | ~ (v0 = cell62)) & ( ~ (v1 = cell60) | ~ (v0 =
% 13.43/2.60 | cell70)) & ( ~ (v1 = cell59) | ~ (v0 = cell69)) & ( ~ (v1 =
% 13.43/2.60 | cell59) | ~ (v0 = cell60)) & ( ~ (v1 = cell58) | ~ (v0 =
% 13.43/2.60 | cell68)) & ( ~ (v1 = cell58) | ~ (v0 = cell59)) & ( ~ (v1 =
% 13.43/2.60 | cell57) | ~ (v0 = cell67)) & ( ~ (v1 = cell57) | ~ (v0 =
% 13.43/2.60 | cell58)) & ( ~ (v1 = cell56) | ~ (v0 = cell66)) & ( ~ (v1 =
% 13.43/2.60 | cell56) | ~ (v0 = cell57)) & ( ~ (v1 = cell55) | ~ (v0 =
% 13.43/2.60 | cell65)) & ( ~ (v1 = cell55) | ~ (v0 = cell56)) & ( ~ (v1 =
% 13.43/2.60 | cell54) | ~ (v0 = cell64)) & ( ~ (v1 = cell54) | ~ (v0 =
% 13.43/2.60 | cell55)) & ( ~ (v1 = cell53) | ~ (v0 = cell63)) & ( ~ (v1 =
% 13.43/2.60 | cell53) | ~ (v0 = cell54)) & ( ~ (v1 = cell52) | ~ (v0 =
% 13.43/2.60 | cell62)) & ( ~ (v1 = cell52) | ~ (v0 = cell53)) & ( ~ (v1 =
% 13.43/2.60 | cell51) | ~ (v0 = cell61)) & ( ~ (v1 = cell51) | ~ (v0 =
% 13.43/2.60 | cell52)) & ( ~ (v1 = cell50) | ~ (v0 = cell60)) & ( ~ (v1 =
% 13.43/2.60 | cell49) | ~ (v0 = cell59)) & ( ~ (v1 = cell49) | ~ (v0 =
% 13.43/2.60 | cell50)) & ( ~ (v1 = cell48) | ~ (v0 = cell58)) & ( ~ (v1 =
% 13.43/2.60 | cell48) | ~ (v0 = cell49)) & ( ~ (v1 = cell47) | ~ (v0 =
% 13.43/2.60 | cell57)) & ( ~ (v1 = cell47) | ~ (v0 = cell48)) & ( ~ (v1 =
% 13.43/2.60 | cell46) | ~ (v0 = cell56)) & ( ~ (v1 = cell46) | ~ (v0 =
% 13.43/2.60 | cell47)) & ( ~ (v1 = cell45) | ~ (v0 = cell55)) & ( ~ (v1 =
% 13.43/2.60 | cell45) | ~ (v0 = cell46)) & ( ~ (v1 = cell44) | ~ (v0 =
% 13.43/2.60 | cell54)) & ( ~ (v1 = cell44) | ~ (v0 = cell45)) & ( ~ (v1 =
% 13.43/2.60 | cell43) | ~ (v0 = cell53)) & ( ~ (v1 = cell43) | ~ (v0 =
% 13.43/2.60 | cell44)) & ( ~ (v1 = cell42) | ~ (v0 = cell52)) & ( ~ (v1 =
% 13.43/2.60 | cell42) | ~ (v0 = cell43)) & ( ~ (v1 = cell41) | ~ (v0 =
% 13.43/2.60 | cell51)) & ( ~ (v1 = cell41) | ~ (v0 = cell42)) & ( ~ (v1 =
% 13.43/2.60 | cell40) | ~ (v0 = cell50)) & ( ~ (v1 = cell39) | ~ (v0 =
% 13.43/2.60 | cell49)) & ( ~ (v1 = cell39) | ~ (v0 = cell40)) & ( ~ (v1 =
% 13.43/2.60 | cell38) | ~ (v0 = cell48)) & ( ~ (v1 = cell38) | ~ (v0 =
% 13.43/2.60 | cell39)) & ( ~ (v1 = cell37) | ~ (v0 = cell47)) & ( ~ (v1 =
% 13.43/2.60 | cell37) | ~ (v0 = cell38)) & ( ~ (v1 = cell36) | ~ (v0 =
% 13.43/2.60 | cell46)) & ( ~ (v1 = cell36) | ~ (v0 = cell37)) & ( ~ (v1 =
% 13.43/2.60 | cell35) | ~ (v0 = cell45)) & ( ~ (v1 = cell35) | ~ (v0 =
% 13.43/2.60 | cell36)) & ( ~ (v1 = cell34) | ~ (v0 = cell44)) & ( ~ (v1 =
% 13.43/2.60 | cell34) | ~ (v0 = cell35)) & ( ~ (v1 = cell33) | ~ (v0 =
% 13.43/2.60 | cell43)) & ( ~ (v1 = cell33) | ~ (v0 = cell34)) & ( ~ (v1 =
% 13.43/2.60 | cell32) | ~ (v0 = cell42)) & ( ~ (v1 = cell32) | ~ (v0 =
% 13.43/2.60 | cell33)) & ( ~ (v1 = cell31) | ~ (v0 = cell41)) & ( ~ (v1 =
% 13.43/2.60 | cell31) | ~ (v0 = cell32)) & ( ~ (v1 = cell30) | ~ (v0 =
% 13.43/2.60 | cell40)) & ( ~ (v1 = cell29) | ~ (v0 = cell39)) & ( ~ (v1 =
% 13.43/2.60 | cell29) | ~ (v0 = cell30)) & ( ~ (v1 = cell28) | ~ (v0 =
% 13.43/2.60 | cell38)) & ( ~ (v1 = cell28) | ~ (v0 = cell29)) & ( ~ (v1 =
% 13.43/2.60 | cell27) | ~ (v0 = cell37)) & ( ~ (v1 = cell27) | ~ (v0 =
% 13.43/2.60 | cell28)) & ( ~ (v1 = cell26) | ~ (v0 = cell36)) & ( ~ (v1 =
% 13.43/2.60 | cell26) | ~ (v0 = cell27)) & ( ~ (v1 = cell25) | ~ (v0 =
% 13.43/2.60 | cell35)) & ( ~ (v1 = cell25) | ~ (v0 = cell26)) & ( ~ (v1 =
% 13.43/2.60 | cell24) | ~ (v0 = cell34)) & ( ~ (v1 = cell24) | ~ (v0 =
% 13.43/2.60 | cell25)) & ( ~ (v1 = cell23) | ~ (v0 = cell33)) & ( ~ (v1 =
% 13.43/2.60 | cell23) | ~ (v0 = cell24)) & ( ~ (v1 = cell22) | ~ (v0 =
% 13.43/2.60 | cell32)) & ( ~ (v1 = cell22) | ~ (v0 = cell23)) & ( ~ (v1 =
% 13.43/2.60 | cell21) | ~ (v0 = cell31)) & ( ~ (v1 = cell21) | ~ (v0 =
% 13.43/2.60 | cell22)) & ( ~ (v1 = cell20) | ~ (v0 = cell30)) & ( ~ (v1 =
% 13.43/2.60 | cell19) | ~ (v0 = cell29)) & ( ~ (v1 = cell19) | ~ (v0 =
% 13.43/2.60 | cell20)) & ( ~ (v1 = cell18) | ~ (v0 = cell28)) & ( ~ (v1 =
% 13.43/2.60 | cell18) | ~ (v0 = cell19)) & ( ~ (v1 = cell17) | ~ (v0 =
% 13.43/2.60 | cell27)) & ( ~ (v1 = cell17) | ~ (v0 = cell18)) & ( ~ (v1 =
% 13.43/2.60 | cell16) | ~ (v0 = cell26)) & ( ~ (v1 = cell16) | ~ (v0 =
% 13.43/2.60 | cell17)) & ( ~ (v1 = cell15) | ~ (v0 = cell25)) & ( ~ (v1 =
% 13.43/2.60 | cell15) | ~ (v0 = cell16)) & ( ~ (v1 = cell14) | ~ (v0 =
% 13.43/2.60 | cell24)) & ( ~ (v1 = cell14) | ~ (v0 = cell15)) & ( ~ (v1 =
% 13.43/2.60 | cell13) | ~ (v0 = cell23)) & ( ~ (v1 = cell13) | ~ (v0 =
% 13.43/2.60 | cell14)) & ( ~ (v1 = cell12) | ~ (v0 = cell22)) & ( ~ (v1 =
% 13.43/2.60 | cell12) | ~ (v0 = cell13)) & ( ~ (v1 = cell11) | ~ (v0 =
% 13.43/2.60 | cell21)) & ( ~ (v1 = cell11) | ~ (v0 = cell12)) & ( ~ (v1 =
% 13.43/2.60 | cell10) | ~ (v0 = cell20)) & ( ~ (v1 = cell9) | ~ (v0 =
% 13.43/2.60 | cell19)) & ( ~ (v1 = cell9) | ~ (v0 = cell10)) & ( ~ (v1 =
% 13.43/2.60 | cell8) | ~ (v0 = cell18)) & ( ~ (v1 = cell8) | ~ (v0 =
% 13.43/2.60 | cell9)) & ( ~ (v1 = cell7) | ~ (v0 = cell17)) & ( ~ (v1 =
% 13.43/2.60 | cell7) | ~ (v0 = cell8)) & ( ~ (v1 = cell6) | ~ (v0 =
% 13.43/2.60 | cell16)) & ( ~ (v1 = cell6) | ~ (v0 = cell7)) & ( ~ (v1 =
% 13.43/2.60 | cell5) | ~ (v0 = cell15)) & ( ~ (v1 = cell5) | ~ (v0 =
% 13.43/2.60 | cell6)) & ( ~ (v1 = cell4) | ~ (v0 = cell14)) & ( ~ (v1 =
% 13.43/2.60 | cell4) | ~ (v0 = cell5)) & ( ~ (v1 = cell3) | ~ (v0 =
% 13.43/2.60 | cell13)) & ( ~ (v1 = cell3) | ~ (v0 = cell4)) & ( ~ (v1 =
% 13.43/2.60 | cell2) | ~ (v0 = cell12)) & ( ~ (v1 = cell2) | ~ (v0 =
% 13.43/2.60 | cell3)) & ( ~ (v1 = cell1) | ~ (v0 = cell11)) & ( ~ (v1 =
% 13.43/2.60 | cell1) | ~ (v0 = cell2))))
% 13.43/2.60 |
% 13.43/2.60 | ALPHA: (tlhfof24988) implies:
% 13.43/2.60 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (adj(v1, v0) =
% 13.43/2.60 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ( ~ (v4
% 13.43/2.60 | = 0) & ~ (v3 = 0) & edge(v1, v0) = v3 & edge(v0, v1) = v4))
% 13.43/2.60 |
% 13.43/2.60 | ALPHA: (tlhfof24989) implies:
% 13.43/2.60 | (3) $i(cell12)
% 13.43/2.60 | (4) $i(cell13)
% 13.43/2.60 | (5) ? [v0: int] : ( ~ (v0 = 0) & adj(cell12, cell13) = v0)
% 13.43/2.60 |
% 13.43/2.60 | DELTA: instantiating (5) with fresh symbol all_6_0 gives:
% 13.43/2.60 | (6) ~ (all_6_0 = 0) & adj(cell12, cell13) = all_6_0
% 13.43/2.60 |
% 13.43/2.60 | ALPHA: (6) implies:
% 13.43/2.61 | (7) ~ (all_6_0 = 0)
% 13.43/2.61 | (8) adj(cell12, cell13) = all_6_0
% 13.43/2.61 |
% 13.43/2.61 | GROUND_INST: instantiating (2) with cell13, cell12, all_6_0, simplifying with
% 13.43/2.61 | (3), (4), (8) gives:
% 13.43/2.61 | (9) all_6_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0)
% 13.43/2.61 | & edge(cell13, cell12) = v1 & edge(cell12, cell13) = v0)
% 13.43/2.61 |
% 13.43/2.61 | BETA: splitting (9) gives:
% 13.43/2.61 |
% 13.43/2.61 | Case 1:
% 13.43/2.61 | |
% 13.43/2.61 | | (10) all_6_0 = 0
% 13.43/2.61 | |
% 13.43/2.61 | | REDUCE: (7), (10) imply:
% 13.43/2.61 | | (11) $false
% 13.43/2.61 | |
% 13.43/2.61 | | CLOSE: (11) is inconsistent.
% 13.43/2.61 | |
% 13.43/2.61 | Case 2:
% 13.43/2.61 | |
% 13.43/2.61 | | (12) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) &
% 13.43/2.61 | | edge(cell13, cell12) = v1 & edge(cell12, cell13) = v0)
% 13.43/2.61 | |
% 13.43/2.61 | | DELTA: instantiating (12) with fresh symbols all_15_0, all_15_1 gives:
% 13.43/2.61 | | (13) ~ (all_15_0 = 0) & ~ (all_15_1 = 0) & edge(cell13, cell12) =
% 13.43/2.61 | | all_15_0 & edge(cell12, cell13) = all_15_1
% 13.43/2.61 | |
% 13.43/2.61 | | ALPHA: (13) implies:
% 13.43/2.61 | | (14) ~ (all_15_1 = 0)
% 13.43/2.61 | | (15) edge(cell12, cell13) = all_15_1
% 13.43/2.61 | |
% 13.43/2.61 | | GROUND_INST: instantiating (1) with cell13, cell12, all_15_1, simplifying
% 13.43/2.61 | | with (3), (4), (15) gives:
% 13.43/2.61 | | (16) all_15_1 = 0
% 13.43/2.61 | |
% 13.43/2.61 | | REDUCE: (14), (16) imply:
% 13.43/2.61 | | (17) $false
% 13.43/2.61 | |
% 13.43/2.61 | | CLOSE: (17) is inconsistent.
% 13.43/2.61 | |
% 13.43/2.61 | End of split
% 13.43/2.61 |
% 13.43/2.61 End of proof
% 13.43/2.61 % SZS output end Proof for theBenchmark
% 13.43/2.61
% 13.43/2.61 1987ms
%------------------------------------------------------------------------------