TSTP Solution File: SYO901_11 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SYO901_11 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n021.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 : Fri Sep 1 04:54:11 EDT 2023
% Result : Theorem 3.67s 1.28s
% Output : Proof 5.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYO901_11 : TPTP v8.2.0. Released v8.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 02:11:41 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.70/0.98 Prover 4: Preprocessing ...
% 1.70/0.98 Prover 1: Preprocessing ...
% 2.29/1.02 Prover 6: Preprocessing ...
% 2.29/1.02 Prover 5: Preprocessing ...
% 2.29/1.02 Prover 0: Preprocessing ...
% 2.29/1.02 Prover 3: Preprocessing ...
% 2.29/1.02 Prover 2: Preprocessing ...
% 3.02/1.13 Prover 2: Proving ...
% 3.02/1.13 Prover 5: Proving ...
% 3.02/1.15 Prover 3: Constructing countermodel ...
% 3.02/1.16 Prover 1: Constructing countermodel ...
% 3.02/1.16 Prover 6: Proving ...
% 3.02/1.18 Prover 4: Constructing countermodel ...
% 3.67/1.20 Prover 0: Proving ...
% 3.67/1.28 Prover 3: gave up
% 3.67/1.28 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.67/1.28 Prover 2: proved (646ms)
% 3.67/1.28
% 3.67/1.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.67/1.28
% 3.67/1.28 Prover 0: stopped
% 3.67/1.28 Prover 6: stopped
% 3.67/1.28 Prover 5: stopped
% 3.67/1.29 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.67/1.29 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.67/1.29 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.33/1.29 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.33/1.30 Prover 7: Preprocessing ...
% 4.33/1.30 Prover 8: Preprocessing ...
% 4.33/1.31 Prover 11: Preprocessing ...
% 4.33/1.31 Prover 13: Preprocessing ...
% 4.33/1.31 Prover 10: Preprocessing ...
% 4.33/1.32 Prover 1: gave up
% 4.33/1.32 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 4.33/1.32 Prover 13: Warning: ignoring some quantifiers
% 4.33/1.33 Prover 10: Warning: ignoring some quantifiers
% 4.33/1.33 Prover 7: Warning: ignoring some quantifiers
% 4.33/1.33 Prover 13: Constructing countermodel ...
% 4.33/1.33 Prover 10: Constructing countermodel ...
% 4.33/1.33 Prover 16: Preprocessing ...
% 4.33/1.35 Prover 7: Constructing countermodel ...
% 4.33/1.36 Prover 13: gave up
% 4.33/1.36 Prover 10: gave up
% 4.33/1.37 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 4.33/1.37 Prover 8: Warning: ignoring some quantifiers
% 4.33/1.37 Prover 8: Constructing countermodel ...
% 4.33/1.37 Prover 16: Warning: ignoring some quantifiers
% 4.33/1.38 Prover 16: Constructing countermodel ...
% 5.01/1.39 Prover 19: Preprocessing ...
% 5.01/1.40 Prover 7: gave up
% 5.01/1.43 Prover 11: Constructing countermodel ...
% 5.01/1.44 Prover 16: gave up
% 5.01/1.45 Prover 4: Found proof (size 37)
% 5.01/1.45 Prover 4: proved (805ms)
% 5.01/1.45 Prover 8: stopped
% 5.01/1.45 Prover 11: stopped
% 5.01/1.46 Prover 19: Warning: ignoring some quantifiers
% 5.01/1.46 Prover 19: Constructing countermodel ...
% 5.01/1.46 Prover 19: stopped
% 5.01/1.46
% 5.01/1.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.01/1.46
% 5.01/1.47 % SZS output start Proof for theBenchmark
% 5.01/1.47 Assumptions after simplification:
% 5.01/1.47 ---------------------------------
% 5.01/1.47
% 5.01/1.47 (mrel_universal)
% 5.62/1.50 ! [v0: $ki_world] : ! [v1: $ki_world] : ! [v2: int] : (v2 = 0 | ~
% 5.62/1.50 ($ki_accessible(v0, v1) = v2) | ~ $ki_world(v1) | ~ $ki_world(v0))
% 5.62/1.50
% 5.62/1.50 (verify)
% 5.64/1.51 $ki_world($ki_local_world) & ? [v0: $ki_world] : ? [v1: $ki_world] : ? [v2:
% 5.64/1.51 int] : ? [v3: int] : ? [v4: $ki_world] : ? [v5: int] : ? [v6: int] :
% 5.64/1.51 ($ki_accessible($ki_local_world, v0) = 0 & $ki_world(v4) & $ki_world(v1) &
% 5.64/1.51 $ki_world(v0) & ! [v7: $ki_world] : ! [v8: any] : ( ~ (q(v7) = v8) | ~
% 5.64/1.51 $ki_world(v7) | ? [v9: any] : ? [v10: any] : (p(v7) = v10 &
% 5.64/1.51 $ki_accessible($ki_local_world, v7) = v9 & ( ~ (v9 = 0) | (( ~ (v10 = 0)
% 5.64/1.51 | v8 = 0) & ( ~ (v8 = 0) | v10 = 0))))) & ! [v7: $ki_world] : !
% 5.64/1.51 [v8: any] : ( ~ (p(v7) = v8) | ~ $ki_world(v7) | ? [v9: any] : ? [v10:
% 5.64/1.51 any] : (q(v7) = v10 & $ki_accessible($ki_local_world, v7) = v9 & ( ~ (v9
% 5.64/1.51 = 0) | (( ~ (v10 = 0) | v8 = 0) & ( ~ (v8 = 0) | v10 = 0))))) & !
% 5.64/1.51 [v7: $ki_world] : ( ~ ($ki_accessible($ki_local_world, v7) = 0) | ~
% 5.64/1.51 $ki_world(v7) | ? [v8: any] : ? [v9: any] : (q(v7) = v9 & p(v7) = v8 & (
% 5.64/1.51 ~ (v9 = 0) | v8 = 0) & ( ~ (v8 = 0) | v9 = 0))) & ((v5 = 0 & ~ (v6 =
% 5.64/1.51 0) & q(v4) = v6 & $ki_accessible(v0, v4) = 0 & ! [v7: $ki_world] : !
% 5.64/1.51 [v8: int] : (v8 = 0 | ~ (p(v7) = v8) | ~ $ki_world(v7) | ? [v9: int]
% 5.64/1.51 : ( ~ (v9 = 0) & $ki_accessible(v0, v7) = v9)) & ! [v7: $ki_world] :
% 5.64/1.51 ( ~ ($ki_accessible(v0, v7) = 0) | ~ $ki_world(v7) | p(v7) = 0)) | (v2
% 5.64/1.51 = 0 & ~ (v3 = 0) & p(v1) = v3 & $ki_accessible(v0, v1) = 0 & ! [v7:
% 5.64/1.51 $ki_world] : ! [v8: int] : (v8 = 0 | ~ (q(v7) = v8) | ~
% 5.64/1.51 $ki_world(v7) | ? [v9: int] : ( ~ (v9 = 0) & $ki_accessible(v0, v7) =
% 5.64/1.51 v9)) & ! [v7: $ki_world] : ( ~ ($ki_accessible(v0, v7) = 0) | ~
% 5.64/1.51 $ki_world(v7) | q(v7) = 0))))
% 5.64/1.51
% 5.64/1.51 (function-axioms)
% 5.64/1.52 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $ki_world] :
% 5.64/1.52 ! [v3: $ki_world] : (v1 = v0 | ~ ($ki_accessible(v3, v2) = v1) | ~
% 5.64/1.52 ($ki_accessible(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 5.64/1.52 MultipleValueBool] : ! [v2: $ki_world] : (v1 = v0 | ~ (q(v2) = v1) | ~
% 5.64/1.52 (q(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : !
% 5.64/1.52 [v2: $ki_world] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0))
% 5.64/1.52
% 5.64/1.52 Those formulas are unsatisfiable:
% 5.64/1.52 ---------------------------------
% 5.64/1.52
% 5.64/1.52 Begin of proof
% 5.64/1.52 |
% 5.64/1.52 | ALPHA: (verify) implies:
% 5.64/1.52 | (1) $ki_world($ki_local_world)
% 5.64/1.53 | (2) ? [v0: $ki_world] : ? [v1: $ki_world] : ? [v2: int] : ? [v3: int] :
% 5.64/1.53 | ? [v4: $ki_world] : ? [v5: int] : ? [v6: int] :
% 5.64/1.53 | ($ki_accessible($ki_local_world, v0) = 0 & $ki_world(v4) &
% 5.64/1.53 | $ki_world(v1) & $ki_world(v0) & ! [v7: $ki_world] : ! [v8: any] : (
% 5.64/1.53 | ~ (q(v7) = v8) | ~ $ki_world(v7) | ? [v9: any] : ? [v10: any] :
% 5.64/1.53 | (p(v7) = v10 & $ki_accessible($ki_local_world, v7) = v9 & ( ~ (v9 =
% 5.64/1.53 | 0) | (( ~ (v10 = 0) | v8 = 0) & ( ~ (v8 = 0) | v10 = 0))))) &
% 5.64/1.53 | ! [v7: $ki_world] : ! [v8: any] : ( ~ (p(v7) = v8) | ~
% 5.64/1.53 | $ki_world(v7) | ? [v9: any] : ? [v10: any] : (q(v7) = v10 &
% 5.64/1.53 | $ki_accessible($ki_local_world, v7) = v9 & ( ~ (v9 = 0) | (( ~
% 5.64/1.53 | (v10 = 0) | v8 = 0) & ( ~ (v8 = 0) | v10 = 0))))) & ! [v7:
% 5.64/1.53 | $ki_world] : ( ~ ($ki_accessible($ki_local_world, v7) = 0) | ~
% 5.64/1.53 | $ki_world(v7) | ? [v8: any] : ? [v9: any] : (q(v7) = v9 & p(v7) =
% 5.64/1.53 | v8 & ( ~ (v9 = 0) | v8 = 0) & ( ~ (v8 = 0) | v9 = 0))) & ((v5 = 0
% 5.64/1.53 | & ~ (v6 = 0) & q(v4) = v6 & $ki_accessible(v0, v4) = 0 & ! [v7:
% 5.64/1.53 | $ki_world] : ! [v8: int] : (v8 = 0 | ~ (p(v7) = v8) | ~
% 5.64/1.53 | $ki_world(v7) | ? [v9: int] : ( ~ (v9 = 0) &
% 5.64/1.53 | $ki_accessible(v0, v7) = v9)) & ! [v7: $ki_world] : ( ~
% 5.64/1.53 | ($ki_accessible(v0, v7) = 0) | ~ $ki_world(v7) | p(v7) = 0)) |
% 5.64/1.53 | (v2 = 0 & ~ (v3 = 0) & p(v1) = v3 & $ki_accessible(v0, v1) = 0 &
% 5.64/1.53 | ! [v7: $ki_world] : ! [v8: int] : (v8 = 0 | ~ (q(v7) = v8) | ~
% 5.64/1.53 | $ki_world(v7) | ? [v9: int] : ( ~ (v9 = 0) &
% 5.64/1.53 | $ki_accessible(v0, v7) = v9)) & ! [v7: $ki_world] : ( ~
% 5.64/1.53 | ($ki_accessible(v0, v7) = 0) | ~ $ki_world(v7) | q(v7) = 0))))
% 5.64/1.53 |
% 5.64/1.53 | ALPHA: (function-axioms) implies:
% 5.64/1.53 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 5.64/1.53 | $ki_world] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0))
% 5.64/1.53 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 5.64/1.53 | $ki_world] : (v1 = v0 | ~ (q(v2) = v1) | ~ (q(v2) = v0))
% 5.64/1.53 |
% 5.64/1.53 | DELTA: instantiating (2) with fresh symbols all_7_0, all_7_1, all_7_2,
% 5.64/1.53 | all_7_3, all_7_4, all_7_5, all_7_6 gives:
% 5.64/1.54 | (5) $ki_accessible($ki_local_world, all_7_6) = 0 & $ki_world(all_7_2) &
% 5.64/1.54 | $ki_world(all_7_5) & $ki_world(all_7_6) & ! [v0: $ki_world] : ! [v1:
% 5.64/1.54 | any] : ( ~ (q(v0) = v1) | ~ $ki_world(v0) | ? [v2: any] : ? [v3:
% 5.64/1.54 | any] : (p(v0) = v3 & $ki_accessible($ki_local_world, v0) = v2 & ( ~
% 5.64/1.54 | (v2 = 0) | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0))))) &
% 5.64/1.54 | ! [v0: $ki_world] : ! [v1: any] : ( ~ (p(v0) = v1) | ~ $ki_world(v0)
% 5.64/1.54 | | ? [v2: any] : ? [v3: any] : (q(v0) = v3 &
% 5.64/1.54 | $ki_accessible($ki_local_world, v0) = v2 & ( ~ (v2 = 0) | (( ~ (v3
% 5.64/1.54 | = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0))))) & ! [v0:
% 5.64/1.54 | $ki_world] : ( ~ ($ki_accessible($ki_local_world, v0) = 0) | ~
% 5.64/1.54 | $ki_world(v0) | ? [v1: any] : ? [v2: any] : (q(v0) = v2 & p(v0) =
% 5.64/1.54 | v1 & ( ~ (v2 = 0) | v1 = 0) & ( ~ (v1 = 0) | v2 = 0))) & ((all_7_1
% 5.64/1.54 | = 0 & ~ (all_7_0 = 0) & q(all_7_2) = all_7_0 &
% 5.64/1.54 | $ki_accessible(all_7_6, all_7_2) = 0 & ! [v0: $ki_world] : ! [v1:
% 5.64/1.54 | int] : (v1 = 0 | ~ (p(v0) = v1) | ~ $ki_world(v0) | ? [v2:
% 5.64/1.54 | int] : ( ~ (v2 = 0) & $ki_accessible(all_7_6, v0) = v2)) & !
% 5.64/1.54 | [v0: $ki_world] : ( ~ ($ki_accessible(all_7_6, v0) = 0) | ~
% 5.64/1.54 | $ki_world(v0) | p(v0) = 0)) | (all_7_4 = 0 & ~ (all_7_3 = 0) &
% 5.64/1.54 | p(all_7_5) = all_7_3 & $ki_accessible(all_7_6, all_7_5) = 0 & !
% 5.64/1.54 | [v0: $ki_world] : ! [v1: int] : (v1 = 0 | ~ (q(v0) = v1) | ~
% 5.64/1.54 | $ki_world(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 5.64/1.54 | $ki_accessible(all_7_6, v0) = v2)) & ! [v0: $ki_world] : ( ~
% 5.64/1.54 | ($ki_accessible(all_7_6, v0) = 0) | ~ $ki_world(v0) | q(v0) =
% 5.64/1.54 | 0)))
% 5.64/1.54 |
% 5.64/1.54 | ALPHA: (5) implies:
% 5.64/1.54 | (6) $ki_world(all_7_5)
% 5.64/1.54 | (7) $ki_world(all_7_2)
% 5.64/1.54 | (8) (all_7_1 = 0 & ~ (all_7_0 = 0) & q(all_7_2) = all_7_0 &
% 5.64/1.54 | $ki_accessible(all_7_6, all_7_2) = 0 & ! [v0: $ki_world] : ! [v1:
% 5.64/1.54 | int] : (v1 = 0 | ~ (p(v0) = v1) | ~ $ki_world(v0) | ? [v2: int]
% 5.64/1.54 | : ( ~ (v2 = 0) & $ki_accessible(all_7_6, v0) = v2)) & ! [v0:
% 5.64/1.54 | $ki_world] : ( ~ ($ki_accessible(all_7_6, v0) = 0) | ~
% 5.64/1.54 | $ki_world(v0) | p(v0) = 0)) | (all_7_4 = 0 & ~ (all_7_3 = 0) &
% 5.64/1.54 | p(all_7_5) = all_7_3 & $ki_accessible(all_7_6, all_7_5) = 0 & ! [v0:
% 5.64/1.54 | $ki_world] : ! [v1: int] : (v1 = 0 | ~ (q(v0) = v1) | ~
% 5.64/1.54 | $ki_world(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 5.64/1.54 | $ki_accessible(all_7_6, v0) = v2)) & ! [v0: $ki_world] : ( ~
% 5.64/1.54 | ($ki_accessible(all_7_6, v0) = 0) | ~ $ki_world(v0) | q(v0) = 0))
% 5.64/1.54 | (9) ! [v0: $ki_world] : ! [v1: any] : ( ~ (p(v0) = v1) | ~ $ki_world(v0)
% 5.64/1.54 | | ? [v2: any] : ? [v3: any] : (q(v0) = v3 &
% 5.64/1.54 | $ki_accessible($ki_local_world, v0) = v2 & ( ~ (v2 = 0) | (( ~ (v3
% 5.64/1.54 | = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0)))))
% 5.64/1.54 | (10) ! [v0: $ki_world] : ! [v1: any] : ( ~ (q(v0) = v1) | ~
% 5.64/1.54 | $ki_world(v0) | ? [v2: any] : ? [v3: any] : (p(v0) = v3 &
% 5.64/1.54 | $ki_accessible($ki_local_world, v0) = v2 & ( ~ (v2 = 0) | (( ~ (v3
% 5.64/1.54 | = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0)))))
% 5.64/1.54 |
% 5.64/1.54 | BETA: splitting (8) gives:
% 5.64/1.54 |
% 5.64/1.54 | Case 1:
% 5.64/1.54 | |
% 5.64/1.55 | | (11) all_7_1 = 0 & ~ (all_7_0 = 0) & q(all_7_2) = all_7_0 &
% 5.64/1.55 | | $ki_accessible(all_7_6, all_7_2) = 0 & ! [v0: $ki_world] : ! [v1:
% 5.64/1.55 | | int] : (v1 = 0 | ~ (p(v0) = v1) | ~ $ki_world(v0) | ? [v2: int]
% 5.64/1.55 | | : ( ~ (v2 = 0) & $ki_accessible(all_7_6, v0) = v2)) & ! [v0:
% 5.64/1.55 | | $ki_world] : ( ~ ($ki_accessible(all_7_6, v0) = 0) | ~
% 5.64/1.55 | | $ki_world(v0) | p(v0) = 0)
% 5.64/1.55 | |
% 5.64/1.55 | | ALPHA: (11) implies:
% 5.64/1.55 | | (12) ~ (all_7_0 = 0)
% 5.64/1.55 | | (13) $ki_accessible(all_7_6, all_7_2) = 0
% 5.64/1.55 | | (14) q(all_7_2) = all_7_0
% 5.64/1.55 | | (15) ! [v0: $ki_world] : ( ~ ($ki_accessible(all_7_6, v0) = 0) | ~
% 5.64/1.55 | | $ki_world(v0) | p(v0) = 0)
% 5.64/1.55 | |
% 5.64/1.55 | | GROUND_INST: instantiating (15) with all_7_2, simplifying with (7), (13)
% 5.64/1.55 | | gives:
% 5.64/1.55 | | (16) p(all_7_2) = 0
% 5.64/1.55 | |
% 5.64/1.55 | | GROUND_INST: instantiating (10) with all_7_2, all_7_0, simplifying with (7),
% 5.64/1.55 | | (14) gives:
% 5.64/1.55 | | (17) ? [v0: any] : ? [v1: any] : (p(all_7_2) = v1 &
% 5.64/1.55 | | $ki_accessible($ki_local_world, all_7_2) = v0 & ( ~ (v0 = 0) | ((
% 5.64/1.55 | | ~ (v1 = 0) | all_7_0 = 0) & ( ~ (all_7_0 = 0) | v1 = 0))))
% 5.64/1.55 | |
% 5.64/1.55 | | DELTA: instantiating (17) with fresh symbols all_44_0, all_44_1 gives:
% 5.64/1.55 | | (18) p(all_7_2) = all_44_0 & $ki_accessible($ki_local_world, all_7_2) =
% 5.64/1.55 | | all_44_1 & ( ~ (all_44_1 = 0) | (( ~ (all_44_0 = 0) | all_7_0 = 0) &
% 5.64/1.55 | | ( ~ (all_7_0 = 0) | all_44_0 = 0)))
% 5.64/1.55 | |
% 5.64/1.55 | | ALPHA: (18) implies:
% 5.64/1.55 | | (19) $ki_accessible($ki_local_world, all_7_2) = all_44_1
% 5.64/1.55 | | (20) p(all_7_2) = all_44_0
% 5.64/1.55 | | (21) ~ (all_44_1 = 0) | (( ~ (all_44_0 = 0) | all_7_0 = 0) & ( ~
% 5.64/1.55 | | (all_7_0 = 0) | all_44_0 = 0))
% 5.64/1.55 | |
% 5.64/1.55 | | GROUND_INST: instantiating (3) with 0, all_44_0, all_7_2, simplifying with
% 5.64/1.55 | | (16), (20) gives:
% 5.64/1.55 | | (22) all_44_0 = 0
% 5.64/1.55 | |
% 5.64/1.55 | | BETA: splitting (21) gives:
% 5.64/1.55 | |
% 5.64/1.55 | | Case 1:
% 5.64/1.55 | | |
% 5.64/1.55 | | | (23) ~ (all_44_1 = 0)
% 5.64/1.55 | | |
% 5.64/1.55 | | | GROUND_INST: instantiating (mrel_universal) with $ki_local_world, all_7_2,
% 5.64/1.55 | | | all_44_1, simplifying with (1), (7), (19) gives:
% 5.64/1.55 | | | (24) all_44_1 = 0
% 5.64/1.55 | | |
% 5.64/1.55 | | | REDUCE: (23), (24) imply:
% 5.64/1.55 | | | (25) $false
% 5.64/1.55 | | |
% 5.64/1.55 | | | CLOSE: (25) is inconsistent.
% 5.64/1.55 | | |
% 5.64/1.55 | | Case 2:
% 5.64/1.55 | | |
% 5.64/1.55 | | | (26) ( ~ (all_44_0 = 0) | all_7_0 = 0) & ( ~ (all_7_0 = 0) | all_44_0 =
% 5.64/1.55 | | | 0)
% 5.64/1.55 | | |
% 5.64/1.55 | | | ALPHA: (26) implies:
% 5.64/1.56 | | | (27) ~ (all_44_0 = 0) | all_7_0 = 0
% 5.64/1.56 | | |
% 5.64/1.56 | | | BETA: splitting (27) gives:
% 5.64/1.56 | | |
% 5.64/1.56 | | | Case 1:
% 5.64/1.56 | | | |
% 5.64/1.56 | | | | (28) ~ (all_44_0 = 0)
% 5.64/1.56 | | | |
% 5.64/1.56 | | | | REDUCE: (22), (28) imply:
% 5.64/1.56 | | | | (29) $false
% 5.64/1.56 | | | |
% 5.64/1.56 | | | | CLOSE: (29) is inconsistent.
% 5.64/1.56 | | | |
% 5.64/1.56 | | | Case 2:
% 5.64/1.56 | | | |
% 5.64/1.56 | | | | (30) all_7_0 = 0
% 5.64/1.56 | | | |
% 5.64/1.56 | | | | REDUCE: (12), (30) imply:
% 5.64/1.56 | | | | (31) $false
% 5.64/1.56 | | | |
% 5.64/1.56 | | | | CLOSE: (31) is inconsistent.
% 5.64/1.56 | | | |
% 5.64/1.56 | | | End of split
% 5.64/1.56 | | |
% 5.64/1.56 | | End of split
% 5.64/1.56 | |
% 5.64/1.56 | Case 2:
% 5.64/1.56 | |
% 5.64/1.56 | | (32) all_7_4 = 0 & ~ (all_7_3 = 0) & p(all_7_5) = all_7_3 &
% 5.64/1.56 | | $ki_accessible(all_7_6, all_7_5) = 0 & ! [v0: $ki_world] : ! [v1:
% 5.64/1.56 | | int] : (v1 = 0 | ~ (q(v0) = v1) | ~ $ki_world(v0) | ? [v2: int]
% 5.64/1.56 | | : ( ~ (v2 = 0) & $ki_accessible(all_7_6, v0) = v2)) & ! [v0:
% 5.64/1.56 | | $ki_world] : ( ~ ($ki_accessible(all_7_6, v0) = 0) | ~
% 5.64/1.56 | | $ki_world(v0) | q(v0) = 0)
% 5.64/1.56 | |
% 5.64/1.56 | | ALPHA: (32) implies:
% 5.64/1.56 | | (33) ~ (all_7_3 = 0)
% 5.64/1.56 | | (34) $ki_accessible(all_7_6, all_7_5) = 0
% 5.64/1.56 | | (35) p(all_7_5) = all_7_3
% 5.64/1.56 | | (36) ! [v0: $ki_world] : ( ~ ($ki_accessible(all_7_6, v0) = 0) | ~
% 5.64/1.56 | | $ki_world(v0) | q(v0) = 0)
% 5.64/1.56 | |
% 5.64/1.56 | | GROUND_INST: instantiating (36) with all_7_5, simplifying with (6), (34)
% 5.64/1.56 | | gives:
% 5.64/1.56 | | (37) q(all_7_5) = 0
% 5.64/1.56 | |
% 5.64/1.56 | | GROUND_INST: instantiating (9) with all_7_5, all_7_3, simplifying with (6),
% 5.64/1.56 | | (35) gives:
% 5.64/1.56 | | (38) ? [v0: any] : ? [v1: any] : (q(all_7_5) = v1 &
% 5.64/1.56 | | $ki_accessible($ki_local_world, all_7_5) = v0 & ( ~ (v0 = 0) | ((
% 5.64/1.56 | | ~ (v1 = 0) | all_7_3 = 0) & ( ~ (all_7_3 = 0) | v1 = 0))))
% 5.64/1.56 | |
% 5.64/1.56 | | DELTA: instantiating (38) with fresh symbols all_44_0, all_44_1 gives:
% 5.64/1.56 | | (39) q(all_7_5) = all_44_0 & $ki_accessible($ki_local_world, all_7_5) =
% 5.64/1.56 | | all_44_1 & ( ~ (all_44_1 = 0) | (( ~ (all_44_0 = 0) | all_7_3 = 0) &
% 5.64/1.56 | | ( ~ (all_7_3 = 0) | all_44_0 = 0)))
% 5.64/1.56 | |
% 5.64/1.56 | | ALPHA: (39) implies:
% 5.64/1.56 | | (40) $ki_accessible($ki_local_world, all_7_5) = all_44_1
% 5.64/1.56 | | (41) q(all_7_5) = all_44_0
% 5.64/1.56 | | (42) ~ (all_44_1 = 0) | (( ~ (all_44_0 = 0) | all_7_3 = 0) & ( ~
% 5.64/1.56 | | (all_7_3 = 0) | all_44_0 = 0))
% 5.64/1.56 | |
% 5.64/1.56 | | GROUND_INST: instantiating (4) with 0, all_44_0, all_7_5, simplifying with
% 5.64/1.56 | | (37), (41) gives:
% 5.64/1.56 | | (43) all_44_0 = 0
% 5.64/1.56 | |
% 5.64/1.56 | | BETA: splitting (42) gives:
% 5.64/1.56 | |
% 5.64/1.56 | | Case 1:
% 5.64/1.56 | | |
% 5.64/1.56 | | | (44) ~ (all_44_1 = 0)
% 5.64/1.56 | | |
% 5.64/1.56 | | | GROUND_INST: instantiating (mrel_universal) with $ki_local_world, all_7_5,
% 5.64/1.56 | | | all_44_1, simplifying with (1), (6), (40) gives:
% 5.64/1.56 | | | (45) all_44_1 = 0
% 5.64/1.56 | | |
% 5.64/1.56 | | | REDUCE: (44), (45) imply:
% 5.64/1.56 | | | (46) $false
% 5.64/1.56 | | |
% 5.64/1.56 | | | CLOSE: (46) is inconsistent.
% 5.64/1.56 | | |
% 5.64/1.56 | | Case 2:
% 5.64/1.56 | | |
% 5.64/1.56 | | | (47) ( ~ (all_44_0 = 0) | all_7_3 = 0) & ( ~ (all_7_3 = 0) | all_44_0 =
% 5.64/1.56 | | | 0)
% 5.64/1.56 | | |
% 5.64/1.56 | | | ALPHA: (47) implies:
% 5.64/1.56 | | | (48) ~ (all_44_0 = 0) | all_7_3 = 0
% 5.64/1.56 | | |
% 5.64/1.56 | | | BETA: splitting (48) gives:
% 5.64/1.56 | | |
% 5.64/1.56 | | | Case 1:
% 5.64/1.56 | | | |
% 5.64/1.56 | | | | (49) ~ (all_44_0 = 0)
% 5.64/1.56 | | | |
% 5.64/1.56 | | | | REDUCE: (43), (49) imply:
% 5.64/1.57 | | | | (50) $false
% 5.64/1.57 | | | |
% 5.64/1.57 | | | | CLOSE: (50) is inconsistent.
% 5.64/1.57 | | | |
% 5.64/1.57 | | | Case 2:
% 5.64/1.57 | | | |
% 5.64/1.57 | | | | (51) all_7_3 = 0
% 5.64/1.57 | | | |
% 5.64/1.57 | | | | REDUCE: (33), (51) imply:
% 5.64/1.57 | | | | (52) $false
% 5.64/1.57 | | | |
% 5.64/1.57 | | | | CLOSE: (52) is inconsistent.
% 5.64/1.57 | | | |
% 5.64/1.57 | | | End of split
% 5.64/1.57 | | |
% 5.64/1.57 | | End of split
% 5.64/1.57 | |
% 5.64/1.57 | End of split
% 5.64/1.57 |
% 5.64/1.57 End of proof
% 5.64/1.57 % SZS output end Proof for theBenchmark
% 5.64/1.57
% 5.64/1.57 954ms
%------------------------------------------------------------------------------