TSTP Solution File: SYO888_10 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SYO888_10 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n025.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 04:54:07 EDT 2023
% Result : Theorem 4.98s 1.38s
% Output : Proof 6.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO888_10 : TPTP v8.2.0. Released v8.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 07:45:52 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.21/1.00 Prover 4: Preprocessing ...
% 2.21/1.00 Prover 1: Preprocessing ...
% 2.21/1.04 Prover 2: Preprocessing ...
% 2.21/1.04 Prover 3: Preprocessing ...
% 2.21/1.04 Prover 0: Preprocessing ...
% 2.21/1.04 Prover 5: Preprocessing ...
% 2.21/1.04 Prover 6: Preprocessing ...
% 3.17/1.15 Prover 2: Proving ...
% 3.17/1.16 Prover 5: Proving ...
% 3.17/1.17 Prover 6: Proving ...
% 3.17/1.17 Prover 3: Warning: ignoring some quantifiers
% 3.17/1.18 Prover 3: Constructing countermodel ...
% 3.17/1.18 Prover 1: Warning: ignoring some quantifiers
% 3.17/1.20 Prover 1: Constructing countermodel ...
% 3.87/1.23 Prover 4: Warning: ignoring some quantifiers
% 3.87/1.27 Prover 4: Constructing countermodel ...
% 4.42/1.32 Prover 0: Proving ...
% 4.42/1.34 Prover 3: gave up
% 4.42/1.35 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.42/1.37 Prover 7: Preprocessing ...
% 4.42/1.38 Prover 2: proved (741ms)
% 4.98/1.38
% 4.98/1.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.98/1.38
% 4.98/1.38 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.98/1.38 Prover 7: Warning: ignoring some quantifiers
% 4.98/1.39 Prover 0: stopped
% 4.98/1.39 Prover 6: stopped
% 4.98/1.39 Prover 5: stopped
% 4.98/1.40 Prover 1: gave up
% 4.98/1.40 Prover 7: Constructing countermodel ...
% 4.98/1.40 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.98/1.40 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.98/1.40 Prover 8: Preprocessing ...
% 4.98/1.40 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.98/1.40 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 4.98/1.41 Prover 10: Preprocessing ...
% 4.98/1.42 Prover 10: Warning: ignoring some quantifiers
% 4.98/1.42 Prover 11: Preprocessing ...
% 4.98/1.42 Prover 10: Constructing countermodel ...
% 4.98/1.43 Prover 13: Preprocessing ...
% 4.98/1.44 Prover 7: gave up
% 4.98/1.44 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 4.98/1.44 Prover 16: Preprocessing ...
% 4.98/1.45 Prover 13: Warning: ignoring some quantifiers
% 4.98/1.45 Prover 10: gave up
% 4.98/1.46 Prover 13: Constructing countermodel ...
% 4.98/1.46 Prover 19: Preprocessing ...
% 4.98/1.47 Prover 8: Warning: ignoring some quantifiers
% 4.98/1.47 Prover 16: Warning: ignoring some quantifiers
% 4.98/1.47 Prover 16: Constructing countermodel ...
% 5.66/1.49 Prover 8: Constructing countermodel ...
% 5.66/1.49 Prover 13: gave up
% 5.66/1.50 Prover 16: gave up
% 5.66/1.52 Prover 11: Warning: ignoring some quantifiers
% 5.66/1.53 Prover 11: Constructing countermodel ...
% 5.66/1.54 Prover 8: gave up
% 5.66/1.54 Prover 19: Warning: ignoring some quantifiers
% 5.66/1.55 Prover 19: Constructing countermodel ...
% 5.66/1.56 Prover 4: Found proof (size 44)
% 5.66/1.56 Prover 4: proved (916ms)
% 5.66/1.56 Prover 19: stopped
% 5.66/1.56 Prover 11: stopped
% 5.66/1.57
% 5.66/1.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.66/1.57
% 5.66/1.57 % SZS output start Proof for theBenchmark
% 5.66/1.58 Assumptions after simplification:
% 5.66/1.58 ---------------------------------
% 5.66/1.58
% 5.66/1.58 (mrel_reflexive)
% 5.96/1.61 ! [v0: $ki_world] : ! [v1: int] : (v1 = 0 | ~ ($ki_accessible(v0, v0) = v1)
% 5.96/1.61 | ~ $ki_world(v0))
% 5.96/1.61
% 5.96/1.61 (verify)
% 6.50/1.62 $ki_world($ki_local_world) & ? [v0: $i] : ? [v1: $ki_world] : ? [v2: int] :
% 6.50/1.62 ( ~ (v2 = 0) & h(v1, v0) = v2 & f($ki_local_world, v0) = 0 &
% 6.50/1.62 $ki_exists_in_world_$i($ki_local_world, v0) = 0 &
% 6.50/1.62 $ki_accessible($ki_local_world, v1) = 0 & $ki_world(v1) & $i(v0) & ! [v3:
% 6.50/1.62 $i] : ! [v4: $ki_world] : ! [v5: int] : (v5 = 0 | ~ (h(v4, v3) = v5) |
% 6.50/1.62 ~ (g($ki_local_world, v3) = 0) | ~ $ki_world(v4) | ~ $i(v3) | ? [v6:
% 6.50/1.62 int] : (( ~ (v6 = 0) & $ki_exists_in_world_$i($ki_local_world, v3) = v6)
% 6.50/1.62 | ( ~ (v6 = 0) & $ki_accessible($ki_local_world, v4) = v6))) & ! [v3:
% 6.50/1.62 $i] : ! [v4: $ki_world] : ! [v5: int] : (v5 = 0 | ~ (h(v4, v3) = v5) |
% 6.50/1.62 ~ ($ki_exists_in_world_$i($ki_local_world, v3) = 0) | ~ $ki_world(v4) |
% 6.50/1.62 ~ $i(v3) | ? [v6: int] : (( ~ (v6 = 0) & g($ki_local_world, v3) = v6) | (
% 6.50/1.62 ~ (v6 = 0) & $ki_accessible($ki_local_world, v4) = v6))) & ! [v3: $i]
% 6.50/1.62 : ! [v4: $ki_world] : ! [v5: int] : (v5 = 0 | ~ (f($ki_local_world, v3) =
% 6.50/1.62 0) | ~ (g(v4, v3) = v5) | ~ $ki_world(v4) | ~ $i(v3) | ? [v6: int] :
% 6.50/1.62 (( ~ (v6 = 0) & $ki_exists_in_world_$i($ki_local_world, v3) = v6) | ( ~
% 6.50/1.62 (v6 = 0) & $ki_accessible($ki_local_world, v4) = v6))) & ! [v3: $i] :
% 6.50/1.62 ! [v4: $ki_world] : ! [v5: int] : (v5 = 0 | ~ (g(v4, v3) = v5) | ~
% 6.50/1.62 ($ki_exists_in_world_$i($ki_local_world, v3) = 0) | ~ $ki_world(v4) | ~
% 6.50/1.62 $i(v3) | ? [v6: int] : (( ~ (v6 = 0) & f($ki_local_world, v3) = v6) | ( ~
% 6.50/1.62 (v6 = 0) & $ki_accessible($ki_local_world, v4) = v6))) & ! [v3: $i] :
% 6.50/1.62 ! [v4: $ki_world] : ( ~ (f($ki_local_world, v3) = 0) | ~
% 6.50/1.62 ($ki_accessible($ki_local_world, v4) = 0) | ~ $ki_world(v4) | ~ $i(v3) |
% 6.50/1.62 ? [v5: int] : ((v5 = 0 & g(v4, v3) = 0) | ( ~ (v5 = 0) &
% 6.50/1.62 $ki_exists_in_world_$i($ki_local_world, v3) = v5))) & ! [v3: $i] : !
% 6.50/1.62 [v4: $ki_world] : ( ~ (g($ki_local_world, v3) = 0) | ~
% 6.50/1.62 ($ki_accessible($ki_local_world, v4) = 0) | ~ $ki_world(v4) | ~ $i(v3) |
% 6.50/1.62 ? [v5: int] : ((v5 = 0 & h(v4, v3) = 0) | ( ~ (v5 = 0) &
% 6.50/1.62 $ki_exists_in_world_$i($ki_local_world, v3) = v5))) & ! [v3: $i] : !
% 6.50/1.62 [v4: $ki_world] : ( ~ ($ki_exists_in_world_$i($ki_local_world, v3) = 0) | ~
% 6.50/1.62 ($ki_accessible($ki_local_world, v4) = 0) | ~ $ki_world(v4) | ~ $i(v3) |
% 6.50/1.62 ? [v5: int] : ((v5 = 0 & h(v4, v3) = 0) | ( ~ (v5 = 0) &
% 6.50/1.62 g($ki_local_world, v3) = v5))) & ! [v3: $i] : ! [v4: $ki_world] : (
% 6.50/1.62 ~ ($ki_exists_in_world_$i($ki_local_world, v3) = 0) | ~
% 6.50/1.62 ($ki_accessible($ki_local_world, v4) = 0) | ~ $ki_world(v4) | ~ $i(v3) |
% 6.50/1.62 ? [v5: int] : ((v5 = 0 & g(v4, v3) = 0) | ( ~ (v5 = 0) &
% 6.50/1.62 f($ki_local_world, v3) = v5))))
% 6.50/1.62
% 6.50/1.62 (function-axioms)
% 6.50/1.63 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 6.50/1.63 [v3: $ki_world] : (v1 = v0 | ~ (h(v3, v2) = v1) | ~ (h(v3, v2) = v0)) & !
% 6.50/1.63 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 6.50/1.63 $ki_world] : (v1 = v0 | ~ (f(v3, v2) = v1) | ~ (f(v3, v2) = v0)) & ! [v0:
% 6.50/1.63 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 6.50/1.63 $ki_world] : (v1 = v0 | ~ (g(v3, v2) = v1) | ~ (g(v3, v2) = v0)) & ! [v0:
% 6.50/1.63 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 6.50/1.63 $ki_world] : (v1 = v0 | ~ ($ki_exists_in_world_$i(v3, v2) = v1) | ~
% 6.50/1.63 ($ki_exists_in_world_$i(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 6.50/1.63 [v1: MultipleValueBool] : ! [v2: $ki_world] : ! [v3: $ki_world] : (v1 = v0 |
% 6.50/1.63 ~ ($ki_accessible(v3, v2) = v1) | ~ ($ki_accessible(v3, v2) = v0))
% 6.50/1.63
% 6.50/1.63 Further assumptions not needed in the proof:
% 6.50/1.63 --------------------------------------------
% 6.50/1.63 $ki_exists_in_world_$i_nonempty, mrel_transitive
% 6.50/1.63
% 6.50/1.63 Those formulas are unsatisfiable:
% 6.50/1.63 ---------------------------------
% 6.50/1.63
% 6.50/1.63 Begin of proof
% 6.50/1.63 |
% 6.50/1.63 | ALPHA: (verify) implies:
% 6.50/1.63 | (1) $ki_world($ki_local_world)
% 6.50/1.64 | (2) ? [v0: $i] : ? [v1: $ki_world] : ? [v2: int] : ( ~ (v2 = 0) & h(v1,
% 6.50/1.64 | v0) = v2 & f($ki_local_world, v0) = 0 &
% 6.50/1.64 | $ki_exists_in_world_$i($ki_local_world, v0) = 0 &
% 6.50/1.64 | $ki_accessible($ki_local_world, v1) = 0 & $ki_world(v1) & $i(v0) & !
% 6.50/1.64 | [v3: $i] : ! [v4: $ki_world] : ! [v5: int] : (v5 = 0 | ~ (h(v4,
% 6.50/1.64 | v3) = v5) | ~ (g($ki_local_world, v3) = 0) | ~ $ki_world(v4)
% 6.50/1.64 | | ~ $i(v3) | ? [v6: int] : (( ~ (v6 = 0) &
% 6.50/1.64 | $ki_exists_in_world_$i($ki_local_world, v3) = v6) | ( ~ (v6 =
% 6.50/1.64 | 0) & $ki_accessible($ki_local_world, v4) = v6))) & ! [v3:
% 6.50/1.64 | $i] : ! [v4: $ki_world] : ! [v5: int] : (v5 = 0 | ~ (h(v4, v3) =
% 6.50/1.64 | v5) | ~ ($ki_exists_in_world_$i($ki_local_world, v3) = 0) | ~
% 6.50/1.64 | $ki_world(v4) | ~ $i(v3) | ? [v6: int] : (( ~ (v6 = 0) &
% 6.50/1.64 | g($ki_local_world, v3) = v6) | ( ~ (v6 = 0) &
% 6.50/1.64 | $ki_accessible($ki_local_world, v4) = v6))) & ! [v3: $i] : !
% 6.50/1.64 | [v4: $ki_world] : ! [v5: int] : (v5 = 0 | ~ (f($ki_local_world, v3)
% 6.50/1.64 | = 0) | ~ (g(v4, v3) = v5) | ~ $ki_world(v4) | ~ $i(v3) | ?
% 6.50/1.64 | [v6: int] : (( ~ (v6 = 0) & $ki_exists_in_world_$i($ki_local_world,
% 6.50/1.64 | v3) = v6) | ( ~ (v6 = 0) & $ki_accessible($ki_local_world,
% 6.50/1.64 | v4) = v6))) & ! [v3: $i] : ! [v4: $ki_world] : ! [v5: int]
% 6.50/1.64 | : (v5 = 0 | ~ (g(v4, v3) = v5) | ~
% 6.50/1.64 | ($ki_exists_in_world_$i($ki_local_world, v3) = 0) | ~
% 6.50/1.64 | $ki_world(v4) | ~ $i(v3) | ? [v6: int] : (( ~ (v6 = 0) &
% 6.50/1.64 | f($ki_local_world, v3) = v6) | ( ~ (v6 = 0) &
% 6.50/1.64 | $ki_accessible($ki_local_world, v4) = v6))) & ! [v3: $i] : !
% 6.50/1.64 | [v4: $ki_world] : ( ~ (f($ki_local_world, v3) = 0) | ~
% 6.50/1.64 | ($ki_accessible($ki_local_world, v4) = 0) | ~ $ki_world(v4) | ~
% 6.50/1.64 | $i(v3) | ? [v5: int] : ((v5 = 0 & g(v4, v3) = 0) | ( ~ (v5 = 0) &
% 6.50/1.64 | $ki_exists_in_world_$i($ki_local_world, v3) = v5))) & ! [v3:
% 6.50/1.64 | $i] : ! [v4: $ki_world] : ( ~ (g($ki_local_world, v3) = 0) | ~
% 6.50/1.64 | ($ki_accessible($ki_local_world, v4) = 0) | ~ $ki_world(v4) | ~
% 6.50/1.64 | $i(v3) | ? [v5: int] : ((v5 = 0 & h(v4, v3) = 0) | ( ~ (v5 = 0) &
% 6.50/1.64 | $ki_exists_in_world_$i($ki_local_world, v3) = v5))) & ! [v3:
% 6.50/1.64 | $i] : ! [v4: $ki_world] : ( ~
% 6.50/1.64 | ($ki_exists_in_world_$i($ki_local_world, v3) = 0) | ~
% 6.50/1.64 | ($ki_accessible($ki_local_world, v4) = 0) | ~ $ki_world(v4) | ~
% 6.50/1.65 | $i(v3) | ? [v5: int] : ((v5 = 0 & h(v4, v3) = 0) | ( ~ (v5 = 0) &
% 6.50/1.65 | g($ki_local_world, v3) = v5))) & ! [v3: $i] : ! [v4:
% 6.50/1.65 | $ki_world] : ( ~ ($ki_exists_in_world_$i($ki_local_world, v3) = 0)
% 6.50/1.65 | | ~ ($ki_accessible($ki_local_world, v4) = 0) | ~ $ki_world(v4) |
% 6.50/1.65 | ~ $i(v3) | ? [v5: int] : ((v5 = 0 & g(v4, v3) = 0) | ( ~ (v5 = 0)
% 6.50/1.65 | & f($ki_local_world, v3) = v5))))
% 6.50/1.65 |
% 6.50/1.65 | ALPHA: (function-axioms) implies:
% 6.50/1.65 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 6.50/1.65 | $ki_world] : ! [v3: $ki_world] : (v1 = v0 | ~ ($ki_accessible(v3,
% 6.50/1.65 | v2) = v1) | ~ ($ki_accessible(v3, v2) = v0))
% 6.50/1.65 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 6.50/1.65 | ! [v3: $ki_world] : (v1 = v0 | ~ (g(v3, v2) = v1) | ~ (g(v3, v2) =
% 6.50/1.65 | v0))
% 6.50/1.65 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 6.50/1.65 | ! [v3: $ki_world] : (v1 = v0 | ~ (f(v3, v2) = v1) | ~ (f(v3, v2) =
% 6.50/1.65 | v0))
% 6.50/1.65 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 6.50/1.65 | ! [v3: $ki_world] : (v1 = v0 | ~ (h(v3, v2) = v1) | ~ (h(v3, v2) =
% 6.50/1.65 | v0))
% 6.50/1.65 |
% 6.50/1.65 | DELTA: instantiating (2) with fresh symbols all_9_0, all_9_1, all_9_2 gives:
% 6.50/1.66 | (7) ~ (all_9_0 = 0) & h(all_9_1, all_9_2) = all_9_0 & f($ki_local_world,
% 6.50/1.66 | all_9_2) = 0 & $ki_exists_in_world_$i($ki_local_world, all_9_2) = 0 &
% 6.50/1.66 | $ki_accessible($ki_local_world, all_9_1) = 0 & $ki_world(all_9_1) &
% 6.50/1.66 | $i(all_9_2) & ! [v0: $i] : ! [v1: $ki_world] : ! [v2: int] : (v2 = 0
% 6.50/1.66 | | ~ (h(v1, v0) = v2) | ~ (g($ki_local_world, v0) = 0) | ~
% 6.50/1.66 | $ki_world(v1) | ~ $i(v0) | ? [v3: int] : (( ~ (v3 = 0) &
% 6.50/1.66 | $ki_exists_in_world_$i($ki_local_world, v0) = v3) | ( ~ (v3 = 0)
% 6.50/1.66 | & $ki_accessible($ki_local_world, v1) = v3))) & ! [v0: $i] : !
% 6.50/1.66 | [v1: $ki_world] : ! [v2: int] : (v2 = 0 | ~ (h(v1, v0) = v2) | ~
% 6.50/1.66 | ($ki_exists_in_world_$i($ki_local_world, v0) = 0) | ~ $ki_world(v1)
% 6.50/1.66 | | ~ $i(v0) | ? [v3: int] : (( ~ (v3 = 0) & g($ki_local_world, v0) =
% 6.50/1.66 | v3) | ( ~ (v3 = 0) & $ki_accessible($ki_local_world, v1) = v3)))
% 6.50/1.66 | & ! [v0: $i] : ! [v1: $ki_world] : ! [v2: int] : (v2 = 0 | ~
% 6.50/1.66 | (f($ki_local_world, v0) = 0) | ~ (g(v1, v0) = v2) | ~ $ki_world(v1)
% 6.50/1.66 | | ~ $i(v0) | ? [v3: int] : (( ~ (v3 = 0) &
% 6.50/1.66 | $ki_exists_in_world_$i($ki_local_world, v0) = v3) | ( ~ (v3 = 0)
% 6.50/1.66 | & $ki_accessible($ki_local_world, v1) = v3))) & ! [v0: $i] : !
% 6.50/1.66 | [v1: $ki_world] : ! [v2: int] : (v2 = 0 | ~ (g(v1, v0) = v2) | ~
% 6.50/1.66 | ($ki_exists_in_world_$i($ki_local_world, v0) = 0) | ~ $ki_world(v1)
% 6.50/1.66 | | ~ $i(v0) | ? [v3: int] : (( ~ (v3 = 0) & f($ki_local_world, v0) =
% 6.50/1.66 | v3) | ( ~ (v3 = 0) & $ki_accessible($ki_local_world, v1) = v3)))
% 6.50/1.66 | & ! [v0: $i] : ! [v1: $ki_world] : ( ~ (f($ki_local_world, v0) = 0) |
% 6.50/1.66 | ~ ($ki_accessible($ki_local_world, v1) = 0) | ~ $ki_world(v1) | ~
% 6.50/1.66 | $i(v0) | ? [v2: int] : ((v2 = 0 & g(v1, v0) = 0) | ( ~ (v2 = 0) &
% 6.50/1.66 | $ki_exists_in_world_$i($ki_local_world, v0) = v2))) & ! [v0: $i]
% 6.50/1.66 | : ! [v1: $ki_world] : ( ~ (g($ki_local_world, v0) = 0) | ~
% 6.50/1.66 | ($ki_accessible($ki_local_world, v1) = 0) | ~ $ki_world(v1) | ~
% 6.50/1.66 | $i(v0) | ? [v2: int] : ((v2 = 0 & h(v1, v0) = 0) | ( ~ (v2 = 0) &
% 6.50/1.66 | $ki_exists_in_world_$i($ki_local_world, v0) = v2))) & ! [v0: $i]
% 6.50/1.66 | : ! [v1: $ki_world] : ( ~ ($ki_exists_in_world_$i($ki_local_world, v0)
% 6.50/1.66 | = 0) | ~ ($ki_accessible($ki_local_world, v1) = 0) | ~
% 6.50/1.66 | $ki_world(v1) | ~ $i(v0) | ? [v2: int] : ((v2 = 0 & h(v1, v0) = 0)
% 6.50/1.66 | | ( ~ (v2 = 0) & g($ki_local_world, v0) = v2))) & ! [v0: $i] : !
% 6.50/1.66 | [v1: $ki_world] : ( ~ ($ki_exists_in_world_$i($ki_local_world, v0) = 0)
% 6.50/1.66 | | ~ ($ki_accessible($ki_local_world, v1) = 0) | ~ $ki_world(v1) |
% 6.50/1.66 | ~ $i(v0) | ? [v2: int] : ((v2 = 0 & g(v1, v0) = 0) | ( ~ (v2 = 0) &
% 6.50/1.66 | f($ki_local_world, v0) = v2)))
% 6.50/1.66 |
% 6.50/1.66 | ALPHA: (7) implies:
% 6.50/1.66 | (8) ~ (all_9_0 = 0)
% 6.50/1.66 | (9) $i(all_9_2)
% 6.50/1.66 | (10) $ki_world(all_9_1)
% 6.50/1.66 | (11) $ki_accessible($ki_local_world, all_9_1) = 0
% 6.50/1.66 | (12) $ki_exists_in_world_$i($ki_local_world, all_9_2) = 0
% 6.50/1.66 | (13) f($ki_local_world, all_9_2) = 0
% 6.50/1.66 | (14) h(all_9_1, all_9_2) = all_9_0
% 6.50/1.66 | (15) ! [v0: $i] : ! [v1: $ki_world] : ( ~
% 6.50/1.66 | ($ki_exists_in_world_$i($ki_local_world, v0) = 0) | ~
% 6.50/1.66 | ($ki_accessible($ki_local_world, v1) = 0) | ~ $ki_world(v1) | ~
% 6.50/1.66 | $i(v0) | ? [v2: int] : ((v2 = 0 & h(v1, v0) = 0) | ( ~ (v2 = 0) &
% 6.50/1.66 | g($ki_local_world, v0) = v2)))
% 6.50/1.66 | (16) ! [v0: $i] : ! [v1: $ki_world] : ! [v2: int] : (v2 = 0 | ~ (g(v1,
% 6.50/1.66 | v0) = v2) | ~ ($ki_exists_in_world_$i($ki_local_world, v0) = 0)
% 6.50/1.66 | | ~ $ki_world(v1) | ~ $i(v0) | ? [v3: int] : (( ~ (v3 = 0) &
% 6.50/1.66 | f($ki_local_world, v0) = v3) | ( ~ (v3 = 0) &
% 6.50/1.66 | $ki_accessible($ki_local_world, v1) = v3)))
% 6.50/1.66 | (17) ! [v0: $i] : ! [v1: $ki_world] : ! [v2: int] : (v2 = 0 | ~ (h(v1,
% 6.50/1.66 | v0) = v2) | ~ ($ki_exists_in_world_$i($ki_local_world, v0) = 0)
% 6.50/1.66 | | ~ $ki_world(v1) | ~ $i(v0) | ? [v3: int] : (( ~ (v3 = 0) &
% 6.50/1.66 | g($ki_local_world, v0) = v3) | ( ~ (v3 = 0) &
% 6.50/1.66 | $ki_accessible($ki_local_world, v1) = v3)))
% 6.50/1.67 |
% 6.50/1.67 | GROUND_INST: instantiating (15) with all_9_2, all_9_1, simplifying with (9),
% 6.50/1.67 | (10), (11), (12) gives:
% 6.50/1.67 | (18) ? [v0: int] : ((v0 = 0 & h(all_9_1, all_9_2) = 0) | ( ~ (v0 = 0) &
% 6.50/1.67 | g($ki_local_world, all_9_2) = v0))
% 6.50/1.67 |
% 6.50/1.67 | GROUND_INST: instantiating (17) with all_9_2, all_9_1, all_9_0, simplifying
% 6.50/1.67 | with (9), (10), (12), (14) gives:
% 6.50/1.67 | (19) all_9_0 = 0 | ? [v0: int] : (( ~ (v0 = 0) & g($ki_local_world,
% 6.50/1.67 | all_9_2) = v0) | ( ~ (v0 = 0) & $ki_accessible($ki_local_world,
% 6.50/1.67 | all_9_1) = v0))
% 6.50/1.67 |
% 6.50/1.67 | DELTA: instantiating (18) with fresh symbol all_19_0 gives:
% 6.50/1.67 | (20) (all_19_0 = 0 & h(all_9_1, all_9_2) = 0) | ( ~ (all_19_0 = 0) &
% 6.50/1.67 | g($ki_local_world, all_9_2) = all_19_0)
% 6.50/1.67 |
% 6.50/1.67 | BETA: splitting (19) gives:
% 6.50/1.67 |
% 6.50/1.67 | Case 1:
% 6.50/1.67 | |
% 6.50/1.67 | | (21) all_9_0 = 0
% 6.50/1.67 | |
% 6.50/1.67 | | REDUCE: (8), (21) imply:
% 6.50/1.67 | | (22) $false
% 6.50/1.67 | |
% 6.50/1.67 | | CLOSE: (22) is inconsistent.
% 6.50/1.67 | |
% 6.50/1.67 | Case 2:
% 6.50/1.67 | |
% 6.50/1.67 | | (23) ? [v0: int] : (( ~ (v0 = 0) & g($ki_local_world, all_9_2) = v0) | (
% 6.50/1.67 | | ~ (v0 = 0) & $ki_accessible($ki_local_world, all_9_1) = v0))
% 6.50/1.67 | |
% 6.50/1.67 | | DELTA: instantiating (23) with fresh symbol all_31_0 gives:
% 6.50/1.67 | | (24) ( ~ (all_31_0 = 0) & g($ki_local_world, all_9_2) = all_31_0) | ( ~
% 6.50/1.67 | | (all_31_0 = 0) & $ki_accessible($ki_local_world, all_9_1) =
% 6.50/1.67 | | all_31_0)
% 6.50/1.67 | |
% 6.50/1.67 | | BETA: splitting (20) gives:
% 6.50/1.67 | |
% 6.50/1.67 | | Case 1:
% 6.50/1.67 | | |
% 6.50/1.67 | | | (25) all_19_0 = 0 & h(all_9_1, all_9_2) = 0
% 6.50/1.67 | | |
% 6.50/1.67 | | | ALPHA: (25) implies:
% 6.50/1.67 | | | (26) h(all_9_1, all_9_2) = 0
% 6.50/1.67 | | |
% 6.50/1.67 | | | GROUND_INST: instantiating (6) with all_9_0, 0, all_9_2, all_9_1,
% 6.50/1.67 | | | simplifying with (14), (26) gives:
% 6.50/1.67 | | | (27) all_9_0 = 0
% 6.50/1.67 | | |
% 6.50/1.67 | | | REDUCE: (8), (27) imply:
% 6.50/1.67 | | | (28) $false
% 6.50/1.67 | | |
% 6.50/1.67 | | | CLOSE: (28) is inconsistent.
% 6.50/1.67 | | |
% 6.50/1.67 | | Case 2:
% 6.50/1.67 | | |
% 6.50/1.67 | | | (29) ~ (all_19_0 = 0) & g($ki_local_world, all_9_2) = all_19_0
% 6.50/1.67 | | |
% 6.50/1.67 | | | ALPHA: (29) implies:
% 6.50/1.68 | | | (30) g($ki_local_world, all_9_2) = all_19_0
% 6.50/1.68 | | |
% 6.50/1.68 | | | BETA: splitting (24) gives:
% 6.50/1.68 | | |
% 6.50/1.68 | | | Case 1:
% 6.50/1.68 | | | |
% 6.50/1.68 | | | | (31) ~ (all_31_0 = 0) & g($ki_local_world, all_9_2) = all_31_0
% 6.50/1.68 | | | |
% 6.50/1.68 | | | | ALPHA: (31) implies:
% 6.50/1.68 | | | | (32) ~ (all_31_0 = 0)
% 6.50/1.68 | | | | (33) g($ki_local_world, all_9_2) = all_31_0
% 6.50/1.68 | | | |
% 6.50/1.68 | | | | GROUND_INST: instantiating (4) with all_19_0, all_31_0, all_9_2,
% 6.50/1.68 | | | | $ki_local_world, simplifying with (30), (33) gives:
% 6.50/1.68 | | | | (34) all_31_0 = all_19_0
% 6.50/1.68 | | | |
% 6.50/1.68 | | | | REDUCE: (32), (34) imply:
% 6.50/1.68 | | | | (35) ~ (all_19_0 = 0)
% 6.50/1.68 | | | |
% 6.50/1.68 | | | | GROUND_INST: instantiating (16) with all_9_2, $ki_local_world, all_19_0,
% 6.50/1.68 | | | | simplifying with (1), (9), (12), (30) gives:
% 6.50/1.68 | | | | (36) all_19_0 = 0 | ? [v0: int] : (( ~ (v0 = 0) & f($ki_local_world,
% 6.50/1.68 | | | | all_9_2) = v0) | ( ~ (v0 = 0) &
% 6.50/1.68 | | | | $ki_accessible($ki_local_world, $ki_local_world) = v0))
% 6.50/1.68 | | | |
% 6.50/1.68 | | | | BETA: splitting (36) gives:
% 6.50/1.68 | | | |
% 6.50/1.68 | | | | Case 1:
% 6.50/1.68 | | | | |
% 6.50/1.68 | | | | | (37) all_19_0 = 0
% 6.50/1.68 | | | | |
% 6.50/1.68 | | | | | REDUCE: (35), (37) imply:
% 6.50/1.68 | | | | | (38) $false
% 6.50/1.68 | | | | |
% 6.50/1.68 | | | | | CLOSE: (38) is inconsistent.
% 6.50/1.68 | | | | |
% 6.50/1.68 | | | | Case 2:
% 6.50/1.68 | | | | |
% 6.50/1.68 | | | | | (39) ? [v0: int] : (( ~ (v0 = 0) & f($ki_local_world, all_9_2) =
% 6.50/1.68 | | | | | v0) | ( ~ (v0 = 0) & $ki_accessible($ki_local_world,
% 6.50/1.68 | | | | | $ki_local_world) = v0))
% 6.50/1.68 | | | | |
% 6.50/1.68 | | | | | DELTA: instantiating (39) with fresh symbol all_55_0 gives:
% 6.50/1.68 | | | | | (40) ( ~ (all_55_0 = 0) & f($ki_local_world, all_9_2) = all_55_0) |
% 6.50/1.68 | | | | | ( ~ (all_55_0 = 0) & $ki_accessible($ki_local_world,
% 6.50/1.68 | | | | | $ki_local_world) = all_55_0)
% 6.50/1.68 | | | | |
% 6.50/1.68 | | | | | BETA: splitting (40) gives:
% 6.50/1.68 | | | | |
% 6.50/1.68 | | | | | Case 1:
% 6.50/1.68 | | | | | |
% 6.50/1.68 | | | | | | (41) ~ (all_55_0 = 0) & f($ki_local_world, all_9_2) = all_55_0
% 6.50/1.68 | | | | | |
% 6.50/1.68 | | | | | | ALPHA: (41) implies:
% 6.50/1.68 | | | | | | (42) ~ (all_55_0 = 0)
% 6.50/1.68 | | | | | | (43) f($ki_local_world, all_9_2) = all_55_0
% 6.50/1.68 | | | | | |
% 6.50/1.68 | | | | | | GROUND_INST: instantiating (5) with 0, all_55_0, all_9_2,
% 6.50/1.68 | | | | | | $ki_local_world, simplifying with (13), (43) gives:
% 6.50/1.68 | | | | | | (44) all_55_0 = 0
% 6.50/1.68 | | | | | |
% 6.50/1.68 | | | | | | REDUCE: (42), (44) imply:
% 6.50/1.68 | | | | | | (45) $false
% 6.50/1.68 | | | | | |
% 6.50/1.68 | | | | | | CLOSE: (45) is inconsistent.
% 6.50/1.68 | | | | | |
% 6.50/1.68 | | | | | Case 2:
% 6.50/1.68 | | | | | |
% 6.50/1.68 | | | | | | (46) ~ (all_55_0 = 0) & $ki_accessible($ki_local_world,
% 6.50/1.68 | | | | | | $ki_local_world) = all_55_0
% 6.50/1.68 | | | | | |
% 6.50/1.68 | | | | | | ALPHA: (46) implies:
% 6.50/1.68 | | | | | | (47) ~ (all_55_0 = 0)
% 6.50/1.68 | | | | | | (48) $ki_accessible($ki_local_world, $ki_local_world) = all_55_0
% 6.50/1.68 | | | | | |
% 6.50/1.68 | | | | | | GROUND_INST: instantiating (mrel_reflexive) with $ki_local_world,
% 6.50/1.68 | | | | | | all_55_0, simplifying with (1), (48) gives:
% 6.50/1.68 | | | | | | (49) all_55_0 = 0
% 6.50/1.68 | | | | | |
% 6.50/1.68 | | | | | | REDUCE: (47), (49) imply:
% 6.50/1.68 | | | | | | (50) $false
% 6.50/1.68 | | | | | |
% 6.50/1.68 | | | | | | CLOSE: (50) is inconsistent.
% 6.50/1.68 | | | | | |
% 6.50/1.68 | | | | | End of split
% 6.50/1.68 | | | | |
% 6.50/1.68 | | | | End of split
% 6.50/1.68 | | | |
% 6.50/1.68 | | | Case 2:
% 6.50/1.68 | | | |
% 6.50/1.69 | | | | (51) ~ (all_31_0 = 0) & $ki_accessible($ki_local_world, all_9_1) =
% 6.50/1.69 | | | | all_31_0
% 6.50/1.69 | | | |
% 6.50/1.69 | | | | ALPHA: (51) implies:
% 6.50/1.69 | | | | (52) ~ (all_31_0 = 0)
% 6.50/1.69 | | | | (53) $ki_accessible($ki_local_world, all_9_1) = all_31_0
% 6.50/1.69 | | | |
% 6.50/1.69 | | | | GROUND_INST: instantiating (3) with 0, all_31_0, all_9_1,
% 6.50/1.69 | | | | $ki_local_world, simplifying with (11), (53) gives:
% 6.50/1.69 | | | | (54) all_31_0 = 0
% 6.50/1.69 | | | |
% 6.50/1.69 | | | | REDUCE: (52), (54) imply:
% 6.50/1.69 | | | | (55) $false
% 6.50/1.69 | | | |
% 6.50/1.69 | | | | CLOSE: (55) is inconsistent.
% 6.50/1.69 | | | |
% 6.50/1.69 | | | End of split
% 6.50/1.69 | | |
% 6.50/1.69 | | End of split
% 6.50/1.69 | |
% 6.50/1.69 | End of split
% 6.50/1.69 |
% 6.50/1.69 End of proof
% 6.50/1.69 % SZS output end Proof for theBenchmark
% 6.50/1.69
% 6.50/1.69 1077ms
%------------------------------------------------------------------------------