TSTP Solution File: SYO889_16 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SYO889_16 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n027.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 4.22s 1.38s
% Output : Proof 6.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO889_16 : TPTP v8.2.0. Released v8.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n027.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 : Sat Aug 26 07:16:34 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 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
% 2.14/1.00 Prover 4: Preprocessing ...
% 2.14/1.00 Prover 1: Preprocessing ...
% 2.50/1.04 Prover 5: Preprocessing ...
% 2.50/1.04 Prover 3: Preprocessing ...
% 2.50/1.04 Prover 0: Preprocessing ...
% 2.50/1.04 Prover 6: Preprocessing ...
% 2.72/1.05 Prover 2: Preprocessing ...
% 3.61/1.18 Prover 2: Proving ...
% 3.61/1.18 Prover 5: Proving ...
% 3.61/1.20 Prover 1: Warning: ignoring some quantifiers
% 3.61/1.21 Prover 6: Proving ...
% 3.61/1.22 Prover 1: Constructing countermodel ...
% 3.61/1.22 Prover 3: Warning: ignoring some quantifiers
% 3.61/1.24 Prover 3: Constructing countermodel ...
% 4.22/1.28 Prover 4: Warning: ignoring some quantifiers
% 4.22/1.29 Prover 4: Constructing countermodel ...
% 4.22/1.30 Prover 0: Proving ...
% 4.22/1.38 Prover 2: proved (756ms)
% 4.22/1.38
% 4.22/1.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.22/1.38
% 4.22/1.38 Prover 5: stopped
% 4.22/1.38 Prover 0: stopped
% 4.22/1.39 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.22/1.39 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.22/1.39 Prover 6: stopped
% 4.22/1.39 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.22/1.39 Prover 3: stopped
% 4.22/1.42 Prover 7: Preprocessing ...
% 4.22/1.42 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.22/1.42 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.22/1.43 Prover 10: Preprocessing ...
% 4.22/1.43 Prover 7: Warning: ignoring some quantifiers
% 4.22/1.43 Prover 8: Preprocessing ...
% 4.22/1.44 Prover 7: Constructing countermodel ...
% 4.22/1.45 Prover 10: Warning: ignoring some quantifiers
% 4.22/1.46 Prover 10: Constructing countermodel ...
% 4.86/1.48 Prover 13: Preprocessing ...
% 4.86/1.50 Prover 4: Found proof (size 18)
% 5.65/1.50 Prover 4: proved (863ms)
% 5.65/1.50 Prover 7: stopped
% 5.65/1.50 Prover 11: Preprocessing ...
% 5.65/1.50 Prover 10: stopped
% 5.65/1.50 Prover 1: stopped
% 5.65/1.51 Prover 13: Warning: ignoring some quantifiers
% 5.65/1.51 Prover 13: Constructing countermodel ...
% 5.65/1.52 Prover 8: Warning: ignoring some quantifiers
% 5.65/1.52 Prover 13: stopped
% 5.65/1.52 Prover 11: stopped
% 5.65/1.52 Prover 8: Constructing countermodel ...
% 5.65/1.53 Prover 8: stopped
% 5.65/1.53
% 5.65/1.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.65/1.53
% 5.65/1.53 % SZS output start Proof for theBenchmark
% 5.65/1.54 Assumptions after simplification:
% 5.65/1.54 ---------------------------------
% 5.65/1.54
% 5.65/1.54 (verify)
% 5.65/1.57 $ki_world($ki_local_world) & ? [v0: $ki_world] : ? [v1: $i] :
% 5.65/1.57 ($ki_exists_in_world_$i(v0, v1) = 0 & $ki_accessible($ki_local_world, v0) = 0
% 5.65/1.57 & $ki_world(v0) & $i(v1) & ! [v2: $ki_world] : ! [v3: $i] : ! [v4:
% 5.65/1.57 $ki_world] : ( ~ (b(v4, v3) = 0) | ~ ($ki_exists_in_world_$i(v2, v3) = 0)
% 5.65/1.57 | ~ ($ki_accessible($ki_local_world, v2) = 0) | ~ $ki_world(v4) | ~
% 5.65/1.57 $ki_world(v2) | ~ $i(v3) | ? [v5: any] : ? [v6: any] : (a(v4, v3) = v6
% 5.65/1.57 & $ki_accessible(v2, v4) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v2:
% 5.65/1.57 $ki_world] : ! [v3: $i] : ! [v4: $ki_world] : ( ~ (a(v4, v3) = 0) | ~
% 5.65/1.57 ($ki_exists_in_world_$i(v2, v3) = 0) | ~ ($ki_accessible($ki_local_world,
% 5.65/1.57 v2) = 0) | ~ $ki_world(v4) | ~ $ki_world(v2) | ~ $i(v3) | ? [v5:
% 5.65/1.57 any] : ? [v6: any] : (b(v4, v3) = v6 & $ki_accessible(v2, v4) = v5 & (
% 5.65/1.57 ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v2: $ki_world] : ! [v3: $i] : !
% 5.65/1.58 [v4: $ki_world] : ( ~ ($ki_exists_in_world_$i(v2, v3) = 0) | ~
% 5.65/1.58 ($ki_accessible(v2, v4) = 0) | ~ ($ki_accessible($ki_local_world, v2) =
% 5.65/1.58 0) | ~ $ki_world(v4) | ~ $ki_world(v2) | ~ $i(v3) | ? [v5: any] : ?
% 5.65/1.58 [v6: any] : (b(v4, v3) = v6 & a(v4, v3) = v5 & ( ~ (v6 = 0) | ~ (v5 =
% 5.65/1.58 0)))) & ! [v2: $ki_world] : ! [v3: int] : (v3 = 0 | ~ (a(v2, v1)
% 5.65/1.58 = v3) | ~ $ki_world(v2) | ? [v4: int] : ( ~ (v4 = 0) &
% 5.65/1.58 $ki_accessible(v0, v2) = v4)) & ! [v2: $ki_world] : ! [v3: $i] : ( ~
% 5.65/1.58 ($ki_exists_in_world_$i(v2, v3) = 0) | ~ ($ki_accessible($ki_local_world,
% 5.65/1.58 v2) = 0) | ~ $ki_world(v2) | ~ $i(v3) | ? [v4: $ki_world] : (b(v4,
% 5.65/1.58 v3) = 0 & $ki_accessible(v2, v4) = 0 & $ki_world(v4))) & ! [v2:
% 5.65/1.58 $ki_world] : ( ~ ($ki_accessible(v0, v2) = 0) | ~ $ki_world(v2) | a(v2,
% 5.65/1.58 v1) = 0))
% 5.65/1.58
% 5.65/1.58 (function-axioms)
% 5.65/1.58 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 5.65/1.58 [v3: $ki_world] : (v1 = v0 | ~ (b(v3, v2) = v1) | ~ (b(v3, v2) = v0)) & !
% 5.65/1.58 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 5.65/1.58 $ki_world] : (v1 = v0 | ~ (a(v3, v2) = v1) | ~ (a(v3, v2) = v0)) & ! [v0:
% 5.65/1.58 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 5.65/1.58 $ki_world] : (v1 = v0 | ~ ($ki_exists_in_world_$i(v3, v2) = v1) | ~
% 5.65/1.58 ($ki_exists_in_world_$i(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 5.65/1.58 [v1: MultipleValueBool] : ! [v2: $ki_world] : ! [v3: $ki_world] : (v1 = v0 |
% 5.65/1.58 ~ ($ki_accessible(v3, v2) = v1) | ~ ($ki_accessible(v3, v2) = v0))
% 5.65/1.58
% 5.65/1.58 Further assumptions not needed in the proof:
% 5.65/1.58 --------------------------------------------
% 5.65/1.58 $ki_exists_in_world_$i_cumul, $ki_exists_in_world_$i_nonempty, mrel_reflexive,
% 5.65/1.58 mrel_transitive
% 5.65/1.58
% 5.65/1.58 Those formulas are unsatisfiable:
% 5.65/1.58 ---------------------------------
% 5.65/1.58
% 5.65/1.58 Begin of proof
% 6.10/1.58 |
% 6.10/1.58 | ALPHA: (verify) implies:
% 6.10/1.59 | (1) ? [v0: $ki_world] : ? [v1: $i] : ($ki_exists_in_world_$i(v0, v1) = 0
% 6.10/1.59 | & $ki_accessible($ki_local_world, v0) = 0 & $ki_world(v0) & $i(v1) &
% 6.10/1.59 | ! [v2: $ki_world] : ! [v3: $i] : ! [v4: $ki_world] : ( ~ (b(v4, v3)
% 6.10/1.59 | = 0) | ~ ($ki_exists_in_world_$i(v2, v3) = 0) | ~
% 6.10/1.59 | ($ki_accessible($ki_local_world, v2) = 0) | ~ $ki_world(v4) | ~
% 6.10/1.59 | $ki_world(v2) | ~ $i(v3) | ? [v5: any] : ? [v6: any] : (a(v4,
% 6.10/1.59 | v3) = v6 & $ki_accessible(v2, v4) = v5 & ( ~ (v6 = 0) | ~ (v5
% 6.10/1.59 | = 0)))) & ! [v2: $ki_world] : ! [v3: $i] : ! [v4:
% 6.10/1.59 | $ki_world] : ( ~ (a(v4, v3) = 0) | ~ ($ki_exists_in_world_$i(v2,
% 6.10/1.59 | v3) = 0) | ~ ($ki_accessible($ki_local_world, v2) = 0) | ~
% 6.10/1.59 | $ki_world(v4) | ~ $ki_world(v2) | ~ $i(v3) | ? [v5: any] : ?
% 6.10/1.59 | [v6: any] : (b(v4, v3) = v6 & $ki_accessible(v2, v4) = v5 & ( ~ (v6
% 6.10/1.59 | = 0) | ~ (v5 = 0)))) & ! [v2: $ki_world] : ! [v3: $i] : !
% 6.10/1.59 | [v4: $ki_world] : ( ~ ($ki_exists_in_world_$i(v2, v3) = 0) | ~
% 6.10/1.59 | ($ki_accessible(v2, v4) = 0) | ~ ($ki_accessible($ki_local_world,
% 6.10/1.59 | v2) = 0) | ~ $ki_world(v4) | ~ $ki_world(v2) | ~ $i(v3) | ?
% 6.10/1.59 | [v5: any] : ? [v6: any] : (b(v4, v3) = v6 & a(v4, v3) = v5 & ( ~
% 6.10/1.59 | (v6 = 0) | ~ (v5 = 0)))) & ! [v2: $ki_world] : ! [v3: int] :
% 6.10/1.59 | (v3 = 0 | ~ (a(v2, v1) = v3) | ~ $ki_world(v2) | ? [v4: int] : ( ~
% 6.10/1.59 | (v4 = 0) & $ki_accessible(v0, v2) = v4)) & ! [v2: $ki_world] :
% 6.10/1.59 | ! [v3: $i] : ( ~ ($ki_exists_in_world_$i(v2, v3) = 0) | ~
% 6.10/1.59 | ($ki_accessible($ki_local_world, v2) = 0) | ~ $ki_world(v2) | ~
% 6.10/1.59 | $i(v3) | ? [v4: $ki_world] : (b(v4, v3) = 0 & $ki_accessible(v2,
% 6.10/1.59 | v4) = 0 & $ki_world(v4))) & ! [v2: $ki_world] : ( ~
% 6.10/1.59 | ($ki_accessible(v0, v2) = 0) | ~ $ki_world(v2) | a(v2, v1) = 0))
% 6.10/1.59 |
% 6.10/1.59 | ALPHA: (function-axioms) implies:
% 6.10/1.60 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 6.10/1.60 | $ki_world] : ! [v3: $ki_world] : (v1 = v0 | ~ ($ki_accessible(v3,
% 6.10/1.60 | v2) = v1) | ~ ($ki_accessible(v3, v2) = v0))
% 6.10/1.60 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 6.10/1.60 | ! [v3: $ki_world] : (v1 = v0 | ~ (a(v3, v2) = v1) | ~ (a(v3, v2) =
% 6.10/1.60 | v0))
% 6.10/1.60 |
% 6.10/1.60 | DELTA: instantiating (1) with fresh symbols all_10_0, all_10_1 gives:
% 6.10/1.60 | (4) $ki_exists_in_world_$i(all_10_1, all_10_0) = 0 &
% 6.10/1.60 | $ki_accessible($ki_local_world, all_10_1) = 0 & $ki_world(all_10_1) &
% 6.10/1.60 | $i(all_10_0) & ! [v0: $ki_world] : ! [v1: $i] : ! [v2: $ki_world] :
% 6.10/1.60 | ( ~ (b(v2, v1) = 0) | ~ ($ki_exists_in_world_$i(v0, v1) = 0) | ~
% 6.10/1.60 | ($ki_accessible($ki_local_world, v0) = 0) | ~ $ki_world(v2) | ~
% 6.10/1.60 | $ki_world(v0) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : (a(v2, v1)
% 6.10/1.60 | = v4 & $ki_accessible(v0, v2) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 6.10/1.60 | & ! [v0: $ki_world] : ! [v1: $i] : ! [v2: $ki_world] : ( ~ (a(v2,
% 6.10/1.60 | v1) = 0) | ~ ($ki_exists_in_world_$i(v0, v1) = 0) | ~
% 6.10/1.60 | ($ki_accessible($ki_local_world, v0) = 0) | ~ $ki_world(v2) | ~
% 6.10/1.60 | $ki_world(v0) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : (b(v2, v1)
% 6.10/1.60 | = v4 & $ki_accessible(v0, v2) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 6.10/1.60 | & ! [v0: $ki_world] : ! [v1: $i] : ! [v2: $ki_world] : ( ~
% 6.10/1.60 | ($ki_exists_in_world_$i(v0, v1) = 0) | ~ ($ki_accessible(v0, v2) =
% 6.10/1.60 | 0) | ~ ($ki_accessible($ki_local_world, v0) = 0) | ~
% 6.10/1.60 | $ki_world(v2) | ~ $ki_world(v0) | ~ $i(v1) | ? [v3: any] : ? [v4:
% 6.10/1.60 | any] : (b(v2, v1) = v4 & a(v2, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 =
% 6.10/1.60 | 0)))) & ! [v0: $ki_world] : ! [v1: int] : (v1 = 0 | ~ (a(v0,
% 6.10/1.60 | all_10_0) = v1) | ~ $ki_world(v0) | ? [v2: int] : ( ~ (v2 = 0)
% 6.10/1.60 | & $ki_accessible(all_10_1, v0) = v2)) & ! [v0: $ki_world] : !
% 6.10/1.60 | [v1: $i] : ( ~ ($ki_exists_in_world_$i(v0, v1) = 0) | ~
% 6.10/1.60 | ($ki_accessible($ki_local_world, v0) = 0) | ~ $ki_world(v0) | ~
% 6.10/1.60 | $i(v1) | ? [v2: $ki_world] : (b(v2, v1) = 0 & $ki_accessible(v0, v2)
% 6.10/1.60 | = 0 & $ki_world(v2))) & ! [v0: $ki_world] : ( ~
% 6.10/1.60 | ($ki_accessible(all_10_1, v0) = 0) | ~ $ki_world(v0) | a(v0,
% 6.10/1.60 | all_10_0) = 0)
% 6.10/1.60 |
% 6.10/1.60 | ALPHA: (4) implies:
% 6.10/1.61 | (5) $i(all_10_0)
% 6.10/1.61 | (6) $ki_world(all_10_1)
% 6.10/1.61 | (7) $ki_accessible($ki_local_world, all_10_1) = 0
% 6.10/1.61 | (8) $ki_exists_in_world_$i(all_10_1, all_10_0) = 0
% 6.10/1.61 | (9) ! [v0: $ki_world] : ( ~ ($ki_accessible(all_10_1, v0) = 0) | ~
% 6.10/1.61 | $ki_world(v0) | a(v0, all_10_0) = 0)
% 6.10/1.61 | (10) ! [v0: $ki_world] : ! [v1: $i] : ( ~ ($ki_exists_in_world_$i(v0, v1)
% 6.10/1.61 | = 0) | ~ ($ki_accessible($ki_local_world, v0) = 0) | ~
% 6.10/1.61 | $ki_world(v0) | ~ $i(v1) | ? [v2: $ki_world] : (b(v2, v1) = 0 &
% 6.10/1.61 | $ki_accessible(v0, v2) = 0 & $ki_world(v2)))
% 6.10/1.61 | (11) ! [v0: $ki_world] : ! [v1: $i] : ! [v2: $ki_world] : ( ~ (b(v2, v1)
% 6.10/1.61 | = 0) | ~ ($ki_exists_in_world_$i(v0, v1) = 0) | ~
% 6.10/1.61 | ($ki_accessible($ki_local_world, v0) = 0) | ~ $ki_world(v2) | ~
% 6.10/1.61 | $ki_world(v0) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : (a(v2, v1)
% 6.10/1.61 | = v4 & $ki_accessible(v0, v2) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 6.10/1.61 |
% 6.10/1.61 | GROUND_INST: instantiating (10) with all_10_1, all_10_0, simplifying with (5),
% 6.10/1.61 | (6), (7), (8) gives:
% 6.10/1.61 | (12) ? [v0: $ki_world] : (b(v0, all_10_0) = 0 & $ki_accessible(all_10_1,
% 6.10/1.61 | v0) = 0 & $ki_world(v0))
% 6.10/1.61 |
% 6.10/1.61 | DELTA: instantiating (12) with fresh symbol all_18_0 gives:
% 6.10/1.61 | (13) b(all_18_0, all_10_0) = 0 & $ki_accessible(all_10_1, all_18_0) = 0 &
% 6.10/1.61 | $ki_world(all_18_0)
% 6.10/1.61 |
% 6.10/1.61 | ALPHA: (13) implies:
% 6.10/1.61 | (14) $ki_world(all_18_0)
% 6.10/1.61 | (15) $ki_accessible(all_10_1, all_18_0) = 0
% 6.10/1.61 | (16) b(all_18_0, all_10_0) = 0
% 6.10/1.61 |
% 6.10/1.61 | GROUND_INST: instantiating (9) with all_18_0, simplifying with (14), (15)
% 6.10/1.61 | gives:
% 6.10/1.61 | (17) a(all_18_0, all_10_0) = 0
% 6.10/1.61 |
% 6.10/1.61 | GROUND_INST: instantiating (11) with all_10_1, all_10_0, all_18_0, simplifying
% 6.10/1.61 | with (5), (6), (7), (8), (14), (16) gives:
% 6.10/1.61 | (18) ? [v0: any] : ? [v1: any] : (a(all_18_0, all_10_0) = v1 &
% 6.10/1.62 | $ki_accessible(all_10_1, all_18_0) = v0 & ( ~ (v1 = 0) | ~ (v0 =
% 6.10/1.62 | 0)))
% 6.10/1.62 |
% 6.10/1.62 | DELTA: instantiating (18) with fresh symbols all_28_0, all_28_1 gives:
% 6.10/1.62 | (19) a(all_18_0, all_10_0) = all_28_0 & $ki_accessible(all_10_1, all_18_0)
% 6.10/1.62 | = all_28_1 & ( ~ (all_28_0 = 0) | ~ (all_28_1 = 0))
% 6.10/1.62 |
% 6.10/1.62 | ALPHA: (19) implies:
% 6.10/1.62 | (20) $ki_accessible(all_10_1, all_18_0) = all_28_1
% 6.10/1.62 | (21) a(all_18_0, all_10_0) = all_28_0
% 6.10/1.62 | (22) ~ (all_28_0 = 0) | ~ (all_28_1 = 0)
% 6.10/1.62 |
% 6.10/1.62 | GROUND_INST: instantiating (2) with 0, all_28_1, all_18_0, all_10_1,
% 6.10/1.62 | simplifying with (15), (20) gives:
% 6.10/1.62 | (23) all_28_1 = 0
% 6.10/1.62 |
% 6.10/1.62 | GROUND_INST: instantiating (3) with 0, all_28_0, all_10_0, all_18_0,
% 6.10/1.62 | simplifying with (17), (21) gives:
% 6.10/1.62 | (24) all_28_0 = 0
% 6.10/1.62 |
% 6.10/1.62 | BETA: splitting (22) gives:
% 6.10/1.62 |
% 6.10/1.62 | Case 1:
% 6.10/1.62 | |
% 6.10/1.62 | | (25) ~ (all_28_0 = 0)
% 6.10/1.62 | |
% 6.10/1.62 | | REDUCE: (24), (25) imply:
% 6.10/1.62 | | (26) $false
% 6.10/1.62 | |
% 6.10/1.62 | | CLOSE: (26) is inconsistent.
% 6.10/1.62 | |
% 6.10/1.62 | Case 2:
% 6.10/1.62 | |
% 6.10/1.62 | | (27) ~ (all_28_1 = 0)
% 6.10/1.62 | |
% 6.10/1.62 | | REDUCE: (23), (27) imply:
% 6.10/1.62 | | (28) $false
% 6.10/1.62 | |
% 6.10/1.62 | | CLOSE: (28) is inconsistent.
% 6.10/1.62 | |
% 6.10/1.62 | End of split
% 6.10/1.62 |
% 6.10/1.62 End of proof
% 6.10/1.62 % SZS output end Proof for theBenchmark
% 6.10/1.62
% 6.10/1.62 1018ms
%------------------------------------------------------------------------------