TSTP Solution File: LCL962_16 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : LCL962_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 : n018.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 08:13:27 EDT 2023
% Result : Theorem 4.62s 1.37s
% Output : Proof 6.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL962_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 : n018.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 : Thu Aug 24 20:36:13 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.58 ________ _____
% 0.20/0.58 ___ __ \_________(_)________________________________
% 0.20/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.58
% 0.20/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.58 (2023-06-19)
% 0.20/0.58
% 0.20/0.58 (c) Philipp Rümmer, 2009-2023
% 0.20/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.58 Amanda Stjerna.
% 0.20/0.58 Free software under BSD-3-Clause.
% 0.20/0.58
% 0.20/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.58
% 0.20/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.59 Running up to 7 provers in parallel.
% 0.20/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.77/1.00 Prover 1: Preprocessing ...
% 2.43/1.00 Prover 4: Preprocessing ...
% 2.43/1.05 Prover 0: Preprocessing ...
% 2.43/1.05 Prover 2: Preprocessing ...
% 2.43/1.05 Prover 6: Preprocessing ...
% 2.43/1.05 Prover 5: Preprocessing ...
% 2.43/1.05 Prover 3: Preprocessing ...
% 3.05/1.17 Prover 5: Proving ...
% 3.05/1.17 Prover 2: Proving ...
% 3.76/1.20 Prover 3: Constructing countermodel ...
% 3.86/1.20 Prover 6: Proving ...
% 3.92/1.21 Prover 1: Constructing countermodel ...
% 3.92/1.27 Prover 4: Constructing countermodel ...
% 3.92/1.27 Prover 0: Proving ...
% 4.62/1.35 Prover 3: gave up
% 4.62/1.36 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.62/1.36 Prover 5: proved (758ms)
% 4.62/1.37
% 4.62/1.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.62/1.37
% 4.62/1.37 Prover 2: stopped
% 4.62/1.37 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.62/1.37 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.62/1.37 Prover 6: stopped
% 4.62/1.37 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.62/1.37 Prover 0: stopped
% 4.62/1.38 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.18/1.40 Prover 7: Preprocessing ...
% 5.18/1.41 Prover 11: Preprocessing ...
% 5.18/1.41 Prover 8: Preprocessing ...
% 5.18/1.41 Prover 10: Preprocessing ...
% 5.18/1.41 Prover 1: gave up
% 5.18/1.43 Prover 13: Preprocessing ...
% 5.18/1.43 Prover 7: Warning: ignoring some quantifiers
% 5.18/1.43 Prover 10: Warning: ignoring some quantifiers
% 5.18/1.43 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 5.18/1.43 Prover 7: Constructing countermodel ...
% 5.18/1.43 Prover 10: Constructing countermodel ...
% 5.18/1.44 Prover 13: Warning: ignoring some quantifiers
% 5.18/1.45 Prover 13: Constructing countermodel ...
% 5.18/1.45 Prover 16: Preprocessing ...
% 5.18/1.45 Prover 8: Warning: ignoring some quantifiers
% 5.18/1.46 Prover 10: gave up
% 5.18/1.46 Prover 8: Constructing countermodel ...
% 5.18/1.47 Prover 7: gave up
% 5.18/1.47 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 5.18/1.47 Prover 13: gave up
% 5.18/1.48 Prover 16: Warning: ignoring some quantifiers
% 5.18/1.49 Prover 16: Constructing countermodel ...
% 5.18/1.50 Prover 19: Preprocessing ...
% 5.18/1.52 Prover 8: gave up
% 5.18/1.53 Prover 16: gave up
% 5.18/1.54 Prover 11: Constructing countermodel ...
% 5.18/1.55 Prover 19: Warning: ignoring some quantifiers
% 5.18/1.55 Prover 19: Constructing countermodel ...
% 5.18/1.56 Prover 4: Found proof (size 43)
% 5.18/1.56 Prover 4: proved (961ms)
% 5.18/1.56 Prover 19: stopped
% 5.18/1.57 Prover 11: stopped
% 5.18/1.57
% 5.18/1.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.18/1.57
% 5.18/1.57 % SZS output start Proof for theBenchmark
% 5.18/1.58 Assumptions after simplification:
% 5.18/1.58 ---------------------------------
% 5.18/1.58
% 5.18/1.58 (ab_axiom_1)
% 6.65/1.61 $ki_index(#idx(b)) & $ki_index(#idx(a)) & $ki_world($ki_local_world) & ! [v0:
% 6.65/1.61 $ki_world] : ! [v1: $ki_world] : ! [v2: int] : (v2 = 0 | ~ (p(v1) = v2) |
% 6.65/1.61 ~ (p(v0) = 0) | ~ $ki_world(v1) | ~ $ki_world(v0) | ? [v3: int] : (( ~
% 6.65/1.61 (v3 = 0) & $ki_accessible(#idx(b), v0, v1) = v3) | ( ~ (v3 = 0) &
% 6.65/1.61 $ki_accessible(#idx(a), $ki_local_world, v0) = v3))) & ! [v0:
% 6.65/1.61 $ki_world] : ! [v1: $ki_world] : ! [v2: int] : (v2 = 0 | ~ (p(v1) = v2) |
% 6.65/1.61 ~ ($ki_accessible(#idx(a), $ki_local_world, v0) = 0) | ~ $ki_world(v1) |
% 6.65/1.61 ~ $ki_world(v0) | ? [v3: int] : (( ~ (v3 = 0) & p(v0) = v3) | ( ~ (v3 = 0)
% 6.65/1.61 & $ki_accessible(#idx(b), v0, v1) = v3))) & ! [v0: $ki_world] : ! [v1:
% 6.65/1.61 $ki_world] : ( ~ (p(v0) = 0) | ~ ($ki_accessible(#idx(b), v0, v1) = 0) | ~
% 6.65/1.61 $ki_world(v1) | ~ $ki_world(v0) | ? [v2: int] : ((v2 = 0 & p(v1) = 0) | (
% 6.65/1.61 ~ (v2 = 0) & $ki_accessible(#idx(a), $ki_local_world, v0) = v2))) & !
% 6.65/1.61 [v0: $ki_world] : ! [v1: $ki_world] : ( ~ ($ki_accessible(#idx(b), v0, v1) =
% 6.65/1.61 0) | ~ ($ki_accessible(#idx(a), $ki_local_world, v0) = 0) | ~
% 6.65/1.61 $ki_world(v1) | ~ $ki_world(v0) | ? [v2: int] : ((v2 = 0 & p(v1) = 0) | (
% 6.65/1.61 ~ (v2 = 0) & p(v0) = v2)))
% 6.65/1.61
% 6.65/1.61 (ab_axiom_2)
% 6.65/1.62 $ki_index(#idx(b)) & $ki_index(#idx(a)) & $ki_world($ki_local_world) & ( !
% 6.65/1.62 [v0: $ki_world] : ( ~ ($ki_accessible(#idx(a), $ki_local_world, v0) = 0) |
% 6.65/1.62 ~ $ki_world(v0) | ? [v1: $ki_world] : ? [v2: int] : ( ~ (v2 = 0) & p(v1)
% 6.65/1.62 = v2 & $ki_accessible(#idx(b), v0, v1) = 0 & $ki_world(v1))) | ( ! [v0:
% 6.65/1.62 $ki_world] : ! [v1: int] : (v1 = 0 | ~ (p(v0) = v1) | ~ $ki_world(v0)
% 6.65/1.62 | ? [v2: int] : ( ~ (v2 = 0) & $ki_accessible(#idx(b), $ki_local_world,
% 6.65/1.62 v0) = v2)) & ! [v0: $ki_world] : ( ~ ($ki_accessible(#idx(b),
% 6.65/1.62 $ki_local_world, v0) = 0) | ~ $ki_world(v0) | p(v0) = 0)))
% 6.65/1.62
% 6.65/1.62 (mrel_reflexive_#idx(b))
% 6.65/1.62 $ki_index(#idx(b)) & ! [v0: $ki_world] : ! [v1: int] : (v1 = 0 | ~
% 6.65/1.62 ($ki_accessible(#idx(b), v0, v0) = v1) | ~ $ki_world(v0))
% 6.65/1.62
% 6.65/1.62 (not_a_axiom_1)
% 6.65/1.62 $ki_world($ki_local_world) & ? [v0: int] : ( ~ (v0 = 0) & p($ki_local_world)
% 6.65/1.62 = v0)
% 6.65/1.62
% 6.65/1.62 (verify)
% 6.65/1.62 $ki_index(#idx(a)) & $ki_world($ki_local_world) & ? [v0: $ki_world] : (p(v0)
% 6.65/1.62 = 0 & $ki_accessible(#idx(a), $ki_local_world, v0) = 0 & $ki_world(v0))
% 6.65/1.62
% 6.65/1.62 (function-axioms)
% 6.65/1.62 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $ki_world] :
% 6.65/1.62 ! [v3: $ki_world] : ! [v4: $ki_index] : (v1 = v0 | ~ ($ki_accessible(v4,
% 6.65/1.62 v3, v2) = v1) | ~ ($ki_accessible(v4, v3, v2) = v0)) & ! [v0:
% 6.65/1.62 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $ki_world] : (v1 =
% 6.65/1.62 v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0))
% 6.65/1.62
% 6.65/1.62 Further assumptions not needed in the proof:
% 6.65/1.62 --------------------------------------------
% 6.65/1.62 mrel_reflexive_#idx(a), mrel_transitive_#idx(a), mrel_transitive_#idx(b)
% 6.65/1.62
% 6.65/1.62 Those formulas are unsatisfiable:
% 6.65/1.62 ---------------------------------
% 6.65/1.62
% 6.65/1.62 Begin of proof
% 6.65/1.62 |
% 6.65/1.62 | ALPHA: (mrel_reflexive_#idx(b)) implies:
% 6.65/1.62 | (1) ! [v0: $ki_world] : ! [v1: int] : (v1 = 0 | ~
% 6.65/1.62 | ($ki_accessible(#idx(b), v0, v0) = v1) | ~ $ki_world(v0))
% 6.65/1.62 |
% 6.65/1.62 | ALPHA: (ab_axiom_1) implies:
% 6.65/1.63 | (2) ! [v0: $ki_world] : ! [v1: $ki_world] : ( ~ (p(v0) = 0) | ~
% 6.65/1.63 | ($ki_accessible(#idx(b), v0, v1) = 0) | ~ $ki_world(v1) | ~
% 6.65/1.63 | $ki_world(v0) | ? [v2: int] : ((v2 = 0 & p(v1) = 0) | ( ~ (v2 = 0) &
% 6.65/1.63 | $ki_accessible(#idx(a), $ki_local_world, v0) = v2)))
% 6.65/1.63 | (3) ! [v0: $ki_world] : ! [v1: $ki_world] : ! [v2: int] : (v2 = 0 | ~
% 6.65/1.63 | (p(v1) = v2) | ~ (p(v0) = 0) | ~ $ki_world(v1) | ~ $ki_world(v0) |
% 6.65/1.63 | ? [v3: int] : (( ~ (v3 = 0) & $ki_accessible(#idx(b), v0, v1) = v3)
% 6.65/1.63 | | ( ~ (v3 = 0) & $ki_accessible(#idx(a), $ki_local_world, v0) =
% 6.65/1.63 | v3)))
% 6.65/1.63 |
% 6.65/1.63 | ALPHA: (ab_axiom_2) implies:
% 6.65/1.63 | (4) ! [v0: $ki_world] : ( ~ ($ki_accessible(#idx(a), $ki_local_world, v0)
% 6.65/1.63 | = 0) | ~ $ki_world(v0) | ? [v1: $ki_world] : ? [v2: int] : ( ~
% 6.65/1.63 | (v2 = 0) & p(v1) = v2 & $ki_accessible(#idx(b), v0, v1) = 0 &
% 6.65/1.63 | $ki_world(v1))) | ( ! [v0: $ki_world] : ! [v1: int] : (v1 = 0 | ~
% 6.65/1.63 | (p(v0) = v1) | ~ $ki_world(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 6.65/1.63 | $ki_accessible(#idx(b), $ki_local_world, v0) = v2)) & ! [v0:
% 6.65/1.63 | $ki_world] : ( ~ ($ki_accessible(#idx(b), $ki_local_world, v0) = 0)
% 6.65/1.63 | | ~ $ki_world(v0) | p(v0) = 0))
% 6.65/1.63 |
% 6.65/1.63 | ALPHA: (not_a_axiom_1) implies:
% 6.65/1.63 | (5) ? [v0: int] : ( ~ (v0 = 0) & p($ki_local_world) = v0)
% 6.65/1.63 |
% 6.65/1.63 | ALPHA: (verify) implies:
% 6.65/1.63 | (6) $ki_world($ki_local_world)
% 6.65/1.63 | (7) ? [v0: $ki_world] : (p(v0) = 0 & $ki_accessible(#idx(a),
% 6.65/1.63 | $ki_local_world, v0) = 0 & $ki_world(v0))
% 6.65/1.63 |
% 6.65/1.63 | ALPHA: (function-axioms) implies:
% 6.65/1.63 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 6.65/1.63 | $ki_world] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0))
% 6.65/1.63 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 6.65/1.63 | $ki_world] : ! [v3: $ki_world] : ! [v4: $ki_index] : (v1 = v0 | ~
% 6.65/1.63 | ($ki_accessible(v4, v3, v2) = v1) | ~ ($ki_accessible(v4, v3, v2) =
% 6.65/1.63 | v0))
% 6.65/1.63 |
% 6.65/1.63 | DELTA: instantiating (5) with fresh symbol all_13_0 gives:
% 6.65/1.64 | (10) ~ (all_13_0 = 0) & p($ki_local_world) = all_13_0
% 6.65/1.64 |
% 6.65/1.64 | ALPHA: (10) implies:
% 6.65/1.64 | (11) ~ (all_13_0 = 0)
% 6.65/1.64 | (12) p($ki_local_world) = all_13_0
% 6.65/1.64 |
% 6.65/1.64 | DELTA: instantiating (7) with fresh symbol all_15_0 gives:
% 6.65/1.64 | (13) p(all_15_0) = 0 & $ki_accessible(#idx(a), $ki_local_world, all_15_0) =
% 6.65/1.64 | 0 & $ki_world(all_15_0)
% 6.65/1.64 |
% 6.65/1.64 | ALPHA: (13) implies:
% 6.65/1.64 | (14) $ki_world(all_15_0)
% 6.65/1.64 | (15) $ki_accessible(#idx(a), $ki_local_world, all_15_0) = 0
% 6.65/1.64 | (16) p(all_15_0) = 0
% 6.65/1.64 |
% 6.65/1.64 | GROUND_INST: instantiating (3) with all_15_0, $ki_local_world, all_13_0,
% 6.65/1.64 | simplifying with (6), (12), (14), (16) gives:
% 6.65/1.64 | (17) all_13_0 = 0 | ? [v0: int] : (( ~ (v0 = 0) & $ki_accessible(#idx(b),
% 6.65/1.64 | all_15_0, $ki_local_world) = v0) | ( ~ (v0 = 0) &
% 6.65/1.64 | $ki_accessible(#idx(a), $ki_local_world, all_15_0) = v0))
% 6.65/1.64 |
% 6.65/1.64 | BETA: splitting (4) gives:
% 6.65/1.64 |
% 6.65/1.64 | Case 1:
% 6.65/1.64 | |
% 6.65/1.64 | | (18) ! [v0: $ki_world] : ( ~ ($ki_accessible(#idx(a), $ki_local_world,
% 6.65/1.64 | | v0) = 0) | ~ $ki_world(v0) | ? [v1: $ki_world] : ? [v2:
% 6.65/1.64 | | int] : ( ~ (v2 = 0) & p(v1) = v2 & $ki_accessible(#idx(b), v0,
% 6.65/1.64 | | v1) = 0 & $ki_world(v1)))
% 6.65/1.64 | |
% 6.65/1.64 | | GROUND_INST: instantiating (18) with all_15_0, simplifying with (14), (15)
% 6.65/1.64 | | gives:
% 6.65/1.64 | | (19) ? [v0: $ki_world] : ? [v1: int] : ( ~ (v1 = 0) & p(v0) = v1 &
% 6.65/1.64 | | $ki_accessible(#idx(b), all_15_0, v0) = 0 & $ki_world(v0))
% 6.65/1.64 | |
% 6.65/1.64 | | DELTA: instantiating (19) with fresh symbols all_24_0, all_24_1 gives:
% 6.65/1.64 | | (20) ~ (all_24_0 = 0) & p(all_24_1) = all_24_0 & $ki_accessible(#idx(b),
% 6.65/1.64 | | all_15_0, all_24_1) = 0 & $ki_world(all_24_1)
% 6.65/1.64 | |
% 6.65/1.64 | | ALPHA: (20) implies:
% 6.65/1.64 | | (21) ~ (all_24_0 = 0)
% 6.65/1.64 | | (22) $ki_world(all_24_1)
% 6.65/1.64 | | (23) $ki_accessible(#idx(b), all_15_0, all_24_1) = 0
% 6.65/1.64 | | (24) p(all_24_1) = all_24_0
% 6.65/1.64 | |
% 6.65/1.64 | | BETA: splitting (17) gives:
% 6.65/1.64 | |
% 6.65/1.64 | | Case 1:
% 6.65/1.64 | | |
% 6.65/1.64 | | | (25) all_13_0 = 0
% 6.65/1.64 | | |
% 6.65/1.64 | | | REDUCE: (11), (25) imply:
% 6.65/1.64 | | | (26) $false
% 6.65/1.64 | | |
% 6.65/1.64 | | | CLOSE: (26) is inconsistent.
% 6.65/1.64 | | |
% 6.65/1.64 | | Case 2:
% 6.65/1.64 | | |
% 6.65/1.64 | | |
% 6.65/1.64 | | | GROUND_INST: instantiating (2) with all_15_0, all_24_1, simplifying with
% 6.65/1.64 | | | (14), (16), (22), (23) gives:
% 6.65/1.64 | | | (27) ? [v0: int] : ((v0 = 0 & p(all_24_1) = 0) | ( ~ (v0 = 0) &
% 6.65/1.64 | | | $ki_accessible(#idx(a), $ki_local_world, all_15_0) = v0))
% 6.65/1.64 | | |
% 6.65/1.64 | | | DELTA: instantiating (27) with fresh symbol all_52_0 gives:
% 6.65/1.65 | | | (28) (all_52_0 = 0 & p(all_24_1) = 0) | ( ~ (all_52_0 = 0) &
% 6.65/1.65 | | | $ki_accessible(#idx(a), $ki_local_world, all_15_0) = all_52_0)
% 6.65/1.65 | | |
% 6.65/1.65 | | | BETA: splitting (28) gives:
% 6.65/1.65 | | |
% 6.65/1.65 | | | Case 1:
% 6.65/1.65 | | | |
% 6.65/1.65 | | | | (29) all_52_0 = 0 & p(all_24_1) = 0
% 6.65/1.65 | | | |
% 6.65/1.65 | | | | ALPHA: (29) implies:
% 6.65/1.65 | | | | (30) p(all_24_1) = 0
% 6.65/1.65 | | | |
% 6.65/1.65 | | | | GROUND_INST: instantiating (8) with all_24_0, 0, all_24_1, simplifying
% 6.65/1.65 | | | | with (24), (30) gives:
% 6.65/1.65 | | | | (31) all_24_0 = 0
% 6.65/1.65 | | | |
% 6.65/1.65 | | | | REDUCE: (21), (31) imply:
% 6.65/1.65 | | | | (32) $false
% 6.65/1.65 | | | |
% 6.65/1.65 | | | | CLOSE: (32) is inconsistent.
% 6.65/1.65 | | | |
% 6.65/1.65 | | | Case 2:
% 6.65/1.65 | | | |
% 6.65/1.65 | | | | (33) ~ (all_52_0 = 0) & $ki_accessible(#idx(a), $ki_local_world,
% 6.65/1.65 | | | | all_15_0) = all_52_0
% 6.65/1.65 | | | |
% 6.65/1.65 | | | | ALPHA: (33) implies:
% 6.65/1.65 | | | | (34) ~ (all_52_0 = 0)
% 6.65/1.65 | | | | (35) $ki_accessible(#idx(a), $ki_local_world, all_15_0) = all_52_0
% 6.65/1.65 | | | |
% 6.65/1.65 | | | | GROUND_INST: instantiating (9) with 0, all_52_0, all_15_0,
% 6.65/1.65 | | | | $ki_local_world, #idx(a), simplifying with (15), (35)
% 6.65/1.65 | | | | gives:
% 6.65/1.65 | | | | (36) all_52_0 = 0
% 6.65/1.65 | | | |
% 6.65/1.65 | | | | REDUCE: (34), (36) imply:
% 6.65/1.65 | | | | (37) $false
% 6.65/1.65 | | | |
% 6.65/1.65 | | | | CLOSE: (37) is inconsistent.
% 6.65/1.65 | | | |
% 6.65/1.65 | | | End of split
% 6.65/1.65 | | |
% 6.65/1.65 | | End of split
% 6.65/1.65 | |
% 6.65/1.65 | Case 2:
% 6.65/1.65 | |
% 6.65/1.65 | | (38) ! [v0: $ki_world] : ! [v1: int] : (v1 = 0 | ~ (p(v0) = v1) | ~
% 6.65/1.65 | | $ki_world(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 6.65/1.65 | | $ki_accessible(#idx(b), $ki_local_world, v0) = v2)) & ! [v0:
% 6.65/1.65 | | $ki_world] : ( ~ ($ki_accessible(#idx(b), $ki_local_world, v0) =
% 6.65/1.65 | | 0) | ~ $ki_world(v0) | p(v0) = 0)
% 6.65/1.65 | |
% 6.65/1.65 | | ALPHA: (38) implies:
% 6.65/1.65 | | (39) ! [v0: $ki_world] : ! [v1: int] : (v1 = 0 | ~ (p(v0) = v1) | ~
% 6.65/1.65 | | $ki_world(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 6.65/1.65 | | $ki_accessible(#idx(b), $ki_local_world, v0) = v2))
% 6.65/1.65 | |
% 6.65/1.65 | | GROUND_INST: instantiating (39) with $ki_local_world, all_13_0, simplifying
% 6.65/1.65 | | with (6), (12) gives:
% 6.65/1.65 | | (40) all_13_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & $ki_accessible(#idx(b),
% 6.65/1.65 | | $ki_local_world, $ki_local_world) = v0)
% 6.65/1.65 | |
% 6.65/1.65 | | BETA: splitting (40) gives:
% 6.65/1.65 | |
% 6.65/1.65 | | Case 1:
% 6.65/1.65 | | |
% 6.65/1.65 | | | (41) all_13_0 = 0
% 6.65/1.65 | | |
% 6.65/1.65 | | | REDUCE: (11), (41) imply:
% 6.65/1.65 | | | (42) $false
% 6.65/1.65 | | |
% 6.65/1.65 | | | CLOSE: (42) is inconsistent.
% 6.65/1.65 | | |
% 6.65/1.65 | | Case 2:
% 6.65/1.65 | | |
% 6.65/1.65 | | | (43) ? [v0: int] : ( ~ (v0 = 0) & $ki_accessible(#idx(b),
% 6.65/1.65 | | | $ki_local_world, $ki_local_world) = v0)
% 6.65/1.65 | | |
% 6.65/1.65 | | | DELTA: instantiating (43) with fresh symbol all_37_0 gives:
% 6.65/1.65 | | | (44) ~ (all_37_0 = 0) & $ki_accessible(#idx(b), $ki_local_world,
% 6.65/1.65 | | | $ki_local_world) = all_37_0
% 6.65/1.65 | | |
% 6.65/1.65 | | | ALPHA: (44) implies:
% 6.65/1.65 | | | (45) ~ (all_37_0 = 0)
% 6.65/1.65 | | | (46) $ki_accessible(#idx(b), $ki_local_world, $ki_local_world) =
% 6.65/1.65 | | | all_37_0
% 6.65/1.65 | | |
% 6.65/1.65 | | | GROUND_INST: instantiating (1) with $ki_local_world, all_37_0, simplifying
% 6.65/1.65 | | | with (6), (46) gives:
% 6.65/1.65 | | | (47) all_37_0 = 0
% 6.65/1.65 | | |
% 6.65/1.65 | | | REDUCE: (45), (47) imply:
% 6.65/1.65 | | | (48) $false
% 6.65/1.65 | | |
% 6.65/1.65 | | | CLOSE: (48) is inconsistent.
% 6.65/1.65 | | |
% 6.65/1.65 | | End of split
% 6.65/1.65 | |
% 6.65/1.65 | End of split
% 6.65/1.65 |
% 6.65/1.65 End of proof
% 6.65/1.65 % SZS output end Proof for theBenchmark
% 6.65/1.65
% 6.65/1.65 1072ms
%------------------------------------------------------------------------------