TSTP Solution File: LCL953_8 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : LCL953_8 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n011.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 08:13:26 EDT 2023
% Result : Theorem 8.50s 1.93s
% Output : Proof 10.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : LCL953_8 : TPTP v8.2.0. Released v8.2.0.
% 0.08/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n011.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 : Fri Aug 25 02:04:23 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.88/1.13 Prover 1: Preprocessing ...
% 2.88/1.13 Prover 4: Preprocessing ...
% 2.88/1.17 Prover 6: Preprocessing ...
% 2.88/1.17 Prover 5: Preprocessing ...
% 2.88/1.18 Prover 3: Preprocessing ...
% 2.88/1.18 Prover 0: Preprocessing ...
% 2.88/1.18 Prover 2: Preprocessing ...
% 5.13/1.42 Prover 2: Proving ...
% 5.31/1.45 Prover 5: Proving ...
% 5.90/1.55 Prover 6: Proving ...
% 5.90/1.56 Prover 1: Warning: ignoring some quantifiers
% 5.90/1.56 Prover 4: Warning: ignoring some quantifiers
% 5.90/1.57 Prover 1: Constructing countermodel ...
% 5.90/1.57 Prover 3: Warning: ignoring some quantifiers
% 5.90/1.57 Prover 0: Proving ...
% 6.29/1.59 Prover 3: Constructing countermodel ...
% 6.29/1.59 Prover 4: Constructing countermodel ...
% 8.50/1.92 Prover 0: proved (1284ms)
% 8.50/1.93
% 8.50/1.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.50/1.93
% 8.50/1.93 Prover 5: stopped
% 8.50/1.93 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.50/1.93 Prover 2: proved (1289ms)
% 8.50/1.93
% 8.50/1.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.50/1.93
% 8.50/1.93 Prover 6: stopped
% 8.50/1.94 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.94/1.95 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.94/1.95 Prover 3: stopped
% 8.94/1.96 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.94/1.96 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.45/2.03 Prover 13: Preprocessing ...
% 9.45/2.04 Prover 10: Preprocessing ...
% 9.45/2.04 Prover 8: Preprocessing ...
% 9.45/2.05 Prover 7: Preprocessing ...
% 9.45/2.05 Prover 11: Preprocessing ...
% 9.45/2.06 Prover 1: Found proof (size 52)
% 9.45/2.06 Prover 1: proved (1417ms)
% 9.45/2.06 Prover 4: stopped
% 9.45/2.07 Prover 13: stopped
% 9.81/2.07 Prover 7: stopped
% 9.81/2.07 Prover 10: stopped
% 9.81/2.09 Prover 11: stopped
% 9.81/2.13 Prover 8: Warning: ignoring some quantifiers
% 10.20/2.14 Prover 8: Constructing countermodel ...
% 10.20/2.15 Prover 8: stopped
% 10.20/2.15
% 10.20/2.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.20/2.15
% 10.20/2.15 % SZS output start Proof for theBenchmark
% 10.20/2.15 Assumptions after simplification:
% 10.20/2.15 ---------------------------------
% 10.20/2.15
% 10.20/2.15 (l28_zfmisc_1)
% 10.36/2.18 $ki_world($ki_local_world) & ! [v0: $ki_world] : ( ~
% 10.36/2.18 ($ki_accessible($ki_local_world, v0) = 0) | ~ $ki_world(v0) | ! [v1: $i] :
% 10.36/2.18 ! [v2: $i] : ( ~ (singleton(v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3
% 10.36/2.18 = 0) & $ki_exists_in_world_$i(v0, v1) = v3) | ! [v3: $ki_world] : ( ~
% 10.36/2.18 ($ki_accessible(v0, v3) = 0) | ~ $ki_world(v3) | ! [v4: $i] : ( ~
% 10.36/2.18 ($ki_exists_in_world_$i(v3, v4) = 0) | ~ $i(v4) | ! [v5: $ki_world]
% 10.36/2.18 : ( ~ ($ki_accessible(v3, v5) = 0) | ~ $ki_world(v5) | ? [v6:
% 10.36/2.18 $ki_world] : ($ki_accessible(v5, v6) = 0 & $ki_world(v6) & ! [v7:
% 10.36/2.18 $ki_world] : ! [v8: int] : (v8 = 0 | ~ (in(v7, v1, v4) = v8) |
% 10.36/2.18 ~ $ki_world(v7) | ? [v9: int] : ( ~ (v9 = 0) &
% 10.36/2.18 $ki_accessible(v6, v7) = v9))) | ! [v6: $ki_world] : ! [v7:
% 10.36/2.18 int] : (v7 = 0 | ~ (disjoint(v6, v2, v4) = v7) | ~ $ki_world(v6)
% 10.36/2.18 | ? [v8: int] : ( ~ (v8 = 0) & $ki_accessible(v5, v6) = v8)))))))
% 10.36/2.18
% 10.36/2.18 (verify)
% 10.36/2.19 $ki_world($ki_local_world) & ? [v0: $ki_world] :
% 10.36/2.19 ($ki_accessible($ki_local_world, v0) = 0 & $ki_world(v0) & ? [v1: $i] : ?
% 10.36/2.19 [v2: $i] : (singleton(v1) = v2 & $ki_exists_in_world_$i(v0, v1) = 0 & $i(v2)
% 10.36/2.19 & $i(v1) & ? [v3: $ki_world] : ($ki_accessible(v0, v3) = 0 &
% 10.36/2.19 $ki_world(v3) & ? [v4: $i] : ($ki_exists_in_world_$i(v3, v4) = 0 &
% 10.36/2.19 $i(v4) & ? [v5: $ki_world] : ($ki_accessible(v3, v5) = 0 &
% 10.36/2.19 $ki_world(v5) & ! [v6: $ki_world] : ( ~ ($ki_accessible(v5, v6) =
% 10.36/2.19 0) | ~ $ki_world(v6) | ? [v7: $ki_world] : ? [v8: int] : ( ~
% 10.36/2.19 (v8 = 0) & in(v7, v1, v4) = v8 & $ki_accessible(v6, v7) = 0 &
% 10.36/2.19 $ki_world(v7))) & ? [v6: $ki_world] : ? [v7: int] : ( ~ (v7 =
% 10.36/2.19 0) & disjoint(v6, v2, v4) = v7 & $ki_accessible(v5, v6) = 0 &
% 10.36/2.19 $ki_world(v6)))))))
% 10.36/2.19
% 10.36/2.19 (function-axioms)
% 10.36/2.19 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 10.36/2.19 [v3: $i] : ! [v4: $ki_world] : (v1 = v0 | ~ (in(v4, v3, v2) = v1) | ~
% 10.36/2.19 (in(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.36/2.19 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $ki_world] : (v1 =
% 10.36/2.19 v0 | ~ (disjoint(v4, v3, v2) = v1) | ~ (disjoint(v4, v3, v2) = v0)) & !
% 10.36/2.19 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 10.36/2.19 $ki_world] : (v1 = v0 | ~ (empty(v3, v2) = v1) | ~ (empty(v3, v2) = v0)) &
% 10.36/2.19 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 10.36/2.19 [v3: $ki_world] : (v1 = v0 | ~ ($ki_exists_in_world_$i(v3, v2) = v1) | ~
% 10.36/2.19 ($ki_exists_in_world_$i(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 10.36/2.19 [v1: MultipleValueBool] : ! [v2: $ki_world] : ! [v3: $ki_world] : (v1 = v0 |
% 10.36/2.19 ~ ($ki_accessible(v3, v2) = v1) | ~ ($ki_accessible(v3, v2) = v0)) & !
% 10.36/2.19 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 10.36/2.19 (singleton(v2) = v0))
% 10.36/2.19
% 10.36/2.19 Further assumptions not needed in the proof:
% 10.36/2.19 --------------------------------------------
% 10.36/2.19 $ki_exists_in_world_$i_nonempty, antisymmetry_r2_hidden, mrel_reflexive,
% 10.36/2.19 rc1_xboole_0, rc2_xboole_0, symmetry_r1_xboole_0
% 10.36/2.19
% 10.36/2.19 Those formulas are unsatisfiable:
% 10.36/2.19 ---------------------------------
% 10.36/2.19
% 10.36/2.19 Begin of proof
% 10.36/2.19 |
% 10.36/2.19 | ALPHA: (l28_zfmisc_1) implies:
% 10.36/2.20 | (1) ! [v0: $ki_world] : ( ~ ($ki_accessible($ki_local_world, v0) = 0) | ~
% 10.36/2.20 | $ki_world(v0) | ! [v1: $i] : ! [v2: $i] : ( ~ (singleton(v1) = v2)
% 10.36/2.20 | | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 10.36/2.20 | $ki_exists_in_world_$i(v0, v1) = v3) | ! [v3: $ki_world] : ( ~
% 10.36/2.20 | ($ki_accessible(v0, v3) = 0) | ~ $ki_world(v3) | ! [v4: $i] : (
% 10.36/2.20 | ~ ($ki_exists_in_world_$i(v3, v4) = 0) | ~ $i(v4) | ! [v5:
% 10.36/2.20 | $ki_world] : ( ~ ($ki_accessible(v3, v5) = 0) | ~
% 10.36/2.20 | $ki_world(v5) | ? [v6: $ki_world] : ($ki_accessible(v5, v6)
% 10.36/2.20 | = 0 & $ki_world(v6) & ! [v7: $ki_world] : ! [v8: int] :
% 10.36/2.20 | (v8 = 0 | ~ (in(v7, v1, v4) = v8) | ~ $ki_world(v7) | ?
% 10.36/2.20 | [v9: int] : ( ~ (v9 = 0) & $ki_accessible(v6, v7) = v9)))
% 10.36/2.20 | | ! [v6: $ki_world] : ! [v7: int] : (v7 = 0 | ~
% 10.36/2.20 | (disjoint(v6, v2, v4) = v7) | ~ $ki_world(v6) | ? [v8:
% 10.36/2.20 | int] : ( ~ (v8 = 0) & $ki_accessible(v5, v6) = v8)))))))
% 10.36/2.20 |
% 10.36/2.20 | ALPHA: (verify) implies:
% 10.36/2.20 | (2) ? [v0: $ki_world] : ($ki_accessible($ki_local_world, v0) = 0 &
% 10.36/2.20 | $ki_world(v0) & ? [v1: $i] : ? [v2: $i] : (singleton(v1) = v2 &
% 10.36/2.20 | $ki_exists_in_world_$i(v0, v1) = 0 & $i(v2) & $i(v1) & ? [v3:
% 10.36/2.20 | $ki_world] : ($ki_accessible(v0, v3) = 0 & $ki_world(v3) & ?
% 10.36/2.20 | [v4: $i] : ($ki_exists_in_world_$i(v3, v4) = 0 & $i(v4) & ? [v5:
% 10.36/2.20 | $ki_world] : ($ki_accessible(v3, v5) = 0 & $ki_world(v5) & !
% 10.36/2.20 | [v6: $ki_world] : ( ~ ($ki_accessible(v5, v6) = 0) | ~
% 10.36/2.20 | $ki_world(v6) | ? [v7: $ki_world] : ? [v8: int] : ( ~ (v8
% 10.36/2.20 | = 0) & in(v7, v1, v4) = v8 & $ki_accessible(v6, v7) = 0
% 10.36/2.20 | & $ki_world(v7))) & ? [v6: $ki_world] : ? [v7: int] : (
% 10.36/2.20 | ~ (v7 = 0) & disjoint(v6, v2, v4) = v7 & $ki_accessible(v5,
% 10.36/2.20 | v6) = 0 & $ki_world(v6)))))))
% 10.36/2.20 |
% 10.36/2.20 | ALPHA: (function-axioms) implies:
% 10.36/2.20 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 10.36/2.20 | $ki_world] : ! [v3: $ki_world] : (v1 = v0 | ~ ($ki_accessible(v3,
% 10.36/2.20 | v2) = v1) | ~ ($ki_accessible(v3, v2) = v0))
% 10.36/2.20 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.36/2.20 | ! [v3: $ki_world] : (v1 = v0 | ~ ($ki_exists_in_world_$i(v3, v2) =
% 10.36/2.20 | v1) | ~ ($ki_exists_in_world_$i(v3, v2) = v0))
% 10.36/2.20 |
% 10.36/2.20 | DELTA: instantiating (2) with fresh symbol all_17_0 gives:
% 10.36/2.20 | (5) $ki_accessible($ki_local_world, all_17_0) = 0 & $ki_world(all_17_0) &
% 10.36/2.20 | ? [v0: $i] : ? [v1: $i] : (singleton(v0) = v1 &
% 10.36/2.20 | $ki_exists_in_world_$i(all_17_0, v0) = 0 & $i(v1) & $i(v0) & ? [v2:
% 10.36/2.20 | $ki_world] : ($ki_accessible(all_17_0, v2) = 0 & $ki_world(v2) & ?
% 10.36/2.20 | [v3: $i] : ($ki_exists_in_world_$i(v2, v3) = 0 & $i(v3) & ? [v4:
% 10.36/2.20 | $ki_world] : ($ki_accessible(v2, v4) = 0 & $ki_world(v4) & !
% 10.36/2.20 | [v5: $ki_world] : ( ~ ($ki_accessible(v4, v5) = 0) | ~
% 10.36/2.20 | $ki_world(v5) | ? [v6: $ki_world] : ? [v7: int] : ( ~ (v7 =
% 10.36/2.20 | 0) & in(v6, v0, v3) = v7 & $ki_accessible(v5, v6) = 0 &
% 10.36/2.20 | $ki_world(v6))) & ? [v5: $ki_world] : ? [v6: int] : ( ~
% 10.36/2.20 | (v6 = 0) & disjoint(v5, v1, v3) = v6 & $ki_accessible(v4, v5)
% 10.36/2.20 | = 0 & $ki_world(v5))))))
% 10.36/2.20 |
% 10.36/2.20 | ALPHA: (5) implies:
% 10.36/2.20 | (6) $ki_world(all_17_0)
% 10.36/2.20 | (7) $ki_accessible($ki_local_world, all_17_0) = 0
% 10.36/2.21 | (8) ? [v0: $i] : ? [v1: $i] : (singleton(v0) = v1 &
% 10.36/2.21 | $ki_exists_in_world_$i(all_17_0, v0) = 0 & $i(v1) & $i(v0) & ? [v2:
% 10.36/2.21 | $ki_world] : ($ki_accessible(all_17_0, v2) = 0 & $ki_world(v2) & ?
% 10.36/2.21 | [v3: $i] : ($ki_exists_in_world_$i(v2, v3) = 0 & $i(v3) & ? [v4:
% 10.36/2.21 | $ki_world] : ($ki_accessible(v2, v4) = 0 & $ki_world(v4) & !
% 10.36/2.21 | [v5: $ki_world] : ( ~ ($ki_accessible(v4, v5) = 0) | ~
% 10.36/2.21 | $ki_world(v5) | ? [v6: $ki_world] : ? [v7: int] : ( ~ (v7 =
% 10.36/2.21 | 0) & in(v6, v0, v3) = v7 & $ki_accessible(v5, v6) = 0 &
% 10.36/2.21 | $ki_world(v6))) & ? [v5: $ki_world] : ? [v6: int] : ( ~
% 10.36/2.21 | (v6 = 0) & disjoint(v5, v1, v3) = v6 & $ki_accessible(v4, v5)
% 10.36/2.21 | = 0 & $ki_world(v5))))))
% 10.36/2.21 |
% 10.36/2.21 | DELTA: instantiating (8) with fresh symbols all_19_0, all_19_1 gives:
% 10.36/2.21 | (9) singleton(all_19_1) = all_19_0 & $ki_exists_in_world_$i(all_17_0,
% 10.36/2.21 | all_19_1) = 0 & $i(all_19_0) & $i(all_19_1) & ? [v0: $ki_world] :
% 10.36/2.21 | ($ki_accessible(all_17_0, v0) = 0 & $ki_world(v0) & ? [v1: $i] :
% 10.36/2.21 | ($ki_exists_in_world_$i(v0, v1) = 0 & $i(v1) & ? [v2: $ki_world] :
% 10.36/2.21 | ($ki_accessible(v0, v2) = 0 & $ki_world(v2) & ! [v3: $ki_world] :
% 10.36/2.21 | ( ~ ($ki_accessible(v2, v3) = 0) | ~ $ki_world(v3) | ? [v4:
% 10.36/2.21 | $ki_world] : ? [v5: int] : ( ~ (v5 = 0) & in(v4, all_19_1,
% 10.36/2.21 | v1) = v5 & $ki_accessible(v3, v4) = 0 & $ki_world(v4))) &
% 10.36/2.21 | ? [v3: $ki_world] : ? [v4: int] : ( ~ (v4 = 0) & disjoint(v3,
% 10.36/2.21 | all_19_0, v1) = v4 & $ki_accessible(v2, v3) = 0 &
% 10.36/2.21 | $ki_world(v3)))))
% 10.36/2.21 |
% 10.36/2.21 | ALPHA: (9) implies:
% 10.36/2.21 | (10) $i(all_19_1)
% 10.36/2.21 | (11) $ki_exists_in_world_$i(all_17_0, all_19_1) = 0
% 10.36/2.21 | (12) singleton(all_19_1) = all_19_0
% 10.36/2.21 | (13) ? [v0: $ki_world] : ($ki_accessible(all_17_0, v0) = 0 & $ki_world(v0)
% 10.36/2.21 | & ? [v1: $i] : ($ki_exists_in_world_$i(v0, v1) = 0 & $i(v1) & ?
% 10.36/2.21 | [v2: $ki_world] : ($ki_accessible(v0, v2) = 0 & $ki_world(v2) & !
% 10.36/2.21 | [v3: $ki_world] : ( ~ ($ki_accessible(v2, v3) = 0) | ~
% 10.36/2.21 | $ki_world(v3) | ? [v4: $ki_world] : ? [v5: int] : ( ~ (v5 =
% 10.36/2.21 | 0) & in(v4, all_19_1, v1) = v5 & $ki_accessible(v3, v4) =
% 10.36/2.21 | 0 & $ki_world(v4))) & ? [v3: $ki_world] : ? [v4: int] : (
% 10.36/2.21 | ~ (v4 = 0) & disjoint(v3, all_19_0, v1) = v4 &
% 10.36/2.21 | $ki_accessible(v2, v3) = 0 & $ki_world(v3)))))
% 10.36/2.21 |
% 10.36/2.21 | DELTA: instantiating (13) with fresh symbol all_21_0 gives:
% 10.36/2.21 | (14) $ki_accessible(all_17_0, all_21_0) = 0 & $ki_world(all_21_0) & ? [v0:
% 10.36/2.21 | $i] : ($ki_exists_in_world_$i(all_21_0, v0) = 0 & $i(v0) & ? [v1:
% 10.36/2.21 | $ki_world] : ($ki_accessible(all_21_0, v1) = 0 & $ki_world(v1) &
% 10.36/2.21 | ! [v2: $ki_world] : ( ~ ($ki_accessible(v1, v2) = 0) | ~
% 10.36/2.21 | $ki_world(v2) | ? [v3: $ki_world] : ? [v4: int] : ( ~ (v4 = 0)
% 10.36/2.21 | & in(v3, all_19_1, v0) = v4 & $ki_accessible(v2, v3) = 0 &
% 10.36/2.21 | $ki_world(v3))) & ? [v2: $ki_world] : ? [v3: int] : ( ~ (v3
% 10.36/2.21 | = 0) & disjoint(v2, all_19_0, v0) = v3 & $ki_accessible(v1,
% 10.36/2.21 | v2) = 0 & $ki_world(v2))))
% 10.36/2.21 |
% 10.36/2.21 | ALPHA: (14) implies:
% 10.36/2.21 | (15) $ki_world(all_21_0)
% 10.36/2.21 | (16) $ki_accessible(all_17_0, all_21_0) = 0
% 10.36/2.22 | (17) ? [v0: $i] : ($ki_exists_in_world_$i(all_21_0, v0) = 0 & $i(v0) & ?
% 10.36/2.22 | [v1: $ki_world] : ($ki_accessible(all_21_0, v1) = 0 & $ki_world(v1)
% 10.36/2.22 | & ! [v2: $ki_world] : ( ~ ($ki_accessible(v1, v2) = 0) | ~
% 10.36/2.22 | $ki_world(v2) | ? [v3: $ki_world] : ? [v4: int] : ( ~ (v4 = 0)
% 10.36/2.22 | & in(v3, all_19_1, v0) = v4 & $ki_accessible(v2, v3) = 0 &
% 10.36/2.22 | $ki_world(v3))) & ? [v2: $ki_world] : ? [v3: int] : ( ~ (v3
% 10.36/2.22 | = 0) & disjoint(v2, all_19_0, v0) = v3 & $ki_accessible(v1,
% 10.36/2.22 | v2) = 0 & $ki_world(v2))))
% 10.36/2.22 |
% 10.36/2.22 | DELTA: instantiating (17) with fresh symbol all_23_0 gives:
% 10.36/2.22 | (18) $ki_exists_in_world_$i(all_21_0, all_23_0) = 0 & $i(all_23_0) & ?
% 10.36/2.22 | [v0: $ki_world] : ($ki_accessible(all_21_0, v0) = 0 & $ki_world(v0) &
% 10.36/2.22 | ! [v1: $ki_world] : ( ~ ($ki_accessible(v0, v1) = 0) | ~
% 10.36/2.22 | $ki_world(v1) | ? [v2: $ki_world] : ? [v3: int] : ( ~ (v3 = 0) &
% 10.36/2.22 | in(v2, all_19_1, all_23_0) = v3 & $ki_accessible(v1, v2) = 0 &
% 10.36/2.22 | $ki_world(v2))) & ? [v1: $ki_world] : ? [v2: int] : ( ~ (v2 =
% 10.36/2.22 | 0) & disjoint(v1, all_19_0, all_23_0) = v2 & $ki_accessible(v0,
% 10.36/2.22 | v1) = 0 & $ki_world(v1)))
% 10.36/2.22 |
% 10.36/2.22 | ALPHA: (18) implies:
% 10.36/2.22 | (19) $i(all_23_0)
% 10.36/2.22 | (20) $ki_exists_in_world_$i(all_21_0, all_23_0) = 0
% 10.36/2.22 | (21) ? [v0: $ki_world] : ($ki_accessible(all_21_0, v0) = 0 & $ki_world(v0)
% 10.36/2.22 | & ! [v1: $ki_world] : ( ~ ($ki_accessible(v0, v1) = 0) | ~
% 10.36/2.22 | $ki_world(v1) | ? [v2: $ki_world] : ? [v3: int] : ( ~ (v3 = 0) &
% 10.36/2.22 | in(v2, all_19_1, all_23_0) = v3 & $ki_accessible(v1, v2) = 0 &
% 10.36/2.22 | $ki_world(v2))) & ? [v1: $ki_world] : ? [v2: int] : ( ~ (v2 =
% 10.36/2.22 | 0) & disjoint(v1, all_19_0, all_23_0) = v2 & $ki_accessible(v0,
% 10.36/2.22 | v1) = 0 & $ki_world(v1)))
% 10.36/2.22 |
% 10.36/2.22 | DELTA: instantiating (21) with fresh symbol all_25_0 gives:
% 10.36/2.22 | (22) $ki_accessible(all_21_0, all_25_0) = 0 & $ki_world(all_25_0) & ! [v0:
% 10.36/2.22 | $ki_world] : ( ~ ($ki_accessible(all_25_0, v0) = 0) | ~
% 10.36/2.22 | $ki_world(v0) | ? [v1: $ki_world] : ? [v2: int] : ( ~ (v2 = 0) &
% 10.36/2.22 | in(v1, all_19_1, all_23_0) = v2 & $ki_accessible(v0, v1) = 0 &
% 10.36/2.22 | $ki_world(v1))) & ? [v0: $ki_world] : ? [v1: int] : ( ~ (v1 = 0)
% 10.36/2.22 | & disjoint(v0, all_19_0, all_23_0) = v1 & $ki_accessible(all_25_0,
% 10.36/2.22 | v0) = 0 & $ki_world(v0))
% 10.36/2.22 |
% 10.36/2.22 | ALPHA: (22) implies:
% 10.36/2.22 | (23) $ki_world(all_25_0)
% 10.36/2.22 | (24) $ki_accessible(all_21_0, all_25_0) = 0
% 10.36/2.22 | (25) ! [v0: $ki_world] : ( ~ ($ki_accessible(all_25_0, v0) = 0) | ~
% 10.36/2.22 | $ki_world(v0) | ? [v1: $ki_world] : ? [v2: int] : ( ~ (v2 = 0) &
% 10.36/2.22 | in(v1, all_19_1, all_23_0) = v2 & $ki_accessible(v0, v1) = 0 &
% 10.36/2.22 | $ki_world(v1)))
% 10.36/2.22 | (26) ? [v0: $ki_world] : ? [v1: int] : ( ~ (v1 = 0) & disjoint(v0,
% 10.36/2.22 | all_19_0, all_23_0) = v1 & $ki_accessible(all_25_0, v0) = 0 &
% 10.36/2.22 | $ki_world(v0))
% 10.36/2.22 |
% 10.36/2.22 | DELTA: instantiating (26) with fresh symbols all_28_0, all_28_1 gives:
% 10.36/2.22 | (27) ~ (all_28_0 = 0) & disjoint(all_28_1, all_19_0, all_23_0) = all_28_0
% 10.36/2.22 | & $ki_accessible(all_25_0, all_28_1) = 0 & $ki_world(all_28_1)
% 10.36/2.22 |
% 10.36/2.22 | ALPHA: (27) implies:
% 10.36/2.22 | (28) ~ (all_28_0 = 0)
% 10.36/2.22 | (29) $ki_world(all_28_1)
% 10.36/2.22 | (30) $ki_accessible(all_25_0, all_28_1) = 0
% 10.36/2.22 | (31) disjoint(all_28_1, all_19_0, all_23_0) = all_28_0
% 10.36/2.22 |
% 10.36/2.22 | GROUND_INST: instantiating (1) with all_17_0, simplifying with (6), (7) gives:
% 10.36/2.23 | (32) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | ?
% 10.36/2.23 | [v2: int] : ( ~ (v2 = 0) & $ki_exists_in_world_$i(all_17_0, v0) =
% 10.36/2.23 | v2) | ! [v2: $ki_world] : ( ~ ($ki_accessible(all_17_0, v2) = 0)
% 10.36/2.23 | | ~ $ki_world(v2) | ! [v3: $i] : ( ~ ($ki_exists_in_world_$i(v2,
% 10.36/2.23 | v3) = 0) | ~ $i(v3) | ! [v4: $ki_world] : ( ~
% 10.36/2.23 | ($ki_accessible(v2, v4) = 0) | ~ $ki_world(v4) | ? [v5:
% 10.36/2.23 | $ki_world] : ($ki_accessible(v4, v5) = 0 & $ki_world(v5) &
% 10.36/2.23 | ! [v6: $ki_world] : ! [v7: int] : (v7 = 0 | ~ (in(v6, v0,
% 10.63/2.23 | v3) = v7) | ~ $ki_world(v6) | ? [v8: int] : ( ~ (v8
% 10.63/2.23 | = 0) & $ki_accessible(v5, v6) = v8))) | ! [v5:
% 10.63/2.23 | $ki_world] : ! [v6: int] : (v6 = 0 | ~ (disjoint(v5, v1,
% 10.63/2.23 | v3) = v6) | ~ $ki_world(v5) | ? [v7: int] : ( ~ (v7 =
% 10.63/2.23 | 0) & $ki_accessible(v4, v5) = v7))))))
% 10.63/2.23 |
% 10.63/2.23 | GROUND_INST: instantiating (32) with all_19_1, all_19_0, simplifying with
% 10.63/2.23 | (10), (12) gives:
% 10.63/2.23 | (33) ? [v0: int] : ( ~ (v0 = 0) & $ki_exists_in_world_$i(all_17_0,
% 10.63/2.23 | all_19_1) = v0) | ! [v0: $ki_world] : ( ~
% 10.63/2.23 | ($ki_accessible(all_17_0, v0) = 0) | ~ $ki_world(v0) | ! [v1: $i]
% 10.63/2.23 | : ( ~ ($ki_exists_in_world_$i(v0, v1) = 0) | ~ $i(v1) | ! [v2:
% 10.63/2.23 | $ki_world] : ( ~ ($ki_accessible(v0, v2) = 0) | ~ $ki_world(v2)
% 10.63/2.23 | | ? [v3: $ki_world] : ($ki_accessible(v2, v3) = 0 &
% 10.63/2.23 | $ki_world(v3) & ! [v4: $ki_world] : ! [v5: int] : (v5 = 0 |
% 10.63/2.23 | ~ (in(v4, all_19_1, v1) = v5) | ~ $ki_world(v4) | ? [v6:
% 10.63/2.23 | int] : ( ~ (v6 = 0) & $ki_accessible(v3, v4) = v6))) | !
% 10.63/2.23 | [v3: $ki_world] : ! [v4: int] : (v4 = 0 | ~ (disjoint(v3,
% 10.63/2.23 | all_19_0, v1) = v4) | ~ $ki_world(v3) | ? [v5: int] : (
% 10.63/2.23 | ~ (v5 = 0) & $ki_accessible(v2, v3) = v5)))))
% 10.63/2.23 |
% 10.63/2.23 | BETA: splitting (33) gives:
% 10.63/2.23 |
% 10.63/2.23 | Case 1:
% 10.63/2.23 | |
% 10.63/2.23 | | (34) ? [v0: int] : ( ~ (v0 = 0) & $ki_exists_in_world_$i(all_17_0,
% 10.63/2.23 | | all_19_1) = v0)
% 10.63/2.23 | |
% 10.63/2.23 | | DELTA: instantiating (34) with fresh symbol all_52_0 gives:
% 10.63/2.23 | | (35) ~ (all_52_0 = 0) & $ki_exists_in_world_$i(all_17_0, all_19_1) =
% 10.63/2.23 | | all_52_0
% 10.63/2.23 | |
% 10.63/2.23 | | ALPHA: (35) implies:
% 10.63/2.23 | | (36) ~ (all_52_0 = 0)
% 10.63/2.23 | | (37) $ki_exists_in_world_$i(all_17_0, all_19_1) = all_52_0
% 10.63/2.23 | |
% 10.63/2.23 | | GROUND_INST: instantiating (4) with 0, all_52_0, all_19_1, all_17_0,
% 10.63/2.23 | | simplifying with (11), (37) gives:
% 10.63/2.23 | | (38) all_52_0 = 0
% 10.63/2.23 | |
% 10.63/2.23 | | REDUCE: (36), (38) imply:
% 10.63/2.23 | | (39) $false
% 10.63/2.23 | |
% 10.63/2.23 | | CLOSE: (39) is inconsistent.
% 10.63/2.23 | |
% 10.63/2.23 | Case 2:
% 10.63/2.23 | |
% 10.63/2.23 | | (40) ! [v0: $ki_world] : ( ~ ($ki_accessible(all_17_0, v0) = 0) | ~
% 10.63/2.23 | | $ki_world(v0) | ! [v1: $i] : ( ~ ($ki_exists_in_world_$i(v0, v1)
% 10.63/2.23 | | = 0) | ~ $i(v1) | ! [v2: $ki_world] : ( ~
% 10.63/2.23 | | ($ki_accessible(v0, v2) = 0) | ~ $ki_world(v2) | ? [v3:
% 10.63/2.23 | | $ki_world] : ($ki_accessible(v2, v3) = 0 & $ki_world(v3) &
% 10.63/2.23 | | ! [v4: $ki_world] : ! [v5: int] : (v5 = 0 | ~ (in(v4,
% 10.63/2.23 | | all_19_1, v1) = v5) | ~ $ki_world(v4) | ? [v6: int]
% 10.63/2.23 | | : ( ~ (v6 = 0) & $ki_accessible(v3, v4) = v6))) | ! [v3:
% 10.63/2.23 | | $ki_world] : ! [v4: int] : (v4 = 0 | ~ (disjoint(v3,
% 10.63/2.23 | | all_19_0, v1) = v4) | ~ $ki_world(v3) | ? [v5: int] :
% 10.63/2.23 | | ( ~ (v5 = 0) & $ki_accessible(v2, v3) = v5)))))
% 10.63/2.23 | |
% 10.63/2.24 | | GROUND_INST: instantiating (40) with all_21_0, simplifying with (15), (16)
% 10.63/2.24 | | gives:
% 10.63/2.24 | | (41) ! [v0: $i] : ( ~ ($ki_exists_in_world_$i(all_21_0, v0) = 0) | ~
% 10.63/2.24 | | $i(v0) | ! [v1: $ki_world] : ( ~ ($ki_accessible(all_21_0, v1) =
% 10.63/2.24 | | 0) | ~ $ki_world(v1) | ? [v2: $ki_world] :
% 10.63/2.24 | | ($ki_accessible(v1, v2) = 0 & $ki_world(v2) & ! [v3: $ki_world]
% 10.63/2.24 | | : ! [v4: int] : (v4 = 0 | ~ (in(v3, all_19_1, v0) = v4) | ~
% 10.63/2.24 | | $ki_world(v3) | ? [v5: int] : ( ~ (v5 = 0) &
% 10.63/2.24 | | $ki_accessible(v2, v3) = v5))) | ! [v2: $ki_world] : !
% 10.63/2.24 | | [v3: int] : (v3 = 0 | ~ (disjoint(v2, all_19_0, v0) = v3) | ~
% 10.63/2.24 | | $ki_world(v2) | ? [v4: int] : ( ~ (v4 = 0) &
% 10.63/2.24 | | $ki_accessible(v1, v2) = v4))))
% 10.63/2.24 | |
% 10.63/2.24 | | GROUND_INST: instantiating (41) with all_23_0, simplifying with (19), (20)
% 10.63/2.24 | | gives:
% 10.63/2.24 | | (42) ! [v0: $ki_world] : ( ~ ($ki_accessible(all_21_0, v0) = 0) | ~
% 10.63/2.24 | | $ki_world(v0) | ? [v1: $ki_world] : ($ki_accessible(v0, v1) = 0 &
% 10.63/2.24 | | $ki_world(v1) & ! [v2: $ki_world] : ! [v3: int] : (v3 = 0 | ~
% 10.63/2.24 | | (in(v2, all_19_1, all_23_0) = v3) | ~ $ki_world(v2) | ? [v4:
% 10.63/2.24 | | int] : ( ~ (v4 = 0) & $ki_accessible(v1, v2) = v4))) | !
% 10.63/2.24 | | [v1: $ki_world] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v1,
% 10.63/2.24 | | all_19_0, all_23_0) = v2) | ~ $ki_world(v1) | ? [v3: int]
% 10.63/2.24 | | : ( ~ (v3 = 0) & $ki_accessible(v0, v1) = v3)))
% 10.63/2.24 | |
% 10.63/2.24 | | GROUND_INST: instantiating (42) with all_25_0, simplifying with (23), (24)
% 10.63/2.24 | | gives:
% 10.63/2.24 | | (43) ? [v0: $ki_world] : ($ki_accessible(all_25_0, v0) = 0 &
% 10.63/2.24 | | $ki_world(v0) & ! [v1: $ki_world] : ! [v2: int] : (v2 = 0 | ~
% 10.63/2.24 | | (in(v1, all_19_1, all_23_0) = v2) | ~ $ki_world(v1) | ? [v3:
% 10.63/2.24 | | int] : ( ~ (v3 = 0) & $ki_accessible(v0, v1) = v3))) | ! [v0:
% 10.63/2.24 | | $ki_world] : ! [v1: int] : (v1 = 0 | ~ (disjoint(v0, all_19_0,
% 10.63/2.24 | | all_23_0) = v1) | ~ $ki_world(v0) | ? [v2: int] : ( ~ (v2 =
% 10.63/2.24 | | 0) & $ki_accessible(all_25_0, v0) = v2))
% 10.63/2.24 | |
% 10.63/2.24 | | BETA: splitting (43) gives:
% 10.63/2.24 | |
% 10.63/2.24 | | Case 1:
% 10.63/2.24 | | |
% 10.63/2.24 | | | (44) ? [v0: $ki_world] : ($ki_accessible(all_25_0, v0) = 0 &
% 10.63/2.24 | | | $ki_world(v0) & ! [v1: $ki_world] : ! [v2: int] : (v2 = 0 | ~
% 10.63/2.24 | | | (in(v1, all_19_1, all_23_0) = v2) | ~ $ki_world(v1) | ? [v3:
% 10.63/2.24 | | | int] : ( ~ (v3 = 0) & $ki_accessible(v0, v1) = v3)))
% 10.63/2.24 | | |
% 10.63/2.24 | | | DELTA: instantiating (44) with fresh symbol all_86_0 gives:
% 10.63/2.24 | | | (45) $ki_accessible(all_25_0, all_86_0) = 0 & $ki_world(all_86_0) & !
% 10.63/2.24 | | | [v0: $ki_world] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_19_1,
% 10.63/2.24 | | | all_23_0) = v1) | ~ $ki_world(v0) | ? [v2: int] : ( ~ (v2
% 10.63/2.24 | | | = 0) & $ki_accessible(all_86_0, v0) = v2))
% 10.63/2.24 | | |
% 10.63/2.24 | | | ALPHA: (45) implies:
% 10.63/2.24 | | | (46) $ki_world(all_86_0)
% 10.63/2.24 | | | (47) $ki_accessible(all_25_0, all_86_0) = 0
% 10.63/2.24 | | | (48) ! [v0: $ki_world] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_19_1,
% 10.63/2.24 | | | all_23_0) = v1) | ~ $ki_world(v0) | ? [v2: int] : ( ~ (v2
% 10.63/2.24 | | | = 0) & $ki_accessible(all_86_0, v0) = v2))
% 10.63/2.24 | | |
% 10.63/2.24 | | | GROUND_INST: instantiating (25) with all_86_0, simplifying with (46), (47)
% 10.63/2.24 | | | gives:
% 10.63/2.24 | | | (49) ? [v0: $ki_world] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 10.63/2.24 | | | all_19_1, all_23_0) = v1 & $ki_accessible(all_86_0, v0) = 0 &
% 10.63/2.24 | | | $ki_world(v0))
% 10.63/2.24 | | |
% 10.63/2.24 | | | DELTA: instantiating (49) with fresh symbols all_100_0, all_100_1 gives:
% 10.63/2.24 | | | (50) ~ (all_100_0 = 0) & in(all_100_1, all_19_1, all_23_0) = all_100_0
% 10.63/2.24 | | | & $ki_accessible(all_86_0, all_100_1) = 0 & $ki_world(all_100_1)
% 10.63/2.24 | | |
% 10.63/2.24 | | | ALPHA: (50) implies:
% 10.63/2.24 | | | (51) ~ (all_100_0 = 0)
% 10.63/2.25 | | | (52) $ki_world(all_100_1)
% 10.63/2.25 | | | (53) $ki_accessible(all_86_0, all_100_1) = 0
% 10.63/2.25 | | | (54) in(all_100_1, all_19_1, all_23_0) = all_100_0
% 10.63/2.25 | | |
% 10.63/2.25 | | | GROUND_INST: instantiating (48) with all_100_1, all_100_0, simplifying
% 10.63/2.25 | | | with (52), (54) gives:
% 10.63/2.25 | | | (55) all_100_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 10.63/2.25 | | | $ki_accessible(all_86_0, all_100_1) = v0)
% 10.63/2.25 | | |
% 10.63/2.25 | | | BETA: splitting (55) gives:
% 10.63/2.25 | | |
% 10.63/2.25 | | | Case 1:
% 10.63/2.25 | | | |
% 10.63/2.25 | | | | (56) all_100_0 = 0
% 10.63/2.25 | | | |
% 10.63/2.25 | | | | REDUCE: (51), (56) imply:
% 10.63/2.25 | | | | (57) $false
% 10.63/2.25 | | | |
% 10.63/2.25 | | | | CLOSE: (57) is inconsistent.
% 10.63/2.25 | | | |
% 10.63/2.25 | | | Case 2:
% 10.63/2.25 | | | |
% 10.63/2.25 | | | | (58) ? [v0: int] : ( ~ (v0 = 0) & $ki_accessible(all_86_0,
% 10.63/2.25 | | | | all_100_1) = v0)
% 10.63/2.25 | | | |
% 10.63/2.25 | | | | DELTA: instantiating (58) with fresh symbol all_111_0 gives:
% 10.63/2.25 | | | | (59) ~ (all_111_0 = 0) & $ki_accessible(all_86_0, all_100_1) =
% 10.63/2.25 | | | | all_111_0
% 10.63/2.25 | | | |
% 10.63/2.25 | | | | ALPHA: (59) implies:
% 10.63/2.25 | | | | (60) ~ (all_111_0 = 0)
% 10.63/2.25 | | | | (61) $ki_accessible(all_86_0, all_100_1) = all_111_0
% 10.63/2.25 | | | |
% 10.63/2.25 | | | | GROUND_INST: instantiating (3) with 0, all_111_0, all_100_1, all_86_0,
% 10.63/2.25 | | | | simplifying with (53), (61) gives:
% 10.63/2.25 | | | | (62) all_111_0 = 0
% 10.63/2.25 | | | |
% 10.63/2.25 | | | | REDUCE: (60), (62) imply:
% 10.63/2.25 | | | | (63) $false
% 10.63/2.25 | | | |
% 10.63/2.25 | | | | CLOSE: (63) is inconsistent.
% 10.63/2.25 | | | |
% 10.63/2.25 | | | End of split
% 10.63/2.25 | | |
% 10.63/2.25 | | Case 2:
% 10.63/2.25 | | |
% 10.63/2.25 | | | (64) ! [v0: $ki_world] : ! [v1: int] : (v1 = 0 | ~ (disjoint(v0,
% 10.63/2.25 | | | all_19_0, all_23_0) = v1) | ~ $ki_world(v0) | ? [v2: int]
% 10.63/2.25 | | | : ( ~ (v2 = 0) & $ki_accessible(all_25_0, v0) = v2))
% 10.63/2.25 | | |
% 10.63/2.25 | | | GROUND_INST: instantiating (64) with all_28_1, all_28_0, simplifying with
% 10.63/2.25 | | | (29), (31) gives:
% 10.63/2.25 | | | (65) all_28_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 10.63/2.25 | | | $ki_accessible(all_25_0, all_28_1) = v0)
% 10.63/2.25 | | |
% 10.63/2.25 | | | BETA: splitting (65) gives:
% 10.63/2.25 | | |
% 10.63/2.25 | | | Case 1:
% 10.63/2.25 | | | |
% 10.63/2.25 | | | | (66) all_28_0 = 0
% 10.63/2.25 | | | |
% 10.63/2.25 | | | | REDUCE: (28), (66) imply:
% 10.63/2.25 | | | | (67) $false
% 10.63/2.25 | | | |
% 10.63/2.25 | | | | CLOSE: (67) is inconsistent.
% 10.63/2.25 | | | |
% 10.63/2.25 | | | Case 2:
% 10.63/2.25 | | | |
% 10.63/2.25 | | | | (68) ? [v0: int] : ( ~ (v0 = 0) & $ki_accessible(all_25_0, all_28_1)
% 10.63/2.25 | | | | = v0)
% 10.63/2.25 | | | |
% 10.63/2.25 | | | | DELTA: instantiating (68) with fresh symbol all_91_0 gives:
% 10.63/2.25 | | | | (69) ~ (all_91_0 = 0) & $ki_accessible(all_25_0, all_28_1) =
% 10.63/2.25 | | | | all_91_0
% 10.63/2.25 | | | |
% 10.63/2.25 | | | | ALPHA: (69) implies:
% 10.63/2.25 | | | | (70) ~ (all_91_0 = 0)
% 10.63/2.25 | | | | (71) $ki_accessible(all_25_0, all_28_1) = all_91_0
% 10.63/2.25 | | | |
% 10.63/2.25 | | | | GROUND_INST: instantiating (3) with 0, all_91_0, all_28_1, all_25_0,
% 10.63/2.25 | | | | simplifying with (30), (71) gives:
% 10.63/2.25 | | | | (72) all_91_0 = 0
% 10.63/2.25 | | | |
% 10.63/2.25 | | | | REDUCE: (70), (72) imply:
% 10.63/2.25 | | | | (73) $false
% 10.63/2.25 | | | |
% 10.63/2.25 | | | | CLOSE: (73) is inconsistent.
% 10.63/2.25 | | | |
% 10.63/2.25 | | | End of split
% 10.63/2.25 | | |
% 10.63/2.25 | | End of split
% 10.63/2.25 | |
% 10.63/2.25 | End of split
% 10.63/2.25 |
% 10.63/2.25 End of proof
% 10.76/2.25 % SZS output end Proof for theBenchmark
% 10.76/2.25
% 10.76/2.25 1643ms
%------------------------------------------------------------------------------