TSTP Solution File: PLA053_4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : PLA053_4 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n023.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 13:02:56 EDT 2023
% Result : Theorem 7.86s 1.76s
% Output : Proof 8.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : PLA053_4 : TPTP v8.2.0. Released v8.2.0.
% 0.06/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Aug 27 05:59:11 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.53/0.58 ________ _____
% 0.53/0.58 ___ __ \_________(_)________________________________
% 0.53/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.53/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.53/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.53/0.58
% 0.53/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.53/0.58 (2023-06-19)
% 0.53/0.58
% 0.53/0.58 (c) Philipp Rümmer, 2009-2023
% 0.53/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.53/0.58 Amanda Stjerna.
% 0.53/0.58 Free software under BSD-3-Clause.
% 0.53/0.58
% 0.53/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.53/0.58
% 0.53/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.53/0.60 Running up to 7 provers in parallel.
% 0.53/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.53/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.53/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.53/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.53/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.53/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.53/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.16/1.04 Prover 1: Preprocessing ...
% 2.64/1.04 Prover 4: Preprocessing ...
% 2.85/1.08 Prover 6: Preprocessing ...
% 2.85/1.08 Prover 0: Preprocessing ...
% 2.85/1.08 Prover 2: Preprocessing ...
% 2.85/1.08 Prover 3: Preprocessing ...
% 2.85/1.08 Prover 5: Preprocessing ...
% 4.00/1.24 Prover 5: Proving ...
% 4.00/1.24 Prover 2: Proving ...
% 4.25/1.28 Prover 3: Warning: ignoring some quantifiers
% 4.25/1.29 Prover 3: Constructing countermodel ...
% 4.25/1.29 Prover 1: Warning: ignoring some quantifiers
% 4.25/1.31 Prover 1: Constructing countermodel ...
% 4.25/1.33 Prover 6: Proving ...
% 5.50/1.46 Prover 4: Warning: ignoring some quantifiers
% 5.50/1.46 Prover 0: Proving ...
% 5.75/1.47 Prover 4: Constructing countermodel ...
% 7.86/1.75 Prover 4: Found proof (size 37)
% 7.86/1.76 Prover 4: proved (1148ms)
% 7.86/1.76 Prover 1: stopped
% 7.86/1.76 Prover 6: stopped
% 7.86/1.76 Prover 5: stopped
% 7.86/1.76 Prover 2: stopped
% 7.86/1.76 Prover 0: stopped
% 7.86/1.76 Prover 3: stopped
% 7.86/1.76
% 7.86/1.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.86/1.76
% 8.00/1.77 % SZS output start Proof for theBenchmark
% 8.00/1.77 Assumptions after simplification:
% 8.00/1.77 ---------------------------------
% 8.00/1.77
% 8.00/1.77 (ax3)
% 8.00/1.81 $ki_world($ki_local_world) & ! [v0: $ki_world] : ! [v1: $i] : ( ~
% 8.00/1.81 ($ki_exists_in_world_$i(v0, v1) = 0) | ~ ($ki_accessible($ki_local_world,
% 8.00/1.81 v0) = 0) | ~ $ki_world(v0) | ~ $i(v1) | ? [v2: $i] :
% 8.00/1.81 ($ki_exists_in_world_$i(v0, v2) = 0 & $i(v2) & ! [v3: $ki_world] : ! [v4:
% 8.00/1.81 int] : (v4 = 0 | ~ (defused(v3, v1) = v4) | ~ $ki_world(v3) | ? [v5:
% 8.00/1.81 any] : ? [v6: any] : ? [v7: any] : (h(v3, v2) = v7 & bomb(v3, v1) =
% 8.00/1.81 v6 & $ki_accessible(v0, v3) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5
% 8.00/1.81 = 0)))) & ! [v3: $ki_world] : ( ~ (h(v3, v2) = 0) | ~
% 8.00/1.81 $ki_world(v3) | ? [v4: any] : ? [v5: any] : ? [v6: any] :
% 8.00/1.81 (defused(v3, v1) = v6 & bomb(v3, v1) = v5 & $ki_accessible(v0, v3) = v4
% 8.00/1.81 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0))) & ! [v3: $ki_world] : ( ~
% 8.00/1.81 (bomb(v3, v1) = 0) | ~ $ki_world(v3) | ? [v4: any] : ? [v5: any] : ?
% 8.00/1.81 [v6: any] : (defused(v3, v1) = v6 & h(v3, v2) = v5 & $ki_accessible(v0,
% 8.00/1.81 v3) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0))) & ! [v3:
% 8.00/1.81 $ki_world] : ( ~ ($ki_accessible(v0, v3) = 0) | ~ $ki_world(v3) | ?
% 8.00/1.81 [v4: any] : ? [v5: any] : ? [v6: any] : (defused(v3, v1) = v6 & h(v3,
% 8.00/1.81 v2) = v5 & bomb(v3, v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 =
% 8.00/1.81 0)))))
% 8.00/1.81
% 8.00/1.81 (mrel_reflexive)
% 8.00/1.81 ! [v0: $ki_world] : ! [v1: int] : (v1 = 0 | ~ ($ki_accessible(v0, v0) = v1)
% 8.00/1.81 | ~ $ki_world(v0))
% 8.00/1.81
% 8.00/1.81 (verify)
% 8.00/1.82 $ki_world($ki_local_world) & ? [v0: $ki_world] : ? [v1: $i] : ? [v2: any] :
% 8.00/1.82 ? [v3: any] : (defused(v0, v1) = v3 & bomb(v0, v1) = v2 &
% 8.00/1.82 $ki_exists_in_world_$i(v0, v1) = 0 & $ki_accessible($ki_local_world, v0) = 0
% 8.00/1.82 & $ki_world(v0) & $i(v1) & ! [v4: $i] : ! [v5: MultipleValueBool] : ( ~
% 8.00/1.82 (v3 = 0) | ~ (h(v0, v4) = v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) &
% 8.00/1.82 $ki_exists_in_world_$i(v0, v4) = v6)) & ! [v4: $i] : ! [v5: int] : (v5
% 8.00/1.82 = 0 | ~ (h(v0, v4) = v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) &
% 8.00/1.82 $ki_exists_in_world_$i(v0, v4) = v6)) & ! [v4: $i] : ! [v5:
% 8.00/1.82 MultipleValueBool] : (v2 = 0 | ~ (h(v0, v4) = v5) | ~ $i(v4) | ? [v6:
% 8.00/1.82 int] : ( ~ (v6 = 0) & $ki_exists_in_world_$i(v0, v4) = v6)) & ! [v4:
% 8.00/1.82 $i] : ( ~ (v3 = 0) | ~ ($ki_exists_in_world_$i(v0, v4) = 0) | ~ $i(v4))
% 8.00/1.82 & ! [v4: $i] : (v2 = 0 | ~ ($ki_exists_in_world_$i(v0, v4) = 0) | ~
% 8.00/1.82 $i(v4)) & ! [v4: $i] : ( ~ ($ki_exists_in_world_$i(v0, v4) = 0) | ~
% 8.00/1.82 $i(v4) | h(v0, v4) = 0))
% 8.00/1.82
% 8.00/1.82 (function-axioms)
% 8.28/1.82 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 8.28/1.82 [v3: $ki_world] : (v1 = v0 | ~ (defused(v3, v2) = v1) | ~ (defused(v3, v2) =
% 8.28/1.82 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 8.28/1.82 $i] : ! [v3: $ki_world] : (v1 = v0 | ~ (h(v3, v2) = v1) | ~ (h(v3, v2) =
% 8.28/1.82 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 8.28/1.82 $i] : ! [v3: $ki_world] : (v1 = v0 | ~ (bomb(v3, v2) = v1) | ~ (bomb(v3,
% 8.28/1.82 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 8.28/1.82 ! [v2: $i] : ! [v3: $ki_world] : (v1 = v0 | ~ ($ki_exists_in_world_$i(v3,
% 8.28/1.82 v2) = v1) | ~ ($ki_exists_in_world_$i(v3, v2) = v0)) & ! [v0:
% 8.28/1.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $ki_world] : !
% 8.28/1.82 [v3: $ki_world] : (v1 = v0 | ~ ($ki_accessible(v3, v2) = v1) | ~
% 8.28/1.82 ($ki_accessible(v3, v2) = v0))
% 8.28/1.82
% 8.28/1.82 Further assumptions not needed in the proof:
% 8.28/1.82 --------------------------------------------
% 8.28/1.82 $ki_exists_in_world_$i_const, $ki_exists_in_world_$i_nonempty, ax1, ax2,
% 8.28/1.82 mrel_transitive
% 8.28/1.82
% 8.28/1.82 Those formulas are unsatisfiable:
% 8.28/1.82 ---------------------------------
% 8.28/1.82
% 8.28/1.82 Begin of proof
% 8.28/1.82 |
% 8.28/1.82 | ALPHA: (ax3) implies:
% 8.28/1.83 | (1) ! [v0: $ki_world] : ! [v1: $i] : ( ~ ($ki_exists_in_world_$i(v0, v1)
% 8.28/1.83 | = 0) | ~ ($ki_accessible($ki_local_world, v0) = 0) | ~
% 8.28/1.83 | $ki_world(v0) | ~ $i(v1) | ? [v2: $i] : ($ki_exists_in_world_$i(v0,
% 8.28/1.83 | v2) = 0 & $i(v2) & ! [v3: $ki_world] : ! [v4: int] : (v4 = 0 |
% 8.28/1.83 | ~ (defused(v3, v1) = v4) | ~ $ki_world(v3) | ? [v5: any] : ?
% 8.28/1.83 | [v6: any] : ? [v7: any] : (h(v3, v2) = v7 & bomb(v3, v1) = v6 &
% 8.28/1.83 | $ki_accessible(v0, v3) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~
% 8.28/1.83 | (v5 = 0)))) & ! [v3: $ki_world] : ( ~ (h(v3, v2) = 0) | ~
% 8.28/1.83 | $ki_world(v3) | ? [v4: any] : ? [v5: any] : ? [v6: any] :
% 8.28/1.83 | (defused(v3, v1) = v6 & bomb(v3, v1) = v5 & $ki_accessible(v0,
% 8.28/1.83 | v3) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0))) & ! [v3:
% 8.28/1.83 | $ki_world] : ( ~ (bomb(v3, v1) = 0) | ~ $ki_world(v3) | ? [v4:
% 8.28/1.83 | any] : ? [v5: any] : ? [v6: any] : (defused(v3, v1) = v6 &
% 8.28/1.83 | h(v3, v2) = v5 & $ki_accessible(v0, v3) = v4 & ( ~ (v5 = 0) |
% 8.28/1.83 | ~ (v4 = 0) | v6 = 0))) & ! [v3: $ki_world] : ( ~
% 8.28/1.83 | ($ki_accessible(v0, v3) = 0) | ~ $ki_world(v3) | ? [v4: any] :
% 8.28/1.83 | ? [v5: any] : ? [v6: any] : (defused(v3, v1) = v6 & h(v3, v2) =
% 8.28/1.83 | v5 & bomb(v3, v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 =
% 8.28/1.83 | 0)))))
% 8.28/1.83 |
% 8.28/1.83 | ALPHA: (verify) implies:
% 8.28/1.83 | (2) ? [v0: $ki_world] : ? [v1: $i] : ? [v2: any] : ? [v3: any] :
% 8.28/1.83 | (defused(v0, v1) = v3 & bomb(v0, v1) = v2 & $ki_exists_in_world_$i(v0,
% 8.28/1.83 | v1) = 0 & $ki_accessible($ki_local_world, v0) = 0 & $ki_world(v0) &
% 8.28/1.83 | $i(v1) & ! [v4: $i] : ! [v5: MultipleValueBool] : ( ~ (v3 = 0) | ~
% 8.28/1.83 | (h(v0, v4) = v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) &
% 8.28/1.83 | $ki_exists_in_world_$i(v0, v4) = v6)) & ! [v4: $i] : ! [v5:
% 8.28/1.83 | int] : (v5 = 0 | ~ (h(v0, v4) = v5) | ~ $i(v4) | ? [v6: int] : (
% 8.28/1.83 | ~ (v6 = 0) & $ki_exists_in_world_$i(v0, v4) = v6)) & ! [v4: $i]
% 8.28/1.83 | : ! [v5: MultipleValueBool] : (v2 = 0 | ~ (h(v0, v4) = v5) | ~
% 8.28/1.83 | $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & $ki_exists_in_world_$i(v0,
% 8.28/1.83 | v4) = v6)) & ! [v4: $i] : ( ~ (v3 = 0) | ~
% 8.28/1.83 | ($ki_exists_in_world_$i(v0, v4) = 0) | ~ $i(v4)) & ! [v4: $i] :
% 8.28/1.83 | (v2 = 0 | ~ ($ki_exists_in_world_$i(v0, v4) = 0) | ~ $i(v4)) & !
% 8.28/1.83 | [v4: $i] : ( ~ ($ki_exists_in_world_$i(v0, v4) = 0) | ~ $i(v4) |
% 8.28/1.83 | h(v0, v4) = 0))
% 8.28/1.83 |
% 8.28/1.83 | ALPHA: (function-axioms) implies:
% 8.28/1.83 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.28/1.83 | ! [v3: $ki_world] : (v1 = v0 | ~ (bomb(v3, v2) = v1) | ~ (bomb(v3,
% 8.28/1.83 | v2) = v0))
% 8.28/1.83 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.28/1.83 | ! [v3: $ki_world] : (v1 = v0 | ~ (h(v3, v2) = v1) | ~ (h(v3, v2) =
% 8.28/1.83 | v0))
% 8.28/1.83 |
% 8.28/1.83 | DELTA: instantiating (2) with fresh symbols all_12_0, all_12_1, all_12_2,
% 8.28/1.83 | all_12_3 gives:
% 8.28/1.84 | (5) defused(all_12_3, all_12_2) = all_12_0 & bomb(all_12_3, all_12_2) =
% 8.28/1.84 | all_12_1 & $ki_exists_in_world_$i(all_12_3, all_12_2) = 0 &
% 8.28/1.84 | $ki_accessible($ki_local_world, all_12_3) = 0 & $ki_world(all_12_3) &
% 8.28/1.84 | $i(all_12_2) & ! [v0: $i] : ! [v1: MultipleValueBool] : ( ~ (all_12_0
% 8.28/1.84 | = 0) | ~ (h(all_12_3, v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~
% 8.28/1.84 | (v2 = 0) & $ki_exists_in_world_$i(all_12_3, v0) = v2)) & ! [v0:
% 8.28/1.84 | $i] : ! [v1: int] : (v1 = 0 | ~ (h(all_12_3, v0) = v1) | ~ $i(v0)
% 8.28/1.84 | | ? [v2: int] : ( ~ (v2 = 0) & $ki_exists_in_world_$i(all_12_3, v0)
% 8.28/1.84 | = v2)) & ! [v0: $i] : ! [v1: MultipleValueBool] : (all_12_1 = 0 |
% 8.28/1.84 | ~ (h(all_12_3, v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 8.28/1.84 | $ki_exists_in_world_$i(all_12_3, v0) = v2)) & ! [v0: $i] : ( ~
% 8.28/1.84 | (all_12_0 = 0) | ~ ($ki_exists_in_world_$i(all_12_3, v0) = 0) | ~
% 8.28/1.84 | $i(v0)) & ! [v0: $i] : (all_12_1 = 0 | ~
% 8.28/1.84 | ($ki_exists_in_world_$i(all_12_3, v0) = 0) | ~ $i(v0)) & ! [v0: $i]
% 8.28/1.84 | : ( ~ ($ki_exists_in_world_$i(all_12_3, v0) = 0) | ~ $i(v0) |
% 8.28/1.84 | h(all_12_3, v0) = 0)
% 8.28/1.84 |
% 8.28/1.84 | ALPHA: (5) implies:
% 8.28/1.84 | (6) $i(all_12_2)
% 8.28/1.84 | (7) $ki_world(all_12_3)
% 8.28/1.84 | (8) $ki_accessible($ki_local_world, all_12_3) = 0
% 8.28/1.84 | (9) $ki_exists_in_world_$i(all_12_3, all_12_2) = 0
% 8.28/1.84 | (10) bomb(all_12_3, all_12_2) = all_12_1
% 8.28/1.84 | (11) defused(all_12_3, all_12_2) = all_12_0
% 8.28/1.84 | (12) ! [v0: $i] : ( ~ ($ki_exists_in_world_$i(all_12_3, v0) = 0) | ~
% 8.28/1.84 | $i(v0) | h(all_12_3, v0) = 0)
% 8.28/1.84 | (13) ! [v0: $i] : (all_12_1 = 0 | ~ ($ki_exists_in_world_$i(all_12_3, v0)
% 8.28/1.84 | = 0) | ~ $i(v0))
% 8.28/1.84 | (14) ! [v0: $i] : ( ~ (all_12_0 = 0) | ~
% 8.28/1.84 | ($ki_exists_in_world_$i(all_12_3, v0) = 0) | ~ $i(v0))
% 8.28/1.84 |
% 8.28/1.84 | GROUND_INST: instantiating (1) with all_12_3, all_12_2, simplifying with (6),
% 8.28/1.84 | (7), (8), (9) gives:
% 8.28/1.84 | (15) ? [v0: $i] : ($ki_exists_in_world_$i(all_12_3, v0) = 0 & $i(v0) & !
% 8.28/1.84 | [v1: $ki_world] : ! [v2: int] : (v2 = 0 | ~ (defused(v1, all_12_2)
% 8.28/1.84 | = v2) | ~ $ki_world(v1) | ? [v3: any] : ? [v4: any] : ? [v5:
% 8.28/1.84 | any] : (h(v1, v0) = v5 & bomb(v1, all_12_2) = v4 &
% 8.28/1.84 | $ki_accessible(all_12_3, v1) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) |
% 8.28/1.84 | ~ (v3 = 0)))) & ! [v1: $ki_world] : ( ~ (h(v1, v0) = 0) | ~
% 8.28/1.84 | $ki_world(v1) | ? [v2: any] : ? [v3: any] : ? [v4: any] :
% 8.28/1.84 | (defused(v1, all_12_2) = v4 & bomb(v1, all_12_2) = v3 &
% 8.28/1.84 | $ki_accessible(all_12_3, v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) |
% 8.28/1.84 | v4 = 0))) & ! [v1: $ki_world] : ( ~ (bomb(v1, all_12_2) = 0)
% 8.28/1.84 | | ~ $ki_world(v1) | ? [v2: any] : ? [v3: any] : ? [v4: any] :
% 8.28/1.84 | (defused(v1, all_12_2) = v4 & h(v1, v0) = v3 &
% 8.28/1.84 | $ki_accessible(all_12_3, v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) |
% 8.28/1.84 | v4 = 0))) & ! [v1: $ki_world] : ( ~ ($ki_accessible(all_12_3,
% 8.28/1.84 | v1) = 0) | ~ $ki_world(v1) | ? [v2: any] : ? [v3: any] : ?
% 8.28/1.84 | [v4: any] : (defused(v1, all_12_2) = v4 & h(v1, v0) = v3 &
% 8.28/1.84 | bomb(v1, all_12_2) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 =
% 8.28/1.84 | 0))))
% 8.28/1.84 |
% 8.28/1.84 | GROUND_INST: instantiating (14) with all_12_2, simplifying with (6), (9)
% 8.28/1.84 | gives:
% 8.28/1.84 | (16) ~ (all_12_0 = 0)
% 8.28/1.84 |
% 8.28/1.84 | GROUND_INST: instantiating (13) with all_12_2, simplifying with (6), (9)
% 8.28/1.84 | gives:
% 8.28/1.84 | (17) all_12_1 = 0
% 8.28/1.84 |
% 8.28/1.84 | DELTA: instantiating (15) with fresh symbol all_26_0 gives:
% 8.28/1.85 | (18) $ki_exists_in_world_$i(all_12_3, all_26_0) = 0 & $i(all_26_0) & !
% 8.28/1.85 | [v0: $ki_world] : ! [v1: int] : (v1 = 0 | ~ (defused(v0, all_12_2) =
% 8.28/1.85 | v1) | ~ $ki_world(v0) | ? [v2: any] : ? [v3: any] : ? [v4:
% 8.28/1.85 | any] : (h(v0, all_26_0) = v4 & bomb(v0, all_12_2) = v3 &
% 8.28/1.85 | $ki_accessible(all_12_3, v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) |
% 8.28/1.85 | ~ (v2 = 0)))) & ! [v0: $ki_world] : ( ~ (h(v0, all_26_0) = 0) |
% 8.28/1.85 | ~ $ki_world(v0) | ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 8.28/1.85 | (defused(v0, all_12_2) = v3 & bomb(v0, all_12_2) = v2 &
% 8.28/1.85 | $ki_accessible(all_12_3, v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) |
% 8.28/1.85 | v3 = 0))) & ! [v0: $ki_world] : ( ~ (bomb(v0, all_12_2) = 0) |
% 8.28/1.85 | ~ $ki_world(v0) | ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 8.28/1.85 | (defused(v0, all_12_2) = v3 & h(v0, all_26_0) = v2 &
% 8.28/1.85 | $ki_accessible(all_12_3, v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) |
% 8.28/1.85 | v3 = 0))) & ! [v0: $ki_world] : ( ~ ($ki_accessible(all_12_3,
% 8.28/1.85 | v0) = 0) | ~ $ki_world(v0) | ? [v1: any] : ? [v2: any] : ?
% 8.28/1.85 | [v3: any] : (defused(v0, all_12_2) = v3 & h(v0, all_26_0) = v2 &
% 8.28/1.85 | bomb(v0, all_12_2) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)))
% 8.28/1.85 |
% 8.28/1.85 | ALPHA: (18) implies:
% 8.28/1.85 | (19) $i(all_26_0)
% 8.28/1.85 | (20) $ki_exists_in_world_$i(all_12_3, all_26_0) = 0
% 8.28/1.85 | (21) ! [v0: $ki_world] : ( ~ (bomb(v0, all_12_2) = 0) | ~ $ki_world(v0) |
% 8.28/1.85 | ? [v1: any] : ? [v2: any] : ? [v3: any] : (defused(v0, all_12_2)
% 8.28/1.85 | = v3 & h(v0, all_26_0) = v2 & $ki_accessible(all_12_3, v0) = v1 &
% 8.28/1.85 | ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)))
% 8.28/1.85 | (22) ! [v0: $ki_world] : ! [v1: int] : (v1 = 0 | ~ (defused(v0,
% 8.28/1.85 | all_12_2) = v1) | ~ $ki_world(v0) | ? [v2: any] : ? [v3: any]
% 8.28/1.85 | : ? [v4: any] : (h(v0, all_26_0) = v4 & bomb(v0, all_12_2) = v3 &
% 8.28/1.85 | $ki_accessible(all_12_3, v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) |
% 8.28/1.85 | ~ (v2 = 0))))
% 8.28/1.85 |
% 8.28/1.85 | GROUND_INST: instantiating (22) with all_12_3, all_12_0, simplifying with (7),
% 8.28/1.85 | (11) gives:
% 8.28/1.85 | (23) all_12_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 8.45/1.85 | (h(all_12_3, all_26_0) = v2 & bomb(all_12_3, all_12_2) = v1 &
% 8.45/1.85 | $ki_accessible(all_12_3, all_12_3) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0)
% 8.45/1.85 | | ~ (v0 = 0)))
% 8.45/1.85 |
% 8.45/1.85 | REDUCE: (10), (17) imply:
% 8.45/1.85 | (24) bomb(all_12_3, all_12_2) = 0
% 8.45/1.85 |
% 8.45/1.85 | BETA: splitting (23) gives:
% 8.45/1.85 |
% 8.45/1.85 | Case 1:
% 8.45/1.85 | |
% 8.45/1.85 | | (25) all_12_0 = 0
% 8.45/1.85 | |
% 8.45/1.85 | | REDUCE: (16), (25) imply:
% 8.45/1.85 | | (26) $false
% 8.45/1.85 | |
% 8.45/1.86 | | CLOSE: (26) is inconsistent.
% 8.45/1.86 | |
% 8.45/1.86 | Case 2:
% 8.45/1.86 | |
% 8.45/1.86 | | (27) ? [v0: any] : ? [v1: any] : ? [v2: any] : (h(all_12_3, all_26_0)
% 8.45/1.86 | | = v2 & bomb(all_12_3, all_12_2) = v1 & $ki_accessible(all_12_3,
% 8.45/1.86 | | all_12_3) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 8.45/1.86 | |
% 8.45/1.86 | | DELTA: instantiating (27) with fresh symbols all_36_0, all_36_1, all_36_2
% 8.45/1.86 | | gives:
% 8.45/1.86 | | (28) h(all_12_3, all_26_0) = all_36_0 & bomb(all_12_3, all_12_2) =
% 8.45/1.86 | | all_36_1 & $ki_accessible(all_12_3, all_12_3) = all_36_2 & ( ~
% 8.45/1.86 | | (all_36_0 = 0) | ~ (all_36_1 = 0) | ~ (all_36_2 = 0))
% 8.45/1.86 | |
% 8.45/1.86 | | ALPHA: (28) implies:
% 8.45/1.86 | | (29) $ki_accessible(all_12_3, all_12_3) = all_36_2
% 8.45/1.86 | | (30) bomb(all_12_3, all_12_2) = all_36_1
% 8.45/1.86 | | (31) h(all_12_3, all_26_0) = all_36_0
% 8.45/1.86 | | (32) ~ (all_36_0 = 0) | ~ (all_36_1 = 0) | ~ (all_36_2 = 0)
% 8.45/1.86 | |
% 8.45/1.86 | | GROUND_INST: instantiating (3) with 0, all_36_1, all_12_2, all_12_3,
% 8.45/1.86 | | simplifying with (24), (30) gives:
% 8.45/1.86 | | (33) all_36_1 = 0
% 8.45/1.86 | |
% 8.45/1.86 | | GROUND_INST: instantiating (mrel_reflexive) with all_12_3, all_36_2,
% 8.45/1.86 | | simplifying with (7), (29) gives:
% 8.45/1.86 | | (34) all_36_2 = 0
% 8.45/1.86 | |
% 8.45/1.86 | | GROUND_INST: instantiating (12) with all_26_0, simplifying with (19), (20)
% 8.45/1.86 | | gives:
% 8.45/1.86 | | (35) h(all_12_3, all_26_0) = 0
% 8.45/1.86 | |
% 8.45/1.86 | | GROUND_INST: instantiating (21) with all_12_3, simplifying with (7), (24)
% 8.45/1.86 | | gives:
% 8.45/1.86 | | (36) ? [v0: any] : ? [v1: any] : ? [v2: any] : (defused(all_12_3,
% 8.45/1.86 | | all_12_2) = v2 & h(all_12_3, all_26_0) = v1 &
% 8.45/1.86 | | $ki_accessible(all_12_3, all_12_3) = v0 & ( ~ (v1 = 0) | ~ (v0 =
% 8.45/1.86 | | 0) | v2 = 0))
% 8.45/1.86 | |
% 8.45/1.86 | | DELTA: instantiating (36) with fresh symbols all_48_0, all_48_1, all_48_2
% 8.45/1.86 | | gives:
% 8.45/1.86 | | (37) defused(all_12_3, all_12_2) = all_48_0 & h(all_12_3, all_26_0) =
% 8.45/1.86 | | all_48_1 & $ki_accessible(all_12_3, all_12_3) = all_48_2 & ( ~
% 8.45/1.86 | | (all_48_1 = 0) | ~ (all_48_2 = 0) | all_48_0 = 0)
% 8.45/1.86 | |
% 8.45/1.86 | | ALPHA: (37) implies:
% 8.45/1.86 | | (38) h(all_12_3, all_26_0) = all_48_1
% 8.45/1.86 | |
% 8.45/1.86 | | BETA: splitting (32) gives:
% 8.45/1.86 | |
% 8.45/1.86 | | Case 1:
% 8.45/1.86 | | |
% 8.45/1.86 | | | (39) ~ (all_36_0 = 0)
% 8.45/1.86 | | |
% 8.45/1.86 | | | GROUND_INST: instantiating (4) with all_36_0, all_48_1, all_26_0,
% 8.45/1.86 | | | all_12_3, simplifying with (31), (38) gives:
% 8.45/1.86 | | | (40) all_48_1 = all_36_0
% 8.45/1.86 | | |
% 8.45/1.86 | | | GROUND_INST: instantiating (4) with 0, all_48_1, all_26_0, all_12_3,
% 8.45/1.86 | | | simplifying with (35), (38) gives:
% 8.45/1.86 | | | (41) all_48_1 = 0
% 8.45/1.86 | | |
% 8.45/1.86 | | | COMBINE_EQS: (40), (41) imply:
% 8.45/1.86 | | | (42) all_36_0 = 0
% 8.45/1.86 | | |
% 8.45/1.86 | | | REDUCE: (39), (42) imply:
% 8.45/1.86 | | | (43) $false
% 8.45/1.86 | | |
% 8.45/1.86 | | | CLOSE: (43) is inconsistent.
% 8.45/1.86 | | |
% 8.45/1.86 | | Case 2:
% 8.45/1.86 | | |
% 8.45/1.86 | | | (44) ~ (all_36_1 = 0) | ~ (all_36_2 = 0)
% 8.45/1.86 | | |
% 8.45/1.86 | | | BETA: splitting (44) gives:
% 8.45/1.86 | | |
% 8.45/1.86 | | | Case 1:
% 8.45/1.86 | | | |
% 8.45/1.86 | | | | (45) ~ (all_36_1 = 0)
% 8.45/1.86 | | | |
% 8.45/1.86 | | | | REDUCE: (33), (45) imply:
% 8.45/1.86 | | | | (46) $false
% 8.45/1.86 | | | |
% 8.45/1.86 | | | | CLOSE: (46) is inconsistent.
% 8.45/1.86 | | | |
% 8.45/1.86 | | | Case 2:
% 8.45/1.86 | | | |
% 8.45/1.86 | | | | (47) ~ (all_36_2 = 0)
% 8.45/1.86 | | | |
% 8.45/1.86 | | | | REDUCE: (34), (47) imply:
% 8.45/1.86 | | | | (48) $false
% 8.45/1.86 | | | |
% 8.45/1.86 | | | | CLOSE: (48) is inconsistent.
% 8.45/1.86 | | | |
% 8.45/1.86 | | | End of split
% 8.45/1.86 | | |
% 8.45/1.86 | | End of split
% 8.45/1.86 | |
% 8.45/1.86 | End of split
% 8.45/1.86 |
% 8.45/1.86 End of proof
% 8.45/1.87 % SZS output end Proof for theBenchmark
% 8.45/1.87
% 8.45/1.87 1281ms
%------------------------------------------------------------------------------