TSTP Solution File: SET801+4 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET801+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n004.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 15:26:30 EDT 2023
% Result : Theorem 10.76s 2.22s
% Output : Proof 12.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SET801+4 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 15:05:37 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.63 ________ _____
% 0.21/0.63 ___ __ \_________(_)________________________________
% 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.63
% 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.63 (2023-06-19)
% 0.21/0.63
% 0.21/0.63 (c) Philipp Rümmer, 2009-2023
% 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.63 Amanda Stjerna.
% 0.21/0.63 Free software under BSD-3-Clause.
% 0.21/0.63
% 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.63
% 0.21/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.64 Running up to 7 provers in parallel.
% 0.21/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.49/1.17 Prover 1: Preprocessing ...
% 3.49/1.18 Prover 4: Preprocessing ...
% 3.49/1.21 Prover 2: Preprocessing ...
% 3.49/1.21 Prover 5: Preprocessing ...
% 3.49/1.21 Prover 6: Preprocessing ...
% 3.49/1.21 Prover 0: Preprocessing ...
% 3.49/1.21 Prover 3: Preprocessing ...
% 7.92/1.79 Prover 5: Proving ...
% 7.92/1.81 Prover 2: Proving ...
% 8.35/1.88 Prover 6: Proving ...
% 8.35/1.92 Prover 1: Constructing countermodel ...
% 8.35/1.93 Prover 3: Constructing countermodel ...
% 9.13/2.05 Prover 0: Proving ...
% 9.88/2.08 Prover 4: Constructing countermodel ...
% 10.76/2.22 Prover 3: proved (1552ms)
% 10.76/2.22
% 10.76/2.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.76/2.22
% 10.76/2.22 Prover 0: stopped
% 10.76/2.22 Prover 6: stopped
% 10.96/2.22 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.96/2.22 Prover 2: stopped
% 11.02/2.24 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.02/2.24 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.02/2.24 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.02/2.24 Prover 5: stopped
% 11.02/2.25 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.02/2.27 Prover 8: Preprocessing ...
% 11.02/2.27 Prover 7: Preprocessing ...
% 11.02/2.29 Prover 10: Preprocessing ...
% 11.60/2.31 Prover 11: Preprocessing ...
% 11.60/2.32 Prover 13: Preprocessing ...
% 11.60/2.37 Prover 10: Warning: ignoring some quantifiers
% 12.10/2.38 Prover 7: Warning: ignoring some quantifiers
% 12.10/2.38 Prover 1: Found proof (size 87)
% 12.10/2.38 Prover 1: proved (1728ms)
% 12.10/2.38 Prover 4: stopped
% 12.10/2.38 Prover 13: stopped
% 12.10/2.38 Prover 10: Constructing countermodel ...
% 12.10/2.39 Prover 7: Constructing countermodel ...
% 12.10/2.39 Prover 10: stopped
% 12.10/2.40 Prover 7: stopped
% 12.10/2.41 Prover 11: stopped
% 12.10/2.43 Prover 8: Warning: ignoring some quantifiers
% 12.10/2.44 Prover 8: Constructing countermodel ...
% 12.10/2.45 Prover 8: stopped
% 12.10/2.45
% 12.10/2.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.10/2.45
% 12.10/2.46 % SZS output start Proof for theBenchmark
% 12.10/2.46 Assumptions after simplification:
% 12.10/2.46 ---------------------------------
% 12.10/2.46
% 12.10/2.46 (greatest)
% 12.76/2.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 12.76/2.49 (greatest(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 12.76/2.49 $i] : ? [v5: int] : ( ~ (v5 = 0) & apply(v0, v4, v2) = v5 & member(v4,
% 12.76/2.49 v1) = 0 & $i(v4)) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) = v4))
% 12.76/2.49 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (greatest(v2, v0, v1) = 0) |
% 12.76/2.49 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v2, v1) = 0 & ! [v3: $i] : !
% 12.76/2.49 [v4: int] : (v4 = 0 | ~ (apply(v0, v3, v2) = v4) | ~ $i(v3) | ? [v5:
% 12.76/2.49 int] : ( ~ (v5 = 0) & member(v3, v1) = v5))))
% 12.76/2.49
% 12.76/2.49 (least_upper_bound)
% 12.76/2.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 12.76/2.50 | ~ (least_upper_bound(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 12.76/2.50 $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) &
% 12.76/2.50 upper_bound(v5, v2, v1) = 0 & apply(v2, v0, v5) = v6 & member(v5, v3) = 0
% 12.76/2.50 & $i(v5)) | ? [v5: any] : ? [v6: any] : (upper_bound(v0, v2, v1) = v6 &
% 12.76/2.50 member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : !
% 12.76/2.50 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (least_upper_bound(v0, v1, v2, v3)
% 12.76/2.50 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (upper_bound(v0,
% 12.76/2.50 v2, v1) = 0 & member(v0, v1) = 0 & ! [v4: $i] : ( ~ (upper_bound(v4,
% 12.76/2.50 v2, v1) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6: any] : (apply(v2,
% 12.76/2.50 v0, v4) = v6 & member(v4, v3) = v5 & ( ~ (v5 = 0) | v6 = 0)))))
% 12.76/2.50
% 12.76/2.50 (thIV13)
% 12.76/2.50 ? [v0: $i] : ? [v1: $i] : (order(v0, v1) = 0 & $i(v1) & $i(v0) & ? [v2: $i]
% 12.76/2.50 : (subset(v2, v1) = 0 & $i(v2) & ? [v3: $i] : ? [v4: any] : ? [v5: any] :
% 12.76/2.50 ? [v6: any] : (least_upper_bound(v3, v2, v0, v1) = v6 & greatest(v3, v0,
% 12.76/2.50 v2) = v4 & member(v3, v2) = v5 & $i(v3) & ((v6 = 0 & v5 = 0 & ~ (v4 =
% 12.76/2.50 0)) | (v4 = 0 & ( ~ (v6 = 0) | ~ (v5 = 0)))))))
% 12.76/2.50
% 12.76/2.50 (upper_bound)
% 12.76/2.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 12.76/2.50 (upper_bound(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 12.76/2.50 $i] : ? [v5: int] : ( ~ (v5 = 0) & apply(v0, v4, v2) = v5 & member(v4,
% 12.76/2.50 v1) = 0 & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 12.76/2.50 (upper_bound(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v3:
% 12.76/2.50 $i] : ! [v4: int] : (v4 = 0 | ~ (apply(v0, v3, v2) = v4) | ~ $i(v3) |
% 12.76/2.50 ? [v5: int] : ( ~ (v5 = 0) & member(v3, v1) = v5)))
% 12.76/2.50
% 12.76/2.50 (function-axioms)
% 12.76/2.51 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 12.76/2.51 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (greatest_lower_bound(v5,
% 12.76/2.51 v4, v3, v2) = v1) | ~ (greatest_lower_bound(v5, v4, v3, v2) = v0)) & !
% 12.76/2.51 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 12.76/2.51 $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (least_upper_bound(v5, v4,
% 12.76/2.51 v3, v2) = v1) | ~ (least_upper_bound(v5, v4, v3, v2) = v0)) & ! [v0:
% 12.76/2.51 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 12.76/2.51 : ! [v4: $i] : (v1 = v0 | ~ (min(v4, v3, v2) = v1) | ~ (min(v4, v3, v2) =
% 12.76/2.51 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 12.76/2.51 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (max(v4, v3, v2) = v1) | ~
% 12.76/2.51 (max(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.76/2.51 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 12.76/2.51 (least(v4, v3, v2) = v1) | ~ (least(v4, v3, v2) = v0)) & ! [v0:
% 12.76/2.51 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 12.76/2.51 : ! [v4: $i] : (v1 = v0 | ~ (greatest(v4, v3, v2) = v1) | ~ (greatest(v4,
% 12.76/2.51 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 12.76/2.51 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (lower_bound(v4, v3,
% 12.76/2.51 v2) = v1) | ~ (lower_bound(v4, v3, v2) = v0)) & ! [v0:
% 12.76/2.51 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 12.76/2.51 : ! [v4: $i] : (v1 = v0 | ~ (upper_bound(v4, v3, v2) = v1) | ~
% 12.76/2.51 (upper_bound(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.76/2.51 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 12.76/2.51 (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0:
% 12.76/2.51 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 12.76/2.51 : (v1 = v0 | ~ (total_order(v3, v2) = v1) | ~ (total_order(v3, v2) = v0)) &
% 12.76/2.51 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 12.76/2.51 $i] : (v1 = v0 | ~ (order(v3, v2) = v1) | ~ (order(v3, v2) = v0)) & !
% 12.76/2.51 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.76/2.51 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 12.76/2.51 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.76/2.51 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 12.76/2.51 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 12.76/2.51 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 12.76/2.51 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 12.76/2.51 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 12.76/2.51 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 12.76/2.51 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.76/2.51 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 12.76/2.51 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 12.76/2.51 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.76/2.51 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 12.76/2.51 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 12.76/2.51 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 12.76/2.51 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 12.76/2.51 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 12.76/2.51 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 12.76/2.51 (power_set(v2) = v0))
% 12.76/2.51
% 12.76/2.51 Further assumptions not needed in the proof:
% 12.76/2.51 --------------------------------------------
% 12.76/2.51 difference, empty_set, equal_set, greatest_lower_bound, intersection, least,
% 12.76/2.51 lower_bound, max, min, order, power_set, product, singleton, subset, sum,
% 12.76/2.51 total_order, union, unordered_pair
% 12.76/2.51
% 12.76/2.51 Those formulas are unsatisfiable:
% 12.76/2.51 ---------------------------------
% 12.76/2.51
% 12.76/2.51 Begin of proof
% 12.76/2.51 |
% 12.76/2.51 | ALPHA: (upper_bound) implies:
% 12.76/2.52 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (upper_bound(v2, v0, v1)
% 12.76/2.52 | = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ! [v4:
% 12.76/2.52 | int] : (v4 = 0 | ~ (apply(v0, v3, v2) = v4) | ~ $i(v3) | ? [v5:
% 12.76/2.52 | int] : ( ~ (v5 = 0) & member(v3, v1) = v5)))
% 12.76/2.52 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 12.76/2.52 | (upper_bound(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 12.76/2.52 | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & apply(v0, v4, v2) = v5 &
% 12.76/2.52 | member(v4, v1) = 0 & $i(v4)))
% 12.76/2.52 |
% 12.76/2.52 | ALPHA: (greatest) implies:
% 12.76/2.52 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (greatest(v2, v0, v1) =
% 12.76/2.52 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v2, v1) = 0 & !
% 12.76/2.52 | [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (apply(v0, v3, v2) = v4) |
% 12.76/2.52 | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = 0) & member(v3, v1) = v5))))
% 12.92/2.52 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 12.92/2.52 | (greatest(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 12.92/2.52 | [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & apply(v0, v4, v2) = v5 &
% 12.92/2.52 | member(v4, v1) = 0 & $i(v4)) | ? [v4: int] : ( ~ (v4 = 0) &
% 12.92/2.52 | member(v2, v1) = v4))
% 12.92/2.52 |
% 12.92/2.52 | ALPHA: (least_upper_bound) implies:
% 12.92/2.52 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 12.92/2.52 | (least_upper_bound(v0, v1, v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~
% 12.92/2.52 | $i(v1) | ~ $i(v0) | (upper_bound(v0, v2, v1) = 0 & member(v0, v1) =
% 12.92/2.52 | 0 & ! [v4: $i] : ( ~ (upper_bound(v4, v2, v1) = 0) | ~ $i(v4) |
% 12.92/2.52 | ? [v5: any] : ? [v6: any] : (apply(v2, v0, v4) = v6 & member(v4,
% 12.92/2.52 | v3) = v5 & ( ~ (v5 = 0) | v6 = 0)))))
% 12.92/2.52 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 12.92/2.52 | (v4 = 0 | ~ (least_upper_bound(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~
% 12.92/2.52 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: int] : ( ~ (v6
% 12.92/2.52 | = 0) & upper_bound(v5, v2, v1) = 0 & apply(v2, v0, v5) = v6 &
% 12.92/2.52 | member(v5, v3) = 0 & $i(v5)) | ? [v5: any] : ? [v6: any] :
% 12.92/2.52 | (upper_bound(v0, v2, v1) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) |
% 12.92/2.52 | ~ (v5 = 0))))
% 12.92/2.52 |
% 12.92/2.52 | ALPHA: (function-axioms) implies:
% 12.92/2.53 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 12.92/2.53 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 12.92/2.53 | = v0))
% 12.92/2.53 |
% 12.92/2.53 | DELTA: instantiating (thIV13) with fresh symbols all_25_0, all_25_1 gives:
% 12.92/2.53 | (8) order(all_25_1, all_25_0) = 0 & $i(all_25_0) & $i(all_25_1) & ? [v0:
% 12.92/2.53 | $i] : (subset(v0, all_25_0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: any]
% 12.92/2.53 | : ? [v3: any] : ? [v4: any] : (least_upper_bound(v1, v0, all_25_1,
% 12.92/2.53 | all_25_0) = v4 & greatest(v1, all_25_1, v0) = v2 & member(v1, v0)
% 12.92/2.53 | = v3 & $i(v1) & ((v4 = 0 & v3 = 0 & ~ (v2 = 0)) | (v2 = 0 & ( ~
% 12.92/2.53 | (v4 = 0) | ~ (v3 = 0))))))
% 12.92/2.53 |
% 12.92/2.53 | ALPHA: (8) implies:
% 12.92/2.53 | (9) $i(all_25_1)
% 12.92/2.53 | (10) $i(all_25_0)
% 12.92/2.53 | (11) ? [v0: $i] : (subset(v0, all_25_0) = 0 & $i(v0) & ? [v1: $i] : ?
% 12.92/2.53 | [v2: any] : ? [v3: any] : ? [v4: any] : (least_upper_bound(v1, v0,
% 12.92/2.53 | all_25_1, all_25_0) = v4 & greatest(v1, all_25_1, v0) = v2 &
% 12.92/2.53 | member(v1, v0) = v3 & $i(v1) & ((v4 = 0 & v3 = 0 & ~ (v2 = 0)) |
% 12.92/2.53 | (v2 = 0 & ( ~ (v4 = 0) | ~ (v3 = 0))))))
% 12.92/2.53 |
% 12.92/2.53 | DELTA: instantiating (11) with fresh symbol all_27_0 gives:
% 12.92/2.53 | (12) subset(all_27_0, all_25_0) = 0 & $i(all_27_0) & ? [v0: $i] : ? [v1:
% 12.92/2.53 | any] : ? [v2: any] : ? [v3: any] : (least_upper_bound(v0,
% 12.92/2.53 | all_27_0, all_25_1, all_25_0) = v3 & greatest(v0, all_25_1,
% 12.92/2.53 | all_27_0) = v1 & member(v0, all_27_0) = v2 & $i(v0) & ((v3 = 0 &
% 12.92/2.53 | v2 = 0 & ~ (v1 = 0)) | (v1 = 0 & ( ~ (v3 = 0) | ~ (v2 = 0)))))
% 12.92/2.53 |
% 12.92/2.53 | ALPHA: (12) implies:
% 12.92/2.53 | (13) $i(all_27_0)
% 12.92/2.53 | (14) ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 12.92/2.53 | (least_upper_bound(v0, all_27_0, all_25_1, all_25_0) = v3 &
% 12.92/2.53 | greatest(v0, all_25_1, all_27_0) = v1 & member(v0, all_27_0) = v2 &
% 12.92/2.53 | $i(v0) & ((v3 = 0 & v2 = 0 & ~ (v1 = 0)) | (v1 = 0 & ( ~ (v3 = 0) |
% 12.92/2.53 | ~ (v2 = 0)))))
% 12.92/2.53 |
% 12.92/2.53 | DELTA: instantiating (14) with fresh symbols all_29_0, all_29_1, all_29_2,
% 12.92/2.53 | all_29_3 gives:
% 12.92/2.53 | (15) least_upper_bound(all_29_3, all_27_0, all_25_1, all_25_0) = all_29_0 &
% 12.92/2.53 | greatest(all_29_3, all_25_1, all_27_0) = all_29_2 & member(all_29_3,
% 12.92/2.53 | all_27_0) = all_29_1 & $i(all_29_3) & ((all_29_0 = 0 & all_29_1 = 0
% 12.92/2.53 | & ~ (all_29_2 = 0)) | (all_29_2 = 0 & ( ~ (all_29_0 = 0) | ~
% 12.92/2.53 | (all_29_1 = 0))))
% 12.92/2.53 |
% 12.92/2.53 | ALPHA: (15) implies:
% 12.92/2.53 | (16) $i(all_29_3)
% 12.92/2.54 | (17) member(all_29_3, all_27_0) = all_29_1
% 12.92/2.54 | (18) greatest(all_29_3, all_25_1, all_27_0) = all_29_2
% 12.92/2.54 | (19) least_upper_bound(all_29_3, all_27_0, all_25_1, all_25_0) = all_29_0
% 12.92/2.54 | (20) (all_29_0 = 0 & all_29_1 = 0 & ~ (all_29_2 = 0)) | (all_29_2 = 0 & (
% 12.92/2.54 | ~ (all_29_0 = 0) | ~ (all_29_1 = 0)))
% 12.92/2.54 |
% 12.92/2.54 | GROUND_INST: instantiating (4) with all_25_1, all_27_0, all_29_3, all_29_2,
% 12.92/2.54 | simplifying with (9), (13), (16), (18) gives:
% 12.92/2.54 | (21) all_29_2 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 12.92/2.54 | apply(all_25_1, v0, all_29_3) = v1 & member(v0, all_27_0) = 0 &
% 12.92/2.54 | $i(v0)) | ? [v0: int] : ( ~ (v0 = 0) & member(all_29_3, all_27_0) =
% 12.92/2.54 | v0)
% 12.92/2.54 |
% 12.92/2.54 | GROUND_INST: instantiating (6) with all_29_3, all_27_0, all_25_1, all_25_0,
% 12.92/2.54 | all_29_0, simplifying with (9), (10), (13), (16), (19) gives:
% 12.92/2.54 | (22) all_29_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 12.92/2.54 | upper_bound(v0, all_25_1, all_27_0) = 0 & apply(all_25_1, all_29_3,
% 12.92/2.54 | v0) = v1 & member(v0, all_25_0) = 0 & $i(v0)) | ? [v0: any] : ?
% 12.92/2.54 | [v1: any] : (upper_bound(all_29_3, all_25_1, all_27_0) = v1 &
% 12.92/2.54 | member(all_29_3, all_27_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 12.92/2.54 |
% 12.92/2.54 | BETA: splitting (20) gives:
% 12.92/2.54 |
% 12.92/2.54 | Case 1:
% 12.92/2.54 | |
% 12.92/2.54 | | (23) all_29_0 = 0 & all_29_1 = 0 & ~ (all_29_2 = 0)
% 12.92/2.54 | |
% 12.92/2.54 | | ALPHA: (23) implies:
% 12.92/2.54 | | (24) all_29_1 = 0
% 12.92/2.54 | | (25) all_29_0 = 0
% 12.92/2.54 | | (26) ~ (all_29_2 = 0)
% 12.92/2.54 | |
% 12.92/2.54 | | REDUCE: (19), (25) imply:
% 12.92/2.54 | | (27) least_upper_bound(all_29_3, all_27_0, all_25_1, all_25_0) = 0
% 12.92/2.54 | |
% 12.92/2.54 | | REDUCE: (17), (24) imply:
% 12.92/2.54 | | (28) member(all_29_3, all_27_0) = 0
% 12.92/2.54 | |
% 12.92/2.54 | | BETA: splitting (21) gives:
% 12.92/2.54 | |
% 12.92/2.54 | | Case 1:
% 12.92/2.54 | | |
% 12.92/2.54 | | | (29) all_29_2 = 0
% 12.92/2.54 | | |
% 12.92/2.54 | | | REDUCE: (26), (29) imply:
% 12.92/2.54 | | | (30) $false
% 12.92/2.54 | | |
% 12.92/2.54 | | | CLOSE: (30) is inconsistent.
% 12.92/2.54 | | |
% 12.92/2.54 | | Case 2:
% 12.92/2.54 | | |
% 12.92/2.55 | | | (31) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & apply(all_25_1, v0,
% 12.92/2.55 | | | all_29_3) = v1 & member(v0, all_27_0) = 0 & $i(v0)) | ? [v0:
% 12.92/2.55 | | | int] : ( ~ (v0 = 0) & member(all_29_3, all_27_0) = v0)
% 12.92/2.55 | | |
% 12.92/2.55 | | | BETA: splitting (31) gives:
% 12.92/2.55 | | |
% 12.92/2.55 | | | Case 1:
% 12.92/2.55 | | | |
% 12.92/2.55 | | | | (32) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & apply(all_25_1, v0,
% 12.92/2.55 | | | | all_29_3) = v1 & member(v0, all_27_0) = 0 & $i(v0))
% 12.92/2.55 | | | |
% 12.92/2.55 | | | | GROUND_INST: instantiating (5) with all_29_3, all_27_0, all_25_1,
% 12.92/2.55 | | | | all_25_0, simplifying with (9), (10), (13), (16), (27)
% 12.92/2.55 | | | | gives:
% 12.92/2.55 | | | | (33) upper_bound(all_29_3, all_25_1, all_27_0) = 0 & member(all_29_3,
% 12.92/2.55 | | | | all_27_0) = 0 & ! [v0: $i] : ( ~ (upper_bound(v0, all_25_1,
% 12.92/2.55 | | | | all_27_0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] :
% 12.92/2.55 | | | | (apply(all_25_1, all_29_3, v0) = v2 & member(v0, all_25_0) =
% 12.92/2.55 | | | | v1 & ( ~ (v1 = 0) | v2 = 0)))
% 12.92/2.55 | | | |
% 12.92/2.55 | | | | ALPHA: (33) implies:
% 12.92/2.55 | | | | (34) upper_bound(all_29_3, all_25_1, all_27_0) = 0
% 12.92/2.55 | | | |
% 12.92/2.55 | | | | GROUND_INST: instantiating (1) with all_25_1, all_27_0, all_29_3,
% 12.92/2.55 | | | | simplifying with (9), (13), (16), (34) gives:
% 12.92/2.55 | | | | (35) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (apply(all_25_1, v0,
% 12.92/2.55 | | | | all_29_3) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0)
% 12.92/2.55 | | | | & member(v0, all_27_0) = v2))
% 12.92/2.55 | | | |
% 12.92/2.55 | | | | DELTA: instantiating (32) with fresh symbols all_94_0, all_94_1 gives:
% 12.92/2.55 | | | | (36) ~ (all_94_0 = 0) & apply(all_25_1, all_94_1, all_29_3) =
% 12.92/2.55 | | | | all_94_0 & member(all_94_1, all_27_0) = 0 & $i(all_94_1)
% 12.92/2.55 | | | |
% 12.92/2.55 | | | | REF_CLOSE: (7), (35), (36) are inconsistent by sub-proof #2.
% 12.92/2.55 | | | |
% 12.92/2.55 | | | Case 2:
% 12.92/2.55 | | | |
% 12.92/2.55 | | | | (37) ? [v0: int] : ( ~ (v0 = 0) & member(all_29_3, all_27_0) = v0)
% 12.92/2.55 | | | |
% 12.92/2.55 | | | | DELTA: instantiating (37) with fresh symbol all_89_0 gives:
% 12.92/2.55 | | | | (38) ~ (all_89_0 = 0) & member(all_29_3, all_27_0) = all_89_0
% 12.92/2.55 | | | |
% 12.92/2.55 | | | | REF_CLOSE: (7), (28), (38) are inconsistent by sub-proof #1.
% 12.92/2.55 | | | |
% 12.92/2.55 | | | End of split
% 12.92/2.55 | | |
% 12.92/2.55 | | End of split
% 12.92/2.55 | |
% 12.92/2.55 | Case 2:
% 12.92/2.55 | |
% 12.92/2.55 | | (39) all_29_2 = 0 & ( ~ (all_29_0 = 0) | ~ (all_29_1 = 0))
% 12.92/2.55 | |
% 12.92/2.55 | | ALPHA: (39) implies:
% 12.92/2.55 | | (40) all_29_2 = 0
% 12.92/2.55 | | (41) ~ (all_29_0 = 0) | ~ (all_29_1 = 0)
% 12.92/2.55 | |
% 12.92/2.55 | | REDUCE: (18), (40) imply:
% 12.92/2.55 | | (42) greatest(all_29_3, all_25_1, all_27_0) = 0
% 12.92/2.55 | |
% 12.92/2.55 | | GROUND_INST: instantiating (3) with all_25_1, all_27_0, all_29_3,
% 12.92/2.55 | | simplifying with (9), (13), (16), (42) gives:
% 12.92/2.55 | | (43) member(all_29_3, all_27_0) = 0 & ! [v0: $i] : ! [v1: int] : (v1 =
% 12.92/2.55 | | 0 | ~ (apply(all_25_1, v0, all_29_3) = v1) | ~ $i(v0) | ? [v2:
% 12.92/2.55 | | int] : ( ~ (v2 = 0) & member(v0, all_27_0) = v2))
% 12.92/2.55 | |
% 12.92/2.55 | | ALPHA: (43) implies:
% 12.92/2.56 | | (44) member(all_29_3, all_27_0) = 0
% 12.92/2.56 | | (45) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (apply(all_25_1, v0,
% 12.92/2.56 | | all_29_3) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 12.92/2.56 | | member(v0, all_27_0) = v2))
% 12.92/2.56 | |
% 12.92/2.56 | | GROUND_INST: instantiating (7) with all_29_1, 0, all_27_0, all_29_3,
% 12.92/2.56 | | simplifying with (17), (44) gives:
% 12.92/2.56 | | (46) all_29_1 = 0
% 12.92/2.56 | |
% 12.92/2.56 | | BETA: splitting (41) gives:
% 12.92/2.56 | |
% 12.92/2.56 | | Case 1:
% 12.92/2.56 | | |
% 12.92/2.56 | | | (47) ~ (all_29_0 = 0)
% 12.92/2.56 | | |
% 12.92/2.56 | | | BETA: splitting (22) gives:
% 12.92/2.56 | | |
% 12.92/2.56 | | | Case 1:
% 12.92/2.56 | | | |
% 12.92/2.56 | | | | (48) all_29_0 = 0
% 12.92/2.56 | | | |
% 12.92/2.56 | | | | REDUCE: (47), (48) imply:
% 12.92/2.56 | | | | (49) $false
% 12.92/2.56 | | | |
% 12.92/2.56 | | | | CLOSE: (49) is inconsistent.
% 12.92/2.56 | | | |
% 12.92/2.56 | | | Case 2:
% 12.92/2.56 | | | |
% 12.92/2.56 | | | | (50) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & upper_bound(v0,
% 12.92/2.56 | | | | all_25_1, all_27_0) = 0 & apply(all_25_1, all_29_3, v0) = v1
% 12.92/2.56 | | | | & member(v0, all_25_0) = 0 & $i(v0)) | ? [v0: any] : ? [v1:
% 12.92/2.56 | | | | any] : (upper_bound(all_29_3, all_25_1, all_27_0) = v1 &
% 12.92/2.56 | | | | member(all_29_3, all_27_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 12.92/2.56 | | | |
% 12.92/2.56 | | | | BETA: splitting (50) gives:
% 12.92/2.56 | | | |
% 12.92/2.56 | | | | Case 1:
% 12.92/2.56 | | | | |
% 12.92/2.56 | | | | | (51) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & upper_bound(v0,
% 12.92/2.56 | | | | | all_25_1, all_27_0) = 0 & apply(all_25_1, all_29_3, v0) =
% 12.92/2.56 | | | | | v1 & member(v0, all_25_0) = 0 & $i(v0))
% 12.92/2.56 | | | | |
% 12.92/2.56 | | | | | DELTA: instantiating (51) with fresh symbols all_77_0, all_77_1 gives:
% 12.92/2.56 | | | | | (52) ~ (all_77_0 = 0) & upper_bound(all_77_1, all_25_1, all_27_0)
% 12.92/2.56 | | | | | = 0 & apply(all_25_1, all_29_3, all_77_1) = all_77_0 &
% 12.92/2.56 | | | | | member(all_77_1, all_25_0) = 0 & $i(all_77_1)
% 12.92/2.56 | | | | |
% 12.92/2.56 | | | | | ALPHA: (52) implies:
% 12.92/2.56 | | | | | (53) ~ (all_77_0 = 0)
% 12.92/2.56 | | | | | (54) $i(all_77_1)
% 12.92/2.56 | | | | | (55) apply(all_25_1, all_29_3, all_77_1) = all_77_0
% 12.92/2.56 | | | | | (56) upper_bound(all_77_1, all_25_1, all_27_0) = 0
% 12.92/2.56 | | | | |
% 12.92/2.56 | | | | | GROUND_INST: instantiating (1) with all_25_1, all_27_0, all_77_1,
% 12.92/2.56 | | | | | simplifying with (9), (13), (54), (56) gives:
% 12.92/2.56 | | | | | (57) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (apply(all_25_1, v0,
% 12.92/2.56 | | | | | all_77_1) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 =
% 12.92/2.56 | | | | | 0) & member(v0, all_27_0) = v2))
% 12.92/2.56 | | | | |
% 12.92/2.56 | | | | | GROUND_INST: instantiating (57) with all_29_3, all_77_0, simplifying
% 12.92/2.56 | | | | | with (16), (55) gives:
% 12.92/2.56 | | | | | (58) all_77_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_29_3,
% 12.92/2.56 | | | | | all_27_0) = v0)
% 12.92/2.56 | | | | |
% 12.92/2.56 | | | | | BETA: splitting (58) gives:
% 12.92/2.56 | | | | |
% 12.92/2.56 | | | | | Case 1:
% 12.92/2.56 | | | | | |
% 12.92/2.56 | | | | | | (59) all_77_0 = 0
% 12.92/2.56 | | | | | |
% 12.92/2.56 | | | | | | REDUCE: (53), (59) imply:
% 12.92/2.56 | | | | | | (60) $false
% 12.92/2.56 | | | | | |
% 12.92/2.56 | | | | | | CLOSE: (60) is inconsistent.
% 12.92/2.56 | | | | | |
% 12.92/2.56 | | | | | Case 2:
% 12.92/2.56 | | | | | |
% 12.92/2.56 | | | | | | (61) ? [v0: int] : ( ~ (v0 = 0) & member(all_29_3, all_27_0) =
% 12.92/2.56 | | | | | | v0)
% 12.92/2.56 | | | | | |
% 12.92/2.56 | | | | | | DELTA: instantiating (61) with fresh symbol all_89_0 gives:
% 12.92/2.56 | | | | | | (62) ~ (all_89_0 = 0) & member(all_29_3, all_27_0) = all_89_0
% 12.92/2.56 | | | | | |
% 12.92/2.56 | | | | | | REF_CLOSE: (7), (44), (62) are inconsistent by sub-proof #1.
% 12.92/2.56 | | | | | |
% 12.92/2.56 | | | | | End of split
% 12.92/2.56 | | | | |
% 12.92/2.56 | | | | Case 2:
% 12.92/2.56 | | | | |
% 12.92/2.56 | | | | | (63) ? [v0: any] : ? [v1: any] : (upper_bound(all_29_3, all_25_1,
% 12.92/2.56 | | | | | all_27_0) = v1 & member(all_29_3, all_27_0) = v0 & ( ~ (v1
% 12.92/2.56 | | | | | = 0) | ~ (v0 = 0)))
% 12.92/2.56 | | | | |
% 12.92/2.56 | | | | | DELTA: instantiating (63) with fresh symbols all_77_0, all_77_1 gives:
% 12.92/2.57 | | | | | (64) upper_bound(all_29_3, all_25_1, all_27_0) = all_77_0 &
% 12.92/2.57 | | | | | member(all_29_3, all_27_0) = all_77_1 & ( ~ (all_77_0 = 0) |
% 12.92/2.57 | | | | | ~ (all_77_1 = 0))
% 12.92/2.57 | | | | |
% 12.92/2.57 | | | | | ALPHA: (64) implies:
% 12.92/2.57 | | | | | (65) member(all_29_3, all_27_0) = all_77_1
% 12.92/2.57 | | | | | (66) upper_bound(all_29_3, all_25_1, all_27_0) = all_77_0
% 12.92/2.57 | | | | | (67) ~ (all_77_0 = 0) | ~ (all_77_1 = 0)
% 12.92/2.57 | | | | |
% 12.92/2.57 | | | | | GROUND_INST: instantiating (7) with 0, all_77_1, all_27_0, all_29_3,
% 12.92/2.57 | | | | | simplifying with (44), (65) gives:
% 12.92/2.57 | | | | | (68) all_77_1 = 0
% 12.92/2.57 | | | | |
% 12.92/2.57 | | | | | BETA: splitting (67) gives:
% 12.92/2.57 | | | | |
% 12.92/2.57 | | | | | Case 1:
% 12.92/2.57 | | | | | |
% 12.92/2.57 | | | | | | (69) ~ (all_77_0 = 0)
% 12.92/2.57 | | | | | |
% 12.92/2.57 | | | | | | GROUND_INST: instantiating (2) with all_25_1, all_27_0, all_29_3,
% 12.92/2.57 | | | | | | all_77_0, simplifying with (9), (13), (16), (66) gives:
% 12.92/2.57 | | | | | | (70) all_77_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 12.92/2.57 | | | | | | apply(all_25_1, v0, all_29_3) = v1 & member(v0, all_27_0)
% 12.92/2.57 | | | | | | = 0 & $i(v0))
% 12.92/2.57 | | | | | |
% 12.92/2.57 | | | | | | BETA: splitting (70) gives:
% 12.92/2.57 | | | | | |
% 12.92/2.57 | | | | | | Case 1:
% 12.92/2.57 | | | | | | |
% 12.92/2.57 | | | | | | | (71) all_77_0 = 0
% 12.92/2.57 | | | | | | |
% 12.92/2.57 | | | | | | | REDUCE: (69), (71) imply:
% 12.92/2.57 | | | | | | | (72) $false
% 12.92/2.57 | | | | | | |
% 12.92/2.57 | | | | | | | CLOSE: (72) is inconsistent.
% 12.92/2.57 | | | | | | |
% 12.92/2.57 | | | | | | Case 2:
% 12.92/2.57 | | | | | | |
% 12.92/2.57 | | | | | | | (73) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 12.92/2.57 | | | | | | | apply(all_25_1, v0, all_29_3) = v1 & member(v0,
% 12.92/2.57 | | | | | | | all_27_0) = 0 & $i(v0))
% 12.92/2.57 | | | | | | |
% 12.92/2.57 | | | | | | | DELTA: instantiating (73) with fresh symbols all_94_0, all_94_1
% 12.92/2.57 | | | | | | | gives:
% 12.92/2.57 | | | | | | | (74) ~ (all_94_0 = 0) & apply(all_25_1, all_94_1, all_29_3) =
% 12.92/2.57 | | | | | | | all_94_0 & member(all_94_1, all_27_0) = 0 & $i(all_94_1)
% 12.92/2.57 | | | | | | |
% 12.92/2.57 | | | | | | | REF_CLOSE: (7), (45), (74) are inconsistent by sub-proof #2.
% 12.92/2.57 | | | | | | |
% 12.92/2.57 | | | | | | End of split
% 12.92/2.57 | | | | | |
% 12.92/2.57 | | | | | Case 2:
% 12.92/2.57 | | | | | |
% 12.92/2.57 | | | | | | (75) ~ (all_77_1 = 0)
% 12.92/2.57 | | | | | |
% 12.92/2.57 | | | | | | REDUCE: (68), (75) imply:
% 12.92/2.57 | | | | | | (76) $false
% 12.92/2.57 | | | | | |
% 12.92/2.57 | | | | | | CLOSE: (76) is inconsistent.
% 12.92/2.57 | | | | | |
% 12.92/2.57 | | | | | End of split
% 12.92/2.57 | | | | |
% 12.92/2.57 | | | | End of split
% 12.92/2.57 | | | |
% 12.92/2.57 | | | End of split
% 12.92/2.57 | | |
% 12.92/2.57 | | Case 2:
% 12.92/2.57 | | |
% 12.92/2.57 | | | (77) ~ (all_29_1 = 0)
% 12.92/2.57 | | |
% 12.92/2.57 | | | REDUCE: (46), (77) imply:
% 12.92/2.57 | | | (78) $false
% 12.92/2.57 | | |
% 12.92/2.57 | | | CLOSE: (78) is inconsistent.
% 12.92/2.57 | | |
% 12.92/2.57 | | End of split
% 12.92/2.57 | |
% 12.92/2.57 | End of split
% 12.92/2.57 |
% 12.92/2.57 End of proof
% 12.92/2.57
% 12.92/2.57 Sub-proof #1 shows that the following formulas are inconsistent:
% 12.92/2.57 ----------------------------------------------------------------
% 12.92/2.57 (1) ~ (all_89_0 = 0) & member(all_29_3, all_27_0) = all_89_0
% 12.92/2.57 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 12.92/2.57 ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) =
% 12.92/2.57 v0))
% 12.92/2.57 (3) member(all_29_3, all_27_0) = 0
% 12.92/2.57
% 12.92/2.57 Begin of proof
% 12.92/2.57 |
% 12.92/2.57 | ALPHA: (1) implies:
% 12.92/2.57 | (4) ~ (all_89_0 = 0)
% 12.92/2.57 | (5) member(all_29_3, all_27_0) = all_89_0
% 12.92/2.57 |
% 12.92/2.57 | GROUND_INST: instantiating (2) with 0, all_89_0, all_27_0, all_29_3,
% 12.92/2.57 | simplifying with (3), (5) gives:
% 12.92/2.57 | (6) all_89_0 = 0
% 12.92/2.57 |
% 12.92/2.57 | REDUCE: (4), (6) imply:
% 12.92/2.57 | (7) $false
% 12.92/2.57 |
% 12.92/2.57 | CLOSE: (7) is inconsistent.
% 12.92/2.57 |
% 12.92/2.57 End of proof
% 12.92/2.57
% 12.92/2.57 Sub-proof #2 shows that the following formulas are inconsistent:
% 12.92/2.57 ----------------------------------------------------------------
% 12.92/2.57 (1) ~ (all_94_0 = 0) & apply(all_25_1, all_94_1, all_29_3) = all_94_0 &
% 12.92/2.57 member(all_94_1, all_27_0) = 0 & $i(all_94_1)
% 12.92/2.57 (2) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (apply(all_25_1, v0, all_29_3)
% 12.92/2.57 = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & member(v0,
% 12.92/2.57 all_27_0) = v2))
% 12.92/2.57 (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 12.92/2.57 ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) =
% 12.92/2.57 v0))
% 12.92/2.57
% 12.92/2.57 Begin of proof
% 12.92/2.57 |
% 12.92/2.57 | ALPHA: (1) implies:
% 12.92/2.57 | (4) ~ (all_94_0 = 0)
% 12.92/2.57 | (5) $i(all_94_1)
% 12.92/2.57 | (6) member(all_94_1, all_27_0) = 0
% 12.92/2.58 | (7) apply(all_25_1, all_94_1, all_29_3) = all_94_0
% 12.92/2.58 |
% 12.92/2.58 | GROUND_INST: instantiating (2) with all_94_1, all_94_0, simplifying with (5),
% 12.92/2.58 | (7) gives:
% 12.92/2.58 | (8) all_94_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_94_1, all_27_0)
% 12.92/2.58 | = v0)
% 12.92/2.58 |
% 12.92/2.58 | BETA: splitting (8) gives:
% 12.92/2.58 |
% 12.92/2.58 | Case 1:
% 12.92/2.58 | |
% 12.92/2.58 | | (9) all_94_0 = 0
% 12.92/2.58 | |
% 12.92/2.58 | | REDUCE: (4), (9) imply:
% 12.92/2.58 | | (10) $false
% 12.92/2.58 | |
% 12.92/2.58 | | CLOSE: (10) is inconsistent.
% 12.92/2.58 | |
% 12.92/2.58 | Case 2:
% 12.92/2.58 | |
% 12.92/2.58 | | (11) ? [v0: int] : ( ~ (v0 = 0) & member(all_94_1, all_27_0) = v0)
% 12.92/2.58 | |
% 12.92/2.58 | | DELTA: instantiating (11) with fresh symbol all_106_0 gives:
% 12.92/2.58 | | (12) ~ (all_106_0 = 0) & member(all_94_1, all_27_0) = all_106_0
% 12.92/2.58 | |
% 12.92/2.58 | | ALPHA: (12) implies:
% 12.92/2.58 | | (13) ~ (all_106_0 = 0)
% 12.92/2.58 | | (14) member(all_94_1, all_27_0) = all_106_0
% 12.92/2.58 | |
% 12.92/2.58 | | GROUND_INST: instantiating (3) with 0, all_106_0, all_27_0, all_94_1,
% 12.92/2.58 | | simplifying with (6), (14) gives:
% 12.92/2.58 | | (15) all_106_0 = 0
% 12.92/2.58 | |
% 12.92/2.58 | | REDUCE: (13), (15) imply:
% 12.92/2.58 | | (16) $false
% 12.92/2.58 | |
% 12.92/2.58 | | CLOSE: (16) is inconsistent.
% 12.92/2.58 | |
% 12.92/2.58 | End of split
% 12.92/2.58 |
% 12.92/2.58 End of proof
% 12.92/2.58 % SZS output end Proof for theBenchmark
% 12.92/2.58
% 12.92/2.58 1947ms
%------------------------------------------------------------------------------