TSTP Solution File: SET796+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET796+4 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n003.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 15:26:29 EDT 2023
% Result : Theorem 13.73s 2.72s
% Output : Proof 17.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.14 % Problem : SET796+4 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.12/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 16:34:24 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.16/0.63 ________ _____
% 0.16/0.63 ___ __ \_________(_)________________________________
% 0.16/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.16/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.16/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.16/0.63
% 0.16/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.16/0.63 (2023-06-19)
% 0.16/0.63
% 0.16/0.63 (c) Philipp Rümmer, 2009-2023
% 0.16/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.16/0.63 Amanda Stjerna.
% 0.16/0.63 Free software under BSD-3-Clause.
% 0.16/0.63
% 0.16/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.16/0.63
% 0.16/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.16/0.65 Running up to 7 provers in parallel.
% 0.16/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.16/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.16/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.16/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.16/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.16/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.16/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.12/1.20 Prover 1: Preprocessing ...
% 3.12/1.20 Prover 4: Preprocessing ...
% 3.43/1.27 Prover 2: Preprocessing ...
% 3.43/1.27 Prover 3: Preprocessing ...
% 3.43/1.27 Prover 6: Preprocessing ...
% 3.43/1.27 Prover 5: Preprocessing ...
% 3.43/1.27 Prover 0: Preprocessing ...
% 9.17/2.05 Prover 5: Proving ...
% 9.17/2.08 Prover 2: Proving ...
% 9.17/2.14 Prover 6: Proving ...
% 9.17/2.21 Prover 3: Constructing countermodel ...
% 9.17/2.22 Prover 1: Constructing countermodel ...
% 11.68/2.44 Prover 4: Constructing countermodel ...
% 11.68/2.44 Prover 0: Proving ...
% 13.73/2.72 Prover 3: proved (2046ms)
% 13.73/2.72
% 13.73/2.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.73/2.72
% 13.73/2.72 Prover 0: stopped
% 13.73/2.73 Prover 2: stopped
% 13.73/2.73 Prover 5: stopped
% 13.73/2.74 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.73/2.74 Prover 6: stopped
% 13.73/2.74 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.73/2.74 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.73/2.75 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.73/2.75 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.44/2.79 Prover 8: Preprocessing ...
% 14.48/2.80 Prover 7: Preprocessing ...
% 14.55/2.81 Prover 10: Preprocessing ...
% 14.55/2.82 Prover 13: Preprocessing ...
% 14.55/2.84 Prover 11: Preprocessing ...
% 14.55/2.93 Prover 7: Warning: ignoring some quantifiers
% 14.55/2.95 Prover 1: Found proof (size 93)
% 14.55/2.95 Prover 1: proved (2292ms)
% 14.55/2.95 Prover 4: stopped
% 14.55/2.99 Prover 10: Warning: ignoring some quantifiers
% 14.55/2.99 Prover 7: Constructing countermodel ...
% 15.55/3.01 Prover 7: stopped
% 15.55/3.02 Prover 10: Constructing countermodel ...
% 15.55/3.02 Prover 11: stopped
% 15.55/3.03 Prover 13: Warning: ignoring some quantifiers
% 15.55/3.04 Prover 10: stopped
% 15.55/3.05 Prover 13: Constructing countermodel ...
% 15.55/3.06 Prover 13: stopped
% 16.49/3.15 Prover 8: Warning: ignoring some quantifiers
% 16.49/3.16 Prover 8: Constructing countermodel ...
% 16.94/3.18 Prover 8: stopped
% 16.94/3.18
% 16.94/3.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.94/3.18
% 16.98/3.20 % SZS output start Proof for theBenchmark
% 16.98/3.20 Assumptions after simplification:
% 16.98/3.20 ---------------------------------
% 16.98/3.20
% 16.98/3.20 (greatest_lower_bound)
% 17.11/3.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 17.11/3.23 | ~ (greatest_lower_bound(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) |
% 17.11/3.23 ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) &
% 17.11/3.23 lower_bound(v5, v2, v1) = 0 & apply(v2, v5, v0) = v6 & member(v5, v3) = 0
% 17.11/3.23 & $i(v5)) | ? [v5: any] : ? [v6: any] : (lower_bound(v0, v2, v1) = v6 &
% 17.11/3.23 member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : !
% 17.11/3.23 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (greatest_lower_bound(v0, v1, v2,
% 17.11/3.24 v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 17.11/3.24 (lower_bound(v0, v2, v1) = 0 & member(v0, v1) = 0 & ! [v4: $i] : ( ~
% 17.11/3.24 (lower_bound(v4, v2, v1) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6: any]
% 17.11/3.24 : (apply(v2, v4, v0) = v6 & member(v4, v3) = v5 & ( ~ (v5 = 0) | v6 =
% 17.11/3.24 0)))))
% 17.11/3.24
% 17.11/3.24 (lower_bound)
% 17.11/3.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 17.11/3.24 (lower_bound(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 17.11/3.24 $i] : ? [v5: int] : ( ~ (v5 = 0) & apply(v0, v2, v4) = v5 & member(v4,
% 17.11/3.24 v1) = 0 & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 17.11/3.24 (lower_bound(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v3:
% 17.11/3.24 $i] : ! [v4: int] : (v4 = 0 | ~ (apply(v0, v2, v3) = v4) | ~ $i(v3) |
% 17.11/3.24 ? [v5: int] : ( ~ (v5 = 0) & member(v3, v1) = v5)))
% 17.11/3.24
% 17.11/3.24 (order)
% 17.11/3.25 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (order(v0, v1) = v2) |
% 17.11/3.25 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6:
% 17.11/3.25 int] : ( ~ (v6 = 0) & apply(v0, v4, v5) = 0 & apply(v0, v3, v5) = v6 &
% 17.11/3.25 apply(v0, v3, v4) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0 &
% 17.11/3.25 member(v3, v1) = 0 & $i(v5) & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: $i]
% 17.11/3.25 : ( ~ (v4 = v3) & apply(v0, v4, v3) = 0 & apply(v0, v3, v4) = 0 & member(v4,
% 17.11/3.25 v1) = 0 & member(v3, v1) = 0 & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4:
% 17.11/3.25 int] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0 &
% 17.11/3.25 $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (order(v0, v1) = 0) | ~ $i(v1)
% 17.11/3.25 | ~ $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5
% 17.11/3.25 = 0 | ~ (apply(v0, v2, v4) = v5) | ~ (apply(v0, v2, v3) = 0) | ~
% 17.11/3.25 $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any] : ? [v8:
% 17.11/3.25 any] : ? [v9: any] : (apply(v0, v3, v4) = v9 & member(v4, v1) = v8 &
% 17.11/3.25 member(v3, v1) = v7 & member(v2, v1) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0)
% 17.11/3.25 | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v2: $i] : ! [v3: $i] : (v3 =
% 17.11/3.25 v2 | ~ (apply(v0, v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v4: any] :
% 17.11/3.25 ? [v5: any] : ? [v6: any] : (apply(v0, v3, v2) = v6 & member(v3, v1) =
% 17.11/3.25 v5 & member(v2, v1) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))
% 17.11/3.25 & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apply(v0, v2, v2) = v3) | ~
% 17.11/3.25 $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) = v4))))
% 17.11/3.25
% 17.11/3.25 (thIV8)
% 17.11/3.26 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 17.11/3.26 int] : ( ~ (v5 = 0) & greatest_lower_bound(v2, v4, v0, v1) = v5 & order(v0,
% 17.11/3.26 v1) = 0 & apply(v0, v2, v3) = 0 & unordered_pair(v2, v3) = v4 & member(v3,
% 17.11/3.26 v1) = 0 & member(v2, v1) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 17.11/3.26
% 17.11/3.26 (unordered_pair)
% 17.11/3.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 17.11/3.26 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) |
% 17.11/3.26 ~ $i(v1) | ~ $i(v0) | ( ~ (v2 = v0) & ~ (v1 = v0))) & ! [v0: $i] : !
% 17.11/3.26 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | v1 = v0 | ~
% 17.11/3.26 (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~
% 17.11/3.26 $i(v1) | ~ $i(v0))
% 17.11/3.26
% 17.11/3.26 (function-axioms)
% 17.11/3.27 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 17.11/3.27 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (greatest_lower_bound(v5,
% 17.11/3.27 v4, v3, v2) = v1) | ~ (greatest_lower_bound(v5, v4, v3, v2) = v0)) & !
% 17.11/3.27 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 17.11/3.27 $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (least_upper_bound(v5, v4,
% 17.11/3.27 v3, v2) = v1) | ~ (least_upper_bound(v5, v4, v3, v2) = v0)) & ! [v0:
% 17.11/3.27 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.11/3.27 : ! [v4: $i] : (v1 = v0 | ~ (min(v4, v3, v2) = v1) | ~ (min(v4, v3, v2) =
% 17.11/3.27 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 17.11/3.27 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (max(v4, v3, v2) = v1) | ~
% 17.11/3.27 (max(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 17.11/3.27 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 17.11/3.27 (least(v4, v3, v2) = v1) | ~ (least(v4, v3, v2) = v0)) & ! [v0:
% 17.11/3.27 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.11/3.27 : ! [v4: $i] : (v1 = v0 | ~ (greatest(v4, v3, v2) = v1) | ~ (greatest(v4,
% 17.11/3.27 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 17.11/3.27 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (lower_bound(v4, v3,
% 17.11/3.27 v2) = v1) | ~ (lower_bound(v4, v3, v2) = v0)) & ! [v0:
% 17.11/3.27 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.11/3.27 : ! [v4: $i] : (v1 = v0 | ~ (upper_bound(v4, v3, v2) = v1) | ~
% 17.11/3.27 (upper_bound(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 17.11/3.27 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 17.11/3.27 (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0:
% 17.11/3.27 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.11/3.27 : (v1 = v0 | ~ (total_order(v3, v2) = v1) | ~ (total_order(v3, v2) = v0)) &
% 17.11/3.27 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 17.11/3.27 $i] : (v1 = v0 | ~ (order(v3, v2) = v1) | ~ (order(v3, v2) = v0)) & !
% 17.11/3.27 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.11/3.27 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 17.11/3.27 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.11/3.27 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 17.11/3.27 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 17.11/3.27 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 17.11/3.27 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 17.11/3.27 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 17.11/3.27 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 17.11/3.27 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 17.11/3.27 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 17.11/3.27 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 17.11/3.27 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.11/3.27 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 17.11/3.27 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 17.11/3.27 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 17.11/3.27 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 17.11/3.27 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 17.11/3.27 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 17.11/3.27 (power_set(v2) = v0))
% 17.11/3.27
% 17.11/3.27 Further assumptions not needed in the proof:
% 17.11/3.27 --------------------------------------------
% 17.11/3.28 difference, empty_set, equal_set, greatest, intersection, least,
% 17.11/3.28 least_upper_bound, max, min, power_set, product, singleton, subset, sum,
% 17.11/3.28 total_order, union, upper_bound
% 17.11/3.28
% 17.11/3.28 Those formulas are unsatisfiable:
% 17.11/3.28 ---------------------------------
% 17.11/3.28
% 17.11/3.28 Begin of proof
% 17.11/3.28 |
% 17.11/3.28 | ALPHA: (unordered_pair) implies:
% 17.11/3.28 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | v1 =
% 17.11/3.28 | v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~
% 17.11/3.28 | $i(v2) | ~ $i(v1) | ~ $i(v0))
% 17.11/3.28 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 17.11/3.28 | (v4 = 0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = v4) |
% 17.11/3.28 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ~ (v2 = v0) & ~ (v1 = v0)))
% 17.11/3.28 |
% 17.11/3.28 | ALPHA: (order) implies:
% 17.11/3.29 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (order(v0, v1) = 0) | ~ $i(v1) | ~
% 17.11/3.29 | $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] :
% 17.11/3.29 | (v5 = 0 | ~ (apply(v0, v2, v4) = v5) | ~ (apply(v0, v2, v3) = 0)
% 17.11/3.29 | | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any]
% 17.11/3.29 | : ? [v8: any] : ? [v9: any] : (apply(v0, v3, v4) = v9 &
% 17.11/3.29 | member(v4, v1) = v8 & member(v3, v1) = v7 & member(v2, v1) = v6
% 17.11/3.29 | & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) &
% 17.11/3.29 | ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ (apply(v0, v2, v3) = 0) |
% 17.11/3.29 | ~ $i(v3) | ~ $i(v2) | ? [v4: any] : ? [v5: any] : ? [v6: any]
% 17.11/3.29 | : (apply(v0, v3, v2) = v6 & member(v3, v1) = v5 & member(v2, v1)
% 17.11/3.29 | = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v2:
% 17.11/3.29 | $i] : ! [v3: int] : (v3 = 0 | ~ (apply(v0, v2, v2) = v3) | ~
% 17.11/3.29 | $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) = v4))))
% 17.11/3.29 |
% 17.11/3.29 | ALPHA: (lower_bound) implies:
% 17.11/3.29 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (lower_bound(v2, v0, v1)
% 17.11/3.29 | = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ! [v4:
% 17.11/3.29 | int] : (v4 = 0 | ~ (apply(v0, v2, v3) = v4) | ~ $i(v3) | ? [v5:
% 17.11/3.29 | int] : ( ~ (v5 = 0) & member(v3, v1) = v5)))
% 17.11/3.29 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 17.11/3.29 | (lower_bound(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 17.11/3.29 | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & apply(v0, v2, v4) = v5 &
% 17.11/3.29 | member(v4, v1) = 0 & $i(v4)))
% 17.11/3.29 |
% 17.11/3.29 | ALPHA: (greatest_lower_bound) implies:
% 17.11/3.29 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 17.11/3.29 | (v4 = 0 | ~ (greatest_lower_bound(v0, v1, v2, v3) = v4) | ~ $i(v3) |
% 17.11/3.29 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: int] : ( ~
% 17.11/3.29 | (v6 = 0) & lower_bound(v5, v2, v1) = 0 & apply(v2, v5, v0) = v6 &
% 17.11/3.29 | member(v5, v3) = 0 & $i(v5)) | ? [v5: any] : ? [v6: any] :
% 17.11/3.29 | (lower_bound(v0, v2, v1) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) |
% 17.11/3.29 | ~ (v5 = 0))))
% 17.11/3.29 |
% 17.11/3.29 | ALPHA: (function-axioms) implies:
% 17.11/3.30 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 17.11/3.30 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 17.11/3.30 | = v0))
% 17.11/3.30 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 17.11/3.30 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~
% 17.11/3.30 | (apply(v4, v3, v2) = v0))
% 17.11/3.30 |
% 17.11/3.30 | DELTA: instantiating (thIV8) with fresh symbols all_25_0, all_25_1, all_25_2,
% 17.11/3.30 | all_25_3, all_25_4, all_25_5 gives:
% 17.11/3.30 | (9) ~ (all_25_0 = 0) & greatest_lower_bound(all_25_3, all_25_1, all_25_5,
% 17.11/3.30 | all_25_4) = all_25_0 & order(all_25_5, all_25_4) = 0 &
% 17.11/3.30 | apply(all_25_5, all_25_3, all_25_2) = 0 & unordered_pair(all_25_3,
% 17.11/3.30 | all_25_2) = all_25_1 & member(all_25_2, all_25_4) = 0 &
% 17.11/3.30 | member(all_25_3, all_25_4) = 0 & $i(all_25_1) & $i(all_25_2) &
% 17.11/3.30 | $i(all_25_3) & $i(all_25_4) & $i(all_25_5)
% 17.11/3.30 |
% 17.11/3.30 | ALPHA: (9) implies:
% 17.11/3.30 | (10) ~ (all_25_0 = 0)
% 17.11/3.30 | (11) $i(all_25_5)
% 17.11/3.30 | (12) $i(all_25_4)
% 17.11/3.30 | (13) $i(all_25_3)
% 17.11/3.30 | (14) $i(all_25_2)
% 17.11/3.30 | (15) $i(all_25_1)
% 17.11/3.30 | (16) member(all_25_3, all_25_4) = 0
% 17.11/3.30 | (17) unordered_pair(all_25_3, all_25_2) = all_25_1
% 17.11/3.30 | (18) apply(all_25_5, all_25_3, all_25_2) = 0
% 17.11/3.30 | (19) order(all_25_5, all_25_4) = 0
% 17.11/3.30 | (20) greatest_lower_bound(all_25_3, all_25_1, all_25_5, all_25_4) =
% 17.11/3.30 | all_25_0
% 17.11/3.30 |
% 17.11/3.31 | GROUND_INST: instantiating (3) with all_25_5, all_25_4, simplifying with (11),
% 17.11/3.31 | (12), (19) gives:
% 17.56/3.31 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 17.56/3.31 | (apply(all_25_5, v0, v2) = v3) | ~ (apply(all_25_5, v0, v1) = 0) |
% 17.56/3.31 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ?
% 17.56/3.31 | [v6: any] : ? [v7: any] : (apply(all_25_5, v1, v2) = v7 &
% 17.56/3.31 | member(v2, all_25_4) = v6 & member(v1, all_25_4) = v5 & member(v0,
% 17.56/3.31 | all_25_4) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~
% 17.56/3.31 | (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~
% 17.56/3.31 | (apply(all_25_5, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any]
% 17.56/3.31 | : ? [v3: any] : ? [v4: any] : (apply(all_25_5, v1, v0) = v4 &
% 17.56/3.31 | member(v1, all_25_4) = v3 & member(v0, all_25_4) = v2 & ( ~ (v4 =
% 17.56/3.31 | 0) | ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: int]
% 17.56/3.31 | : (v1 = 0 | ~ (apply(all_25_5, v0, v0) = v1) | ~ $i(v0) | ? [v2:
% 17.56/3.31 | int] : ( ~ (v2 = 0) & member(v0, all_25_4) = v2))
% 17.56/3.31 |
% 17.56/3.31 | ALPHA: (21) implies:
% 17.56/3.31 | (22) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (apply(all_25_5, v0, v0) =
% 17.56/3.31 | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & member(v0,
% 17.56/3.31 | all_25_4) = v2))
% 17.56/3.31 | (23) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (apply(all_25_5, v0, v1) =
% 17.56/3.31 | 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4:
% 17.56/3.31 | any] : (apply(all_25_5, v1, v0) = v4 & member(v1, all_25_4) = v3 &
% 17.56/3.31 | member(v0, all_25_4) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 =
% 17.56/3.31 | 0))))
% 17.56/3.32 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 17.56/3.32 | (apply(all_25_5, v0, v2) = v3) | ~ (apply(all_25_5, v0, v1) = 0) |
% 17.56/3.32 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ?
% 17.56/3.32 | [v6: any] : ? [v7: any] : (apply(all_25_5, v1, v2) = v7 &
% 17.56/3.32 | member(v2, all_25_4) = v6 & member(v1, all_25_4) = v5 & member(v0,
% 17.56/3.32 | all_25_4) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~
% 17.56/3.32 | (v4 = 0))))
% 17.56/3.32 |
% 17.56/3.32 | GROUND_INST: instantiating (6) with all_25_3, all_25_1, all_25_5, all_25_4,
% 17.56/3.32 | all_25_0, simplifying with (11), (12), (13), (15), (20) gives:
% 17.56/3.32 | (25) all_25_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 17.56/3.32 | lower_bound(v0, all_25_5, all_25_1) = 0 & apply(all_25_5, v0,
% 17.56/3.32 | all_25_3) = v1 & member(v0, all_25_4) = 0 & $i(v0)) | ? [v0: any]
% 17.56/3.32 | : ? [v1: any] : (lower_bound(all_25_3, all_25_5, all_25_1) = v1 &
% 17.56/3.32 | member(all_25_3, all_25_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 17.56/3.32 |
% 17.56/3.32 | GROUND_INST: instantiating (23) with all_25_3, all_25_2, simplifying with
% 17.56/3.32 | (13), (14), (18) gives:
% 17.56/3.32 | (26) all_25_2 = all_25_3 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 17.56/3.32 | (apply(all_25_5, all_25_2, all_25_3) = v2 & member(all_25_2, all_25_4)
% 17.56/3.32 | = v1 & member(all_25_3, all_25_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0)
% 17.56/3.32 | | ~ (v0 = 0)))
% 17.56/3.32 |
% 17.56/3.32 | BETA: splitting (25) gives:
% 17.56/3.32 |
% 17.56/3.32 | Case 1:
% 17.56/3.32 | |
% 17.56/3.32 | | (27) all_25_0 = 0
% 17.56/3.32 | |
% 17.56/3.32 | | REDUCE: (10), (27) imply:
% 17.56/3.32 | | (28) $false
% 17.56/3.33 | |
% 17.56/3.33 | | CLOSE: (28) is inconsistent.
% 17.56/3.33 | |
% 17.56/3.33 | Case 2:
% 17.56/3.33 | |
% 17.56/3.33 | | (29) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & lower_bound(v0,
% 17.56/3.33 | | all_25_5, all_25_1) = 0 & apply(all_25_5, v0, all_25_3) = v1 &
% 17.56/3.33 | | member(v0, all_25_4) = 0 & $i(v0)) | ? [v0: any] : ? [v1: any] :
% 17.56/3.33 | | (lower_bound(all_25_3, all_25_5, all_25_1) = v1 & member(all_25_3,
% 17.56/3.33 | | all_25_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 17.56/3.33 | |
% 17.56/3.33 | | BETA: splitting (29) gives:
% 17.56/3.33 | |
% 17.56/3.33 | | Case 1:
% 17.56/3.33 | | |
% 17.56/3.33 | | | (30) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & lower_bound(v0,
% 17.56/3.33 | | | all_25_5, all_25_1) = 0 & apply(all_25_5, v0, all_25_3) = v1 &
% 17.56/3.33 | | | member(v0, all_25_4) = 0 & $i(v0))
% 17.56/3.33 | | |
% 17.56/3.33 | | | DELTA: instantiating (30) with fresh symbols all_43_0, all_43_1 gives:
% 17.56/3.33 | | | (31) ~ (all_43_0 = 0) & lower_bound(all_43_1, all_25_5, all_25_1) = 0
% 17.56/3.33 | | | & apply(all_25_5, all_43_1, all_25_3) = all_43_0 &
% 17.56/3.33 | | | member(all_43_1, all_25_4) = 0 & $i(all_43_1)
% 17.56/3.33 | | |
% 17.56/3.33 | | | ALPHA: (31) implies:
% 17.56/3.33 | | | (32) ~ (all_43_0 = 0)
% 17.56/3.33 | | | (33) $i(all_43_1)
% 17.56/3.33 | | | (34) apply(all_25_5, all_43_1, all_25_3) = all_43_0
% 17.56/3.33 | | | (35) lower_bound(all_43_1, all_25_5, all_25_1) = 0
% 17.56/3.33 | | |
% 17.56/3.33 | | | GROUND_INST: instantiating (4) with all_25_5, all_25_1, all_43_1,
% 17.56/3.33 | | | simplifying with (11), (15), (33), (35) gives:
% 17.56/3.33 | | | (36) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (apply(all_25_5,
% 17.56/3.33 | | | all_43_1, v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 =
% 17.56/3.33 | | | 0) & member(v0, all_25_1) = v2))
% 17.56/3.33 | | |
% 17.56/3.33 | | | GROUND_INST: instantiating (36) with all_25_3, all_43_0, simplifying with
% 17.56/3.33 | | | (13), (34) gives:
% 17.56/3.33 | | | (37) all_43_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_25_3,
% 17.56/3.33 | | | all_25_1) = v0)
% 17.56/3.33 | | |
% 17.56/3.33 | | | BETA: splitting (37) gives:
% 17.56/3.33 | | |
% 17.56/3.33 | | | Case 1:
% 17.56/3.33 | | | |
% 17.56/3.33 | | | | (38) all_43_0 = 0
% 17.56/3.33 | | | |
% 17.56/3.33 | | | | REDUCE: (32), (38) imply:
% 17.56/3.33 | | | | (39) $false
% 17.56/3.33 | | | |
% 17.56/3.33 | | | | CLOSE: (39) is inconsistent.
% 17.56/3.33 | | | |
% 17.56/3.34 | | | Case 2:
% 17.56/3.34 | | | |
% 17.56/3.34 | | | | (40) ? [v0: int] : ( ~ (v0 = 0) & member(all_25_3, all_25_1) = v0)
% 17.56/3.34 | | | |
% 17.56/3.34 | | | | DELTA: instantiating (40) with fresh symbol all_61_0 gives:
% 17.56/3.34 | | | | (41) ~ (all_61_0 = 0) & member(all_25_3, all_25_1) = all_61_0
% 17.56/3.34 | | | |
% 17.56/3.34 | | | | ALPHA: (41) implies:
% 17.56/3.34 | | | | (42) ~ (all_61_0 = 0)
% 17.56/3.34 | | | | (43) member(all_25_3, all_25_1) = all_61_0
% 17.56/3.34 | | | |
% 17.56/3.34 | | | | GROUND_INST: instantiating (2) with all_25_3, all_25_3, all_25_2,
% 17.56/3.34 | | | | all_25_1, all_61_0, simplifying with (13), (14), (17), (43)
% 17.56/3.34 | | | | gives:
% 17.56/3.34 | | | | (44) all_61_0 = 0
% 17.56/3.34 | | | |
% 17.56/3.34 | | | | REDUCE: (42), (44) imply:
% 17.56/3.34 | | | | (45) $false
% 17.56/3.34 | | | |
% 17.56/3.34 | | | | CLOSE: (45) is inconsistent.
% 17.56/3.34 | | | |
% 17.56/3.34 | | | End of split
% 17.56/3.34 | | |
% 17.56/3.34 | | Case 2:
% 17.56/3.34 | | |
% 17.56/3.34 | | | (46) ? [v0: any] : ? [v1: any] : (lower_bound(all_25_3, all_25_5,
% 17.56/3.34 | | | all_25_1) = v1 & member(all_25_3, all_25_1) = v0 & ( ~ (v1 =
% 17.56/3.34 | | | 0) | ~ (v0 = 0)))
% 17.56/3.34 | | |
% 17.56/3.34 | | | DELTA: instantiating (46) with fresh symbols all_43_0, all_43_1 gives:
% 17.56/3.34 | | | (47) lower_bound(all_25_3, all_25_5, all_25_1) = all_43_0 &
% 17.56/3.34 | | | member(all_25_3, all_25_1) = all_43_1 & ( ~ (all_43_0 = 0) | ~
% 17.56/3.34 | | | (all_43_1 = 0))
% 17.56/3.34 | | |
% 17.56/3.34 | | | ALPHA: (47) implies:
% 17.56/3.34 | | | (48) member(all_25_3, all_25_1) = all_43_1
% 17.56/3.34 | | | (49) lower_bound(all_25_3, all_25_5, all_25_1) = all_43_0
% 17.56/3.34 | | | (50) ~ (all_43_0 = 0) | ~ (all_43_1 = 0)
% 17.56/3.34 | | |
% 17.56/3.35 | | | GROUND_INST: instantiating (2) with all_25_3, all_25_3, all_25_2,
% 17.56/3.35 | | | all_25_1, all_43_1, simplifying with (13), (14), (17), (48)
% 17.56/3.35 | | | gives:
% 17.56/3.35 | | | (51) all_43_1 = 0
% 17.56/3.35 | | |
% 17.56/3.35 | | | GROUND_INST: instantiating (5) with all_25_5, all_25_1, all_25_3,
% 17.56/3.35 | | | all_43_0, simplifying with (11), (13), (15), (49) gives:
% 17.56/3.35 | | | (52) all_43_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 17.56/3.35 | | | apply(all_25_5, all_25_3, v0) = v1 & member(v0, all_25_1) = 0 &
% 17.56/3.35 | | | $i(v0))
% 17.56/3.35 | | |
% 17.56/3.35 | | | BETA: splitting (50) gives:
% 17.56/3.35 | | |
% 17.56/3.35 | | | Case 1:
% 17.56/3.35 | | | |
% 17.56/3.35 | | | | (53) ~ (all_43_0 = 0)
% 17.56/3.35 | | | |
% 17.56/3.35 | | | | BETA: splitting (52) gives:
% 17.56/3.35 | | | |
% 17.56/3.35 | | | | Case 1:
% 17.56/3.35 | | | | |
% 17.56/3.35 | | | | | (54) all_43_0 = 0
% 17.56/3.35 | | | | |
% 17.56/3.35 | | | | | REDUCE: (53), (54) imply:
% 17.56/3.35 | | | | | (55) $false
% 17.56/3.35 | | | | |
% 17.56/3.35 | | | | | CLOSE: (55) is inconsistent.
% 17.56/3.35 | | | | |
% 17.56/3.35 | | | | Case 2:
% 17.56/3.35 | | | | |
% 17.56/3.35 | | | | | (56) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & apply(all_25_5,
% 17.56/3.35 | | | | | all_25_3, v0) = v1 & member(v0, all_25_1) = 0 & $i(v0))
% 17.56/3.35 | | | | |
% 17.56/3.35 | | | | | DELTA: instantiating (56) with fresh symbols all_59_0, all_59_1 gives:
% 17.56/3.35 | | | | | (57) ~ (all_59_0 = 0) & apply(all_25_5, all_25_3, all_59_1) =
% 17.56/3.35 | | | | | all_59_0 & member(all_59_1, all_25_1) = 0 & $i(all_59_1)
% 17.56/3.35 | | | | |
% 17.56/3.35 | | | | | ALPHA: (57) implies:
% 17.56/3.35 | | | | | (58) ~ (all_59_0 = 0)
% 17.56/3.35 | | | | | (59) $i(all_59_1)
% 17.56/3.35 | | | | | (60) member(all_59_1, all_25_1) = 0
% 17.56/3.35 | | | | | (61) apply(all_25_5, all_25_3, all_59_1) = all_59_0
% 17.56/3.35 | | | | |
% 17.56/3.35 | | | | | GROUND_INST: instantiating (1) with all_59_1, all_25_3, all_25_2,
% 17.56/3.35 | | | | | all_25_1, simplifying with (13), (14), (17), (59), (60)
% 17.56/3.35 | | | | | gives:
% 17.56/3.35 | | | | | (62) all_59_1 = all_25_2 | all_59_1 = all_25_3
% 17.56/3.35 | | | | |
% 17.56/3.35 | | | | | GROUND_INST: instantiating (24) with all_25_3, all_25_2, all_59_1,
% 17.56/3.35 | | | | | all_59_0, simplifying with (13), (14), (18), (59), (61)
% 17.56/3.35 | | | | | gives:
% 17.56/3.35 | | | | | (63) all_59_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 17.56/3.35 | | | | | [v3: any] : (apply(all_25_5, all_25_2, all_59_1) = v3 &
% 17.56/3.35 | | | | | member(all_59_1, all_25_4) = v2 & member(all_25_2, all_25_4)
% 17.56/3.35 | | | | | = v1 & member(all_25_3, all_25_4) = v0 & ( ~ (v3 = 0) | ~
% 17.56/3.35 | | | | | (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 17.56/3.35 | | | | |
% 17.56/3.35 | | | | | BETA: splitting (26) gives:
% 17.56/3.35 | | | | |
% 17.56/3.36 | | | | | Case 1:
% 17.56/3.36 | | | | | |
% 17.56/3.36 | | | | | | (64) all_25_2 = all_25_3
% 17.56/3.36 | | | | | |
% 17.56/3.36 | | | | | | REDUCE: (18), (64) imply:
% 17.56/3.36 | | | | | | (65) apply(all_25_5, all_25_3, all_25_3) = 0
% 17.56/3.36 | | | | | |
% 17.56/3.36 | | | | | | BETA: splitting (62) gives:
% 17.56/3.36 | | | | | |
% 17.56/3.36 | | | | | | Case 1:
% 17.56/3.36 | | | | | | |
% 17.56/3.36 | | | | | | | (66) all_59_1 = all_25_2
% 17.56/3.36 | | | | | | |
% 17.56/3.36 | | | | | | | COMBINE_EQS: (64), (66) imply:
% 17.56/3.36 | | | | | | | (67) all_59_1 = all_25_3
% 17.56/3.36 | | | | | | |
% 17.56/3.36 | | | | | | | REDUCE: (61), (67) imply:
% 17.56/3.36 | | | | | | | (68) apply(all_25_5, all_25_3, all_25_3) = all_59_0
% 17.56/3.36 | | | | | | |
% 17.56/3.36 | | | | | | | BETA: splitting (63) gives:
% 17.56/3.36 | | | | | | |
% 17.56/3.36 | | | | | | | Case 1:
% 17.56/3.36 | | | | | | | |
% 17.56/3.36 | | | | | | | | (69) all_59_0 = 0
% 17.56/3.36 | | | | | | | |
% 17.56/3.36 | | | | | | | | REDUCE: (58), (69) imply:
% 17.56/3.36 | | | | | | | | (70) $false
% 17.56/3.36 | | | | | | | |
% 17.56/3.36 | | | | | | | | CLOSE: (70) is inconsistent.
% 17.56/3.36 | | | | | | | |
% 17.56/3.36 | | | | | | | Case 2:
% 17.56/3.36 | | | | | | | |
% 17.56/3.36 | | | | | | | | (71) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3:
% 17.56/3.36 | | | | | | | | any] : (apply(all_25_5, all_25_2, all_59_1) = v3 &
% 17.56/3.36 | | | | | | | | member(all_59_1, all_25_4) = v2 & member(all_25_2,
% 17.56/3.36 | | | | | | | | all_25_4) = v1 & member(all_25_3, all_25_4) = v0 & (
% 17.56/3.36 | | | | | | | | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 17.56/3.36 | | | | | | | | 0)))
% 17.56/3.36 | | | | | | | |
% 17.56/3.36 | | | | | | | | DELTA: instantiating (71) with fresh symbols all_75_0, all_75_1,
% 17.56/3.36 | | | | | | | | all_75_2, all_75_3 gives:
% 17.56/3.36 | | | | | | | | (72) apply(all_25_5, all_25_2, all_59_1) = all_75_0 &
% 17.56/3.36 | | | | | | | | member(all_59_1, all_25_4) = all_75_1 & member(all_25_2,
% 17.56/3.36 | | | | | | | | all_25_4) = all_75_2 & member(all_25_3, all_25_4) =
% 17.56/3.36 | | | | | | | | all_75_3 & ( ~ (all_75_0 = 0) | ~ (all_75_1 = 0) | ~
% 17.56/3.36 | | | | | | | | (all_75_2 = 0) | ~ (all_75_3 = 0))
% 17.56/3.36 | | | | | | | |
% 17.56/3.36 | | | | | | | | ALPHA: (72) implies:
% 17.56/3.36 | | | | | | | | (73) apply(all_25_5, all_25_2, all_59_1) = all_75_0
% 17.56/3.36 | | | | | | | |
% 17.56/3.36 | | | | | | | | REDUCE: (64), (67), (73) imply:
% 17.56/3.36 | | | | | | | | (74) apply(all_25_5, all_25_3, all_25_3) = all_75_0
% 17.56/3.36 | | | | | | | |
% 17.56/3.36 | | | | | | | | GROUND_INST: instantiating (8) with all_59_0, all_75_0,
% 17.56/3.36 | | | | | | | | all_25_3, all_25_3, all_25_5, simplifying with
% 17.56/3.36 | | | | | | | | (68), (74) gives:
% 17.56/3.36 | | | | | | | | (75) all_75_0 = all_59_0
% 17.56/3.36 | | | | | | | |
% 17.56/3.36 | | | | | | | | GROUND_INST: instantiating (8) with 0, all_75_0, all_25_3,
% 17.56/3.36 | | | | | | | | all_25_3, all_25_5, simplifying with (65), (74)
% 17.56/3.36 | | | | | | | | gives:
% 17.56/3.36 | | | | | | | | (76) all_75_0 = 0
% 17.56/3.36 | | | | | | | |
% 17.56/3.36 | | | | | | | | COMBINE_EQS: (75), (76) imply:
% 17.56/3.36 | | | | | | | | (77) all_59_0 = 0
% 17.56/3.36 | | | | | | | |
% 17.56/3.36 | | | | | | | | SIMP: (77) implies:
% 17.56/3.36 | | | | | | | | (78) all_59_0 = 0
% 17.56/3.36 | | | | | | | |
% 17.56/3.36 | | | | | | | | REDUCE: (58), (78) imply:
% 17.56/3.36 | | | | | | | | (79) $false
% 17.56/3.36 | | | | | | | |
% 17.56/3.36 | | | | | | | | CLOSE: (79) is inconsistent.
% 17.56/3.36 | | | | | | | |
% 17.56/3.36 | | | | | | | End of split
% 17.56/3.36 | | | | | | |
% 17.56/3.36 | | | | | | Case 2:
% 17.56/3.36 | | | | | | |
% 17.56/3.36 | | | | | | | (80) all_59_1 = all_25_3
% 17.56/3.36 | | | | | | | (81) ~ (all_59_1 = all_25_2)
% 17.56/3.36 | | | | | | |
% 17.56/3.36 | | | | | | | REDUCE: (64), (80), (81) imply:
% 17.56/3.36 | | | | | | | (82) $false
% 17.56/3.36 | | | | | | |
% 17.56/3.36 | | | | | | | CLOSE: (82) is inconsistent.
% 17.56/3.36 | | | | | | |
% 17.56/3.36 | | | | | | End of split
% 17.56/3.36 | | | | | |
% 17.56/3.36 | | | | | Case 2:
% 17.56/3.36 | | | | | |
% 17.56/3.37 | | | | | | (83) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 17.56/3.37 | | | | | | (apply(all_25_5, all_25_2, all_25_3) = v2 & member(all_25_2,
% 17.56/3.37 | | | | | | all_25_4) = v1 & member(all_25_3, all_25_4) = v0 & ( ~
% 17.56/3.37 | | | | | | (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 17.56/3.37 | | | | | |
% 17.56/3.37 | | | | | | DELTA: instantiating (83) with fresh symbols all_68_0, all_68_1,
% 17.56/3.37 | | | | | | all_68_2 gives:
% 17.56/3.37 | | | | | | (84) apply(all_25_5, all_25_2, all_25_3) = all_68_0 &
% 17.56/3.37 | | | | | | member(all_25_2, all_25_4) = all_68_1 & member(all_25_3,
% 17.56/3.37 | | | | | | all_25_4) = all_68_2 & ( ~ (all_68_0 = 0) | ~ (all_68_1 =
% 17.56/3.37 | | | | | | 0) | ~ (all_68_2 = 0))
% 17.56/3.37 | | | | | |
% 17.56/3.37 | | | | | | ALPHA: (84) implies:
% 17.56/3.37 | | | | | | (85) member(all_25_3, all_25_4) = all_68_2
% 17.56/3.37 | | | | | |
% 17.56/3.37 | | | | | | BETA: splitting (63) gives:
% 17.56/3.37 | | | | | |
% 17.56/3.37 | | | | | | Case 1:
% 17.56/3.37 | | | | | | |
% 17.56/3.37 | | | | | | | (86) all_59_0 = 0
% 17.56/3.37 | | | | | | |
% 17.56/3.37 | | | | | | | REDUCE: (58), (86) imply:
% 17.56/3.37 | | | | | | | (87) $false
% 17.56/3.37 | | | | | | |
% 17.56/3.37 | | | | | | | CLOSE: (87) is inconsistent.
% 17.56/3.37 | | | | | | |
% 17.56/3.37 | | | | | | Case 2:
% 17.56/3.37 | | | | | | |
% 17.56/3.37 | | | | | | | (88) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any]
% 17.56/3.37 | | | | | | | : (apply(all_25_5, all_25_2, all_59_1) = v3 &
% 17.56/3.37 | | | | | | | member(all_59_1, all_25_4) = v2 & member(all_25_2,
% 17.56/3.37 | | | | | | | all_25_4) = v1 & member(all_25_3, all_25_4) = v0 & ( ~
% 17.56/3.37 | | | | | | | (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 17.56/3.37 | | | | | | |
% 17.56/3.37 | | | | | | | DELTA: instantiating (88) with fresh symbols all_74_0, all_74_1,
% 17.56/3.37 | | | | | | | all_74_2, all_74_3 gives:
% 17.56/3.37 | | | | | | | (89) apply(all_25_5, all_25_2, all_59_1) = all_74_0 &
% 17.56/3.37 | | | | | | | member(all_59_1, all_25_4) = all_74_1 & member(all_25_2,
% 17.56/3.37 | | | | | | | all_25_4) = all_74_2 & member(all_25_3, all_25_4) =
% 17.56/3.37 | | | | | | | all_74_3 & ( ~ (all_74_0 = 0) | ~ (all_74_1 = 0) | ~
% 17.56/3.37 | | | | | | | (all_74_2 = 0) | ~ (all_74_3 = 0))
% 17.56/3.37 | | | | | | |
% 17.56/3.37 | | | | | | | ALPHA: (89) implies:
% 17.56/3.37 | | | | | | | (90) member(all_25_3, all_25_4) = all_74_3
% 17.56/3.37 | | | | | | | (91) member(all_59_1, all_25_4) = all_74_1
% 17.56/3.37 | | | | | | |
% 17.56/3.37 | | | | | | | GROUND_INST: instantiating (7) with 0, all_74_3, all_25_4,
% 17.56/3.37 | | | | | | | all_25_3, simplifying with (16), (90) gives:
% 17.56/3.37 | | | | | | | (92) all_74_3 = 0
% 17.56/3.37 | | | | | | |
% 17.56/3.37 | | | | | | | GROUND_INST: instantiating (7) with all_68_2, all_74_3, all_25_4,
% 17.56/3.37 | | | | | | | all_25_3, simplifying with (85), (90) gives:
% 17.56/3.37 | | | | | | | (93) all_74_3 = all_68_2
% 17.56/3.37 | | | | | | |
% 17.56/3.37 | | | | | | | COMBINE_EQS: (92), (93) imply:
% 17.56/3.37 | | | | | | | (94) all_68_2 = 0
% 17.56/3.37 | | | | | | |
% 17.56/3.37 | | | | | | | BETA: splitting (62) gives:
% 17.56/3.37 | | | | | | |
% 17.56/3.37 | | | | | | | Case 1:
% 17.56/3.37 | | | | | | | |
% 17.56/3.37 | | | | | | | | (95) all_59_1 = all_25_2
% 17.56/3.37 | | | | | | | |
% 17.56/3.37 | | | | | | | | REDUCE: (61), (95) imply:
% 17.56/3.37 | | | | | | | | (96) apply(all_25_5, all_25_3, all_25_2) = all_59_0
% 17.56/3.37 | | | | | | | |
% 17.56/3.37 | | | | | | | | GROUND_INST: instantiating (8) with 0, all_59_0, all_25_2,
% 17.56/3.37 | | | | | | | | all_25_3, all_25_5, simplifying with (18), (96)
% 17.56/3.37 | | | | | | | | gives:
% 17.56/3.37 | | | | | | | | (97) all_59_0 = 0
% 17.56/3.37 | | | | | | | |
% 17.56/3.37 | | | | | | | | REDUCE: (58), (97) imply:
% 17.56/3.37 | | | | | | | | (98) $false
% 17.56/3.37 | | | | | | | |
% 17.56/3.37 | | | | | | | | CLOSE: (98) is inconsistent.
% 17.56/3.37 | | | | | | | |
% 17.56/3.37 | | | | | | | Case 2:
% 17.56/3.37 | | | | | | | |
% 17.56/3.37 | | | | | | | | (99) all_59_1 = all_25_3
% 17.56/3.38 | | | | | | | |
% 17.56/3.38 | | | | | | | | REDUCE: (61), (99) imply:
% 17.56/3.38 | | | | | | | | (100) apply(all_25_5, all_25_3, all_25_3) = all_59_0
% 17.56/3.38 | | | | | | | |
% 17.56/3.38 | | | | | | | | REDUCE: (91), (99) imply:
% 17.56/3.38 | | | | | | | | (101) member(all_25_3, all_25_4) = all_74_1
% 17.56/3.38 | | | | | | | |
% 17.56/3.38 | | | | | | | | GROUND_INST: instantiating (7) with 0, all_74_1, all_25_4,
% 17.56/3.38 | | | | | | | | all_25_3, simplifying with (16), (101) gives:
% 17.56/3.38 | | | | | | | | (102) all_74_1 = 0
% 17.56/3.38 | | | | | | | |
% 17.56/3.38 | | | | | | | | GROUND_INST: instantiating (22) with all_25_3, all_59_0,
% 17.56/3.38 | | | | | | | | simplifying with (13), (100) gives:
% 17.56/3.38 | | | | | | | | (103) all_59_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 17.56/3.38 | | | | | | | | member(all_25_3, all_25_4) = v0)
% 17.56/3.38 | | | | | | | |
% 17.56/3.38 | | | | | | | | BETA: splitting (103) gives:
% 17.56/3.38 | | | | | | | |
% 17.56/3.38 | | | | | | | | Case 1:
% 17.56/3.38 | | | | | | | | |
% 17.56/3.38 | | | | | | | | | (104) all_59_0 = 0
% 17.56/3.38 | | | | | | | | |
% 17.56/3.38 | | | | | | | | | REDUCE: (58), (104) imply:
% 17.56/3.38 | | | | | | | | | (105) $false
% 17.56/3.38 | | | | | | | | |
% 17.56/3.38 | | | | | | | | | CLOSE: (105) is inconsistent.
% 17.56/3.38 | | | | | | | | |
% 17.56/3.38 | | | | | | | | Case 2:
% 17.56/3.38 | | | | | | | | |
% 17.56/3.38 | | | | | | | | | (106) ? [v0: int] : ( ~ (v0 = 0) & member(all_25_3,
% 17.56/3.38 | | | | | | | | | all_25_4) = v0)
% 17.56/3.38 | | | | | | | | |
% 17.56/3.38 | | | | | | | | | DELTA: instantiating (106) with fresh symbol all_102_0 gives:
% 17.56/3.38 | | | | | | | | | (107) ~ (all_102_0 = 0) & member(all_25_3, all_25_4) =
% 17.56/3.38 | | | | | | | | | all_102_0
% 17.56/3.38 | | | | | | | | |
% 17.56/3.38 | | | | | | | | | ALPHA: (107) implies:
% 17.56/3.38 | | | | | | | | | (108) ~ (all_102_0 = 0)
% 17.56/3.38 | | | | | | | | | (109) member(all_25_3, all_25_4) = all_102_0
% 17.56/3.38 | | | | | | | | |
% 17.56/3.38 | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_102_0, all_25_4,
% 17.56/3.38 | | | | | | | | | all_25_3, simplifying with (16), (109) gives:
% 17.56/3.38 | | | | | | | | | (110) all_102_0 = 0
% 17.56/3.38 | | | | | | | | |
% 17.56/3.38 | | | | | | | | | REDUCE: (108), (110) imply:
% 17.56/3.38 | | | | | | | | | (111) $false
% 17.56/3.38 | | | | | | | | |
% 17.56/3.38 | | | | | | | | | CLOSE: (111) is inconsistent.
% 17.56/3.38 | | | | | | | | |
% 17.56/3.38 | | | | | | | | End of split
% 17.56/3.38 | | | | | | | |
% 17.56/3.38 | | | | | | | End of split
% 17.56/3.38 | | | | | | |
% 17.56/3.38 | | | | | | End of split
% 17.56/3.38 | | | | | |
% 17.56/3.38 | | | | | End of split
% 17.56/3.38 | | | | |
% 17.56/3.38 | | | | End of split
% 17.56/3.38 | | | |
% 17.56/3.38 | | | Case 2:
% 17.56/3.38 | | | |
% 17.56/3.38 | | | | (112) ~ (all_43_1 = 0)
% 17.56/3.38 | | | |
% 17.56/3.38 | | | | REDUCE: (51), (112) imply:
% 17.56/3.38 | | | | (113) $false
% 17.56/3.38 | | | |
% 17.56/3.38 | | | | CLOSE: (113) is inconsistent.
% 17.56/3.38 | | | |
% 17.56/3.38 | | | End of split
% 17.56/3.38 | | |
% 17.56/3.38 | | End of split
% 17.56/3.38 | |
% 17.56/3.38 | End of split
% 17.56/3.38 |
% 17.56/3.38 End of proof
% 17.56/3.38 % SZS output end Proof for theBenchmark
% 17.56/3.38
% 17.56/3.38 2751ms
%------------------------------------------------------------------------------