TSTP Solution File: SEU044+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU044+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n014.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 17:42:23 EDT 2023
% Result : Theorem 45.76s 7.10s
% Output : Proof 100.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU044+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.10/0.32 % Computer : n014.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Wed Aug 23 12:26:49 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.16/0.60 ________ _____
% 0.16/0.60 ___ __ \_________(_)________________________________
% 0.16/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.16/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.16/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.16/0.60
% 0.16/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.16/0.60 (2023-06-19)
% 0.16/0.60
% 0.16/0.60 (c) Philipp Rümmer, 2009-2023
% 0.16/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.16/0.60 Amanda Stjerna.
% 0.16/0.60 Free software under BSD-3-Clause.
% 0.16/0.60
% 0.16/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.16/0.60
% 0.16/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.16/0.62 Running up to 7 provers in parallel.
% 0.16/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.16/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.16/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.16/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.16/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.16/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.16/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.90/1.23 Prover 1: Preprocessing ...
% 2.90/1.23 Prover 4: Preprocessing ...
% 3.06/1.31 Prover 5: Preprocessing ...
% 3.06/1.31 Prover 2: Preprocessing ...
% 3.06/1.32 Prover 3: Preprocessing ...
% 3.06/1.32 Prover 6: Preprocessing ...
% 3.06/1.32 Prover 0: Preprocessing ...
% 7.62/1.96 Prover 1: Warning: ignoring some quantifiers
% 7.62/1.98 Prover 3: Warning: ignoring some quantifiers
% 7.62/2.00 Prover 3: Constructing countermodel ...
% 7.62/2.00 Prover 5: Proving ...
% 7.62/2.01 Prover 6: Proving ...
% 7.62/2.01 Prover 1: Constructing countermodel ...
% 8.83/2.26 Prover 2: Proving ...
% 13.15/2.88 Prover 4: Warning: ignoring some quantifiers
% 13.15/2.94 Prover 4: Constructing countermodel ...
% 15.46/3.10 Prover 0: Proving ...
% 17.37/3.33 Prover 3: gave up
% 17.37/3.34 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 17.73/3.40 Prover 7: Preprocessing ...
% 19.18/3.63 Prover 7: Warning: ignoring some quantifiers
% 19.18/3.66 Prover 7: Constructing countermodel ...
% 20.83/3.78 Prover 1: gave up
% 20.83/3.78 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 21.21/3.82 Prover 8: Preprocessing ...
% 22.28/3.97 Prover 8: Warning: ignoring some quantifiers
% 22.28/3.99 Prover 8: Constructing countermodel ...
% 26.34/4.60 Prover 8: gave up
% 26.34/4.62 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 27.02/4.69 Prover 9: Preprocessing ...
% 32.91/5.45 Prover 9: Warning: ignoring some quantifiers
% 32.91/5.46 Prover 9: Constructing countermodel ...
% 45.76/7.10 Prover 2: proved (6441ms)
% 45.76/7.10
% 45.76/7.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 45.76/7.10
% 45.76/7.11 Prover 5: stopped
% 45.76/7.11 Prover 6: stopped
% 45.76/7.13 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 45.76/7.13 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 45.76/7.13 Prover 9: stopped
% 45.76/7.14 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 45.76/7.14 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 46.15/7.16 Prover 11: Preprocessing ...
% 46.15/7.16 Prover 10: Preprocessing ...
% 46.15/7.19 Prover 13: Preprocessing ...
% 46.15/7.19 Prover 0: stopped
% 46.15/7.20 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 46.15/7.20 Prover 16: Preprocessing ...
% 46.15/7.20 Prover 10: Warning: ignoring some quantifiers
% 46.15/7.20 Prover 10: Constructing countermodel ...
% 46.15/7.23 Prover 19: Preprocessing ...
% 46.15/7.35 Prover 16: Warning: ignoring some quantifiers
% 46.15/7.35 Prover 16: Constructing countermodel ...
% 46.15/7.38 Prover 13: Warning: ignoring some quantifiers
% 46.15/7.39 Prover 13: Constructing countermodel ...
% 47.40/7.45 Prover 19: Warning: ignoring some quantifiers
% 47.40/7.46 Prover 19: Constructing countermodel ...
% 47.40/7.46 Prover 10: gave up
% 48.64/7.57 Prover 11: Warning: ignoring some quantifiers
% 48.64/7.58 Prover 11: Constructing countermodel ...
% 51.82/8.02 Prover 19: gave up
% 79.72/11.66 Prover 13: stopped
% 88.51/12.92 Prover 16: stopped
% 97.85/15.04 Prover 4: Found proof (size 199)
% 97.85/15.04 Prover 4: proved (14406ms)
% 97.85/15.04 Prover 7: stopped
% 97.85/15.06 Prover 11: stopped
% 97.85/15.06
% 97.85/15.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 97.85/15.06
% 98.54/15.09 % SZS output start Proof for theBenchmark
% 98.54/15.10 Assumptions after simplification:
% 98.54/15.10 ---------------------------------
% 98.54/15.10
% 98.54/15.10 (cc2_funct_1)
% 99.01/15.14 ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? [v2:
% 99.01/15.14 any] : ? [v3: any] : ? [v4: any] : (function(v0) = v4 & empty(v0) = v3 &
% 99.01/15.14 relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0))) &
% 99.01/15.14 ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any]
% 99.01/15.14 : ? [v3: any] : (one_to_one(v0) = v3 & empty(v0) = v2 & relation(v0) = v1 &
% 99.01/15.14 ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (empty(v0) = 0)
% 99.01/15.14 | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: any] : (one_to_one(v0) =
% 99.01/15.14 v3 & function(v0) = v2 & relation(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) |
% 99.01/15.14 v3 = 0))) & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1:
% 99.01/15.14 any] : ? [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) =
% 99.01/15.14 v2 & empty(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)))
% 99.01/15.14
% 99.01/15.14 (dt_k8_relat_1)
% 99.01/15.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0,
% 99.01/15.15 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 99.01/15.15 (relation(v2) = v4 & relation(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 99.01/15.15
% 99.01/15.15 (fc5_funct_1)
% 99.01/15.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0,
% 99.01/15.15 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ?
% 99.01/15.15 [v5: any] : ? [v6: any] : (function(v2) = v6 & function(v1) = v4 &
% 99.01/15.15 relation(v2) = v5 & relation(v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 =
% 99.01/15.15 0 & v5 = 0))))
% 99.01/15.15
% 99.01/15.15 (fc5_relat_1)
% 99.01/15.15 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ?
% 99.01/15.15 [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_dom(v0) = v3 & empty(v3)
% 99.01/15.15 = v4 & relation(v0) = v2 & $i(v3) & ( ~ (v4 = 0) | ~ (v2 = 0)))) & !
% 99.01/15.15 [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2:
% 99.01/15.15 any] : ? [v3: any] : ? [v4: any] : (empty(v1) = v4 & empty(v0) = v2 &
% 99.01/15.15 relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) & ! [v0: $i] :
% 99.01/15.15 ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] : ? [v3: any]
% 99.01/15.15 : (relation_dom(v0) = v2 & empty(v2) = v3 & empty(v0) = v1 & $i(v2) & ( ~
% 99.01/15.15 (v3 = 0) | v1 = 0)))
% 99.01/15.15
% 99.01/15.15 (t85_funct_1)
% 99.72/15.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 99.72/15.29 (relation_rng_restriction(v0, v3) = v4) | ~ (relation_dom(v1) = v2) | ~
% 99.72/15.29 $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any]
% 99.72/15.29 : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ? [v11: int] : ? [v12: $i] :
% 99.72/15.29 ? [v13: $i] : ? [v14: $i] : ? [v15: any] : ? [v16: any] : ? [v17: $i] :
% 99.72/15.29 ? [v18: any] : ($i(v14) & $i(v10) & ((relation_dom(v3) = v9 & function(v3)
% 99.72/15.29 = v8 & relation(v3) = v7 & $i(v9) & ( ~ (v8 = 0) | ~ (v7 = 0) | (( ~
% 99.72/15.29 (v4 = v1) | ( ! [v19: $i] : ! [v20: int] : (v20 = 0 | ~
% 99.72/15.29 (in(v19, v2) = v20) | ~ $i(v19) | ? [v21: any] : ? [v22:
% 99.72/15.29 $i] : ? [v23: any] : (apply(v3, v19) = v22 & in(v22, v0)
% 99.72/15.29 = v23 & in(v19, v9) = v21 & $i(v22) & ( ~ (v23 = 0) | ~
% 99.72/15.29 (v21 = 0)))) & ! [v19: $i] : ! [v20: $i] : ( ~
% 99.72/15.29 (apply(v3, v19) = v20) | ~ $i(v19) | ? [v21: any] : ?
% 99.72/15.29 [v22: any] : ? [v23: any] : (in(v20, v0) = v23 & in(v19,
% 99.72/15.29 v9) = v22 & in(v19, v2) = v21 & ( ~ (v21 = 0) | (v23 = 0
% 99.72/15.29 & v22 = 0)))) & ! [v19: $i] : ! [v20: $i] : ( ~
% 99.72/15.29 (apply(v3, v19) = v20) | ~ $i(v19) | ? [v21: any] : ?
% 99.72/15.29 [v22: any] : ? [v23: any] : (in(v20, v0) = v22 & in(v19,
% 99.72/15.29 v9) = v21 & in(v19, v2) = v23 & ( ~ (v22 = 0) | ~ (v21
% 99.72/15.29 = 0) | v23 = 0))) & ! [v19: $i] : ! [v20: $i] : ( ~
% 99.72/15.29 (apply(v3, v19) = v20) | ~ $i(v19) | ? [v21: any] : ?
% 99.72/15.29 [v22: $i] : (apply(v1, v19) = v22 & in(v19, v2) = v21 &
% 99.72/15.29 $i(v22) & ( ~ (v21 = 0) | v22 = v20))) & ! [v19: $i] : !
% 99.72/15.29 [v20: $i] : ( ~ (apply(v1, v19) = v20) | ~ $i(v19) | ? [v21:
% 99.72/15.29 any] : ? [v22: $i] : (apply(v3, v19) = v22 & in(v19, v2)
% 99.72/15.29 = v21 & $i(v22) & ( ~ (v21 = 0) | v22 = v20))) & ! [v19:
% 99.72/15.29 $i] : ! [v20: any] : ( ~ (in(v19, v9) = v20) | ~ $i(v19) |
% 99.72/15.29 ? [v21: any] : ? [v22: $i] : ? [v23: any] : (apply(v3,
% 99.72/15.29 v19) = v22 & in(v22, v0) = v23 & in(v19, v2) = v21 &
% 99.72/15.29 $i(v22) & ( ~ (v21 = 0) | (v23 = 0 & v20 = 0)))) & !
% 99.72/15.29 [v19: $i] : ( ~ (in(v19, v9) = 0) | ~ $i(v19) | ? [v20: $i]
% 99.72/15.29 : ? [v21: any] : ? [v22: any] : (apply(v3, v19) = v20 &
% 99.72/15.29 in(v20, v0) = v21 & in(v19, v2) = v22 & $i(v20) & ( ~ (v21
% 99.72/15.29 = 0) | v22 = 0))) & ! [v19: $i] : ( ~ (in(v19, v2) =
% 99.72/15.29 0) | ~ $i(v19) | ? [v20: $i] : (apply(v3, v19) = v20 &
% 99.72/15.29 apply(v1, v19) = v20 & $i(v20))) & ! [v19: $i] : ( ~
% 99.72/15.29 (in(v19, v2) = 0) | ~ $i(v19) | ? [v20: $i] : (apply(v3,
% 99.72/15.29 v19) = v20 & in(v20, v0) = 0 & in(v19, v9) = 0 &
% 99.72/15.29 $i(v20))))) & (v4 = v1 | (v11 = 0 & ~ (v13 = v12) &
% 99.72/15.29 apply(v3, v10) = v13 & apply(v1, v10) = v12 & in(v10, v2) = 0
% 99.72/15.29 & $i(v13) & $i(v12)) | (apply(v3, v14) = v17 & in(v17, v0) =
% 99.72/15.29 v18 & in(v14, v9) = v16 & in(v14, v2) = v15 & $i(v17) & ( ~
% 99.72/15.29 (v18 = 0) | ~ (v16 = 0) | ~ (v15 = 0)) & (v15 = 0 | (v18 =
% 99.72/15.29 0 & v16 = 0))))))) | (function(v1) = v6 & relation(v1) =
% 99.72/15.29 v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))))) & ? [v0: $i] : ! [v1: $i] : !
% 99.72/15.29 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (relation_dom(v3) = v4) | ~
% 99.72/15.29 (relation_dom(v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] :
% 99.72/15.29 ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ?
% 99.72/15.29 [v11: int] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: any] : ?
% 99.72/15.29 [v16: any] : ? [v17: $i] : ? [v18: any] : ($i(v14) & $i(v10) &
% 99.72/15.29 ((relation_rng_restriction(v0, v3) = v9 & function(v3) = v8 & relation(v3)
% 99.72/15.29 = v7 & $i(v9) & ( ~ (v8 = 0) | ~ (v7 = 0) | (( ~ (v9 = v1) | ( !
% 99.72/15.29 [v19: $i] : ! [v20: int] : (v20 = 0 | ~ (in(v19, v2) = v20)
% 99.72/15.29 | ~ $i(v19) | ? [v21: any] : ? [v22: $i] : ? [v23: any]
% 99.72/15.29 : (apply(v3, v19) = v22 & in(v22, v0) = v23 & in(v19, v4) =
% 99.72/15.29 v21 & $i(v22) & ( ~ (v23 = 0) | ~ (v21 = 0)))) & ! [v19:
% 99.72/15.29 $i] : ! [v20: $i] : ( ~ (apply(v3, v19) = v20) | ~ $i(v19)
% 99.72/15.29 | ? [v21: any] : ? [v22: any] : ? [v23: any] : (in(v20,
% 99.72/15.29 v0) = v23 & in(v19, v4) = v22 & in(v19, v2) = v21 & ( ~
% 99.72/15.29 (v21 = 0) | (v23 = 0 & v22 = 0)))) & ! [v19: $i] : !
% 99.72/15.29 [v20: $i] : ( ~ (apply(v3, v19) = v20) | ~ $i(v19) | ? [v21:
% 99.72/15.29 any] : ? [v22: any] : ? [v23: any] : (in(v20, v0) = v22
% 99.72/15.29 & in(v19, v4) = v21 & in(v19, v2) = v23 & ( ~ (v22 = 0) |
% 99.72/15.29 ~ (v21 = 0) | v23 = 0))) & ! [v19: $i] : ! [v20: $i] :
% 99.72/15.29 ( ~ (apply(v3, v19) = v20) | ~ $i(v19) | ? [v21: any] : ?
% 99.72/15.29 [v22: $i] : (apply(v1, v19) = v22 & in(v19, v2) = v21 &
% 99.72/15.29 $i(v22) & ( ~ (v21 = 0) | v22 = v20))) & ! [v19: $i] : !
% 99.72/15.29 [v20: $i] : ( ~ (apply(v1, v19) = v20) | ~ $i(v19) | ? [v21:
% 99.72/15.29 any] : ? [v22: $i] : (apply(v3, v19) = v22 & in(v19, v2)
% 99.72/15.29 = v21 & $i(v22) & ( ~ (v21 = 0) | v22 = v20))) & ! [v19:
% 99.72/15.29 $i] : ! [v20: any] : ( ~ (in(v19, v4) = v20) | ~ $i(v19) |
% 99.72/15.29 ? [v21: any] : ? [v22: $i] : ? [v23: any] : (apply(v3,
% 99.72/15.29 v19) = v22 & in(v22, v0) = v23 & in(v19, v2) = v21 &
% 99.72/15.29 $i(v22) & ( ~ (v21 = 0) | (v23 = 0 & v20 = 0)))) & !
% 99.72/15.29 [v19: $i] : ( ~ (in(v19, v4) = 0) | ~ $i(v19) | ? [v20: $i]
% 99.72/15.30 : ? [v21: any] : ? [v22: any] : (apply(v3, v19) = v20 &
% 99.72/15.30 in(v20, v0) = v21 & in(v19, v2) = v22 & $i(v20) & ( ~ (v21
% 99.72/15.30 = 0) | v22 = 0))) & ! [v19: $i] : ( ~ (in(v19, v2) =
% 99.72/15.30 0) | ~ $i(v19) | ? [v20: $i] : (apply(v3, v19) = v20 &
% 99.72/15.30 apply(v1, v19) = v20 & $i(v20))) & ! [v19: $i] : ( ~
% 99.72/15.30 (in(v19, v2) = 0) | ~ $i(v19) | ? [v20: $i] : (apply(v3,
% 99.72/15.30 v19) = v20 & in(v20, v0) = 0 & in(v19, v4) = 0 &
% 99.72/15.30 $i(v20))))) & (v9 = v1 | (v11 = 0 & ~ (v13 = v12) &
% 99.72/15.30 apply(v3, v10) = v13 & apply(v1, v10) = v12 & in(v10, v2) = 0
% 99.72/15.30 & $i(v13) & $i(v12)) | (apply(v3, v14) = v17 & in(v17, v0) =
% 99.72/15.30 v18 & in(v14, v4) = v16 & in(v14, v2) = v15 & $i(v17) & ( ~
% 99.72/15.30 (v18 = 0) | ~ (v16 = 0) | ~ (v15 = 0)) & (v15 = 0 | (v18 =
% 99.72/15.30 0 & v16 = 0))))))) | (function(v1) = v6 & relation(v1) =
% 99.72/15.30 v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))))) & ? [v0: $i] : ! [v1: $i] : !
% 99.72/15.30 [v2: $i] : ! [v3: $i] : ( ~ (relation_dom(v1) = v2) | ~ (function(v3) = 0) |
% 99.72/15.30 ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6:
% 99.72/15.30 any] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: int] : ? [v11:
% 99.72/15.30 $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: any] : ? [v15: any] : ?
% 99.72/15.30 [v16: $i] : ? [v17: any] : ($i(v13) & $i(v9) &
% 99.72/15.30 ((relation_rng_restriction(v0, v3) = v7 & relation_dom(v3) = v8 &
% 99.72/15.30 relation(v3) = v6 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | (( ~ (v7 = v1) |
% 99.72/15.30 ( ! [v18: $i] : ! [v19: int] : (v19 = 0 | ~ (in(v18, v2) =
% 99.72/15.30 v19) | ~ $i(v18) | ? [v20: any] : ? [v21: $i] : ?
% 99.72/15.30 [v22: any] : (apply(v3, v18) = v21 & in(v21, v0) = v22 &
% 99.72/15.30 in(v18, v8) = v20 & $i(v21) & ( ~ (v22 = 0) | ~ (v20 =
% 99.72/15.30 0)))) & ! [v18: $i] : ! [v19: $i] : ( ~ (apply(v3,
% 99.72/15.30 v18) = v19) | ~ $i(v18) | ? [v20: any] : ? [v21: any]
% 99.72/15.30 : ? [v22: any] : (in(v19, v0) = v22 & in(v18, v8) = v21 &
% 99.72/15.30 in(v18, v2) = v20 & ( ~ (v20 = 0) | (v22 = 0 & v21 = 0))))
% 99.72/15.30 & ! [v18: $i] : ! [v19: $i] : ( ~ (apply(v3, v18) = v19) |
% 99.72/15.30 ~ $i(v18) | ? [v20: any] : ? [v21: any] : ? [v22: any] :
% 99.72/15.30 (in(v19, v0) = v21 & in(v18, v8) = v20 & in(v18, v2) = v22 &
% 99.72/15.30 ( ~ (v21 = 0) | ~ (v20 = 0) | v22 = 0))) & ! [v18: $i] :
% 99.72/15.30 ! [v19: $i] : ( ~ (apply(v3, v18) = v19) | ~ $i(v18) | ?
% 99.72/15.30 [v20: any] : ? [v21: $i] : (apply(v1, v18) = v21 & in(v18,
% 99.72/15.30 v2) = v20 & $i(v21) & ( ~ (v20 = 0) | v21 = v19))) & !
% 99.72/15.30 [v18: $i] : ! [v19: $i] : ( ~ (apply(v1, v18) = v19) | ~
% 99.72/15.30 $i(v18) | ? [v20: any] : ? [v21: $i] : (apply(v3, v18) =
% 99.72/15.30 v21 & in(v18, v2) = v20 & $i(v21) & ( ~ (v20 = 0) | v21 =
% 99.72/15.30 v19))) & ! [v18: $i] : ! [v19: any] : ( ~ (in(v18, v8)
% 99.72/15.30 = v19) | ~ $i(v18) | ? [v20: any] : ? [v21: $i] : ?
% 99.72/15.30 [v22: any] : (apply(v3, v18) = v21 & in(v21, v0) = v22 &
% 99.72/15.30 in(v18, v2) = v20 & $i(v21) & ( ~ (v20 = 0) | (v22 = 0 &
% 99.72/15.30 v19 = 0)))) & ! [v18: $i] : ( ~ (in(v18, v8) = 0) |
% 99.72/15.30 ~ $i(v18) | ? [v19: $i] : ? [v20: any] : ? [v21: any] :
% 99.72/15.30 (apply(v3, v18) = v19 & in(v19, v0) = v20 & in(v18, v2) =
% 99.72/15.30 v21 & $i(v19) & ( ~ (v20 = 0) | v21 = 0))) & ! [v18: $i]
% 99.72/15.30 : ( ~ (in(v18, v2) = 0) | ~ $i(v18) | ? [v19: $i] :
% 99.72/15.30 (apply(v3, v18) = v19 & apply(v1, v18) = v19 & $i(v19))) &
% 99.72/15.30 ! [v18: $i] : ( ~ (in(v18, v2) = 0) | ~ $i(v18) | ? [v19:
% 99.72/15.30 $i] : (apply(v3, v18) = v19 & in(v19, v0) = 0 & in(v18,
% 99.72/15.30 v8) = 0 & $i(v19))))) & (v7 = v1 | (v10 = 0 & ~ (v12 =
% 99.72/15.30 v11) & apply(v3, v9) = v12 & apply(v1, v9) = v11 & in(v9,
% 99.72/15.30 v2) = 0 & $i(v12) & $i(v11)) | (apply(v3, v13) = v16 &
% 99.72/15.30 in(v16, v0) = v17 & in(v13, v8) = v15 & in(v13, v2) = v14 &
% 99.72/15.30 $i(v16) & ( ~ (v17 = 0) | ~ (v15 = 0) | ~ (v14 = 0)) & (v14
% 99.72/15.30 = 0 | (v17 = 0 & v15 = 0))))))) | (function(v1) = v5 &
% 99.72/15.30 relation(v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))) & ? [v0: $i] : !
% 99.72/15.30 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (relation_dom(v1) = v2) | ~
% 99.72/15.30 (relation(v3) = 0) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ?
% 99.72/15.30 [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 99.72/15.30 [v10: int] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: any] : ?
% 99.72/15.30 [v15: any] : ? [v16: $i] : ? [v17: any] : ($i(v13) & $i(v9) &
% 99.72/15.30 ((relation_rng_restriction(v0, v3) = v7 & relation_dom(v3) = v8 &
% 99.72/15.30 function(v3) = v6 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | (( ~ (v7 = v1) |
% 99.72/15.30 ( ! [v18: $i] : ! [v19: int] : (v19 = 0 | ~ (in(v18, v2) =
% 99.72/15.30 v19) | ~ $i(v18) | ? [v20: any] : ? [v21: $i] : ?
% 99.72/15.30 [v22: any] : (apply(v3, v18) = v21 & in(v21, v0) = v22 &
% 99.72/15.30 in(v18, v8) = v20 & $i(v21) & ( ~ (v22 = 0) | ~ (v20 =
% 99.72/15.30 0)))) & ! [v18: $i] : ! [v19: $i] : ( ~ (apply(v3,
% 99.72/15.30 v18) = v19) | ~ $i(v18) | ? [v20: any] : ? [v21: any]
% 99.72/15.30 : ? [v22: any] : (in(v19, v0) = v22 & in(v18, v8) = v21 &
% 99.72/15.30 in(v18, v2) = v20 & ( ~ (v20 = 0) | (v22 = 0 & v21 = 0))))
% 99.72/15.30 & ! [v18: $i] : ! [v19: $i] : ( ~ (apply(v3, v18) = v19) |
% 99.72/15.30 ~ $i(v18) | ? [v20: any] : ? [v21: any] : ? [v22: any] :
% 99.72/15.30 (in(v19, v0) = v21 & in(v18, v8) = v20 & in(v18, v2) = v22 &
% 99.72/15.30 ( ~ (v21 = 0) | ~ (v20 = 0) | v22 = 0))) & ! [v18: $i] :
% 99.72/15.30 ! [v19: $i] : ( ~ (apply(v3, v18) = v19) | ~ $i(v18) | ?
% 99.72/15.30 [v20: any] : ? [v21: $i] : (apply(v1, v18) = v21 & in(v18,
% 99.72/15.30 v2) = v20 & $i(v21) & ( ~ (v20 = 0) | v21 = v19))) & !
% 99.72/15.30 [v18: $i] : ! [v19: $i] : ( ~ (apply(v1, v18) = v19) | ~
% 99.72/15.30 $i(v18) | ? [v20: any] : ? [v21: $i] : (apply(v3, v18) =
% 99.72/15.30 v21 & in(v18, v2) = v20 & $i(v21) & ( ~ (v20 = 0) | v21 =
% 99.72/15.30 v19))) & ! [v18: $i] : ! [v19: any] : ( ~ (in(v18, v8)
% 99.72/15.30 = v19) | ~ $i(v18) | ? [v20: any] : ? [v21: $i] : ?
% 99.72/15.30 [v22: any] : (apply(v3, v18) = v21 & in(v21, v0) = v22 &
% 99.72/15.30 in(v18, v2) = v20 & $i(v21) & ( ~ (v20 = 0) | (v22 = 0 &
% 99.72/15.30 v19 = 0)))) & ! [v18: $i] : ( ~ (in(v18, v8) = 0) |
% 99.72/15.30 ~ $i(v18) | ? [v19: $i] : ? [v20: any] : ? [v21: any] :
% 99.72/15.30 (apply(v3, v18) = v19 & in(v19, v0) = v20 & in(v18, v2) =
% 99.72/15.30 v21 & $i(v19) & ( ~ (v20 = 0) | v21 = 0))) & ! [v18: $i]
% 99.72/15.31 : ( ~ (in(v18, v2) = 0) | ~ $i(v18) | ? [v19: $i] :
% 99.72/15.31 (apply(v3, v18) = v19 & apply(v1, v18) = v19 & $i(v19))) &
% 99.72/15.31 ! [v18: $i] : ( ~ (in(v18, v2) = 0) | ~ $i(v18) | ? [v19:
% 99.72/15.31 $i] : (apply(v3, v18) = v19 & in(v19, v0) = 0 & in(v18,
% 99.72/15.31 v8) = 0 & $i(v19))))) & (v7 = v1 | (v10 = 0 & ~ (v12 =
% 99.72/15.31 v11) & apply(v3, v9) = v12 & apply(v1, v9) = v11 & in(v9,
% 99.72/15.31 v2) = 0 & $i(v12) & $i(v11)) | (apply(v3, v13) = v16 &
% 99.72/15.31 in(v16, v0) = v17 & in(v13, v8) = v15 & in(v13, v2) = v14 &
% 99.72/15.31 $i(v16) & ( ~ (v17 = 0) | ~ (v15 = 0) | ~ (v14 = 0)) & (v14
% 99.72/15.31 = 0 | (v17 = 0 & v15 = 0))))))) | (function(v1) = v5 &
% 99.72/15.31 relation(v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))) & ? [v0: $i] : !
% 99.72/15.31 [v1: $i] : ( ~ (function(v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ?
% 99.72/15.31 [v3: $i] : (relation_dom(v1) = v3 & relation(v1) = v2 & $i(v3) & ( ~ (v2 =
% 99.72/15.31 0) | ( ! [v4: $i] : ! [v5: $i] : ( ~ (relation_rng_restriction(v0,
% 99.72/15.31 v4) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: any] : ? [v8:
% 99.72/15.31 $i] : ? [v9: $i] : ? [v10: int] : ? [v11: $i] : ? [v12: $i] :
% 99.72/15.31 ? [v13: $i] : ? [v14: any] : ? [v15: any] : ? [v16: $i] : ?
% 99.72/15.31 [v17: any] : (relation_dom(v4) = v8 & function(v4) = v7 &
% 99.72/15.31 relation(v4) = v6 & $i(v13) & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~
% 99.72/15.31 (v6 = 0) | (( ~ (v5 = v1) | ( ! [v18: $i] : ! [v19: int] : (v19
% 99.72/15.31 = 0 | ~ (in(v18, v3) = v19) | ~ $i(v18) | ? [v20:
% 99.72/15.31 any] : ? [v21: $i] : ? [v22: any] : (apply(v4, v18)
% 99.72/15.31 = v21 & in(v21, v0) = v22 & in(v18, v8) = v20 &
% 99.72/15.31 $i(v21) & ( ~ (v22 = 0) | ~ (v20 = 0)))) & ! [v18:
% 99.72/15.31 $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~
% 99.72/15.31 $i(v18) | ? [v20: any] : ? [v21: any] : ? [v22: any]
% 99.72/15.31 : (in(v19, v0) = v22 & in(v18, v8) = v21 & in(v18, v3) =
% 99.72/15.31 v20 & ( ~ (v20 = 0) | (v22 = 0 & v21 = 0)))) & !
% 99.72/15.31 [v18: $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~
% 99.72/15.31 $i(v18) | ? [v20: any] : ? [v21: any] : ? [v22: any]
% 99.72/15.31 : (in(v19, v0) = v21 & in(v18, v8) = v20 & in(v18, v3) =
% 99.72/15.31 v22 & ( ~ (v21 = 0) | ~ (v20 = 0) | v22 = 0))) & !
% 99.72/15.31 [v18: $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~
% 99.72/15.31 $i(v18) | ? [v20: any] : ? [v21: $i] : (apply(v1, v18)
% 99.72/15.31 = v21 & in(v18, v3) = v20 & $i(v21) & ( ~ (v20 = 0) |
% 99.72/15.31 v21 = v19))) & ! [v18: $i] : ! [v19: $i] : ( ~
% 99.72/15.31 (apply(v1, v18) = v19) | ~ $i(v18) | ? [v20: any] : ?
% 99.72/15.31 [v21: $i] : (apply(v4, v18) = v21 & in(v18, v3) = v20 &
% 99.72/15.31 $i(v21) & ( ~ (v20 = 0) | v21 = v19))) & ! [v18: $i]
% 99.72/15.31 : ! [v19: any] : ( ~ (in(v18, v8) = v19) | ~ $i(v18) |
% 99.72/15.31 ? [v20: any] : ? [v21: $i] : ? [v22: any] : (apply(v4,
% 99.72/15.31 v18) = v21 & in(v21, v0) = v22 & in(v18, v3) = v20 &
% 99.72/15.31 $i(v21) & ( ~ (v20 = 0) | (v22 = 0 & v19 = 0)))) & !
% 99.72/15.31 [v18: $i] : ( ~ (in(v18, v8) = 0) | ~ $i(v18) | ? [v19:
% 99.72/15.31 $i] : ? [v20: any] : ? [v21: any] : (apply(v4, v18)
% 99.72/15.31 = v19 & in(v19, v0) = v20 & in(v18, v3) = v21 &
% 99.72/15.31 $i(v19) & ( ~ (v20 = 0) | v21 = 0))) & ! [v18: $i] :
% 99.72/15.31 ( ~ (in(v18, v3) = 0) | ~ $i(v18) | ? [v19: $i] :
% 99.72/15.31 (apply(v4, v18) = v19 & apply(v1, v18) = v19 & $i(v19)))
% 99.72/15.31 & ! [v18: $i] : ( ~ (in(v18, v3) = 0) | ~ $i(v18) | ?
% 99.72/15.31 [v19: $i] : (apply(v4, v18) = v19 & in(v19, v0) = 0 &
% 99.72/15.31 in(v18, v8) = 0 & $i(v19))))) & (v5 = v1 | (v10 = 0 &
% 99.72/15.31 ~ (v12 = v11) & apply(v4, v9) = v12 & apply(v1, v9) = v11
% 99.72/15.31 & in(v9, v3) = 0 & $i(v12) & $i(v11)) | (apply(v4, v13) =
% 99.72/15.31 v16 & in(v16, v0) = v17 & in(v13, v8) = v15 & in(v13, v3)
% 99.72/15.31 = v14 & $i(v16) & ( ~ (v17 = 0) | ~ (v15 = 0) | ~ (v14 =
% 99.72/15.31 0)) & (v14 = 0 | (v17 = 0 & v15 = 0)))))))) & ! [v4:
% 99.72/15.31 $i] : ! [v5: $i] : ( ~ (relation_dom(v4) = v5) | ~ $i(v4) | ?
% 99.72/15.31 [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: $i] : ? [v10: int]
% 99.72/15.31 : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: any] : ?
% 99.72/15.31 [v15: any] : ? [v16: $i] : ? [v17: any] :
% 99.72/15.31 (relation_rng_restriction(v0, v4) = v8 & function(v4) = v7 &
% 99.72/15.31 relation(v4) = v6 & $i(v13) & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~
% 99.72/15.31 (v6 = 0) | (( ~ (v8 = v1) | ( ! [v18: $i] : ! [v19: int] : (v19
% 99.72/15.31 = 0 | ~ (in(v18, v3) = v19) | ~ $i(v18) | ? [v20:
% 99.72/15.31 any] : ? [v21: $i] : ? [v22: any] : (apply(v4, v18)
% 99.72/15.31 = v21 & in(v21, v0) = v22 & in(v18, v5) = v20 &
% 99.72/15.31 $i(v21) & ( ~ (v22 = 0) | ~ (v20 = 0)))) & ! [v18:
% 99.72/15.31 $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~
% 99.72/15.31 $i(v18) | ? [v20: any] : ? [v21: any] : ? [v22: any]
% 99.72/15.31 : (in(v19, v0) = v22 & in(v18, v5) = v21 & in(v18, v3) =
% 99.72/15.31 v20 & ( ~ (v20 = 0) | (v22 = 0 & v21 = 0)))) & !
% 99.72/15.31 [v18: $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~
% 99.72/15.31 $i(v18) | ? [v20: any] : ? [v21: any] : ? [v22: any]
% 99.72/15.31 : (in(v19, v0) = v21 & in(v18, v5) = v20 & in(v18, v3) =
% 99.72/15.31 v22 & ( ~ (v21 = 0) | ~ (v20 = 0) | v22 = 0))) & !
% 99.72/15.31 [v18: $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~
% 99.72/15.31 $i(v18) | ? [v20: any] : ? [v21: $i] : (apply(v1, v18)
% 99.72/15.31 = v21 & in(v18, v3) = v20 & $i(v21) & ( ~ (v20 = 0) |
% 99.72/15.31 v21 = v19))) & ! [v18: $i] : ! [v19: $i] : ( ~
% 99.72/15.31 (apply(v1, v18) = v19) | ~ $i(v18) | ? [v20: any] : ?
% 99.72/15.31 [v21: $i] : (apply(v4, v18) = v21 & in(v18, v3) = v20 &
% 99.72/15.31 $i(v21) & ( ~ (v20 = 0) | v21 = v19))) & ! [v18: $i]
% 99.72/15.31 : ! [v19: any] : ( ~ (in(v18, v5) = v19) | ~ $i(v18) |
% 99.72/15.31 ? [v20: any] : ? [v21: $i] : ? [v22: any] : (apply(v4,
% 99.72/15.31 v18) = v21 & in(v21, v0) = v22 & in(v18, v3) = v20 &
% 99.72/15.31 $i(v21) & ( ~ (v20 = 0) | (v22 = 0 & v19 = 0)))) & !
% 99.72/15.31 [v18: $i] : ( ~ (in(v18, v5) = 0) | ~ $i(v18) | ? [v19:
% 99.72/15.31 $i] : ? [v20: any] : ? [v21: any] : (apply(v4, v18)
% 99.72/15.31 = v19 & in(v19, v0) = v20 & in(v18, v3) = v21 &
% 99.72/15.31 $i(v19) & ( ~ (v20 = 0) | v21 = 0))) & ! [v18: $i] :
% 99.72/15.31 ( ~ (in(v18, v3) = 0) | ~ $i(v18) | ? [v19: $i] :
% 99.72/15.31 (apply(v4, v18) = v19 & apply(v1, v18) = v19 & $i(v19)))
% 99.72/15.31 & ! [v18: $i] : ( ~ (in(v18, v3) = 0) | ~ $i(v18) | ?
% 99.72/15.31 [v19: $i] : (apply(v4, v18) = v19 & in(v19, v0) = 0 &
% 99.72/15.31 in(v18, v5) = 0 & $i(v19))))) & (v8 = v1 | (v10 = 0 &
% 99.72/15.31 ~ (v12 = v11) & apply(v4, v9) = v12 & apply(v1, v9) = v11
% 99.72/15.31 & in(v9, v3) = 0 & $i(v12) & $i(v11)) | (apply(v4, v13) =
% 99.72/15.31 v16 & in(v16, v0) = v17 & in(v13, v5) = v15 & in(v13, v3)
% 99.72/15.31 = v14 & $i(v16) & ( ~ (v17 = 0) | ~ (v15 = 0) | ~ (v14 =
% 99.72/15.31 0)) & (v14 = 0 | (v17 = 0 & v15 = 0)))))))) & ! [v4:
% 99.72/15.31 $i] : ( ~ (function(v4) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6:
% 99.72/15.31 $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: int] : ? [v10: $i] : ?
% 99.72/15.31 [v11: $i] : ? [v12: $i] : ? [v13: any] : ? [v14: any] : ? [v15:
% 99.72/15.31 $i] : ? [v16: any] : (relation_rng_restriction(v0, v4) = v6 &
% 99.72/15.31 relation_dom(v4) = v7 & relation(v4) = v5 & $i(v12) & $i(v8) &
% 99.72/15.31 $i(v7) & $i(v6) & ( ~ (v5 = 0) | (( ~ (v6 = v1) | ( ! [v17: $i] :
% 99.72/15.31 ! [v18: int] : (v18 = 0 | ~ (in(v17, v3) = v18) | ~
% 99.72/15.31 $i(v17) | ? [v19: any] : ? [v20: $i] : ? [v21: any] :
% 99.72/15.31 (apply(v4, v17) = v20 & in(v20, v0) = v21 & in(v17, v7)
% 99.72/15.31 = v19 & $i(v20) & ( ~ (v21 = 0) | ~ (v19 = 0)))) & !
% 99.72/15.31 [v17: $i] : ! [v18: $i] : ( ~ (apply(v4, v17) = v18) | ~
% 99.72/15.31 $i(v17) | ? [v19: any] : ? [v20: any] : ? [v21: any]
% 99.72/15.31 : (in(v18, v0) = v21 & in(v17, v7) = v20 & in(v17, v3) =
% 99.72/15.31 v19 & ( ~ (v19 = 0) | (v21 = 0 & v20 = 0)))) & !
% 99.72/15.31 [v17: $i] : ! [v18: $i] : ( ~ (apply(v4, v17) = v18) | ~
% 99.72/15.31 $i(v17) | ? [v19: any] : ? [v20: any] : ? [v21: any]
% 99.72/15.31 : (in(v18, v0) = v20 & in(v17, v7) = v19 & in(v17, v3) =
% 99.72/15.31 v21 & ( ~ (v20 = 0) | ~ (v19 = 0) | v21 = 0))) & !
% 99.72/15.31 [v17: $i] : ! [v18: $i] : ( ~ (apply(v4, v17) = v18) | ~
% 99.72/15.31 $i(v17) | ? [v19: any] : ? [v20: $i] : (apply(v1, v17)
% 99.72/15.31 = v20 & in(v17, v3) = v19 & $i(v20) & ( ~ (v19 = 0) |
% 99.72/15.31 v20 = v18))) & ! [v17: $i] : ! [v18: $i] : ( ~
% 99.72/15.31 (apply(v1, v17) = v18) | ~ $i(v17) | ? [v19: any] : ?
% 99.72/15.31 [v20: $i] : (apply(v4, v17) = v20 & in(v17, v3) = v19 &
% 99.72/15.31 $i(v20) & ( ~ (v19 = 0) | v20 = v18))) & ! [v17: $i]
% 99.72/15.31 : ! [v18: any] : ( ~ (in(v17, v7) = v18) | ~ $i(v17) |
% 99.72/15.31 ? [v19: any] : ? [v20: $i] : ? [v21: any] : (apply(v4,
% 99.72/15.31 v17) = v20 & in(v20, v0) = v21 & in(v17, v3) = v19 &
% 99.72/15.31 $i(v20) & ( ~ (v19 = 0) | (v21 = 0 & v18 = 0)))) & !
% 99.72/15.31 [v17: $i] : ( ~ (in(v17, v7) = 0) | ~ $i(v17) | ? [v18:
% 99.72/15.31 $i] : ? [v19: any] : ? [v20: any] : (apply(v4, v17)
% 99.72/15.31 = v18 & in(v18, v0) = v19 & in(v17, v3) = v20 &
% 99.72/15.31 $i(v18) & ( ~ (v19 = 0) | v20 = 0))) & ! [v17: $i] :
% 99.72/15.31 ( ~ (in(v17, v3) = 0) | ~ $i(v17) | ? [v18: $i] :
% 99.72/15.31 (apply(v4, v17) = v18 & apply(v1, v17) = v18 & $i(v18)))
% 99.72/15.31 & ! [v17: $i] : ( ~ (in(v17, v3) = 0) | ~ $i(v17) | ?
% 99.72/15.31 [v18: $i] : (apply(v4, v17) = v18 & in(v18, v0) = 0 &
% 99.72/15.31 in(v17, v7) = 0 & $i(v18))))) & (v6 = v1 | (v9 = 0 &
% 99.72/15.31 ~ (v11 = v10) & apply(v4, v8) = v11 & apply(v1, v8) = v10
% 99.72/15.31 & in(v8, v3) = 0 & $i(v11) & $i(v10)) | (apply(v4, v12) =
% 99.72/15.31 v15 & in(v15, v0) = v16 & in(v12, v7) = v14 & in(v12, v3)
% 99.72/15.31 = v13 & $i(v15) & ( ~ (v16 = 0) | ~ (v14 = 0) | ~ (v13 =
% 99.72/15.31 0)) & (v13 = 0 | (v16 = 0 & v14 = 0)))))))) & ! [v4:
% 99.72/15.31 $i] : ( ~ (relation(v4) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6:
% 99.72/15.31 $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: int] : ? [v10: $i] : ?
% 99.72/15.31 [v11: $i] : ? [v12: $i] : ? [v13: any] : ? [v14: any] : ? [v15:
% 99.72/15.31 $i] : ? [v16: any] : (relation_rng_restriction(v0, v4) = v6 &
% 99.72/15.31 relation_dom(v4) = v7 & function(v4) = v5 & $i(v12) & $i(v8) &
% 99.72/15.32 $i(v7) & $i(v6) & ( ~ (v5 = 0) | (( ~ (v6 = v1) | ( ! [v17: $i] :
% 99.72/15.32 ! [v18: int] : (v18 = 0 | ~ (in(v17, v3) = v18) | ~
% 99.72/15.32 $i(v17) | ? [v19: any] : ? [v20: $i] : ? [v21: any] :
% 99.72/15.32 (apply(v4, v17) = v20 & in(v20, v0) = v21 & in(v17, v7)
% 99.72/15.32 = v19 & $i(v20) & ( ~ (v21 = 0) | ~ (v19 = 0)))) & !
% 99.72/15.32 [v17: $i] : ! [v18: $i] : ( ~ (apply(v4, v17) = v18) | ~
% 99.72/15.32 $i(v17) | ? [v19: any] : ? [v20: any] : ? [v21: any]
% 99.72/15.32 : (in(v18, v0) = v21 & in(v17, v7) = v20 & in(v17, v3) =
% 99.72/15.32 v19 & ( ~ (v19 = 0) | (v21 = 0 & v20 = 0)))) & !
% 99.72/15.32 [v17: $i] : ! [v18: $i] : ( ~ (apply(v4, v17) = v18) | ~
% 99.72/15.32 $i(v17) | ? [v19: any] : ? [v20: any] : ? [v21: any]
% 99.72/15.32 : (in(v18, v0) = v20 & in(v17, v7) = v19 & in(v17, v3) =
% 99.72/15.32 v21 & ( ~ (v20 = 0) | ~ (v19 = 0) | v21 = 0))) & !
% 99.72/15.32 [v17: $i] : ! [v18: $i] : ( ~ (apply(v4, v17) = v18) | ~
% 99.72/15.32 $i(v17) | ? [v19: any] : ? [v20: $i] : (apply(v1, v17)
% 99.72/15.32 = v20 & in(v17, v3) = v19 & $i(v20) & ( ~ (v19 = 0) |
% 99.72/15.32 v20 = v18))) & ! [v17: $i] : ! [v18: $i] : ( ~
% 99.72/15.32 (apply(v1, v17) = v18) | ~ $i(v17) | ? [v19: any] : ?
% 99.72/15.32 [v20: $i] : (apply(v4, v17) = v20 & in(v17, v3) = v19 &
% 99.72/15.32 $i(v20) & ( ~ (v19 = 0) | v20 = v18))) & ! [v17: $i]
% 99.72/15.32 : ! [v18: any] : ( ~ (in(v17, v7) = v18) | ~ $i(v17) |
% 99.72/15.32 ? [v19: any] : ? [v20: $i] : ? [v21: any] : (apply(v4,
% 99.72/15.32 v17) = v20 & in(v20, v0) = v21 & in(v17, v3) = v19 &
% 99.72/15.32 $i(v20) & ( ~ (v19 = 0) | (v21 = 0 & v18 = 0)))) & !
% 99.72/15.32 [v17: $i] : ( ~ (in(v17, v7) = 0) | ~ $i(v17) | ? [v18:
% 99.72/15.32 $i] : ? [v19: any] : ? [v20: any] : (apply(v4, v17)
% 99.72/15.32 = v18 & in(v18, v0) = v19 & in(v17, v3) = v20 &
% 99.72/15.32 $i(v18) & ( ~ (v19 = 0) | v20 = 0))) & ! [v17: $i] :
% 99.72/15.32 ( ~ (in(v17, v3) = 0) | ~ $i(v17) | ? [v18: $i] :
% 99.72/15.32 (apply(v4, v17) = v18 & apply(v1, v17) = v18 & $i(v18)))
% 99.72/15.32 & ! [v17: $i] : ( ~ (in(v17, v3) = 0) | ~ $i(v17) | ?
% 99.72/15.32 [v18: $i] : (apply(v4, v17) = v18 & in(v18, v0) = 0 &
% 99.72/15.32 in(v17, v7) = 0 & $i(v18))))) & (v6 = v1 | (v9 = 0 &
% 99.72/15.32 ~ (v11 = v10) & apply(v4, v8) = v11 & apply(v1, v8) = v10
% 99.72/15.32 & in(v8, v3) = 0 & $i(v11) & $i(v10)) | (apply(v4, v12) =
% 99.72/15.32 v15 & in(v15, v0) = v16 & in(v12, v7) = v14 & in(v12, v3)
% 99.72/15.32 = v13 & $i(v15) & ( ~ (v16 = 0) | ~ (v14 = 0) | ~ (v13 =
% 99.72/15.32 0)) & (v13 = 0 | (v16 = 0 & v14 = 0)))))))))))) & ?
% 99.72/15.32 [v0: $i] : ! [v1: $i] : ( ~ (relation(v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 99.72/15.32 [v2: any] : ? [v3: $i] : (relation_dom(v1) = v3 & function(v1) = v2 &
% 99.72/15.32 $i(v3) & ( ~ (v2 = 0) | ( ! [v4: $i] : ! [v5: $i] : ( ~
% 99.72/15.32 (relation_rng_restriction(v0, v4) = v5) | ~ $i(v4) | ? [v6: any] :
% 99.72/15.32 ? [v7: any] : ? [v8: $i] : ? [v9: $i] : ? [v10: int] : ? [v11:
% 99.72/15.32 $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: any] : ? [v15: any]
% 99.72/15.32 : ? [v16: $i] : ? [v17: any] : (relation_dom(v4) = v8 &
% 99.72/15.32 function(v4) = v7 & relation(v4) = v6 & $i(v13) & $i(v9) & $i(v8)
% 99.72/15.32 & ( ~ (v7 = 0) | ~ (v6 = 0) | (( ~ (v5 = v1) | ( ! [v18: $i] : !
% 99.72/15.32 [v19: int] : (v19 = 0 | ~ (in(v18, v3) = v19) | ~
% 99.72/15.32 $i(v18) | ? [v20: any] : ? [v21: $i] : ? [v22: any] :
% 99.72/15.32 (apply(v4, v18) = v21 & in(v21, v0) = v22 & in(v18, v8)
% 99.72/15.32 = v20 & $i(v21) & ( ~ (v22 = 0) | ~ (v20 = 0)))) & !
% 99.72/15.32 [v18: $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~
% 99.72/15.32 $i(v18) | ? [v20: any] : ? [v21: any] : ? [v22: any]
% 99.72/15.32 : (in(v19, v0) = v22 & in(v18, v8) = v21 & in(v18, v3) =
% 99.72/15.32 v20 & ( ~ (v20 = 0) | (v22 = 0 & v21 = 0)))) & !
% 99.72/15.32 [v18: $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~
% 99.72/15.32 $i(v18) | ? [v20: any] : ? [v21: any] : ? [v22: any]
% 99.72/15.32 : (in(v19, v0) = v21 & in(v18, v8) = v20 & in(v18, v3) =
% 99.72/15.32 v22 & ( ~ (v21 = 0) | ~ (v20 = 0) | v22 = 0))) & !
% 99.72/15.32 [v18: $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~
% 99.72/15.32 $i(v18) | ? [v20: any] : ? [v21: $i] : (apply(v1, v18)
% 99.72/15.32 = v21 & in(v18, v3) = v20 & $i(v21) & ( ~ (v20 = 0) |
% 99.72/15.32 v21 = v19))) & ! [v18: $i] : ! [v19: $i] : ( ~
% 99.72/15.32 (apply(v1, v18) = v19) | ~ $i(v18) | ? [v20: any] : ?
% 99.72/15.32 [v21: $i] : (apply(v4, v18) = v21 & in(v18, v3) = v20 &
% 99.72/15.32 $i(v21) & ( ~ (v20 = 0) | v21 = v19))) & ! [v18: $i]
% 99.72/15.32 : ! [v19: any] : ( ~ (in(v18, v8) = v19) | ~ $i(v18) |
% 99.72/15.32 ? [v20: any] : ? [v21: $i] : ? [v22: any] : (apply(v4,
% 99.72/15.32 v18) = v21 & in(v21, v0) = v22 & in(v18, v3) = v20 &
% 99.72/15.32 $i(v21) & ( ~ (v20 = 0) | (v22 = 0 & v19 = 0)))) & !
% 99.72/15.32 [v18: $i] : ( ~ (in(v18, v8) = 0) | ~ $i(v18) | ? [v19:
% 99.72/15.32 $i] : ? [v20: any] : ? [v21: any] : (apply(v4, v18)
% 99.72/15.32 = v19 & in(v19, v0) = v20 & in(v18, v3) = v21 &
% 99.72/15.32 $i(v19) & ( ~ (v20 = 0) | v21 = 0))) & ! [v18: $i] :
% 99.72/15.32 ( ~ (in(v18, v3) = 0) | ~ $i(v18) | ? [v19: $i] :
% 99.72/15.32 (apply(v4, v18) = v19 & apply(v1, v18) = v19 & $i(v19)))
% 99.72/15.32 & ! [v18: $i] : ( ~ (in(v18, v3) = 0) | ~ $i(v18) | ?
% 99.72/15.32 [v19: $i] : (apply(v4, v18) = v19 & in(v19, v0) = 0 &
% 99.72/15.32 in(v18, v8) = 0 & $i(v19))))) & (v5 = v1 | (v10 = 0 &
% 99.72/15.32 ~ (v12 = v11) & apply(v4, v9) = v12 & apply(v1, v9) = v11
% 99.72/15.32 & in(v9, v3) = 0 & $i(v12) & $i(v11)) | (apply(v4, v13) =
% 99.72/15.32 v16 & in(v16, v0) = v17 & in(v13, v8) = v15 & in(v13, v3)
% 99.72/15.32 = v14 & $i(v16) & ( ~ (v17 = 0) | ~ (v15 = 0) | ~ (v14 =
% 99.72/15.32 0)) & (v14 = 0 | (v17 = 0 & v15 = 0)))))))) & ! [v4:
% 99.72/15.32 $i] : ! [v5: $i] : ( ~ (relation_dom(v4) = v5) | ~ $i(v4) | ?
% 99.72/15.32 [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: $i] : ? [v10: int]
% 99.72/15.32 : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: any] : ?
% 99.72/15.32 [v15: any] : ? [v16: $i] : ? [v17: any] :
% 99.72/15.32 (relation_rng_restriction(v0, v4) = v8 & function(v4) = v7 &
% 99.72/15.32 relation(v4) = v6 & $i(v13) & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~
% 99.72/15.32 (v6 = 0) | (( ~ (v8 = v1) | ( ! [v18: $i] : ! [v19: int] : (v19
% 99.72/15.32 = 0 | ~ (in(v18, v3) = v19) | ~ $i(v18) | ? [v20:
% 99.72/15.32 any] : ? [v21: $i] : ? [v22: any] : (apply(v4, v18)
% 99.72/15.32 = v21 & in(v21, v0) = v22 & in(v18, v5) = v20 &
% 99.72/15.32 $i(v21) & ( ~ (v22 = 0) | ~ (v20 = 0)))) & ! [v18:
% 99.72/15.32 $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~
% 99.72/15.32 $i(v18) | ? [v20: any] : ? [v21: any] : ? [v22: any]
% 99.72/15.32 : (in(v19, v0) = v22 & in(v18, v5) = v21 & in(v18, v3) =
% 99.72/15.32 v20 & ( ~ (v20 = 0) | (v22 = 0 & v21 = 0)))) & !
% 99.72/15.32 [v18: $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~
% 99.72/15.32 $i(v18) | ? [v20: any] : ? [v21: any] : ? [v22: any]
% 99.72/15.32 : (in(v19, v0) = v21 & in(v18, v5) = v20 & in(v18, v3) =
% 99.72/15.32 v22 & ( ~ (v21 = 0) | ~ (v20 = 0) | v22 = 0))) & !
% 99.72/15.32 [v18: $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~
% 99.72/15.32 $i(v18) | ? [v20: any] : ? [v21: $i] : (apply(v1, v18)
% 99.72/15.32 = v21 & in(v18, v3) = v20 & $i(v21) & ( ~ (v20 = 0) |
% 99.72/15.32 v21 = v19))) & ! [v18: $i] : ! [v19: $i] : ( ~
% 99.72/15.32 (apply(v1, v18) = v19) | ~ $i(v18) | ? [v20: any] : ?
% 99.72/15.32 [v21: $i] : (apply(v4, v18) = v21 & in(v18, v3) = v20 &
% 99.72/15.32 $i(v21) & ( ~ (v20 = 0) | v21 = v19))) & ! [v18: $i]
% 99.72/15.32 : ! [v19: any] : ( ~ (in(v18, v5) = v19) | ~ $i(v18) |
% 99.72/15.32 ? [v20: any] : ? [v21: $i] : ? [v22: any] : (apply(v4,
% 99.72/15.32 v18) = v21 & in(v21, v0) = v22 & in(v18, v3) = v20 &
% 99.72/15.32 $i(v21) & ( ~ (v20 = 0) | (v22 = 0 & v19 = 0)))) & !
% 99.72/15.32 [v18: $i] : ( ~ (in(v18, v5) = 0) | ~ $i(v18) | ? [v19:
% 99.72/15.32 $i] : ? [v20: any] : ? [v21: any] : (apply(v4, v18)
% 99.72/15.32 = v19 & in(v19, v0) = v20 & in(v18, v3) = v21 &
% 99.72/15.32 $i(v19) & ( ~ (v20 = 0) | v21 = 0))) & ! [v18: $i] :
% 99.72/15.32 ( ~ (in(v18, v3) = 0) | ~ $i(v18) | ? [v19: $i] :
% 99.72/15.32 (apply(v4, v18) = v19 & apply(v1, v18) = v19 & $i(v19)))
% 99.72/15.32 & ! [v18: $i] : ( ~ (in(v18, v3) = 0) | ~ $i(v18) | ?
% 99.72/15.32 [v19: $i] : (apply(v4, v18) = v19 & in(v19, v0) = 0 &
% 99.72/15.32 in(v18, v5) = 0 & $i(v19))))) & (v8 = v1 | (v10 = 0 &
% 99.72/15.32 ~ (v12 = v11) & apply(v4, v9) = v12 & apply(v1, v9) = v11
% 99.72/15.32 & in(v9, v3) = 0 & $i(v12) & $i(v11)) | (apply(v4, v13) =
% 99.72/15.32 v16 & in(v16, v0) = v17 & in(v13, v5) = v15 & in(v13, v3)
% 99.72/15.32 = v14 & $i(v16) & ( ~ (v17 = 0) | ~ (v15 = 0) | ~ (v14 =
% 99.72/15.32 0)) & (v14 = 0 | (v17 = 0 & v15 = 0)))))))) & ! [v4:
% 99.72/15.32 $i] : ( ~ (function(v4) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6:
% 99.72/15.32 $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: int] : ? [v10: $i] : ?
% 99.72/15.32 [v11: $i] : ? [v12: $i] : ? [v13: any] : ? [v14: any] : ? [v15:
% 99.72/15.32 $i] : ? [v16: any] : (relation_rng_restriction(v0, v4) = v6 &
% 99.72/15.32 relation_dom(v4) = v7 & relation(v4) = v5 & $i(v12) & $i(v8) &
% 99.72/15.32 $i(v7) & $i(v6) & ( ~ (v5 = 0) | (( ~ (v6 = v1) | ( ! [v17: $i] :
% 99.72/15.32 ! [v18: int] : (v18 = 0 | ~ (in(v17, v3) = v18) | ~
% 99.72/15.32 $i(v17) | ? [v19: any] : ? [v20: $i] : ? [v21: any] :
% 99.72/15.32 (apply(v4, v17) = v20 & in(v20, v0) = v21 & in(v17, v7)
% 99.72/15.32 = v19 & $i(v20) & ( ~ (v21 = 0) | ~ (v19 = 0)))) & !
% 99.72/15.32 [v17: $i] : ! [v18: $i] : ( ~ (apply(v4, v17) = v18) | ~
% 99.72/15.32 $i(v17) | ? [v19: any] : ? [v20: any] : ? [v21: any]
% 99.72/15.32 : (in(v18, v0) = v21 & in(v17, v7) = v20 & in(v17, v3) =
% 99.72/15.32 v19 & ( ~ (v19 = 0) | (v21 = 0 & v20 = 0)))) & !
% 99.72/15.32 [v17: $i] : ! [v18: $i] : ( ~ (apply(v4, v17) = v18) | ~
% 99.72/15.32 $i(v17) | ? [v19: any] : ? [v20: any] : ? [v21: any]
% 99.72/15.32 : (in(v18, v0) = v20 & in(v17, v7) = v19 & in(v17, v3) =
% 99.72/15.32 v21 & ( ~ (v20 = 0) | ~ (v19 = 0) | v21 = 0))) & !
% 99.72/15.32 [v17: $i] : ! [v18: $i] : ( ~ (apply(v4, v17) = v18) | ~
% 99.72/15.32 $i(v17) | ? [v19: any] : ? [v20: $i] : (apply(v1, v17)
% 99.72/15.32 = v20 & in(v17, v3) = v19 & $i(v20) & ( ~ (v19 = 0) |
% 99.72/15.32 v20 = v18))) & ! [v17: $i] : ! [v18: $i] : ( ~
% 99.72/15.32 (apply(v1, v17) = v18) | ~ $i(v17) | ? [v19: any] : ?
% 99.72/15.32 [v20: $i] : (apply(v4, v17) = v20 & in(v17, v3) = v19 &
% 99.72/15.32 $i(v20) & ( ~ (v19 = 0) | v20 = v18))) & ! [v17: $i]
% 99.72/15.32 : ! [v18: any] : ( ~ (in(v17, v7) = v18) | ~ $i(v17) |
% 99.72/15.32 ? [v19: any] : ? [v20: $i] : ? [v21: any] : (apply(v4,
% 99.72/15.32 v17) = v20 & in(v20, v0) = v21 & in(v17, v3) = v19 &
% 99.72/15.32 $i(v20) & ( ~ (v19 = 0) | (v21 = 0 & v18 = 0)))) & !
% 99.72/15.32 [v17: $i] : ( ~ (in(v17, v7) = 0) | ~ $i(v17) | ? [v18:
% 99.72/15.32 $i] : ? [v19: any] : ? [v20: any] : (apply(v4, v17)
% 99.72/15.32 = v18 & in(v18, v0) = v19 & in(v17, v3) = v20 &
% 99.72/15.32 $i(v18) & ( ~ (v19 = 0) | v20 = 0))) & ! [v17: $i] :
% 99.72/15.32 ( ~ (in(v17, v3) = 0) | ~ $i(v17) | ? [v18: $i] :
% 99.72/15.32 (apply(v4, v17) = v18 & apply(v1, v17) = v18 & $i(v18)))
% 99.72/15.32 & ! [v17: $i] : ( ~ (in(v17, v3) = 0) | ~ $i(v17) | ?
% 99.72/15.32 [v18: $i] : (apply(v4, v17) = v18 & in(v18, v0) = 0 &
% 99.72/15.32 in(v17, v7) = 0 & $i(v18))))) & (v6 = v1 | (v9 = 0 &
% 99.72/15.32 ~ (v11 = v10) & apply(v4, v8) = v11 & apply(v1, v8) = v10
% 99.72/15.32 & in(v8, v3) = 0 & $i(v11) & $i(v10)) | (apply(v4, v12) =
% 99.72/15.32 v15 & in(v15, v0) = v16 & in(v12, v7) = v14 & in(v12, v3)
% 99.72/15.32 = v13 & $i(v15) & ( ~ (v16 = 0) | ~ (v14 = 0) | ~ (v13 =
% 99.72/15.32 0)) & (v13 = 0 | (v16 = 0 & v14 = 0)))))))) & ! [v4:
% 99.72/15.32 $i] : ( ~ (relation(v4) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6:
% 99.72/15.32 $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: int] : ? [v10: $i] : ?
% 99.72/15.32 [v11: $i] : ? [v12: $i] : ? [v13: any] : ? [v14: any] : ? [v15:
% 99.72/15.32 $i] : ? [v16: any] : (relation_rng_restriction(v0, v4) = v6 &
% 99.72/15.32 relation_dom(v4) = v7 & function(v4) = v5 & $i(v12) & $i(v8) &
% 99.72/15.32 $i(v7) & $i(v6) & ( ~ (v5 = 0) | (( ~ (v6 = v1) | ( ! [v17: $i] :
% 99.72/15.32 ! [v18: int] : (v18 = 0 | ~ (in(v17, v3) = v18) | ~
% 99.72/15.32 $i(v17) | ? [v19: any] : ? [v20: $i] : ? [v21: any] :
% 99.72/15.32 (apply(v4, v17) = v20 & in(v20, v0) = v21 & in(v17, v7)
% 99.72/15.32 = v19 & $i(v20) & ( ~ (v21 = 0) | ~ (v19 = 0)))) & !
% 99.72/15.32 [v17: $i] : ! [v18: $i] : ( ~ (apply(v4, v17) = v18) | ~
% 99.72/15.32 $i(v17) | ? [v19: any] : ? [v20: any] : ? [v21: any]
% 99.72/15.32 : (in(v18, v0) = v21 & in(v17, v7) = v20 & in(v17, v3) =
% 99.72/15.32 v19 & ( ~ (v19 = 0) | (v21 = 0 & v20 = 0)))) & !
% 99.72/15.32 [v17: $i] : ! [v18: $i] : ( ~ (apply(v4, v17) = v18) | ~
% 99.72/15.32 $i(v17) | ? [v19: any] : ? [v20: any] : ? [v21: any]
% 99.72/15.32 : (in(v18, v0) = v20 & in(v17, v7) = v19 & in(v17, v3) =
% 99.72/15.32 v21 & ( ~ (v20 = 0) | ~ (v19 = 0) | v21 = 0))) & !
% 99.72/15.32 [v17: $i] : ! [v18: $i] : ( ~ (apply(v4, v17) = v18) | ~
% 99.72/15.32 $i(v17) | ? [v19: any] : ? [v20: $i] : (apply(v1, v17)
% 99.72/15.32 = v20 & in(v17, v3) = v19 & $i(v20) & ( ~ (v19 = 0) |
% 99.72/15.32 v20 = v18))) & ! [v17: $i] : ! [v18: $i] : ( ~
% 99.72/15.32 (apply(v1, v17) = v18) | ~ $i(v17) | ? [v19: any] : ?
% 99.72/15.32 [v20: $i] : (apply(v4, v17) = v20 & in(v17, v3) = v19 &
% 99.72/15.32 $i(v20) & ( ~ (v19 = 0) | v20 = v18))) & ! [v17: $i]
% 99.72/15.32 : ! [v18: any] : ( ~ (in(v17, v7) = v18) | ~ $i(v17) |
% 99.72/15.32 ? [v19: any] : ? [v20: $i] : ? [v21: any] : (apply(v4,
% 99.72/15.32 v17) = v20 & in(v20, v0) = v21 & in(v17, v3) = v19 &
% 99.72/15.32 $i(v20) & ( ~ (v19 = 0) | (v21 = 0 & v18 = 0)))) & !
% 99.72/15.32 [v17: $i] : ( ~ (in(v17, v7) = 0) | ~ $i(v17) | ? [v18:
% 99.72/15.32 $i] : ? [v19: any] : ? [v20: any] : (apply(v4, v17)
% 99.72/15.32 = v18 & in(v18, v0) = v19 & in(v17, v3) = v20 &
% 99.72/15.32 $i(v18) & ( ~ (v19 = 0) | v20 = 0))) & ! [v17: $i] :
% 99.72/15.32 ( ~ (in(v17, v3) = 0) | ~ $i(v17) | ? [v18: $i] :
% 99.72/15.32 (apply(v4, v17) = v18 & apply(v1, v17) = v18 & $i(v18)))
% 99.72/15.32 & ! [v17: $i] : ( ~ (in(v17, v3) = 0) | ~ $i(v17) | ?
% 99.72/15.32 [v18: $i] : (apply(v4, v17) = v18 & in(v18, v0) = 0 &
% 99.72/15.32 in(v17, v7) = 0 & $i(v18))))) & (v6 = v1 | (v9 = 0 &
% 99.72/15.32 ~ (v11 = v10) & apply(v4, v8) = v11 & apply(v1, v8) = v10
% 99.72/15.32 & in(v8, v3) = 0 & $i(v11) & $i(v10)) | (apply(v4, v12) =
% 99.72/15.33 v15 & in(v15, v0) = v16 & in(v12, v7) = v14 & in(v12, v3)
% 99.72/15.33 = v13 & $i(v15) & ( ~ (v16 = 0) | ~ (v14 = 0) | ~ (v13 =
% 99.72/15.33 0)) & (v13 = 0 | (v16 = 0 & v14 = 0))))))))))))
% 99.72/15.33
% 99.72/15.33 (t86_funct_1)
% 99.72/15.33 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 99.72/15.33 any] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9: any] : (apply(v2,
% 99.72/15.33 v1) = v8 & relation_rng_restriction(v0, v2) = v3 & in(v8, v0) = v9 &
% 99.72/15.33 in(v1, v6) = v7 & in(v1, v4) = v5 & relation_dom(v3) = v4 & relation_dom(v2)
% 99.72/15.33 = v6 & function(v2) = 0 & relation(v2) = 0 & $i(v8) & $i(v6) & $i(v4) &
% 99.72/15.33 $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v9 = 0 & v7 = 0 & ~ (v5 = 0)) | (v5 =
% 99.72/15.33 0 & ( ~ (v9 = 0) | ~ (v7 = 0)))))
% 99.72/15.33
% 99.72/15.33 (function-axioms)
% 99.72/15.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 99.72/15.33 (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 99.72/15.33 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2)
% 99.72/15.33 = v1) | ~ (relation_rng_restriction(v3, v2) = v0)) & ! [v0:
% 99.72/15.33 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 99.72/15.33 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 99.72/15.33 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 99.72/15.33 : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0:
% 99.72/15.33 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 99.72/15.33 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0:
% 99.72/15.33 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~
% 99.72/15.33 (relation_dom(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 99.72/15.33 v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0:
% 99.72/15.33 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 99.72/15.33 ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0:
% 99.72/15.33 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 99.72/15.33 ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool]
% 99.72/15.33 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 99.72/15.33 (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0))
% 99.72/15.33 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 99.72/15.33 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0:
% 99.72/15.33 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 99.72/15.33 ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 99.72/15.33
% 99.72/15.33 Further assumptions not needed in the proof:
% 99.72/15.33 --------------------------------------------
% 99.72/15.33 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, existence_m1_subset_1,
% 99.72/15.33 fc12_relat_1, fc1_subset_1, fc1_xboole_0, fc4_relat_1, fc7_relat_1, rc1_funct_1,
% 99.72/15.34 rc1_relat_1, rc1_subset_1, rc1_xboole_0, rc2_funct_1, rc2_relat_1, rc2_subset_1,
% 99.72/15.34 rc2_xboole_0, rc3_funct_1, rc3_relat_1, reflexivity_r1_tarski, t1_subset,
% 99.72/15.34 t2_subset, t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole
% 99.72/15.34
% 99.72/15.34 Those formulas are unsatisfiable:
% 99.72/15.34 ---------------------------------
% 99.72/15.34
% 99.72/15.34 Begin of proof
% 99.72/15.34 |
% 99.72/15.34 | ALPHA: (cc2_funct_1) implies:
% 99.72/15.34 | (1) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 99.72/15.34 | [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 &
% 99.72/15.34 | empty(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)))
% 99.72/15.34 | (2) ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 99.72/15.34 | [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & empty(v0) = v2 &
% 99.72/15.34 | relation(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)))
% 99.72/15.34 |
% 99.72/15.34 | ALPHA: (fc5_relat_1) implies:
% 99.72/15.34 | (3) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 99.72/15.34 | [v2: $i] : ? [v3: any] : (relation_dom(v0) = v2 & empty(v2) = v3 &
% 99.72/15.34 | empty(v0) = v1 & $i(v2) & ( ~ (v3 = 0) | v1 = 0)))
% 99.72/15.34 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) |
% 99.72/15.34 | ? [v2: any] : ? [v3: any] : ? [v4: any] : (empty(v1) = v4 &
% 99.72/15.34 | empty(v0) = v2 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) |
% 99.72/15.34 | v2 = 0)))
% 99.72/15.34 |
% 99.72/15.34 | ALPHA: (t85_funct_1) implies:
% 99.72/15.35 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 99.72/15.35 | ~ (relation_rng_restriction(v0, v3) = v4) | ~ (relation_dom(v1) =
% 99.72/15.35 | v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6:
% 99.72/15.35 | any] : ? [v7: any] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] :
% 99.72/15.36 | ? [v11: int] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15:
% 99.72/15.36 | any] : ? [v16: any] : ? [v17: $i] : ? [v18: any] : ($i(v14) &
% 99.72/15.36 | $i(v10) & ((relation_dom(v3) = v9 & function(v3) = v8 &
% 99.72/15.36 | relation(v3) = v7 & $i(v9) & ( ~ (v8 = 0) | ~ (v7 = 0) | (( ~
% 99.72/15.36 | (v4 = v1) | ( ! [v19: $i] : ! [v20: int] : (v20 = 0 | ~
% 99.72/15.36 | (in(v19, v2) = v20) | ~ $i(v19) | ? [v21: any] : ?
% 99.72/15.36 | [v22: $i] : ? [v23: any] : (apply(v3, v19) = v22 &
% 99.72/15.36 | in(v22, v0) = v23 & in(v19, v9) = v21 & $i(v22) & (
% 99.72/15.36 | ~ (v23 = 0) | ~ (v21 = 0)))) & ! [v19: $i] : !
% 99.72/15.36 | [v20: $i] : ( ~ (apply(v3, v19) = v20) | ~ $i(v19) |
% 99.72/15.36 | ? [v21: any] : ? [v22: any] : ? [v23: any] :
% 99.72/15.36 | (in(v20, v0) = v23 & in(v19, v9) = v22 & in(v19, v2)
% 99.72/15.36 | = v21 & ( ~ (v21 = 0) | (v23 = 0 & v22 = 0)))) & !
% 99.72/15.36 | [v19: $i] : ! [v20: $i] : ( ~ (apply(v3, v19) = v20) |
% 99.72/15.36 | ~ $i(v19) | ? [v21: any] : ? [v22: any] : ? [v23:
% 99.72/15.36 | any] : (in(v20, v0) = v22 & in(v19, v9) = v21 &
% 99.72/15.36 | in(v19, v2) = v23 & ( ~ (v22 = 0) | ~ (v21 = 0) |
% 99.72/15.36 | v23 = 0))) & ! [v19: $i] : ! [v20: $i] : ( ~
% 99.72/15.36 | (apply(v3, v19) = v20) | ~ $i(v19) | ? [v21: any] :
% 99.72/15.36 | ? [v22: $i] : (apply(v1, v19) = v22 & in(v19, v2) =
% 99.72/15.36 | v21 & $i(v22) & ( ~ (v21 = 0) | v22 = v20))) & !
% 99.72/15.36 | [v19: $i] : ! [v20: $i] : ( ~ (apply(v1, v19) = v20) |
% 99.72/15.36 | ~ $i(v19) | ? [v21: any] : ? [v22: $i] :
% 99.72/15.36 | (apply(v3, v19) = v22 & in(v19, v2) = v21 & $i(v22) &
% 99.72/15.36 | ( ~ (v21 = 0) | v22 = v20))) & ! [v19: $i] : !
% 99.72/15.36 | [v20: any] : ( ~ (in(v19, v9) = v20) | ~ $i(v19) | ?
% 99.72/15.36 | [v21: any] : ? [v22: $i] : ? [v23: any] :
% 99.72/15.36 | (apply(v3, v19) = v22 & in(v22, v0) = v23 & in(v19,
% 99.72/15.36 | v2) = v21 & $i(v22) & ( ~ (v21 = 0) | (v23 = 0 &
% 99.72/15.36 | v20 = 0)))) & ! [v19: $i] : ( ~ (in(v19, v9) =
% 99.72/15.36 | 0) | ~ $i(v19) | ? [v20: $i] : ? [v21: any] : ?
% 99.72/15.36 | [v22: any] : (apply(v3, v19) = v20 & in(v20, v0) =
% 99.72/15.36 | v21 & in(v19, v2) = v22 & $i(v20) & ( ~ (v21 = 0) |
% 99.72/15.36 | v22 = 0))) & ! [v19: $i] : ( ~ (in(v19, v2) = 0)
% 99.72/15.36 | | ~ $i(v19) | ? [v20: $i] : (apply(v3, v19) = v20 &
% 99.72/15.36 | apply(v1, v19) = v20 & $i(v20))) & ! [v19: $i] : (
% 99.72/15.36 | ~ (in(v19, v2) = 0) | ~ $i(v19) | ? [v20: $i] :
% 99.72/15.36 | (apply(v3, v19) = v20 & in(v20, v0) = 0 & in(v19, v9)
% 99.72/15.36 | = 0 & $i(v20))))) & (v4 = v1 | (v11 = 0 & ~ (v13 =
% 99.72/15.36 | v12) & apply(v3, v10) = v13 & apply(v1, v10) = v12 &
% 99.72/15.36 | in(v10, v2) = 0 & $i(v13) & $i(v12)) | (apply(v3, v14)
% 99.72/15.36 | = v17 & in(v17, v0) = v18 & in(v14, v9) = v16 & in(v14,
% 99.72/15.36 | v2) = v15 & $i(v17) & ( ~ (v18 = 0) | ~ (v16 = 0) |
% 99.72/15.36 | ~ (v15 = 0)) & (v15 = 0 | (v18 = 0 & v16 = 0))))))) |
% 99.72/15.36 | (function(v1) = v6 & relation(v1) = v5 & ( ~ (v6 = 0) | ~ (v5 =
% 99.72/15.36 | 0))))))
% 99.72/15.36 |
% 99.72/15.36 | ALPHA: (function-axioms) implies:
% 99.72/15.36 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 99.72/15.36 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 99.72/15.36 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 99.72/15.36 | (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 99.72/15.36 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 99.72/15.36 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 99.72/15.36 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 99.72/15.36 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 99.72/15.36 |
% 99.72/15.36 | DELTA: instantiating (t86_funct_1) with fresh symbols all_42_0, all_42_1,
% 99.72/15.36 | all_42_2, all_42_3, all_42_4, all_42_5, all_42_6, all_42_7, all_42_8,
% 99.72/15.36 | all_42_9 gives:
% 99.72/15.36 | (10) apply(all_42_7, all_42_8) = all_42_1 &
% 99.72/15.36 | relation_rng_restriction(all_42_9, all_42_7) = all_42_6 & in(all_42_1,
% 99.72/15.36 | all_42_9) = all_42_0 & in(all_42_8, all_42_3) = all_42_2 &
% 99.72/15.36 | in(all_42_8, all_42_5) = all_42_4 & relation_dom(all_42_6) = all_42_5
% 99.72/15.36 | & relation_dom(all_42_7) = all_42_3 & function(all_42_7) = 0 &
% 99.72/15.36 | relation(all_42_7) = 0 & $i(all_42_1) & $i(all_42_3) & $i(all_42_5) &
% 99.72/15.36 | $i(all_42_6) & $i(all_42_7) & $i(all_42_8) & $i(all_42_9) & ((all_42_0
% 99.72/15.36 | = 0 & all_42_2 = 0 & ~ (all_42_4 = 0)) | (all_42_4 = 0 & ( ~
% 99.72/15.36 | (all_42_0 = 0) | ~ (all_42_2 = 0))))
% 99.72/15.36 |
% 99.72/15.36 | ALPHA: (10) implies:
% 99.72/15.36 | (11) $i(all_42_9)
% 99.72/15.36 | (12) $i(all_42_8)
% 99.72/15.36 | (13) $i(all_42_7)
% 99.72/15.36 | (14) $i(all_42_6)
% 99.72/15.36 | (15) relation(all_42_7) = 0
% 99.72/15.36 | (16) function(all_42_7) = 0
% 99.72/15.36 | (17) relation_dom(all_42_7) = all_42_3
% 99.72/15.36 | (18) relation_dom(all_42_6) = all_42_5
% 99.72/15.36 | (19) in(all_42_8, all_42_5) = all_42_4
% 99.72/15.36 | (20) in(all_42_8, all_42_3) = all_42_2
% 99.72/15.36 | (21) in(all_42_1, all_42_9) = all_42_0
% 99.72/15.36 | (22) relation_rng_restriction(all_42_9, all_42_7) = all_42_6
% 99.72/15.36 | (23) apply(all_42_7, all_42_8) = all_42_1
% 99.72/15.36 | (24) (all_42_0 = 0 & all_42_2 = 0 & ~ (all_42_4 = 0)) | (all_42_4 = 0 & (
% 99.72/15.36 | ~ (all_42_0 = 0) | ~ (all_42_2 = 0)))
% 99.72/15.36 |
% 99.72/15.37 | GROUND_INST: instantiating (3) with all_42_7, simplifying with (13), (15)
% 99.72/15.37 | gives:
% 99.72/15.37 | (25) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_dom(all_42_7) =
% 99.72/15.37 | v1 & empty(v1) = v2 & empty(all_42_7) = v0 & $i(v1) & ( ~ (v2 = 0) |
% 99.72/15.37 | v0 = 0))
% 99.72/15.37 |
% 99.72/15.37 | GROUND_INST: instantiating (1) with all_42_7, simplifying with (13), (15)
% 99.72/15.37 | gives:
% 99.72/15.37 | (26) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_42_7) =
% 99.72/15.37 | v2 & function(all_42_7) = v1 & empty(all_42_7) = v0 & ( ~ (v1 = 0) |
% 99.72/15.37 | ~ (v0 = 0) | v2 = 0))
% 99.72/15.37 |
% 99.72/15.37 | GROUND_INST: instantiating (2) with all_42_7, simplifying with (13), (16)
% 99.72/15.37 | gives:
% 99.72/15.37 | (27) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_42_7) =
% 99.72/15.37 | v2 & empty(all_42_7) = v1 & relation(all_42_7) = v0 & ( ~ (v1 = 0) |
% 99.72/15.37 | ~ (v0 = 0) | v2 = 0))
% 99.72/15.37 |
% 99.72/15.37 | GROUND_INST: instantiating (4) with all_42_7, all_42_3, simplifying with (13),
% 99.72/15.37 | (17) gives:
% 99.72/15.37 | (28) ? [v0: any] : ? [v1: any] : ? [v2: any] : (empty(all_42_3) = v2 &
% 99.72/15.37 | empty(all_42_7) = v0 & relation(all_42_7) = v1 & ( ~ (v2 = 0) | ~
% 99.72/15.37 | (v1 = 0) | v0 = 0))
% 99.72/15.37 |
% 99.72/15.37 | GROUND_INST: instantiating (4) with all_42_6, all_42_5, simplifying with (14),
% 99.72/15.37 | (18) gives:
% 99.72/15.37 | (29) ? [v0: any] : ? [v1: any] : ? [v2: any] : (empty(all_42_5) = v2 &
% 99.72/15.37 | empty(all_42_6) = v0 & relation(all_42_6) = v1 & ( ~ (v2 = 0) | ~
% 99.72/15.37 | (v1 = 0) | v0 = 0))
% 99.72/15.37 |
% 99.72/15.37 | GROUND_INST: instantiating (5) with all_42_9, all_42_6, all_42_5, all_42_7,
% 99.72/15.37 | all_42_6, simplifying with (11), (13), (14), (18), (22) gives:
% 100.16/15.38 | (30) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 100.16/15.38 | $i] : ? [v5: $i] : ? [v6: $i] : ($i(v6) & $i(v5) &
% 100.16/15.38 | ((relation_dom(all_42_7) = v4 & function(all_42_7) = v3 &
% 100.16/15.38 | relation(all_42_7) = v2 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) |
% 100.16/15.38 | ( ! [v7: $i] : ! [v8: int] : (v8 = 0 | ~ (in(v7, all_42_5) =
% 100.16/15.38 | v8) | ~ $i(v7) | ? [v9: any] : ? [v10: $i] : ? [v11:
% 100.16/15.38 | any] : (apply(all_42_7, v7) = v10 & in(v10, all_42_9) =
% 100.16/15.38 | v11 & in(v7, v4) = v9 & $i(v10) & ( ~ (v11 = 0) | ~ (v9
% 100.16/15.38 | = 0)))) & ! [v7: $i] : ! [v8: $i] : ( ~
% 100.16/15.38 | (apply(all_42_6, v7) = v8) | ~ $i(v7) | ? [v9: any] : ?
% 100.16/15.38 | [v10: $i] : (apply(all_42_7, v7) = v10 & in(v7, all_42_5)
% 100.16/15.38 | = v9 & $i(v10) & ( ~ (v9 = 0) | v10 = v8))) & ! [v7:
% 100.16/15.38 | $i] : ! [v8: $i] : ( ~ (apply(all_42_7, v7) = v8) | ~
% 100.16/15.38 | $i(v7) | ? [v9: any] : ? [v10: any] : ? [v11: any] :
% 100.16/15.38 | (in(v8, all_42_9) = v11 & in(v7, v4) = v10 & in(v7,
% 100.16/15.38 | all_42_5) = v9 & ( ~ (v9 = 0) | (v11 = 0 & v10 = 0))))
% 100.16/15.38 | & ! [v7: $i] : ! [v8: $i] : ( ~ (apply(all_42_7, v7) = v8)
% 100.16/15.38 | | ~ $i(v7) | ? [v9: any] : ? [v10: any] : ? [v11: any]
% 100.16/15.38 | : (in(v8, all_42_9) = v10 & in(v7, v4) = v9 & in(v7,
% 100.16/15.38 | all_42_5) = v11 & ( ~ (v10 = 0) | ~ (v9 = 0) | v11 =
% 100.16/15.38 | 0))) & ! [v7: $i] : ! [v8: $i] : ( ~
% 100.16/15.38 | (apply(all_42_7, v7) = v8) | ~ $i(v7) | ? [v9: any] : ?
% 100.16/15.38 | [v10: $i] : (apply(all_42_6, v7) = v10 & in(v7, all_42_5)
% 100.16/15.38 | = v9 & $i(v10) & ( ~ (v9 = 0) | v10 = v8))) & ! [v7:
% 100.16/15.38 | $i] : ! [v8: any] : ( ~ (in(v7, v4) = v8) | ~ $i(v7) |
% 100.16/15.38 | ? [v9: any] : ? [v10: $i] : ? [v11: any] :
% 100.16/15.38 | (apply(all_42_7, v7) = v10 & in(v10, all_42_9) = v11 &
% 100.16/15.38 | in(v7, all_42_5) = v9 & $i(v10) & ( ~ (v9 = 0) | (v11 =
% 100.16/15.38 | 0 & v8 = 0)))) & ! [v7: $i] : ( ~ (in(v7, v4) = 0)
% 100.16/15.38 | | ~ $i(v7) | ? [v8: $i] : ? [v9: any] : ? [v10: any] :
% 100.16/15.38 | (apply(all_42_7, v7) = v8 & in(v8, all_42_9) = v9 & in(v7,
% 100.16/15.38 | all_42_5) = v10 & $i(v8) & ( ~ (v9 = 0) | v10 = 0))) &
% 100.16/15.38 | ! [v7: $i] : ( ~ (in(v7, all_42_5) = 0) | ~ $i(v7) | ?
% 100.16/15.38 | [v8: $i] : (apply(all_42_6, v7) = v8 & apply(all_42_7, v7)
% 100.16/15.38 | = v8 & $i(v8))) & ! [v7: $i] : ( ~ (in(v7, all_42_5) =
% 100.16/15.38 | 0) | ~ $i(v7) | ? [v8: $i] : (apply(all_42_7, v7) = v8
% 100.16/15.38 | & in(v8, all_42_9) = 0 & in(v7, v4) = 0 & $i(v8)))))) |
% 100.16/15.38 | (function(all_42_6) = v1 & relation(all_42_6) = v0 & ( ~ (v1 = 0)
% 100.16/15.38 | | ~ (v0 = 0)))))
% 100.16/15.38 |
% 100.16/15.38 | GROUND_INST: instantiating (5) with all_42_9, all_42_7, all_42_3, all_42_7,
% 100.16/15.38 | all_42_6, simplifying with (11), (13), (17), (22) gives:
% 100.16/15.39 | (31) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 100.16/15.39 | $i] : ? [v5: $i] : ? [v6: int] : ? [v7: $i] : ? [v8: $i] : ?
% 100.16/15.39 | [v9: $i] : ? [v10: any] : ? [v11: any] : ? [v12: $i] : ? [v13:
% 100.16/15.39 | any] : ($i(v9) & $i(v5) & ((relation_dom(all_42_7) = v4 &
% 100.16/15.39 | function(all_42_7) = v3 & relation(all_42_7) = v2 & $i(v4) & ( ~
% 100.16/15.39 | (v3 = 0) | ~ (v2 = 0) | (( ~ (all_42_6 = all_42_7) | ( !
% 100.16/15.39 | [v14: $i] : ! [v15: int] : (v15 = 0 | ~ (in(v14,
% 100.16/15.39 | all_42_3) = v15) | ~ $i(v14) | ? [v16: any] : ?
% 100.16/15.39 | [v17: $i] : ? [v18: any] : (apply(all_42_7, v14) =
% 100.16/15.39 | v17 & in(v17, all_42_9) = v18 & in(v14, v4) = v16 &
% 100.16/15.39 | $i(v17) & ( ~ (v18 = 0) | ~ (v16 = 0)))) & ! [v14:
% 100.16/15.39 | $i] : ! [v15: $i] : ( ~ (apply(all_42_7, v14) = v15)
% 100.16/15.39 | | ~ $i(v14) | ? [v16: any] : ? [v17: any] : ?
% 100.16/15.39 | [v18: any] : (in(v15, all_42_9) = v18 & in(v14, v4) =
% 100.16/15.39 | v17 & in(v14, all_42_3) = v16 & ( ~ (v16 = 0) | (v18
% 100.16/15.39 | = 0 & v17 = 0)))) & ! [v14: $i] : ! [v15: $i]
% 100.16/15.39 | : ( ~ (apply(all_42_7, v14) = v15) | ~ $i(v14) | ?
% 100.16/15.39 | [v16: any] : ? [v17: any] : ? [v18: any] : (in(v15,
% 100.16/15.39 | all_42_9) = v17 & in(v14, v4) = v16 & in(v14,
% 100.16/15.39 | all_42_3) = v18 & ( ~ (v17 = 0) | ~ (v16 = 0) |
% 100.16/15.39 | v18 = 0))) & ! [v14: $i] : ! [v15: $i] : ( ~
% 100.16/15.39 | (apply(all_42_7, v14) = v15) | ~ $i(v14) | ? [v16:
% 100.16/15.39 | any] : ? [v17: $i] : (apply(all_42_7, v14) = v17 &
% 100.16/15.39 | in(v14, all_42_3) = v16 & $i(v17) & ( ~ (v16 = 0) |
% 100.16/15.39 | v17 = v15))) & ! [v14: $i] : ! [v15: any] : ( ~
% 100.16/15.39 | (in(v14, v4) = v15) | ~ $i(v14) | ? [v16: any] : ?
% 100.16/15.39 | [v17: $i] : ? [v18: any] : (apply(all_42_7, v14) =
% 100.16/15.39 | v17 & in(v17, all_42_9) = v18 & in(v14, all_42_3) =
% 100.16/15.39 | v16 & $i(v17) & ( ~ (v16 = 0) | (v18 = 0 & v15 =
% 100.16/15.39 | 0)))) & ! [v14: $i] : ( ~ (in(v14, v4) = 0) |
% 100.16/15.39 | ~ $i(v14) | ? [v15: $i] : ? [v16: any] : ? [v17:
% 100.16/15.39 | any] : (apply(all_42_7, v14) = v15 & in(v15,
% 100.16/15.39 | all_42_9) = v16 & in(v14, all_42_3) = v17 &
% 100.16/15.39 | $i(v15) & ( ~ (v16 = 0) | v17 = 0))) & ! [v14: $i]
% 100.16/15.39 | : ( ~ (in(v14, all_42_3) = 0) | ~ $i(v14) | ? [v15:
% 100.16/15.39 | $i] : (apply(all_42_7, v14) = v15 & in(v15,
% 100.16/15.39 | all_42_9) = 0 & in(v14, v4) = 0 & $i(v15))) & !
% 100.16/15.39 | [v14: $i] : ( ~ (in(v14, all_42_3) = 0) | ~ $i(v14) |
% 100.16/15.39 | ? [v15: $i] : (apply(all_42_7, v14) = v15 &
% 100.16/15.39 | $i(v15))))) & (all_42_6 = all_42_7 | (v6 = 0 & ~
% 100.16/15.39 | (v8 = v7) & apply(all_42_7, v5) = v8 & apply(all_42_7,
% 100.16/15.39 | v5) = v7 & in(v5, all_42_3) = 0 & $i(v8) & $i(v7)) |
% 100.16/15.39 | (apply(all_42_7, v9) = v12 & in(v12, all_42_9) = v13 &
% 100.16/15.39 | in(v9, v4) = v11 & in(v9, all_42_3) = v10 & $i(v12) & (
% 100.16/15.39 | ~ (v13 = 0) | ~ (v11 = 0) | ~ (v10 = 0)) & (v10 = 0
% 100.16/15.39 | | (v13 = 0 & v11 = 0))))))) | (function(all_42_7) = v1
% 100.16/15.39 | & relation(all_42_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))))
% 100.16/15.39 |
% 100.16/15.39 | GROUND_INST: instantiating (fc5_funct_1) with all_42_9, all_42_7, all_42_6,
% 100.16/15.39 | simplifying with (11), (13), (22) gives:
% 100.16/15.39 | (32) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 100.16/15.39 | (function(all_42_6) = v3 & function(all_42_7) = v1 &
% 100.16/15.39 | relation(all_42_6) = v2 & relation(all_42_7) = v0 & ( ~ (v1 = 0) |
% 100.16/15.39 | ~ (v0 = 0) | (v3 = 0 & v2 = 0)))
% 100.16/15.39 |
% 100.16/15.39 | GROUND_INST: instantiating (dt_k8_relat_1) with all_42_9, all_42_7, all_42_6,
% 100.16/15.39 | simplifying with (11), (13), (22) gives:
% 100.16/15.39 | (33) ? [v0: any] : ? [v1: any] : (relation(all_42_6) = v1 &
% 100.16/15.39 | relation(all_42_7) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 100.16/15.39 |
% 100.16/15.39 | DELTA: instantiating (33) with fresh symbols all_62_0, all_62_1 gives:
% 100.16/15.39 | (34) relation(all_42_6) = all_62_0 & relation(all_42_7) = all_62_1 & ( ~
% 100.16/15.39 | (all_62_1 = 0) | all_62_0 = 0)
% 100.16/15.39 |
% 100.16/15.39 | ALPHA: (34) implies:
% 100.16/15.39 | (35) relation(all_42_7) = all_62_1
% 100.16/15.39 | (36) relation(all_42_6) = all_62_0
% 100.16/15.39 | (37) ~ (all_62_1 = 0) | all_62_0 = 0
% 100.16/15.39 |
% 100.16/15.39 | DELTA: instantiating (29) with fresh symbols all_72_0, all_72_1, all_72_2
% 100.16/15.39 | gives:
% 100.16/15.39 | (38) empty(all_42_5) = all_72_0 & empty(all_42_6) = all_72_2 &
% 100.16/15.39 | relation(all_42_6) = all_72_1 & ( ~ (all_72_0 = 0) | ~ (all_72_1 = 0)
% 100.16/15.39 | | all_72_2 = 0)
% 100.16/15.39 |
% 100.16/15.39 | ALPHA: (38) implies:
% 100.16/15.39 | (39) relation(all_42_6) = all_72_1
% 100.16/15.39 |
% 100.16/15.39 | DELTA: instantiating (27) with fresh symbols all_78_0, all_78_1, all_78_2
% 100.16/15.39 | gives:
% 100.16/15.39 | (40) one_to_one(all_42_7) = all_78_0 & empty(all_42_7) = all_78_1 &
% 100.16/15.39 | relation(all_42_7) = all_78_2 & ( ~ (all_78_1 = 0) | ~ (all_78_2 = 0)
% 100.16/15.39 | | all_78_0 = 0)
% 100.16/15.39 |
% 100.16/15.39 | ALPHA: (40) implies:
% 100.16/15.39 | (41) relation(all_42_7) = all_78_2
% 100.16/15.39 |
% 100.16/15.39 | DELTA: instantiating (26) with fresh symbols all_88_0, all_88_1, all_88_2
% 100.16/15.39 | gives:
% 100.24/15.39 | (42) one_to_one(all_42_7) = all_88_0 & function(all_42_7) = all_88_1 &
% 100.24/15.39 | empty(all_42_7) = all_88_2 & ( ~ (all_88_1 = 0) | ~ (all_88_2 = 0) |
% 100.24/15.39 | all_88_0 = 0)
% 100.24/15.39 |
% 100.24/15.39 | ALPHA: (42) implies:
% 100.24/15.39 | (43) function(all_42_7) = all_88_1
% 100.24/15.39 |
% 100.24/15.39 | DELTA: instantiating (25) with fresh symbols all_90_0, all_90_1, all_90_2
% 100.24/15.39 | gives:
% 100.24/15.40 | (44) relation_dom(all_42_7) = all_90_1 & empty(all_90_1) = all_90_0 &
% 100.24/15.40 | empty(all_42_7) = all_90_2 & $i(all_90_1) & ( ~ (all_90_0 = 0) |
% 100.24/15.40 | all_90_2 = 0)
% 100.24/15.40 |
% 100.24/15.40 | ALPHA: (44) implies:
% 100.24/15.40 | (45) relation_dom(all_42_7) = all_90_1
% 100.24/15.40 |
% 100.24/15.40 | DELTA: instantiating (28) with fresh symbols all_92_0, all_92_1, all_92_2
% 100.24/15.40 | gives:
% 100.24/15.40 | (46) empty(all_42_3) = all_92_0 & empty(all_42_7) = all_92_2 &
% 100.24/15.40 | relation(all_42_7) = all_92_1 & ( ~ (all_92_0 = 0) | ~ (all_92_1 = 0)
% 100.24/15.40 | | all_92_2 = 0)
% 100.24/15.40 |
% 100.24/15.40 | ALPHA: (46) implies:
% 100.24/15.40 | (47) relation(all_42_7) = all_92_1
% 100.24/15.40 |
% 100.24/15.40 | DELTA: instantiating (32) with fresh symbols all_128_0, all_128_1, all_128_2,
% 100.24/15.40 | all_128_3 gives:
% 100.24/15.40 | (48) function(all_42_6) = all_128_0 & function(all_42_7) = all_128_2 &
% 100.24/15.40 | relation(all_42_6) = all_128_1 & relation(all_42_7) = all_128_3 & ( ~
% 100.24/15.40 | (all_128_2 = 0) | ~ (all_128_3 = 0) | (all_128_0 = 0 & all_128_1 =
% 100.24/15.40 | 0))
% 100.24/15.40 |
% 100.24/15.40 | ALPHA: (48) implies:
% 100.24/15.40 | (49) relation(all_42_7) = all_128_3
% 100.24/15.40 | (50) relation(all_42_6) = all_128_1
% 100.24/15.40 | (51) function(all_42_7) = all_128_2
% 100.24/15.40 | (52) function(all_42_6) = all_128_0
% 100.24/15.40 | (53) ~ (all_128_2 = 0) | ~ (all_128_3 = 0) | (all_128_0 = 0 & all_128_1 =
% 100.24/15.40 | 0)
% 100.24/15.40 |
% 100.24/15.40 | DELTA: instantiating (30) with fresh symbols all_130_0, all_130_1, all_130_2,
% 100.24/15.40 | all_130_3, all_130_4, all_130_5, all_130_6 gives:
% 100.24/15.41 | (54) $i(all_130_0) & $i(all_130_1) & ((relation_dom(all_42_7) = all_130_2 &
% 100.24/15.41 | function(all_42_7) = all_130_3 & relation(all_42_7) = all_130_4 &
% 100.24/15.41 | $i(all_130_2) & ( ~ (all_130_3 = 0) | ~ (all_130_4 = 0) | ( !
% 100.24/15.41 | [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_42_5) = v1)
% 100.24/15.41 | | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] :
% 100.24/15.41 | (apply(all_42_7, v0) = v3 & in(v3, all_42_9) = v4 & in(v0,
% 100.24/15.41 | all_130_2) = v2 & $i(v3) & ( ~ (v4 = 0) | ~ (v2 = 0))))
% 100.24/15.41 | & ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_42_6, v0) = v1) |
% 100.24/15.41 | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : (apply(all_42_7,
% 100.24/15.41 | v0) = v3 & in(v0, all_42_5) = v2 & $i(v3) & ( ~ (v2 = 0)
% 100.24/15.41 | | v3 = v1))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 100.24/15.41 | (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 100.24/15.41 | [v3: any] : ? [v4: any] : (in(v1, all_42_9) = v4 & in(v0,
% 100.24/15.41 | all_130_2) = v3 & in(v0, all_42_5) = v2 & ( ~ (v2 = 0) |
% 100.24/15.41 | (v4 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 100.24/15.41 | (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 100.24/15.41 | [v3: any] : ? [v4: any] : (in(v1, all_42_9) = v3 & in(v0,
% 100.24/15.41 | all_130_2) = v2 & in(v0, all_42_5) = v4 & ( ~ (v3 = 0) |
% 100.24/15.41 | ~ (v2 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : (
% 100.24/15.41 | ~ (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 100.24/15.41 | [v3: $i] : (apply(all_42_6, v0) = v3 & in(v0, all_42_5) = v2
% 100.24/15.41 | & $i(v3) & ( ~ (v2 = 0) | v3 = v1))) & ! [v0: $i] : !
% 100.24/15.41 | [v1: any] : ( ~ (in(v0, all_130_2) = v1) | ~ $i(v0) | ? [v2:
% 100.24/15.41 | any] : ? [v3: $i] : ? [v4: any] : (apply(all_42_7, v0) =
% 100.24/15.41 | v3 & in(v3, all_42_9) = v4 & in(v0, all_42_5) = v2 &
% 100.24/15.41 | $i(v3) & ( ~ (v2 = 0) | (v4 = 0 & v1 = 0)))) & ! [v0: $i]
% 100.24/15.41 | : ( ~ (in(v0, all_130_2) = 0) | ~ $i(v0) | ? [v1: $i] : ?
% 100.24/15.41 | [v2: any] : ? [v3: any] : (apply(all_42_7, v0) = v1 &
% 100.24/15.41 | in(v1, all_42_9) = v2 & in(v0, all_42_5) = v3 & $i(v1) & (
% 100.24/15.41 | ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (in(v0,
% 100.24/15.41 | all_42_5) = 0) | ~ $i(v0) | ? [v1: $i] :
% 100.24/15.41 | (apply(all_42_6, v0) = v1 & apply(all_42_7, v0) = v1 &
% 100.24/15.41 | $i(v1))) & ! [v0: $i] : ( ~ (in(v0, all_42_5) = 0) | ~
% 100.24/15.41 | $i(v0) | ? [v1: $i] : (apply(all_42_7, v0) = v1 & in(v1,
% 100.24/15.41 | all_42_9) = 0 & in(v0, all_130_2) = 0 & $i(v1)))))) |
% 100.24/15.41 | (function(all_42_6) = all_130_5 & relation(all_42_6) = all_130_6 & (
% 100.24/15.41 | ~ (all_130_5 = 0) | ~ (all_130_6 = 0))))
% 100.24/15.41 |
% 100.24/15.41 | ALPHA: (54) implies:
% 100.33/15.42 | (55) (relation_dom(all_42_7) = all_130_2 & function(all_42_7) = all_130_3 &
% 100.33/15.42 | relation(all_42_7) = all_130_4 & $i(all_130_2) & ( ~ (all_130_3 = 0)
% 100.33/15.42 | | ~ (all_130_4 = 0) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 100.33/15.42 | (in(v0, all_42_5) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 100.33/15.42 | $i] : ? [v4: any] : (apply(all_42_7, v0) = v3 & in(v3,
% 100.33/15.42 | all_42_9) = v4 & in(v0, all_130_2) = v2 & $i(v3) & ( ~ (v4
% 100.33/15.42 | = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 100.33/15.42 | (apply(all_42_6, v0) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 100.33/15.42 | [v3: $i] : (apply(all_42_7, v0) = v3 & in(v0, all_42_5) = v2 &
% 100.33/15.42 | $i(v3) & ( ~ (v2 = 0) | v3 = v1))) & ! [v0: $i] : ! [v1:
% 100.33/15.42 | $i] : ( ~ (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2:
% 100.33/15.42 | any] : ? [v3: any] : ? [v4: any] : (in(v1, all_42_9) = v4
% 100.33/15.42 | & in(v0, all_130_2) = v3 & in(v0, all_42_5) = v2 & ( ~ (v2 =
% 100.33/15.42 | 0) | (v4 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] :
% 100.33/15.42 | ( ~ (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 100.33/15.42 | [v3: any] : ? [v4: any] : (in(v1, all_42_9) = v3 & in(v0,
% 100.33/15.42 | all_130_2) = v2 & in(v0, all_42_5) = v4 & ( ~ (v3 = 0) |
% 100.33/15.42 | ~ (v2 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 100.33/15.42 | (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 100.33/15.42 | [v3: $i] : (apply(all_42_6, v0) = v3 & in(v0, all_42_5) = v2 &
% 100.33/15.42 | $i(v3) & ( ~ (v2 = 0) | v3 = v1))) & ! [v0: $i] : ! [v1:
% 100.33/15.42 | any] : ( ~ (in(v0, all_130_2) = v1) | ~ $i(v0) | ? [v2: any]
% 100.33/15.42 | : ? [v3: $i] : ? [v4: any] : (apply(all_42_7, v0) = v3 &
% 100.33/15.42 | in(v3, all_42_9) = v4 & in(v0, all_42_5) = v2 & $i(v3) & ( ~
% 100.33/15.42 | (v2 = 0) | (v4 = 0 & v1 = 0)))) & ! [v0: $i] : ( ~
% 100.33/15.42 | (in(v0, all_130_2) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 100.33/15.42 | any] : ? [v3: any] : (apply(all_42_7, v0) = v1 & in(v1,
% 100.33/15.42 | all_42_9) = v2 & in(v0, all_42_5) = v3 & $i(v1) & ( ~ (v2
% 100.33/15.42 | = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (in(v0, all_42_5) =
% 100.33/15.42 | 0) | ~ $i(v0) | ? [v1: $i] : (apply(all_42_6, v0) = v1 &
% 100.33/15.42 | apply(all_42_7, v0) = v1 & $i(v1))) & ! [v0: $i] : ( ~
% 100.33/15.42 | (in(v0, all_42_5) = 0) | ~ $i(v0) | ? [v1: $i] :
% 100.33/15.42 | (apply(all_42_7, v0) = v1 & in(v1, all_42_9) = 0 & in(v0,
% 100.33/15.42 | all_130_2) = 0 & $i(v1)))))) | (function(all_42_6) =
% 100.33/15.42 | all_130_5 & relation(all_42_6) = all_130_6 & ( ~ (all_130_5 = 0) |
% 100.33/15.42 | ~ (all_130_6 = 0)))
% 100.33/15.42 |
% 100.33/15.42 | DELTA: instantiating (31) with fresh symbols all_132_0, all_132_1, all_132_2,
% 100.33/15.42 | all_132_3, all_132_4, all_132_5, all_132_6, all_132_7, all_132_8,
% 100.33/15.42 | all_132_9, all_132_10, all_132_11, all_132_12, all_132_13 gives:
% 100.34/15.42 | (56) $i(all_132_4) & $i(all_132_8) & ((relation_dom(all_42_7) = all_132_9 &
% 100.34/15.42 | function(all_42_7) = all_132_10 & relation(all_42_7) = all_132_11
% 100.34/15.42 | & $i(all_132_9) & ( ~ (all_132_10 = 0) | ~ (all_132_11 = 0) | ((
% 100.34/15.42 | ~ (all_42_6 = all_42_7) | ( ! [v0: $i] : ! [v1: int] : (v1
% 100.34/15.42 | = 0 | ~ (in(v0, all_42_3) = v1) | ~ $i(v0) | ? [v2:
% 100.34/15.42 | any] : ? [v3: $i] : ? [v4: any] : (apply(all_42_7,
% 100.34/15.42 | v0) = v3 & in(v3, all_42_9) = v4 & in(v0, all_132_9)
% 100.34/15.42 | = v2 & $i(v3) & ( ~ (v4 = 0) | ~ (v2 = 0)))) & !
% 100.34/15.42 | [v0: $i] : ! [v1: $i] : ( ~ (apply(all_42_7, v0) = v1) |
% 100.34/15.42 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] :
% 100.34/15.42 | (in(v1, all_42_9) = v4 & in(v0, all_132_9) = v3 & in(v0,
% 100.34/15.42 | all_42_3) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0))))
% 100.34/15.42 | & ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_42_7, v0) =
% 100.34/15.42 | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ?
% 100.34/15.42 | [v4: any] : (in(v1, all_42_9) = v3 & in(v0, all_132_9) =
% 100.34/15.42 | v2 & in(v0, all_42_3) = v4 & ( ~ (v3 = 0) | ~ (v2 =
% 100.34/15.42 | 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 100.34/15.42 | (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any] :
% 100.34/15.42 | ? [v3: $i] : (apply(all_42_7, v0) = v3 & in(v0,
% 100.34/15.42 | all_42_3) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = v1)))
% 100.34/15.42 | & ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_132_9) =
% 100.34/15.42 | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4:
% 100.34/15.42 | any] : (apply(all_42_7, v0) = v3 & in(v3, all_42_9) =
% 100.34/15.42 | v4 & in(v0, all_42_3) = v2 & $i(v3) & ( ~ (v2 = 0) |
% 100.34/15.42 | (v4 = 0 & v1 = 0)))) & ! [v0: $i] : ( ~ (in(v0,
% 100.34/15.42 | all_132_9) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 100.34/15.42 | any] : ? [v3: any] : (apply(all_42_7, v0) = v1 &
% 100.34/15.42 | in(v1, all_42_9) = v2 & in(v0, all_42_3) = v3 & $i(v1)
% 100.34/15.42 | & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (in(v0,
% 100.34/15.42 | all_42_3) = 0) | ~ $i(v0) | ? [v1: $i] :
% 100.34/15.42 | (apply(all_42_7, v0) = v1 & in(v1, all_42_9) = 0 &
% 100.34/15.42 | in(v0, all_132_9) = 0 & $i(v1))) & ! [v0: $i] : ( ~
% 100.34/15.42 | (in(v0, all_42_3) = 0) | ~ $i(v0) | ? [v1: $i] :
% 100.34/15.42 | (apply(all_42_7, v0) = v1 & $i(v1))))) & (all_42_6 =
% 100.34/15.42 | all_42_7 | (all_132_7 = 0 & ~ (all_132_5 = all_132_6) &
% 100.34/15.42 | apply(all_42_7, all_132_8) = all_132_5 & apply(all_42_7,
% 100.34/15.42 | all_132_8) = all_132_6 & in(all_132_8, all_42_3) = 0 &
% 100.34/15.42 | $i(all_132_5) & $i(all_132_6)) | (apply(all_42_7,
% 100.34/15.42 | all_132_4) = all_132_1 & in(all_132_1, all_42_9) =
% 100.34/15.42 | all_132_0 & in(all_132_4, all_132_9) = all_132_2 &
% 100.34/15.42 | in(all_132_4, all_42_3) = all_132_3 & $i(all_132_1) & ( ~
% 100.34/15.42 | (all_132_0 = 0) | ~ (all_132_2 = 0) | ~ (all_132_3 =
% 100.34/15.42 | 0)) & (all_132_3 = 0 | (all_132_0 = 0 & all_132_2 =
% 100.34/15.42 | 0))))))) | (function(all_42_7) = all_132_12 &
% 100.34/15.42 | relation(all_42_7) = all_132_13 & ( ~ (all_132_12 = 0) | ~
% 100.34/15.42 | (all_132_13 = 0))))
% 100.34/15.42 |
% 100.34/15.42 | ALPHA: (56) implies:
% 100.34/15.43 | (57) (relation_dom(all_42_7) = all_132_9 & function(all_42_7) = all_132_10
% 100.34/15.43 | & relation(all_42_7) = all_132_11 & $i(all_132_9) & ( ~ (all_132_10
% 100.34/15.43 | = 0) | ~ (all_132_11 = 0) | (( ~ (all_42_6 = all_42_7) | ( !
% 100.34/15.43 | [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_42_3) =
% 100.34/15.43 | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4:
% 100.34/15.43 | any] : (apply(all_42_7, v0) = v3 & in(v3, all_42_9) = v4
% 100.34/15.43 | & in(v0, all_132_9) = v2 & $i(v3) & ( ~ (v4 = 0) | ~
% 100.34/15.43 | (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 100.34/15.43 | (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 100.34/15.43 | [v3: any] : ? [v4: any] : (in(v1, all_42_9) = v4 & in(v0,
% 100.34/15.43 | all_132_9) = v3 & in(v0, all_42_3) = v2 & ( ~ (v2 = 0)
% 100.34/15.43 | | (v4 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : (
% 100.34/15.43 | ~ (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any] :
% 100.34/15.43 | ? [v3: any] : ? [v4: any] : (in(v1, all_42_9) = v3 &
% 100.34/15.43 | in(v0, all_132_9) = v2 & in(v0, all_42_3) = v4 & ( ~ (v3
% 100.34/15.43 | = 0) | ~ (v2 = 0) | v4 = 0))) & ! [v0: $i] : !
% 100.34/15.43 | [v1: $i] : ( ~ (apply(all_42_7, v0) = v1) | ~ $i(v0) | ?
% 100.34/15.43 | [v2: any] : ? [v3: $i] : (apply(all_42_7, v0) = v3 &
% 100.34/15.43 | in(v0, all_42_3) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 =
% 100.34/15.43 | v1))) & ! [v0: $i] : ! [v1: any] : ( ~ (in(v0,
% 100.34/15.43 | all_132_9) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 100.34/15.43 | $i] : ? [v4: any] : (apply(all_42_7, v0) = v3 & in(v3,
% 100.34/15.43 | all_42_9) = v4 & in(v0, all_42_3) = v2 & $i(v3) & ( ~
% 100.34/15.43 | (v2 = 0) | (v4 = 0 & v1 = 0)))) & ! [v0: $i] : ( ~
% 100.34/15.43 | (in(v0, all_132_9) = 0) | ~ $i(v0) | ? [v1: $i] : ?
% 100.34/15.43 | [v2: any] : ? [v3: any] : (apply(all_42_7, v0) = v1 &
% 100.34/15.43 | in(v1, all_42_9) = v2 & in(v0, all_42_3) = v3 & $i(v1) &
% 100.34/15.43 | ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (in(v0,
% 100.34/15.43 | all_42_3) = 0) | ~ $i(v0) | ? [v1: $i] :
% 100.34/15.43 | (apply(all_42_7, v0) = v1 & in(v1, all_42_9) = 0 & in(v0,
% 100.34/15.43 | all_132_9) = 0 & $i(v1))) & ! [v0: $i] : ( ~ (in(v0,
% 100.34/15.43 | all_42_3) = 0) | ~ $i(v0) | ? [v1: $i] :
% 100.34/15.43 | (apply(all_42_7, v0) = v1 & $i(v1))))) & (all_42_6 =
% 100.34/15.43 | all_42_7 | (all_132_7 = 0 & ~ (all_132_5 = all_132_6) &
% 100.34/15.43 | apply(all_42_7, all_132_8) = all_132_5 & apply(all_42_7,
% 100.34/15.43 | all_132_8) = all_132_6 & in(all_132_8, all_42_3) = 0 &
% 100.34/15.43 | $i(all_132_5) & $i(all_132_6)) | (apply(all_42_7, all_132_4)
% 100.34/15.43 | = all_132_1 & in(all_132_1, all_42_9) = all_132_0 &
% 100.34/15.43 | in(all_132_4, all_132_9) = all_132_2 & in(all_132_4,
% 100.34/15.43 | all_42_3) = all_132_3 & $i(all_132_1) & ( ~ (all_132_0 =
% 100.34/15.43 | 0) | ~ (all_132_2 = 0) | ~ (all_132_3 = 0)) &
% 100.34/15.43 | (all_132_3 = 0 | (all_132_0 = 0 & all_132_2 = 0))))))) |
% 100.34/15.43 | (function(all_42_7) = all_132_12 & relation(all_42_7) = all_132_13 & (
% 100.34/15.43 | ~ (all_132_12 = 0) | ~ (all_132_13 = 0)))
% 100.34/15.43 |
% 100.34/15.44 | GROUND_INST: instantiating (6) with 0, all_128_3, all_42_7, simplifying with
% 100.34/15.44 | (15), (49) gives:
% 100.34/15.44 | (58) all_128_3 = 0
% 100.34/15.44 |
% 100.34/15.44 | GROUND_INST: instantiating (6) with all_92_1, all_128_3, all_42_7, simplifying
% 100.34/15.44 | with (47), (49) gives:
% 100.34/15.44 | (59) all_128_3 = all_92_1
% 100.34/15.44 |
% 100.34/15.44 | GROUND_INST: instantiating (6) with all_78_2, all_128_3, all_42_7, simplifying
% 100.34/15.44 | with (41), (49) gives:
% 100.34/15.44 | (60) all_128_3 = all_78_2
% 100.34/15.44 |
% 100.34/15.44 | GROUND_INST: instantiating (6) with all_62_1, all_128_3, all_42_7, simplifying
% 100.34/15.44 | with (35), (49) gives:
% 100.34/15.44 | (61) all_128_3 = all_62_1
% 100.34/15.44 |
% 100.34/15.44 | GROUND_INST: instantiating (6) with all_72_1, all_128_1, all_42_6, simplifying
% 100.34/15.44 | with (39), (50) gives:
% 100.34/15.44 | (62) all_128_1 = all_72_1
% 100.34/15.44 |
% 100.34/15.44 | GROUND_INST: instantiating (6) with all_62_0, all_128_1, all_42_6, simplifying
% 100.34/15.44 | with (36), (50) gives:
% 100.34/15.44 | (63) all_128_1 = all_62_0
% 100.34/15.44 |
% 100.34/15.44 | GROUND_INST: instantiating (7) with 0, all_128_2, all_42_7, simplifying with
% 100.34/15.44 | (16), (51) gives:
% 100.34/15.44 | (64) all_128_2 = 0
% 100.34/15.44 |
% 100.34/15.44 | GROUND_INST: instantiating (7) with all_88_1, all_128_2, all_42_7, simplifying
% 100.34/15.44 | with (43), (51) gives:
% 100.34/15.44 | (65) all_128_2 = all_88_1
% 100.34/15.44 |
% 100.34/15.44 | GROUND_INST: instantiating (8) with all_42_3, all_90_1, all_42_7, simplifying
% 100.34/15.44 | with (17), (45) gives:
% 100.34/15.44 | (66) all_90_1 = all_42_3
% 100.34/15.44 |
% 100.34/15.44 | COMBINE_EQS: (62), (63) imply:
% 100.34/15.44 | (67) all_72_1 = all_62_0
% 100.34/15.44 |
% 100.34/15.44 | COMBINE_EQS: (64), (65) imply:
% 100.34/15.44 | (68) all_88_1 = 0
% 100.34/15.44 |
% 100.34/15.44 | SIMP: (68) implies:
% 100.34/15.44 | (69) all_88_1 = 0
% 100.34/15.44 |
% 100.34/15.44 | COMBINE_EQS: (58), (59) imply:
% 100.34/15.44 | (70) all_92_1 = 0
% 100.34/15.44 |
% 100.34/15.44 | COMBINE_EQS: (59), (61) imply:
% 100.34/15.44 | (71) all_92_1 = all_62_1
% 100.34/15.44 |
% 100.34/15.44 | COMBINE_EQS: (59), (60) imply:
% 100.34/15.44 | (72) all_92_1 = all_78_2
% 100.34/15.44 |
% 100.34/15.44 | COMBINE_EQS: (70), (72) imply:
% 100.34/15.44 | (73) all_78_2 = 0
% 100.34/15.44 |
% 100.34/15.45 | COMBINE_EQS: (71), (72) imply:
% 100.34/15.45 | (74) all_78_2 = all_62_1
% 100.34/15.45 |
% 100.34/15.45 | COMBINE_EQS: (73), (74) imply:
% 100.34/15.45 | (75) all_62_1 = 0
% 100.34/15.45 |
% 100.34/15.45 | SIMP: (75) implies:
% 100.34/15.45 | (76) all_62_1 = 0
% 100.34/15.45 |
% 100.34/15.45 | BETA: splitting (57) gives:
% 100.34/15.45 |
% 100.34/15.45 | Case 1:
% 100.34/15.45 | |
% 100.34/15.45 | | (77) relation_dom(all_42_7) = all_132_9 & function(all_42_7) = all_132_10
% 100.34/15.45 | | & relation(all_42_7) = all_132_11 & $i(all_132_9) & ( ~ (all_132_10
% 100.34/15.45 | | = 0) | ~ (all_132_11 = 0) | (( ~ (all_42_6 = all_42_7) | ( !
% 100.34/15.45 | | [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_42_3) =
% 100.34/15.45 | | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4:
% 100.34/15.45 | | any] : (apply(all_42_7, v0) = v3 & in(v3, all_42_9) = v4
% 100.34/15.45 | | & in(v0, all_132_9) = v2 & $i(v3) & ( ~ (v4 = 0) | ~
% 100.34/15.45 | | (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 100.34/15.45 | | (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 100.34/15.45 | | [v3: any] : ? [v4: any] : (in(v1, all_42_9) = v4 & in(v0,
% 100.34/15.45 | | all_132_9) = v3 & in(v0, all_42_3) = v2 & ( ~ (v2 = 0)
% 100.34/15.45 | | | (v4 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : (
% 100.34/15.45 | | ~ (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any] :
% 100.34/15.45 | | ? [v3: any] : ? [v4: any] : (in(v1, all_42_9) = v3 &
% 100.34/15.46 | | in(v0, all_132_9) = v2 & in(v0, all_42_3) = v4 & ( ~ (v3
% 100.34/15.46 | | = 0) | ~ (v2 = 0) | v4 = 0))) & ! [v0: $i] : !
% 100.34/15.46 | | [v1: $i] : ( ~ (apply(all_42_7, v0) = v1) | ~ $i(v0) | ?
% 100.34/15.46 | | [v2: any] : ? [v3: $i] : (apply(all_42_7, v0) = v3 &
% 100.34/15.46 | | in(v0, all_42_3) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 =
% 100.34/15.46 | | v1))) & ! [v0: $i] : ! [v1: any] : ( ~ (in(v0,
% 100.34/15.46 | | all_132_9) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 100.34/15.46 | | $i] : ? [v4: any] : (apply(all_42_7, v0) = v3 & in(v3,
% 100.34/15.46 | | all_42_9) = v4 & in(v0, all_42_3) = v2 & $i(v3) & ( ~
% 100.34/15.46 | | (v2 = 0) | (v4 = 0 & v1 = 0)))) & ! [v0: $i] : ( ~
% 100.34/15.46 | | (in(v0, all_132_9) = 0) | ~ $i(v0) | ? [v1: $i] : ?
% 100.34/15.46 | | [v2: any] : ? [v3: any] : (apply(all_42_7, v0) = v1 &
% 100.34/15.46 | | in(v1, all_42_9) = v2 & in(v0, all_42_3) = v3 & $i(v1) &
% 100.34/15.46 | | ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (in(v0,
% 100.34/15.46 | | all_42_3) = 0) | ~ $i(v0) | ? [v1: $i] :
% 100.34/15.46 | | (apply(all_42_7, v0) = v1 & in(v1, all_42_9) = 0 & in(v0,
% 100.34/15.46 | | all_132_9) = 0 & $i(v1))) & ! [v0: $i] : ( ~ (in(v0,
% 100.34/15.46 | | all_42_3) = 0) | ~ $i(v0) | ? [v1: $i] :
% 100.34/15.46 | | (apply(all_42_7, v0) = v1 & $i(v1))))) & (all_42_6 =
% 100.34/15.46 | | all_42_7 | (all_132_7 = 0 & ~ (all_132_5 = all_132_6) &
% 100.34/15.46 | | apply(all_42_7, all_132_8) = all_132_5 & apply(all_42_7,
% 100.34/15.46 | | all_132_8) = all_132_6 & in(all_132_8, all_42_3) = 0 &
% 100.34/15.46 | | $i(all_132_5) & $i(all_132_6)) | (apply(all_42_7, all_132_4)
% 100.34/15.46 | | = all_132_1 & in(all_132_1, all_42_9) = all_132_0 &
% 100.34/15.46 | | in(all_132_4, all_132_9) = all_132_2 & in(all_132_4,
% 100.34/15.46 | | all_42_3) = all_132_3 & $i(all_132_1) & ( ~ (all_132_0 =
% 100.34/15.46 | | 0) | ~ (all_132_2 = 0) | ~ (all_132_3 = 0)) &
% 100.34/15.46 | | (all_132_3 = 0 | (all_132_0 = 0 & all_132_2 = 0))))))
% 100.34/15.46 | |
% 100.34/15.46 | | ALPHA: (77) implies:
% 100.34/15.46 | | (78) relation(all_42_7) = all_132_11
% 100.34/15.46 | | (79) function(all_42_7) = all_132_10
% 100.34/15.46 | | (80) relation_dom(all_42_7) = all_132_9
% 100.34/15.46 | |
% 100.34/15.46 | | BETA: splitting (37) gives:
% 100.34/15.46 | |
% 100.34/15.46 | | Case 1:
% 100.34/15.46 | | |
% 100.34/15.46 | | | (81) ~ (all_62_1 = 0)
% 100.34/15.46 | | |
% 100.34/15.46 | | | REDUCE: (76), (81) imply:
% 100.34/15.46 | | | (82) $false
% 100.34/15.46 | | |
% 100.34/15.46 | | | CLOSE: (82) is inconsistent.
% 100.34/15.46 | | |
% 100.34/15.46 | | Case 2:
% 100.34/15.46 | | |
% 100.34/15.46 | | | (83) all_62_0 = 0
% 100.34/15.46 | | |
% 100.34/15.46 | | | REDUCE: (36), (83) imply:
% 100.34/15.46 | | | (84) relation(all_42_6) = 0
% 100.34/15.46 | | |
% 100.34/15.46 | | | BETA: splitting (53) gives:
% 100.34/15.46 | | |
% 100.34/15.46 | | | Case 1:
% 100.34/15.46 | | | |
% 100.34/15.46 | | | | (85) ~ (all_128_2 = 0)
% 100.34/15.46 | | | |
% 100.34/15.46 | | | | REDUCE: (64), (85) imply:
% 100.34/15.46 | | | | (86) $false
% 100.34/15.46 | | | |
% 100.34/15.46 | | | | CLOSE: (86) is inconsistent.
% 100.34/15.46 | | | |
% 100.34/15.46 | | | Case 2:
% 100.34/15.46 | | | |
% 100.34/15.46 | | | | (87) ~ (all_128_3 = 0) | (all_128_0 = 0 & all_128_1 = 0)
% 100.34/15.46 | | | |
% 100.34/15.46 | | | | BETA: splitting (87) gives:
% 100.34/15.46 | | | |
% 100.34/15.46 | | | | Case 1:
% 100.34/15.46 | | | | |
% 100.34/15.46 | | | | | (88) ~ (all_128_3 = 0)
% 100.34/15.46 | | | | |
% 100.34/15.46 | | | | | REDUCE: (58), (88) imply:
% 100.34/15.46 | | | | | (89) $false
% 100.34/15.46 | | | | |
% 100.34/15.46 | | | | | CLOSE: (89) is inconsistent.
% 100.34/15.46 | | | | |
% 100.34/15.46 | | | | Case 2:
% 100.34/15.46 | | | | |
% 100.34/15.46 | | | | | (90) all_128_0 = 0 & all_128_1 = 0
% 100.34/15.46 | | | | |
% 100.34/15.46 | | | | | ALPHA: (90) implies:
% 100.34/15.46 | | | | | (91) all_128_0 = 0
% 100.34/15.46 | | | | |
% 100.34/15.46 | | | | | REDUCE: (52), (91) imply:
% 100.34/15.46 | | | | | (92) function(all_42_6) = 0
% 100.34/15.46 | | | | |
% 100.34/15.46 | | | | | BETA: splitting (55) gives:
% 100.34/15.46 | | | | |
% 100.34/15.46 | | | | | Case 1:
% 100.34/15.46 | | | | | |
% 100.34/15.47 | | | | | | (93) relation_dom(all_42_7) = all_130_2 & function(all_42_7) =
% 100.34/15.47 | | | | | | all_130_3 & relation(all_42_7) = all_130_4 & $i(all_130_2) &
% 100.34/15.47 | | | | | | ( ~ (all_130_3 = 0) | ~ (all_130_4 = 0) | ( ! [v0: $i] : !
% 100.34/15.47 | | | | | | [v1: int] : (v1 = 0 | ~ (in(v0, all_42_5) = v1) | ~
% 100.34/15.47 | | | | | | $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] :
% 100.34/15.47 | | | | | | (apply(all_42_7, v0) = v3 & in(v3, all_42_9) = v4 &
% 100.34/15.47 | | | | | | in(v0, all_130_2) = v2 & $i(v3) & ( ~ (v4 = 0) | ~
% 100.34/15.47 | | | | | | (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 100.34/15.47 | | | | | | (apply(all_42_6, v0) = v1) | ~ $i(v0) | ? [v2: any]
% 100.34/15.47 | | | | | | : ? [v3: $i] : (apply(all_42_7, v0) = v3 & in(v0,
% 100.34/15.47 | | | | | | all_42_5) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 =
% 100.34/15.47 | | | | | | v1))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 100.34/15.47 | | | | | | (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any]
% 100.34/15.47 | | | | | | : ? [v3: any] : ? [v4: any] : (in(v1, all_42_9) = v4
% 100.34/15.47 | | | | | | & in(v0, all_130_2) = v3 & in(v0, all_42_5) = v2 & (
% 100.34/15.47 | | | | | | ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0: $i] :
% 100.34/15.47 | | | | | | ! [v1: $i] : ( ~ (apply(all_42_7, v0) = v1) | ~ $i(v0)
% 100.34/15.47 | | | | | | | ? [v2: any] : ? [v3: any] : ? [v4: any] : (in(v1,
% 100.34/15.47 | | | | | | all_42_9) = v3 & in(v0, all_130_2) = v2 & in(v0,
% 100.34/15.47 | | | | | | all_42_5) = v4 & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 =
% 100.34/15.47 | | | | | | 0))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 100.34/15.47 | | | | | | (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any]
% 100.34/15.47 | | | | | | : ? [v3: $i] : (apply(all_42_6, v0) = v3 & in(v0,
% 100.34/15.47 | | | | | | all_42_5) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 =
% 100.34/15.47 | | | | | | v1))) & ! [v0: $i] : ! [v1: any] : ( ~ (in(v0,
% 100.34/15.47 | | | | | | all_130_2) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 100.34/15.47 | | | | | | [v3: $i] : ? [v4: any] : (apply(all_42_7, v0) = v3 &
% 100.34/15.47 | | | | | | in(v3, all_42_9) = v4 & in(v0, all_42_5) = v2 &
% 100.34/15.47 | | | | | | $i(v3) & ( ~ (v2 = 0) | (v4 = 0 & v1 = 0)))) & !
% 100.34/15.47 | | | | | | [v0: $i] : ( ~ (in(v0, all_130_2) = 0) | ~ $i(v0) | ?
% 100.34/15.47 | | | | | | [v1: $i] : ? [v2: any] : ? [v3: any] :
% 100.34/15.47 | | | | | | (apply(all_42_7, v0) = v1 & in(v1, all_42_9) = v2 &
% 100.34/15.47 | | | | | | in(v0, all_42_5) = v3 & $i(v1) & ( ~ (v2 = 0) | v3 =
% 100.34/15.47 | | | | | | 0))) & ! [v0: $i] : ( ~ (in(v0, all_42_5) = 0) |
% 100.34/15.47 | | | | | | ~ $i(v0) | ? [v1: $i] : (apply(all_42_6, v0) = v1 &
% 100.34/15.47 | | | | | | apply(all_42_7, v0) = v1 & $i(v1))) & ! [v0: $i] :
% 100.34/15.47 | | | | | | ( ~ (in(v0, all_42_5) = 0) | ~ $i(v0) | ? [v1: $i] :
% 100.34/15.47 | | | | | | (apply(all_42_7, v0) = v1 & in(v1, all_42_9) = 0 &
% 100.34/15.47 | | | | | | in(v0, all_130_2) = 0 & $i(v1)))))
% 100.34/15.47 | | | | | |
% 100.34/15.47 | | | | | | ALPHA: (93) implies:
% 100.34/15.47 | | | | | | (94) relation(all_42_7) = all_130_4
% 100.34/15.47 | | | | | | (95) function(all_42_7) = all_130_3
% 100.34/15.47 | | | | | | (96) relation_dom(all_42_7) = all_130_2
% 100.34/15.48 | | | | | | (97) ~ (all_130_3 = 0) | ~ (all_130_4 = 0) | ( ! [v0: $i] : !
% 100.34/15.48 | | | | | | [v1: int] : (v1 = 0 | ~ (in(v0, all_42_5) = v1) | ~
% 100.34/15.48 | | | | | | $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] :
% 100.34/15.48 | | | | | | (apply(all_42_7, v0) = v3 & in(v3, all_42_9) = v4 &
% 100.34/15.48 | | | | | | in(v0, all_130_2) = v2 & $i(v3) & ( ~ (v4 = 0) | ~
% 100.34/15.48 | | | | | | (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 100.34/15.48 | | | | | | (apply(all_42_6, v0) = v1) | ~ $i(v0) | ? [v2: any] :
% 100.34/15.48 | | | | | | ? [v3: $i] : (apply(all_42_7, v0) = v3 & in(v0,
% 100.34/15.48 | | | | | | all_42_5) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = v1)))
% 100.34/15.48 | | | | | | & ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_42_7, v0) =
% 100.34/15.48 | | | | | | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ?
% 100.34/15.48 | | | | | | [v4: any] : (in(v1, all_42_9) = v4 & in(v0, all_130_2) =
% 100.34/15.48 | | | | | | v3 & in(v0, all_42_5) = v2 & ( ~ (v2 = 0) | (v4 = 0 &
% 100.34/15.48 | | | | | | v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 100.34/15.48 | | | | | | (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any] :
% 100.34/15.48 | | | | | | ? [v3: any] : ? [v4: any] : (in(v1, all_42_9) = v3 &
% 100.34/15.48 | | | | | | in(v0, all_130_2) = v2 & in(v0, all_42_5) = v4 & ( ~
% 100.34/15.48 | | | | | | (v3 = 0) | ~ (v2 = 0) | v4 = 0))) & ! [v0: $i] :
% 100.34/15.48 | | | | | | ! [v1: $i] : ( ~ (apply(all_42_7, v0) = v1) | ~ $i(v0) |
% 100.34/15.48 | | | | | | ? [v2: any] : ? [v3: $i] : (apply(all_42_6, v0) = v3 &
% 100.34/15.48 | | | | | | in(v0, all_42_5) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 =
% 100.34/15.48 | | | | | | v1))) & ! [v0: $i] : ! [v1: any] : ( ~ (in(v0,
% 100.34/15.48 | | | | | | all_130_2) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 100.34/15.48 | | | | | | [v3: $i] : ? [v4: any] : (apply(all_42_7, v0) = v3 &
% 100.34/15.48 | | | | | | in(v3, all_42_9) = v4 & in(v0, all_42_5) = v2 & $i(v3)
% 100.34/15.48 | | | | | | & ( ~ (v2 = 0) | (v4 = 0 & v1 = 0)))) & ! [v0: $i] :
% 100.34/15.48 | | | | | | ( ~ (in(v0, all_130_2) = 0) | ~ $i(v0) | ? [v1: $i] : ?
% 100.34/15.48 | | | | | | [v2: any] : ? [v3: any] : (apply(all_42_7, v0) = v1 &
% 100.34/15.48 | | | | | | in(v1, all_42_9) = v2 & in(v0, all_42_5) = v3 & $i(v1)
% 100.34/15.48 | | | | | | & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (in(v0,
% 100.34/15.48 | | | | | | all_42_5) = 0) | ~ $i(v0) | ? [v1: $i] :
% 100.34/15.48 | | | | | | (apply(all_42_6, v0) = v1 & apply(all_42_7, v0) = v1 &
% 100.34/15.48 | | | | | | $i(v1))) & ! [v0: $i] : ( ~ (in(v0, all_42_5) = 0) |
% 100.34/15.48 | | | | | | ~ $i(v0) | ? [v1: $i] : (apply(all_42_7, v0) = v1 &
% 100.34/15.48 | | | | | | in(v1, all_42_9) = 0 & in(v0, all_130_2) = 0 &
% 100.34/15.48 | | | | | | $i(v1))))
% 100.34/15.48 | | | | | |
% 100.34/15.48 | | | | | | GROUND_INST: instantiating (6) with 0, all_132_11, all_42_7,
% 100.34/15.48 | | | | | | simplifying with (15), (78) gives:
% 100.34/15.48 | | | | | | (98) all_132_11 = 0
% 100.34/15.48 | | | | | |
% 100.34/15.48 | | | | | | GROUND_INST: instantiating (6) with all_130_4, all_132_11, all_42_7,
% 100.34/15.48 | | | | | | simplifying with (78), (94) gives:
% 100.34/15.48 | | | | | | (99) all_132_11 = all_130_4
% 100.34/15.48 | | | | | |
% 100.34/15.48 | | | | | | GROUND_INST: instantiating (7) with 0, all_132_10, all_42_7,
% 100.34/15.48 | | | | | | simplifying with (16), (79) gives:
% 100.34/15.48 | | | | | | (100) all_132_10 = 0
% 100.34/15.48 | | | | | |
% 100.34/15.48 | | | | | | GROUND_INST: instantiating (7) with all_130_3, all_132_10, all_42_7,
% 100.34/15.48 | | | | | | simplifying with (79), (95) gives:
% 100.34/15.49 | | | | | | (101) all_132_10 = all_130_3
% 100.34/15.49 | | | | | |
% 100.34/15.49 | | | | | | GROUND_INST: instantiating (8) with all_42_3, all_132_9, all_42_7,
% 100.34/15.49 | | | | | | simplifying with (17), (80) gives:
% 100.34/15.49 | | | | | | (102) all_132_9 = all_42_3
% 100.34/15.49 | | | | | |
% 100.34/15.49 | | | | | | GROUND_INST: instantiating (8) with all_130_2, all_132_9, all_42_7,
% 100.34/15.49 | | | | | | simplifying with (80), (96) gives:
% 100.34/15.49 | | | | | | (103) all_132_9 = all_130_2
% 100.34/15.49 | | | | | |
% 100.34/15.49 | | | | | | COMBINE_EQS: (102), (103) imply:
% 100.34/15.49 | | | | | | (104) all_130_2 = all_42_3
% 100.34/15.49 | | | | | |
% 100.34/15.49 | | | | | | COMBINE_EQS: (100), (101) imply:
% 100.34/15.49 | | | | | | (105) all_130_3 = 0
% 100.34/15.49 | | | | | |
% 100.34/15.49 | | | | | | COMBINE_EQS: (98), (99) imply:
% 100.34/15.49 | | | | | | (106) all_130_4 = 0
% 100.34/15.49 | | | | | |
% 100.34/15.49 | | | | | | SIMP: (106) implies:
% 100.34/15.49 | | | | | | (107) all_130_4 = 0
% 100.34/15.49 | | | | | |
% 100.34/15.49 | | | | | | BETA: splitting (97) gives:
% 100.34/15.49 | | | | | |
% 100.34/15.49 | | | | | | Case 1:
% 100.34/15.49 | | | | | | |
% 100.34/15.49 | | | | | | | (108) ~ (all_130_3 = 0)
% 100.34/15.49 | | | | | | |
% 100.34/15.49 | | | | | | | REDUCE: (105), (108) imply:
% 100.34/15.49 | | | | | | | (109) $false
% 100.34/15.49 | | | | | | |
% 100.34/15.49 | | | | | | | CLOSE: (109) is inconsistent.
% 100.34/15.49 | | | | | | |
% 100.34/15.49 | | | | | | Case 2:
% 100.34/15.49 | | | | | | |
% 100.34/15.49 | | | | | | | (110) ~ (all_130_4 = 0) | ( ! [v0: $i] : ! [v1: int] : (v1 =
% 100.34/15.49 | | | | | | | 0 | ~ (in(v0, all_42_5) = v1) | ~ $i(v0) | ? [v2:
% 100.34/15.49 | | | | | | | any] : ? [v3: $i] : ? [v4: any] :
% 100.34/15.49 | | | | | | | (apply(all_42_7, v0) = v3 & in(v3, all_42_9) = v4 &
% 100.34/15.49 | | | | | | | in(v0, all_130_2) = v2 & $i(v3) & ( ~ (v4 = 0) | ~
% 100.34/15.49 | | | | | | | (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 100.34/15.49 | | | | | | | (apply(all_42_6, v0) = v1) | ~ $i(v0) | ? [v2: any]
% 100.34/15.49 | | | | | | | : ? [v3: $i] : (apply(all_42_7, v0) = v3 & in(v0,
% 100.34/15.49 | | | | | | | all_42_5) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 =
% 100.34/15.49 | | | | | | | v1))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 100.34/15.49 | | | | | | | (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any]
% 100.34/15.49 | | | | | | | : ? [v3: any] : ? [v4: any] : (in(v1, all_42_9) =
% 100.34/15.49 | | | | | | | v4 & in(v0, all_130_2) = v3 & in(v0, all_42_5) = v2
% 100.34/15.49 | | | | | | | & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0: $i]
% 100.34/15.49 | | | | | | | : ! [v1: $i] : ( ~ (apply(all_42_7, v0) = v1) | ~
% 100.34/15.49 | | | | | | | $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] :
% 100.34/15.49 | | | | | | | (in(v1, all_42_9) = v3 & in(v0, all_130_2) = v2 &
% 100.34/15.49 | | | | | | | in(v0, all_42_5) = v4 & ( ~ (v3 = 0) | ~ (v2 = 0)
% 100.34/15.49 | | | | | | | | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 100.34/15.49 | | | | | | | (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any]
% 100.34/15.49 | | | | | | | : ? [v3: $i] : (apply(all_42_6, v0) = v3 & in(v0,
% 100.34/15.49 | | | | | | | all_42_5) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 =
% 100.34/15.49 | | | | | | | v1))) & ! [v0: $i] : ! [v1: any] : ( ~ (in(v0,
% 100.34/15.49 | | | | | | | all_130_2) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 100.34/15.49 | | | | | | | [v3: $i] : ? [v4: any] : (apply(all_42_7, v0) = v3 &
% 100.34/15.49 | | | | | | | in(v3, all_42_9) = v4 & in(v0, all_42_5) = v2 &
% 100.34/15.49 | | | | | | | $i(v3) & ( ~ (v2 = 0) | (v4 = 0 & v1 = 0)))) & !
% 100.34/15.49 | | | | | | | [v0: $i] : ( ~ (in(v0, all_130_2) = 0) | ~ $i(v0) | ?
% 100.34/15.49 | | | | | | | [v1: $i] : ? [v2: any] : ? [v3: any] :
% 100.34/15.49 | | | | | | | (apply(all_42_7, v0) = v1 & in(v1, all_42_9) = v2 &
% 100.34/15.49 | | | | | | | in(v0, all_42_5) = v3 & $i(v1) & ( ~ (v2 = 0) | v3
% 100.34/15.49 | | | | | | | = 0))) & ! [v0: $i] : ( ~ (in(v0, all_42_5) = 0)
% 100.34/15.49 | | | | | | | | ~ $i(v0) | ? [v1: $i] : (apply(all_42_6, v0) = v1
% 100.34/15.49 | | | | | | | & apply(all_42_7, v0) = v1 & $i(v1))) & ! [v0: $i]
% 100.34/15.49 | | | | | | | : ( ~ (in(v0, all_42_5) = 0) | ~ $i(v0) | ? [v1: $i]
% 100.34/15.49 | | | | | | | : (apply(all_42_7, v0) = v1 & in(v1, all_42_9) = 0 &
% 100.34/15.49 | | | | | | | in(v0, all_130_2) = 0 & $i(v1))))
% 100.34/15.49 | | | | | | |
% 100.34/15.49 | | | | | | | BETA: splitting (110) gives:
% 100.34/15.49 | | | | | | |
% 100.34/15.49 | | | | | | | Case 1:
% 100.34/15.49 | | | | | | | |
% 100.34/15.49 | | | | | | | | (111) ~ (all_130_4 = 0)
% 100.34/15.49 | | | | | | | |
% 100.34/15.49 | | | | | | | | REDUCE: (107), (111) imply:
% 100.34/15.49 | | | | | | | | (112) $false
% 100.34/15.49 | | | | | | | |
% 100.34/15.49 | | | | | | | | CLOSE: (112) is inconsistent.
% 100.34/15.49 | | | | | | | |
% 100.34/15.49 | | | | | | | Case 2:
% 100.34/15.49 | | | | | | | |
% 100.66/15.50 | | | | | | | | (113) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0,
% 100.66/15.50 | | | | | | | | all_42_5) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 100.66/15.50 | | | | | | | | [v3: $i] : ? [v4: any] : (apply(all_42_7, v0) = v3 &
% 100.66/15.50 | | | | | | | | in(v3, all_42_9) = v4 & in(v0, all_130_2) = v2 &
% 100.66/15.50 | | | | | | | | $i(v3) & ( ~ (v4 = 0) | ~ (v2 = 0)))) & ! [v0:
% 100.66/15.50 | | | | | | | | $i] : ! [v1: $i] : ( ~ (apply(all_42_6, v0) = v1) |
% 100.66/15.50 | | | | | | | | ~ $i(v0) | ? [v2: any] : ? [v3: $i] :
% 100.66/15.50 | | | | | | | | (apply(all_42_7, v0) = v3 & in(v0, all_42_5) = v2 &
% 100.66/15.50 | | | | | | | | $i(v3) & ( ~ (v2 = 0) | v3 = v1))) & ! [v0: $i] :
% 100.66/15.50 | | | | | | | | ! [v1: $i] : ( ~ (apply(all_42_7, v0) = v1) | ~ $i(v0)
% 100.66/15.50 | | | | | | | | | ? [v2: any] : ? [v3: any] : ? [v4: any] :
% 100.66/15.50 | | | | | | | | (in(v1, all_42_9) = v4 & in(v0, all_130_2) = v3 &
% 100.66/15.50 | | | | | | | | in(v0, all_42_5) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3
% 100.66/15.50 | | | | | | | | = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 100.66/15.50 | | | | | | | | (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any]
% 100.66/15.50 | | | | | | | | : ? [v3: any] : ? [v4: any] : (in(v1, all_42_9) =
% 100.66/15.50 | | | | | | | | v3 & in(v0, all_130_2) = v2 & in(v0, all_42_5) = v4
% 100.66/15.50 | | | | | | | | & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = 0))) & ! [v0:
% 100.66/15.50 | | | | | | | | $i] : ! [v1: $i] : ( ~ (apply(all_42_7, v0) = v1) |
% 100.66/15.50 | | | | | | | | ~ $i(v0) | ? [v2: any] : ? [v3: $i] :
% 100.66/15.50 | | | | | | | | (apply(all_42_6, v0) = v3 & in(v0, all_42_5) = v2 &
% 100.66/15.50 | | | | | | | | $i(v3) & ( ~ (v2 = 0) | v3 = v1))) & ! [v0: $i] :
% 100.66/15.50 | | | | | | | | ! [v1: any] : ( ~ (in(v0, all_130_2) = v1) | ~ $i(v0)
% 100.66/15.50 | | | | | | | | | ? [v2: any] : ? [v3: $i] : ? [v4: any] :
% 100.66/15.50 | | | | | | | | (apply(all_42_7, v0) = v3 & in(v3, all_42_9) = v4 &
% 100.66/15.50 | | | | | | | | in(v0, all_42_5) = v2 & $i(v3) & ( ~ (v2 = 0) | (v4
% 100.66/15.50 | | | | | | | | = 0 & v1 = 0)))) & ! [v0: $i] : ( ~ (in(v0,
% 100.66/15.50 | | | | | | | | all_130_2) = 0) | ~ $i(v0) | ? [v1: $i] : ?
% 100.66/15.50 | | | | | | | | [v2: any] : ? [v3: any] : (apply(all_42_7, v0) = v1
% 100.66/15.50 | | | | | | | | & in(v1, all_42_9) = v2 & in(v0, all_42_5) = v3 &
% 100.66/15.50 | | | | | | | | $i(v1) & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : (
% 100.66/15.50 | | | | | | | | ~ (in(v0, all_42_5) = 0) | ~ $i(v0) | ? [v1: $i] :
% 100.66/15.50 | | | | | | | | (apply(all_42_6, v0) = v1 & apply(all_42_7, v0) = v1
% 100.66/15.50 | | | | | | | | & $i(v1))) & ! [v0: $i] : ( ~ (in(v0, all_42_5) =
% 100.66/15.50 | | | | | | | | 0) | ~ $i(v0) | ? [v1: $i] : (apply(all_42_7, v0)
% 100.66/15.50 | | | | | | | | = v1 & in(v1, all_42_9) = 0 & in(v0, all_130_2) = 0
% 100.66/15.50 | | | | | | | | & $i(v1)))
% 100.66/15.50 | | | | | | | |
% 100.66/15.50 | | | | | | | | ALPHA: (113) implies:
% 100.66/15.50 | | | | | | | | (114) ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_42_7, v0) =
% 100.66/15.50 | | | | | | | | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] :
% 100.66/15.50 | | | | | | | | (apply(all_42_6, v0) = v3 & in(v0, all_42_5) = v2 &
% 100.66/15.50 | | | | | | | | $i(v3) & ( ~ (v2 = 0) | v3 = v1)))
% 100.66/15.51 | | | | | | | | (115) ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_42_7, v0) =
% 100.66/15.51 | | | | | | | | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ?
% 100.66/15.51 | | | | | | | | [v4: any] : (in(v1, all_42_9) = v3 & in(v0,
% 100.66/15.51 | | | | | | | | all_130_2) = v2 & in(v0, all_42_5) = v4 & ( ~ (v3
% 100.66/15.51 | | | | | | | | = 0) | ~ (v2 = 0) | v4 = 0)))
% 100.66/15.51 | | | | | | | | (116) ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_42_7, v0) =
% 100.66/15.51 | | | | | | | | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ?
% 100.66/15.51 | | | | | | | | [v4: any] : (in(v1, all_42_9) = v4 & in(v0,
% 100.66/15.51 | | | | | | | | all_130_2) = v3 & in(v0, all_42_5) = v2 & ( ~ (v2
% 100.66/15.51 | | | | | | | | = 0) | (v4 = 0 & v3 = 0))))
% 100.66/15.51 | | | | | | | |
% 100.66/15.51 | | | | | | | | GROUND_INST: instantiating (116) with all_42_8, all_42_1,
% 100.66/15.51 | | | | | | | | simplifying with (12), (23) gives:
% 100.66/15.51 | | | | | | | | (117) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 100.66/15.51 | | | | | | | | (in(all_42_1, all_42_9) = v2 & in(all_42_8, all_130_2)
% 100.66/15.51 | | | | | | | | = v1 & in(all_42_8, all_42_5) = v0 & ( ~ (v0 = 0) |
% 100.66/15.51 | | | | | | | | (v2 = 0 & v1 = 0)))
% 100.66/15.51 | | | | | | | |
% 100.66/15.51 | | | | | | | | GROUND_INST: instantiating (115) with all_42_8, all_42_1,
% 100.66/15.51 | | | | | | | | simplifying with (12), (23) gives:
% 100.66/15.51 | | | | | | | | (118) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 100.66/15.51 | | | | | | | | (in(all_42_1, all_42_9) = v1 & in(all_42_8, all_130_2)
% 100.66/15.51 | | | | | | | | = v0 & in(all_42_8, all_42_5) = v2 & ( ~ (v1 = 0) |
% 100.66/15.51 | | | | | | | | ~ (v0 = 0) | v2 = 0))
% 100.66/15.51 | | | | | | | |
% 100.66/15.51 | | | | | | | | GROUND_INST: instantiating (114) with all_42_8, all_42_1,
% 100.66/15.51 | | | | | | | | simplifying with (12), (23) gives:
% 100.66/15.51 | | | | | | | | (119) ? [v0: any] : ? [v1: $i] : (apply(all_42_6, all_42_8)
% 100.66/15.51 | | | | | | | | = v1 & in(all_42_8, all_42_5) = v0 & $i(v1) & ( ~ (v0
% 100.66/15.51 | | | | | | | | = 0) | v1 = all_42_1))
% 100.66/15.51 | | | | | | | |
% 100.66/15.51 | | | | | | | | DELTA: instantiating (119) with fresh symbols all_213_0,
% 100.66/15.51 | | | | | | | | all_213_1 gives:
% 100.66/15.51 | | | | | | | | (120) apply(all_42_6, all_42_8) = all_213_0 & in(all_42_8,
% 100.66/15.51 | | | | | | | | all_42_5) = all_213_1 & $i(all_213_0) & ( ~
% 100.66/15.51 | | | | | | | | (all_213_1 = 0) | all_213_0 = all_42_1)
% 100.66/15.51 | | | | | | | |
% 100.66/15.51 | | | | | | | | ALPHA: (120) implies:
% 100.66/15.51 | | | | | | | | (121) in(all_42_8, all_42_5) = all_213_1
% 100.66/15.51 | | | | | | | |
% 100.66/15.51 | | | | | | | | DELTA: instantiating (118) with fresh symbols all_215_0,
% 100.66/15.51 | | | | | | | | all_215_1, all_215_2 gives:
% 100.66/15.51 | | | | | | | | (122) in(all_42_1, all_42_9) = all_215_1 & in(all_42_8,
% 100.66/15.51 | | | | | | | | all_130_2) = all_215_2 & in(all_42_8, all_42_5) =
% 100.66/15.51 | | | | | | | | all_215_0 & ( ~ (all_215_1 = 0) | ~ (all_215_2 = 0) |
% 100.66/15.51 | | | | | | | | all_215_0 = 0)
% 100.66/15.51 | | | | | | | |
% 100.66/15.51 | | | | | | | | ALPHA: (122) implies:
% 100.66/15.51 | | | | | | | | (123) in(all_42_8, all_42_5) = all_215_0
% 100.66/15.51 | | | | | | | | (124) in(all_42_8, all_130_2) = all_215_2
% 100.66/15.51 | | | | | | | | (125) in(all_42_1, all_42_9) = all_215_1
% 100.66/15.51 | | | | | | | | (126) ~ (all_215_1 = 0) | ~ (all_215_2 = 0) | all_215_0 = 0
% 100.66/15.51 | | | | | | | |
% 100.66/15.51 | | | | | | | | DELTA: instantiating (117) with fresh symbols all_217_0,
% 100.66/15.51 | | | | | | | | all_217_1, all_217_2 gives:
% 100.66/15.52 | | | | | | | | (127) in(all_42_1, all_42_9) = all_217_0 & in(all_42_8,
% 100.66/15.52 | | | | | | | | all_130_2) = all_217_1 & in(all_42_8, all_42_5) =
% 100.66/15.52 | | | | | | | | all_217_2 & ( ~ (all_217_2 = 0) | (all_217_0 = 0 &
% 100.66/15.52 | | | | | | | | all_217_1 = 0))
% 100.66/15.52 | | | | | | | |
% 100.66/15.52 | | | | | | | | ALPHA: (127) implies:
% 100.66/15.52 | | | | | | | | (128) in(all_42_8, all_42_5) = all_217_2
% 100.66/15.52 | | | | | | | | (129) in(all_42_8, all_130_2) = all_217_1
% 100.66/15.52 | | | | | | | | (130) in(all_42_1, all_42_9) = all_217_0
% 100.66/15.52 | | | | | | | | (131) ~ (all_217_2 = 0) | (all_217_0 = 0 & all_217_1 = 0)
% 100.66/15.52 | | | | | | | |
% 100.66/15.52 | | | | | | | | REDUCE: (104), (129) imply:
% 100.66/15.52 | | | | | | | | (132) in(all_42_8, all_42_3) = all_217_1
% 100.66/15.52 | | | | | | | |
% 100.66/15.52 | | | | | | | | REDUCE: (104), (124) imply:
% 100.66/15.52 | | | | | | | | (133) in(all_42_8, all_42_3) = all_215_2
% 100.66/15.52 | | | | | | | |
% 100.66/15.52 | | | | | | | | GROUND_INST: instantiating (9) with all_42_4, all_215_0,
% 100.66/15.52 | | | | | | | | all_42_5, all_42_8, simplifying with (19), (123)
% 100.66/15.52 | | | | | | | | gives:
% 100.66/15.52 | | | | | | | | (134) all_215_0 = all_42_4
% 100.66/15.52 | | | | | | | |
% 100.66/15.52 | | | | | | | | GROUND_INST: instantiating (9) with all_215_0, all_217_2,
% 100.66/15.52 | | | | | | | | all_42_5, all_42_8, simplifying with (123), (128)
% 100.66/15.52 | | | | | | | | gives:
% 100.66/15.52 | | | | | | | | (135) all_217_2 = all_215_0
% 100.66/15.52 | | | | | | | |
% 100.66/15.52 | | | | | | | | GROUND_INST: instantiating (9) with all_213_1, all_217_2,
% 100.66/15.52 | | | | | | | | all_42_5, all_42_8, simplifying with (121), (128)
% 100.66/15.52 | | | | | | | | gives:
% 100.66/15.52 | | | | | | | | (136) all_217_2 = all_213_1
% 100.66/15.52 | | | | | | | |
% 100.66/15.52 | | | | | | | | GROUND_INST: instantiating (9) with all_42_2, all_217_1,
% 100.66/15.52 | | | | | | | | all_42_3, all_42_8, simplifying with (20), (132)
% 100.66/15.52 | | | | | | | | gives:
% 100.66/15.52 | | | | | | | | (137) all_217_1 = all_42_2
% 100.66/15.52 | | | | | | | |
% 100.66/15.52 | | | | | | | | GROUND_INST: instantiating (9) with all_215_2, all_217_1,
% 100.66/15.52 | | | | | | | | all_42_3, all_42_8, simplifying with (132), (133)
% 100.66/15.52 | | | | | | | | gives:
% 100.66/15.52 | | | | | | | | (138) all_217_1 = all_215_2
% 100.66/15.52 | | | | | | | |
% 100.66/15.52 | | | | | | | | GROUND_INST: instantiating (9) with all_42_0, all_217_0,
% 100.66/15.52 | | | | | | | | all_42_9, all_42_1, simplifying with (21), (130)
% 100.66/15.52 | | | | | | | | gives:
% 100.66/15.52 | | | | | | | | (139) all_217_0 = all_42_0
% 100.66/15.52 | | | | | | | |
% 100.66/15.52 | | | | | | | | GROUND_INST: instantiating (9) with all_215_1, all_217_0,
% 100.66/15.52 | | | | | | | | all_42_9, all_42_1, simplifying with (125), (130)
% 100.66/15.52 | | | | | | | | gives:
% 100.66/15.52 | | | | | | | | (140) all_217_0 = all_215_1
% 100.66/15.52 | | | | | | | |
% 100.66/15.52 | | | | | | | | COMBINE_EQS: (139), (140) imply:
% 100.66/15.52 | | | | | | | | (141) all_215_1 = all_42_0
% 100.66/15.52 | | | | | | | |
% 100.66/15.52 | | | | | | | | COMBINE_EQS: (137), (138) imply:
% 100.66/15.52 | | | | | | | | (142) all_215_2 = all_42_2
% 100.66/15.52 | | | | | | | |
% 100.66/15.52 | | | | | | | | COMBINE_EQS: (135), (136) imply:
% 100.66/15.52 | | | | | | | | (143) all_215_0 = all_213_1
% 100.66/15.52 | | | | | | | |
% 100.66/15.52 | | | | | | | | SIMP: (143) implies:
% 100.66/15.52 | | | | | | | | (144) all_215_0 = all_213_1
% 100.66/15.52 | | | | | | | |
% 100.66/15.52 | | | | | | | | COMBINE_EQS: (134), (144) imply:
% 100.66/15.52 | | | | | | | | (145) all_213_1 = all_42_4
% 100.66/15.52 | | | | | | | |
% 100.66/15.52 | | | | | | | | COMBINE_EQS: (136), (145) imply:
% 100.66/15.52 | | | | | | | | (146) all_217_2 = all_42_4
% 100.66/15.52 | | | | | | | |
% 100.66/15.52 | | | | | | | | BETA: splitting (24) gives:
% 100.66/15.52 | | | | | | | |
% 100.66/15.52 | | | | | | | | Case 1:
% 100.66/15.52 | | | | | | | | |
% 100.66/15.52 | | | | | | | | | (147) all_42_0 = 0 & all_42_2 = 0 & ~ (all_42_4 = 0)
% 100.66/15.52 | | | | | | | | |
% 100.66/15.52 | | | | | | | | | ALPHA: (147) implies:
% 100.66/15.52 | | | | | | | | | (148) all_42_2 = 0
% 100.66/15.52 | | | | | | | | | (149) all_42_0 = 0
% 100.66/15.52 | | | | | | | | | (150) ~ (all_42_4 = 0)
% 100.66/15.52 | | | | | | | | |
% 100.66/15.52 | | | | | | | | | COMBINE_EQS: (142), (148) imply:
% 100.66/15.52 | | | | | | | | | (151) all_215_2 = 0
% 100.66/15.52 | | | | | | | | |
% 100.66/15.52 | | | | | | | | | COMBINE_EQS: (141), (149) imply:
% 100.66/15.52 | | | | | | | | | (152) all_215_1 = 0
% 100.66/15.52 | | | | | | | | |
% 100.66/15.52 | | | | | | | | | BETA: splitting (126) gives:
% 100.66/15.52 | | | | | | | | |
% 100.66/15.52 | | | | | | | | | Case 1:
% 100.66/15.52 | | | | | | | | | |
% 100.66/15.52 | | | | | | | | | | (153) ~ (all_215_1 = 0)
% 100.66/15.52 | | | | | | | | | |
% 100.66/15.52 | | | | | | | | | | REDUCE: (152), (153) imply:
% 100.66/15.52 | | | | | | | | | | (154) $false
% 100.66/15.52 | | | | | | | | | |
% 100.66/15.52 | | | | | | | | | | CLOSE: (154) is inconsistent.
% 100.66/15.52 | | | | | | | | | |
% 100.66/15.52 | | | | | | | | | Case 2:
% 100.66/15.52 | | | | | | | | | |
% 100.66/15.52 | | | | | | | | | | (155) ~ (all_215_2 = 0) | all_215_0 = 0
% 100.66/15.52 | | | | | | | | | |
% 100.66/15.52 | | | | | | | | | | BETA: splitting (155) gives:
% 100.66/15.52 | | | | | | | | | |
% 100.66/15.52 | | | | | | | | | | Case 1:
% 100.66/15.52 | | | | | | | | | | |
% 100.66/15.52 | | | | | | | | | | | (156) ~ (all_215_2 = 0)
% 100.66/15.52 | | | | | | | | | | |
% 100.66/15.52 | | | | | | | | | | | REDUCE: (151), (156) imply:
% 100.66/15.52 | | | | | | | | | | | (157) $false
% 100.66/15.52 | | | | | | | | | | |
% 100.66/15.52 | | | | | | | | | | | CLOSE: (157) is inconsistent.
% 100.66/15.52 | | | | | | | | | | |
% 100.66/15.52 | | | | | | | | | | Case 2:
% 100.66/15.52 | | | | | | | | | | |
% 100.66/15.52 | | | | | | | | | | | (158) all_215_0 = 0
% 100.66/15.52 | | | | | | | | | | |
% 100.66/15.53 | | | | | | | | | | | COMBINE_EQS: (134), (158) imply:
% 100.66/15.53 | | | | | | | | | | | (159) all_42_4 = 0
% 100.66/15.53 | | | | | | | | | | |
% 100.66/15.53 | | | | | | | | | | | SIMP: (159) implies:
% 100.66/15.53 | | | | | | | | | | | (160) all_42_4 = 0
% 100.66/15.53 | | | | | | | | | | |
% 100.66/15.53 | | | | | | | | | | | REDUCE: (150), (160) imply:
% 100.66/15.53 | | | | | | | | | | | (161) $false
% 100.66/15.53 | | | | | | | | | | |
% 100.66/15.53 | | | | | | | | | | | CLOSE: (161) is inconsistent.
% 100.66/15.53 | | | | | | | | | | |
% 100.66/15.53 | | | | | | | | | | End of split
% 100.66/15.53 | | | | | | | | | |
% 100.66/15.53 | | | | | | | | | End of split
% 100.66/15.53 | | | | | | | | |
% 100.66/15.53 | | | | | | | | Case 2:
% 100.66/15.53 | | | | | | | | |
% 100.66/15.53 | | | | | | | | | (162) all_42_4 = 0 & ( ~ (all_42_0 = 0) | ~ (all_42_2 =
% 100.66/15.53 | | | | | | | | | 0))
% 100.66/15.53 | | | | | | | | |
% 100.66/15.53 | | | | | | | | | ALPHA: (162) implies:
% 100.66/15.53 | | | | | | | | | (163) all_42_4 = 0
% 100.66/15.53 | | | | | | | | | (164) ~ (all_42_0 = 0) | ~ (all_42_2 = 0)
% 100.66/15.53 | | | | | | | | |
% 100.66/15.53 | | | | | | | | | COMBINE_EQS: (146), (163) imply:
% 100.66/15.53 | | | | | | | | | (165) all_217_2 = 0
% 100.66/15.53 | | | | | | | | |
% 100.66/15.53 | | | | | | | | | BETA: splitting (131) gives:
% 100.66/15.53 | | | | | | | | |
% 100.66/15.53 | | | | | | | | | Case 1:
% 100.66/15.53 | | | | | | | | | |
% 100.66/15.53 | | | | | | | | | | (166) ~ (all_217_2 = 0)
% 100.66/15.53 | | | | | | | | | |
% 100.66/15.53 | | | | | | | | | | REDUCE: (165), (166) imply:
% 100.66/15.53 | | | | | | | | | | (167) $false
% 100.66/15.53 | | | | | | | | | |
% 100.66/15.53 | | | | | | | | | | CLOSE: (167) is inconsistent.
% 100.66/15.53 | | | | | | | | | |
% 100.66/15.53 | | | | | | | | | Case 2:
% 100.66/15.53 | | | | | | | | | |
% 100.66/15.53 | | | | | | | | | | (168) all_217_0 = 0 & all_217_1 = 0
% 100.66/15.53 | | | | | | | | | |
% 100.66/15.53 | | | | | | | | | | ALPHA: (168) implies:
% 100.66/15.53 | | | | | | | | | | (169) all_217_1 = 0
% 100.66/15.53 | | | | | | | | | | (170) all_217_0 = 0
% 100.66/15.53 | | | | | | | | | |
% 100.66/15.53 | | | | | | | | | | COMBINE_EQS: (139), (170) imply:
% 100.66/15.53 | | | | | | | | | | (171) all_42_0 = 0
% 100.66/15.53 | | | | | | | | | |
% 100.66/15.53 | | | | | | | | | | COMBINE_EQS: (137), (169) imply:
% 100.66/15.53 | | | | | | | | | | (172) all_42_2 = 0
% 100.66/15.53 | | | | | | | | | |
% 100.66/15.53 | | | | | | | | | | SIMP: (172) implies:
% 100.66/15.53 | | | | | | | | | | (173) all_42_2 = 0
% 100.66/15.53 | | | | | | | | | |
% 100.66/15.53 | | | | | | | | | | BETA: splitting (164) gives:
% 100.66/15.53 | | | | | | | | | |
% 100.66/15.53 | | | | | | | | | | Case 1:
% 100.66/15.53 | | | | | | | | | | |
% 100.66/15.53 | | | | | | | | | | | (174) ~ (all_42_0 = 0)
% 100.66/15.53 | | | | | | | | | | |
% 100.66/15.53 | | | | | | | | | | | REDUCE: (171), (174) imply:
% 100.66/15.53 | | | | | | | | | | | (175) $false
% 100.66/15.53 | | | | | | | | | | |
% 100.66/15.53 | | | | | | | | | | | CLOSE: (175) is inconsistent.
% 100.66/15.53 | | | | | | | | | | |
% 100.66/15.53 | | | | | | | | | | Case 2:
% 100.66/15.53 | | | | | | | | | | |
% 100.66/15.53 | | | | | | | | | | | (176) ~ (all_42_2 = 0)
% 100.66/15.53 | | | | | | | | | | |
% 100.66/15.53 | | | | | | | | | | | REDUCE: (173), (176) imply:
% 100.66/15.53 | | | | | | | | | | | (177) $false
% 100.66/15.53 | | | | | | | | | | |
% 100.66/15.53 | | | | | | | | | | | CLOSE: (177) is inconsistent.
% 100.66/15.53 | | | | | | | | | | |
% 100.66/15.53 | | | | | | | | | | End of split
% 100.66/15.53 | | | | | | | | | |
% 100.66/15.53 | | | | | | | | | End of split
% 100.66/15.53 | | | | | | | | |
% 100.66/15.53 | | | | | | | | End of split
% 100.66/15.53 | | | | | | | |
% 100.66/15.53 | | | | | | | End of split
% 100.66/15.53 | | | | | | |
% 100.66/15.53 | | | | | | End of split
% 100.66/15.53 | | | | | |
% 100.66/15.53 | | | | | Case 2:
% 100.66/15.53 | | | | | |
% 100.66/15.53 | | | | | | (178) function(all_42_6) = all_130_5 & relation(all_42_6) =
% 100.66/15.53 | | | | | | all_130_6 & ( ~ (all_130_5 = 0) | ~ (all_130_6 = 0))
% 100.66/15.53 | | | | | |
% 100.66/15.53 | | | | | | ALPHA: (178) implies:
% 100.66/15.53 | | | | | | (179) relation(all_42_6) = all_130_6
% 100.66/15.53 | | | | | | (180) function(all_42_6) = all_130_5
% 100.66/15.53 | | | | | | (181) ~ (all_130_5 = 0) | ~ (all_130_6 = 0)
% 100.66/15.53 | | | | | |
% 100.66/15.53 | | | | | | REF_CLOSE: (6), (7), (84), (92), (179), (180), (181) are
% 100.66/15.53 | | | | | | inconsistent by sub-proof #1.
% 100.66/15.53 | | | | | |
% 100.66/15.53 | | | | | End of split
% 100.66/15.53 | | | | |
% 100.66/15.53 | | | | End of split
% 100.66/15.53 | | | |
% 100.66/15.53 | | | End of split
% 100.66/15.53 | | |
% 100.66/15.53 | | End of split
% 100.66/15.53 | |
% 100.66/15.53 | Case 2:
% 100.66/15.53 | |
% 100.66/15.53 | | (182) function(all_42_7) = all_132_12 & relation(all_42_7) = all_132_13 &
% 100.66/15.53 | | ( ~ (all_132_12 = 0) | ~ (all_132_13 = 0))
% 100.66/15.53 | |
% 100.66/15.53 | | ALPHA: (182) implies:
% 100.66/15.53 | | (183) relation(all_42_7) = all_132_13
% 100.66/15.53 | | (184) function(all_42_7) = all_132_12
% 100.66/15.53 | | (185) ~ (all_132_12 = 0) | ~ (all_132_13 = 0)
% 100.66/15.53 | |
% 100.66/15.53 | | BETA: splitting (37) gives:
% 100.66/15.53 | |
% 100.66/15.53 | | Case 1:
% 100.66/15.53 | | |
% 100.66/15.53 | | | (186) ~ (all_62_1 = 0)
% 100.66/15.53 | | |
% 100.66/15.53 | | | REDUCE: (76), (186) imply:
% 100.66/15.53 | | | (187) $false
% 100.66/15.53 | | |
% 100.66/15.53 | | | CLOSE: (187) is inconsistent.
% 100.66/15.53 | | |
% 100.66/15.53 | | Case 2:
% 100.66/15.53 | | |
% 100.66/15.53 | | | (188) all_62_0 = 0
% 100.66/15.53 | | |
% 100.66/15.53 | | | REDUCE: (36), (188) imply:
% 100.66/15.53 | | | (189) relation(all_42_6) = 0
% 100.66/15.53 | | |
% 100.66/15.53 | | | BETA: splitting (53) gives:
% 100.66/15.53 | | |
% 100.66/15.53 | | | Case 1:
% 100.66/15.53 | | | |
% 100.66/15.53 | | | | (190) ~ (all_128_2 = 0)
% 100.66/15.53 | | | |
% 100.66/15.53 | | | | REDUCE: (64), (190) imply:
% 100.66/15.53 | | | | (191) $false
% 100.66/15.53 | | | |
% 100.66/15.53 | | | | CLOSE: (191) is inconsistent.
% 100.66/15.53 | | | |
% 100.66/15.53 | | | Case 2:
% 100.66/15.53 | | | |
% 100.66/15.53 | | | | (192) ~ (all_128_3 = 0) | (all_128_0 = 0 & all_128_1 = 0)
% 100.66/15.53 | | | |
% 100.66/15.53 | | | | BETA: splitting (192) gives:
% 100.66/15.53 | | | |
% 100.66/15.53 | | | | Case 1:
% 100.66/15.53 | | | | |
% 100.66/15.53 | | | | | (193) ~ (all_128_3 = 0)
% 100.66/15.53 | | | | |
% 100.66/15.53 | | | | | REDUCE: (58), (193) imply:
% 100.66/15.53 | | | | | (194) $false
% 100.66/15.53 | | | | |
% 100.66/15.53 | | | | | CLOSE: (194) is inconsistent.
% 100.66/15.53 | | | | |
% 100.66/15.53 | | | | Case 2:
% 100.66/15.53 | | | | |
% 100.66/15.53 | | | | | (195) all_128_0 = 0 & all_128_1 = 0
% 100.66/15.53 | | | | |
% 100.66/15.53 | | | | | ALPHA: (195) implies:
% 100.66/15.53 | | | | | (196) all_128_0 = 0
% 100.66/15.53 | | | | |
% 100.66/15.53 | | | | | REDUCE: (52), (196) imply:
% 100.66/15.53 | | | | | (197) function(all_42_6) = 0
% 100.66/15.53 | | | | |
% 100.66/15.53 | | | | | BETA: splitting (55) gives:
% 100.66/15.53 | | | | |
% 100.66/15.53 | | | | | Case 1:
% 100.66/15.53 | | | | | |
% 100.66/15.54 | | | | | | (198) relation_dom(all_42_7) = all_130_2 & function(all_42_7) =
% 100.66/15.54 | | | | | | all_130_3 & relation(all_42_7) = all_130_4 & $i(all_130_2)
% 100.66/15.54 | | | | | | & ( ~ (all_130_3 = 0) | ~ (all_130_4 = 0) | ( ! [v0: $i] :
% 100.66/15.54 | | | | | | ! [v1: int] : (v1 = 0 | ~ (in(v0, all_42_5) = v1) |
% 100.66/15.54 | | | | | | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any]
% 100.66/15.54 | | | | | | : (apply(all_42_7, v0) = v3 & in(v3, all_42_9) = v4 &
% 100.66/15.54 | | | | | | in(v0, all_130_2) = v2 & $i(v3) & ( ~ (v4 = 0) | ~
% 100.66/15.54 | | | | | | (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 100.66/15.54 | | | | | | (apply(all_42_6, v0) = v1) | ~ $i(v0) | ? [v2: any]
% 100.66/15.54 | | | | | | : ? [v3: $i] : (apply(all_42_7, v0) = v3 & in(v0,
% 100.66/15.54 | | | | | | all_42_5) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 =
% 100.66/15.54 | | | | | | v1))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 100.66/15.54 | | | | | | (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any]
% 100.66/15.54 | | | | | | : ? [v3: any] : ? [v4: any] : (in(v1, all_42_9) =
% 100.66/15.54 | | | | | | v4 & in(v0, all_130_2) = v3 & in(v0, all_42_5) = v2
% 100.66/15.54 | | | | | | & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0: $i]
% 100.66/15.54 | | | | | | : ! [v1: $i] : ( ~ (apply(all_42_7, v0) = v1) | ~
% 100.66/15.54 | | | | | | $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] :
% 100.66/15.54 | | | | | | (in(v1, all_42_9) = v3 & in(v0, all_130_2) = v2 &
% 100.66/15.54 | | | | | | in(v0, all_42_5) = v4 & ( ~ (v3 = 0) | ~ (v2 = 0)
% 100.66/15.54 | | | | | | | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 100.66/15.54 | | | | | | (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any]
% 100.66/15.54 | | | | | | : ? [v3: $i] : (apply(all_42_6, v0) = v3 & in(v0,
% 100.66/15.54 | | | | | | all_42_5) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 =
% 100.66/15.54 | | | | | | v1))) & ! [v0: $i] : ! [v1: any] : ( ~ (in(v0,
% 100.66/15.54 | | | | | | all_130_2) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 100.66/15.54 | | | | | | [v3: $i] : ? [v4: any] : (apply(all_42_7, v0) = v3 &
% 100.66/15.54 | | | | | | in(v3, all_42_9) = v4 & in(v0, all_42_5) = v2 &
% 100.66/15.54 | | | | | | $i(v3) & ( ~ (v2 = 0) | (v4 = 0 & v1 = 0)))) & !
% 100.66/15.54 | | | | | | [v0: $i] : ( ~ (in(v0, all_130_2) = 0) | ~ $i(v0) | ?
% 100.66/15.54 | | | | | | [v1: $i] : ? [v2: any] : ? [v3: any] :
% 100.66/15.54 | | | | | | (apply(all_42_7, v0) = v1 & in(v1, all_42_9) = v2 &
% 100.66/15.54 | | | | | | in(v0, all_42_5) = v3 & $i(v1) & ( ~ (v2 = 0) | v3
% 100.66/15.54 | | | | | | = 0))) & ! [v0: $i] : ( ~ (in(v0, all_42_5) = 0)
% 100.66/15.54 | | | | | | | ~ $i(v0) | ? [v1: $i] : (apply(all_42_6, v0) = v1
% 100.66/15.54 | | | | | | & apply(all_42_7, v0) = v1 & $i(v1))) & ! [v0: $i]
% 100.66/15.54 | | | | | | : ( ~ (in(v0, all_42_5) = 0) | ~ $i(v0) | ? [v1: $i]
% 100.66/15.54 | | | | | | : (apply(all_42_7, v0) = v1 & in(v1, all_42_9) = 0 &
% 100.66/15.54 | | | | | | in(v0, all_130_2) = 0 & $i(v1)))))
% 100.66/15.54 | | | | | |
% 100.66/15.54 | | | | | | ALPHA: (198) implies:
% 100.66/15.54 | | | | | | (199) relation(all_42_7) = all_130_4
% 100.66/15.54 | | | | | | (200) function(all_42_7) = all_130_3
% 100.66/15.54 | | | | | |
% 100.66/15.54 | | | | | | GROUND_INST: instantiating (6) with 0, all_132_13, all_42_7,
% 100.66/15.54 | | | | | | simplifying with (15), (183) gives:
% 100.66/15.54 | | | | | | (201) all_132_13 = 0
% 100.66/15.54 | | | | | |
% 100.66/15.54 | | | | | | GROUND_INST: instantiating (6) with all_130_4, all_132_13, all_42_7,
% 100.66/15.54 | | | | | | simplifying with (183), (199) gives:
% 100.66/15.54 | | | | | | (202) all_132_13 = all_130_4
% 100.66/15.54 | | | | | |
% 100.66/15.54 | | | | | | GROUND_INST: instantiating (7) with 0, all_132_12, all_42_7,
% 100.66/15.54 | | | | | | simplifying with (16), (184) gives:
% 100.66/15.54 | | | | | | (203) all_132_12 = 0
% 100.66/15.54 | | | | | |
% 100.66/15.54 | | | | | | GROUND_INST: instantiating (7) with all_130_3, all_132_12, all_42_7,
% 100.66/15.54 | | | | | | simplifying with (184), (200) gives:
% 100.66/15.54 | | | | | | (204) all_132_12 = all_130_3
% 100.66/15.54 | | | | | |
% 100.66/15.54 | | | | | | COMBINE_EQS: (203), (204) imply:
% 100.66/15.54 | | | | | | (205) all_130_3 = 0
% 100.66/15.54 | | | | | |
% 100.66/15.54 | | | | | | COMBINE_EQS: (201), (202) imply:
% 100.66/15.54 | | | | | | (206) all_130_4 = 0
% 100.66/15.54 | | | | | |
% 100.66/15.54 | | | | | | BETA: splitting (185) gives:
% 100.66/15.54 | | | | | |
% 100.66/15.54 | | | | | | Case 1:
% 100.66/15.54 | | | | | | |
% 100.66/15.54 | | | | | | | (207) ~ (all_132_12 = 0)
% 100.66/15.54 | | | | | | |
% 100.66/15.54 | | | | | | | REDUCE: (203), (207) imply:
% 100.66/15.54 | | | | | | | (208) $false
% 100.66/15.54 | | | | | | |
% 100.66/15.54 | | | | | | | CLOSE: (208) is inconsistent.
% 100.66/15.54 | | | | | | |
% 100.66/15.54 | | | | | | Case 2:
% 100.66/15.54 | | | | | | |
% 100.66/15.54 | | | | | | | (209) ~ (all_132_13 = 0)
% 100.66/15.54 | | | | | | |
% 100.66/15.54 | | | | | | | REDUCE: (201), (209) imply:
% 100.66/15.54 | | | | | | | (210) $false
% 100.66/15.54 | | | | | | |
% 100.66/15.54 | | | | | | | CLOSE: (210) is inconsistent.
% 100.66/15.54 | | | | | | |
% 100.66/15.54 | | | | | | End of split
% 100.66/15.54 | | | | | |
% 100.66/15.54 | | | | | Case 2:
% 100.66/15.54 | | | | | |
% 100.66/15.55 | | | | | | (211) function(all_42_6) = all_130_5 & relation(all_42_6) =
% 100.66/15.55 | | | | | | all_130_6 & ( ~ (all_130_5 = 0) | ~ (all_130_6 = 0))
% 100.66/15.55 | | | | | |
% 100.66/15.55 | | | | | | ALPHA: (211) implies:
% 100.66/15.55 | | | | | | (212) relation(all_42_6) = all_130_6
% 100.66/15.55 | | | | | | (213) function(all_42_6) = all_130_5
% 100.66/15.55 | | | | | | (214) ~ (all_130_5 = 0) | ~ (all_130_6 = 0)
% 100.66/15.55 | | | | | |
% 100.66/15.55 | | | | | | REF_CLOSE: (6), (7), (189), (197), (212), (213), (214) are
% 100.66/15.55 | | | | | | inconsistent by sub-proof #1.
% 100.66/15.55 | | | | | |
% 100.66/15.55 | | | | | End of split
% 100.66/15.55 | | | | |
% 100.66/15.55 | | | | End of split
% 100.66/15.55 | | | |
% 100.66/15.55 | | | End of split
% 100.66/15.55 | | |
% 100.66/15.55 | | End of split
% 100.66/15.55 | |
% 100.66/15.55 | End of split
% 100.66/15.55 |
% 100.66/15.55 End of proof
% 100.66/15.55
% 100.66/15.55 Sub-proof #1 shows that the following formulas are inconsistent:
% 100.66/15.55 ----------------------------------------------------------------
% 100.66/15.55 (1) ~ (all_130_5 = 0) | ~ (all_130_6 = 0)
% 100.66/15.55 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 100.66/15.55 (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 100.66/15.55 (3) function(all_42_6) = 0
% 100.66/15.55 (4) relation(all_42_6) = all_130_6
% 100.66/15.55 (5) function(all_42_6) = all_130_5
% 100.66/15.55 (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 100.66/15.55 (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 100.66/15.55 (7) relation(all_42_6) = 0
% 100.66/15.55
% 100.66/15.55 Begin of proof
% 100.66/15.55 |
% 100.66/15.55 | GROUND_INST: instantiating (6) with 0, all_130_6, all_42_6, simplifying with
% 100.66/15.55 | (4), (7) gives:
% 100.66/15.55 | (8) all_130_6 = 0
% 100.66/15.55 |
% 100.66/15.55 | GROUND_INST: instantiating (2) with 0, all_130_5, all_42_6, simplifying with
% 100.66/15.55 | (3), (5) gives:
% 100.66/15.55 | (9) all_130_5 = 0
% 100.66/15.55 |
% 100.66/15.55 | BETA: splitting (1) gives:
% 100.66/15.55 |
% 100.66/15.55 | Case 1:
% 100.66/15.55 | |
% 100.66/15.55 | | (10) ~ (all_130_5 = 0)
% 100.66/15.55 | |
% 100.66/15.55 | | REDUCE: (9), (10) imply:
% 100.66/15.55 | | (11) $false
% 100.66/15.55 | |
% 100.66/15.55 | | CLOSE: (11) is inconsistent.
% 100.66/15.55 | |
% 100.66/15.55 | Case 2:
% 100.66/15.55 | |
% 100.66/15.55 | | (12) ~ (all_130_6 = 0)
% 100.66/15.55 | |
% 100.66/15.55 | | REDUCE: (8), (12) imply:
% 100.66/15.55 | | (13) $false
% 100.66/15.55 | |
% 100.66/15.55 | | CLOSE: (13) is inconsistent.
% 100.66/15.55 | |
% 100.66/15.55 | End of split
% 100.66/15.55 |
% 100.66/15.55 End of proof
% 100.66/15.55 % SZS output end Proof for theBenchmark
% 100.66/15.55
% 100.66/15.55 14949ms
%------------------------------------------------------------------------------