TSTP Solution File: SEU046+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU046+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 : n029.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 62.55s 9.11s
% Output : Proof 63.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU046+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 23 16:47:52 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.78/1.12 Prover 4: Preprocessing ...
% 2.78/1.12 Prover 1: Preprocessing ...
% 2.78/1.15 Prover 2: Preprocessing ...
% 2.78/1.15 Prover 6: Preprocessing ...
% 2.78/1.15 Prover 0: Preprocessing ...
% 2.78/1.15 Prover 5: Preprocessing ...
% 2.78/1.15 Prover 3: Preprocessing ...
% 6.42/1.68 Prover 1: Warning: ignoring some quantifiers
% 6.98/1.73 Prover 3: Warning: ignoring some quantifiers
% 6.98/1.73 Prover 5: Proving ...
% 6.98/1.75 Prover 3: Constructing countermodel ...
% 6.98/1.77 Prover 1: Constructing countermodel ...
% 7.45/1.80 Prover 6: Proving ...
% 8.24/1.91 Prover 2: Proving ...
% 12.21/2.44 Prover 4: Warning: ignoring some quantifiers
% 12.21/2.52 Prover 4: Constructing countermodel ...
% 12.21/2.52 Prover 0: Proving ...
% 13.48/2.65 Prover 3: gave up
% 14.00/2.68 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.55/2.74 Prover 7: Preprocessing ...
% 14.55/2.78 Prover 1: gave up
% 14.55/2.78 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.55/2.81 Prover 8: Preprocessing ...
% 15.30/2.88 Prover 7: Warning: ignoring some quantifiers
% 15.30/2.89 Prover 7: Constructing countermodel ...
% 15.30/2.96 Prover 8: Warning: ignoring some quantifiers
% 15.30/2.96 Prover 8: Constructing countermodel ...
% 20.30/3.56 Prover 8: gave up
% 20.30/3.58 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 21.06/3.64 Prover 9: Preprocessing ...
% 24.40/4.05 Prover 9: Warning: ignoring some quantifiers
% 24.40/4.06 Prover 9: Constructing countermodel ...
% 60.18/8.79 Prover 2: stopped
% 60.18/8.80 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 60.18/8.83 Prover 10: Preprocessing ...
% 60.18/8.88 Prover 10: Warning: ignoring some quantifiers
% 60.18/8.88 Prover 10: Constructing countermodel ...
% 60.18/9.00 Prover 10: gave up
% 60.18/9.01 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 62.27/9.06 Prover 11: Preprocessing ...
% 62.55/9.10 Prover 4: Found proof (size 138)
% 62.55/9.10 Prover 4: proved (8471ms)
% 62.55/9.10 Prover 5: stopped
% 62.55/9.10 Prover 9: stopped
% 62.55/9.10 Prover 7: stopped
% 62.55/9.10 Prover 6: stopped
% 62.55/9.10 Prover 0: stopped
% 62.55/9.11 Prover 11: stopped
% 62.55/9.11
% 62.55/9.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 62.55/9.11
% 62.55/9.13 % SZS output start Proof for theBenchmark
% 62.79/9.13 Assumptions after simplification:
% 62.79/9.13 ---------------------------------
% 62.79/9.13
% 62.79/9.13 (cc2_funct_1)
% 62.83/9.16 ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? [v2:
% 62.83/9.16 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 & function(v0) =
% 62.83/9.16 v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0)))
% 62.83/9.16 & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2:
% 62.83/9.16 any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 & empty(v0)
% 62.83/9.16 = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~
% 62.83/9.16 (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: any]
% 62.83/9.16 : (one_to_one(v0) = v3 & relation(v0) = v1 & empty(v0) = v2 & ( ~ (v2 = 0) |
% 62.83/9.16 ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0)
% 62.83/9.16 | ? [v1: any] : ? [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 &
% 62.83/9.16 relation(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 =
% 62.83/9.16 0)))
% 62.83/9.16
% 62.83/9.16 (d3_tarski)
% 62.83/9.17 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 62.83/9.17 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 62.83/9.17 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : !
% 62.83/9.17 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~
% 62.83/9.17 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 &
% 62.83/9.17 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 62.83/9.17 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 62.83/9.17 $i(v0) | in(v2, v1) = 0)
% 62.83/9.17
% 62.83/9.17 (dt_k8_relat_1)
% 62.83/9.17 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0,
% 62.83/9.17 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 62.83/9.17 (relation(v2) = v4 & relation(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 62.83/9.17
% 62.83/9.17 (fc5_funct_1)
% 62.83/9.17 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0,
% 62.83/9.17 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ?
% 62.83/9.17 [v5: any] : ? [v6: any] : (relation(v2) = v5 & relation(v1) = v3 &
% 62.83/9.17 function(v2) = v6 & function(v1) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 =
% 62.83/9.17 0 & v5 = 0))))
% 62.83/9.17
% 62.83/9.17 (fc5_relat_1)
% 62.83/9.17 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ?
% 62.83/9.17 [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_dom(v0) = v3 &
% 62.83/9.17 relation(v0) = v2 & empty(v3) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v2 =
% 62.83/9.17 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~
% 62.83/9.17 $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 &
% 62.83/9.17 empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) &
% 62.83/9.17 ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i]
% 62.83/9.17 : ? [v3: any] : (relation_dom(v0) = v2 & empty(v2) = v3 & empty(v0) = v1 &
% 62.83/9.17 $i(v2) & ( ~ (v3 = 0) | v1 = 0)))
% 62.83/9.17
% 62.83/9.17 (fc6_relat_1)
% 62.83/9.18 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ?
% 62.83/9.18 [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_rng(v0) = v3 &
% 62.83/9.18 relation(v0) = v2 & empty(v3) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v2 =
% 62.83/9.18 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~
% 62.83/9.18 $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 &
% 62.83/9.18 empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) &
% 62.83/9.18 ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i]
% 62.83/9.18 : ? [v3: any] : (relation_rng(v0) = v2 & empty(v2) = v3 & empty(v0) = v1 &
% 62.83/9.18 $i(v2) & ( ~ (v3 = 0) | v1 = 0)))
% 62.83/9.18
% 62.83/9.18 (t118_relat_1)
% 62.83/9.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0,
% 62.83/9.18 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5:
% 62.83/9.18 $i] : ? [v6: any] : (relation_rng(v2) = v4 & relation_rng(v1) = v5 &
% 62.83/9.18 subset(v4, v5) = v6 & relation(v1) = v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0) |
% 62.83/9.18 v6 = 0)))
% 62.83/9.18
% 62.83/9.18 (t85_funct_1)
% 63.13/9.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 63.13/9.25 (relation_dom(v1) = v2) | ~ (relation_rng_restriction(v0, v3) = v4) | ~
% 63.13/9.25 $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any]
% 63.13/9.25 : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ? [v11: int] : ? [v12: $i] :
% 63.13/9.25 ? [v13: $i] : ? [v14: $i] : ? [v15: any] : ? [v16: any] : ? [v17: $i] :
% 63.13/9.25 ? [v18: any] : ($i(v14) & $i(v10) & ((relation_dom(v3) = v9 & relation(v3)
% 63.13/9.25 = v7 & function(v3) = v8 & $i(v9) & ( ~ (v8 = 0) | ~ (v7 = 0) | (( ~
% 63.13/9.25 (v4 = v1) | ( ! [v19: $i] : ! [v20: int] : (v20 = 0 | ~
% 63.13/9.25 (in(v19, v2) = v20) | ~ $i(v19) | ? [v21: any] : ? [v22:
% 63.13/9.25 $i] : ? [v23: any] : (apply(v3, v19) = v22 & in(v22, v0)
% 63.13/9.26 = v23 & in(v19, v9) = v21 & $i(v22) & ( ~ (v23 = 0) | ~
% 63.13/9.26 (v21 = 0)))) & ! [v19: $i] : ! [v20: $i] : ( ~
% 63.13/9.26 (apply(v3, v19) = v20) | ~ $i(v19) | ? [v21: any] : ?
% 63.13/9.26 [v22: any] : ? [v23: any] : (in(v20, v0) = v23 & in(v19,
% 63.13/9.26 v9) = v22 & in(v19, v2) = v21 & ( ~ (v21 = 0) | (v23 = 0
% 63.13/9.26 & v22 = 0)))) & ! [v19: $i] : ! [v20: $i] : ( ~
% 63.13/9.26 (apply(v3, v19) = v20) | ~ $i(v19) | ? [v21: any] : ?
% 63.13/9.26 [v22: any] : ? [v23: any] : (in(v20, v0) = v22 & in(v19,
% 63.13/9.26 v9) = v21 & in(v19, v2) = v23 & ( ~ (v22 = 0) | ~ (v21
% 63.13/9.26 = 0) | v23 = 0))) & ! [v19: $i] : ! [v20: $i] : ( ~
% 63.13/9.26 (apply(v3, v19) = v20) | ~ $i(v19) | ? [v21: any] : ?
% 63.13/9.26 [v22: $i] : (apply(v1, v19) = v22 & in(v19, v2) = v21 &
% 63.13/9.26 $i(v22) & ( ~ (v21 = 0) | v22 = v20))) & ! [v19: $i] : !
% 63.13/9.26 [v20: $i] : ( ~ (apply(v1, v19) = v20) | ~ $i(v19) | ? [v21:
% 63.13/9.26 any] : ? [v22: $i] : (apply(v3, v19) = v22 & in(v19, v2)
% 63.13/9.26 = v21 & $i(v22) & ( ~ (v21 = 0) | v22 = v20))) & ! [v19:
% 63.13/9.26 $i] : ! [v20: any] : ( ~ (in(v19, v9) = v20) | ~ $i(v19) |
% 63.13/9.26 ? [v21: any] : ? [v22: $i] : ? [v23: any] : (apply(v3,
% 63.13/9.26 v19) = v22 & in(v22, v0) = v23 & in(v19, v2) = v21 &
% 63.13/9.26 $i(v22) & ( ~ (v21 = 0) | (v23 = 0 & v20 = 0)))) & !
% 63.13/9.26 [v19: $i] : ( ~ (in(v19, v9) = 0) | ~ $i(v19) | ? [v20: $i]
% 63.13/9.26 : ? [v21: any] : ? [v22: any] : (apply(v3, v19) = v20 &
% 63.13/9.26 in(v20, v0) = v21 & in(v19, v2) = v22 & $i(v20) & ( ~ (v21
% 63.13/9.26 = 0) | v22 = 0))) & ! [v19: $i] : ( ~ (in(v19, v2) =
% 63.13/9.26 0) | ~ $i(v19) | ? [v20: $i] : (apply(v3, v19) = v20 &
% 63.13/9.26 apply(v1, v19) = v20 & $i(v20))) & ! [v19: $i] : ( ~
% 63.13/9.26 (in(v19, v2) = 0) | ~ $i(v19) | ? [v20: $i] : (apply(v3,
% 63.13/9.26 v19) = v20 & in(v20, v0) = 0 & in(v19, v9) = 0 &
% 63.13/9.26 $i(v20))))) & (v4 = v1 | (v11 = 0 & ~ (v13 = v12) &
% 63.13/9.26 apply(v3, v10) = v13 & apply(v1, v10) = v12 & in(v10, v2) = 0
% 63.13/9.26 & $i(v13) & $i(v12)) | (apply(v3, v14) = v17 & in(v17, v0) =
% 63.13/9.26 v18 & in(v14, v9) = v16 & in(v14, v2) = v15 & $i(v17) & ( ~
% 63.13/9.26 (v18 = 0) | ~ (v16 = 0) | ~ (v15 = 0)) & (v15 = 0 | (v18 =
% 63.13/9.26 0 & v16 = 0))))))) | (relation(v1) = v5 & function(v1) =
% 63.13/9.26 v6 & ( ~ (v6 = 0) | ~ (v5 = 0)))))) & ? [v0: $i] : ! [v1: $i] : !
% 63.13/9.26 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (relation_dom(v3) = v4) | ~
% 63.13/9.26 (relation_dom(v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] :
% 63.13/9.26 ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ?
% 63.13/9.26 [v11: int] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: any] : ?
% 63.13/9.26 [v16: any] : ? [v17: $i] : ? [v18: any] : ($i(v14) & $i(v10) &
% 63.13/9.26 ((relation_rng_restriction(v0, v3) = v9 & relation(v3) = v7 & function(v3)
% 63.13/9.26 = v8 & $i(v9) & ( ~ (v8 = 0) | ~ (v7 = 0) | (( ~ (v9 = v1) | ( !
% 63.13/9.26 [v19: $i] : ! [v20: int] : (v20 = 0 | ~ (in(v19, v2) = v20)
% 63.13/9.26 | ~ $i(v19) | ? [v21: any] : ? [v22: $i] : ? [v23: any]
% 63.13/9.26 : (apply(v3, v19) = v22 & in(v22, v0) = v23 & in(v19, v4) =
% 63.13/9.26 v21 & $i(v22) & ( ~ (v23 = 0) | ~ (v21 = 0)))) & ! [v19:
% 63.13/9.26 $i] : ! [v20: $i] : ( ~ (apply(v3, v19) = v20) | ~ $i(v19)
% 63.13/9.26 | ? [v21: any] : ? [v22: any] : ? [v23: any] : (in(v20,
% 63.13/9.26 v0) = v23 & in(v19, v4) = v22 & in(v19, v2) = v21 & ( ~
% 63.13/9.26 (v21 = 0) | (v23 = 0 & v22 = 0)))) & ! [v19: $i] : !
% 63.13/9.26 [v20: $i] : ( ~ (apply(v3, v19) = v20) | ~ $i(v19) | ? [v21:
% 63.13/9.26 any] : ? [v22: any] : ? [v23: any] : (in(v20, v0) = v22
% 63.13/9.26 & in(v19, v4) = v21 & in(v19, v2) = v23 & ( ~ (v22 = 0) |
% 63.13/9.26 ~ (v21 = 0) | v23 = 0))) & ! [v19: $i] : ! [v20: $i] :
% 63.13/9.26 ( ~ (apply(v3, v19) = v20) | ~ $i(v19) | ? [v21: any] : ?
% 63.13/9.26 [v22: $i] : (apply(v1, v19) = v22 & in(v19, v2) = v21 &
% 63.13/9.26 $i(v22) & ( ~ (v21 = 0) | v22 = v20))) & ! [v19: $i] : !
% 63.13/9.26 [v20: $i] : ( ~ (apply(v1, v19) = v20) | ~ $i(v19) | ? [v21:
% 63.13/9.26 any] : ? [v22: $i] : (apply(v3, v19) = v22 & in(v19, v2)
% 63.13/9.26 = v21 & $i(v22) & ( ~ (v21 = 0) | v22 = v20))) & ! [v19:
% 63.13/9.26 $i] : ! [v20: any] : ( ~ (in(v19, v4) = v20) | ~ $i(v19) |
% 63.13/9.26 ? [v21: any] : ? [v22: $i] : ? [v23: any] : (apply(v3,
% 63.13/9.26 v19) = v22 & in(v22, v0) = v23 & in(v19, v2) = v21 &
% 63.13/9.26 $i(v22) & ( ~ (v21 = 0) | (v23 = 0 & v20 = 0)))) & !
% 63.13/9.26 [v19: $i] : ( ~ (in(v19, v4) = 0) | ~ $i(v19) | ? [v20: $i]
% 63.13/9.26 : ? [v21: any] : ? [v22: any] : (apply(v3, v19) = v20 &
% 63.13/9.26 in(v20, v0) = v21 & in(v19, v2) = v22 & $i(v20) & ( ~ (v21
% 63.13/9.26 = 0) | v22 = 0))) & ! [v19: $i] : ( ~ (in(v19, v2) =
% 63.13/9.26 0) | ~ $i(v19) | ? [v20: $i] : (apply(v3, v19) = v20 &
% 63.13/9.26 apply(v1, v19) = v20 & $i(v20))) & ! [v19: $i] : ( ~
% 63.13/9.26 (in(v19, v2) = 0) | ~ $i(v19) | ? [v20: $i] : (apply(v3,
% 63.13/9.26 v19) = v20 & in(v20, v0) = 0 & in(v19, v4) = 0 &
% 63.13/9.26 $i(v20))))) & (v9 = v1 | (v11 = 0 & ~ (v13 = v12) &
% 63.13/9.26 apply(v3, v10) = v13 & apply(v1, v10) = v12 & in(v10, v2) = 0
% 63.13/9.26 & $i(v13) & $i(v12)) | (apply(v3, v14) = v17 & in(v17, v0) =
% 63.13/9.26 v18 & in(v14, v4) = v16 & in(v14, v2) = v15 & $i(v17) & ( ~
% 63.13/9.26 (v18 = 0) | ~ (v16 = 0) | ~ (v15 = 0)) & (v15 = 0 | (v18 =
% 63.13/9.26 0 & v16 = 0))))))) | (relation(v1) = v5 & function(v1) =
% 63.13/9.26 v6 & ( ~ (v6 = 0) | ~ (v5 = 0)))))) & ? [v0: $i] : ! [v1: $i] : !
% 63.13/9.26 [v2: $i] : ! [v3: $i] : ( ~ (relation_dom(v1) = v2) | ~ (relation(v3) = 0) |
% 63.13/9.26 ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6:
% 63.13/9.26 any] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: int] : ? [v11:
% 63.13/9.26 $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: any] : ? [v15: any] : ?
% 63.13/9.26 [v16: $i] : ? [v17: any] : ($i(v13) & $i(v9) & ((relation_dom(v3) = v8 &
% 63.13/9.26 relation_rng_restriction(v0, v3) = v7 & function(v3) = v6 & $i(v8) &
% 63.13/9.26 $i(v7) & ( ~ (v6 = 0) | (( ~ (v7 = v1) | ( ! [v18: $i] : ! [v19: int]
% 63.13/9.26 : (v19 = 0 | ~ (in(v18, v2) = v19) | ~ $i(v18) | ? [v20:
% 63.13/9.26 any] : ? [v21: $i] : ? [v22: any] : (apply(v3, v18) =
% 63.13/9.26 v21 & in(v21, v0) = v22 & in(v18, v8) = v20 & $i(v21) & (
% 63.13/9.26 ~ (v22 = 0) | ~ (v20 = 0)))) & ! [v18: $i] : ! [v19:
% 63.13/9.26 $i] : ( ~ (apply(v3, v18) = v19) | ~ $i(v18) | ? [v20:
% 63.13/9.26 any] : ? [v21: any] : ? [v22: any] : (in(v19, v0) = v22
% 63.13/9.26 & in(v18, v8) = v21 & in(v18, v2) = v20 & ( ~ (v20 = 0) |
% 63.13/9.26 (v22 = 0 & v21 = 0)))) & ! [v18: $i] : ! [v19: $i] : (
% 63.13/9.26 ~ (apply(v3, v18) = v19) | ~ $i(v18) | ? [v20: any] : ?
% 63.13/9.26 [v21: any] : ? [v22: any] : (in(v19, v0) = v21 & in(v18,
% 63.13/9.26 v8) = v20 & in(v18, v2) = v22 & ( ~ (v21 = 0) | ~ (v20
% 63.13/9.26 = 0) | v22 = 0))) & ! [v18: $i] : ! [v19: $i] : ( ~
% 63.13/9.26 (apply(v3, v18) = v19) | ~ $i(v18) | ? [v20: any] : ?
% 63.13/9.26 [v21: $i] : (apply(v1, v18) = v21 & in(v18, v2) = v20 &
% 63.13/9.26 $i(v21) & ( ~ (v20 = 0) | v21 = v19))) & ! [v18: $i] : !
% 63.13/9.26 [v19: $i] : ( ~ (apply(v1, v18) = v19) | ~ $i(v18) | ? [v20:
% 63.13/9.26 any] : ? [v21: $i] : (apply(v3, v18) = v21 & in(v18, v2)
% 63.13/9.26 = v20 & $i(v21) & ( ~ (v20 = 0) | v21 = v19))) & ! [v18:
% 63.13/9.26 $i] : ! [v19: any] : ( ~ (in(v18, v8) = v19) | ~ $i(v18) |
% 63.13/9.26 ? [v20: any] : ? [v21: $i] : ? [v22: any] : (apply(v3,
% 63.13/9.26 v18) = v21 & in(v21, v0) = v22 & in(v18, v2) = v20 &
% 63.13/9.26 $i(v21) & ( ~ (v20 = 0) | (v22 = 0 & v19 = 0)))) & !
% 63.13/9.26 [v18: $i] : ( ~ (in(v18, v8) = 0) | ~ $i(v18) | ? [v19: $i]
% 63.13/9.26 : ? [v20: any] : ? [v21: any] : (apply(v3, v18) = v19 &
% 63.13/9.26 in(v19, v0) = v20 & in(v18, v2) = v21 & $i(v19) & ( ~ (v20
% 63.13/9.26 = 0) | v21 = 0))) & ! [v18: $i] : ( ~ (in(v18, v2) =
% 63.13/9.26 0) | ~ $i(v18) | ? [v19: $i] : (apply(v3, v18) = v19 &
% 63.13/9.26 apply(v1, v18) = v19 & $i(v19))) & ! [v18: $i] : ( ~
% 63.13/9.26 (in(v18, v2) = 0) | ~ $i(v18) | ? [v19: $i] : (apply(v3,
% 63.13/9.26 v18) = v19 & in(v19, v0) = 0 & in(v18, v8) = 0 &
% 63.13/9.26 $i(v19))))) & (v7 = v1 | (v10 = 0 & ~ (v12 = v11) &
% 63.13/9.26 apply(v3, v9) = v12 & apply(v1, v9) = v11 & in(v9, v2) = 0 &
% 63.13/9.26 $i(v12) & $i(v11)) | (apply(v3, v13) = v16 & in(v16, v0) = v17
% 63.13/9.26 & in(v13, v8) = v15 & in(v13, v2) = v14 & $i(v16) & ( ~ (v17 =
% 63.13/9.26 0) | ~ (v15 = 0) | ~ (v14 = 0)) & (v14 = 0 | (v17 = 0 &
% 63.13/9.26 v15 = 0))))))) | (relation(v1) = v4 & function(v1) = v5 &
% 63.13/9.26 ( ~ (v5 = 0) | ~ (v4 = 0)))))) & ? [v0: $i] : ! [v1: $i] : ! [v2:
% 63.13/9.26 $i] : ! [v3: $i] : ( ~ (relation_dom(v1) = v2) | ~ (function(v3) = 0) | ~
% 63.13/9.26 $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any]
% 63.13/9.26 : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: int] : ? [v11: $i] :
% 63.13/9.26 ? [v12: $i] : ? [v13: $i] : ? [v14: any] : ? [v15: any] : ? [v16: $i] :
% 63.13/9.26 ? [v17: any] : ($i(v13) & $i(v9) & ((relation_dom(v3) = v8 &
% 63.13/9.26 relation_rng_restriction(v0, v3) = v7 & relation(v3) = v6 & $i(v8) &
% 63.13/9.26 $i(v7) & ( ~ (v6 = 0) | (( ~ (v7 = v1) | ( ! [v18: $i] : ! [v19: int]
% 63.13/9.26 : (v19 = 0 | ~ (in(v18, v2) = v19) | ~ $i(v18) | ? [v20:
% 63.13/9.26 any] : ? [v21: $i] : ? [v22: any] : (apply(v3, v18) =
% 63.13/9.26 v21 & in(v21, v0) = v22 & in(v18, v8) = v20 & $i(v21) & (
% 63.13/9.26 ~ (v22 = 0) | ~ (v20 = 0)))) & ! [v18: $i] : ! [v19:
% 63.13/9.26 $i] : ( ~ (apply(v3, v18) = v19) | ~ $i(v18) | ? [v20:
% 63.13/9.26 any] : ? [v21: any] : ? [v22: any] : (in(v19, v0) = v22
% 63.13/9.26 & in(v18, v8) = v21 & in(v18, v2) = v20 & ( ~ (v20 = 0) |
% 63.13/9.26 (v22 = 0 & v21 = 0)))) & ! [v18: $i] : ! [v19: $i] : (
% 63.13/9.26 ~ (apply(v3, v18) = v19) | ~ $i(v18) | ? [v20: any] : ?
% 63.13/9.26 [v21: any] : ? [v22: any] : (in(v19, v0) = v21 & in(v18,
% 63.13/9.26 v8) = v20 & in(v18, v2) = v22 & ( ~ (v21 = 0) | ~ (v20
% 63.13/9.26 = 0) | v22 = 0))) & ! [v18: $i] : ! [v19: $i] : ( ~
% 63.13/9.26 (apply(v3, v18) = v19) | ~ $i(v18) | ? [v20: any] : ?
% 63.13/9.26 [v21: $i] : (apply(v1, v18) = v21 & in(v18, v2) = v20 &
% 63.13/9.26 $i(v21) & ( ~ (v20 = 0) | v21 = v19))) & ! [v18: $i] : !
% 63.13/9.26 [v19: $i] : ( ~ (apply(v1, v18) = v19) | ~ $i(v18) | ? [v20:
% 63.13/9.26 any] : ? [v21: $i] : (apply(v3, v18) = v21 & in(v18, v2)
% 63.13/9.26 = v20 & $i(v21) & ( ~ (v20 = 0) | v21 = v19))) & ! [v18:
% 63.13/9.26 $i] : ! [v19: any] : ( ~ (in(v18, v8) = v19) | ~ $i(v18) |
% 63.13/9.26 ? [v20: any] : ? [v21: $i] : ? [v22: any] : (apply(v3,
% 63.13/9.26 v18) = v21 & in(v21, v0) = v22 & in(v18, v2) = v20 &
% 63.13/9.26 $i(v21) & ( ~ (v20 = 0) | (v22 = 0 & v19 = 0)))) & !
% 63.13/9.26 [v18: $i] : ( ~ (in(v18, v8) = 0) | ~ $i(v18) | ? [v19: $i]
% 63.13/9.26 : ? [v20: any] : ? [v21: any] : (apply(v3, v18) = v19 &
% 63.13/9.26 in(v19, v0) = v20 & in(v18, v2) = v21 & $i(v19) & ( ~ (v20
% 63.13/9.26 = 0) | v21 = 0))) & ! [v18: $i] : ( ~ (in(v18, v2) =
% 63.13/9.26 0) | ~ $i(v18) | ? [v19: $i] : (apply(v3, v18) = v19 &
% 63.13/9.26 apply(v1, v18) = v19 & $i(v19))) & ! [v18: $i] : ( ~
% 63.13/9.26 (in(v18, v2) = 0) | ~ $i(v18) | ? [v19: $i] : (apply(v3,
% 63.13/9.26 v18) = v19 & in(v19, v0) = 0 & in(v18, v8) = 0 &
% 63.13/9.26 $i(v19))))) & (v7 = v1 | (v10 = 0 & ~ (v12 = v11) &
% 63.13/9.26 apply(v3, v9) = v12 & apply(v1, v9) = v11 & in(v9, v2) = 0 &
% 63.13/9.26 $i(v12) & $i(v11)) | (apply(v3, v13) = v16 & in(v16, v0) = v17
% 63.13/9.26 & in(v13, v8) = v15 & in(v13, v2) = v14 & $i(v16) & ( ~ (v17 =
% 63.13/9.26 0) | ~ (v15 = 0) | ~ (v14 = 0)) & (v14 = 0 | (v17 = 0 &
% 63.13/9.26 v15 = 0))))))) | (relation(v1) = v4 & function(v1) = v5 &
% 63.13/9.26 ( ~ (v5 = 0) | ~ (v4 = 0)))))) & ? [v0: $i] : ! [v1: $i] : ( ~
% 63.13/9.26 (relation(v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] :
% 63.13/9.26 (relation_dom(v1) = v3 & function(v1) = v2 & $i(v3) & ( ~ (v2 = 0) | ( !
% 63.13/9.26 [v4: $i] : ! [v5: $i] : ( ~ (relation_dom(v4) = v5) | ~ $i(v4) | ?
% 63.13/9.26 [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: $i] : ? [v10: int]
% 63.13/9.26 : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: any] : ?
% 63.13/9.26 [v15: any] : ? [v16: $i] : ? [v17: any] :
% 63.13/9.26 (relation_rng_restriction(v0, v4) = v8 & relation(v4) = v6 &
% 63.13/9.26 function(v4) = v7 & $i(v13) & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~
% 63.13/9.26 (v6 = 0) | (( ~ (v8 = v1) | ( ! [v18: $i] : ! [v19: int] : (v19
% 63.13/9.26 = 0 | ~ (in(v18, v3) = v19) | ~ $i(v18) | ? [v20:
% 63.13/9.26 any] : ? [v21: $i] : ? [v22: any] : (apply(v4, v18)
% 63.13/9.26 = v21 & in(v21, v0) = v22 & in(v18, v5) = v20 &
% 63.13/9.26 $i(v21) & ( ~ (v22 = 0) | ~ (v20 = 0)))) & ! [v18:
% 63.13/9.26 $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~
% 63.13/9.26 $i(v18) | ? [v20: any] : ? [v21: any] : ? [v22: any]
% 63.13/9.26 : (in(v19, v0) = v22 & in(v18, v5) = v21 & in(v18, v3) =
% 63.13/9.26 v20 & ( ~ (v20 = 0) | (v22 = 0 & v21 = 0)))) & !
% 63.13/9.26 [v18: $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~
% 63.13/9.26 $i(v18) | ? [v20: any] : ? [v21: any] : ? [v22: any]
% 63.13/9.26 : (in(v19, v0) = v21 & in(v18, v5) = v20 & in(v18, v3) =
% 63.13/9.26 v22 & ( ~ (v21 = 0) | ~ (v20 = 0) | v22 = 0))) & !
% 63.13/9.26 [v18: $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~
% 63.13/9.26 $i(v18) | ? [v20: any] : ? [v21: $i] : (apply(v1, v18)
% 63.13/9.26 = v21 & in(v18, v3) = v20 & $i(v21) & ( ~ (v20 = 0) |
% 63.13/9.26 v21 = v19))) & ! [v18: $i] : ! [v19: $i] : ( ~
% 63.13/9.26 (apply(v1, v18) = v19) | ~ $i(v18) | ? [v20: any] : ?
% 63.13/9.26 [v21: $i] : (apply(v4, v18) = v21 & in(v18, v3) = v20 &
% 63.13/9.26 $i(v21) & ( ~ (v20 = 0) | v21 = v19))) & ! [v18: $i]
% 63.13/9.26 : ! [v19: any] : ( ~ (in(v18, v5) = v19) | ~ $i(v18) |
% 63.13/9.26 ? [v20: any] : ? [v21: $i] : ? [v22: any] : (apply(v4,
% 63.13/9.26 v18) = v21 & in(v21, v0) = v22 & in(v18, v3) = v20 &
% 63.13/9.26 $i(v21) & ( ~ (v20 = 0) | (v22 = 0 & v19 = 0)))) & !
% 63.13/9.26 [v18: $i] : ( ~ (in(v18, v5) = 0) | ~ $i(v18) | ? [v19:
% 63.13/9.26 $i] : ? [v20: any] : ? [v21: any] : (apply(v4, v18)
% 63.13/9.26 = v19 & in(v19, v0) = v20 & in(v18, v3) = v21 &
% 63.13/9.26 $i(v19) & ( ~ (v20 = 0) | v21 = 0))) & ! [v18: $i] :
% 63.13/9.26 ( ~ (in(v18, v3) = 0) | ~ $i(v18) | ? [v19: $i] :
% 63.13/9.26 (apply(v4, v18) = v19 & apply(v1, v18) = v19 & $i(v19)))
% 63.13/9.26 & ! [v18: $i] : ( ~ (in(v18, v3) = 0) | ~ $i(v18) | ?
% 63.13/9.26 [v19: $i] : (apply(v4, v18) = v19 & in(v19, v0) = 0 &
% 63.13/9.26 in(v18, v5) = 0 & $i(v19))))) & (v8 = v1 | (v10 = 0 &
% 63.13/9.26 ~ (v12 = v11) & apply(v4, v9) = v12 & apply(v1, v9) = v11
% 63.13/9.26 & in(v9, v3) = 0 & $i(v12) & $i(v11)) | (apply(v4, v13) =
% 63.13/9.26 v16 & in(v16, v0) = v17 & in(v13, v5) = v15 & in(v13, v3)
% 63.13/9.26 = v14 & $i(v16) & ( ~ (v17 = 0) | ~ (v15 = 0) | ~ (v14 =
% 63.13/9.26 0)) & (v14 = 0 | (v17 = 0 & v15 = 0)))))))) & ! [v4:
% 63.13/9.26 $i] : ! [v5: $i] : ( ~ (relation_rng_restriction(v0, v4) = v5) | ~
% 63.13/9.26 $i(v4) | ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: $i] :
% 63.13/9.26 ? [v10: int] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14:
% 63.13/9.26 any] : ? [v15: any] : ? [v16: $i] : ? [v17: any] :
% 63.13/9.26 (relation_dom(v4) = v8 & relation(v4) = v6 & function(v4) = v7 &
% 63.13/9.26 $i(v13) & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | (( ~ (v5
% 63.13/9.26 = v1) | ( ! [v18: $i] : ! [v19: int] : (v19 = 0 | ~
% 63.13/9.26 (in(v18, v3) = v19) | ~ $i(v18) | ? [v20: any] : ?
% 63.13/9.26 [v21: $i] : ? [v22: any] : (apply(v4, v18) = v21 &
% 63.13/9.26 in(v21, v0) = v22 & in(v18, v8) = v20 & $i(v21) & ( ~
% 63.13/9.26 (v22 = 0) | ~ (v20 = 0)))) & ! [v18: $i] : !
% 63.13/9.26 [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~ $i(v18) | ?
% 63.13/9.26 [v20: any] : ? [v21: any] : ? [v22: any] : (in(v19,
% 63.13/9.26 v0) = v22 & in(v18, v8) = v21 & in(v18, v3) = v20 &
% 63.13/9.26 ( ~ (v20 = 0) | (v22 = 0 & v21 = 0)))) & ! [v18: $i]
% 63.13/9.26 : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~ $i(v18) |
% 63.13/9.26 ? [v20: any] : ? [v21: any] : ? [v22: any] : (in(v19,
% 63.13/9.26 v0) = v21 & in(v18, v8) = v20 & in(v18, v3) = v22 &
% 63.13/9.26 ( ~ (v21 = 0) | ~ (v20 = 0) | v22 = 0))) & ! [v18:
% 63.13/9.26 $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~
% 63.13/9.26 $i(v18) | ? [v20: any] : ? [v21: $i] : (apply(v1, v18)
% 63.13/9.26 = v21 & in(v18, v3) = v20 & $i(v21) & ( ~ (v20 = 0) |
% 63.13/9.26 v21 = v19))) & ! [v18: $i] : ! [v19: $i] : ( ~
% 63.13/9.26 (apply(v1, v18) = v19) | ~ $i(v18) | ? [v20: any] : ?
% 63.13/9.26 [v21: $i] : (apply(v4, v18) = v21 & in(v18, v3) = v20 &
% 63.13/9.26 $i(v21) & ( ~ (v20 = 0) | v21 = v19))) & ! [v18: $i]
% 63.13/9.26 : ! [v19: any] : ( ~ (in(v18, v8) = v19) | ~ $i(v18) |
% 63.13/9.26 ? [v20: any] : ? [v21: $i] : ? [v22: any] : (apply(v4,
% 63.13/9.26 v18) = v21 & in(v21, v0) = v22 & in(v18, v3) = v20 &
% 63.13/9.26 $i(v21) & ( ~ (v20 = 0) | (v22 = 0 & v19 = 0)))) & !
% 63.13/9.26 [v18: $i] : ( ~ (in(v18, v8) = 0) | ~ $i(v18) | ? [v19:
% 63.13/9.26 $i] : ? [v20: any] : ? [v21: any] : (apply(v4, v18)
% 63.13/9.26 = v19 & in(v19, v0) = v20 & in(v18, v3) = v21 &
% 63.13/9.26 $i(v19) & ( ~ (v20 = 0) | v21 = 0))) & ! [v18: $i] :
% 63.13/9.26 ( ~ (in(v18, v3) = 0) | ~ $i(v18) | ? [v19: $i] :
% 63.13/9.26 (apply(v4, v18) = v19 & apply(v1, v18) = v19 & $i(v19)))
% 63.13/9.26 & ! [v18: $i] : ( ~ (in(v18, v3) = 0) | ~ $i(v18) | ?
% 63.13/9.26 [v19: $i] : (apply(v4, v18) = v19 & in(v19, v0) = 0 &
% 63.13/9.26 in(v18, v8) = 0 & $i(v19))))) & (v5 = v1 | (v10 = 0 &
% 63.13/9.26 ~ (v12 = v11) & apply(v4, v9) = v12 & apply(v1, v9) = v11
% 63.13/9.26 & in(v9, v3) = 0 & $i(v12) & $i(v11)) | (apply(v4, v13) =
% 63.13/9.26 v16 & in(v16, v0) = v17 & in(v13, v8) = v15 & in(v13, v3)
% 63.13/9.26 = v14 & $i(v16) & ( ~ (v17 = 0) | ~ (v15 = 0) | ~ (v14 =
% 63.13/9.26 0)) & (v14 = 0 | (v17 = 0 & v15 = 0)))))))) & ! [v4:
% 63.13/9.26 $i] : ( ~ (relation(v4) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6:
% 63.13/9.26 $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: int] : ? [v10: $i] : ?
% 63.13/9.26 [v11: $i] : ? [v12: $i] : ? [v13: any] : ? [v14: any] : ? [v15:
% 63.13/9.26 $i] : ? [v16: any] : (relation_dom(v4) = v7 &
% 63.13/9.26 relation_rng_restriction(v0, v4) = v6 & function(v4) = v5 &
% 63.13/9.26 $i(v12) & $i(v8) & $i(v7) & $i(v6) & ( ~ (v5 = 0) | (( ~ (v6 = v1)
% 63.13/9.26 | ( ! [v17: $i] : ! [v18: int] : (v18 = 0 | ~ (in(v17, v3)
% 63.13/9.26 = v18) | ~ $i(v17) | ? [v19: any] : ? [v20: $i] :
% 63.13/9.26 ? [v21: any] : (apply(v4, v17) = v20 & in(v20, v0) = v21
% 63.13/9.26 & in(v17, v7) = v19 & $i(v20) & ( ~ (v21 = 0) | ~
% 63.13/9.26 (v19 = 0)))) & ! [v17: $i] : ! [v18: $i] : ( ~
% 63.13/9.26 (apply(v4, v17) = v18) | ~ $i(v17) | ? [v19: any] : ?
% 63.13/9.26 [v20: any] : ? [v21: any] : (in(v18, v0) = v21 &
% 63.13/9.26 in(v17, v7) = v20 & in(v17, v3) = v19 & ( ~ (v19 = 0)
% 63.13/9.26 | (v21 = 0 & v20 = 0)))) & ! [v17: $i] : ! [v18:
% 63.13/9.26 $i] : ( ~ (apply(v4, v17) = v18) | ~ $i(v17) | ? [v19:
% 63.13/9.26 any] : ? [v20: any] : ? [v21: any] : (in(v18, v0) =
% 63.13/9.26 v20 & in(v17, v7) = v19 & in(v17, v3) = v21 & ( ~ (v20
% 63.13/9.26 = 0) | ~ (v19 = 0) | v21 = 0))) & ! [v17: $i] :
% 63.13/9.26 ! [v18: $i] : ( ~ (apply(v4, v17) = v18) | ~ $i(v17) | ?
% 63.13/9.26 [v19: any] : ? [v20: $i] : (apply(v1, v17) = v20 &
% 63.13/9.26 in(v17, v3) = v19 & $i(v20) & ( ~ (v19 = 0) | v20 =
% 63.13/9.26 v18))) & ! [v17: $i] : ! [v18: $i] : ( ~
% 63.13/9.26 (apply(v1, v17) = v18) | ~ $i(v17) | ? [v19: any] : ?
% 63.13/9.26 [v20: $i] : (apply(v4, v17) = v20 & in(v17, v3) = v19 &
% 63.13/9.26 $i(v20) & ( ~ (v19 = 0) | v20 = v18))) & ! [v17: $i]
% 63.13/9.26 : ! [v18: any] : ( ~ (in(v17, v7) = v18) | ~ $i(v17) |
% 63.13/9.26 ? [v19: any] : ? [v20: $i] : ? [v21: any] : (apply(v4,
% 63.13/9.26 v17) = v20 & in(v20, v0) = v21 & in(v17, v3) = v19 &
% 63.13/9.26 $i(v20) & ( ~ (v19 = 0) | (v21 = 0 & v18 = 0)))) & !
% 63.13/9.26 [v17: $i] : ( ~ (in(v17, v7) = 0) | ~ $i(v17) | ? [v18:
% 63.39/9.26 $i] : ? [v19: any] : ? [v20: any] : (apply(v4, v17)
% 63.39/9.26 = v18 & in(v18, v0) = v19 & in(v17, v3) = v20 &
% 63.39/9.26 $i(v18) & ( ~ (v19 = 0) | v20 = 0))) & ! [v17: $i] :
% 63.39/9.26 ( ~ (in(v17, v3) = 0) | ~ $i(v17) | ? [v18: $i] :
% 63.39/9.26 (apply(v4, v17) = v18 & apply(v1, v17) = v18 & $i(v18)))
% 63.39/9.26 & ! [v17: $i] : ( ~ (in(v17, v3) = 0) | ~ $i(v17) | ?
% 63.39/9.26 [v18: $i] : (apply(v4, v17) = v18 & in(v18, v0) = 0 &
% 63.39/9.26 in(v17, v7) = 0 & $i(v18))))) & (v6 = v1 | (v9 = 0 &
% 63.39/9.26 ~ (v11 = v10) & apply(v4, v8) = v11 & apply(v1, v8) = v10
% 63.39/9.26 & in(v8, v3) = 0 & $i(v11) & $i(v10)) | (apply(v4, v12) =
% 63.39/9.26 v15 & in(v15, v0) = v16 & in(v12, v7) = v14 & in(v12, v3)
% 63.39/9.26 = v13 & $i(v15) & ( ~ (v16 = 0) | ~ (v14 = 0) | ~ (v13 =
% 63.39/9.26 0)) & (v13 = 0 | (v16 = 0 & v14 = 0)))))))) & ! [v4:
% 63.39/9.26 $i] : ( ~ (function(v4) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6:
% 63.39/9.26 $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: int] : ? [v10: $i] : ?
% 63.39/9.26 [v11: $i] : ? [v12: $i] : ? [v13: any] : ? [v14: any] : ? [v15:
% 63.39/9.26 $i] : ? [v16: any] : (relation_dom(v4) = v7 &
% 63.39/9.26 relation_rng_restriction(v0, v4) = v6 & relation(v4) = v5 &
% 63.39/9.26 $i(v12) & $i(v8) & $i(v7) & $i(v6) & ( ~ (v5 = 0) | (( ~ (v6 = v1)
% 63.39/9.26 | ( ! [v17: $i] : ! [v18: int] : (v18 = 0 | ~ (in(v17, v3)
% 63.39/9.26 = v18) | ~ $i(v17) | ? [v19: any] : ? [v20: $i] :
% 63.39/9.26 ? [v21: any] : (apply(v4, v17) = v20 & in(v20, v0) = v21
% 63.39/9.26 & in(v17, v7) = v19 & $i(v20) & ( ~ (v21 = 0) | ~
% 63.39/9.26 (v19 = 0)))) & ! [v17: $i] : ! [v18: $i] : ( ~
% 63.39/9.26 (apply(v4, v17) = v18) | ~ $i(v17) | ? [v19: any] : ?
% 63.39/9.26 [v20: any] : ? [v21: any] : (in(v18, v0) = v21 &
% 63.39/9.26 in(v17, v7) = v20 & in(v17, v3) = v19 & ( ~ (v19 = 0)
% 63.39/9.26 | (v21 = 0 & v20 = 0)))) & ! [v17: $i] : ! [v18:
% 63.39/9.26 $i] : ( ~ (apply(v4, v17) = v18) | ~ $i(v17) | ? [v19:
% 63.39/9.26 any] : ? [v20: any] : ? [v21: any] : (in(v18, v0) =
% 63.39/9.26 v20 & in(v17, v7) = v19 & in(v17, v3) = v21 & ( ~ (v20
% 63.39/9.26 = 0) | ~ (v19 = 0) | v21 = 0))) & ! [v17: $i] :
% 63.39/9.26 ! [v18: $i] : ( ~ (apply(v4, v17) = v18) | ~ $i(v17) | ?
% 63.39/9.26 [v19: any] : ? [v20: $i] : (apply(v1, v17) = v20 &
% 63.39/9.26 in(v17, v3) = v19 & $i(v20) & ( ~ (v19 = 0) | v20 =
% 63.39/9.26 v18))) & ! [v17: $i] : ! [v18: $i] : ( ~
% 63.39/9.26 (apply(v1, v17) = v18) | ~ $i(v17) | ? [v19: any] : ?
% 63.39/9.26 [v20: $i] : (apply(v4, v17) = v20 & in(v17, v3) = v19 &
% 63.39/9.26 $i(v20) & ( ~ (v19 = 0) | v20 = v18))) & ! [v17: $i]
% 63.39/9.26 : ! [v18: any] : ( ~ (in(v17, v7) = v18) | ~ $i(v17) |
% 63.39/9.26 ? [v19: any] : ? [v20: $i] : ? [v21: any] : (apply(v4,
% 63.39/9.26 v17) = v20 & in(v20, v0) = v21 & in(v17, v3) = v19 &
% 63.39/9.26 $i(v20) & ( ~ (v19 = 0) | (v21 = 0 & v18 = 0)))) & !
% 63.39/9.26 [v17: $i] : ( ~ (in(v17, v7) = 0) | ~ $i(v17) | ? [v18:
% 63.39/9.26 $i] : ? [v19: any] : ? [v20: any] : (apply(v4, v17)
% 63.39/9.26 = v18 & in(v18, v0) = v19 & in(v17, v3) = v20 &
% 63.39/9.26 $i(v18) & ( ~ (v19 = 0) | v20 = 0))) & ! [v17: $i] :
% 63.39/9.26 ( ~ (in(v17, v3) = 0) | ~ $i(v17) | ? [v18: $i] :
% 63.39/9.26 (apply(v4, v17) = v18 & apply(v1, v17) = v18 & $i(v18)))
% 63.39/9.26 & ! [v17: $i] : ( ~ (in(v17, v3) = 0) | ~ $i(v17) | ?
% 63.39/9.26 [v18: $i] : (apply(v4, v17) = v18 & in(v18, v0) = 0 &
% 63.39/9.26 in(v17, v7) = 0 & $i(v18))))) & (v6 = v1 | (v9 = 0 &
% 63.39/9.26 ~ (v11 = v10) & apply(v4, v8) = v11 & apply(v1, v8) = v10
% 63.39/9.26 & in(v8, v3) = 0 & $i(v11) & $i(v10)) | (apply(v4, v12) =
% 63.39/9.26 v15 & in(v15, v0) = v16 & in(v12, v7) = v14 & in(v12, v3)
% 63.39/9.26 = v13 & $i(v15) & ( ~ (v16 = 0) | ~ (v14 = 0) | ~ (v13 =
% 63.39/9.26 0)) & (v13 = 0 | (v16 = 0 & v14 = 0)))))))))))) & ?
% 63.39/9.26 [v0: $i] : ! [v1: $i] : ( ~ (function(v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 63.39/9.26 [v2: any] : ? [v3: $i] : (relation_dom(v1) = v3 & relation(v1) = v2 &
% 63.39/9.26 $i(v3) & ( ~ (v2 = 0) | ( ! [v4: $i] : ! [v5: $i] : ( ~ (relation_dom(v4)
% 63.39/9.26 = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: any] : ? [v8: $i] : ?
% 63.39/9.26 [v9: $i] : ? [v10: int] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 63.39/9.26 $i] : ? [v14: any] : ? [v15: any] : ? [v16: $i] : ? [v17: any]
% 63.39/9.26 : (relation_rng_restriction(v0, v4) = v8 & relation(v4) = v6 &
% 63.39/9.26 function(v4) = v7 & $i(v13) & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~
% 63.39/9.26 (v6 = 0) | (( ~ (v8 = v1) | ( ! [v18: $i] : ! [v19: int] : (v19
% 63.39/9.26 = 0 | ~ (in(v18, v3) = v19) | ~ $i(v18) | ? [v20:
% 63.39/9.26 any] : ? [v21: $i] : ? [v22: any] : (apply(v4, v18)
% 63.39/9.26 = v21 & in(v21, v0) = v22 & in(v18, v5) = v20 &
% 63.39/9.26 $i(v21) & ( ~ (v22 = 0) | ~ (v20 = 0)))) & ! [v18:
% 63.39/9.26 $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~
% 63.39/9.26 $i(v18) | ? [v20: any] : ? [v21: any] : ? [v22: any]
% 63.39/9.26 : (in(v19, v0) = v22 & in(v18, v5) = v21 & in(v18, v3) =
% 63.39/9.26 v20 & ( ~ (v20 = 0) | (v22 = 0 & v21 = 0)))) & !
% 63.39/9.26 [v18: $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~
% 63.39/9.26 $i(v18) | ? [v20: any] : ? [v21: any] : ? [v22: any]
% 63.39/9.26 : (in(v19, v0) = v21 & in(v18, v5) = v20 & in(v18, v3) =
% 63.39/9.26 v22 & ( ~ (v21 = 0) | ~ (v20 = 0) | v22 = 0))) & !
% 63.39/9.26 [v18: $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~
% 63.39/9.26 $i(v18) | ? [v20: any] : ? [v21: $i] : (apply(v1, v18)
% 63.39/9.26 = v21 & in(v18, v3) = v20 & $i(v21) & ( ~ (v20 = 0) |
% 63.39/9.26 v21 = v19))) & ! [v18: $i] : ! [v19: $i] : ( ~
% 63.39/9.26 (apply(v1, v18) = v19) | ~ $i(v18) | ? [v20: any] : ?
% 63.39/9.26 [v21: $i] : (apply(v4, v18) = v21 & in(v18, v3) = v20 &
% 63.39/9.26 $i(v21) & ( ~ (v20 = 0) | v21 = v19))) & ! [v18: $i]
% 63.39/9.26 : ! [v19: any] : ( ~ (in(v18, v5) = v19) | ~ $i(v18) |
% 63.39/9.26 ? [v20: any] : ? [v21: $i] : ? [v22: any] : (apply(v4,
% 63.39/9.26 v18) = v21 & in(v21, v0) = v22 & in(v18, v3) = v20 &
% 63.39/9.26 $i(v21) & ( ~ (v20 = 0) | (v22 = 0 & v19 = 0)))) & !
% 63.39/9.26 [v18: $i] : ( ~ (in(v18, v5) = 0) | ~ $i(v18) | ? [v19:
% 63.39/9.26 $i] : ? [v20: any] : ? [v21: any] : (apply(v4, v18)
% 63.39/9.26 = v19 & in(v19, v0) = v20 & in(v18, v3) = v21 &
% 63.39/9.26 $i(v19) & ( ~ (v20 = 0) | v21 = 0))) & ! [v18: $i] :
% 63.39/9.26 ( ~ (in(v18, v3) = 0) | ~ $i(v18) | ? [v19: $i] :
% 63.39/9.26 (apply(v4, v18) = v19 & apply(v1, v18) = v19 & $i(v19)))
% 63.39/9.26 & ! [v18: $i] : ( ~ (in(v18, v3) = 0) | ~ $i(v18) | ?
% 63.39/9.26 [v19: $i] : (apply(v4, v18) = v19 & in(v19, v0) = 0 &
% 63.39/9.26 in(v18, v5) = 0 & $i(v19))))) & (v8 = v1 | (v10 = 0 &
% 63.39/9.26 ~ (v12 = v11) & apply(v4, v9) = v12 & apply(v1, v9) = v11
% 63.39/9.26 & in(v9, v3) = 0 & $i(v12) & $i(v11)) | (apply(v4, v13) =
% 63.39/9.26 v16 & in(v16, v0) = v17 & in(v13, v5) = v15 & in(v13, v3)
% 63.39/9.26 = v14 & $i(v16) & ( ~ (v17 = 0) | ~ (v15 = 0) | ~ (v14 =
% 63.39/9.26 0)) & (v14 = 0 | (v17 = 0 & v15 = 0)))))))) & ! [v4:
% 63.39/9.26 $i] : ! [v5: $i] : ( ~ (relation_rng_restriction(v0, v4) = v5) | ~
% 63.39/9.26 $i(v4) | ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: $i] :
% 63.39/9.26 ? [v10: int] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14:
% 63.39/9.26 any] : ? [v15: any] : ? [v16: $i] : ? [v17: any] :
% 63.39/9.26 (relation_dom(v4) = v8 & relation(v4) = v6 & function(v4) = v7 &
% 63.39/9.26 $i(v13) & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | (( ~ (v5
% 63.39/9.26 = v1) | ( ! [v18: $i] : ! [v19: int] : (v19 = 0 | ~
% 63.39/9.26 (in(v18, v3) = v19) | ~ $i(v18) | ? [v20: any] : ?
% 63.39/9.26 [v21: $i] : ? [v22: any] : (apply(v4, v18) = v21 &
% 63.39/9.26 in(v21, v0) = v22 & in(v18, v8) = v20 & $i(v21) & ( ~
% 63.39/9.26 (v22 = 0) | ~ (v20 = 0)))) & ! [v18: $i] : !
% 63.39/9.26 [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~ $i(v18) | ?
% 63.39/9.26 [v20: any] : ? [v21: any] : ? [v22: any] : (in(v19,
% 63.39/9.26 v0) = v22 & in(v18, v8) = v21 & in(v18, v3) = v20 &
% 63.39/9.26 ( ~ (v20 = 0) | (v22 = 0 & v21 = 0)))) & ! [v18: $i]
% 63.39/9.26 : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~ $i(v18) |
% 63.39/9.26 ? [v20: any] : ? [v21: any] : ? [v22: any] : (in(v19,
% 63.39/9.26 v0) = v21 & in(v18, v8) = v20 & in(v18, v3) = v22 &
% 63.39/9.26 ( ~ (v21 = 0) | ~ (v20 = 0) | v22 = 0))) & ! [v18:
% 63.39/9.26 $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~
% 63.39/9.26 $i(v18) | ? [v20: any] : ? [v21: $i] : (apply(v1, v18)
% 63.39/9.26 = v21 & in(v18, v3) = v20 & $i(v21) & ( ~ (v20 = 0) |
% 63.39/9.26 v21 = v19))) & ! [v18: $i] : ! [v19: $i] : ( ~
% 63.39/9.26 (apply(v1, v18) = v19) | ~ $i(v18) | ? [v20: any] : ?
% 63.39/9.26 [v21: $i] : (apply(v4, v18) = v21 & in(v18, v3) = v20 &
% 63.39/9.26 $i(v21) & ( ~ (v20 = 0) | v21 = v19))) & ! [v18: $i]
% 63.39/9.26 : ! [v19: any] : ( ~ (in(v18, v8) = v19) | ~ $i(v18) |
% 63.39/9.26 ? [v20: any] : ? [v21: $i] : ? [v22: any] : (apply(v4,
% 63.39/9.26 v18) = v21 & in(v21, v0) = v22 & in(v18, v3) = v20 &
% 63.39/9.26 $i(v21) & ( ~ (v20 = 0) | (v22 = 0 & v19 = 0)))) & !
% 63.39/9.26 [v18: $i] : ( ~ (in(v18, v8) = 0) | ~ $i(v18) | ? [v19:
% 63.39/9.26 $i] : ? [v20: any] : ? [v21: any] : (apply(v4, v18)
% 63.39/9.26 = v19 & in(v19, v0) = v20 & in(v18, v3) = v21 &
% 63.39/9.26 $i(v19) & ( ~ (v20 = 0) | v21 = 0))) & ! [v18: $i] :
% 63.39/9.26 ( ~ (in(v18, v3) = 0) | ~ $i(v18) | ? [v19: $i] :
% 63.39/9.26 (apply(v4, v18) = v19 & apply(v1, v18) = v19 & $i(v19)))
% 63.39/9.26 & ! [v18: $i] : ( ~ (in(v18, v3) = 0) | ~ $i(v18) | ?
% 63.39/9.26 [v19: $i] : (apply(v4, v18) = v19 & in(v19, v0) = 0 &
% 63.39/9.26 in(v18, v8) = 0 & $i(v19))))) & (v5 = v1 | (v10 = 0 &
% 63.39/9.26 ~ (v12 = v11) & apply(v4, v9) = v12 & apply(v1, v9) = v11
% 63.39/9.26 & in(v9, v3) = 0 & $i(v12) & $i(v11)) | (apply(v4, v13) =
% 63.39/9.26 v16 & in(v16, v0) = v17 & in(v13, v8) = v15 & in(v13, v3)
% 63.39/9.26 = v14 & $i(v16) & ( ~ (v17 = 0) | ~ (v15 = 0) | ~ (v14 =
% 63.39/9.26 0)) & (v14 = 0 | (v17 = 0 & v15 = 0)))))))) & ! [v4:
% 63.39/9.26 $i] : ( ~ (relation(v4) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6:
% 63.39/9.26 $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: int] : ? [v10: $i] : ?
% 63.39/9.26 [v11: $i] : ? [v12: $i] : ? [v13: any] : ? [v14: any] : ? [v15:
% 63.39/9.26 $i] : ? [v16: any] : (relation_dom(v4) = v7 &
% 63.39/9.26 relation_rng_restriction(v0, v4) = v6 & function(v4) = v5 &
% 63.39/9.26 $i(v12) & $i(v8) & $i(v7) & $i(v6) & ( ~ (v5 = 0) | (( ~ (v6 = v1)
% 63.39/9.26 | ( ! [v17: $i] : ! [v18: int] : (v18 = 0 | ~ (in(v17, v3)
% 63.39/9.26 = v18) | ~ $i(v17) | ? [v19: any] : ? [v20: $i] :
% 63.39/9.26 ? [v21: any] : (apply(v4, v17) = v20 & in(v20, v0) = v21
% 63.39/9.26 & in(v17, v7) = v19 & $i(v20) & ( ~ (v21 = 0) | ~
% 63.39/9.26 (v19 = 0)))) & ! [v17: $i] : ! [v18: $i] : ( ~
% 63.39/9.26 (apply(v4, v17) = v18) | ~ $i(v17) | ? [v19: any] : ?
% 63.39/9.26 [v20: any] : ? [v21: any] : (in(v18, v0) = v21 &
% 63.39/9.26 in(v17, v7) = v20 & in(v17, v3) = v19 & ( ~ (v19 = 0)
% 63.39/9.26 | (v21 = 0 & v20 = 0)))) & ! [v17: $i] : ! [v18:
% 63.39/9.26 $i] : ( ~ (apply(v4, v17) = v18) | ~ $i(v17) | ? [v19:
% 63.39/9.26 any] : ? [v20: any] : ? [v21: any] : (in(v18, v0) =
% 63.39/9.27 v20 & in(v17, v7) = v19 & in(v17, v3) = v21 & ( ~ (v20
% 63.39/9.27 = 0) | ~ (v19 = 0) | v21 = 0))) & ! [v17: $i] :
% 63.39/9.27 ! [v18: $i] : ( ~ (apply(v4, v17) = v18) | ~ $i(v17) | ?
% 63.39/9.27 [v19: any] : ? [v20: $i] : (apply(v1, v17) = v20 &
% 63.39/9.27 in(v17, v3) = v19 & $i(v20) & ( ~ (v19 = 0) | v20 =
% 63.39/9.27 v18))) & ! [v17: $i] : ! [v18: $i] : ( ~
% 63.39/9.27 (apply(v1, v17) = v18) | ~ $i(v17) | ? [v19: any] : ?
% 63.39/9.27 [v20: $i] : (apply(v4, v17) = v20 & in(v17, v3) = v19 &
% 63.39/9.27 $i(v20) & ( ~ (v19 = 0) | v20 = v18))) & ! [v17: $i]
% 63.39/9.27 : ! [v18: any] : ( ~ (in(v17, v7) = v18) | ~ $i(v17) |
% 63.39/9.27 ? [v19: any] : ? [v20: $i] : ? [v21: any] : (apply(v4,
% 63.39/9.27 v17) = v20 & in(v20, v0) = v21 & in(v17, v3) = v19 &
% 63.39/9.27 $i(v20) & ( ~ (v19 = 0) | (v21 = 0 & v18 = 0)))) & !
% 63.39/9.27 [v17: $i] : ( ~ (in(v17, v7) = 0) | ~ $i(v17) | ? [v18:
% 63.39/9.27 $i] : ? [v19: any] : ? [v20: any] : (apply(v4, v17)
% 63.39/9.27 = v18 & in(v18, v0) = v19 & in(v17, v3) = v20 &
% 63.39/9.27 $i(v18) & ( ~ (v19 = 0) | v20 = 0))) & ! [v17: $i] :
% 63.39/9.27 ( ~ (in(v17, v3) = 0) | ~ $i(v17) | ? [v18: $i] :
% 63.39/9.27 (apply(v4, v17) = v18 & apply(v1, v17) = v18 & $i(v18)))
% 63.39/9.27 & ! [v17: $i] : ( ~ (in(v17, v3) = 0) | ~ $i(v17) | ?
% 63.39/9.27 [v18: $i] : (apply(v4, v17) = v18 & in(v18, v0) = 0 &
% 63.39/9.27 in(v17, v7) = 0 & $i(v18))))) & (v6 = v1 | (v9 = 0 &
% 63.39/9.27 ~ (v11 = v10) & apply(v4, v8) = v11 & apply(v1, v8) = v10
% 63.39/9.27 & in(v8, v3) = 0 & $i(v11) & $i(v10)) | (apply(v4, v12) =
% 63.39/9.27 v15 & in(v15, v0) = v16 & in(v12, v7) = v14 & in(v12, v3)
% 63.39/9.27 = v13 & $i(v15) & ( ~ (v16 = 0) | ~ (v14 = 0) | ~ (v13 =
% 63.39/9.27 0)) & (v13 = 0 | (v16 = 0 & v14 = 0)))))))) & ! [v4:
% 63.39/9.27 $i] : ( ~ (function(v4) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6:
% 63.39/9.27 $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: int] : ? [v10: $i] : ?
% 63.39/9.27 [v11: $i] : ? [v12: $i] : ? [v13: any] : ? [v14: any] : ? [v15:
% 63.39/9.27 $i] : ? [v16: any] : (relation_dom(v4) = v7 &
% 63.39/9.27 relation_rng_restriction(v0, v4) = v6 & relation(v4) = v5 &
% 63.39/9.27 $i(v12) & $i(v8) & $i(v7) & $i(v6) & ( ~ (v5 = 0) | (( ~ (v6 = v1)
% 63.39/9.27 | ( ! [v17: $i] : ! [v18: int] : (v18 = 0 | ~ (in(v17, v3)
% 63.39/9.27 = v18) | ~ $i(v17) | ? [v19: any] : ? [v20: $i] :
% 63.39/9.27 ? [v21: any] : (apply(v4, v17) = v20 & in(v20, v0) = v21
% 63.39/9.27 & in(v17, v7) = v19 & $i(v20) & ( ~ (v21 = 0) | ~
% 63.39/9.27 (v19 = 0)))) & ! [v17: $i] : ! [v18: $i] : ( ~
% 63.39/9.27 (apply(v4, v17) = v18) | ~ $i(v17) | ? [v19: any] : ?
% 63.39/9.27 [v20: any] : ? [v21: any] : (in(v18, v0) = v21 &
% 63.39/9.27 in(v17, v7) = v20 & in(v17, v3) = v19 & ( ~ (v19 = 0)
% 63.39/9.27 | (v21 = 0 & v20 = 0)))) & ! [v17: $i] : ! [v18:
% 63.39/9.27 $i] : ( ~ (apply(v4, v17) = v18) | ~ $i(v17) | ? [v19:
% 63.39/9.27 any] : ? [v20: any] : ? [v21: any] : (in(v18, v0) =
% 63.39/9.27 v20 & in(v17, v7) = v19 & in(v17, v3) = v21 & ( ~ (v20
% 63.39/9.27 = 0) | ~ (v19 = 0) | v21 = 0))) & ! [v17: $i] :
% 63.39/9.27 ! [v18: $i] : ( ~ (apply(v4, v17) = v18) | ~ $i(v17) | ?
% 63.39/9.27 [v19: any] : ? [v20: $i] : (apply(v1, v17) = v20 &
% 63.39/9.27 in(v17, v3) = v19 & $i(v20) & ( ~ (v19 = 0) | v20 =
% 63.39/9.27 v18))) & ! [v17: $i] : ! [v18: $i] : ( ~
% 63.39/9.27 (apply(v1, v17) = v18) | ~ $i(v17) | ? [v19: any] : ?
% 63.39/9.27 [v20: $i] : (apply(v4, v17) = v20 & in(v17, v3) = v19 &
% 63.39/9.27 $i(v20) & ( ~ (v19 = 0) | v20 = v18))) & ! [v17: $i]
% 63.39/9.27 : ! [v18: any] : ( ~ (in(v17, v7) = v18) | ~ $i(v17) |
% 63.39/9.27 ? [v19: any] : ? [v20: $i] : ? [v21: any] : (apply(v4,
% 63.39/9.27 v17) = v20 & in(v20, v0) = v21 & in(v17, v3) = v19 &
% 63.39/9.27 $i(v20) & ( ~ (v19 = 0) | (v21 = 0 & v18 = 0)))) & !
% 63.39/9.27 [v17: $i] : ( ~ (in(v17, v7) = 0) | ~ $i(v17) | ? [v18:
% 63.39/9.27 $i] : ? [v19: any] : ? [v20: any] : (apply(v4, v17)
% 63.39/9.27 = v18 & in(v18, v0) = v19 & in(v17, v3) = v20 &
% 63.39/9.27 $i(v18) & ( ~ (v19 = 0) | v20 = 0))) & ! [v17: $i] :
% 63.39/9.27 ( ~ (in(v17, v3) = 0) | ~ $i(v17) | ? [v18: $i] :
% 63.39/9.27 (apply(v4, v17) = v18 & apply(v1, v17) = v18 & $i(v18)))
% 63.39/9.27 & ! [v17: $i] : ( ~ (in(v17, v3) = 0) | ~ $i(v17) | ?
% 63.39/9.27 [v18: $i] : (apply(v4, v17) = v18 & in(v18, v0) = 0 &
% 63.39/9.27 in(v17, v7) = 0 & $i(v18))))) & (v6 = v1 | (v9 = 0 &
% 63.39/9.27 ~ (v11 = v10) & apply(v4, v8) = v11 & apply(v1, v8) = v10
% 63.39/9.27 & in(v8, v3) = 0 & $i(v11) & $i(v10)) | (apply(v4, v12) =
% 63.39/9.27 v15 & in(v15, v0) = v16 & in(v12, v7) = v14 & in(v12, v3)
% 63.39/9.27 = v13 & $i(v15) & ( ~ (v16 = 0) | ~ (v14 = 0) | ~ (v13 =
% 63.39/9.27 0)) & (v13 = 0 | (v16 = 0 & v14 = 0))))))))))))
% 63.39/9.27
% 63.39/9.27 (t89_funct_1)
% 63.39/9.27 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 63.39/9.27 any] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] : (relation_rng(v2) = v6 &
% 63.39/9.27 relation_rng(v1) = v7 & relation_dom(v2) = v3 & relation_dom(v1) = v4 &
% 63.39/9.27 relation_rng_restriction(v0, v1) = v2 & subset(v6, v7) = v8 & subset(v3, v4)
% 63.39/9.27 = v5 & relation(v1) = 0 & function(v1) = 0 & $i(v7) & $i(v6) & $i(v4) &
% 63.39/9.27 $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v8 = 0) | ~ (v5 = 0)))
% 63.39/9.27
% 63.39/9.27 (function-axioms)
% 63.39/9.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 63.39/9.27 (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: MultipleValueBool]
% 63.39/9.27 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 63.39/9.27 (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 63.39/9.27 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 63.39/9.27 (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3,
% 63.39/9.27 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 63.39/9.27 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~
% 63.39/9.27 (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 63.39/9.27 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) =
% 63.39/9.27 v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 63.39/9.27 (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0:
% 63.39/9.27 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~
% 63.39/9.27 (relation_dom(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 63.39/9.27 v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0:
% 63.39/9.27 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 63.39/9.27 ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) =
% 63.39/9.27 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 63.39/9.27 $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & !
% 63.39/9.27 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 63.39/9.27 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0:
% 63.39/9.27 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 63.39/9.27 ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool]
% 63.39/9.27 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) |
% 63.39/9.27 ~ (empty(v2) = v0))
% 63.39/9.27
% 63.39/9.27 Further assumptions not needed in the proof:
% 63.39/9.27 --------------------------------------------
% 63.39/9.27 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, existence_m1_subset_1,
% 63.39/9.27 fc12_relat_1, fc1_subset_1, fc1_xboole_0, fc4_relat_1, fc7_relat_1, fc8_relat_1,
% 63.39/9.27 rc1_funct_1, rc1_relat_1, rc1_subset_1, rc1_xboole_0, rc2_funct_1, rc2_relat_1,
% 63.39/9.27 rc2_subset_1, rc2_xboole_0, rc3_funct_1, rc3_relat_1, reflexivity_r1_tarski,
% 63.39/9.27 t1_subset, t2_subset, t3_subset, t4_subset, t5_subset, t6_boole, t7_boole,
% 63.39/9.27 t8_boole
% 63.39/9.27
% 63.39/9.27 Those formulas are unsatisfiable:
% 63.39/9.27 ---------------------------------
% 63.39/9.27
% 63.39/9.27 Begin of proof
% 63.39/9.28 |
% 63.39/9.28 | ALPHA: (cc2_funct_1) implies:
% 63.39/9.28 | (1) ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 63.39/9.28 | [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & relation(v0) = v1 &
% 63.39/9.28 | empty(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)))
% 63.39/9.28 | (2) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 63.39/9.28 | [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 &
% 63.39/9.28 | empty(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)))
% 63.39/9.28 |
% 63.39/9.28 | ALPHA: (d3_tarski) implies:
% 63.39/9.28 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 63.39/9.28 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 63.39/9.28 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 63.39/9.28 |
% 63.39/9.28 | ALPHA: (fc5_relat_1) implies:
% 63.39/9.28 | (4) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 63.39/9.28 | [v2: $i] : ? [v3: any] : (relation_dom(v0) = v2 & empty(v2) = v3 &
% 63.39/9.28 | empty(v0) = v1 & $i(v2) & ( ~ (v3 = 0) | v1 = 0)))
% 63.39/9.28 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) |
% 63.39/9.28 | ? [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 &
% 63.39/9.28 | empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 =
% 63.39/9.28 | 0)))
% 63.39/9.28 |
% 63.39/9.28 | ALPHA: (fc6_relat_1) implies:
% 63.39/9.28 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) |
% 63.39/9.28 | ? [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 &
% 63.39/9.28 | empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 =
% 63.39/9.28 | 0)))
% 63.39/9.28 |
% 63.39/9.28 | ALPHA: (t85_funct_1) implies:
% 63.39/9.29 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 63.39/9.29 | ~ (relation_dom(v1) = v2) | ~ (relation_rng_restriction(v0, v3) =
% 63.39/9.29 | v4) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6:
% 63.39/9.29 | any] : ? [v7: any] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] :
% 63.39/9.29 | ? [v11: int] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15:
% 63.39/9.29 | any] : ? [v16: any] : ? [v17: $i] : ? [v18: any] : ($i(v14) &
% 63.39/9.29 | $i(v10) & ((relation_dom(v3) = v9 & relation(v3) = v7 &
% 63.39/9.29 | function(v3) = v8 & $i(v9) & ( ~ (v8 = 0) | ~ (v7 = 0) | (( ~
% 63.39/9.29 | (v4 = v1) | ( ! [v19: $i] : ! [v20: int] : (v20 = 0 | ~
% 63.39/9.29 | (in(v19, v2) = v20) | ~ $i(v19) | ? [v21: any] : ?
% 63.39/9.29 | [v22: $i] : ? [v23: any] : (apply(v3, v19) = v22 &
% 63.39/9.29 | in(v22, v0) = v23 & in(v19, v9) = v21 & $i(v22) & (
% 63.39/9.29 | ~ (v23 = 0) | ~ (v21 = 0)))) & ! [v19: $i] : !
% 63.39/9.29 | [v20: $i] : ( ~ (apply(v3, v19) = v20) | ~ $i(v19) |
% 63.39/9.29 | ? [v21: any] : ? [v22: any] : ? [v23: any] :
% 63.39/9.29 | (in(v20, v0) = v23 & in(v19, v9) = v22 & in(v19, v2)
% 63.39/9.29 | = v21 & ( ~ (v21 = 0) | (v23 = 0 & v22 = 0)))) & !
% 63.39/9.29 | [v19: $i] : ! [v20: $i] : ( ~ (apply(v3, v19) = v20) |
% 63.39/9.29 | ~ $i(v19) | ? [v21: any] : ? [v22: any] : ? [v23:
% 63.39/9.29 | any] : (in(v20, v0) = v22 & in(v19, v9) = v21 &
% 63.39/9.29 | in(v19, v2) = v23 & ( ~ (v22 = 0) | ~ (v21 = 0) |
% 63.39/9.29 | v23 = 0))) & ! [v19: $i] : ! [v20: $i] : ( ~
% 63.39/9.29 | (apply(v3, v19) = v20) | ~ $i(v19) | ? [v21: any] :
% 63.39/9.29 | ? [v22: $i] : (apply(v1, v19) = v22 & in(v19, v2) =
% 63.39/9.29 | v21 & $i(v22) & ( ~ (v21 = 0) | v22 = v20))) & !
% 63.39/9.29 | [v19: $i] : ! [v20: $i] : ( ~ (apply(v1, v19) = v20) |
% 63.39/9.29 | ~ $i(v19) | ? [v21: any] : ? [v22: $i] :
% 63.39/9.29 | (apply(v3, v19) = v22 & in(v19, v2) = v21 & $i(v22) &
% 63.39/9.29 | ( ~ (v21 = 0) | v22 = v20))) & ! [v19: $i] : !
% 63.39/9.29 | [v20: any] : ( ~ (in(v19, v9) = v20) | ~ $i(v19) | ?
% 63.39/9.29 | [v21: any] : ? [v22: $i] : ? [v23: any] :
% 63.39/9.29 | (apply(v3, v19) = v22 & in(v22, v0) = v23 & in(v19,
% 63.39/9.29 | v2) = v21 & $i(v22) & ( ~ (v21 = 0) | (v23 = 0 &
% 63.39/9.29 | v20 = 0)))) & ! [v19: $i] : ( ~ (in(v19, v9) =
% 63.39/9.29 | 0) | ~ $i(v19) | ? [v20: $i] : ? [v21: any] : ?
% 63.39/9.29 | [v22: any] : (apply(v3, v19) = v20 & in(v20, v0) =
% 63.39/9.29 | v21 & in(v19, v2) = v22 & $i(v20) & ( ~ (v21 = 0) |
% 63.39/9.29 | v22 = 0))) & ! [v19: $i] : ( ~ (in(v19, v2) = 0)
% 63.39/9.29 | | ~ $i(v19) | ? [v20: $i] : (apply(v3, v19) = v20 &
% 63.39/9.29 | apply(v1, v19) = v20 & $i(v20))) & ! [v19: $i] : (
% 63.39/9.29 | ~ (in(v19, v2) = 0) | ~ $i(v19) | ? [v20: $i] :
% 63.39/9.29 | (apply(v3, v19) = v20 & in(v20, v0) = 0 & in(v19, v9)
% 63.39/9.29 | = 0 & $i(v20))))) & (v4 = v1 | (v11 = 0 & ~ (v13 =
% 63.39/9.29 | v12) & apply(v3, v10) = v13 & apply(v1, v10) = v12 &
% 63.39/9.29 | in(v10, v2) = 0 & $i(v13) & $i(v12)) | (apply(v3, v14)
% 63.39/9.29 | = v17 & in(v17, v0) = v18 & in(v14, v9) = v16 & in(v14,
% 63.39/9.29 | v2) = v15 & $i(v17) & ( ~ (v18 = 0) | ~ (v16 = 0) |
% 63.39/9.29 | ~ (v15 = 0)) & (v15 = 0 | (v18 = 0 & v16 = 0))))))) |
% 63.39/9.29 | (relation(v1) = v5 & function(v1) = v6 & ( ~ (v6 = 0) | ~ (v5 =
% 63.39/9.29 | 0))))))
% 63.39/9.29 |
% 63.39/9.29 | ALPHA: (function-axioms) implies:
% 63.39/9.29 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 63.39/9.29 | (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 63.39/9.29 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 63.39/9.29 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 63.39/9.29 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 63.39/9.29 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 63.39/9.30 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 63.39/9.30 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 63.39/9.30 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 63.39/9.30 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) =
% 63.39/9.30 | v0))
% 63.39/9.30 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 63.39/9.30 | : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3,
% 63.39/9.30 | v2) = v0))
% 63.39/9.30 |
% 63.39/9.30 | DELTA: instantiating (t89_funct_1) with fresh symbols all_46_0, all_46_1,
% 63.39/9.30 | all_46_2, all_46_3, all_46_4, all_46_5, all_46_6, all_46_7, all_46_8
% 63.39/9.30 | gives:
% 63.39/9.30 | (14) relation_rng(all_46_6) = all_46_2 & relation_rng(all_46_7) = all_46_1
% 63.39/9.30 | & relation_dom(all_46_6) = all_46_5 & relation_dom(all_46_7) =
% 63.39/9.30 | all_46_4 & relation_rng_restriction(all_46_8, all_46_7) = all_46_6 &
% 63.39/9.30 | subset(all_46_2, all_46_1) = all_46_0 & subset(all_46_5, all_46_4) =
% 63.39/9.30 | all_46_3 & relation(all_46_7) = 0 & function(all_46_7) = 0 &
% 63.39/9.30 | $i(all_46_1) & $i(all_46_2) & $i(all_46_4) & $i(all_46_5) &
% 63.39/9.30 | $i(all_46_6) & $i(all_46_7) & $i(all_46_8) & ( ~ (all_46_0 = 0) | ~
% 63.39/9.30 | (all_46_3 = 0))
% 63.39/9.30 |
% 63.39/9.30 | ALPHA: (14) implies:
% 63.39/9.30 | (15) $i(all_46_8)
% 63.39/9.30 | (16) $i(all_46_7)
% 63.39/9.30 | (17) $i(all_46_6)
% 63.39/9.30 | (18) $i(all_46_5)
% 63.39/9.30 | (19) $i(all_46_4)
% 63.39/9.30 | (20) function(all_46_7) = 0
% 63.39/9.30 | (21) relation(all_46_7) = 0
% 63.39/9.30 | (22) subset(all_46_5, all_46_4) = all_46_3
% 63.39/9.30 | (23) subset(all_46_2, all_46_1) = all_46_0
% 63.39/9.30 | (24) relation_rng_restriction(all_46_8, all_46_7) = all_46_6
% 63.39/9.30 | (25) relation_dom(all_46_7) = all_46_4
% 63.39/9.30 | (26) relation_dom(all_46_6) = all_46_5
% 63.39/9.30 | (27) relation_rng(all_46_7) = all_46_1
% 63.39/9.30 | (28) relation_rng(all_46_6) = all_46_2
% 63.39/9.30 | (29) ~ (all_46_0 = 0) | ~ (all_46_3 = 0)
% 63.39/9.30 |
% 63.39/9.30 | GROUND_INST: instantiating (1) with all_46_7, simplifying with (16), (20)
% 63.39/9.30 | gives:
% 63.39/9.30 | (30) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_46_7) =
% 63.39/9.30 | v2 & relation(all_46_7) = v0 & empty(all_46_7) = v1 & ( ~ (v1 = 0) |
% 63.39/9.30 | ~ (v0 = 0) | v2 = 0))
% 63.39/9.30 |
% 63.39/9.30 | GROUND_INST: instantiating (4) with all_46_7, simplifying with (16), (21)
% 63.39/9.30 | gives:
% 63.39/9.30 | (31) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_dom(all_46_7) =
% 63.39/9.30 | v1 & empty(v1) = v2 & empty(all_46_7) = v0 & $i(v1) & ( ~ (v2 = 0) |
% 63.39/9.30 | v0 = 0))
% 63.39/9.30 |
% 63.39/9.30 | GROUND_INST: instantiating (2) with all_46_7, simplifying with (16), (21)
% 63.39/9.30 | gives:
% 63.39/9.30 | (32) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_46_7) =
% 63.39/9.30 | v2 & function(all_46_7) = v1 & empty(all_46_7) = v0 & ( ~ (v1 = 0) |
% 63.39/9.30 | ~ (v0 = 0) | v2 = 0))
% 63.39/9.30 |
% 63.39/9.30 | GROUND_INST: instantiating (3) with all_46_5, all_46_4, all_46_3, simplifying
% 63.39/9.30 | with (18), (19), (22) gives:
% 63.39/9.31 | (33) all_46_3 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 63.39/9.31 | all_46_4) = v1 & in(v0, all_46_5) = 0 & $i(v0))
% 63.39/9.31 |
% 63.39/9.31 | GROUND_INST: instantiating (t118_relat_1) with all_46_8, all_46_7, all_46_6,
% 63.39/9.31 | simplifying with (15), (16), (24) gives:
% 63.39/9.31 | (34) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] :
% 63.39/9.31 | (relation_rng(all_46_6) = v1 & relation_rng(all_46_7) = v2 &
% 63.39/9.31 | subset(v1, v2) = v3 & relation(all_46_7) = v0 & $i(v2) & $i(v1) & (
% 63.39/9.31 | ~ (v0 = 0) | v3 = 0))
% 63.39/9.31 |
% 63.39/9.31 | GROUND_INST: instantiating (fc5_funct_1) with all_46_8, all_46_7, all_46_6,
% 63.39/9.31 | simplifying with (15), (16), (24) gives:
% 63.39/9.31 | (35) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 63.39/9.31 | (relation(all_46_6) = v2 & relation(all_46_7) = v0 &
% 63.39/9.31 | function(all_46_6) = v3 & function(all_46_7) = v1 & ( ~ (v1 = 0) |
% 63.39/9.31 | ~ (v0 = 0) | (v3 = 0 & v2 = 0)))
% 63.39/9.31 |
% 63.39/9.31 | GROUND_INST: instantiating (dt_k8_relat_1) with all_46_8, all_46_7, all_46_6,
% 63.39/9.31 | simplifying with (15), (16), (24) gives:
% 63.39/9.31 | (36) ? [v0: any] : ? [v1: any] : (relation(all_46_6) = v1 &
% 63.39/9.31 | relation(all_46_7) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 63.39/9.31 |
% 63.39/9.31 | GROUND_INST: instantiating (5) with all_46_7, all_46_4, simplifying with (16),
% 63.39/9.31 | (25) gives:
% 63.39/9.31 | (37) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_46_7) = v1
% 63.39/9.31 | & empty(all_46_4) = v2 & empty(all_46_7) = v0 & ( ~ (v2 = 0) | ~
% 63.39/9.31 | (v1 = 0) | v0 = 0))
% 63.39/9.31 |
% 63.39/9.31 | GROUND_INST: instantiating (7) with all_46_8, all_46_6, all_46_5, all_46_7,
% 63.39/9.31 | all_46_6, simplifying with (15), (16), (17), (24), (26) gives:
% 63.39/9.32 | (38) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 63.39/9.32 | $i] : ? [v5: $i] : ? [v6: $i] : ($i(v6) & $i(v5) &
% 63.39/9.32 | ((relation_dom(all_46_7) = v4 & relation(all_46_7) = v2 &
% 63.39/9.32 | function(all_46_7) = v3 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) |
% 63.39/9.32 | ( ! [v7: $i] : ! [v8: int] : (v8 = 0 | ~ (in(v7, all_46_5) =
% 63.39/9.32 | v8) | ~ $i(v7) | ? [v9: any] : ? [v10: $i] : ? [v11:
% 63.39/9.32 | any] : (apply(all_46_7, v7) = v10 & in(v10, all_46_8) =
% 63.39/9.32 | v11 & in(v7, v4) = v9 & $i(v10) & ( ~ (v11 = 0) | ~ (v9
% 63.39/9.32 | = 0)))) & ! [v7: $i] : ! [v8: $i] : ( ~
% 63.39/9.32 | (apply(all_46_6, v7) = v8) | ~ $i(v7) | ? [v9: any] : ?
% 63.39/9.32 | [v10: $i] : (apply(all_46_7, v7) = v10 & in(v7, all_46_5)
% 63.39/9.32 | = v9 & $i(v10) & ( ~ (v9 = 0) | v10 = v8))) & ! [v7:
% 63.39/9.32 | $i] : ! [v8: $i] : ( ~ (apply(all_46_7, v7) = v8) | ~
% 63.39/9.32 | $i(v7) | ? [v9: any] : ? [v10: any] : ? [v11: any] :
% 63.39/9.32 | (in(v8, all_46_8) = v11 & in(v7, v4) = v10 & in(v7,
% 63.39/9.32 | all_46_5) = v9 & ( ~ (v9 = 0) | (v11 = 0 & v10 = 0))))
% 63.39/9.32 | & ! [v7: $i] : ! [v8: $i] : ( ~ (apply(all_46_7, v7) = v8)
% 63.39/9.32 | | ~ $i(v7) | ? [v9: any] : ? [v10: any] : ? [v11: any]
% 63.39/9.32 | : (in(v8, all_46_8) = v10 & in(v7, v4) = v9 & in(v7,
% 63.39/9.32 | all_46_5) = v11 & ( ~ (v10 = 0) | ~ (v9 = 0) | v11 =
% 63.39/9.32 | 0))) & ! [v7: $i] : ! [v8: $i] : ( ~
% 63.39/9.32 | (apply(all_46_7, v7) = v8) | ~ $i(v7) | ? [v9: any] : ?
% 63.39/9.32 | [v10: $i] : (apply(all_46_6, v7) = v10 & in(v7, all_46_5)
% 63.39/9.32 | = v9 & $i(v10) & ( ~ (v9 = 0) | v10 = v8))) & ! [v7:
% 63.39/9.32 | $i] : ! [v8: any] : ( ~ (in(v7, v4) = v8) | ~ $i(v7) |
% 63.39/9.32 | ? [v9: any] : ? [v10: $i] : ? [v11: any] :
% 63.39/9.32 | (apply(all_46_7, v7) = v10 & in(v10, all_46_8) = v11 &
% 63.39/9.32 | in(v7, all_46_5) = v9 & $i(v10) & ( ~ (v9 = 0) | (v11 =
% 63.39/9.32 | 0 & v8 = 0)))) & ! [v7: $i] : ( ~ (in(v7, v4) = 0)
% 63.39/9.32 | | ~ $i(v7) | ? [v8: $i] : ? [v9: any] : ? [v10: any] :
% 63.39/9.32 | (apply(all_46_7, v7) = v8 & in(v8, all_46_8) = v9 & in(v7,
% 63.39/9.32 | all_46_5) = v10 & $i(v8) & ( ~ (v9 = 0) | v10 = 0))) &
% 63.39/9.32 | ! [v7: $i] : ( ~ (in(v7, all_46_5) = 0) | ~ $i(v7) | ?
% 63.39/9.32 | [v8: $i] : (apply(all_46_6, v7) = v8 & apply(all_46_7, v7)
% 63.39/9.32 | = v8 & $i(v8))) & ! [v7: $i] : ( ~ (in(v7, all_46_5) =
% 63.39/9.32 | 0) | ~ $i(v7) | ? [v8: $i] : (apply(all_46_7, v7) = v8
% 63.39/9.32 | & in(v8, all_46_8) = 0 & in(v7, v4) = 0 & $i(v8)))))) |
% 63.39/9.32 | (relation(all_46_6) = v0 & function(all_46_6) = v1 & ( ~ (v1 = 0)
% 63.39/9.32 | | ~ (v0 = 0)))))
% 63.39/9.32 |
% 63.39/9.32 | GROUND_INST: instantiating (5) with all_46_6, all_46_5, simplifying with (17),
% 63.39/9.32 | (26) gives:
% 63.39/9.32 | (39) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_46_6) = v1
% 63.39/9.32 | & empty(all_46_5) = v2 & empty(all_46_6) = v0 & ( ~ (v2 = 0) | ~
% 63.39/9.32 | (v1 = 0) | v0 = 0))
% 63.39/9.32 |
% 63.39/9.32 | GROUND_INST: instantiating (6) with all_46_7, all_46_1, simplifying with (16),
% 63.39/9.32 | (27) gives:
% 63.39/9.32 | (40) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_46_7) = v1
% 63.39/9.32 | & empty(all_46_1) = v2 & empty(all_46_7) = v0 & ( ~ (v2 = 0) | ~
% 63.39/9.32 | (v1 = 0) | v0 = 0))
% 63.39/9.32 |
% 63.39/9.32 | GROUND_INST: instantiating (6) with all_46_6, all_46_2, simplifying with (17),
% 63.39/9.32 | (28) gives:
% 63.39/9.32 | (41) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_46_6) = v1
% 63.39/9.32 | & empty(all_46_2) = v2 & empty(all_46_6) = v0 & ( ~ (v2 = 0) | ~
% 63.39/9.32 | (v1 = 0) | v0 = 0))
% 63.39/9.32 |
% 63.39/9.32 | DELTA: instantiating (36) with fresh symbols all_68_0, all_68_1 gives:
% 63.39/9.32 | (42) relation(all_46_6) = all_68_0 & relation(all_46_7) = all_68_1 & ( ~
% 63.39/9.32 | (all_68_1 = 0) | all_68_0 = 0)
% 63.39/9.32 |
% 63.39/9.32 | ALPHA: (42) implies:
% 63.39/9.32 | (43) relation(all_46_7) = all_68_1
% 63.39/9.32 | (44) relation(all_46_6) = all_68_0
% 63.39/9.32 | (45) ~ (all_68_1 = 0) | all_68_0 = 0
% 63.39/9.32 |
% 63.39/9.32 | DELTA: instantiating (37) with fresh symbols all_88_0, all_88_1, all_88_2
% 63.39/9.32 | gives:
% 63.39/9.32 | (46) relation(all_46_7) = all_88_1 & empty(all_46_4) = all_88_0 &
% 63.39/9.32 | empty(all_46_7) = all_88_2 & ( ~ (all_88_0 = 0) | ~ (all_88_1 = 0) |
% 63.39/9.32 | all_88_2 = 0)
% 63.39/9.32 |
% 63.39/9.32 | ALPHA: (46) implies:
% 63.39/9.32 | (47) relation(all_46_7) = all_88_1
% 63.39/9.32 |
% 63.39/9.32 | DELTA: instantiating (41) with fresh symbols all_102_0, all_102_1, all_102_2
% 63.39/9.32 | gives:
% 63.39/9.32 | (48) relation(all_46_6) = all_102_1 & empty(all_46_2) = all_102_0 &
% 63.39/9.32 | empty(all_46_6) = all_102_2 & ( ~ (all_102_0 = 0) | ~ (all_102_1 = 0)
% 63.39/9.32 | | all_102_2 = 0)
% 63.39/9.32 |
% 63.39/9.32 | ALPHA: (48) implies:
% 63.39/9.32 | (49) relation(all_46_6) = all_102_1
% 63.39/9.32 |
% 63.39/9.32 | DELTA: instantiating (32) with fresh symbols all_106_0, all_106_1, all_106_2
% 63.39/9.32 | gives:
% 63.39/9.32 | (50) one_to_one(all_46_7) = all_106_0 & function(all_46_7) = all_106_1 &
% 63.39/9.32 | empty(all_46_7) = all_106_2 & ( ~ (all_106_1 = 0) | ~ (all_106_2 = 0)
% 63.39/9.32 | | all_106_0 = 0)
% 63.39/9.32 |
% 63.39/9.32 | ALPHA: (50) implies:
% 63.39/9.32 | (51) function(all_46_7) = all_106_1
% 63.39/9.32 |
% 63.39/9.32 | DELTA: instantiating (31) with fresh symbols all_108_0, all_108_1, all_108_2
% 63.39/9.32 | gives:
% 63.39/9.32 | (52) relation_dom(all_46_7) = all_108_1 & empty(all_108_1) = all_108_0 &
% 63.39/9.32 | empty(all_46_7) = all_108_2 & $i(all_108_1) & ( ~ (all_108_0 = 0) |
% 63.39/9.32 | all_108_2 = 0)
% 63.39/9.32 |
% 63.39/9.32 | ALPHA: (52) implies:
% 63.39/9.32 | (53) relation_dom(all_46_7) = all_108_1
% 63.39/9.32 |
% 63.39/9.32 | DELTA: instantiating (39) with fresh symbols all_134_0, all_134_1, all_134_2
% 63.39/9.32 | gives:
% 63.39/9.33 | (54) relation(all_46_6) = all_134_1 & empty(all_46_5) = all_134_0 &
% 63.39/9.33 | empty(all_46_6) = all_134_2 & ( ~ (all_134_0 = 0) | ~ (all_134_1 = 0)
% 63.39/9.33 | | all_134_2 = 0)
% 63.39/9.33 |
% 63.39/9.33 | ALPHA: (54) implies:
% 63.39/9.33 | (55) relation(all_46_6) = all_134_1
% 63.39/9.33 |
% 63.39/9.33 | DELTA: instantiating (30) with fresh symbols all_150_0, all_150_1, all_150_2
% 63.39/9.33 | gives:
% 63.39/9.33 | (56) one_to_one(all_46_7) = all_150_0 & relation(all_46_7) = all_150_2 &
% 63.39/9.33 | empty(all_46_7) = all_150_1 & ( ~ (all_150_1 = 0) | ~ (all_150_2 = 0)
% 63.39/9.33 | | all_150_0 = 0)
% 63.39/9.33 |
% 63.39/9.33 | ALPHA: (56) implies:
% 63.39/9.33 | (57) relation(all_46_7) = all_150_2
% 63.39/9.33 |
% 63.39/9.33 | DELTA: instantiating (40) with fresh symbols all_152_0, all_152_1, all_152_2
% 63.39/9.33 | gives:
% 63.39/9.33 | (58) relation(all_46_7) = all_152_1 & empty(all_46_1) = all_152_0 &
% 63.39/9.33 | empty(all_46_7) = all_152_2 & ( ~ (all_152_0 = 0) | ~ (all_152_1 = 0)
% 63.39/9.33 | | all_152_2 = 0)
% 63.39/9.33 |
% 63.39/9.33 | ALPHA: (58) implies:
% 63.39/9.33 | (59) relation(all_46_7) = all_152_1
% 63.39/9.33 |
% 63.39/9.33 | DELTA: instantiating (35) with fresh symbols all_164_0, all_164_1, all_164_2,
% 63.39/9.33 | all_164_3 gives:
% 63.39/9.33 | (60) relation(all_46_6) = all_164_1 & relation(all_46_7) = all_164_3 &
% 63.39/9.33 | function(all_46_6) = all_164_0 & function(all_46_7) = all_164_2 & ( ~
% 63.39/9.33 | (all_164_2 = 0) | ~ (all_164_3 = 0) | (all_164_0 = 0 & all_164_1 =
% 63.39/9.33 | 0))
% 63.39/9.33 |
% 63.39/9.33 | ALPHA: (60) implies:
% 63.39/9.33 | (61) function(all_46_7) = all_164_2
% 63.39/9.33 | (62) function(all_46_6) = all_164_0
% 63.39/9.33 | (63) relation(all_46_7) = all_164_3
% 63.39/9.33 | (64) relation(all_46_6) = all_164_1
% 63.39/9.33 | (65) ~ (all_164_2 = 0) | ~ (all_164_3 = 0) | (all_164_0 = 0 & all_164_1 =
% 63.39/9.33 | 0)
% 63.39/9.33 |
% 63.39/9.33 | DELTA: instantiating (34) with fresh symbols all_166_0, all_166_1, all_166_2,
% 63.39/9.33 | all_166_3 gives:
% 63.39/9.33 | (66) relation_rng(all_46_6) = all_166_2 & relation_rng(all_46_7) =
% 63.39/9.33 | all_166_1 & subset(all_166_2, all_166_1) = all_166_0 &
% 63.39/9.33 | relation(all_46_7) = all_166_3 & $i(all_166_1) & $i(all_166_2) & ( ~
% 63.39/9.33 | (all_166_3 = 0) | all_166_0 = 0)
% 63.39/9.33 |
% 63.39/9.33 | ALPHA: (66) implies:
% 63.39/9.33 | (67) relation(all_46_7) = all_166_3
% 63.39/9.33 | (68) subset(all_166_2, all_166_1) = all_166_0
% 63.39/9.33 | (69) relation_rng(all_46_7) = all_166_1
% 63.39/9.33 | (70) relation_rng(all_46_6) = all_166_2
% 63.39/9.33 | (71) ~ (all_166_3 = 0) | all_166_0 = 0
% 63.39/9.33 |
% 63.39/9.33 | DELTA: instantiating (38) with fresh symbols all_168_0, all_168_1, all_168_2,
% 63.39/9.33 | all_168_3, all_168_4, all_168_5, all_168_6 gives:
% 63.39/9.34 | (72) $i(all_168_0) & $i(all_168_1) & ((relation_dom(all_46_7) = all_168_2 &
% 63.39/9.34 | relation(all_46_7) = all_168_4 & function(all_46_7) = all_168_3 &
% 63.39/9.34 | $i(all_168_2) & ( ~ (all_168_3 = 0) | ~ (all_168_4 = 0) | ( !
% 63.39/9.34 | [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_46_5) = v1)
% 63.39/9.34 | | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] :
% 63.39/9.34 | (apply(all_46_7, v0) = v3 & in(v3, all_46_8) = v4 & in(v0,
% 63.39/9.34 | all_168_2) = v2 & $i(v3) & ( ~ (v4 = 0) | ~ (v2 = 0))))
% 63.39/9.34 | & ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_46_6, v0) = v1) |
% 63.39/9.34 | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : (apply(all_46_7,
% 63.39/9.34 | v0) = v3 & in(v0, all_46_5) = v2 & $i(v3) & ( ~ (v2 = 0)
% 63.39/9.34 | | v3 = v1))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 63.39/9.34 | (apply(all_46_7, v0) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 63.39/9.34 | [v3: any] : ? [v4: any] : (in(v1, all_46_8) = v4 & in(v0,
% 63.39/9.34 | all_168_2) = v3 & in(v0, all_46_5) = v2 & ( ~ (v2 = 0) |
% 63.39/9.34 | (v4 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 63.39/9.34 | (apply(all_46_7, v0) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 63.39/9.34 | [v3: any] : ? [v4: any] : (in(v1, all_46_8) = v3 & in(v0,
% 63.39/9.34 | all_168_2) = v2 & in(v0, all_46_5) = v4 & ( ~ (v3 = 0) |
% 63.39/9.34 | ~ (v2 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : (
% 63.39/9.34 | ~ (apply(all_46_7, v0) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 63.39/9.34 | [v3: $i] : (apply(all_46_6, v0) = v3 & in(v0, all_46_5) = v2
% 63.39/9.34 | & $i(v3) & ( ~ (v2 = 0) | v3 = v1))) & ! [v0: $i] : !
% 63.39/9.34 | [v1: any] : ( ~ (in(v0, all_168_2) = v1) | ~ $i(v0) | ? [v2:
% 63.39/9.34 | any] : ? [v3: $i] : ? [v4: any] : (apply(all_46_7, v0) =
% 63.39/9.34 | v3 & in(v3, all_46_8) = v4 & in(v0, all_46_5) = v2 &
% 63.39/9.34 | $i(v3) & ( ~ (v2 = 0) | (v4 = 0 & v1 = 0)))) & ! [v0: $i]
% 63.39/9.34 | : ( ~ (in(v0, all_168_2) = 0) | ~ $i(v0) | ? [v1: $i] : ?
% 63.39/9.34 | [v2: any] : ? [v3: any] : (apply(all_46_7, v0) = v1 &
% 63.39/9.34 | in(v1, all_46_8) = v2 & in(v0, all_46_5) = v3 & $i(v1) & (
% 63.39/9.34 | ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (in(v0,
% 63.39/9.34 | all_46_5) = 0) | ~ $i(v0) | ? [v1: $i] :
% 63.39/9.34 | (apply(all_46_6, v0) = v1 & apply(all_46_7, v0) = v1 &
% 63.39/9.34 | $i(v1))) & ! [v0: $i] : ( ~ (in(v0, all_46_5) = 0) | ~
% 63.39/9.34 | $i(v0) | ? [v1: $i] : (apply(all_46_7, v0) = v1 & in(v1,
% 63.39/9.34 | all_46_8) = 0 & in(v0, all_168_2) = 0 & $i(v1)))))) |
% 63.39/9.34 | (relation(all_46_6) = all_168_6 & function(all_46_6) = all_168_5 & (
% 63.39/9.34 | ~ (all_168_5 = 0) | ~ (all_168_6 = 0))))
% 63.39/9.34 |
% 63.39/9.34 | ALPHA: (72) implies:
% 63.39/9.34 | (73) (relation_dom(all_46_7) = all_168_2 & relation(all_46_7) = all_168_4 &
% 63.39/9.34 | function(all_46_7) = all_168_3 & $i(all_168_2) & ( ~ (all_168_3 = 0)
% 63.39/9.34 | | ~ (all_168_4 = 0) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 63.39/9.34 | (in(v0, all_46_5) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 63.39/9.34 | $i] : ? [v4: any] : (apply(all_46_7, v0) = v3 & in(v3,
% 63.39/9.34 | all_46_8) = v4 & in(v0, all_168_2) = v2 & $i(v3) & ( ~ (v4
% 63.39/9.34 | = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 63.39/9.34 | (apply(all_46_6, v0) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 63.39/9.34 | [v3: $i] : (apply(all_46_7, v0) = v3 & in(v0, all_46_5) = v2 &
% 63.39/9.34 | $i(v3) & ( ~ (v2 = 0) | v3 = v1))) & ! [v0: $i] : ! [v1:
% 63.39/9.34 | $i] : ( ~ (apply(all_46_7, v0) = v1) | ~ $i(v0) | ? [v2:
% 63.39/9.34 | any] : ? [v3: any] : ? [v4: any] : (in(v1, all_46_8) = v4
% 63.39/9.34 | & in(v0, all_168_2) = v3 & in(v0, all_46_5) = v2 & ( ~ (v2 =
% 63.39/9.34 | 0) | (v4 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] :
% 63.39/9.34 | ( ~ (apply(all_46_7, v0) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 63.39/9.34 | [v3: any] : ? [v4: any] : (in(v1, all_46_8) = v3 & in(v0,
% 63.39/9.34 | all_168_2) = v2 & in(v0, all_46_5) = v4 & ( ~ (v3 = 0) |
% 63.39/9.34 | ~ (v2 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 63.39/9.34 | (apply(all_46_7, v0) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 63.39/9.34 | [v3: $i] : (apply(all_46_6, v0) = v3 & in(v0, all_46_5) = v2 &
% 63.39/9.34 | $i(v3) & ( ~ (v2 = 0) | v3 = v1))) & ! [v0: $i] : ! [v1:
% 63.39/9.34 | any] : ( ~ (in(v0, all_168_2) = v1) | ~ $i(v0) | ? [v2: any]
% 63.39/9.34 | : ? [v3: $i] : ? [v4: any] : (apply(all_46_7, v0) = v3 &
% 63.39/9.34 | in(v3, all_46_8) = v4 & in(v0, all_46_5) = v2 & $i(v3) & ( ~
% 63.39/9.34 | (v2 = 0) | (v4 = 0 & v1 = 0)))) & ! [v0: $i] : ( ~
% 63.39/9.34 | (in(v0, all_168_2) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 63.39/9.34 | any] : ? [v3: any] : (apply(all_46_7, v0) = v1 & in(v1,
% 63.39/9.34 | all_46_8) = v2 & in(v0, all_46_5) = v3 & $i(v1) & ( ~ (v2
% 63.39/9.34 | = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (in(v0, all_46_5) =
% 63.39/9.34 | 0) | ~ $i(v0) | ? [v1: $i] : (apply(all_46_6, v0) = v1 &
% 63.39/9.34 | apply(all_46_7, v0) = v1 & $i(v1))) & ! [v0: $i] : ( ~
% 63.39/9.34 | (in(v0, all_46_5) = 0) | ~ $i(v0) | ? [v1: $i] :
% 63.39/9.34 | (apply(all_46_7, v0) = v1 & in(v1, all_46_8) = 0 & in(v0,
% 63.39/9.34 | all_168_2) = 0 & $i(v1)))))) | (relation(all_46_6) =
% 63.39/9.34 | all_168_6 & function(all_46_6) = all_168_5 & ( ~ (all_168_5 = 0) |
% 63.39/9.34 | ~ (all_168_6 = 0)))
% 63.39/9.34 |
% 63.39/9.34 | GROUND_INST: instantiating (8) with 0, all_164_2, all_46_7, simplifying with
% 63.39/9.34 | (20), (61) gives:
% 63.39/9.34 | (74) all_164_2 = 0
% 63.39/9.34 |
% 63.39/9.34 | GROUND_INST: instantiating (8) with all_106_1, all_164_2, all_46_7,
% 63.39/9.34 | simplifying with (51), (61) gives:
% 63.39/9.34 | (75) all_164_2 = all_106_1
% 63.39/9.34 |
% 63.39/9.35 | GROUND_INST: instantiating (9) with 0, all_150_2, all_46_7, simplifying with
% 63.39/9.35 | (21), (57) gives:
% 63.39/9.35 | (76) all_150_2 = 0
% 63.39/9.35 |
% 63.39/9.35 | GROUND_INST: instantiating (9) with all_68_1, all_150_2, all_46_7, simplifying
% 63.39/9.35 | with (43), (57) gives:
% 63.39/9.35 | (77) all_150_2 = all_68_1
% 63.39/9.35 |
% 63.39/9.35 | GROUND_INST: instantiating (9) with all_150_2, all_152_1, all_46_7,
% 63.39/9.35 | simplifying with (57), (59) gives:
% 63.39/9.35 | (78) all_152_1 = all_150_2
% 63.39/9.35 |
% 63.39/9.35 | GROUND_INST: instantiating (9) with all_164_3, all_166_3, all_46_7,
% 63.39/9.35 | simplifying with (63), (67) gives:
% 63.39/9.35 | (79) all_166_3 = all_164_3
% 63.39/9.35 |
% 63.39/9.35 | GROUND_INST: instantiating (9) with all_152_1, all_166_3, all_46_7,
% 63.39/9.35 | simplifying with (59), (67) gives:
% 63.39/9.35 | (80) all_166_3 = all_152_1
% 63.39/9.35 |
% 63.39/9.35 | GROUND_INST: instantiating (9) with all_88_1, all_166_3, all_46_7, simplifying
% 63.39/9.35 | with (47), (67) gives:
% 63.39/9.35 | (81) all_166_3 = all_88_1
% 63.39/9.35 |
% 63.39/9.35 | GROUND_INST: instantiating (9) with all_102_1, all_134_1, all_46_6,
% 63.39/9.35 | simplifying with (49), (55) gives:
% 63.39/9.35 | (82) all_134_1 = all_102_1
% 63.39/9.35 |
% 63.39/9.35 | GROUND_INST: instantiating (9) with all_134_1, all_164_1, all_46_6,
% 63.39/9.35 | simplifying with (55), (64) gives:
% 63.39/9.35 | (83) all_164_1 = all_134_1
% 63.39/9.35 |
% 63.39/9.35 | GROUND_INST: instantiating (9) with all_68_0, all_164_1, all_46_6, simplifying
% 63.39/9.35 | with (44), (64) gives:
% 63.39/9.35 | (84) all_164_1 = all_68_0
% 63.39/9.35 |
% 63.39/9.35 | GROUND_INST: instantiating (10) with all_46_4, all_108_1, all_46_7,
% 63.39/9.35 | simplifying with (25), (53) gives:
% 63.39/9.35 | (85) all_108_1 = all_46_4
% 63.39/9.35 |
% 63.39/9.35 | GROUND_INST: instantiating (11) with all_46_1, all_166_1, all_46_7,
% 63.39/9.35 | simplifying with (27), (69) gives:
% 63.39/9.35 | (86) all_166_1 = all_46_1
% 63.39/9.35 |
% 63.39/9.35 | GROUND_INST: instantiating (11) with all_46_2, all_166_2, all_46_6,
% 63.39/9.35 | simplifying with (28), (70) gives:
% 63.39/9.35 | (87) all_166_2 = all_46_2
% 63.39/9.35 |
% 63.39/9.35 | COMBINE_EQS: (79), (81) imply:
% 63.39/9.35 | (88) all_164_3 = all_88_1
% 63.39/9.35 |
% 63.39/9.35 | COMBINE_EQS: (79), (80) imply:
% 63.39/9.35 | (89) all_164_3 = all_152_1
% 63.39/9.35 |
% 63.39/9.35 | COMBINE_EQS: (83), (84) imply:
% 63.39/9.35 | (90) all_134_1 = all_68_0
% 63.39/9.35 |
% 63.39/9.35 | SIMP: (90) implies:
% 63.39/9.35 | (91) all_134_1 = all_68_0
% 63.39/9.35 |
% 63.39/9.35 | COMBINE_EQS: (74), (75) imply:
% 63.39/9.35 | (92) all_106_1 = 0
% 63.39/9.35 |
% 63.39/9.35 | COMBINE_EQS: (88), (89) imply:
% 63.39/9.35 | (93) all_152_1 = all_88_1
% 63.39/9.35 |
% 63.39/9.35 | SIMP: (93) implies:
% 63.39/9.35 | (94) all_152_1 = all_88_1
% 63.39/9.35 |
% 63.39/9.35 | COMBINE_EQS: (78), (94) imply:
% 63.39/9.35 | (95) all_150_2 = all_88_1
% 63.39/9.35 |
% 63.39/9.35 | SIMP: (95) implies:
% 63.39/9.35 | (96) all_150_2 = all_88_1
% 63.39/9.35 |
% 63.39/9.35 | COMBINE_EQS: (77), (96) imply:
% 63.39/9.35 | (97) all_88_1 = all_68_1
% 63.39/9.35 |
% 63.39/9.35 | COMBINE_EQS: (76), (96) imply:
% 63.39/9.35 | (98) all_88_1 = 0
% 63.39/9.35 |
% 63.39/9.35 | COMBINE_EQS: (82), (91) imply:
% 63.78/9.35 | (99) all_102_1 = all_68_0
% 63.78/9.35 |
% 63.78/9.35 | SIMP: (99) implies:
% 63.78/9.35 | (100) all_102_1 = all_68_0
% 63.78/9.35 |
% 63.78/9.35 | COMBINE_EQS: (97), (98) imply:
% 63.78/9.35 | (101) all_68_1 = 0
% 63.78/9.35 |
% 63.78/9.35 | COMBINE_EQS: (88), (98) imply:
% 63.78/9.35 | (102) all_164_3 = 0
% 63.78/9.35 |
% 63.78/9.35 | COMBINE_EQS: (79), (102) imply:
% 63.78/9.35 | (103) all_166_3 = 0
% 63.78/9.35 |
% 63.78/9.35 | REDUCE: (68), (86), (87) imply:
% 63.78/9.35 | (104) subset(all_46_2, all_46_1) = all_166_0
% 63.78/9.35 |
% 63.78/9.35 | BETA: splitting (71) gives:
% 63.78/9.35 |
% 63.78/9.35 | Case 1:
% 63.78/9.35 | |
% 63.78/9.35 | | (105) ~ (all_166_3 = 0)
% 63.78/9.35 | |
% 63.78/9.35 | | REDUCE: (103), (105) imply:
% 63.78/9.35 | | (106) $false
% 63.78/9.36 | |
% 63.78/9.36 | | CLOSE: (106) is inconsistent.
% 63.78/9.36 | |
% 63.78/9.36 | Case 2:
% 63.78/9.36 | |
% 63.78/9.36 | | (107) all_166_0 = 0
% 63.78/9.36 | |
% 63.78/9.36 | | REDUCE: (104), (107) imply:
% 63.78/9.36 | | (108) subset(all_46_2, all_46_1) = 0
% 63.78/9.36 | |
% 63.78/9.36 | | BETA: splitting (45) gives:
% 63.78/9.36 | |
% 63.78/9.36 | | Case 1:
% 63.78/9.36 | | |
% 63.78/9.36 | | | (109) ~ (all_68_1 = 0)
% 63.78/9.36 | | |
% 63.78/9.36 | | | REDUCE: (101), (109) imply:
% 63.78/9.36 | | | (110) $false
% 63.78/9.36 | | |
% 63.78/9.36 | | | CLOSE: (110) is inconsistent.
% 63.78/9.36 | | |
% 63.78/9.36 | | Case 2:
% 63.78/9.36 | | |
% 63.78/9.36 | | | (111) all_68_0 = 0
% 63.78/9.36 | | |
% 63.78/9.36 | | | REDUCE: (44), (111) imply:
% 63.78/9.36 | | | (112) relation(all_46_6) = 0
% 63.78/9.36 | | |
% 63.78/9.36 | | | BETA: splitting (65) gives:
% 63.78/9.36 | | |
% 63.78/9.36 | | | Case 1:
% 63.78/9.36 | | | |
% 63.78/9.36 | | | | (113) ~ (all_164_2 = 0)
% 63.78/9.36 | | | |
% 63.78/9.36 | | | | REDUCE: (74), (113) imply:
% 63.78/9.36 | | | | (114) $false
% 63.78/9.36 | | | |
% 63.78/9.36 | | | | CLOSE: (114) is inconsistent.
% 63.78/9.36 | | | |
% 63.78/9.36 | | | Case 2:
% 63.78/9.36 | | | |
% 63.78/9.36 | | | | (115) ~ (all_164_3 = 0) | (all_164_0 = 0 & all_164_1 = 0)
% 63.78/9.36 | | | |
% 63.78/9.36 | | | | BETA: splitting (115) gives:
% 63.78/9.36 | | | |
% 63.78/9.36 | | | | Case 1:
% 63.78/9.36 | | | | |
% 63.78/9.36 | | | | | (116) ~ (all_164_3 = 0)
% 63.78/9.36 | | | | |
% 63.78/9.36 | | | | | REDUCE: (102), (116) imply:
% 63.78/9.36 | | | | | (117) $false
% 63.78/9.36 | | | | |
% 63.78/9.36 | | | | | CLOSE: (117) is inconsistent.
% 63.78/9.36 | | | | |
% 63.78/9.36 | | | | Case 2:
% 63.78/9.36 | | | | |
% 63.78/9.36 | | | | | (118) all_164_0 = 0 & all_164_1 = 0
% 63.78/9.36 | | | | |
% 63.78/9.36 | | | | | ALPHA: (118) implies:
% 63.78/9.36 | | | | | (119) all_164_0 = 0
% 63.78/9.36 | | | | |
% 63.78/9.36 | | | | | REDUCE: (62), (119) imply:
% 63.78/9.36 | | | | | (120) function(all_46_6) = 0
% 63.78/9.36 | | | | |
% 63.78/9.36 | | | | | BETA: splitting (73) gives:
% 63.78/9.36 | | | | |
% 63.78/9.36 | | | | | Case 1:
% 63.78/9.36 | | | | | |
% 63.78/9.37 | | | | | | (121) relation_dom(all_46_7) = all_168_2 & relation(all_46_7) =
% 63.78/9.37 | | | | | | all_168_4 & function(all_46_7) = all_168_3 & $i(all_168_2)
% 63.78/9.37 | | | | | | & ( ~ (all_168_3 = 0) | ~ (all_168_4 = 0) | ( ! [v0: $i] :
% 63.78/9.37 | | | | | | ! [v1: int] : (v1 = 0 | ~ (in(v0, all_46_5) = v1) |
% 63.78/9.37 | | | | | | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any]
% 63.78/9.37 | | | | | | : (apply(all_46_7, v0) = v3 & in(v3, all_46_8) = v4 &
% 63.78/9.37 | | | | | | in(v0, all_168_2) = v2 & $i(v3) & ( ~ (v4 = 0) | ~
% 63.78/9.37 | | | | | | (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 63.78/9.37 | | | | | | (apply(all_46_6, v0) = v1) | ~ $i(v0) | ? [v2: any]
% 63.78/9.37 | | | | | | : ? [v3: $i] : (apply(all_46_7, v0) = v3 & in(v0,
% 63.78/9.37 | | | | | | all_46_5) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 =
% 63.78/9.37 | | | | | | v1))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 63.78/9.37 | | | | | | (apply(all_46_7, v0) = v1) | ~ $i(v0) | ? [v2: any]
% 63.78/9.37 | | | | | | : ? [v3: any] : ? [v4: any] : (in(v1, all_46_8) =
% 63.78/9.37 | | | | | | v4 & in(v0, all_168_2) = v3 & in(v0, all_46_5) = v2
% 63.78/9.37 | | | | | | & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0: $i]
% 63.78/9.37 | | | | | | : ! [v1: $i] : ( ~ (apply(all_46_7, v0) = v1) | ~
% 63.78/9.37 | | | | | | $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] :
% 63.78/9.37 | | | | | | (in(v1, all_46_8) = v3 & in(v0, all_168_2) = v2 &
% 63.78/9.37 | | | | | | in(v0, all_46_5) = v4 & ( ~ (v3 = 0) | ~ (v2 = 0)
% 63.78/9.37 | | | | | | | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 63.78/9.37 | | | | | | (apply(all_46_7, v0) = v1) | ~ $i(v0) | ? [v2: any]
% 63.78/9.37 | | | | | | : ? [v3: $i] : (apply(all_46_6, v0) = v3 & in(v0,
% 63.78/9.37 | | | | | | all_46_5) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 =
% 63.78/9.37 | | | | | | v1))) & ! [v0: $i] : ! [v1: any] : ( ~ (in(v0,
% 63.78/9.37 | | | | | | all_168_2) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 63.78/9.37 | | | | | | [v3: $i] : ? [v4: any] : (apply(all_46_7, v0) = v3 &
% 63.78/9.37 | | | | | | in(v3, all_46_8) = v4 & in(v0, all_46_5) = v2 &
% 63.78/9.37 | | | | | | $i(v3) & ( ~ (v2 = 0) | (v4 = 0 & v1 = 0)))) & !
% 63.78/9.37 | | | | | | [v0: $i] : ( ~ (in(v0, all_168_2) = 0) | ~ $i(v0) | ?
% 63.78/9.37 | | | | | | [v1: $i] : ? [v2: any] : ? [v3: any] :
% 63.78/9.37 | | | | | | (apply(all_46_7, v0) = v1 & in(v1, all_46_8) = v2 &
% 63.78/9.37 | | | | | | in(v0, all_46_5) = v3 & $i(v1) & ( ~ (v2 = 0) | v3
% 63.78/9.37 | | | | | | = 0))) & ! [v0: $i] : ( ~ (in(v0, all_46_5) = 0)
% 63.78/9.37 | | | | | | | ~ $i(v0) | ? [v1: $i] : (apply(all_46_6, v0) = v1
% 63.78/9.37 | | | | | | & apply(all_46_7, v0) = v1 & $i(v1))) & ! [v0: $i]
% 63.78/9.37 | | | | | | : ( ~ (in(v0, all_46_5) = 0) | ~ $i(v0) | ? [v1: $i]
% 63.78/9.37 | | | | | | : (apply(all_46_7, v0) = v1 & in(v1, all_46_8) = 0 &
% 63.78/9.37 | | | | | | in(v0, all_168_2) = 0 & $i(v1)))))
% 63.78/9.37 | | | | | |
% 63.78/9.37 | | | | | | ALPHA: (121) implies:
% 63.78/9.37 | | | | | | (122) function(all_46_7) = all_168_3
% 63.78/9.37 | | | | | | (123) relation(all_46_7) = all_168_4
% 63.78/9.37 | | | | | | (124) relation_dom(all_46_7) = all_168_2
% 63.78/9.37 | | | | | | (125) ~ (all_168_3 = 0) | ~ (all_168_4 = 0) | ( ! [v0: $i] : !
% 63.78/9.37 | | | | | | [v1: int] : (v1 = 0 | ~ (in(v0, all_46_5) = v1) | ~
% 63.78/9.37 | | | | | | $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] :
% 63.78/9.37 | | | | | | (apply(all_46_7, v0) = v3 & in(v3, all_46_8) = v4 &
% 63.78/9.37 | | | | | | in(v0, all_168_2) = v2 & $i(v3) & ( ~ (v4 = 0) | ~
% 63.78/9.37 | | | | | | (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 63.78/9.37 | | | | | | (apply(all_46_6, v0) = v1) | ~ $i(v0) | ? [v2: any] :
% 63.78/9.37 | | | | | | ? [v3: $i] : (apply(all_46_7, v0) = v3 & in(v0,
% 63.78/9.38 | | | | | | all_46_5) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = v1)))
% 63.78/9.38 | | | | | | & ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_46_7, v0) =
% 63.78/9.38 | | | | | | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ?
% 63.78/9.38 | | | | | | [v4: any] : (in(v1, all_46_8) = v4 & in(v0, all_168_2)
% 63.78/9.38 | | | | | | = v3 & in(v0, all_46_5) = v2 & ( ~ (v2 = 0) | (v4 = 0
% 63.78/9.38 | | | | | | & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 63.78/9.38 | | | | | | (apply(all_46_7, v0) = v1) | ~ $i(v0) | ? [v2: any] :
% 63.78/9.38 | | | | | | ? [v3: any] : ? [v4: any] : (in(v1, all_46_8) = v3 &
% 63.78/9.38 | | | | | | in(v0, all_168_2) = v2 & in(v0, all_46_5) = v4 & ( ~
% 63.78/9.38 | | | | | | (v3 = 0) | ~ (v2 = 0) | v4 = 0))) & ! [v0: $i] :
% 63.78/9.38 | | | | | | ! [v1: $i] : ( ~ (apply(all_46_7, v0) = v1) | ~ $i(v0) |
% 63.78/9.38 | | | | | | ? [v2: any] : ? [v3: $i] : (apply(all_46_6, v0) = v3
% 63.78/9.38 | | | | | | & in(v0, all_46_5) = v2 & $i(v3) & ( ~ (v2 = 0) | v3
% 63.78/9.38 | | | | | | = v1))) & ! [v0: $i] : ! [v1: any] : ( ~ (in(v0,
% 63.78/9.38 | | | | | | all_168_2) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 63.78/9.38 | | | | | | [v3: $i] : ? [v4: any] : (apply(all_46_7, v0) = v3 &
% 63.78/9.38 | | | | | | in(v3, all_46_8) = v4 & in(v0, all_46_5) = v2 &
% 63.78/9.38 | | | | | | $i(v3) & ( ~ (v2 = 0) | (v4 = 0 & v1 = 0)))) & !
% 63.78/9.38 | | | | | | [v0: $i] : ( ~ (in(v0, all_168_2) = 0) | ~ $i(v0) | ?
% 63.78/9.38 | | | | | | [v1: $i] : ? [v2: any] : ? [v3: any] :
% 63.78/9.38 | | | | | | (apply(all_46_7, v0) = v1 & in(v1, all_46_8) = v2 &
% 63.78/9.38 | | | | | | in(v0, all_46_5) = v3 & $i(v1) & ( ~ (v2 = 0) | v3 =
% 63.78/9.38 | | | | | | 0))) & ! [v0: $i] : ( ~ (in(v0, all_46_5) = 0) |
% 63.78/9.38 | | | | | | ~ $i(v0) | ? [v1: $i] : (apply(all_46_6, v0) = v1 &
% 63.78/9.38 | | | | | | apply(all_46_7, v0) = v1 & $i(v1))) & ! [v0: $i] : (
% 63.78/9.38 | | | | | | ~ (in(v0, all_46_5) = 0) | ~ $i(v0) | ? [v1: $i] :
% 63.78/9.38 | | | | | | (apply(all_46_7, v0) = v1 & in(v1, all_46_8) = 0 &
% 63.78/9.38 | | | | | | in(v0, all_168_2) = 0 & $i(v1))))
% 63.78/9.38 | | | | | |
% 63.78/9.38 | | | | | | GROUND_INST: instantiating (8) with 0, all_168_3, all_46_7,
% 63.78/9.38 | | | | | | simplifying with (20), (122) gives:
% 63.78/9.38 | | | | | | (126) all_168_3 = 0
% 63.78/9.38 | | | | | |
% 63.78/9.38 | | | | | | GROUND_INST: instantiating (9) with 0, all_168_4, all_46_7,
% 63.78/9.38 | | | | | | simplifying with (21), (123) gives:
% 63.78/9.38 | | | | | | (127) all_168_4 = 0
% 63.78/9.38 | | | | | |
% 63.78/9.38 | | | | | | GROUND_INST: instantiating (13) with all_46_0, 0, all_46_1,
% 63.78/9.38 | | | | | | all_46_2, simplifying with (23), (108) gives:
% 63.78/9.38 | | | | | | (128) all_46_0 = 0
% 63.78/9.38 | | | | | |
% 63.78/9.38 | | | | | | GROUND_INST: instantiating (10) with all_46_4, all_168_2, all_46_7,
% 63.78/9.38 | | | | | | simplifying with (25), (124) gives:
% 63.78/9.38 | | | | | | (129) all_168_2 = all_46_4
% 63.78/9.38 | | | | | |
% 63.78/9.38 | | | | | | BETA: splitting (29) gives:
% 63.78/9.38 | | | | | |
% 63.78/9.38 | | | | | | Case 1:
% 63.78/9.38 | | | | | | |
% 63.78/9.38 | | | | | | | (130) ~ (all_46_0 = 0)
% 63.78/9.38 | | | | | | |
% 63.78/9.38 | | | | | | | REDUCE: (128), (130) imply:
% 63.78/9.38 | | | | | | | (131) $false
% 63.78/9.38 | | | | | | |
% 63.78/9.38 | | | | | | | CLOSE: (131) is inconsistent.
% 63.78/9.38 | | | | | | |
% 63.78/9.38 | | | | | | Case 2:
% 63.78/9.38 | | | | | | |
% 63.78/9.38 | | | | | | | (132) ~ (all_46_3 = 0)
% 63.78/9.38 | | | | | | |
% 63.78/9.38 | | | | | | | BETA: splitting (125) gives:
% 63.78/9.38 | | | | | | |
% 63.78/9.38 | | | | | | | Case 1:
% 63.78/9.38 | | | | | | | |
% 63.78/9.38 | | | | | | | | (133) ~ (all_168_3 = 0)
% 63.78/9.38 | | | | | | | |
% 63.78/9.38 | | | | | | | | REDUCE: (126), (133) imply:
% 63.78/9.38 | | | | | | | | (134) $false
% 63.78/9.38 | | | | | | | |
% 63.78/9.38 | | | | | | | | CLOSE: (134) is inconsistent.
% 63.78/9.38 | | | | | | | |
% 63.78/9.38 | | | | | | | Case 2:
% 63.78/9.38 | | | | | | | |
% 63.78/9.39 | | | | | | | | (135) ~ (all_168_4 = 0) | ( ! [v0: $i] : ! [v1: int] : (v1
% 63.78/9.39 | | | | | | | | = 0 | ~ (in(v0, all_46_5) = v1) | ~ $i(v0) | ?
% 63.78/9.39 | | | | | | | | [v2: any] : ? [v3: $i] : ? [v4: any] :
% 63.78/9.39 | | | | | | | | (apply(all_46_7, v0) = v3 & in(v3, all_46_8) = v4 &
% 63.78/9.39 | | | | | | | | in(v0, all_168_2) = v2 & $i(v3) & ( ~ (v4 = 0) |
% 63.78/9.39 | | | | | | | | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 63.78/9.39 | | | | | | | | (apply(all_46_6, v0) = v1) | ~ $i(v0) | ? [v2:
% 63.78/9.39 | | | | | | | | any] : ? [v3: $i] : (apply(all_46_7, v0) = v3 &
% 63.78/9.39 | | | | | | | | in(v0, all_46_5) = v2 & $i(v3) & ( ~ (v2 = 0) |
% 63.78/9.39 | | | | | | | | v3 = v1))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 63.78/9.39 | | | | | | | | (apply(all_46_7, v0) = v1) | ~ $i(v0) | ? [v2:
% 63.78/9.39 | | | | | | | | any] : ? [v3: any] : ? [v4: any] : (in(v1,
% 63.78/9.39 | | | | | | | | all_46_8) = v4 & in(v0, all_168_2) = v3 &
% 63.78/9.39 | | | | | | | | in(v0, all_46_5) = v2 & ( ~ (v2 = 0) | (v4 = 0 &
% 63.78/9.39 | | | | | | | | v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 63.78/9.39 | | | | | | | | (apply(all_46_7, v0) = v1) | ~ $i(v0) | ? [v2:
% 63.78/9.39 | | | | | | | | any] : ? [v3: any] : ? [v4: any] : (in(v1,
% 63.78/9.39 | | | | | | | | all_46_8) = v3 & in(v0, all_168_2) = v2 &
% 63.78/9.39 | | | | | | | | in(v0, all_46_5) = v4 & ( ~ (v3 = 0) | ~ (v2 =
% 63.78/9.39 | | | | | | | | 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] :
% 63.78/9.39 | | | | | | | | ( ~ (apply(all_46_7, v0) = v1) | ~ $i(v0) | ? [v2:
% 63.78/9.39 | | | | | | | | any] : ? [v3: $i] : (apply(all_46_6, v0) = v3 &
% 63.78/9.39 | | | | | | | | in(v0, all_46_5) = v2 & $i(v3) & ( ~ (v2 = 0) |
% 63.78/9.39 | | | | | | | | v3 = v1))) & ! [v0: $i] : ! [v1: any] : ( ~
% 63.78/9.39 | | | | | | | | (in(v0, all_168_2) = v1) | ~ $i(v0) | ? [v2: any]
% 63.78/9.39 | | | | | | | | : ? [v3: $i] : ? [v4: any] : (apply(all_46_7, v0)
% 63.78/9.39 | | | | | | | | = v3 & in(v3, all_46_8) = v4 & in(v0, all_46_5) =
% 63.78/9.39 | | | | | | | | v2 & $i(v3) & ( ~ (v2 = 0) | (v4 = 0 & v1 = 0))))
% 63.78/9.39 | | | | | | | | & ! [v0: $i] : ( ~ (in(v0, all_168_2) = 0) | ~
% 63.78/9.39 | | | | | | | | $i(v0) | ? [v1: $i] : ? [v2: any] : ? [v3: any]
% 63.78/9.39 | | | | | | | | : (apply(all_46_7, v0) = v1 & in(v1, all_46_8) = v2
% 63.78/9.39 | | | | | | | | & in(v0, all_46_5) = v3 & $i(v1) & ( ~ (v2 = 0) |
% 63.78/9.39 | | | | | | | | v3 = 0))) & ! [v0: $i] : ( ~ (in(v0, all_46_5)
% 63.78/9.39 | | | | | | | | = 0) | ~ $i(v0) | ? [v1: $i] : (apply(all_46_6,
% 63.78/9.39 | | | | | | | | v0) = v1 & apply(all_46_7, v0) = v1 & $i(v1)))
% 63.78/9.39 | | | | | | | | & ! [v0: $i] : ( ~ (in(v0, all_46_5) = 0) | ~
% 63.78/9.39 | | | | | | | | $i(v0) | ? [v1: $i] : (apply(all_46_7, v0) = v1 &
% 63.78/9.39 | | | | | | | | in(v1, all_46_8) = 0 & in(v0, all_168_2) = 0 &
% 63.78/9.39 | | | | | | | | $i(v1))))
% 63.78/9.39 | | | | | | | |
% 63.78/9.39 | | | | | | | | BETA: splitting (33) gives:
% 63.78/9.39 | | | | | | | |
% 63.78/9.39 | | | | | | | | Case 1:
% 63.78/9.39 | | | | | | | | |
% 63.78/9.39 | | | | | | | | | (136) all_46_3 = 0
% 63.78/9.39 | | | | | | | | |
% 63.78/9.39 | | | | | | | | | REDUCE: (132), (136) imply:
% 63.93/9.39 | | | | | | | | | (137) $false
% 63.93/9.39 | | | | | | | | |
% 63.93/9.39 | | | | | | | | | CLOSE: (137) is inconsistent.
% 63.93/9.39 | | | | | | | | |
% 63.93/9.39 | | | | | | | | Case 2:
% 63.93/9.39 | | | | | | | | |
% 63.93/9.39 | | | | | | | | | (138) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 63.93/9.39 | | | | | | | | | all_46_4) = v1 & in(v0, all_46_5) = 0 & $i(v0))
% 63.93/9.39 | | | | | | | | |
% 63.93/9.39 | | | | | | | | | DELTA: instantiating (138) with fresh symbols all_277_0,
% 63.93/9.39 | | | | | | | | | all_277_1 gives:
% 63.93/9.39 | | | | | | | | | (139) ~ (all_277_0 = 0) & in(all_277_1, all_46_4) =
% 63.93/9.39 | | | | | | | | | all_277_0 & in(all_277_1, all_46_5) = 0 &
% 63.93/9.39 | | | | | | | | | $i(all_277_1)
% 63.93/9.39 | | | | | | | | |
% 63.93/9.39 | | | | | | | | | ALPHA: (139) implies:
% 63.93/9.39 | | | | | | | | | (140) ~ (all_277_0 = 0)
% 63.93/9.39 | | | | | | | | | (141) $i(all_277_1)
% 63.93/9.39 | | | | | | | | | (142) in(all_277_1, all_46_5) = 0
% 63.93/9.39 | | | | | | | | | (143) in(all_277_1, all_46_4) = all_277_0
% 63.93/9.39 | | | | | | | | |
% 63.93/9.39 | | | | | | | | | BETA: splitting (135) gives:
% 63.93/9.39 | | | | | | | | |
% 63.93/9.39 | | | | | | | | | Case 1:
% 63.93/9.39 | | | | | | | | | |
% 63.93/9.39 | | | | | | | | | | (144) ~ (all_168_4 = 0)
% 63.93/9.39 | | | | | | | | | |
% 63.93/9.39 | | | | | | | | | | REDUCE: (127), (144) imply:
% 63.93/9.39 | | | | | | | | | | (145) $false
% 63.93/9.39 | | | | | | | | | |
% 63.93/9.39 | | | | | | | | | | CLOSE: (145) is inconsistent.
% 63.93/9.39 | | | | | | | | | |
% 63.93/9.39 | | | | | | | | | Case 2:
% 63.93/9.39 | | | | | | | | | |
% 63.93/9.40 | | | | | | | | | | (146) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0,
% 63.93/9.40 | | | | | | | | | | all_46_5) = v1) | ~ $i(v0) | ? [v2: any] :
% 63.93/9.40 | | | | | | | | | | ? [v3: $i] : ? [v4: any] : (apply(all_46_7, v0)
% 63.93/9.40 | | | | | | | | | | = v3 & in(v3, all_46_8) = v4 & in(v0,
% 63.93/9.40 | | | | | | | | | | all_168_2) = v2 & $i(v3) & ( ~ (v4 = 0) | ~
% 63.93/9.40 | | | | | | | | | | (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 63.93/9.40 | | | | | | | | | | (apply(all_46_6, v0) = v1) | ~ $i(v0) | ? [v2:
% 63.93/9.40 | | | | | | | | | | any] : ? [v3: $i] : (apply(all_46_7, v0) = v3
% 63.93/9.40 | | | | | | | | | | & in(v0, all_46_5) = v2 & $i(v3) & ( ~ (v2 = 0)
% 63.93/9.40 | | | | | | | | | | | v3 = v1))) & ! [v0: $i] : ! [v1: $i] : (
% 63.93/9.40 | | | | | | | | | | ~ (apply(all_46_7, v0) = v1) | ~ $i(v0) | ?
% 63.93/9.40 | | | | | | | | | | [v2: any] : ? [v3: any] : ? [v4: any] : (in(v1,
% 63.93/9.40 | | | | | | | | | | all_46_8) = v4 & in(v0, all_168_2) = v3 &
% 63.93/9.40 | | | | | | | | | | in(v0, all_46_5) = v2 & ( ~ (v2 = 0) | (v4 = 0
% 63.93/9.40 | | | | | | | | | | & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] :
% 63.93/9.40 | | | | | | | | | | ( ~ (apply(all_46_7, v0) = v1) | ~ $i(v0) | ?
% 63.93/9.40 | | | | | | | | | | [v2: any] : ? [v3: any] : ? [v4: any] : (in(v1,
% 63.93/9.40 | | | | | | | | | | all_46_8) = v3 & in(v0, all_168_2) = v2 &
% 63.93/9.40 | | | | | | | | | | in(v0, all_46_5) = v4 & ( ~ (v3 = 0) | ~ (v2 =
% 63.93/9.40 | | | | | | | | | | 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i]
% 63.93/9.40 | | | | | | | | | | : ( ~ (apply(all_46_7, v0) = v1) | ~ $i(v0) | ?
% 63.93/9.40 | | | | | | | | | | [v2: any] : ? [v3: $i] : (apply(all_46_6, v0) =
% 63.93/9.40 | | | | | | | | | | v3 & in(v0, all_46_5) = v2 & $i(v3) & ( ~ (v2 =
% 63.93/9.40 | | | | | | | | | | 0) | v3 = v1))) & ! [v0: $i] : ! [v1:
% 63.93/9.40 | | | | | | | | | | any] : ( ~ (in(v0, all_168_2) = v1) | ~ $i(v0) |
% 63.93/9.40 | | | | | | | | | | ? [v2: any] : ? [v3: $i] : ? [v4: any] :
% 63.93/9.40 | | | | | | | | | | (apply(all_46_7, v0) = v3 & in(v3, all_46_8) = v4
% 63.93/9.40 | | | | | | | | | | & in(v0, all_46_5) = v2 & $i(v3) & ( ~ (v2 = 0)
% 63.93/9.40 | | | | | | | | | | | (v4 = 0 & v1 = 0)))) & ! [v0: $i] : ( ~
% 63.93/9.40 | | | | | | | | | | (in(v0, all_168_2) = 0) | ~ $i(v0) | ? [v1: $i]
% 63.93/9.40 | | | | | | | | | | : ? [v2: any] : ? [v3: any] : (apply(all_46_7,
% 63.93/9.40 | | | | | | | | | | v0) = v1 & in(v1, all_46_8) = v2 & in(v0,
% 63.93/9.40 | | | | | | | | | | all_46_5) = v3 & $i(v1) & ( ~ (v2 = 0) | v3 =
% 63.93/9.40 | | | | | | | | | | 0))) & ! [v0: $i] : ( ~ (in(v0, all_46_5) =
% 63.93/9.40 | | | | | | | | | | 0) | ~ $i(v0) | ? [v1: $i] : (apply(all_46_6,
% 63.93/9.40 | | | | | | | | | | v0) = v1 & apply(all_46_7, v0) = v1 &
% 63.93/9.40 | | | | | | | | | | $i(v1))) & ! [v0: $i] : ( ~ (in(v0, all_46_5)
% 63.93/9.40 | | | | | | | | | | = 0) | ~ $i(v0) | ? [v1: $i] :
% 63.93/9.40 | | | | | | | | | | (apply(all_46_7, v0) = v1 & in(v1, all_46_8) = 0
% 63.93/9.40 | | | | | | | | | | & in(v0, all_168_2) = 0 & $i(v1)))
% 63.93/9.40 | | | | | | | | | |
% 63.93/9.40 | | | | | | | | | | ALPHA: (146) implies:
% 63.93/9.40 | | | | | | | | | | (147) ! [v0: $i] : ( ~ (in(v0, all_46_5) = 0) | ~
% 63.93/9.40 | | | | | | | | | | $i(v0) | ? [v1: $i] : (apply(all_46_7, v0) = v1
% 63.93/9.40 | | | | | | | | | | & in(v1, all_46_8) = 0 & in(v0, all_168_2) = 0
% 63.93/9.40 | | | | | | | | | | & $i(v1)))
% 63.93/9.40 | | | | | | | | | |
% 63.93/9.40 | | | | | | | | | | GROUND_INST: instantiating (147) with all_277_1, simplifying
% 63.93/9.40 | | | | | | | | | | with (141), (142) gives:
% 63.93/9.40 | | | | | | | | | | (148) ? [v0: $i] : (apply(all_46_7, all_277_1) = v0 &
% 63.93/9.40 | | | | | | | | | | in(v0, all_46_8) = 0 & in(all_277_1, all_168_2) =
% 63.93/9.40 | | | | | | | | | | 0 & $i(v0))
% 63.93/9.40 | | | | | | | | | |
% 63.93/9.40 | | | | | | | | | | DELTA: instantiating (148) with fresh symbol all_326_0
% 63.93/9.40 | | | | | | | | | | gives:
% 63.93/9.40 | | | | | | | | | | (149) apply(all_46_7, all_277_1) = all_326_0 &
% 63.93/9.40 | | | | | | | | | | in(all_326_0, all_46_8) = 0 & in(all_277_1,
% 63.93/9.40 | | | | | | | | | | all_168_2) = 0 & $i(all_326_0)
% 63.93/9.40 | | | | | | | | | |
% 63.93/9.40 | | | | | | | | | | ALPHA: (149) implies:
% 63.93/9.40 | | | | | | | | | | (150) in(all_277_1, all_168_2) = 0
% 63.93/9.40 | | | | | | | | | |
% 63.93/9.40 | | | | | | | | | | REDUCE: (129), (150) imply:
% 63.93/9.40 | | | | | | | | | | (151) in(all_277_1, all_46_4) = 0
% 63.93/9.40 | | | | | | | | | |
% 63.93/9.40 | | | | | | | | | | GROUND_INST: instantiating (12) with all_277_0, 0, all_46_4,
% 63.93/9.40 | | | | | | | | | | all_277_1, simplifying with (143), (151) gives:
% 63.93/9.40 | | | | | | | | | | (152) all_277_0 = 0
% 63.93/9.40 | | | | | | | | | |
% 63.93/9.40 | | | | | | | | | | REDUCE: (140), (152) imply:
% 63.93/9.40 | | | | | | | | | | (153) $false
% 63.93/9.40 | | | | | | | | | |
% 63.93/9.40 | | | | | | | | | | CLOSE: (153) is inconsistent.
% 63.93/9.40 | | | | | | | | | |
% 63.93/9.40 | | | | | | | | | End of split
% 63.93/9.40 | | | | | | | | |
% 63.93/9.40 | | | | | | | | End of split
% 63.93/9.40 | | | | | | | |
% 63.93/9.40 | | | | | | | End of split
% 63.93/9.40 | | | | | | |
% 63.93/9.40 | | | | | | End of split
% 63.93/9.40 | | | | | |
% 63.93/9.40 | | | | | Case 2:
% 63.93/9.40 | | | | | |
% 63.93/9.40 | | | | | | (154) relation(all_46_6) = all_168_6 & function(all_46_6) =
% 63.93/9.40 | | | | | | all_168_5 & ( ~ (all_168_5 = 0) | ~ (all_168_6 = 0))
% 63.93/9.40 | | | | | |
% 63.93/9.40 | | | | | | ALPHA: (154) implies:
% 63.93/9.40 | | | | | | (155) function(all_46_6) = all_168_5
% 63.93/9.40 | | | | | | (156) relation(all_46_6) = all_168_6
% 63.93/9.40 | | | | | | (157) ~ (all_168_5 = 0) | ~ (all_168_6 = 0)
% 63.93/9.40 | | | | | |
% 63.93/9.40 | | | | | | GROUND_INST: instantiating (8) with 0, all_168_5, all_46_6,
% 63.93/9.40 | | | | | | simplifying with (120), (155) gives:
% 63.93/9.40 | | | | | | (158) all_168_5 = 0
% 63.93/9.40 | | | | | |
% 63.93/9.40 | | | | | | GROUND_INST: instantiating (9) with 0, all_168_6, all_46_6,
% 63.93/9.40 | | | | | | simplifying with (112), (156) gives:
% 63.93/9.40 | | | | | | (159) all_168_6 = 0
% 63.93/9.40 | | | | | |
% 63.93/9.40 | | | | | | BETA: splitting (157) gives:
% 63.93/9.40 | | | | | |
% 63.93/9.40 | | | | | | Case 1:
% 63.93/9.40 | | | | | | |
% 63.93/9.40 | | | | | | | (160) ~ (all_168_5 = 0)
% 63.93/9.40 | | | | | | |
% 63.93/9.40 | | | | | | | REDUCE: (158), (160) imply:
% 63.93/9.40 | | | | | | | (161) $false
% 63.93/9.40 | | | | | | |
% 63.93/9.40 | | | | | | | CLOSE: (161) is inconsistent.
% 63.93/9.40 | | | | | | |
% 63.93/9.40 | | | | | | Case 2:
% 63.93/9.40 | | | | | | |
% 63.93/9.40 | | | | | | | (162) ~ (all_168_6 = 0)
% 63.93/9.40 | | | | | | |
% 63.93/9.40 | | | | | | | REDUCE: (159), (162) imply:
% 63.93/9.40 | | | | | | | (163) $false
% 63.93/9.40 | | | | | | |
% 63.93/9.40 | | | | | | | CLOSE: (163) is inconsistent.
% 63.93/9.40 | | | | | | |
% 63.93/9.40 | | | | | | End of split
% 63.93/9.40 | | | | | |
% 63.93/9.40 | | | | | End of split
% 63.93/9.40 | | | | |
% 63.93/9.40 | | | | End of split
% 63.93/9.40 | | | |
% 63.93/9.40 | | | End of split
% 63.93/9.40 | | |
% 63.93/9.40 | | End of split
% 63.93/9.40 | |
% 63.93/9.40 | End of split
% 63.93/9.40 |
% 63.93/9.40 End of proof
% 63.93/9.41 % SZS output end Proof for theBenchmark
% 63.93/9.41
% 63.93/9.41 8806ms
%------------------------------------------------------------------------------