TSTP Solution File: SEU292+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU292+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n016.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 17:43:53 EDT 2023
% Result : Theorem 13.14s 2.61s
% Output : Proof 25.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU292+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 20:27:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.62 ________ _____
% 0.19/0.62 ___ __ \_________(_)________________________________
% 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.62
% 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.62 (2023-06-19)
% 0.19/0.62
% 0.19/0.62 (c) Philipp Rümmer, 2009-2023
% 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.62 Amanda Stjerna.
% 0.19/0.62 Free software under BSD-3-Clause.
% 0.19/0.62
% 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.62
% 0.19/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.63 Running up to 7 provers in parallel.
% 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.25/1.17 Prover 4: Preprocessing ...
% 3.25/1.17 Prover 1: Preprocessing ...
% 3.41/1.21 Prover 3: Preprocessing ...
% 3.41/1.21 Prover 6: Preprocessing ...
% 3.41/1.21 Prover 5: Preprocessing ...
% 3.41/1.21 Prover 0: Preprocessing ...
% 3.41/1.21 Prover 2: Preprocessing ...
% 6.98/1.78 Prover 1: Warning: ignoring some quantifiers
% 6.98/1.83 Prover 5: Proving ...
% 6.98/1.83 Prover 2: Proving ...
% 7.74/1.84 Prover 1: Constructing countermodel ...
% 7.74/1.86 Prover 3: Warning: ignoring some quantifiers
% 7.74/1.88 Prover 4: Warning: ignoring some quantifiers
% 7.74/1.88 Prover 3: Constructing countermodel ...
% 7.74/1.88 Prover 6: Proving ...
% 8.22/1.94 Prover 4: Constructing countermodel ...
% 8.73/2.05 Prover 0: Proving ...
% 9.97/2.22 Prover 3: gave up
% 9.97/2.22 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.97/2.26 Prover 7: Preprocessing ...
% 11.33/2.37 Prover 7: Warning: ignoring some quantifiers
% 11.33/2.39 Prover 7: Constructing countermodel ...
% 12.78/2.54 Prover 1: gave up
% 12.78/2.54 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.14/2.60 Prover 8: Preprocessing ...
% 13.14/2.61 Prover 0: proved (1965ms)
% 13.14/2.61
% 13.14/2.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.14/2.61
% 13.14/2.61 Prover 2: stopped
% 13.14/2.62 Prover 5: stopped
% 13.14/2.62 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.14/2.62 Prover 6: stopped
% 13.14/2.63 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.14/2.63 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 13.14/2.63 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.78/2.68 Prover 10: Preprocessing ...
% 14.00/2.69 Prover 11: Preprocessing ...
% 14.00/2.69 Prover 13: Preprocessing ...
% 14.00/2.70 Prover 16: Preprocessing ...
% 14.00/2.70 Prover 8: Warning: ignoring some quantifiers
% 14.00/2.72 Prover 8: Constructing countermodel ...
% 14.45/2.80 Prover 16: Warning: ignoring some quantifiers
% 14.45/2.81 Prover 10: Warning: ignoring some quantifiers
% 14.94/2.82 Prover 16: Constructing countermodel ...
% 14.94/2.82 Prover 10: Constructing countermodel ...
% 14.94/2.83 Prover 13: Warning: ignoring some quantifiers
% 14.94/2.84 Prover 13: Constructing countermodel ...
% 15.33/2.94 Prover 11: Warning: ignoring some quantifiers
% 16.00/2.95 Prover 11: Constructing countermodel ...
% 16.00/2.97 Prover 10: gave up
% 16.00/3.01 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 16.00/3.06 Prover 19: Preprocessing ...
% 16.00/3.12 Prover 8: gave up
% 16.88/3.18 Prover 7: gave up
% 17.89/3.23 Prover 19: Warning: ignoring some quantifiers
% 17.89/3.25 Prover 19: Constructing countermodel ...
% 20.02/3.48 Prover 19: gave up
% 23.70/4.05 Prover 4: Found proof (size 295)
% 23.70/4.06 Prover 4: proved (3409ms)
% 23.70/4.06 Prover 11: stopped
% 23.70/4.06 Prover 13: stopped
% 23.70/4.06 Prover 16: stopped
% 23.70/4.06
% 23.70/4.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.70/4.06
% 24.18/4.09 % SZS output start Proof for theBenchmark
% 24.18/4.09 Assumptions after simplification:
% 24.18/4.09 ---------------------------------
% 24.18/4.09
% 24.18/4.09 (cc1_relset_1)
% 24.18/4.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 24.18/4.12 (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = v4) | ~ (element(v2,
% 24.18/4.12 v4) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | relation(v2) = 0)
% 24.18/4.12
% 24.18/4.12 (cc2_funct_1)
% 24.18/4.12 ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? [v2:
% 24.18/4.12 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 & function(v0) =
% 24.18/4.12 v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0)))
% 24.18/4.12 & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2:
% 24.18/4.12 any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 & empty(v0)
% 24.18/4.12 = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~
% 24.18/4.12 (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: any]
% 24.18/4.12 : (one_to_one(v0) = v3 & relation(v0) = v1 & empty(v0) = v2 & ( ~ (v2 = 0) |
% 24.18/4.12 ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0)
% 24.18/4.12 | ? [v1: any] : ? [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 &
% 24.18/4.12 relation(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 =
% 24.18/4.12 0)))
% 24.18/4.12
% 24.18/4.12 (d1_funct_2)
% 24.18/4.13 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 24.18/4.13 (relation_dom_as_subset(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 24.18/4.13 $i(v0) | ? [v4: any] : ? [v5: any] : (relation_of2_as_subset(v2, v0, v1) =
% 24.18/4.13 v4 & quasi_total(v2, v0, v1) = v5 & ( ~ (v4 = 0) | (( ~ (v1 = empty_set) |
% 24.18/4.13 v0 = empty_set | (( ~ (v5 = 0) | v2 = empty_set) & ( ~ (v2 =
% 24.18/4.13 empty_set) | v5 = 0))) & ((v1 = empty_set & ~ (v0 =
% 24.18/4.13 empty_set)) | (( ~ (v5 = 0) | v3 = v0) & ( ~ (v3 = v0) | v5 =
% 24.18/4.13 0))))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 24.18/4.13 any] : ( ~ (quasi_total(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 24.18/4.13 $i(v0) | ? [v4: any] : ? [v5: $i] : (relation_dom_as_subset(v0, v1, v2) =
% 24.18/4.13 v5 & relation_of2_as_subset(v2, v0, v1) = v4 & $i(v5) & ( ~ (v4 = 0) | ((
% 24.18/4.13 ~ (v1 = empty_set) | v0 = empty_set | (( ~ (v3 = 0) | v2 =
% 24.18/4.13 empty_set) & ( ~ (v2 = empty_set) | v3 = 0))) & ((v1 = empty_set
% 24.18/4.13 & ~ (v0 = empty_set)) | (( ~ (v5 = v0) | v3 = 0) & ( ~ (v3 = 0) |
% 24.18/4.13 v5 = v0))))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 24.18/4.13 (relation_of2_as_subset(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 24.18/4.13 | ? [v3: any] : ? [v4: $i] : (relation_dom_as_subset(v0, v1, v2) = v4 &
% 24.18/4.13 quasi_total(v2, v0, v1) = v3 & $i(v4) & ( ~ (v1 = empty_set) | v0 =
% 24.18/4.13 empty_set | (( ~ (v3 = 0) | v2 = empty_set) & ( ~ (v2 = empty_set) | v3
% 24.18/4.13 = 0))) & ((v1 = empty_set & ~ (v0 = empty_set)) | (( ~ (v4 = v0) |
% 24.18/4.13 v3 = 0) & ( ~ (v3 = 0) | v4 = v0)))))
% 24.18/4.13
% 24.18/4.13 (dt_k4_relset_1)
% 24.18/4.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 24.18/4.13 (relation_dom_as_subset(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 24.18/4.13 $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: any] : (relation_of2(v2, v0,
% 24.18/4.13 v1) = v4 & powerset(v0) = v5 & element(v3, v5) = v6 & $i(v5) & ( ~ (v4 =
% 24.18/4.13 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 24.18/4.13 (relation_of2(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 24.18/4.13 $i] : ? [v4: $i] : (relation_dom_as_subset(v0, v1, v2) = v3 &
% 24.18/4.13 powerset(v0) = v4 & element(v3, v4) = 0 & $i(v4) & $i(v3)))
% 24.18/4.13
% 24.18/4.13 (dt_k5_relat_1)
% 24.18/4.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_composition(v0, v1) =
% 24.18/4.13 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 24.18/4.13 (relation(v2) = v5 & relation(v1) = v4 & relation(v0) = v3 & ( ~ (v4 = 0) |
% 24.18/4.13 ~ (v3 = 0) | v5 = 0)))
% 24.18/4.13
% 24.18/4.13 (dt_m2_relset_1)
% 24.18/4.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 24.18/4.14 int] : (v5 = 0 | ~ (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) =
% 24.18/4.14 v4) | ~ (element(v2, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 24.18/4.14 [v6: int] : ( ~ (v6 = 0) & relation_of2_as_subset(v2, v0, v1) = v6)) & !
% 24.18/4.14 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_of2_as_subset(v2, v0, v1)
% 24.18/4.14 = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 24.18/4.14 (cartesian_product2(v0, v1) = v3 & powerset(v3) = v4 & element(v2, v4) = 0 &
% 24.18/4.14 $i(v4) & $i(v3)))
% 24.18/4.14
% 24.18/4.14 (fc10_relat_1)
% 24.18/4.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_composition(v1, v0) =
% 24.18/4.14 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 24.18/4.14 ? [v6: any] : (relation(v2) = v6 & relation(v1) = v4 & empty(v2) = v5 &
% 24.18/4.14 empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v5 = 0))))
% 24.18/4.14
% 24.18/4.14 (fc1_funct_1)
% 24.18/4.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_composition(v0, v1) =
% 24.18/4.14 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 24.18/4.14 ? [v6: any] : ? [v7: any] : ? [v8: any] : (relation(v2) = v7 &
% 24.18/4.14 relation(v1) = v5 & relation(v0) = v3 & function(v2) = v8 & function(v1) =
% 24.18/4.14 v6 & function(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3
% 24.18/4.14 = 0) | (v8 = 0 & v7 = 0))))
% 24.18/4.14
% 24.18/4.14 (fc5_relat_1)
% 24.18/4.14 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ?
% 24.18/4.14 [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_dom(v0) = v3 &
% 24.18/4.14 relation(v0) = v2 & empty(v3) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v2 =
% 24.18/4.14 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~
% 24.18/4.14 $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 &
% 24.18/4.14 empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) &
% 24.18/4.14 ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i]
% 24.18/4.14 : ? [v3: any] : (relation_dom(v0) = v2 & empty(v2) = v3 & empty(v0) = v1 &
% 24.18/4.14 $i(v2) & ( ~ (v3 = 0) | v1 = 0)))
% 24.18/4.14
% 24.18/4.14 (fc7_relat_1)
% 24.18/4.14 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2:
% 24.18/4.14 any] : ? [v3: any] : ? [v4: any] : (relation(v1) = v4 & empty(v1) = v3 &
% 24.18/4.14 empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0: $i] : ( ~
% 24.18/4.14 (empty(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (relation_dom(v0) = v1 &
% 24.18/4.14 relation(v1) = 0 & empty(v1) = 0 & $i(v1)))
% 24.18/4.14
% 24.18/4.14 (fc9_relat_1)
% 24.18/4.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_composition(v0, v1) =
% 24.18/4.14 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 24.18/4.14 ? [v6: any] : (relation(v2) = v6 & relation(v1) = v4 & empty(v2) = v5 &
% 24.18/4.14 empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v5 = 0))))
% 24.18/4.14
% 24.18/4.14 (rc1_subset_1)
% 24.18/4.14 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ?
% 24.18/4.14 [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & powerset(v0) = v2 &
% 24.18/4.14 element(v3, v2) = 0 & empty(v3) = v4 & $i(v3) & $i(v2))) & ! [v0: $i] :
% 24.18/4.14 ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i]
% 24.18/4.14 : ? [v4: int] : ? [v5: int] : ($i(v3) & ((v4 = 0 & ~ (v5 = 0) &
% 24.18/4.14 element(v3, v1) = 0 & empty(v3) = v5) | (v2 = 0 & empty(v0) = 0))))
% 24.18/4.14
% 24.18/4.14 (rc2_relat_1)
% 24.18/4.15 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & relation(v0) = 0 & empty(v0) = v1
% 24.18/4.15 & $i(v0))
% 24.18/4.15
% 24.18/4.15 (redefinition_k4_relset_1)
% 24.18/4.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 24.18/4.15 (relation_dom_as_subset(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 24.18/4.15 $i(v0) | ? [v4: any] : ? [v5: $i] : (relation_dom(v2) = v5 &
% 24.18/4.15 relation_of2(v2, v0, v1) = v4 & $i(v5) & ( ~ (v4 = 0) | v5 = v3))) & !
% 24.18/4.15 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_of2(v2, v0, v1) = 0) | ~
% 24.18/4.15 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (relation_dom(v2) = v3 &
% 24.18/4.15 relation_dom_as_subset(v0, v1, v2) = v3 & $i(v3)))
% 24.18/4.15
% 24.18/4.15 (redefinition_m2_relset_1)
% 24.18/4.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 24.18/4.15 (relation_of2(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 24.18/4.15 [v4: int] : ( ~ (v4 = 0) & relation_of2_as_subset(v2, v0, v1) = v4)) & !
% 24.18/4.15 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 24.18/4.15 (relation_of2_as_subset(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 24.18/4.15 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & relation_of2(v2, v0, v1) = v4)) & !
% 24.18/4.15 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_of2(v2, v0, v1) = 0) | ~
% 24.18/4.15 $i(v2) | ~ $i(v1) | ~ $i(v0) | relation_of2_as_subset(v2, v0, v1) = 0) &
% 24.18/4.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_of2_as_subset(v2, v0,
% 24.18/4.15 v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | relation_of2(v2, v0, v1)
% 24.18/4.15 = 0)
% 24.18/4.15
% 24.18/4.15 (t21_funct_2)
% 24.18/4.15 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 24.18/4.15 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ( ~ (v8 =
% 24.18/4.15 v7) & ~ (v1 = empty_set) & apply(v6, v2) = v7 & apply(v5, v4) = v8 &
% 24.18/4.15 apply(v3, v2) = v4 & relation_composition(v3, v5) = v6 &
% 24.18/4.15 relation_of2_as_subset(v3, v0, v1) = 0 & quasi_total(v3, v0, v1) = 0 &
% 24.18/4.15 relation(v5) = 0 & function(v5) = 0 & function(v3) = 0 & in(v2, v0) = 0 &
% 24.18/4.15 $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 24.18/4.15 $i(v0))
% 24.18/4.15
% 24.18/4.15 (t23_funct_1)
% 24.18/4.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (relation_dom(v1)
% 24.18/4.16 = v2) | ~ (in(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ?
% 24.18/4.16 [v5: any] : ? [v6: $i] : (apply(v1, v0) = v6 & relation(v1) = v4 &
% 24.18/4.16 function(v1) = v5 & $i(v6) & ( ~ (v5 = 0) | ~ (v4 = 0) | ( ! [v7: $i] :
% 24.18/4.16 ! [v8: $i] : ( ~ (v3 = 0) | ~ (apply(v7, v6) = v8) | ~ $i(v7) | ?
% 24.18/4.16 [v9: any] : ? [v10: any] : ? [v11: $i] : ? [v12: $i] :
% 24.18/4.16 (apply(v11, v0) = v12 & relation_composition(v1, v7) = v11 &
% 24.18/4.16 relation(v7) = v9 & function(v7) = v10 & $i(v12) & $i(v11) & ( ~
% 24.18/4.16 (v10 = 0) | ~ (v9 = 0) | v12 = v8))) & ! [v7: $i] : ! [v8:
% 24.18/4.16 $i] : ( ~ (v3 = 0) | ~ (relation_composition(v1, v7) = v8) | ~
% 24.18/4.16 $i(v7) | ? [v9: any] : ? [v10: any] : ? [v11: $i] : ? [v12: $i]
% 24.18/4.16 : (apply(v8, v0) = v11 & apply(v7, v6) = v12 & relation(v7) = v9 &
% 24.18/4.16 function(v7) = v10 & $i(v12) & $i(v11) & ( ~ (v10 = 0) | ~ (v9 =
% 24.18/4.16 0) | v12 = v11))) & ! [v7: $i] : ( ~ (v3 = 0) | ~
% 24.18/4.16 (relation(v7) = 0) | ~ $i(v7) | ? [v8: any] : ? [v9: $i] : ?
% 24.18/4.16 [v10: $i] : ? [v11: $i] : (apply(v9, v0) = v10 & apply(v7, v6) =
% 24.18/4.16 v11 & relation_composition(v1, v7) = v9 & function(v7) = v8 &
% 24.18/4.16 $i(v11) & $i(v10) & $i(v9) & ( ~ (v8 = 0) | v11 = v10))) & ! [v7:
% 24.18/4.16 $i] : ( ~ (v3 = 0) | ~ (function(v7) = 0) | ~ $i(v7) | ? [v8:
% 24.18/4.16 any] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : (apply(v9, v0)
% 24.18/4.16 = v10 & apply(v7, v6) = v11 & relation_composition(v1, v7) = v9 &
% 24.18/4.16 relation(v7) = v8 & $i(v11) & $i(v10) & $i(v9) & ( ~ (v8 = 0) |
% 24.18/4.16 v11 = v10))))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 24.18/4.16 (apply(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 24.18/4.16 ? [v5: $i] : ? [v6: any] : (relation_dom(v1) = v5 & relation(v1) = v3 &
% 24.18/4.16 function(v1) = v4 & in(v0, v5) = v6 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0)
% 24.18/4.16 | ( ! [v7: $i] : ! [v8: $i] : ( ~ (v6 = 0) | ~ (apply(v7, v2) = v8) |
% 24.18/4.16 ~ $i(v7) | ? [v9: any] : ? [v10: any] : ? [v11: $i] : ? [v12:
% 24.18/4.16 $i] : (apply(v11, v0) = v12 & relation_composition(v1, v7) = v11 &
% 24.18/4.16 relation(v7) = v9 & function(v7) = v10 & $i(v12) & $i(v11) & ( ~
% 24.18/4.16 (v10 = 0) | ~ (v9 = 0) | v12 = v8))) & ! [v7: $i] : ! [v8:
% 24.18/4.16 $i] : ( ~ (v6 = 0) | ~ (relation_composition(v1, v7) = v8) | ~
% 24.18/4.16 $i(v7) | ? [v9: any] : ? [v10: any] : ? [v11: $i] : ? [v12: $i]
% 24.18/4.16 : (apply(v8, v0) = v11 & apply(v7, v2) = v12 & relation(v7) = v9 &
% 24.18/4.16 function(v7) = v10 & $i(v12) & $i(v11) & ( ~ (v10 = 0) | ~ (v9 =
% 24.18/4.16 0) | v12 = v11))) & ! [v7: $i] : ( ~ (v6 = 0) | ~
% 24.18/4.16 (relation(v7) = 0) | ~ $i(v7) | ? [v8: any] : ? [v9: $i] : ?
% 24.18/4.16 [v10: $i] : ? [v11: $i] : (apply(v9, v0) = v10 & apply(v7, v2) =
% 24.18/4.16 v11 & relation_composition(v1, v7) = v9 & function(v7) = v8 &
% 24.18/4.16 $i(v11) & $i(v10) & $i(v9) & ( ~ (v8 = 0) | v11 = v10))) & ! [v7:
% 24.18/4.16 $i] : ( ~ (v6 = 0) | ~ (function(v7) = 0) | ~ $i(v7) | ? [v8:
% 24.18/4.16 any] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : (apply(v9, v0)
% 24.18/4.16 = v10 & apply(v7, v2) = v11 & relation_composition(v1, v7) = v9 &
% 24.18/4.16 relation(v7) = v8 & $i(v11) & $i(v10) & $i(v9) & ( ~ (v8 = 0) |
% 24.18/4.16 v11 = v10)))))))
% 24.18/4.16
% 24.18/4.16 (function-axioms)
% 24.62/4.17 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 24.62/4.17 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (relation_of2(v4, v3, v2) = v1) | ~
% 24.62/4.17 (relation_of2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 24.62/4.17 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (relation_dom_as_subset(v4, v3, v2)
% 24.62/4.17 = v1) | ~ (relation_dom_as_subset(v4, v3, v2) = v0)) & ! [v0:
% 24.62/4.17 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 24.62/4.17 : ! [v4: $i] : (v1 = v0 | ~ (relation_of2_as_subset(v4, v3, v2) = v1) | ~
% 24.62/4.17 (relation_of2_as_subset(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 24.62/4.17 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 |
% 24.62/4.17 ~ (quasi_total(v4, v3, v2) = v1) | ~ (quasi_total(v4, v3, v2) = v0)) & !
% 24.62/4.17 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apply(v3,
% 24.62/4.17 v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 24.62/4.17 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.62/4.17 (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 24.62/4.17 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_composition(v3,
% 24.62/4.17 v2) = v1) | ~ (relation_composition(v3, v2) = v0)) & ! [v0: $i] : !
% 24.62/4.17 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3,
% 24.62/4.17 v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0:
% 24.62/4.17 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 24.62/4.17 : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0:
% 24.62/4.17 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 24.62/4.17 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : !
% 24.62/4.17 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~
% 24.62/4.17 (relation_dom(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 24.62/4.17 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 24.62/4.17 (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0))
% 24.62/4.17 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 24.62/4.17 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0: $i] :
% 24.62/4.17 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~
% 24.62/4.17 (powerset(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 24.62/4.17 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~
% 24.62/4.17 (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 24.62/4.17 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) | ~
% 24.62/4.17 (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 24.62/4.17 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 24.62/4.17 (empty(v2) = v0))
% 24.62/4.17
% 24.62/4.17 Further assumptions not needed in the proof:
% 24.62/4.17 --------------------------------------------
% 24.62/4.17 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, dt_k1_funct_1, dt_k1_relat_1,
% 24.62/4.17 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_zfmisc_1, dt_m1_relset_1, dt_m1_subset_1,
% 24.62/4.17 existence_m1_relset_1, existence_m1_subset_1, existence_m2_relset_1,
% 24.62/4.17 fc12_relat_1, fc1_subset_1, fc1_xboole_0, fc4_relat_1, fc4_subset_1,
% 24.62/4.17 rc1_funct_1, rc1_funct_2, rc1_partfun1, rc1_relat_1, rc1_xboole_0, rc2_funct_1,
% 24.62/4.17 rc2_partfun1, rc2_subset_1, rc2_xboole_0, rc3_funct_1, rc3_relat_1, rc4_funct_1,
% 24.62/4.17 reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, t5_subset,
% 24.62/4.17 t6_boole, t7_boole, t8_boole
% 24.62/4.17
% 24.62/4.17 Those formulas are unsatisfiable:
% 24.62/4.17 ---------------------------------
% 24.62/4.17
% 24.62/4.17 Begin of proof
% 24.62/4.17 |
% 24.62/4.17 | ALPHA: (cc2_funct_1) implies:
% 24.62/4.17 | (1) ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 24.62/4.17 | [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & relation(v0) = v1 &
% 24.62/4.17 | empty(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)))
% 24.62/4.17 | (2) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 24.62/4.17 | [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 &
% 24.62/4.17 | empty(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)))
% 24.62/4.17 | (3) ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ?
% 24.62/4.17 | [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 &
% 24.62/4.17 | function(v0) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) |
% 24.62/4.17 | ~ (v2 = 0) | v1 = 0)))
% 24.62/4.17 |
% 24.62/4.17 | ALPHA: (d1_funct_2) implies:
% 24.62/4.18 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 24.62/4.18 | (relation_of2_as_subset(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 24.62/4.18 | $i(v0) | ? [v3: any] : ? [v4: $i] : (relation_dom_as_subset(v0, v1,
% 24.62/4.18 | v2) = v4 & quasi_total(v2, v0, v1) = v3 & $i(v4) & ( ~ (v1 =
% 24.62/4.18 | empty_set) | v0 = empty_set | (( ~ (v3 = 0) | v2 = empty_set) &
% 24.62/4.18 | ( ~ (v2 = empty_set) | v3 = 0))) & ((v1 = empty_set & ~ (v0 =
% 24.62/4.18 | empty_set)) | (( ~ (v4 = v0) | v3 = 0) & ( ~ (v3 = 0) | v4 =
% 24.62/4.18 | v0)))))
% 24.62/4.18 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 24.62/4.18 | (quasi_total(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 24.62/4.18 | ? [v4: any] : ? [v5: $i] : (relation_dom_as_subset(v0, v1, v2) = v5
% 24.62/4.18 | & relation_of2_as_subset(v2, v0, v1) = v4 & $i(v5) & ( ~ (v4 = 0) |
% 24.62/4.18 | (( ~ (v1 = empty_set) | v0 = empty_set | (( ~ (v3 = 0) | v2 =
% 24.62/4.18 | empty_set) & ( ~ (v2 = empty_set) | v3 = 0))) & ((v1 =
% 24.62/4.18 | empty_set & ~ (v0 = empty_set)) | (( ~ (v5 = v0) | v3 = 0)
% 24.62/4.18 | & ( ~ (v3 = 0) | v5 = v0)))))))
% 24.62/4.18 |
% 24.62/4.18 | ALPHA: (dt_k4_relset_1) implies:
% 24.62/4.18 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_of2(v2, v0, v1)
% 24.62/4.18 | = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4:
% 24.62/4.18 | $i] : (relation_dom_as_subset(v0, v1, v2) = v3 & powerset(v0) = v4
% 24.62/4.18 | & element(v3, v4) = 0 & $i(v4) & $i(v3)))
% 24.62/4.18 |
% 24.62/4.18 | ALPHA: (dt_m2_relset_1) implies:
% 24.62/4.18 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 24.62/4.18 | (relation_of2_as_subset(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 24.62/4.18 | $i(v0) | ? [v3: $i] : ? [v4: $i] : (cartesian_product2(v0, v1) = v3
% 24.62/4.18 | & powerset(v3) = v4 & element(v2, v4) = 0 & $i(v4) & $i(v3)))
% 24.62/4.18 |
% 24.62/4.18 | ALPHA: (fc5_relat_1) implies:
% 24.62/4.18 | (8) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 24.62/4.18 | [v2: $i] : ? [v3: any] : (relation_dom(v0) = v2 & empty(v2) = v3 &
% 24.62/4.18 | empty(v0) = v1 & $i(v2) & ( ~ (v3 = 0) | v1 = 0)))
% 24.62/4.18 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) |
% 24.62/4.18 | ? [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 &
% 24.62/4.18 | empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 =
% 24.62/4.18 | 0)))
% 24.62/4.18 | (10) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0)
% 24.62/4.18 | | ? [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_dom(v0) = v3
% 24.62/4.18 | & relation(v0) = v2 & empty(v3) = v4 & $i(v3) & ( ~ (v4 = 0) | ~
% 24.62/4.18 | (v2 = 0))))
% 24.62/4.18 |
% 24.62/4.18 | ALPHA: (fc7_relat_1) implies:
% 24.62/4.18 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) |
% 24.62/4.18 | ? [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v1) = v4 &
% 24.62/4.18 | empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 =
% 24.62/4.18 | 0))))
% 24.62/4.18 |
% 24.62/4.18 | ALPHA: (rc1_subset_1) implies:
% 24.62/4.18 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ?
% 24.62/4.18 | [v2: int] : ? [v3: $i] : ? [v4: int] : ? [v5: int] : ($i(v3) &
% 24.62/4.18 | ((v4 = 0 & ~ (v5 = 0) & element(v3, v1) = 0 & empty(v3) = v5) |
% 24.62/4.18 | (v2 = 0 & empty(v0) = 0))))
% 24.62/4.19 | (13) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0)
% 24.62/4.19 | | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 24.62/4.19 | powerset(v0) = v2 & element(v3, v2) = 0 & empty(v3) = v4 & $i(v3)
% 24.62/4.19 | & $i(v2)))
% 24.62/4.19 |
% 24.62/4.19 | ALPHA: (redefinition_k4_relset_1) implies:
% 24.62/4.19 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_of2(v2, v0,
% 24.62/4.19 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 24.62/4.19 | (relation_dom(v2) = v3 & relation_dom_as_subset(v0, v1, v2) = v3 &
% 24.62/4.19 | $i(v3)))
% 24.62/4.19 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 24.62/4.19 | (relation_dom_as_subset(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 24.62/4.19 | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : (relation_dom(v2) = v5 &
% 24.62/4.19 | relation_of2(v2, v0, v1) = v4 & $i(v5) & ( ~ (v4 = 0) | v5 = v3)))
% 24.62/4.19 |
% 24.62/4.19 | ALPHA: (redefinition_m2_relset_1) implies:
% 24.62/4.19 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 24.62/4.19 | (relation_of2_as_subset(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) |
% 24.62/4.19 | ~ $i(v0) | relation_of2(v2, v0, v1) = 0)
% 24.62/4.19 |
% 24.62/4.19 | ALPHA: (t23_funct_1) implies:
% 24.62/4.19 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (apply(v1, v0) = v2) |
% 24.62/4.19 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 24.62/4.19 | ? [v6: any] : (relation_dom(v1) = v5 & relation(v1) = v3 &
% 24.62/4.19 | function(v1) = v4 & in(v0, v5) = v6 & $i(v5) & ( ~ (v4 = 0) | ~
% 24.62/4.19 | (v3 = 0) | ( ! [v7: $i] : ! [v8: $i] : ( ~ (v6 = 0) | ~
% 24.62/4.19 | (apply(v7, v2) = v8) | ~ $i(v7) | ? [v9: any] : ? [v10:
% 24.62/4.19 | any] : ? [v11: $i] : ? [v12: $i] : (apply(v11, v0) = v12
% 24.62/4.19 | & relation_composition(v1, v7) = v11 & relation(v7) = v9 &
% 24.62/4.19 | function(v7) = v10 & $i(v12) & $i(v11) & ( ~ (v10 = 0) |
% 24.62/4.19 | ~ (v9 = 0) | v12 = v8))) & ! [v7: $i] : ! [v8: $i] : (
% 24.62/4.19 | ~ (v6 = 0) | ~ (relation_composition(v1, v7) = v8) | ~
% 24.62/4.19 | $i(v7) | ? [v9: any] : ? [v10: any] : ? [v11: $i] : ?
% 24.62/4.19 | [v12: $i] : (apply(v8, v0) = v11 & apply(v7, v2) = v12 &
% 24.62/4.19 | relation(v7) = v9 & function(v7) = v10 & $i(v12) & $i(v11)
% 24.62/4.19 | & ( ~ (v10 = 0) | ~ (v9 = 0) | v12 = v11))) & ! [v7: $i]
% 24.62/4.19 | : ( ~ (v6 = 0) | ~ (relation(v7) = 0) | ~ $i(v7) | ? [v8:
% 24.62/4.19 | any] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] :
% 24.62/4.19 | (apply(v9, v0) = v10 & apply(v7, v2) = v11 &
% 24.62/4.19 | relation_composition(v1, v7) = v9 & function(v7) = v8 &
% 24.62/4.19 | $i(v11) & $i(v10) & $i(v9) & ( ~ (v8 = 0) | v11 = v10))) &
% 24.62/4.19 | ! [v7: $i] : ( ~ (v6 = 0) | ~ (function(v7) = 0) | ~ $i(v7)
% 24.62/4.19 | | ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] :
% 24.62/4.19 | (apply(v9, v0) = v10 & apply(v7, v2) = v11 &
% 24.62/4.19 | relation_composition(v1, v7) = v9 & relation(v7) = v8 &
% 24.62/4.19 | $i(v11) & $i(v10) & $i(v9) & ( ~ (v8 = 0) | v11 =
% 24.62/4.19 | v10)))))))
% 24.75/4.19 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 24.75/4.19 | (relation_dom(v1) = v2) | ~ (in(v0, v2) = v3) | ~ $i(v1) | ~
% 24.75/4.19 | $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: $i] : (apply(v1, v0)
% 24.75/4.19 | = v6 & relation(v1) = v4 & function(v1) = v5 & $i(v6) & ( ~ (v5 =
% 24.75/4.19 | 0) | ~ (v4 = 0) | ( ! [v7: $i] : ! [v8: $i] : ( ~ (v3 = 0) |
% 24.75/4.19 | ~ (apply(v7, v6) = v8) | ~ $i(v7) | ? [v9: any] : ?
% 24.75/4.20 | [v10: any] : ? [v11: $i] : ? [v12: $i] : (apply(v11, v0) =
% 24.75/4.20 | v12 & relation_composition(v1, v7) = v11 & relation(v7) =
% 24.75/4.20 | v9 & function(v7) = v10 & $i(v12) & $i(v11) & ( ~ (v10 =
% 24.75/4.20 | 0) | ~ (v9 = 0) | v12 = v8))) & ! [v7: $i] : ! [v8:
% 24.75/4.20 | $i] : ( ~ (v3 = 0) | ~ (relation_composition(v1, v7) = v8)
% 24.75/4.20 | | ~ $i(v7) | ? [v9: any] : ? [v10: any] : ? [v11: $i] :
% 24.75/4.20 | ? [v12: $i] : (apply(v8, v0) = v11 & apply(v7, v6) = v12 &
% 24.75/4.20 | relation(v7) = v9 & function(v7) = v10 & $i(v12) & $i(v11)
% 24.75/4.20 | & ( ~ (v10 = 0) | ~ (v9 = 0) | v12 = v11))) & ! [v7: $i]
% 24.75/4.20 | : ( ~ (v3 = 0) | ~ (relation(v7) = 0) | ~ $i(v7) | ? [v8:
% 24.75/4.20 | any] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] :
% 24.75/4.20 | (apply(v9, v0) = v10 & apply(v7, v6) = v11 &
% 24.75/4.20 | relation_composition(v1, v7) = v9 & function(v7) = v8 &
% 24.75/4.20 | $i(v11) & $i(v10) & $i(v9) & ( ~ (v8 = 0) | v11 = v10))) &
% 24.75/4.20 | ! [v7: $i] : ( ~ (v3 = 0) | ~ (function(v7) = 0) | ~ $i(v7)
% 24.75/4.20 | | ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] :
% 24.75/4.20 | (apply(v9, v0) = v10 & apply(v7, v6) = v11 &
% 24.75/4.20 | relation_composition(v1, v7) = v9 & relation(v7) = v8 &
% 24.75/4.20 | $i(v11) & $i(v10) & $i(v9) & ( ~ (v8 = 0) | v11 =
% 24.75/4.20 | v10)))))))
% 24.75/4.20 |
% 24.75/4.20 | ALPHA: (t21_funct_2) implies:
% 24.75/4.20 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 24.75/4.20 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ( ~ (v8 = v7) &
% 24.75/4.20 | ~ (v1 = empty_set) & apply(v6, v2) = v7 & apply(v5, v4) = v8 &
% 24.75/4.20 | apply(v3, v2) = v4 & relation_composition(v3, v5) = v6 &
% 24.75/4.20 | relation_of2_as_subset(v3, v0, v1) = 0 & quasi_total(v3, v0, v1) = 0
% 24.75/4.20 | & relation(v5) = 0 & function(v5) = 0 & function(v3) = 0 & in(v2,
% 24.75/4.20 | v0) = 0 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 24.75/4.20 | $i(v2) & $i(v1) & $i(v0))
% 24.75/4.20 |
% 24.75/4.20 | ALPHA: (function-axioms) implies:
% 24.75/4.20 | (20) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 24.75/4.20 | : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 24.75/4.20 | (21) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 24.75/4.20 | : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 24.75/4.20 | (22) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 24.75/4.20 | : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 24.75/4.20 | (23) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 24.75/4.20 | : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0))
% 24.75/4.20 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 24.75/4.20 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 24.75/4.20 | (25) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 24.75/4.20 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) =
% 24.75/4.20 | v0))
% 24.75/4.20 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.75/4.20 | (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3,
% 24.75/4.20 | v2) = v0))
% 24.75/4.20 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.75/4.20 | (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 24.75/4.20 | (28) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 24.75/4.20 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (quasi_total(v4, v3, v2) =
% 24.75/4.20 | v1) | ~ (quasi_total(v4, v3, v2) = v0))
% 24.75/4.20 | (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 24.75/4.20 | (v1 = v0 | ~ (relation_dom_as_subset(v4, v3, v2) = v1) | ~
% 24.75/4.20 | (relation_dom_as_subset(v4, v3, v2) = v0))
% 24.75/4.20 |
% 24.75/4.20 | DELTA: instantiating (rc2_relat_1) with fresh symbols all_45_0, all_45_1
% 24.75/4.20 | gives:
% 24.75/4.20 | (30) ~ (all_45_0 = 0) & relation(all_45_1) = 0 & empty(all_45_1) =
% 24.75/4.20 | all_45_0 & $i(all_45_1)
% 24.75/4.20 |
% 24.75/4.20 | ALPHA: (30) implies:
% 24.75/4.20 | (31) ~ (all_45_0 = 0)
% 24.75/4.20 | (32) $i(all_45_1)
% 24.75/4.20 | (33) empty(all_45_1) = all_45_0
% 24.75/4.20 | (34) relation(all_45_1) = 0
% 24.75/4.20 |
% 24.75/4.20 | DELTA: instantiating (19) with fresh symbols all_59_0, all_59_1, all_59_2,
% 24.75/4.20 | all_59_3, all_59_4, all_59_5, all_59_6, all_59_7, all_59_8 gives:
% 24.75/4.20 | (35) ~ (all_59_0 = all_59_1) & ~ (all_59_7 = empty_set) & apply(all_59_2,
% 24.75/4.20 | all_59_6) = all_59_1 & apply(all_59_3, all_59_4) = all_59_0 &
% 24.75/4.20 | apply(all_59_5, all_59_6) = all_59_4 & relation_composition(all_59_5,
% 24.75/4.20 | all_59_3) = all_59_2 & relation_of2_as_subset(all_59_5, all_59_8,
% 24.75/4.20 | all_59_7) = 0 & quasi_total(all_59_5, all_59_8, all_59_7) = 0 &
% 24.75/4.20 | relation(all_59_3) = 0 & function(all_59_3) = 0 & function(all_59_5) =
% 24.75/4.20 | 0 & in(all_59_6, all_59_8) = 0 & $i(all_59_0) & $i(all_59_1) &
% 24.75/4.20 | $i(all_59_2) & $i(all_59_3) & $i(all_59_4) & $i(all_59_5) &
% 24.75/4.20 | $i(all_59_6) & $i(all_59_7) & $i(all_59_8)
% 24.75/4.20 |
% 24.75/4.20 | ALPHA: (35) implies:
% 24.75/4.20 | (36) ~ (all_59_7 = empty_set)
% 24.75/4.20 | (37) ~ (all_59_0 = all_59_1)
% 24.75/4.20 | (38) $i(all_59_8)
% 24.75/4.20 | (39) $i(all_59_7)
% 24.75/4.20 | (40) $i(all_59_6)
% 24.75/4.20 | (41) $i(all_59_5)
% 24.75/4.20 | (42) $i(all_59_4)
% 24.75/4.20 | (43) $i(all_59_3)
% 24.75/4.20 | (44) $i(all_59_2)
% 24.75/4.20 | (45) in(all_59_6, all_59_8) = 0
% 24.75/4.20 | (46) function(all_59_5) = 0
% 24.75/4.20 | (47) function(all_59_3) = 0
% 24.75/4.20 | (48) relation(all_59_3) = 0
% 24.75/4.20 | (49) quasi_total(all_59_5, all_59_8, all_59_7) = 0
% 24.75/4.21 | (50) relation_of2_as_subset(all_59_5, all_59_8, all_59_7) = 0
% 24.75/4.21 | (51) relation_composition(all_59_5, all_59_3) = all_59_2
% 24.75/4.21 | (52) apply(all_59_5, all_59_6) = all_59_4
% 24.75/4.21 | (53) apply(all_59_3, all_59_4) = all_59_0
% 24.75/4.21 | (54) apply(all_59_2, all_59_6) = all_59_1
% 24.75/4.21 |
% 24.75/4.21 | GROUND_INST: instantiating (13) with all_45_1, all_45_0, simplifying with
% 24.75/4.21 | (32), (33) gives:
% 24.75/4.21 | (55) all_45_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0)
% 24.75/4.21 | & powerset(all_45_1) = v0 & element(v1, v0) = 0 & empty(v1) = v2 &
% 24.75/4.21 | $i(v1) & $i(v0))
% 24.75/4.21 |
% 24.75/4.21 | GROUND_INST: instantiating (10) with all_45_1, all_45_0, simplifying with
% 24.75/4.21 | (32), (33) gives:
% 24.75/4.21 | (56) all_45_0 = 0 | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 24.75/4.21 | (relation_dom(all_45_1) = v1 & relation(all_45_1) = v0 & empty(v1) =
% 24.75/4.21 | v2 & $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 24.75/4.21 |
% 24.75/4.21 | GROUND_INST: instantiating (1) with all_59_5, simplifying with (41), (46)
% 24.75/4.21 | gives:
% 24.75/4.21 | (57) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_59_5) =
% 24.75/4.21 | v2 & relation(all_59_5) = v0 & empty(all_59_5) = v1 & ( ~ (v1 = 0) |
% 24.75/4.21 | ~ (v0 = 0) | v2 = 0))
% 24.75/4.21 |
% 24.75/4.21 | GROUND_INST: instantiating (1) with all_59_3, simplifying with (43), (47)
% 24.75/4.21 | gives:
% 24.75/4.21 | (58) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_59_3) =
% 24.75/4.21 | v2 & relation(all_59_3) = v0 & empty(all_59_3) = v1 & ( ~ (v1 = 0) |
% 24.75/4.21 | ~ (v0 = 0) | v2 = 0))
% 24.75/4.21 |
% 24.75/4.21 | GROUND_INST: instantiating (8) with all_45_1, simplifying with (32), (34)
% 24.75/4.21 | gives:
% 24.75/4.21 | (59) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_dom(all_45_1) =
% 24.75/4.21 | v1 & empty(v1) = v2 & empty(all_45_1) = v0 & $i(v1) & ( ~ (v2 = 0) |
% 24.75/4.21 | v0 = 0))
% 24.75/4.21 |
% 24.75/4.21 | GROUND_INST: instantiating (2) with all_45_1, simplifying with (32), (34)
% 24.75/4.21 | gives:
% 24.75/4.21 | (60) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_45_1) =
% 24.75/4.21 | v2 & function(all_45_1) = v1 & empty(all_45_1) = v0 & ( ~ (v1 = 0) |
% 24.75/4.21 | ~ (v0 = 0) | v2 = 0))
% 24.75/4.21 |
% 24.75/4.21 | GROUND_INST: instantiating (8) with all_59_3, simplifying with (43), (48)
% 24.75/4.21 | gives:
% 24.75/4.21 | (61) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_dom(all_59_3) =
% 24.75/4.21 | v1 & empty(v1) = v2 & empty(all_59_3) = v0 & $i(v1) & ( ~ (v2 = 0) |
% 24.75/4.21 | v0 = 0))
% 24.75/4.21 |
% 24.75/4.21 | GROUND_INST: instantiating (2) with all_59_3, simplifying with (43), (48)
% 24.75/4.21 | gives:
% 24.75/4.21 | (62) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_59_3) =
% 24.75/4.21 | v2 & function(all_59_3) = v1 & empty(all_59_3) = v0 & ( ~ (v1 = 0) |
% 24.75/4.21 | ~ (v0 = 0) | v2 = 0))
% 24.75/4.21 |
% 24.75/4.21 | GROUND_INST: instantiating (5) with all_59_8, all_59_7, all_59_5, 0,
% 24.75/4.21 | simplifying with (38), (39), (41), (49) gives:
% 24.75/4.21 | (63) ? [v0: any] : ? [v1: $i] : (relation_dom_as_subset(all_59_8,
% 24.75/4.21 | all_59_7, all_59_5) = v1 & relation_of2_as_subset(all_59_5,
% 24.75/4.21 | all_59_8, all_59_7) = v0 & $i(v1) & ( ~ (v0 = 0) | (( ~ (all_59_7
% 24.75/4.21 | = empty_set) | all_59_5 = empty_set | all_59_8 = empty_set)
% 24.75/4.21 | & (v1 = all_59_8 | (all_59_7 = empty_set & ~ (all_59_8 =
% 24.75/4.21 | empty_set))))))
% 24.75/4.21 |
% 24.75/4.21 | GROUND_INST: instantiating (16) with all_59_8, all_59_7, all_59_5, simplifying
% 24.75/4.21 | with (38), (39), (41), (50) gives:
% 24.75/4.21 | (64) relation_of2(all_59_5, all_59_8, all_59_7) = 0
% 24.75/4.21 |
% 24.75/4.21 | GROUND_INST: instantiating (4) with all_59_8, all_59_7, all_59_5, simplifying
% 24.75/4.21 | with (38), (39), (41), (50) gives:
% 24.75/4.21 | (65) ? [v0: any] : ? [v1: $i] : (relation_dom_as_subset(all_59_8,
% 24.75/4.21 | all_59_7, all_59_5) = v1 & quasi_total(all_59_5, all_59_8,
% 24.75/4.21 | all_59_7) = v0 & $i(v1) & ( ~ (all_59_7 = empty_set) | all_59_8 =
% 24.75/4.21 | empty_set | (( ~ (v0 = 0) | all_59_5 = empty_set) & ( ~ (all_59_5
% 24.75/4.21 | = empty_set) | v0 = 0))) & ((all_59_7 = empty_set & ~
% 24.75/4.21 | (all_59_8 = empty_set)) | (( ~ (v1 = all_59_8) | v0 = 0) & ( ~
% 24.75/4.21 | (v0 = 0) | v1 = all_59_8))))
% 24.75/4.21 |
% 24.75/4.21 | GROUND_INST: instantiating (7) with all_59_8, all_59_7, all_59_5, simplifying
% 24.75/4.21 | with (38), (39), (41), (50) gives:
% 24.75/4.21 | (66) ? [v0: $i] : ? [v1: $i] : (cartesian_product2(all_59_8, all_59_7) =
% 24.75/4.21 | v0 & powerset(v0) = v1 & element(all_59_5, v1) = 0 & $i(v1) &
% 24.75/4.21 | $i(v0))
% 24.75/4.21 |
% 24.75/4.21 | GROUND_INST: instantiating (fc10_relat_1) with all_59_3, all_59_5, all_59_2,
% 24.75/4.21 | simplifying with (41), (43), (51) gives:
% 24.75/4.21 | (67) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 24.75/4.21 | (relation(all_59_2) = v3 & relation(all_59_5) = v1 & empty(all_59_2) =
% 24.75/4.21 | v2 & empty(all_59_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = 0 &
% 24.75/4.21 | v2 = 0)))
% 24.75/4.21 |
% 24.75/4.21 | GROUND_INST: instantiating (fc1_funct_1) with all_59_5, all_59_3, all_59_2,
% 24.75/4.21 | simplifying with (41), (43), (51) gives:
% 24.75/4.22 | (68) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 24.75/4.22 | any] : ? [v5: any] : (relation(all_59_2) = v4 & relation(all_59_3)
% 24.75/4.22 | = v2 & relation(all_59_5) = v0 & function(all_59_2) = v5 &
% 24.75/4.22 | function(all_59_3) = v3 & function(all_59_5) = v1 & ( ~ (v3 = 0) |
% 24.75/4.22 | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v5 = 0 & v4 = 0)))
% 24.75/4.22 |
% 24.75/4.22 | GROUND_INST: instantiating (fc9_relat_1) with all_59_5, all_59_3, all_59_2,
% 24.75/4.22 | simplifying with (41), (43), (51) gives:
% 24.75/4.22 | (69) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 24.75/4.22 | (relation(all_59_2) = v3 & relation(all_59_3) = v1 & empty(all_59_2) =
% 24.75/4.22 | v2 & empty(all_59_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = 0 &
% 24.75/4.22 | v2 = 0)))
% 24.75/4.22 |
% 24.75/4.22 | GROUND_INST: instantiating (dt_k5_relat_1) with all_59_5, all_59_3, all_59_2,
% 24.75/4.22 | simplifying with (41), (43), (51) gives:
% 24.75/4.22 | (70) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_59_2) = v2
% 24.75/4.22 | & relation(all_59_3) = v1 & relation(all_59_5) = v0 & ( ~ (v1 = 0) |
% 24.75/4.22 | ~ (v0 = 0) | v2 = 0))
% 24.75/4.22 |
% 24.75/4.22 | GROUND_INST: instantiating (17) with all_59_6, all_59_5, all_59_4, simplifying
% 24.75/4.22 | with (40), (41), (52) gives:
% 24.75/4.22 | (71) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 24.75/4.22 | (relation_dom(all_59_5) = v2 & relation(all_59_5) = v0 &
% 24.75/4.22 | function(all_59_5) = v1 & in(all_59_6, v2) = v3 & $i(v2) & ( ~ (v1 =
% 24.75/4.22 | 0) | ~ (v0 = 0) | ( ! [v4: $i] : ! [v5: $i] : ( ~ (v3 = 0) |
% 24.75/4.22 | ~ (apply(v4, all_59_4) = v5) | ~ $i(v4) | ? [v6: any] : ?
% 24.75/4.22 | [v7: any] : ? [v8: $i] : ? [v9: $i] : (apply(v8, all_59_6) =
% 24.75/4.22 | v9 & relation_composition(all_59_5, v4) = v8 & relation(v4)
% 24.75/4.22 | = v6 & function(v4) = v7 & $i(v9) & $i(v8) & ( ~ (v7 = 0) |
% 24.75/4.22 | ~ (v6 = 0) | v9 = v5))) & ! [v4: $i] : ! [v5: $i] : ( ~
% 24.75/4.22 | (v3 = 0) | ~ (relation_composition(all_59_5, v4) = v5) | ~
% 24.75/4.22 | $i(v4) | ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9:
% 24.75/4.22 | $i] : (apply(v5, all_59_6) = v8 & apply(v4, all_59_4) = v9 &
% 24.75/4.22 | relation(v4) = v6 & function(v4) = v7 & $i(v9) & $i(v8) & (
% 24.75/4.22 | ~ (v7 = 0) | ~ (v6 = 0) | v9 = v8))) & ! [v4: $i] : ( ~
% 24.75/4.22 | (v3 = 0) | ~ (relation(v4) = 0) | ~ $i(v4) | ? [v5: any] :
% 24.75/4.22 | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (apply(v6, all_59_6)
% 24.75/4.22 | = v7 & apply(v4, all_59_4) = v8 &
% 24.75/4.22 | relation_composition(all_59_5, v4) = v6 & function(v4) = v5
% 24.75/4.22 | & $i(v8) & $i(v7) & $i(v6) & ( ~ (v5 = 0) | v8 = v7))) & !
% 24.75/4.22 | [v4: $i] : ( ~ (v3 = 0) | ~ (function(v4) = 0) | ~ $i(v4) | ?
% 24.75/4.22 | [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 24.75/4.22 | (apply(v6, all_59_6) = v7 & apply(v4, all_59_4) = v8 &
% 24.75/4.22 | relation_composition(all_59_5, v4) = v6 & relation(v4) = v5
% 24.75/4.22 | & $i(v8) & $i(v7) & $i(v6) & ( ~ (v5 = 0) | v8 = v7))))))
% 24.75/4.22 |
% 24.75/4.22 | GROUND_INST: instantiating (17) with all_59_4, all_59_3, all_59_0, simplifying
% 24.75/4.22 | with (42), (43), (53) gives:
% 24.75/4.22 | (72) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 24.75/4.22 | (relation_dom(all_59_3) = v2 & relation(all_59_3) = v0 &
% 24.75/4.22 | function(all_59_3) = v1 & in(all_59_4, v2) = v3 & $i(v2) & ( ~ (v1 =
% 24.75/4.22 | 0) | ~ (v0 = 0) | ( ! [v4: $i] : ! [v5: $i] : ( ~ (v3 = 0) |
% 24.75/4.22 | ~ (apply(v4, all_59_0) = v5) | ~ $i(v4) | ? [v6: any] : ?
% 24.75/4.22 | [v7: any] : ? [v8: $i] : ? [v9: $i] : (apply(v8, all_59_4) =
% 24.75/4.22 | v9 & relation_composition(all_59_3, v4) = v8 & relation(v4)
% 24.75/4.22 | = v6 & function(v4) = v7 & $i(v9) & $i(v8) & ( ~ (v7 = 0) |
% 24.75/4.22 | ~ (v6 = 0) | v9 = v5))) & ! [v4: $i] : ! [v5: $i] : ( ~
% 24.75/4.22 | (v3 = 0) | ~ (relation_composition(all_59_3, v4) = v5) | ~
% 24.75/4.22 | $i(v4) | ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9:
% 24.75/4.22 | $i] : (apply(v5, all_59_4) = v8 & apply(v4, all_59_0) = v9 &
% 24.75/4.22 | relation(v4) = v6 & function(v4) = v7 & $i(v9) & $i(v8) & (
% 24.75/4.22 | ~ (v7 = 0) | ~ (v6 = 0) | v9 = v8))) & ! [v4: $i] : ( ~
% 24.75/4.22 | (v3 = 0) | ~ (relation(v4) = 0) | ~ $i(v4) | ? [v5: any] :
% 24.75/4.22 | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (apply(v6, all_59_4)
% 24.75/4.22 | = v7 & apply(v4, all_59_0) = v8 &
% 24.75/4.22 | relation_composition(all_59_3, v4) = v6 & function(v4) = v5
% 24.75/4.22 | & $i(v8) & $i(v7) & $i(v6) & ( ~ (v5 = 0) | v8 = v7))) & !
% 24.75/4.22 | [v4: $i] : ( ~ (v3 = 0) | ~ (function(v4) = 0) | ~ $i(v4) | ?
% 24.75/4.22 | [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 24.75/4.22 | (apply(v6, all_59_4) = v7 & apply(v4, all_59_0) = v8 &
% 24.75/4.22 | relation_composition(all_59_3, v4) = v6 & relation(v4) = v5
% 24.75/4.22 | & $i(v8) & $i(v7) & $i(v6) & ( ~ (v5 = 0) | v8 = v7))))))
% 24.75/4.22 |
% 24.75/4.22 | GROUND_INST: instantiating (17) with all_59_6, all_59_2, all_59_1, simplifying
% 24.75/4.22 | with (40), (44), (54) gives:
% 24.90/4.23 | (73) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 24.90/4.23 | (relation_dom(all_59_2) = v2 & relation(all_59_2) = v0 &
% 24.90/4.23 | function(all_59_2) = v1 & in(all_59_6, v2) = v3 & $i(v2) & ( ~ (v1 =
% 24.90/4.23 | 0) | ~ (v0 = 0) | ( ! [v4: $i] : ! [v5: $i] : ( ~ (v3 = 0) |
% 24.90/4.23 | ~ (apply(v4, all_59_1) = v5) | ~ $i(v4) | ? [v6: any] : ?
% 24.90/4.23 | [v7: any] : ? [v8: $i] : ? [v9: $i] : (apply(v8, all_59_6) =
% 24.90/4.23 | v9 & relation_composition(all_59_2, v4) = v8 & relation(v4)
% 24.90/4.23 | = v6 & function(v4) = v7 & $i(v9) & $i(v8) & ( ~ (v7 = 0) |
% 24.90/4.23 | ~ (v6 = 0) | v9 = v5))) & ! [v4: $i] : ! [v5: $i] : ( ~
% 24.90/4.23 | (v3 = 0) | ~ (relation_composition(all_59_2, v4) = v5) | ~
% 24.90/4.23 | $i(v4) | ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9:
% 24.90/4.23 | $i] : (apply(v5, all_59_6) = v8 & apply(v4, all_59_1) = v9 &
% 24.90/4.23 | relation(v4) = v6 & function(v4) = v7 & $i(v9) & $i(v8) & (
% 24.90/4.23 | ~ (v7 = 0) | ~ (v6 = 0) | v9 = v8))) & ! [v4: $i] : ( ~
% 24.90/4.23 | (v3 = 0) | ~ (relation(v4) = 0) | ~ $i(v4) | ? [v5: any] :
% 24.90/4.23 | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (apply(v6, all_59_6)
% 24.90/4.23 | = v7 & apply(v4, all_59_1) = v8 &
% 24.90/4.23 | relation_composition(all_59_2, v4) = v6 & function(v4) = v5
% 24.90/4.23 | & $i(v8) & $i(v7) & $i(v6) & ( ~ (v5 = 0) | v8 = v7))) & !
% 24.90/4.23 | [v4: $i] : ( ~ (v3 = 0) | ~ (function(v4) = 0) | ~ $i(v4) | ?
% 24.90/4.23 | [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 24.90/4.23 | (apply(v6, all_59_6) = v7 & apply(v4, all_59_1) = v8 &
% 24.90/4.23 | relation_composition(all_59_2, v4) = v6 & relation(v4) = v5
% 24.90/4.23 | & $i(v8) & $i(v7) & $i(v6) & ( ~ (v5 = 0) | v8 = v7))))))
% 24.90/4.23 |
% 24.90/4.23 | DELTA: instantiating (66) with fresh symbols all_93_0, all_93_1 gives:
% 24.90/4.23 | (74) cartesian_product2(all_59_8, all_59_7) = all_93_1 & powerset(all_93_1)
% 24.90/4.23 | = all_93_0 & element(all_59_5, all_93_0) = 0 & $i(all_93_0) &
% 24.90/4.23 | $i(all_93_1)
% 24.90/4.23 |
% 24.90/4.23 | ALPHA: (74) implies:
% 24.90/4.23 | (75) element(all_59_5, all_93_0) = 0
% 24.90/4.23 | (76) powerset(all_93_1) = all_93_0
% 24.90/4.23 | (77) cartesian_product2(all_59_8, all_59_7) = all_93_1
% 24.90/4.23 |
% 24.90/4.23 | DELTA: instantiating (62) with fresh symbols all_97_0, all_97_1, all_97_2
% 24.90/4.23 | gives:
% 24.92/4.23 | (78) one_to_one(all_59_3) = all_97_0 & function(all_59_3) = all_97_1 &
% 24.92/4.23 | empty(all_59_3) = all_97_2 & ( ~ (all_97_1 = 0) | ~ (all_97_2 = 0) |
% 24.92/4.23 | all_97_0 = 0)
% 24.92/4.23 |
% 24.92/4.23 | ALPHA: (78) implies:
% 24.92/4.23 | (79) function(all_59_3) = all_97_1
% 24.92/4.23 | (80) one_to_one(all_59_3) = all_97_0
% 24.92/4.23 |
% 24.92/4.23 | DELTA: instantiating (61) with fresh symbols all_99_0, all_99_1, all_99_2
% 24.92/4.23 | gives:
% 24.92/4.23 | (81) relation_dom(all_59_3) = all_99_1 & empty(all_99_1) = all_99_0 &
% 24.92/4.23 | empty(all_59_3) = all_99_2 & $i(all_99_1) & ( ~ (all_99_0 = 0) |
% 24.92/4.23 | all_99_2 = 0)
% 24.92/4.23 |
% 24.92/4.23 | ALPHA: (81) implies:
% 24.92/4.23 | (82) relation_dom(all_59_3) = all_99_1
% 24.92/4.23 |
% 24.92/4.23 | DELTA: instantiating (57) with fresh symbols all_109_0, all_109_1, all_109_2
% 24.92/4.23 | gives:
% 24.92/4.23 | (83) one_to_one(all_59_5) = all_109_0 & relation(all_59_5) = all_109_2 &
% 24.92/4.23 | empty(all_59_5) = all_109_1 & ( ~ (all_109_1 = 0) | ~ (all_109_2 = 0)
% 24.92/4.23 | | all_109_0 = 0)
% 24.92/4.23 |
% 24.92/4.23 | ALPHA: (83) implies:
% 24.92/4.23 | (84) relation(all_59_5) = all_109_2
% 24.92/4.23 | (85) one_to_one(all_59_5) = all_109_0
% 24.92/4.23 |
% 24.92/4.23 | DELTA: instantiating (59) with fresh symbols all_125_0, all_125_1, all_125_2
% 24.92/4.23 | gives:
% 24.92/4.23 | (86) relation_dom(all_45_1) = all_125_1 & empty(all_125_1) = all_125_0 &
% 24.92/4.23 | empty(all_45_1) = all_125_2 & $i(all_125_1) & ( ~ (all_125_0 = 0) |
% 24.92/4.23 | all_125_2 = 0)
% 24.92/4.23 |
% 24.92/4.23 | ALPHA: (86) implies:
% 24.92/4.23 | (87) empty(all_45_1) = all_125_2
% 24.92/4.23 | (88) relation_dom(all_45_1) = all_125_1
% 24.92/4.23 |
% 24.92/4.23 | DELTA: instantiating (60) with fresh symbols all_129_0, all_129_1, all_129_2
% 24.92/4.23 | gives:
% 24.92/4.23 | (89) one_to_one(all_45_1) = all_129_0 & function(all_45_1) = all_129_1 &
% 24.92/4.23 | empty(all_45_1) = all_129_2 & ( ~ (all_129_1 = 0) | ~ (all_129_2 = 0)
% 24.92/4.23 | | all_129_0 = 0)
% 24.92/4.23 |
% 24.92/4.23 | ALPHA: (89) implies:
% 24.92/4.23 | (90) empty(all_45_1) = all_129_2
% 24.92/4.23 |
% 24.92/4.23 | DELTA: instantiating (70) with fresh symbols all_131_0, all_131_1, all_131_2
% 24.92/4.23 | gives:
% 24.92/4.23 | (91) relation(all_59_2) = all_131_0 & relation(all_59_3) = all_131_1 &
% 24.92/4.23 | relation(all_59_5) = all_131_2 & ( ~ (all_131_1 = 0) | ~ (all_131_2 =
% 24.92/4.23 | 0) | all_131_0 = 0)
% 24.92/4.23 |
% 24.92/4.23 | ALPHA: (91) implies:
% 24.92/4.23 | (92) relation(all_59_5) = all_131_2
% 24.92/4.23 | (93) relation(all_59_3) = all_131_1
% 24.92/4.23 |
% 24.92/4.23 | DELTA: instantiating (58) with fresh symbols all_153_0, all_153_1, all_153_2
% 24.92/4.23 | gives:
% 24.92/4.23 | (94) one_to_one(all_59_3) = all_153_0 & relation(all_59_3) = all_153_2 &
% 24.92/4.23 | empty(all_59_3) = all_153_1 & ( ~ (all_153_1 = 0) | ~ (all_153_2 = 0)
% 24.92/4.23 | | all_153_0 = 0)
% 24.92/4.23 |
% 24.92/4.23 | ALPHA: (94) implies:
% 24.92/4.23 | (95) relation(all_59_3) = all_153_2
% 24.92/4.23 | (96) one_to_one(all_59_3) = all_153_0
% 24.92/4.23 |
% 24.92/4.23 | DELTA: instantiating (69) with fresh symbols all_155_0, all_155_1, all_155_2,
% 24.92/4.23 | all_155_3 gives:
% 24.92/4.23 | (97) relation(all_59_2) = all_155_0 & relation(all_59_3) = all_155_2 &
% 24.92/4.23 | empty(all_59_2) = all_155_1 & empty(all_59_5) = all_155_3 & ( ~
% 24.92/4.23 | (all_155_2 = 0) | ~ (all_155_3 = 0) | (all_155_0 = 0 & all_155_1 =
% 24.92/4.23 | 0))
% 24.92/4.23 |
% 24.92/4.23 | ALPHA: (97) implies:
% 24.92/4.23 | (98) relation(all_59_3) = all_155_2
% 24.92/4.23 |
% 24.92/4.23 | DELTA: instantiating (67) with fresh symbols all_157_0, all_157_1, all_157_2,
% 24.92/4.23 | all_157_3 gives:
% 24.92/4.23 | (99) relation(all_59_2) = all_157_0 & relation(all_59_5) = all_157_2 &
% 24.92/4.23 | empty(all_59_2) = all_157_1 & empty(all_59_3) = all_157_3 & ( ~
% 24.92/4.23 | (all_157_2 = 0) | ~ (all_157_3 = 0) | (all_157_0 = 0 & all_157_1 =
% 24.92/4.23 | 0))
% 24.92/4.23 |
% 24.92/4.23 | ALPHA: (99) implies:
% 24.92/4.23 | (100) relation(all_59_5) = all_157_2
% 24.92/4.23 |
% 24.92/4.23 | DELTA: instantiating (63) with fresh symbols all_159_0, all_159_1 gives:
% 24.92/4.23 | (101) relation_dom_as_subset(all_59_8, all_59_7, all_59_5) = all_159_0 &
% 24.92/4.23 | relation_of2_as_subset(all_59_5, all_59_8, all_59_7) = all_159_1 &
% 24.92/4.23 | $i(all_159_0) & ( ~ (all_159_1 = 0) | (( ~ (all_59_7 = empty_set) |
% 24.92/4.23 | all_59_5 = empty_set | all_59_8 = empty_set) & (all_159_0 =
% 24.92/4.23 | all_59_8 | (all_59_7 = empty_set & ~ (all_59_8 =
% 24.92/4.23 | empty_set)))))
% 24.92/4.23 |
% 24.92/4.23 | ALPHA: (101) implies:
% 24.92/4.23 | (102) relation_dom_as_subset(all_59_8, all_59_7, all_59_5) = all_159_0
% 24.92/4.23 |
% 24.92/4.23 | DELTA: instantiating (68) with fresh symbols all_161_0, all_161_1, all_161_2,
% 24.92/4.23 | all_161_3, all_161_4, all_161_5 gives:
% 24.92/4.23 | (103) relation(all_59_2) = all_161_1 & relation(all_59_3) = all_161_3 &
% 24.92/4.23 | relation(all_59_5) = all_161_5 & function(all_59_2) = all_161_0 &
% 24.92/4.23 | function(all_59_3) = all_161_2 & function(all_59_5) = all_161_4 & ( ~
% 24.92/4.23 | (all_161_2 = 0) | ~ (all_161_3 = 0) | ~ (all_161_4 = 0) | ~
% 24.92/4.23 | (all_161_5 = 0) | (all_161_0 = 0 & all_161_1 = 0))
% 24.92/4.23 |
% 24.92/4.23 | ALPHA: (103) implies:
% 24.92/4.23 | (104) function(all_59_5) = all_161_4
% 24.92/4.23 | (105) function(all_59_3) = all_161_2
% 24.92/4.23 | (106) relation(all_59_5) = all_161_5
% 24.92/4.23 | (107) relation(all_59_3) = all_161_3
% 24.92/4.23 |
% 24.92/4.23 | DELTA: instantiating (65) with fresh symbols all_163_0, all_163_1 gives:
% 24.92/4.23 | (108) relation_dom_as_subset(all_59_8, all_59_7, all_59_5) = all_163_0 &
% 24.92/4.23 | quasi_total(all_59_5, all_59_8, all_59_7) = all_163_1 & $i(all_163_0)
% 24.92/4.23 | & ( ~ (all_59_7 = empty_set) | all_59_8 = empty_set | (( ~ (all_163_1
% 24.92/4.23 | = 0) | all_59_5 = empty_set) & ( ~ (all_59_5 = empty_set) |
% 24.92/4.23 | all_163_1 = 0))) & ((all_59_7 = empty_set & ~ (all_59_8 =
% 24.92/4.23 | empty_set)) | (( ~ (all_163_0 = all_59_8) | all_163_1 = 0) & (
% 24.92/4.23 | ~ (all_163_1 = 0) | all_163_0 = all_59_8)))
% 24.92/4.23 |
% 24.92/4.23 | ALPHA: (108) implies:
% 24.92/4.23 | (109) $i(all_163_0)
% 24.92/4.23 | (110) quasi_total(all_59_5, all_59_8, all_59_7) = all_163_1
% 24.92/4.23 | (111) relation_dom_as_subset(all_59_8, all_59_7, all_59_5) = all_163_0
% 24.92/4.24 | (112) (all_59_7 = empty_set & ~ (all_59_8 = empty_set)) | (( ~ (all_163_0
% 24.92/4.24 | = all_59_8) | all_163_1 = 0) & ( ~ (all_163_1 = 0) | all_163_0
% 24.92/4.24 | = all_59_8))
% 24.92/4.24 |
% 24.92/4.24 | DELTA: instantiating (71) with fresh symbols all_165_0, all_165_1, all_165_2,
% 24.92/4.24 | all_165_3 gives:
% 24.92/4.24 | (113) relation_dom(all_59_5) = all_165_1 & relation(all_59_5) = all_165_3 &
% 24.92/4.24 | function(all_59_5) = all_165_2 & in(all_59_6, all_165_1) = all_165_0
% 24.92/4.24 | & $i(all_165_1) & ( ~ (all_165_2 = 0) | ~ (all_165_3 = 0) | ( ! [v0:
% 24.92/4.24 | $i] : ! [v1: $i] : ( ~ (all_165_0 = 0) | ~ (apply(v0,
% 24.92/4.24 | all_59_4) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 24.92/4.24 | ? [v4: $i] : ? [v5: $i] : (apply(v4, all_59_6) = v5 &
% 24.92/4.24 | relation_composition(all_59_5, v0) = v4 & relation(v0) = v2 &
% 24.92/4.24 | function(v0) = v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | ~ (v2 =
% 24.92/4.24 | 0) | v5 = v1))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 24.92/4.24 | (all_165_0 = 0) | ~ (relation_composition(all_59_5, v0) = v1)
% 24.92/4.24 | | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ?
% 24.92/4.24 | [v5: $i] : (apply(v1, all_59_6) = v4 & apply(v0, all_59_4) = v5
% 24.92/4.24 | & relation(v0) = v2 & function(v0) = v3 & $i(v5) & $i(v4) & (
% 24.92/4.24 | ~ (v3 = 0) | ~ (v2 = 0) | v5 = v4))) & ! [v0: $i] : ( ~
% 24.92/4.24 | (all_165_0 = 0) | ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1:
% 24.92/4.24 | any] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (apply(v2,
% 24.92/4.24 | all_59_6) = v3 & apply(v0, all_59_4) = v4 &
% 24.92/4.24 | relation_composition(all_59_5, v0) = v2 & function(v0) = v1 &
% 24.92/4.24 | $i(v4) & $i(v3) & $i(v2) & ( ~ (v1 = 0) | v4 = v3))) & !
% 24.92/4.24 | [v0: $i] : ( ~ (all_165_0 = 0) | ~ (function(v0) = 0) | ~
% 24.92/4.24 | $i(v0) | ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 24.92/4.24 | : (apply(v2, all_59_6) = v3 & apply(v0, all_59_4) = v4 &
% 24.92/4.24 | relation_composition(all_59_5, v0) = v2 & relation(v0) = v1 &
% 24.92/4.24 | $i(v4) & $i(v3) & $i(v2) & ( ~ (v1 = 0) | v4 = v3)))))
% 24.92/4.24 |
% 24.92/4.24 | ALPHA: (113) implies:
% 24.92/4.24 | (114) in(all_59_6, all_165_1) = all_165_0
% 24.92/4.24 | (115) function(all_59_5) = all_165_2
% 24.92/4.24 | (116) relation(all_59_5) = all_165_3
% 24.92/4.24 | (117) relation_dom(all_59_5) = all_165_1
% 24.92/4.24 | (118) ~ (all_165_2 = 0) | ~ (all_165_3 = 0) | ( ! [v0: $i] : ! [v1: $i]
% 24.92/4.24 | : ( ~ (all_165_0 = 0) | ~ (apply(v0, all_59_4) = v1) | ~ $i(v0) |
% 24.92/4.24 | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5: $i] :
% 24.92/4.24 | (apply(v4, all_59_6) = v5 & relation_composition(all_59_5, v0) =
% 24.92/4.24 | v4 & relation(v0) = v2 & function(v0) = v3 & $i(v5) & $i(v4) &
% 24.92/4.24 | ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = v1))) & ! [v0: $i] : ! [v1:
% 24.92/4.24 | $i] : ( ~ (all_165_0 = 0) | ~ (relation_composition(all_59_5,
% 24.92/4.24 | v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4:
% 24.92/4.24 | $i] : ? [v5: $i] : (apply(v1, all_59_6) = v4 & apply(v0,
% 24.92/4.24 | all_59_4) = v5 & relation(v0) = v2 & function(v0) = v3 &
% 24.92/4.24 | $i(v5) & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = v4))) & !
% 24.92/4.24 | [v0: $i] : ( ~ (all_165_0 = 0) | ~ (relation(v0) = 0) | ~ $i(v0)
% 24.92/4.24 | | ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 24.92/4.24 | (apply(v2, all_59_6) = v3 & apply(v0, all_59_4) = v4 &
% 24.92/4.24 | relation_composition(all_59_5, v0) = v2 & function(v0) = v1 &
% 24.92/4.24 | $i(v4) & $i(v3) & $i(v2) & ( ~ (v1 = 0) | v4 = v3))) & ! [v0:
% 24.92/4.24 | $i] : ( ~ (all_165_0 = 0) | ~ (function(v0) = 0) | ~ $i(v0) |
% 24.92/4.24 | ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 24.92/4.24 | (apply(v2, all_59_6) = v3 & apply(v0, all_59_4) = v4 &
% 24.92/4.24 | relation_composition(all_59_5, v0) = v2 & relation(v0) = v1 &
% 24.92/4.24 | $i(v4) & $i(v3) & $i(v2) & ( ~ (v1 = 0) | v4 = v3))))
% 24.92/4.24 |
% 24.92/4.24 | DELTA: instantiating (73) with fresh symbols all_167_0, all_167_1, all_167_2,
% 24.92/4.24 | all_167_3 gives:
% 24.92/4.24 | (119) relation_dom(all_59_2) = all_167_1 & relation(all_59_2) = all_167_3 &
% 24.92/4.24 | function(all_59_2) = all_167_2 & in(all_59_6, all_167_1) = all_167_0
% 24.92/4.24 | & $i(all_167_1) & ( ~ (all_167_2 = 0) | ~ (all_167_3 = 0) | ( ! [v0:
% 24.92/4.24 | $i] : ! [v1: $i] : ( ~ (all_167_0 = 0) | ~ (apply(v0,
% 24.92/4.24 | all_59_1) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 24.92/4.24 | ? [v4: $i] : ? [v5: $i] : (apply(v4, all_59_6) = v5 &
% 24.92/4.24 | relation_composition(all_59_2, v0) = v4 & relation(v0) = v2 &
% 24.92/4.24 | function(v0) = v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | ~ (v2 =
% 24.92/4.24 | 0) | v5 = v1))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 24.92/4.24 | (all_167_0 = 0) | ~ (relation_composition(all_59_2, v0) = v1)
% 24.92/4.24 | | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ?
% 24.92/4.24 | [v5: $i] : (apply(v1, all_59_6) = v4 & apply(v0, all_59_1) = v5
% 24.92/4.24 | & relation(v0) = v2 & function(v0) = v3 & $i(v5) & $i(v4) & (
% 24.92/4.24 | ~ (v3 = 0) | ~ (v2 = 0) | v5 = v4))) & ! [v0: $i] : ( ~
% 24.92/4.24 | (all_167_0 = 0) | ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1:
% 24.92/4.24 | any] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (apply(v2,
% 24.92/4.24 | all_59_6) = v3 & apply(v0, all_59_1) = v4 &
% 24.92/4.24 | relation_composition(all_59_2, v0) = v2 & function(v0) = v1 &
% 24.92/4.24 | $i(v4) & $i(v3) & $i(v2) & ( ~ (v1 = 0) | v4 = v3))) & !
% 24.92/4.24 | [v0: $i] : ( ~ (all_167_0 = 0) | ~ (function(v0) = 0) | ~
% 24.92/4.24 | $i(v0) | ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 24.92/4.24 | : (apply(v2, all_59_6) = v3 & apply(v0, all_59_1) = v4 &
% 24.92/4.24 | relation_composition(all_59_2, v0) = v2 & relation(v0) = v1 &
% 24.92/4.24 | $i(v4) & $i(v3) & $i(v2) & ( ~ (v1 = 0) | v4 = v3)))))
% 24.92/4.24 |
% 24.92/4.24 | ALPHA: (119) implies:
% 24.92/4.24 | (120) in(all_59_6, all_167_1) = all_167_0
% 24.92/4.24 | (121) relation_dom(all_59_2) = all_167_1
% 24.92/4.24 |
% 24.92/4.24 | DELTA: instantiating (72) with fresh symbols all_169_0, all_169_1, all_169_2,
% 24.92/4.24 | all_169_3 gives:
% 24.92/4.24 | (122) relation_dom(all_59_3) = all_169_1 & relation(all_59_3) = all_169_3 &
% 24.92/4.24 | function(all_59_3) = all_169_2 & in(all_59_4, all_169_1) = all_169_0
% 24.92/4.24 | & $i(all_169_1) & ( ~ (all_169_2 = 0) | ~ (all_169_3 = 0) | ( ! [v0:
% 24.92/4.24 | $i] : ! [v1: $i] : ( ~ (all_169_0 = 0) | ~ (apply(v0,
% 24.92/4.24 | all_59_0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 24.92/4.24 | ? [v4: $i] : ? [v5: $i] : (apply(v4, all_59_4) = v5 &
% 24.92/4.24 | relation_composition(all_59_3, v0) = v4 & relation(v0) = v2 &
% 24.92/4.24 | function(v0) = v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | ~ (v2 =
% 24.92/4.24 | 0) | v5 = v1))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 24.92/4.24 | (all_169_0 = 0) | ~ (relation_composition(all_59_3, v0) = v1)
% 24.92/4.24 | | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ?
% 24.92/4.24 | [v5: $i] : (apply(v1, all_59_4) = v4 & apply(v0, all_59_0) = v5
% 24.92/4.25 | & relation(v0) = v2 & function(v0) = v3 & $i(v5) & $i(v4) & (
% 24.92/4.25 | ~ (v3 = 0) | ~ (v2 = 0) | v5 = v4))) & ! [v0: $i] : ( ~
% 24.92/4.25 | (all_169_0 = 0) | ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1:
% 24.92/4.25 | any] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (apply(v2,
% 24.92/4.25 | all_59_4) = v3 & apply(v0, all_59_0) = v4 &
% 24.92/4.25 | relation_composition(all_59_3, v0) = v2 & function(v0) = v1 &
% 24.92/4.25 | $i(v4) & $i(v3) & $i(v2) & ( ~ (v1 = 0) | v4 = v3))) & !
% 24.92/4.25 | [v0: $i] : ( ~ (all_169_0 = 0) | ~ (function(v0) = 0) | ~
% 24.92/4.25 | $i(v0) | ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 24.92/4.25 | : (apply(v2, all_59_4) = v3 & apply(v0, all_59_0) = v4 &
% 24.92/4.25 | relation_composition(all_59_3, v0) = v2 & relation(v0) = v1 &
% 24.92/4.25 | $i(v4) & $i(v3) & $i(v2) & ( ~ (v1 = 0) | v4 = v3)))))
% 24.92/4.25 |
% 24.92/4.25 | ALPHA: (122) implies:
% 24.92/4.25 | (123) in(all_59_4, all_169_1) = all_169_0
% 24.92/4.25 | (124) function(all_59_3) = all_169_2
% 24.92/4.25 | (125) relation(all_59_3) = all_169_3
% 24.92/4.25 | (126) relation_dom(all_59_3) = all_169_1
% 24.92/4.25 |
% 24.92/4.25 | BETA: splitting (56) gives:
% 24.92/4.25 |
% 24.92/4.25 | Case 1:
% 24.92/4.25 | |
% 24.92/4.25 | | (127) all_45_0 = 0
% 24.92/4.25 | |
% 24.92/4.25 | | REDUCE: (31), (127) imply:
% 24.92/4.25 | | (128) $false
% 24.92/4.25 | |
% 24.92/4.25 | | CLOSE: (128) is inconsistent.
% 24.92/4.25 | |
% 24.92/4.25 | Case 2:
% 24.92/4.25 | |
% 24.92/4.25 | | (129) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_dom(all_45_1)
% 24.92/4.25 | | = v1 & relation(all_45_1) = v0 & empty(v1) = v2 & $i(v1) & ( ~
% 24.92/4.25 | | (v2 = 0) | ~ (v0 = 0)))
% 24.92/4.25 | |
% 24.92/4.25 | | DELTA: instantiating (129) with fresh symbols all_175_0, all_175_1,
% 24.92/4.25 | | all_175_2 gives:
% 24.92/4.25 | | (130) relation_dom(all_45_1) = all_175_1 & relation(all_45_1) = all_175_2
% 24.92/4.25 | | & empty(all_175_1) = all_175_0 & $i(all_175_1) & ( ~ (all_175_0 =
% 24.92/4.25 | | 0) | ~ (all_175_2 = 0))
% 24.92/4.25 | |
% 24.92/4.25 | | ALPHA: (130) implies:
% 24.92/4.25 | | (131) relation_dom(all_45_1) = all_175_1
% 24.92/4.25 | |
% 24.92/4.25 | | BETA: splitting (55) gives:
% 24.92/4.25 | |
% 24.92/4.25 | | Case 1:
% 24.92/4.25 | | |
% 24.92/4.25 | | | (132) all_45_0 = 0
% 24.92/4.25 | | |
% 24.92/4.25 | | | REDUCE: (31), (132) imply:
% 24.92/4.25 | | | (133) $false
% 24.92/4.25 | | |
% 24.92/4.25 | | | CLOSE: (133) is inconsistent.
% 24.92/4.25 | | |
% 24.92/4.25 | | Case 2:
% 24.92/4.25 | | |
% 24.92/4.25 | | | (134) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 24.92/4.25 | | | powerset(all_45_1) = v0 & element(v1, v0) = 0 & empty(v1) = v2
% 24.92/4.25 | | | & $i(v1) & $i(v0))
% 24.92/4.25 | | |
% 24.92/4.25 | | | DELTA: instantiating (134) with fresh symbols all_181_0, all_181_1,
% 24.92/4.25 | | | all_181_2 gives:
% 24.92/4.25 | | | (135) ~ (all_181_0 = 0) & powerset(all_45_1) = all_181_2 &
% 24.92/4.25 | | | element(all_181_1, all_181_2) = 0 & empty(all_181_1) = all_181_0
% 24.92/4.25 | | | & $i(all_181_1) & $i(all_181_2)
% 24.92/4.25 | | |
% 24.92/4.25 | | | ALPHA: (135) implies:
% 24.92/4.25 | | | (136) powerset(all_45_1) = all_181_2
% 24.92/4.25 | | |
% 24.92/4.25 | | | GROUND_INST: instantiating (20) with all_45_0, all_129_2, all_45_1,
% 24.92/4.25 | | | simplifying with (33), (90) gives:
% 24.92/4.25 | | | (137) all_129_2 = all_45_0
% 24.92/4.25 | | |
% 24.92/4.25 | | | GROUND_INST: instantiating (20) with all_125_2, all_129_2, all_45_1,
% 24.92/4.25 | | | simplifying with (87), (90) gives:
% 24.92/4.25 | | | (138) all_129_2 = all_125_2
% 24.92/4.25 | | |
% 24.92/4.25 | | | GROUND_INST: instantiating (21) with 0, all_165_2, all_59_5, simplifying
% 24.92/4.25 | | | with (46), (115) gives:
% 24.92/4.25 | | | (139) all_165_2 = 0
% 24.92/4.25 | | |
% 24.92/4.25 | | | GROUND_INST: instantiating (21) with all_161_4, all_165_2, all_59_5,
% 24.92/4.25 | | | simplifying with (104), (115) gives:
% 24.92/4.25 | | | (140) all_165_2 = all_161_4
% 24.92/4.25 | | |
% 24.92/4.25 | | | GROUND_INST: instantiating (21) with all_97_1, all_161_2, all_59_3,
% 24.92/4.25 | | | simplifying with (79), (105) gives:
% 24.92/4.25 | | | (141) all_161_2 = all_97_1
% 24.92/4.25 | | |
% 24.92/4.25 | | | GROUND_INST: instantiating (21) with 0, all_169_2, all_59_3, simplifying
% 24.92/4.25 | | | with (47), (124) gives:
% 24.92/4.25 | | | (142) all_169_2 = 0
% 24.92/4.25 | | |
% 24.92/4.25 | | | GROUND_INST: instantiating (21) with all_161_2, all_169_2, all_59_3,
% 24.92/4.25 | | | simplifying with (105), (124) gives:
% 24.92/4.25 | | | (143) all_169_2 = all_161_2
% 24.92/4.25 | | |
% 24.92/4.25 | | | GROUND_INST: instantiating (22) with all_109_2, all_161_5, all_59_5,
% 24.92/4.25 | | | simplifying with (84), (106) gives:
% 24.92/4.25 | | | (144) all_161_5 = all_109_2
% 24.92/4.25 | | |
% 24.92/4.25 | | | GROUND_INST: instantiating (22) with all_161_5, all_165_3, all_59_5,
% 24.92/4.25 | | | simplifying with (106), (116) gives:
% 24.92/4.25 | | | (145) all_165_3 = all_161_5
% 24.92/4.25 | | |
% 24.92/4.25 | | | GROUND_INST: instantiating (22) with all_157_2, all_165_3, all_59_5,
% 24.92/4.25 | | | simplifying with (100), (116) gives:
% 24.92/4.25 | | | (146) all_165_3 = all_157_2
% 24.92/4.25 | | |
% 24.92/4.25 | | | GROUND_INST: instantiating (22) with all_131_2, all_165_3, all_59_5,
% 24.92/4.25 | | | simplifying with (92), (116) gives:
% 24.92/4.25 | | | (147) all_165_3 = all_131_2
% 24.92/4.25 | | |
% 24.92/4.25 | | | GROUND_INST: instantiating (22) with 0, all_155_2, all_59_3, simplifying
% 24.92/4.25 | | | with (48), (98) gives:
% 24.92/4.25 | | | (148) all_155_2 = 0
% 24.92/4.25 | | |
% 24.92/4.25 | | | GROUND_INST: instantiating (22) with all_153_2, all_155_2, all_59_3,
% 24.92/4.25 | | | simplifying with (95), (98) gives:
% 24.92/4.25 | | | (149) all_155_2 = all_153_2
% 24.92/4.25 | | |
% 24.92/4.25 | | | GROUND_INST: instantiating (22) with all_161_3, all_169_3, all_59_3,
% 24.92/4.25 | | | simplifying with (107), (125) gives:
% 24.92/4.25 | | | (150) all_169_3 = all_161_3
% 24.92/4.25 | | |
% 24.92/4.25 | | | GROUND_INST: instantiating (22) with all_153_2, all_169_3, all_59_3,
% 24.92/4.25 | | | simplifying with (95), (125) gives:
% 24.92/4.25 | | | (151) all_169_3 = all_153_2
% 24.92/4.25 | | |
% 24.92/4.25 | | | GROUND_INST: instantiating (22) with all_131_1, all_169_3, all_59_3,
% 24.92/4.25 | | | simplifying with (93), (125) gives:
% 24.92/4.25 | | | (152) all_169_3 = all_131_1
% 24.92/4.25 | | |
% 24.92/4.25 | | | GROUND_INST: instantiating (23) with all_97_0, all_153_0, all_59_3,
% 24.92/4.25 | | | simplifying with (80), (96) gives:
% 24.92/4.25 | | | (153) all_153_0 = all_97_0
% 24.92/4.25 | | |
% 24.92/4.25 | | | GROUND_INST: instantiating (28) with 0, all_163_1, all_59_7, all_59_8,
% 24.92/4.25 | | | all_59_5, simplifying with (49), (110) gives:
% 24.92/4.25 | | | (154) all_163_1 = 0
% 24.92/4.25 | | |
% 24.92/4.25 | | | GROUND_INST: instantiating (29) with all_159_0, all_163_0, all_59_5,
% 24.92/4.25 | | | all_59_7, all_59_8, simplifying with (102), (111) gives:
% 24.92/4.25 | | | (155) all_163_0 = all_159_0
% 24.92/4.25 | | |
% 24.92/4.25 | | | GROUND_INST: instantiating (24) with all_125_1, all_175_1, all_45_1,
% 24.92/4.25 | | | simplifying with (88), (131) gives:
% 24.92/4.25 | | | (156) all_175_1 = all_125_1
% 24.92/4.25 | | |
% 24.92/4.25 | | | GROUND_INST: instantiating (24) with all_99_1, all_169_1, all_59_3,
% 24.92/4.25 | | | simplifying with (82), (126) gives:
% 24.92/4.25 | | | (157) all_169_1 = all_99_1
% 24.92/4.25 | | |
% 24.92/4.25 | | | COMBINE_EQS: (142), (143) imply:
% 24.92/4.25 | | | (158) all_161_2 = 0
% 24.92/4.25 | | |
% 24.92/4.25 | | | SIMP: (158) implies:
% 24.92/4.25 | | | (159) all_161_2 = 0
% 24.92/4.25 | | |
% 24.92/4.25 | | | COMBINE_EQS: (150), (151) imply:
% 24.92/4.26 | | | (160) all_161_3 = all_153_2
% 24.92/4.26 | | |
% 24.92/4.26 | | | COMBINE_EQS: (150), (152) imply:
% 24.92/4.26 | | | (161) all_161_3 = all_131_1
% 24.92/4.26 | | |
% 24.92/4.26 | | | COMBINE_EQS: (139), (140) imply:
% 24.92/4.26 | | | (162) all_161_4 = 0
% 24.92/4.26 | | |
% 24.92/4.26 | | | COMBINE_EQS: (145), (146) imply:
% 24.92/4.26 | | | (163) all_161_5 = all_157_2
% 24.92/4.26 | | |
% 24.92/4.26 | | | SIMP: (163) implies:
% 24.92/4.26 | | | (164) all_161_5 = all_157_2
% 24.92/4.26 | | |
% 24.92/4.26 | | | COMBINE_EQS: (146), (147) imply:
% 24.92/4.26 | | | (165) all_157_2 = all_131_2
% 24.92/4.26 | | |
% 24.92/4.26 | | | COMBINE_EQS: (141), (159) imply:
% 24.92/4.26 | | | (166) all_97_1 = 0
% 24.92/4.26 | | |
% 24.92/4.26 | | | COMBINE_EQS: (160), (161) imply:
% 24.92/4.26 | | | (167) all_153_2 = all_131_1
% 24.92/4.26 | | |
% 24.92/4.26 | | | SIMP: (167) implies:
% 24.92/4.26 | | | (168) all_153_2 = all_131_1
% 24.92/4.26 | | |
% 24.92/4.26 | | | COMBINE_EQS: (144), (164) imply:
% 24.92/4.26 | | | (169) all_157_2 = all_109_2
% 24.92/4.26 | | |
% 24.92/4.26 | | | SIMP: (169) implies:
% 24.92/4.26 | | | (170) all_157_2 = all_109_2
% 24.92/4.26 | | |
% 24.92/4.26 | | | COMBINE_EQS: (165), (170) imply:
% 24.92/4.26 | | | (171) all_131_2 = all_109_2
% 24.92/4.26 | | |
% 24.92/4.26 | | | SIMP: (171) implies:
% 24.92/4.26 | | | (172) all_131_2 = all_109_2
% 24.92/4.26 | | |
% 24.92/4.26 | | | COMBINE_EQS: (148), (149) imply:
% 24.92/4.26 | | | (173) all_153_2 = 0
% 24.92/4.26 | | |
% 24.92/4.26 | | | SIMP: (173) implies:
% 24.92/4.26 | | | (174) all_153_2 = 0
% 24.92/4.26 | | |
% 24.92/4.26 | | | COMBINE_EQS: (168), (174) imply:
% 24.92/4.26 | | | (175) all_131_1 = 0
% 24.92/4.26 | | |
% 24.92/4.26 | | | COMBINE_EQS: (137), (138) imply:
% 24.92/4.26 | | | (176) all_125_2 = all_45_0
% 24.92/4.26 | | |
% 24.92/4.26 | | | COMBINE_EQS: (146), (170) imply:
% 24.92/4.26 | | | (177) all_165_3 = all_109_2
% 24.92/4.26 | | |
% 24.92/4.26 | | | REDUCE: (123), (157) imply:
% 24.92/4.26 | | | (178) in(all_59_4, all_99_1) = all_169_0
% 24.92/4.26 | | |
% 24.92/4.26 | | | REDUCE: (109), (155) imply:
% 24.92/4.26 | | | (179) $i(all_159_0)
% 24.92/4.26 | | |
% 24.92/4.26 | | | BETA: splitting (112) gives:
% 24.92/4.26 | | |
% 24.92/4.26 | | | Case 1:
% 24.92/4.26 | | | |
% 24.92/4.26 | | | | (180) all_59_7 = empty_set & ~ (all_59_8 = empty_set)
% 24.92/4.26 | | | |
% 24.92/4.26 | | | | ALPHA: (180) implies:
% 24.92/4.26 | | | | (181) all_59_7 = empty_set
% 24.92/4.26 | | | |
% 24.92/4.26 | | | | REDUCE: (36), (181) imply:
% 24.92/4.26 | | | | (182) $false
% 24.92/4.26 | | | |
% 24.92/4.26 | | | | CLOSE: (182) is inconsistent.
% 24.92/4.26 | | | |
% 24.92/4.26 | | | Case 2:
% 24.92/4.26 | | | |
% 24.92/4.26 | | | | (183) ( ~ (all_163_0 = all_59_8) | all_163_1 = 0) & ( ~ (all_163_1 =
% 24.92/4.26 | | | | 0) | all_163_0 = all_59_8)
% 24.92/4.26 | | | |
% 24.92/4.26 | | | | ALPHA: (183) implies:
% 24.92/4.26 | | | | (184) ~ (all_163_1 = 0) | all_163_0 = all_59_8
% 24.92/4.26 | | | |
% 24.92/4.26 | | | | BETA: splitting (184) gives:
% 24.92/4.26 | | | |
% 24.92/4.26 | | | | Case 1:
% 24.92/4.26 | | | | |
% 24.92/4.26 | | | | | (185) ~ (all_163_1 = 0)
% 24.92/4.26 | | | | |
% 24.92/4.26 | | | | | REDUCE: (154), (185) imply:
% 24.92/4.26 | | | | | (186) $false
% 24.92/4.26 | | | | |
% 24.92/4.26 | | | | | CLOSE: (186) is inconsistent.
% 24.92/4.26 | | | | |
% 24.92/4.26 | | | | Case 2:
% 24.92/4.26 | | | | |
% 24.92/4.26 | | | | | (187) all_163_0 = all_59_8
% 24.92/4.26 | | | | |
% 24.92/4.26 | | | | | COMBINE_EQS: (155), (187) imply:
% 24.92/4.26 | | | | | (188) all_159_0 = all_59_8
% 24.92/4.26 | | | | |
% 24.92/4.26 | | | | | REDUCE: (102), (188) imply:
% 24.92/4.26 | | | | | (189) relation_dom_as_subset(all_59_8, all_59_7, all_59_5) =
% 24.92/4.26 | | | | | all_59_8
% 24.92/4.26 | | | | |
% 24.92/4.26 | | | | | GROUND_INST: instantiating (12) with all_45_1, all_181_2, simplifying
% 24.92/4.26 | | | | | with (32), (136) gives:
% 24.92/4.26 | | | | | (190) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ? [v3: int] :
% 24.92/4.26 | | | | | ($i(v1) & ((v2 = 0 & ~ (v3 = 0) & element(v1, all_181_2) = 0
% 24.92/4.26 | | | | | & empty(v1) = v3) | (v0 = 0 & empty(all_45_1) = 0)))
% 24.92/4.26 | | | | |
% 24.92/4.26 | | | | | GROUND_INST: instantiating (cc1_relset_1) with all_59_8, all_59_7,
% 24.92/4.26 | | | | | all_59_5, all_93_1, all_93_0, simplifying with (38),
% 24.92/4.26 | | | | | (39), (41), (75), (76), (77) gives:
% 24.92/4.26 | | | | | (191) relation(all_59_5) = 0
% 24.92/4.26 | | | | |
% 24.92/4.26 | | | | | GROUND_INST: instantiating (3) with all_59_5, all_109_0, simplifying
% 24.92/4.26 | | | | | with (41), (85) gives:
% 24.92/4.26 | | | | | (192) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 24.92/4.26 | | | | | (relation(all_59_5) = v0 & function(all_59_5) = v2 &
% 24.92/4.26 | | | | | empty(all_59_5) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0
% 24.92/4.26 | | | | | = 0) | all_109_0 = 0))
% 24.92/4.26 | | | | |
% 24.92/4.26 | | | | | GROUND_INST: instantiating (3) with all_59_3, all_97_0, simplifying
% 24.92/4.26 | | | | | with (43), (80) gives:
% 24.92/4.26 | | | | | (193) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 24.92/4.26 | | | | | (relation(all_59_3) = v0 & function(all_59_3) = v2 &
% 24.92/4.26 | | | | | empty(all_59_3) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0
% 24.92/4.26 | | | | | = 0) | all_97_0 = 0))
% 24.92/4.26 | | | | |
% 24.92/4.26 | | | | | GROUND_INST: instantiating (15) with all_59_8, all_59_7, all_59_5,
% 24.92/4.26 | | | | | all_59_8, simplifying with (38), (39), (41), (189) gives:
% 24.92/4.26 | | | | | (194) ? [v0: any] : ? [v1: $i] : (relation_dom(all_59_5) = v1 &
% 24.92/4.26 | | | | | relation_of2(all_59_5, all_59_8, all_59_7) = v0 & $i(v1) &
% 24.92/4.26 | | | | | ( ~ (v0 = 0) | v1 = all_59_8))
% 24.92/4.26 | | | | |
% 24.92/4.26 | | | | | GROUND_INST: instantiating (6) with all_59_8, all_59_7, all_59_5,
% 24.92/4.26 | | | | | simplifying with (38), (39), (41), (64) gives:
% 24.92/4.26 | | | | | (195) ? [v0: $i] : ? [v1: $i] : (relation_dom_as_subset(all_59_8,
% 24.92/4.26 | | | | | all_59_7, all_59_5) = v0 & powerset(all_59_8) = v1 &
% 24.92/4.26 | | | | | element(v0, v1) = 0 & $i(v1) & $i(v0))
% 24.92/4.26 | | | | |
% 24.92/4.26 | | | | | GROUND_INST: instantiating (14) with all_59_8, all_59_7, all_59_5,
% 24.92/4.26 | | | | | simplifying with (38), (39), (41), (64) gives:
% 24.92/4.26 | | | | | (196) ? [v0: $i] : (relation_dom(all_59_5) = v0 &
% 24.92/4.26 | | | | | relation_dom_as_subset(all_59_8, all_59_7, all_59_5) = v0 &
% 24.92/4.26 | | | | | $i(v0))
% 24.92/4.26 | | | | |
% 24.92/4.26 | | | | | GROUND_INST: instantiating (11) with all_45_1, all_125_1, simplifying
% 24.92/4.26 | | | | | with (32), (88) gives:
% 24.92/4.26 | | | | | (197) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 24.92/4.26 | | | | | (relation(all_125_1) = v2 & empty(all_125_1) = v1 &
% 24.92/4.26 | | | | | empty(all_45_1) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0)))
% 24.92/4.26 | | | | |
% 24.92/4.26 | | | | | GROUND_INST: instantiating (18) with all_59_6, all_59_5, all_165_1,
% 24.92/4.26 | | | | | all_165_0, simplifying with (40), (41), (114), (117)
% 24.92/4.26 | | | | | gives:
% 24.92/4.27 | | | | | (198) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (apply(all_59_5,
% 24.92/4.27 | | | | | all_59_6) = v2 & relation(all_59_5) = v0 &
% 24.92/4.27 | | | | | function(all_59_5) = v1 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 =
% 24.92/4.27 | | | | | 0) | ( ! [v3: $i] : ! [v4: $i] : ( ~ (all_165_0 = 0) |
% 24.92/4.27 | | | | | ~ (apply(v3, v2) = v4) | ~ $i(v3) | ? [v5: any] :
% 24.92/4.27 | | | | | ? [v6: any] : ? [v7: $i] : ? [v8: $i] : (apply(v7,
% 24.92/4.27 | | | | | all_59_6) = v8 & relation_composition(all_59_5,
% 24.92/4.27 | | | | | v3) = v7 & relation(v3) = v5 & function(v3) = v6
% 24.92/4.27 | | | | | & $i(v8) & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | v8
% 24.92/4.27 | | | | | = v4))) & ! [v3: $i] : ! [v4: $i] : ( ~
% 24.92/4.27 | | | | | (all_165_0 = 0) | ~ (relation_composition(all_59_5,
% 24.92/4.27 | | | | | v3) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6:
% 24.92/4.27 | | | | | any] : ? [v7: $i] : ? [v8: $i] : (apply(v4,
% 24.92/4.27 | | | | | all_59_6) = v7 & apply(v3, v2) = v8 &
% 24.92/4.27 | | | | | relation(v3) = v5 & function(v3) = v6 & $i(v8) &
% 24.92/4.27 | | | | | $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | v8 = v7))) &
% 24.92/4.27 | | | | | ! [v3: $i] : ( ~ (all_165_0 = 0) | ~ (relation(v3) =
% 24.92/4.27 | | | | | 0) | ~ $i(v3) | ? [v4: any] : ? [v5: $i] : ?
% 24.92/4.27 | | | | | [v6: $i] : ? [v7: $i] : (apply(v5, all_59_6) = v6 &
% 24.92/4.27 | | | | | apply(v3, v2) = v7 & relation_composition(all_59_5,
% 24.92/4.27 | | | | | v3) = v5 & function(v3) = v4 & $i(v7) & $i(v6) &
% 24.92/4.27 | | | | | $i(v5) & ( ~ (v4 = 0) | v7 = v6))) & ! [v3: $i] :
% 24.92/4.27 | | | | | ( ~ (all_165_0 = 0) | ~ (function(v3) = 0) | ~ $i(v3)
% 24.92/4.27 | | | | | | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7:
% 24.92/4.27 | | | | | $i] : (apply(v5, all_59_6) = v6 & apply(v3, v2) =
% 24.92/4.27 | | | | | v7 & relation_composition(all_59_5, v3) = v5 &
% 24.92/4.27 | | | | | relation(v3) = v4 & $i(v7) & $i(v6) & $i(v5) & ( ~
% 24.92/4.27 | | | | | (v4 = 0) | v7 = v6))))))
% 24.92/4.27 | | | | |
% 24.92/4.27 | | | | | GROUND_INST: instantiating (9) with all_59_5, all_165_1, simplifying
% 24.92/4.27 | | | | | with (41), (117) gives:
% 24.92/4.27 | | | | | (199) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 24.92/4.27 | | | | | (relation(all_59_5) = v1 & empty(all_165_1) = v2 &
% 24.92/4.27 | | | | | empty(all_59_5) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | v0 =
% 24.92/4.27 | | | | | 0))
% 24.92/4.27 | | | | |
% 24.92/4.27 | | | | | GROUND_INST: instantiating (18) with all_59_4, all_59_3, all_99_1,
% 24.92/4.27 | | | | | all_169_0, simplifying with (42), (43), (82), (178)
% 24.92/4.27 | | | | | gives:
% 24.92/4.27 | | | | | (200) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (apply(all_59_3,
% 24.92/4.27 | | | | | all_59_4) = v2 & relation(all_59_3) = v0 &
% 24.92/4.27 | | | | | function(all_59_3) = v1 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 =
% 24.92/4.27 | | | | | 0) | ( ! [v3: $i] : ! [v4: $i] : ( ~ (all_169_0 = 0) |
% 24.92/4.27 | | | | | ~ (apply(v3, v2) = v4) | ~ $i(v3) | ? [v5: any] :
% 24.92/4.27 | | | | | ? [v6: any] : ? [v7: $i] : ? [v8: $i] : (apply(v7,
% 24.92/4.27 | | | | | all_59_4) = v8 & relation_composition(all_59_3,
% 24.92/4.27 | | | | | v3) = v7 & relation(v3) = v5 & function(v3) = v6
% 24.92/4.27 | | | | | & $i(v8) & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | v8
% 24.92/4.27 | | | | | = v4))) & ! [v3: $i] : ! [v4: $i] : ( ~
% 24.92/4.27 | | | | | (all_169_0 = 0) | ~ (relation_composition(all_59_3,
% 24.92/4.27 | | | | | v3) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6:
% 24.92/4.27 | | | | | any] : ? [v7: $i] : ? [v8: $i] : (apply(v4,
% 24.92/4.27 | | | | | all_59_4) = v7 & apply(v3, v2) = v8 &
% 24.92/4.27 | | | | | relation(v3) = v5 & function(v3) = v6 & $i(v8) &
% 24.92/4.27 | | | | | $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | v8 = v7))) &
% 24.92/4.27 | | | | | ! [v3: $i] : ( ~ (all_169_0 = 0) | ~ (relation(v3) =
% 24.92/4.27 | | | | | 0) | ~ $i(v3) | ? [v4: any] : ? [v5: $i] : ?
% 24.92/4.27 | | | | | [v6: $i] : ? [v7: $i] : (apply(v5, all_59_4) = v6 &
% 24.92/4.27 | | | | | apply(v3, v2) = v7 & relation_composition(all_59_3,
% 24.92/4.27 | | | | | v3) = v5 & function(v3) = v4 & $i(v7) & $i(v6) &
% 24.92/4.27 | | | | | $i(v5) & ( ~ (v4 = 0) | v7 = v6))) & ! [v3: $i] :
% 24.92/4.27 | | | | | ( ~ (all_169_0 = 0) | ~ (function(v3) = 0) | ~ $i(v3)
% 24.92/4.27 | | | | | | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7:
% 24.92/4.27 | | | | | $i] : (apply(v5, all_59_4) = v6 & apply(v3, v2) =
% 24.92/4.27 | | | | | v7 & relation_composition(all_59_3, v3) = v5 &
% 24.92/4.27 | | | | | relation(v3) = v4 & $i(v7) & $i(v6) & $i(v5) & ( ~
% 24.92/4.27 | | | | | (v4 = 0) | v7 = v6))))))
% 24.92/4.27 | | | | |
% 24.92/4.27 | | | | | GROUND_INST: instantiating (9) with all_59_3, all_99_1, simplifying
% 24.92/4.27 | | | | | with (43), (82) gives:
% 24.92/4.27 | | | | | (201) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 24.92/4.27 | | | | | (relation(all_59_3) = v1 & empty(all_99_1) = v2 &
% 24.92/4.27 | | | | | empty(all_59_3) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | v0 =
% 24.92/4.27 | | | | | 0))
% 24.92/4.27 | | | | |
% 24.92/4.27 | | | | | GROUND_INST: instantiating (18) with all_59_6, all_59_2, all_167_1,
% 24.92/4.27 | | | | | all_167_0, simplifying with (40), (44), (120), (121)
% 24.92/4.27 | | | | | gives:
% 24.92/4.27 | | | | | (202) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (apply(all_59_2,
% 24.92/4.27 | | | | | all_59_6) = v2 & relation(all_59_2) = v0 &
% 24.92/4.27 | | | | | function(all_59_2) = v1 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 =
% 24.92/4.27 | | | | | 0) | ( ! [v3: $i] : ! [v4: $i] : ( ~ (all_167_0 = 0) |
% 24.92/4.27 | | | | | ~ (apply(v3, v2) = v4) | ~ $i(v3) | ? [v5: any] :
% 24.92/4.27 | | | | | ? [v6: any] : ? [v7: $i] : ? [v8: $i] : (apply(v7,
% 24.92/4.27 | | | | | all_59_6) = v8 & relation_composition(all_59_2,
% 24.92/4.27 | | | | | v3) = v7 & relation(v3) = v5 & function(v3) = v6
% 24.92/4.27 | | | | | & $i(v8) & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | v8
% 24.92/4.27 | | | | | = v4))) & ! [v3: $i] : ! [v4: $i] : ( ~
% 24.92/4.27 | | | | | (all_167_0 = 0) | ~ (relation_composition(all_59_2,
% 24.92/4.27 | | | | | v3) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6:
% 24.92/4.27 | | | | | any] : ? [v7: $i] : ? [v8: $i] : (apply(v4,
% 24.92/4.27 | | | | | all_59_6) = v7 & apply(v3, v2) = v8 &
% 24.92/4.27 | | | | | relation(v3) = v5 & function(v3) = v6 & $i(v8) &
% 24.92/4.27 | | | | | $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | v8 = v7))) &
% 24.92/4.27 | | | | | ! [v3: $i] : ( ~ (all_167_0 = 0) | ~ (relation(v3) =
% 24.92/4.27 | | | | | 0) | ~ $i(v3) | ? [v4: any] : ? [v5: $i] : ?
% 24.92/4.27 | | | | | [v6: $i] : ? [v7: $i] : (apply(v5, all_59_6) = v6 &
% 24.92/4.27 | | | | | apply(v3, v2) = v7 & relation_composition(all_59_2,
% 24.92/4.27 | | | | | v3) = v5 & function(v3) = v4 & $i(v7) & $i(v6) &
% 24.92/4.27 | | | | | $i(v5) & ( ~ (v4 = 0) | v7 = v6))) & ! [v3: $i] :
% 24.92/4.27 | | | | | ( ~ (all_167_0 = 0) | ~ (function(v3) = 0) | ~ $i(v3)
% 24.92/4.27 | | | | | | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7:
% 24.92/4.27 | | | | | $i] : (apply(v5, all_59_6) = v6 & apply(v3, v2) =
% 24.92/4.27 | | | | | v7 & relation_composition(all_59_2, v3) = v5 &
% 24.92/4.27 | | | | | relation(v3) = v4 & $i(v7) & $i(v6) & $i(v5) & ( ~
% 24.92/4.27 | | | | | (v4 = 0) | v7 = v6))))))
% 24.92/4.27 | | | | |
% 24.92/4.27 | | | | | DELTA: instantiating (196) with fresh symbol all_241_0 gives:
% 24.92/4.27 | | | | | (203) relation_dom(all_59_5) = all_241_0 &
% 24.92/4.27 | | | | | relation_dom_as_subset(all_59_8, all_59_7, all_59_5) =
% 24.92/4.27 | | | | | all_241_0 & $i(all_241_0)
% 24.92/4.27 | | | | |
% 24.92/4.27 | | | | | ALPHA: (203) implies:
% 24.92/4.27 | | | | | (204) relation_dom_as_subset(all_59_8, all_59_7, all_59_5) =
% 24.92/4.27 | | | | | all_241_0
% 24.92/4.27 | | | | | (205) relation_dom(all_59_5) = all_241_0
% 24.92/4.27 | | | | |
% 24.92/4.27 | | | | | DELTA: instantiating (194) with fresh symbols all_257_0, all_257_1
% 24.92/4.27 | | | | | gives:
% 24.92/4.27 | | | | | (206) relation_dom(all_59_5) = all_257_0 & relation_of2(all_59_5,
% 24.92/4.27 | | | | | all_59_8, all_59_7) = all_257_1 & $i(all_257_0) & ( ~
% 24.92/4.27 | | | | | (all_257_1 = 0) | all_257_0 = all_59_8)
% 24.92/4.27 | | | | |
% 24.92/4.27 | | | | | ALPHA: (206) implies:
% 24.92/4.27 | | | | | (207) relation_dom(all_59_5) = all_257_0
% 24.92/4.27 | | | | |
% 24.92/4.27 | | | | | DELTA: instantiating (195) with fresh symbols all_259_0, all_259_1
% 24.92/4.27 | | | | | gives:
% 24.92/4.27 | | | | | (208) relation_dom_as_subset(all_59_8, all_59_7, all_59_5) =
% 24.92/4.27 | | | | | all_259_1 & powerset(all_59_8) = all_259_0 &
% 24.92/4.27 | | | | | element(all_259_1, all_259_0) = 0 & $i(all_259_0) &
% 24.92/4.27 | | | | | $i(all_259_1)
% 24.92/4.27 | | | | |
% 24.92/4.27 | | | | | ALPHA: (208) implies:
% 24.92/4.27 | | | | | (209) relation_dom_as_subset(all_59_8, all_59_7, all_59_5) =
% 24.92/4.27 | | | | | all_259_1
% 24.92/4.27 | | | | |
% 24.92/4.27 | | | | | DELTA: instantiating (201) with fresh symbols all_267_0, all_267_1,
% 24.92/4.27 | | | | | all_267_2 gives:
% 24.92/4.27 | | | | | (210) relation(all_59_3) = all_267_1 & empty(all_99_1) = all_267_0
% 24.92/4.27 | | | | | & empty(all_59_3) = all_267_2 & ( ~ (all_267_0 = 0) | ~
% 24.92/4.27 | | | | | (all_267_1 = 0) | all_267_2 = 0)
% 24.92/4.27 | | | | |
% 24.92/4.27 | | | | | ALPHA: (210) implies:
% 24.92/4.27 | | | | | (211) relation(all_59_3) = all_267_1
% 24.92/4.27 | | | | |
% 24.92/4.27 | | | | | DELTA: instantiating (199) with fresh symbols all_285_0, all_285_1,
% 24.92/4.27 | | | | | all_285_2 gives:
% 24.92/4.27 | | | | | (212) relation(all_59_5) = all_285_1 & empty(all_165_1) = all_285_0
% 24.92/4.27 | | | | | & empty(all_59_5) = all_285_2 & ( ~ (all_285_0 = 0) | ~
% 24.92/4.27 | | | | | (all_285_1 = 0) | all_285_2 = 0)
% 24.92/4.27 | | | | |
% 24.92/4.27 | | | | | ALPHA: (212) implies:
% 24.92/4.27 | | | | | (213) relation(all_59_5) = all_285_1
% 24.92/4.27 | | | | |
% 24.92/4.27 | | | | | DELTA: instantiating (197) with fresh symbols all_303_0, all_303_1,
% 24.92/4.27 | | | | | all_303_2 gives:
% 24.92/4.27 | | | | | (214) relation(all_125_1) = all_303_0 & empty(all_125_1) =
% 24.92/4.27 | | | | | all_303_1 & empty(all_45_1) = all_303_2 & ( ~ (all_303_2 = 0)
% 24.92/4.27 | | | | | | (all_303_0 = 0 & all_303_1 = 0))
% 24.92/4.27 | | | | |
% 24.92/4.27 | | | | | ALPHA: (214) implies:
% 24.92/4.27 | | | | | (215) empty(all_45_1) = all_303_2
% 24.92/4.27 | | | | |
% 24.92/4.27 | | | | | DELTA: instantiating (190) with fresh symbols all_305_0, all_305_1,
% 24.92/4.27 | | | | | all_305_2, all_305_3 gives:
% 24.92/4.27 | | | | | (216) $i(all_305_2) & ((all_305_1 = 0 & ~ (all_305_0 = 0) &
% 24.92/4.27 | | | | | element(all_305_2, all_181_2) = 0 & empty(all_305_2) =
% 24.92/4.27 | | | | | all_305_0) | (all_305_3 = 0 & empty(all_45_1) = 0))
% 24.92/4.27 | | | | |
% 24.92/4.27 | | | | | ALPHA: (216) implies:
% 24.92/4.27 | | | | | (217) (all_305_1 = 0 & ~ (all_305_0 = 0) & element(all_305_2,
% 24.92/4.27 | | | | | all_181_2) = 0 & empty(all_305_2) = all_305_0) |
% 24.92/4.27 | | | | | (all_305_3 = 0 & empty(all_45_1) = 0)
% 24.92/4.27 | | | | |
% 24.92/4.27 | | | | | DELTA: instantiating (193) with fresh symbols all_307_0, all_307_1,
% 24.92/4.27 | | | | | all_307_2 gives:
% 24.92/4.28 | | | | | (218) relation(all_59_3) = all_307_2 & function(all_59_3) =
% 24.92/4.28 | | | | | all_307_0 & empty(all_59_3) = all_307_1 & ( ~ (all_307_0 = 0)
% 24.92/4.28 | | | | | | ~ (all_307_1 = 0) | ~ (all_307_2 = 0) | all_97_0 = 0)
% 24.92/4.28 | | | | |
% 24.92/4.28 | | | | | ALPHA: (218) implies:
% 24.92/4.28 | | | | | (219) function(all_59_3) = all_307_0
% 24.92/4.28 | | | | | (220) relation(all_59_3) = all_307_2
% 24.92/4.28 | | | | |
% 24.92/4.28 | | | | | DELTA: instantiating (192) with fresh symbols all_315_0, all_315_1,
% 24.92/4.28 | | | | | all_315_2 gives:
% 24.92/4.28 | | | | | (221) relation(all_59_5) = all_315_2 & function(all_59_5) =
% 24.92/4.28 | | | | | all_315_0 & empty(all_59_5) = all_315_1 & ( ~ (all_315_0 = 0)
% 24.92/4.28 | | | | | | ~ (all_315_1 = 0) | ~ (all_315_2 = 0) | all_109_0 = 0)
% 24.92/4.28 | | | | |
% 24.92/4.28 | | | | | ALPHA: (221) implies:
% 24.92/4.28 | | | | | (222) relation(all_59_5) = all_315_2
% 24.92/4.28 | | | | |
% 24.92/4.28 | | | | | DELTA: instantiating (198) with fresh symbols all_323_0, all_323_1,
% 24.92/4.28 | | | | | all_323_2 gives:
% 24.92/4.28 | | | | | (223) apply(all_59_5, all_59_6) = all_323_0 & relation(all_59_5) =
% 24.92/4.28 | | | | | all_323_2 & function(all_59_5) = all_323_1 & $i(all_323_0) &
% 24.92/4.28 | | | | | ( ~ (all_323_1 = 0) | ~ (all_323_2 = 0) | ( ! [v0: $i] : !
% 24.92/4.28 | | | | | [v1: $i] : ( ~ (all_165_0 = 0) | ~ (apply(v0, all_323_0)
% 24.92/4.28 | | | | | = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ?
% 24.92/4.28 | | | | | [v4: $i] : ? [v5: $i] : (apply(v4, all_59_6) = v5 &
% 24.92/4.28 | | | | | relation_composition(all_59_5, v0) = v4 &
% 24.92/4.28 | | | | | relation(v0) = v2 & function(v0) = v3 & $i(v5) &
% 24.92/4.28 | | | | | $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = v1))) & !
% 24.92/4.28 | | | | | [v0: $i] : ! [v1: $i] : ( ~ (all_165_0 = 0) | ~
% 24.92/4.28 | | | | | (relation_composition(all_59_5, v0) = v1) | ~ $i(v0) |
% 24.92/4.28 | | | | | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5: $i]
% 24.92/4.28 | | | | | : (apply(v1, all_59_6) = v4 & apply(v0, all_323_0) = v5
% 24.92/4.28 | | | | | & relation(v0) = v2 & function(v0) = v3 & $i(v5) &
% 24.92/4.28 | | | | | $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = v4))) & !
% 24.92/4.28 | | | | | [v0: $i] : ( ~ (all_165_0 = 0) | ~ (relation(v0) = 0) |
% 24.92/4.28 | | | | | ~ $i(v0) | ? [v1: any] : ? [v2: $i] : ? [v3: $i] :
% 24.92/4.28 | | | | | ? [v4: $i] : (apply(v2, all_59_6) = v3 & apply(v0,
% 24.92/4.28 | | | | | all_323_0) = v4 & relation_composition(all_59_5,
% 24.92/4.28 | | | | | v0) = v2 & function(v0) = v1 & $i(v4) & $i(v3) &
% 24.92/4.28 | | | | | $i(v2) & ( ~ (v1 = 0) | v4 = v3))) & ! [v0: $i] : (
% 24.92/4.28 | | | | | ~ (all_165_0 = 0) | ~ (function(v0) = 0) | ~ $i(v0) |
% 24.92/4.28 | | | | | ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 24.92/4.28 | | | | | : (apply(v2, all_59_6) = v3 & apply(v0, all_323_0) = v4
% 24.92/4.28 | | | | | & relation_composition(all_59_5, v0) = v2 &
% 24.92/4.28 | | | | | relation(v0) = v1 & $i(v4) & $i(v3) & $i(v2) & ( ~
% 24.92/4.28 | | | | | (v1 = 0) | v4 = v3)))))
% 24.92/4.28 | | | | |
% 24.92/4.28 | | | | | ALPHA: (223) implies:
% 24.92/4.28 | | | | | (224) function(all_59_5) = all_323_1
% 24.92/4.28 | | | | | (225) relation(all_59_5) = all_323_2
% 24.92/4.28 | | | | | (226) ~ (all_323_1 = 0) | ~ (all_323_2 = 0) | ( ! [v0: $i] : !
% 24.92/4.28 | | | | | [v1: $i] : ( ~ (all_165_0 = 0) | ~ (apply(v0, all_323_0) =
% 24.92/4.28 | | | | | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4:
% 24.92/4.28 | | | | | $i] : ? [v5: $i] : (apply(v4, all_59_6) = v5 &
% 24.92/4.28 | | | | | relation_composition(all_59_5, v0) = v4 & relation(v0)
% 24.92/4.28 | | | | | = v2 & function(v0) = v3 & $i(v5) & $i(v4) & ( ~ (v3 =
% 24.92/4.28 | | | | | 0) | ~ (v2 = 0) | v5 = v1))) & ! [v0: $i] : !
% 24.92/4.28 | | | | | [v1: $i] : ( ~ (all_165_0 = 0) | ~
% 24.92/4.28 | | | | | (relation_composition(all_59_5, v0) = v1) | ~ $i(v0) |
% 24.92/4.28 | | | | | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5: $i] :
% 24.92/4.28 | | | | | (apply(v1, all_59_6) = v4 & apply(v0, all_323_0) = v5 &
% 24.92/4.28 | | | | | relation(v0) = v2 & function(v0) = v3 & $i(v5) & $i(v4)
% 24.92/4.28 | | | | | & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = v4))) & ! [v0: $i]
% 24.92/4.28 | | | | | : ( ~ (all_165_0 = 0) | ~ (relation(v0) = 0) | ~ $i(v0) |
% 24.92/4.28 | | | | | ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 24.92/4.28 | | | | | (apply(v2, all_59_6) = v3 & apply(v0, all_323_0) = v4 &
% 24.92/4.28 | | | | | relation_composition(all_59_5, v0) = v2 & function(v0)
% 24.92/4.28 | | | | | = v1 & $i(v4) & $i(v3) & $i(v2) & ( ~ (v1 = 0) | v4 =
% 24.92/4.28 | | | | | v3))) & ! [v0: $i] : ( ~ (all_165_0 = 0) | ~
% 24.92/4.28 | | | | | (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2:
% 24.92/4.28 | | | | | $i] : ? [v3: $i] : ? [v4: $i] : (apply(v2, all_59_6)
% 24.92/4.28 | | | | | = v3 & apply(v0, all_323_0) = v4 &
% 24.92/4.28 | | | | | relation_composition(all_59_5, v0) = v2 & relation(v0)
% 24.92/4.28 | | | | | = v1 & $i(v4) & $i(v3) & $i(v2) & ( ~ (v1 = 0) | v4 =
% 24.92/4.28 | | | | | v3))))
% 24.92/4.28 | | | | |
% 24.92/4.28 | | | | | DELTA: instantiating (200) with fresh symbols all_325_0, all_325_1,
% 24.92/4.28 | | | | | all_325_2 gives:
% 24.92/4.28 | | | | | (227) apply(all_59_3, all_59_4) = all_325_0 & relation(all_59_3) =
% 24.92/4.28 | | | | | all_325_2 & function(all_59_3) = all_325_1 & $i(all_325_0) &
% 24.92/4.28 | | | | | ( ~ (all_325_1 = 0) | ~ (all_325_2 = 0) | ( ! [v0: $i] : !
% 24.92/4.28 | | | | | [v1: $i] : ( ~ (all_169_0 = 0) | ~ (apply(v0, all_325_0)
% 24.92/4.28 | | | | | = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ?
% 24.92/4.28 | | | | | [v4: $i] : ? [v5: $i] : (apply(v4, all_59_4) = v5 &
% 24.92/4.28 | | | | | relation_composition(all_59_3, v0) = v4 &
% 24.92/4.28 | | | | | relation(v0) = v2 & function(v0) = v3 & $i(v5) &
% 24.92/4.28 | | | | | $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = v1))) & !
% 24.92/4.28 | | | | | [v0: $i] : ! [v1: $i] : ( ~ (all_169_0 = 0) | ~
% 24.92/4.28 | | | | | (relation_composition(all_59_3, v0) = v1) | ~ $i(v0) |
% 24.92/4.28 | | | | | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5: $i]
% 24.92/4.28 | | | | | : (apply(v1, all_59_4) = v4 & apply(v0, all_325_0) = v5
% 24.92/4.28 | | | | | & relation(v0) = v2 & function(v0) = v3 & $i(v5) &
% 24.92/4.28 | | | | | $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = v4))) & !
% 24.92/4.28 | | | | | [v0: $i] : ( ~ (all_169_0 = 0) | ~ (relation(v0) = 0) |
% 24.92/4.28 | | | | | ~ $i(v0) | ? [v1: any] : ? [v2: $i] : ? [v3: $i] :
% 24.92/4.28 | | | | | ? [v4: $i] : (apply(v2, all_59_4) = v3 & apply(v0,
% 24.92/4.28 | | | | | all_325_0) = v4 & relation_composition(all_59_3,
% 24.92/4.28 | | | | | v0) = v2 & function(v0) = v1 & $i(v4) & $i(v3) &
% 24.92/4.28 | | | | | $i(v2) & ( ~ (v1 = 0) | v4 = v3))) & ! [v0: $i] : (
% 24.92/4.28 | | | | | ~ (all_169_0 = 0) | ~ (function(v0) = 0) | ~ $i(v0) |
% 24.92/4.28 | | | | | ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 24.92/4.28 | | | | | : (apply(v2, all_59_4) = v3 & apply(v0, all_325_0) = v4
% 24.92/4.28 | | | | | & relation_composition(all_59_3, v0) = v2 &
% 24.92/4.28 | | | | | relation(v0) = v1 & $i(v4) & $i(v3) & $i(v2) & ( ~
% 24.92/4.28 | | | | | (v1 = 0) | v4 = v3)))))
% 24.92/4.28 | | | | |
% 24.92/4.28 | | | | | ALPHA: (227) implies:
% 24.92/4.28 | | | | | (228) function(all_59_3) = all_325_1
% 24.92/4.28 | | | | | (229) relation(all_59_3) = all_325_2
% 24.92/4.28 | | | | | (230) apply(all_59_3, all_59_4) = all_325_0
% 24.92/4.28 | | | | |
% 24.92/4.28 | | | | | DELTA: instantiating (202) with fresh symbols all_327_0, all_327_1,
% 24.92/4.28 | | | | | all_327_2 gives:
% 24.92/4.29 | | | | | (231) apply(all_59_2, all_59_6) = all_327_0 & relation(all_59_2) =
% 24.92/4.29 | | | | | all_327_2 & function(all_59_2) = all_327_1 & $i(all_327_0) &
% 24.92/4.29 | | | | | ( ~ (all_327_1 = 0) | ~ (all_327_2 = 0) | ( ! [v0: $i] : !
% 24.92/4.29 | | | | | [v1: $i] : ( ~ (all_167_0 = 0) | ~ (apply(v0, all_327_0)
% 24.92/4.29 | | | | | = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ?
% 24.92/4.29 | | | | | [v4: $i] : ? [v5: $i] : (apply(v4, all_59_6) = v5 &
% 24.92/4.29 | | | | | relation_composition(all_59_2, v0) = v4 &
% 24.92/4.29 | | | | | relation(v0) = v2 & function(v0) = v3 & $i(v5) &
% 24.92/4.29 | | | | | $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = v1))) & !
% 24.92/4.29 | | | | | [v0: $i] : ! [v1: $i] : ( ~ (all_167_0 = 0) | ~
% 24.92/4.29 | | | | | (relation_composition(all_59_2, v0) = v1) | ~ $i(v0) |
% 24.92/4.29 | | | | | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5: $i]
% 24.92/4.29 | | | | | : (apply(v1, all_59_6) = v4 & apply(v0, all_327_0) = v5
% 24.92/4.29 | | | | | & relation(v0) = v2 & function(v0) = v3 & $i(v5) &
% 24.92/4.29 | | | | | $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = v4))) & !
% 24.92/4.29 | | | | | [v0: $i] : ( ~ (all_167_0 = 0) | ~ (relation(v0) = 0) |
% 24.92/4.29 | | | | | ~ $i(v0) | ? [v1: any] : ? [v2: $i] : ? [v3: $i] :
% 24.92/4.29 | | | | | ? [v4: $i] : (apply(v2, all_59_6) = v3 & apply(v0,
% 24.92/4.29 | | | | | all_327_0) = v4 & relation_composition(all_59_2,
% 24.92/4.29 | | | | | v0) = v2 & function(v0) = v1 & $i(v4) & $i(v3) &
% 24.92/4.29 | | | | | $i(v2) & ( ~ (v1 = 0) | v4 = v3))) & ! [v0: $i] : (
% 24.92/4.29 | | | | | ~ (all_167_0 = 0) | ~ (function(v0) = 0) | ~ $i(v0) |
% 24.92/4.29 | | | | | ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 24.92/4.29 | | | | | : (apply(v2, all_59_6) = v3 & apply(v0, all_327_0) = v4
% 24.92/4.29 | | | | | & relation_composition(all_59_2, v0) = v2 &
% 24.92/4.29 | | | | | relation(v0) = v1 & $i(v4) & $i(v3) & $i(v2) & ( ~
% 24.92/4.29 | | | | | (v1 = 0) | v4 = v3)))))
% 24.92/4.29 | | | | |
% 24.92/4.29 | | | | | ALPHA: (231) implies:
% 24.92/4.29 | | | | | (232) apply(all_59_2, all_59_6) = all_327_0
% 24.92/4.29 | | | | |
% 24.92/4.29 | | | | | BETA: splitting (217) gives:
% 24.92/4.29 | | | | |
% 24.92/4.29 | | | | | Case 1:
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | GROUND_INST: instantiating (21) with 0, all_323_1, all_59_5,
% 24.92/4.29 | | | | | | simplifying with (46), (224) gives:
% 24.92/4.29 | | | | | | (233) all_323_1 = 0
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | GROUND_INST: instantiating (21) with 0, all_325_1, all_59_3,
% 24.92/4.29 | | | | | | simplifying with (47), (228) gives:
% 24.92/4.29 | | | | | | (234) all_325_1 = 0
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | GROUND_INST: instantiating (21) with all_307_0, all_325_1, all_59_3,
% 24.92/4.29 | | | | | | simplifying with (219), (228) gives:
% 24.92/4.29 | | | | | | (235) all_325_1 = all_307_0
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | GROUND_INST: instantiating (22) with all_109_2, all_323_2, all_59_5,
% 24.92/4.29 | | | | | | simplifying with (84), (225) gives:
% 24.92/4.29 | | | | | | (236) all_323_2 = all_109_2
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | GROUND_INST: instantiating (22) with all_315_2, all_323_2, all_59_5,
% 24.92/4.29 | | | | | | simplifying with (222), (225) gives:
% 24.92/4.29 | | | | | | (237) all_323_2 = all_315_2
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | GROUND_INST: instantiating (22) with all_285_1, all_323_2, all_59_5,
% 24.92/4.29 | | | | | | simplifying with (213), (225) gives:
% 24.92/4.29 | | | | | | (238) all_323_2 = all_285_1
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | GROUND_INST: instantiating (22) with 0, all_323_2, all_59_5,
% 24.92/4.29 | | | | | | simplifying with (191), (225) gives:
% 24.92/4.29 | | | | | | (239) all_323_2 = 0
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | GROUND_INST: instantiating (22) with all_267_1, all_307_2, all_59_3,
% 24.92/4.29 | | | | | | simplifying with (211), (220) gives:
% 24.92/4.29 | | | | | | (240) all_307_2 = all_267_1
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | GROUND_INST: instantiating (22) with 0, all_325_2, all_59_3,
% 24.92/4.29 | | | | | | simplifying with (48), (229) gives:
% 24.92/4.29 | | | | | | (241) all_325_2 = 0
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | GROUND_INST: instantiating (22) with all_307_2, all_325_2, all_59_3,
% 24.92/4.29 | | | | | | simplifying with (220), (229) gives:
% 24.92/4.29 | | | | | | (242) all_325_2 = all_307_2
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | GROUND_INST: instantiating (29) with all_59_8, all_259_1, all_59_5,
% 24.92/4.29 | | | | | | all_59_7, all_59_8, simplifying with (189), (209)
% 24.92/4.29 | | | | | | gives:
% 24.92/4.29 | | | | | | (243) all_259_1 = all_59_8
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | GROUND_INST: instantiating (29) with all_241_0, all_259_1, all_59_5,
% 24.92/4.29 | | | | | | all_59_7, all_59_8, simplifying with (204), (209)
% 24.92/4.29 | | | | | | gives:
% 24.92/4.29 | | | | | | (244) all_259_1 = all_241_0
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | GROUND_INST: instantiating (24) with all_165_1, all_257_0, all_59_5,
% 24.92/4.29 | | | | | | simplifying with (117), (207) gives:
% 24.92/4.29 | | | | | | (245) all_257_0 = all_165_1
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | GROUND_INST: instantiating (24) with all_241_0, all_257_0, all_59_5,
% 24.92/4.29 | | | | | | simplifying with (205), (207) gives:
% 24.92/4.29 | | | | | | (246) all_257_0 = all_241_0
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | GROUND_INST: instantiating (27) with all_59_0, all_325_0, all_59_4,
% 24.92/4.29 | | | | | | all_59_3, simplifying with (53), (230) gives:
% 24.92/4.29 | | | | | | (247) all_325_0 = all_59_0
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | GROUND_INST: instantiating (27) with all_59_1, all_327_0, all_59_6,
% 24.92/4.29 | | | | | | all_59_2, simplifying with (54), (232) gives:
% 24.92/4.29 | | | | | | (248) all_327_0 = all_59_1
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | COMBINE_EQS: (234), (235) imply:
% 24.92/4.29 | | | | | | (249) all_307_0 = 0
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | COMBINE_EQS: (241), (242) imply:
% 24.92/4.29 | | | | | | (250) all_307_2 = 0
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | SIMP: (250) implies:
% 24.92/4.29 | | | | | | (251) all_307_2 = 0
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | COMBINE_EQS: (236), (237) imply:
% 24.92/4.29 | | | | | | (252) all_315_2 = all_109_2
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | COMBINE_EQS: (237), (239) imply:
% 24.92/4.29 | | | | | | (253) all_315_2 = 0
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | COMBINE_EQS: (237), (238) imply:
% 24.92/4.29 | | | | | | (254) all_315_2 = all_285_1
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | COMBINE_EQS: (252), (254) imply:
% 24.92/4.29 | | | | | | (255) all_285_1 = all_109_2
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | COMBINE_EQS: (253), (254) imply:
% 24.92/4.29 | | | | | | (256) all_285_1 = 0
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | COMBINE_EQS: (240), (251) imply:
% 24.92/4.29 | | | | | | (257) all_267_1 = 0
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | SIMP: (257) implies:
% 24.92/4.29 | | | | | | (258) all_267_1 = 0
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | COMBINE_EQS: (255), (256) imply:
% 24.92/4.29 | | | | | | (259) all_109_2 = 0
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | COMBINE_EQS: (243), (244) imply:
% 24.92/4.29 | | | | | | (260) all_241_0 = all_59_8
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | SIMP: (260) implies:
% 24.92/4.29 | | | | | | (261) all_241_0 = all_59_8
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | COMBINE_EQS: (245), (246) imply:
% 24.92/4.29 | | | | | | (262) all_241_0 = all_165_1
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | SIMP: (262) implies:
% 24.92/4.29 | | | | | | (263) all_241_0 = all_165_1
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | COMBINE_EQS: (261), (263) imply:
% 24.92/4.29 | | | | | | (264) all_165_1 = all_59_8
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | COMBINE_EQS: (177), (259) imply:
% 24.92/4.29 | | | | | | (265) all_165_3 = 0
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | REDUCE: (114), (264) imply:
% 24.92/4.29 | | | | | | (266) in(all_59_6, all_59_8) = all_165_0
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | BETA: splitting (226) gives:
% 24.92/4.29 | | | | | |
% 24.92/4.29 | | | | | | Case 1:
% 24.92/4.29 | | | | | | |
% 24.92/4.29 | | | | | | | (267) ~ (all_323_1 = 0)
% 24.92/4.29 | | | | | | |
% 24.92/4.29 | | | | | | | REDUCE: (233), (267) imply:
% 24.92/4.29 | | | | | | | (268) $false
% 24.92/4.29 | | | | | | |
% 24.92/4.29 | | | | | | | CLOSE: (268) is inconsistent.
% 24.92/4.29 | | | | | | |
% 24.92/4.29 | | | | | | Case 2:
% 24.92/4.29 | | | | | | |
% 24.92/4.29 | | | | | | | (269) ~ (all_323_2 = 0) | ( ! [v0: $i] : ! [v1: $i] : ( ~
% 24.92/4.29 | | | | | | | (all_165_0 = 0) | ~ (apply(v0, all_323_0) = v1) | ~
% 24.92/4.29 | | | | | | | $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] :
% 24.92/4.29 | | | | | | | ? [v5: $i] : (apply(v4, all_59_6) = v5 &
% 24.92/4.29 | | | | | | | relation_composition(all_59_5, v0) = v4 &
% 24.92/4.29 | | | | | | | relation(v0) = v2 & function(v0) = v3 & $i(v5) &
% 24.92/4.29 | | | | | | | $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = v1))) &
% 24.92/4.29 | | | | | | | ! [v0: $i] : ! [v1: $i] : ( ~ (all_165_0 = 0) | ~
% 24.92/4.29 | | | | | | | (relation_composition(all_59_5, v0) = v1) | ~ $i(v0)
% 24.92/4.29 | | | | | | | | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5:
% 24.92/4.29 | | | | | | | $i] : (apply(v1, all_59_6) = v4 & apply(v0,
% 24.92/4.29 | | | | | | | all_323_0) = v5 & relation(v0) = v2 &
% 24.92/4.29 | | | | | | | function(v0) = v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0)
% 24.92/4.29 | | | | | | | | ~ (v2 = 0) | v5 = v4))) & ! [v0: $i] : ( ~
% 24.92/4.29 | | | | | | | (all_165_0 = 0) | ~ (relation(v0) = 0) | ~ $i(v0) |
% 24.92/4.29 | | | | | | | ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 24.92/4.29 | | | | | | | $i] : (apply(v2, all_59_6) = v3 & apply(v0,
% 24.92/4.29 | | | | | | | all_323_0) = v4 & relation_composition(all_59_5,
% 24.92/4.29 | | | | | | | v0) = v2 & function(v0) = v1 & $i(v4) & $i(v3) &
% 24.92/4.29 | | | | | | | $i(v2) & ( ~ (v1 = 0) | v4 = v3))) & ! [v0: $i] :
% 24.92/4.29 | | | | | | | ( ~ (all_165_0 = 0) | ~ (function(v0) = 0) | ~ $i(v0)
% 24.92/4.29 | | | | | | | | ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 24.92/4.29 | | | | | | | $i] : (apply(v2, all_59_6) = v3 & apply(v0,
% 24.92/4.29 | | | | | | | all_323_0) = v4 & relation_composition(all_59_5,
% 24.92/4.29 | | | | | | | v0) = v2 & relation(v0) = v1 & $i(v4) & $i(v3) &
% 24.92/4.29 | | | | | | | $i(v2) & ( ~ (v1 = 0) | v4 = v3))))
% 24.92/4.29 | | | | | | |
% 24.92/4.29 | | | | | | | BETA: splitting (118) gives:
% 24.92/4.29 | | | | | | |
% 24.92/4.29 | | | | | | | Case 1:
% 24.92/4.29 | | | | | | | |
% 24.92/4.29 | | | | | | | | (270) ~ (all_165_2 = 0)
% 24.92/4.29 | | | | | | | |
% 24.92/4.29 | | | | | | | | REDUCE: (139), (270) imply:
% 24.92/4.29 | | | | | | | | (271) $false
% 24.92/4.29 | | | | | | | |
% 24.92/4.29 | | | | | | | | CLOSE: (271) is inconsistent.
% 24.92/4.29 | | | | | | | |
% 24.92/4.29 | | | | | | | Case 2:
% 24.92/4.29 | | | | | | | |
% 24.92/4.30 | | | | | | | | (272) ~ (all_165_3 = 0) | ( ! [v0: $i] : ! [v1: $i] : ( ~
% 24.92/4.30 | | | | | | | | (all_165_0 = 0) | ~ (apply(v0, all_59_4) = v1) |
% 24.92/4.30 | | | | | | | | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4:
% 24.92/4.30 | | | | | | | | $i] : ? [v5: $i] : (apply(v4, all_59_6) = v5 &
% 24.92/4.30 | | | | | | | | relation_composition(all_59_5, v0) = v4 &
% 24.92/4.30 | | | | | | | | relation(v0) = v2 & function(v0) = v3 & $i(v5) &
% 24.92/4.30 | | | | | | | | $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = v1)))
% 24.92/4.30 | | | | | | | | & ! [v0: $i] : ! [v1: $i] : ( ~ (all_165_0 = 0) |
% 24.92/4.30 | | | | | | | | ~ (relation_composition(all_59_5, v0) = v1) | ~
% 24.92/4.30 | | | | | | | | $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i]
% 24.92/4.30 | | | | | | | | : ? [v5: $i] : (apply(v1, all_59_6) = v4 &
% 24.92/4.30 | | | | | | | | apply(v0, all_59_4) = v5 & relation(v0) = v2 &
% 24.92/4.30 | | | | | | | | function(v0) = v3 & $i(v5) & $i(v4) & ( ~ (v3 =
% 24.92/4.30 | | | | | | | | 0) | ~ (v2 = 0) | v5 = v4))) & ! [v0: $i] :
% 24.92/4.30 | | | | | | | | ( ~ (all_165_0 = 0) | ~ (relation(v0) = 0) | ~
% 24.92/4.30 | | | | | | | | $i(v0) | ? [v1: any] : ? [v2: $i] : ? [v3: $i] :
% 24.92/4.30 | | | | | | | | ? [v4: $i] : (apply(v2, all_59_6) = v3 & apply(v0,
% 24.92/4.30 | | | | | | | | all_59_4) = v4 & relation_composition(all_59_5,
% 24.92/4.30 | | | | | | | | v0) = v2 & function(v0) = v1 & $i(v4) & $i(v3)
% 24.92/4.30 | | | | | | | | & $i(v2) & ( ~ (v1 = 0) | v4 = v3))) & ! [v0:
% 24.92/4.30 | | | | | | | | $i] : ( ~ (all_165_0 = 0) | ~ (function(v0) = 0) |
% 24.92/4.30 | | | | | | | | ~ $i(v0) | ? [v1: any] : ? [v2: $i] : ? [v3:
% 24.92/4.30 | | | | | | | | $i] : ? [v4: $i] : (apply(v2, all_59_6) = v3 &
% 24.92/4.30 | | | | | | | | apply(v0, all_59_4) = v4 &
% 24.92/4.30 | | | | | | | | relation_composition(all_59_5, v0) = v2 &
% 24.92/4.30 | | | | | | | | relation(v0) = v1 & $i(v4) & $i(v3) & $i(v2) & (
% 24.92/4.30 | | | | | | | | ~ (v1 = 0) | v4 = v3))))
% 24.92/4.30 | | | | | | | |
% 24.92/4.30 | | | | | | | | BETA: splitting (269) gives:
% 24.92/4.30 | | | | | | | |
% 24.92/4.30 | | | | | | | | Case 1:
% 24.92/4.30 | | | | | | | | |
% 24.92/4.30 | | | | | | | | | (273) ~ (all_323_2 = 0)
% 24.92/4.30 | | | | | | | | |
% 24.92/4.30 | | | | | | | | | REDUCE: (239), (273) imply:
% 24.92/4.30 | | | | | | | | | (274) $false
% 24.92/4.30 | | | | | | | | |
% 24.92/4.30 | | | | | | | | | CLOSE: (274) is inconsistent.
% 24.92/4.30 | | | | | | | | |
% 24.92/4.30 | | | | | | | | Case 2:
% 24.92/4.30 | | | | | | | | |
% 24.92/4.30 | | | | | | | | | (275) ! [v0: $i] : ! [v1: $i] : ( ~ (all_165_0 = 0) | ~
% 24.92/4.30 | | | | | | | | | (apply(v0, all_323_0) = v1) | ~ $i(v0) | ? [v2:
% 24.92/4.30 | | | | | | | | | any] : ? [v3: any] : ? [v4: $i] : ? [v5: $i] :
% 24.92/4.30 | | | | | | | | | (apply(v4, all_59_6) = v5 &
% 24.92/4.30 | | | | | | | | | relation_composition(all_59_5, v0) = v4 &
% 24.92/4.30 | | | | | | | | | relation(v0) = v2 & function(v0) = v3 & $i(v5) &
% 24.92/4.30 | | | | | | | | | $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = v1)))
% 24.92/4.30 | | | | | | | | | & ! [v0: $i] : ! [v1: $i] : ( ~ (all_165_0 = 0) |
% 24.92/4.30 | | | | | | | | | ~ (relation_composition(all_59_5, v0) = v1) | ~
% 24.92/4.30 | | | | | | | | | $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i]
% 24.92/4.30 | | | | | | | | | : ? [v5: $i] : (apply(v1, all_59_6) = v4 &
% 24.92/4.30 | | | | | | | | | apply(v0, all_323_0) = v5 & relation(v0) = v2 &
% 24.92/4.30 | | | | | | | | | function(v0) = v3 & $i(v5) & $i(v4) & ( ~ (v3 =
% 24.92/4.30 | | | | | | | | | 0) | ~ (v2 = 0) | v5 = v4))) & ! [v0: $i] :
% 24.92/4.30 | | | | | | | | | ( ~ (all_165_0 = 0) | ~ (relation(v0) = 0) | ~
% 24.92/4.30 | | | | | | | | | $i(v0) | ? [v1: any] : ? [v2: $i] : ? [v3: $i] :
% 24.92/4.30 | | | | | | | | | ? [v4: $i] : (apply(v2, all_59_6) = v3 & apply(v0,
% 24.92/4.30 | | | | | | | | | all_323_0) = v4 &
% 24.92/4.30 | | | | | | | | | relation_composition(all_59_5, v0) = v2 &
% 24.92/4.30 | | | | | | | | | function(v0) = v1 & $i(v4) & $i(v3) & $i(v2) & (
% 24.92/4.30 | | | | | | | | | ~ (v1 = 0) | v4 = v3))) & ! [v0: $i] : ( ~
% 24.92/4.30 | | | | | | | | | (all_165_0 = 0) | ~ (function(v0) = 0) | ~ $i(v0)
% 24.92/4.30 | | | | | | | | | | ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ?
% 24.92/4.30 | | | | | | | | | [v4: $i] : (apply(v2, all_59_6) = v3 & apply(v0,
% 24.92/4.30 | | | | | | | | | all_323_0) = v4 &
% 24.92/4.30 | | | | | | | | | relation_composition(all_59_5, v0) = v2 &
% 24.92/4.30 | | | | | | | | | relation(v0) = v1 & $i(v4) & $i(v3) & $i(v2) & (
% 24.92/4.30 | | | | | | | | | ~ (v1 = 0) | v4 = v3)))
% 24.92/4.30 | | | | | | | | |
% 24.92/4.30 | | | | | | | | | ALPHA: (275) implies:
% 24.92/4.30 | | | | | | | | | (276) ! [v0: $i] : ! [v1: $i] : ( ~ (all_165_0 = 0) | ~
% 24.92/4.30 | | | | | | | | | (relation_composition(all_59_5, v0) = v1) | ~
% 24.92/4.30 | | | | | | | | | $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i]
% 24.92/4.30 | | | | | | | | | : ? [v5: $i] : (apply(v1, all_59_6) = v4 &
% 24.92/4.30 | | | | | | | | | apply(v0, all_323_0) = v5 & relation(v0) = v2 &
% 24.92/4.30 | | | | | | | | | function(v0) = v3 & $i(v5) & $i(v4) & ( ~ (v3 =
% 24.92/4.30 | | | | | | | | | 0) | ~ (v2 = 0) | v5 = v4)))
% 24.92/4.30 | | | | | | | | |
% 24.92/4.30 | | | | | | | | | GROUND_INST: instantiating (276) with all_59_3, all_59_2,
% 24.92/4.30 | | | | | | | | | simplifying with (43), (51) gives:
% 24.92/4.30 | | | | | | | | | (277) ~ (all_165_0 = 0) | ? [v0: any] : ? [v1: any] : ?
% 24.92/4.30 | | | | | | | | | [v2: $i] : ? [v3: $i] : (apply(all_59_2, all_59_6) =
% 24.92/4.30 | | | | | | | | | v2 & apply(all_59_3, all_323_0) = v3 &
% 24.92/4.30 | | | | | | | | | relation(all_59_3) = v0 & function(all_59_3) = v1 &
% 24.92/4.30 | | | | | | | | | $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 =
% 24.92/4.30 | | | | | | | | | v2))
% 24.92/4.30 | | | | | | | | |
% 24.92/4.30 | | | | | | | | | BETA: splitting (272) gives:
% 24.92/4.30 | | | | | | | | |
% 24.92/4.30 | | | | | | | | | Case 1:
% 24.92/4.30 | | | | | | | | | |
% 24.92/4.30 | | | | | | | | | | (278) ~ (all_165_3 = 0)
% 24.92/4.30 | | | | | | | | | |
% 24.92/4.30 | | | | | | | | | | REDUCE: (265), (278) imply:
% 24.92/4.30 | | | | | | | | | | (279) $false
% 24.92/4.30 | | | | | | | | | |
% 24.92/4.30 | | | | | | | | | | CLOSE: (279) is inconsistent.
% 25.24/4.30 | | | | | | | | | |
% 25.24/4.30 | | | | | | | | | Case 2:
% 25.24/4.30 | | | | | | | | | |
% 25.24/4.30 | | | | | | | | | | (280) ! [v0: $i] : ! [v1: $i] : ( ~ (all_165_0 = 0) |
% 25.24/4.30 | | | | | | | | | | ~ (apply(v0, all_59_4) = v1) | ~ $i(v0) | ?
% 25.24/4.30 | | | | | | | | | | [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5:
% 25.24/4.30 | | | | | | | | | | $i] : (apply(v4, all_59_6) = v5 &
% 25.24/4.30 | | | | | | | | | | relation_composition(all_59_5, v0) = v4 &
% 25.24/4.30 | | | | | | | | | | relation(v0) = v2 & function(v0) = v3 & $i(v5)
% 25.24/4.30 | | | | | | | | | | & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 =
% 25.24/4.30 | | | | | | | | | | v1))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 25.24/4.30 | | | | | | | | | | (all_165_0 = 0) | ~
% 25.24/4.30 | | | | | | | | | | (relation_composition(all_59_5, v0) = v1) | ~
% 25.24/4.30 | | | | | | | | | | $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4:
% 25.24/4.30 | | | | | | | | | | $i] : ? [v5: $i] : (apply(v1, all_59_6) = v4 &
% 25.24/4.30 | | | | | | | | | | apply(v0, all_59_4) = v5 & relation(v0) = v2 &
% 25.24/4.30 | | | | | | | | | | function(v0) = v3 & $i(v5) & $i(v4) & ( ~ (v3 =
% 25.24/4.30 | | | | | | | | | | 0) | ~ (v2 = 0) | v5 = v4))) & ! [v0: $i]
% 25.24/4.30 | | | | | | | | | | : ( ~ (all_165_0 = 0) | ~ (relation(v0) = 0) | ~
% 25.24/4.30 | | | | | | | | | | $i(v0) | ? [v1: any] : ? [v2: $i] : ? [v3: $i]
% 25.24/4.30 | | | | | | | | | | : ? [v4: $i] : (apply(v2, all_59_6) = v3 &
% 25.24/4.30 | | | | | | | | | | apply(v0, all_59_4) = v4 &
% 25.24/4.30 | | | | | | | | | | relation_composition(all_59_5, v0) = v2 &
% 25.24/4.30 | | | | | | | | | | function(v0) = v1 & $i(v4) & $i(v3) & $i(v2) &
% 25.24/4.30 | | | | | | | | | | ( ~ (v1 = 0) | v4 = v3))) & ! [v0: $i] : ( ~
% 25.24/4.30 | | | | | | | | | | (all_165_0 = 0) | ~ (function(v0) = 0) | ~
% 25.24/4.30 | | | | | | | | | | $i(v0) | ? [v1: any] : ? [v2: $i] : ? [v3: $i]
% 25.24/4.30 | | | | | | | | | | : ? [v4: $i] : (apply(v2, all_59_6) = v3 &
% 25.24/4.30 | | | | | | | | | | apply(v0, all_59_4) = v4 &
% 25.24/4.30 | | | | | | | | | | relation_composition(all_59_5, v0) = v2 &
% 25.24/4.30 | | | | | | | | | | relation(v0) = v1 & $i(v4) & $i(v3) & $i(v2) &
% 25.24/4.30 | | | | | | | | | | ( ~ (v1 = 0) | v4 = v3)))
% 25.24/4.30 | | | | | | | | | |
% 25.24/4.30 | | | | | | | | | | ALPHA: (280) implies:
% 25.24/4.30 | | | | | | | | | | (281) ! [v0: $i] : ! [v1: $i] : ( ~ (all_165_0 = 0) |
% 25.24/4.30 | | | | | | | | | | ~ (relation_composition(all_59_5, v0) = v1) | ~
% 25.24/4.30 | | | | | | | | | | $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4:
% 25.24/4.30 | | | | | | | | | | $i] : ? [v5: $i] : (apply(v1, all_59_6) = v4 &
% 25.24/4.30 | | | | | | | | | | apply(v0, all_59_4) = v5 & relation(v0) = v2 &
% 25.24/4.30 | | | | | | | | | | function(v0) = v3 & $i(v5) & $i(v4) & ( ~ (v3 =
% 25.24/4.30 | | | | | | | | | | 0) | ~ (v2 = 0) | v5 = v4)))
% 25.24/4.30 | | | | | | | | | | (282) ! [v0: $i] : ! [v1: $i] : ( ~ (all_165_0 = 0) |
% 25.24/4.30 | | | | | | | | | | ~ (apply(v0, all_59_4) = v1) | ~ $i(v0) | ?
% 25.24/4.30 | | | | | | | | | | [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5:
% 25.24/4.30 | | | | | | | | | | $i] : (apply(v4, all_59_6) = v5 &
% 25.24/4.30 | | | | | | | | | | relation_composition(all_59_5, v0) = v4 &
% 25.24/4.30 | | | | | | | | | | relation(v0) = v2 & function(v0) = v3 & $i(v5)
% 25.24/4.30 | | | | | | | | | | & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 =
% 25.24/4.30 | | | | | | | | | | v1)))
% 25.24/4.30 | | | | | | | | | |
% 25.24/4.30 | | | | | | | | | | GROUND_INST: instantiating (281) with all_59_3, all_59_2,
% 25.24/4.30 | | | | | | | | | | simplifying with (43), (51) gives:
% 25.24/4.30 | | | | | | | | | | (283) ~ (all_165_0 = 0) | ? [v0: any] : ? [v1: any] :
% 25.24/4.30 | | | | | | | | | | ? [v2: $i] : ? [v3: $i] : (apply(all_59_2,
% 25.24/4.30 | | | | | | | | | | all_59_6) = v2 & apply(all_59_3, all_59_4) = v3
% 25.24/4.30 | | | | | | | | | | & relation(all_59_3) = v0 & function(all_59_3) =
% 25.24/4.30 | | | | | | | | | | v1 & $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0)
% 25.24/4.30 | | | | | | | | | | | v3 = v2))
% 25.24/4.30 | | | | | | | | | |
% 25.24/4.30 | | | | | | | | | | GROUND_INST: instantiating (282) with all_59_3, all_59_0,
% 25.24/4.30 | | | | | | | | | | simplifying with (43), (53) gives:
% 25.24/4.30 | | | | | | | | | | (284) ~ (all_165_0 = 0) | ? [v0: any] : ? [v1: any] :
% 25.24/4.30 | | | | | | | | | | ? [v2: $i] : ? [v3: $i] : (apply(v2, all_59_6) =
% 25.24/4.30 | | | | | | | | | | v3 & relation_composition(all_59_5, all_59_3) =
% 25.24/4.30 | | | | | | | | | | v2 & relation(all_59_3) = v0 & function(all_59_3)
% 25.24/4.30 | | | | | | | | | | = v1 & $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 =
% 25.24/4.30 | | | | | | | | | | 0) | v3 = all_59_0))
% 25.24/4.30 | | | | | | | | | |
% 25.24/4.30 | | | | | | | | | | BETA: splitting (284) gives:
% 25.24/4.30 | | | | | | | | | |
% 25.24/4.30 | | | | | | | | | | Case 1:
% 25.24/4.30 | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | (285) ~ (all_165_0 = 0)
% 25.24/4.31 | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | REF_CLOSE: (25), (45), (266), (285) are inconsistent by
% 25.24/4.31 | | | | | | | | | | | sub-proof #1.
% 25.24/4.31 | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | Case 2:
% 25.24/4.31 | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | (286) all_165_0 = 0
% 25.24/4.31 | | | | | | | | | | | (287) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ?
% 25.24/4.31 | | | | | | | | | | | [v3: $i] : (apply(v2, all_59_6) = v3 &
% 25.24/4.31 | | | | | | | | | | | relation_composition(all_59_5, all_59_3) = v2 &
% 25.24/4.31 | | | | | | | | | | | relation(all_59_3) = v0 & function(all_59_3) =
% 25.24/4.31 | | | | | | | | | | | v1 & $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 =
% 25.24/4.31 | | | | | | | | | | | 0) | v3 = all_59_0))
% 25.24/4.31 | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | DELTA: instantiating (287) with fresh symbols all_453_0,
% 25.24/4.31 | | | | | | | | | | | all_453_1, all_453_2, all_453_3 gives:
% 25.24/4.31 | | | | | | | | | | | (288) apply(all_453_1, all_59_6) = all_453_0 &
% 25.24/4.31 | | | | | | | | | | | relation_composition(all_59_5, all_59_3) =
% 25.24/4.31 | | | | | | | | | | | all_453_1 & relation(all_59_3) = all_453_3 &
% 25.24/4.31 | | | | | | | | | | | function(all_59_3) = all_453_2 & $i(all_453_0) &
% 25.24/4.31 | | | | | | | | | | | $i(all_453_1) & ( ~ (all_453_2 = 0) | ~
% 25.24/4.31 | | | | | | | | | | | (all_453_3 = 0) | all_453_0 = all_59_0)
% 25.24/4.31 | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | ALPHA: (288) implies:
% 25.24/4.31 | | | | | | | | | | | (289) function(all_59_3) = all_453_2
% 25.24/4.31 | | | | | | | | | | | (290) relation(all_59_3) = all_453_3
% 25.24/4.31 | | | | | | | | | | | (291) relation_composition(all_59_5, all_59_3) =
% 25.24/4.31 | | | | | | | | | | | all_453_1
% 25.24/4.31 | | | | | | | | | | | (292) apply(all_453_1, all_59_6) = all_453_0
% 25.24/4.31 | | | | | | | | | | | (293) ~ (all_453_2 = 0) | ~ (all_453_3 = 0) |
% 25.24/4.31 | | | | | | | | | | | all_453_0 = all_59_0
% 25.24/4.31 | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | GROUND_INST: instantiating (21) with 0, all_453_2, all_59_3,
% 25.24/4.31 | | | | | | | | | | | simplifying with (47), (289) gives:
% 25.24/4.31 | | | | | | | | | | | (294) all_453_2 = 0
% 25.24/4.31 | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | GROUND_INST: instantiating (22) with 0, all_453_3, all_59_3,
% 25.24/4.31 | | | | | | | | | | | simplifying with (48), (290) gives:
% 25.24/4.31 | | | | | | | | | | | (295) all_453_3 = 0
% 25.24/4.31 | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | GROUND_INST: instantiating (26) with all_59_2, all_453_1,
% 25.24/4.31 | | | | | | | | | | | all_59_3, all_59_5, simplifying with (51), (291)
% 25.24/4.31 | | | | | | | | | | | gives:
% 25.24/4.31 | | | | | | | | | | | (296) all_453_1 = all_59_2
% 25.24/4.31 | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | REDUCE: (292), (296) imply:
% 25.24/4.31 | | | | | | | | | | | (297) apply(all_59_2, all_59_6) = all_453_0
% 25.24/4.31 | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | BETA: splitting (283) gives:
% 25.24/4.31 | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | Case 1:
% 25.24/4.31 | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | (298) ~ (all_165_0 = 0)
% 25.24/4.31 | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | REF_CLOSE: (25), (45), (266), (298) are inconsistent by
% 25.24/4.31 | | | | | | | | | | | | sub-proof #1.
% 25.24/4.31 | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | Case 2:
% 25.24/4.31 | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | (299) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ?
% 25.24/4.31 | | | | | | | | | | | | [v3: $i] : (apply(all_59_2, all_59_6) = v2 &
% 25.24/4.31 | | | | | | | | | | | | apply(all_59_3, all_59_4) = v3 &
% 25.24/4.31 | | | | | | | | | | | | relation(all_59_3) = v0 & function(all_59_3) =
% 25.24/4.31 | | | | | | | | | | | | v1 & $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 =
% 25.24/4.31 | | | | | | | | | | | | 0) | v3 = v2))
% 25.24/4.31 | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | DELTA: instantiating (299) with fresh symbols all_542_0,
% 25.24/4.31 | | | | | | | | | | | | all_542_1, all_542_2, all_542_3 gives:
% 25.24/4.31 | | | | | | | | | | | | (300) apply(all_59_2, all_59_6) = all_542_1 &
% 25.24/4.31 | | | | | | | | | | | | apply(all_59_3, all_59_4) = all_542_0 &
% 25.24/4.31 | | | | | | | | | | | | relation(all_59_3) = all_542_3 &
% 25.24/4.31 | | | | | | | | | | | | function(all_59_3) = all_542_2 & $i(all_542_0) &
% 25.24/4.31 | | | | | | | | | | | | $i(all_542_1) & ( ~ (all_542_2 = 0) | ~
% 25.24/4.31 | | | | | | | | | | | | (all_542_3 = 0) | all_542_0 = all_542_1)
% 25.24/4.31 | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | ALPHA: (300) implies:
% 25.24/4.31 | | | | | | | | | | | | (301) apply(all_59_2, all_59_6) = all_542_1
% 25.24/4.31 | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | BETA: splitting (277) gives:
% 25.24/4.31 | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | Case 1:
% 25.24/4.31 | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | | (302) ~ (all_165_0 = 0)
% 25.24/4.31 | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | | REF_CLOSE: (25), (45), (266), (302) are inconsistent by
% 25.24/4.31 | | | | | | | | | | | | | sub-proof #1.
% 25.24/4.31 | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | Case 2:
% 25.24/4.31 | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | | (303) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ?
% 25.24/4.31 | | | | | | | | | | | | | [v3: $i] : (apply(all_59_2, all_59_6) = v2 &
% 25.24/4.31 | | | | | | | | | | | | | apply(all_59_3, all_323_0) = v3 &
% 25.24/4.31 | | | | | | | | | | | | | relation(all_59_3) = v0 & function(all_59_3) =
% 25.24/4.31 | | | | | | | | | | | | | v1 & $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 =
% 25.24/4.31 | | | | | | | | | | | | | 0) | v3 = v2))
% 25.24/4.31 | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | | DELTA: instantiating (303) with fresh symbols all_552_0,
% 25.24/4.31 | | | | | | | | | | | | | all_552_1, all_552_2, all_552_3 gives:
% 25.24/4.31 | | | | | | | | | | | | | (304) apply(all_59_2, all_59_6) = all_552_1 &
% 25.24/4.31 | | | | | | | | | | | | | apply(all_59_3, all_323_0) = all_552_0 &
% 25.24/4.31 | | | | | | | | | | | | | relation(all_59_3) = all_552_3 &
% 25.24/4.31 | | | | | | | | | | | | | function(all_59_3) = all_552_2 & $i(all_552_0) &
% 25.24/4.31 | | | | | | | | | | | | | $i(all_552_1) & ( ~ (all_552_2 = 0) | ~
% 25.24/4.31 | | | | | | | | | | | | | (all_552_3 = 0) | all_552_0 = all_552_1)
% 25.24/4.31 | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | | ALPHA: (304) implies:
% 25.24/4.31 | | | | | | | | | | | | | (305) apply(all_59_2, all_59_6) = all_552_1
% 25.24/4.31 | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | | BETA: splitting (293) gives:
% 25.24/4.31 | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | | Case 1:
% 25.24/4.31 | | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | | | (306) ~ (all_453_2 = 0)
% 25.24/4.31 | | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | | | REDUCE: (294), (306) imply:
% 25.24/4.31 | | | | | | | | | | | | | | (307) $false
% 25.24/4.31 | | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | | | CLOSE: (307) is inconsistent.
% 25.24/4.31 | | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | | Case 2:
% 25.24/4.31 | | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | | | (308) ~ (all_453_3 = 0) | all_453_0 = all_59_0
% 25.24/4.31 | | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | | | BETA: splitting (308) gives:
% 25.24/4.31 | | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | | | Case 1:
% 25.24/4.31 | | | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | | | | (309) ~ (all_453_3 = 0)
% 25.24/4.31 | | | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | | | | REDUCE: (295), (309) imply:
% 25.24/4.31 | | | | | | | | | | | | | | | (310) $false
% 25.24/4.31 | | | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | | | | CLOSE: (310) is inconsistent.
% 25.24/4.31 | | | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | | | Case 2:
% 25.24/4.31 | | | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | | | | (311) all_453_0 = all_59_0
% 25.24/4.31 | | | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | | | | REDUCE: (297), (311) imply:
% 25.24/4.31 | | | | | | | | | | | | | | | (312) apply(all_59_2, all_59_6) = all_59_0
% 25.24/4.31 | | | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_59_1, all_552_1,
% 25.24/4.31 | | | | | | | | | | | | | | | all_59_6, all_59_2, simplifying with (54), (305)
% 25.24/4.31 | | | | | | | | | | | | | | | gives:
% 25.24/4.31 | | | | | | | | | | | | | | | (313) all_552_1 = all_59_1
% 25.24/4.31 | | | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_542_1, all_552_1,
% 25.24/4.31 | | | | | | | | | | | | | | | all_59_6, all_59_2, simplifying with (301), (305)
% 25.24/4.31 | | | | | | | | | | | | | | | gives:
% 25.24/4.31 | | | | | | | | | | | | | | | (314) all_552_1 = all_542_1
% 25.24/4.31 | | | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_59_0, all_552_1,
% 25.24/4.31 | | | | | | | | | | | | | | | all_59_6, all_59_2, simplifying with (305), (312)
% 25.24/4.31 | | | | | | | | | | | | | | | gives:
% 25.24/4.31 | | | | | | | | | | | | | | | (315) all_552_1 = all_59_0
% 25.24/4.31 | | | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | | | | COMBINE_EQS: (314), (315) imply:
% 25.24/4.31 | | | | | | | | | | | | | | | (316) all_542_1 = all_59_0
% 25.24/4.31 | | | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | | | | COMBINE_EQS: (313), (314) imply:
% 25.24/4.31 | | | | | | | | | | | | | | | (317) all_542_1 = all_59_1
% 25.24/4.31 | | | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | | | | COMBINE_EQS: (316), (317) imply:
% 25.24/4.31 | | | | | | | | | | | | | | | (318) all_59_0 = all_59_1
% 25.24/4.31 | | | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | | | | REDUCE: (37), (318) imply:
% 25.24/4.31 | | | | | | | | | | | | | | | (319) $false
% 25.24/4.31 | | | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | | | | CLOSE: (319) is inconsistent.
% 25.24/4.31 | | | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | | | End of split
% 25.24/4.31 | | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | | End of split
% 25.24/4.31 | | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | | End of split
% 25.24/4.31 | | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | | End of split
% 25.24/4.31 | | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | | End of split
% 25.24/4.31 | | | | | | | | | |
% 25.24/4.31 | | | | | | | | | End of split
% 25.24/4.31 | | | | | | | | |
% 25.24/4.31 | | | | | | | | End of split
% 25.24/4.31 | | | | | | | |
% 25.24/4.31 | | | | | | | End of split
% 25.24/4.31 | | | | | | |
% 25.24/4.31 | | | | | | End of split
% 25.24/4.31 | | | | | |
% 25.24/4.31 | | | | | Case 2:
% 25.24/4.31 | | | | | |
% 25.24/4.31 | | | | | | (320) all_305_3 = 0 & empty(all_45_1) = 0
% 25.24/4.31 | | | | | |
% 25.24/4.31 | | | | | | ALPHA: (320) implies:
% 25.24/4.31 | | | | | | (321) empty(all_45_1) = 0
% 25.24/4.31 | | | | | |
% 25.24/4.31 | | | | | | GROUND_INST: instantiating (20) with all_45_0, all_303_2, all_45_1,
% 25.24/4.31 | | | | | | simplifying with (33), (215) gives:
% 25.24/4.31 | | | | | | (322) all_303_2 = all_45_0
% 25.24/4.31 | | | | | |
% 25.24/4.31 | | | | | | GROUND_INST: instantiating (20) with 0, all_303_2, all_45_1,
% 25.24/4.31 | | | | | | simplifying with (215), (321) gives:
% 25.24/4.31 | | | | | | (323) all_303_2 = 0
% 25.24/4.31 | | | | | |
% 25.24/4.31 | | | | | | COMBINE_EQS: (322), (323) imply:
% 25.24/4.31 | | | | | | (324) all_45_0 = 0
% 25.24/4.31 | | | | | |
% 25.24/4.31 | | | | | | SIMP: (324) implies:
% 25.24/4.31 | | | | | | (325) all_45_0 = 0
% 25.24/4.31 | | | | | |
% 25.24/4.31 | | | | | | REDUCE: (31), (325) imply:
% 25.24/4.31 | | | | | | (326) $false
% 25.24/4.31 | | | | | |
% 25.24/4.31 | | | | | | CLOSE: (326) is inconsistent.
% 25.24/4.31 | | | | | |
% 25.24/4.31 | | | | | End of split
% 25.24/4.31 | | | | |
% 25.24/4.31 | | | | End of split
% 25.24/4.31 | | | |
% 25.24/4.31 | | | End of split
% 25.24/4.31 | | |
% 25.24/4.31 | | End of split
% 25.24/4.31 | |
% 25.24/4.31 | End of split
% 25.24/4.31 |
% 25.24/4.31 End of proof
% 25.24/4.31
% 25.24/4.31 Sub-proof #1 shows that the following formulas are inconsistent:
% 25.24/4.31 ----------------------------------------------------------------
% 25.24/4.32 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 25.24/4.32 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 25.24/4.32 (2) in(all_59_6, all_59_8) = all_165_0
% 25.24/4.32 (3) in(all_59_6, all_59_8) = 0
% 25.24/4.32 (4) ~ (all_165_0 = 0)
% 25.24/4.32
% 25.24/4.32 Begin of proof
% 25.24/4.32 |
% 25.24/4.32 | GROUND_INST: instantiating (1) with 0, all_165_0, all_59_8, all_59_6,
% 25.24/4.32 | simplifying with (2), (3) gives:
% 25.24/4.32 | (5) all_165_0 = 0
% 25.24/4.32 |
% 25.24/4.32 | REDUCE: (4), (5) imply:
% 25.24/4.32 | (6) $false
% 25.24/4.32 |
% 25.24/4.32 | CLOSE: (6) is inconsistent.
% 25.24/4.32 |
% 25.24/4.32 End of proof
% 25.24/4.32 % SZS output end Proof for theBenchmark
% 25.24/4.32
% 25.24/4.32 3693ms
%------------------------------------------------------------------------------