TSTP Solution File: SEU249+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU249+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 : n026.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 17:43:38 EDT 2023
% Result : Theorem 158.54s 22.00s
% Output : Proof 161.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU249+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 : n026.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 13:40:31 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.05/1.15 Prover 4: Preprocessing ...
% 3.05/1.15 Prover 1: Preprocessing ...
% 3.05/1.19 Prover 2: Preprocessing ...
% 3.05/1.19 Prover 5: Preprocessing ...
% 3.05/1.19 Prover 3: Preprocessing ...
% 3.05/1.19 Prover 0: Preprocessing ...
% 3.05/1.19 Prover 6: Preprocessing ...
% 6.47/1.70 Prover 1: Warning: ignoring some quantifiers
% 7.13/1.74 Prover 3: Warning: ignoring some quantifiers
% 7.13/1.76 Prover 5: Proving ...
% 7.13/1.77 Prover 6: Proving ...
% 7.13/1.78 Prover 1: Constructing countermodel ...
% 7.13/1.78 Prover 3: Constructing countermodel ...
% 7.51/1.80 Prover 4: Warning: ignoring some quantifiers
% 7.51/1.83 Prover 2: Proving ...
% 7.99/1.85 Prover 4: Constructing countermodel ...
% 8.07/1.87 Prover 0: Proving ...
% 9.36/2.10 Prover 3: gave up
% 9.36/2.10 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.36/2.14 Prover 7: Preprocessing ...
% 9.36/2.15 Prover 1: gave up
% 9.36/2.16 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.36/2.24 Prover 8: Preprocessing ...
% 10.25/2.32 Prover 7: Warning: ignoring some quantifiers
% 11.43/2.34 Prover 7: Constructing countermodel ...
% 11.54/2.39 Prover 8: Warning: ignoring some quantifiers
% 12.08/2.41 Prover 8: Constructing countermodel ...
% 14.90/2.80 Prover 8: gave up
% 14.90/2.81 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 14.90/2.90 Prover 9: Preprocessing ...
% 16.86/3.05 Prover 9: Warning: ignoring some quantifiers
% 16.86/3.06 Prover 9: Constructing countermodel ...
% 63.03/9.11 Prover 2: stopped
% 63.03/9.11 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 63.03/9.19 Prover 10: Preprocessing ...
% 63.03/9.29 Prover 10: Warning: ignoring some quantifiers
% 63.03/9.32 Prover 10: Constructing countermodel ...
% 64.89/9.36 Prover 10: gave up
% 64.89/9.36 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 64.89/9.39 Prover 11: Preprocessing ...
% 65.56/9.52 Prover 11: Warning: ignoring some quantifiers
% 65.56/9.52 Prover 11: Constructing countermodel ...
% 99.30/13.97 Prover 5: stopped
% 99.69/13.98 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 99.69/14.03 Prover 12: Preprocessing ...
% 100.48/14.10 Prover 12: Proving ...
% 110.23/15.42 Prover 12: stopped
% 110.23/15.44 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 110.92/15.49 Prover 13: Preprocessing ...
% 110.92/15.56 Prover 13: Warning: ignoring some quantifiers
% 110.92/15.56 Prover 13: Constructing countermodel ...
% 128.95/17.88 Prover 6: stopped
% 128.95/17.88 Prover 14: Options: -triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=414236379
% 128.95/17.90 Prover 14: Preprocessing ...
% 129.82/17.98 Prover 14: Proving ...
% 139.28/19.24 Prover 13: stopped
% 139.28/19.24 Prover 15: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=723048181
% 139.28/19.26 Prover 15: Preprocessing ...
% 139.85/19.37 Prover 15: Proving ...
% 158.54/21.99 Prover 4: Found proof (size 588)
% 158.54/21.99 Prover 4: proved (21356ms)
% 158.54/21.99 Prover 14: stopped
% 158.54/21.99 Prover 15: stopped
% 158.54/21.99 Prover 9: stopped
% 158.54/22.00 Prover 0: stopped
% 158.54/22.00 Prover 7: stopped
% 158.54/22.00 Prover 11: stopped
% 158.54/22.00
% 158.54/22.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 158.54/22.00
% 160.10/22.06 % SZS output start Proof for theBenchmark
% 160.10/22.06 Assumptions after simplification:
% 160.10/22.06 ---------------------------------
% 160.10/22.06
% 160.10/22.06 (cc1_funct_1)
% 160.10/22.09 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (function(v0) = v1) | ~ $i(v0) | ?
% 160.10/22.09 [v2: int] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0: $i] : ( ~ (empty(v0) =
% 160.10/22.09 0) | ~ $i(v0) | function(v0) = 0)
% 160.10/22.09
% 160.10/22.09 (cc2_funct_1)
% 160.10/22.09 ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? [v2:
% 160.10/22.09 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 & function(v0) =
% 160.10/22.09 v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0)))
% 160.10/22.09 & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2:
% 160.10/22.10 any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 & empty(v0)
% 160.10/22.10 = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~
% 160.10/22.10 (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: any]
% 160.10/22.10 : (one_to_one(v0) = v3 & relation(v0) = v1 & empty(v0) = v2 & ( ~ (v2 = 0) |
% 160.10/22.10 ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0)
% 160.10/22.10 | ? [v1: any] : ? [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 &
% 160.10/22.10 relation(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 =
% 160.10/22.10 0)))
% 160.10/22.10
% 160.10/22.10 (commutativity_k2_xboole_0)
% 160.10/22.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~
% 160.10/22.10 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 160.10/22.10 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 160.10/22.10 | (set_union2(v1, v0) = v2 & $i(v2)))
% 160.10/22.10
% 160.10/22.10 (commutativity_k3_xboole_0)
% 160.10/22.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1, v0) = v2)
% 160.10/22.10 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) = v2 & $i(v2))) & !
% 160.10/22.10 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) |
% 160.10/22.10 ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2)))
% 160.10/22.10
% 160.10/22.10 (d2_xboole_0)
% 160.35/22.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 160.35/22.11 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) | ~
% 160.35/22.11 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0)
% 160.35/22.11 & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5)) & ! [v0: $i] : !
% 160.35/22.11 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~
% 160.35/22.11 (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ $i(v2) |
% 160.35/22.11 ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 &
% 160.35/22.11 in(v3, v0) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] :
% 160.35/22.11 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (set_union2(v0, v1) =
% 160.35/22.11 v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 160.35/22.11 | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5
% 160.35/22.11 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 160.35/22.11 $i] : ! [v4: any] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) |
% 160.35/22.11 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] :
% 160.35/22.11 (in(v3, v2) = v6 & in(v3, v0) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 =
% 160.35/22.11 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 160.35/22.11 [v4: any] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) |
% 160.35/22.11 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3,
% 160.35/22.11 v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0))))) &
% 160.35/22.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0, v1)
% 160.35/22.11 = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 160.35/22.11 $i(v0) | ? [v4: any] : ? [v5: any] : (in(v3, v1) = v5 & in(v3, v0) = v4 &
% 160.35/22.11 (v5 = 0 | v4 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 160.35/22.11 $i] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 160.35/22.11 $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : (in(v4,
% 160.35/22.11 v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | (
% 160.35/22.11 ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0)))
% 160.35/22.11
% 160.35/22.11 (d3_xboole_0)
% 160.35/22.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 160.35/22.12 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) |
% 160.35/22.12 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v1)
% 160.35/22.12 = v6 & in(v3, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : !
% 160.35/22.12 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 160.35/22.12 (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~
% 160.35/22.12 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) =
% 160.35/22.12 v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0: $i] :
% 160.35/22.12 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 160.35/22.12 (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~
% 160.35/22.12 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) =
% 160.35/22.12 v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0: $i] :
% 160.35/22.12 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2)
% 160.35/22.12 | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 160.35/22.12 (in(v3, v1) = 0 & in(v3, v0) = 0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 160.35/22.12 : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = 0) |
% 160.35/22.12 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 160.35/22.12 (in(v3, v2) = v5 & in(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v0: $i]
% 160.35/22.12 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) =
% 160.35/22.12 v2) | ~ (in(v3, v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 160.35/22.12 | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4
% 160.35/22.12 = 0) | v5 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 160.35/22.12 $i] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1)
% 160.35/22.12 | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 160.35/22.12 (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v7 = 0)
% 160.35/22.12 | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0))))
% 160.35/22.12
% 160.35/22.12 (d6_relat_1)
% 160.35/22.12 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2:
% 160.35/22.12 any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (relation_field(v0) = v3
% 160.35/22.12 & relation_rng(v0) = v4 & set_union2(v1, v4) = v5 & relation(v0) = v2 &
% 160.35/22.12 $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = v3))) & ! [v0: $i] : !
% 160.35/22.12 [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 160.35/22.12 $i] : ? [v4: $i] : ? [v5: $i] : (relation_dom(v0) = v3 &
% 160.35/22.12 relation_rng(v0) = v4 & set_union2(v3, v4) = v5 & relation(v0) = v2 &
% 160.35/22.12 $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = v1))) & ! [v0: $i] : !
% 160.35/22.12 [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 160.35/22.12 $i] : ? [v4: $i] : ? [v5: $i] : (relation_dom(v0) = v4 &
% 160.35/22.12 relation_field(v0) = v3 & set_union2(v4, v1) = v5 & relation(v0) = v2 &
% 160.35/22.12 $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = v3))) & ! [v0: $i] : ( ~
% 160.35/22.12 (relation(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 160.35/22.12 (relation_dom(v0) = v2 & relation_field(v0) = v1 & relation_rng(v0) = v3 &
% 160.35/22.12 set_union2(v2, v3) = v1 & $i(v3) & $i(v2) & $i(v1)))
% 160.35/22.12
% 160.35/22.12 (d6_wellord1)
% 160.35/22.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_restriction(v0, v1) =
% 160.35/22.13 v2) | ~ (relation(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 160.35/22.13 (cartesian_product2(v1, v1) = v3 & set_intersection2(v0, v3) = v2 & $i(v3) &
% 160.35/22.13 $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 160.35/22.13 (cartesian_product2(v1, v1) = v2) | ~ (relation(v0) = 0) | ~ $i(v1) | ~
% 160.35/22.13 $i(v0) | ? [v3: $i] : (relation_restriction(v0, v1) = v3 &
% 160.35/22.13 set_intersection2(v0, v2) = v3 & $i(v3)))
% 160.35/22.13
% 160.35/22.13 (dt_k2_wellord1)
% 160.35/22.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_restriction(v0, v1) =
% 160.35/22.13 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (relation(v2)
% 160.35/22.13 = v4 & relation(v0) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 160.35/22.13
% 160.35/22.13 (dt_k7_relat_1)
% 160.35/22.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom_restriction(v0,
% 160.35/22.13 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 160.35/22.13 (relation(v2) = v4 & relation(v0) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 160.35/22.13
% 160.35/22.13 (dt_k8_relat_1)
% 160.35/22.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0,
% 160.35/22.13 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 160.35/22.13 (relation(v2) = v4 & relation(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 160.35/22.13
% 160.35/22.13 (fc2_xboole_0)
% 160.35/22.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~
% 160.35/22.13 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (empty(v2) = v4 &
% 160.35/22.13 empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 160.35/22.13
% 160.35/22.13 (fc3_xboole_0)
% 160.35/22.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~
% 160.35/22.13 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (empty(v2) = v4 &
% 160.35/22.13 empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 160.35/22.13
% 160.35/22.13 (fc4_funct_1)
% 160.35/22.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom_restriction(v0,
% 160.35/22.13 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ?
% 160.35/22.13 [v5: any] : ? [v6: any] : (relation(v2) = v5 & relation(v0) = v3 &
% 160.35/22.13 function(v2) = v6 & function(v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 =
% 160.35/22.13 0 & v5 = 0))))
% 160.35/22.13
% 160.35/22.13 (fc5_funct_1)
% 160.35/22.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0,
% 160.35/22.13 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ?
% 160.35/22.13 [v5: any] : ? [v6: any] : (relation(v2) = v5 & relation(v1) = v3 &
% 160.35/22.13 function(v2) = v6 & function(v1) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 =
% 160.35/22.13 0 & v5 = 0))))
% 160.35/22.13
% 160.35/22.13 (l29_wellord1)
% 160.35/22.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0,
% 160.35/22.13 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5:
% 160.35/22.13 $i] : ? [v6: any] : (subset(v4, v5) = v6 & relation_dom(v2) = v4 &
% 160.35/22.13 relation_dom(v1) = v5 & relation(v1) = v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0)
% 160.35/22.13 | v6 = 0)))
% 160.35/22.13
% 160.35/22.13 (t119_relat_1)
% 160.35/22.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (relation_rng(v1)
% 160.35/22.14 = v2) | ~ (set_intersection2(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ?
% 160.35/22.14 [v4: any] : ? [v5: $i] : ? [v6: $i] : (relation_rng_restriction(v0, v1) =
% 160.35/22.14 v5 & relation_rng(v5) = v6 & relation(v1) = v4 & $i(v6) & $i(v5) & ( ~ (v4
% 160.35/22.14 = 0) | v6 = v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 160.35/22.14 (relation_rng_restriction(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 160.35/22.14 any] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (relation_rng(v2) = v4 &
% 160.35/22.14 relation_rng(v1) = v5 & set_intersection2(v5, v0) = v6 & relation(v1) = v3
% 160.35/22.14 & $i(v6) & $i(v5) & $i(v4) & ( ~ (v3 = 0) | v6 = v4)))
% 160.35/22.14
% 160.35/22.14 (t17_wellord1)
% 160.35/22.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0,
% 160.35/22.14 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5:
% 160.35/22.14 $i] : (relation_dom_restriction(v2, v0) = v5 & relation_restriction(v1,
% 160.35/22.14 v0) = v4 & relation(v1) = v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | v5 =
% 160.35/22.14 v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 160.35/22.14 (relation_restriction(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] :
% 160.35/22.14 ? [v4: $i] : ? [v5: $i] : (relation_rng_restriction(v0, v1) = v4 &
% 160.35/22.14 relation_dom_restriction(v4, v0) = v5 & relation(v1) = v3 & $i(v5) &
% 160.35/22.14 $i(v4) & ( ~ (v3 = 0) | v5 = v2)))
% 160.35/22.14
% 160.35/22.14 (t18_wellord1)
% 160.35/22.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom_restriction(v1,
% 160.35/22.14 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5:
% 160.35/22.14 $i] : (relation_rng_restriction(v0, v2) = v5 & relation_restriction(v1,
% 160.35/22.14 v0) = v4 & relation(v1) = v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | v5 =
% 160.35/22.14 v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 160.35/22.14 (relation_restriction(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] :
% 160.35/22.14 ? [v4: $i] : ? [v5: $i] : (relation_rng_restriction(v0, v4) = v5 &
% 160.35/22.14 relation_dom_restriction(v1, v0) = v4 & relation(v1) = v3 & $i(v5) &
% 160.35/22.14 $i(v4) & ( ~ (v3 = 0) | v5 = v2)))
% 160.35/22.14
% 160.35/22.14 (t19_wellord1)
% 160.35/22.14 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 160.35/22.14 $i] : ? [v6: any] : ? [v7: any] : (relation_restriction(v2, v1) = v3 &
% 160.35/22.14 relation_field(v3) = v4 & relation_field(v2) = v5 & relation(v2) = 0 &
% 160.35/22.14 in(v0, v5) = v6 & in(v0, v4) = 0 & in(v0, v1) = v7 & $i(v5) & $i(v4) &
% 160.35/22.14 $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v7 = 0) | ~ (v6 = 0)))
% 160.35/22.14
% 160.35/22.14 (t2_subset)
% 160.35/22.14 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2) | ~
% 160.35/22.14 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (element(v0, v1) = v3 &
% 160.35/22.14 empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : (
% 160.35/22.14 ~ (element(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 160.35/22.14 any] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0)))
% 160.35/22.14
% 160.35/22.14 (t3_subset)
% 160.35/22.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 160.35/22.15 (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ?
% 160.35/22.15 [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i]
% 160.35/22.15 : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 160.35/22.15 ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0,
% 160.35/22.15 v3) = v4 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 160.35/22.15 (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) |
% 160.35/22.15 subset(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) |
% 160.35/22.15 ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : (powerset(v1) = v2 & element(v0, v2) =
% 160.35/22.15 0 & $i(v2)))
% 160.35/22.15
% 160.35/22.15 (t4_subset)
% 160.35/22.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 160.35/22.15 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) =
% 160.35/22.15 v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) &
% 160.35/22.15 in(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int]
% 160.35/22.15 : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (in(v0, v1) = 0) | ~ $i(v2) | ~
% 160.35/22.15 $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) &
% 160.35/22.15 powerset(v2) = v4 & element(v1, v4) = v5 & $i(v4))) & ! [v0: $i] : !
% 160.35/22.15 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (powerset(v2) = v3) | ~
% 160.35/22.15 (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 160.35/22.15 $i(v0) | element(v0, v2) = 0)
% 160.35/22.15
% 160.35/22.15 (t5_subset)
% 160.35/22.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (powerset(v2) =
% 160.35/22.15 v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ~ $i(v2) | ~
% 160.35/22.15 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & empty(v2) = v4)) & !
% 160.35/22.15 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) =
% 160.35/22.15 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 160.35/22.15 (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4 & $i(v3)))
% 160.35/22.15
% 160.35/22.15 (t90_relat_1)
% 160.35/22.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (relation_dom(v1)
% 160.35/22.15 = v2) | ~ (set_intersection2(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ?
% 160.35/22.15 [v4: any] : ? [v5: $i] : ? [v6: $i] : (relation_dom_restriction(v1, v0) =
% 160.35/22.15 v5 & relation_dom(v5) = v6 & relation(v1) = v4 & $i(v6) & $i(v5) & ( ~ (v4
% 160.35/22.15 = 0) | v6 = v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 160.35/22.15 (relation_dom_restriction(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 160.35/22.15 any] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (relation_dom(v2) = v4 &
% 160.35/22.15 relation_dom(v1) = v5 & set_intersection2(v5, v0) = v6 & relation(v1) = v3
% 160.35/22.15 & $i(v6) & $i(v5) & $i(v4) & ( ~ (v3 = 0) | v6 = v4)))
% 160.35/22.15
% 160.35/22.15 (t99_relat_1)
% 160.35/22.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom_restriction(v1,
% 160.35/22.16 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5:
% 160.35/22.16 $i] : ? [v6: any] : (subset(v4, v5) = v6 & relation_rng(v2) = v4 &
% 160.35/22.16 relation_rng(v1) = v5 & relation(v1) = v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0)
% 160.35/22.16 | v6 = 0)))
% 160.35/22.16
% 160.35/22.16 (function-axioms)
% 160.35/22.16 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 160.35/22.16 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 160.35/22.16 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 160.35/22.16 $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & !
% 160.35/22.16 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 160.35/22.16 (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3,
% 160.35/22.16 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 160.35/22.16 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~
% 160.35/22.16 (relation_dom_restriction(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 160.35/22.16 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_restriction(v3, v2) = v1) |
% 160.35/22.16 ~ (relation_restriction(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 160.35/22.16 $i] : ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~
% 160.35/22.16 (cartesian_product2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 160.35/22.16 : ! [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~
% 160.35/22.16 (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 160.35/22.16 : ! [v3: $i] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3,
% 160.35/22.16 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 160.35/22.16 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) =
% 160.35/22.16 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 160.35/22.16 (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 160.35/22.16 ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) =
% 160.35/22.16 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 160.35/22.16 (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & ! [v0: $i] : !
% 160.35/22.16 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~
% 160.35/22.16 (relation_rng(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 160.35/22.16 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~
% 160.35/22.16 (one_to_one(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 160.35/22.16 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~
% 160.35/22.16 (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 160.35/22.16 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) | ~
% 160.35/22.16 (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 160.35/22.16 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 160.35/22.16 (empty(v2) = v0))
% 160.35/22.16
% 160.35/22.16 Further assumptions not needed in the proof:
% 160.35/22.16 --------------------------------------------
% 160.35/22.16 antisymmetry_r2_hidden, dt_k1_relat_1, dt_k1_xboole_0, dt_k1_zfmisc_1,
% 160.35/22.16 dt_k2_relat_1, dt_k2_xboole_0, dt_k2_zfmisc_1, dt_k3_relat_1, dt_k3_xboole_0,
% 160.35/22.16 dt_m1_subset_1, existence_m1_subset_1, fc1_xboole_0, idempotence_k2_xboole_0,
% 160.35/22.16 idempotence_k3_xboole_0, rc1_funct_1, rc1_xboole_0, rc2_funct_1, rc2_xboole_0,
% 160.35/22.16 rc3_funct_1, reflexivity_r1_tarski, t1_boole, t1_subset, t2_boole, t6_boole,
% 160.35/22.16 t7_boole, t8_boole
% 160.35/22.16
% 160.35/22.16 Those formulas are unsatisfiable:
% 160.35/22.16 ---------------------------------
% 160.35/22.16
% 160.35/22.16 Begin of proof
% 160.35/22.16 |
% 160.35/22.16 | ALPHA: (cc1_funct_1) implies:
% 160.64/22.17 | (1) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (function(v0) = v1) | ~
% 160.64/22.17 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & empty(v0) = v2))
% 160.64/22.17 |
% 160.64/22.17 | ALPHA: (cc2_funct_1) implies:
% 160.64/22.17 | (2) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 160.64/22.17 | [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 &
% 160.64/22.17 | empty(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)))
% 160.64/22.17 | (3) ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ?
% 160.64/22.17 | [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 &
% 160.64/22.17 | function(v0) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) |
% 160.64/22.17 | ~ (v2 = 0) | v1 = 0)))
% 160.64/22.17 |
% 160.64/22.17 | ALPHA: (commutativity_k2_xboole_0) implies:
% 160.64/22.17 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2)
% 160.64/22.17 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2)))
% 160.64/22.17 |
% 160.64/22.17 | ALPHA: (commutativity_k3_xboole_0) implies:
% 160.64/22.17 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1,
% 160.64/22.17 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) =
% 160.64/22.17 | v2 & $i(v2)))
% 160.64/22.17 |
% 160.64/22.17 | ALPHA: (d2_xboole_0) implies:
% 160.64/22.17 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 160.64/22.17 | (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~
% 160.64/22.17 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 160.64/22.17 | (in(v3, v1) = v5 & in(v3, v0) = v4 & (v5 = 0 | v4 = 0)))
% 160.64/22.17 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 160.64/22.17 | (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~
% 160.64/22.17 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6:
% 160.64/22.17 | any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | v6 =
% 160.64/22.17 | 0)))
% 160.64/22.17 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 160.64/22.17 | (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~
% 160.64/22.17 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6:
% 160.64/22.17 | any] : (in(v3, v2) = v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | v6 =
% 160.64/22.17 | 0)))
% 160.64/22.17 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 160.64/22.18 | (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~
% 160.64/22.18 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6:
% 160.64/22.18 | int] : ( ~ (v6 = 0) & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) =
% 160.64/22.18 | v5))
% 160.64/22.18 |
% 160.64/22.18 | ALPHA: (d3_xboole_0) implies:
% 160.64/22.18 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 160.64/22.18 | (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = 0) | ~ $i(v3) |
% 160.64/22.18 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 160.64/22.18 | (in(v3, v2) = v5 & in(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0)))
% 160.64/22.18 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] :
% 160.64/22.18 | ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~
% 160.64/22.18 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6:
% 160.64/22.18 | any] : (in(v3, v2) = v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0
% 160.64/22.18 | & v4 = 0))))
% 160.64/22.18 |
% 160.64/22.18 | ALPHA: (d6_relat_1) implies:
% 160.64/22.18 | (12) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ?
% 160.64/22.18 | [v2: $i] : ? [v3: $i] : (relation_dom(v0) = v2 & relation_field(v0)
% 160.64/22.18 | = v1 & relation_rng(v0) = v3 & set_union2(v2, v3) = v1 & $i(v3) &
% 160.64/22.18 | $i(v2) & $i(v1)))
% 160.64/22.18 | (13) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) |
% 160.64/22.18 | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 160.64/22.18 | (relation_dom(v0) = v4 & relation_field(v0) = v3 & set_union2(v4,
% 160.64/22.18 | v1) = v5 & relation(v0) = v2 & $i(v5) & $i(v4) & $i(v3) & ( ~
% 160.64/22.18 | (v2 = 0) | v5 = v3)))
% 160.64/22.18 | (14) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0)
% 160.64/22.18 | | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 160.64/22.18 | (relation_dom(v0) = v3 & relation_rng(v0) = v4 & set_union2(v3, v4)
% 160.64/22.18 | = v5 & relation(v0) = v2 & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0)
% 160.64/22.18 | | v5 = v1)))
% 160.64/22.18 | (15) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) |
% 160.64/22.18 | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 160.64/22.18 | (relation_field(v0) = v3 & relation_rng(v0) = v4 & set_union2(v1,
% 160.64/22.18 | v4) = v5 & relation(v0) = v2 & $i(v5) & $i(v4) & $i(v3) & ( ~
% 160.64/22.18 | (v2 = 0) | v5 = v3)))
% 160.64/22.18 |
% 160.64/22.18 | ALPHA: (d6_wellord1) implies:
% 160.64/22.19 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 160.64/22.19 | (relation_restriction(v0, v1) = v2) | ~ (relation(v0) = 0) | ~
% 160.64/22.19 | $i(v1) | ~ $i(v0) | ? [v3: $i] : (cartesian_product2(v1, v1) = v3
% 160.64/22.19 | & set_intersection2(v0, v3) = v2 & $i(v3) & $i(v2)))
% 160.64/22.19 |
% 160.64/22.19 | ALPHA: (t119_relat_1) implies:
% 160.64/22.19 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 160.64/22.19 | (relation_rng_restriction(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 160.64/22.19 | [v3: any] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 160.64/22.19 | (relation_rng(v2) = v4 & relation_rng(v1) = v5 &
% 160.64/22.19 | set_intersection2(v5, v0) = v6 & relation(v1) = v3 & $i(v6) &
% 160.64/22.19 | $i(v5) & $i(v4) & ( ~ (v3 = 0) | v6 = v4)))
% 160.64/22.19 |
% 160.64/22.19 | ALPHA: (t17_wellord1) implies:
% 160.64/22.19 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 160.64/22.19 | (relation_restriction(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 160.64/22.19 | [v3: any] : ? [v4: $i] : ? [v5: $i] :
% 160.64/22.19 | (relation_rng_restriction(v0, v1) = v4 &
% 160.64/22.19 | relation_dom_restriction(v4, v0) = v5 & relation(v1) = v3 & $i(v5)
% 160.64/22.19 | & $i(v4) & ( ~ (v3 = 0) | v5 = v2)))
% 160.64/22.19 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 160.64/22.19 | (relation_rng_restriction(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 160.64/22.19 | [v3: any] : ? [v4: $i] : ? [v5: $i] :
% 160.64/22.19 | (relation_dom_restriction(v2, v0) = v5 & relation_restriction(v1,
% 160.64/22.19 | v0) = v4 & relation(v1) = v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0) |
% 160.64/22.19 | v5 = v4)))
% 160.64/22.19 |
% 160.64/22.19 | ALPHA: (t18_wellord1) implies:
% 160.64/22.19 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 160.64/22.19 | (relation_restriction(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 160.64/22.19 | [v3: any] : ? [v4: $i] : ? [v5: $i] :
% 160.64/22.19 | (relation_rng_restriction(v0, v4) = v5 &
% 160.64/22.19 | relation_dom_restriction(v1, v0) = v4 & relation(v1) = v3 & $i(v5)
% 160.64/22.19 | & $i(v4) & ( ~ (v3 = 0) | v5 = v2)))
% 160.64/22.19 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 160.64/22.19 | (relation_dom_restriction(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 160.64/22.19 | [v3: any] : ? [v4: $i] : ? [v5: $i] :
% 160.64/22.19 | (relation_rng_restriction(v0, v2) = v5 & relation_restriction(v1,
% 160.64/22.19 | v0) = v4 & relation(v1) = v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0) |
% 160.64/22.19 | v5 = v4)))
% 160.64/22.19 |
% 160.64/22.19 | ALPHA: (t2_subset) implies:
% 160.64/22.19 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) =
% 160.64/22.19 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 160.64/22.19 | (element(v0, v1) = v3 & empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0)))
% 160.64/22.19 |
% 160.64/22.19 | ALPHA: (t3_subset) implies:
% 160.64/22.19 | (23) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 160.64/22.19 | $i(v0) | ? [v2: $i] : (powerset(v1) = v2 & element(v0, v2) = 0 &
% 160.64/22.19 | $i(v2)))
% 160.64/22.19 |
% 160.64/22.19 | ALPHA: (t4_subset) implies:
% 160.64/22.19 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 160.64/22.19 | (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0)
% 160.64/22.19 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | element(v0, v2) = 0)
% 160.64/22.19 |
% 160.64/22.19 | ALPHA: (t5_subset) implies:
% 160.64/22.19 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 160.64/22.19 | (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0)
% 160.64/22.19 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) &
% 160.64/22.19 | empty(v2) = v4))
% 160.64/22.19 |
% 160.64/22.19 | ALPHA: (t90_relat_1) implies:
% 160.64/22.20 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 160.64/22.20 | (relation_dom_restriction(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 160.64/22.20 | [v3: any] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 160.64/22.20 | (relation_dom(v2) = v4 & relation_dom(v1) = v5 &
% 160.64/22.20 | set_intersection2(v5, v0) = v6 & relation(v1) = v3 & $i(v6) &
% 160.64/22.20 | $i(v5) & $i(v4) & ( ~ (v3 = 0) | v6 = v4)))
% 160.64/22.20 |
% 160.64/22.20 | ALPHA: (function-axioms) implies:
% 160.64/22.20 | (27) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 160.64/22.20 | : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 160.64/22.20 | (28) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 160.64/22.20 | : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 160.64/22.20 | (29) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 160.64/22.20 | : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 160.64/22.20 | (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 160.64/22.20 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 160.64/22.20 | (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 160.64/22.20 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 160.64/22.20 | (32) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 160.64/22.20 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) =
% 160.64/22.20 | v0))
% 160.64/22.20 | (33) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 160.64/22.20 | : ! [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3,
% 160.64/22.20 | v2) = v0))
% 160.64/22.20 |
% 160.64/22.20 | DELTA: instantiating (t19_wellord1) with fresh symbols all_52_0, all_52_1,
% 160.64/22.20 | all_52_2, all_52_3, all_52_4, all_52_5, all_52_6, all_52_7 gives:
% 160.64/22.20 | (34) relation_restriction(all_52_5, all_52_6) = all_52_4 &
% 160.64/22.20 | relation_field(all_52_4) = all_52_3 & relation_field(all_52_5) =
% 160.64/22.20 | all_52_2 & relation(all_52_5) = 0 & in(all_52_7, all_52_2) = all_52_1
% 160.64/22.20 | & in(all_52_7, all_52_3) = 0 & in(all_52_7, all_52_6) = all_52_0 &
% 160.64/22.20 | $i(all_52_2) & $i(all_52_3) & $i(all_52_4) & $i(all_52_5) &
% 160.64/22.20 | $i(all_52_6) & $i(all_52_7) & ( ~ (all_52_0 = 0) | ~ (all_52_1 = 0))
% 160.64/22.20 |
% 160.64/22.20 | ALPHA: (34) implies:
% 160.64/22.20 | (35) $i(all_52_7)
% 160.64/22.20 | (36) $i(all_52_6)
% 160.64/22.20 | (37) $i(all_52_5)
% 160.64/22.20 | (38) $i(all_52_4)
% 160.64/22.20 | (39) in(all_52_7, all_52_6) = all_52_0
% 160.64/22.20 | (40) in(all_52_7, all_52_3) = 0
% 160.64/22.20 | (41) in(all_52_7, all_52_2) = all_52_1
% 160.64/22.20 | (42) relation(all_52_5) = 0
% 160.64/22.20 | (43) relation_field(all_52_5) = all_52_2
% 160.64/22.20 | (44) relation_field(all_52_4) = all_52_3
% 160.64/22.20 | (45) relation_restriction(all_52_5, all_52_6) = all_52_4
% 160.64/22.20 | (46) ~ (all_52_0 = 0) | ~ (all_52_1 = 0)
% 160.64/22.20 |
% 160.64/22.20 | GROUND_INST: instantiating (12) with all_52_5, simplifying with (37), (42)
% 160.64/22.20 | gives:
% 160.64/22.20 | (47) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (relation_dom(all_52_5) = v1
% 160.64/22.20 | & relation_field(all_52_5) = v0 & relation_rng(all_52_5) = v2 &
% 160.64/22.20 | set_union2(v1, v2) = v0 & $i(v2) & $i(v1) & $i(v0))
% 160.64/22.20 |
% 160.64/22.20 | GROUND_INST: instantiating (2) with all_52_5, simplifying with (37), (42)
% 160.64/22.20 | gives:
% 160.64/22.20 | (48) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_52_5) =
% 160.64/22.20 | v2 & function(all_52_5) = v1 & empty(all_52_5) = v0 & ( ~ (v1 = 0) |
% 160.64/22.20 | ~ (v0 = 0) | v2 = 0))
% 160.64/22.20 |
% 160.64/22.20 | GROUND_INST: instantiating (14) with all_52_5, all_52_2, simplifying with
% 160.64/22.20 | (37), (43) gives:
% 160.64/22.21 | (49) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 160.64/22.21 | (relation_dom(all_52_5) = v1 & relation_rng(all_52_5) = v2 &
% 160.64/22.21 | set_union2(v1, v2) = v3 & relation(all_52_5) = v0 & $i(v3) & $i(v2)
% 160.64/22.21 | & $i(v1) & ( ~ (v0 = 0) | v3 = all_52_2))
% 160.64/22.21 |
% 160.64/22.21 | GROUND_INST: instantiating (14) with all_52_4, all_52_3, simplifying with
% 160.64/22.21 | (38), (44) gives:
% 160.64/22.21 | (50) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 160.64/22.21 | (relation_dom(all_52_4) = v1 & relation_rng(all_52_4) = v2 &
% 160.64/22.21 | set_union2(v1, v2) = v3 & relation(all_52_4) = v0 & $i(v3) & $i(v2)
% 160.64/22.21 | & $i(v1) & ( ~ (v0 = 0) | v3 = all_52_3))
% 160.64/22.21 |
% 160.64/22.21 | GROUND_INST: instantiating (16) with all_52_5, all_52_6, all_52_4, simplifying
% 160.64/22.21 | with (36), (37), (42), (45) gives:
% 160.64/22.21 | (51) ? [v0: $i] : (cartesian_product2(all_52_6, all_52_6) = v0 &
% 160.64/22.21 | set_intersection2(all_52_5, v0) = all_52_4 & $i(v0) & $i(all_52_4))
% 160.64/22.21 |
% 160.64/22.21 | GROUND_INST: instantiating (20) with all_52_6, all_52_5, all_52_4, simplifying
% 160.64/22.21 | with (36), (37), (45) gives:
% 160.64/22.21 | (52) ? [v0: any] : ? [v1: $i] : ? [v2: $i] :
% 160.64/22.21 | (relation_rng_restriction(all_52_6, v1) = v2 &
% 160.64/22.21 | relation_dom_restriction(all_52_5, all_52_6) = v1 &
% 160.64/22.21 | relation(all_52_5) = v0 & $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 =
% 160.64/22.21 | all_52_4))
% 160.64/22.21 |
% 160.64/22.21 | GROUND_INST: instantiating (18) with all_52_6, all_52_5, all_52_4, simplifying
% 160.64/22.21 | with (36), (37), (45) gives:
% 160.64/22.21 | (53) ? [v0: any] : ? [v1: $i] : ? [v2: $i] :
% 160.64/22.21 | (relation_rng_restriction(all_52_6, all_52_5) = v1 &
% 160.64/22.21 | relation_dom_restriction(v1, all_52_6) = v2 & relation(all_52_5) =
% 160.64/22.21 | v0 & $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = all_52_4))
% 160.64/22.21 |
% 160.64/22.21 | GROUND_INST: instantiating (dt_k2_wellord1) with all_52_5, all_52_6, all_52_4,
% 160.64/22.21 | simplifying with (36), (37), (45) gives:
% 160.64/22.21 | (54) ? [v0: any] : ? [v1: any] : (relation(all_52_4) = v1 &
% 160.64/22.21 | relation(all_52_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 160.64/22.21 |
% 160.64/22.21 | DELTA: instantiating (54) with fresh symbols all_74_0, all_74_1 gives:
% 160.64/22.21 | (55) relation(all_52_4) = all_74_0 & relation(all_52_5) = all_74_1 & ( ~
% 160.64/22.21 | (all_74_1 = 0) | all_74_0 = 0)
% 160.64/22.21 |
% 160.64/22.21 | ALPHA: (55) implies:
% 160.64/22.21 | (56) relation(all_52_5) = all_74_1
% 160.64/22.21 | (57) relation(all_52_4) = all_74_0
% 160.64/22.21 | (58) ~ (all_74_1 = 0) | all_74_0 = 0
% 160.64/22.21 |
% 160.64/22.21 | DELTA: instantiating (51) with fresh symbol all_76_0 gives:
% 160.64/22.21 | (59) cartesian_product2(all_52_6, all_52_6) = all_76_0 &
% 160.64/22.21 | set_intersection2(all_52_5, all_76_0) = all_52_4 & $i(all_76_0) &
% 160.64/22.21 | $i(all_52_4)
% 160.64/22.21 |
% 160.64/22.21 | ALPHA: (59) implies:
% 160.64/22.21 | (60) $i(all_76_0)
% 160.64/22.21 | (61) set_intersection2(all_52_5, all_76_0) = all_52_4
% 160.64/22.21 |
% 160.64/22.21 | DELTA: instantiating (48) with fresh symbols all_90_0, all_90_1, all_90_2
% 160.64/22.21 | gives:
% 160.64/22.21 | (62) one_to_one(all_52_5) = all_90_0 & function(all_52_5) = all_90_1 &
% 160.64/22.21 | empty(all_52_5) = all_90_2 & ( ~ (all_90_1 = 0) | ~ (all_90_2 = 0) |
% 160.64/22.21 | all_90_0 = 0)
% 160.64/22.21 |
% 160.64/22.21 | ALPHA: (62) implies:
% 160.64/22.21 | (63) one_to_one(all_52_5) = all_90_0
% 160.64/22.21 |
% 160.64/22.21 | DELTA: instantiating (52) with fresh symbols all_100_0, all_100_1, all_100_2
% 160.64/22.21 | gives:
% 160.64/22.21 | (64) relation_rng_restriction(all_52_6, all_100_1) = all_100_0 &
% 160.64/22.21 | relation_dom_restriction(all_52_5, all_52_6) = all_100_1 &
% 160.64/22.21 | relation(all_52_5) = all_100_2 & $i(all_100_0) & $i(all_100_1) & ( ~
% 160.64/22.21 | (all_100_2 = 0) | all_100_0 = all_52_4)
% 160.64/22.21 |
% 160.64/22.21 | ALPHA: (64) implies:
% 160.64/22.21 | (65) $i(all_100_1)
% 160.64/22.21 | (66) relation(all_52_5) = all_100_2
% 160.64/22.21 | (67) relation_dom_restriction(all_52_5, all_52_6) = all_100_1
% 160.64/22.21 | (68) relation_rng_restriction(all_52_6, all_100_1) = all_100_0
% 160.64/22.21 | (69) ~ (all_100_2 = 0) | all_100_0 = all_52_4
% 160.64/22.21 |
% 160.64/22.21 | DELTA: instantiating (53) with fresh symbols all_104_0, all_104_1, all_104_2
% 160.64/22.21 | gives:
% 160.64/22.21 | (70) relation_rng_restriction(all_52_6, all_52_5) = all_104_1 &
% 160.64/22.21 | relation_dom_restriction(all_104_1, all_52_6) = all_104_0 &
% 160.64/22.21 | relation(all_52_5) = all_104_2 & $i(all_104_0) & $i(all_104_1) & ( ~
% 160.64/22.21 | (all_104_2 = 0) | all_104_0 = all_52_4)
% 160.64/22.21 |
% 160.64/22.21 | ALPHA: (70) implies:
% 160.64/22.21 | (71) $i(all_104_1)
% 160.64/22.21 | (72) $i(all_104_0)
% 160.64/22.21 | (73) relation(all_52_5) = all_104_2
% 160.64/22.21 | (74) relation_dom_restriction(all_104_1, all_52_6) = all_104_0
% 160.64/22.21 | (75) relation_rng_restriction(all_52_6, all_52_5) = all_104_1
% 160.64/22.21 | (76) ~ (all_104_2 = 0) | all_104_0 = all_52_4
% 160.64/22.21 |
% 160.64/22.21 | DELTA: instantiating (47) with fresh symbols all_106_0, all_106_1, all_106_2
% 160.64/22.21 | gives:
% 160.64/22.21 | (77) relation_dom(all_52_5) = all_106_1 & relation_field(all_52_5) =
% 160.64/22.21 | all_106_2 & relation_rng(all_52_5) = all_106_0 & set_union2(all_106_1,
% 160.64/22.21 | all_106_0) = all_106_2 & $i(all_106_0) & $i(all_106_1) &
% 160.64/22.21 | $i(all_106_2)
% 160.64/22.21 |
% 160.64/22.21 | ALPHA: (77) implies:
% 160.64/22.21 | (78) relation_rng(all_52_5) = all_106_0
% 160.64/22.21 | (79) relation_dom(all_52_5) = all_106_1
% 160.64/22.21 |
% 160.64/22.21 | DELTA: instantiating (50) with fresh symbols all_110_0, all_110_1, all_110_2,
% 160.64/22.21 | all_110_3 gives:
% 160.64/22.22 | (80) relation_dom(all_52_4) = all_110_2 & relation_rng(all_52_4) =
% 160.64/22.22 | all_110_1 & set_union2(all_110_2, all_110_1) = all_110_0 &
% 160.64/22.22 | relation(all_52_4) = all_110_3 & $i(all_110_0) & $i(all_110_1) &
% 160.64/22.22 | $i(all_110_2) & ( ~ (all_110_3 = 0) | all_110_0 = all_52_3)
% 160.64/22.22 |
% 160.64/22.22 | ALPHA: (80) implies:
% 160.64/22.22 | (81) $i(all_110_2)
% 160.64/22.22 | (82) $i(all_110_1)
% 160.64/22.22 | (83) $i(all_110_0)
% 160.64/22.22 | (84) relation(all_52_4) = all_110_3
% 160.64/22.22 | (85) set_union2(all_110_2, all_110_1) = all_110_0
% 160.64/22.22 | (86) relation_rng(all_52_4) = all_110_1
% 160.64/22.22 | (87) relation_dom(all_52_4) = all_110_2
% 160.64/22.22 | (88) ~ (all_110_3 = 0) | all_110_0 = all_52_3
% 160.64/22.22 |
% 160.64/22.22 | DELTA: instantiating (49) with fresh symbols all_112_0, all_112_1, all_112_2,
% 160.64/22.22 | all_112_3 gives:
% 160.64/22.22 | (89) relation_dom(all_52_5) = all_112_2 & relation_rng(all_52_5) =
% 160.64/22.22 | all_112_1 & set_union2(all_112_2, all_112_1) = all_112_0 &
% 160.64/22.22 | relation(all_52_5) = all_112_3 & $i(all_112_0) & $i(all_112_1) &
% 160.64/22.22 | $i(all_112_2) & ( ~ (all_112_3 = 0) | all_112_0 = all_52_2)
% 160.64/22.22 |
% 160.64/22.22 | ALPHA: (89) implies:
% 160.64/22.22 | (90) $i(all_112_2)
% 160.64/22.22 | (91) $i(all_112_1)
% 160.64/22.22 | (92) $i(all_112_0)
% 160.64/22.22 | (93) relation(all_52_5) = all_112_3
% 160.64/22.22 | (94) set_union2(all_112_2, all_112_1) = all_112_0
% 160.64/22.22 | (95) relation_rng(all_52_5) = all_112_1
% 160.64/22.22 | (96) relation_dom(all_52_5) = all_112_2
% 160.64/22.22 | (97) ~ (all_112_3 = 0) | all_112_0 = all_52_2
% 160.64/22.22 |
% 160.64/22.22 | GROUND_INST: instantiating (29) with 0, all_104_2, all_52_5, simplifying with
% 160.64/22.22 | (42), (73) gives:
% 160.64/22.22 | (98) all_104_2 = 0
% 160.64/22.22 |
% 160.64/22.22 | GROUND_INST: instantiating (29) with all_100_2, all_104_2, all_52_5,
% 160.64/22.22 | simplifying with (66), (73) gives:
% 160.64/22.22 | (99) all_104_2 = all_100_2
% 160.64/22.22 |
% 160.64/22.22 | GROUND_INST: instantiating (29) with all_104_2, all_112_3, all_52_5,
% 160.64/22.22 | simplifying with (73), (93) gives:
% 160.64/22.22 | (100) all_112_3 = all_104_2
% 160.64/22.22 |
% 160.64/22.22 | GROUND_INST: instantiating (29) with all_74_1, all_112_3, all_52_5,
% 160.64/22.22 | simplifying with (56), (93) gives:
% 160.64/22.22 | (101) all_112_3 = all_74_1
% 160.64/22.22 |
% 160.64/22.22 | GROUND_INST: instantiating (29) with all_74_0, all_110_3, all_52_4,
% 160.64/22.22 | simplifying with (57), (84) gives:
% 160.64/22.22 | (102) all_110_3 = all_74_0
% 160.64/22.22 |
% 160.64/22.22 | GROUND_INST: instantiating (30) with all_106_0, all_112_1, all_52_5,
% 160.64/22.22 | simplifying with (78), (95) gives:
% 160.64/22.22 | (103) all_112_1 = all_106_0
% 160.64/22.22 |
% 160.64/22.22 | GROUND_INST: instantiating (31) with all_106_1, all_112_2, all_52_5,
% 160.64/22.22 | simplifying with (79), (96) gives:
% 160.64/22.22 | (104) all_112_2 = all_106_1
% 160.64/22.22 |
% 160.64/22.22 | COMBINE_EQS: (100), (101) imply:
% 160.64/22.22 | (105) all_104_2 = all_74_1
% 160.64/22.22 |
% 160.64/22.22 | SIMP: (105) implies:
% 160.64/22.22 | (106) all_104_2 = all_74_1
% 160.64/22.22 |
% 160.64/22.22 | COMBINE_EQS: (98), (99) imply:
% 160.64/22.22 | (107) all_100_2 = 0
% 160.64/22.22 |
% 160.64/22.22 | COMBINE_EQS: (99), (106) imply:
% 160.64/22.22 | (108) all_100_2 = all_74_1
% 160.64/22.22 |
% 160.64/22.22 | COMBINE_EQS: (107), (108) imply:
% 160.64/22.22 | (109) all_74_1 = 0
% 160.64/22.22 |
% 160.64/22.22 | COMBINE_EQS: (101), (109) imply:
% 160.64/22.22 | (110) all_112_3 = 0
% 160.64/22.22 |
% 160.64/22.22 | REDUCE: (94), (103), (104) imply:
% 160.64/22.22 | (111) set_union2(all_106_1, all_106_0) = all_112_0
% 160.64/22.22 |
% 160.64/22.22 | REDUCE: (91), (103) imply:
% 160.64/22.22 | (112) $i(all_106_0)
% 160.64/22.22 |
% 160.64/22.22 | REDUCE: (90), (104) imply:
% 160.64/22.22 | (113) $i(all_106_1)
% 160.64/22.22 |
% 160.64/22.22 | BETA: splitting (69) gives:
% 160.64/22.22 |
% 160.64/22.22 | Case 1:
% 160.64/22.22 | |
% 160.64/22.22 | | (114) ~ (all_100_2 = 0)
% 160.64/22.22 | |
% 160.64/22.22 | | REDUCE: (107), (114) imply:
% 160.64/22.22 | | (115) $false
% 160.64/22.22 | |
% 160.64/22.22 | | CLOSE: (115) is inconsistent.
% 160.64/22.22 | |
% 160.64/22.22 | Case 2:
% 160.64/22.22 | |
% 160.64/22.22 | | (116) all_100_0 = all_52_4
% 160.64/22.22 | |
% 160.64/22.22 | | REDUCE: (68), (116) imply:
% 160.64/22.22 | | (117) relation_rng_restriction(all_52_6, all_100_1) = all_52_4
% 160.64/22.22 | |
% 160.64/22.22 | | BETA: splitting (76) gives:
% 160.64/22.22 | |
% 160.64/22.22 | | Case 1:
% 160.64/22.22 | | |
% 160.64/22.22 | | | (118) ~ (all_104_2 = 0)
% 160.64/22.22 | | |
% 160.64/22.22 | | | REDUCE: (98), (118) imply:
% 160.64/22.22 | | | (119) $false
% 160.64/22.22 | | |
% 160.64/22.22 | | | CLOSE: (119) is inconsistent.
% 160.64/22.22 | | |
% 160.64/22.22 | | Case 2:
% 160.64/22.22 | | |
% 160.64/22.22 | | | (120) all_104_0 = all_52_4
% 160.64/22.22 | | |
% 160.64/22.22 | | | REDUCE: (74), (120) imply:
% 160.64/22.22 | | | (121) relation_dom_restriction(all_104_1, all_52_6) = all_52_4
% 160.64/22.22 | | |
% 160.64/22.22 | | | BETA: splitting (58) gives:
% 160.64/22.22 | | |
% 160.64/22.22 | | | Case 1:
% 160.64/22.22 | | | |
% 160.64/22.22 | | | | (122) ~ (all_74_1 = 0)
% 160.64/22.22 | | | |
% 160.64/22.22 | | | | REDUCE: (109), (122) imply:
% 160.64/22.22 | | | | (123) $false
% 160.64/22.22 | | | |
% 160.64/22.22 | | | | CLOSE: (123) is inconsistent.
% 160.64/22.22 | | | |
% 160.64/22.22 | | | Case 2:
% 160.64/22.22 | | | |
% 160.64/22.22 | | | | (124) all_74_0 = 0
% 160.64/22.22 | | | |
% 160.64/22.22 | | | | COMBINE_EQS: (102), (124) imply:
% 160.64/22.23 | | | | (125) all_110_3 = 0
% 160.64/22.23 | | | |
% 160.64/22.23 | | | | REDUCE: (57), (124) imply:
% 160.64/22.23 | | | | (126) relation(all_52_4) = 0
% 160.64/22.23 | | | |
% 160.64/22.23 | | | | BETA: splitting (88) gives:
% 160.64/22.23 | | | |
% 160.64/22.23 | | | | Case 1:
% 160.64/22.23 | | | | |
% 160.64/22.23 | | | | | (127) ~ (all_110_3 = 0)
% 160.64/22.23 | | | | |
% 160.64/22.23 | | | | | REDUCE: (125), (127) imply:
% 160.64/22.23 | | | | | (128) $false
% 160.64/22.23 | | | | |
% 160.64/22.23 | | | | | CLOSE: (128) is inconsistent.
% 160.64/22.23 | | | | |
% 160.64/22.23 | | | | Case 2:
% 160.64/22.23 | | | | |
% 160.64/22.23 | | | | | (129) all_110_0 = all_52_3
% 160.64/22.23 | | | | |
% 160.64/22.23 | | | | | REDUCE: (85), (129) imply:
% 160.64/22.23 | | | | | (130) set_union2(all_110_2, all_110_1) = all_52_3
% 160.64/22.23 | | | | |
% 160.64/22.23 | | | | | REDUCE: (83), (129) imply:
% 160.64/22.23 | | | | | (131) $i(all_52_3)
% 160.64/22.23 | | | | |
% 160.64/22.23 | | | | | BETA: splitting (97) gives:
% 160.64/22.23 | | | | |
% 160.64/22.23 | | | | | Case 1:
% 160.64/22.23 | | | | | |
% 160.64/22.23 | | | | | | (132) ~ (all_112_3 = 0)
% 160.64/22.23 | | | | | |
% 160.64/22.23 | | | | | | REDUCE: (110), (132) imply:
% 160.64/22.23 | | | | | | (133) $false
% 160.64/22.23 | | | | | |
% 160.64/22.23 | | | | | | CLOSE: (133) is inconsistent.
% 160.64/22.23 | | | | | |
% 160.64/22.23 | | | | | Case 2:
% 160.64/22.23 | | | | | |
% 160.64/22.23 | | | | | | (134) all_112_0 = all_52_2
% 160.64/22.23 | | | | | |
% 160.64/22.23 | | | | | | REDUCE: (111), (134) imply:
% 160.64/22.23 | | | | | | (135) set_union2(all_106_1, all_106_0) = all_52_2
% 160.64/22.23 | | | | | |
% 160.64/22.23 | | | | | | REDUCE: (92), (134) imply:
% 160.64/22.23 | | | | | | (136) $i(all_52_2)
% 160.64/22.23 | | | | | |
% 160.64/22.23 | | | | | | GROUND_INST: instantiating (2) with all_52_4, simplifying with (38),
% 160.64/22.23 | | | | | | (126) gives:
% 160.64/22.23 | | | | | | (137) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 160.64/22.23 | | | | | | (one_to_one(all_52_4) = v2 & function(all_52_4) = v1 &
% 160.64/22.23 | | | | | | empty(all_52_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 =
% 160.64/22.23 | | | | | | 0))
% 160.64/22.23 | | | | | |
% 160.64/22.23 | | | | | | GROUND_INST: instantiating (3) with all_52_5, all_90_0, simplifying
% 160.64/22.23 | | | | | | with (37), (63) gives:
% 160.64/22.23 | | | | | | (138) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 160.64/22.23 | | | | | | (relation(all_52_5) = v0 & function(all_52_5) = v2 &
% 160.64/22.23 | | | | | | empty(all_52_5) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~
% 160.64/22.23 | | | | | | (v0 = 0) | all_90_0 = 0))
% 160.64/22.23 | | | | | |
% 160.64/22.23 | | | | | | GROUND_INST: instantiating (9) with all_106_1, all_106_0, all_52_2,
% 160.64/22.23 | | | | | | all_52_7, all_52_1, simplifying with (35), (41), (112),
% 160.64/22.23 | | | | | | (113), (135), (136) gives:
% 160.64/22.23 | | | | | | (139) all_52_1 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) &
% 160.64/22.23 | | | | | | ~ (v0 = 0) & in(all_52_7, all_106_0) = v1 & in(all_52_7,
% 160.64/22.23 | | | | | | all_106_1) = v0)
% 160.64/22.23 | | | | | |
% 160.64/22.23 | | | | | | GROUND_INST: instantiating (fc3_xboole_0) with all_106_0, all_106_1,
% 160.64/22.23 | | | | | | all_52_2, simplifying with (112), (113), (135) gives:
% 160.64/22.23 | | | | | | (140) ? [v0: any] : ? [v1: any] : (empty(all_106_0) = v0 &
% 160.64/22.23 | | | | | | empty(all_52_2) = v1 & ( ~ (v1 = 0) | v0 = 0))
% 160.64/22.23 | | | | | |
% 160.64/22.23 | | | | | | GROUND_INST: instantiating (4) with all_106_0, all_106_1, all_52_2,
% 160.64/22.23 | | | | | | simplifying with (112), (113), (135) gives:
% 160.64/22.23 | | | | | | (141) set_union2(all_106_0, all_106_1) = all_52_2 & $i(all_52_2)
% 160.64/22.23 | | | | | |
% 160.64/22.23 | | | | | | ALPHA: (141) implies:
% 160.64/22.23 | | | | | | (142) set_union2(all_106_0, all_106_1) = all_52_2
% 160.64/22.23 | | | | | |
% 160.64/22.23 | | | | | | GROUND_INST: instantiating (fc2_xboole_0) with all_106_1, all_106_0,
% 160.64/22.23 | | | | | | all_52_2, simplifying with (112), (113), (135) gives:
% 160.64/22.23 | | | | | | (143) ? [v0: any] : ? [v1: any] : (empty(all_106_1) = v0 &
% 160.64/22.23 | | | | | | empty(all_52_2) = v1 & ( ~ (v1 = 0) | v0 = 0))
% 160.64/22.23 | | | | | |
% 160.64/22.23 | | | | | | GROUND_INST: instantiating (6) with all_110_2, all_110_1, all_52_3,
% 160.64/22.23 | | | | | | all_52_7, simplifying with (35), (40), (81), (82),
% 160.64/22.23 | | | | | | (130), (131) gives:
% 160.64/22.23 | | | | | | (144) ? [v0: any] : ? [v1: any] : (in(all_52_7, all_110_1) = v1
% 160.64/22.23 | | | | | | & in(all_52_7, all_110_2) = v0 & (v1 = 0 | v0 = 0))
% 160.64/22.23 | | | | | |
% 160.64/22.23 | | | | | | GROUND_INST: instantiating (4) with all_110_1, all_110_2, all_52_3,
% 160.64/22.23 | | | | | | simplifying with (81), (82), (130) gives:
% 160.64/22.23 | | | | | | (145) set_union2(all_110_1, all_110_2) = all_52_3 & $i(all_52_3)
% 160.64/22.23 | | | | | |
% 160.64/22.23 | | | | | | ALPHA: (145) implies:
% 160.64/22.23 | | | | | | (146) set_union2(all_110_1, all_110_2) = all_52_3
% 160.64/22.23 | | | | | |
% 160.64/22.23 | | | | | | GROUND_INST: instantiating (5) with all_76_0, all_52_5, all_52_4,
% 160.64/22.23 | | | | | | simplifying with (37), (60), (61) gives:
% 160.64/22.23 | | | | | | (147) set_intersection2(all_76_0, all_52_5) = all_52_4 &
% 160.64/22.23 | | | | | | $i(all_52_4)
% 160.64/22.23 | | | | | |
% 160.64/22.23 | | | | | | GROUND_INST: instantiating (t99_relat_1) with all_52_6, all_52_5,
% 160.64/22.23 | | | | | | all_100_1, simplifying with (36), (37), (67) gives:
% 160.64/22.23 | | | | | | (148) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] :
% 160.64/22.23 | | | | | | (subset(v1, v2) = v3 & relation_rng(all_100_1) = v1 &
% 160.64/22.23 | | | | | | relation_rng(all_52_5) = v2 & relation(all_52_5) = v0 &
% 160.64/22.23 | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v3 = 0))
% 160.64/22.23 | | | | | |
% 160.64/22.23 | | | | | | GROUND_INST: instantiating (26) with all_52_6, all_52_5, all_100_1,
% 160.64/22.23 | | | | | | simplifying with (36), (37), (67) gives:
% 160.64/22.24 | | | | | | (149) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 160.64/22.24 | | | | | | (relation_dom(all_100_1) = v1 & relation_dom(all_52_5) = v2
% 160.64/22.24 | | | | | | & set_intersection2(v2, all_52_6) = v3 &
% 160.64/22.24 | | | | | | relation(all_52_5) = v0 & $i(v3) & $i(v2) & $i(v1) & ( ~
% 160.64/22.24 | | | | | | (v0 = 0) | v3 = v1))
% 160.64/22.24 | | | | | |
% 160.64/22.24 | | | | | | GROUND_INST: instantiating (fc4_funct_1) with all_52_5, all_52_6,
% 160.64/22.24 | | | | | | all_100_1, simplifying with (36), (37), (67) gives:
% 160.64/22.24 | | | | | | (150) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 160.64/22.24 | | | | | | (relation(all_100_1) = v2 & relation(all_52_5) = v0 &
% 160.64/22.24 | | | | | | function(all_100_1) = v3 & function(all_52_5) = v1 & ( ~
% 160.64/22.24 | | | | | | (v1 = 0) | ~ (v0 = 0) | (v3 = 0 & v2 = 0)))
% 160.64/22.24 | | | | | |
% 160.64/22.24 | | | | | | GROUND_INST: instantiating (dt_k7_relat_1) with all_52_5, all_52_6,
% 160.64/22.24 | | | | | | all_100_1, simplifying with (36), (37), (67) gives:
% 160.64/22.24 | | | | | | (151) ? [v0: any] : ? [v1: any] : (relation(all_100_1) = v1 &
% 160.64/22.24 | | | | | | relation(all_52_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 160.64/22.24 | | | | | |
% 160.64/22.24 | | | | | | GROUND_INST: instantiating (t99_relat_1) with all_52_6, all_104_1,
% 160.64/22.24 | | | | | | all_52_4, simplifying with (36), (71), (121) gives:
% 160.64/22.24 | | | | | | (152) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] :
% 160.64/22.24 | | | | | | (subset(v1, v2) = v3 & relation_rng(all_104_1) = v2 &
% 160.64/22.24 | | | | | | relation_rng(all_52_4) = v1 & relation(all_104_1) = v0 &
% 160.64/22.24 | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v3 = 0))
% 160.64/22.24 | | | | | |
% 160.64/22.24 | | | | | | GROUND_INST: instantiating (26) with all_52_6, all_104_1, all_52_4,
% 160.64/22.24 | | | | | | simplifying with (36), (71), (121) gives:
% 160.64/22.24 | | | | | | (153) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 160.64/22.24 | | | | | | (relation_dom(all_104_1) = v2 & relation_dom(all_52_4) = v1
% 160.64/22.24 | | | | | | & set_intersection2(v2, all_52_6) = v3 &
% 160.64/22.24 | | | | | | relation(all_104_1) = v0 & $i(v3) & $i(v2) & $i(v1) & ( ~
% 160.64/22.24 | | | | | | (v0 = 0) | v3 = v1))
% 160.64/22.24 | | | | | |
% 160.64/22.24 | | | | | | GROUND_INST: instantiating (21) with all_52_6, all_104_1, all_52_4,
% 160.64/22.24 | | | | | | simplifying with (36), (71), (121) gives:
% 160.64/22.24 | | | | | | (154) ? [v0: any] : ? [v1: $i] : ? [v2: $i] :
% 160.64/22.24 | | | | | | (relation_rng_restriction(all_52_6, all_52_4) = v2 &
% 160.64/22.24 | | | | | | relation_restriction(all_104_1, all_52_6) = v1 &
% 160.64/22.24 | | | | | | relation(all_104_1) = v0 & $i(v2) & $i(v1) & ( ~ (v0 = 0)
% 160.64/22.24 | | | | | | | v2 = v1))
% 160.64/22.24 | | | | | |
% 160.64/22.24 | | | | | | GROUND_INST: instantiating (fc4_funct_1) with all_104_1, all_52_6,
% 160.64/22.24 | | | | | | all_52_4, simplifying with (36), (71), (121) gives:
% 160.64/22.24 | | | | | | (155) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 160.64/22.24 | | | | | | (relation(all_104_1) = v0 & relation(all_52_4) = v2 &
% 160.64/22.24 | | | | | | function(all_104_1) = v1 & function(all_52_4) = v3 & ( ~
% 160.64/22.24 | | | | | | (v1 = 0) | ~ (v0 = 0) | (v3 = 0 & v2 = 0)))
% 160.64/22.24 | | | | | |
% 160.64/22.24 | | | | | | GROUND_INST: instantiating (dt_k7_relat_1) with all_104_1, all_52_6,
% 160.64/22.24 | | | | | | all_52_4, simplifying with (36), (71), (121) gives:
% 160.64/22.24 | | | | | | (156) ? [v0: any] : ? [v1: any] : (relation(all_104_1) = v0 &
% 160.64/22.24 | | | | | | relation(all_52_4) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 160.64/22.24 | | | | | |
% 160.64/22.24 | | | | | | GROUND_INST: instantiating (l29_wellord1) with all_52_6, all_52_5,
% 160.64/22.24 | | | | | | all_104_1, simplifying with (36), (37), (75) gives:
% 160.64/22.24 | | | | | | (157) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] :
% 160.64/22.24 | | | | | | (subset(v1, v2) = v3 & relation_dom(all_104_1) = v1 &
% 160.64/22.24 | | | | | | relation_dom(all_52_5) = v2 & relation(all_52_5) = v0 &
% 160.64/22.24 | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v3 = 0))
% 160.64/22.24 | | | | | |
% 160.64/22.24 | | | | | | GROUND_INST: instantiating (17) with all_52_6, all_52_5, all_104_1,
% 160.64/22.24 | | | | | | simplifying with (36), (37), (75) gives:
% 160.64/22.24 | | | | | | (158) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 160.64/22.24 | | | | | | (relation_rng(all_104_1) = v1 & relation_rng(all_52_5) = v2
% 160.64/22.24 | | | | | | & set_intersection2(v2, all_52_6) = v3 &
% 160.64/22.24 | | | | | | relation(all_52_5) = v0 & $i(v3) & $i(v2) & $i(v1) & ( ~
% 160.64/22.24 | | | | | | (v0 = 0) | v3 = v1))
% 160.64/22.24 | | | | | |
% 160.64/22.24 | | | | | | GROUND_INST: instantiating (fc5_funct_1) with all_52_6, all_52_5,
% 160.64/22.24 | | | | | | all_104_1, simplifying with (36), (37), (75) gives:
% 160.64/22.24 | | | | | | (159) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 160.64/22.24 | | | | | | (relation(all_104_1) = v2 & relation(all_52_5) = v0 &
% 160.64/22.24 | | | | | | function(all_104_1) = v3 & function(all_52_5) = v1 & ( ~
% 160.64/22.24 | | | | | | (v1 = 0) | ~ (v0 = 0) | (v3 = 0 & v2 = 0)))
% 160.64/22.24 | | | | | |
% 160.64/22.24 | | | | | | GROUND_INST: instantiating (dt_k8_relat_1) with all_52_6, all_52_5,
% 160.64/22.24 | | | | | | all_104_1, simplifying with (36), (37), (75) gives:
% 160.64/22.24 | | | | | | (160) ? [v0: any] : ? [v1: any] : (relation(all_104_1) = v1 &
% 160.64/22.24 | | | | | | relation(all_52_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 160.64/22.24 | | | | | |
% 160.64/22.24 | | | | | | GROUND_INST: instantiating (l29_wellord1) with all_52_6, all_100_1,
% 160.64/22.24 | | | | | | all_52_4, simplifying with (36), (65), (117) gives:
% 160.64/22.24 | | | | | | (161) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] :
% 160.64/22.24 | | | | | | (subset(v1, v2) = v3 & relation_dom(all_100_1) = v2 &
% 160.64/22.24 | | | | | | relation_dom(all_52_4) = v1 & relation(all_100_1) = v0 &
% 160.64/22.24 | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v3 = 0))
% 160.64/22.24 | | | | | |
% 160.64/22.24 | | | | | | GROUND_INST: instantiating (17) with all_52_6, all_100_1, all_52_4,
% 160.64/22.24 | | | | | | simplifying with (36), (65), (117) gives:
% 160.64/22.24 | | | | | | (162) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 160.64/22.24 | | | | | | (relation_rng(all_100_1) = v2 & relation_rng(all_52_4) = v1
% 160.64/22.24 | | | | | | & set_intersection2(v2, all_52_6) = v3 &
% 160.64/22.24 | | | | | | relation(all_100_1) = v0 & $i(v3) & $i(v2) & $i(v1) & ( ~
% 160.64/22.24 | | | | | | (v0 = 0) | v3 = v1))
% 160.64/22.24 | | | | | |
% 160.64/22.25 | | | | | | GROUND_INST: instantiating (fc5_funct_1) with all_52_6, all_100_1,
% 160.64/22.25 | | | | | | all_52_4, simplifying with (36), (65), (117) gives:
% 160.64/22.25 | | | | | | (163) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 160.64/22.25 | | | | | | (relation(all_100_1) = v0 & relation(all_52_4) = v2 &
% 160.64/22.25 | | | | | | function(all_100_1) = v1 & function(all_52_4) = v3 & ( ~
% 160.64/22.25 | | | | | | (v1 = 0) | ~ (v0 = 0) | (v3 = 0 & v2 = 0)))
% 160.64/22.25 | | | | | |
% 160.64/22.25 | | | | | | GROUND_INST: instantiating (19) with all_52_6, all_100_1, all_52_4,
% 160.64/22.25 | | | | | | simplifying with (36), (65), (117) gives:
% 160.64/22.25 | | | | | | (164) ? [v0: any] : ? [v1: $i] : ? [v2: $i] :
% 160.64/22.25 | | | | | | (relation_dom_restriction(all_52_4, all_52_6) = v2 &
% 160.64/22.25 | | | | | | relation_restriction(all_100_1, all_52_6) = v1 &
% 160.64/22.25 | | | | | | relation(all_100_1) = v0 & $i(v2) & $i(v1) & ( ~ (v0 = 0)
% 160.64/22.25 | | | | | | | v2 = v1))
% 160.64/22.25 | | | | | |
% 160.64/22.25 | | | | | | GROUND_INST: instantiating (dt_k8_relat_1) with all_52_6, all_100_1,
% 160.64/22.25 | | | | | | all_52_4, simplifying with (36), (65), (117) gives:
% 160.64/22.25 | | | | | | (165) ? [v0: any] : ? [v1: any] : (relation(all_100_1) = v0 &
% 160.64/22.25 | | | | | | relation(all_52_4) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 160.64/22.25 | | | | | |
% 160.64/22.25 | | | | | | DELTA: instantiating (165) with fresh symbols all_176_0, all_176_1
% 160.64/22.25 | | | | | | gives:
% 160.64/22.25 | | | | | | (166) relation(all_100_1) = all_176_1 & relation(all_52_4) =
% 160.64/22.25 | | | | | | all_176_0 & ( ~ (all_176_1 = 0) | all_176_0 = 0)
% 160.64/22.25 | | | | | |
% 160.64/22.25 | | | | | | ALPHA: (166) implies:
% 160.64/22.25 | | | | | | (167) relation(all_100_1) = all_176_1
% 160.64/22.25 | | | | | |
% 160.64/22.25 | | | | | | DELTA: instantiating (144) with fresh symbols all_180_0, all_180_1
% 160.64/22.25 | | | | | | gives:
% 160.64/22.25 | | | | | | (168) in(all_52_7, all_110_1) = all_180_0 & in(all_52_7,
% 160.64/22.25 | | | | | | all_110_2) = all_180_1 & (all_180_0 = 0 | all_180_1 = 0)
% 160.64/22.25 | | | | | |
% 160.64/22.25 | | | | | | ALPHA: (168) implies:
% 160.64/22.25 | | | | | | (169) in(all_52_7, all_110_2) = all_180_1
% 160.64/22.25 | | | | | | (170) in(all_52_7, all_110_1) = all_180_0
% 160.64/22.25 | | | | | | (171) all_180_0 = 0 | all_180_1 = 0
% 160.64/22.25 | | | | | |
% 160.64/22.25 | | | | | | DELTA: instantiating (160) with fresh symbols all_186_0, all_186_1
% 160.64/22.25 | | | | | | gives:
% 160.64/22.25 | | | | | | (172) relation(all_104_1) = all_186_0 & relation(all_52_5) =
% 160.64/22.25 | | | | | | all_186_1 & ( ~ (all_186_1 = 0) | all_186_0 = 0)
% 160.64/22.25 | | | | | |
% 160.64/22.25 | | | | | | ALPHA: (172) implies:
% 160.64/22.25 | | | | | | (173) relation(all_52_5) = all_186_1
% 160.64/22.25 | | | | | | (174) relation(all_104_1) = all_186_0
% 160.64/22.25 | | | | | | (175) ~ (all_186_1 = 0) | all_186_0 = 0
% 160.64/22.25 | | | | | |
% 160.64/22.25 | | | | | | DELTA: instantiating (140) with fresh symbols all_188_0, all_188_1
% 160.64/22.25 | | | | | | gives:
% 160.64/22.25 | | | | | | (176) empty(all_106_0) = all_188_1 & empty(all_52_2) = all_188_0
% 160.64/22.25 | | | | | | & ( ~ (all_188_0 = 0) | all_188_1 = 0)
% 160.64/22.25 | | | | | |
% 160.64/22.25 | | | | | | ALPHA: (176) implies:
% 160.64/22.25 | | | | | | (177) empty(all_106_0) = all_188_1
% 160.64/22.25 | | | | | |
% 160.64/22.25 | | | | | | DELTA: instantiating (156) with fresh symbols all_194_0, all_194_1
% 160.64/22.25 | | | | | | gives:
% 160.64/22.25 | | | | | | (178) relation(all_104_1) = all_194_1 & relation(all_52_4) =
% 160.64/22.25 | | | | | | all_194_0 & ( ~ (all_194_1 = 0) | all_194_0 = 0)
% 160.64/22.25 | | | | | |
% 160.64/22.25 | | | | | | ALPHA: (178) implies:
% 160.64/22.25 | | | | | | (179) relation(all_104_1) = all_194_1
% 160.64/22.25 | | | | | |
% 160.64/22.25 | | | | | | DELTA: instantiating (143) with fresh symbols all_202_0, all_202_1
% 160.64/22.25 | | | | | | gives:
% 160.64/22.25 | | | | | | (180) empty(all_106_1) = all_202_1 & empty(all_52_2) = all_202_0
% 160.64/22.25 | | | | | | & ( ~ (all_202_0 = 0) | all_202_1 = 0)
% 160.64/22.25 | | | | | |
% 160.64/22.25 | | | | | | ALPHA: (180) implies:
% 160.64/22.25 | | | | | | (181) empty(all_106_1) = all_202_1
% 160.64/22.25 | | | | | |
% 160.64/22.25 | | | | | | DELTA: instantiating (151) with fresh symbols all_204_0, all_204_1
% 160.64/22.25 | | | | | | gives:
% 160.64/22.25 | | | | | | (182) relation(all_100_1) = all_204_0 & relation(all_52_5) =
% 160.64/22.25 | | | | | | all_204_1 & ( ~ (all_204_1 = 0) | all_204_0 = 0)
% 160.64/22.25 | | | | | |
% 160.64/22.25 | | | | | | ALPHA: (182) implies:
% 160.64/22.25 | | | | | | (183) relation(all_52_5) = all_204_1
% 160.64/22.25 | | | | | | (184) relation(all_100_1) = all_204_0
% 160.64/22.25 | | | | | | (185) ~ (all_204_1 = 0) | all_204_0 = 0
% 160.64/22.25 | | | | | |
% 160.64/22.25 | | | | | | DELTA: instantiating (137) with fresh symbols all_206_0, all_206_1,
% 160.64/22.25 | | | | | | all_206_2 gives:
% 160.64/22.25 | | | | | | (186) one_to_one(all_52_4) = all_206_0 & function(all_52_4) =
% 160.64/22.25 | | | | | | all_206_1 & empty(all_52_4) = all_206_2 & ( ~ (all_206_1 =
% 160.64/22.25 | | | | | | 0) | ~ (all_206_2 = 0) | all_206_0 = 0)
% 160.64/22.25 | | | | | |
% 160.64/22.25 | | | | | | ALPHA: (186) implies:
% 160.64/22.25 | | | | | | (187) function(all_52_4) = all_206_1
% 160.64/22.25 | | | | | | (188) one_to_one(all_52_4) = all_206_0
% 160.64/22.25 | | | | | | (189) ~ (all_206_1 = 0) | ~ (all_206_2 = 0) | all_206_0 = 0
% 160.64/22.25 | | | | | |
% 160.64/22.25 | | | | | | DELTA: instantiating (164) with fresh symbols all_208_0, all_208_1,
% 160.64/22.25 | | | | | | all_208_2 gives:
% 160.64/22.25 | | | | | | (190) relation_dom_restriction(all_52_4, all_52_6) = all_208_0 &
% 160.64/22.25 | | | | | | relation_restriction(all_100_1, all_52_6) = all_208_1 &
% 160.64/22.25 | | | | | | relation(all_100_1) = all_208_2 & $i(all_208_0) &
% 160.64/22.25 | | | | | | $i(all_208_1) & ( ~ (all_208_2 = 0) | all_208_0 =
% 160.64/22.25 | | | | | | all_208_1)
% 160.64/22.25 | | | | | |
% 160.64/22.25 | | | | | | ALPHA: (190) implies:
% 160.64/22.25 | | | | | | (191) relation(all_100_1) = all_208_2
% 160.64/22.25 | | | | | | (192) relation_dom_restriction(all_52_4, all_52_6) = all_208_0
% 160.64/22.25 | | | | | | (193) ~ (all_208_2 = 0) | all_208_0 = all_208_1
% 160.64/22.25 | | | | | |
% 160.64/22.25 | | | | | | DELTA: instantiating (154) with fresh symbols all_210_0, all_210_1,
% 160.64/22.25 | | | | | | all_210_2 gives:
% 160.64/22.25 | | | | | | (194) relation_rng_restriction(all_52_6, all_52_4) = all_210_0 &
% 160.64/22.25 | | | | | | relation_restriction(all_104_1, all_52_6) = all_210_1 &
% 160.64/22.25 | | | | | | relation(all_104_1) = all_210_2 & $i(all_210_0) &
% 160.64/22.25 | | | | | | $i(all_210_1) & ( ~ (all_210_2 = 0) | all_210_0 =
% 160.64/22.25 | | | | | | all_210_1)
% 160.64/22.25 | | | | | |
% 160.64/22.25 | | | | | | ALPHA: (194) implies:
% 160.64/22.25 | | | | | | (195) relation(all_104_1) = all_210_2
% 160.64/22.25 | | | | | | (196) relation_rng_restriction(all_52_6, all_52_4) = all_210_0
% 160.64/22.25 | | | | | | (197) ~ (all_210_2 = 0) | all_210_0 = all_210_1
% 160.64/22.25 | | | | | |
% 160.64/22.25 | | | | | | DELTA: instantiating (138) with fresh symbols all_214_0, all_214_1,
% 160.64/22.25 | | | | | | all_214_2 gives:
% 160.64/22.25 | | | | | | (198) relation(all_52_5) = all_214_2 & function(all_52_5) =
% 160.64/22.25 | | | | | | all_214_0 & empty(all_52_5) = all_214_1 & ( ~ (all_214_0 =
% 160.64/22.25 | | | | | | 0) | ~ (all_214_1 = 0) | ~ (all_214_2 = 0) | all_90_0
% 160.64/22.25 | | | | | | = 0)
% 160.64/22.25 | | | | | |
% 160.64/22.25 | | | | | | ALPHA: (198) implies:
% 161.05/22.25 | | | | | | (199) relation(all_52_5) = all_214_2
% 161.05/22.25 | | | | | |
% 161.05/22.25 | | | | | | DELTA: instantiating (152) with fresh symbols all_216_0, all_216_1,
% 161.05/22.25 | | | | | | all_216_2, all_216_3 gives:
% 161.05/22.25 | | | | | | (200) subset(all_216_2, all_216_1) = all_216_0 &
% 161.05/22.25 | | | | | | relation_rng(all_104_1) = all_216_1 &
% 161.05/22.25 | | | | | | relation_rng(all_52_4) = all_216_2 & relation(all_104_1) =
% 161.05/22.25 | | | | | | all_216_3 & $i(all_216_1) & $i(all_216_2) & ( ~ (all_216_3
% 161.05/22.25 | | | | | | = 0) | all_216_0 = 0)
% 161.05/22.25 | | | | | |
% 161.05/22.25 | | | | | | ALPHA: (200) implies:
% 161.05/22.25 | | | | | | (201) relation(all_104_1) = all_216_3
% 161.05/22.25 | | | | | | (202) relation_rng(all_104_1) = all_216_1
% 161.05/22.25 | | | | | |
% 161.05/22.25 | | | | | | DELTA: instantiating (148) with fresh symbols all_218_0, all_218_1,
% 161.05/22.25 | | | | | | all_218_2, all_218_3 gives:
% 161.05/22.25 | | | | | | (203) subset(all_218_2, all_218_1) = all_218_0 &
% 161.05/22.25 | | | | | | relation_rng(all_100_1) = all_218_2 &
% 161.05/22.25 | | | | | | relation_rng(all_52_5) = all_218_1 & relation(all_52_5) =
% 161.05/22.25 | | | | | | all_218_3 & $i(all_218_1) & $i(all_218_2) & ( ~ (all_218_3
% 161.05/22.25 | | | | | | = 0) | all_218_0 = 0)
% 161.05/22.25 | | | | | |
% 161.05/22.25 | | | | | | ALPHA: (203) implies:
% 161.05/22.26 | | | | | | (204) $i(all_218_1)
% 161.05/22.26 | | | | | | (205) relation(all_52_5) = all_218_3
% 161.05/22.26 | | | | | | (206) relation_rng(all_52_5) = all_218_1
% 161.05/22.26 | | | | | | (207) relation_rng(all_100_1) = all_218_2
% 161.05/22.26 | | | | | | (208) subset(all_218_2, all_218_1) = all_218_0
% 161.05/22.26 | | | | | | (209) ~ (all_218_3 = 0) | all_218_0 = 0
% 161.05/22.26 | | | | | |
% 161.05/22.26 | | | | | | DELTA: instantiating (161) with fresh symbols all_220_0, all_220_1,
% 161.05/22.26 | | | | | | all_220_2, all_220_3 gives:
% 161.05/22.26 | | | | | | (210) subset(all_220_2, all_220_1) = all_220_0 &
% 161.05/22.26 | | | | | | relation_dom(all_100_1) = all_220_1 &
% 161.05/22.26 | | | | | | relation_dom(all_52_4) = all_220_2 & relation(all_100_1) =
% 161.05/22.26 | | | | | | all_220_3 & $i(all_220_1) & $i(all_220_2) & ( ~ (all_220_3
% 161.05/22.26 | | | | | | = 0) | all_220_0 = 0)
% 161.05/22.26 | | | | | |
% 161.05/22.26 | | | | | | ALPHA: (210) implies:
% 161.05/22.26 | | | | | | (211) relation(all_100_1) = all_220_3
% 161.05/22.26 | | | | | | (212) relation_dom(all_100_1) = all_220_1
% 161.05/22.26 | | | | | |
% 161.05/22.26 | | | | | | DELTA: instantiating (163) with fresh symbols all_222_0, all_222_1,
% 161.05/22.26 | | | | | | all_222_2, all_222_3 gives:
% 161.05/22.26 | | | | | | (213) relation(all_100_1) = all_222_3 & relation(all_52_4) =
% 161.05/22.26 | | | | | | all_222_1 & function(all_100_1) = all_222_2 &
% 161.05/22.26 | | | | | | function(all_52_4) = all_222_0 & ( ~ (all_222_2 = 0) | ~
% 161.05/22.26 | | | | | | (all_222_3 = 0) | (all_222_0 = 0 & all_222_1 = 0))
% 161.05/22.26 | | | | | |
% 161.05/22.26 | | | | | | ALPHA: (213) implies:
% 161.05/22.26 | | | | | | (214) function(all_52_4) = all_222_0
% 161.05/22.26 | | | | | | (215) function(all_100_1) = all_222_2
% 161.05/22.26 | | | | | | (216) relation(all_100_1) = all_222_3
% 161.05/22.26 | | | | | | (217) ~ (all_222_2 = 0) | ~ (all_222_3 = 0) | (all_222_0 = 0 &
% 161.05/22.26 | | | | | | all_222_1 = 0)
% 161.05/22.26 | | | | | |
% 161.05/22.26 | | | | | | DELTA: instantiating (150) with fresh symbols all_224_0, all_224_1,
% 161.05/22.26 | | | | | | all_224_2, all_224_3 gives:
% 161.05/22.26 | | | | | | (218) relation(all_100_1) = all_224_1 & relation(all_52_5) =
% 161.05/22.26 | | | | | | all_224_3 & function(all_100_1) = all_224_0 &
% 161.05/22.26 | | | | | | function(all_52_5) = all_224_2 & ( ~ (all_224_2 = 0) | ~
% 161.05/22.26 | | | | | | (all_224_3 = 0) | (all_224_0 = 0 & all_224_1 = 0))
% 161.05/22.26 | | | | | |
% 161.05/22.26 | | | | | | ALPHA: (218) implies:
% 161.05/22.26 | | | | | | (219) function(all_100_1) = all_224_0
% 161.05/22.26 | | | | | | (220) relation(all_52_5) = all_224_3
% 161.05/22.26 | | | | | | (221) relation(all_100_1) = all_224_1
% 161.05/22.26 | | | | | |
% 161.05/22.26 | | | | | | DELTA: instantiating (157) with fresh symbols all_226_0, all_226_1,
% 161.05/22.26 | | | | | | all_226_2, all_226_3 gives:
% 161.05/22.26 | | | | | | (222) subset(all_226_2, all_226_1) = all_226_0 &
% 161.05/22.26 | | | | | | relation_dom(all_104_1) = all_226_2 &
% 161.05/22.26 | | | | | | relation_dom(all_52_5) = all_226_1 & relation(all_52_5) =
% 161.05/22.26 | | | | | | all_226_3 & $i(all_226_1) & $i(all_226_2) & ( ~ (all_226_3
% 161.05/22.26 | | | | | | = 0) | all_226_0 = 0)
% 161.05/22.26 | | | | | |
% 161.05/22.26 | | | | | | ALPHA: (222) implies:
% 161.05/22.26 | | | | | | (223) $i(all_226_1)
% 161.05/22.26 | | | | | | (224) relation(all_52_5) = all_226_3
% 161.05/22.26 | | | | | | (225) relation_dom(all_52_5) = all_226_1
% 161.05/22.26 | | | | | | (226) relation_dom(all_104_1) = all_226_2
% 161.05/22.26 | | | | | | (227) subset(all_226_2, all_226_1) = all_226_0
% 161.05/22.26 | | | | | | (228) ~ (all_226_3 = 0) | all_226_0 = 0
% 161.05/22.26 | | | | | |
% 161.05/22.26 | | | | | | DELTA: instantiating (159) with fresh symbols all_228_0, all_228_1,
% 161.05/22.26 | | | | | | all_228_2, all_228_3 gives:
% 161.05/22.26 | | | | | | (229) relation(all_104_1) = all_228_1 & relation(all_52_5) =
% 161.05/22.26 | | | | | | all_228_3 & function(all_104_1) = all_228_0 &
% 161.05/22.26 | | | | | | function(all_52_5) = all_228_2 & ( ~ (all_228_2 = 0) | ~
% 161.05/22.26 | | | | | | (all_228_3 = 0) | (all_228_0 = 0 & all_228_1 = 0))
% 161.05/22.26 | | | | | |
% 161.05/22.26 | | | | | | ALPHA: (229) implies:
% 161.05/22.26 | | | | | | (230) relation(all_52_5) = all_228_3
% 161.05/22.26 | | | | | | (231) relation(all_104_1) = all_228_1
% 161.05/22.26 | | | | | |
% 161.05/22.26 | | | | | | DELTA: instantiating (155) with fresh symbols all_230_0, all_230_1,
% 161.05/22.26 | | | | | | all_230_2, all_230_3 gives:
% 161.05/22.26 | | | | | | (232) relation(all_104_1) = all_230_3 & relation(all_52_4) =
% 161.05/22.26 | | | | | | all_230_1 & function(all_104_1) = all_230_2 &
% 161.05/22.26 | | | | | | function(all_52_4) = all_230_0 & ( ~ (all_230_2 = 0) | ~
% 161.05/22.26 | | | | | | (all_230_3 = 0) | (all_230_0 = 0 & all_230_1 = 0))
% 161.05/22.26 | | | | | |
% 161.05/22.26 | | | | | | ALPHA: (232) implies:
% 161.05/22.26 | | | | | | (233) function(all_52_4) = all_230_0
% 161.05/22.26 | | | | | | (234) relation(all_104_1) = all_230_3
% 161.05/22.26 | | | | | |
% 161.05/22.26 | | | | | | DELTA: instantiating (162) with fresh symbols all_232_0, all_232_1,
% 161.05/22.26 | | | | | | all_232_2, all_232_3 gives:
% 161.05/22.26 | | | | | | (235) relation_rng(all_100_1) = all_232_1 &
% 161.05/22.26 | | | | | | relation_rng(all_52_4) = all_232_2 &
% 161.05/22.26 | | | | | | set_intersection2(all_232_1, all_52_6) = all_232_0 &
% 161.05/22.26 | | | | | | relation(all_100_1) = all_232_3 & $i(all_232_0) &
% 161.05/22.26 | | | | | | $i(all_232_1) & $i(all_232_2) & ( ~ (all_232_3 = 0) |
% 161.05/22.26 | | | | | | all_232_0 = all_232_2)
% 161.05/22.26 | | | | | |
% 161.05/22.26 | | | | | | ALPHA: (235) implies:
% 161.05/22.26 | | | | | | (236) $i(all_232_1)
% 161.05/22.26 | | | | | | (237) $i(all_232_0)
% 161.05/22.26 | | | | | | (238) relation(all_100_1) = all_232_3
% 161.05/22.26 | | | | | | (239) set_intersection2(all_232_1, all_52_6) = all_232_0
% 161.05/22.26 | | | | | | (240) relation_rng(all_52_4) = all_232_2
% 161.05/22.26 | | | | | | (241) relation_rng(all_100_1) = all_232_1
% 161.05/22.26 | | | | | | (242) ~ (all_232_3 = 0) | all_232_0 = all_232_2
% 161.05/22.26 | | | | | |
% 161.05/22.26 | | | | | | DELTA: instantiating (158) with fresh symbols all_234_0, all_234_1,
% 161.05/22.26 | | | | | | all_234_2, all_234_3 gives:
% 161.05/22.26 | | | | | | (243) relation_rng(all_104_1) = all_234_2 &
% 161.05/22.26 | | | | | | relation_rng(all_52_5) = all_234_1 &
% 161.05/22.26 | | | | | | set_intersection2(all_234_1, all_52_6) = all_234_0 &
% 161.05/22.26 | | | | | | relation(all_52_5) = all_234_3 & $i(all_234_0) &
% 161.05/22.26 | | | | | | $i(all_234_1) & $i(all_234_2) & ( ~ (all_234_3 = 0) |
% 161.05/22.26 | | | | | | all_234_0 = all_234_2)
% 161.05/22.26 | | | | | |
% 161.05/22.26 | | | | | | ALPHA: (243) implies:
% 161.05/22.26 | | | | | | (244) relation(all_52_5) = all_234_3
% 161.05/22.26 | | | | | | (245) relation_rng(all_52_5) = all_234_1
% 161.05/22.26 | | | | | | (246) relation_rng(all_104_1) = all_234_2
% 161.05/22.26 | | | | | |
% 161.05/22.26 | | | | | | DELTA: instantiating (149) with fresh symbols all_236_0, all_236_1,
% 161.05/22.26 | | | | | | all_236_2, all_236_3 gives:
% 161.05/22.26 | | | | | | (247) relation_dom(all_100_1) = all_236_2 &
% 161.05/22.26 | | | | | | relation_dom(all_52_5) = all_236_1 &
% 161.05/22.26 | | | | | | set_intersection2(all_236_1, all_52_6) = all_236_0 &
% 161.05/22.26 | | | | | | relation(all_52_5) = all_236_3 & $i(all_236_0) &
% 161.05/22.26 | | | | | | $i(all_236_1) & $i(all_236_2) & ( ~ (all_236_3 = 0) |
% 161.05/22.26 | | | | | | all_236_0 = all_236_2)
% 161.05/22.26 | | | | | |
% 161.05/22.26 | | | | | | ALPHA: (247) implies:
% 161.05/22.26 | | | | | | (248) relation(all_52_5) = all_236_3
% 161.05/22.26 | | | | | | (249) relation_dom(all_52_5) = all_236_1
% 161.05/22.26 | | | | | | (250) relation_dom(all_100_1) = all_236_2
% 161.05/22.26 | | | | | |
% 161.05/22.26 | | | | | | DELTA: instantiating (153) with fresh symbols all_238_0, all_238_1,
% 161.05/22.26 | | | | | | all_238_2, all_238_3 gives:
% 161.05/22.26 | | | | | | (251) relation_dom(all_104_1) = all_238_1 &
% 161.05/22.26 | | | | | | relation_dom(all_52_4) = all_238_2 &
% 161.05/22.26 | | | | | | set_intersection2(all_238_1, all_52_6) = all_238_0 &
% 161.05/22.26 | | | | | | relation(all_104_1) = all_238_3 & $i(all_238_0) &
% 161.05/22.26 | | | | | | $i(all_238_1) & $i(all_238_2) & ( ~ (all_238_3 = 0) |
% 161.05/22.26 | | | | | | all_238_0 = all_238_2)
% 161.05/22.26 | | | | | |
% 161.05/22.26 | | | | | | ALPHA: (251) implies:
% 161.05/22.26 | | | | | | (252) $i(all_238_1)
% 161.05/22.26 | | | | | | (253) $i(all_238_0)
% 161.05/22.26 | | | | | | (254) relation(all_104_1) = all_238_3
% 161.05/22.26 | | | | | | (255) set_intersection2(all_238_1, all_52_6) = all_238_0
% 161.05/22.26 | | | | | | (256) relation_dom(all_52_4) = all_238_2
% 161.05/22.26 | | | | | | (257) relation_dom(all_104_1) = all_238_1
% 161.05/22.26 | | | | | | (258) ~ (all_238_3 = 0) | all_238_0 = all_238_2
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (28) with all_222_0, all_230_0, all_52_4,
% 161.05/22.27 | | | | | | simplifying with (214), (233) gives:
% 161.05/22.27 | | | | | | (259) all_230_0 = all_222_0
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (28) with all_206_1, all_230_0, all_52_4,
% 161.05/22.27 | | | | | | simplifying with (187), (233) gives:
% 161.05/22.27 | | | | | | (260) all_230_0 = all_206_1
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (28) with all_222_2, all_224_0,
% 161.05/22.27 | | | | | | all_100_1, simplifying with (215), (219) gives:
% 161.05/22.27 | | | | | | (261) all_224_0 = all_222_2
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (29) with all_186_1, all_218_3, all_52_5,
% 161.05/22.27 | | | | | | simplifying with (173), (205) gives:
% 161.05/22.27 | | | | | | (262) all_218_3 = all_186_1
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (29) with all_204_1, all_224_3, all_52_5,
% 161.05/22.27 | | | | | | simplifying with (183), (220) gives:
% 161.05/22.27 | | | | | | (263) all_224_3 = all_204_1
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (29) with all_224_3, all_226_3, all_52_5,
% 161.05/22.27 | | | | | | simplifying with (220), (224) gives:
% 161.05/22.27 | | | | | | (264) all_226_3 = all_224_3
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (29) with all_218_3, all_226_3, all_52_5,
% 161.05/22.27 | | | | | | simplifying with (205), (224) gives:
% 161.05/22.27 | | | | | | (265) all_226_3 = all_218_3
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (29) with all_214_2, all_226_3, all_52_5,
% 161.05/22.27 | | | | | | simplifying with (199), (224) gives:
% 161.05/22.27 | | | | | | (266) all_226_3 = all_214_2
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (29) with 0, all_236_3, all_52_5,
% 161.05/22.27 | | | | | | simplifying with (42), (248) gives:
% 161.05/22.27 | | | | | | (267) all_236_3 = 0
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (29) with all_234_3, all_236_3, all_52_5,
% 161.05/22.27 | | | | | | simplifying with (244), (248) gives:
% 161.05/22.27 | | | | | | (268) all_236_3 = all_234_3
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (29) with all_228_3, all_236_3, all_52_5,
% 161.05/22.27 | | | | | | simplifying with (230), (248) gives:
% 161.05/22.27 | | | | | | (269) all_236_3 = all_228_3
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (29) with all_226_3, all_236_3, all_52_5,
% 161.05/22.27 | | | | | | simplifying with (224), (248) gives:
% 161.05/22.27 | | | | | | (270) all_236_3 = all_226_3
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (29) with all_204_0, all_220_3,
% 161.05/22.27 | | | | | | all_100_1, simplifying with (184), (211) gives:
% 161.05/22.27 | | | | | | (271) all_220_3 = all_204_0
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (29) with all_220_3, all_222_3,
% 161.05/22.27 | | | | | | all_100_1, simplifying with (211), (216) gives:
% 161.05/22.27 | | | | | | (272) all_222_3 = all_220_3
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (29) with all_176_1, all_222_3,
% 161.05/22.27 | | | | | | all_100_1, simplifying with (167), (216) gives:
% 161.05/22.27 | | | | | | (273) all_222_3 = all_176_1
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (29) with all_220_3, all_224_1,
% 161.05/22.27 | | | | | | all_100_1, simplifying with (211), (221) gives:
% 161.05/22.27 | | | | | | (274) all_224_1 = all_220_3
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (29) with all_224_1, all_232_3,
% 161.05/22.27 | | | | | | all_100_1, simplifying with (221), (238) gives:
% 161.05/22.27 | | | | | | (275) all_232_3 = all_224_1
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (29) with all_208_2, all_232_3,
% 161.05/22.27 | | | | | | all_100_1, simplifying with (191), (238) gives:
% 161.05/22.27 | | | | | | (276) all_232_3 = all_208_2
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (29) with all_210_2, all_216_3,
% 161.05/22.27 | | | | | | all_104_1, simplifying with (195), (201) gives:
% 161.05/22.27 | | | | | | (277) all_216_3 = all_210_2
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (29) with all_216_3, all_228_1,
% 161.05/22.27 | | | | | | all_104_1, simplifying with (201), (231) gives:
% 161.05/22.27 | | | | | | (278) all_228_1 = all_216_3
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (29) with all_210_2, all_230_3,
% 161.05/22.27 | | | | | | all_104_1, simplifying with (195), (234) gives:
% 161.05/22.27 | | | | | | (279) all_230_3 = all_210_2
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (29) with all_194_1, all_230_3,
% 161.05/22.27 | | | | | | all_104_1, simplifying with (179), (234) gives:
% 161.05/22.27 | | | | | | (280) all_230_3 = all_194_1
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (29) with all_228_1, all_238_3,
% 161.05/22.27 | | | | | | all_104_1, simplifying with (231), (254) gives:
% 161.05/22.27 | | | | | | (281) all_238_3 = all_228_1
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (29) with all_186_0, all_238_3,
% 161.05/22.27 | | | | | | all_104_1, simplifying with (174), (254) gives:
% 161.05/22.27 | | | | | | (282) all_238_3 = all_186_0
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (30) with all_106_0, all_234_1, all_52_5,
% 161.05/22.27 | | | | | | simplifying with (78), (245) gives:
% 161.05/22.27 | | | | | | (283) all_234_1 = all_106_0
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (30) with all_218_1, all_234_1, all_52_5,
% 161.05/22.27 | | | | | | simplifying with (206), (245) gives:
% 161.05/22.27 | | | | | | (284) all_234_1 = all_218_1
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (30) with all_110_1, all_232_2, all_52_4,
% 161.05/22.27 | | | | | | simplifying with (86), (240) gives:
% 161.05/22.27 | | | | | | (285) all_232_2 = all_110_1
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (30) with all_218_2, all_232_1,
% 161.05/22.27 | | | | | | all_100_1, simplifying with (207), (241) gives:
% 161.05/22.27 | | | | | | (286) all_232_1 = all_218_2
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (30) with all_216_1, all_234_2,
% 161.05/22.27 | | | | | | all_104_1, simplifying with (202), (246) gives:
% 161.05/22.27 | | | | | | (287) all_234_2 = all_216_1
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (31) with all_106_1, all_236_1, all_52_5,
% 161.05/22.27 | | | | | | simplifying with (79), (249) gives:
% 161.05/22.27 | | | | | | (288) all_236_1 = all_106_1
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (31) with all_226_1, all_236_1, all_52_5,
% 161.05/22.27 | | | | | | simplifying with (225), (249) gives:
% 161.05/22.27 | | | | | | (289) all_236_1 = all_226_1
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (31) with all_110_2, all_238_2, all_52_4,
% 161.05/22.27 | | | | | | simplifying with (87), (256) gives:
% 161.05/22.27 | | | | | | (290) all_238_2 = all_110_2
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (31) with all_220_1, all_236_2,
% 161.05/22.27 | | | | | | all_100_1, simplifying with (212), (250) gives:
% 161.05/22.27 | | | | | | (291) all_236_2 = all_220_1
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | GROUND_INST: instantiating (31) with all_226_2, all_238_1,
% 161.05/22.27 | | | | | | all_104_1, simplifying with (226), (257) gives:
% 161.05/22.27 | | | | | | (292) all_238_1 = all_226_2
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | COMBINE_EQS: (281), (282) imply:
% 161.05/22.27 | | | | | | (293) all_228_1 = all_186_0
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | SIMP: (293) implies:
% 161.05/22.27 | | | | | | (294) all_228_1 = all_186_0
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | COMBINE_EQS: (288), (289) imply:
% 161.05/22.27 | | | | | | (295) all_226_1 = all_106_1
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | SIMP: (295) implies:
% 161.05/22.27 | | | | | | (296) all_226_1 = all_106_1
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | COMBINE_EQS: (267), (268) imply:
% 161.05/22.27 | | | | | | (297) all_234_3 = 0
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | COMBINE_EQS: (268), (270) imply:
% 161.05/22.27 | | | | | | (298) all_234_3 = all_226_3
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | COMBINE_EQS: (268), (269) imply:
% 161.05/22.27 | | | | | | (299) all_234_3 = all_228_3
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | COMBINE_EQS: (283), (284) imply:
% 161.05/22.27 | | | | | | (300) all_218_1 = all_106_0
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | COMBINE_EQS: (298), (299) imply:
% 161.05/22.27 | | | | | | (301) all_228_3 = all_226_3
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | COMBINE_EQS: (297), (299) imply:
% 161.05/22.27 | | | | | | (302) all_228_3 = 0
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | COMBINE_EQS: (275), (276) imply:
% 161.05/22.27 | | | | | | (303) all_224_1 = all_208_2
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | SIMP: (303) implies:
% 161.05/22.27 | | | | | | (304) all_224_1 = all_208_2
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | COMBINE_EQS: (259), (260) imply:
% 161.05/22.27 | | | | | | (305) all_222_0 = all_206_1
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | COMBINE_EQS: (279), (280) imply:
% 161.05/22.27 | | | | | | (306) all_210_2 = all_194_1
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | SIMP: (306) implies:
% 161.05/22.27 | | | | | | (307) all_210_2 = all_194_1
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | COMBINE_EQS: (278), (294) imply:
% 161.05/22.27 | | | | | | (308) all_216_3 = all_186_0
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | SIMP: (308) implies:
% 161.05/22.27 | | | | | | (309) all_216_3 = all_186_0
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | COMBINE_EQS: (301), (302) imply:
% 161.05/22.27 | | | | | | (310) all_226_3 = 0
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | SIMP: (310) implies:
% 161.05/22.27 | | | | | | (311) all_226_3 = 0
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | COMBINE_EQS: (265), (266) imply:
% 161.05/22.27 | | | | | | (312) all_218_3 = all_214_2
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | SIMP: (312) implies:
% 161.05/22.27 | | | | | | (313) all_218_3 = all_214_2
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | COMBINE_EQS: (264), (266) imply:
% 161.05/22.27 | | | | | | (314) all_224_3 = all_214_2
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | SIMP: (314) implies:
% 161.05/22.27 | | | | | | (315) all_224_3 = all_214_2
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | COMBINE_EQS: (266), (311) imply:
% 161.05/22.27 | | | | | | (316) all_214_2 = 0
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | COMBINE_EQS: (274), (304) imply:
% 161.05/22.27 | | | | | | (317) all_220_3 = all_208_2
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | SIMP: (317) implies:
% 161.05/22.27 | | | | | | (318) all_220_3 = all_208_2
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | COMBINE_EQS: (263), (315) imply:
% 161.05/22.27 | | | | | | (319) all_214_2 = all_204_1
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | SIMP: (319) implies:
% 161.05/22.27 | | | | | | (320) all_214_2 = all_204_1
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | COMBINE_EQS: (272), (273) imply:
% 161.05/22.27 | | | | | | (321) all_220_3 = all_176_1
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | SIMP: (321) implies:
% 161.05/22.27 | | | | | | (322) all_220_3 = all_176_1
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | COMBINE_EQS: (271), (318) imply:
% 161.05/22.27 | | | | | | (323) all_208_2 = all_204_0
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | COMBINE_EQS: (318), (322) imply:
% 161.05/22.27 | | | | | | (324) all_208_2 = all_176_1
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | COMBINE_EQS: (262), (313) imply:
% 161.05/22.27 | | | | | | (325) all_214_2 = all_186_1
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | SIMP: (325) implies:
% 161.05/22.27 | | | | | | (326) all_214_2 = all_186_1
% 161.05/22.27 | | | | | |
% 161.05/22.27 | | | | | | COMBINE_EQS: (277), (309) imply:
% 161.05/22.28 | | | | | | (327) all_210_2 = all_186_0
% 161.05/22.28 | | | | | |
% 161.05/22.28 | | | | | | SIMP: (327) implies:
% 161.05/22.28 | | | | | | (328) all_210_2 = all_186_0
% 161.05/22.28 | | | | | |
% 161.05/22.28 | | | | | | COMBINE_EQS: (320), (326) imply:
% 161.05/22.28 | | | | | | (329) all_204_1 = all_186_1
% 161.05/22.28 | | | | | |
% 161.05/22.28 | | | | | | COMBINE_EQS: (316), (320) imply:
% 161.05/22.28 | | | | | | (330) all_204_1 = 0
% 161.05/22.28 | | | | | |
% 161.05/22.28 | | | | | | COMBINE_EQS: (307), (328) imply:
% 161.05/22.28 | | | | | | (331) all_194_1 = all_186_0
% 161.05/22.28 | | | | | |
% 161.05/22.28 | | | | | | SIMP: (331) implies:
% 161.05/22.28 | | | | | | (332) all_194_1 = all_186_0
% 161.05/22.28 | | | | | |
% 161.05/22.28 | | | | | | COMBINE_EQS: (323), (324) imply:
% 161.05/22.28 | | | | | | (333) all_204_0 = all_176_1
% 161.05/22.28 | | | | | |
% 161.05/22.28 | | | | | | SIMP: (333) implies:
% 161.05/22.28 | | | | | | (334) all_204_0 = all_176_1
% 161.05/22.28 | | | | | |
% 161.05/22.28 | | | | | | COMBINE_EQS: (329), (330) imply:
% 161.05/22.28 | | | | | | (335) all_186_1 = 0
% 161.05/22.28 | | | | | |
% 161.05/22.28 | | | | | | SIMP: (335) implies:
% 161.05/22.28 | | | | | | (336) all_186_1 = 0
% 161.05/22.28 | | | | | |
% 161.05/22.28 | | | | | | COMBINE_EQS: (262), (336) imply:
% 161.05/22.28 | | | | | | (337) all_218_3 = 0
% 161.05/22.28 | | | | | |
% 161.05/22.28 | | | | | | COMBINE_EQS: (276), (324) imply:
% 161.05/22.28 | | | | | | (338) all_232_3 = all_176_1
% 161.05/22.28 | | | | | |
% 161.05/22.28 | | | | | | REDUCE: (227), (296) imply:
% 161.05/22.28 | | | | | | (339) subset(all_226_2, all_106_1) = all_226_0
% 161.05/22.28 | | | | | |
% 161.05/22.28 | | | | | | REDUCE: (208), (300) imply:
% 161.05/22.28 | | | | | | (340) subset(all_218_2, all_106_0) = all_218_0
% 161.05/22.28 | | | | | |
% 161.05/22.28 | | | | | | REDUCE: (255), (292) imply:
% 161.05/22.28 | | | | | | (341) set_intersection2(all_226_2, all_52_6) = all_238_0
% 161.05/22.28 | | | | | |
% 161.05/22.28 | | | | | | REDUCE: (239), (286) imply:
% 161.05/22.28 | | | | | | (342) set_intersection2(all_218_2, all_52_6) = all_232_0
% 161.05/22.28 | | | | | |
% 161.05/22.28 | | | | | | REDUCE: (252), (292) imply:
% 161.05/22.28 | | | | | | (343) $i(all_226_2)
% 161.05/22.28 | | | | | |
% 161.05/22.28 | | | | | | REDUCE: (236), (286) imply:
% 161.05/22.28 | | | | | | (344) $i(all_218_2)
% 161.05/22.28 | | | | | |
% 161.05/22.28 | | | | | | BETA: splitting (209) gives:
% 161.05/22.28 | | | | | |
% 161.05/22.28 | | | | | | Case 1:
% 161.05/22.28 | | | | | | |
% 161.05/22.28 | | | | | | | (345) ~ (all_218_3 = 0)
% 161.05/22.28 | | | | | | |
% 161.05/22.28 | | | | | | | REDUCE: (337), (345) imply:
% 161.05/22.28 | | | | | | | (346) $false
% 161.05/22.28 | | | | | | |
% 161.05/22.28 | | | | | | | CLOSE: (346) is inconsistent.
% 161.05/22.28 | | | | | | |
% 161.05/22.28 | | | | | | Case 2:
% 161.05/22.28 | | | | | | |
% 161.05/22.28 | | | | | | | (347) all_218_0 = 0
% 161.05/22.28 | | | | | | |
% 161.05/22.28 | | | | | | | REDUCE: (340), (347) imply:
% 161.05/22.28 | | | | | | | (348) subset(all_218_2, all_106_0) = 0
% 161.05/22.28 | | | | | | |
% 161.05/22.28 | | | | | | | BETA: splitting (185) gives:
% 161.05/22.28 | | | | | | |
% 161.05/22.28 | | | | | | | Case 1:
% 161.05/22.28 | | | | | | | |
% 161.05/22.28 | | | | | | | | (349) ~ (all_204_1 = 0)
% 161.05/22.28 | | | | | | | |
% 161.05/22.28 | | | | | | | | REDUCE: (330), (349) imply:
% 161.05/22.28 | | | | | | | | (350) $false
% 161.05/22.28 | | | | | | | |
% 161.05/22.28 | | | | | | | | CLOSE: (350) is inconsistent.
% 161.05/22.28 | | | | | | | |
% 161.05/22.28 | | | | | | | Case 2:
% 161.05/22.28 | | | | | | | |
% 161.05/22.28 | | | | | | | | (351) all_204_0 = 0
% 161.05/22.28 | | | | | | | |
% 161.05/22.28 | | | | | | | | COMBINE_EQS: (334), (351) imply:
% 161.05/22.28 | | | | | | | | (352) all_176_1 = 0
% 161.05/22.28 | | | | | | | |
% 161.05/22.28 | | | | | | | | SIMP: (352) implies:
% 161.05/22.28 | | | | | | | | (353) all_176_1 = 0
% 161.05/22.28 | | | | | | | |
% 161.05/22.28 | | | | | | | | COMBINE_EQS: (324), (353) imply:
% 161.05/22.28 | | | | | | | | (354) all_208_2 = 0
% 161.05/22.28 | | | | | | | |
% 161.05/22.28 | | | | | | | | COMBINE_EQS: (273), (353) imply:
% 161.05/22.28 | | | | | | | | (355) all_222_3 = 0
% 161.05/22.28 | | | | | | | |
% 161.05/22.28 | | | | | | | | COMBINE_EQS: (338), (353) imply:
% 161.05/22.28 | | | | | | | | (356) all_232_3 = 0
% 161.05/22.28 | | | | | | | |
% 161.05/22.28 | | | | | | | | REDUCE: (167), (353) imply:
% 161.05/22.28 | | | | | | | | (357) relation(all_100_1) = 0
% 161.05/22.28 | | | | | | | |
% 161.05/22.28 | | | | | | | | BETA: splitting (228) gives:
% 161.05/22.28 | | | | | | | |
% 161.05/22.28 | | | | | | | | Case 1:
% 161.05/22.28 | | | | | | | | |
% 161.05/22.28 | | | | | | | | | (358) ~ (all_226_3 = 0)
% 161.05/22.28 | | | | | | | | |
% 161.05/22.28 | | | | | | | | | REDUCE: (311), (358) imply:
% 161.05/22.28 | | | | | | | | | (359) $false
% 161.05/22.28 | | | | | | | | |
% 161.05/22.28 | | | | | | | | | CLOSE: (359) is inconsistent.
% 161.05/22.28 | | | | | | | | |
% 161.05/22.28 | | | | | | | | Case 2:
% 161.05/22.28 | | | | | | | | |
% 161.05/22.28 | | | | | | | | | (360) all_226_0 = 0
% 161.05/22.28 | | | | | | | | |
% 161.05/22.28 | | | | | | | | | REDUCE: (339), (360) imply:
% 161.05/22.28 | | | | | | | | | (361) subset(all_226_2, all_106_1) = 0
% 161.05/22.28 | | | | | | | | |
% 161.05/22.28 | | | | | | | | | BETA: splitting (175) gives:
% 161.05/22.28 | | | | | | | | |
% 161.05/22.28 | | | | | | | | | Case 1:
% 161.05/22.28 | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | (362) ~ (all_186_1 = 0)
% 161.05/22.28 | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | REDUCE: (336), (362) imply:
% 161.05/22.28 | | | | | | | | | | (363) $false
% 161.05/22.28 | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | CLOSE: (363) is inconsistent.
% 161.05/22.28 | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | Case 2:
% 161.05/22.28 | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | (364) all_186_0 = 0
% 161.05/22.28 | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | COMBINE_EQS: (328), (364) imply:
% 161.05/22.28 | | | | | | | | | | (365) all_210_2 = 0
% 161.05/22.28 | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | COMBINE_EQS: (282), (364) imply:
% 161.05/22.28 | | | | | | | | | | (366) all_238_3 = 0
% 161.05/22.28 | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | REDUCE: (174), (364) imply:
% 161.05/22.28 | | | | | | | | | | (367) relation(all_104_1) = 0
% 161.05/22.28 | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | BETA: splitting (197) gives:
% 161.05/22.28 | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | Case 1:
% 161.05/22.28 | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | (368) ~ (all_210_2 = 0)
% 161.05/22.28 | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | REDUCE: (365), (368) imply:
% 161.05/22.28 | | | | | | | | | | | (369) $false
% 161.05/22.28 | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | CLOSE: (369) is inconsistent.
% 161.05/22.28 | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | Case 2:
% 161.05/22.28 | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | (370) all_210_0 = all_210_1
% 161.05/22.28 | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | REDUCE: (196), (370) imply:
% 161.05/22.28 | | | | | | | | | | | (371) relation_rng_restriction(all_52_6, all_52_4) =
% 161.05/22.28 | | | | | | | | | | | all_210_1
% 161.05/22.28 | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | BETA: splitting (258) gives:
% 161.05/22.28 | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | Case 1:
% 161.05/22.28 | | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | | (372) ~ (all_238_3 = 0)
% 161.05/22.28 | | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | | REDUCE: (366), (372) imply:
% 161.05/22.28 | | | | | | | | | | | | (373) $false
% 161.05/22.28 | | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | | CLOSE: (373) is inconsistent.
% 161.05/22.28 | | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | Case 2:
% 161.05/22.28 | | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | | (374) all_238_0 = all_238_2
% 161.05/22.28 | | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | | COMBINE_EQS: (290), (374) imply:
% 161.05/22.28 | | | | | | | | | | | | (375) all_238_0 = all_110_2
% 161.05/22.28 | | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | | REDUCE: (341), (375) imply:
% 161.05/22.28 | | | | | | | | | | | | (376) set_intersection2(all_226_2, all_52_6) = all_110_2
% 161.05/22.28 | | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | | BETA: splitting (193) gives:
% 161.05/22.28 | | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | | Case 1:
% 161.05/22.28 | | | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | | | (377) ~ (all_208_2 = 0)
% 161.05/22.28 | | | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | | | REDUCE: (354), (377) imply:
% 161.05/22.28 | | | | | | | | | | | | | (378) $false
% 161.05/22.28 | | | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | | | CLOSE: (378) is inconsistent.
% 161.05/22.28 | | | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | | Case 2:
% 161.05/22.28 | | | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | | | (379) all_208_0 = all_208_1
% 161.05/22.28 | | | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | | | REDUCE: (192), (379) imply:
% 161.05/22.28 | | | | | | | | | | | | | (380) relation_dom_restriction(all_52_4, all_52_6) =
% 161.05/22.28 | | | | | | | | | | | | | all_208_1
% 161.05/22.28 | | | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | | | BETA: splitting (242) gives:
% 161.05/22.28 | | | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | | | Case 1:
% 161.05/22.28 | | | | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | | | | (381) ~ (all_232_3 = 0)
% 161.05/22.28 | | | | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | | | | REDUCE: (356), (381) imply:
% 161.05/22.28 | | | | | | | | | | | | | | (382) $false
% 161.05/22.28 | | | | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | | | | CLOSE: (382) is inconsistent.
% 161.05/22.28 | | | | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | | | Case 2:
% 161.05/22.28 | | | | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | | | | (383) all_232_0 = all_232_2
% 161.05/22.28 | | | | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | | | | COMBINE_EQS: (285), (383) imply:
% 161.05/22.28 | | | | | | | | | | | | | | (384) all_232_0 = all_110_1
% 161.05/22.28 | | | | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | | | | REDUCE: (342), (384) imply:
% 161.05/22.28 | | | | | | | | | | | | | | (385) set_intersection2(all_218_2, all_52_6) = all_110_1
% 161.05/22.28 | | | | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 161.05/22.28 | | | | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | | | | Case 1:
% 161.05/22.28 | | | | | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | | | | | (386) ~ (all_52_0 = 0)
% 161.05/22.28 | | | | | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_110_1, all_110_2,
% 161.05/22.28 | | | | | | | | | | | | | | | all_52_3, all_52_7, all_180_0, simplifying with
% 161.05/22.28 | | | | | | | | | | | | | | | (35), (81), (82), (131), (146), (170) gives:
% 161.05/22.28 | | | | | | | | | | | | | | | (387) all_180_0 = 0 | ? [v0: any] : ? [v1: any] :
% 161.05/22.28 | | | | | | | | | | | | | | | (in(all_52_7, all_110_2) = v1 & in(all_52_7,
% 161.05/22.28 | | | | | | | | | | | | | | | all_52_3) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 161.05/22.28 | | | | | | | | | | | | | | |
% 161.05/22.28 | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_110_1, all_110_2,
% 161.05/22.28 | | | | | | | | | | | | | | | all_52_3, all_52_7, all_180_1, simplifying with
% 161.05/22.28 | | | | | | | | | | | | | | | (35), (81), (82), (131), (146), (169) gives:
% 161.05/22.28 | | | | | | | | | | | | | | | (388) all_180_1 = 0 | ? [v0: any] : ? [v1: any] :
% 161.05/22.28 | | | | | | | | | | | | | | | (in(all_52_7, all_110_1) = v1 & in(all_52_7,
% 161.05/22.28 | | | | | | | | | | | | | | | all_52_3) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 161.05/22.28 | | | | | | | | | | | | | | |
% 161.19/22.28 | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_218_2, all_52_6,
% 161.19/22.28 | | | | | | | | | | | | | | | all_110_1, all_52_7, all_52_0, simplifying with
% 161.19/22.28 | | | | | | | | | | | | | | | (35), (36), (39), (82), (344), (385) gives:
% 161.19/22.28 | | | | | | | | | | | | | | | (389) ? [v0: any] : ? [v1: any] : (in(all_52_7,
% 161.19/22.28 | | | | | | | | | | | | | | | all_218_2) = v1 & in(all_52_7, all_110_1) = v0
% 161.19/22.28 | | | | | | | | | | | | | | | & ( ~ (v0 = 0) | (v1 = 0 & all_52_0 = 0)))
% 161.19/22.28 | | | | | | | | | | | | | | |
% 161.19/22.28 | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_226_2, all_52_6,
% 161.19/22.28 | | | | | | | | | | | | | | | all_110_2, all_52_7, all_52_0, simplifying with
% 161.19/22.28 | | | | | | | | | | | | | | | (35), (36), (39), (81), (343), (376) gives:
% 161.19/22.28 | | | | | | | | | | | | | | | (390) ? [v0: any] : ? [v1: any] : (in(all_52_7,
% 161.19/22.28 | | | | | | | | | | | | | | | all_226_2) = v1 & in(all_52_7, all_110_2) = v0
% 161.19/22.28 | | | | | | | | | | | | | | | & ( ~ (v0 = 0) | (v1 = 0 & all_52_0 = 0)))
% 161.19/22.28 | | | | | | | | | | | | | | |
% 161.19/22.28 | | | | | | | | | | | | | | | DELTA: instantiating (390) with fresh symbols all_406_0,
% 161.19/22.28 | | | | | | | | | | | | | | | all_406_1 gives:
% 161.19/22.29 | | | | | | | | | | | | | | | (391) in(all_52_7, all_226_2) = all_406_0 & in(all_52_7,
% 161.19/22.29 | | | | | | | | | | | | | | | all_110_2) = all_406_1 & ( ~ (all_406_1 = 0) |
% 161.19/22.29 | | | | | | | | | | | | | | | (all_406_0 = 0 & all_52_0 = 0))
% 161.19/22.29 | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | ALPHA: (391) implies:
% 161.19/22.29 | | | | | | | | | | | | | | | (392) in(all_52_7, all_110_2) = all_406_1
% 161.19/22.29 | | | | | | | | | | | | | | | (393) ~ (all_406_1 = 0) | (all_406_0 = 0 & all_52_0 =
% 161.19/22.29 | | | | | | | | | | | | | | | 0)
% 161.19/22.29 | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | DELTA: instantiating (389) with fresh symbols all_408_0,
% 161.19/22.29 | | | | | | | | | | | | | | | all_408_1 gives:
% 161.19/22.29 | | | | | | | | | | | | | | | (394) in(all_52_7, all_218_2) = all_408_0 & in(all_52_7,
% 161.19/22.29 | | | | | | | | | | | | | | | all_110_1) = all_408_1 & ( ~ (all_408_1 = 0) |
% 161.19/22.29 | | | | | | | | | | | | | | | (all_408_0 = 0 & all_52_0 = 0))
% 161.19/22.29 | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | ALPHA: (394) implies:
% 161.19/22.29 | | | | | | | | | | | | | | | (395) in(all_52_7, all_110_1) = all_408_1
% 161.19/22.29 | | | | | | | | | | | | | | | (396) ~ (all_408_1 = 0) | (all_408_0 = 0 & all_52_0 =
% 161.19/22.29 | | | | | | | | | | | | | | | 0)
% 161.19/22.29 | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | BETA: splitting (393) gives:
% 161.19/22.29 | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | Case 1:
% 161.19/22.29 | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | (397) ~ (all_406_1 = 0)
% 161.19/22.29 | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | BETA: splitting (396) gives:
% 161.19/22.29 | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | Case 1:
% 161.19/22.29 | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | (398) ~ (all_408_1 = 0)
% 161.19/22.29 | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | BETA: splitting (387) gives:
% 161.19/22.29 | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | Case 1:
% 161.19/22.29 | | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | | (399) all_180_0 = 0
% 161.19/22.29 | | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | | REDUCE: (170), (399) imply:
% 161.19/22.29 | | | | | | | | | | | | | | | | | | (400) in(all_52_7, all_110_1) = 0
% 161.19/22.29 | | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | | BETA: splitting (388) gives:
% 161.19/22.29 | | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | | Case 1:
% 161.19/22.29 | | | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | (401) all_180_1 = 0
% 161.19/22.29 | | | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | REDUCE: (169), (401) imply:
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | (402) in(all_52_7, all_110_2) = 0
% 161.19/22.29 | | | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (392), (397), (402) are inconsistent by
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | sub-proof #4.
% 161.19/22.29 | | | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | | Case 2:
% 161.19/22.29 | | | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | (403) ? [v0: any] : ? [v1: any] : (in(all_52_7,
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | all_110_1) = v1 & in(all_52_7, all_52_3) = v0
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | & ( ~ (v0 = 0) | v1 = 0))
% 161.19/22.29 | | | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (403) with fresh symbols all_489_0,
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | all_489_1 gives:
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | (404) in(all_52_7, all_110_1) = all_489_0 & in(all_52_7,
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | all_52_3) = all_489_1 & ( ~ (all_489_1 = 0) |
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | all_489_0 = 0)
% 161.19/22.29 | | | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | ALPHA: (404) implies:
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | (405) in(all_52_7, all_110_1) = all_489_0
% 161.19/22.29 | | | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_408_1, all_489_0,
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | all_110_1, all_52_7, simplifying with (395), (405)
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | gives:
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | (406) all_489_0 = all_408_1
% 161.19/22.29 | | | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_489_0, all_110_1,
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | all_52_7, simplifying with (400), (405) gives:
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | (407) all_489_0 = 0
% 161.19/22.29 | | | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (406), (407) imply:
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | (408) all_408_1 = 0
% 161.19/22.29 | | | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | SIMP: (408) implies:
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | (409) all_408_1 = 0
% 161.19/22.29 | | | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | REDUCE: (398), (409) imply:
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | (410) $false
% 161.19/22.29 | | | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | CLOSE: (410) is inconsistent.
% 161.19/22.29 | | | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | | End of split
% 161.19/22.29 | | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | Case 2:
% 161.19/22.29 | | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | | (411) ~ (all_180_0 = 0)
% 161.19/22.29 | | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 161.19/22.29 | | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | | Case 1:
% 161.19/22.29 | | | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | (412) all_180_0 = 0
% 161.19/22.29 | | | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | REDUCE: (411), (412) imply:
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | (413) $false
% 161.19/22.29 | | | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | CLOSE: (413) is inconsistent.
% 161.19/22.29 | | | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | | Case 2:
% 161.19/22.29 | | | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | (414) all_180_1 = 0
% 161.19/22.29 | | | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | REDUCE: (169), (414) imply:
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | (415) in(all_52_7, all_110_2) = 0
% 161.19/22.29 | | | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (392), (397), (415) are inconsistent by
% 161.19/22.29 | | | | | | | | | | | | | | | | | | | sub-proof #4.
% 161.19/22.29 | | | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | | End of split
% 161.19/22.29 | | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | End of split
% 161.19/22.29 | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | Case 2:
% 161.19/22.29 | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | (416) all_408_0 = 0 & all_52_0 = 0
% 161.19/22.29 | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | ALPHA: (416) implies:
% 161.19/22.29 | | | | | | | | | | | | | | | | | (417) all_52_0 = 0
% 161.19/22.29 | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | REDUCE: (386), (417) imply:
% 161.19/22.29 | | | | | | | | | | | | | | | | | (418) $false
% 161.19/22.29 | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | | CLOSE: (418) is inconsistent.
% 161.19/22.29 | | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | End of split
% 161.19/22.29 | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | Case 2:
% 161.19/22.29 | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | (419) all_406_0 = 0 & all_52_0 = 0
% 161.19/22.29 | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | ALPHA: (419) implies:
% 161.19/22.29 | | | | | | | | | | | | | | | | (420) all_52_0 = 0
% 161.19/22.29 | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | REDUCE: (386), (420) imply:
% 161.19/22.29 | | | | | | | | | | | | | | | | (421) $false
% 161.19/22.29 | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | CLOSE: (421) is inconsistent.
% 161.19/22.29 | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | End of split
% 161.19/22.29 | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | Case 2:
% 161.19/22.29 | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | (422) all_52_0 = 0
% 161.19/22.29 | | | | | | | | | | | | | | | (423) ~ (all_52_1 = 0)
% 161.19/22.29 | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | REDUCE: (39), (422) imply:
% 161.19/22.29 | | | | | | | | | | | | | | | (424) in(all_52_7, all_52_6) = 0
% 161.19/22.29 | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | BETA: splitting (139) gives:
% 161.19/22.29 | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | Case 1:
% 161.19/22.29 | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | (425) all_52_1 = 0
% 161.19/22.29 | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | REDUCE: (423), (425) imply:
% 161.19/22.29 | | | | | | | | | | | | | | | | (426) $false
% 161.19/22.29 | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | CLOSE: (426) is inconsistent.
% 161.19/22.29 | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | Case 2:
% 161.19/22.29 | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | (427) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~
% 161.19/22.29 | | | | | | | | | | | | | | | | (v0 = 0) & in(all_52_7, all_106_0) = v1 &
% 161.19/22.29 | | | | | | | | | | | | | | | | in(all_52_7, all_106_1) = v0)
% 161.19/22.29 | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | DELTA: instantiating (427) with fresh symbols all_329_0,
% 161.19/22.29 | | | | | | | | | | | | | | | | all_329_1 gives:
% 161.19/22.29 | | | | | | | | | | | | | | | | (428) ~ (all_329_0 = 0) & ~ (all_329_1 = 0) &
% 161.19/22.29 | | | | | | | | | | | | | | | | in(all_52_7, all_106_0) = all_329_0 & in(all_52_7,
% 161.19/22.29 | | | | | | | | | | | | | | | | all_106_1) = all_329_1
% 161.19/22.29 | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | ALPHA: (428) implies:
% 161.19/22.29 | | | | | | | | | | | | | | | | (429) ~ (all_329_1 = 0)
% 161.19/22.29 | | | | | | | | | | | | | | | | (430) ~ (all_329_0 = 0)
% 161.19/22.29 | | | | | | | | | | | | | | | | (431) in(all_52_7, all_106_1) = all_329_1
% 161.19/22.29 | | | | | | | | | | | | | | | | (432) in(all_52_7, all_106_0) = all_329_0
% 161.19/22.29 | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (22) with all_52_7, all_106_1,
% 161.19/22.29 | | | | | | | | | | | | | | | | all_329_1, simplifying with (35), (113), (431)
% 161.19/22.29 | | | | | | | | | | | | | | | | gives:
% 161.19/22.29 | | | | | | | | | | | | | | | | (433) all_329_1 = 0 | ? [v0: any] : ? [v1: any] :
% 161.19/22.29 | | | | | | | | | | | | | | | | (element(all_52_7, all_106_1) = v0 &
% 161.19/22.29 | | | | | | | | | | | | | | | | empty(all_106_1) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 161.19/22.29 | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (22) with all_52_7, all_106_0,
% 161.19/22.29 | | | | | | | | | | | | | | | | all_329_0, simplifying with (35), (112), (432)
% 161.19/22.29 | | | | | | | | | | | | | | | | gives:
% 161.19/22.29 | | | | | | | | | | | | | | | | (434) all_329_0 = 0 | ? [v0: any] : ? [v1: any] :
% 161.19/22.29 | | | | | | | | | | | | | | | | (element(all_52_7, all_106_0) = v0 &
% 161.19/22.29 | | | | | | | | | | | | | | | | empty(all_106_0) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 161.19/22.29 | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_100_1, all_222_2,
% 161.19/22.29 | | | | | | | | | | | | | | | | simplifying with (65), (215) gives:
% 161.19/22.29 | | | | | | | | | | | | | | | | (435) all_222_2 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 161.19/22.29 | | | | | | | | | | | | | | | | empty(all_100_1) = v0)
% 161.19/22.29 | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_100_1, simplifying
% 161.19/22.29 | | | | | | | | | | | | | | | | with (65), (357) gives:
% 161.19/22.29 | | | | | | | | | | | | | | | | (436) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 161.19/22.29 | | | | | | | | | | | | | | | | (relation_dom(all_100_1) = v1 &
% 161.19/22.29 | | | | | | | | | | | | | | | | relation_field(all_100_1) = v0 &
% 161.19/22.29 | | | | | | | | | | | | | | | | relation_rng(all_100_1) = v2 & set_union2(v1,
% 161.19/22.29 | | | | | | | | | | | | | | | | v2) = v0 & $i(v2) & $i(v1) & $i(v0))
% 161.19/22.29 | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_104_1, simplifying
% 161.19/22.29 | | | | | | | | | | | | | | | | with (71), (367) gives:
% 161.19/22.29 | | | | | | | | | | | | | | | | (437) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 161.19/22.29 | | | | | | | | | | | | | | | | (relation_dom(all_104_1) = v1 &
% 161.19/22.29 | | | | | | | | | | | | | | | | relation_field(all_104_1) = v0 &
% 161.19/22.29 | | | | | | | | | | | | | | | | relation_rng(all_104_1) = v2 & set_union2(v1,
% 161.19/22.29 | | | | | | | | | | | | | | | | v2) = v0 & $i(v2) & $i(v1) & $i(v0))
% 161.19/22.29 | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_52_4, all_206_0,
% 161.19/22.29 | | | | | | | | | | | | | | | | simplifying with (38), (188) gives:
% 161.19/22.29 | | | | | | | | | | | | | | | | (438) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 161.19/22.29 | | | | | | | | | | | | | | | | (relation(all_52_4) = v0 & function(all_52_4) = v2
% 161.19/22.29 | | | | | | | | | | | | | | | | & empty(all_52_4) = v1 & ( ~ (v2 = 0) | ~ (v1 =
% 161.19/22.29 | | | | | | | | | | | | | | | | 0) | ~ (v0 = 0) | all_206_0 = 0))
% 161.19/22.29 | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_110_1, all_110_2,
% 161.19/22.29 | | | | | | | | | | | | | | | | all_52_3, all_52_7, simplifying with (35), (40),
% 161.19/22.29 | | | | | | | | | | | | | | | | (81), (82), (131), (146) gives:
% 161.19/22.29 | | | | | | | | | | | | | | | | (439) ? [v0: any] : ? [v1: any] : (in(all_52_7,
% 161.19/22.29 | | | | | | | | | | | | | | | | all_110_1) = v0 & in(all_52_7, all_110_2) = v1
% 161.19/22.29 | | | | | | | | | | | | | | | | & (v1 = 0 | v0 = 0))
% 161.19/22.29 | | | | | | | | | | | | | | | |
% 161.19/22.29 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_218_2, all_52_6,
% 161.19/22.29 | | | | | | | | | | | | | | | | all_110_1, all_52_7, simplifying with (35), (36),
% 161.19/22.29 | | | | | | | | | | | | | | | | (82), (344), (385), (424) gives:
% 161.19/22.30 | | | | | | | | | | | | | | | | (440) ? [v0: any] : ? [v1: any] : (in(all_52_7,
% 161.19/22.30 | | | | | | | | | | | | | | | | all_218_2) = v0 & in(all_52_7, all_110_1) = v1
% 161.19/22.30 | | | | | | | | | | | | | | | | & ( ~ (v0 = 0) | v1 = 0))
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_218_2, all_52_6,
% 161.19/22.30 | | | | | | | | | | | | | | | | all_110_1, all_52_7, 0, simplifying with (35),
% 161.19/22.30 | | | | | | | | | | | | | | | | (36), (82), (344), (385), (424) gives:
% 161.19/22.30 | | | | | | | | | | | | | | | | (441) ? [v0: any] : ? [v1: any] : (in(all_52_7,
% 161.19/22.30 | | | | | | | | | | | | | | | | all_218_2) = v1 & in(all_52_7, all_110_1) = v0
% 161.19/22.30 | | | | | | | | | | | | | | | | & ( ~ (v0 = 0) | v1 = 0))
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_226_2, all_52_6,
% 161.19/22.30 | | | | | | | | | | | | | | | | all_110_2, all_52_7, simplifying with (35), (36),
% 161.19/22.30 | | | | | | | | | | | | | | | | (81), (343), (376), (424) gives:
% 161.19/22.30 | | | | | | | | | | | | | | | | (442) ? [v0: any] : ? [v1: any] : (in(all_52_7,
% 161.19/22.30 | | | | | | | | | | | | | | | | all_226_2) = v0 & in(all_52_7, all_110_2) = v1
% 161.19/22.30 | | | | | | | | | | | | | | | | & ( ~ (v0 = 0) | v1 = 0))
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_226_2, all_52_6,
% 161.19/22.30 | | | | | | | | | | | | | | | | all_110_2, all_52_7, 0, simplifying with (35),
% 161.19/22.30 | | | | | | | | | | | | | | | | (36), (81), (343), (376), (424) gives:
% 161.19/22.30 | | | | | | | | | | | | | | | | (443) ? [v0: any] : ? [v1: any] : (in(all_52_7,
% 161.19/22.30 | | | | | | | | | | | | | | | | all_226_2) = v1 & in(all_52_7, all_110_2) = v0
% 161.19/22.30 | | | | | | | | | | | | | | | | & ( ~ (v0 = 0) | v1 = 0))
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_104_1, all_216_1,
% 161.19/22.30 | | | | | | | | | | | | | | | | simplifying with (71), (202) gives:
% 161.19/22.30 | | | | | | | | | | | | | | | | (444) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 161.19/22.30 | | | | | | | | | | | | | | | | $i] : (relation_dom(all_104_1) = v2 &
% 161.19/22.30 | | | | | | | | | | | | | | | | relation_field(all_104_1) = v1 & set_union2(v2,
% 161.19/22.30 | | | | | | | | | | | | | | | | all_216_1) = v3 & relation(all_104_1) = v0 &
% 161.19/22.30 | | | | | | | | | | | | | | | | $i(v3) & $i(v2) & $i(v1) & ( ~ (v0 = 0) | v3 =
% 161.19/22.30 | | | | | | | | | | | | | | | | v1))
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_100_1, all_220_1,
% 161.19/22.30 | | | | | | | | | | | | | | | | simplifying with (65), (212) gives:
% 161.19/22.30 | | | | | | | | | | | | | | | | (445) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 161.19/22.30 | | | | | | | | | | | | | | | | $i] : (relation_field(all_100_1) = v1 &
% 161.19/22.30 | | | | | | | | | | | | | | | | relation_rng(all_100_1) = v2 &
% 161.19/22.30 | | | | | | | | | | | | | | | | set_union2(all_220_1, v2) = v3 &
% 161.19/22.30 | | | | | | | | | | | | | | | | relation(all_100_1) = v0 & $i(v3) & $i(v2) &
% 161.19/22.30 | | | | | | | | | | | | | | | | $i(v1) & ( ~ (v0 = 0) | v3 = v1))
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (fc4_funct_1) with all_52_4,
% 161.19/22.30 | | | | | | | | | | | | | | | | all_52_6, all_208_1, simplifying with (36), (38),
% 161.19/22.30 | | | | | | | | | | | | | | | | (380) gives:
% 161.19/22.30 | | | | | | | | | | | | | | | | (446) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 161.19/22.30 | | | | | | | | | | | | | | | | [v3: any] : (relation(all_208_1) = v2 &
% 161.19/22.30 | | | | | | | | | | | | | | | | relation(all_52_4) = v0 & function(all_208_1) =
% 161.19/22.30 | | | | | | | | | | | | | | | | v3 & function(all_52_4) = v1 & ( ~ (v1 = 0) | ~
% 161.19/22.30 | | | | | | | | | | | | | | | | (v0 = 0) | (v3 = 0 & v2 = 0)))
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (fc5_funct_1) with all_52_6,
% 161.19/22.30 | | | | | | | | | | | | | | | | all_52_4, all_210_1, simplifying with (36), (38),
% 161.19/22.30 | | | | | | | | | | | | | | | | (371) gives:
% 161.19/22.30 | | | | | | | | | | | | | | | | (447) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 161.19/22.30 | | | | | | | | | | | | | | | | [v3: any] : (relation(all_210_1) = v2 &
% 161.19/22.30 | | | | | | | | | | | | | | | | relation(all_52_4) = v0 & function(all_210_1) =
% 161.19/22.30 | | | | | | | | | | | | | | | | v3 & function(all_52_4) = v1 & ( ~ (v1 = 0) | ~
% 161.19/22.30 | | | | | | | | | | | | | | | | (v0 = 0) | (v3 = 0 & v2 = 0)))
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (23) with all_218_2, all_106_0,
% 161.19/22.30 | | | | | | | | | | | | | | | | simplifying with (112), (344), (348) gives:
% 161.19/22.30 | | | | | | | | | | | | | | | | (448) ? [v0: $i] : (powerset(all_106_0) = v0 &
% 161.19/22.30 | | | | | | | | | | | | | | | | element(all_218_2, v0) = 0 & $i(v0))
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (23) with all_226_2, all_106_1,
% 161.19/22.30 | | | | | | | | | | | | | | | | simplifying with (113), (343), (361) gives:
% 161.19/22.30 | | | | | | | | | | | | | | | | (449) ? [v0: $i] : (powerset(all_106_1) = v0 &
% 161.19/22.30 | | | | | | | | | | | | | | | | element(all_226_2, v0) = 0 & $i(v0))
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | DELTA: instantiating (449) with fresh symbol all_347_0
% 161.19/22.30 | | | | | | | | | | | | | | | | gives:
% 161.19/22.30 | | | | | | | | | | | | | | | | (450) powerset(all_106_1) = all_347_0 &
% 161.19/22.30 | | | | | | | | | | | | | | | | element(all_226_2, all_347_0) = 0 & $i(all_347_0)
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | ALPHA: (450) implies:
% 161.19/22.30 | | | | | | | | | | | | | | | | (451) element(all_226_2, all_347_0) = 0
% 161.19/22.30 | | | | | | | | | | | | | | | | (452) powerset(all_106_1) = all_347_0
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | DELTA: instantiating (448) with fresh symbol all_355_0
% 161.19/22.30 | | | | | | | | | | | | | | | | gives:
% 161.19/22.30 | | | | | | | | | | | | | | | | (453) powerset(all_106_0) = all_355_0 &
% 161.19/22.30 | | | | | | | | | | | | | | | | element(all_218_2, all_355_0) = 0 & $i(all_355_0)
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | ALPHA: (453) implies:
% 161.19/22.30 | | | | | | | | | | | | | | | | (454) element(all_218_2, all_355_0) = 0
% 161.19/22.30 | | | | | | | | | | | | | | | | (455) powerset(all_106_0) = all_355_0
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | DELTA: instantiating (439) with fresh symbols all_363_0,
% 161.19/22.30 | | | | | | | | | | | | | | | | all_363_1 gives:
% 161.19/22.30 | | | | | | | | | | | | | | | | (456) in(all_52_7, all_110_1) = all_363_1 & in(all_52_7,
% 161.19/22.30 | | | | | | | | | | | | | | | | all_110_2) = all_363_0 & (all_363_0 = 0 |
% 161.19/22.30 | | | | | | | | | | | | | | | | all_363_1 = 0)
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | ALPHA: (456) implies:
% 161.19/22.30 | | | | | | | | | | | | | | | | (457) in(all_52_7, all_110_2) = all_363_0
% 161.19/22.30 | | | | | | | | | | | | | | | | (458) in(all_52_7, all_110_1) = all_363_1
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | DELTA: instantiating (140) with fresh symbols all_369_0,
% 161.19/22.30 | | | | | | | | | | | | | | | | all_369_1 gives:
% 161.19/22.30 | | | | | | | | | | | | | | | | (459) empty(all_106_0) = all_369_1 & empty(all_52_2) =
% 161.19/22.30 | | | | | | | | | | | | | | | | all_369_0 & ( ~ (all_369_0 = 0) | all_369_1 = 0)
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | ALPHA: (459) implies:
% 161.19/22.30 | | | | | | | | | | | | | | | | (460) empty(all_106_0) = all_369_1
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | DELTA: instantiating (143) with fresh symbols all_371_0,
% 161.19/22.30 | | | | | | | | | | | | | | | | all_371_1 gives:
% 161.19/22.30 | | | | | | | | | | | | | | | | (461) empty(all_106_1) = all_371_1 & empty(all_52_2) =
% 161.19/22.30 | | | | | | | | | | | | | | | | all_371_0 & ( ~ (all_371_0 = 0) | all_371_1 = 0)
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | ALPHA: (461) implies:
% 161.19/22.30 | | | | | | | | | | | | | | | | (462) empty(all_106_1) = all_371_1
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | DELTA: instantiating (443) with fresh symbols all_379_0,
% 161.19/22.30 | | | | | | | | | | | | | | | | all_379_1 gives:
% 161.19/22.30 | | | | | | | | | | | | | | | | (463) in(all_52_7, all_226_2) = all_379_0 & in(all_52_7,
% 161.19/22.30 | | | | | | | | | | | | | | | | all_110_2) = all_379_1 & ( ~ (all_379_1 = 0) |
% 161.19/22.30 | | | | | | | | | | | | | | | | all_379_0 = 0)
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | ALPHA: (463) implies:
% 161.19/22.30 | | | | | | | | | | | | | | | | (464) in(all_52_7, all_110_2) = all_379_1
% 161.19/22.30 | | | | | | | | | | | | | | | | (465) in(all_52_7, all_226_2) = all_379_0
% 161.19/22.30 | | | | | | | | | | | | | | | | (466) ~ (all_379_1 = 0) | all_379_0 = 0
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | DELTA: instantiating (442) with fresh symbols all_381_0,
% 161.19/22.30 | | | | | | | | | | | | | | | | all_381_1 gives:
% 161.19/22.30 | | | | | | | | | | | | | | | | (467) in(all_52_7, all_226_2) = all_381_1 & in(all_52_7,
% 161.19/22.30 | | | | | | | | | | | | | | | | all_110_2) = all_381_0 & ( ~ (all_381_1 = 0) |
% 161.19/22.30 | | | | | | | | | | | | | | | | all_381_0 = 0)
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | ALPHA: (467) implies:
% 161.19/22.30 | | | | | | | | | | | | | | | | (468) in(all_52_7, all_110_2) = all_381_0
% 161.19/22.30 | | | | | | | | | | | | | | | | (469) in(all_52_7, all_226_2) = all_381_1
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | DELTA: instantiating (441) with fresh symbols all_397_0,
% 161.19/22.30 | | | | | | | | | | | | | | | | all_397_1 gives:
% 161.19/22.30 | | | | | | | | | | | | | | | | (470) in(all_52_7, all_218_2) = all_397_0 & in(all_52_7,
% 161.19/22.30 | | | | | | | | | | | | | | | | all_110_1) = all_397_1 & ( ~ (all_397_1 = 0) |
% 161.19/22.30 | | | | | | | | | | | | | | | | all_397_0 = 0)
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | ALPHA: (470) implies:
% 161.19/22.30 | | | | | | | | | | | | | | | | (471) in(all_52_7, all_110_1) = all_397_1
% 161.19/22.30 | | | | | | | | | | | | | | | | (472) in(all_52_7, all_218_2) = all_397_0
% 161.19/22.30 | | | | | | | | | | | | | | | | (473) ~ (all_397_1 = 0) | all_397_0 = 0
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | DELTA: instantiating (440) with fresh symbols all_401_0,
% 161.19/22.30 | | | | | | | | | | | | | | | | all_401_1 gives:
% 161.19/22.30 | | | | | | | | | | | | | | | | (474) in(all_52_7, all_218_2) = all_401_1 & in(all_52_7,
% 161.19/22.30 | | | | | | | | | | | | | | | | all_110_1) = all_401_0 & ( ~ (all_401_1 = 0) |
% 161.19/22.30 | | | | | | | | | | | | | | | | all_401_0 = 0)
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | ALPHA: (474) implies:
% 161.19/22.30 | | | | | | | | | | | | | | | | (475) in(all_52_7, all_110_1) = all_401_0
% 161.19/22.30 | | | | | | | | | | | | | | | | (476) in(all_52_7, all_218_2) = all_401_1
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | DELTA: instantiating (438) with fresh symbols all_429_0,
% 161.19/22.30 | | | | | | | | | | | | | | | | all_429_1, all_429_2 gives:
% 161.19/22.30 | | | | | | | | | | | | | | | | (477) relation(all_52_4) = all_429_2 &
% 161.19/22.30 | | | | | | | | | | | | | | | | function(all_52_4) = all_429_0 & empty(all_52_4) =
% 161.19/22.30 | | | | | | | | | | | | | | | | all_429_1 & ( ~ (all_429_0 = 0) | ~ (all_429_1 =
% 161.19/22.30 | | | | | | | | | | | | | | | | 0) | ~ (all_429_2 = 0) | all_206_0 = 0)
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | ALPHA: (477) implies:
% 161.19/22.30 | | | | | | | | | | | | | | | | (478) function(all_52_4) = all_429_0
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | DELTA: instantiating (436) with fresh symbols all_441_0,
% 161.19/22.30 | | | | | | | | | | | | | | | | all_441_1, all_441_2 gives:
% 161.19/22.30 | | | | | | | | | | | | | | | | (479) relation_dom(all_100_1) = all_441_1 &
% 161.19/22.30 | | | | | | | | | | | | | | | | relation_field(all_100_1) = all_441_2 &
% 161.19/22.30 | | | | | | | | | | | | | | | | relation_rng(all_100_1) = all_441_0 &
% 161.19/22.30 | | | | | | | | | | | | | | | | set_union2(all_441_1, all_441_0) = all_441_2 &
% 161.19/22.30 | | | | | | | | | | | | | | | | $i(all_441_0) & $i(all_441_1) & $i(all_441_2)
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | ALPHA: (479) implies:
% 161.19/22.30 | | | | | | | | | | | | | | | | (480) $i(all_441_0)
% 161.19/22.30 | | | | | | | | | | | | | | | | (481) relation_rng(all_100_1) = all_441_0
% 161.19/22.30 | | | | | | | | | | | | | | | |
% 161.19/22.30 | | | | | | | | | | | | | | | | DELTA: instantiating (437) with fresh symbols all_445_0,
% 161.19/22.30 | | | | | | | | | | | | | | | | all_445_1, all_445_2 gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | (482) relation_dom(all_104_1) = all_445_1 &
% 161.19/22.31 | | | | | | | | | | | | | | | | relation_field(all_104_1) = all_445_2 &
% 161.19/22.31 | | | | | | | | | | | | | | | | relation_rng(all_104_1) = all_445_0 &
% 161.19/22.31 | | | | | | | | | | | | | | | | set_union2(all_445_1, all_445_0) = all_445_2 &
% 161.19/22.31 | | | | | | | | | | | | | | | | $i(all_445_0) & $i(all_445_1) & $i(all_445_2)
% 161.19/22.31 | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | ALPHA: (482) implies:
% 161.19/22.31 | | | | | | | | | | | | | | | | (483) $i(all_445_1)
% 161.19/22.31 | | | | | | | | | | | | | | | | (484) relation_dom(all_104_1) = all_445_1
% 161.19/22.31 | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | DELTA: instantiating (446) with fresh symbols all_457_0,
% 161.19/22.31 | | | | | | | | | | | | | | | | all_457_1, all_457_2, all_457_3 gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | (485) relation(all_208_1) = all_457_1 &
% 161.19/22.31 | | | | | | | | | | | | | | | | relation(all_52_4) = all_457_3 &
% 161.19/22.31 | | | | | | | | | | | | | | | | function(all_208_1) = all_457_0 &
% 161.19/22.31 | | | | | | | | | | | | | | | | function(all_52_4) = all_457_2 & ( ~ (all_457_2 =
% 161.19/22.31 | | | | | | | | | | | | | | | | 0) | ~ (all_457_3 = 0) | (all_457_0 = 0 &
% 161.19/22.31 | | | | | | | | | | | | | | | | all_457_1 = 0))
% 161.19/22.31 | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | ALPHA: (485) implies:
% 161.19/22.31 | | | | | | | | | | | | | | | | (486) function(all_52_4) = all_457_2
% 161.19/22.31 | | | | | | | | | | | | | | | | (487) ~ (all_457_2 = 0) | ~ (all_457_3 = 0) |
% 161.19/22.31 | | | | | | | | | | | | | | | | (all_457_0 = 0 & all_457_1 = 0)
% 161.19/22.31 | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | DELTA: instantiating (447) with fresh symbols all_459_0,
% 161.19/22.31 | | | | | | | | | | | | | | | | all_459_1, all_459_2, all_459_3 gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | (488) relation(all_210_1) = all_459_1 &
% 161.19/22.31 | | | | | | | | | | | | | | | | relation(all_52_4) = all_459_3 &
% 161.19/22.31 | | | | | | | | | | | | | | | | function(all_210_1) = all_459_0 &
% 161.19/22.31 | | | | | | | | | | | | | | | | function(all_52_4) = all_459_2 & ( ~ (all_459_2 =
% 161.19/22.31 | | | | | | | | | | | | | | | | 0) | ~ (all_459_3 = 0) | (all_459_0 = 0 &
% 161.19/22.31 | | | | | | | | | | | | | | | | all_459_1 = 0))
% 161.19/22.31 | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | ALPHA: (488) implies:
% 161.19/22.31 | | | | | | | | | | | | | | | | (489) function(all_52_4) = all_459_2
% 161.19/22.31 | | | | | | | | | | | | | | | | (490) ~ (all_459_2 = 0) | ~ (all_459_3 = 0) |
% 161.19/22.31 | | | | | | | | | | | | | | | | (all_459_0 = 0 & all_459_1 = 0)
% 161.19/22.31 | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | DELTA: instantiating (445) with fresh symbols all_465_0,
% 161.19/22.31 | | | | | | | | | | | | | | | | all_465_1, all_465_2, all_465_3 gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | (491) relation_field(all_100_1) = all_465_2 &
% 161.19/22.31 | | | | | | | | | | | | | | | | relation_rng(all_100_1) = all_465_1 &
% 161.19/22.31 | | | | | | | | | | | | | | | | set_union2(all_220_1, all_465_1) = all_465_0 &
% 161.19/22.31 | | | | | | | | | | | | | | | | relation(all_100_1) = all_465_3 & $i(all_465_0) &
% 161.19/22.31 | | | | | | | | | | | | | | | | $i(all_465_1) & $i(all_465_2) & ( ~ (all_465_3 =
% 161.19/22.31 | | | | | | | | | | | | | | | | 0) | all_465_0 = all_465_2)
% 161.19/22.31 | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | ALPHA: (491) implies:
% 161.19/22.31 | | | | | | | | | | | | | | | | (492) relation_rng(all_100_1) = all_465_1
% 161.19/22.31 | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | DELTA: instantiating (444) with fresh symbols all_469_0,
% 161.19/22.31 | | | | | | | | | | | | | | | | all_469_1, all_469_2, all_469_3 gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | (493) relation_dom(all_104_1) = all_469_1 &
% 161.19/22.31 | | | | | | | | | | | | | | | | relation_field(all_104_1) = all_469_2 &
% 161.19/22.31 | | | | | | | | | | | | | | | | set_union2(all_469_1, all_216_1) = all_469_0 &
% 161.19/22.31 | | | | | | | | | | | | | | | | relation(all_104_1) = all_469_3 & $i(all_469_0) &
% 161.19/22.31 | | | | | | | | | | | | | | | | $i(all_469_1) & $i(all_469_2) & ( ~ (all_469_3 =
% 161.19/22.31 | | | | | | | | | | | | | | | | 0) | all_469_0 = all_469_2)
% 161.19/22.31 | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | ALPHA: (493) implies:
% 161.19/22.31 | | | | | | | | | | | | | | | | (494) relation_dom(all_104_1) = all_469_1
% 161.19/22.31 | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | BETA: splitting (434) gives:
% 161.19/22.31 | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | Case 1:
% 161.19/22.31 | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | (495) all_329_0 = 0
% 161.19/22.31 | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | REDUCE: (430), (495) imply:
% 161.19/22.31 | | | | | | | | | | | | | | | | | (496) $false
% 161.19/22.31 | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | CLOSE: (496) is inconsistent.
% 161.19/22.31 | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | Case 2:
% 161.19/22.31 | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | (497) ? [v0: any] : ? [v1: any] : (element(all_52_7,
% 161.19/22.31 | | | | | | | | | | | | | | | | | all_106_0) = v0 & empty(all_106_0) = v1 & ( ~
% 161.19/22.31 | | | | | | | | | | | | | | | | | (v0 = 0) | v1 = 0))
% 161.19/22.31 | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | DELTA: instantiating (497) with fresh symbols all_487_0,
% 161.19/22.31 | | | | | | | | | | | | | | | | | all_487_1 gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | | (498) element(all_52_7, all_106_0) = all_487_1 &
% 161.19/22.31 | | | | | | | | | | | | | | | | | empty(all_106_0) = all_487_0 & ( ~ (all_487_1 = 0)
% 161.19/22.31 | | | | | | | | | | | | | | | | | | all_487_0 = 0)
% 161.19/22.31 | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | ALPHA: (498) implies:
% 161.19/22.31 | | | | | | | | | | | | | | | | | (499) empty(all_106_0) = all_487_0
% 161.19/22.31 | | | | | | | | | | | | | | | | | (500) element(all_52_7, all_106_0) = all_487_1
% 161.19/22.31 | | | | | | | | | | | | | | | | | (501) ~ (all_487_1 = 0) | all_487_0 = 0
% 161.19/22.31 | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | BETA: splitting (433) gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | Case 1:
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (502) all_329_1 = 0
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | REDUCE: (429), (502) imply:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (503) $false
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | CLOSE: (503) is inconsistent.
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | Case 2:
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (504) ? [v0: any] : ? [v1: any] : (element(all_52_7,
% 161.19/22.31 | | | | | | | | | | | | | | | | | | all_106_1) = v0 & empty(all_106_1) = v1 & ( ~
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (v0 = 0) | v1 = 0))
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | DELTA: instantiating (504) with fresh symbols all_492_0,
% 161.19/22.31 | | | | | | | | | | | | | | | | | | all_492_1 gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (505) element(all_52_7, all_106_1) = all_492_1 &
% 161.19/22.31 | | | | | | | | | | | | | | | | | | empty(all_106_1) = all_492_0 & ( ~ (all_492_1 = 0)
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | all_492_0 = 0)
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | ALPHA: (505) implies:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (506) empty(all_106_1) = all_492_0
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (507) element(all_52_7, all_106_1) = all_492_1
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (508) ~ (all_492_1 = 0) | all_492_0 = 0
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_363_0, all_379_1,
% 161.19/22.31 | | | | | | | | | | | | | | | | | | all_110_2, all_52_7, simplifying with (457), (464)
% 161.19/22.31 | | | | | | | | | | | | | | | | | | gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (509) all_379_1 = all_363_0
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_180_1, all_381_0,
% 161.19/22.31 | | | | | | | | | | | | | | | | | | all_110_2, all_52_7, simplifying with (169), (468)
% 161.19/22.31 | | | | | | | | | | | | | | | | | | gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (510) all_381_0 = all_180_1
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_379_1, all_381_0,
% 161.19/22.31 | | | | | | | | | | | | | | | | | | all_110_2, all_52_7, simplifying with (464), (468)
% 161.19/22.31 | | | | | | | | | | | | | | | | | | gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (511) all_381_0 = all_379_1
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_363_1, all_397_1,
% 161.19/22.31 | | | | | | | | | | | | | | | | | | all_110_1, all_52_7, simplifying with (458), (471)
% 161.19/22.31 | | | | | | | | | | | | | | | | | | gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (512) all_397_1 = all_363_1
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_180_0, all_401_0,
% 161.19/22.31 | | | | | | | | | | | | | | | | | | all_110_1, all_52_7, simplifying with (170), (475)
% 161.19/22.31 | | | | | | | | | | | | | | | | | | gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (513) all_401_0 = all_180_0
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_397_1, all_401_0,
% 161.19/22.31 | | | | | | | | | | | | | | | | | | all_110_1, all_52_7, simplifying with (471), (475)
% 161.19/22.31 | | | | | | | | | | | | | | | | | | gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (514) all_401_0 = all_397_1
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_397_0, all_401_1,
% 161.19/22.31 | | | | | | | | | | | | | | | | | | all_218_2, all_52_7, simplifying with (472), (476)
% 161.19/22.31 | | | | | | | | | | | | | | | | | | gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (515) all_401_1 = all_397_0
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_379_0, all_381_1,
% 161.19/22.31 | | | | | | | | | | | | | | | | | | all_226_2, all_52_7, simplifying with (465), (469)
% 161.19/22.31 | | | | | | | | | | | | | | | | | | gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (516) all_381_1 = all_379_0
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_202_1, all_492_0,
% 161.19/22.31 | | | | | | | | | | | | | | | | | | all_106_1, simplifying with (181), (506) gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (517) all_492_0 = all_202_1
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_371_1, all_492_0,
% 161.19/22.31 | | | | | | | | | | | | | | | | | | all_106_1, simplifying with (462), (506) gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (518) all_492_0 = all_371_1
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_188_1, all_487_0,
% 161.19/22.31 | | | | | | | | | | | | | | | | | | all_106_0, simplifying with (177), (499) gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (519) all_487_0 = all_188_1
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_369_1, all_487_0,
% 161.19/22.31 | | | | | | | | | | | | | | | | | | all_106_0, simplifying with (460), (499) gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (520) all_487_0 = all_369_1
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_206_1, all_459_2,
% 161.19/22.31 | | | | | | | | | | | | | | | | | | all_52_4, simplifying with (187), (489) gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (521) all_459_2 = all_206_1
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_457_2, all_459_2,
% 161.19/22.31 | | | | | | | | | | | | | | | | | | all_52_4, simplifying with (486), (489) gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (522) all_459_2 = all_457_2
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_429_0, all_459_2,
% 161.19/22.31 | | | | | | | | | | | | | | | | | | all_52_4, simplifying with (478), (489) gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (523) all_459_2 = all_429_0
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with all_218_2, all_465_1,
% 161.19/22.31 | | | | | | | | | | | | | | | | | | all_100_1, simplifying with (207), (492) gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (524) all_465_1 = all_218_2
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with all_441_0, all_465_1,
% 161.19/22.31 | | | | | | | | | | | | | | | | | | all_100_1, simplifying with (481), (492) gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (525) all_465_1 = all_441_0
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with all_226_2, all_469_1,
% 161.19/22.31 | | | | | | | | | | | | | | | | | | all_104_1, simplifying with (226), (494) gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (526) all_469_1 = all_226_2
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with all_445_1, all_469_1,
% 161.19/22.31 | | | | | | | | | | | | | | | | | | all_104_1, simplifying with (484), (494) gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (527) all_469_1 = all_445_1
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (517), (518) imply:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (528) all_371_1 = all_202_1
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | SIMP: (528) implies:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (529) all_371_1 = all_202_1
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (519), (520) imply:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (530) all_369_1 = all_188_1
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (526), (527) imply:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (531) all_445_1 = all_226_2
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (524), (525) imply:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (532) all_441_0 = all_218_2
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (522), (523) imply:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (533) all_457_2 = all_429_0
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (521), (522) imply:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (534) all_457_2 = all_206_1
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (533), (534) imply:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (535) all_429_0 = all_206_1
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (513), (514) imply:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (536) all_397_1 = all_180_0
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | SIMP: (536) implies:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (537) all_397_1 = all_180_0
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (512), (537) imply:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (538) all_363_1 = all_180_0
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (510), (511) imply:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (539) all_379_1 = all_180_1
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | SIMP: (539) implies:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (540) all_379_1 = all_180_1
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (509), (540) imply:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | (541) all_363_0 = all_180_1
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | Case 1:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | (542) all_180_0 = 0
% 161.19/22.31 | | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (537), (542) imply:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | (543) all_397_1 = 0
% 161.19/22.31 | | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | BETA: splitting (473) gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | Case 1:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | (544) ~ (all_397_1 = 0)
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | REDUCE: (543), (544) imply:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | (545) $false
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | CLOSE: (545) is inconsistent.
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | Case 2:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | (546) all_397_0 = 0
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | REDUCE: (472), (546) imply:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | (547) in(all_52_7, all_218_2) = 0
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | Case 1:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | | (548) ~ (all_206_1 = 0)
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | | | (549) ~ (all_222_2 = 0)
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (435) gives:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | | | | (550) all_222_2 = 0
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (549), (550) imply:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | | | | (551) $false
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (551) is inconsistent.
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.31 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_52_7, all_218_2,
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | all_106_0, all_355_0, simplifying with (35),
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | (112), (344), (454), (455), (547) gives:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | (552) element(all_52_7, all_106_0) = 0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_52_7, all_218_2,
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | all_106_0, all_355_0, simplifying with (35),
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | (112), (344), (454), (455), (547) gives:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | (553) ? [v0: int] : ( ~ (v0 = 0) & empty(all_106_0) =
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | v0)
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (553) with fresh symbol all_765_0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | gives:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | (554) ~ (all_765_0 = 0) & empty(all_106_0) = all_765_0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (554) implies:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | (555) ~ (all_765_0 = 0)
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | (556) empty(all_106_0) = all_765_0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (501) gives:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | | (557) ~ (all_487_1 = 0)
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (500), (552), (557) are inconsistent by
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #3.
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | | (558) all_487_0 = 0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (519), (558) imply:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | | (559) all_188_1 = 0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (177), (559) imply:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | | (560) empty(all_106_0) = 0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with 0, all_765_0, all_106_0,
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (556), (560) gives:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | | (561) all_765_0 = 0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (555), (561) imply:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | | (562) $false
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (562) is inconsistent.
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | End of split
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | (563) ~ (all_222_3 = 0) | (all_222_0 = 0 & all_222_1 =
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | 0)
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (305), (355), (548), (563) are inconsistent by
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | sub-proof #2.
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | End of split
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | Case 2:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | (564) all_206_1 = 0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (521), (564) imply:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | (565) all_459_2 = 0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (490) gives:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | (566) ~ (all_459_2 = 0)
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (565), (566) imply:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | (567) $false
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (567) is inconsistent.
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_52_7, all_218_2,
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | all_106_0, all_355_0, simplifying with (35),
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | (112), (344), (454), (455), (547) gives:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | (568) element(all_52_7, all_106_0) = 0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_52_7, all_218_2,
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | all_106_0, all_355_0, simplifying with (35),
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | (112), (344), (454), (455), (547) gives:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | (569) ? [v0: int] : ( ~ (v0 = 0) & empty(all_106_0) =
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | v0)
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (569) with fresh symbol all_745_0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | gives:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | (570) ~ (all_745_0 = 0) & empty(all_106_0) = all_745_0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (570) implies:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | (571) ~ (all_745_0 = 0)
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | (572) empty(all_106_0) = all_745_0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (501) gives:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | (573) ~ (all_487_1 = 0)
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (500), (568), (573) are inconsistent by
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #3.
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | (574) all_487_0 = 0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (519), (574) imply:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | (575) all_188_1 = 0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (177), (575) imply:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | (576) empty(all_106_0) = 0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with 0, all_745_0, all_106_0,
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (572), (576) gives:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | (577) all_745_0 = 0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (571), (577) imply:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | (578) $false
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (578) is inconsistent.
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | End of split
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | End of split
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | End of split
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | End of split
% 161.19/22.32 | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | Case 2:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | (579) all_180_1 = 0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (579) imply:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | (580) all_379_1 = 0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | BETA: splitting (466) gives:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | Case 1:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | (581) ~ (all_379_1 = 0)
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | REDUCE: (580), (581) imply:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | (582) $false
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | CLOSE: (582) is inconsistent.
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | Case 2:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | (583) all_379_0 = 0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | REDUCE: (465), (583) imply:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | (584) in(all_52_7, all_226_2) = 0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | Case 1:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | (585) ~ (all_206_1 = 0)
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | (586) ~ (all_222_2 = 0)
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (435) gives:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | (587) all_222_2 = 0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (586), (587) imply:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | (588) $false
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (588) is inconsistent.
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_52_7, all_226_2,
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | all_106_1, all_347_0, simplifying with (35),
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | (113), (343), (451), (452), (584) gives:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | (589) element(all_52_7, all_106_1) = 0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_52_7, all_226_2,
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | all_106_1, all_347_0, simplifying with (35),
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | (113), (343), (451), (452), (584) gives:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | (590) ? [v0: int] : ( ~ (v0 = 0) & empty(all_106_1) =
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | v0)
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (590) with fresh symbol all_770_0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | gives:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | (591) ~ (all_770_0 = 0) & empty(all_106_1) = all_770_0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (591) implies:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | (592) ~ (all_770_0 = 0)
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | (593) empty(all_106_1) = all_770_0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (508) gives:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | | (594) ~ (all_492_1 = 0)
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (507), (589), (594) are inconsistent by
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1.
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | | (595) all_492_0 = 0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (517), (595) imply:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | | (596) all_202_1 = 0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (596) imply:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | | (597) empty(all_106_1) = 0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with 0, all_770_0, all_106_1,
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (593), (597) gives:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | | (598) all_770_0 = 0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (592), (598) imply:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | | (599) $false
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (599) is inconsistent.
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | End of split
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | (600) ~ (all_222_3 = 0) | (all_222_0 = 0 & all_222_1 =
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | 0)
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (305), (355), (585), (600) are inconsistent by
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | sub-proof #2.
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | End of split
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | Case 2:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | (601) all_206_1 = 0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (534), (601) imply:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | (602) all_457_2 = 0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (487) gives:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | (603) ~ (all_457_2 = 0)
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (602), (603) imply:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | (604) $false
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (604) is inconsistent.
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_52_7, all_226_2,
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | all_106_1, all_347_0, simplifying with (35),
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | (113), (343), (451), (452), (584) gives:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | (605) element(all_52_7, all_106_1) = 0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_52_7, all_226_2,
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | all_106_1, all_347_0, simplifying with (35),
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | (113), (343), (451), (452), (584) gives:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | (606) ? [v0: int] : ( ~ (v0 = 0) & empty(all_106_1) =
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | v0)
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (606) with fresh symbol all_760_0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | gives:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | (607) ~ (all_760_0 = 0) & empty(all_106_1) = all_760_0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (607) implies:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | (608) ~ (all_760_0 = 0)
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | (609) empty(all_106_1) = all_760_0
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (508) gives:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 161.19/22.32 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.33 | | | | | | | | | | | | | | | | | | | | | | | (610) ~ (all_492_1 = 0)
% 161.19/22.33 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.33 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (507), (605), (610) are inconsistent by
% 161.19/22.33 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1.
% 161.19/22.33 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.33 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 161.19/22.33 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.33 | | | | | | | | | | | | | | | | | | | | | | | (611) all_492_0 = 0
% 161.19/22.33 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.33 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (517), (611) imply:
% 161.19/22.33 | | | | | | | | | | | | | | | | | | | | | | | (612) all_202_1 = 0
% 161.19/22.33 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.33 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (612) imply:
% 161.19/22.33 | | | | | | | | | | | | | | | | | | | | | | | (613) empty(all_106_1) = 0
% 161.19/22.33 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.33 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with 0, all_760_0, all_106_1,
% 161.19/22.33 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (609), (613) gives:
% 161.19/22.33 | | | | | | | | | | | | | | | | | | | | | | | (614) all_760_0 = 0
% 161.19/22.33 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.33 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (608), (614) imply:
% 161.19/22.33 | | | | | | | | | | | | | | | | | | | | | | | (615) $false
% 161.19/22.33 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.33 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (615) is inconsistent.
% 161.19/22.33 | | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.33 | | | | | | | | | | | | | | | | | | | | | | End of split
% 161.19/22.33 | | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.33 | | | | | | | | | | | | | | | | | | | | | End of split
% 161.19/22.33 | | | | | | | | | | | | | | | | | | | | |
% 161.19/22.33 | | | | | | | | | | | | | | | | | | | | End of split
% 161.19/22.33 | | | | | | | | | | | | | | | | | | | |
% 161.19/22.33 | | | | | | | | | | | | | | | | | | | End of split
% 161.19/22.33 | | | | | | | | | | | | | | | | | | |
% 161.19/22.33 | | | | | | | | | | | | | | | | | | End of split
% 161.19/22.33 | | | | | | | | | | | | | | | | | |
% 161.19/22.33 | | | | | | | | | | | | | | | | | End of split
% 161.19/22.33 | | | | | | | | | | | | | | | | |
% 161.19/22.33 | | | | | | | | | | | | | | | | End of split
% 161.19/22.33 | | | | | | | | | | | | | | | |
% 161.38/22.33 | | | | | | | | | | | | | | | End of split
% 161.38/22.33 | | | | | | | | | | | | | | |
% 161.38/22.33 | | | | | | | | | | | | | | End of split
% 161.38/22.33 | | | | | | | | | | | | | |
% 161.38/22.33 | | | | | | | | | | | | | End of split
% 161.38/22.33 | | | | | | | | | | | | |
% 161.38/22.33 | | | | | | | | | | | | End of split
% 161.38/22.33 | | | | | | | | | | | |
% 161.38/22.33 | | | | | | | | | | | End of split
% 161.38/22.33 | | | | | | | | | | |
% 161.38/22.33 | | | | | | | | | | End of split
% 161.38/22.33 | | | | | | | | | |
% 161.38/22.33 | | | | | | | | | End of split
% 161.38/22.33 | | | | | | | | |
% 161.38/22.33 | | | | | | | | End of split
% 161.38/22.33 | | | | | | | |
% 161.38/22.33 | | | | | | | End of split
% 161.38/22.33 | | | | | | |
% 161.38/22.33 | | | | | | End of split
% 161.38/22.33 | | | | | |
% 161.38/22.33 | | | | | End of split
% 161.38/22.33 | | | | |
% 161.38/22.33 | | | | End of split
% 161.38/22.33 | | | |
% 161.38/22.33 | | | End of split
% 161.38/22.33 | | |
% 161.38/22.33 | | End of split
% 161.38/22.33 | |
% 161.38/22.33 | End of split
% 161.38/22.33 |
% 161.38/22.33 End of proof
% 161.38/22.33
% 161.38/22.33 Sub-proof #1 shows that the following formulas are inconsistent:
% 161.38/22.33 ----------------------------------------------------------------
% 161.38/22.33 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 161.38/22.33 ! [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) =
% 161.38/22.33 v0))
% 161.38/22.33 (2) element(all_52_7, all_106_1) = all_492_1
% 161.38/22.33 (3) element(all_52_7, all_106_1) = 0
% 161.38/22.33 (4) ~ (all_492_1 = 0)
% 161.38/22.33
% 161.38/22.33 Begin of proof
% 161.38/22.33 |
% 161.38/22.33 | GROUND_INST: instantiating (1) with all_492_1, 0, all_106_1, all_52_7,
% 161.38/22.33 | simplifying with (2), (3) gives:
% 161.38/22.33 | (5) all_492_1 = 0
% 161.38/22.33 |
% 161.38/22.33 | REDUCE: (4), (5) imply:
% 161.38/22.33 | (6) $false
% 161.38/22.33 |
% 161.38/22.33 | CLOSE: (6) is inconsistent.
% 161.38/22.33 |
% 161.38/22.33 End of proof
% 161.38/22.33
% 161.38/22.33 Sub-proof #2 shows that the following formulas are inconsistent:
% 161.38/22.33 ----------------------------------------------------------------
% 161.38/22.33 (1) ~ (all_222_3 = 0) | (all_222_0 = 0 & all_222_1 = 0)
% 161.38/22.33 (2) all_222_3 = 0
% 161.38/22.33 (3) all_222_0 = all_206_1
% 161.38/22.33 (4) ~ (all_206_1 = 0)
% 161.38/22.33
% 161.38/22.33 Begin of proof
% 161.38/22.33 |
% 161.38/22.33 | BETA: splitting (1) gives:
% 161.38/22.33 |
% 161.38/22.33 | Case 1:
% 161.38/22.33 | |
% 161.38/22.33 | | (5) ~ (all_222_3 = 0)
% 161.38/22.33 | |
% 161.38/22.33 | | REDUCE: (2), (5) imply:
% 161.38/22.33 | | (6) $false
% 161.38/22.33 | |
% 161.38/22.33 | | CLOSE: (6) is inconsistent.
% 161.38/22.33 | |
% 161.38/22.33 | Case 2:
% 161.38/22.33 | |
% 161.38/22.33 | | (7) all_222_0 = 0 & all_222_1 = 0
% 161.38/22.33 | |
% 161.38/22.33 | | ALPHA: (7) implies:
% 161.38/22.33 | | (8) all_222_0 = 0
% 161.38/22.33 | |
% 161.38/22.33 | | COMBINE_EQS: (3), (8) imply:
% 161.38/22.33 | | (9) all_206_1 = 0
% 161.38/22.33 | |
% 161.38/22.33 | | REDUCE: (4), (9) imply:
% 161.38/22.33 | | (10) $false
% 161.38/22.33 | |
% 161.38/22.33 | | CLOSE: (10) is inconsistent.
% 161.38/22.33 | |
% 161.38/22.33 | End of split
% 161.38/22.33 |
% 161.38/22.33 End of proof
% 161.38/22.33
% 161.38/22.33 Sub-proof #3 shows that the following formulas are inconsistent:
% 161.38/22.33 ----------------------------------------------------------------
% 161.38/22.33 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 161.38/22.33 ! [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) =
% 161.38/22.33 v0))
% 161.38/22.33 (2) element(all_52_7, all_106_0) = all_487_1
% 161.38/22.33 (3) element(all_52_7, all_106_0) = 0
% 161.38/22.33 (4) ~ (all_487_1 = 0)
% 161.38/22.33
% 161.38/22.33 Begin of proof
% 161.38/22.33 |
% 161.38/22.33 | GROUND_INST: instantiating (1) with all_487_1, 0, all_106_0, all_52_7,
% 161.38/22.33 | simplifying with (2), (3) gives:
% 161.38/22.33 | (5) all_487_1 = 0
% 161.38/22.33 |
% 161.38/22.33 | REDUCE: (4), (5) imply:
% 161.38/22.33 | (6) $false
% 161.38/22.33 |
% 161.38/22.33 | CLOSE: (6) is inconsistent.
% 161.38/22.33 |
% 161.38/22.33 End of proof
% 161.38/22.33
% 161.38/22.33 Sub-proof #4 shows that the following formulas are inconsistent:
% 161.38/22.33 ----------------------------------------------------------------
% 161.38/22.33 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 161.38/22.33 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 161.38/22.33 (2) in(all_52_7, all_110_2) = all_406_1
% 161.38/22.33 (3) in(all_52_7, all_110_2) = 0
% 161.38/22.33 (4) ~ (all_406_1 = 0)
% 161.38/22.33
% 161.38/22.33 Begin of proof
% 161.38/22.33 |
% 161.38/22.33 | GROUND_INST: instantiating (1) with 0, all_406_1, all_110_2, all_52_7,
% 161.38/22.33 | simplifying with (2), (3) gives:
% 161.38/22.33 | (5) all_406_1 = 0
% 161.38/22.33 |
% 161.38/22.33 | REDUCE: (4), (5) imply:
% 161.38/22.33 | (6) $false
% 161.38/22.33 |
% 161.38/22.33 | CLOSE: (6) is inconsistent.
% 161.38/22.33 |
% 161.38/22.33 End of proof
% 161.38/22.33 % SZS output end Proof for theBenchmark
% 161.38/22.33
% 161.38/22.33 21722ms
%------------------------------------------------------------------------------