TSTP Solution File: SEU362+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU362+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 : n007.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 17:44:18 EDT 2023
% Result : Theorem 21.74s 3.74s
% Output : Proof 99.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU362+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.35 % Computer : n007.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Wed Aug 23 13:17:24 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.74/1.09 Prover 4: Preprocessing ...
% 2.74/1.09 Prover 1: Preprocessing ...
% 3.31/1.13 Prover 3: Preprocessing ...
% 3.31/1.13 Prover 6: Preprocessing ...
% 3.31/1.13 Prover 2: Preprocessing ...
% 3.31/1.13 Prover 5: Preprocessing ...
% 3.31/1.13 Prover 0: Preprocessing ...
% 6.84/1.70 Prover 1: Warning: ignoring some quantifiers
% 7.53/1.75 Prover 5: Proving ...
% 7.53/1.75 Prover 2: Proving ...
% 7.53/1.75 Prover 3: Warning: ignoring some quantifiers
% 7.53/1.76 Prover 1: Constructing countermodel ...
% 7.53/1.77 Prover 6: Proving ...
% 7.53/1.77 Prover 3: Constructing countermodel ...
% 8.05/1.85 Prover 4: Warning: ignoring some quantifiers
% 8.46/1.90 Prover 4: Constructing countermodel ...
% 9.64/2.05 Prover 0: Proving ...
% 21.74/3.73 Prover 0: proved (3110ms)
% 21.74/3.74
% 21.74/3.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.74/3.74
% 21.74/3.74 Prover 5: stopped
% 21.74/3.74 Prover 6: stopped
% 21.74/3.74 Prover 2: stopped
% 21.74/3.75 Prover 3: stopped
% 21.74/3.77 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 21.74/3.77 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 21.74/3.77 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 21.74/3.77 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 21.74/3.77 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 22.46/3.80 Prover 10: Preprocessing ...
% 22.46/3.81 Prover 13: Preprocessing ...
% 22.46/3.81 Prover 7: Preprocessing ...
% 22.46/3.83 Prover 11: Preprocessing ...
% 22.46/3.84 Prover 8: Preprocessing ...
% 22.46/3.93 Prover 10: Warning: ignoring some quantifiers
% 22.46/3.93 Prover 10: Constructing countermodel ...
% 22.46/3.96 Prover 7: Warning: ignoring some quantifiers
% 22.46/3.98 Prover 7: Constructing countermodel ...
% 22.46/3.98 Prover 13: Warning: ignoring some quantifiers
% 22.46/3.99 Prover 13: Constructing countermodel ...
% 22.46/4.00 Prover 8: Warning: ignoring some quantifiers
% 24.17/4.01 Prover 8: Constructing countermodel ...
% 24.91/4.14 Prover 11: Warning: ignoring some quantifiers
% 25.35/4.18 Prover 11: Constructing countermodel ...
% 63.35/9.34 Prover 13: stopped
% 63.35/9.36 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 64.29/9.41 Prover 16: Preprocessing ...
% 64.52/9.45 Prover 16: Warning: ignoring some quantifiers
% 64.52/9.46 Prover 16: Constructing countermodel ...
% 97.99/13.89 Prover 11: Found proof (size 244)
% 97.99/13.89 Prover 11: proved (10132ms)
% 97.99/13.90 Prover 7: stopped
% 97.99/13.90 Prover 16: stopped
% 97.99/13.90 Prover 4: stopped
% 97.99/13.90 Prover 10: stopped
% 98.41/13.92 Prover 1: stopped
% 98.41/13.93 Prover 8: stopped
% 98.41/13.93
% 98.41/13.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 98.41/13.93
% 98.41/13.96 % SZS output start Proof for theBenchmark
% 98.41/13.96 Assumptions after simplification:
% 98.41/13.96 ---------------------------------
% 98.41/13.96
% 98.41/13.96 (d13_yellow_0)
% 98.60/14.02 ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ? [v2:
% 98.60/14.02 int] : ? [v3: $i] : (( ~ (v2 = 0) & rel_str(v0) = v2) |
% 98.60/14.02 (the_InternalRel(v0) = v3 & $i(v3) & ! [v4: $i] : ! [v5: $i] : ( ~
% 98.60/14.02 (the_carrier(v4) = v5) | ~ $i(v4) | ? [v6: int] : ? [v7: int] : ?
% 98.60/14.02 [v8: int] : ? [v9: $i] : ? [v10: int] : (( ~ (v6 = 0) & rel_str(v4)
% 98.60/14.02 = v6) | (((v10 = 0 & v8 = 0 & the_InternalRel(v4) = v9 &
% 98.60/14.02 subset(v9, v3) = 0 & subset(v5, v1) = 0 & $i(v9)) | ( ~ (v7 =
% 98.60/14.02 0) & subrelstr(v4, v0) = v7)) & ((v7 = 0 & subrelstr(v4, v0)
% 98.60/14.02 = 0) | ( ~ (v10 = 0) & the_InternalRel(v4) = v9 & subset(v9,
% 98.60/14.02 v3) = v10 & $i(v9)) | ( ~ (v8 = 0) & subset(v5, v1) =
% 98.60/14.02 v8))))) & ! [v4: $i] : ! [v5: any] : ( ~ (subrelstr(v4, v0)
% 98.60/14.02 = v5) | ~ $i(v4) | ? [v6: int] : ? [v7: $i] : ? [v8: int] : ?
% 98.60/14.02 [v9: $i] : ? [v10: int] : (( ~ (v6 = 0) & rel_str(v4) = v6) | (( ~
% 98.60/14.02 (v5 = 0) | (v10 = 0 & v8 = 0 & the_carrier(v4) = v7 &
% 98.60/14.02 the_InternalRel(v4) = v9 & subset(v9, v3) = 0 & subset(v7, v1)
% 98.60/14.02 = 0 & $i(v9) & $i(v7))) & (v5 = 0 | ( ~ (v10 = 0) &
% 98.60/14.02 the_InternalRel(v4) = v9 & subset(v9, v3) = v10 & $i(v9)) | (
% 98.60/14.02 ~ (v8 = 0) & the_carrier(v4) = v7 & subset(v7, v1) = v8 &
% 98.60/14.02 $i(v7)))))) & ! [v4: $i] : ! [v5: $i] : ( ~
% 98.60/14.02 (the_InternalRel(v4) = v5) | ~ $i(v4) | ? [v6: int] : ? [v7: int] :
% 98.60/14.02 ? [v8: $i] : ? [v9: int] : ? [v10: int] : (( ~ (v6 = 0) &
% 98.60/14.02 rel_str(v4) = v6) | (((v10 = 0 & v9 = 0 & the_carrier(v4) = v8 &
% 98.60/14.02 subset(v8, v1) = 0 & subset(v5, v3) = 0 & $i(v8)) | ( ~ (v7 =
% 98.60/14.02 0) & subrelstr(v4, v0) = v7)) & ((v7 = 0 & subrelstr(v4, v0)
% 98.60/14.02 = 0) | ( ~ (v10 = 0) & subset(v5, v3) = v10) | ( ~ (v9 = 0) &
% 98.60/14.02 the_carrier(v4) = v8 & subset(v8, v1) = v9 & $i(v8)))))) & !
% 98.60/14.02 [v4: $i] : ( ~ (rel_str(v4) = 0) | ~ $i(v4) | ? [v5: int] : ? [v6:
% 98.60/14.02 $i] : ? [v7: int] : ? [v8: $i] : ? [v9: int] : (((v9 = 0 & v7 = 0
% 98.60/14.02 & the_carrier(v4) = v6 & the_InternalRel(v4) = v8 & subset(v8,
% 98.60/14.02 v3) = 0 & subset(v6, v1) = 0 & $i(v8) & $i(v6)) | ( ~ (v5 = 0)
% 98.60/14.02 & subrelstr(v4, v0) = v5)) & ((v5 = 0 & subrelstr(v4, v0) = 0) |
% 98.60/14.02 ( ~ (v9 = 0) & the_InternalRel(v4) = v8 & subset(v8, v3) = v9 &
% 98.60/14.02 $i(v8)) | ( ~ (v7 = 0) & the_carrier(v4) = v6 & subset(v6, v1) =
% 98.60/14.02 v7 & $i(v6)))))))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 98.60/14.02 (the_InternalRel(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : (( ~
% 98.60/14.02 (v2 = 0) & rel_str(v0) = v2) | (the_carrier(v0) = v3 & $i(v3) & ! [v4:
% 98.60/14.02 $i] : ! [v5: $i] : ( ~ (the_carrier(v4) = v5) | ~ $i(v4) | ? [v6:
% 98.60/14.02 int] : ? [v7: int] : ? [v8: int] : ? [v9: $i] : ? [v10: int] :
% 98.60/14.02 (( ~ (v6 = 0) & rel_str(v4) = v6) | (((v10 = 0 & v8 = 0 &
% 98.60/14.02 the_InternalRel(v4) = v9 & subset(v9, v1) = 0 & subset(v5, v3)
% 98.60/14.02 = 0 & $i(v9)) | ( ~ (v7 = 0) & subrelstr(v4, v0) = v7)) & ((v7
% 98.60/14.02 = 0 & subrelstr(v4, v0) = 0) | ( ~ (v10 = 0) &
% 98.60/14.02 the_InternalRel(v4) = v9 & subset(v9, v1) = v10 & $i(v9)) | (
% 98.60/14.02 ~ (v8 = 0) & subset(v5, v3) = v8))))) & ! [v4: $i] : ! [v5:
% 98.60/14.02 any] : ( ~ (subrelstr(v4, v0) = v5) | ~ $i(v4) | ? [v6: int] : ?
% 98.60/14.02 [v7: $i] : ? [v8: int] : ? [v9: $i] : ? [v10: int] : (( ~ (v6 = 0)
% 98.60/14.02 & rel_str(v4) = v6) | (( ~ (v5 = 0) | (v10 = 0 & v8 = 0 &
% 98.60/14.02 the_carrier(v4) = v7 & the_InternalRel(v4) = v9 & subset(v9,
% 98.60/14.02 v1) = 0 & subset(v7, v3) = 0 & $i(v9) & $i(v7))) & (v5 = 0 |
% 98.60/14.03 ( ~ (v10 = 0) & the_InternalRel(v4) = v9 & subset(v9, v1) = v10
% 98.60/14.03 & $i(v9)) | ( ~ (v8 = 0) & the_carrier(v4) = v7 & subset(v7,
% 98.60/14.03 v3) = v8 & $i(v7)))))) & ! [v4: $i] : ! [v5: $i] : ( ~
% 98.60/14.03 (the_InternalRel(v4) = v5) | ~ $i(v4) | ? [v6: int] : ? [v7: int] :
% 98.60/14.03 ? [v8: $i] : ? [v9: int] : ? [v10: int] : (( ~ (v6 = 0) &
% 98.60/14.03 rel_str(v4) = v6) | (((v10 = 0 & v9 = 0 & the_carrier(v4) = v8 &
% 98.60/14.03 subset(v8, v3) = 0 & subset(v5, v1) = 0 & $i(v8)) | ( ~ (v7 =
% 98.60/14.03 0) & subrelstr(v4, v0) = v7)) & ((v7 = 0 & subrelstr(v4, v0)
% 98.60/14.03 = 0) | ( ~ (v10 = 0) & subset(v5, v1) = v10) | ( ~ (v9 = 0) &
% 98.60/14.03 the_carrier(v4) = v8 & subset(v8, v3) = v9 & $i(v8)))))) & !
% 98.60/14.03 [v4: $i] : ( ~ (rel_str(v4) = 0) | ~ $i(v4) | ? [v5: int] : ? [v6:
% 98.60/14.03 $i] : ? [v7: int] : ? [v8: $i] : ? [v9: int] : (((v9 = 0 & v7 = 0
% 98.60/14.03 & the_carrier(v4) = v6 & the_InternalRel(v4) = v8 & subset(v8,
% 98.60/14.03 v1) = 0 & subset(v6, v3) = 0 & $i(v8) & $i(v6)) | ( ~ (v5 = 0)
% 98.60/14.03 & subrelstr(v4, v0) = v5)) & ((v5 = 0 & subrelstr(v4, v0) = 0) |
% 98.60/14.03 ( ~ (v9 = 0) & the_InternalRel(v4) = v8 & subset(v8, v1) = v9 &
% 98.60/14.03 $i(v8)) | ( ~ (v7 = 0) & the_carrier(v4) = v6 & subset(v6, v3) =
% 98.60/14.03 v7 & $i(v6)))))))) & ! [v0: $i] : ( ~ (rel_str(v0) = 0) | ~
% 98.60/14.03 $i(v0) | ? [v1: $i] : ? [v2: $i] : (the_carrier(v0) = v1 &
% 98.60/14.03 the_InternalRel(v0) = v2 & $i(v2) & $i(v1) & ! [v3: $i] : ! [v4: $i] : (
% 98.60/14.03 ~ (the_carrier(v3) = v4) | ~ $i(v3) | ? [v5: int] : ? [v6: int] : ?
% 98.60/14.03 [v7: int] : ? [v8: $i] : ? [v9: int] : (( ~ (v5 = 0) & rel_str(v3) =
% 98.60/14.03 v5) | (((v9 = 0 & v7 = 0 & the_InternalRel(v3) = v8 & subset(v8, v2)
% 98.60/14.03 = 0 & subset(v4, v1) = 0 & $i(v8)) | ( ~ (v6 = 0) &
% 98.60/14.03 subrelstr(v3, v0) = v6)) & ((v6 = 0 & subrelstr(v3, v0) = 0) | (
% 98.60/14.03 ~ (v9 = 0) & the_InternalRel(v3) = v8 & subset(v8, v2) = v9 &
% 98.60/14.03 $i(v8)) | ( ~ (v7 = 0) & subset(v4, v1) = v7))))) & ! [v3: $i]
% 98.60/14.03 : ! [v4: any] : ( ~ (subrelstr(v3, v0) = v4) | ~ $i(v3) | ? [v5: int] :
% 98.60/14.03 ? [v6: $i] : ? [v7: int] : ? [v8: $i] : ? [v9: int] : (( ~ (v5 = 0)
% 98.60/14.03 & rel_str(v3) = v5) | (( ~ (v4 = 0) | (v9 = 0 & v7 = 0 &
% 98.60/14.03 the_carrier(v3) = v6 & the_InternalRel(v3) = v8 & subset(v8, v2)
% 98.60/14.03 = 0 & subset(v6, v1) = 0 & $i(v8) & $i(v6))) & (v4 = 0 | ( ~ (v9
% 98.60/14.03 = 0) & the_InternalRel(v3) = v8 & subset(v8, v2) = v9 &
% 98.60/14.03 $i(v8)) | ( ~ (v7 = 0) & the_carrier(v3) = v6 & subset(v6, v1) =
% 98.60/14.03 v7 & $i(v6)))))) & ! [v3: $i] : ! [v4: $i] : ( ~
% 98.60/14.03 (the_InternalRel(v3) = v4) | ~ $i(v3) | ? [v5: int] : ? [v6: int] :
% 98.60/14.03 ? [v7: $i] : ? [v8: int] : ? [v9: int] : (( ~ (v5 = 0) & rel_str(v3) =
% 98.60/14.03 v5) | (((v9 = 0 & v8 = 0 & the_carrier(v3) = v7 & subset(v7, v1) = 0
% 98.60/14.03 & subset(v4, v2) = 0 & $i(v7)) | ( ~ (v6 = 0) & subrelstr(v3,
% 98.60/14.03 v0) = v6)) & ((v6 = 0 & subrelstr(v3, v0) = 0) | ( ~ (v9 = 0)
% 98.60/14.03 & subset(v4, v2) = v9) | ( ~ (v8 = 0) & the_carrier(v3) = v7 &
% 98.60/14.03 subset(v7, v1) = v8 & $i(v7)))))) & ! [v3: $i] : ( ~
% 98.60/14.03 (rel_str(v3) = 0) | ~ $i(v3) | ? [v4: int] : ? [v5: $i] : ? [v6:
% 98.60/14.03 int] : ? [v7: $i] : ? [v8: int] : (((v8 = 0 & v6 = 0 &
% 98.60/14.03 the_carrier(v3) = v5 & the_InternalRel(v3) = v7 & subset(v7, v2) =
% 98.60/14.03 0 & subset(v5, v1) = 0 & $i(v7) & $i(v5)) | ( ~ (v4 = 0) &
% 98.60/14.03 subrelstr(v3, v0) = v4)) & ((v4 = 0 & subrelstr(v3, v0) = 0) | ( ~
% 98.60/14.03 (v8 = 0) & the_InternalRel(v3) = v7 & subset(v7, v2) = v8 &
% 98.60/14.03 $i(v7)) | ( ~ (v6 = 0) & the_carrier(v3) = v5 & subset(v5, v1) =
% 98.60/14.03 v6 & $i(v5)))))))
% 98.60/14.03
% 98.60/14.03 (d9_orders_2)
% 98.60/14.04 ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ? [v2:
% 98.60/14.04 int] : ? [v3: $i] : (( ~ (v2 = 0) & rel_str(v0) = v2) |
% 98.60/14.04 (the_InternalRel(v0) = v3 & $i(v3) & ! [v4: $i] : ! [v5: $i] : ! [v6:
% 98.60/14.04 $i] : ( ~ (ordered_pair(v4, v5) = v6) | ~ (element(v4, v1) = 0) | ~
% 98.60/14.04 $i(v5) | ~ $i(v4) | ? [v7: int] : ? [v8: int] : ? [v9: int] : (( ~
% 98.60/14.04 (v7 = 0) & element(v5, v1) = v7) | (((v9 = 0 & in(v6, v3) = 0) | (
% 98.60/14.04 ~ (v8 = 0) & related(v0, v4, v5) = v8)) & ((v8 = 0 &
% 98.60/14.04 related(v0, v4, v5) = 0) | ( ~ (v9 = 0) & in(v6, v3) = v9)))))
% 98.60/14.04 & ! [v4: $i] : ! [v5: $i] : ! [v6: any] : ( ~ (related(v0, v4, v5) =
% 98.60/14.04 v6) | ~ (element(v4, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ? [v7:
% 98.60/14.04 int] : ? [v8: $i] : ? [v9: int] : (( ~ (v7 = 0) & element(v5, v1)
% 98.60/14.04 = v7) | (( ~ (v6 = 0) | (v9 = 0 & ordered_pair(v4, v5) = v8 &
% 98.60/14.04 in(v8, v3) = 0 & $i(v8))) & (v6 = 0 | ( ~ (v9 = 0) &
% 98.60/14.04 ordered_pair(v4, v5) = v8 & in(v8, v3) = v9 & $i(v8)))))) & !
% 98.60/14.04 [v4: $i] : ! [v5: $i] : ( ~ (element(v5, v1) = 0) | ~ (element(v4, v1)
% 98.60/14.04 = 0) | ~ $i(v5) | ~ $i(v4) | ? [v6: int] : ? [v7: $i] : ? [v8:
% 98.60/14.04 int] : (((v8 = 0 & ordered_pair(v4, v5) = v7 & in(v7, v3) = 0 &
% 98.60/14.04 $i(v7)) | ( ~ (v6 = 0) & related(v0, v4, v5) = v6)) & ((v6 = 0 &
% 98.60/14.04 related(v0, v4, v5) = 0) | ( ~ (v8 = 0) & ordered_pair(v4, v5) =
% 98.60/14.04 v7 & in(v7, v3) = v8 & $i(v7)))))))) & ! [v0: $i] : ! [v1: $i]
% 98.60/14.04 : ( ~ (the_InternalRel(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ((
% 98.60/14.04 ~ (v2 = 0) & rel_str(v0) = v2) | (the_carrier(v0) = v3 & $i(v3) & !
% 98.60/14.04 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v4, v5) = v6) |
% 98.60/14.04 ~ (element(v4, v3) = 0) | ~ $i(v5) | ~ $i(v4) | ? [v7: int] : ?
% 98.60/14.04 [v8: int] : ? [v9: int] : (( ~ (v7 = 0) & element(v5, v3) = v7) |
% 98.60/14.04 (((v9 = 0 & in(v6, v1) = 0) | ( ~ (v8 = 0) & related(v0, v4, v5) =
% 98.60/14.04 v8)) & ((v8 = 0 & related(v0, v4, v5) = 0) | ( ~ (v9 = 0) &
% 98.60/14.04 in(v6, v1) = v9))))) & ! [v4: $i] : ! [v5: $i] : ! [v6:
% 98.60/14.04 any] : ( ~ (related(v0, v4, v5) = v6) | ~ (element(v4, v3) = 0) | ~
% 98.60/14.04 $i(v5) | ~ $i(v4) | ? [v7: int] : ? [v8: $i] : ? [v9: int] : (( ~
% 98.60/14.04 (v7 = 0) & element(v5, v3) = v7) | (( ~ (v6 = 0) | (v9 = 0 &
% 98.60/14.04 ordered_pair(v4, v5) = v8 & in(v8, v1) = 0 & $i(v8))) & (v6 =
% 98.60/14.04 0 | ( ~ (v9 = 0) & ordered_pair(v4, v5) = v8 & in(v8, v1) = v9 &
% 98.60/14.04 $i(v8)))))) & ! [v4: $i] : ! [v5: $i] : ( ~ (element(v5, v3)
% 98.60/14.04 = 0) | ~ (element(v4, v3) = 0) | ~ $i(v5) | ~ $i(v4) | ? [v6:
% 98.60/14.04 int] : ? [v7: $i] : ? [v8: int] : (((v8 = 0 & ordered_pair(v4, v5)
% 98.60/14.04 = v7 & in(v7, v1) = 0 & $i(v7)) | ( ~ (v6 = 0) & related(v0, v4,
% 98.60/14.04 v5) = v6)) & ((v6 = 0 & related(v0, v4, v5) = 0) | ( ~ (v8 =
% 98.60/14.04 0) & ordered_pair(v4, v5) = v7 & in(v7, v1) = v8 &
% 98.60/14.04 $i(v7)))))))) & ! [v0: $i] : ( ~ (rel_str(v0) = 0) | ~ $i(v0)
% 98.60/14.04 | ? [v1: $i] : ? [v2: $i] : (the_carrier(v0) = v1 & the_InternalRel(v0) =
% 98.60/14.04 v2 & $i(v2) & $i(v1) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 98.60/14.04 (ordered_pair(v3, v4) = v5) | ~ (element(v3, v1) = 0) | ~ $i(v4) | ~
% 98.60/14.04 $i(v3) | ? [v6: int] : ? [v7: int] : ? [v8: int] : (( ~ (v6 = 0) &
% 98.60/14.04 element(v4, v1) = v6) | (((v8 = 0 & in(v5, v2) = 0) | ( ~ (v7 = 0) &
% 98.60/14.04 related(v0, v3, v4) = v7)) & ((v7 = 0 & related(v0, v3, v4) = 0)
% 98.60/14.04 | ( ~ (v8 = 0) & in(v5, v2) = v8))))) & ! [v3: $i] : ! [v4: $i]
% 98.60/14.04 : ! [v5: any] : ( ~ (related(v0, v3, v4) = v5) | ~ (element(v3, v1) = 0)
% 98.60/14.04 | ~ $i(v4) | ~ $i(v3) | ? [v6: int] : ? [v7: $i] : ? [v8: int] : ((
% 98.60/14.04 ~ (v6 = 0) & element(v4, v1) = v6) | (( ~ (v5 = 0) | (v8 = 0 &
% 98.60/14.04 ordered_pair(v3, v4) = v7 & in(v7, v2) = 0 & $i(v7))) & (v5 = 0
% 98.60/14.04 | ( ~ (v8 = 0) & ordered_pair(v3, v4) = v7 & in(v7, v2) = v8 &
% 98.60/14.04 $i(v7)))))) & ! [v3: $i] : ! [v4: $i] : ( ~ (element(v4, v1) =
% 98.60/14.04 0) | ~ (element(v3, v1) = 0) | ~ $i(v4) | ~ $i(v3) | ? [v5: int] :
% 98.60/14.04 ? [v6: $i] : ? [v7: int] : (((v7 = 0 & ordered_pair(v3, v4) = v6 &
% 98.60/14.04 in(v6, v2) = 0 & $i(v6)) | ( ~ (v5 = 0) & related(v0, v3, v4) =
% 98.60/14.04 v5)) & ((v5 = 0 & related(v0, v3, v4) = 0) | ( ~ (v7 = 0) &
% 98.60/14.04 ordered_pair(v3, v4) = v6 & in(v6, v2) = v7 & $i(v6)))))))
% 98.60/14.04
% 98.60/14.04 (dt_m1_yellow_0)
% 98.60/14.04 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (rel_str(v1) = v2) |
% 98.60/14.04 ~ (rel_str(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 98.60/14.04 subrelstr(v1, v0) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ (rel_str(v0) =
% 98.60/14.04 0) | ~ (subrelstr(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | rel_str(v1) = 0)
% 98.60/14.04
% 98.60/14.04 (dt_u1_orders_2)
% 99.00/14.04 ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ? [v2:
% 99.00/14.04 int] : ? [v3: $i] : ? [v4: int] : ((v4 = 0 & relation_of2_as_subset(v3,
% 99.00/14.04 v1, v1) = 0 & the_InternalRel(v0) = v3 & $i(v3)) | ( ~ (v2 = 0) &
% 99.00/14.04 rel_str(v0) = v2))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 99.00/14.04 (the_InternalRel(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ?
% 99.00/14.04 [v4: int] : ((v4 = 0 & relation_of2_as_subset(v1, v3, v3) = 0 &
% 99.00/14.04 the_carrier(v0) = v3 & $i(v3)) | ( ~ (v2 = 0) & rel_str(v0) = v2))) & !
% 99.00/14.04 [v0: $i] : ( ~ (rel_str(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] :
% 99.00/14.04 (relation_of2_as_subset(v1, v2, v2) = 0 & the_carrier(v0) = v2 &
% 99.00/14.04 the_InternalRel(v0) = v1 & $i(v2) & $i(v1)))
% 99.00/14.04
% 99.00/14.04 (t2_subset)
% 99.00/14.04 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2) | ~
% 99.00/14.04 $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ((v4 = 0 & empty(v1) = 0)
% 99.00/14.04 | ( ~ (v3 = 0) & element(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 99.00/14.04 (element(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int]
% 99.00/14.04 : ((v3 = 0 & in(v0, v1) = 0) | (v2 = 0 & empty(v1) = 0)))
% 99.00/14.04
% 99.00/14.05 (t3_subset)
% 99.00/14.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 99.00/14.05 (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ?
% 99.00/14.05 [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i]
% 99.00/14.05 : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 99.00/14.05 ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0,
% 99.00/14.05 v3) = v4 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 99.00/14.05 (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) |
% 99.00/14.05 subset(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) |
% 99.00/14.05 ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : (powerset(v1) = v2 & element(v0, v2) =
% 99.00/14.05 0 & $i(v2)))
% 99.00/14.05
% 99.00/14.05 (t4_subset)
% 99.00/14.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 99.00/14.05 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) =
% 99.00/14.05 v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) &
% 99.00/14.05 in(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int]
% 99.00/14.05 : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (in(v0, v1) = 0) | ~ $i(v2) | ~
% 99.00/14.05 $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) &
% 99.00/14.05 powerset(v2) = v4 & element(v1, v4) = v5 & $i(v4))) & ! [v0: $i] : !
% 99.00/14.05 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (powerset(v2) = v3) | ~
% 99.00/14.05 (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 99.00/14.05 $i(v0) | element(v0, v2) = 0)
% 99.00/14.05
% 99.00/14.05 (t5_subset)
% 99.00/14.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (powerset(v2) =
% 99.00/14.05 v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ~ $i(v2) | ~
% 99.00/14.05 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & empty(v2) = v4)) & !
% 99.00/14.05 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) =
% 99.00/14.05 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 99.00/14.05 (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4 & $i(v3)))
% 99.00/14.05
% 99.00/14.05 (t60_yellow_0)
% 99.00/14.05 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 99.00/14.05 $i] : ? [v6: int] : ( ~ (v6 = 0) & related(v2, v4, v5) = 0 & related(v0,
% 99.00/14.05 v4, v5) = v6 & the_carrier(v2) = v3 & the_carrier(v0) = v1 & rel_str(v0) =
% 99.00/14.05 0 & subrelstr(v2, v0) = 0 & element(v5, v3) = 0 & element(v5, v1) = 0 &
% 99.00/14.05 element(v4, v3) = 0 & element(v4, v1) = 0 & $i(v5) & $i(v4) & $i(v3) &
% 99.00/14.05 $i(v2) & $i(v1) & $i(v0))
% 99.00/14.05
% 99.00/14.05 (function-axioms)
% 99.00/14.06 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 99.00/14.06 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (relation_of2(v4, v3, v2) = v1) | ~
% 99.00/14.06 (relation_of2(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 99.00/14.06 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 99.00/14.06 (relation_of2_as_subset(v4, v3, v2) = v1) | ~ (relation_of2_as_subset(v4,
% 99.00/14.06 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 99.00/14.06 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (related(v4, v3, v2)
% 99.00/14.06 = v1) | ~ (related(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 99.00/14.06 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~
% 99.00/14.06 (ordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 99.00/14.06 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 99.00/14.06 (subrelstr(v3, v2) = v1) | ~ (subrelstr(v3, v2) = v0)) & ! [v0:
% 99.00/14.06 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 99.00/14.06 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0:
% 99.00/14.06 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 99.00/14.06 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) &
% 99.00/14.06 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 99.00/14.06 $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & !
% 99.00/14.06 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 99.00/14.06 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 99.00/14.06 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 99.00/14.06 ~ (one_sorted_str(v2) = v1) | ~ (one_sorted_str(v2) = v0)) & ! [v0: $i] :
% 99.00/14.06 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~
% 99.00/14.06 (the_carrier(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 99.00/14.06 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (rel_str(v2) = v1) | ~
% 99.00/14.06 (rel_str(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 99.00/14.06 ~ (the_InternalRel(v2) = v1) | ~ (the_InternalRel(v2) = v0)) & ! [v0: $i]
% 99.00/14.06 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~
% 99.00/14.06 (powerset(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 99.00/14.06 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~
% 99.00/14.06 (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 99.00/14.06 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (finite(v2) = v1) | ~
% 99.00/14.06 (finite(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 99.00/14.06 : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 99.00/14.06
% 99.00/14.06 Further assumptions not needed in the proof:
% 99.00/14.06 --------------------------------------------
% 99.00/14.06 antisymmetry_r2_hidden, cc1_finset_1, cc1_relset_1, cc2_finset_1,
% 99.00/14.06 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_zfmisc_1, dt_k4_tarski, dt_l1_orders_2,
% 99.00/14.06 dt_l1_struct_0, dt_m1_relset_1, dt_m1_subset_1, dt_m2_relset_1, dt_u1_struct_0,
% 99.00/14.06 existence_l1_orders_2, existence_l1_struct_0, existence_m1_relset_1,
% 99.00/14.06 existence_m1_subset_1, existence_m1_yellow_0, existence_m2_relset_1,
% 99.00/14.06 fc14_finset_1, fc1_xboole_0, rc1_finset_1, rc1_xboole_0, rc2_xboole_0,
% 99.00/14.06 rc3_finset_1, rc4_finset_1, redefinition_m2_relset_1, reflexivity_r1_tarski,
% 99.00/14.06 t1_subset, t6_boole, t7_boole, t8_boole
% 99.00/14.06
% 99.00/14.06 Those formulas are unsatisfiable:
% 99.00/14.06 ---------------------------------
% 99.00/14.06
% 99.00/14.06 Begin of proof
% 99.00/14.06 |
% 99.00/14.06 | ALPHA: (d13_yellow_0) implies:
% 99.00/14.07 | (1) ! [v0: $i] : ( ~ (rel_str(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 99.00/14.07 | $i] : (the_carrier(v0) = v1 & the_InternalRel(v0) = v2 & $i(v2) &
% 99.00/14.07 | $i(v1) & ! [v3: $i] : ! [v4: $i] : ( ~ (the_carrier(v3) = v4) |
% 99.00/14.07 | ~ $i(v3) | ? [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8:
% 99.00/14.07 | $i] : ? [v9: int] : (( ~ (v5 = 0) & rel_str(v3) = v5) | (((v9
% 99.00/14.07 | = 0 & v7 = 0 & the_InternalRel(v3) = v8 & subset(v8, v2)
% 99.00/14.07 | = 0 & subset(v4, v1) = 0 & $i(v8)) | ( ~ (v6 = 0) &
% 99.00/14.07 | subrelstr(v3, v0) = v6)) & ((v6 = 0 & subrelstr(v3, v0) =
% 99.00/14.07 | 0) | ( ~ (v9 = 0) & the_InternalRel(v3) = v8 & subset(v8,
% 99.00/14.07 | v2) = v9 & $i(v8)) | ( ~ (v7 = 0) & subset(v4, v1) =
% 99.00/14.07 | v7))))) & ! [v3: $i] : ! [v4: any] : ( ~ (subrelstr(v3,
% 99.00/14.07 | v0) = v4) | ~ $i(v3) | ? [v5: int] : ? [v6: $i] : ? [v7:
% 99.00/14.07 | int] : ? [v8: $i] : ? [v9: int] : (( ~ (v5 = 0) & rel_str(v3)
% 99.00/14.07 | = v5) | (( ~ (v4 = 0) | (v9 = 0 & v7 = 0 & the_carrier(v3) =
% 99.00/14.07 | v6 & the_InternalRel(v3) = v8 & subset(v8, v2) = 0 &
% 99.00/14.07 | subset(v6, v1) = 0 & $i(v8) & $i(v6))) & (v4 = 0 | ( ~
% 99.00/14.07 | (v9 = 0) & the_InternalRel(v3) = v8 & subset(v8, v2) = v9
% 99.00/14.07 | & $i(v8)) | ( ~ (v7 = 0) & the_carrier(v3) = v6 &
% 99.00/14.07 | subset(v6, v1) = v7 & $i(v6)))))) & ! [v3: $i] : ! [v4:
% 99.00/14.07 | $i] : ( ~ (the_InternalRel(v3) = v4) | ~ $i(v3) | ? [v5: int] :
% 99.00/14.07 | ? [v6: int] : ? [v7: $i] : ? [v8: int] : ? [v9: int] : (( ~
% 99.00/14.07 | (v5 = 0) & rel_str(v3) = v5) | (((v9 = 0 & v8 = 0 &
% 99.00/14.07 | the_carrier(v3) = v7 & subset(v7, v1) = 0 & subset(v4,
% 99.00/14.07 | v2) = 0 & $i(v7)) | ( ~ (v6 = 0) & subrelstr(v3, v0) =
% 99.00/14.07 | v6)) & ((v6 = 0 & subrelstr(v3, v0) = 0) | ( ~ (v9 = 0) &
% 99.00/14.07 | subset(v4, v2) = v9) | ( ~ (v8 = 0) & the_carrier(v3) =
% 99.00/14.07 | v7 & subset(v7, v1) = v8 & $i(v7)))))) & ! [v3: $i] : (
% 99.00/14.07 | ~ (rel_str(v3) = 0) | ~ $i(v3) | ? [v4: int] : ? [v5: $i] : ?
% 99.00/14.07 | [v6: int] : ? [v7: $i] : ? [v8: int] : (((v8 = 0 & v6 = 0 &
% 99.00/14.07 | the_carrier(v3) = v5 & the_InternalRel(v3) = v7 &
% 99.00/14.07 | subset(v7, v2) = 0 & subset(v5, v1) = 0 & $i(v7) & $i(v5))
% 99.00/14.07 | | ( ~ (v4 = 0) & subrelstr(v3, v0) = v4)) & ((v4 = 0 &
% 99.00/14.07 | subrelstr(v3, v0) = 0) | ( ~ (v8 = 0) & the_InternalRel(v3)
% 99.00/14.07 | = v7 & subset(v7, v2) = v8 & $i(v7)) | ( ~ (v6 = 0) &
% 99.00/14.07 | the_carrier(v3) = v5 & subset(v5, v1) = v6 & $i(v5)))))))
% 99.00/14.08 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ?
% 99.00/14.08 | [v2: int] : ? [v3: $i] : (( ~ (v2 = 0) & rel_str(v0) = v2) |
% 99.00/14.08 | (the_InternalRel(v0) = v3 & $i(v3) & ! [v4: $i] : ! [v5: $i] : (
% 99.00/14.08 | ~ (the_carrier(v4) = v5) | ~ $i(v4) | ? [v6: int] : ? [v7:
% 99.00/14.08 | int] : ? [v8: int] : ? [v9: $i] : ? [v10: int] : (( ~ (v6
% 99.00/14.08 | = 0) & rel_str(v4) = v6) | (((v10 = 0 & v8 = 0 &
% 99.00/14.08 | the_InternalRel(v4) = v9 & subset(v9, v3) = 0 &
% 99.00/14.08 | subset(v5, v1) = 0 & $i(v9)) | ( ~ (v7 = 0) &
% 99.00/14.08 | subrelstr(v4, v0) = v7)) & ((v7 = 0 & subrelstr(v4, v0)
% 99.00/14.08 | = 0) | ( ~ (v10 = 0) & the_InternalRel(v4) = v9 &
% 99.00/14.08 | subset(v9, v3) = v10 & $i(v9)) | ( ~ (v8 = 0) &
% 99.00/14.08 | subset(v5, v1) = v8))))) & ! [v4: $i] : ! [v5: any] :
% 99.00/14.08 | ( ~ (subrelstr(v4, v0) = v5) | ~ $i(v4) | ? [v6: int] : ? [v7:
% 99.00/14.08 | $i] : ? [v8: int] : ? [v9: $i] : ? [v10: int] : (( ~ (v6 =
% 99.00/14.08 | 0) & rel_str(v4) = v6) | (( ~ (v5 = 0) | (v10 = 0 & v8 =
% 99.00/14.08 | 0 & the_carrier(v4) = v7 & the_InternalRel(v4) = v9 &
% 99.00/14.08 | subset(v9, v3) = 0 & subset(v7, v1) = 0 & $i(v9) &
% 99.00/14.08 | $i(v7))) & (v5 = 0 | ( ~ (v10 = 0) &
% 99.00/14.08 | the_InternalRel(v4) = v9 & subset(v9, v3) = v10 &
% 99.00/14.08 | $i(v9)) | ( ~ (v8 = 0) & the_carrier(v4) = v7 &
% 99.00/14.08 | subset(v7, v1) = v8 & $i(v7)))))) & ! [v4: $i] : !
% 99.00/14.08 | [v5: $i] : ( ~ (the_InternalRel(v4) = v5) | ~ $i(v4) | ? [v6:
% 99.00/14.08 | int] : ? [v7: int] : ? [v8: $i] : ? [v9: int] : ? [v10:
% 99.00/14.08 | int] : (( ~ (v6 = 0) & rel_str(v4) = v6) | (((v10 = 0 & v9 =
% 99.00/14.08 | 0 & the_carrier(v4) = v8 & subset(v8, v1) = 0 &
% 99.00/14.08 | subset(v5, v3) = 0 & $i(v8)) | ( ~ (v7 = 0) &
% 99.00/14.08 | subrelstr(v4, v0) = v7)) & ((v7 = 0 & subrelstr(v4, v0)
% 99.00/14.08 | = 0) | ( ~ (v10 = 0) & subset(v5, v3) = v10) | ( ~ (v9
% 99.00/14.08 | = 0) & the_carrier(v4) = v8 & subset(v8, v1) = v9 &
% 99.00/14.08 | $i(v8)))))) & ! [v4: $i] : ( ~ (rel_str(v4) = 0) | ~
% 99.00/14.08 | $i(v4) | ? [v5: int] : ? [v6: $i] : ? [v7: int] : ? [v8:
% 99.00/14.08 | $i] : ? [v9: int] : (((v9 = 0 & v7 = 0 & the_carrier(v4) =
% 99.00/14.08 | v6 & the_InternalRel(v4) = v8 & subset(v8, v3) = 0 &
% 99.00/14.08 | subset(v6, v1) = 0 & $i(v8) & $i(v6)) | ( ~ (v5 = 0) &
% 99.00/14.08 | subrelstr(v4, v0) = v5)) & ((v5 = 0 & subrelstr(v4, v0) =
% 99.00/14.08 | 0) | ( ~ (v9 = 0) & the_InternalRel(v4) = v8 & subset(v8,
% 99.00/14.08 | v3) = v9 & $i(v8)) | ( ~ (v7 = 0) & the_carrier(v4) =
% 99.00/14.08 | v6 & subset(v6, v1) = v7 & $i(v6))))))))
% 99.00/14.08 |
% 99.00/14.08 | ALPHA: (d9_orders_2) implies:
% 99.18/14.08 | (3) ! [v0: $i] : ( ~ (rel_str(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 99.18/14.08 | $i] : (the_carrier(v0) = v1 & the_InternalRel(v0) = v2 & $i(v2) &
% 99.18/14.08 | $i(v1) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 99.18/14.08 | (ordered_pair(v3, v4) = v5) | ~ (element(v3, v1) = 0) | ~
% 99.18/14.08 | $i(v4) | ~ $i(v3) | ? [v6: int] : ? [v7: int] : ? [v8: int] :
% 99.18/14.08 | (( ~ (v6 = 0) & element(v4, v1) = v6) | (((v8 = 0 & in(v5, v2) =
% 99.18/14.08 | 0) | ( ~ (v7 = 0) & related(v0, v3, v4) = v7)) & ((v7 = 0
% 99.18/14.08 | & related(v0, v3, v4) = 0) | ( ~ (v8 = 0) & in(v5, v2) =
% 99.18/14.08 | v8))))) & ! [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~
% 99.18/14.08 | (related(v0, v3, v4) = v5) | ~ (element(v3, v1) = 0) | ~ $i(v4)
% 99.18/14.08 | | ~ $i(v3) | ? [v6: int] : ? [v7: $i] : ? [v8: int] : (( ~
% 99.18/14.08 | (v6 = 0) & element(v4, v1) = v6) | (( ~ (v5 = 0) | (v8 = 0 &
% 99.18/14.08 | ordered_pair(v3, v4) = v7 & in(v7, v2) = 0 & $i(v7))) &
% 99.18/14.08 | (v5 = 0 | ( ~ (v8 = 0) & ordered_pair(v3, v4) = v7 & in(v7,
% 99.18/14.08 | v2) = v8 & $i(v7)))))) & ! [v3: $i] : ! [v4: $i] : (
% 99.18/14.08 | ~ (element(v4, v1) = 0) | ~ (element(v3, v1) = 0) | ~ $i(v4) |
% 99.18/14.08 | ~ $i(v3) | ? [v5: int] : ? [v6: $i] : ? [v7: int] : (((v7 = 0
% 99.18/14.08 | & ordered_pair(v3, v4) = v6 & in(v6, v2) = 0 & $i(v6)) | (
% 99.18/14.08 | ~ (v5 = 0) & related(v0, v3, v4) = v5)) & ((v5 = 0 &
% 99.18/14.08 | related(v0, v3, v4) = 0) | ( ~ (v7 = 0) & ordered_pair(v3,
% 99.18/14.08 | v4) = v6 & in(v6, v2) = v7 & $i(v6)))))))
% 99.18/14.09 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ?
% 99.18/14.09 | [v2: int] : ? [v3: $i] : (( ~ (v2 = 0) & rel_str(v0) = v2) |
% 99.18/14.09 | (the_InternalRel(v0) = v3 & $i(v3) & ! [v4: $i] : ! [v5: $i] : !
% 99.18/14.09 | [v6: $i] : ( ~ (ordered_pair(v4, v5) = v6) | ~ (element(v4, v1)
% 99.18/14.09 | = 0) | ~ $i(v5) | ~ $i(v4) | ? [v7: int] : ? [v8: int] :
% 99.18/14.09 | ? [v9: int] : (( ~ (v7 = 0) & element(v5, v1) = v7) | (((v9 = 0
% 99.18/14.09 | & in(v6, v3) = 0) | ( ~ (v8 = 0) & related(v0, v4, v5)
% 99.18/14.09 | = v8)) & ((v8 = 0 & related(v0, v4, v5) = 0) | ( ~ (v9
% 99.18/14.09 | = 0) & in(v6, v3) = v9))))) & ! [v4: $i] : ! [v5:
% 99.18/14.09 | $i] : ! [v6: any] : ( ~ (related(v0, v4, v5) = v6) | ~
% 99.18/14.09 | (element(v4, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ? [v7: int] :
% 99.18/14.09 | ? [v8: $i] : ? [v9: int] : (( ~ (v7 = 0) & element(v5, v1) =
% 99.18/14.09 | v7) | (( ~ (v6 = 0) | (v9 = 0 & ordered_pair(v4, v5) = v8 &
% 99.18/14.09 | in(v8, v3) = 0 & $i(v8))) & (v6 = 0 | ( ~ (v9 = 0) &
% 99.18/14.09 | ordered_pair(v4, v5) = v8 & in(v8, v3) = v9 &
% 99.18/14.09 | $i(v8)))))) & ! [v4: $i] : ! [v5: $i] : ( ~
% 99.18/14.09 | (element(v5, v1) = 0) | ~ (element(v4, v1) = 0) | ~ $i(v5) |
% 99.18/14.09 | ~ $i(v4) | ? [v6: int] : ? [v7: $i] : ? [v8: int] : (((v8 =
% 99.18/14.09 | 0 & ordered_pair(v4, v5) = v7 & in(v7, v3) = 0 & $i(v7))
% 99.18/14.09 | | ( ~ (v6 = 0) & related(v0, v4, v5) = v6)) & ((v6 = 0 &
% 99.18/14.09 | related(v0, v4, v5) = 0) | ( ~ (v8 = 0) &
% 99.18/14.09 | ordered_pair(v4, v5) = v7 & in(v7, v3) = v8 &
% 99.18/14.09 | $i(v7))))))))
% 99.18/14.09 |
% 99.18/14.09 | ALPHA: (dt_m1_yellow_0) implies:
% 99.18/14.09 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (rel_str(v0) = 0) | ~ (subrelstr(v1,
% 99.18/14.09 | v0) = 0) | ~ $i(v1) | ~ $i(v0) | rel_str(v1) = 0)
% 99.18/14.09 |
% 99.18/14.09 | ALPHA: (dt_u1_orders_2) implies:
% 99.18/14.09 | (6) ! [v0: $i] : ( ~ (rel_str(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 99.18/14.09 | $i] : (relation_of2_as_subset(v1, v2, v2) = 0 & the_carrier(v0) =
% 99.18/14.09 | v2 & the_InternalRel(v0) = v1 & $i(v2) & $i(v1)))
% 99.18/14.09 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ?
% 99.18/14.09 | [v2: int] : ? [v3: $i] : ? [v4: int] : ((v4 = 0 &
% 99.18/14.09 | relation_of2_as_subset(v3, v1, v1) = 0 & the_InternalRel(v0) = v3
% 99.18/14.09 | & $i(v3)) | ( ~ (v2 = 0) & rel_str(v0) = v2)))
% 99.18/14.09 |
% 99.18/14.09 | ALPHA: (t2_subset) implies:
% 99.18/14.09 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) =
% 99.18/14.09 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ((v4 =
% 99.18/14.09 | 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 99.18/14.09 |
% 99.18/14.09 | ALPHA: (t3_subset) implies:
% 99.18/14.10 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 99.18/14.10 | $i(v0) | ? [v2: $i] : (powerset(v1) = v2 & element(v0, v2) = 0 &
% 99.18/14.10 | $i(v2)))
% 99.18/14.10 |
% 99.18/14.10 | ALPHA: (t4_subset) implies:
% 99.18/14.10 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 99.18/14.10 | (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0)
% 99.18/14.10 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | element(v0, v2) = 0)
% 99.18/14.10 |
% 99.18/14.10 | ALPHA: (t5_subset) implies:
% 99.18/14.10 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 99.18/14.10 | (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0)
% 99.18/14.10 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) &
% 99.18/14.10 | empty(v2) = v4))
% 99.18/14.10 |
% 99.18/14.10 | ALPHA: (function-axioms) implies:
% 99.18/14.10 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 99.18/14.10 | : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 99.18/14.10 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 99.18/14.10 | (the_InternalRel(v2) = v1) | ~ (the_InternalRel(v2) = v0))
% 99.18/14.10 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 99.18/14.10 | : (v1 = v0 | ~ (rel_str(v2) = v1) | ~ (rel_str(v2) = v0))
% 99.18/14.10 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 99.18/14.10 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) =
% 99.18/14.10 | v0))
% 99.18/14.10 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 99.18/14.10 | : ! [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3,
% 99.18/14.10 | v2) = v0))
% 99.18/14.10 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 99.18/14.10 | : ! [v3: $i] : (v1 = v0 | ~ (subrelstr(v3, v2) = v1) | ~
% 99.18/14.10 | (subrelstr(v3, v2) = v0))
% 99.18/14.10 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 99.18/14.10 | (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 99.18/14.10 | (19) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 99.18/14.10 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (related(v4, v3, v2) = v1)
% 99.18/14.10 | | ~ (related(v4, v3, v2) = v0))
% 99.18/14.10 |
% 99.18/14.10 | DELTA: instantiating (t60_yellow_0) with fresh symbols all_41_0, all_41_1,
% 99.18/14.10 | all_41_2, all_41_3, all_41_4, all_41_5, all_41_6 gives:
% 99.18/14.10 | (20) ~ (all_41_0 = 0) & related(all_41_4, all_41_2, all_41_1) = 0 &
% 99.18/14.10 | related(all_41_6, all_41_2, all_41_1) = all_41_0 &
% 99.18/14.10 | the_carrier(all_41_4) = all_41_3 & the_carrier(all_41_6) = all_41_5 &
% 99.18/14.10 | rel_str(all_41_6) = 0 & subrelstr(all_41_4, all_41_6) = 0 &
% 99.18/14.10 | element(all_41_1, all_41_3) = 0 & element(all_41_1, all_41_5) = 0 &
% 99.18/14.10 | element(all_41_2, all_41_3) = 0 & element(all_41_2, all_41_5) = 0 &
% 99.18/14.10 | $i(all_41_1) & $i(all_41_2) & $i(all_41_3) & $i(all_41_4) &
% 99.18/14.10 | $i(all_41_5) & $i(all_41_6)
% 99.18/14.10 |
% 99.18/14.10 | ALPHA: (20) implies:
% 99.18/14.10 | (21) ~ (all_41_0 = 0)
% 99.18/14.10 | (22) $i(all_41_6)
% 99.18/14.10 | (23) $i(all_41_4)
% 99.18/14.10 | (24) $i(all_41_2)
% 99.18/14.10 | (25) $i(all_41_1)
% 99.18/14.10 | (26) element(all_41_2, all_41_5) = 0
% 99.18/14.10 | (27) element(all_41_2, all_41_3) = 0
% 99.18/14.10 | (28) element(all_41_1, all_41_5) = 0
% 99.18/14.10 | (29) element(all_41_1, all_41_3) = 0
% 99.18/14.10 | (30) subrelstr(all_41_4, all_41_6) = 0
% 99.18/14.10 | (31) rel_str(all_41_6) = 0
% 99.18/14.10 | (32) the_carrier(all_41_6) = all_41_5
% 99.18/14.10 | (33) the_carrier(all_41_4) = all_41_3
% 99.18/14.10 | (34) related(all_41_6, all_41_2, all_41_1) = all_41_0
% 99.18/14.10 | (35) related(all_41_4, all_41_2, all_41_1) = 0
% 99.18/14.10 |
% 99.18/14.11 | GROUND_INST: instantiating (5) with all_41_6, all_41_4, simplifying with (22),
% 99.18/14.11 | (23), (30), (31) gives:
% 99.18/14.11 | (36) rel_str(all_41_4) = 0
% 99.18/14.11 |
% 99.18/14.11 | GROUND_INST: instantiating (6) with all_41_6, simplifying with (22), (31)
% 99.18/14.11 | gives:
% 99.18/14.11 | (37) ? [v0: $i] : ? [v1: $i] : (relation_of2_as_subset(v0, v1, v1) = 0 &
% 99.18/14.11 | the_carrier(all_41_6) = v1 & the_InternalRel(all_41_6) = v0 & $i(v1)
% 99.18/14.11 | & $i(v0))
% 99.18/14.11 |
% 99.18/14.11 | GROUND_INST: instantiating (3) with all_41_6, simplifying with (22), (31)
% 99.18/14.11 | gives:
% 99.18/14.11 | (38) ? [v0: $i] : ? [v1: $i] : (the_carrier(all_41_6) = v0 &
% 99.18/14.11 | the_InternalRel(all_41_6) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : !
% 99.18/14.11 | [v3: $i] : ! [v4: $i] : ( ~ (ordered_pair(v2, v3) = v4) | ~
% 99.18/14.11 | (element(v2, v0) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v5: int] : ?
% 99.18/14.11 | [v6: int] : ? [v7: int] : (( ~ (v5 = 0) & element(v3, v0) = v5) |
% 99.18/14.11 | (((v7 = 0 & in(v4, v1) = 0) | ( ~ (v6 = 0) & related(all_41_6,
% 99.18/14.11 | v2, v3) = v6)) & ((v6 = 0 & related(all_41_6, v2, v3) =
% 99.18/14.11 | 0) | ( ~ (v7 = 0) & in(v4, v1) = v7))))) & ! [v2: $i] :
% 99.18/14.11 | ! [v3: $i] : ! [v4: any] : ( ~ (related(all_41_6, v2, v3) = v4) |
% 99.18/14.11 | ~ (element(v2, v0) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v5: int] :
% 99.18/14.11 | ? [v6: $i] : ? [v7: int] : (( ~ (v5 = 0) & element(v3, v0) = v5)
% 99.18/14.11 | | (( ~ (v4 = 0) | (v7 = 0 & ordered_pair(v2, v3) = v6 & in(v6,
% 99.18/14.11 | v1) = 0 & $i(v6))) & (v4 = 0 | ( ~ (v7 = 0) &
% 99.18/14.11 | ordered_pair(v2, v3) = v6 & in(v6, v1) = v7 & $i(v6))))))
% 99.18/14.11 | & ! [v2: $i] : ! [v3: $i] : ( ~ (element(v3, v0) = 0) | ~
% 99.18/14.11 | (element(v2, v0) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v4: int] : ?
% 99.18/14.11 | [v5: $i] : ? [v6: int] : (((v6 = 0 & ordered_pair(v2, v3) = v5 &
% 99.18/14.11 | in(v5, v1) = 0 & $i(v5)) | ( ~ (v4 = 0) & related(all_41_6,
% 99.18/14.11 | v2, v3) = v4)) & ((v4 = 0 & related(all_41_6, v2, v3) = 0)
% 99.18/14.11 | | ( ~ (v6 = 0) & ordered_pair(v2, v3) = v5 & in(v5, v1) = v6 &
% 99.18/14.11 | $i(v5))))))
% 99.18/14.11 |
% 99.18/14.11 | GROUND_INST: instantiating (1) with all_41_6, simplifying with (22), (31)
% 99.18/14.11 | gives:
% 99.18/14.11 | (39) ? [v0: $i] : ? [v1: $i] : (the_carrier(all_41_6) = v0 &
% 99.18/14.11 | the_InternalRel(all_41_6) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : !
% 99.18/14.11 | [v3: $i] : ( ~ (the_carrier(v2) = v3) | ~ $i(v2) | ? [v4: int] :
% 99.18/14.11 | ? [v5: int] : ? [v6: int] : ? [v7: $i] : ? [v8: int] : (( ~ (v4
% 99.18/14.11 | = 0) & rel_str(v2) = v4) | (((v8 = 0 & v6 = 0 &
% 99.18/14.11 | the_InternalRel(v2) = v7 & subset(v7, v1) = 0 & subset(v3,
% 99.18/14.11 | v0) = 0 & $i(v7)) | ( ~ (v5 = 0) & subrelstr(v2,
% 99.18/14.11 | all_41_6) = v5)) & ((v5 = 0 & subrelstr(v2, all_41_6) =
% 99.18/14.11 | 0) | ( ~ (v8 = 0) & the_InternalRel(v2) = v7 & subset(v7,
% 99.18/14.11 | v1) = v8 & $i(v7)) | ( ~ (v6 = 0) & subset(v3, v0) =
% 99.18/14.11 | v6))))) & ! [v2: $i] : ! [v3: any] : ( ~ (subrelstr(v2,
% 99.18/14.11 | all_41_6) = v3) | ~ $i(v2) | ? [v4: int] : ? [v5: $i] : ?
% 99.18/14.11 | [v6: int] : ? [v7: $i] : ? [v8: int] : (( ~ (v4 = 0) &
% 99.18/14.11 | rel_str(v2) = v4) | (( ~ (v3 = 0) | (v8 = 0 & v6 = 0 &
% 99.18/14.11 | the_carrier(v2) = v5 & the_InternalRel(v2) = v7 &
% 99.18/14.11 | subset(v7, v1) = 0 & subset(v5, v0) = 0 & $i(v7) &
% 99.18/14.11 | $i(v5))) & (v3 = 0 | ( ~ (v8 = 0) & the_InternalRel(v2) =
% 99.18/14.11 | v7 & subset(v7, v1) = v8 & $i(v7)) | ( ~ (v6 = 0) &
% 99.18/14.11 | the_carrier(v2) = v5 & subset(v5, v0) = v6 & $i(v5)))))) &
% 99.18/14.11 | ! [v2: $i] : ! [v3: $i] : ( ~ (the_InternalRel(v2) = v3) | ~
% 99.18/14.11 | $i(v2) | ? [v4: int] : ? [v5: int] : ? [v6: $i] : ? [v7: int]
% 99.18/14.11 | : ? [v8: int] : (( ~ (v4 = 0) & rel_str(v2) = v4) | (((v8 = 0 &
% 99.18/14.11 | v7 = 0 & the_carrier(v2) = v6 & subset(v6, v0) = 0 &
% 99.18/14.11 | subset(v3, v1) = 0 & $i(v6)) | ( ~ (v5 = 0) &
% 99.18/14.11 | subrelstr(v2, all_41_6) = v5)) & ((v5 = 0 & subrelstr(v2,
% 99.18/14.11 | all_41_6) = 0) | ( ~ (v8 = 0) & subset(v3, v1) = v8) | (
% 99.18/14.11 | ~ (v7 = 0) & the_carrier(v2) = v6 & subset(v6, v0) = v7 &
% 99.18/14.11 | $i(v6)))))) & ! [v2: $i] : ( ~ (rel_str(v2) = 0) | ~
% 99.18/14.11 | $i(v2) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : ? [v6: $i] :
% 99.18/14.11 | ? [v7: int] : (((v7 = 0 & v5 = 0 & the_carrier(v2) = v4 &
% 99.18/14.11 | the_InternalRel(v2) = v6 & subset(v6, v1) = 0 & subset(v4,
% 99.18/14.11 | v0) = 0 & $i(v6) & $i(v4)) | ( ~ (v3 = 0) & subrelstr(v2,
% 99.18/14.11 | all_41_6) = v3)) & ((v3 = 0 & subrelstr(v2, all_41_6) = 0)
% 99.18/14.11 | | ( ~ (v7 = 0) & the_InternalRel(v2) = v6 & subset(v6, v1) =
% 99.18/14.11 | v7 & $i(v6)) | ( ~ (v5 = 0) & the_carrier(v2) = v4 &
% 99.18/14.11 | subset(v4, v0) = v5 & $i(v4))))))
% 99.18/14.11 |
% 99.18/14.11 | GROUND_INST: instantiating (7) with all_41_6, all_41_5, simplifying with (22),
% 99.18/14.11 | (32) gives:
% 99.18/14.12 | (40) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ((v2 = 0 &
% 99.18/14.12 | relation_of2_as_subset(v1, all_41_5, all_41_5) = 0 &
% 99.18/14.12 | the_InternalRel(all_41_6) = v1 & $i(v1)) | ( ~ (v0 = 0) &
% 99.18/14.12 | rel_str(all_41_6) = v0))
% 99.18/14.12 |
% 99.18/14.12 | GROUND_INST: instantiating (4) with all_41_6, all_41_5, simplifying with (22),
% 99.18/14.12 | (32) gives:
% 99.18/14.12 | (41) ? [v0: int] : ? [v1: $i] : (( ~ (v0 = 0) & rel_str(all_41_6) = v0) |
% 99.18/14.12 | (the_InternalRel(all_41_6) = v1 & $i(v1) & ! [v2: $i] : ! [v3: $i]
% 99.18/14.12 | : ! [v4: $i] : ( ~ (ordered_pair(v2, v3) = v4) | ~ (element(v2,
% 99.18/14.12 | all_41_5) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v5: int] : ?
% 99.18/14.12 | [v6: int] : ? [v7: int] : (( ~ (v5 = 0) & element(v3, all_41_5)
% 99.18/14.12 | = v5) | (((v7 = 0 & in(v4, v1) = 0) | ( ~ (v6 = 0) &
% 99.18/14.12 | related(all_41_6, v2, v3) = v6)) & ((v6 = 0 &
% 99.18/14.12 | related(all_41_6, v2, v3) = 0) | ( ~ (v7 = 0) & in(v4,
% 99.18/14.12 | v1) = v7))))) & ! [v2: $i] : ! [v3: $i] : ! [v4:
% 99.18/14.12 | any] : ( ~ (related(all_41_6, v2, v3) = v4) | ~ (element(v2,
% 99.18/14.12 | all_41_5) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v5: int] : ?
% 99.18/14.12 | [v6: $i] : ? [v7: int] : (( ~ (v5 = 0) & element(v3, all_41_5)
% 99.18/14.12 | = v5) | (( ~ (v4 = 0) | (v7 = 0 & ordered_pair(v2, v3) = v6
% 99.18/14.12 | & in(v6, v1) = 0 & $i(v6))) & (v4 = 0 | ( ~ (v7 = 0) &
% 99.18/14.12 | ordered_pair(v2, v3) = v6 & in(v6, v1) = v7 &
% 99.18/14.12 | $i(v6)))))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 99.18/14.12 | (element(v3, all_41_5) = 0) | ~ (element(v2, all_41_5) = 0) |
% 99.18/14.12 | ~ $i(v3) | ~ $i(v2) | ? [v4: int] : ? [v5: $i] : ? [v6: int]
% 99.18/14.12 | : (((v6 = 0 & ordered_pair(v2, v3) = v5 & in(v5, v1) = 0 &
% 99.18/14.12 | $i(v5)) | ( ~ (v4 = 0) & related(all_41_6, v2, v3) = v4))
% 99.18/14.12 | & ((v4 = 0 & related(all_41_6, v2, v3) = 0) | ( ~ (v6 = 0) &
% 99.18/14.12 | ordered_pair(v2, v3) = v5 & in(v5, v1) = v6 & $i(v5)))))))
% 99.18/14.12 |
% 99.18/14.12 | GROUND_INST: instantiating (2) with all_41_6, all_41_5, simplifying with (22),
% 99.18/14.12 | (32) gives:
% 99.18/14.12 | (42) ? [v0: int] : ? [v1: $i] : (( ~ (v0 = 0) & rel_str(all_41_6) = v0) |
% 99.18/14.12 | (the_InternalRel(all_41_6) = v1 & $i(v1) & ! [v2: $i] : ! [v3: $i]
% 99.18/14.12 | : ( ~ (the_carrier(v2) = v3) | ~ $i(v2) | ? [v4: int] : ? [v5:
% 99.18/14.12 | int] : ? [v6: int] : ? [v7: $i] : ? [v8: int] : (( ~ (v4 =
% 99.18/14.12 | 0) & rel_str(v2) = v4) | (((v8 = 0 & v6 = 0 &
% 99.18/14.12 | the_InternalRel(v2) = v7 & subset(v7, v1) = 0 &
% 99.18/14.12 | subset(v3, all_41_5) = 0 & $i(v7)) | ( ~ (v5 = 0) &
% 99.18/14.12 | subrelstr(v2, all_41_6) = v5)) & ((v5 = 0 &
% 99.18/14.12 | subrelstr(v2, all_41_6) = 0) | ( ~ (v8 = 0) &
% 99.18/14.12 | the_InternalRel(v2) = v7 & subset(v7, v1) = v8 & $i(v7))
% 99.18/14.12 | | ( ~ (v6 = 0) & subset(v3, all_41_5) = v6))))) & ! [v2:
% 99.18/14.12 | $i] : ! [v3: any] : ( ~ (subrelstr(v2, all_41_6) = v3) | ~
% 99.18/14.12 | $i(v2) | ? [v4: int] : ? [v5: $i] : ? [v6: int] : ? [v7: $i]
% 99.18/14.12 | : ? [v8: int] : (( ~ (v4 = 0) & rel_str(v2) = v4) | (( ~ (v3 =
% 99.18/14.12 | 0) | (v8 = 0 & v6 = 0 & the_carrier(v2) = v5 &
% 99.18/14.12 | the_InternalRel(v2) = v7 & subset(v7, v1) = 0 &
% 99.18/14.12 | subset(v5, all_41_5) = 0 & $i(v7) & $i(v5))) & (v3 = 0 |
% 99.18/14.12 | ( ~ (v8 = 0) & the_InternalRel(v2) = v7 & subset(v7, v1) =
% 99.18/14.12 | v8 & $i(v7)) | ( ~ (v6 = 0) & the_carrier(v2) = v5 &
% 99.18/14.12 | subset(v5, all_41_5) = v6 & $i(v5)))))) & ! [v2: $i] :
% 99.18/14.12 | ! [v3: $i] : ( ~ (the_InternalRel(v2) = v3) | ~ $i(v2) | ? [v4:
% 99.18/14.12 | int] : ? [v5: int] : ? [v6: $i] : ? [v7: int] : ? [v8:
% 99.18/14.12 | int] : (( ~ (v4 = 0) & rel_str(v2) = v4) | (((v8 = 0 & v7 = 0
% 99.18/14.12 | & the_carrier(v2) = v6 & subset(v6, all_41_5) = 0 &
% 99.18/14.12 | subset(v3, v1) = 0 & $i(v6)) | ( ~ (v5 = 0) &
% 99.18/14.12 | subrelstr(v2, all_41_6) = v5)) & ((v5 = 0 &
% 99.18/14.12 | subrelstr(v2, all_41_6) = 0) | ( ~ (v8 = 0) & subset(v3,
% 99.18/14.12 | v1) = v8) | ( ~ (v7 = 0) & the_carrier(v2) = v6 &
% 99.18/14.12 | subset(v6, all_41_5) = v7 & $i(v6)))))) & ! [v2: $i] :
% 99.18/14.12 | ( ~ (rel_str(v2) = 0) | ~ $i(v2) | ? [v3: int] : ? [v4: $i] :
% 99.18/14.12 | ? [v5: int] : ? [v6: $i] : ? [v7: int] : (((v7 = 0 & v5 = 0 &
% 99.18/14.12 | the_carrier(v2) = v4 & the_InternalRel(v2) = v6 &
% 99.18/14.12 | subset(v6, v1) = 0 & subset(v4, all_41_5) = 0 & $i(v6) &
% 99.18/14.12 | $i(v4)) | ( ~ (v3 = 0) & subrelstr(v2, all_41_6) = v3)) &
% 99.18/14.12 | ((v3 = 0 & subrelstr(v2, all_41_6) = 0) | ( ~ (v7 = 0) &
% 99.18/14.12 | the_InternalRel(v2) = v6 & subset(v6, v1) = v7 & $i(v6)) |
% 99.18/14.12 | ( ~ (v5 = 0) & the_carrier(v2) = v4 & subset(v4, all_41_5) =
% 99.18/14.12 | v5 & $i(v4)))))))
% 99.18/14.12 |
% 99.18/14.12 | GROUND_INST: instantiating (7) with all_41_4, all_41_3, simplifying with (23),
% 99.18/14.12 | (33) gives:
% 99.18/14.12 | (43) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ((v2 = 0 &
% 99.18/14.12 | relation_of2_as_subset(v1, all_41_3, all_41_3) = 0 &
% 99.18/14.12 | the_InternalRel(all_41_4) = v1 & $i(v1)) | ( ~ (v0 = 0) &
% 99.18/14.12 | rel_str(all_41_4) = v0))
% 99.18/14.12 |
% 99.18/14.12 | GROUND_INST: instantiating (4) with all_41_4, all_41_3, simplifying with (23),
% 99.18/14.12 | (33) gives:
% 99.18/14.13 | (44) ? [v0: int] : ? [v1: $i] : (( ~ (v0 = 0) & rel_str(all_41_4) = v0) |
% 99.18/14.13 | (the_InternalRel(all_41_4) = v1 & $i(v1) & ! [v2: $i] : ! [v3: $i]
% 99.18/14.13 | : ! [v4: $i] : ( ~ (ordered_pair(v2, v3) = v4) | ~ (element(v2,
% 99.18/14.13 | all_41_3) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v5: int] : ?
% 99.18/14.13 | [v6: int] : ? [v7: int] : (( ~ (v5 = 0) & element(v3, all_41_3)
% 99.18/14.13 | = v5) | (((v7 = 0 & in(v4, v1) = 0) | ( ~ (v6 = 0) &
% 99.18/14.13 | related(all_41_4, v2, v3) = v6)) & ((v6 = 0 &
% 99.18/14.13 | related(all_41_4, v2, v3) = 0) | ( ~ (v7 = 0) & in(v4,
% 99.18/14.13 | v1) = v7))))) & ! [v2: $i] : ! [v3: $i] : ! [v4:
% 99.18/14.13 | any] : ( ~ (related(all_41_4, v2, v3) = v4) | ~ (element(v2,
% 99.18/14.13 | all_41_3) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v5: int] : ?
% 99.18/14.13 | [v6: $i] : ? [v7: int] : (( ~ (v5 = 0) & element(v3, all_41_3)
% 99.18/14.13 | = v5) | (( ~ (v4 = 0) | (v7 = 0 & ordered_pair(v2, v3) = v6
% 99.18/14.13 | & in(v6, v1) = 0 & $i(v6))) & (v4 = 0 | ( ~ (v7 = 0) &
% 99.18/14.13 | ordered_pair(v2, v3) = v6 & in(v6, v1) = v7 &
% 99.18/14.13 | $i(v6)))))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 99.18/14.13 | (element(v3, all_41_3) = 0) | ~ (element(v2, all_41_3) = 0) |
% 99.18/14.13 | ~ $i(v3) | ~ $i(v2) | ? [v4: int] : ? [v5: $i] : ? [v6: int]
% 99.18/14.13 | : (((v6 = 0 & ordered_pair(v2, v3) = v5 & in(v5, v1) = 0 &
% 99.18/14.13 | $i(v5)) | ( ~ (v4 = 0) & related(all_41_4, v2, v3) = v4))
% 99.18/14.13 | & ((v4 = 0 & related(all_41_4, v2, v3) = 0) | ( ~ (v6 = 0) &
% 99.18/14.13 | ordered_pair(v2, v3) = v5 & in(v5, v1) = v6 & $i(v5)))))))
% 99.18/14.13 |
% 99.18/14.13 | GROUND_INST: instantiating (2) with all_41_4, all_41_3, simplifying with (23),
% 99.18/14.13 | (33) gives:
% 99.43/14.13 | (45) ? [v0: int] : ? [v1: $i] : (( ~ (v0 = 0) & rel_str(all_41_4) = v0) |
% 99.43/14.13 | (the_InternalRel(all_41_4) = v1 & $i(v1) & ! [v2: $i] : ! [v3: $i]
% 99.43/14.13 | : ( ~ (the_carrier(v2) = v3) | ~ $i(v2) | ? [v4: int] : ? [v5:
% 99.43/14.13 | int] : ? [v6: int] : ? [v7: $i] : ? [v8: int] : (( ~ (v4 =
% 99.43/14.13 | 0) & rel_str(v2) = v4) | (((v8 = 0 & v6 = 0 &
% 99.43/14.13 | the_InternalRel(v2) = v7 & subset(v7, v1) = 0 &
% 99.43/14.13 | subset(v3, all_41_3) = 0 & $i(v7)) | ( ~ (v5 = 0) &
% 99.43/14.13 | subrelstr(v2, all_41_4) = v5)) & ((v5 = 0 &
% 99.43/14.13 | subrelstr(v2, all_41_4) = 0) | ( ~ (v8 = 0) &
% 99.43/14.13 | the_InternalRel(v2) = v7 & subset(v7, v1) = v8 & $i(v7))
% 99.43/14.13 | | ( ~ (v6 = 0) & subset(v3, all_41_3) = v6))))) & ! [v2:
% 99.43/14.13 | $i] : ! [v3: any] : ( ~ (subrelstr(v2, all_41_4) = v3) | ~
% 99.43/14.13 | $i(v2) | ? [v4: int] : ? [v5: $i] : ? [v6: int] : ? [v7: $i]
% 99.43/14.13 | : ? [v8: int] : (( ~ (v4 = 0) & rel_str(v2) = v4) | (( ~ (v3 =
% 99.43/14.13 | 0) | (v8 = 0 & v6 = 0 & the_carrier(v2) = v5 &
% 99.43/14.13 | the_InternalRel(v2) = v7 & subset(v7, v1) = 0 &
% 99.43/14.13 | subset(v5, all_41_3) = 0 & $i(v7) & $i(v5))) & (v3 = 0 |
% 99.43/14.13 | ( ~ (v8 = 0) & the_InternalRel(v2) = v7 & subset(v7, v1) =
% 99.43/14.13 | v8 & $i(v7)) | ( ~ (v6 = 0) & the_carrier(v2) = v5 &
% 99.43/14.13 | subset(v5, all_41_3) = v6 & $i(v5)))))) & ! [v2: $i] :
% 99.43/14.13 | ! [v3: $i] : ( ~ (the_InternalRel(v2) = v3) | ~ $i(v2) | ? [v4:
% 99.43/14.13 | int] : ? [v5: int] : ? [v6: $i] : ? [v7: int] : ? [v8:
% 99.43/14.13 | int] : (( ~ (v4 = 0) & rel_str(v2) = v4) | (((v8 = 0 & v7 = 0
% 99.43/14.13 | & the_carrier(v2) = v6 & subset(v6, all_41_3) = 0 &
% 99.43/14.13 | subset(v3, v1) = 0 & $i(v6)) | ( ~ (v5 = 0) &
% 99.43/14.13 | subrelstr(v2, all_41_4) = v5)) & ((v5 = 0 &
% 99.43/14.13 | subrelstr(v2, all_41_4) = 0) | ( ~ (v8 = 0) & subset(v3,
% 99.43/14.13 | v1) = v8) | ( ~ (v7 = 0) & the_carrier(v2) = v6 &
% 99.43/14.13 | subset(v6, all_41_3) = v7 & $i(v6)))))) & ! [v2: $i] :
% 99.43/14.13 | ( ~ (rel_str(v2) = 0) | ~ $i(v2) | ? [v3: int] : ? [v4: $i] :
% 99.43/14.13 | ? [v5: int] : ? [v6: $i] : ? [v7: int] : (((v7 = 0 & v5 = 0 &
% 99.43/14.13 | the_carrier(v2) = v4 & the_InternalRel(v2) = v6 &
% 99.43/14.13 | subset(v6, v1) = 0 & subset(v4, all_41_3) = 0 & $i(v6) &
% 99.43/14.13 | $i(v4)) | ( ~ (v3 = 0) & subrelstr(v2, all_41_4) = v3)) &
% 99.43/14.13 | ((v3 = 0 & subrelstr(v2, all_41_4) = 0) | ( ~ (v7 = 0) &
% 99.43/14.13 | the_InternalRel(v2) = v6 & subset(v6, v1) = v7 & $i(v6)) |
% 99.43/14.13 | ( ~ (v5 = 0) & the_carrier(v2) = v4 & subset(v4, all_41_3) =
% 99.43/14.13 | v5 & $i(v4)))))))
% 99.43/14.13 |
% 99.43/14.13 | DELTA: instantiating (37) with fresh symbols all_57_0, all_57_1 gives:
% 99.43/14.13 | (46) relation_of2_as_subset(all_57_1, all_57_0, all_57_0) = 0 &
% 99.43/14.13 | the_carrier(all_41_6) = all_57_0 & the_InternalRel(all_41_6) =
% 99.43/14.13 | all_57_1 & $i(all_57_0) & $i(all_57_1)
% 99.43/14.13 |
% 99.43/14.13 | ALPHA: (46) implies:
% 99.43/14.13 | (47) the_InternalRel(all_41_6) = all_57_1
% 99.43/14.13 |
% 99.43/14.13 | DELTA: instantiating (43) with fresh symbols all_61_0, all_61_1, all_61_2
% 99.43/14.13 | gives:
% 99.43/14.13 | (48) (all_61_0 = 0 & relation_of2_as_subset(all_61_1, all_41_3, all_41_3) =
% 99.43/14.13 | 0 & the_InternalRel(all_41_4) = all_61_1 & $i(all_61_1)) | ( ~
% 99.43/14.13 | (all_61_2 = 0) & rel_str(all_41_4) = all_61_2)
% 99.43/14.13 |
% 99.43/14.13 | DELTA: instantiating (40) with fresh symbols all_62_0, all_62_1, all_62_2
% 99.43/14.13 | gives:
% 99.43/14.13 | (49) (all_62_0 = 0 & relation_of2_as_subset(all_62_1, all_41_5, all_41_5) =
% 99.43/14.13 | 0 & the_InternalRel(all_41_6) = all_62_1 & $i(all_62_1)) | ( ~
% 99.43/14.13 | (all_62_2 = 0) & rel_str(all_41_6) = all_62_2)
% 99.43/14.13 |
% 99.43/14.13 | DELTA: instantiating (44) with fresh symbols all_69_0, all_69_1 gives:
% 99.43/14.14 | (50) ( ~ (all_69_1 = 0) & rel_str(all_41_4) = all_69_1) |
% 99.43/14.14 | (the_InternalRel(all_41_4) = all_69_0 & $i(all_69_0) & ! [v0: $i] :
% 99.43/14.14 | ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~
% 99.43/14.14 | (element(v0, all_41_3) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int]
% 99.43/14.14 | : ? [v4: int] : ? [v5: int] : (( ~ (v3 = 0) & element(v1,
% 99.43/14.14 | all_41_3) = v3) | (((v5 = 0 & in(v2, all_69_0) = 0) | ( ~
% 99.43/14.14 | (v4 = 0) & related(all_41_4, v0, v1) = v4)) & ((v4 = 0 &
% 99.43/14.14 | related(all_41_4, v0, v1) = 0) | ( ~ (v5 = 0) & in(v2,
% 99.43/14.14 | all_69_0) = v5))))) & ! [v0: $i] : ! [v1: $i] : !
% 99.43/14.14 | [v2: any] : ( ~ (related(all_41_4, v0, v1) = v2) | ~ (element(v0,
% 99.43/14.14 | all_41_3) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ?
% 99.43/14.14 | [v4: $i] : ? [v5: int] : (( ~ (v3 = 0) & element(v1, all_41_3) =
% 99.43/14.14 | v3) | (( ~ (v2 = 0) | (v5 = 0 & ordered_pair(v0, v1) = v4 &
% 99.43/14.14 | in(v4, all_69_0) = 0 & $i(v4))) & (v2 = 0 | ( ~ (v5 = 0) &
% 99.43/14.14 | ordered_pair(v0, v1) = v4 & in(v4, all_69_0) = v5 &
% 99.43/14.14 | $i(v4)))))) & ! [v0: $i] : ! [v1: $i] : ( ~ (element(v1,
% 99.43/14.14 | all_41_3) = 0) | ~ (element(v0, all_41_3) = 0) | ~ $i(v1) |
% 99.43/14.14 | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: int] : (((v4 = 0 &
% 99.43/14.14 | ordered_pair(v0, v1) = v3 & in(v3, all_69_0) = 0 & $i(v3)) |
% 99.43/14.14 | ( ~ (v2 = 0) & related(all_41_4, v0, v1) = v2)) & ((v2 = 0 &
% 99.43/14.14 | related(all_41_4, v0, v1) = 0) | ( ~ (v4 = 0) &
% 99.43/14.14 | ordered_pair(v0, v1) = v3 & in(v3, all_69_0) = v4 &
% 99.43/14.14 | $i(v3))))))
% 99.43/14.14 |
% 99.43/14.14 | DELTA: instantiating (41) with fresh symbols all_70_0, all_70_1 gives:
% 99.43/14.14 | (51) ( ~ (all_70_1 = 0) & rel_str(all_41_6) = all_70_1) |
% 99.43/14.14 | (the_InternalRel(all_41_6) = all_70_0 & $i(all_70_0) & ! [v0: $i] :
% 99.43/14.14 | ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~
% 99.43/14.14 | (element(v0, all_41_5) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int]
% 99.43/14.14 | : ? [v4: int] : ? [v5: int] : (( ~ (v3 = 0) & element(v1,
% 99.43/14.14 | all_41_5) = v3) | (((v5 = 0 & in(v2, all_70_0) = 0) | ( ~
% 99.43/14.14 | (v4 = 0) & related(all_41_6, v0, v1) = v4)) & ((v4 = 0 &
% 99.43/14.14 | related(all_41_6, v0, v1) = 0) | ( ~ (v5 = 0) & in(v2,
% 99.43/14.14 | all_70_0) = v5))))) & ! [v0: $i] : ! [v1: $i] : !
% 99.43/14.14 | [v2: any] : ( ~ (related(all_41_6, v0, v1) = v2) | ~ (element(v0,
% 99.43/14.14 | all_41_5) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ?
% 99.43/14.14 | [v4: $i] : ? [v5: int] : (( ~ (v3 = 0) & element(v1, all_41_5) =
% 99.43/14.14 | v3) | (( ~ (v2 = 0) | (v5 = 0 & ordered_pair(v0, v1) = v4 &
% 99.43/14.14 | in(v4, all_70_0) = 0 & $i(v4))) & (v2 = 0 | ( ~ (v5 = 0) &
% 99.43/14.14 | ordered_pair(v0, v1) = v4 & in(v4, all_70_0) = v5 &
% 99.43/14.14 | $i(v4)))))) & ! [v0: $i] : ! [v1: $i] : ( ~ (element(v1,
% 99.43/14.14 | all_41_5) = 0) | ~ (element(v0, all_41_5) = 0) | ~ $i(v1) |
% 99.43/14.14 | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: int] : (((v4 = 0 &
% 99.43/14.14 | ordered_pair(v0, v1) = v3 & in(v3, all_70_0) = 0 & $i(v3)) |
% 99.43/14.14 | ( ~ (v2 = 0) & related(all_41_6, v0, v1) = v2)) & ((v2 = 0 &
% 99.43/14.14 | related(all_41_6, v0, v1) = 0) | ( ~ (v4 = 0) &
% 99.43/14.14 | ordered_pair(v0, v1) = v3 & in(v3, all_70_0) = v4 &
% 99.43/14.14 | $i(v3))))))
% 99.43/14.14 |
% 99.43/14.14 | DELTA: instantiating (38) with fresh symbols all_71_0, all_71_1 gives:
% 99.43/14.14 | (52) the_carrier(all_41_6) = all_71_1 & the_InternalRel(all_41_6) =
% 99.43/14.14 | all_71_0 & $i(all_71_0) & $i(all_71_1) & ! [v0: $i] : ! [v1: $i] :
% 99.43/14.14 | ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ (element(v0,
% 99.43/14.14 | all_71_1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4:
% 99.43/14.14 | int] : ? [v5: int] : (( ~ (v3 = 0) & element(v1, all_71_1) = v3)
% 99.43/14.14 | | (((v5 = 0 & in(v2, all_71_0) = 0) | ( ~ (v4 = 0) &
% 99.43/14.14 | related(all_41_6, v0, v1) = v4)) & ((v4 = 0 &
% 99.43/14.14 | related(all_41_6, v0, v1) = 0) | ( ~ (v5 = 0) & in(v2,
% 99.43/14.14 | all_71_0) = v5))))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 99.43/14.14 | any] : ( ~ (related(all_41_6, v0, v1) = v2) | ~ (element(v0,
% 99.43/14.14 | all_71_1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4:
% 99.43/14.14 | $i] : ? [v5: int] : (( ~ (v3 = 0) & element(v1, all_71_1) = v3) |
% 99.43/14.14 | (( ~ (v2 = 0) | (v5 = 0 & ordered_pair(v0, v1) = v4 & in(v4,
% 99.43/14.14 | all_71_0) = 0 & $i(v4))) & (v2 = 0 | ( ~ (v5 = 0) &
% 99.43/14.14 | ordered_pair(v0, v1) = v4 & in(v4, all_71_0) = v5 &
% 99.43/14.14 | $i(v4)))))) & ! [v0: $i] : ! [v1: $i] : ( ~ (element(v1,
% 99.43/14.14 | all_71_1) = 0) | ~ (element(v0, all_71_1) = 0) | ~ $i(v1) | ~
% 99.43/14.14 | $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: int] : (((v4 = 0 &
% 99.43/14.14 | ordered_pair(v0, v1) = v3 & in(v3, all_71_0) = 0 & $i(v3)) | (
% 99.43/14.14 | ~ (v2 = 0) & related(all_41_6, v0, v1) = v2)) & ((v2 = 0 &
% 99.43/14.14 | related(all_41_6, v0, v1) = 0) | ( ~ (v4 = 0) &
% 99.43/14.14 | ordered_pair(v0, v1) = v3 & in(v3, all_71_0) = v4 & $i(v3)))))
% 99.43/14.14 |
% 99.43/14.14 | ALPHA: (52) implies:
% 99.43/14.14 | (53) the_InternalRel(all_41_6) = all_71_0
% 99.43/14.14 |
% 99.43/14.14 | DELTA: instantiating (39) with fresh symbols all_81_0, all_81_1 gives:
% 99.43/14.15 | (54) the_carrier(all_41_6) = all_81_1 & the_InternalRel(all_41_6) =
% 99.43/14.15 | all_81_0 & $i(all_81_0) & $i(all_81_1) & ! [v0: $i] : ! [v1: $i] : (
% 99.43/14.15 | ~ (the_carrier(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int] :
% 99.43/14.15 | ? [v4: int] : ? [v5: $i] : ? [v6: int] : (( ~ (v2 = 0) &
% 99.43/14.15 | rel_str(v0) = v2) | (((v6 = 0 & v4 = 0 & the_InternalRel(v0) =
% 99.43/14.15 | v5 & subset(v5, all_81_0) = 0 & subset(v1, all_81_1) = 0 &
% 99.43/14.15 | $i(v5)) | ( ~ (v3 = 0) & subrelstr(v0, all_41_6) = v3)) &
% 99.43/14.15 | ((v3 = 0 & subrelstr(v0, all_41_6) = 0) | ( ~ (v6 = 0) &
% 99.43/14.15 | the_InternalRel(v0) = v5 & subset(v5, all_81_0) = v6 &
% 99.43/14.15 | $i(v5)) | ( ~ (v4 = 0) & subset(v1, all_81_1) = v4))))) & !
% 99.43/14.15 | [v0: $i] : ! [v1: any] : ( ~ (subrelstr(v0, all_41_6) = v1) | ~
% 99.43/14.15 | $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: int] : ? [v5: $i] :
% 99.43/14.15 | ? [v6: int] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (( ~ (v1 = 0) |
% 99.43/14.15 | (v6 = 0 & v4 = 0 & the_carrier(v0) = v3 & the_InternalRel(v0)
% 99.43/14.15 | = v5 & subset(v5, all_81_0) = 0 & subset(v3, all_81_1) = 0 &
% 99.43/14.15 | $i(v5) & $i(v3))) & (v1 = 0 | ( ~ (v6 = 0) &
% 99.43/14.15 | the_InternalRel(v0) = v5 & subset(v5, all_81_0) = v6 &
% 99.43/14.15 | $i(v5)) | ( ~ (v4 = 0) & the_carrier(v0) = v3 & subset(v3,
% 99.43/14.15 | all_81_1) = v4 & $i(v3)))))) & ! [v0: $i] : ! [v1: $i] :
% 99.43/14.15 | ( ~ (the_InternalRel(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3:
% 99.43/14.15 | int] : ? [v4: $i] : ? [v5: int] : ? [v6: int] : (( ~ (v2 = 0) &
% 99.43/14.15 | rel_str(v0) = v2) | (((v6 = 0 & v5 = 0 & the_carrier(v0) = v4 &
% 99.43/14.15 | subset(v4, all_81_1) = 0 & subset(v1, all_81_0) = 0 &
% 99.43/14.15 | $i(v4)) | ( ~ (v3 = 0) & subrelstr(v0, all_41_6) = v3)) &
% 99.43/14.15 | ((v3 = 0 & subrelstr(v0, all_41_6) = 0) | ( ~ (v6 = 0) &
% 99.43/14.15 | subset(v1, all_81_0) = v6) | ( ~ (v5 = 0) & the_carrier(v0)
% 99.43/14.15 | = v4 & subset(v4, all_81_1) = v5 & $i(v4)))))) & ! [v0: $i]
% 99.43/14.15 | : ( ~ (rel_str(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? [v2: $i] : ?
% 99.43/14.15 | [v3: int] : ? [v4: $i] : ? [v5: int] : (((v5 = 0 & v3 = 0 &
% 99.43/14.15 | the_carrier(v0) = v2 & the_InternalRel(v0) = v4 & subset(v4,
% 99.43/14.15 | all_81_0) = 0 & subset(v2, all_81_1) = 0 & $i(v4) & $i(v2))
% 99.43/14.15 | | ( ~ (v1 = 0) & subrelstr(v0, all_41_6) = v1)) & ((v1 = 0 &
% 99.43/14.15 | subrelstr(v0, all_41_6) = 0) | ( ~ (v5 = 0) &
% 99.43/14.15 | the_InternalRel(v0) = v4 & subset(v4, all_81_0) = v5 & $i(v4))
% 99.43/14.15 | | ( ~ (v3 = 0) & the_carrier(v0) = v2 & subset(v2, all_81_1) =
% 99.43/14.15 | v3 & $i(v2)))))
% 99.43/14.15 |
% 99.43/14.15 | ALPHA: (54) implies:
% 99.43/14.15 | (55) the_InternalRel(all_41_6) = all_81_0
% 99.43/14.15 | (56) ! [v0: $i] : ! [v1: any] : ( ~ (subrelstr(v0, all_41_6) = v1) | ~
% 99.43/14.15 | $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: int] : ? [v5: $i] :
% 99.43/14.15 | ? [v6: int] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (( ~ (v1 = 0) |
% 99.43/14.15 | (v6 = 0 & v4 = 0 & the_carrier(v0) = v3 & the_InternalRel(v0)
% 99.43/14.15 | = v5 & subset(v5, all_81_0) = 0 & subset(v3, all_81_1) = 0 &
% 99.43/14.15 | $i(v5) & $i(v3))) & (v1 = 0 | ( ~ (v6 = 0) &
% 99.43/14.15 | the_InternalRel(v0) = v5 & subset(v5, all_81_0) = v6 &
% 99.43/14.15 | $i(v5)) | ( ~ (v4 = 0) & the_carrier(v0) = v3 & subset(v3,
% 99.43/14.15 | all_81_1) = v4 & $i(v3))))))
% 99.50/14.15 | (57) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) |
% 99.50/14.15 | ? [v2: int] : ? [v3: int] : ? [v4: int] : ? [v5: $i] : ? [v6:
% 99.50/14.15 | int] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (((v6 = 0 & v4 = 0 &
% 99.50/14.15 | the_InternalRel(v0) = v5 & subset(v5, all_81_0) = 0 &
% 99.50/14.15 | subset(v1, all_81_1) = 0 & $i(v5)) | ( ~ (v3 = 0) &
% 99.50/14.15 | subrelstr(v0, all_41_6) = v3)) & ((v3 = 0 & subrelstr(v0,
% 99.50/14.15 | all_41_6) = 0) | ( ~ (v6 = 0) & the_InternalRel(v0) = v5 &
% 99.50/14.15 | subset(v5, all_81_0) = v6 & $i(v5)) | ( ~ (v4 = 0) &
% 99.50/14.15 | subset(v1, all_81_1) = v4)))))
% 99.50/14.15 |
% 99.50/14.15 | GROUND_INST: instantiating (56) with all_41_4, 0, simplifying with (23), (30)
% 99.50/14.15 | gives:
% 99.50/14.15 | (58) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ? [v3: $i] : ? [v4: int]
% 99.50/14.15 | : ((v4 = 0 & v2 = 0 & the_carrier(all_41_4) = v1 &
% 99.50/14.15 | the_InternalRel(all_41_4) = v3 & subset(v3, all_81_0) = 0 &
% 99.50/14.15 | subset(v1, all_81_1) = 0 & $i(v3) & $i(v1)) | ( ~ (v0 = 0) &
% 99.50/14.15 | rel_str(all_41_4) = v0))
% 99.50/14.15 |
% 99.50/14.15 | GROUND_INST: instantiating (57) with all_41_4, all_41_3, simplifying with
% 99.50/14.15 | (23), (33) gives:
% 99.50/14.15 | (59) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: $i] : ? [v4:
% 99.50/14.15 | int] : (( ~ (v0 = 0) & rel_str(all_41_4) = v0) | (((v4 = 0 & v2 = 0
% 99.50/14.15 | & the_InternalRel(all_41_4) = v3 & subset(v3, all_81_0) = 0 &
% 99.50/14.15 | subset(all_41_3, all_81_1) = 0 & $i(v3)) | ( ~ (v1 = 0) &
% 99.50/14.15 | subrelstr(all_41_4, all_41_6) = v1)) & ((v1 = 0 &
% 99.50/14.15 | subrelstr(all_41_4, all_41_6) = 0) | ( ~ (v4 = 0) &
% 99.50/14.15 | the_InternalRel(all_41_4) = v3 & subset(v3, all_81_0) = v4 &
% 99.50/14.15 | $i(v3)) | ( ~ (v2 = 0) & subset(all_41_3, all_81_1) = v2))))
% 99.50/14.15 |
% 99.50/14.15 | DELTA: instantiating (58) with fresh symbols all_84_0, all_84_1, all_84_2,
% 99.50/14.15 | all_84_3, all_84_4 gives:
% 99.50/14.16 | (60) (all_84_0 = 0 & all_84_2 = 0 & the_carrier(all_41_4) = all_84_3 &
% 99.50/14.16 | the_InternalRel(all_41_4) = all_84_1 & subset(all_84_1, all_81_0) =
% 99.50/14.16 | 0 & subset(all_84_3, all_81_1) = 0 & $i(all_84_1) & $i(all_84_3)) |
% 99.50/14.16 | ( ~ (all_84_4 = 0) & rel_str(all_41_4) = all_84_4)
% 99.50/14.16 |
% 99.50/14.16 | DELTA: instantiating (59) with fresh symbols all_86_0, all_86_1, all_86_2,
% 99.50/14.16 | all_86_3, all_86_4 gives:
% 99.50/14.16 | (61) ( ~ (all_86_4 = 0) & rel_str(all_41_4) = all_86_4) | (((all_86_0 = 0 &
% 99.50/14.16 | all_86_2 = 0 & the_InternalRel(all_41_4) = all_86_1 &
% 99.50/14.16 | subset(all_86_1, all_81_0) = 0 & subset(all_41_3, all_81_1) = 0
% 99.50/14.16 | & $i(all_86_1)) | ( ~ (all_86_3 = 0) & subrelstr(all_41_4,
% 99.50/14.16 | all_41_6) = all_86_3)) & ((all_86_3 = 0 & subrelstr(all_41_4,
% 99.50/14.16 | all_41_6) = 0) | ( ~ (all_86_0 = 0) &
% 99.50/14.16 | the_InternalRel(all_41_4) = all_86_1 & subset(all_86_1,
% 99.50/14.16 | all_81_0) = all_86_0 & $i(all_86_1)) | ( ~ (all_86_2 = 0) &
% 99.50/14.16 | subset(all_41_3, all_81_1) = all_86_2)))
% 99.50/14.16 |
% 99.50/14.16 | DELTA: instantiating (45) with fresh symbols all_89_0, all_89_1 gives:
% 99.50/14.16 | (62) ( ~ (all_89_1 = 0) & rel_str(all_41_4) = all_89_1) |
% 99.50/14.16 | (the_InternalRel(all_41_4) = all_89_0 & $i(all_89_0) & ! [v0: $i] :
% 99.50/14.16 | ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ? [v2: int] :
% 99.50/14.16 | ? [v3: int] : ? [v4: int] : ? [v5: $i] : ? [v6: int] : (( ~
% 99.50/14.16 | (v2 = 0) & rel_str(v0) = v2) | (((v6 = 0 & v4 = 0 &
% 99.50/14.16 | the_InternalRel(v0) = v5 & subset(v5, all_89_0) = 0 &
% 99.50/14.16 | subset(v1, all_41_3) = 0 & $i(v5)) | ( ~ (v3 = 0) &
% 99.50/14.16 | subrelstr(v0, all_41_4) = v3)) & ((v3 = 0 & subrelstr(v0,
% 99.50/14.16 | all_41_4) = 0) | ( ~ (v6 = 0) & the_InternalRel(v0) = v5
% 99.50/14.16 | & subset(v5, all_89_0) = v6 & $i(v5)) | ( ~ (v4 = 0) &
% 99.50/14.16 | subset(v1, all_41_3) = v4))))) & ! [v0: $i] : ! [v1:
% 99.50/14.16 | any] : ( ~ (subrelstr(v0, all_41_4) = v1) | ~ $i(v0) | ? [v2:
% 99.50/14.16 | int] : ? [v3: $i] : ? [v4: int] : ? [v5: $i] : ? [v6: int] :
% 99.50/14.16 | (( ~ (v2 = 0) & rel_str(v0) = v2) | (( ~ (v1 = 0) | (v6 = 0 & v4 =
% 99.50/14.16 | 0 & the_carrier(v0) = v3 & the_InternalRel(v0) = v5 &
% 99.50/14.16 | subset(v5, all_89_0) = 0 & subset(v3, all_41_3) = 0 &
% 99.50/14.16 | $i(v5) & $i(v3))) & (v1 = 0 | ( ~ (v6 = 0) &
% 99.50/14.16 | the_InternalRel(v0) = v5 & subset(v5, all_89_0) = v6 &
% 99.50/14.16 | $i(v5)) | ( ~ (v4 = 0) & the_carrier(v0) = v3 & subset(v3,
% 99.50/14.16 | all_41_3) = v4 & $i(v3)))))) & ! [v0: $i] : ! [v1: $i]
% 99.50/14.16 | : ( ~ (the_InternalRel(v0) = v1) | ~ $i(v0) | ? [v2: int] : ?
% 99.50/14.16 | [v3: int] : ? [v4: $i] : ? [v5: int] : ? [v6: int] : (( ~ (v2 =
% 99.50/14.16 | 0) & rel_str(v0) = v2) | (((v6 = 0 & v5 = 0 &
% 99.50/14.16 | the_carrier(v0) = v4 & subset(v4, all_41_3) = 0 &
% 99.50/14.16 | subset(v1, all_89_0) = 0 & $i(v4)) | ( ~ (v3 = 0) &
% 99.50/14.16 | subrelstr(v0, all_41_4) = v3)) & ((v3 = 0 & subrelstr(v0,
% 99.50/14.16 | all_41_4) = 0) | ( ~ (v6 = 0) & subset(v1, all_89_0) =
% 99.50/14.16 | v6) | ( ~ (v5 = 0) & the_carrier(v0) = v4 & subset(v4,
% 99.50/14.16 | all_41_3) = v5 & $i(v4)))))) & ! [v0: $i] : ( ~
% 99.50/14.16 | (rel_str(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? [v2: $i] : ?
% 99.50/14.16 | [v3: int] : ? [v4: $i] : ? [v5: int] : (((v5 = 0 & v3 = 0 &
% 99.50/14.16 | the_carrier(v0) = v2 & the_InternalRel(v0) = v4 & subset(v4,
% 99.50/14.16 | all_89_0) = 0 & subset(v2, all_41_3) = 0 & $i(v4) &
% 99.50/14.16 | $i(v2)) | ( ~ (v1 = 0) & subrelstr(v0, all_41_4) = v1)) &
% 99.50/14.16 | ((v1 = 0 & subrelstr(v0, all_41_4) = 0) | ( ~ (v5 = 0) &
% 99.50/14.16 | the_InternalRel(v0) = v4 & subset(v4, all_89_0) = v5 &
% 99.50/14.16 | $i(v4)) | ( ~ (v3 = 0) & the_carrier(v0) = v2 & subset(v2,
% 99.50/14.16 | all_41_3) = v3 & $i(v2))))))
% 99.50/14.16 |
% 99.50/14.16 | DELTA: instantiating (42) with fresh symbols all_90_0, all_90_1 gives:
% 99.50/14.17 | (63) ( ~ (all_90_1 = 0) & rel_str(all_41_6) = all_90_1) |
% 99.50/14.17 | (the_InternalRel(all_41_6) = all_90_0 & $i(all_90_0) & ! [v0: $i] :
% 99.50/14.17 | ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ? [v2: int] :
% 99.50/14.17 | ? [v3: int] : ? [v4: int] : ? [v5: $i] : ? [v6: int] : (( ~
% 99.50/14.17 | (v2 = 0) & rel_str(v0) = v2) | (((v6 = 0 & v4 = 0 &
% 99.50/14.17 | the_InternalRel(v0) = v5 & subset(v5, all_90_0) = 0 &
% 99.50/14.17 | subset(v1, all_41_5) = 0 & $i(v5)) | ( ~ (v3 = 0) &
% 99.50/14.17 | subrelstr(v0, all_41_6) = v3)) & ((v3 = 0 & subrelstr(v0,
% 99.50/14.17 | all_41_6) = 0) | ( ~ (v6 = 0) & the_InternalRel(v0) = v5
% 99.50/14.17 | & subset(v5, all_90_0) = v6 & $i(v5)) | ( ~ (v4 = 0) &
% 99.50/14.17 | subset(v1, all_41_5) = v4))))) & ! [v0: $i] : ! [v1:
% 99.50/14.17 | any] : ( ~ (subrelstr(v0, all_41_6) = v1) | ~ $i(v0) | ? [v2:
% 99.50/14.17 | int] : ? [v3: $i] : ? [v4: int] : ? [v5: $i] : ? [v6: int] :
% 99.50/14.17 | (( ~ (v2 = 0) & rel_str(v0) = v2) | (( ~ (v1 = 0) | (v6 = 0 & v4 =
% 99.50/14.17 | 0 & the_carrier(v0) = v3 & the_InternalRel(v0) = v5 &
% 99.50/14.17 | subset(v5, all_90_0) = 0 & subset(v3, all_41_5) = 0 &
% 99.50/14.17 | $i(v5) & $i(v3))) & (v1 = 0 | ( ~ (v6 = 0) &
% 99.50/14.17 | the_InternalRel(v0) = v5 & subset(v5, all_90_0) = v6 &
% 99.50/14.17 | $i(v5)) | ( ~ (v4 = 0) & the_carrier(v0) = v3 & subset(v3,
% 99.50/14.17 | all_41_5) = v4 & $i(v3)))))) & ! [v0: $i] : ! [v1: $i]
% 99.50/14.17 | : ( ~ (the_InternalRel(v0) = v1) | ~ $i(v0) | ? [v2: int] : ?
% 99.50/14.17 | [v3: int] : ? [v4: $i] : ? [v5: int] : ? [v6: int] : (( ~ (v2 =
% 99.50/14.17 | 0) & rel_str(v0) = v2) | (((v6 = 0 & v5 = 0 &
% 99.50/14.17 | the_carrier(v0) = v4 & subset(v4, all_41_5) = 0 &
% 99.50/14.17 | subset(v1, all_90_0) = 0 & $i(v4)) | ( ~ (v3 = 0) &
% 99.50/14.17 | subrelstr(v0, all_41_6) = v3)) & ((v3 = 0 & subrelstr(v0,
% 99.50/14.17 | all_41_6) = 0) | ( ~ (v6 = 0) & subset(v1, all_90_0) =
% 99.50/14.17 | v6) | ( ~ (v5 = 0) & the_carrier(v0) = v4 & subset(v4,
% 99.50/14.17 | all_41_5) = v5 & $i(v4)))))) & ! [v0: $i] : ( ~
% 99.50/14.17 | (rel_str(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? [v2: $i] : ?
% 99.50/14.17 | [v3: int] : ? [v4: $i] : ? [v5: int] : (((v5 = 0 & v3 = 0 &
% 99.50/14.17 | the_carrier(v0) = v2 & the_InternalRel(v0) = v4 & subset(v4,
% 99.50/14.17 | all_90_0) = 0 & subset(v2, all_41_5) = 0 & $i(v4) &
% 99.50/14.17 | $i(v2)) | ( ~ (v1 = 0) & subrelstr(v0, all_41_6) = v1)) &
% 99.50/14.17 | ((v1 = 0 & subrelstr(v0, all_41_6) = 0) | ( ~ (v5 = 0) &
% 99.50/14.17 | the_InternalRel(v0) = v4 & subset(v4, all_90_0) = v5 &
% 99.50/14.17 | $i(v4)) | ( ~ (v3 = 0) & the_carrier(v0) = v2 & subset(v2,
% 99.50/14.17 | all_41_5) = v3 & $i(v2))))))
% 99.50/14.17 |
% 99.50/14.17 | BETA: splitting (48) gives:
% 99.50/14.17 |
% 99.50/14.17 | Case 1:
% 99.50/14.17 | |
% 99.50/14.17 | | (64) all_61_0 = 0 & relation_of2_as_subset(all_61_1, all_41_3, all_41_3)
% 99.50/14.17 | | = 0 & the_InternalRel(all_41_4) = all_61_1 & $i(all_61_1)
% 99.50/14.17 | |
% 99.50/14.17 | | ALPHA: (64) implies:
% 99.50/14.17 | | (65) the_InternalRel(all_41_4) = all_61_1
% 99.50/14.17 | |
% 99.50/14.17 | | BETA: splitting (63) gives:
% 99.50/14.17 | |
% 99.50/14.17 | | Case 1:
% 99.50/14.17 | | |
% 99.50/14.17 | | | (66) ~ (all_90_1 = 0) & rel_str(all_41_6) = all_90_1
% 99.50/14.17 | | |
% 99.50/14.17 | | | ALPHA: (66) implies:
% 99.50/14.17 | | | (67) ~ (all_90_1 = 0)
% 99.50/14.17 | | | (68) rel_str(all_41_6) = all_90_1
% 99.50/14.17 | | |
% 99.50/14.17 | | | GROUND_INST: instantiating (14) with 0, all_90_1, all_41_6, simplifying
% 99.50/14.17 | | | with (31), (68) gives:
% 99.50/14.17 | | | (69) all_90_1 = 0
% 99.50/14.17 | | |
% 99.50/14.17 | | | REDUCE: (67), (69) imply:
% 99.50/14.17 | | | (70) $false
% 99.50/14.17 | | |
% 99.50/14.17 | | | CLOSE: (70) is inconsistent.
% 99.50/14.17 | | |
% 99.50/14.17 | | Case 2:
% 99.50/14.17 | | |
% 99.50/14.17 | | | (71) the_InternalRel(all_41_6) = all_90_0 & $i(all_90_0) & ! [v0: $i]
% 99.50/14.17 | | | : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ? [v2:
% 99.50/14.17 | | | int] : ? [v3: int] : ? [v4: int] : ? [v5: $i] : ? [v6:
% 99.50/14.17 | | | int] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (((v6 = 0 & v4 = 0
% 99.50/14.17 | | | & the_InternalRel(v0) = v5 & subset(v5, all_90_0) = 0 &
% 99.50/14.17 | | | subset(v1, all_41_5) = 0 & $i(v5)) | ( ~ (v3 = 0) &
% 99.50/14.17 | | | subrelstr(v0, all_41_6) = v3)) & ((v3 = 0 &
% 99.50/14.17 | | | subrelstr(v0, all_41_6) = 0) | ( ~ (v6 = 0) &
% 99.50/14.17 | | | the_InternalRel(v0) = v5 & subset(v5, all_90_0) = v6 &
% 99.50/14.17 | | | $i(v5)) | ( ~ (v4 = 0) & subset(v1, all_41_5) = v4)))))
% 99.50/14.17 | | | & ! [v0: $i] : ! [v1: any] : ( ~ (subrelstr(v0, all_41_6) = v1)
% 99.50/14.17 | | | | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: int] : ?
% 99.50/14.17 | | | [v5: $i] : ? [v6: int] : (( ~ (v2 = 0) & rel_str(v0) = v2) | ((
% 99.50/14.17 | | | ~ (v1 = 0) | (v6 = 0 & v4 = 0 & the_carrier(v0) = v3 &
% 99.50/14.17 | | | the_InternalRel(v0) = v5 & subset(v5, all_90_0) = 0 &
% 99.50/14.17 | | | subset(v3, all_41_5) = 0 & $i(v5) & $i(v3))) & (v1 = 0 |
% 99.50/14.17 | | | ( ~ (v6 = 0) & the_InternalRel(v0) = v5 & subset(v5,
% 99.50/14.17 | | | all_90_0) = v6 & $i(v5)) | ( ~ (v4 = 0) &
% 99.50/14.17 | | | the_carrier(v0) = v3 & subset(v3, all_41_5) = v4 &
% 99.50/14.17 | | | $i(v3)))))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 99.50/14.17 | | | (the_InternalRel(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3:
% 99.50/14.17 | | | int] : ? [v4: $i] : ? [v5: int] : ? [v6: int] : (( ~ (v2 =
% 99.50/14.17 | | | 0) & rel_str(v0) = v2) | (((v6 = 0 & v5 = 0 &
% 99.50/14.17 | | | the_carrier(v0) = v4 & subset(v4, all_41_5) = 0 &
% 99.50/14.17 | | | subset(v1, all_90_0) = 0 & $i(v4)) | ( ~ (v3 = 0) &
% 99.50/14.17 | | | subrelstr(v0, all_41_6) = v3)) & ((v3 = 0 &
% 99.50/14.17 | | | subrelstr(v0, all_41_6) = 0) | ( ~ (v6 = 0) & subset(v1,
% 99.50/14.17 | | | all_90_0) = v6) | ( ~ (v5 = 0) & the_carrier(v0) = v4
% 99.50/14.17 | | | & subset(v4, all_41_5) = v5 & $i(v4)))))) & ! [v0: $i]
% 99.50/14.17 | | | : ( ~ (rel_str(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? [v2: $i] :
% 99.50/14.17 | | | ? [v3: int] : ? [v4: $i] : ? [v5: int] : (((v5 = 0 & v3 = 0 &
% 99.50/14.17 | | | the_carrier(v0) = v2 & the_InternalRel(v0) = v4 &
% 99.50/14.17 | | | subset(v4, all_90_0) = 0 & subset(v2, all_41_5) = 0 &
% 99.50/14.17 | | | $i(v4) & $i(v2)) | ( ~ (v1 = 0) & subrelstr(v0, all_41_6)
% 99.50/14.17 | | | = v1)) & ((v1 = 0 & subrelstr(v0, all_41_6) = 0) | ( ~ (v5
% 99.50/14.17 | | | = 0) & the_InternalRel(v0) = v4 & subset(v4, all_90_0) =
% 99.50/14.17 | | | v5 & $i(v4)) | ( ~ (v3 = 0) & the_carrier(v0) = v2 &
% 99.50/14.17 | | | subset(v2, all_41_5) = v3 & $i(v2)))))
% 99.50/14.17 | | |
% 99.50/14.17 | | | ALPHA: (71) implies:
% 99.50/14.17 | | | (72) the_InternalRel(all_41_6) = all_90_0
% 99.50/14.18 | | | (73) ! [v0: $i] : ! [v1: any] : ( ~ (subrelstr(v0, all_41_6) = v1) |
% 99.50/14.18 | | | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: int] : ? [v5:
% 99.50/14.18 | | | $i] : ? [v6: int] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (( ~
% 99.50/14.18 | | | (v1 = 0) | (v6 = 0 & v4 = 0 & the_carrier(v0) = v3 &
% 99.50/14.18 | | | the_InternalRel(v0) = v5 & subset(v5, all_90_0) = 0 &
% 99.50/14.18 | | | subset(v3, all_41_5) = 0 & $i(v5) & $i(v3))) & (v1 = 0 |
% 99.50/14.18 | | | ( ~ (v6 = 0) & the_InternalRel(v0) = v5 & subset(v5,
% 99.50/14.18 | | | all_90_0) = v6 & $i(v5)) | ( ~ (v4 = 0) &
% 99.50/14.18 | | | the_carrier(v0) = v3 & subset(v3, all_41_5) = v4 &
% 99.50/14.18 | | | $i(v3))))))
% 99.50/14.18 | | | (74) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0)
% 99.50/14.18 | | | | ? [v2: int] : ? [v3: int] : ? [v4: int] : ? [v5: $i] : ?
% 99.50/14.18 | | | [v6: int] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (((v6 = 0 & v4 =
% 99.50/14.18 | | | 0 & the_InternalRel(v0) = v5 & subset(v5, all_90_0) = 0
% 99.50/14.18 | | | & subset(v1, all_41_5) = 0 & $i(v5)) | ( ~ (v3 = 0) &
% 99.50/14.18 | | | subrelstr(v0, all_41_6) = v3)) & ((v3 = 0 &
% 99.50/14.18 | | | subrelstr(v0, all_41_6) = 0) | ( ~ (v6 = 0) &
% 99.50/14.18 | | | the_InternalRel(v0) = v5 & subset(v5, all_90_0) = v6 &
% 99.50/14.18 | | | $i(v5)) | ( ~ (v4 = 0) & subset(v1, all_41_5) = v4)))))
% 99.50/14.18 | | |
% 99.50/14.18 | | | GROUND_INST: instantiating (73) with all_41_4, 0, simplifying with (23),
% 99.50/14.18 | | | (30) gives:
% 99.50/14.18 | | | (75) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ? [v3: $i] : ? [v4:
% 99.50/14.18 | | | int] : ((v4 = 0 & v2 = 0 & the_carrier(all_41_4) = v1 &
% 99.50/14.18 | | | the_InternalRel(all_41_4) = v3 & subset(v3, all_90_0) = 0 &
% 99.50/14.18 | | | subset(v1, all_41_5) = 0 & $i(v3) & $i(v1)) | ( ~ (v0 = 0) &
% 99.50/14.18 | | | rel_str(all_41_4) = v0))
% 99.50/14.18 | | |
% 99.50/14.18 | | | GROUND_INST: instantiating (74) with all_41_4, all_41_3, simplifying with
% 99.50/14.18 | | | (23), (33) gives:
% 99.50/14.18 | | | (76) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: $i] : ? [v4:
% 99.50/14.18 | | | int] : (( ~ (v0 = 0) & rel_str(all_41_4) = v0) | (((v4 = 0 & v2
% 99.50/14.18 | | | = 0 & the_InternalRel(all_41_4) = v3 & subset(v3,
% 99.50/14.18 | | | all_90_0) = 0 & subset(all_41_3, all_41_5) = 0 & $i(v3))
% 99.50/14.18 | | | | ( ~ (v1 = 0) & subrelstr(all_41_4, all_41_6) = v1)) & ((v1
% 99.50/14.18 | | | = 0 & subrelstr(all_41_4, all_41_6) = 0) | ( ~ (v4 = 0) &
% 99.50/14.18 | | | the_InternalRel(all_41_4) = v3 & subset(v3, all_90_0) = v4
% 99.50/14.18 | | | & $i(v3)) | ( ~ (v2 = 0) & subset(all_41_3, all_41_5) =
% 99.50/14.18 | | | v2))))
% 99.50/14.18 | | |
% 99.50/14.18 | | | DELTA: instantiating (75) with fresh symbols all_100_0, all_100_1,
% 99.50/14.18 | | | all_100_2, all_100_3, all_100_4 gives:
% 99.50/14.18 | | | (77) (all_100_0 = 0 & all_100_2 = 0 & the_carrier(all_41_4) = all_100_3
% 99.50/14.18 | | | & the_InternalRel(all_41_4) = all_100_1 & subset(all_100_1,
% 99.50/14.18 | | | all_90_0) = 0 & subset(all_100_3, all_41_5) = 0 &
% 99.50/14.18 | | | $i(all_100_1) & $i(all_100_3)) | ( ~ (all_100_4 = 0) &
% 99.50/14.18 | | | rel_str(all_41_4) = all_100_4)
% 99.50/14.18 | | |
% 99.50/14.18 | | | DELTA: instantiating (76) with fresh symbols all_102_0, all_102_1,
% 99.50/14.18 | | | all_102_2, all_102_3, all_102_4 gives:
% 99.50/14.18 | | | (78) ( ~ (all_102_4 = 0) & rel_str(all_41_4) = all_102_4) |
% 99.50/14.18 | | | (((all_102_0 = 0 & all_102_2 = 0 & the_InternalRel(all_41_4) =
% 99.50/14.18 | | | all_102_1 & subset(all_102_1, all_90_0) = 0 &
% 99.50/14.18 | | | subset(all_41_3, all_41_5) = 0 & $i(all_102_1)) | ( ~
% 99.50/14.18 | | | (all_102_3 = 0) & subrelstr(all_41_4, all_41_6) =
% 99.50/14.18 | | | all_102_3)) & ((all_102_3 = 0 & subrelstr(all_41_4,
% 99.50/14.18 | | | all_41_6) = 0) | ( ~ (all_102_0 = 0) &
% 99.50/14.18 | | | the_InternalRel(all_41_4) = all_102_1 & subset(all_102_1,
% 99.50/14.18 | | | all_90_0) = all_102_0 & $i(all_102_1)) | ( ~ (all_102_2 =
% 99.50/14.18 | | | 0) & subset(all_41_3, all_41_5) = all_102_2)))
% 99.50/14.18 | | |
% 99.50/14.18 | | | BETA: splitting (60) gives:
% 99.50/14.18 | | |
% 99.50/14.18 | | | Case 1:
% 99.50/14.18 | | | |
% 99.50/14.18 | | | | (79) all_84_0 = 0 & all_84_2 = 0 & the_carrier(all_41_4) = all_84_3 &
% 99.50/14.18 | | | | the_InternalRel(all_41_4) = all_84_1 & subset(all_84_1,
% 99.50/14.18 | | | | all_81_0) = 0 & subset(all_84_3, all_81_1) = 0 & $i(all_84_1)
% 99.50/14.18 | | | | & $i(all_84_3)
% 99.50/14.18 | | | |
% 99.50/14.18 | | | | ALPHA: (79) implies:
% 99.50/14.18 | | | | (80) subset(all_84_1, all_81_0) = 0
% 99.50/14.18 | | | | (81) the_InternalRel(all_41_4) = all_84_1
% 99.50/14.18 | | | |
% 99.50/14.18 | | | | BETA: splitting (50) gives:
% 99.50/14.18 | | | |
% 99.50/14.18 | | | | Case 1:
% 99.50/14.18 | | | | |
% 99.50/14.18 | | | | | (82) ~ (all_69_1 = 0) & rel_str(all_41_4) = all_69_1
% 99.50/14.18 | | | | |
% 99.50/14.18 | | | | | ALPHA: (82) implies:
% 99.50/14.18 | | | | | (83) ~ (all_69_1 = 0)
% 99.50/14.18 | | | | | (84) rel_str(all_41_4) = all_69_1
% 99.50/14.18 | | | | |
% 99.50/14.18 | | | | | GROUND_INST: instantiating (14) with 0, all_69_1, all_41_4,
% 99.50/14.18 | | | | | simplifying with (36), (84) gives:
% 99.50/14.18 | | | | | (85) all_69_1 = 0
% 99.50/14.18 | | | | |
% 99.50/14.18 | | | | | REDUCE: (83), (85) imply:
% 99.50/14.18 | | | | | (86) $false
% 99.50/14.18 | | | | |
% 99.50/14.18 | | | | | CLOSE: (86) is inconsistent.
% 99.50/14.18 | | | | |
% 99.50/14.18 | | | | Case 2:
% 99.50/14.18 | | | | |
% 99.50/14.19 | | | | | (87) the_InternalRel(all_41_4) = all_69_0 & $i(all_69_0) & ! [v0:
% 99.50/14.19 | | | | | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1)
% 99.50/14.19 | | | | | = v2) | ~ (element(v0, all_41_3) = 0) | ~ $i(v1) | ~
% 99.50/14.19 | | | | | $i(v0) | ? [v3: int] : ? [v4: int] : ? [v5: int] : (( ~
% 99.50/14.19 | | | | | (v3 = 0) & element(v1, all_41_3) = v3) | (((v5 = 0 &
% 99.50/14.19 | | | | | in(v2, all_69_0) = 0) | ( ~ (v4 = 0) &
% 99.50/14.19 | | | | | related(all_41_4, v0, v1) = v4)) & ((v4 = 0 &
% 99.50/14.19 | | | | | related(all_41_4, v0, v1) = 0) | ( ~ (v5 = 0) &
% 99.50/14.19 | | | | | in(v2, all_69_0) = v5))))) & ! [v0: $i] : ! [v1:
% 99.50/14.19 | | | | | $i] : ! [v2: any] : ( ~ (related(all_41_4, v0, v1) = v2) |
% 99.50/14.19 | | | | | ~ (element(v0, all_41_3) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 99.50/14.19 | | | | | [v3: int] : ? [v4: $i] : ? [v5: int] : (( ~ (v3 = 0) &
% 99.50/14.19 | | | | | element(v1, all_41_3) = v3) | (( ~ (v2 = 0) | (v5 = 0 &
% 99.50/14.19 | | | | | ordered_pair(v0, v1) = v4 & in(v4, all_69_0) = 0 &
% 99.50/14.19 | | | | | $i(v4))) & (v2 = 0 | ( ~ (v5 = 0) & ordered_pair(v0,
% 99.50/14.19 | | | | | v1) = v4 & in(v4, all_69_0) = v5 & $i(v4)))))) &
% 99.50/14.19 | | | | | ! [v0: $i] : ! [v1: $i] : ( ~ (element(v1, all_41_3) = 0) |
% 99.50/14.19 | | | | | ~ (element(v0, all_41_3) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 99.50/14.19 | | | | | [v2: int] : ? [v3: $i] : ? [v4: int] : (((v4 = 0 &
% 99.50/14.19 | | | | | ordered_pair(v0, v1) = v3 & in(v3, all_69_0) = 0 &
% 99.50/14.19 | | | | | $i(v3)) | ( ~ (v2 = 0) & related(all_41_4, v0, v1) =
% 99.50/14.19 | | | | | v2)) & ((v2 = 0 & related(all_41_4, v0, v1) = 0) | ( ~
% 99.50/14.19 | | | | | (v4 = 0) & ordered_pair(v0, v1) = v3 & in(v3,
% 99.50/14.19 | | | | | all_69_0) = v4 & $i(v3)))))
% 99.50/14.19 | | | | |
% 99.50/14.19 | | | | | ALPHA: (87) implies:
% 99.50/14.19 | | | | | (88) $i(all_69_0)
% 99.50/14.19 | | | | | (89) the_InternalRel(all_41_4) = all_69_0
% 99.50/14.19 | | | | | (90) ! [v0: $i] : ! [v1: $i] : ( ~ (element(v1, all_41_3) = 0) |
% 99.50/14.19 | | | | | ~ (element(v0, all_41_3) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 99.50/14.19 | | | | | [v2: int] : ? [v3: $i] : ? [v4: int] : (((v4 = 0 &
% 99.50/14.19 | | | | | ordered_pair(v0, v1) = v3 & in(v3, all_69_0) = 0 &
% 99.50/14.19 | | | | | $i(v3)) | ( ~ (v2 = 0) & related(all_41_4, v0, v1) =
% 99.50/14.19 | | | | | v2)) & ((v2 = 0 & related(all_41_4, v0, v1) = 0) | ( ~
% 99.50/14.19 | | | | | (v4 = 0) & ordered_pair(v0, v1) = v3 & in(v3,
% 99.50/14.19 | | | | | all_69_0) = v4 & $i(v3)))))
% 99.50/14.19 | | | | | (91) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 99.50/14.19 | | | | | (related(all_41_4, v0, v1) = v2) | ~ (element(v0, all_41_3)
% 99.50/14.19 | | | | | = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i]
% 99.50/14.19 | | | | | : ? [v5: int] : (( ~ (v3 = 0) & element(v1, all_41_3) = v3)
% 99.50/14.19 | | | | | | (( ~ (v2 = 0) | (v5 = 0 & ordered_pair(v0, v1) = v4 &
% 99.50/14.19 | | | | | in(v4, all_69_0) = 0 & $i(v4))) & (v2 = 0 | ( ~ (v5
% 99.50/14.19 | | | | | = 0) & ordered_pair(v0, v1) = v4 & in(v4,
% 99.50/14.19 | | | | | all_69_0) = v5 & $i(v4))))))
% 99.50/14.19 | | | | |
% 99.50/14.19 | | | | | GROUND_INST: instantiating (90) with all_41_2, all_41_1, simplifying
% 99.50/14.19 | | | | | with (24), (25), (27), (29) gives:
% 99.50/14.19 | | | | | (92) ? [v0: int] : ? [v1: $i] : ? [v2: int] : (((v2 = 0 &
% 99.50/14.19 | | | | | ordered_pair(all_41_2, all_41_1) = v1 & in(v1, all_69_0)
% 99.50/14.19 | | | | | = 0 & $i(v1)) | ( ~ (v0 = 0) & related(all_41_4,
% 99.50/14.19 | | | | | all_41_2, all_41_1) = v0)) & ((v0 = 0 &
% 99.50/14.19 | | | | | related(all_41_4, all_41_2, all_41_1) = 0) | ( ~ (v2 =
% 99.50/14.19 | | | | | 0) & ordered_pair(all_41_2, all_41_1) = v1 & in(v1,
% 99.50/14.19 | | | | | all_69_0) = v2 & $i(v1))))
% 99.50/14.19 | | | | |
% 99.50/14.19 | | | | | GROUND_INST: instantiating (91) with all_41_2, all_41_1, 0,
% 99.50/14.19 | | | | | simplifying with (24), (25), (27), (35) gives:
% 99.50/14.19 | | | | | (93) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ((v2 = 0 &
% 99.50/14.19 | | | | | ordered_pair(all_41_2, all_41_1) = v1 & in(v1, all_69_0) =
% 99.50/14.19 | | | | | 0 & $i(v1)) | ( ~ (v0 = 0) & element(all_41_1, all_41_3) =
% 99.50/14.19 | | | | | v0))
% 99.50/14.19 | | | | |
% 99.50/14.19 | | | | | DELTA: instantiating (93) with fresh symbols all_119_0, all_119_1,
% 99.50/14.19 | | | | | all_119_2 gives:
% 99.50/14.19 | | | | | (94) (all_119_0 = 0 & ordered_pair(all_41_2, all_41_1) = all_119_1
% 99.50/14.19 | | | | | & in(all_119_1, all_69_0) = 0 & $i(all_119_1)) | ( ~
% 99.50/14.19 | | | | | (all_119_2 = 0) & element(all_41_1, all_41_3) = all_119_2)
% 99.50/14.19 | | | | |
% 99.50/14.19 | | | | | DELTA: instantiating (92) with fresh symbols all_123_0, all_123_1,
% 99.50/14.19 | | | | | all_123_2 gives:
% 99.50/14.19 | | | | | (95) ((all_123_0 = 0 & ordered_pair(all_41_2, all_41_1) = all_123_1
% 99.50/14.19 | | | | | & in(all_123_1, all_69_0) = 0 & $i(all_123_1)) | ( ~
% 99.50/14.19 | | | | | (all_123_2 = 0) & related(all_41_4, all_41_2, all_41_1) =
% 99.50/14.19 | | | | | all_123_2)) & ((all_123_2 = 0 & related(all_41_4,
% 99.50/14.19 | | | | | all_41_2, all_41_1) = 0) | ( ~ (all_123_0 = 0) &
% 99.50/14.19 | | | | | ordered_pair(all_41_2, all_41_1) = all_123_1 &
% 99.50/14.19 | | | | | in(all_123_1, all_69_0) = all_123_0 & $i(all_123_1)))
% 99.50/14.19 | | | | |
% 99.50/14.19 | | | | | ALPHA: (95) implies:
% 99.50/14.19 | | | | | (96) (all_123_0 = 0 & ordered_pair(all_41_2, all_41_1) = all_123_1
% 99.50/14.19 | | | | | & in(all_123_1, all_69_0) = 0 & $i(all_123_1)) | ( ~
% 99.50/14.19 | | | | | (all_123_2 = 0) & related(all_41_4, all_41_2, all_41_1) =
% 99.50/14.19 | | | | | all_123_2)
% 99.50/14.19 | | | | |
% 99.50/14.19 | | | | | BETA: splitting (94) gives:
% 99.50/14.19 | | | | |
% 99.50/14.19 | | | | | Case 1:
% 99.50/14.19 | | | | | |
% 99.50/14.19 | | | | | | (97) all_119_0 = 0 & ordered_pair(all_41_2, all_41_1) = all_119_1
% 99.50/14.19 | | | | | | & in(all_119_1, all_69_0) = 0 & $i(all_119_1)
% 99.50/14.19 | | | | | |
% 99.50/14.19 | | | | | | ALPHA: (97) implies:
% 99.50/14.19 | | | | | | (98) in(all_119_1, all_69_0) = 0
% 99.50/14.19 | | | | | | (99) ordered_pair(all_41_2, all_41_1) = all_119_1
% 99.50/14.19 | | | | | |
% 99.50/14.19 | | | | | | BETA: splitting (61) gives:
% 99.50/14.19 | | | | | |
% 99.50/14.19 | | | | | | Case 1:
% 99.50/14.19 | | | | | | |
% 99.50/14.19 | | | | | | | (100) ~ (all_86_4 = 0) & rel_str(all_41_4) = all_86_4
% 99.50/14.19 | | | | | | |
% 99.50/14.19 | | | | | | | ALPHA: (100) implies:
% 99.50/14.19 | | | | | | | (101) ~ (all_86_4 = 0)
% 99.50/14.19 | | | | | | | (102) rel_str(all_41_4) = all_86_4
% 99.50/14.19 | | | | | | |
% 99.50/14.19 | | | | | | | GROUND_INST: instantiating (14) with 0, all_86_4, all_41_4,
% 99.50/14.19 | | | | | | | simplifying with (36), (102) gives:
% 99.50/14.20 | | | | | | | (103) all_86_4 = 0
% 99.50/14.20 | | | | | | |
% 99.50/14.20 | | | | | | | REDUCE: (101), (103) imply:
% 99.50/14.20 | | | | | | | (104) $false
% 99.50/14.20 | | | | | | |
% 99.50/14.20 | | | | | | | CLOSE: (104) is inconsistent.
% 99.50/14.20 | | | | | | |
% 99.50/14.20 | | | | | | Case 2:
% 99.50/14.20 | | | | | | |
% 99.50/14.20 | | | | | | | (105) ((all_86_0 = 0 & all_86_2 = 0 & the_InternalRel(all_41_4)
% 99.50/14.20 | | | | | | | = all_86_1 & subset(all_86_1, all_81_0) = 0 &
% 99.50/14.20 | | | | | | | subset(all_41_3, all_81_1) = 0 & $i(all_86_1)) | ( ~
% 99.50/14.20 | | | | | | | (all_86_3 = 0) & subrelstr(all_41_4, all_41_6) =
% 99.50/14.20 | | | | | | | all_86_3)) & ((all_86_3 = 0 & subrelstr(all_41_4,
% 99.50/14.20 | | | | | | | all_41_6) = 0) | ( ~ (all_86_0 = 0) &
% 99.50/14.20 | | | | | | | the_InternalRel(all_41_4) = all_86_1 &
% 99.50/14.20 | | | | | | | subset(all_86_1, all_81_0) = all_86_0 & $i(all_86_1))
% 99.50/14.20 | | | | | | | | ( ~ (all_86_2 = 0) & subset(all_41_3, all_81_1) =
% 99.50/14.20 | | | | | | | all_86_2))
% 99.50/14.20 | | | | | | |
% 99.50/14.20 | | | | | | | ALPHA: (105) implies:
% 99.50/14.20 | | | | | | | (106) (all_86_0 = 0 & all_86_2 = 0 & the_InternalRel(all_41_4)
% 99.50/14.20 | | | | | | | = all_86_1 & subset(all_86_1, all_81_0) = 0 &
% 99.50/14.20 | | | | | | | subset(all_41_3, all_81_1) = 0 & $i(all_86_1)) | ( ~
% 99.50/14.20 | | | | | | | (all_86_3 = 0) & subrelstr(all_41_4, all_41_6) =
% 99.50/14.20 | | | | | | | all_86_3)
% 99.50/14.20 | | | | | | |
% 99.50/14.20 | | | | | | | BETA: splitting (77) gives:
% 99.50/14.20 | | | | | | |
% 99.50/14.20 | | | | | | | Case 1:
% 99.50/14.20 | | | | | | | |
% 99.50/14.20 | | | | | | | | (107) all_100_0 = 0 & all_100_2 = 0 & the_carrier(all_41_4) =
% 99.50/14.20 | | | | | | | | all_100_3 & the_InternalRel(all_41_4) = all_100_1 &
% 99.50/14.20 | | | | | | | | subset(all_100_1, all_90_0) = 0 & subset(all_100_3,
% 99.50/14.20 | | | | | | | | all_41_5) = 0 & $i(all_100_1) & $i(all_100_3)
% 99.50/14.20 | | | | | | | |
% 99.50/14.20 | | | | | | | | ALPHA: (107) implies:
% 99.50/14.20 | | | | | | | | (108) the_InternalRel(all_41_4) = all_100_1
% 99.50/14.20 | | | | | | | |
% 99.50/14.20 | | | | | | | | BETA: splitting (51) gives:
% 99.50/14.20 | | | | | | | |
% 99.50/14.20 | | | | | | | | Case 1:
% 99.50/14.20 | | | | | | | | |
% 99.50/14.20 | | | | | | | | | (109) ~ (all_70_1 = 0) & rel_str(all_41_6) = all_70_1
% 99.50/14.20 | | | | | | | | |
% 99.50/14.20 | | | | | | | | | ALPHA: (109) implies:
% 99.50/14.20 | | | | | | | | | (110) ~ (all_70_1 = 0)
% 99.50/14.20 | | | | | | | | | (111) rel_str(all_41_6) = all_70_1
% 99.50/14.20 | | | | | | | | |
% 99.50/14.20 | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_70_1, all_41_6,
% 99.50/14.20 | | | | | | | | | simplifying with (31), (111) gives:
% 99.50/14.20 | | | | | | | | | (112) all_70_1 = 0
% 99.50/14.20 | | | | | | | | |
% 99.50/14.20 | | | | | | | | | REDUCE: (110), (112) imply:
% 99.50/14.20 | | | | | | | | | (113) $false
% 99.50/14.20 | | | | | | | | |
% 99.50/14.20 | | | | | | | | | CLOSE: (113) is inconsistent.
% 99.50/14.20 | | | | | | | | |
% 99.50/14.20 | | | | | | | | Case 2:
% 99.50/14.20 | | | | | | | | |
% 99.50/14.20 | | | | | | | | | (114) the_InternalRel(all_41_6) = all_70_0 & $i(all_70_0) &
% 99.50/14.20 | | | | | | | | | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 99.50/14.20 | | | | | | | | | (ordered_pair(v0, v1) = v2) | ~ (element(v0,
% 99.50/14.20 | | | | | | | | | all_41_5) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 99.50/14.20 | | | | | | | | | [v3: int] : ? [v4: int] : ? [v5: int] : (( ~ (v3
% 99.50/14.20 | | | | | | | | | = 0) & element(v1, all_41_5) = v3) | (((v5 =
% 99.50/14.20 | | | | | | | | | 0 & in(v2, all_70_0) = 0) | ( ~ (v4 = 0) &
% 99.50/14.20 | | | | | | | | | related(all_41_6, v0, v1) = v4)) & ((v4 = 0
% 99.50/14.20 | | | | | | | | | & related(all_41_6, v0, v1) = 0) | ( ~ (v5
% 99.50/14.20 | | | | | | | | | = 0) & in(v2, all_70_0) = v5))))) & !
% 99.50/14.20 | | | | | | | | | [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 99.50/14.20 | | | | | | | | | (related(all_41_6, v0, v1) = v2) | ~ (element(v0,
% 99.50/14.20 | | | | | | | | | all_41_5) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 99.50/14.20 | | | | | | | | | [v3: int] : ? [v4: $i] : ? [v5: int] : (( ~ (v3 =
% 99.50/14.20 | | | | | | | | | 0) & element(v1, all_41_5) = v3) | (( ~ (v2 =
% 99.50/14.20 | | | | | | | | | 0) | (v5 = 0 & ordered_pair(v0, v1) = v4 &
% 99.50/14.20 | | | | | | | | | in(v4, all_70_0) = 0 & $i(v4))) & (v2 = 0 |
% 99.50/14.20 | | | | | | | | | ( ~ (v5 = 0) & ordered_pair(v0, v1) = v4 &
% 99.50/14.20 | | | | | | | | | in(v4, all_70_0) = v5 & $i(v4)))))) & !
% 99.50/14.20 | | | | | | | | | [v0: $i] : ! [v1: $i] : ( ~ (element(v1, all_41_5) =
% 99.50/14.20 | | | | | | | | | 0) | ~ (element(v0, all_41_5) = 0) | ~ $i(v1) |
% 99.50/14.20 | | | | | | | | | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4:
% 99.50/14.20 | | | | | | | | | int] : (((v4 = 0 & ordered_pair(v0, v1) = v3 &
% 99.50/14.20 | | | | | | | | | in(v3, all_70_0) = 0 & $i(v3)) | ( ~ (v2 = 0)
% 99.50/14.20 | | | | | | | | | & related(all_41_6, v0, v1) = v2)) & ((v2 = 0
% 99.50/14.20 | | | | | | | | | & related(all_41_6, v0, v1) = 0) | ( ~ (v4 =
% 99.50/14.20 | | | | | | | | | 0) & ordered_pair(v0, v1) = v3 & in(v3,
% 99.50/14.20 | | | | | | | | | all_70_0) = v4 & $i(v3)))))
% 99.50/14.20 | | | | | | | | |
% 99.50/14.20 | | | | | | | | | ALPHA: (114) implies:
% 99.50/14.20 | | | | | | | | | (115) the_InternalRel(all_41_6) = all_70_0
% 99.50/14.20 | | | | | | | | | (116) ! [v0: $i] : ! [v1: $i] : ( ~ (element(v1,
% 99.50/14.20 | | | | | | | | | all_41_5) = 0) | ~ (element(v0, all_41_5) = 0)
% 99.50/14.20 | | | | | | | | | | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ? [v3:
% 99.50/14.20 | | | | | | | | | $i] : ? [v4: int] : (((v4 = 0 & ordered_pair(v0,
% 99.50/14.20 | | | | | | | | | v1) = v3 & in(v3, all_70_0) = 0 & $i(v3)) |
% 99.50/14.20 | | | | | | | | | ( ~ (v2 = 0) & related(all_41_6, v0, v1) = v2))
% 99.50/14.20 | | | | | | | | | & ((v2 = 0 & related(all_41_6, v0, v1) = 0) | ( ~
% 99.50/14.20 | | | | | | | | | (v4 = 0) & ordered_pair(v0, v1) = v3 & in(v3,
% 99.50/14.20 | | | | | | | | | all_70_0) = v4 & $i(v3)))))
% 99.50/14.20 | | | | | | | | | (117) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 99.50/14.20 | | | | | | | | | (related(all_41_6, v0, v1) = v2) | ~ (element(v0,
% 99.50/14.20 | | | | | | | | | all_41_5) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 99.50/14.20 | | | | | | | | | [v3: int] : ? [v4: $i] : ? [v5: int] : (( ~ (v3 =
% 99.50/14.20 | | | | | | | | | 0) & element(v1, all_41_5) = v3) | (( ~ (v2 =
% 99.50/14.20 | | | | | | | | | 0) | (v5 = 0 & ordered_pair(v0, v1) = v4 &
% 99.50/14.20 | | | | | | | | | in(v4, all_70_0) = 0 & $i(v4))) & (v2 = 0 |
% 99.50/14.20 | | | | | | | | | ( ~ (v5 = 0) & ordered_pair(v0, v1) = v4 &
% 99.50/14.20 | | | | | | | | | in(v4, all_70_0) = v5 & $i(v4))))))
% 99.50/14.20 | | | | | | | | |
% 99.50/14.20 | | | | | | | | | GROUND_INST: instantiating (116) with all_41_2, all_41_1,
% 99.50/14.20 | | | | | | | | | simplifying with (24), (25), (26), (28) gives:
% 99.50/14.20 | | | | | | | | | (118) ? [v0: int] : ? [v1: $i] : ? [v2: int] : (((v2 = 0
% 99.50/14.20 | | | | | | | | | & ordered_pair(all_41_2, all_41_1) = v1 &
% 99.50/14.20 | | | | | | | | | in(v1, all_70_0) = 0 & $i(v1)) | ( ~ (v0 = 0) &
% 99.50/14.20 | | | | | | | | | related(all_41_6, all_41_2, all_41_1) = v0)) &
% 99.50/14.20 | | | | | | | | | ((v0 = 0 & related(all_41_6, all_41_2, all_41_1) =
% 99.50/14.20 | | | | | | | | | 0) | ( ~ (v2 = 0) & ordered_pair(all_41_2,
% 99.50/14.20 | | | | | | | | | all_41_1) = v1 & in(v1, all_70_0) = v2 &
% 99.50/14.20 | | | | | | | | | $i(v1))))
% 99.50/14.20 | | | | | | | | |
% 99.50/14.20 | | | | | | | | | GROUND_INST: instantiating (117) with all_41_2, all_41_1,
% 99.50/14.20 | | | | | | | | | all_41_0, simplifying with (24), (25), (26), (34)
% 99.50/14.20 | | | | | | | | | gives:
% 99.50/14.21 | | | | | | | | | (119) ? [v0: int] : ? [v1: $i] : ? [v2: int] : (( ~ (v0
% 99.50/14.21 | | | | | | | | | = 0) & element(all_41_1, all_41_5) = v0) | (( ~
% 99.50/14.21 | | | | | | | | | (all_41_0 = 0) | (v2 = 0 &
% 99.50/14.21 | | | | | | | | | ordered_pair(all_41_2, all_41_1) = v1 &
% 99.50/14.21 | | | | | | | | | in(v1, all_70_0) = 0 & $i(v1))) & (all_41_0 =
% 99.50/14.21 | | | | | | | | | 0 | ( ~ (v2 = 0) & ordered_pair(all_41_2,
% 99.50/14.21 | | | | | | | | | all_41_1) = v1 & in(v1, all_70_0) = v2 &
% 99.50/14.21 | | | | | | | | | $i(v1)))))
% 99.50/14.21 | | | | | | | | |
% 99.50/14.21 | | | | | | | | | DELTA: instantiating (119) with fresh symbols all_148_0,
% 99.50/14.21 | | | | | | | | | all_148_1, all_148_2 gives:
% 99.50/14.21 | | | | | | | | | (120) ( ~ (all_148_2 = 0) & element(all_41_1, all_41_5) =
% 99.50/14.21 | | | | | | | | | all_148_2) | (( ~ (all_41_0 = 0) | (all_148_0 = 0 &
% 99.50/14.21 | | | | | | | | | ordered_pair(all_41_2, all_41_1) = all_148_1 &
% 99.50/14.21 | | | | | | | | | in(all_148_1, all_70_0) = 0 & $i(all_148_1))) &
% 99.50/14.21 | | | | | | | | | (all_41_0 = 0 | ( ~ (all_148_0 = 0) &
% 99.50/14.21 | | | | | | | | | ordered_pair(all_41_2, all_41_1) = all_148_1 &
% 99.50/14.21 | | | | | | | | | in(all_148_1, all_70_0) = all_148_0 &
% 99.50/14.21 | | | | | | | | | $i(all_148_1))))
% 99.50/14.21 | | | | | | | | |
% 99.50/14.21 | | | | | | | | | DELTA: instantiating (118) with fresh symbols all_152_0,
% 99.50/14.21 | | | | | | | | | all_152_1, all_152_2 gives:
% 99.50/14.21 | | | | | | | | | (121) ((all_152_0 = 0 & ordered_pair(all_41_2, all_41_1) =
% 99.50/14.21 | | | | | | | | | all_152_1 & in(all_152_1, all_70_0) = 0 &
% 99.50/14.21 | | | | | | | | | $i(all_152_1)) | ( ~ (all_152_2 = 0) &
% 99.50/14.21 | | | | | | | | | related(all_41_6, all_41_2, all_41_1) =
% 99.50/14.21 | | | | | | | | | all_152_2)) & ((all_152_2 = 0 & related(all_41_6,
% 99.50/14.21 | | | | | | | | | all_41_2, all_41_1) = 0) | ( ~ (all_152_0 = 0)
% 99.50/14.21 | | | | | | | | | & ordered_pair(all_41_2, all_41_1) = all_152_1 &
% 99.50/14.21 | | | | | | | | | in(all_152_1, all_70_0) = all_152_0 &
% 99.50/14.21 | | | | | | | | | $i(all_152_1)))
% 99.50/14.21 | | | | | | | | |
% 99.50/14.21 | | | | | | | | | ALPHA: (121) implies:
% 99.50/14.21 | | | | | | | | | (122) (all_152_2 = 0 & related(all_41_6, all_41_2,
% 99.50/14.21 | | | | | | | | | all_41_1) = 0) | ( ~ (all_152_0 = 0) &
% 99.50/14.21 | | | | | | | | | ordered_pair(all_41_2, all_41_1) = all_152_1 &
% 99.50/14.21 | | | | | | | | | in(all_152_1, all_70_0) = all_152_0 &
% 99.50/14.21 | | | | | | | | | $i(all_152_1))
% 99.50/14.21 | | | | | | | | |
% 99.50/14.21 | | | | | | | | | BETA: splitting (96) gives:
% 99.50/14.21 | | | | | | | | |
% 99.50/14.21 | | | | | | | | | Case 1:
% 99.50/14.21 | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | (123) all_123_0 = 0 & ordered_pair(all_41_2, all_41_1) =
% 99.50/14.21 | | | | | | | | | | all_123_1 & in(all_123_1, all_69_0) = 0 &
% 99.50/14.21 | | | | | | | | | | $i(all_123_1)
% 99.50/14.21 | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | ALPHA: (123) implies:
% 99.50/14.21 | | | | | | | | | | (124) $i(all_123_1)
% 99.50/14.21 | | | | | | | | | | (125) ordered_pair(all_41_2, all_41_1) = all_123_1
% 99.50/14.21 | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | BETA: splitting (49) gives:
% 99.50/14.21 | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | Case 1:
% 99.50/14.21 | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | (126) all_62_0 = 0 & relation_of2_as_subset(all_62_1,
% 99.50/14.21 | | | | | | | | | | | all_41_5, all_41_5) = 0 &
% 99.50/14.21 | | | | | | | | | | | the_InternalRel(all_41_6) = all_62_1 &
% 99.50/14.21 | | | | | | | | | | | $i(all_62_1)
% 99.50/14.21 | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | ALPHA: (126) implies:
% 99.50/14.21 | | | | | | | | | | | (127) $i(all_62_1)
% 99.50/14.21 | | | | | | | | | | | (128) the_InternalRel(all_41_6) = all_62_1
% 99.50/14.21 | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | BETA: splitting (122) gives:
% 99.50/14.21 | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | Case 1:
% 99.50/14.21 | | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | | (129) all_152_2 = 0 & related(all_41_6, all_41_2,
% 99.50/14.21 | | | | | | | | | | | | all_41_1) = 0
% 99.50/14.21 | | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | | ALPHA: (129) implies:
% 99.50/14.21 | | | | | | | | | | | | (130) related(all_41_6, all_41_2, all_41_1) = 0
% 99.50/14.21 | | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_41_0, 0, all_41_1,
% 99.50/14.21 | | | | | | | | | | | | all_41_2, all_41_6, simplifying with (34), (130)
% 99.50/14.21 | | | | | | | | | | | | gives:
% 99.50/14.21 | | | | | | | | | | | | (131) all_41_0 = 0
% 99.50/14.21 | | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | | REDUCE: (21), (131) imply:
% 99.50/14.21 | | | | | | | | | | | | (132) $false
% 99.50/14.21 | | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | | CLOSE: (132) is inconsistent.
% 99.50/14.21 | | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | Case 2:
% 99.50/14.21 | | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | | (133) ~ (all_152_0 = 0) & ordered_pair(all_41_2,
% 99.50/14.21 | | | | | | | | | | | | all_41_1) = all_152_1 & in(all_152_1, all_70_0)
% 99.50/14.21 | | | | | | | | | | | | = all_152_0 & $i(all_152_1)
% 99.50/14.21 | | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | | ALPHA: (133) implies:
% 99.50/14.21 | | | | | | | | | | | | (134) ~ (all_152_0 = 0)
% 99.50/14.21 | | | | | | | | | | | | (135) in(all_152_1, all_70_0) = all_152_0
% 99.50/14.21 | | | | | | | | | | | | (136) ordered_pair(all_41_2, all_41_1) = all_152_1
% 99.50/14.21 | | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | | BETA: splitting (78) gives:
% 99.50/14.21 | | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | | Case 1:
% 99.50/14.21 | | | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | | | (137) ~ (all_102_4 = 0) & rel_str(all_41_4) = all_102_4
% 99.50/14.21 | | | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | | | ALPHA: (137) implies:
% 99.50/14.21 | | | | | | | | | | | | | (138) ~ (all_102_4 = 0)
% 99.50/14.21 | | | | | | | | | | | | | (139) rel_str(all_41_4) = all_102_4
% 99.50/14.21 | | | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_102_4, all_41_4,
% 99.50/14.21 | | | | | | | | | | | | | simplifying with (36), (139) gives:
% 99.50/14.21 | | | | | | | | | | | | | (140) all_102_4 = 0
% 99.50/14.21 | | | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | | | REDUCE: (138), (140) imply:
% 99.50/14.21 | | | | | | | | | | | | | (141) $false
% 99.50/14.21 | | | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | | | CLOSE: (141) is inconsistent.
% 99.50/14.21 | | | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | | Case 2:
% 99.50/14.21 | | | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | | | (142) ((all_102_0 = 0 & all_102_2 = 0 &
% 99.50/14.21 | | | | | | | | | | | | | the_InternalRel(all_41_4) = all_102_1 &
% 99.50/14.21 | | | | | | | | | | | | | subset(all_102_1, all_90_0) = 0 &
% 99.50/14.21 | | | | | | | | | | | | | subset(all_41_3, all_41_5) = 0 &
% 99.50/14.21 | | | | | | | | | | | | | $i(all_102_1)) | ( ~ (all_102_3 = 0) &
% 99.50/14.21 | | | | | | | | | | | | | subrelstr(all_41_4, all_41_6) = all_102_3)) &
% 99.50/14.21 | | | | | | | | | | | | | ((all_102_3 = 0 & subrelstr(all_41_4, all_41_6) =
% 99.50/14.21 | | | | | | | | | | | | | 0) | ( ~ (all_102_0 = 0) &
% 99.50/14.21 | | | | | | | | | | | | | the_InternalRel(all_41_4) = all_102_1 &
% 99.50/14.21 | | | | | | | | | | | | | subset(all_102_1, all_90_0) = all_102_0 &
% 99.50/14.21 | | | | | | | | | | | | | $i(all_102_1)) | ( ~ (all_102_2 = 0) &
% 99.50/14.21 | | | | | | | | | | | | | subset(all_41_3, all_41_5) = all_102_2))
% 99.50/14.21 | | | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | | | ALPHA: (142) implies:
% 99.50/14.21 | | | | | | | | | | | | | (143) (all_102_0 = 0 & all_102_2 = 0 &
% 99.50/14.21 | | | | | | | | | | | | | the_InternalRel(all_41_4) = all_102_1 &
% 99.50/14.21 | | | | | | | | | | | | | subset(all_102_1, all_90_0) = 0 &
% 99.50/14.21 | | | | | | | | | | | | | subset(all_41_3, all_41_5) = 0 & $i(all_102_1))
% 99.50/14.21 | | | | | | | | | | | | | | ( ~ (all_102_3 = 0) & subrelstr(all_41_4,
% 99.50/14.21 | | | | | | | | | | | | | all_41_6) = all_102_3)
% 99.50/14.21 | | | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | | | BETA: splitting (143) gives:
% 99.50/14.21 | | | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | | | Case 1:
% 99.50/14.21 | | | | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | | | | (144) all_102_0 = 0 & all_102_2 = 0 &
% 99.50/14.21 | | | | | | | | | | | | | | the_InternalRel(all_41_4) = all_102_1 &
% 99.50/14.21 | | | | | | | | | | | | | | subset(all_102_1, all_90_0) = 0 & subset(all_41_3,
% 99.50/14.21 | | | | | | | | | | | | | | all_41_5) = 0 & $i(all_102_1)
% 99.50/14.21 | | | | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | | | | ALPHA: (144) implies:
% 99.50/14.21 | | | | | | | | | | | | | | (145) the_InternalRel(all_41_4) = all_102_1
% 99.50/14.21 | | | | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | | | | BETA: splitting (62) gives:
% 99.50/14.21 | | | | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | | | | Case 1:
% 99.50/14.21 | | | | | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | | | | | (146) ~ (all_89_1 = 0) & rel_str(all_41_4) = all_89_1
% 99.50/14.21 | | | | | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | | | | | ALPHA: (146) implies:
% 99.50/14.21 | | | | | | | | | | | | | | | (147) ~ (all_89_1 = 0)
% 99.50/14.21 | | | | | | | | | | | | | | | (148) rel_str(all_41_4) = all_89_1
% 99.50/14.21 | | | | | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_89_1, all_41_4,
% 99.50/14.21 | | | | | | | | | | | | | | | simplifying with (36), (148) gives:
% 99.50/14.21 | | | | | | | | | | | | | | | (149) all_89_1 = 0
% 99.50/14.21 | | | | | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | | | | | REDUCE: (147), (149) imply:
% 99.50/14.21 | | | | | | | | | | | | | | | (150) $false
% 99.50/14.21 | | | | | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | | | | | CLOSE: (150) is inconsistent.
% 99.50/14.21 | | | | | | | | | | | | | | |
% 99.50/14.21 | | | | | | | | | | | | | | Case 2:
% 99.50/14.21 | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | (151) the_InternalRel(all_41_4) = all_89_0 &
% 99.50/14.22 | | | | | | | | | | | | | | | $i(all_89_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 99.50/14.22 | | | | | | | | | | | | | | | (the_carrier(v0) = v1) | ~ $i(v0) | ? [v2:
% 99.50/14.22 | | | | | | | | | | | | | | | int] : ? [v3: int] : ? [v4: int] : ? [v5:
% 99.50/14.22 | | | | | | | | | | | | | | | $i] : ? [v6: int] : (( ~ (v2 = 0) &
% 99.50/14.22 | | | | | | | | | | | | | | | rel_str(v0) = v2) | (((v6 = 0 & v4 = 0 &
% 99.50/14.22 | | | | | | | | | | | | | | | the_InternalRel(v0) = v5 & subset(v5,
% 99.50/14.22 | | | | | | | | | | | | | | | all_89_0) = 0 & subset(v1, all_41_3) =
% 99.50/14.22 | | | | | | | | | | | | | | | 0 & $i(v5)) | ( ~ (v3 = 0) &
% 99.50/14.22 | | | | | | | | | | | | | | | subrelstr(v0, all_41_4) = v3)) & ((v3 =
% 99.50/14.22 | | | | | | | | | | | | | | | 0 & subrelstr(v0, all_41_4) = 0) | ( ~
% 99.50/14.22 | | | | | | | | | | | | | | | (v6 = 0) & the_InternalRel(v0) = v5 &
% 99.50/14.22 | | | | | | | | | | | | | | | subset(v5, all_89_0) = v6 & $i(v5)) | (
% 99.50/14.22 | | | | | | | | | | | | | | | ~ (v4 = 0) & subset(v1, all_41_3) =
% 99.50/14.22 | | | | | | | | | | | | | | | v4))))) & ! [v0: $i] : ! [v1: any] : (
% 99.50/14.22 | | | | | | | | | | | | | | | ~ (subrelstr(v0, all_41_4) = v1) | ~ $i(v0) |
% 99.50/14.22 | | | | | | | | | | | | | | | ? [v2: int] : ? [v3: $i] : ? [v4: int] : ?
% 99.50/14.22 | | | | | | | | | | | | | | | [v5: $i] : ? [v6: int] : (( ~ (v2 = 0) &
% 99.50/14.22 | | | | | | | | | | | | | | | rel_str(v0) = v2) | (( ~ (v1 = 0) | (v6 = 0
% 99.50/14.22 | | | | | | | | | | | | | | | & v4 = 0 & the_carrier(v0) = v3 &
% 99.50/14.22 | | | | | | | | | | | | | | | the_InternalRel(v0) = v5 & subset(v5,
% 99.50/14.22 | | | | | | | | | | | | | | | all_89_0) = 0 & subset(v3, all_41_3) =
% 99.50/14.22 | | | | | | | | | | | | | | | 0 & $i(v5) & $i(v3))) & (v1 = 0 | ( ~
% 99.50/14.22 | | | | | | | | | | | | | | | (v6 = 0) & the_InternalRel(v0) = v5 &
% 99.50/14.22 | | | | | | | | | | | | | | | subset(v5, all_89_0) = v6 & $i(v5)) | (
% 99.50/14.22 | | | | | | | | | | | | | | | ~ (v4 = 0) & the_carrier(v0) = v3 &
% 99.50/14.22 | | | | | | | | | | | | | | | subset(v3, all_41_3) = v4 & $i(v3))))))
% 99.50/14.22 | | | | | | | | | | | | | | | & ! [v0: $i] : ! [v1: $i] : ( ~
% 99.50/14.22 | | | | | | | | | | | | | | | (the_InternalRel(v0) = v1) | ~ $i(v0) | ? [v2:
% 99.50/14.22 | | | | | | | | | | | | | | | int] : ? [v3: int] : ? [v4: $i] : ? [v5:
% 99.50/14.22 | | | | | | | | | | | | | | | int] : ? [v6: int] : (( ~ (v2 = 0) &
% 99.50/14.22 | | | | | | | | | | | | | | | rel_str(v0) = v2) | (((v6 = 0 & v5 = 0 &
% 99.50/14.22 | | | | | | | | | | | | | | | the_carrier(v0) = v4 & subset(v4,
% 99.50/14.22 | | | | | | | | | | | | | | | all_41_3) = 0 & subset(v1, all_89_0) =
% 99.50/14.22 | | | | | | | | | | | | | | | 0 & $i(v4)) | ( ~ (v3 = 0) &
% 99.50/14.22 | | | | | | | | | | | | | | | subrelstr(v0, all_41_4) = v3)) & ((v3 =
% 99.50/14.22 | | | | | | | | | | | | | | | 0 & subrelstr(v0, all_41_4) = 0) | ( ~
% 99.50/14.22 | | | | | | | | | | | | | | | (v6 = 0) & subset(v1, all_89_0) = v6) |
% 99.50/14.22 | | | | | | | | | | | | | | | ( ~ (v5 = 0) & the_carrier(v0) = v4 &
% 99.50/14.22 | | | | | | | | | | | | | | | subset(v4, all_41_3) = v5 & $i(v4))))))
% 99.50/14.22 | | | | | | | | | | | | | | | & ! [v0: $i] : ( ~ (rel_str(v0) = 0) | ~ $i(v0)
% 99.50/14.22 | | | | | | | | | | | | | | | | ? [v1: int] : ? [v2: $i] : ? [v3: int] : ?
% 99.50/14.22 | | | | | | | | | | | | | | | [v4: $i] : ? [v5: int] : (((v5 = 0 & v3 = 0 &
% 99.50/14.22 | | | | | | | | | | | | | | | the_carrier(v0) = v2 & the_InternalRel(v0)
% 99.50/14.22 | | | | | | | | | | | | | | | = v4 & subset(v4, all_89_0) = 0 &
% 99.50/14.22 | | | | | | | | | | | | | | | subset(v2, all_41_3) = 0 & $i(v4) &
% 99.50/14.22 | | | | | | | | | | | | | | | $i(v2)) | ( ~ (v1 = 0) & subrelstr(v0,
% 99.50/14.22 | | | | | | | | | | | | | | | all_41_4) = v1)) & ((v1 = 0 &
% 99.50/14.22 | | | | | | | | | | | | | | | subrelstr(v0, all_41_4) = 0) | ( ~ (v5 =
% 99.50/14.22 | | | | | | | | | | | | | | | 0) & the_InternalRel(v0) = v4 &
% 99.50/14.22 | | | | | | | | | | | | | | | subset(v4, all_89_0) = v5 & $i(v4)) | ( ~
% 99.50/14.22 | | | | | | | | | | | | | | | (v3 = 0) & the_carrier(v0) = v2 &
% 99.50/14.22 | | | | | | | | | | | | | | | subset(v2, all_41_3) = v3 & $i(v2)))))
% 99.50/14.22 | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | ALPHA: (151) implies:
% 99.50/14.22 | | | | | | | | | | | | | | | (152) the_InternalRel(all_41_4) = all_89_0
% 99.50/14.22 | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 99.50/14.22 | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | Case 1:
% 99.50/14.22 | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | (153) all_86_0 = 0 & all_86_2 = 0 &
% 99.50/14.22 | | | | | | | | | | | | | | | | the_InternalRel(all_41_4) = all_86_1 &
% 99.50/14.22 | | | | | | | | | | | | | | | | subset(all_86_1, all_81_0) = 0 & subset(all_41_3,
% 99.50/14.22 | | | | | | | | | | | | | | | | all_81_1) = 0 & $i(all_86_1)
% 99.50/14.22 | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | ALPHA: (153) implies:
% 99.50/14.22 | | | | | | | | | | | | | | | | (154) the_InternalRel(all_41_4) = all_86_1
% 99.50/14.22 | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | BETA: splitting (120) gives:
% 99.50/14.22 | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | Case 1:
% 99.50/14.22 | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | (155) ~ (all_148_2 = 0) & element(all_41_1, all_41_5) =
% 99.50/14.22 | | | | | | | | | | | | | | | | | all_148_2
% 99.50/14.22 | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | ALPHA: (155) implies:
% 99.50/14.22 | | | | | | | | | | | | | | | | | (156) ~ (all_148_2 = 0)
% 99.50/14.22 | | | | | | | | | | | | | | | | | (157) element(all_41_1, all_41_5) = all_148_2
% 99.50/14.22 | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_148_2, all_41_5,
% 99.50/14.22 | | | | | | | | | | | | | | | | | all_41_1, simplifying with (28), (157) gives:
% 99.50/14.22 | | | | | | | | | | | | | | | | | (158) all_148_2 = 0
% 99.50/14.22 | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | REDUCE: (156), (158) imply:
% 99.50/14.22 | | | | | | | | | | | | | | | | | (159) $false
% 99.50/14.22 | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | CLOSE: (159) is inconsistent.
% 99.50/14.22 | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | Case 2:
% 99.50/14.22 | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | (160) ( ~ (all_41_0 = 0) | (all_148_0 = 0 &
% 99.50/14.22 | | | | | | | | | | | | | | | | | ordered_pair(all_41_2, all_41_1) = all_148_1 &
% 99.50/14.22 | | | | | | | | | | | | | | | | | in(all_148_1, all_70_0) = 0 & $i(all_148_1)))
% 99.50/14.22 | | | | | | | | | | | | | | | | | & (all_41_0 = 0 | ( ~ (all_148_0 = 0) &
% 99.50/14.22 | | | | | | | | | | | | | | | | | ordered_pair(all_41_2, all_41_1) = all_148_1 &
% 99.50/14.22 | | | | | | | | | | | | | | | | | in(all_148_1, all_70_0) = all_148_0 &
% 99.50/14.22 | | | | | | | | | | | | | | | | | $i(all_148_1)))
% 99.50/14.22 | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | ALPHA: (160) implies:
% 99.50/14.22 | | | | | | | | | | | | | | | | | (161) all_41_0 = 0 | ( ~ (all_148_0 = 0) &
% 99.50/14.22 | | | | | | | | | | | | | | | | | ordered_pair(all_41_2, all_41_1) = all_148_1 &
% 99.50/14.22 | | | | | | | | | | | | | | | | | in(all_148_1, all_70_0) = all_148_0 &
% 99.50/14.22 | | | | | | | | | | | | | | | | | $i(all_148_1))
% 99.50/14.22 | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | BETA: splitting (161) gives:
% 99.50/14.22 | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | Case 1:
% 99.50/14.22 | | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | | (162) all_41_0 = 0
% 99.50/14.22 | | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | | REDUCE: (21), (162) imply:
% 99.50/14.22 | | | | | | | | | | | | | | | | | | (163) $false
% 99.50/14.22 | | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | | CLOSE: (163) is inconsistent.
% 99.50/14.22 | | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | Case 2:
% 99.50/14.22 | | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | | (164) ~ (all_148_0 = 0) & ordered_pair(all_41_2,
% 99.50/14.22 | | | | | | | | | | | | | | | | | | all_41_1) = all_148_1 & in(all_148_1, all_70_0)
% 99.50/14.22 | | | | | | | | | | | | | | | | | | = all_148_0 & $i(all_148_1)
% 99.50/14.22 | | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | | ALPHA: (164) implies:
% 99.50/14.22 | | | | | | | | | | | | | | | | | | (165) in(all_148_1, all_70_0) = all_148_0
% 99.50/14.22 | | | | | | | | | | | | | | | | | | (166) ordered_pair(all_41_2, all_41_1) = all_148_1
% 99.50/14.22 | | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_57_1, all_81_0,
% 99.50/14.22 | | | | | | | | | | | | | | | | | | all_41_6, simplifying with (47), (55) gives:
% 99.50/14.22 | | | | | | | | | | | | | | | | | | (167) all_81_0 = all_57_1
% 99.50/14.22 | | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_81_0, all_90_0,
% 99.50/14.22 | | | | | | | | | | | | | | | | | | all_41_6, simplifying with (55), (72) gives:
% 99.50/14.22 | | | | | | | | | | | | | | | | | | (168) all_90_0 = all_81_0
% 99.50/14.22 | | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_71_0, all_90_0,
% 99.50/14.22 | | | | | | | | | | | | | | | | | | all_41_6, simplifying with (53), (72) gives:
% 99.50/14.22 | | | | | | | | | | | | | | | | | | (169) all_90_0 = all_71_0
% 99.50/14.22 | | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_70_0, all_90_0,
% 99.50/14.22 | | | | | | | | | | | | | | | | | | all_41_6, simplifying with (72), (115) gives:
% 99.50/14.22 | | | | | | | | | | | | | | | | | | (170) all_90_0 = all_70_0
% 99.50/14.22 | | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_62_1, all_90_0,
% 99.50/14.22 | | | | | | | | | | | | | | | | | | all_41_6, simplifying with (72), (128) gives:
% 99.50/14.22 | | | | | | | | | | | | | | | | | | (171) all_90_0 = all_62_1
% 99.50/14.22 | | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_84_1, all_86_1,
% 99.50/14.22 | | | | | | | | | | | | | | | | | | all_41_4, simplifying with (81), (154) gives:
% 99.50/14.22 | | | | | | | | | | | | | | | | | | (172) all_86_1 = all_84_1
% 99.50/14.22 | | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_86_1, all_100_1,
% 99.50/14.22 | | | | | | | | | | | | | | | | | | all_41_4, simplifying with (108), (154) gives:
% 99.50/14.22 | | | | | | | | | | | | | | | | | | (173) all_100_1 = all_86_1
% 99.50/14.22 | | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_61_1, all_100_1,
% 99.50/14.22 | | | | | | | | | | | | | | | | | | all_41_4, simplifying with (65), (108) gives:
% 99.50/14.22 | | | | | | | | | | | | | | | | | | (174) all_100_1 = all_61_1
% 99.50/14.22 | | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_89_0, all_102_1,
% 99.50/14.22 | | | | | | | | | | | | | | | | | | all_41_4, simplifying with (145), (152) gives:
% 99.50/14.22 | | | | | | | | | | | | | | | | | | (175) all_102_1 = all_89_0
% 99.50/14.22 | | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_84_1, all_102_1,
% 99.50/14.22 | | | | | | | | | | | | | | | | | | all_41_4, simplifying with (81), (145) gives:
% 99.50/14.22 | | | | | | | | | | | | | | | | | | (176) all_102_1 = all_84_1
% 99.50/14.22 | | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_69_0, all_102_1,
% 99.50/14.22 | | | | | | | | | | | | | | | | | | all_41_4, simplifying with (89), (145) gives:
% 99.50/14.22 | | | | | | | | | | | | | | | | | | (177) all_102_1 = all_69_0
% 99.50/14.22 | | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_123_1, all_148_1,
% 99.50/14.22 | | | | | | | | | | | | | | | | | | all_41_1, all_41_2, simplifying with (125), (166)
% 99.50/14.22 | | | | | | | | | | | | | | | | | | gives:
% 99.50/14.22 | | | | | | | | | | | | | | | | | | (178) all_148_1 = all_123_1
% 99.50/14.22 | | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_148_1, all_152_1,
% 99.50/14.22 | | | | | | | | | | | | | | | | | | all_41_1, all_41_2, simplifying with (136), (166)
% 99.50/14.22 | | | | | | | | | | | | | | | | | | gives:
% 99.50/14.22 | | | | | | | | | | | | | | | | | | (179) all_152_1 = all_148_1
% 99.50/14.22 | | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_119_1, all_152_1,
% 99.50/14.22 | | | | | | | | | | | | | | | | | | all_41_1, all_41_2, simplifying with (99), (136)
% 99.50/14.22 | | | | | | | | | | | | | | | | | | gives:
% 99.50/14.22 | | | | | | | | | | | | | | | | | | (180) all_152_1 = all_119_1
% 99.50/14.22 | | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (179), (180) imply:
% 99.50/14.22 | | | | | | | | | | | | | | | | | | (181) all_148_1 = all_119_1
% 99.50/14.22 | | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | | SIMP: (181) implies:
% 99.50/14.22 | | | | | | | | | | | | | | | | | | (182) all_148_1 = all_119_1
% 99.50/14.22 | | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (178), (182) imply:
% 99.50/14.22 | | | | | | | | | | | | | | | | | | (183) all_123_1 = all_119_1
% 99.50/14.22 | | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | | SIMP: (183) implies:
% 99.50/14.22 | | | | | | | | | | | | | | | | | | (184) all_123_1 = all_119_1
% 99.50/14.22 | | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (175), (176) imply:
% 99.50/14.22 | | | | | | | | | | | | | | | | | | (185) all_89_0 = all_84_1
% 99.50/14.22 | | | | | | | | | | | | | | | | | |
% 99.50/14.22 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (175), (177) imply:
% 99.50/14.22 | | | | | | | | | | | | | | | | | | (186) all_89_0 = all_69_0
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (173), (174) imply:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | (187) all_86_1 = all_61_1
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | SIMP: (187) implies:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | (188) all_86_1 = all_61_1
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (168), (169) imply:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | (189) all_81_0 = all_71_0
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | SIMP: (189) implies:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | (190) all_81_0 = all_71_0
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (169), (171) imply:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | (191) all_71_0 = all_62_1
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (169), (170) imply:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | (192) all_71_0 = all_70_0
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (185), (186) imply:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | (193) all_84_1 = all_69_0
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | SIMP: (193) implies:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | (194) all_84_1 = all_69_0
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (172), (188) imply:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | (195) all_84_1 = all_61_1
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | SIMP: (195) implies:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | (196) all_84_1 = all_61_1
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (194), (196) imply:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | (197) all_69_0 = all_61_1
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | SIMP: (197) implies:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | (198) all_69_0 = all_61_1
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (167), (190) imply:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | (199) all_71_0 = all_57_1
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | SIMP: (199) implies:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | (200) all_71_0 = all_57_1
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (191), (192) imply:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | (201) all_70_0 = all_62_1
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (192), (200) imply:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | (202) all_70_0 = all_57_1
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (201), (202) imply:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | (203) all_62_1 = all_57_1
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | REDUCE: (80), (167), (196) imply:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | (204) subset(all_61_1, all_57_1) = 0
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | REDUCE: (135), (180), (202) imply:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | (205) in(all_119_1, all_57_1) = all_152_0
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | REDUCE: (165), (182), (202) imply:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | (206) in(all_119_1, all_57_1) = all_148_0
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | REDUCE: (98), (198) imply:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | (207) in(all_119_1, all_61_1) = 0
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | REDUCE: (124), (184) imply:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | (208) $i(all_119_1)
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | REDUCE: (88), (198) imply:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | (209) $i(all_61_1)
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | REDUCE: (127), (203) imply:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | (210) $i(all_57_1)
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_148_0, all_152_0,
% 99.50/14.23 | | | | | | | | | | | | | | | | | | all_57_1, all_119_1, simplifying with (205), (206)
% 99.50/14.23 | | | | | | | | | | | | | | | | | | gives:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | (211) all_152_0 = all_148_0
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | REDUCE: (134), (211) imply:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | (212) ~ (all_148_0 = 0)
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_119_1, all_57_1,
% 99.50/14.23 | | | | | | | | | | | | | | | | | | all_148_0, simplifying with (206), (208), (210)
% 99.50/14.23 | | | | | | | | | | | | | | | | | | gives:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | (213) all_148_0 = 0 | ? [v0: int] : ? [v1: int] : ((v1
% 99.50/14.23 | | | | | | | | | | | | | | | | | | = 0 & empty(all_57_1) = 0) | ( ~ (v0 = 0) &
% 99.50/14.23 | | | | | | | | | | | | | | | | | | element(all_119_1, all_57_1) = v0))
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_61_1, all_57_1,
% 99.50/14.23 | | | | | | | | | | | | | | | | | | simplifying with (204), (209), (210) gives:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | (214) ? [v0: $i] : (powerset(all_57_1) = v0 &
% 99.50/14.23 | | | | | | | | | | | | | | | | | | element(all_61_1, v0) = 0 & $i(v0))
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | DELTA: instantiating (214) with fresh symbol all_222_0
% 99.50/14.23 | | | | | | | | | | | | | | | | | | gives:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | (215) powerset(all_57_1) = all_222_0 & element(all_61_1,
% 99.50/14.23 | | | | | | | | | | | | | | | | | | all_222_0) = 0 & $i(all_222_0)
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | ALPHA: (215) implies:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | (216) element(all_61_1, all_222_0) = 0
% 99.50/14.23 | | | | | | | | | | | | | | | | | | (217) powerset(all_57_1) = all_222_0
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | Case 1:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | (218) all_148_0 = 0
% 99.50/14.23 | | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | REDUCE: (212), (218) imply:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | (219) $false
% 99.50/14.23 | | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | CLOSE: (219) is inconsistent.
% 99.50/14.23 | | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | Case 2:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | (220) ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | empty(all_57_1) = 0) | ( ~ (v0 = 0) &
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | element(all_119_1, all_57_1) = v0))
% 99.50/14.23 | | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (220) with fresh symbols all_328_0,
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | all_328_1 gives:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | (221) (all_328_0 = 0 & empty(all_57_1) = 0) | ( ~
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | (all_328_1 = 0) & element(all_119_1, all_57_1) =
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | all_328_1)
% 99.50/14.23 | | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_119_1, all_61_1,
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | all_57_1, all_222_0, simplifying with (207),
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | (208), (209), (210), (216), (217) gives:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | (222) element(all_119_1, all_57_1) = 0
% 99.50/14.23 | | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_119_1, all_61_1,
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | all_57_1, all_222_0, simplifying with (207),
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | (208), (209), (210), (216), (217) gives:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | (223) ? [v0: int] : ( ~ (v0 = 0) & empty(all_57_1) =
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | v0)
% 99.50/14.23 | | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (223) with fresh symbol all_839_0
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | gives:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | (224) ~ (all_839_0 = 0) & empty(all_57_1) = all_839_0
% 99.50/14.23 | | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | ALPHA: (224) implies:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | (225) ~ (all_839_0 = 0)
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | (226) empty(all_57_1) = all_839_0
% 99.50/14.23 | | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | Case 1:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | | (227) all_328_0 = 0 & empty(all_57_1) = 0
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | | ALPHA: (227) implies:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | | (228) empty(all_57_1) = 0
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with 0, all_839_0, all_57_1,
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | | simplifying with (226), (228) gives:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | | (229) all_839_0 = 0
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | | REDUCE: (225), (229) imply:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | | (230) $false
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | | CLOSE: (230) is inconsistent.
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | Case 2:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | | (231) ~ (all_328_1 = 0) & element(all_119_1, all_57_1)
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | | = all_328_1
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | | ALPHA: (231) implies:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | | (232) ~ (all_328_1 = 0)
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | | (233) element(all_119_1, all_57_1) = all_328_1
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_328_1, all_57_1,
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | | all_119_1, simplifying with (222), (233) gives:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | | (234) all_328_1 = 0
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | | REDUCE: (232), (234) imply:
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | | (235) $false
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | | CLOSE: (235) is inconsistent.
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | | End of split
% 99.50/14.23 | | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | | End of split
% 99.50/14.23 | | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | | End of split
% 99.50/14.23 | | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | End of split
% 99.50/14.23 | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | Case 2:
% 99.50/14.23 | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | (236) ~ (all_86_3 = 0) & subrelstr(all_41_4, all_41_6)
% 99.50/14.23 | | | | | | | | | | | | | | | | = all_86_3
% 99.50/14.23 | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | ALPHA: (236) implies:
% 99.50/14.23 | | | | | | | | | | | | | | | | (237) ~ (all_86_3 = 0)
% 99.50/14.23 | | | | | | | | | | | | | | | | (238) subrelstr(all_41_4, all_41_6) = all_86_3
% 99.50/14.23 | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_86_3, all_41_6,
% 99.50/14.23 | | | | | | | | | | | | | | | | all_41_4, simplifying with (30), (238) gives:
% 99.50/14.23 | | | | | | | | | | | | | | | | (239) all_86_3 = 0
% 99.50/14.23 | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | REDUCE: (237), (239) imply:
% 99.50/14.23 | | | | | | | | | | | | | | | | (240) $false
% 99.50/14.23 | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | | CLOSE: (240) is inconsistent.
% 99.50/14.23 | | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | | End of split
% 99.50/14.23 | | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | End of split
% 99.50/14.23 | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | Case 2:
% 99.50/14.23 | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | (241) ~ (all_102_3 = 0) & subrelstr(all_41_4, all_41_6)
% 99.50/14.23 | | | | | | | | | | | | | | = all_102_3
% 99.50/14.23 | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | ALPHA: (241) implies:
% 99.50/14.23 | | | | | | | | | | | | | | (242) ~ (all_102_3 = 0)
% 99.50/14.23 | | | | | | | | | | | | | | (243) subrelstr(all_41_4, all_41_6) = all_102_3
% 99.50/14.23 | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_102_3, all_41_6,
% 99.50/14.23 | | | | | | | | | | | | | | all_41_4, simplifying with (30), (243) gives:
% 99.50/14.23 | | | | | | | | | | | | | | (244) all_102_3 = 0
% 99.50/14.23 | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | REDUCE: (242), (244) imply:
% 99.50/14.23 | | | | | | | | | | | | | | (245) $false
% 99.50/14.23 | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | | CLOSE: (245) is inconsistent.
% 99.50/14.23 | | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | | End of split
% 99.50/14.23 | | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | | End of split
% 99.50/14.23 | | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | End of split
% 99.50/14.23 | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | Case 2:
% 99.50/14.23 | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | (246) ~ (all_62_2 = 0) & rel_str(all_41_6) = all_62_2
% 99.50/14.23 | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | ALPHA: (246) implies:
% 99.50/14.23 | | | | | | | | | | | (247) ~ (all_62_2 = 0)
% 99.50/14.23 | | | | | | | | | | | (248) rel_str(all_41_6) = all_62_2
% 99.50/14.23 | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_62_2, all_41_6,
% 99.50/14.23 | | | | | | | | | | | simplifying with (31), (248) gives:
% 99.50/14.23 | | | | | | | | | | | (249) all_62_2 = 0
% 99.50/14.23 | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | REDUCE: (247), (249) imply:
% 99.50/14.23 | | | | | | | | | | | (250) $false
% 99.50/14.23 | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | | CLOSE: (250) is inconsistent.
% 99.50/14.23 | | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | End of split
% 99.50/14.23 | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | Case 2:
% 99.50/14.23 | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | (251) ~ (all_123_2 = 0) & related(all_41_4, all_41_2,
% 99.50/14.23 | | | | | | | | | | all_41_1) = all_123_2
% 99.50/14.23 | | | | | | | | | |
% 99.50/14.23 | | | | | | | | | | ALPHA: (251) implies:
% 99.50/14.24 | | | | | | | | | | (252) ~ (all_123_2 = 0)
% 99.50/14.24 | | | | | | | | | | (253) related(all_41_4, all_41_2, all_41_1) = all_123_2
% 99.50/14.24 | | | | | | | | | |
% 99.50/14.24 | | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_123_2, all_41_1,
% 99.50/14.24 | | | | | | | | | | all_41_2, all_41_4, simplifying with (35), (253)
% 99.50/14.24 | | | | | | | | | | gives:
% 99.50/14.24 | | | | | | | | | | (254) all_123_2 = 0
% 99.50/14.24 | | | | | | | | | |
% 99.50/14.24 | | | | | | | | | | REDUCE: (252), (254) imply:
% 99.50/14.24 | | | | | | | | | | (255) $false
% 99.50/14.24 | | | | | | | | | |
% 99.50/14.24 | | | | | | | | | | CLOSE: (255) is inconsistent.
% 99.50/14.24 | | | | | | | | | |
% 99.50/14.24 | | | | | | | | | End of split
% 99.50/14.24 | | | | | | | | |
% 99.50/14.24 | | | | | | | | End of split
% 99.50/14.24 | | | | | | | |
% 99.50/14.24 | | | | | | | Case 2:
% 99.50/14.24 | | | | | | | |
% 99.50/14.24 | | | | | | | | (256) ~ (all_100_4 = 0) & rel_str(all_41_4) = all_100_4
% 99.50/14.24 | | | | | | | |
% 99.50/14.24 | | | | | | | | ALPHA: (256) implies:
% 99.50/14.24 | | | | | | | | (257) ~ (all_100_4 = 0)
% 99.50/14.24 | | | | | | | | (258) rel_str(all_41_4) = all_100_4
% 99.50/14.24 | | | | | | | |
% 99.50/14.24 | | | | | | | | GROUND_INST: instantiating (14) with 0, all_100_4, all_41_4,
% 99.50/14.24 | | | | | | | | simplifying with (36), (258) gives:
% 99.50/14.24 | | | | | | | | (259) all_100_4 = 0
% 99.50/14.24 | | | | | | | |
% 99.50/14.24 | | | | | | | | REDUCE: (257), (259) imply:
% 99.50/14.24 | | | | | | | | (260) $false
% 99.50/14.24 | | | | | | | |
% 99.50/14.24 | | | | | | | | CLOSE: (260) is inconsistent.
% 99.50/14.24 | | | | | | | |
% 99.50/14.24 | | | | | | | End of split
% 99.50/14.24 | | | | | | |
% 99.50/14.24 | | | | | | End of split
% 99.50/14.24 | | | | | |
% 99.50/14.24 | | | | | Case 2:
% 99.50/14.24 | | | | | |
% 99.50/14.24 | | | | | | (261) ~ (all_119_2 = 0) & element(all_41_1, all_41_3) =
% 99.50/14.24 | | | | | | all_119_2
% 99.50/14.24 | | | | | |
% 99.50/14.24 | | | | | | ALPHA: (261) implies:
% 99.50/14.24 | | | | | | (262) ~ (all_119_2 = 0)
% 99.50/14.24 | | | | | | (263) element(all_41_1, all_41_3) = all_119_2
% 99.50/14.24 | | | | | |
% 99.50/14.24 | | | | | | GROUND_INST: instantiating (16) with 0, all_119_2, all_41_3,
% 99.50/14.24 | | | | | | all_41_1, simplifying with (29), (263) gives:
% 99.50/14.24 | | | | | | (264) all_119_2 = 0
% 99.50/14.24 | | | | | |
% 99.50/14.24 | | | | | | REDUCE: (262), (264) imply:
% 99.50/14.24 | | | | | | (265) $false
% 99.50/14.24 | | | | | |
% 99.50/14.24 | | | | | | CLOSE: (265) is inconsistent.
% 99.50/14.24 | | | | | |
% 99.50/14.24 | | | | | End of split
% 99.50/14.24 | | | | |
% 99.50/14.24 | | | | End of split
% 99.50/14.24 | | | |
% 99.50/14.24 | | | Case 2:
% 99.50/14.24 | | | |
% 99.50/14.24 | | | | (266) ~ (all_84_4 = 0) & rel_str(all_41_4) = all_84_4
% 99.50/14.24 | | | |
% 99.50/14.24 | | | | ALPHA: (266) implies:
% 99.50/14.24 | | | | (267) ~ (all_84_4 = 0)
% 99.50/14.24 | | | | (268) rel_str(all_41_4) = all_84_4
% 99.50/14.24 | | | |
% 99.50/14.24 | | | | GROUND_INST: instantiating (14) with 0, all_84_4, all_41_4, simplifying
% 99.50/14.24 | | | | with (36), (268) gives:
% 99.50/14.24 | | | | (269) all_84_4 = 0
% 99.50/14.24 | | | |
% 99.50/14.24 | | | | REDUCE: (267), (269) imply:
% 99.50/14.24 | | | | (270) $false
% 99.50/14.24 | | | |
% 99.50/14.24 | | | | CLOSE: (270) is inconsistent.
% 99.50/14.24 | | | |
% 99.50/14.24 | | | End of split
% 99.50/14.24 | | |
% 99.50/14.24 | | End of split
% 99.50/14.24 | |
% 99.50/14.24 | Case 2:
% 99.50/14.24 | |
% 99.50/14.24 | | (271) ~ (all_61_2 = 0) & rel_str(all_41_4) = all_61_2
% 99.50/14.24 | |
% 99.50/14.24 | | ALPHA: (271) implies:
% 99.50/14.24 | | (272) ~ (all_61_2 = 0)
% 99.50/14.24 | | (273) rel_str(all_41_4) = all_61_2
% 99.50/14.24 | |
% 99.50/14.24 | | GROUND_INST: instantiating (14) with 0, all_61_2, all_41_4, simplifying with
% 99.50/14.24 | | (36), (273) gives:
% 99.50/14.24 | | (274) all_61_2 = 0
% 99.50/14.24 | |
% 99.50/14.24 | | REDUCE: (272), (274) imply:
% 99.50/14.24 | | (275) $false
% 99.50/14.24 | |
% 99.50/14.24 | | CLOSE: (275) is inconsistent.
% 99.50/14.24 | |
% 99.50/14.24 | End of split
% 99.50/14.24 |
% 99.50/14.24 End of proof
% 99.50/14.24 % SZS output end Proof for theBenchmark
% 99.50/14.24
% 99.50/14.24 13633ms
%------------------------------------------------------------------------------