TSTP Solution File: SET771+4 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET771+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n024.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 15:26:22 EDT 2023
% Result : Theorem 13.15s 2.48s
% Output : Proof 20.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET771+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 11:02:39 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.63 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.32/1.19 Prover 1: Preprocessing ...
% 3.32/1.20 Prover 4: Preprocessing ...
% 3.86/1.24 Prover 5: Preprocessing ...
% 3.86/1.24 Prover 0: Preprocessing ...
% 3.86/1.24 Prover 6: Preprocessing ...
% 3.86/1.24 Prover 2: Preprocessing ...
% 3.86/1.24 Prover 3: Preprocessing ...
% 9.56/2.04 Prover 5: Proving ...
% 9.94/2.05 Prover 2: Proving ...
% 9.94/2.09 Prover 6: Proving ...
% 10.85/2.19 Prover 3: Constructing countermodel ...
% 10.85/2.20 Prover 1: Constructing countermodel ...
% 13.15/2.48 Prover 3: proved (1828ms)
% 13.15/2.48
% 13.15/2.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.15/2.48
% 13.15/2.48 Prover 5: stopped
% 13.15/2.48 Prover 6: stopped
% 13.15/2.48 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.15/2.49 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.15/2.49 Prover 2: stopped
% 13.15/2.50 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.15/2.50 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.73/2.58 Prover 8: Preprocessing ...
% 13.73/2.60 Prover 7: Preprocessing ...
% 13.73/2.60 Prover 11: Preprocessing ...
% 13.73/2.64 Prover 10: Preprocessing ...
% 15.03/2.78 Prover 7: Warning: ignoring some quantifiers
% 15.03/2.79 Prover 4: Constructing countermodel ...
% 15.03/2.79 Prover 0: Proving ...
% 15.03/2.80 Prover 0: stopped
% 15.03/2.80 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 15.03/2.80 Prover 10: Warning: ignoring some quantifiers
% 15.03/2.80 Prover 7: Constructing countermodel ...
% 15.74/2.82 Prover 10: Constructing countermodel ...
% 15.74/2.86 Prover 13: Preprocessing ...
% 16.30/2.96 Prover 8: Warning: ignoring some quantifiers
% 16.95/3.00 Prover 8: Constructing countermodel ...
% 17.31/3.07 Prover 13: Warning: ignoring some quantifiers
% 18.04/3.12 Prover 13: Constructing countermodel ...
% 18.04/3.15 Prover 10: gave up
% 18.04/3.15 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 18.65/3.24 Prover 16: Preprocessing ...
% 18.65/3.27 Prover 1: Found proof (size 351)
% 18.65/3.27 Prover 1: proved (2638ms)
% 18.65/3.27 Prover 7: stopped
% 18.65/3.27 Prover 8: stopped
% 18.65/3.27 Prover 11: stopped
% 18.65/3.27 Prover 4: stopped
% 18.65/3.28 Prover 13: stopped
% 18.65/3.29 Prover 16: stopped
% 18.65/3.29
% 18.65/3.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.65/3.29
% 18.65/3.31 % SZS output start Proof for theBenchmark
% 18.65/3.31 Assumptions after simplification:
% 18.65/3.31 ---------------------------------
% 18.65/3.31
% 18.65/3.32 (equivalence)
% 19.48/3.34 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equivalence(v1, v0) =
% 19.48/3.34 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ?
% 19.48/3.34 [v6: int] : ( ~ (v6 = 0) & apply(v1, v4, v5) = 0 & apply(v1, v3, v5) = v6 &
% 19.48/3.34 apply(v1, v3, v4) = 0 & member(v5, v0) = 0 & member(v4, v0) = 0 &
% 19.48/3.34 member(v3, v0) = 0 & $i(v5) & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: $i]
% 19.48/3.34 : ? [v5: int] : ( ~ (v5 = 0) & apply(v1, v4, v3) = v5 & apply(v1, v3, v4) =
% 19.48/3.34 0 & member(v4, v0) = 0 & member(v3, v0) = 0 & $i(v4) & $i(v3)) | ? [v3:
% 19.48/3.34 $i] : ? [v4: int] : ( ~ (v4 = 0) & apply(v1, v3, v3) = v4 & member(v3,
% 19.48/3.34 v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (equivalence(v1,
% 19.48/3.34 v0) = 0) | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4:
% 19.48/3.34 $i] : ! [v5: int] : (v5 = 0 | ~ (apply(v1, v2, v4) = v5) | ~
% 19.48/3.34 (apply(v1, v2, v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6:
% 19.48/3.34 any] : ? [v7: any] : ? [v8: any] : ? [v9: any] : (apply(v1, v3, v4)
% 19.48/3.34 = v9 & member(v4, v0) = v8 & member(v3, v0) = v7 & member(v2, v0) = v6
% 19.48/3.34 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v2:
% 19.48/3.34 $i] : ! [v3: int] : (v3 = 0 | ~ (apply(v1, v2, v2) = v3) | ~ $i(v2) |
% 19.48/3.34 ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v2: $i] : !
% 19.48/3.34 [v3: $i] : ( ~ (apply(v1, v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v4:
% 19.48/3.34 any] : ? [v5: any] : ? [v6: any] : (apply(v1, v3, v2) = v6 &
% 19.48/3.34 member(v3, v0) = v5 & member(v2, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)
% 19.48/3.34 | v6 = 0)))))
% 19.48/3.34
% 19.48/3.34 (maps)
% 19.48/3.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 19.48/3.35 (maps(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] :
% 19.48/3.35 ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & apply(v0, v4, v6) = 0 & apply(v0,
% 19.48/3.35 v4, v5) = 0 & member(v6, v2) = 0 & member(v5, v2) = 0 & member(v4, v1) =
% 19.48/3.35 0 & $i(v6) & $i(v5) & $i(v4)) | ? [v4: $i] : (member(v4, v1) = 0 & $i(v4)
% 19.48/3.35 & ! [v5: $i] : ( ~ (apply(v0, v4, v5) = 0) | ~ $i(v5) | ? [v6: int] : (
% 19.48/3.35 ~ (v6 = 0) & member(v5, v2) = v6)))) & ! [v0: $i] : ! [v1: $i] : !
% 19.48/3.35 [v2: $i] : ( ~ (maps(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (
% 19.48/3.35 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (apply(v0, v3, v5)
% 19.48/3.35 = 0) | ~ (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3)
% 19.48/3.35 | ? [v6: any] : ? [v7: any] : ? [v8: any] : (member(v5, v2) = v8 &
% 19.48/3.35 member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0)
% 19.48/3.35 | ~ (v6 = 0)))) & ! [v3: $i] : ( ~ (member(v3, v1) = 0) | ~
% 19.48/3.35 $i(v3) | ? [v4: $i] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0 &
% 19.48/3.35 $i(v4)))))
% 19.48/3.35
% 19.48/3.35 (thIII07)
% 19.48/3.35 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4
% 19.48/3.35 = 0) & equivalence(v3, v1) = v4 & maps(v0, v1, v2) = 0 & $i(v3) & $i(v2) &
% 19.48/3.35 $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : ! [v7: any] : ( ~ (apply(v3,
% 19.48/3.35 v5, v6) = v7) | ~ $i(v6) | ~ $i(v5) | ? [v8: any] : ? [v9: any] :
% 19.48/3.35 (member(v6, v1) = v9 & member(v5, v1) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0)))
% 19.48/3.35 | (( ~ (v7 = 0) | ? [v8: $i] : (apply(v0, v6, v8) = 0 & apply(v0, v5, v8)
% 19.48/3.35 = 0 & member(v8, v2) = 0 & $i(v8))) & (v7 = 0 | ! [v8: $i] : ( ~
% 19.48/3.35 (apply(v0, v5, v8) = 0) | ~ $i(v8) | ? [v9: any] : ? [v10: any] :
% 19.48/3.35 (apply(v0, v6, v8) = v10 & member(v8, v2) = v9 & ( ~ (v10 = 0) | ~
% 19.48/3.35 (v9 = 0))))))))
% 19.48/3.35
% 19.48/3.35 (function-axioms)
% 19.48/3.36 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 19.48/3.36 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 |
% 19.48/3.36 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~
% 19.48/3.36 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 19.48/3.36 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 19.48/3.36 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5,
% 19.48/3.36 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 19.48/3.36 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 19.48/3.36 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5,
% 19.48/3.36 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 19.48/3.36 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 19.48/3.36 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5,
% 19.48/3.36 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 19.48/3.36 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 19.48/3.36 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~
% 19.48/3.36 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 19.48/3.36 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 19.48/3.36 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~
% 19.48/3.36 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 19.48/3.36 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 19.48/3.36 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5,
% 19.48/3.36 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 19.48/3.36 $i] : ! [v4: $i] : (v1 = v0 | ~ (equivalence_class(v4, v3, v2) = v1) | ~
% 19.48/3.36 (equivalence_class(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 19.48/3.36 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2)
% 19.48/3.36 = v1) | ~ (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 19.48/3.36 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2)
% 19.48/3.36 = v1) | ~ (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 19.48/3.36 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3,
% 19.48/3.36 v2) = v1) | ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0:
% 19.48/3.36 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 19.48/3.36 : ! [v4: $i] : (v1 = v0 | ~ (one_to_one(v4, v3, v2) = v1) | ~
% 19.48/3.36 (one_to_one(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 19.48/3.36 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 19.48/3.36 (surjective(v4, v3, v2) = v1) | ~ (surjective(v4, v3, v2) = v0)) & ! [v0:
% 19.48/3.36 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 19.48/3.36 : ! [v4: $i] : (v1 = v0 | ~ (injective(v4, v3, v2) = v1) | ~ (injective(v4,
% 19.48/3.36 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 19.48/3.36 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) =
% 19.48/3.36 v1) | ~ (maps(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 19.48/3.36 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 19.48/3.36 (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0:
% 19.48/3.36 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 19.48/3.36 : (v1 = v0 | ~ (pre_order(v3, v2) = v1) | ~ (pre_order(v3, v2) = v0)) & !
% 19.48/3.36 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 19.48/3.36 $i] : (v1 = v0 | ~ (equivalence(v3, v2) = v1) | ~ (equivalence(v3, v2) =
% 19.48/3.36 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 19.48/3.36 $i] : ! [v3: $i] : (v1 = v0 | ~ (partition(v3, v2) = v1) | ~
% 19.48/3.36 (partition(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 19.48/3.36 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disjoint(v3,
% 19.48/3.36 v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 19.48/3.36 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~
% 19.48/3.36 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 19.48/3.36 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) &
% 19.48/3.36 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 19.48/3.36 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0))
% 19.48/3.36 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 19.48/3.36 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 19.48/3.36 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 19.48/3.36 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 19.48/3.36 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 19.48/3.36 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 19.48/3.36 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 19.48/3.36 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 19.48/3.36 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 19.48/3.36 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 19.48/3.36 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 19.48/3.36 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 19.48/3.36 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 19.48/3.36 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 19.48/3.36 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 19.48/3.36 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 19.48/3.36 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 19.48/3.36 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 19.48/3.36 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 19.48/3.36 (power_set(v2) = v0))
% 19.48/3.36
% 19.48/3.36 Further assumptions not needed in the proof:
% 19.48/3.36 --------------------------------------------
% 19.48/3.36 compose_function, compose_predicate, decreasing_function, difference, disjoint,
% 19.48/3.36 empty_set, equal_maps, equal_set, equivalence_class, identity, image2, image3,
% 19.48/3.36 increasing_function, injective, intersection, inverse_function, inverse_image2,
% 19.48/3.36 inverse_image3, inverse_predicate, isomorphism, one_to_one, partition,
% 19.48/3.36 power_set, pre_order, product, singleton, subset, sum, surjective, union,
% 19.48/3.36 unordered_pair
% 19.48/3.36
% 19.48/3.36 Those formulas are unsatisfiable:
% 19.48/3.36 ---------------------------------
% 19.48/3.36
% 19.48/3.36 Begin of proof
% 19.48/3.36 |
% 19.48/3.36 | ALPHA: (maps) implies:
% 19.48/3.36 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (maps(v0, v1, v2) = 0) |
% 19.48/3.36 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: $i] : !
% 19.48/3.36 | [v5: $i] : (v5 = v4 | ~ (apply(v0, v3, v5) = 0) | ~ (apply(v0,
% 19.48/3.36 | v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v6:
% 19.48/3.36 | any] : ? [v7: any] : ? [v8: any] : (member(v5, v2) = v8 &
% 19.48/3.36 | member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~
% 19.48/3.36 | (v7 = 0) | ~ (v6 = 0)))) & ! [v3: $i] : ( ~ (member(v3, v1)
% 19.48/3.36 | = 0) | ~ $i(v3) | ? [v4: $i] : (apply(v0, v3, v4) = 0 &
% 19.48/3.36 | member(v4, v2) = 0 & $i(v4)))))
% 19.48/3.36 |
% 19.48/3.36 | ALPHA: (equivalence) implies:
% 19.48/3.37 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 19.48/3.37 | (equivalence(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ?
% 19.48/3.37 | [v4: $i] : ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & apply(v1, v4,
% 19.48/3.37 | v5) = 0 & apply(v1, v3, v5) = v6 & apply(v1, v3, v4) = 0 &
% 19.48/3.37 | member(v5, v0) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0 &
% 19.48/3.37 | $i(v5) & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: $i] : ? [v5:
% 19.48/3.37 | int] : ( ~ (v5 = 0) & apply(v1, v4, v3) = v5 & apply(v1, v3, v4) =
% 19.48/3.37 | 0 & member(v4, v0) = 0 & member(v3, v0) = 0 & $i(v4) & $i(v3)) | ?
% 19.48/3.37 | [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & apply(v1, v3, v3) = v4 &
% 19.48/3.37 | member(v3, v0) = 0 & $i(v3)))
% 19.48/3.37 |
% 19.48/3.37 | ALPHA: (function-axioms) implies:
% 19.48/3.37 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 19.48/3.37 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 19.48/3.37 | = v0))
% 19.48/3.37 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 19.48/3.37 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~
% 19.48/3.37 | (apply(v4, v3, v2) = v0))
% 19.48/3.37 |
% 19.48/3.37 | DELTA: instantiating (thIII07) with fresh symbols all_37_0, all_37_1,
% 19.48/3.37 | all_37_2, all_37_3, all_37_4 gives:
% 19.48/3.37 | (5) ~ (all_37_0 = 0) & equivalence(all_37_1, all_37_3) = all_37_0 &
% 19.48/3.37 | maps(all_37_4, all_37_3, all_37_2) = 0 & $i(all_37_1) & $i(all_37_2) &
% 19.48/3.37 | $i(all_37_3) & $i(all_37_4) & ! [v0: $i] : ! [v1: $i] : ! [v2: any]
% 19.48/3.37 | : ( ~ (apply(all_37_1, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 19.48/3.37 | any] : ? [v4: any] : (member(v1, all_37_3) = v4 & member(v0,
% 19.48/3.37 | all_37_3) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))) | (( ~ (v2 = 0) |
% 19.48/3.37 | ? [v3: $i] : (apply(all_37_4, v1, v3) = 0 & apply(all_37_4, v0,
% 19.48/3.37 | v3) = 0 & member(v3, all_37_2) = 0 & $i(v3))) & (v2 = 0 | !
% 19.48/3.37 | [v3: $i] : ( ~ (apply(all_37_4, v0, v3) = 0) | ~ $i(v3) | ?
% 19.48/3.37 | [v4: any] : ? [v5: any] : (apply(all_37_4, v1, v3) = v5 &
% 19.48/3.37 | member(v3, all_37_2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))))
% 19.48/3.37 |
% 19.48/3.37 | ALPHA: (5) implies:
% 19.48/3.37 | (6) ~ (all_37_0 = 0)
% 19.48/3.37 | (7) $i(all_37_4)
% 19.48/3.37 | (8) $i(all_37_3)
% 19.48/3.37 | (9) $i(all_37_2)
% 19.48/3.37 | (10) $i(all_37_1)
% 19.48/3.37 | (11) maps(all_37_4, all_37_3, all_37_2) = 0
% 19.48/3.37 | (12) equivalence(all_37_1, all_37_3) = all_37_0
% 19.48/3.37 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (apply(all_37_1, v0,
% 19.48/3.37 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any]
% 19.48/3.37 | : (member(v1, all_37_3) = v4 & member(v0, all_37_3) = v3 & ( ~ (v4 =
% 19.48/3.37 | 0) | ~ (v3 = 0))) | (( ~ (v2 = 0) | ? [v3: $i] :
% 19.48/3.37 | (apply(all_37_4, v1, v3) = 0 & apply(all_37_4, v0, v3) = 0 &
% 19.48/3.37 | member(v3, all_37_2) = 0 & $i(v3))) & (v2 = 0 | ! [v3: $i] :
% 19.48/3.37 | ( ~ (apply(all_37_4, v0, v3) = 0) | ~ $i(v3) | ? [v4: any] :
% 19.48/3.37 | ? [v5: any] : (apply(all_37_4, v1, v3) = v5 & member(v3,
% 19.48/3.37 | all_37_2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))))
% 19.48/3.37 |
% 19.48/3.37 | GROUND_INST: instantiating (1) with all_37_4, all_37_3, all_37_2, simplifying
% 19.48/3.37 | with (7), (8), (9), (11) gives:
% 19.48/3.37 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 19.48/3.37 | (apply(all_37_4, v0, v2) = 0) | ~ (apply(all_37_4, v0, v1) = 0) |
% 19.48/3.37 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ?
% 19.48/3.37 | [v5: any] : (member(v2, all_37_2) = v5 & member(v1, all_37_2) = v4 &
% 19.48/3.37 | member(v0, all_37_3) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 =
% 19.48/3.37 | 0)))) & ! [v0: $i] : ( ~ (member(v0, all_37_3) = 0) | ~
% 19.48/3.37 | $i(v0) | ? [v1: $i] : (apply(all_37_4, v0, v1) = 0 & member(v1,
% 19.48/3.37 | all_37_2) = 0 & $i(v1)))
% 19.48/3.37 |
% 19.48/3.37 | ALPHA: (14) implies:
% 19.48/3.38 | (15) ! [v0: $i] : ( ~ (member(v0, all_37_3) = 0) | ~ $i(v0) | ? [v1: $i]
% 19.48/3.38 | : (apply(all_37_4, v0, v1) = 0 & member(v1, all_37_2) = 0 & $i(v1)))
% 19.48/3.38 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 19.48/3.38 | (apply(all_37_4, v0, v2) = 0) | ~ (apply(all_37_4, v0, v1) = 0) |
% 19.48/3.38 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ?
% 19.48/3.38 | [v5: any] : (member(v2, all_37_2) = v5 & member(v1, all_37_2) = v4 &
% 19.48/3.38 | member(v0, all_37_3) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 =
% 19.48/3.38 | 0))))
% 19.48/3.38 |
% 19.48/3.38 | GROUND_INST: instantiating (2) with all_37_3, all_37_1, all_37_0, simplifying
% 19.48/3.38 | with (8), (10), (12) gives:
% 19.48/3.38 | (17) all_37_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int]
% 19.48/3.38 | : ( ~ (v3 = 0) & apply(all_37_1, v1, v2) = 0 & apply(all_37_1, v0, v2)
% 19.48/3.38 | = v3 & apply(all_37_1, v0, v1) = 0 & member(v2, all_37_3) = 0 &
% 19.48/3.38 | member(v1, all_37_3) = 0 & member(v0, all_37_3) = 0 & $i(v2) &
% 19.48/3.38 | $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~
% 19.48/3.38 | (v2 = 0) & apply(all_37_1, v1, v0) = v2 & apply(all_37_1, v0, v1) =
% 19.48/3.38 | 0 & member(v1, all_37_3) = 0 & member(v0, all_37_3) = 0 & $i(v1) &
% 19.48/3.38 | $i(v0)) | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 19.48/3.38 | apply(all_37_1, v0, v0) = v1 & member(v0, all_37_3) = 0 & $i(v0))
% 19.48/3.38 |
% 19.48/3.38 | BETA: splitting (17) gives:
% 19.48/3.38 |
% 19.48/3.38 | Case 1:
% 19.48/3.38 | |
% 19.48/3.38 | | (18) all_37_0 = 0
% 19.48/3.38 | |
% 19.48/3.38 | | REDUCE: (6), (18) imply:
% 19.48/3.38 | | (19) $false
% 19.48/3.38 | |
% 19.48/3.38 | | CLOSE: (19) is inconsistent.
% 19.48/3.38 | |
% 19.48/3.38 | Case 2:
% 19.48/3.38 | |
% 19.48/3.38 | | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 =
% 19.48/3.38 | | 0) & apply(all_37_1, v1, v2) = 0 & apply(all_37_1, v0, v2) = v3
% 19.48/3.38 | | & apply(all_37_1, v0, v1) = 0 & member(v2, all_37_3) = 0 &
% 19.48/3.38 | | member(v1, all_37_3) = 0 & member(v0, all_37_3) = 0 & $i(v2) &
% 19.48/3.38 | | $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~
% 19.48/3.38 | | (v2 = 0) & apply(all_37_1, v1, v0) = v2 & apply(all_37_1, v0, v1)
% 19.48/3.38 | | = 0 & member(v1, all_37_3) = 0 & member(v0, all_37_3) = 0 & $i(v1)
% 19.48/3.38 | | & $i(v0)) | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 19.48/3.38 | | apply(all_37_1, v0, v0) = v1 & member(v0, all_37_3) = 0 & $i(v0))
% 19.48/3.38 | |
% 19.48/3.38 | | BETA: splitting (20) gives:
% 19.48/3.38 | |
% 19.48/3.38 | | Case 1:
% 19.48/3.38 | | |
% 19.48/3.38 | | | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 =
% 19.48/3.38 | | | 0) & apply(all_37_1, v1, v2) = 0 & apply(all_37_1, v0, v2) =
% 19.48/3.38 | | | v3 & apply(all_37_1, v0, v1) = 0 & member(v2, all_37_3) = 0 &
% 19.48/3.38 | | | member(v1, all_37_3) = 0 & member(v0, all_37_3) = 0 & $i(v2) &
% 19.48/3.38 | | | $i(v1) & $i(v0))
% 19.48/3.38 | | |
% 19.48/3.38 | | | DELTA: instantiating (21) with fresh symbols all_56_0, all_56_1, all_56_2,
% 19.48/3.38 | | | all_56_3 gives:
% 19.48/3.38 | | | (22) ~ (all_56_0 = 0) & apply(all_37_1, all_56_2, all_56_1) = 0 &
% 19.48/3.38 | | | apply(all_37_1, all_56_3, all_56_1) = all_56_0 & apply(all_37_1,
% 19.48/3.38 | | | all_56_3, all_56_2) = 0 & member(all_56_1, all_37_3) = 0 &
% 19.48/3.38 | | | member(all_56_2, all_37_3) = 0 & member(all_56_3, all_37_3) = 0 &
% 19.48/3.38 | | | $i(all_56_1) & $i(all_56_2) & $i(all_56_3)
% 19.48/3.38 | | |
% 19.48/3.38 | | | ALPHA: (22) implies:
% 19.48/3.38 | | | (23) ~ (all_56_0 = 0)
% 19.48/3.38 | | | (24) $i(all_56_3)
% 19.48/3.38 | | | (25) $i(all_56_2)
% 19.48/3.38 | | | (26) $i(all_56_1)
% 19.48/3.38 | | | (27) member(all_56_3, all_37_3) = 0
% 19.48/3.38 | | | (28) member(all_56_2, all_37_3) = 0
% 19.48/3.38 | | | (29) member(all_56_1, all_37_3) = 0
% 19.48/3.38 | | | (30) apply(all_37_1, all_56_3, all_56_2) = 0
% 19.48/3.39 | | | (31) apply(all_37_1, all_56_3, all_56_1) = all_56_0
% 19.48/3.39 | | | (32) apply(all_37_1, all_56_2, all_56_1) = 0
% 19.48/3.39 | | |
% 19.48/3.39 | | | GROUND_INST: instantiating (15) with all_56_3, simplifying with (24), (27)
% 19.48/3.39 | | | gives:
% 19.48/3.39 | | | (33) ? [v0: $i] : (apply(all_37_4, all_56_3, v0) = 0 & member(v0,
% 19.48/3.39 | | | all_37_2) = 0 & $i(v0))
% 19.48/3.39 | | |
% 19.48/3.39 | | | GROUND_INST: instantiating (15) with all_56_2, simplifying with (25), (28)
% 19.48/3.39 | | | gives:
% 19.48/3.39 | | | (34) ? [v0: $i] : (apply(all_37_4, all_56_2, v0) = 0 & member(v0,
% 19.48/3.39 | | | all_37_2) = 0 & $i(v0))
% 19.48/3.39 | | |
% 19.48/3.39 | | | GROUND_INST: instantiating (15) with all_56_1, simplifying with (26), (29)
% 19.48/3.39 | | | gives:
% 19.48/3.39 | | | (35) ? [v0: $i] : (apply(all_37_4, all_56_1, v0) = 0 & member(v0,
% 19.48/3.39 | | | all_37_2) = 0 & $i(v0))
% 19.48/3.39 | | |
% 19.48/3.39 | | | GROUND_INST: instantiating (13) with all_56_3, all_56_2, 0, simplifying
% 19.48/3.39 | | | with (24), (25), (30) gives:
% 19.48/3.39 | | | (36) ? [v0: any] : ? [v1: any] : (member(all_56_2, all_37_3) = v1 &
% 19.48/3.39 | | | member(all_56_3, all_37_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) |
% 19.48/3.39 | | | ? [v0: $i] : (apply(all_37_4, all_56_2, v0) = 0 & apply(all_37_4,
% 19.48/3.39 | | | all_56_3, v0) = 0 & member(v0, all_37_2) = 0 & $i(v0))
% 19.48/3.39 | | |
% 19.48/3.39 | | | GROUND_INST: instantiating (13) with all_56_3, all_56_1, all_56_0,
% 19.48/3.39 | | | simplifying with (24), (26), (31) gives:
% 19.48/3.39 | | | (37) ? [v0: any] : ? [v1: any] : (member(all_56_1, all_37_3) = v1 &
% 19.48/3.39 | | | member(all_56_3, all_37_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) |
% 19.48/3.39 | | | (( ~ (all_56_0 = 0) | ? [v0: $i] : (apply(all_37_4, all_56_1, v0)
% 19.48/3.39 | | | = 0 & apply(all_37_4, all_56_3, v0) = 0 & member(v0,
% 19.48/3.39 | | | all_37_2) = 0 & $i(v0))) & (all_56_0 = 0 | ! [v0: $i] : (
% 19.48/3.39 | | | ~ (apply(all_37_4, all_56_3, v0) = 0) | ~ $i(v0) | ? [v1:
% 19.48/3.39 | | | any] : ? [v2: any] : (apply(all_37_4, all_56_1, v0) = v2
% 19.48/3.39 | | | & member(v0, all_37_2) = v1 & ( ~ (v2 = 0) | ~ (v1 =
% 19.48/3.39 | | | 0))))))
% 19.48/3.39 | | |
% 19.48/3.39 | | | GROUND_INST: instantiating (13) with all_56_2, all_56_1, 0, simplifying
% 19.48/3.39 | | | with (25), (26), (32) gives:
% 19.48/3.39 | | | (38) ? [v0: any] : ? [v1: any] : (member(all_56_1, all_37_3) = v1 &
% 19.48/3.39 | | | member(all_56_2, all_37_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) |
% 19.48/3.39 | | | ? [v0: $i] : (apply(all_37_4, all_56_1, v0) = 0 & apply(all_37_4,
% 19.48/3.39 | | | all_56_2, v0) = 0 & member(v0, all_37_2) = 0 & $i(v0))
% 19.48/3.39 | | |
% 19.48/3.39 | | | DELTA: instantiating (35) with fresh symbol all_63_0 gives:
% 19.48/3.39 | | | (39) apply(all_37_4, all_56_1, all_63_0) = 0 & member(all_63_0,
% 19.48/3.39 | | | all_37_2) = 0 & $i(all_63_0)
% 19.48/3.39 | | |
% 19.48/3.39 | | | ALPHA: (39) implies:
% 19.48/3.39 | | | (40) $i(all_63_0)
% 19.48/3.39 | | | (41) member(all_63_0, all_37_2) = 0
% 19.48/3.39 | | | (42) apply(all_37_4, all_56_1, all_63_0) = 0
% 19.48/3.39 | | |
% 19.48/3.39 | | | DELTA: instantiating (34) with fresh symbol all_65_0 gives:
% 19.48/3.39 | | | (43) apply(all_37_4, all_56_2, all_65_0) = 0 & member(all_65_0,
% 19.48/3.39 | | | all_37_2) = 0 & $i(all_65_0)
% 19.48/3.39 | | |
% 19.48/3.39 | | | ALPHA: (43) implies:
% 19.48/3.39 | | | (44) $i(all_65_0)
% 19.48/3.39 | | | (45) member(all_65_0, all_37_2) = 0
% 19.48/3.39 | | | (46) apply(all_37_4, all_56_2, all_65_0) = 0
% 19.48/3.39 | | |
% 19.48/3.39 | | | DELTA: instantiating (33) with fresh symbol all_67_0 gives:
% 19.48/3.39 | | | (47) apply(all_37_4, all_56_3, all_67_0) = 0 & member(all_67_0,
% 19.48/3.39 | | | all_37_2) = 0 & $i(all_67_0)
% 19.48/3.39 | | |
% 19.48/3.39 | | | ALPHA: (47) implies:
% 19.48/3.39 | | | (48) $i(all_67_0)
% 19.48/3.39 | | | (49) apply(all_37_4, all_56_3, all_67_0) = 0
% 19.48/3.39 | | |
% 19.48/3.39 | | | BETA: splitting (37) gives:
% 19.48/3.39 | | |
% 19.48/3.39 | | | Case 1:
% 19.48/3.39 | | | |
% 19.48/3.39 | | | | (50) ? [v0: any] : ? [v1: any] : (member(all_56_1, all_37_3) = v1 &
% 19.48/3.39 | | | | member(all_56_3, all_37_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 19.48/3.39 | | | |
% 19.48/3.39 | | | | DELTA: instantiating (50) with fresh symbols all_72_0, all_72_1 gives:
% 19.48/3.40 | | | | (51) member(all_56_1, all_37_3) = all_72_0 & member(all_56_3,
% 19.48/3.40 | | | | all_37_3) = all_72_1 & ( ~ (all_72_0 = 0) | ~ (all_72_1 = 0))
% 19.48/3.40 | | | |
% 19.48/3.40 | | | | ALPHA: (51) implies:
% 19.48/3.40 | | | | (52) member(all_56_3, all_37_3) = all_72_1
% 19.48/3.40 | | | | (53) member(all_56_1, all_37_3) = all_72_0
% 19.48/3.40 | | | | (54) ~ (all_72_0 = 0) | ~ (all_72_1 = 0)
% 19.48/3.40 | | | |
% 19.48/3.40 | | | | GROUND_INST: instantiating (3) with 0, all_72_1, all_37_3, all_56_3,
% 19.48/3.40 | | | | simplifying with (27), (52) gives:
% 19.48/3.40 | | | | (55) all_72_1 = 0
% 19.48/3.40 | | | |
% 19.48/3.40 | | | | GROUND_INST: instantiating (3) with 0, all_72_0, all_37_3, all_56_1,
% 19.48/3.40 | | | | simplifying with (29), (53) gives:
% 19.48/3.40 | | | | (56) all_72_0 = 0
% 19.48/3.40 | | | |
% 19.48/3.40 | | | | BETA: splitting (54) gives:
% 19.48/3.40 | | | |
% 19.48/3.40 | | | | Case 1:
% 19.48/3.40 | | | | |
% 19.48/3.40 | | | | | (57) ~ (all_72_0 = 0)
% 19.48/3.40 | | | | |
% 19.48/3.40 | | | | | REDUCE: (56), (57) imply:
% 19.48/3.40 | | | | | (58) $false
% 19.48/3.40 | | | | |
% 19.48/3.40 | | | | | CLOSE: (58) is inconsistent.
% 19.48/3.40 | | | | |
% 19.48/3.40 | | | | Case 2:
% 19.48/3.40 | | | | |
% 19.48/3.40 | | | | | (59) ~ (all_72_1 = 0)
% 19.48/3.40 | | | | |
% 19.48/3.40 | | | | | REDUCE: (55), (59) imply:
% 19.48/3.40 | | | | | (60) $false
% 19.48/3.40 | | | | |
% 19.48/3.40 | | | | | CLOSE: (60) is inconsistent.
% 19.48/3.40 | | | | |
% 19.48/3.40 | | | | End of split
% 19.48/3.40 | | | |
% 19.48/3.40 | | | Case 2:
% 19.48/3.40 | | | |
% 19.48/3.40 | | | | (61) ( ~ (all_56_0 = 0) | ? [v0: $i] : (apply(all_37_4, all_56_1,
% 19.48/3.40 | | | | v0) = 0 & apply(all_37_4, all_56_3, v0) = 0 & member(v0,
% 19.48/3.40 | | | | all_37_2) = 0 & $i(v0))) & (all_56_0 = 0 | ! [v0: $i] : (
% 19.48/3.40 | | | | ~ (apply(all_37_4, all_56_3, v0) = 0) | ~ $i(v0) | ? [v1:
% 19.48/3.40 | | | | any] : ? [v2: any] : (apply(all_37_4, all_56_1, v0) = v2
% 19.48/3.40 | | | | & member(v0, all_37_2) = v1 & ( ~ (v2 = 0) | ~ (v1 =
% 19.48/3.40 | | | | 0)))))
% 19.48/3.40 | | | |
% 19.48/3.40 | | | | ALPHA: (61) implies:
% 19.48/3.40 | | | | (62) all_56_0 = 0 | ! [v0: $i] : ( ~ (apply(all_37_4, all_56_3, v0)
% 19.48/3.40 | | | | = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] :
% 19.48/3.40 | | | | (apply(all_37_4, all_56_1, v0) = v2 & member(v0, all_37_2) =
% 19.48/3.40 | | | | v1 & ( ~ (v2 = 0) | ~ (v1 = 0))))
% 19.48/3.40 | | | |
% 19.48/3.40 | | | | BETA: splitting (36) gives:
% 19.48/3.40 | | | |
% 19.48/3.40 | | | | Case 1:
% 19.48/3.40 | | | | |
% 19.48/3.40 | | | | | (63) ? [v0: any] : ? [v1: any] : (member(all_56_2, all_37_3) = v1
% 19.48/3.40 | | | | | & member(all_56_3, all_37_3) = v0 & ( ~ (v1 = 0) | ~ (v0 =
% 19.48/3.40 | | | | | 0)))
% 19.48/3.40 | | | | |
% 19.48/3.40 | | | | | DELTA: instantiating (63) with fresh symbols all_73_0, all_73_1 gives:
% 19.48/3.40 | | | | | (64) member(all_56_2, all_37_3) = all_73_0 & member(all_56_3,
% 19.48/3.40 | | | | | all_37_3) = all_73_1 & ( ~ (all_73_0 = 0) | ~ (all_73_1 =
% 19.48/3.40 | | | | | 0))
% 19.48/3.40 | | | | |
% 19.48/3.40 | | | | | ALPHA: (64) implies:
% 19.48/3.40 | | | | | (65) member(all_56_3, all_37_3) = all_73_1
% 19.48/3.40 | | | | | (66) member(all_56_2, all_37_3) = all_73_0
% 19.48/3.40 | | | | | (67) ~ (all_73_0 = 0) | ~ (all_73_1 = 0)
% 19.48/3.40 | | | | |
% 19.48/3.40 | | | | | GROUND_INST: instantiating (3) with 0, all_73_1, all_37_3, all_56_3,
% 19.48/3.40 | | | | | simplifying with (27), (65) gives:
% 19.48/3.40 | | | | | (68) all_73_1 = 0
% 19.48/3.40 | | | | |
% 19.48/3.40 | | | | | GROUND_INST: instantiating (3) with 0, all_73_0, all_37_3, all_56_2,
% 19.48/3.40 | | | | | simplifying with (28), (66) gives:
% 19.48/3.40 | | | | | (69) all_73_0 = 0
% 19.48/3.40 | | | | |
% 19.48/3.40 | | | | | BETA: splitting (67) gives:
% 19.48/3.40 | | | | |
% 19.48/3.40 | | | | | Case 1:
% 19.48/3.40 | | | | | |
% 19.48/3.40 | | | | | | (70) ~ (all_73_0 = 0)
% 19.48/3.40 | | | | | |
% 19.48/3.40 | | | | | | REDUCE: (69), (70) imply:
% 19.48/3.40 | | | | | | (71) $false
% 19.48/3.40 | | | | | |
% 19.48/3.40 | | | | | | CLOSE: (71) is inconsistent.
% 19.48/3.40 | | | | | |
% 19.48/3.40 | | | | | Case 2:
% 19.48/3.40 | | | | | |
% 19.48/3.40 | | | | | | (72) ~ (all_73_1 = 0)
% 19.48/3.40 | | | | | |
% 19.48/3.40 | | | | | | REDUCE: (68), (72) imply:
% 19.48/3.40 | | | | | | (73) $false
% 19.48/3.40 | | | | | |
% 19.48/3.40 | | | | | | CLOSE: (73) is inconsistent.
% 19.48/3.40 | | | | | |
% 19.48/3.40 | | | | | End of split
% 19.48/3.40 | | | | |
% 19.48/3.40 | | | | Case 2:
% 19.48/3.40 | | | | |
% 19.48/3.40 | | | | | (74) ? [v0: $i] : (apply(all_37_4, all_56_2, v0) = 0 &
% 19.48/3.40 | | | | | apply(all_37_4, all_56_3, v0) = 0 & member(v0, all_37_2) = 0
% 19.48/3.40 | | | | | & $i(v0))
% 19.48/3.40 | | | | |
% 19.48/3.40 | | | | | DELTA: instantiating (74) with fresh symbol all_73_0 gives:
% 19.48/3.40 | | | | | (75) apply(all_37_4, all_56_2, all_73_0) = 0 & apply(all_37_4,
% 19.48/3.40 | | | | | all_56_3, all_73_0) = 0 & member(all_73_0, all_37_2) = 0 &
% 19.48/3.40 | | | | | $i(all_73_0)
% 19.48/3.40 | | | | |
% 19.48/3.40 | | | | | ALPHA: (75) implies:
% 19.48/3.40 | | | | | (76) $i(all_73_0)
% 19.48/3.40 | | | | | (77) member(all_73_0, all_37_2) = 0
% 19.48/3.40 | | | | | (78) apply(all_37_4, all_56_3, all_73_0) = 0
% 19.48/3.40 | | | | | (79) apply(all_37_4, all_56_2, all_73_0) = 0
% 19.48/3.40 | | | | |
% 19.48/3.40 | | | | | BETA: splitting (38) gives:
% 19.48/3.40 | | | | |
% 19.48/3.40 | | | | | Case 1:
% 19.48/3.40 | | | | | |
% 19.48/3.40 | | | | | | (80) ? [v0: any] : ? [v1: any] : (member(all_56_1, all_37_3) =
% 19.48/3.40 | | | | | | v1 & member(all_56_2, all_37_3) = v0 & ( ~ (v1 = 0) | ~
% 19.48/3.40 | | | | | | (v0 = 0)))
% 19.48/3.40 | | | | | |
% 19.48/3.40 | | | | | | DELTA: instantiating (80) with fresh symbols all_77_0, all_77_1
% 19.48/3.41 | | | | | | gives:
% 19.48/3.41 | | | | | | (81) member(all_56_1, all_37_3) = all_77_0 & member(all_56_2,
% 19.48/3.41 | | | | | | all_37_3) = all_77_1 & ( ~ (all_77_0 = 0) | ~ (all_77_1 =
% 19.48/3.41 | | | | | | 0))
% 19.48/3.41 | | | | | |
% 19.48/3.41 | | | | | | ALPHA: (81) implies:
% 19.48/3.41 | | | | | | (82) member(all_56_2, all_37_3) = all_77_1
% 19.48/3.41 | | | | | | (83) member(all_56_1, all_37_3) = all_77_0
% 19.48/3.41 | | | | | | (84) ~ (all_77_0 = 0) | ~ (all_77_1 = 0)
% 19.48/3.41 | | | | | |
% 19.48/3.41 | | | | | | GROUND_INST: instantiating (3) with 0, all_77_1, all_37_3, all_56_2,
% 19.48/3.41 | | | | | | simplifying with (28), (82) gives:
% 19.48/3.41 | | | | | | (85) all_77_1 = 0
% 19.48/3.41 | | | | | |
% 19.48/3.41 | | | | | | GROUND_INST: instantiating (3) with 0, all_77_0, all_37_3, all_56_1,
% 19.48/3.41 | | | | | | simplifying with (29), (83) gives:
% 19.48/3.41 | | | | | | (86) all_77_0 = 0
% 19.48/3.41 | | | | | |
% 19.48/3.41 | | | | | | BETA: splitting (84) gives:
% 19.48/3.41 | | | | | |
% 19.48/3.41 | | | | | | Case 1:
% 19.48/3.41 | | | | | | |
% 19.48/3.41 | | | | | | | (87) ~ (all_77_0 = 0)
% 19.48/3.41 | | | | | | |
% 19.48/3.41 | | | | | | | REDUCE: (86), (87) imply:
% 19.48/3.41 | | | | | | | (88) $false
% 19.48/3.41 | | | | | | |
% 19.48/3.41 | | | | | | | CLOSE: (88) is inconsistent.
% 19.48/3.41 | | | | | | |
% 19.48/3.41 | | | | | | Case 2:
% 19.48/3.41 | | | | | | |
% 19.48/3.41 | | | | | | | (89) ~ (all_77_1 = 0)
% 19.48/3.41 | | | | | | |
% 19.48/3.41 | | | | | | | REDUCE: (85), (89) imply:
% 19.48/3.41 | | | | | | | (90) $false
% 19.48/3.41 | | | | | | |
% 19.48/3.41 | | | | | | | CLOSE: (90) is inconsistent.
% 19.48/3.41 | | | | | | |
% 19.48/3.41 | | | | | | End of split
% 19.48/3.41 | | | | | |
% 19.48/3.41 | | | | | Case 2:
% 19.48/3.41 | | | | | |
% 19.48/3.41 | | | | | | (91) ? [v0: $i] : (apply(all_37_4, all_56_1, v0) = 0 &
% 19.48/3.41 | | | | | | apply(all_37_4, all_56_2, v0) = 0 & member(v0, all_37_2) =
% 19.48/3.41 | | | | | | 0 & $i(v0))
% 19.48/3.41 | | | | | |
% 19.48/3.41 | | | | | | DELTA: instantiating (91) with fresh symbol all_77_0 gives:
% 19.48/3.41 | | | | | | (92) apply(all_37_4, all_56_1, all_77_0) = 0 & apply(all_37_4,
% 19.48/3.41 | | | | | | all_56_2, all_77_0) = 0 & member(all_77_0, all_37_2) = 0 &
% 19.48/3.41 | | | | | | $i(all_77_0)
% 19.48/3.41 | | | | | |
% 19.48/3.41 | | | | | | ALPHA: (92) implies:
% 19.48/3.41 | | | | | | (93) $i(all_77_0)
% 19.48/3.41 | | | | | | (94) member(all_77_0, all_37_2) = 0
% 19.48/3.41 | | | | | | (95) apply(all_37_4, all_56_2, all_77_0) = 0
% 19.48/3.41 | | | | | | (96) apply(all_37_4, all_56_1, all_77_0) = 0
% 19.48/3.41 | | | | | |
% 19.48/3.41 | | | | | | BETA: splitting (62) gives:
% 19.48/3.41 | | | | | |
% 19.48/3.41 | | | | | | Case 1:
% 19.48/3.41 | | | | | | |
% 19.48/3.41 | | | | | | | (97) all_56_0 = 0
% 19.48/3.41 | | | | | | |
% 19.48/3.41 | | | | | | | REDUCE: (23), (97) imply:
% 19.48/3.41 | | | | | | | (98) $false
% 19.48/3.41 | | | | | | |
% 19.48/3.41 | | | | | | | CLOSE: (98) is inconsistent.
% 19.48/3.41 | | | | | | |
% 19.48/3.41 | | | | | | Case 2:
% 19.48/3.41 | | | | | | |
% 19.48/3.41 | | | | | | | (99) ! [v0: $i] : ( ~ (apply(all_37_4, all_56_3, v0) = 0) | ~
% 19.48/3.41 | | | | | | | $i(v0) | ? [v1: any] : ? [v2: any] : (apply(all_37_4,
% 19.48/3.41 | | | | | | | all_56_1, v0) = v2 & member(v0, all_37_2) = v1 & ( ~
% 19.48/3.41 | | | | | | | (v2 = 0) | ~ (v1 = 0))))
% 19.48/3.41 | | | | | | |
% 19.48/3.41 | | | | | | | GROUND_INST: instantiating (16) with all_56_3, all_67_0, all_73_0,
% 19.48/3.41 | | | | | | | simplifying with (24), (48), (49), (76), (78) gives:
% 19.48/3.41 | | | | | | | (100) all_73_0 = all_67_0 | ? [v0: any] : ? [v1: any] : ?
% 19.48/3.41 | | | | | | | [v2: any] : (member(all_73_0, all_37_2) = v2 &
% 19.48/3.41 | | | | | | | member(all_67_0, all_37_2) = v1 & member(all_56_3,
% 19.48/3.41 | | | | | | | all_37_3) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0
% 19.48/3.41 | | | | | | | = 0)))
% 19.48/3.41 | | | | | | |
% 19.48/3.41 | | | | | | | GROUND_INST: instantiating (16) with all_56_3, all_73_0, all_67_0,
% 19.48/3.41 | | | | | | | simplifying with (24), (48), (49), (76), (78) gives:
% 19.48/3.41 | | | | | | | (101) all_73_0 = all_67_0 | ? [v0: any] : ? [v1: any] : ?
% 19.48/3.41 | | | | | | | [v2: any] : (member(all_73_0, all_37_2) = v1 &
% 19.48/3.41 | | | | | | | member(all_67_0, all_37_2) = v2 & member(all_56_3,
% 19.48/3.41 | | | | | | | all_37_3) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0
% 19.48/3.41 | | | | | | | = 0)))
% 19.48/3.41 | | | | | | |
% 19.48/3.41 | | | | | | | GROUND_INST: instantiating (99) with all_73_0, simplifying with
% 19.48/3.41 | | | | | | | (76), (78) gives:
% 19.48/3.41 | | | | | | | (102) ? [v0: any] : ? [v1: any] : (apply(all_37_4, all_56_1,
% 19.48/3.41 | | | | | | | all_73_0) = v1 & member(all_73_0, all_37_2) = v0 & (
% 19.48/3.41 | | | | | | | ~ (v1 = 0) | ~ (v0 = 0)))
% 19.48/3.41 | | | | | | |
% 19.48/3.41 | | | | | | | GROUND_INST: instantiating (16) with all_56_2, all_65_0, all_73_0,
% 19.48/3.41 | | | | | | | simplifying with (25), (44), (46), (76), (79) gives:
% 19.48/3.41 | | | | | | | (103) all_73_0 = all_65_0 | ? [v0: any] : ? [v1: any] : ?
% 19.48/3.41 | | | | | | | [v2: any] : (member(all_73_0, all_37_2) = v2 &
% 19.48/3.41 | | | | | | | member(all_65_0, all_37_2) = v1 & member(all_56_2,
% 19.48/3.41 | | | | | | | all_37_3) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0
% 19.48/3.41 | | | | | | | = 0)))
% 19.48/3.41 | | | | | | |
% 19.48/3.42 | | | | | | | GROUND_INST: instantiating (16) with all_56_2, all_73_0, all_65_0,
% 19.48/3.42 | | | | | | | simplifying with (25), (44), (46), (76), (79) gives:
% 19.48/3.42 | | | | | | | (104) all_73_0 = all_65_0 | ? [v0: any] : ? [v1: any] : ?
% 19.48/3.42 | | | | | | | [v2: any] : (member(all_73_0, all_37_2) = v1 &
% 19.48/3.42 | | | | | | | member(all_65_0, all_37_2) = v2 & member(all_56_2,
% 19.48/3.42 | | | | | | | all_37_3) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0
% 19.48/3.42 | | | | | | | = 0)))
% 19.48/3.42 | | | | | | |
% 19.48/3.42 | | | | | | | GROUND_INST: instantiating (16) with all_56_2, all_73_0, all_77_0,
% 19.48/3.42 | | | | | | | simplifying with (25), (76), (79), (93), (95) gives:
% 19.48/3.42 | | | | | | | (105) all_77_0 = all_73_0 | ? [v0: any] : ? [v1: any] : ?
% 19.48/3.42 | | | | | | | [v2: any] : (member(all_77_0, all_37_2) = v2 &
% 19.48/3.42 | | | | | | | member(all_73_0, all_37_2) = v1 & member(all_56_2,
% 19.48/3.42 | | | | | | | all_37_3) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0
% 19.48/3.42 | | | | | | | = 0)))
% 19.48/3.42 | | | | | | |
% 19.48/3.42 | | | | | | | GROUND_INST: instantiating (16) with all_56_2, all_77_0, all_73_0,
% 19.48/3.42 | | | | | | | simplifying with (25), (76), (79), (93), (95) gives:
% 19.48/3.42 | | | | | | | (106) all_77_0 = all_73_0 | ? [v0: any] : ? [v1: any] : ?
% 19.48/3.42 | | | | | | | [v2: any] : (member(all_77_0, all_37_2) = v1 &
% 19.48/3.42 | | | | | | | member(all_73_0, all_37_2) = v2 & member(all_56_2,
% 19.48/3.42 | | | | | | | all_37_3) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0
% 19.48/3.42 | | | | | | | = 0)))
% 19.48/3.42 | | | | | | |
% 19.48/3.42 | | | | | | | GROUND_INST: instantiating (16) with all_56_2, all_77_0, all_65_0,
% 19.48/3.42 | | | | | | | simplifying with (25), (44), (46), (93), (95) gives:
% 19.48/3.42 | | | | | | | (107) all_77_0 = all_65_0 | ? [v0: any] : ? [v1: any] : ?
% 19.48/3.42 | | | | | | | [v2: any] : (member(all_77_0, all_37_2) = v1 &
% 19.48/3.42 | | | | | | | member(all_65_0, all_37_2) = v2 & member(all_56_2,
% 19.48/3.42 | | | | | | | all_37_3) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0
% 19.48/3.42 | | | | | | | = 0)))
% 19.48/3.42 | | | | | | |
% 19.48/3.42 | | | | | | | GROUND_INST: instantiating (16) with all_56_1, all_77_0, all_63_0,
% 19.48/3.42 | | | | | | | simplifying with (26), (40), (42), (93), (96) gives:
% 19.48/3.42 | | | | | | | (108) all_77_0 = all_63_0 | ? [v0: any] : ? [v1: any] : ?
% 19.48/3.42 | | | | | | | [v2: any] : (member(all_77_0, all_37_2) = v1 &
% 19.48/3.42 | | | | | | | member(all_63_0, all_37_2) = v2 & member(all_56_1,
% 19.48/3.42 | | | | | | | all_37_3) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0
% 19.48/3.42 | | | | | | | = 0)))
% 19.48/3.42 | | | | | | |
% 19.48/3.42 | | | | | | | DELTA: instantiating (102) with fresh symbols all_89_0, all_89_1
% 19.48/3.42 | | | | | | | gives:
% 19.48/3.42 | | | | | | | (109) apply(all_37_4, all_56_1, all_73_0) = all_89_0 &
% 19.48/3.42 | | | | | | | member(all_73_0, all_37_2) = all_89_1 & ( ~ (all_89_0 =
% 19.48/3.42 | | | | | | | 0) | ~ (all_89_1 = 0))
% 19.48/3.42 | | | | | | |
% 19.48/3.42 | | | | | | | ALPHA: (109) implies:
% 19.48/3.42 | | | | | | | (110) member(all_73_0, all_37_2) = all_89_1
% 19.48/3.42 | | | | | | | (111) apply(all_37_4, all_56_1, all_73_0) = all_89_0
% 19.48/3.42 | | | | | | | (112) ~ (all_89_0 = 0) | ~ (all_89_1 = 0)
% 19.48/3.42 | | | | | | |
% 19.48/3.42 | | | | | | | BETA: splitting (108) gives:
% 19.48/3.42 | | | | | | |
% 19.48/3.42 | | | | | | | Case 1:
% 19.48/3.42 | | | | | | | |
% 19.48/3.42 | | | | | | | | (113) all_77_0 = all_63_0
% 19.48/3.42 | | | | | | | |
% 19.48/3.42 | | | | | | | | BETA: splitting (107) gives:
% 19.48/3.42 | | | | | | | |
% 19.48/3.42 | | | | | | | | Case 1:
% 19.48/3.42 | | | | | | | | |
% 19.48/3.42 | | | | | | | | | (114) all_77_0 = all_65_0
% 19.48/3.42 | | | | | | | | |
% 19.48/3.42 | | | | | | | | | COMBINE_EQS: (113), (114) imply:
% 19.48/3.42 | | | | | | | | | (115) all_65_0 = all_63_0
% 19.48/3.42 | | | | | | | | |
% 19.48/3.42 | | | | | | | | | SIMP: (115) implies:
% 19.48/3.42 | | | | | | | | | (116) all_65_0 = all_63_0
% 19.48/3.42 | | | | | | | | |
% 19.48/3.42 | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_89_1, all_37_2,
% 19.48/3.42 | | | | | | | | | all_73_0, simplifying with (77), (110) gives:
% 19.48/3.42 | | | | | | | | | (117) all_89_1 = 0
% 19.48/3.42 | | | | | | | | |
% 19.48/3.42 | | | | | | | | | BETA: splitting (106) gives:
% 19.48/3.42 | | | | | | | | |
% 19.48/3.42 | | | | | | | | | Case 1:
% 19.48/3.42 | | | | | | | | | |
% 19.48/3.42 | | | | | | | | | | (118) all_77_0 = all_73_0
% 19.48/3.42 | | | | | | | | | |
% 19.48/3.42 | | | | | | | | | | COMBINE_EQS: (113), (118) imply:
% 19.48/3.42 | | | | | | | | | | (119) all_73_0 = all_63_0
% 19.48/3.42 | | | | | | | | | |
% 19.48/3.42 | | | | | | | | | | REDUCE: (111), (119) imply:
% 19.48/3.42 | | | | | | | | | | (120) apply(all_37_4, all_56_1, all_63_0) = all_89_0
% 19.48/3.42 | | | | | | | | | |
% 19.48/3.42 | | | | | | | | | | BETA: splitting (112) gives:
% 19.48/3.42 | | | | | | | | | |
% 19.48/3.42 | | | | | | | | | | Case 1:
% 19.48/3.42 | | | | | | | | | | |
% 19.48/3.42 | | | | | | | | | | | (121) ~ (all_89_0 = 0)
% 19.48/3.42 | | | | | | | | | | |
% 19.48/3.42 | | | | | | | | | | | GROUND_INST: instantiating (4) with 0, all_89_0, all_63_0,
% 19.48/3.42 | | | | | | | | | | | all_56_1, all_37_4, simplifying with (42), (120)
% 19.48/3.42 | | | | | | | | | | | gives:
% 19.48/3.42 | | | | | | | | | | | (122) all_89_0 = 0
% 19.48/3.42 | | | | | | | | | | |
% 19.48/3.42 | | | | | | | | | | | REDUCE: (121), (122) imply:
% 19.48/3.42 | | | | | | | | | | | (123) $false
% 19.48/3.42 | | | | | | | | | | |
% 19.48/3.42 | | | | | | | | | | | CLOSE: (123) is inconsistent.
% 19.48/3.42 | | | | | | | | | | |
% 19.48/3.42 | | | | | | | | | | Case 2:
% 19.48/3.42 | | | | | | | | | | |
% 19.48/3.42 | | | | | | | | | | | (124) ~ (all_89_1 = 0)
% 19.48/3.42 | | | | | | | | | | |
% 19.48/3.42 | | | | | | | | | | | REDUCE: (117), (124) imply:
% 19.48/3.42 | | | | | | | | | | | (125) $false
% 19.48/3.42 | | | | | | | | | | |
% 19.48/3.42 | | | | | | | | | | | CLOSE: (125) is inconsistent.
% 19.48/3.42 | | | | | | | | | | |
% 19.48/3.42 | | | | | | | | | | End of split
% 19.48/3.42 | | | | | | | | | |
% 19.48/3.42 | | | | | | | | | Case 2:
% 19.48/3.42 | | | | | | | | | |
% 19.48/3.42 | | | | | | | | | | (126) ~ (all_77_0 = all_73_0)
% 19.48/3.42 | | | | | | | | | | (127) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 19.48/3.42 | | | | | | | | | | (member(all_77_0, all_37_2) = v1 & member(all_73_0,
% 19.48/3.42 | | | | | | | | | | all_37_2) = v2 & member(all_56_2, all_37_3) =
% 19.48/3.42 | | | | | | | | | | v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 19.48/3.43 | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | DELTA: instantiating (127) with fresh symbols all_109_0,
% 19.48/3.43 | | | | | | | | | | all_109_1, all_109_2 gives:
% 19.48/3.43 | | | | | | | | | | (128) member(all_77_0, all_37_2) = all_109_1 &
% 19.48/3.43 | | | | | | | | | | member(all_73_0, all_37_2) = all_109_0 &
% 19.48/3.43 | | | | | | | | | | member(all_56_2, all_37_3) = all_109_2 & ( ~
% 19.48/3.43 | | | | | | | | | | (all_109_0 = 0) | ~ (all_109_1 = 0) | ~
% 19.48/3.43 | | | | | | | | | | (all_109_2 = 0))
% 19.48/3.43 | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | ALPHA: (128) implies:
% 19.48/3.43 | | | | | | | | | | (129) member(all_56_2, all_37_3) = all_109_2
% 19.48/3.43 | | | | | | | | | | (130) member(all_73_0, all_37_2) = all_109_0
% 19.48/3.43 | | | | | | | | | | (131) member(all_77_0, all_37_2) = all_109_1
% 19.48/3.43 | | | | | | | | | | (132) ~ (all_109_0 = 0) | ~ (all_109_1 = 0) | ~
% 19.48/3.43 | | | | | | | | | | (all_109_2 = 0)
% 19.48/3.43 | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | REDUCE: (113), (126) imply:
% 19.48/3.43 | | | | | | | | | | (133) ~ (all_73_0 = all_63_0)
% 19.48/3.43 | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | SIMP: (133) implies:
% 19.48/3.43 | | | | | | | | | | (134) ~ (all_73_0 = all_63_0)
% 19.48/3.43 | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | REDUCE: (113), (131) imply:
% 19.48/3.43 | | | | | | | | | | (135) member(all_63_0, all_37_2) = all_109_1
% 19.48/3.43 | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | BETA: splitting (105) gives:
% 19.48/3.43 | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | Case 1:
% 19.48/3.43 | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | (136) all_77_0 = all_73_0
% 19.48/3.43 | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | COMBINE_EQS: (113), (136) imply:
% 19.48/3.43 | | | | | | | | | | | (137) all_73_0 = all_63_0
% 19.48/3.43 | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | REDUCE: (134), (137) imply:
% 19.48/3.43 | | | | | | | | | | | (138) $false
% 19.48/3.43 | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | CLOSE: (138) is inconsistent.
% 19.48/3.43 | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | Case 2:
% 19.48/3.43 | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | (139) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 19.48/3.43 | | | | | | | | | | | (member(all_77_0, all_37_2) = v2 &
% 19.48/3.43 | | | | | | | | | | | member(all_73_0, all_37_2) = v1 &
% 19.48/3.43 | | | | | | | | | | | member(all_56_2, all_37_3) = v0 & ( ~ (v2 = 0) |
% 19.48/3.43 | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0)))
% 19.48/3.43 | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | DELTA: instantiating (139) with fresh symbols all_115_0,
% 19.48/3.43 | | | | | | | | | | | all_115_1, all_115_2 gives:
% 19.48/3.43 | | | | | | | | | | | (140) member(all_77_0, all_37_2) = all_115_0 &
% 19.48/3.43 | | | | | | | | | | | member(all_73_0, all_37_2) = all_115_1 &
% 19.48/3.43 | | | | | | | | | | | member(all_56_2, all_37_3) = all_115_2 & ( ~
% 19.48/3.43 | | | | | | | | | | | (all_115_0 = 0) | ~ (all_115_1 = 0) | ~
% 19.48/3.43 | | | | | | | | | | | (all_115_2 = 0))
% 19.48/3.43 | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | ALPHA: (140) implies:
% 19.48/3.43 | | | | | | | | | | | (141) member(all_56_2, all_37_3) = all_115_2
% 19.48/3.43 | | | | | | | | | | | (142) member(all_73_0, all_37_2) = all_115_1
% 19.48/3.43 | | | | | | | | | | | (143) member(all_77_0, all_37_2) = all_115_0
% 19.48/3.43 | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | REDUCE: (113), (143) imply:
% 19.48/3.43 | | | | | | | | | | | (144) member(all_63_0, all_37_2) = all_115_0
% 19.48/3.43 | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | BETA: splitting (101) gives:
% 19.48/3.43 | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | Case 1:
% 19.48/3.43 | | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | | (145) all_73_0 = all_67_0
% 19.48/3.43 | | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | | REDUCE: (134), (145) imply:
% 19.48/3.43 | | | | | | | | | | | | (146) ~ (all_67_0 = all_63_0)
% 19.48/3.43 | | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | | REDUCE: (142), (145) imply:
% 19.48/3.43 | | | | | | | | | | | | (147) member(all_67_0, all_37_2) = all_115_1
% 19.48/3.43 | | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | | REDUCE: (130), (145) imply:
% 19.48/3.43 | | | | | | | | | | | | (148) member(all_67_0, all_37_2) = all_109_0
% 19.48/3.43 | | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | | REDUCE: (77), (145) imply:
% 19.48/3.43 | | | | | | | | | | | | (149) member(all_67_0, all_37_2) = 0
% 19.48/3.43 | | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | | BETA: splitting (104) gives:
% 19.48/3.43 | | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | | Case 1:
% 19.48/3.43 | | | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | | | (150) all_73_0 = all_65_0
% 19.48/3.43 | | | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | | | COMBINE_EQS: (145), (150) imply:
% 19.48/3.43 | | | | | | | | | | | | | (151) all_67_0 = all_65_0
% 19.48/3.43 | | | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | | | COMBINE_EQS: (116), (151) imply:
% 19.48/3.43 | | | | | | | | | | | | | (152) all_67_0 = all_63_0
% 19.48/3.43 | | | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | | | REDUCE: (146), (152) imply:
% 19.48/3.43 | | | | | | | | | | | | | (153) $false
% 19.48/3.43 | | | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | | | CLOSE: (153) is inconsistent.
% 19.48/3.43 | | | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | | Case 2:
% 19.48/3.43 | | | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | | | (154) ~ (all_73_0 = all_65_0)
% 19.48/3.43 | | | | | | | | | | | | | (155) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 19.48/3.43 | | | | | | | | | | | | | (member(all_73_0, all_37_2) = v1 &
% 19.48/3.43 | | | | | | | | | | | | | member(all_65_0, all_37_2) = v2 &
% 19.48/3.43 | | | | | | | | | | | | | member(all_56_2, all_37_3) = v0 & ( ~ (v2 = 0) |
% 19.48/3.43 | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0)))
% 19.48/3.43 | | | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | | | DELTA: instantiating (155) with fresh symbols all_125_0,
% 19.48/3.43 | | | | | | | | | | | | | all_125_1, all_125_2 gives:
% 19.48/3.43 | | | | | | | | | | | | | (156) member(all_73_0, all_37_2) = all_125_1 &
% 19.48/3.43 | | | | | | | | | | | | | member(all_65_0, all_37_2) = all_125_0 &
% 19.48/3.43 | | | | | | | | | | | | | member(all_56_2, all_37_3) = all_125_2 & ( ~
% 19.48/3.43 | | | | | | | | | | | | | (all_125_0 = 0) | ~ (all_125_1 = 0) | ~
% 19.48/3.43 | | | | | | | | | | | | | (all_125_2 = 0))
% 19.48/3.43 | | | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | | | ALPHA: (156) implies:
% 19.48/3.43 | | | | | | | | | | | | | (157) member(all_56_2, all_37_3) = all_125_2
% 19.48/3.43 | | | | | | | | | | | | | (158) member(all_65_0, all_37_2) = all_125_0
% 19.48/3.43 | | | | | | | | | | | | | (159) member(all_73_0, all_37_2) = all_125_1
% 19.48/3.43 | | | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | | | REDUCE: (145), (159) imply:
% 19.48/3.43 | | | | | | | | | | | | | (160) member(all_67_0, all_37_2) = all_125_1
% 19.48/3.43 | | | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | | | REDUCE: (116), (158) imply:
% 19.48/3.43 | | | | | | | | | | | | | (161) member(all_63_0, all_37_2) = all_125_0
% 19.48/3.43 | | | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | | | BETA: splitting (103) gives:
% 19.48/3.43 | | | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | | | Case 1:
% 19.48/3.43 | | | | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | | | | (162) all_73_0 = all_65_0
% 19.48/3.43 | | | | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | | | | COMBINE_EQS: (145), (162) imply:
% 19.48/3.43 | | | | | | | | | | | | | | (163) all_67_0 = all_65_0
% 19.48/3.43 | | | | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | | | | COMBINE_EQS: (116), (163) imply:
% 19.48/3.43 | | | | | | | | | | | | | | (164) all_67_0 = all_63_0
% 19.48/3.43 | | | | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | | | | REDUCE: (146), (164) imply:
% 19.48/3.43 | | | | | | | | | | | | | | (165) $false
% 19.48/3.43 | | | | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | | | | CLOSE: (165) is inconsistent.
% 19.48/3.43 | | | | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | | | Case 2:
% 19.48/3.43 | | | | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | | | | (166) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 19.48/3.43 | | | | | | | | | | | | | | (member(all_73_0, all_37_2) = v2 &
% 19.48/3.43 | | | | | | | | | | | | | | member(all_65_0, all_37_2) = v1 &
% 19.48/3.43 | | | | | | | | | | | | | | member(all_56_2, all_37_3) = v0 & ( ~ (v2 = 0) |
% 19.48/3.43 | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0)))
% 19.48/3.43 | | | | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | | | | DELTA: instantiating (166) with fresh symbols all_135_0,
% 19.48/3.43 | | | | | | | | | | | | | | all_135_1, all_135_2 gives:
% 19.48/3.43 | | | | | | | | | | | | | | (167) member(all_73_0, all_37_2) = all_135_0 &
% 19.48/3.43 | | | | | | | | | | | | | | member(all_65_0, all_37_2) = all_135_1 &
% 19.48/3.43 | | | | | | | | | | | | | | member(all_56_2, all_37_3) = all_135_2 & ( ~
% 19.48/3.43 | | | | | | | | | | | | | | (all_135_0 = 0) | ~ (all_135_1 = 0) | ~
% 19.48/3.43 | | | | | | | | | | | | | | (all_135_2 = 0))
% 19.48/3.43 | | | | | | | | | | | | | |
% 19.48/3.43 | | | | | | | | | | | | | | ALPHA: (167) implies:
% 19.48/3.44 | | | | | | | | | | | | | | (168) member(all_56_2, all_37_3) = all_135_2
% 19.48/3.44 | | | | | | | | | | | | | | (169) member(all_65_0, all_37_2) = all_135_1
% 19.48/3.44 | | | | | | | | | | | | | | (170) member(all_73_0, all_37_2) = all_135_0
% 19.48/3.44 | | | | | | | | | | | | | |
% 19.48/3.44 | | | | | | | | | | | | | | REDUCE: (145), (170) imply:
% 19.48/3.44 | | | | | | | | | | | | | | (171) member(all_67_0, all_37_2) = all_135_0
% 19.48/3.44 | | | | | | | | | | | | | |
% 19.48/3.44 | | | | | | | | | | | | | | REDUCE: (116), (169) imply:
% 19.48/3.44 | | | | | | | | | | | | | | (172) member(all_63_0, all_37_2) = all_135_1
% 19.48/3.44 | | | | | | | | | | | | | |
% 19.48/3.44 | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_115_2, all_37_3,
% 19.48/3.44 | | | | | | | | | | | | | | all_56_2, simplifying with (28), (141) gives:
% 19.48/3.44 | | | | | | | | | | | | | | (173) all_115_2 = 0
% 19.48/3.44 | | | | | | | | | | | | | |
% 19.48/3.44 | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_115_2, all_125_2,
% 19.48/3.44 | | | | | | | | | | | | | | all_37_3, all_56_2, simplifying with (141), (157)
% 19.48/3.44 | | | | | | | | | | | | | | gives:
% 19.48/3.44 | | | | | | | | | | | | | | (174) all_125_2 = all_115_2
% 19.48/3.44 | | | | | | | | | | | | | |
% 19.48/3.44 | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_125_2, all_135_2,
% 19.48/3.44 | | | | | | | | | | | | | | all_37_3, all_56_2, simplifying with (157), (168)
% 19.48/3.44 | | | | | | | | | | | | | | gives:
% 19.48/3.44 | | | | | | | | | | | | | | (175) all_135_2 = all_125_2
% 19.48/3.44 | | | | | | | | | | | | | |
% 19.48/3.44 | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_109_2, all_135_2,
% 19.48/3.44 | | | | | | | | | | | | | | all_37_3, all_56_2, simplifying with (129), (168)
% 19.48/3.44 | | | | | | | | | | | | | | gives:
% 19.48/3.44 | | | | | | | | | | | | | | (176) all_135_2 = all_109_2
% 19.48/3.44 | | | | | | | | | | | | | |
% 19.48/3.44 | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_115_0, all_37_2,
% 19.48/3.44 | | | | | | | | | | | | | | all_63_0, simplifying with (41), (144) gives:
% 19.48/3.44 | | | | | | | | | | | | | | (177) all_115_0 = 0
% 19.48/3.44 | | | | | | | | | | | | | |
% 19.48/3.44 | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_115_0, all_125_0,
% 19.48/3.44 | | | | | | | | | | | | | | all_37_2, all_63_0, simplifying with (144), (161)
% 19.48/3.44 | | | | | | | | | | | | | | gives:
% 19.48/3.44 | | | | | | | | | | | | | | (178) all_125_0 = all_115_0
% 19.48/3.44 | | | | | | | | | | | | | |
% 19.48/3.44 | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_125_0, all_135_1,
% 19.48/3.44 | | | | | | | | | | | | | | all_37_2, all_63_0, simplifying with (161), (172)
% 19.48/3.44 | | | | | | | | | | | | | | gives:
% 19.48/3.44 | | | | | | | | | | | | | | (179) all_135_1 = all_125_0
% 19.48/3.44 | | | | | | | | | | | | | |
% 19.48/3.44 | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_109_1, all_135_1,
% 19.48/3.44 | | | | | | | | | | | | | | all_37_2, all_63_0, simplifying with (135), (172)
% 19.48/3.44 | | | | | | | | | | | | | | gives:
% 19.48/3.44 | | | | | | | | | | | | | | (180) all_135_1 = all_109_1
% 19.48/3.44 | | | | | | | | | | | | | |
% 19.48/3.44 | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_115_1, all_37_2,
% 19.48/3.44 | | | | | | | | | | | | | | all_67_0, simplifying with (147), (149) gives:
% 19.48/3.44 | | | | | | | | | | | | | | (181) all_115_1 = 0
% 19.48/3.44 | | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_115_1, all_125_1,
% 19.99/3.44 | | | | | | | | | | | | | | all_37_2, all_67_0, simplifying with (147), (160)
% 19.99/3.44 | | | | | | | | | | | | | | gives:
% 19.99/3.44 | | | | | | | | | | | | | | (182) all_125_1 = all_115_1
% 19.99/3.44 | | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_125_1, all_135_0,
% 19.99/3.44 | | | | | | | | | | | | | | all_37_2, all_67_0, simplifying with (160), (171)
% 19.99/3.44 | | | | | | | | | | | | | | gives:
% 19.99/3.44 | | | | | | | | | | | | | | (183) all_135_0 = all_125_1
% 19.99/3.44 | | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_109_0, all_135_0,
% 19.99/3.44 | | | | | | | | | | | | | | all_37_2, all_67_0, simplifying with (148), (171)
% 19.99/3.44 | | | | | | | | | | | | | | gives:
% 19.99/3.44 | | | | | | | | | | | | | | (184) all_135_0 = all_109_0
% 19.99/3.44 | | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | | COMBINE_EQS: (183), (184) imply:
% 19.99/3.44 | | | | | | | | | | | | | | (185) all_125_1 = all_109_0
% 19.99/3.44 | | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | | SIMP: (185) implies:
% 19.99/3.44 | | | | | | | | | | | | | | (186) all_125_1 = all_109_0
% 19.99/3.44 | | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | | COMBINE_EQS: (179), (180) imply:
% 19.99/3.44 | | | | | | | | | | | | | | (187) all_125_0 = all_109_1
% 19.99/3.44 | | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | | SIMP: (187) implies:
% 19.99/3.44 | | | | | | | | | | | | | | (188) all_125_0 = all_109_1
% 19.99/3.44 | | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | | COMBINE_EQS: (175), (176) imply:
% 19.99/3.44 | | | | | | | | | | | | | | (189) all_125_2 = all_109_2
% 19.99/3.44 | | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | | SIMP: (189) implies:
% 19.99/3.44 | | | | | | | | | | | | | | (190) all_125_2 = all_109_2
% 19.99/3.44 | | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | | COMBINE_EQS: (178), (188) imply:
% 19.99/3.44 | | | | | | | | | | | | | | (191) all_115_0 = all_109_1
% 19.99/3.44 | | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | | SIMP: (191) implies:
% 19.99/3.44 | | | | | | | | | | | | | | (192) all_115_0 = all_109_1
% 19.99/3.44 | | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | | COMBINE_EQS: (182), (186) imply:
% 19.99/3.44 | | | | | | | | | | | | | | (193) all_115_1 = all_109_0
% 19.99/3.44 | | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | | SIMP: (193) implies:
% 19.99/3.44 | | | | | | | | | | | | | | (194) all_115_1 = all_109_0
% 19.99/3.44 | | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | | COMBINE_EQS: (174), (190) imply:
% 19.99/3.44 | | | | | | | | | | | | | | (195) all_115_2 = all_109_2
% 19.99/3.44 | | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | | SIMP: (195) implies:
% 19.99/3.44 | | | | | | | | | | | | | | (196) all_115_2 = all_109_2
% 19.99/3.44 | | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | | COMBINE_EQS: (177), (192) imply:
% 19.99/3.44 | | | | | | | | | | | | | | (197) all_109_1 = 0
% 19.99/3.44 | | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | | COMBINE_EQS: (181), (194) imply:
% 19.99/3.44 | | | | | | | | | | | | | | (198) all_109_0 = 0
% 19.99/3.44 | | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | | SIMP: (198) implies:
% 19.99/3.44 | | | | | | | | | | | | | | (199) all_109_0 = 0
% 19.99/3.44 | | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | | COMBINE_EQS: (173), (196) imply:
% 19.99/3.44 | | | | | | | | | | | | | | (200) all_109_2 = 0
% 19.99/3.44 | | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | | SIMP: (200) implies:
% 19.99/3.44 | | | | | | | | | | | | | | (201) all_109_2 = 0
% 19.99/3.44 | | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 19.99/3.44 | | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | | Case 1:
% 19.99/3.44 | | | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | | | (202) ~ (all_109_0 = 0)
% 19.99/3.44 | | | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | | | REDUCE: (199), (202) imply:
% 19.99/3.44 | | | | | | | | | | | | | | | (203) $false
% 19.99/3.44 | | | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | | | CLOSE: (203) is inconsistent.
% 19.99/3.44 | | | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | | Case 2:
% 19.99/3.44 | | | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | | | (204) ~ (all_109_1 = 0) | ~ (all_109_2 = 0)
% 19.99/3.44 | | | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | | | REF_CLOSE: (197), (201), (204) are inconsistent by sub-proof
% 19.99/3.44 | | | | | | | | | | | | | | | #1.
% 19.99/3.44 | | | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | | End of split
% 19.99/3.44 | | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | End of split
% 19.99/3.44 | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | End of split
% 19.99/3.44 | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | Case 2:
% 19.99/3.44 | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | (205) ~ (all_73_0 = all_67_0)
% 19.99/3.44 | | | | | | | | | | | | (206) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 19.99/3.44 | | | | | | | | | | | | (member(all_73_0, all_37_2) = v1 &
% 19.99/3.44 | | | | | | | | | | | | member(all_67_0, all_37_2) = v2 &
% 19.99/3.44 | | | | | | | | | | | | member(all_56_3, all_37_3) = v0 & ( ~ (v2 = 0) |
% 19.99/3.44 | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0)))
% 19.99/3.44 | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | DELTA: instantiating (206) with fresh symbols all_121_0,
% 19.99/3.44 | | | | | | | | | | | | all_121_1, all_121_2 gives:
% 19.99/3.44 | | | | | | | | | | | | (207) member(all_73_0, all_37_2) = all_121_1 &
% 19.99/3.44 | | | | | | | | | | | | member(all_67_0, all_37_2) = all_121_0 &
% 19.99/3.44 | | | | | | | | | | | | member(all_56_3, all_37_3) = all_121_2 & ( ~
% 19.99/3.44 | | | | | | | | | | | | (all_121_0 = 0) | ~ (all_121_1 = 0) | ~
% 19.99/3.44 | | | | | | | | | | | | (all_121_2 = 0))
% 19.99/3.44 | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | ALPHA: (207) implies:
% 19.99/3.44 | | | | | | | | | | | | (208) member(all_73_0, all_37_2) = all_121_1
% 19.99/3.44 | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | BETA: splitting (104) gives:
% 19.99/3.44 | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | Case 1:
% 19.99/3.44 | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | (209) all_73_0 = all_65_0
% 19.99/3.44 | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | COMBINE_EQS: (116), (209) imply:
% 19.99/3.44 | | | | | | | | | | | | | (210) all_73_0 = all_63_0
% 19.99/3.44 | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | REDUCE: (134), (210) imply:
% 19.99/3.44 | | | | | | | | | | | | | (211) $false
% 19.99/3.44 | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | CLOSE: (211) is inconsistent.
% 19.99/3.44 | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | Case 2:
% 19.99/3.44 | | | | | | | | | | | | |
% 19.99/3.44 | | | | | | | | | | | | | (212) ~ (all_73_0 = all_65_0)
% 19.99/3.45 | | | | | | | | | | | | | (213) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 19.99/3.45 | | | | | | | | | | | | | (member(all_73_0, all_37_2) = v1 &
% 19.99/3.45 | | | | | | | | | | | | | member(all_65_0, all_37_2) = v2 &
% 19.99/3.45 | | | | | | | | | | | | | member(all_56_2, all_37_3) = v0 & ( ~ (v2 = 0) |
% 19.99/3.45 | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0)))
% 19.99/3.45 | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | DELTA: instantiating (213) with fresh symbols all_127_0,
% 19.99/3.45 | | | | | | | | | | | | | all_127_1, all_127_2 gives:
% 19.99/3.45 | | | | | | | | | | | | | (214) member(all_73_0, all_37_2) = all_127_1 &
% 19.99/3.45 | | | | | | | | | | | | | member(all_65_0, all_37_2) = all_127_0 &
% 19.99/3.45 | | | | | | | | | | | | | member(all_56_2, all_37_3) = all_127_2 & ( ~
% 19.99/3.45 | | | | | | | | | | | | | (all_127_0 = 0) | ~ (all_127_1 = 0) | ~
% 19.99/3.45 | | | | | | | | | | | | | (all_127_2 = 0))
% 19.99/3.45 | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | ALPHA: (214) implies:
% 19.99/3.45 | | | | | | | | | | | | | (215) member(all_56_2, all_37_3) = all_127_2
% 19.99/3.45 | | | | | | | | | | | | | (216) member(all_65_0, all_37_2) = all_127_0
% 19.99/3.45 | | | | | | | | | | | | | (217) member(all_73_0, all_37_2) = all_127_1
% 19.99/3.45 | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | REDUCE: (116), (216) imply:
% 19.99/3.45 | | | | | | | | | | | | | (218) member(all_63_0, all_37_2) = all_127_0
% 19.99/3.45 | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | BETA: splitting (103) gives:
% 19.99/3.45 | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | Case 1:
% 19.99/3.45 | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | (219) all_73_0 = all_65_0
% 19.99/3.45 | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | COMBINE_EQS: (116), (219) imply:
% 19.99/3.45 | | | | | | | | | | | | | | (220) all_73_0 = all_63_0
% 19.99/3.45 | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | REDUCE: (134), (220) imply:
% 19.99/3.45 | | | | | | | | | | | | | | (221) $false
% 19.99/3.45 | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | CLOSE: (221) is inconsistent.
% 19.99/3.45 | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | Case 2:
% 19.99/3.45 | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | (222) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 19.99/3.45 | | | | | | | | | | | | | | (member(all_73_0, all_37_2) = v2 &
% 19.99/3.45 | | | | | | | | | | | | | | member(all_65_0, all_37_2) = v1 &
% 19.99/3.45 | | | | | | | | | | | | | | member(all_56_2, all_37_3) = v0 & ( ~ (v2 = 0) |
% 19.99/3.45 | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0)))
% 19.99/3.45 | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | DELTA: instantiating (222) with fresh symbols all_137_0,
% 19.99/3.45 | | | | | | | | | | | | | | all_137_1, all_137_2 gives:
% 19.99/3.45 | | | | | | | | | | | | | | (223) member(all_73_0, all_37_2) = all_137_0 &
% 19.99/3.45 | | | | | | | | | | | | | | member(all_65_0, all_37_2) = all_137_1 &
% 19.99/3.45 | | | | | | | | | | | | | | member(all_56_2, all_37_3) = all_137_2 & ( ~
% 19.99/3.45 | | | | | | | | | | | | | | (all_137_0 = 0) | ~ (all_137_1 = 0) | ~
% 19.99/3.45 | | | | | | | | | | | | | | (all_137_2 = 0))
% 19.99/3.45 | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | ALPHA: (223) implies:
% 19.99/3.45 | | | | | | | | | | | | | | (224) member(all_56_2, all_37_3) = all_137_2
% 19.99/3.45 | | | | | | | | | | | | | | (225) member(all_65_0, all_37_2) = all_137_1
% 19.99/3.45 | | | | | | | | | | | | | | (226) member(all_73_0, all_37_2) = all_137_0
% 19.99/3.45 | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | REDUCE: (116), (225) imply:
% 19.99/3.45 | | | | | | | | | | | | | | (227) member(all_63_0, all_37_2) = all_137_1
% 19.99/3.45 | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 19.99/3.45 | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | Case 1:
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | (228) all_73_0 = all_67_0
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | REDUCE: (205), (228) imply:
% 19.99/3.45 | | | | | | | | | | | | | | | (229) $false
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | CLOSE: (229) is inconsistent.
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | Case 2:
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | (230) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 19.99/3.45 | | | | | | | | | | | | | | | (member(all_73_0, all_37_2) = v2 &
% 19.99/3.45 | | | | | | | | | | | | | | | member(all_67_0, all_37_2) = v1 &
% 19.99/3.45 | | | | | | | | | | | | | | | member(all_56_3, all_37_3) = v0 & ( ~ (v2 = 0) |
% 19.99/3.45 | | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0)))
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | DELTA: instantiating (230) with fresh symbols all_147_0,
% 19.99/3.45 | | | | | | | | | | | | | | | all_147_1, all_147_2 gives:
% 19.99/3.45 | | | | | | | | | | | | | | | (231) member(all_73_0, all_37_2) = all_147_0 &
% 19.99/3.45 | | | | | | | | | | | | | | | member(all_67_0, all_37_2) = all_147_1 &
% 19.99/3.45 | | | | | | | | | | | | | | | member(all_56_3, all_37_3) = all_147_2 & ( ~
% 19.99/3.45 | | | | | | | | | | | | | | | (all_147_0 = 0) | ~ (all_147_1 = 0) | ~
% 19.99/3.45 | | | | | | | | | | | | | | | (all_147_2 = 0))
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | ALPHA: (231) implies:
% 19.99/3.45 | | | | | | | | | | | | | | | (232) member(all_73_0, all_37_2) = all_147_0
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_109_2, all_115_2,
% 19.99/3.45 | | | | | | | | | | | | | | | all_37_3, all_56_2, simplifying with (129), (141)
% 19.99/3.45 | | | | | | | | | | | | | | | gives:
% 19.99/3.45 | | | | | | | | | | | | | | | (233) all_115_2 = all_109_2
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_115_2, all_127_2,
% 19.99/3.45 | | | | | | | | | | | | | | | all_37_3, all_56_2, simplifying with (141), (215)
% 19.99/3.45 | | | | | | | | | | | | | | | gives:
% 19.99/3.45 | | | | | | | | | | | | | | | (234) all_127_2 = all_115_2
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_137_2, all_37_3,
% 19.99/3.45 | | | | | | | | | | | | | | | all_56_2, simplifying with (28), (224) gives:
% 19.99/3.45 | | | | | | | | | | | | | | | (235) all_137_2 = 0
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_127_2, all_137_2,
% 19.99/3.45 | | | | | | | | | | | | | | | all_37_3, all_56_2, simplifying with (215), (224)
% 19.99/3.45 | | | | | | | | | | | | | | | gives:
% 19.99/3.45 | | | | | | | | | | | | | | | (236) all_137_2 = all_127_2
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_115_0, all_127_0,
% 19.99/3.45 | | | | | | | | | | | | | | | all_37_2, all_63_0, simplifying with (144), (218)
% 19.99/3.45 | | | | | | | | | | | | | | | gives:
% 19.99/3.45 | | | | | | | | | | | | | | | (237) all_127_0 = all_115_0
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_109_1, all_127_0,
% 19.99/3.45 | | | | | | | | | | | | | | | all_37_2, all_63_0, simplifying with (135), (218)
% 19.99/3.45 | | | | | | | | | | | | | | | gives:
% 19.99/3.45 | | | | | | | | | | | | | | | (238) all_127_0 = all_109_1
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_137_1, all_37_2,
% 19.99/3.45 | | | | | | | | | | | | | | | all_63_0, simplifying with (41), (227) gives:
% 19.99/3.45 | | | | | | | | | | | | | | | (239) all_137_1 = 0
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_127_0, all_137_1,
% 19.99/3.45 | | | | | | | | | | | | | | | all_37_2, all_63_0, simplifying with (218), (227)
% 19.99/3.45 | | | | | | | | | | | | | | | gives:
% 19.99/3.45 | | | | | | | | | | | | | | | (240) all_137_1 = all_127_0
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_121_1, all_127_1,
% 19.99/3.45 | | | | | | | | | | | | | | | all_37_2, all_73_0, simplifying with (208), (217)
% 19.99/3.45 | | | | | | | | | | | | | | | gives:
% 19.99/3.45 | | | | | | | | | | | | | | | (241) all_127_1 = all_121_1
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_137_0, all_37_2,
% 19.99/3.45 | | | | | | | | | | | | | | | all_73_0, simplifying with (77), (226) gives:
% 19.99/3.45 | | | | | | | | | | | | | | | (242) all_137_0 = 0
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_121_1, all_137_0,
% 19.99/3.45 | | | | | | | | | | | | | | | all_37_2, all_73_0, simplifying with (208), (226)
% 19.99/3.45 | | | | | | | | | | | | | | | gives:
% 19.99/3.45 | | | | | | | | | | | | | | | (243) all_137_0 = all_121_1
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_115_1, all_137_0,
% 19.99/3.45 | | | | | | | | | | | | | | | all_37_2, all_73_0, simplifying with (142), (226)
% 19.99/3.45 | | | | | | | | | | | | | | | gives:
% 19.99/3.45 | | | | | | | | | | | | | | | (244) all_137_0 = all_115_1
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_127_1, all_147_0,
% 19.99/3.45 | | | | | | | | | | | | | | | all_37_2, all_73_0, simplifying with (217), (232)
% 19.99/3.45 | | | | | | | | | | | | | | | gives:
% 19.99/3.45 | | | | | | | | | | | | | | | (245) all_147_0 = all_127_1
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_109_0, all_147_0,
% 19.99/3.45 | | | | | | | | | | | | | | | all_37_2, all_73_0, simplifying with (130), (232)
% 19.99/3.45 | | | | | | | | | | | | | | | gives:
% 19.99/3.45 | | | | | | | | | | | | | | | (246) all_147_0 = all_109_0
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | COMBINE_EQS: (245), (246) imply:
% 19.99/3.45 | | | | | | | | | | | | | | | (247) all_127_1 = all_109_0
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | SIMP: (247) implies:
% 19.99/3.45 | | | | | | | | | | | | | | | (248) all_127_1 = all_109_0
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | COMBINE_EQS: (243), (244) imply:
% 19.99/3.45 | | | | | | | | | | | | | | | (249) all_121_1 = all_115_1
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | SIMP: (249) implies:
% 19.99/3.45 | | | | | | | | | | | | | | | (250) all_121_1 = all_115_1
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | COMBINE_EQS: (242), (244) imply:
% 19.99/3.45 | | | | | | | | | | | | | | | (251) all_115_1 = 0
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | COMBINE_EQS: (239), (240) imply:
% 19.99/3.45 | | | | | | | | | | | | | | | (252) all_127_0 = 0
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | SIMP: (252) implies:
% 19.99/3.45 | | | | | | | | | | | | | | | (253) all_127_0 = 0
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | COMBINE_EQS: (235), (236) imply:
% 19.99/3.45 | | | | | | | | | | | | | | | (254) all_127_2 = 0
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | SIMP: (254) implies:
% 19.99/3.45 | | | | | | | | | | | | | | | (255) all_127_2 = 0
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | COMBINE_EQS: (237), (238) imply:
% 19.99/3.45 | | | | | | | | | | | | | | | (256) all_115_0 = all_109_1
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | COMBINE_EQS: (237), (253) imply:
% 19.99/3.45 | | | | | | | | | | | | | | | (257) all_115_0 = 0
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | COMBINE_EQS: (241), (248) imply:
% 19.99/3.45 | | | | | | | | | | | | | | | (258) all_121_1 = all_109_0
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | SIMP: (258) implies:
% 19.99/3.45 | | | | | | | | | | | | | | | (259) all_121_1 = all_109_0
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | COMBINE_EQS: (234), (255) imply:
% 19.99/3.45 | | | | | | | | | | | | | | | (260) all_115_2 = 0
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | SIMP: (260) implies:
% 19.99/3.45 | | | | | | | | | | | | | | | (261) all_115_2 = 0
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | COMBINE_EQS: (250), (259) imply:
% 19.99/3.45 | | | | | | | | | | | | | | | (262) all_115_1 = all_109_0
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | SIMP: (262) implies:
% 19.99/3.45 | | | | | | | | | | | | | | | (263) all_115_1 = all_109_0
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | COMBINE_EQS: (256), (257) imply:
% 19.99/3.45 | | | | | | | | | | | | | | | (264) all_109_1 = 0
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.45 | | | | | | | | | | | | | | | SIMP: (264) implies:
% 19.99/3.45 | | | | | | | | | | | | | | | (265) all_109_1 = 0
% 19.99/3.45 | | | | | | | | | | | | | | |
% 19.99/3.46 | | | | | | | | | | | | | | | COMBINE_EQS: (251), (263) imply:
% 19.99/3.46 | | | | | | | | | | | | | | | (266) all_109_0 = 0
% 19.99/3.46 | | | | | | | | | | | | | | |
% 19.99/3.46 | | | | | | | | | | | | | | | SIMP: (266) implies:
% 19.99/3.46 | | | | | | | | | | | | | | | (267) all_109_0 = 0
% 19.99/3.46 | | | | | | | | | | | | | | |
% 19.99/3.46 | | | | | | | | | | | | | | | COMBINE_EQS: (233), (261) imply:
% 19.99/3.46 | | | | | | | | | | | | | | | (268) all_109_2 = 0
% 19.99/3.46 | | | | | | | | | | | | | | |
% 19.99/3.46 | | | | | | | | | | | | | | | SIMP: (268) implies:
% 19.99/3.46 | | | | | | | | | | | | | | | (269) all_109_2 = 0
% 19.99/3.46 | | | | | | | | | | | | | | |
% 19.99/3.46 | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 19.99/3.46 | | | | | | | | | | | | | | |
% 19.99/3.46 | | | | | | | | | | | | | | | Case 1:
% 19.99/3.46 | | | | | | | | | | | | | | | |
% 19.99/3.46 | | | | | | | | | | | | | | | | (270) ~ (all_109_0 = 0)
% 19.99/3.46 | | | | | | | | | | | | | | | |
% 19.99/3.46 | | | | | | | | | | | | | | | | REDUCE: (267), (270) imply:
% 19.99/3.46 | | | | | | | | | | | | | | | | (271) $false
% 19.99/3.46 | | | | | | | | | | | | | | | |
% 19.99/3.46 | | | | | | | | | | | | | | | | CLOSE: (271) is inconsistent.
% 19.99/3.46 | | | | | | | | | | | | | | | |
% 19.99/3.46 | | | | | | | | | | | | | | | Case 2:
% 19.99/3.46 | | | | | | | | | | | | | | | |
% 19.99/3.46 | | | | | | | | | | | | | | | | (272) ~ (all_109_1 = 0) | ~ (all_109_2 = 0)
% 19.99/3.46 | | | | | | | | | | | | | | | |
% 19.99/3.46 | | | | | | | | | | | | | | | | REF_CLOSE: (265), (269), (272) are inconsistent by sub-proof
% 19.99/3.46 | | | | | | | | | | | | | | | | #1.
% 19.99/3.46 | | | | | | | | | | | | | | | |
% 19.99/3.46 | | | | | | | | | | | | | | | End of split
% 19.99/3.46 | | | | | | | | | | | | | | |
% 19.99/3.46 | | | | | | | | | | | | | | End of split
% 19.99/3.46 | | | | | | | | | | | | | |
% 19.99/3.46 | | | | | | | | | | | | | End of split
% 19.99/3.46 | | | | | | | | | | | | |
% 19.99/3.46 | | | | | | | | | | | | End of split
% 19.99/3.46 | | | | | | | | | | | |
% 19.99/3.46 | | | | | | | | | | | End of split
% 19.99/3.46 | | | | | | | | | | |
% 19.99/3.46 | | | | | | | | | | End of split
% 19.99/3.46 | | | | | | | | | |
% 19.99/3.46 | | | | | | | | | End of split
% 19.99/3.46 | | | | | | | | |
% 19.99/3.46 | | | | | | | | Case 2:
% 19.99/3.46 | | | | | | | | |
% 19.99/3.46 | | | | | | | | | (273) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 19.99/3.46 | | | | | | | | | (member(all_77_0, all_37_2) = v1 & member(all_65_0,
% 19.99/3.46 | | | | | | | | | all_37_2) = v2 & member(all_56_2, all_37_3) = v0
% 19.99/3.46 | | | | | | | | | & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 19.99/3.46 | | | | | | | | |
% 20.08/3.46 | | | | | | | | | DELTA: instantiating (273) with fresh symbols all_101_0,
% 20.08/3.46 | | | | | | | | | all_101_1, all_101_2 gives:
% 20.08/3.46 | | | | | | | | | (274) member(all_77_0, all_37_2) = all_101_1 &
% 20.08/3.46 | | | | | | | | | member(all_65_0, all_37_2) = all_101_0 &
% 20.08/3.46 | | | | | | | | | member(all_56_2, all_37_3) = all_101_2 & ( ~
% 20.08/3.46 | | | | | | | | | (all_101_0 = 0) | ~ (all_101_1 = 0) | ~
% 20.08/3.46 | | | | | | | | | (all_101_2 = 0))
% 20.08/3.46 | | | | | | | | |
% 20.08/3.46 | | | | | | | | | ALPHA: (274) implies:
% 20.08/3.46 | | | | | | | | | (275) member(all_56_2, all_37_3) = all_101_2
% 20.08/3.46 | | | | | | | | | (276) member(all_65_0, all_37_2) = all_101_0
% 20.08/3.46 | | | | | | | | | (277) member(all_77_0, all_37_2) = all_101_1
% 20.08/3.46 | | | | | | | | | (278) ~ (all_101_0 = 0) | ~ (all_101_1 = 0) | ~
% 20.08/3.46 | | | | | | | | | (all_101_2 = 0)
% 20.08/3.46 | | | | | | | | |
% 20.08/3.46 | | | | | | | | | REDUCE: (113), (277) imply:
% 20.08/3.46 | | | | | | | | | (279) member(all_63_0, all_37_2) = all_101_1
% 20.08/3.46 | | | | | | | | |
% 20.08/3.46 | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_101_2, all_37_3,
% 20.08/3.46 | | | | | | | | | all_56_2, simplifying with (28), (275) gives:
% 20.08/3.46 | | | | | | | | | (280) all_101_2 = 0
% 20.08/3.46 | | | | | | | | |
% 20.08/3.46 | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_101_1, all_37_2,
% 20.08/3.46 | | | | | | | | | all_63_0, simplifying with (41), (279) gives:
% 20.08/3.46 | | | | | | | | | (281) all_101_1 = 0
% 20.08/3.46 | | | | | | | | |
% 20.08/3.46 | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_101_0, all_37_2,
% 20.08/3.46 | | | | | | | | | all_65_0, simplifying with (45), (276) gives:
% 20.08/3.46 | | | | | | | | | (282) all_101_0 = 0
% 20.08/3.46 | | | | | | | | |
% 20.08/3.46 | | | | | | | | | BETA: splitting (278) gives:
% 20.08/3.46 | | | | | | | | |
% 20.08/3.46 | | | | | | | | | Case 1:
% 20.08/3.46 | | | | | | | | | |
% 20.08/3.46 | | | | | | | | | | (283) ~ (all_101_0 = 0)
% 20.08/3.46 | | | | | | | | | |
% 20.08/3.46 | | | | | | | | | | REDUCE: (282), (283) imply:
% 20.08/3.46 | | | | | | | | | | (284) $false
% 20.08/3.46 | | | | | | | | | |
% 20.08/3.46 | | | | | | | | | | CLOSE: (284) is inconsistent.
% 20.08/3.46 | | | | | | | | | |
% 20.08/3.46 | | | | | | | | | Case 2:
% 20.08/3.46 | | | | | | | | | |
% 20.08/3.46 | | | | | | | | | | (285) ~ (all_101_1 = 0) | ~ (all_101_2 = 0)
% 20.08/3.46 | | | | | | | | | |
% 20.08/3.46 | | | | | | | | | | BETA: splitting (285) gives:
% 20.08/3.46 | | | | | | | | | |
% 20.08/3.46 | | | | | | | | | | Case 1:
% 20.08/3.46 | | | | | | | | | | |
% 20.08/3.46 | | | | | | | | | | | (286) ~ (all_101_1 = 0)
% 20.08/3.46 | | | | | | | | | | |
% 20.08/3.46 | | | | | | | | | | | REDUCE: (281), (286) imply:
% 20.08/3.46 | | | | | | | | | | | (287) $false
% 20.08/3.46 | | | | | | | | | | |
% 20.08/3.46 | | | | | | | | | | | CLOSE: (287) is inconsistent.
% 20.08/3.46 | | | | | | | | | | |
% 20.08/3.46 | | | | | | | | | | Case 2:
% 20.08/3.46 | | | | | | | | | | |
% 20.08/3.46 | | | | | | | | | | | (288) ~ (all_101_2 = 0)
% 20.08/3.46 | | | | | | | | | | |
% 20.08/3.46 | | | | | | | | | | | REDUCE: (280), (288) imply:
% 20.08/3.46 | | | | | | | | | | | (289) $false
% 20.08/3.46 | | | | | | | | | | |
% 20.08/3.46 | | | | | | | | | | | CLOSE: (289) is inconsistent.
% 20.08/3.46 | | | | | | | | | | |
% 20.08/3.46 | | | | | | | | | | End of split
% 20.08/3.46 | | | | | | | | | |
% 20.08/3.46 | | | | | | | | | End of split
% 20.08/3.46 | | | | | | | | |
% 20.08/3.46 | | | | | | | | End of split
% 20.08/3.46 | | | | | | | |
% 20.08/3.46 | | | | | | | Case 2:
% 20.08/3.46 | | | | | | | |
% 20.08/3.46 | | | | | | | | (290) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 20.08/3.46 | | | | | | | | (member(all_77_0, all_37_2) = v1 & member(all_63_0,
% 20.08/3.46 | | | | | | | | all_37_2) = v2 & member(all_56_1, all_37_3) = v0 &
% 20.08/3.46 | | | | | | | | ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 20.08/3.46 | | | | | | | |
% 20.08/3.46 | | | | | | | | DELTA: instantiating (290) with fresh symbols all_97_0,
% 20.08/3.46 | | | | | | | | all_97_1, all_97_2 gives:
% 20.08/3.46 | | | | | | | | (291) member(all_77_0, all_37_2) = all_97_1 &
% 20.08/3.46 | | | | | | | | member(all_63_0, all_37_2) = all_97_0 &
% 20.08/3.46 | | | | | | | | member(all_56_1, all_37_3) = all_97_2 & ( ~ (all_97_0 =
% 20.08/3.46 | | | | | | | | 0) | ~ (all_97_1 = 0) | ~ (all_97_2 = 0))
% 20.08/3.46 | | | | | | | |
% 20.08/3.46 | | | | | | | | ALPHA: (291) implies:
% 20.08/3.46 | | | | | | | | (292) member(all_56_1, all_37_3) = all_97_2
% 20.08/3.46 | | | | | | | | (293) member(all_63_0, all_37_2) = all_97_0
% 20.08/3.46 | | | | | | | | (294) member(all_77_0, all_37_2) = all_97_1
% 20.08/3.46 | | | | | | | | (295) ~ (all_97_0 = 0) | ~ (all_97_1 = 0) | ~ (all_97_2 =
% 20.08/3.46 | | | | | | | | 0)
% 20.08/3.46 | | | | | | | |
% 20.08/3.46 | | | | | | | | GROUND_INST: instantiating (3) with 0, all_97_2, all_37_3,
% 20.08/3.46 | | | | | | | | all_56_1, simplifying with (29), (292) gives:
% 20.08/3.46 | | | | | | | | (296) all_97_2 = 0
% 20.08/3.46 | | | | | | | |
% 20.08/3.46 | | | | | | | | GROUND_INST: instantiating (3) with 0, all_97_0, all_37_2,
% 20.08/3.46 | | | | | | | | all_63_0, simplifying with (41), (293) gives:
% 20.08/3.46 | | | | | | | | (297) all_97_0 = 0
% 20.08/3.46 | | | | | | | |
% 20.08/3.46 | | | | | | | | GROUND_INST: instantiating (3) with 0, all_97_1, all_37_2,
% 20.08/3.46 | | | | | | | | all_77_0, simplifying with (94), (294) gives:
% 20.08/3.46 | | | | | | | | (298) all_97_1 = 0
% 20.08/3.46 | | | | | | | |
% 20.08/3.46 | | | | | | | | BETA: splitting (295) gives:
% 20.08/3.46 | | | | | | | |
% 20.08/3.46 | | | | | | | | Case 1:
% 20.08/3.46 | | | | | | | | |
% 20.08/3.46 | | | | | | | | | (299) ~ (all_97_0 = 0)
% 20.08/3.46 | | | | | | | | |
% 20.08/3.46 | | | | | | | | | REDUCE: (297), (299) imply:
% 20.08/3.46 | | | | | | | | | (300) $false
% 20.08/3.46 | | | | | | | | |
% 20.08/3.46 | | | | | | | | | CLOSE: (300) is inconsistent.
% 20.08/3.46 | | | | | | | | |
% 20.08/3.46 | | | | | | | | Case 2:
% 20.08/3.46 | | | | | | | | |
% 20.08/3.46 | | | | | | | | | (301) ~ (all_97_1 = 0) | ~ (all_97_2 = 0)
% 20.08/3.46 | | | | | | | | |
% 20.08/3.46 | | | | | | | | | BETA: splitting (301) gives:
% 20.08/3.46 | | | | | | | | |
% 20.08/3.46 | | | | | | | | | Case 1:
% 20.08/3.46 | | | | | | | | | |
% 20.08/3.46 | | | | | | | | | | (302) ~ (all_97_1 = 0)
% 20.08/3.46 | | | | | | | | | |
% 20.08/3.46 | | | | | | | | | | REDUCE: (298), (302) imply:
% 20.08/3.46 | | | | | | | | | | (303) $false
% 20.08/3.46 | | | | | | | | | |
% 20.08/3.46 | | | | | | | | | | CLOSE: (303) is inconsistent.
% 20.08/3.46 | | | | | | | | | |
% 20.08/3.46 | | | | | | | | | Case 2:
% 20.08/3.46 | | | | | | | | | |
% 20.08/3.46 | | | | | | | | | | (304) ~ (all_97_2 = 0)
% 20.08/3.46 | | | | | | | | | |
% 20.08/3.46 | | | | | | | | | | REDUCE: (296), (304) imply:
% 20.08/3.46 | | | | | | | | | | (305) $false
% 20.08/3.46 | | | | | | | | | |
% 20.08/3.46 | | | | | | | | | | CLOSE: (305) is inconsistent.
% 20.08/3.46 | | | | | | | | | |
% 20.08/3.46 | | | | | | | | | End of split
% 20.08/3.46 | | | | | | | | |
% 20.08/3.46 | | | | | | | | End of split
% 20.08/3.46 | | | | | | | |
% 20.08/3.46 | | | | | | | End of split
% 20.08/3.46 | | | | | | |
% 20.08/3.46 | | | | | | End of split
% 20.08/3.46 | | | | | |
% 20.08/3.46 | | | | | End of split
% 20.08/3.46 | | | | |
% 20.08/3.46 | | | | End of split
% 20.08/3.46 | | | |
% 20.08/3.46 | | | End of split
% 20.08/3.46 | | |
% 20.08/3.46 | | Case 2:
% 20.08/3.46 | | |
% 20.08/3.46 | | | (306) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 20.08/3.46 | | | apply(all_37_1, v1, v0) = v2 & apply(all_37_1, v0, v1) = 0 &
% 20.08/3.46 | | | member(v1, all_37_3) = 0 & member(v0, all_37_3) = 0 & $i(v1) &
% 20.08/3.46 | | | $i(v0)) | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 20.08/3.46 | | | apply(all_37_1, v0, v0) = v1 & member(v0, all_37_3) = 0 &
% 20.08/3.46 | | | $i(v0))
% 20.08/3.46 | | |
% 20.08/3.46 | | | BETA: splitting (306) gives:
% 20.08/3.46 | | |
% 20.08/3.46 | | | Case 1:
% 20.08/3.46 | | | |
% 20.08/3.46 | | | | (307) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 20.08/3.46 | | | | apply(all_37_1, v1, v0) = v2 & apply(all_37_1, v0, v1) = 0 &
% 20.08/3.46 | | | | member(v1, all_37_3) = 0 & member(v0, all_37_3) = 0 & $i(v1)
% 20.08/3.46 | | | | & $i(v0))
% 20.08/3.46 | | | |
% 20.08/3.46 | | | | DELTA: instantiating (307) with fresh symbols all_56_0, all_56_1,
% 20.08/3.46 | | | | all_56_2 gives:
% 20.08/3.46 | | | | (308) ~ (all_56_0 = 0) & apply(all_37_1, all_56_1, all_56_2) =
% 20.08/3.46 | | | | all_56_0 & apply(all_37_1, all_56_2, all_56_1) = 0 &
% 20.08/3.46 | | | | member(all_56_1, all_37_3) = 0 & member(all_56_2, all_37_3) = 0
% 20.08/3.46 | | | | & $i(all_56_1) & $i(all_56_2)
% 20.08/3.46 | | | |
% 20.08/3.46 | | | | ALPHA: (308) implies:
% 20.08/3.46 | | | | (309) ~ (all_56_0 = 0)
% 20.08/3.46 | | | | (310) $i(all_56_2)
% 20.08/3.47 | | | | (311) $i(all_56_1)
% 20.08/3.47 | | | | (312) member(all_56_2, all_37_3) = 0
% 20.08/3.47 | | | | (313) member(all_56_1, all_37_3) = 0
% 20.08/3.47 | | | | (314) apply(all_37_1, all_56_2, all_56_1) = 0
% 20.08/3.47 | | | | (315) apply(all_37_1, all_56_1, all_56_2) = all_56_0
% 20.08/3.47 | | | |
% 20.08/3.47 | | | | GROUND_INST: instantiating (13) with all_56_2, all_56_1, 0, simplifying
% 20.08/3.47 | | | | with (310), (311), (314) gives:
% 20.08/3.47 | | | | (316) ? [v0: any] : ? [v1: any] : (member(all_56_1, all_37_3) = v1
% 20.08/3.47 | | | | & member(all_56_2, all_37_3) = v0 & ( ~ (v1 = 0) | ~ (v0 =
% 20.08/3.47 | | | | 0))) | ? [v0: $i] : (apply(all_37_4, all_56_1, v0) = 0 &
% 20.08/3.47 | | | | apply(all_37_4, all_56_2, v0) = 0 & member(v0, all_37_2) = 0
% 20.08/3.47 | | | | & $i(v0))
% 20.08/3.47 | | | |
% 20.08/3.47 | | | | GROUND_INST: instantiating (13) with all_56_1, all_56_2, all_56_0,
% 20.08/3.47 | | | | simplifying with (310), (311), (315) gives:
% 20.08/3.47 | | | | (317) ? [v0: any] : ? [v1: any] : (member(all_56_1, all_37_3) = v0
% 20.08/3.47 | | | | & member(all_56_2, all_37_3) = v1 & ( ~ (v1 = 0) | ~ (v0 =
% 20.08/3.47 | | | | 0))) | (( ~ (all_56_0 = 0) | ? [v0: $i] :
% 20.08/3.47 | | | | (apply(all_37_4, all_56_1, v0) = 0 & apply(all_37_4,
% 20.08/3.47 | | | | all_56_2, v0) = 0 & member(v0, all_37_2) = 0 & $i(v0)))
% 20.08/3.47 | | | | & (all_56_0 = 0 | ! [v0: $i] : ( ~ (apply(all_37_4,
% 20.08/3.47 | | | | all_56_1, v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 20.08/3.47 | | | | [v2: any] : (apply(all_37_4, all_56_2, v0) = v2 &
% 20.08/3.47 | | | | member(v0, all_37_2) = v1 & ( ~ (v2 = 0) | ~ (v1 =
% 20.08/3.47 | | | | 0))))))
% 20.08/3.47 | | | |
% 20.08/3.47 | | | | BETA: splitting (317) gives:
% 20.08/3.47 | | | |
% 20.08/3.47 | | | | Case 1:
% 20.08/3.47 | | | | |
% 20.08/3.47 | | | | | (318) ? [v0: any] : ? [v1: any] : (member(all_56_1, all_37_3) =
% 20.08/3.47 | | | | | v0 & member(all_56_2, all_37_3) = v1 & ( ~ (v1 = 0) | ~
% 20.08/3.47 | | | | | (v0 = 0)))
% 20.08/3.47 | | | | |
% 20.08/3.47 | | | | | DELTA: instantiating (318) with fresh symbols all_70_0, all_70_1
% 20.08/3.47 | | | | | gives:
% 20.08/3.47 | | | | | (319) member(all_56_1, all_37_3) = all_70_1 & member(all_56_2,
% 20.08/3.47 | | | | | all_37_3) = all_70_0 & ( ~ (all_70_0 = 0) | ~ (all_70_1 =
% 20.08/3.47 | | | | | 0))
% 20.08/3.47 | | | | |
% 20.08/3.47 | | | | | ALPHA: (319) implies:
% 20.08/3.47 | | | | | (320) member(all_56_2, all_37_3) = all_70_0
% 20.08/3.47 | | | | | (321) member(all_56_1, all_37_3) = all_70_1
% 20.08/3.47 | | | | | (322) ~ (all_70_0 = 0) | ~ (all_70_1 = 0)
% 20.08/3.47 | | | | |
% 20.08/3.47 | | | | | GROUND_INST: instantiating (3) with 0, all_70_0, all_37_3, all_56_2,
% 20.08/3.47 | | | | | simplifying with (312), (320) gives:
% 20.08/3.47 | | | | | (323) all_70_0 = 0
% 20.08/3.47 | | | | |
% 20.08/3.47 | | | | | GROUND_INST: instantiating (3) with 0, all_70_1, all_37_3, all_56_1,
% 20.08/3.47 | | | | | simplifying with (313), (321) gives:
% 20.08/3.47 | | | | | (324) all_70_1 = 0
% 20.08/3.47 | | | | |
% 20.08/3.47 | | | | | BETA: splitting (322) gives:
% 20.08/3.47 | | | | |
% 20.08/3.47 | | | | | Case 1:
% 20.08/3.47 | | | | | |
% 20.08/3.47 | | | | | | (325) ~ (all_70_0 = 0)
% 20.08/3.47 | | | | | |
% 20.08/3.47 | | | | | | REDUCE: (323), (325) imply:
% 20.08/3.47 | | | | | | (326) $false
% 20.08/3.47 | | | | | |
% 20.08/3.47 | | | | | | CLOSE: (326) is inconsistent.
% 20.08/3.47 | | | | | |
% 20.08/3.47 | | | | | Case 2:
% 20.08/3.47 | | | | | |
% 20.08/3.47 | | | | | | (327) ~ (all_70_1 = 0)
% 20.08/3.47 | | | | | |
% 20.08/3.47 | | | | | | REDUCE: (324), (327) imply:
% 20.08/3.47 | | | | | | (328) $false
% 20.08/3.47 | | | | | |
% 20.08/3.47 | | | | | | CLOSE: (328) is inconsistent.
% 20.08/3.47 | | | | | |
% 20.08/3.47 | | | | | End of split
% 20.08/3.47 | | | | |
% 20.08/3.47 | | | | Case 2:
% 20.08/3.47 | | | | |
% 20.08/3.47 | | | | | (329) ( ~ (all_56_0 = 0) | ? [v0: $i] : (apply(all_37_4, all_56_1,
% 20.08/3.47 | | | | | v0) = 0 & apply(all_37_4, all_56_2, v0) = 0 &
% 20.08/3.47 | | | | | member(v0, all_37_2) = 0 & $i(v0))) & (all_56_0 = 0 | !
% 20.08/3.47 | | | | | [v0: $i] : ( ~ (apply(all_37_4, all_56_1, v0) = 0) | ~
% 20.08/3.47 | | | | | $i(v0) | ? [v1: any] : ? [v2: any] : (apply(all_37_4,
% 20.08/3.47 | | | | | all_56_2, v0) = v2 & member(v0, all_37_2) = v1 & ( ~
% 20.08/3.47 | | | | | (v2 = 0) | ~ (v1 = 0)))))
% 20.08/3.47 | | | | |
% 20.08/3.47 | | | | | ALPHA: (329) implies:
% 20.08/3.47 | | | | | (330) all_56_0 = 0 | ! [v0: $i] : ( ~ (apply(all_37_4, all_56_1,
% 20.08/3.47 | | | | | v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] :
% 20.08/3.47 | | | | | (apply(all_37_4, all_56_2, v0) = v2 & member(v0, all_37_2)
% 20.08/3.47 | | | | | = v1 & ( ~ (v2 = 0) | ~ (v1 = 0))))
% 20.08/3.47 | | | | |
% 20.08/3.47 | | | | | BETA: splitting (316) gives:
% 20.08/3.47 | | | | |
% 20.08/3.47 | | | | | Case 1:
% 20.08/3.47 | | | | | |
% 20.08/3.47 | | | | | | (331) ? [v0: any] : ? [v1: any] : (member(all_56_1, all_37_3) =
% 20.08/3.47 | | | | | | v1 & member(all_56_2, all_37_3) = v0 & ( ~ (v1 = 0) | ~
% 20.08/3.47 | | | | | | (v0 = 0)))
% 20.08/3.47 | | | | | |
% 20.08/3.47 | | | | | | DELTA: instantiating (331) with fresh symbols all_71_0, all_71_1
% 20.08/3.47 | | | | | | gives:
% 20.08/3.47 | | | | | | (332) member(all_56_1, all_37_3) = all_71_0 & member(all_56_2,
% 20.08/3.47 | | | | | | all_37_3) = all_71_1 & ( ~ (all_71_0 = 0) | ~ (all_71_1
% 20.08/3.47 | | | | | | = 0))
% 20.08/3.47 | | | | | |
% 20.08/3.47 | | | | | | ALPHA: (332) implies:
% 20.08/3.47 | | | | | | (333) member(all_56_2, all_37_3) = all_71_1
% 20.08/3.47 | | | | | | (334) member(all_56_1, all_37_3) = all_71_0
% 20.08/3.47 | | | | | | (335) ~ (all_71_0 = 0) | ~ (all_71_1 = 0)
% 20.08/3.47 | | | | | |
% 20.08/3.47 | | | | | | GROUND_INST: instantiating (3) with 0, all_71_1, all_37_3, all_56_2,
% 20.08/3.47 | | | | | | simplifying with (312), (333) gives:
% 20.08/3.47 | | | | | | (336) all_71_1 = 0
% 20.08/3.47 | | | | | |
% 20.08/3.47 | | | | | | GROUND_INST: instantiating (3) with 0, all_71_0, all_37_3, all_56_1,
% 20.08/3.47 | | | | | | simplifying with (313), (334) gives:
% 20.08/3.47 | | | | | | (337) all_71_0 = 0
% 20.08/3.47 | | | | | |
% 20.08/3.47 | | | | | | BETA: splitting (335) gives:
% 20.08/3.47 | | | | | |
% 20.08/3.47 | | | | | | Case 1:
% 20.08/3.47 | | | | | | |
% 20.08/3.47 | | | | | | | (338) ~ (all_71_0 = 0)
% 20.08/3.47 | | | | | | |
% 20.08/3.47 | | | | | | | REDUCE: (337), (338) imply:
% 20.08/3.47 | | | | | | | (339) $false
% 20.08/3.47 | | | | | | |
% 20.08/3.47 | | | | | | | CLOSE: (339) is inconsistent.
% 20.08/3.47 | | | | | | |
% 20.08/3.47 | | | | | | Case 2:
% 20.08/3.47 | | | | | | |
% 20.08/3.47 | | | | | | | (340) ~ (all_71_1 = 0)
% 20.08/3.47 | | | | | | |
% 20.08/3.47 | | | | | | | REDUCE: (336), (340) imply:
% 20.08/3.47 | | | | | | | (341) $false
% 20.08/3.47 | | | | | | |
% 20.08/3.47 | | | | | | | CLOSE: (341) is inconsistent.
% 20.08/3.47 | | | | | | |
% 20.08/3.47 | | | | | | End of split
% 20.08/3.47 | | | | | |
% 20.08/3.47 | | | | | Case 2:
% 20.08/3.47 | | | | | |
% 20.08/3.47 | | | | | | (342) ? [v0: $i] : (apply(all_37_4, all_56_1, v0) = 0 &
% 20.08/3.47 | | | | | | apply(all_37_4, all_56_2, v0) = 0 & member(v0, all_37_2)
% 20.08/3.47 | | | | | | = 0 & $i(v0))
% 20.08/3.47 | | | | | |
% 20.08/3.47 | | | | | | DELTA: instantiating (342) with fresh symbol all_71_0 gives:
% 20.08/3.47 | | | | | | (343) apply(all_37_4, all_56_1, all_71_0) = 0 & apply(all_37_4,
% 20.08/3.47 | | | | | | all_56_2, all_71_0) = 0 & member(all_71_0, all_37_2) = 0
% 20.08/3.47 | | | | | | & $i(all_71_0)
% 20.08/3.47 | | | | | |
% 20.08/3.47 | | | | | | ALPHA: (343) implies:
% 20.08/3.47 | | | | | | (344) $i(all_71_0)
% 20.08/3.47 | | | | | | (345) member(all_71_0, all_37_2) = 0
% 20.08/3.47 | | | | | | (346) apply(all_37_4, all_56_2, all_71_0) = 0
% 20.08/3.47 | | | | | | (347) apply(all_37_4, all_56_1, all_71_0) = 0
% 20.08/3.47 | | | | | |
% 20.08/3.47 | | | | | | BETA: splitting (330) gives:
% 20.08/3.47 | | | | | |
% 20.08/3.47 | | | | | | Case 1:
% 20.08/3.47 | | | | | | |
% 20.08/3.47 | | | | | | | (348) all_56_0 = 0
% 20.08/3.47 | | | | | | |
% 20.08/3.47 | | | | | | | REDUCE: (309), (348) imply:
% 20.08/3.47 | | | | | | | (349) $false
% 20.08/3.47 | | | | | | |
% 20.08/3.47 | | | | | | | CLOSE: (349) is inconsistent.
% 20.08/3.47 | | | | | | |
% 20.08/3.47 | | | | | | Case 2:
% 20.08/3.47 | | | | | | |
% 20.08/3.47 | | | | | | | (350) ! [v0: $i] : ( ~ (apply(all_37_4, all_56_1, v0) = 0) |
% 20.08/3.47 | | | | | | | ~ $i(v0) | ? [v1: any] : ? [v2: any] :
% 20.08/3.47 | | | | | | | (apply(all_37_4, all_56_2, v0) = v2 & member(v0,
% 20.08/3.47 | | | | | | | all_37_2) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0))))
% 20.08/3.47 | | | | | | |
% 20.08/3.47 | | | | | | | GROUND_INST: instantiating (350) with all_71_0, simplifying with
% 20.08/3.47 | | | | | | | (344), (347) gives:
% 20.08/3.47 | | | | | | | (351) ? [v0: any] : ? [v1: any] : (apply(all_37_4, all_56_2,
% 20.08/3.47 | | | | | | | all_71_0) = v1 & member(all_71_0, all_37_2) = v0 & (
% 20.08/3.47 | | | | | | | ~ (v1 = 0) | ~ (v0 = 0)))
% 20.08/3.47 | | | | | | |
% 20.08/3.47 | | | | | | | DELTA: instantiating (351) with fresh symbols all_83_0, all_83_1
% 20.08/3.47 | | | | | | | gives:
% 20.08/3.48 | | | | | | | (352) apply(all_37_4, all_56_2, all_71_0) = all_83_0 &
% 20.08/3.48 | | | | | | | member(all_71_0, all_37_2) = all_83_1 & ( ~ (all_83_0 =
% 20.08/3.48 | | | | | | | 0) | ~ (all_83_1 = 0))
% 20.08/3.48 | | | | | | |
% 20.08/3.48 | | | | | | | ALPHA: (352) implies:
% 20.08/3.48 | | | | | | | (353) member(all_71_0, all_37_2) = all_83_1
% 20.08/3.48 | | | | | | | (354) apply(all_37_4, all_56_2, all_71_0) = all_83_0
% 20.08/3.48 | | | | | | | (355) ~ (all_83_0 = 0) | ~ (all_83_1 = 0)
% 20.08/3.48 | | | | | | |
% 20.08/3.48 | | | | | | | GROUND_INST: instantiating (3) with 0, all_83_1, all_37_2,
% 20.08/3.48 | | | | | | | all_71_0, simplifying with (345), (353) gives:
% 20.08/3.48 | | | | | | | (356) all_83_1 = 0
% 20.08/3.48 | | | | | | |
% 20.08/3.48 | | | | | | | GROUND_INST: instantiating (4) with 0, all_83_0, all_71_0,
% 20.08/3.48 | | | | | | | all_56_2, all_37_4, simplifying with (346), (354)
% 20.08/3.48 | | | | | | | gives:
% 20.08/3.48 | | | | | | | (357) all_83_0 = 0
% 20.08/3.48 | | | | | | |
% 20.08/3.48 | | | | | | | BETA: splitting (355) gives:
% 20.08/3.48 | | | | | | |
% 20.08/3.48 | | | | | | | Case 1:
% 20.08/3.48 | | | | | | | |
% 20.08/3.48 | | | | | | | | (358) ~ (all_83_0 = 0)
% 20.08/3.48 | | | | | | | |
% 20.08/3.48 | | | | | | | | REDUCE: (357), (358) imply:
% 20.08/3.48 | | | | | | | | (359) $false
% 20.08/3.48 | | | | | | | |
% 20.08/3.48 | | | | | | | | CLOSE: (359) is inconsistent.
% 20.08/3.48 | | | | | | | |
% 20.08/3.48 | | | | | | | Case 2:
% 20.08/3.48 | | | | | | | |
% 20.08/3.48 | | | | | | | | (360) ~ (all_83_1 = 0)
% 20.08/3.48 | | | | | | | |
% 20.08/3.48 | | | | | | | | REDUCE: (356), (360) imply:
% 20.08/3.48 | | | | | | | | (361) $false
% 20.08/3.48 | | | | | | | |
% 20.08/3.48 | | | | | | | | CLOSE: (361) is inconsistent.
% 20.08/3.48 | | | | | | | |
% 20.08/3.48 | | | | | | | End of split
% 20.08/3.48 | | | | | | |
% 20.08/3.48 | | | | | | End of split
% 20.08/3.48 | | | | | |
% 20.08/3.48 | | | | | End of split
% 20.08/3.48 | | | | |
% 20.08/3.48 | | | | End of split
% 20.08/3.48 | | | |
% 20.08/3.48 | | | Case 2:
% 20.08/3.48 | | | |
% 20.08/3.48 | | | | (362) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & apply(all_37_1, v0,
% 20.08/3.48 | | | | v0) = v1 & member(v0, all_37_3) = 0 & $i(v0))
% 20.08/3.48 | | | |
% 20.08/3.48 | | | | DELTA: instantiating (362) with fresh symbols all_56_0, all_56_1 gives:
% 20.08/3.48 | | | | (363) ~ (all_56_0 = 0) & apply(all_37_1, all_56_1, all_56_1) =
% 20.08/3.48 | | | | all_56_0 & member(all_56_1, all_37_3) = 0 & $i(all_56_1)
% 20.08/3.48 | | | |
% 20.08/3.48 | | | | ALPHA: (363) implies:
% 20.08/3.48 | | | | (364) ~ (all_56_0 = 0)
% 20.08/3.48 | | | | (365) $i(all_56_1)
% 20.08/3.48 | | | | (366) member(all_56_1, all_37_3) = 0
% 20.08/3.48 | | | | (367) apply(all_37_1, all_56_1, all_56_1) = all_56_0
% 20.08/3.48 | | | |
% 20.08/3.48 | | | | GROUND_INST: instantiating (15) with all_56_1, simplifying with (365),
% 20.08/3.48 | | | | (366) gives:
% 20.08/3.48 | | | | (368) ? [v0: $i] : (apply(all_37_4, all_56_1, v0) = 0 & member(v0,
% 20.08/3.48 | | | | all_37_2) = 0 & $i(v0))
% 20.08/3.48 | | | |
% 20.08/3.48 | | | | GROUND_INST: instantiating (13) with all_56_1, all_56_1, all_56_0,
% 20.08/3.48 | | | | simplifying with (365), (367) gives:
% 20.08/3.48 | | | | (369) ? [v0: any] : ? [v1: any] : (member(all_56_1, all_37_3) = v1
% 20.08/3.48 | | | | & member(all_56_1, all_37_3) = v0 & ( ~ (v1 = 0) | ~ (v0 =
% 20.08/3.48 | | | | 0))) | (( ~ (all_56_0 = 0) | ? [v0: $i] :
% 20.08/3.48 | | | | (apply(all_37_4, all_56_1, v0) = 0 & member(v0, all_37_2) =
% 20.08/3.48 | | | | 0 & $i(v0))) & (all_56_0 = 0 | ! [v0: $i] : ( ~
% 20.08/3.48 | | | | (apply(all_37_4, all_56_1, v0) = 0) | ~ $i(v0) | ? [v1:
% 20.08/3.48 | | | | any] : ? [v2: any] : (apply(all_37_4, all_56_1, v0) =
% 20.08/3.48 | | | | v2 & member(v0, all_37_2) = v1 & ( ~ (v2 = 0) | ~ (v1
% 20.08/3.48 | | | | = 0))))))
% 20.08/3.48 | | | |
% 20.08/3.48 | | | | DELTA: instantiating (368) with fresh symbol all_63_0 gives:
% 20.08/3.48 | | | | (370) apply(all_37_4, all_56_1, all_63_0) = 0 & member(all_63_0,
% 20.08/3.48 | | | | all_37_2) = 0 & $i(all_63_0)
% 20.08/3.48 | | | |
% 20.08/3.48 | | | | ALPHA: (370) implies:
% 20.08/3.48 | | | | (371) $i(all_63_0)
% 20.08/3.48 | | | | (372) member(all_63_0, all_37_2) = 0
% 20.08/3.48 | | | | (373) apply(all_37_4, all_56_1, all_63_0) = 0
% 20.08/3.48 | | | |
% 20.08/3.48 | | | | BETA: splitting (369) gives:
% 20.08/3.48 | | | |
% 20.08/3.48 | | | | Case 1:
% 20.08/3.48 | | | | |
% 20.08/3.48 | | | | | (374) ? [v0: any] : ? [v1: any] : (member(all_56_1, all_37_3) =
% 20.08/3.48 | | | | | v1 & member(all_56_1, all_37_3) = v0 & ( ~ (v1 = 0) | ~
% 20.08/3.48 | | | | | (v0 = 0)))
% 20.08/3.48 | | | | |
% 20.08/3.48 | | | | | DELTA: instantiating (374) with fresh symbols all_68_0, all_68_1
% 20.08/3.48 | | | | | gives:
% 20.08/3.48 | | | | | (375) member(all_56_1, all_37_3) = all_68_0 & member(all_56_1,
% 20.08/3.48 | | | | | all_37_3) = all_68_1 & ( ~ (all_68_0 = 0) | ~ (all_68_1 =
% 20.08/3.48 | | | | | 0))
% 20.08/3.48 | | | | |
% 20.08/3.48 | | | | | ALPHA: (375) implies:
% 20.08/3.48 | | | | | (376) member(all_56_1, all_37_3) = all_68_1
% 20.08/3.48 | | | | | (377) member(all_56_1, all_37_3) = all_68_0
% 20.08/3.48 | | | | | (378) ~ (all_68_0 = 0) | ~ (all_68_1 = 0)
% 20.08/3.48 | | | | |
% 20.08/3.48 | | | | | GROUND_INST: instantiating (3) with 0, all_68_0, all_37_3, all_56_1,
% 20.08/3.48 | | | | | simplifying with (366), (377) gives:
% 20.08/3.48 | | | | | (379) all_68_0 = 0
% 20.08/3.48 | | | | |
% 20.08/3.48 | | | | | GROUND_INST: instantiating (3) with all_68_1, all_68_0, all_37_3,
% 20.08/3.48 | | | | | all_56_1, simplifying with (376), (377) gives:
% 20.08/3.48 | | | | | (380) all_68_0 = all_68_1
% 20.08/3.48 | | | | |
% 20.08/3.48 | | | | | COMBINE_EQS: (379), (380) imply:
% 20.08/3.48 | | | | | (381) all_68_1 = 0
% 20.08/3.48 | | | | |
% 20.08/3.48 | | | | | BETA: splitting (378) gives:
% 20.08/3.48 | | | | |
% 20.08/3.48 | | | | | Case 1:
% 20.08/3.48 | | | | | |
% 20.08/3.48 | | | | | | (382) ~ (all_68_0 = 0)
% 20.08/3.48 | | | | | |
% 20.08/3.48 | | | | | | REDUCE: (379), (382) imply:
% 20.08/3.48 | | | | | | (383) $false
% 20.08/3.48 | | | | | |
% 20.08/3.48 | | | | | | CLOSE: (383) is inconsistent.
% 20.08/3.48 | | | | | |
% 20.08/3.48 | | | | | Case 2:
% 20.08/3.48 | | | | | |
% 20.08/3.48 | | | | | | (384) ~ (all_68_1 = 0)
% 20.08/3.48 | | | | | |
% 20.08/3.48 | | | | | | REDUCE: (381), (384) imply:
% 20.08/3.48 | | | | | | (385) $false
% 20.08/3.48 | | | | | |
% 20.08/3.48 | | | | | | CLOSE: (385) is inconsistent.
% 20.08/3.48 | | | | | |
% 20.08/3.48 | | | | | End of split
% 20.08/3.48 | | | | |
% 20.08/3.48 | | | | Case 2:
% 20.08/3.48 | | | | |
% 20.08/3.48 | | | | | (386) ( ~ (all_56_0 = 0) | ? [v0: $i] : (apply(all_37_4, all_56_1,
% 20.08/3.48 | | | | | v0) = 0 & member(v0, all_37_2) = 0 & $i(v0))) &
% 20.08/3.48 | | | | | (all_56_0 = 0 | ! [v0: $i] : ( ~ (apply(all_37_4, all_56_1,
% 20.08/3.48 | | | | | v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] :
% 20.08/3.48 | | | | | (apply(all_37_4, all_56_1, v0) = v2 & member(v0,
% 20.08/3.48 | | | | | all_37_2) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)))))
% 20.08/3.48 | | | | |
% 20.08/3.48 | | | | | ALPHA: (386) implies:
% 20.08/3.48 | | | | | (387) all_56_0 = 0 | ! [v0: $i] : ( ~ (apply(all_37_4, all_56_1,
% 20.08/3.48 | | | | | v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] :
% 20.08/3.48 | | | | | (apply(all_37_4, all_56_1, v0) = v2 & member(v0, all_37_2)
% 20.08/3.48 | | | | | = v1 & ( ~ (v2 = 0) | ~ (v1 = 0))))
% 20.08/3.48 | | | | |
% 20.08/3.48 | | | | | BETA: splitting (387) gives:
% 20.08/3.48 | | | | |
% 20.08/3.48 | | | | | Case 1:
% 20.08/3.48 | | | | | |
% 20.08/3.48 | | | | | | (388) all_56_0 = 0
% 20.08/3.48 | | | | | |
% 20.08/3.48 | | | | | | REDUCE: (364), (388) imply:
% 20.08/3.48 | | | | | | (389) $false
% 20.08/3.48 | | | | | |
% 20.08/3.48 | | | | | | CLOSE: (389) is inconsistent.
% 20.08/3.48 | | | | | |
% 20.08/3.48 | | | | | Case 2:
% 20.08/3.48 | | | | | |
% 20.08/3.48 | | | | | | (390) ! [v0: $i] : ( ~ (apply(all_37_4, all_56_1, v0) = 0) | ~
% 20.08/3.48 | | | | | | $i(v0) | ? [v1: any] : ? [v2: any] : (apply(all_37_4,
% 20.08/3.48 | | | | | | all_56_1, v0) = v2 & member(v0, all_37_2) = v1 & ( ~
% 20.08/3.48 | | | | | | (v2 = 0) | ~ (v1 = 0))))
% 20.08/3.48 | | | | | |
% 20.08/3.48 | | | | | | GROUND_INST: instantiating (390) with all_63_0, simplifying with
% 20.08/3.48 | | | | | | (371), (373) gives:
% 20.08/3.48 | | | | | | (391) ? [v0: any] : ? [v1: any] : (apply(all_37_4, all_56_1,
% 20.08/3.48 | | | | | | all_63_0) = v1 & member(all_63_0, all_37_2) = v0 & ( ~
% 20.08/3.48 | | | | | | (v1 = 0) | ~ (v0 = 0)))
% 20.08/3.48 | | | | | |
% 20.08/3.48 | | | | | | DELTA: instantiating (391) with fresh symbols all_77_0, all_77_1
% 20.08/3.48 | | | | | | gives:
% 20.08/3.48 | | | | | | (392) apply(all_37_4, all_56_1, all_63_0) = all_77_0 &
% 20.08/3.48 | | | | | | member(all_63_0, all_37_2) = all_77_1 & ( ~ (all_77_0 = 0)
% 20.08/3.48 | | | | | | | ~ (all_77_1 = 0))
% 20.08/3.48 | | | | | |
% 20.08/3.48 | | | | | | ALPHA: (392) implies:
% 20.08/3.48 | | | | | | (393) member(all_63_0, all_37_2) = all_77_1
% 20.08/3.48 | | | | | | (394) apply(all_37_4, all_56_1, all_63_0) = all_77_0
% 20.08/3.48 | | | | | | (395) ~ (all_77_0 = 0) | ~ (all_77_1 = 0)
% 20.08/3.48 | | | | | |
% 20.08/3.48 | | | | | | GROUND_INST: instantiating (3) with 0, all_77_1, all_37_2, all_63_0,
% 20.08/3.48 | | | | | | simplifying with (372), (393) gives:
% 20.08/3.48 | | | | | | (396) all_77_1 = 0
% 20.08/3.48 | | | | | |
% 20.08/3.48 | | | | | | GROUND_INST: instantiating (4) with 0, all_77_0, all_63_0, all_56_1,
% 20.08/3.48 | | | | | | all_37_4, simplifying with (373), (394) gives:
% 20.08/3.48 | | | | | | (397) all_77_0 = 0
% 20.08/3.48 | | | | | |
% 20.08/3.48 | | | | | | BETA: splitting (395) gives:
% 20.08/3.48 | | | | | |
% 20.08/3.48 | | | | | | Case 1:
% 20.08/3.48 | | | | | | |
% 20.08/3.48 | | | | | | | (398) ~ (all_77_0 = 0)
% 20.08/3.48 | | | | | | |
% 20.08/3.48 | | | | | | | REDUCE: (397), (398) imply:
% 20.08/3.48 | | | | | | | (399) $false
% 20.08/3.48 | | | | | | |
% 20.08/3.49 | | | | | | | CLOSE: (399) is inconsistent.
% 20.08/3.49 | | | | | | |
% 20.08/3.49 | | | | | | Case 2:
% 20.08/3.49 | | | | | | |
% 20.08/3.49 | | | | | | | (400) ~ (all_77_1 = 0)
% 20.08/3.49 | | | | | | |
% 20.08/3.49 | | | | | | | REDUCE: (396), (400) imply:
% 20.08/3.49 | | | | | | | (401) $false
% 20.08/3.49 | | | | | | |
% 20.08/3.49 | | | | | | | CLOSE: (401) is inconsistent.
% 20.08/3.49 | | | | | | |
% 20.08/3.49 | | | | | | End of split
% 20.08/3.49 | | | | | |
% 20.08/3.49 | | | | | End of split
% 20.08/3.49 | | | | |
% 20.08/3.49 | | | | End of split
% 20.08/3.49 | | | |
% 20.08/3.49 | | | End of split
% 20.08/3.49 | | |
% 20.08/3.49 | | End of split
% 20.08/3.49 | |
% 20.08/3.49 | End of split
% 20.08/3.49 |
% 20.08/3.49 End of proof
% 20.08/3.49
% 20.08/3.49 Sub-proof #1 shows that the following formulas are inconsistent:
% 20.08/3.49 ----------------------------------------------------------------
% 20.08/3.49 (1) ~ (all_109_1 = 0) | ~ (all_109_2 = 0)
% 20.08/3.49 (2) all_109_1 = 0
% 20.08/3.49 (3) all_109_2 = 0
% 20.08/3.49
% 20.08/3.49 Begin of proof
% 20.08/3.49 |
% 20.08/3.49 | BETA: splitting (1) gives:
% 20.08/3.49 |
% 20.08/3.49 | Case 1:
% 20.08/3.49 | |
% 20.08/3.49 | | (4) ~ (all_109_1 = 0)
% 20.08/3.49 | |
% 20.08/3.49 | | REDUCE: (2), (4) imply:
% 20.08/3.49 | | (5) $false
% 20.08/3.49 | |
% 20.08/3.49 | | CLOSE: (5) is inconsistent.
% 20.08/3.49 | |
% 20.08/3.49 | Case 2:
% 20.08/3.49 | |
% 20.08/3.49 | | (6) ~ (all_109_2 = 0)
% 20.08/3.49 | |
% 20.08/3.49 | | REDUCE: (3), (6) imply:
% 20.08/3.49 | | (7) $false
% 20.08/3.49 | |
% 20.08/3.49 | | CLOSE: (7) is inconsistent.
% 20.08/3.49 | |
% 20.08/3.49 | End of split
% 20.08/3.49 |
% 20.08/3.49 End of proof
% 20.08/3.49 % SZS output end Proof for theBenchmark
% 20.08/3.49
% 20.08/3.49 2872ms
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