TSTP Solution File: SET183+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET183+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 15:24:12 EDT 2023
% Result : Theorem 4.38s 1.45s
% Output : Proof 6.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET183+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 14:37:12 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.59 ________ _____
% 0.20/0.59 ___ __ \_________(_)________________________________
% 0.20/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.59
% 0.20/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.59 (2023-06-19)
% 0.20/0.59
% 0.20/0.59 (c) Philipp Rümmer, 2009-2023
% 0.20/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.59 Amanda Stjerna.
% 0.20/0.59 Free software under BSD-3-Clause.
% 0.20/0.59
% 0.20/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.59
% 0.20/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.60 Running up to 7 provers in parallel.
% 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.70/1.00 Prover 1: Preprocessing ...
% 1.70/1.00 Prover 4: Preprocessing ...
% 2.33/1.04 Prover 3: Preprocessing ...
% 2.33/1.04 Prover 0: Preprocessing ...
% 2.33/1.04 Prover 6: Preprocessing ...
% 2.33/1.04 Prover 2: Preprocessing ...
% 2.33/1.04 Prover 5: Preprocessing ...
% 3.70/1.24 Prover 3: Warning: ignoring some quantifiers
% 3.70/1.24 Prover 1: Warning: ignoring some quantifiers
% 3.70/1.25 Prover 4: Warning: ignoring some quantifiers
% 3.70/1.25 Prover 3: Constructing countermodel ...
% 3.70/1.25 Prover 6: Proving ...
% 3.70/1.25 Prover 5: Proving ...
% 3.70/1.25 Prover 2: Proving ...
% 3.70/1.26 Prover 1: Constructing countermodel ...
% 3.70/1.27 Prover 0: Proving ...
% 3.70/1.28 Prover 4: Constructing countermodel ...
% 4.38/1.42 Prover 3: gave up
% 4.38/1.43 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.38/1.45 Prover 0: proved (838ms)
% 4.38/1.45
% 4.38/1.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.38/1.45
% 4.38/1.45 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.38/1.45 Prover 5: stopped
% 4.38/1.45 Prover 6: stopped
% 4.38/1.45 Prover 1: gave up
% 4.38/1.47 Prover 7: Preprocessing ...
% 4.38/1.47 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.38/1.47 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.38/1.47 Prover 2: stopped
% 4.38/1.48 Prover 8: Preprocessing ...
% 4.38/1.48 Prover 10: Preprocessing ...
% 4.38/1.48 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.38/1.49 Prover 11: Preprocessing ...
% 4.38/1.49 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 4.38/1.51 Prover 16: Preprocessing ...
% 4.38/1.52 Prover 13: Preprocessing ...
% 4.38/1.53 Prover 7: Warning: ignoring some quantifiers
% 4.38/1.53 Prover 7: Constructing countermodel ...
% 4.38/1.54 Prover 10: Warning: ignoring some quantifiers
% 4.38/1.54 Prover 10: Constructing countermodel ...
% 4.38/1.55 Prover 16: Warning: ignoring some quantifiers
% 4.38/1.56 Prover 13: Warning: ignoring some quantifiers
% 5.54/1.56 Prover 13: Constructing countermodel ...
% 5.54/1.56 Prover 8: Warning: ignoring some quantifiers
% 5.54/1.56 Prover 16: Constructing countermodel ...
% 5.54/1.57 Prover 8: Constructing countermodel ...
% 5.54/1.59 Prover 4: Found proof (size 38)
% 5.54/1.59 Prover 4: proved (971ms)
% 5.54/1.59 Prover 7: stopped
% 5.54/1.59 Prover 16: stopped
% 5.54/1.59 Prover 13: stopped
% 5.54/1.59 Prover 8: stopped
% 5.54/1.59 Prover 10: stopped
% 5.54/1.61 Prover 11: Warning: ignoring some quantifiers
% 5.54/1.62 Prover 11: Constructing countermodel ...
% 5.54/1.62 Prover 11: stopped
% 5.54/1.62
% 5.54/1.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.54/1.62
% 5.54/1.63 % SZS output start Proof for theBenchmark
% 5.54/1.63 Assumptions after simplification:
% 5.54/1.63 ---------------------------------
% 5.54/1.63
% 5.54/1.63 (commutativity_of_intersection)
% 6.50/1.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v1, v0) = v2) | ~
% 6.50/1.66 $i(v1) | ~ $i(v0) | (intersection(v0, v1) = v2 & $i(v2))) & ! [v0: $i] :
% 6.50/1.66 ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v0, v1) = v2) | ~ $i(v1) | ~
% 6.50/1.66 $i(v0) | (intersection(v1, v0) = v2 & $i(v2)))
% 6.50/1.66
% 6.50/1.66 (equal_defn)
% 6.50/1.66 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (subset(v1, v0) = 0) | ~ $i(v1) |
% 6.50/1.66 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) & ! [v0: $i]
% 6.50/1.66 : ! [v1: $i] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 6.50/1.66 ? [v2: int] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0: $i] : ! [v1:
% 6.50/1.66 int] : (v1 = 0 | ~ (subset(v0, v0) = v1) | ~ $i(v0))
% 6.50/1.66
% 6.50/1.67 (intersection_defn)
% 6.50/1.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 6.50/1.67 | ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~
% 6.50/1.67 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v2, v1) = v6 &
% 6.50/1.67 member(v2, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : !
% 6.50/1.67 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (intersection(v0, v1) = v3) | ~
% 6.50/1.67 (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v2, v1) =
% 6.50/1.67 0 & member(v2, v0) = 0))
% 6.50/1.67
% 6.50/1.67 (intersection_is_subset)
% 6.50/1.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v0, v1) = v2) | ~
% 6.50/1.67 $i(v1) | ~ $i(v0) | subset(v2, v0) = 0)
% 6.50/1.67
% 6.50/1.67 (prove_subset_intersection)
% 6.50/1.67 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v0) & subset(v0, v1) = 0 &
% 6.50/1.67 intersection(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0))
% 6.50/1.67
% 6.50/1.67 (subset_defn)
% 6.50/1.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 6.50/1.68 (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 6.50/1.68 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0: $i] :
% 6.50/1.68 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) |
% 6.50/1.68 ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4 &
% 6.50/1.68 member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 6.50/1.68 ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) |
% 6.50/1.68 ~ $i(v0) | member(v2, v1) = 0)
% 6.50/1.68
% 6.50/1.68 (function-axioms)
% 6.50/1.68 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 6.50/1.68 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 6.50/1.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.50/1.68 (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0:
% 6.50/1.68 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 6.50/1.68 : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 6.50/1.68
% 6.50/1.68 Further assumptions not needed in the proof:
% 6.50/1.68 --------------------------------------------
% 6.50/1.68 equal_member_defn, reflexivity_of_subset
% 6.50/1.68
% 6.50/1.68 Those formulas are unsatisfiable:
% 6.50/1.68 ---------------------------------
% 6.50/1.68
% 6.50/1.68 Begin of proof
% 6.50/1.68 |
% 6.50/1.68 | ALPHA: (intersection_defn) implies:
% 6.50/1.69 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 6.50/1.69 | (v4 = 0 | ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = v4) |
% 6.50/1.69 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] :
% 6.50/1.69 | (member(v2, v1) = v6 & member(v2, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 =
% 6.50/1.69 | 0))))
% 6.50/1.69 |
% 6.50/1.69 | ALPHA: (subset_defn) implies:
% 6.50/1.69 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v0, v1) = 0) | ~
% 6.50/1.69 | (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | member(v2,
% 6.50/1.69 | v1) = 0)
% 6.50/1.69 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 6.50/1.69 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 6.50/1.69 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 6.50/1.69 |
% 6.50/1.69 | ALPHA: (equal_defn) implies:
% 6.50/1.69 | (4) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (subset(v1, v0) = 0) | ~
% 6.50/1.69 | $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subset(v0, v1) =
% 6.50/1.69 | v2))
% 6.50/1.69 |
% 6.50/1.69 | ALPHA: (commutativity_of_intersection) implies:
% 6.50/1.69 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v1, v0) =
% 6.50/1.69 | v2) | ~ $i(v1) | ~ $i(v0) | (intersection(v0, v1) = v2 & $i(v2)))
% 6.50/1.69 |
% 6.50/1.69 | ALPHA: (function-axioms) implies:
% 6.50/1.69 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 6.50/1.69 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 6.50/1.69 | = v0))
% 6.50/1.69 |
% 6.50/1.70 | DELTA: instantiating (prove_subset_intersection) with fresh symbols all_9_0,
% 6.50/1.70 | all_9_1, all_9_2 gives:
% 6.50/1.70 | (7) ~ (all_9_0 = all_9_2) & subset(all_9_2, all_9_1) = 0 &
% 6.50/1.70 | intersection(all_9_2, all_9_1) = all_9_0 & $i(all_9_0) & $i(all_9_1) &
% 6.50/1.70 | $i(all_9_2)
% 6.50/1.70 |
% 6.50/1.70 | ALPHA: (7) implies:
% 6.50/1.70 | (8) ~ (all_9_0 = all_9_2)
% 6.50/1.70 | (9) $i(all_9_2)
% 6.50/1.70 | (10) $i(all_9_1)
% 6.50/1.70 | (11) intersection(all_9_2, all_9_1) = all_9_0
% 6.50/1.70 | (12) subset(all_9_2, all_9_1) = 0
% 6.50/1.70 |
% 6.50/1.70 | GROUND_INST: instantiating (5) with all_9_1, all_9_2, all_9_0, simplifying
% 6.50/1.70 | with (9), (10), (11) gives:
% 6.50/1.70 | (13) intersection(all_9_1, all_9_2) = all_9_0 & $i(all_9_0)
% 6.50/1.70 |
% 6.50/1.70 | ALPHA: (13) implies:
% 6.50/1.70 | (14) $i(all_9_0)
% 6.50/1.70 |
% 6.50/1.70 | GROUND_INST: instantiating (intersection_is_subset) with all_9_2, all_9_1,
% 6.50/1.70 | all_9_0, simplifying with (9), (10), (11) gives:
% 6.50/1.70 | (15) subset(all_9_0, all_9_2) = 0
% 6.50/1.70 |
% 6.77/1.70 | GROUND_INST: instantiating (4) with all_9_2, all_9_0, simplifying with (9),
% 6.77/1.70 | (14), (15) gives:
% 6.77/1.70 | (16) all_9_0 = all_9_2 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_9_2,
% 6.77/1.70 | all_9_0) = v0)
% 6.77/1.70 |
% 6.77/1.70 | BETA: splitting (16) gives:
% 6.77/1.70 |
% 6.77/1.70 | Case 1:
% 6.77/1.70 | |
% 6.77/1.70 | | (17) all_9_0 = all_9_2
% 6.77/1.70 | |
% 6.77/1.70 | | REDUCE: (8), (17) imply:
% 6.77/1.70 | | (18) $false
% 6.77/1.70 | |
% 6.77/1.70 | | CLOSE: (18) is inconsistent.
% 6.77/1.70 | |
% 6.77/1.70 | Case 2:
% 6.77/1.70 | |
% 6.77/1.70 | | (19) ? [v0: int] : ( ~ (v0 = 0) & subset(all_9_2, all_9_0) = v0)
% 6.77/1.70 | |
% 6.77/1.70 | | DELTA: instantiating (19) with fresh symbol all_28_0 gives:
% 6.77/1.70 | | (20) ~ (all_28_0 = 0) & subset(all_9_2, all_9_0) = all_28_0
% 6.77/1.71 | |
% 6.77/1.71 | | ALPHA: (20) implies:
% 6.77/1.71 | | (21) ~ (all_28_0 = 0)
% 6.77/1.71 | | (22) subset(all_9_2, all_9_0) = all_28_0
% 6.77/1.71 | |
% 6.77/1.71 | | GROUND_INST: instantiating (3) with all_9_2, all_9_0, all_28_0, simplifying
% 6.77/1.71 | | with (9), (14), (22) gives:
% 6.77/1.71 | | (23) all_28_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 6.77/1.71 | | member(v0, all_9_0) = v1 & member(v0, all_9_2) = 0 & $i(v0))
% 6.77/1.71 | |
% 6.77/1.71 | | BETA: splitting (23) gives:
% 6.77/1.71 | |
% 6.77/1.71 | | Case 1:
% 6.77/1.71 | | |
% 6.77/1.71 | | | (24) all_28_0 = 0
% 6.77/1.71 | | |
% 6.77/1.71 | | | REDUCE: (21), (24) imply:
% 6.77/1.71 | | | (25) $false
% 6.77/1.71 | | |
% 6.77/1.71 | | | CLOSE: (25) is inconsistent.
% 6.77/1.71 | | |
% 6.77/1.71 | | Case 2:
% 6.77/1.71 | | |
% 6.77/1.71 | | | (26) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_9_0) =
% 6.77/1.71 | | | v1 & member(v0, all_9_2) = 0 & $i(v0))
% 6.77/1.71 | | |
% 6.77/1.71 | | | DELTA: instantiating (26) with fresh symbols all_41_0, all_41_1 gives:
% 6.77/1.71 | | | (27) ~ (all_41_0 = 0) & member(all_41_1, all_9_0) = all_41_0 &
% 6.77/1.71 | | | member(all_41_1, all_9_2) = 0 & $i(all_41_1)
% 6.77/1.71 | | |
% 6.77/1.71 | | | ALPHA: (27) implies:
% 6.77/1.71 | | | (28) ~ (all_41_0 = 0)
% 6.77/1.71 | | | (29) $i(all_41_1)
% 6.77/1.71 | | | (30) member(all_41_1, all_9_2) = 0
% 6.77/1.71 | | | (31) member(all_41_1, all_9_0) = all_41_0
% 6.77/1.71 | | |
% 6.77/1.71 | | | GROUND_INST: instantiating (2) with all_9_2, all_9_1, all_41_1,
% 6.77/1.71 | | | simplifying with (9), (10), (12), (29), (30) gives:
% 6.77/1.71 | | | (32) member(all_41_1, all_9_1) = 0
% 6.77/1.71 | | |
% 6.77/1.71 | | | GROUND_INST: instantiating (1) with all_9_2, all_9_1, all_41_1, all_9_0,
% 6.77/1.71 | | | all_41_0, simplifying with (9), (10), (11), (29), (31) gives:
% 6.77/1.71 | | | (33) all_41_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_41_1,
% 6.77/1.71 | | | all_9_1) = v1 & member(all_41_1, all_9_2) = v0 & ( ~ (v1 = 0)
% 6.77/1.71 | | | | ~ (v0 = 0)))
% 6.77/1.71 | | |
% 6.77/1.71 | | | BETA: splitting (33) gives:
% 6.77/1.71 | | |
% 6.77/1.71 | | | Case 1:
% 6.77/1.71 | | | |
% 6.77/1.71 | | | | (34) all_41_0 = 0
% 6.77/1.71 | | | |
% 6.77/1.71 | | | | REDUCE: (28), (34) imply:
% 6.77/1.71 | | | | (35) $false
% 6.77/1.71 | | | |
% 6.77/1.71 | | | | CLOSE: (35) is inconsistent.
% 6.77/1.71 | | | |
% 6.77/1.71 | | | Case 2:
% 6.77/1.71 | | | |
% 6.77/1.71 | | | | (36) ? [v0: any] : ? [v1: any] : (member(all_41_1, all_9_1) = v1 &
% 6.77/1.71 | | | | member(all_41_1, all_9_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 6.77/1.71 | | | |
% 6.77/1.71 | | | | DELTA: instantiating (36) with fresh symbols all_53_0, all_53_1 gives:
% 6.77/1.71 | | | | (37) member(all_41_1, all_9_1) = all_53_0 & member(all_41_1, all_9_2)
% 6.77/1.71 | | | | = all_53_1 & ( ~ (all_53_0 = 0) | ~ (all_53_1 = 0))
% 6.77/1.71 | | | |
% 6.77/1.71 | | | | ALPHA: (37) implies:
% 6.77/1.72 | | | | (38) member(all_41_1, all_9_2) = all_53_1
% 6.77/1.72 | | | | (39) member(all_41_1, all_9_1) = all_53_0
% 6.77/1.72 | | | | (40) ~ (all_53_0 = 0) | ~ (all_53_1 = 0)
% 6.77/1.72 | | | |
% 6.77/1.72 | | | | GROUND_INST: instantiating (6) with 0, all_53_1, all_9_2, all_41_1,
% 6.77/1.72 | | | | simplifying with (30), (38) gives:
% 6.77/1.72 | | | | (41) all_53_1 = 0
% 6.77/1.72 | | | |
% 6.77/1.72 | | | | GROUND_INST: instantiating (6) with 0, all_53_0, all_9_1, all_41_1,
% 6.77/1.72 | | | | simplifying with (32), (39) gives:
% 6.77/1.72 | | | | (42) all_53_0 = 0
% 6.77/1.72 | | | |
% 6.77/1.72 | | | | BETA: splitting (40) gives:
% 6.77/1.72 | | | |
% 6.77/1.72 | | | | Case 1:
% 6.77/1.72 | | | | |
% 6.77/1.72 | | | | | (43) ~ (all_53_0 = 0)
% 6.77/1.72 | | | | |
% 6.77/1.72 | | | | | REDUCE: (42), (43) imply:
% 6.77/1.72 | | | | | (44) $false
% 6.77/1.72 | | | | |
% 6.77/1.72 | | | | | CLOSE: (44) is inconsistent.
% 6.77/1.72 | | | | |
% 6.77/1.72 | | | | Case 2:
% 6.77/1.72 | | | | |
% 6.77/1.72 | | | | | (45) ~ (all_53_1 = 0)
% 6.77/1.72 | | | | |
% 6.77/1.72 | | | | | REDUCE: (41), (45) imply:
% 6.77/1.72 | | | | | (46) $false
% 6.77/1.72 | | | | |
% 6.77/1.72 | | | | | CLOSE: (46) is inconsistent.
% 6.77/1.72 | | | | |
% 6.77/1.72 | | | | End of split
% 6.77/1.72 | | | |
% 6.77/1.72 | | | End of split
% 6.77/1.72 | | |
% 6.77/1.72 | | End of split
% 6.77/1.72 | |
% 6.77/1.72 | End of split
% 6.77/1.72 |
% 6.77/1.72 End of proof
% 6.77/1.72 % SZS output end Proof for theBenchmark
% 6.77/1.72
% 6.77/1.72 1130ms
%------------------------------------------------------------------------------