TSTP Solution File: SET015+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET015+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n004.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 15:23:07 EDT 2023
% Result : Theorem 8.25s 1.96s
% Output : Proof 10.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET015+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.32 % Computer : n004.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sat Aug 26 11:09:52 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.16/0.61 ________ _____
% 0.16/0.61 ___ __ \_________(_)________________________________
% 0.16/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.16/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.16/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.16/0.61
% 0.16/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.16/0.61 (2023-06-19)
% 0.16/0.61
% 0.16/0.61 (c) Philipp Rümmer, 2009-2023
% 0.16/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.16/0.61 Amanda Stjerna.
% 0.16/0.61 Free software under BSD-3-Clause.
% 0.16/0.61
% 0.16/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.16/0.61
% 0.16/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.16/0.63 Running up to 7 provers in parallel.
% 0.16/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.16/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.16/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.16/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.16/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.16/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.16/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.41/1.09 Prover 4: Preprocessing ...
% 2.41/1.11 Prover 1: Preprocessing ...
% 2.80/1.15 Prover 0: Preprocessing ...
% 2.80/1.15 Prover 2: Preprocessing ...
% 2.80/1.15 Prover 3: Preprocessing ...
% 2.80/1.15 Prover 5: Preprocessing ...
% 2.80/1.15 Prover 6: Preprocessing ...
% 5.51/1.65 Prover 5: Proving ...
% 6.17/1.66 Prover 6: Proving ...
% 6.17/1.67 Prover 1: Constructing countermodel ...
% 6.17/1.68 Prover 3: Constructing countermodel ...
% 6.40/1.70 Prover 2: Proving ...
% 6.79/1.75 Prover 4: Constructing countermodel ...
% 6.79/1.77 Prover 0: Proving ...
% 8.25/1.95 Prover 3: proved (1313ms)
% 8.25/1.95
% 8.25/1.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.25/1.96
% 8.25/1.96 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.25/1.96 Prover 2: stopped
% 8.25/1.96 Prover 5: stopped
% 8.25/1.96 Prover 0: stopped
% 8.25/1.97 Prover 6: stopped
% 8.25/1.97 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.25/1.97 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.25/1.97 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.25/1.97 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.48/2.01 Prover 8: Preprocessing ...
% 8.48/2.01 Prover 13: Preprocessing ...
% 8.48/2.02 Prover 10: Preprocessing ...
% 8.48/2.03 Prover 11: Preprocessing ...
% 8.48/2.03 Prover 7: Preprocessing ...
% 8.48/2.13 Prover 1: Found proof (size 61)
% 8.48/2.14 Prover 1: proved (1499ms)
% 8.48/2.14 Prover 4: stopped
% 8.48/2.14 Prover 11: stopped
% 8.48/2.15 Prover 10: Warning: ignoring some quantifiers
% 8.48/2.16 Prover 8: Warning: ignoring some quantifiers
% 8.48/2.16 Prover 10: Constructing countermodel ...
% 8.48/2.17 Prover 7: Warning: ignoring some quantifiers
% 9.40/2.18 Prover 10: stopped
% 9.40/2.18 Prover 7: Constructing countermodel ...
% 9.40/2.18 Prover 8: Constructing countermodel ...
% 9.83/2.19 Prover 7: stopped
% 9.83/2.19 Prover 8: stopped
% 9.83/2.20 Prover 13: Warning: ignoring some quantifiers
% 9.83/2.22 Prover 13: Constructing countermodel ...
% 9.83/2.24 Prover 13: stopped
% 9.83/2.24
% 9.83/2.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.83/2.24
% 9.83/2.25 % SZS output start Proof for theBenchmark
% 10.19/2.25 Assumptions after simplification:
% 10.19/2.25 ---------------------------------
% 10.19/2.25
% 10.19/2.25 (equal_set)
% 10.26/2.30 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) =
% 10.26/2.30 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1,
% 10.26/2.30 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0:
% 10.26/2.30 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 10.26/2.30 (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 10.26/2.30
% 10.26/2.30 (subset)
% 10.26/2.31 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 10.26/2.31 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 10.26/2.31 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 10.26/2.31 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 10.26/2.31 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 10.26/2.31
% 10.26/2.31 (thI07)
% 10.26/2.31 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4
% 10.26/2.31 = 0) & union(v1, v0) = v3 & union(v0, v1) = v2 & equal_set(v2, v3) = v4 &
% 10.26/2.31 $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 10.26/2.31
% 10.26/2.31 (union)
% 10.48/2.32 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 10.48/2.32 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1)
% 10.48/2.32 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) &
% 10.48/2.32 member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] :
% 10.48/2.32 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0)
% 10.48/2.32 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 10.48/2.32 (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0)))
% 10.48/2.32
% 10.48/2.32 (function-axioms)
% 10.48/2.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.48/2.33 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 10.48/2.33 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.48/2.33 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 10.48/2.33 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 10.48/2.33 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 10.48/2.33 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 10.48/2.33 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 10.48/2.33 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 10.48/2.33 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.48/2.33 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 10.48/2.33 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 10.48/2.33 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.48/2.33 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 10.48/2.33 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 10.48/2.33 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 10.48/2.33 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 10.48/2.33 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 10.48/2.34 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 10.48/2.34 (power_set(v2) = v0))
% 10.48/2.34
% 10.48/2.34 Further assumptions not needed in the proof:
% 10.48/2.34 --------------------------------------------
% 10.48/2.34 difference, empty_set, intersection, power_set, product, singleton, sum,
% 10.48/2.34 unordered_pair
% 10.48/2.34
% 10.48/2.34 Those formulas are unsatisfiable:
% 10.48/2.34 ---------------------------------
% 10.48/2.34
% 10.48/2.34 Begin of proof
% 10.48/2.34 |
% 10.48/2.34 | ALPHA: (subset) implies:
% 10.63/2.34 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 10.63/2.34 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 10.63/2.34 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 10.63/2.34 |
% 10.63/2.34 | ALPHA: (equal_set) implies:
% 10.63/2.34 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0,
% 10.63/2.34 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 10.63/2.35 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 =
% 10.63/2.35 | 0))))
% 10.63/2.35 |
% 10.63/2.35 | ALPHA: (union) implies:
% 10.63/2.35 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1,
% 10.63/2.35 | v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 10.63/2.35 | $i(v0) | ? [v4: any] : ? [v5: any] : (member(v0, v2) = v5 &
% 10.63/2.35 | member(v0, v1) = v4 & (v5 = 0 | v4 = 0)))
% 10.63/2.35 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 10.63/2.35 | (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~
% 10.63/2.35 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~
% 10.63/2.35 | (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) =
% 10.63/2.35 | v5))
% 10.63/2.35 |
% 10.63/2.35 | ALPHA: (function-axioms) implies:
% 10.63/2.35 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.63/2.35 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 10.63/2.35 | = v0))
% 10.63/2.35 |
% 10.63/2.36 | DELTA: instantiating (thI07) with fresh symbols all_15_0, all_15_1, all_15_2,
% 10.63/2.36 | all_15_3, all_15_4 gives:
% 10.63/2.36 | (6) ~ (all_15_0 = 0) & union(all_15_3, all_15_4) = all_15_1 &
% 10.63/2.36 | union(all_15_4, all_15_3) = all_15_2 & equal_set(all_15_2, all_15_1) =
% 10.63/2.36 | all_15_0 & $i(all_15_1) & $i(all_15_2) & $i(all_15_3) & $i(all_15_4)
% 10.63/2.36 |
% 10.63/2.36 | ALPHA: (6) implies:
% 10.63/2.36 | (7) ~ (all_15_0 = 0)
% 10.63/2.36 | (8) $i(all_15_4)
% 10.63/2.36 | (9) $i(all_15_3)
% 10.63/2.36 | (10) $i(all_15_2)
% 10.63/2.36 | (11) $i(all_15_1)
% 10.63/2.36 | (12) equal_set(all_15_2, all_15_1) = all_15_0
% 10.63/2.36 | (13) union(all_15_4, all_15_3) = all_15_2
% 10.63/2.36 | (14) union(all_15_3, all_15_4) = all_15_1
% 10.63/2.36 |
% 10.63/2.36 | GROUND_INST: instantiating (2) with all_15_2, all_15_1, all_15_0, simplifying
% 10.63/2.36 | with (10), (11), (12) gives:
% 10.63/2.36 | (15) all_15_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_1,
% 10.63/2.36 | all_15_2) = v1 & subset(all_15_2, all_15_1) = v0 & ( ~ (v1 = 0) |
% 10.63/2.36 | ~ (v0 = 0)))
% 10.63/2.36 |
% 10.63/2.36 | BETA: splitting (15) gives:
% 10.63/2.36 |
% 10.63/2.36 | Case 1:
% 10.63/2.36 | |
% 10.63/2.37 | | (16) all_15_0 = 0
% 10.63/2.37 | |
% 10.63/2.37 | | REDUCE: (7), (16) imply:
% 10.63/2.37 | | (17) $false
% 10.63/2.37 | |
% 10.63/2.37 | | CLOSE: (17) is inconsistent.
% 10.63/2.37 | |
% 10.63/2.37 | Case 2:
% 10.63/2.37 | |
% 10.63/2.37 | | (18) ? [v0: any] : ? [v1: any] : (subset(all_15_1, all_15_2) = v1 &
% 10.63/2.37 | | subset(all_15_2, all_15_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 10.63/2.37 | |
% 10.63/2.37 | | DELTA: instantiating (18) with fresh symbols all_24_0, all_24_1 gives:
% 10.63/2.37 | | (19) subset(all_15_1, all_15_2) = all_24_0 & subset(all_15_2, all_15_1) =
% 10.63/2.37 | | all_24_1 & ( ~ (all_24_0 = 0) | ~ (all_24_1 = 0))
% 10.63/2.37 | |
% 10.63/2.37 | | ALPHA: (19) implies:
% 10.63/2.37 | | (20) subset(all_15_2, all_15_1) = all_24_1
% 10.63/2.37 | | (21) subset(all_15_1, all_15_2) = all_24_0
% 10.63/2.37 | | (22) ~ (all_24_0 = 0) | ~ (all_24_1 = 0)
% 10.63/2.37 | |
% 10.63/2.37 | | GROUND_INST: instantiating (1) with all_15_2, all_15_1, all_24_1,
% 10.63/2.37 | | simplifying with (10), (11), (20) gives:
% 10.63/2.37 | | (23) all_24_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 10.63/2.37 | | member(v0, all_15_1) = v1 & member(v0, all_15_2) = 0 & $i(v0))
% 10.63/2.37 | |
% 10.63/2.37 | | GROUND_INST: instantiating (1) with all_15_1, all_15_2, all_24_0,
% 10.63/2.37 | | simplifying with (10), (11), (21) gives:
% 10.63/2.38 | | (24) all_24_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 10.63/2.38 | | member(v0, all_15_1) = 0 & member(v0, all_15_2) = v1 & $i(v0))
% 10.63/2.38 | |
% 10.63/2.38 | | BETA: splitting (22) gives:
% 10.63/2.38 | |
% 10.63/2.38 | | Case 1:
% 10.63/2.38 | | |
% 10.63/2.38 | | | (25) ~ (all_24_0 = 0)
% 10.63/2.38 | | |
% 10.63/2.38 | | | BETA: splitting (24) gives:
% 10.63/2.38 | | |
% 10.63/2.38 | | | Case 1:
% 10.63/2.38 | | | |
% 10.63/2.38 | | | | (26) all_24_0 = 0
% 10.63/2.38 | | | |
% 10.63/2.38 | | | | REDUCE: (25), (26) imply:
% 10.63/2.38 | | | | (27) $false
% 10.63/2.38 | | | |
% 10.63/2.38 | | | | CLOSE: (27) is inconsistent.
% 10.63/2.38 | | | |
% 10.63/2.38 | | | Case 2:
% 10.63/2.38 | | | |
% 10.63/2.38 | | | | (28) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1)
% 10.63/2.38 | | | | = 0 & member(v0, all_15_2) = v1 & $i(v0))
% 10.63/2.38 | | | |
% 10.63/2.38 | | | | DELTA: instantiating (28) with fresh symbols all_37_0, all_37_1 gives:
% 10.63/2.38 | | | | (29) ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = 0 &
% 10.63/2.38 | | | | member(all_37_1, all_15_2) = all_37_0 & $i(all_37_1)
% 10.63/2.38 | | | |
% 10.63/2.38 | | | | ALPHA: (29) implies:
% 10.63/2.38 | | | | (30) ~ (all_37_0 = 0)
% 10.63/2.38 | | | | (31) $i(all_37_1)
% 10.63/2.38 | | | | (32) member(all_37_1, all_15_2) = all_37_0
% 10.63/2.38 | | | | (33) member(all_37_1, all_15_1) = 0
% 10.63/2.38 | | | |
% 10.63/2.38 | | | | GROUND_INST: instantiating (4) with all_37_1, all_15_4, all_15_3,
% 10.63/2.38 | | | | all_15_2, all_37_0, simplifying with (8), (9), (13), (31),
% 10.63/2.38 | | | | (32) gives:
% 10.63/2.38 | | | | (34) all_37_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~
% 10.63/2.38 | | | | (v0 = 0) & member(all_37_1, all_15_3) = v1 & member(all_37_1,
% 10.63/2.38 | | | | all_15_4) = v0)
% 10.63/2.38 | | | |
% 10.63/2.38 | | | | GROUND_INST: instantiating (3) with all_37_1, all_15_3, all_15_4,
% 10.63/2.38 | | | | all_15_1, simplifying with (8), (9), (14), (31), (33)
% 10.63/2.38 | | | | gives:
% 10.63/2.39 | | | | (35) ? [v0: any] : ? [v1: any] : (member(all_37_1, all_15_3) = v0 &
% 10.63/2.39 | | | | member(all_37_1, all_15_4) = v1 & (v1 = 0 | v0 = 0))
% 10.63/2.39 | | | |
% 10.63/2.39 | | | | DELTA: instantiating (35) with fresh symbols all_44_0, all_44_1 gives:
% 10.63/2.39 | | | | (36) member(all_37_1, all_15_3) = all_44_1 & member(all_37_1,
% 10.63/2.39 | | | | all_15_4) = all_44_0 & (all_44_0 = 0 | all_44_1 = 0)
% 10.63/2.39 | | | |
% 10.63/2.39 | | | | ALPHA: (36) implies:
% 10.63/2.39 | | | | (37) member(all_37_1, all_15_4) = all_44_0
% 10.63/2.39 | | | | (38) member(all_37_1, all_15_3) = all_44_1
% 10.63/2.39 | | | | (39) all_44_0 = 0 | all_44_1 = 0
% 10.63/2.39 | | | |
% 10.63/2.39 | | | | BETA: splitting (34) gives:
% 10.63/2.39 | | | |
% 10.63/2.39 | | | | Case 1:
% 10.63/2.39 | | | | |
% 10.63/2.39 | | | | | (40) all_37_0 = 0
% 10.63/2.39 | | | | |
% 10.63/2.39 | | | | | REDUCE: (30), (40) imply:
% 10.63/2.39 | | | | | (41) $false
% 10.63/2.39 | | | | |
% 10.63/2.39 | | | | | CLOSE: (41) is inconsistent.
% 10.63/2.39 | | | | |
% 10.63/2.39 | | | | Case 2:
% 10.63/2.39 | | | | |
% 10.63/2.39 | | | | | (42) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) &
% 10.63/2.39 | | | | | member(all_37_1, all_15_3) = v1 & member(all_37_1, all_15_4)
% 10.63/2.39 | | | | | = v0)
% 10.63/2.39 | | | | |
% 10.63/2.39 | | | | | DELTA: instantiating (42) with fresh symbols all_50_0, all_50_1 gives:
% 10.63/2.39 | | | | | (43) ~ (all_50_0 = 0) & ~ (all_50_1 = 0) & member(all_37_1,
% 10.63/2.39 | | | | | all_15_3) = all_50_0 & member(all_37_1, all_15_4) = all_50_1
% 10.63/2.39 | | | | |
% 10.63/2.39 | | | | | ALPHA: (43) implies:
% 10.63/2.39 | | | | | (44) ~ (all_50_1 = 0)
% 10.63/2.39 | | | | | (45) ~ (all_50_0 = 0)
% 10.63/2.39 | | | | | (46) member(all_37_1, all_15_4) = all_50_1
% 10.63/2.39 | | | | | (47) member(all_37_1, all_15_3) = all_50_0
% 10.63/2.39 | | | | |
% 10.63/2.39 | | | | | GROUND_INST: instantiating (5) with all_44_0, all_50_1, all_15_4,
% 10.63/2.39 | | | | | all_37_1, simplifying with (37), (46) gives:
% 10.63/2.39 | | | | | (48) all_50_1 = all_44_0
% 10.63/2.39 | | | | |
% 10.63/2.40 | | | | | GROUND_INST: instantiating (5) with all_44_1, all_50_0, all_15_3,
% 10.63/2.40 | | | | | all_37_1, simplifying with (38), (47) gives:
% 10.63/2.40 | | | | | (49) all_50_0 = all_44_1
% 10.63/2.40 | | | | |
% 10.63/2.40 | | | | | REDUCE: (45), (49) imply:
% 10.63/2.40 | | | | | (50) ~ (all_44_1 = 0)
% 10.63/2.40 | | | | |
% 10.63/2.40 | | | | | REDUCE: (44), (48) imply:
% 10.63/2.40 | | | | | (51) ~ (all_44_0 = 0)
% 10.63/2.40 | | | | |
% 10.63/2.40 | | | | | BETA: splitting (39) gives:
% 10.63/2.40 | | | | |
% 10.63/2.40 | | | | | Case 1:
% 10.63/2.40 | | | | | |
% 10.63/2.40 | | | | | | (52) all_44_0 = 0
% 10.63/2.40 | | | | | |
% 10.63/2.40 | | | | | | REDUCE: (51), (52) imply:
% 10.63/2.40 | | | | | | (53) $false
% 10.63/2.40 | | | | | |
% 10.63/2.40 | | | | | | CLOSE: (53) is inconsistent.
% 10.63/2.40 | | | | | |
% 10.63/2.40 | | | | | Case 2:
% 10.63/2.40 | | | | | |
% 10.63/2.40 | | | | | | (54) all_44_1 = 0
% 10.63/2.40 | | | | | |
% 10.63/2.40 | | | | | | REDUCE: (50), (54) imply:
% 10.63/2.40 | | | | | | (55) $false
% 10.63/2.40 | | | | | |
% 10.63/2.40 | | | | | | CLOSE: (55) is inconsistent.
% 10.63/2.40 | | | | | |
% 10.63/2.40 | | | | | End of split
% 10.63/2.40 | | | | |
% 10.63/2.40 | | | | End of split
% 10.63/2.40 | | | |
% 10.63/2.40 | | | End of split
% 10.63/2.40 | | |
% 10.63/2.40 | | Case 2:
% 10.63/2.40 | | |
% 10.63/2.40 | | | (56) ~ (all_24_1 = 0)
% 10.63/2.40 | | |
% 10.63/2.40 | | | BETA: splitting (23) gives:
% 10.63/2.40 | | |
% 10.63/2.40 | | | Case 1:
% 10.63/2.40 | | | |
% 10.63/2.40 | | | | (57) all_24_1 = 0
% 10.63/2.40 | | | |
% 10.63/2.40 | | | | REDUCE: (56), (57) imply:
% 10.63/2.40 | | | | (58) $false
% 10.63/2.40 | | | |
% 10.63/2.40 | | | | CLOSE: (58) is inconsistent.
% 10.63/2.40 | | | |
% 10.63/2.40 | | | Case 2:
% 10.63/2.40 | | | |
% 10.63/2.40 | | | | (59) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1)
% 10.63/2.40 | | | | = v1 & member(v0, all_15_2) = 0 & $i(v0))
% 10.63/2.40 | | | |
% 10.63/2.40 | | | | DELTA: instantiating (59) with fresh symbols all_37_0, all_37_1 gives:
% 10.63/2.40 | | | | (60) ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = all_37_0 &
% 10.63/2.40 | | | | member(all_37_1, all_15_2) = 0 & $i(all_37_1)
% 10.63/2.40 | | | |
% 10.63/2.40 | | | | ALPHA: (60) implies:
% 10.63/2.40 | | | | (61) ~ (all_37_0 = 0)
% 10.63/2.40 | | | | (62) $i(all_37_1)
% 10.63/2.40 | | | | (63) member(all_37_1, all_15_2) = 0
% 10.63/2.40 | | | | (64) member(all_37_1, all_15_1) = all_37_0
% 10.63/2.40 | | | |
% 10.63/2.41 | | | | GROUND_INST: instantiating (3) with all_37_1, all_15_4, all_15_3,
% 10.63/2.41 | | | | all_15_2, simplifying with (8), (9), (13), (62), (63)
% 10.63/2.41 | | | | gives:
% 10.63/2.41 | | | | (65) ? [v0: any] : ? [v1: any] : (member(all_37_1, all_15_3) = v1 &
% 10.63/2.41 | | | | member(all_37_1, all_15_4) = v0 & (v1 = 0 | v0 = 0))
% 10.63/2.41 | | | |
% 10.63/2.41 | | | | GROUND_INST: instantiating (4) with all_37_1, all_15_3, all_15_4,
% 10.63/2.41 | | | | all_15_1, all_37_0, simplifying with (8), (9), (14), (62),
% 10.63/2.41 | | | | (64) gives:
% 10.63/2.41 | | | | (66) all_37_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~
% 10.63/2.41 | | | | (v0 = 0) & member(all_37_1, all_15_3) = v0 & member(all_37_1,
% 10.63/2.41 | | | | all_15_4) = v1)
% 10.63/2.41 | | | |
% 10.63/2.41 | | | | DELTA: instantiating (65) with fresh symbols all_45_0, all_45_1 gives:
% 10.63/2.41 | | | | (67) member(all_37_1, all_15_3) = all_45_0 & member(all_37_1,
% 10.63/2.41 | | | | all_15_4) = all_45_1 & (all_45_0 = 0 | all_45_1 = 0)
% 10.63/2.41 | | | |
% 10.63/2.41 | | | | ALPHA: (67) implies:
% 10.63/2.41 | | | | (68) member(all_37_1, all_15_4) = all_45_1
% 10.63/2.41 | | | | (69) member(all_37_1, all_15_3) = all_45_0
% 10.63/2.41 | | | | (70) all_45_0 = 0 | all_45_1 = 0
% 10.63/2.41 | | | |
% 10.63/2.41 | | | | BETA: splitting (66) gives:
% 10.63/2.41 | | | |
% 10.63/2.41 | | | | Case 1:
% 10.63/2.41 | | | | |
% 10.63/2.41 | | | | | (71) all_37_0 = 0
% 10.63/2.41 | | | | |
% 10.63/2.41 | | | | | REDUCE: (61), (71) imply:
% 10.63/2.41 | | | | | (72) $false
% 10.63/2.41 | | | | |
% 10.63/2.41 | | | | | CLOSE: (72) is inconsistent.
% 10.63/2.41 | | | | |
% 10.63/2.41 | | | | Case 2:
% 10.63/2.41 | | | | |
% 10.63/2.41 | | | | | (73) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) &
% 10.63/2.41 | | | | | member(all_37_1, all_15_3) = v0 & member(all_37_1, all_15_4)
% 10.63/2.41 | | | | | = v1)
% 10.63/2.41 | | | | |
% 10.63/2.41 | | | | | DELTA: instantiating (73) with fresh symbols all_51_0, all_51_1 gives:
% 10.63/2.42 | | | | | (74) ~ (all_51_0 = 0) & ~ (all_51_1 = 0) & member(all_37_1,
% 10.63/2.42 | | | | | all_15_3) = all_51_1 & member(all_37_1, all_15_4) = all_51_0
% 10.63/2.42 | | | | |
% 10.63/2.42 | | | | | ALPHA: (74) implies:
% 10.63/2.42 | | | | | (75) ~ (all_51_1 = 0)
% 10.63/2.42 | | | | | (76) ~ (all_51_0 = 0)
% 10.63/2.42 | | | | | (77) member(all_37_1, all_15_4) = all_51_0
% 10.63/2.42 | | | | | (78) member(all_37_1, all_15_3) = all_51_1
% 10.63/2.42 | | | | |
% 10.63/2.42 | | | | | GROUND_INST: instantiating (5) with all_45_1, all_51_0, all_15_4,
% 10.63/2.42 | | | | | all_37_1, simplifying with (68), (77) gives:
% 10.63/2.42 | | | | | (79) all_51_0 = all_45_1
% 10.63/2.42 | | | | |
% 10.63/2.42 | | | | | GROUND_INST: instantiating (5) with all_45_0, all_51_1, all_15_3,
% 10.63/2.42 | | | | | all_37_1, simplifying with (69), (78) gives:
% 10.63/2.42 | | | | | (80) all_51_1 = all_45_0
% 10.63/2.42 | | | | |
% 10.63/2.42 | | | | | REDUCE: (76), (79) imply:
% 10.63/2.42 | | | | | (81) ~ (all_45_1 = 0)
% 10.63/2.42 | | | | |
% 10.63/2.42 | | | | | REDUCE: (75), (80) imply:
% 10.63/2.42 | | | | | (82) ~ (all_45_0 = 0)
% 10.63/2.42 | | | | |
% 10.63/2.42 | | | | | BETA: splitting (70) gives:
% 10.63/2.42 | | | | |
% 10.63/2.42 | | | | | Case 1:
% 10.63/2.42 | | | | | |
% 10.63/2.42 | | | | | | (83) all_45_0 = 0
% 10.63/2.42 | | | | | |
% 10.63/2.42 | | | | | | REDUCE: (82), (83) imply:
% 10.63/2.42 | | | | | | (84) $false
% 10.63/2.42 | | | | | |
% 10.63/2.42 | | | | | | CLOSE: (84) is inconsistent.
% 10.63/2.42 | | | | | |
% 10.63/2.42 | | | | | Case 2:
% 10.63/2.42 | | | | | |
% 10.63/2.42 | | | | | | (85) all_45_1 = 0
% 10.63/2.42 | | | | | |
% 10.63/2.42 | | | | | | REDUCE: (81), (85) imply:
% 10.63/2.42 | | | | | | (86) $false
% 10.63/2.42 | | | | | |
% 10.63/2.42 | | | | | | CLOSE: (86) is inconsistent.
% 10.63/2.42 | | | | | |
% 10.63/2.42 | | | | | End of split
% 10.63/2.42 | | | | |
% 10.63/2.42 | | | | End of split
% 10.63/2.42 | | | |
% 10.63/2.42 | | | End of split
% 10.63/2.42 | | |
% 10.63/2.42 | | End of split
% 10.63/2.42 | |
% 10.63/2.42 | End of split
% 10.63/2.42 |
% 10.63/2.42 End of proof
% 10.63/2.42 % SZS output end Proof for theBenchmark
% 10.63/2.42
% 10.63/2.42 1811ms
%------------------------------------------------------------------------------