TSTP Solution File: SET169+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET169+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 : n001.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 15:24:08 EDT 2023
% Result : Theorem 7.42s 1.72s
% Output : Proof 9.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET169+4 : 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 : n001.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 10:35:45 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.40/1.04 Prover 1: Preprocessing ...
% 2.40/1.04 Prover 4: Preprocessing ...
% 2.88/1.08 Prover 6: Preprocessing ...
% 2.88/1.08 Prover 3: Preprocessing ...
% 2.88/1.08 Prover 2: Preprocessing ...
% 2.88/1.08 Prover 5: Preprocessing ...
% 2.88/1.09 Prover 0: Preprocessing ...
% 4.49/1.44 Prover 5: Proving ...
% 4.49/1.45 Prover 6: Proving ...
% 4.49/1.46 Prover 1: Constructing countermodel ...
% 4.49/1.46 Prover 2: Proving ...
% 4.49/1.47 Prover 3: Constructing countermodel ...
% 4.49/1.50 Prover 4: Constructing countermodel ...
% 5.28/1.53 Prover 0: Proving ...
% 7.42/1.72 Prover 3: proved (1086ms)
% 7.42/1.72
% 7.42/1.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.42/1.72
% 7.42/1.72 Prover 5: stopped
% 7.42/1.72 Prover 6: stopped
% 7.42/1.72 Prover 0: stopped
% 7.42/1.72 Prover 2: stopped
% 7.42/1.72 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.42/1.72 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.42/1.72 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.42/1.73 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.42/1.73 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.42/1.77 Prover 10: Preprocessing ...
% 7.42/1.77 Prover 13: Preprocessing ...
% 7.42/1.77 Prover 8: Preprocessing ...
% 8.04/1.79 Prover 7: Preprocessing ...
% 8.04/1.80 Prover 11: Preprocessing ...
% 8.04/1.87 Prover 1: Found proof (size 119)
% 8.04/1.87 Prover 1: proved (1247ms)
% 8.04/1.88 Prover 7: Warning: ignoring some quantifiers
% 8.04/1.88 Prover 4: stopped
% 8.79/1.88 Prover 7: Constructing countermodel ...
% 8.79/1.89 Prover 10: Warning: ignoring some quantifiers
% 8.79/1.89 Prover 7: stopped
% 8.85/1.89 Prover 13: Warning: ignoring some quantifiers
% 8.85/1.90 Prover 8: Warning: ignoring some quantifiers
% 8.85/1.90 Prover 10: Constructing countermodel ...
% 8.95/1.91 Prover 13: Constructing countermodel ...
% 8.95/1.91 Prover 8: Constructing countermodel ...
% 8.98/1.91 Prover 10: stopped
% 8.98/1.91 Prover 13: stopped
% 8.98/1.92 Prover 8: stopped
% 8.98/1.92 Prover 11: Constructing countermodel ...
% 8.98/1.93 Prover 11: stopped
% 8.98/1.93
% 8.98/1.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.98/1.93
% 8.98/1.94 % SZS output start Proof for theBenchmark
% 8.98/1.94 Assumptions after simplification:
% 8.98/1.94 ---------------------------------
% 8.98/1.94
% 8.98/1.94 (equal_set)
% 8.98/1.97 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) =
% 8.98/1.97 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1,
% 8.98/1.97 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0:
% 8.98/1.97 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 8.98/1.97 (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 8.98/1.97
% 8.98/1.97 (intersection)
% 8.98/1.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 8.98/1.98 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~
% 8.98/1.98 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v0, v2) = v6 &
% 8.98/1.98 member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : !
% 8.98/1.98 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (intersection(v1, v2) = v3) | ~
% 8.98/1.98 (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) =
% 8.98/1.98 0 & member(v0, v1) = 0))
% 8.98/1.98
% 8.98/1.98 (subset)
% 8.98/1.98 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 8.98/1.98 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 8.98/1.98 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 8.98/1.98 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 8.98/1.98 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 8.98/1.98
% 8.98/1.98 (thI10)
% 8.98/1.98 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 8.98/1.98 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & union(v5,
% 8.98/1.98 v6) = v7 & union(v1, v2) = v3 & intersection(v0, v3) = v4 &
% 8.98/1.98 intersection(v0, v2) = v6 & intersection(v0, v1) = v5 & equal_set(v4, v7) =
% 8.98/1.98 v8 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 8.98/1.98
% 8.98/1.98 (union)
% 8.98/1.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 8.98/1.98 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1)
% 8.98/1.98 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) &
% 8.98/1.98 member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] :
% 8.98/1.98 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0)
% 8.98/1.98 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 8.98/1.98 (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0)))
% 8.98/1.98
% 8.98/1.98 (function-axioms)
% 8.98/1.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.98/1.99 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 8.98/1.99 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.98/1.99 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 8.98/1.99 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 8.98/1.99 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 8.98/1.99 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 8.98/1.99 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 8.98/1.99 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 8.98/1.99 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.98/1.99 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 8.98/1.99 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 8.98/1.99 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.98/1.99 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 8.98/1.99 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 8.98/1.99 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 8.98/1.99 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 8.98/1.99 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 8.98/1.99 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 8.98/1.99 (power_set(v2) = v0))
% 8.98/1.99
% 8.98/1.99 Further assumptions not needed in the proof:
% 8.98/1.99 --------------------------------------------
% 8.98/1.99 difference, empty_set, power_set, product, singleton, sum, unordered_pair
% 8.98/1.99
% 8.98/1.99 Those formulas are unsatisfiable:
% 8.98/1.99 ---------------------------------
% 8.98/1.99
% 8.98/1.99 Begin of proof
% 8.98/1.99 |
% 8.98/1.99 | ALPHA: (subset) implies:
% 8.98/1.99 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 8.98/1.99 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 8.98/1.99 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 8.98/1.99 |
% 8.98/1.99 | ALPHA: (equal_set) implies:
% 8.98/1.99 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0,
% 8.98/1.99 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 8.98/1.99 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 =
% 8.98/1.99 | 0))))
% 8.98/1.99 |
% 8.98/1.99 | ALPHA: (intersection) implies:
% 8.98/2.00 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 8.98/2.00 | (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) |
% 8.98/2.00 | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 8.98/2.00 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 8.98/2.00 | (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) |
% 8.98/2.00 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] :
% 8.98/2.00 | (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 =
% 8.98/2.00 | 0))))
% 8.98/2.00 |
% 8.98/2.00 | ALPHA: (union) implies:
% 8.98/2.00 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1,
% 8.98/2.00 | v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 8.98/2.00 | $i(v0) | ? [v4: any] : ? [v5: any] : (member(v0, v2) = v5 &
% 8.98/2.00 | member(v0, v1) = v4 & (v5 = 0 | v4 = 0)))
% 8.98/2.00 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 8.98/2.00 | (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~
% 8.98/2.00 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~
% 8.98/2.00 | (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) =
% 8.98/2.00 | v5))
% 8.98/2.00 |
% 8.98/2.00 | ALPHA: (function-axioms) implies:
% 8.98/2.00 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.98/2.00 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 8.98/2.00 | = v0))
% 8.98/2.00 |
% 9.44/2.00 | DELTA: instantiating (thI10) with fresh symbols all_15_0, all_15_1, all_15_2,
% 9.44/2.00 | all_15_3, all_15_4, all_15_5, all_15_6, all_15_7, all_15_8 gives:
% 9.44/2.00 | (8) ~ (all_15_0 = 0) & union(all_15_3, all_15_2) = all_15_1 &
% 9.44/2.00 | union(all_15_7, all_15_6) = all_15_5 & intersection(all_15_8, all_15_5)
% 9.44/2.00 | = all_15_4 & intersection(all_15_8, all_15_6) = all_15_2 &
% 9.44/2.00 | intersection(all_15_8, all_15_7) = all_15_3 & equal_set(all_15_4,
% 9.44/2.00 | all_15_1) = all_15_0 & $i(all_15_1) & $i(all_15_2) & $i(all_15_3) &
% 9.44/2.00 | $i(all_15_4) & $i(all_15_5) & $i(all_15_6) & $i(all_15_7) &
% 9.44/2.00 | $i(all_15_8)
% 9.44/2.00 |
% 9.44/2.00 | ALPHA: (8) implies:
% 9.44/2.00 | (9) ~ (all_15_0 = 0)
% 9.44/2.00 | (10) $i(all_15_8)
% 9.44/2.00 | (11) $i(all_15_7)
% 9.44/2.00 | (12) $i(all_15_6)
% 9.44/2.00 | (13) $i(all_15_5)
% 9.44/2.00 | (14) $i(all_15_4)
% 9.44/2.00 | (15) $i(all_15_3)
% 9.44/2.00 | (16) $i(all_15_2)
% 9.44/2.00 | (17) $i(all_15_1)
% 9.44/2.00 | (18) equal_set(all_15_4, all_15_1) = all_15_0
% 9.44/2.00 | (19) intersection(all_15_8, all_15_7) = all_15_3
% 9.44/2.00 | (20) intersection(all_15_8, all_15_6) = all_15_2
% 9.44/2.00 | (21) intersection(all_15_8, all_15_5) = all_15_4
% 9.44/2.00 | (22) union(all_15_7, all_15_6) = all_15_5
% 9.44/2.01 | (23) union(all_15_3, all_15_2) = all_15_1
% 9.44/2.01 |
% 9.44/2.01 | GROUND_INST: instantiating (2) with all_15_4, all_15_1, all_15_0, simplifying
% 9.44/2.01 | with (14), (17), (18) gives:
% 9.44/2.01 | (24) all_15_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_1,
% 9.44/2.01 | all_15_4) = v1 & subset(all_15_4, all_15_1) = v0 & ( ~ (v1 = 0) |
% 9.44/2.01 | ~ (v0 = 0)))
% 9.44/2.01 |
% 9.44/2.01 | BETA: splitting (24) gives:
% 9.44/2.01 |
% 9.44/2.01 | Case 1:
% 9.44/2.01 | |
% 9.44/2.01 | | (25) all_15_0 = 0
% 9.44/2.01 | |
% 9.44/2.01 | | REDUCE: (9), (25) imply:
% 9.44/2.01 | | (26) $false
% 9.44/2.01 | |
% 9.44/2.01 | | CLOSE: (26) is inconsistent.
% 9.44/2.01 | |
% 9.44/2.01 | Case 2:
% 9.44/2.01 | |
% 9.44/2.01 | | (27) ? [v0: any] : ? [v1: any] : (subset(all_15_1, all_15_4) = v1 &
% 9.44/2.01 | | subset(all_15_4, all_15_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 9.44/2.01 | |
% 9.44/2.01 | | DELTA: instantiating (27) with fresh symbols all_24_0, all_24_1 gives:
% 9.44/2.01 | | (28) subset(all_15_1, all_15_4) = all_24_0 & subset(all_15_4, all_15_1) =
% 9.44/2.01 | | all_24_1 & ( ~ (all_24_0 = 0) | ~ (all_24_1 = 0))
% 9.44/2.01 | |
% 9.44/2.01 | | ALPHA: (28) implies:
% 9.44/2.01 | | (29) subset(all_15_4, all_15_1) = all_24_1
% 9.44/2.01 | | (30) subset(all_15_1, all_15_4) = all_24_0
% 9.44/2.01 | | (31) ~ (all_24_0 = 0) | ~ (all_24_1 = 0)
% 9.44/2.01 | |
% 9.44/2.01 | | GROUND_INST: instantiating (1) with all_15_4, all_15_1, all_24_1,
% 9.44/2.01 | | simplifying with (14), (17), (29) gives:
% 9.44/2.01 | | (32) all_24_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 9.44/2.01 | | member(v0, all_15_1) = v1 & member(v0, all_15_4) = 0 & $i(v0))
% 9.44/2.01 | |
% 9.44/2.01 | | GROUND_INST: instantiating (1) with all_15_1, all_15_4, all_24_0,
% 9.44/2.01 | | simplifying with (14), (17), (30) gives:
% 9.44/2.01 | | (33) all_24_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 9.44/2.01 | | member(v0, all_15_1) = 0 & member(v0, all_15_4) = v1 & $i(v0))
% 9.44/2.01 | |
% 9.44/2.01 | | BETA: splitting (31) gives:
% 9.44/2.01 | |
% 9.44/2.01 | | Case 1:
% 9.44/2.01 | | |
% 9.44/2.01 | | | (34) ~ (all_24_0 = 0)
% 9.44/2.01 | | |
% 9.44/2.01 | | | BETA: splitting (33) gives:
% 9.44/2.01 | | |
% 9.44/2.01 | | | Case 1:
% 9.44/2.01 | | | |
% 9.44/2.01 | | | | (35) all_24_0 = 0
% 9.44/2.01 | | | |
% 9.44/2.01 | | | | REDUCE: (34), (35) imply:
% 9.44/2.01 | | | | (36) $false
% 9.44/2.01 | | | |
% 9.44/2.01 | | | | CLOSE: (36) is inconsistent.
% 9.44/2.01 | | | |
% 9.44/2.01 | | | Case 2:
% 9.44/2.01 | | | |
% 9.44/2.01 | | | | (37) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1)
% 9.44/2.01 | | | | = 0 & member(v0, all_15_4) = v1 & $i(v0))
% 9.44/2.01 | | | |
% 9.44/2.01 | | | | DELTA: instantiating (37) with fresh symbols all_37_0, all_37_1 gives:
% 9.44/2.01 | | | | (38) ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = 0 &
% 9.44/2.01 | | | | member(all_37_1, all_15_4) = all_37_0 & $i(all_37_1)
% 9.44/2.01 | | | |
% 9.44/2.01 | | | | ALPHA: (38) implies:
% 9.44/2.01 | | | | (39) ~ (all_37_0 = 0)
% 9.44/2.02 | | | | (40) $i(all_37_1)
% 9.44/2.02 | | | | (41) member(all_37_1, all_15_4) = all_37_0
% 9.44/2.02 | | | | (42) member(all_37_1, all_15_1) = 0
% 9.44/2.02 | | | |
% 9.44/2.02 | | | | GROUND_INST: instantiating (4) with all_37_1, all_15_8, all_15_5,
% 9.44/2.02 | | | | all_15_4, all_37_0, simplifying with (10), (13), (21),
% 9.44/2.02 | | | | (40), (41) gives:
% 9.44/2.02 | | | | (43) all_37_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_37_1,
% 9.44/2.02 | | | | all_15_5) = v1 & member(all_37_1, all_15_8) = v0 & ( ~ (v1 =
% 9.44/2.02 | | | | 0) | ~ (v0 = 0)))
% 9.44/2.02 | | | |
% 9.44/2.02 | | | | GROUND_INST: instantiating (5) with all_37_1, all_15_3, all_15_2,
% 9.44/2.02 | | | | all_15_1, simplifying with (15), (16), (23), (40), (42)
% 9.44/2.02 | | | | gives:
% 9.44/2.02 | | | | (44) ? [v0: any] : ? [v1: any] : (member(all_37_1, all_15_2) = v1 &
% 9.44/2.02 | | | | member(all_37_1, all_15_3) = v0 & (v1 = 0 | v0 = 0))
% 9.44/2.02 | | | |
% 9.44/2.02 | | | | DELTA: instantiating (44) with fresh symbols all_44_0, all_44_1 gives:
% 9.44/2.02 | | | | (45) member(all_37_1, all_15_2) = all_44_0 & member(all_37_1,
% 9.44/2.02 | | | | all_15_3) = all_44_1 & (all_44_0 = 0 | all_44_1 = 0)
% 9.44/2.02 | | | |
% 9.44/2.02 | | | | ALPHA: (45) implies:
% 9.44/2.02 | | | | (46) member(all_37_1, all_15_3) = all_44_1
% 9.44/2.02 | | | | (47) member(all_37_1, all_15_2) = all_44_0
% 9.44/2.02 | | | | (48) all_44_0 = 0 | all_44_1 = 0
% 9.44/2.02 | | | |
% 9.44/2.02 | | | | BETA: splitting (43) gives:
% 9.44/2.02 | | | |
% 9.44/2.02 | | | | Case 1:
% 9.44/2.02 | | | | |
% 9.44/2.02 | | | | | (49) all_37_0 = 0
% 9.44/2.02 | | | | |
% 9.44/2.02 | | | | | REDUCE: (39), (49) imply:
% 9.44/2.02 | | | | | (50) $false
% 9.44/2.02 | | | | |
% 9.44/2.02 | | | | | CLOSE: (50) is inconsistent.
% 9.44/2.02 | | | | |
% 9.44/2.02 | | | | Case 2:
% 9.44/2.02 | | | | |
% 9.44/2.02 | | | | | (51) ? [v0: any] : ? [v1: any] : (member(all_37_1, all_15_5) = v1
% 9.44/2.02 | | | | | & member(all_37_1, all_15_8) = v0 & ( ~ (v1 = 0) | ~ (v0 =
% 9.44/2.02 | | | | | 0)))
% 9.44/2.02 | | | | |
% 9.44/2.02 | | | | | DELTA: instantiating (51) with fresh symbols all_50_0, all_50_1 gives:
% 9.44/2.02 | | | | | (52) member(all_37_1, all_15_5) = all_50_0 & member(all_37_1,
% 9.44/2.02 | | | | | all_15_8) = all_50_1 & ( ~ (all_50_0 = 0) | ~ (all_50_1 =
% 9.44/2.02 | | | | | 0))
% 9.44/2.02 | | | | |
% 9.44/2.02 | | | | | ALPHA: (52) implies:
% 9.44/2.02 | | | | | (53) member(all_37_1, all_15_8) = all_50_1
% 9.44/2.02 | | | | | (54) member(all_37_1, all_15_5) = all_50_0
% 9.44/2.02 | | | | | (55) ~ (all_50_0 = 0) | ~ (all_50_1 = 0)
% 9.44/2.02 | | | | |
% 9.44/2.02 | | | | | GROUND_INST: instantiating (6) with all_37_1, all_15_7, all_15_6,
% 9.44/2.02 | | | | | all_15_5, all_50_0, simplifying with (11), (12), (22),
% 9.44/2.02 | | | | | (40), (54) gives:
% 9.44/2.02 | | | | | (56) all_50_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~
% 9.44/2.02 | | | | | (v0 = 0) & member(all_37_1, all_15_6) = v1 &
% 9.44/2.02 | | | | | member(all_37_1, all_15_7) = v0)
% 9.44/2.02 | | | | |
% 9.44/2.02 | | | | | GROUND_INST: instantiating (4) with all_37_1, all_15_8, all_15_6,
% 9.44/2.02 | | | | | all_15_2, all_44_0, simplifying with (10), (12), (20),
% 9.44/2.02 | | | | | (40), (47) gives:
% 9.44/2.03 | | | | | (57) all_44_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_37_1,
% 9.44/2.03 | | | | | all_15_6) = v1 & member(all_37_1, all_15_8) = v0 & ( ~ (v1
% 9.44/2.03 | | | | | = 0) | ~ (v0 = 0)))
% 9.44/2.03 | | | | |
% 9.44/2.03 | | | | | BETA: splitting (48) gives:
% 9.44/2.03 | | | | |
% 9.44/2.03 | | | | | Case 1:
% 9.44/2.03 | | | | | |
% 9.44/2.03 | | | | | | (58) all_44_0 = 0
% 9.44/2.03 | | | | | |
% 9.44/2.03 | | | | | | REDUCE: (47), (58) imply:
% 9.44/2.03 | | | | | | (59) member(all_37_1, all_15_2) = 0
% 9.44/2.03 | | | | | |
% 9.44/2.03 | | | | | | GROUND_INST: instantiating (3) with all_37_1, all_15_8, all_15_6,
% 9.44/2.03 | | | | | | all_15_2, simplifying with (10), (12), (20), (40), (59)
% 9.44/2.03 | | | | | | gives:
% 9.44/2.03 | | | | | | (60) member(all_37_1, all_15_6) = 0 & member(all_37_1, all_15_8)
% 9.44/2.03 | | | | | | = 0
% 9.44/2.03 | | | | | |
% 9.44/2.03 | | | | | | ALPHA: (60) implies:
% 9.44/2.03 | | | | | | (61) member(all_37_1, all_15_8) = 0
% 9.44/2.03 | | | | | | (62) member(all_37_1, all_15_6) = 0
% 9.44/2.03 | | | | | |
% 9.44/2.03 | | | | | | BETA: splitting (56) gives:
% 9.44/2.03 | | | | | |
% 9.44/2.03 | | | | | | Case 1:
% 9.44/2.03 | | | | | | |
% 9.44/2.03 | | | | | | | (63) all_50_0 = 0
% 9.44/2.03 | | | | | | |
% 9.44/2.03 | | | | | | | REF_CLOSE: (7), (53), (55), (61), (63) are inconsistent by
% 9.44/2.03 | | | | | | | sub-proof #1.
% 9.44/2.03 | | | | | | |
% 9.44/2.03 | | | | | | Case 2:
% 9.44/2.03 | | | | | | |
% 9.44/2.03 | | | | | | | (64) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) &
% 9.44/2.03 | | | | | | | member(all_37_1, all_15_6) = v1 & member(all_37_1,
% 9.44/2.03 | | | | | | | all_15_7) = v0)
% 9.44/2.03 | | | | | | |
% 9.44/2.03 | | | | | | | DELTA: instantiating (64) with fresh symbols all_79_0, all_79_1
% 9.44/2.03 | | | | | | | gives:
% 9.44/2.03 | | | | | | | (65) ~ (all_79_0 = 0) & ~ (all_79_1 = 0) & member(all_37_1,
% 9.44/2.03 | | | | | | | all_15_6) = all_79_0 & member(all_37_1, all_15_7) =
% 9.44/2.03 | | | | | | | all_79_1
% 9.44/2.03 | | | | | | |
% 9.44/2.03 | | | | | | | ALPHA: (65) implies:
% 9.44/2.03 | | | | | | | (66) ~ (all_79_0 = 0)
% 9.44/2.03 | | | | | | | (67) member(all_37_1, all_15_6) = all_79_0
% 9.44/2.03 | | | | | | |
% 9.44/2.03 | | | | | | | GROUND_INST: instantiating (7) with 0, all_79_0, all_15_6,
% 9.44/2.03 | | | | | | | all_37_1, simplifying with (62), (67) gives:
% 9.44/2.03 | | | | | | | (68) all_79_0 = 0
% 9.44/2.03 | | | | | | |
% 9.44/2.03 | | | | | | | REDUCE: (66), (68) imply:
% 9.44/2.03 | | | | | | | (69) $false
% 9.44/2.03 | | | | | | |
% 9.44/2.03 | | | | | | | CLOSE: (69) is inconsistent.
% 9.44/2.03 | | | | | | |
% 9.44/2.03 | | | | | | End of split
% 9.44/2.03 | | | | | |
% 9.44/2.03 | | | | | Case 2:
% 9.44/2.03 | | | | | |
% 9.44/2.03 | | | | | | (70) all_44_1 = 0
% 9.44/2.03 | | | | | | (71) ~ (all_44_0 = 0)
% 9.44/2.03 | | | | | |
% 9.44/2.03 | | | | | | REDUCE: (46), (70) imply:
% 9.44/2.03 | | | | | | (72) member(all_37_1, all_15_3) = 0
% 9.44/2.03 | | | | | |
% 9.44/2.03 | | | | | | BETA: splitting (57) gives:
% 9.44/2.03 | | | | | |
% 9.44/2.03 | | | | | | Case 1:
% 9.44/2.03 | | | | | | |
% 9.44/2.03 | | | | | | | (73) all_44_0 = 0
% 9.44/2.03 | | | | | | |
% 9.44/2.03 | | | | | | | REDUCE: (71), (73) imply:
% 9.44/2.03 | | | | | | | (74) $false
% 9.44/2.03 | | | | | | |
% 9.44/2.03 | | | | | | | CLOSE: (74) is inconsistent.
% 9.44/2.03 | | | | | | |
% 9.44/2.03 | | | | | | Case 2:
% 9.44/2.03 | | | | | | |
% 9.44/2.03 | | | | | | | (75) ? [v0: any] : ? [v1: any] : (member(all_37_1, all_15_6)
% 9.44/2.03 | | | | | | | = v1 & member(all_37_1, all_15_8) = v0 & ( ~ (v1 = 0) |
% 9.44/2.03 | | | | | | | ~ (v0 = 0)))
% 9.44/2.03 | | | | | | |
% 9.44/2.03 | | | | | | | DELTA: instantiating (75) with fresh symbols all_73_0, all_73_1
% 9.44/2.03 | | | | | | | gives:
% 9.44/2.03 | | | | | | | (76) member(all_37_1, all_15_6) = all_73_0 & member(all_37_1,
% 9.44/2.03 | | | | | | | all_15_8) = all_73_1 & ( ~ (all_73_0 = 0) | ~ (all_73_1
% 9.44/2.03 | | | | | | | = 0))
% 9.44/2.03 | | | | | | |
% 9.44/2.03 | | | | | | | ALPHA: (76) implies:
% 9.44/2.03 | | | | | | | (77) member(all_37_1, all_15_8) = all_73_1
% 9.44/2.03 | | | | | | |
% 9.44/2.03 | | | | | | | GROUND_INST: instantiating (7) with all_50_1, all_73_1, all_15_8,
% 9.44/2.03 | | | | | | | all_37_1, simplifying with (53), (77) gives:
% 9.44/2.03 | | | | | | | (78) all_73_1 = all_50_1
% 9.44/2.03 | | | | | | |
% 9.44/2.03 | | | | | | | GROUND_INST: instantiating (3) with all_37_1, all_15_8, all_15_7,
% 9.44/2.03 | | | | | | | all_15_3, simplifying with (10), (11), (19), (40),
% 9.44/2.03 | | | | | | | (72) gives:
% 9.44/2.04 | | | | | | | (79) member(all_37_1, all_15_7) = 0 & member(all_37_1,
% 9.44/2.04 | | | | | | | all_15_8) = 0
% 9.44/2.04 | | | | | | |
% 9.44/2.04 | | | | | | | ALPHA: (79) implies:
% 9.44/2.04 | | | | | | | (80) member(all_37_1, all_15_8) = 0
% 9.44/2.04 | | | | | | | (81) member(all_37_1, all_15_7) = 0
% 9.44/2.04 | | | | | | |
% 9.44/2.04 | | | | | | | BETA: splitting (56) gives:
% 9.44/2.04 | | | | | | |
% 9.44/2.04 | | | | | | | Case 1:
% 9.44/2.04 | | | | | | | |
% 9.44/2.04 | | | | | | | | (82) all_50_0 = 0
% 9.44/2.04 | | | | | | | |
% 9.44/2.04 | | | | | | | | REF_CLOSE: (7), (53), (55), (80), (82) are inconsistent by
% 9.44/2.04 | | | | | | | | sub-proof #1.
% 9.44/2.04 | | | | | | | |
% 9.44/2.04 | | | | | | | Case 2:
% 9.44/2.04 | | | | | | | |
% 9.44/2.04 | | | | | | | | (83) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0)
% 9.44/2.04 | | | | | | | | & member(all_37_1, all_15_6) = v1 & member(all_37_1,
% 9.44/2.04 | | | | | | | | all_15_7) = v0)
% 9.44/2.04 | | | | | | | |
% 9.44/2.04 | | | | | | | | DELTA: instantiating (83) with fresh symbols all_89_0, all_89_1
% 9.44/2.04 | | | | | | | | gives:
% 9.44/2.04 | | | | | | | | (84) ~ (all_89_0 = 0) & ~ (all_89_1 = 0) & member(all_37_1,
% 9.44/2.04 | | | | | | | | all_15_6) = all_89_0 & member(all_37_1, all_15_7) =
% 9.44/2.04 | | | | | | | | all_89_1
% 9.44/2.04 | | | | | | | |
% 9.44/2.04 | | | | | | | | ALPHA: (84) implies:
% 9.44/2.04 | | | | | | | | (85) ~ (all_89_1 = 0)
% 9.44/2.04 | | | | | | | | (86) member(all_37_1, all_15_7) = all_89_1
% 9.44/2.04 | | | | | | | |
% 9.44/2.04 | | | | | | | | GROUND_INST: instantiating (7) with 0, all_89_1, all_15_7,
% 9.44/2.04 | | | | | | | | all_37_1, simplifying with (81), (86) gives:
% 9.44/2.04 | | | | | | | | (87) all_89_1 = 0
% 9.44/2.04 | | | | | | | |
% 9.44/2.04 | | | | | | | | REDUCE: (85), (87) imply:
% 9.44/2.04 | | | | | | | | (88) $false
% 9.44/2.04 | | | | | | | |
% 9.44/2.04 | | | | | | | | CLOSE: (88) is inconsistent.
% 9.44/2.04 | | | | | | | |
% 9.44/2.04 | | | | | | | End of split
% 9.44/2.04 | | | | | | |
% 9.44/2.04 | | | | | | End of split
% 9.44/2.04 | | | | | |
% 9.44/2.04 | | | | | End of split
% 9.44/2.04 | | | | |
% 9.44/2.04 | | | | End of split
% 9.44/2.04 | | | |
% 9.44/2.04 | | | End of split
% 9.44/2.04 | | |
% 9.44/2.04 | | Case 2:
% 9.44/2.04 | | |
% 9.44/2.04 | | | (89) ~ (all_24_1 = 0)
% 9.44/2.04 | | |
% 9.44/2.04 | | | BETA: splitting (32) gives:
% 9.44/2.04 | | |
% 9.44/2.04 | | | Case 1:
% 9.44/2.04 | | | |
% 9.44/2.04 | | | | (90) all_24_1 = 0
% 9.44/2.04 | | | |
% 9.44/2.04 | | | | REDUCE: (89), (90) imply:
% 9.44/2.04 | | | | (91) $false
% 9.44/2.04 | | | |
% 9.44/2.04 | | | | CLOSE: (91) is inconsistent.
% 9.44/2.04 | | | |
% 9.44/2.04 | | | Case 2:
% 9.44/2.04 | | | |
% 9.44/2.04 | | | | (92) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1)
% 9.44/2.04 | | | | = v1 & member(v0, all_15_4) = 0 & $i(v0))
% 9.44/2.04 | | | |
% 9.44/2.04 | | | | DELTA: instantiating (92) with fresh symbols all_59_0, all_59_1 gives:
% 9.44/2.04 | | | | (93) ~ (all_59_0 = 0) & member(all_59_1, all_15_1) = all_59_0 &
% 9.44/2.04 | | | | member(all_59_1, all_15_4) = 0 & $i(all_59_1)
% 9.44/2.04 | | | |
% 9.44/2.04 | | | | ALPHA: (93) implies:
% 9.44/2.04 | | | | (94) ~ (all_59_0 = 0)
% 9.44/2.04 | | | | (95) $i(all_59_1)
% 9.44/2.04 | | | | (96) member(all_59_1, all_15_4) = 0
% 9.44/2.04 | | | | (97) member(all_59_1, all_15_1) = all_59_0
% 9.44/2.04 | | | |
% 9.44/2.04 | | | | GROUND_INST: instantiating (3) with all_59_1, all_15_8, all_15_5,
% 9.44/2.04 | | | | all_15_4, simplifying with (10), (13), (21), (95), (96)
% 9.44/2.04 | | | | gives:
% 9.44/2.04 | | | | (98) member(all_59_1, all_15_5) = 0 & member(all_59_1, all_15_8) = 0
% 9.44/2.04 | | | |
% 9.44/2.04 | | | | ALPHA: (98) implies:
% 9.44/2.05 | | | | (99) member(all_59_1, all_15_8) = 0
% 9.44/2.05 | | | | (100) member(all_59_1, all_15_5) = 0
% 9.44/2.05 | | | |
% 9.44/2.05 | | | | GROUND_INST: instantiating (6) with all_59_1, all_15_3, all_15_2,
% 9.44/2.05 | | | | all_15_1, all_59_0, simplifying with (15), (16), (23),
% 9.44/2.05 | | | | (95), (97) gives:
% 9.44/2.05 | | | | (101) all_59_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~
% 9.44/2.05 | | | | (v0 = 0) & member(all_59_1, all_15_2) = v1 & member(all_59_1,
% 9.44/2.05 | | | | all_15_3) = v0)
% 9.44/2.05 | | | |
% 9.44/2.05 | | | | BETA: splitting (101) gives:
% 9.44/2.05 | | | |
% 9.44/2.05 | | | | Case 1:
% 9.44/2.05 | | | | |
% 9.44/2.05 | | | | | (102) all_59_0 = 0
% 9.44/2.05 | | | | |
% 9.44/2.05 | | | | | REDUCE: (94), (102) imply:
% 9.44/2.05 | | | | | (103) $false
% 9.44/2.05 | | | | |
% 9.44/2.05 | | | | | CLOSE: (103) is inconsistent.
% 9.44/2.05 | | | | |
% 9.44/2.05 | | | | Case 2:
% 9.44/2.05 | | | | |
% 9.44/2.05 | | | | | (104) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) &
% 9.44/2.05 | | | | | member(all_59_1, all_15_2) = v1 & member(all_59_1,
% 9.44/2.05 | | | | | all_15_3) = v0)
% 9.44/2.05 | | | | |
% 9.44/2.05 | | | | | DELTA: instantiating (104) with fresh symbols all_71_0, all_71_1
% 9.44/2.05 | | | | | gives:
% 9.44/2.05 | | | | | (105) ~ (all_71_0 = 0) & ~ (all_71_1 = 0) & member(all_59_1,
% 9.44/2.05 | | | | | all_15_2) = all_71_0 & member(all_59_1, all_15_3) =
% 9.44/2.05 | | | | | all_71_1
% 9.44/2.05 | | | | |
% 9.44/2.05 | | | | | ALPHA: (105) implies:
% 9.44/2.05 | | | | | (106) ~ (all_71_1 = 0)
% 9.44/2.05 | | | | | (107) ~ (all_71_0 = 0)
% 9.44/2.05 | | | | | (108) member(all_59_1, all_15_3) = all_71_1
% 9.44/2.05 | | | | | (109) member(all_59_1, all_15_2) = all_71_0
% 9.44/2.05 | | | | |
% 9.44/2.05 | | | | | GROUND_INST: instantiating (5) with all_59_1, all_15_7, all_15_6,
% 9.44/2.05 | | | | | all_15_5, simplifying with (11), (12), (22), (95), (100)
% 9.44/2.05 | | | | | gives:
% 9.44/2.05 | | | | | (110) ? [v0: any] : ? [v1: any] : (member(all_59_1, all_15_6) =
% 9.44/2.05 | | | | | v1 & member(all_59_1, all_15_7) = v0 & (v1 = 0 | v0 = 0))
% 9.44/2.05 | | | | |
% 9.44/2.05 | | | | | GROUND_INST: instantiating (4) with all_59_1, all_15_8, all_15_7,
% 9.44/2.05 | | | | | all_15_3, all_71_1, simplifying with (10), (11), (19),
% 9.44/2.05 | | | | | (95), (108) gives:
% 9.44/2.05 | | | | | (111) all_71_1 = 0 | ? [v0: any] : ? [v1: any] :
% 9.44/2.05 | | | | | (member(all_59_1, all_15_7) = v1 & member(all_59_1, all_15_8)
% 9.44/2.05 | | | | | = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 9.44/2.05 | | | | |
% 9.44/2.05 | | | | | GROUND_INST: instantiating (4) with all_59_1, all_15_8, all_15_6,
% 9.44/2.05 | | | | | all_15_2, all_71_0, simplifying with (10), (12), (20),
% 9.44/2.05 | | | | | (95), (109) gives:
% 9.44/2.05 | | | | | (112) all_71_0 = 0 | ? [v0: any] : ? [v1: any] :
% 9.44/2.05 | | | | | (member(all_59_1, all_15_6) = v1 & member(all_59_1, all_15_8)
% 9.44/2.05 | | | | | = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 9.44/2.05 | | | | |
% 9.44/2.05 | | | | | DELTA: instantiating (110) with fresh symbols all_78_0, all_78_1
% 9.44/2.05 | | | | | gives:
% 9.44/2.05 | | | | | (113) member(all_59_1, all_15_6) = all_78_0 & member(all_59_1,
% 9.44/2.05 | | | | | all_15_7) = all_78_1 & (all_78_0 = 0 | all_78_1 = 0)
% 9.44/2.05 | | | | |
% 9.44/2.05 | | | | | ALPHA: (113) implies:
% 9.44/2.05 | | | | | (114) member(all_59_1, all_15_7) = all_78_1
% 9.44/2.05 | | | | | (115) member(all_59_1, all_15_6) = all_78_0
% 9.44/2.05 | | | | | (116) all_78_0 = 0 | all_78_1 = 0
% 9.44/2.05 | | | | |
% 9.44/2.05 | | | | | BETA: splitting (112) gives:
% 9.44/2.05 | | | | |
% 9.44/2.05 | | | | | Case 1:
% 9.44/2.05 | | | | | |
% 9.44/2.05 | | | | | | (117) all_71_0 = 0
% 9.44/2.06 | | | | | |
% 9.44/2.06 | | | | | | REDUCE: (107), (117) imply:
% 9.44/2.06 | | | | | | (118) $false
% 9.44/2.06 | | | | | |
% 9.44/2.06 | | | | | | CLOSE: (118) is inconsistent.
% 9.44/2.06 | | | | | |
% 9.44/2.06 | | | | | Case 2:
% 9.44/2.06 | | | | | |
% 9.44/2.06 | | | | | | (119) ? [v0: any] : ? [v1: any] : (member(all_59_1, all_15_6) =
% 9.44/2.06 | | | | | | v1 & member(all_59_1, all_15_8) = v0 & ( ~ (v1 = 0) | ~
% 9.44/2.06 | | | | | | (v0 = 0)))
% 9.44/2.06 | | | | | |
% 9.44/2.06 | | | | | | DELTA: instantiating (119) with fresh symbols all_84_0, all_84_1
% 9.44/2.06 | | | | | | gives:
% 9.44/2.06 | | | | | | (120) member(all_59_1, all_15_6) = all_84_0 & member(all_59_1,
% 9.44/2.06 | | | | | | all_15_8) = all_84_1 & ( ~ (all_84_0 = 0) | ~ (all_84_1
% 9.44/2.06 | | | | | | = 0))
% 9.44/2.06 | | | | | |
% 9.44/2.06 | | | | | | ALPHA: (120) implies:
% 9.44/2.06 | | | | | | (121) member(all_59_1, all_15_8) = all_84_1
% 9.44/2.06 | | | | | | (122) member(all_59_1, all_15_6) = all_84_0
% 9.44/2.06 | | | | | | (123) ~ (all_84_0 = 0) | ~ (all_84_1 = 0)
% 9.44/2.06 | | | | | |
% 9.44/2.06 | | | | | | GROUND_INST: instantiating (7) with 0, all_84_1, all_15_8, all_59_1,
% 9.44/2.06 | | | | | | simplifying with (99), (121) gives:
% 9.44/2.06 | | | | | | (124) all_84_1 = 0
% 9.44/2.06 | | | | | |
% 9.44/2.06 | | | | | | GROUND_INST: instantiating (7) with all_78_0, all_84_0, all_15_6,
% 9.44/2.06 | | | | | | all_59_1, simplifying with (115), (122) gives:
% 9.44/2.06 | | | | | | (125) all_84_0 = all_78_0
% 9.44/2.06 | | | | | |
% 9.44/2.06 | | | | | | BETA: splitting (111) gives:
% 9.44/2.06 | | | | | |
% 9.44/2.06 | | | | | | Case 1:
% 9.44/2.06 | | | | | | |
% 9.44/2.06 | | | | | | | (126) all_71_1 = 0
% 9.44/2.06 | | | | | | |
% 9.44/2.06 | | | | | | | REDUCE: (106), (126) imply:
% 9.44/2.06 | | | | | | | (127) $false
% 9.44/2.06 | | | | | | |
% 9.44/2.06 | | | | | | | CLOSE: (127) is inconsistent.
% 9.44/2.06 | | | | | | |
% 9.44/2.06 | | | | | | Case 2:
% 9.44/2.06 | | | | | | |
% 9.44/2.06 | | | | | | | (128) ? [v0: any] : ? [v1: any] : (member(all_59_1, all_15_7)
% 9.44/2.06 | | | | | | | = v1 & member(all_59_1, all_15_8) = v0 & ( ~ (v1 = 0) |
% 9.44/2.06 | | | | | | | ~ (v0 = 0)))
% 9.44/2.06 | | | | | | |
% 9.44/2.06 | | | | | | | DELTA: instantiating (128) with fresh symbols all_94_0, all_94_1
% 9.44/2.06 | | | | | | | gives:
% 9.44/2.06 | | | | | | | (129) member(all_59_1, all_15_7) = all_94_0 & member(all_59_1,
% 9.44/2.06 | | | | | | | all_15_8) = all_94_1 & ( ~ (all_94_0 = 0) | ~
% 9.44/2.06 | | | | | | | (all_94_1 = 0))
% 9.44/2.06 | | | | | | |
% 9.44/2.06 | | | | | | | ALPHA: (129) implies:
% 9.44/2.06 | | | | | | | (130) member(all_59_1, all_15_8) = all_94_1
% 9.44/2.06 | | | | | | | (131) member(all_59_1, all_15_7) = all_94_0
% 9.44/2.06 | | | | | | | (132) ~ (all_94_0 = 0) | ~ (all_94_1 = 0)
% 9.44/2.06 | | | | | | |
% 9.44/2.06 | | | | | | | BETA: splitting (123) gives:
% 9.44/2.06 | | | | | | |
% 9.44/2.06 | | | | | | | Case 1:
% 9.44/2.06 | | | | | | | |
% 9.44/2.06 | | | | | | | | (133) ~ (all_84_0 = 0)
% 9.44/2.06 | | | | | | | |
% 9.44/2.06 | | | | | | | | REDUCE: (125), (133) imply:
% 9.44/2.06 | | | | | | | | (134) ~ (all_78_0 = 0)
% 9.44/2.06 | | | | | | | |
% 9.44/2.06 | | | | | | | | BETA: splitting (116) gives:
% 9.44/2.06 | | | | | | | |
% 9.44/2.06 | | | | | | | | Case 1:
% 9.44/2.06 | | | | | | | | |
% 9.44/2.06 | | | | | | | | | (135) all_78_0 = 0
% 9.44/2.06 | | | | | | | | |
% 9.44/2.06 | | | | | | | | | REDUCE: (134), (135) imply:
% 9.44/2.06 | | | | | | | | | (136) $false
% 9.44/2.06 | | | | | | | | |
% 9.44/2.06 | | | | | | | | | CLOSE: (136) is inconsistent.
% 9.44/2.06 | | | | | | | | |
% 9.44/2.06 | | | | | | | | Case 2:
% 9.44/2.06 | | | | | | | | |
% 9.44/2.06 | | | | | | | | | (137) all_78_1 = 0
% 9.44/2.06 | | | | | | | | |
% 9.44/2.06 | | | | | | | | | REDUCE: (114), (137) imply:
% 9.44/2.06 | | | | | | | | | (138) member(all_59_1, all_15_7) = 0
% 9.44/2.06 | | | | | | | | |
% 9.44/2.06 | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_94_1, all_15_8,
% 9.44/2.06 | | | | | | | | | all_59_1, simplifying with (99), (130) gives:
% 9.44/2.06 | | | | | | | | | (139) all_94_1 = 0
% 9.44/2.06 | | | | | | | | |
% 9.44/2.06 | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_94_0, all_15_7,
% 9.44/2.06 | | | | | | | | | all_59_1, simplifying with (131), (138) gives:
% 9.44/2.06 | | | | | | | | | (140) all_94_0 = 0
% 9.44/2.06 | | | | | | | | |
% 9.44/2.06 | | | | | | | | | BETA: splitting (132) gives:
% 9.44/2.06 | | | | | | | | |
% 9.44/2.06 | | | | | | | | | Case 1:
% 9.44/2.06 | | | | | | | | | |
% 9.44/2.06 | | | | | | | | | | (141) ~ (all_94_0 = 0)
% 9.44/2.06 | | | | | | | | | |
% 9.44/2.06 | | | | | | | | | | REDUCE: (140), (141) imply:
% 9.44/2.06 | | | | | | | | | | (142) $false
% 9.44/2.06 | | | | | | | | | |
% 9.44/2.06 | | | | | | | | | | CLOSE: (142) is inconsistent.
% 9.44/2.06 | | | | | | | | | |
% 9.44/2.06 | | | | | | | | | Case 2:
% 9.44/2.06 | | | | | | | | | |
% 9.44/2.06 | | | | | | | | | | (143) ~ (all_94_1 = 0)
% 9.44/2.06 | | | | | | | | | |
% 9.44/2.06 | | | | | | | | | | REDUCE: (139), (143) imply:
% 9.44/2.06 | | | | | | | | | | (144) $false
% 9.44/2.06 | | | | | | | | | |
% 9.44/2.06 | | | | | | | | | | CLOSE: (144) is inconsistent.
% 9.44/2.06 | | | | | | | | | |
% 9.44/2.06 | | | | | | | | | End of split
% 9.44/2.06 | | | | | | | | |
% 9.44/2.06 | | | | | | | | End of split
% 9.44/2.06 | | | | | | | |
% 9.44/2.06 | | | | | | | Case 2:
% 9.44/2.06 | | | | | | | |
% 9.44/2.06 | | | | | | | | (145) ~ (all_84_1 = 0)
% 9.44/2.06 | | | | | | | |
% 9.44/2.06 | | | | | | | | REDUCE: (124), (145) imply:
% 9.44/2.06 | | | | | | | | (146) $false
% 9.44/2.06 | | | | | | | |
% 9.44/2.06 | | | | | | | | CLOSE: (146) is inconsistent.
% 9.44/2.06 | | | | | | | |
% 9.44/2.06 | | | | | | | End of split
% 9.44/2.06 | | | | | | |
% 9.44/2.06 | | | | | | End of split
% 9.44/2.06 | | | | | |
% 9.44/2.06 | | | | | End of split
% 9.44/2.06 | | | | |
% 9.44/2.07 | | | | End of split
% 9.44/2.07 | | | |
% 9.44/2.07 | | | End of split
% 9.44/2.07 | | |
% 9.44/2.07 | | End of split
% 9.44/2.07 | |
% 9.44/2.07 | End of split
% 9.44/2.07 |
% 9.44/2.07 End of proof
% 9.44/2.07
% 9.44/2.07 Sub-proof #1 shows that the following formulas are inconsistent:
% 9.44/2.07 ----------------------------------------------------------------
% 9.44/2.07 (1) member(all_37_1, all_15_8) = all_50_1
% 9.44/2.07 (2) all_50_0 = 0
% 9.44/2.07 (3) ~ (all_50_0 = 0) | ~ (all_50_1 = 0)
% 9.44/2.07 (4) member(all_37_1, all_15_8) = 0
% 9.44/2.07 (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 9.44/2.07 ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) =
% 9.44/2.07 v0))
% 9.44/2.07
% 9.44/2.07 Begin of proof
% 9.44/2.07 |
% 9.44/2.07 | BETA: splitting (3) gives:
% 9.44/2.07 |
% 9.44/2.07 | Case 1:
% 9.44/2.07 | |
% 9.44/2.07 | | (6) ~ (all_50_0 = 0)
% 9.44/2.07 | |
% 9.44/2.07 | | REDUCE: (2), (6) imply:
% 9.44/2.07 | | (7) $false
% 9.44/2.07 | |
% 9.44/2.07 | | CLOSE: (7) is inconsistent.
% 9.44/2.07 | |
% 9.44/2.07 | Case 2:
% 9.44/2.07 | |
% 9.44/2.07 | | (8) ~ (all_50_1 = 0)
% 9.44/2.07 | |
% 9.44/2.07 | | GROUND_INST: instantiating (5) with all_50_1, 0, all_15_8, all_37_1,
% 9.44/2.07 | | simplifying with (1), (4) gives:
% 9.44/2.07 | | (9) all_50_1 = 0
% 9.44/2.07 | |
% 9.44/2.07 | | REDUCE: (8), (9) imply:
% 9.44/2.07 | | (10) $false
% 9.44/2.07 | |
% 9.44/2.07 | | CLOSE: (10) is inconsistent.
% 9.44/2.07 | |
% 9.44/2.07 | End of split
% 9.44/2.07 |
% 9.44/2.07 End of proof
% 9.44/2.07 % SZS output end Proof for theBenchmark
% 9.44/2.07
% 9.44/2.07 1459ms
%------------------------------------------------------------------------------