TSTP Solution File: SET698+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET698+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 : n012.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 15:26:02 EDT 2023
% Result : Theorem 7.88s 1.85s
% Output : Proof 9.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET698+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 11:17:56 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.61 ________ _____
% 0.18/0.61 ___ __ \_________(_)________________________________
% 0.18/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.61
% 0.18/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.61 (2023-06-19)
% 0.18/0.61
% 0.18/0.61 (c) Philipp Rümmer, 2009-2023
% 0.18/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.61 Amanda Stjerna.
% 0.18/0.61 Free software under BSD-3-Clause.
% 0.18/0.61
% 0.18/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.61
% 0.18/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.63 Running up to 7 provers in parallel.
% 0.18/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.41/1.04 Prover 4: Preprocessing ...
% 2.41/1.04 Prover 1: Preprocessing ...
% 2.41/1.08 Prover 0: Preprocessing ...
% 2.41/1.08 Prover 5: Preprocessing ...
% 2.97/1.08 Prover 3: Preprocessing ...
% 2.97/1.08 Prover 6: Preprocessing ...
% 2.97/1.09 Prover 2: Preprocessing ...
% 4.57/1.46 Prover 1: Constructing countermodel ...
% 4.57/1.46 Prover 5: Proving ...
% 4.57/1.46 Prover 6: Proving ...
% 4.57/1.48 Prover 0: Proving ...
% 4.57/1.49 Prover 2: Proving ...
% 4.57/1.49 Prover 3: Constructing countermodel ...
% 4.57/1.49 Prover 4: Constructing countermodel ...
% 7.88/1.85 Prover 3: proved (1213ms)
% 7.88/1.85
% 7.88/1.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.88/1.85
% 7.88/1.85 Prover 0: stopped
% 7.88/1.85 Prover 5: stopped
% 7.88/1.85 Prover 6: stopped
% 7.88/1.85 Prover 2: stopped
% 8.47/1.88 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.47/1.88 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.47/1.88 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.47/1.88 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.47/1.88 Prover 11: Preprocessing ...
% 8.47/1.88 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.61/1.90 Prover 10: Preprocessing ...
% 8.61/1.90 Prover 8: Preprocessing ...
% 8.61/1.90 Prover 13: Preprocessing ...
% 8.61/1.91 Prover 7: Preprocessing ...
% 8.97/1.94 Prover 10: Warning: ignoring some quantifiers
% 8.97/1.95 Prover 1: Found proof (size 98)
% 8.97/1.95 Prover 1: proved (1317ms)
% 8.97/1.95 Prover 4: stopped
% 8.97/1.96 Prover 10: Constructing countermodel ...
% 8.97/1.96 Prover 7: Warning: ignoring some quantifiers
% 8.97/1.96 Prover 10: stopped
% 8.97/1.99 Prover 7: Constructing countermodel ...
% 8.97/2.00 Prover 7: stopped
% 8.97/2.00 Prover 13: Warning: ignoring some quantifiers
% 9.53/2.01 Prover 8: Warning: ignoring some quantifiers
% 9.53/2.01 Prover 11: Constructing countermodel ...
% 9.53/2.01 Prover 13: Constructing countermodel ...
% 9.53/2.02 Prover 8: Constructing countermodel ...
% 9.53/2.02 Prover 11: stopped
% 9.53/2.02 Prover 13: stopped
% 9.53/2.02 Prover 8: stopped
% 9.53/2.02
% 9.53/2.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.53/2.02
% 9.53/2.03 % SZS output start Proof for theBenchmark
% 9.53/2.04 Assumptions after simplification:
% 9.53/2.04 ---------------------------------
% 9.53/2.04
% 9.53/2.04 (difference)
% 9.53/2.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 9.53/2.06 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~
% 9.53/2.06 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v0, v2) = v5 &
% 9.53/2.06 member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i]
% 9.53/2.06 : ! [v2: $i] : ! [v3: $i] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0,
% 9.53/2.06 v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 =
% 9.53/2.06 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 9.53/2.06
% 9.53/2.06 (equal_set)
% 9.53/2.07 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) =
% 9.53/2.07 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1,
% 9.53/2.07 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0:
% 9.53/2.07 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 9.53/2.07 (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 9.53/2.07
% 9.53/2.07 (subset)
% 9.53/2.07 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 9.53/2.07 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 9.53/2.07 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 9.53/2.07 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 9.53/2.07 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 9.53/2.07
% 9.53/2.07 (thI32)
% 9.53/2.07 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: $i] : ? [v5:
% 9.53/2.07 $i] : ? [v6: any] : (difference(v2, v0) = v4 & union(v4, v1) = v5 &
% 9.53/2.07 equal_set(v5, v2) = v6 & subset(v1, v2) = 0 & subset(v0, v2) = 0 &
% 9.53/2.07 subset(v0, v1) = v3 & $i(v5) & $i(v4) & $i(v2) & $i(v1) & $i(v0) & ((v6 = 0
% 9.53/2.07 & ~ (v3 = 0)) | (v3 = 0 & ~ (v6 = 0))))
% 9.53/2.07
% 9.53/2.07 (union)
% 9.88/2.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 9.88/2.08 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1)
% 9.88/2.08 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) &
% 9.88/2.08 member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] :
% 9.88/2.08 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0)
% 9.88/2.08 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 9.88/2.08 (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0)))
% 9.88/2.08
% 9.88/2.08 (function-axioms)
% 9.88/2.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.88/2.08 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 9.88/2.08 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.88/2.08 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 9.88/2.08 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 9.88/2.08 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 9.88/2.08 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 9.88/2.08 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 9.88/2.08 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 9.88/2.08 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.88/2.08 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 9.88/2.08 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 9.88/2.08 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.88/2.08 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 9.88/2.08 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 9.88/2.08 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 9.88/2.08 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 9.88/2.08 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 9.88/2.08 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 9.88/2.08 (power_set(v2) = v0))
% 9.88/2.08
% 9.88/2.08 Further assumptions not needed in the proof:
% 9.88/2.08 --------------------------------------------
% 9.88/2.08 empty_set, intersection, power_set, product, singleton, sum, unordered_pair
% 9.88/2.08
% 9.88/2.08 Those formulas are unsatisfiable:
% 9.88/2.08 ---------------------------------
% 9.88/2.08
% 9.88/2.08 Begin of proof
% 9.88/2.08 |
% 9.88/2.08 | ALPHA: (subset) implies:
% 9.88/2.09 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 9.88/2.09 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) |
% 9.88/2.09 | member(v2, v1) = 0))
% 9.88/2.09 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 9.88/2.09 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 9.88/2.09 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 9.88/2.09 |
% 9.88/2.09 | ALPHA: (equal_set) implies:
% 9.88/2.09 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) |
% 9.88/2.09 | ~ $i(v0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 9.88/2.09 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0,
% 9.88/2.09 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 9.88/2.09 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 =
% 9.88/2.09 | 0))))
% 9.88/2.09 |
% 9.88/2.09 | ALPHA: (union) implies:
% 9.88/2.09 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1,
% 9.88/2.09 | v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 9.88/2.09 | $i(v0) | ? [v4: any] : ? [v5: any] : (member(v0, v2) = v5 &
% 9.88/2.09 | member(v0, v1) = v4 & (v5 = 0 | v4 = 0)))
% 9.88/2.09 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 9.88/2.09 | (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~
% 9.88/2.09 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~
% 9.88/2.09 | (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) =
% 9.88/2.09 | v5))
% 9.88/2.09 |
% 9.88/2.09 | ALPHA: (difference) implies:
% 9.88/2.09 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 9.88/2.09 | (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~
% 9.88/2.09 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v0, v2) = 0
% 9.88/2.09 | & member(v0, v1) = v4))
% 9.88/2.10 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 9.88/2.10 | (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ~
% 9.88/2.10 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] :
% 9.88/2.10 | (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0)))
% 9.88/2.10 |
% 9.88/2.10 | ALPHA: (function-axioms) implies:
% 9.88/2.10 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 9.88/2.10 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 9.88/2.10 | = v0))
% 9.88/2.10 |
% 9.88/2.10 | DELTA: instantiating (thI32) with fresh symbols all_15_0, all_15_1, all_15_2,
% 9.88/2.10 | all_15_3, all_15_4, all_15_5, all_15_6 gives:
% 9.88/2.10 | (10) difference(all_15_4, all_15_6) = all_15_2 & union(all_15_2, all_15_5)
% 9.88/2.10 | = all_15_1 & equal_set(all_15_1, all_15_4) = all_15_0 &
% 9.88/2.10 | subset(all_15_5, all_15_4) = 0 & subset(all_15_6, all_15_4) = 0 &
% 9.88/2.10 | subset(all_15_6, all_15_5) = all_15_3 & $i(all_15_1) & $i(all_15_2) &
% 9.88/2.10 | $i(all_15_4) & $i(all_15_5) & $i(all_15_6) & ((all_15_0 = 0 & ~
% 9.88/2.10 | (all_15_3 = 0)) | (all_15_3 = 0 & ~ (all_15_0 = 0)))
% 9.88/2.10 |
% 9.88/2.10 | ALPHA: (10) implies:
% 9.88/2.10 | (11) $i(all_15_6)
% 9.88/2.10 | (12) $i(all_15_5)
% 9.88/2.10 | (13) $i(all_15_4)
% 9.88/2.10 | (14) $i(all_15_2)
% 9.88/2.10 | (15) $i(all_15_1)
% 9.88/2.10 | (16) subset(all_15_6, all_15_5) = all_15_3
% 9.88/2.10 | (17) subset(all_15_6, all_15_4) = 0
% 9.88/2.10 | (18) subset(all_15_5, all_15_4) = 0
% 9.88/2.10 | (19) equal_set(all_15_1, all_15_4) = all_15_0
% 9.88/2.10 | (20) union(all_15_2, all_15_5) = all_15_1
% 9.88/2.10 | (21) difference(all_15_4, all_15_6) = all_15_2
% 9.88/2.10 | (22) (all_15_0 = 0 & ~ (all_15_3 = 0)) | (all_15_3 = 0 & ~ (all_15_0 =
% 9.88/2.10 | 0))
% 9.88/2.10 |
% 9.88/2.10 | GROUND_INST: instantiating (2) with all_15_6, all_15_5, all_15_3, simplifying
% 9.88/2.10 | with (11), (12), (16) gives:
% 9.88/2.10 | (23) all_15_3 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 9.88/2.10 | all_15_5) = v1 & member(v0, all_15_6) = 0 & $i(v0))
% 9.88/2.10 |
% 9.88/2.10 | GROUND_INST: instantiating (1) with all_15_6, all_15_4, simplifying with (11),
% 9.88/2.10 | (13), (17) gives:
% 9.88/2.10 | (24) ! [v0: $i] : ( ~ (member(v0, all_15_6) = 0) | ~ $i(v0) | member(v0,
% 9.88/2.10 | all_15_4) = 0)
% 9.88/2.10 |
% 9.88/2.10 | GROUND_INST: instantiating (1) with all_15_5, all_15_4, simplifying with (12),
% 9.88/2.10 | (13), (18) gives:
% 9.88/2.10 | (25) ! [v0: $i] : ( ~ (member(v0, all_15_5) = 0) | ~ $i(v0) | member(v0,
% 9.88/2.10 | all_15_4) = 0)
% 9.88/2.10 |
% 9.88/2.10 | GROUND_INST: instantiating (4) with all_15_1, all_15_4, all_15_0, simplifying
% 9.88/2.11 | with (13), (15), (19) gives:
% 9.88/2.11 | (26) all_15_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_1,
% 9.88/2.11 | all_15_4) = v0 & subset(all_15_4, all_15_1) = v1 & ( ~ (v1 = 0) |
% 9.88/2.11 | ~ (v0 = 0)))
% 9.88/2.11 |
% 9.88/2.11 | BETA: splitting (22) gives:
% 9.88/2.11 |
% 9.88/2.11 | Case 1:
% 9.88/2.11 | |
% 9.88/2.11 | | (27) all_15_0 = 0 & ~ (all_15_3 = 0)
% 9.88/2.11 | |
% 9.88/2.11 | | ALPHA: (27) implies:
% 9.88/2.11 | | (28) all_15_0 = 0
% 9.88/2.11 | | (29) ~ (all_15_3 = 0)
% 9.88/2.11 | |
% 9.88/2.11 | | REDUCE: (19), (28) imply:
% 9.88/2.11 | | (30) equal_set(all_15_1, all_15_4) = 0
% 9.88/2.11 | |
% 9.88/2.11 | | BETA: splitting (23) gives:
% 9.88/2.11 | |
% 9.88/2.11 | | Case 1:
% 9.88/2.11 | | |
% 9.88/2.11 | | | (31) all_15_3 = 0
% 9.88/2.11 | | |
% 9.88/2.11 | | | REDUCE: (29), (31) imply:
% 9.88/2.11 | | | (32) $false
% 9.88/2.11 | | |
% 9.88/2.11 | | | CLOSE: (32) is inconsistent.
% 9.88/2.11 | | |
% 9.88/2.11 | | Case 2:
% 9.88/2.11 | | |
% 9.88/2.11 | | | (33) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_5) =
% 9.88/2.11 | | | v1 & member(v0, all_15_6) = 0 & $i(v0))
% 9.88/2.11 | | |
% 9.88/2.11 | | | DELTA: instantiating (33) with fresh symbols all_33_0, all_33_1 gives:
% 9.88/2.11 | | | (34) ~ (all_33_0 = 0) & member(all_33_1, all_15_5) = all_33_0 &
% 9.88/2.11 | | | member(all_33_1, all_15_6) = 0 & $i(all_33_1)
% 9.88/2.11 | | |
% 9.88/2.11 | | | ALPHA: (34) implies:
% 9.88/2.11 | | | (35) ~ (all_33_0 = 0)
% 9.88/2.11 | | | (36) $i(all_33_1)
% 9.88/2.11 | | | (37) member(all_33_1, all_15_6) = 0
% 9.88/2.11 | | | (38) member(all_33_1, all_15_5) = all_33_0
% 9.88/2.11 | | |
% 9.88/2.11 | | | GROUND_INST: instantiating (24) with all_33_1, simplifying with (36), (37)
% 9.88/2.11 | | | gives:
% 9.88/2.11 | | | (39) member(all_33_1, all_15_4) = 0
% 9.88/2.11 | | |
% 9.88/2.11 | | | GROUND_INST: instantiating (3) with all_15_1, all_15_4, simplifying with
% 9.88/2.11 | | | (13), (15), (30) gives:
% 9.88/2.11 | | | (40) subset(all_15_1, all_15_4) = 0 & subset(all_15_4, all_15_1) = 0
% 9.88/2.11 | | |
% 9.88/2.11 | | | ALPHA: (40) implies:
% 9.88/2.11 | | | (41) subset(all_15_4, all_15_1) = 0
% 9.88/2.11 | | |
% 9.88/2.11 | | | GROUND_INST: instantiating (1) with all_15_4, all_15_1, simplifying with
% 9.88/2.11 | | | (13), (15), (41) gives:
% 9.88/2.11 | | | (42) ! [v0: $i] : ( ~ (member(v0, all_15_4) = 0) | ~ $i(v0) |
% 9.88/2.11 | | | member(v0, all_15_1) = 0)
% 9.88/2.11 | | |
% 9.88/2.11 | | | GROUND_INST: instantiating (42) with all_33_1, simplifying with (36), (39)
% 9.88/2.11 | | | gives:
% 9.88/2.11 | | | (43) member(all_33_1, all_15_1) = 0
% 9.88/2.11 | | |
% 9.88/2.11 | | | GROUND_INST: instantiating (5) with all_33_1, all_15_2, all_15_5,
% 9.88/2.11 | | | all_15_1, simplifying with (12), (14), (20), (36), (43)
% 9.88/2.11 | | | gives:
% 9.88/2.11 | | | (44) ? [v0: any] : ? [v1: any] : (member(all_33_1, all_15_2) = v0 &
% 9.88/2.11 | | | member(all_33_1, all_15_5) = v1 & (v1 = 0 | v0 = 0))
% 9.88/2.11 | | |
% 9.88/2.11 | | | DELTA: instantiating (44) with fresh symbols all_54_0, all_54_1 gives:
% 9.88/2.11 | | | (45) member(all_33_1, all_15_2) = all_54_1 & member(all_33_1, all_15_5)
% 9.88/2.11 | | | = all_54_0 & (all_54_0 = 0 | all_54_1 = 0)
% 9.88/2.11 | | |
% 9.88/2.11 | | | ALPHA: (45) implies:
% 9.88/2.11 | | | (46) member(all_33_1, all_15_5) = all_54_0
% 9.88/2.12 | | | (47) member(all_33_1, all_15_2) = all_54_1
% 9.88/2.12 | | | (48) all_54_0 = 0 | all_54_1 = 0
% 9.88/2.12 | | |
% 9.88/2.12 | | | GROUND_INST: instantiating (9) with all_33_0, all_54_0, all_15_5,
% 9.88/2.12 | | | all_33_1, simplifying with (38), (46) gives:
% 9.88/2.12 | | | (49) all_54_0 = all_33_0
% 9.88/2.12 | | |
% 9.88/2.12 | | | BETA: splitting (48) gives:
% 9.88/2.12 | | |
% 9.88/2.12 | | | Case 1:
% 9.88/2.12 | | | |
% 9.88/2.12 | | | | (50) all_54_0 = 0
% 9.88/2.12 | | | |
% 9.88/2.12 | | | | COMBINE_EQS: (49), (50) imply:
% 9.88/2.12 | | | | (51) all_33_0 = 0
% 9.88/2.12 | | | |
% 9.88/2.12 | | | | REDUCE: (35), (51) imply:
% 9.88/2.12 | | | | (52) $false
% 9.88/2.12 | | | |
% 9.88/2.12 | | | | CLOSE: (52) is inconsistent.
% 9.88/2.12 | | | |
% 9.88/2.12 | | | Case 2:
% 9.88/2.12 | | | |
% 9.88/2.12 | | | | (53) all_54_1 = 0
% 9.88/2.12 | | | |
% 9.88/2.12 | | | | REDUCE: (47), (53) imply:
% 9.88/2.12 | | | | (54) member(all_33_1, all_15_2) = 0
% 9.88/2.12 | | | |
% 9.88/2.12 | | | | GROUND_INST: instantiating (7) with all_33_1, all_15_6, all_15_4,
% 9.88/2.12 | | | | all_15_2, simplifying with (11), (13), (21), (36), (54)
% 9.88/2.12 | | | | gives:
% 9.88/2.12 | | | | (55) ? [v0: int] : ( ~ (v0 = 0) & member(all_33_1, all_15_4) = 0 &
% 9.88/2.12 | | | | member(all_33_1, all_15_6) = v0)
% 9.88/2.12 | | | |
% 9.88/2.12 | | | | DELTA: instantiating (55) with fresh symbol all_69_0 gives:
% 9.88/2.12 | | | | (56) ~ (all_69_0 = 0) & member(all_33_1, all_15_4) = 0 &
% 9.88/2.12 | | | | member(all_33_1, all_15_6) = all_69_0
% 9.88/2.12 | | | |
% 9.88/2.12 | | | | ALPHA: (56) implies:
% 9.88/2.12 | | | | (57) ~ (all_69_0 = 0)
% 9.88/2.12 | | | | (58) member(all_33_1, all_15_6) = all_69_0
% 9.88/2.12 | | | |
% 9.88/2.12 | | | | GROUND_INST: instantiating (9) with 0, all_69_0, all_15_6, all_33_1,
% 9.88/2.12 | | | | simplifying with (37), (58) gives:
% 9.88/2.12 | | | | (59) all_69_0 = 0
% 9.88/2.12 | | | |
% 9.88/2.12 | | | | REDUCE: (57), (59) imply:
% 9.88/2.12 | | | | (60) $false
% 9.88/2.12 | | | |
% 9.88/2.12 | | | | CLOSE: (60) is inconsistent.
% 9.88/2.12 | | | |
% 9.88/2.12 | | | End of split
% 9.88/2.12 | | |
% 9.88/2.12 | | End of split
% 9.88/2.12 | |
% 9.88/2.12 | Case 2:
% 9.88/2.12 | |
% 9.88/2.12 | | (61) all_15_3 = 0 & ~ (all_15_0 = 0)
% 9.88/2.12 | |
% 9.88/2.12 | | ALPHA: (61) implies:
% 9.88/2.12 | | (62) all_15_3 = 0
% 9.88/2.12 | | (63) ~ (all_15_0 = 0)
% 9.88/2.12 | |
% 9.88/2.12 | | REDUCE: (16), (62) imply:
% 9.88/2.12 | | (64) subset(all_15_6, all_15_5) = 0
% 9.88/2.12 | |
% 9.88/2.12 | | BETA: splitting (26) gives:
% 9.88/2.12 | |
% 9.88/2.12 | | Case 1:
% 9.88/2.12 | | |
% 9.88/2.12 | | | (65) all_15_0 = 0
% 9.88/2.12 | | |
% 9.88/2.12 | | | REDUCE: (63), (65) imply:
% 9.88/2.12 | | | (66) $false
% 9.88/2.12 | | |
% 9.88/2.12 | | | CLOSE: (66) is inconsistent.
% 9.88/2.12 | | |
% 9.88/2.12 | | Case 2:
% 9.88/2.12 | | |
% 9.88/2.12 | | | (67) ? [v0: any] : ? [v1: any] : (subset(all_15_1, all_15_4) = v0 &
% 9.88/2.12 | | | subset(all_15_4, all_15_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 9.88/2.12 | | |
% 9.88/2.12 | | | DELTA: instantiating (67) with fresh symbols all_33_0, all_33_1 gives:
% 9.88/2.12 | | | (68) subset(all_15_1, all_15_4) = all_33_1 & subset(all_15_4, all_15_1)
% 9.88/2.12 | | | = all_33_0 & ( ~ (all_33_0 = 0) | ~ (all_33_1 = 0))
% 9.88/2.12 | | |
% 9.88/2.12 | | | ALPHA: (68) implies:
% 9.88/2.12 | | | (69) subset(all_15_4, all_15_1) = all_33_0
% 9.88/2.12 | | | (70) subset(all_15_1, all_15_4) = all_33_1
% 9.88/2.12 | | | (71) ~ (all_33_0 = 0) | ~ (all_33_1 = 0)
% 9.88/2.12 | | |
% 9.88/2.12 | | | GROUND_INST: instantiating (1) with all_15_6, all_15_5, simplifying with
% 9.88/2.12 | | | (11), (12), (64) gives:
% 9.88/2.12 | | | (72) ! [v0: $i] : ( ~ (member(v0, all_15_6) = 0) | ~ $i(v0) |
% 9.88/2.12 | | | member(v0, all_15_5) = 0)
% 9.88/2.12 | | |
% 9.88/2.12 | | | GROUND_INST: instantiating (2) with all_15_4, all_15_1, all_33_0,
% 9.88/2.12 | | | simplifying with (13), (15), (69) gives:
% 9.88/2.12 | | | (73) all_33_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 9.88/2.12 | | | member(v0, all_15_1) = v1 & member(v0, all_15_4) = 0 & $i(v0))
% 9.88/2.12 | | |
% 9.88/2.13 | | | GROUND_INST: instantiating (2) with all_15_1, all_15_4, all_33_1,
% 9.88/2.13 | | | simplifying with (13), (15), (70) gives:
% 9.88/2.13 | | | (74) all_33_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 9.88/2.13 | | | member(v0, all_15_1) = 0 & member(v0, all_15_4) = v1 & $i(v0))
% 9.88/2.13 | | |
% 9.88/2.13 | | | BETA: splitting (71) gives:
% 9.88/2.13 | | |
% 9.88/2.13 | | | Case 1:
% 9.88/2.13 | | | |
% 9.88/2.13 | | | | (75) ~ (all_33_0 = 0)
% 9.88/2.13 | | | |
% 9.88/2.13 | | | | BETA: splitting (73) gives:
% 9.88/2.13 | | | |
% 9.88/2.13 | | | | Case 1:
% 9.88/2.13 | | | | |
% 9.88/2.13 | | | | | (76) all_33_0 = 0
% 9.88/2.13 | | | | |
% 9.88/2.13 | | | | | REDUCE: (75), (76) imply:
% 9.88/2.13 | | | | | (77) $false
% 9.88/2.13 | | | | |
% 9.88/2.13 | | | | | CLOSE: (77) is inconsistent.
% 9.88/2.13 | | | | |
% 9.88/2.13 | | | | Case 2:
% 9.88/2.13 | | | | |
% 9.88/2.13 | | | | | (78) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 9.88/2.13 | | | | | all_15_1) = v1 & member(v0, all_15_4) = 0 & $i(v0))
% 9.88/2.13 | | | | |
% 9.88/2.13 | | | | | DELTA: instantiating (78) with fresh symbols all_49_0, all_49_1 gives:
% 9.88/2.13 | | | | | (79) ~ (all_49_0 = 0) & member(all_49_1, all_15_1) = all_49_0 &
% 9.88/2.13 | | | | | member(all_49_1, all_15_4) = 0 & $i(all_49_1)
% 9.88/2.13 | | | | |
% 9.88/2.13 | | | | | ALPHA: (79) implies:
% 9.88/2.13 | | | | | (80) ~ (all_49_0 = 0)
% 9.88/2.13 | | | | | (81) $i(all_49_1)
% 9.88/2.13 | | | | | (82) member(all_49_1, all_15_4) = 0
% 9.88/2.13 | | | | | (83) member(all_49_1, all_15_1) = all_49_0
% 9.88/2.13 | | | | |
% 9.88/2.13 | | | | | GROUND_INST: instantiating (6) with all_49_1, all_15_2, all_15_5,
% 9.88/2.13 | | | | | all_15_1, all_49_0, simplifying with (12), (14), (20),
% 9.88/2.13 | | | | | (81), (83) gives:
% 9.88/2.13 | | | | | (84) all_49_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~
% 9.88/2.13 | | | | | (v0 = 0) & member(all_49_1, all_15_2) = v0 &
% 9.88/2.13 | | | | | member(all_49_1, all_15_5) = v1)
% 9.88/2.13 | | | | |
% 9.88/2.13 | | | | | BETA: splitting (84) gives:
% 9.88/2.13 | | | | |
% 9.88/2.13 | | | | | Case 1:
% 9.88/2.13 | | | | | |
% 9.88/2.13 | | | | | | (85) all_49_0 = 0
% 9.88/2.13 | | | | | |
% 9.88/2.13 | | | | | | REDUCE: (80), (85) imply:
% 9.88/2.13 | | | | | | (86) $false
% 9.88/2.13 | | | | | |
% 9.88/2.13 | | | | | | CLOSE: (86) is inconsistent.
% 9.88/2.13 | | | | | |
% 9.88/2.13 | | | | | Case 2:
% 9.88/2.13 | | | | | |
% 9.88/2.13 | | | | | | (87) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) &
% 9.88/2.13 | | | | | | member(all_49_1, all_15_2) = v0 & member(all_49_1,
% 9.88/2.13 | | | | | | all_15_5) = v1)
% 9.88/2.13 | | | | | |
% 9.88/2.13 | | | | | | DELTA: instantiating (87) with fresh symbols all_62_0, all_62_1
% 9.88/2.13 | | | | | | gives:
% 9.88/2.13 | | | | | | (88) ~ (all_62_0 = 0) & ~ (all_62_1 = 0) & member(all_49_1,
% 9.88/2.13 | | | | | | all_15_2) = all_62_1 & member(all_49_1, all_15_5) =
% 9.88/2.13 | | | | | | all_62_0
% 9.88/2.13 | | | | | |
% 9.88/2.13 | | | | | | ALPHA: (88) implies:
% 9.88/2.13 | | | | | | (89) ~ (all_62_1 = 0)
% 9.88/2.13 | | | | | | (90) ~ (all_62_0 = 0)
% 9.88/2.13 | | | | | | (91) member(all_49_1, all_15_5) = all_62_0
% 9.88/2.13 | | | | | | (92) member(all_49_1, all_15_2) = all_62_1
% 9.88/2.13 | | | | | |
% 9.88/2.13 | | | | | | GROUND_INST: instantiating (8) with all_49_1, all_15_6, all_15_4,
% 9.88/2.13 | | | | | | all_15_2, all_62_1, simplifying with (11), (13), (21),
% 9.88/2.13 | | | | | | (81), (92) gives:
% 9.88/2.13 | | | | | | (93) all_62_1 = 0 | ? [v0: any] : ? [v1: any] :
% 9.88/2.13 | | | | | | (member(all_49_1, all_15_4) = v0 & member(all_49_1,
% 9.88/2.13 | | | | | | all_15_6) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 9.88/2.13 | | | | | |
% 9.88/2.13 | | | | | | BETA: splitting (93) gives:
% 9.88/2.13 | | | | | |
% 9.88/2.13 | | | | | | Case 1:
% 9.88/2.13 | | | | | | |
% 9.88/2.13 | | | | | | | (94) all_62_1 = 0
% 9.88/2.13 | | | | | | |
% 9.88/2.13 | | | | | | | REDUCE: (89), (94) imply:
% 9.88/2.13 | | | | | | | (95) $false
% 9.88/2.13 | | | | | | |
% 9.88/2.13 | | | | | | | CLOSE: (95) is inconsistent.
% 9.88/2.13 | | | | | | |
% 9.88/2.13 | | | | | | Case 2:
% 9.88/2.13 | | | | | | |
% 9.88/2.13 | | | | | | | (96) ? [v0: any] : ? [v1: any] : (member(all_49_1, all_15_4)
% 9.88/2.13 | | | | | | | = v0 & member(all_49_1, all_15_6) = v1 & ( ~ (v0 = 0) |
% 9.88/2.13 | | | | | | | v1 = 0))
% 9.88/2.13 | | | | | | |
% 9.88/2.13 | | | | | | | DELTA: instantiating (96) with fresh symbols all_74_0, all_74_1
% 9.88/2.13 | | | | | | | gives:
% 9.88/2.13 | | | | | | | (97) member(all_49_1, all_15_4) = all_74_1 & member(all_49_1,
% 9.88/2.13 | | | | | | | all_15_6) = all_74_0 & ( ~ (all_74_1 = 0) | all_74_0 =
% 9.88/2.13 | | | | | | | 0)
% 9.88/2.13 | | | | | | |
% 9.88/2.13 | | | | | | | ALPHA: (97) implies:
% 9.88/2.14 | | | | | | | (98) member(all_49_1, all_15_6) = all_74_0
% 9.88/2.14 | | | | | | | (99) member(all_49_1, all_15_4) = all_74_1
% 9.88/2.14 | | | | | | | (100) ~ (all_74_1 = 0) | all_74_0 = 0
% 9.88/2.14 | | | | | | |
% 9.88/2.14 | | | | | | | GROUND_INST: instantiating (9) with 0, all_74_1, all_15_4,
% 9.88/2.14 | | | | | | | all_49_1, simplifying with (82), (99) gives:
% 9.88/2.14 | | | | | | | (101) all_74_1 = 0
% 9.88/2.14 | | | | | | |
% 9.88/2.14 | | | | | | | BETA: splitting (100) gives:
% 9.88/2.14 | | | | | | |
% 9.88/2.14 | | | | | | | Case 1:
% 9.88/2.14 | | | | | | | |
% 9.88/2.14 | | | | | | | | (102) ~ (all_74_1 = 0)
% 9.88/2.14 | | | | | | | |
% 9.88/2.14 | | | | | | | | REDUCE: (101), (102) imply:
% 9.88/2.14 | | | | | | | | (103) $false
% 9.88/2.14 | | | | | | | |
% 9.88/2.14 | | | | | | | | CLOSE: (103) is inconsistent.
% 9.88/2.14 | | | | | | | |
% 9.88/2.14 | | | | | | | Case 2:
% 9.88/2.14 | | | | | | | |
% 9.88/2.14 | | | | | | | | (104) all_74_0 = 0
% 9.88/2.14 | | | | | | | |
% 9.88/2.14 | | | | | | | | REDUCE: (98), (104) imply:
% 9.88/2.14 | | | | | | | | (105) member(all_49_1, all_15_6) = 0
% 9.88/2.14 | | | | | | | |
% 9.88/2.14 | | | | | | | | GROUND_INST: instantiating (72) with all_49_1, simplifying with
% 9.88/2.14 | | | | | | | | (81), (105) gives:
% 9.88/2.14 | | | | | | | | (106) member(all_49_1, all_15_5) = 0
% 9.88/2.14 | | | | | | | |
% 9.88/2.14 | | | | | | | | GROUND_INST: instantiating (9) with all_62_0, 0, all_15_5,
% 9.88/2.14 | | | | | | | | all_49_1, simplifying with (91), (106) gives:
% 9.88/2.14 | | | | | | | | (107) all_62_0 = 0
% 9.88/2.14 | | | | | | | |
% 9.88/2.14 | | | | | | | | REDUCE: (90), (107) imply:
% 9.88/2.14 | | | | | | | | (108) $false
% 9.88/2.14 | | | | | | | |
% 9.88/2.14 | | | | | | | | CLOSE: (108) is inconsistent.
% 9.88/2.14 | | | | | | | |
% 9.88/2.14 | | | | | | | End of split
% 9.88/2.14 | | | | | | |
% 9.88/2.14 | | | | | | End of split
% 9.88/2.14 | | | | | |
% 9.88/2.14 | | | | | End of split
% 9.88/2.14 | | | | |
% 9.88/2.14 | | | | End of split
% 9.88/2.14 | | | |
% 9.88/2.14 | | | Case 2:
% 9.88/2.14 | | | |
% 9.88/2.14 | | | | (109) ~ (all_33_1 = 0)
% 9.88/2.14 | | | |
% 9.88/2.14 | | | | BETA: splitting (74) gives:
% 9.88/2.14 | | | |
% 9.88/2.14 | | | | Case 1:
% 9.88/2.14 | | | | |
% 9.88/2.14 | | | | | (110) all_33_1 = 0
% 9.88/2.14 | | | | |
% 9.88/2.14 | | | | | REDUCE: (109), (110) imply:
% 9.88/2.14 | | | | | (111) $false
% 9.88/2.14 | | | | |
% 9.88/2.14 | | | | | CLOSE: (111) is inconsistent.
% 9.88/2.14 | | | | |
% 9.88/2.14 | | | | Case 2:
% 9.88/2.14 | | | | |
% 9.88/2.14 | | | | | (112) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 9.88/2.14 | | | | | all_15_1) = 0 & member(v0, all_15_4) = v1 & $i(v0))
% 9.88/2.14 | | | | |
% 9.88/2.14 | | | | | DELTA: instantiating (112) with fresh symbols all_49_0, all_49_1
% 9.88/2.14 | | | | | gives:
% 9.88/2.14 | | | | | (113) ~ (all_49_0 = 0) & member(all_49_1, all_15_1) = 0 &
% 9.88/2.14 | | | | | member(all_49_1, all_15_4) = all_49_0 & $i(all_49_1)
% 9.88/2.14 | | | | |
% 9.88/2.14 | | | | | ALPHA: (113) implies:
% 9.88/2.14 | | | | | (114) ~ (all_49_0 = 0)
% 9.88/2.14 | | | | | (115) $i(all_49_1)
% 9.88/2.14 | | | | | (116) member(all_49_1, all_15_4) = all_49_0
% 9.88/2.14 | | | | | (117) member(all_49_1, all_15_1) = 0
% 9.88/2.14 | | | | |
% 9.88/2.14 | | | | | GROUND_INST: instantiating (5) with all_49_1, all_15_2, all_15_5,
% 9.88/2.14 | | | | | all_15_1, simplifying with (12), (14), (20), (115), (117)
% 9.88/2.14 | | | | | gives:
% 9.88/2.14 | | | | | (118) ? [v0: any] : ? [v1: any] : (member(all_49_1, all_15_2) =
% 9.88/2.14 | | | | | v0 & member(all_49_1, all_15_5) = v1 & (v1 = 0 | v0 = 0))
% 9.88/2.14 | | | | |
% 9.88/2.14 | | | | | DELTA: instantiating (118) with fresh symbols all_57_0, all_57_1
% 9.88/2.14 | | | | | gives:
% 9.88/2.14 | | | | | (119) member(all_49_1, all_15_2) = all_57_1 & member(all_49_1,
% 9.88/2.14 | | | | | all_15_5) = all_57_0 & (all_57_0 = 0 | all_57_1 = 0)
% 9.88/2.14 | | | | |
% 9.88/2.14 | | | | | ALPHA: (119) implies:
% 9.88/2.14 | | | | | (120) member(all_49_1, all_15_5) = all_57_0
% 9.88/2.14 | | | | | (121) member(all_49_1, all_15_2) = all_57_1
% 9.88/2.14 | | | | | (122) all_57_0 = 0 | all_57_1 = 0
% 9.88/2.14 | | | | |
% 9.88/2.14 | | | | | BETA: splitting (122) gives:
% 9.88/2.14 | | | | |
% 9.88/2.14 | | | | | Case 1:
% 9.88/2.14 | | | | | |
% 9.88/2.14 | | | | | | (123) all_57_0 = 0
% 9.88/2.14 | | | | | |
% 9.88/2.14 | | | | | | REDUCE: (120), (123) imply:
% 9.88/2.14 | | | | | | (124) member(all_49_1, all_15_5) = 0
% 9.88/2.14 | | | | | |
% 9.88/2.14 | | | | | | GROUND_INST: instantiating (25) with all_49_1, simplifying with
% 9.88/2.14 | | | | | | (115), (124) gives:
% 9.88/2.14 | | | | | | (125) member(all_49_1, all_15_4) = 0
% 9.88/2.14 | | | | | |
% 9.88/2.14 | | | | | | GROUND_INST: instantiating (9) with all_49_0, 0, all_15_4, all_49_1,
% 9.88/2.14 | | | | | | simplifying with (116), (125) gives:
% 9.88/2.14 | | | | | | (126) all_49_0 = 0
% 9.88/2.14 | | | | | |
% 9.88/2.14 | | | | | | REDUCE: (114), (126) imply:
% 9.88/2.14 | | | | | | (127) $false
% 9.88/2.14 | | | | | |
% 9.88/2.14 | | | | | | CLOSE: (127) is inconsistent.
% 9.88/2.14 | | | | | |
% 9.88/2.14 | | | | | Case 2:
% 9.88/2.14 | | | | | |
% 9.88/2.15 | | | | | | (128) all_57_1 = 0
% 9.88/2.15 | | | | | |
% 9.88/2.15 | | | | | | REDUCE: (121), (128) imply:
% 9.88/2.15 | | | | | | (129) member(all_49_1, all_15_2) = 0
% 9.88/2.15 | | | | | |
% 9.88/2.15 | | | | | | GROUND_INST: instantiating (7) with all_49_1, all_15_6, all_15_4,
% 9.88/2.15 | | | | | | all_15_2, simplifying with (11), (13), (21), (115),
% 9.88/2.15 | | | | | | (129) gives:
% 9.88/2.15 | | | | | | (130) ? [v0: int] : ( ~ (v0 = 0) & member(all_49_1, all_15_4) =
% 9.88/2.15 | | | | | | 0 & member(all_49_1, all_15_6) = v0)
% 9.88/2.15 | | | | | |
% 9.88/2.15 | | | | | | DELTA: instantiating (130) with fresh symbol all_71_0 gives:
% 9.88/2.15 | | | | | | (131) ~ (all_71_0 = 0) & member(all_49_1, all_15_4) = 0 &
% 9.88/2.15 | | | | | | member(all_49_1, all_15_6) = all_71_0
% 9.88/2.15 | | | | | |
% 9.88/2.15 | | | | | | ALPHA: (131) implies:
% 9.88/2.15 | | | | | | (132) member(all_49_1, all_15_4) = 0
% 9.88/2.15 | | | | | |
% 9.88/2.15 | | | | | | GROUND_INST: instantiating (9) with all_49_0, 0, all_15_4, all_49_1,
% 9.88/2.15 | | | | | | simplifying with (116), (132) gives:
% 9.88/2.15 | | | | | | (133) all_49_0 = 0
% 9.88/2.15 | | | | | |
% 9.88/2.15 | | | | | | REDUCE: (114), (133) imply:
% 9.88/2.15 | | | | | | (134) $false
% 9.88/2.15 | | | | | |
% 9.88/2.15 | | | | | | CLOSE: (134) is inconsistent.
% 9.88/2.15 | | | | | |
% 9.88/2.15 | | | | | End of split
% 9.88/2.15 | | | | |
% 9.88/2.15 | | | | End of split
% 9.88/2.15 | | | |
% 9.88/2.15 | | | End of split
% 9.88/2.15 | | |
% 9.88/2.15 | | End of split
% 9.88/2.15 | |
% 9.88/2.15 | End of split
% 9.88/2.15 |
% 9.88/2.15 End of proof
% 9.88/2.15 % SZS output end Proof for theBenchmark
% 9.88/2.15
% 9.88/2.15 1534ms
%------------------------------------------------------------------------------