TSTP Solution File: SET358+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET358+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 : n011.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 15:24:44 EDT 2023
% Result : Theorem 8.39s 1.91s
% Output : Proof 10.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET358+4 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 09:58:39 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.62 Running up to 7 provers in parallel.
% 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.44/1.05 Prover 4: Preprocessing ...
% 2.44/1.05 Prover 1: Preprocessing ...
% 2.63/1.11 Prover 3: Preprocessing ...
% 2.63/1.11 Prover 5: Preprocessing ...
% 2.63/1.11 Prover 2: Preprocessing ...
% 2.63/1.11 Prover 0: Preprocessing ...
% 2.63/1.11 Prover 6: Preprocessing ...
% 5.34/1.47 Prover 1: Constructing countermodel ...
% 5.34/1.48 Prover 3: Constructing countermodel ...
% 5.34/1.49 Prover 6: Proving ...
% 5.34/1.49 Prover 5: Proving ...
% 5.34/1.50 Prover 2: Proving ...
% 5.34/1.51 Prover 0: Proving ...
% 5.87/1.56 Prover 4: Constructing countermodel ...
% 8.39/1.91 Prover 0: proved (1275ms)
% 8.39/1.91
% 8.39/1.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.39/1.91
% 8.39/1.91 Prover 3: stopped
% 8.39/1.92 Prover 2: stopped
% 8.39/1.92 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.39/1.92 Prover 6: stopped
% 8.39/1.92 Prover 5: stopped
% 8.39/1.92 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.39/1.92 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.39/1.92 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.39/1.92 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.39/1.95 Prover 11: Preprocessing ...
% 8.39/1.96 Prover 7: Preprocessing ...
% 8.39/1.96 Prover 8: Preprocessing ...
% 8.39/1.97 Prover 10: Preprocessing ...
% 8.39/1.97 Prover 13: Preprocessing ...
% 9.12/2.04 Prover 10: Warning: ignoring some quantifiers
% 9.62/2.06 Prover 7: Warning: ignoring some quantifiers
% 9.62/2.06 Prover 10: Constructing countermodel ...
% 9.62/2.06 Prover 13: Warning: ignoring some quantifiers
% 9.62/2.07 Prover 7: Constructing countermodel ...
% 9.99/2.10 Prover 10: gave up
% 9.99/2.11 Prover 13: Constructing countermodel ...
% 9.99/2.11 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 9.99/2.12 Prover 8: Warning: ignoring some quantifiers
% 9.99/2.12 Prover 16: Preprocessing ...
% 9.99/2.13 Prover 1: Found proof (size 107)
% 9.99/2.13 Prover 1: proved (1496ms)
% 9.99/2.13 Prover 7: stopped
% 9.99/2.13 Prover 4: stopped
% 9.99/2.13 Prover 13: stopped
% 9.99/2.13 Prover 8: Constructing countermodel ...
% 9.99/2.14 Prover 11: Constructing countermodel ...
% 9.99/2.14 Prover 8: stopped
% 9.99/2.14 Prover 16: stopped
% 9.99/2.14 Prover 11: stopped
% 9.99/2.14
% 9.99/2.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.99/2.14
% 10.35/2.16 % SZS output start Proof for theBenchmark
% 10.35/2.16 Assumptions after simplification:
% 10.35/2.16 ---------------------------------
% 10.35/2.16
% 10.35/2.16 (equal_set)
% 10.35/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) =
% 10.35/2.19 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1,
% 10.35/2.19 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0:
% 10.35/2.19 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 10.35/2.19 (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 10.35/2.19
% 10.35/2.19 (subset)
% 10.35/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 10.35/2.19 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 10.35/2.19 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 10.35/2.19 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 10.35/2.19 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 10.35/2.19
% 10.35/2.19 (sum)
% 10.35/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (sum(v1)
% 10.35/2.19 = v2) | ~ (member(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ! [v4: $i] : (
% 10.35/2.19 ~ (member(v0, v4) = 0) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) &
% 10.35/2.19 member(v4, v1) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 10.35/2.19 (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 10.35/2.19 $i] : (member(v3, v1) = 0 & member(v0, v3) = 0 & $i(v3)))
% 10.35/2.19
% 10.35/2.19 (thI37)
% 10.35/2.19 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 10.35/2.19 $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & sum(v5) = v6 & sum(v1) =
% 10.35/2.20 v3 & sum(v0) = v2 & union(v2, v3) = v4 & union(v0, v1) = v5 & equal_set(v4,
% 10.35/2.20 v6) = v7 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 10.35/2.20
% 10.35/2.20 (union)
% 10.35/2.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 10.35/2.20 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1)
% 10.35/2.20 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) &
% 10.35/2.20 member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] :
% 10.35/2.20 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0)
% 10.35/2.20 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 10.35/2.20 (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0)))
% 10.35/2.20
% 10.35/2.20 (function-axioms)
% 10.35/2.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.35/2.20 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 10.35/2.20 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.35/2.20 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 10.35/2.20 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 10.35/2.20 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 10.35/2.20 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 10.35/2.20 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 10.35/2.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 10.35/2.20 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.35/2.20 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 10.35/2.20 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 10.35/2.20 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.35/2.20 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 10.35/2.20 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 10.35/2.20 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 10.35/2.20 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 10.35/2.20 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 10.35/2.20 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 10.35/2.20 (power_set(v2) = v0))
% 10.35/2.20
% 10.35/2.20 Further assumptions not needed in the proof:
% 10.35/2.20 --------------------------------------------
% 10.35/2.20 difference, empty_set, intersection, power_set, product, singleton,
% 10.35/2.20 unordered_pair
% 10.35/2.20
% 10.35/2.20 Those formulas are unsatisfiable:
% 10.35/2.20 ---------------------------------
% 10.35/2.20
% 10.35/2.20 Begin of proof
% 10.35/2.20 |
% 10.35/2.20 | ALPHA: (subset) implies:
% 10.35/2.21 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 10.35/2.21 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 10.35/2.21 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 10.35/2.21 |
% 10.35/2.21 | ALPHA: (equal_set) implies:
% 10.35/2.21 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0,
% 10.35/2.21 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 10.35/2.21 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 =
% 10.35/2.21 | 0))))
% 10.35/2.21 |
% 10.35/2.21 | ALPHA: (union) implies:
% 10.35/2.21 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1,
% 10.35/2.21 | v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 10.35/2.21 | $i(v0) | ? [v4: any] : ? [v5: any] : (member(v0, v2) = v5 &
% 10.35/2.21 | member(v0, v1) = v4 & (v5 = 0 | v4 = 0)))
% 10.35/2.21 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 10.35/2.21 | (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~
% 10.35/2.21 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~
% 10.35/2.21 | (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) =
% 10.35/2.21 | v5))
% 10.35/2.21 |
% 10.35/2.21 | ALPHA: (sum) implies:
% 10.35/2.21 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sum(v1) = v2) | ~
% 10.35/2.21 | (member(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 10.35/2.21 | (member(v3, v1) = 0 & member(v0, v3) = 0 & $i(v3)))
% 10.35/2.21 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 10.35/2.21 | (sum(v1) = v2) | ~ (member(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) |
% 10.35/2.21 | ! [v4: $i] : ( ~ (member(v0, v4) = 0) | ~ $i(v4) | ? [v5: int] : (
% 10.35/2.21 | ~ (v5 = 0) & member(v4, v1) = v5)))
% 10.35/2.21 |
% 10.35/2.21 | ALPHA: (function-axioms) implies:
% 10.35/2.21 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.35/2.21 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 10.35/2.21 | = v0))
% 10.35/2.21 |
% 10.35/2.21 | DELTA: instantiating (thI37) with fresh symbols all_15_0, all_15_1, all_15_2,
% 10.35/2.21 | all_15_3, all_15_4, all_15_5, all_15_6, all_15_7 gives:
% 10.35/2.21 | (8) ~ (all_15_0 = 0) & sum(all_15_2) = all_15_1 & sum(all_15_6) = all_15_4
% 10.35/2.21 | & sum(all_15_7) = all_15_5 & union(all_15_5, all_15_4) = all_15_3 &
% 10.35/2.21 | union(all_15_7, all_15_6) = all_15_2 & equal_set(all_15_3, all_15_1) =
% 10.35/2.21 | all_15_0 & $i(all_15_1) & $i(all_15_2) & $i(all_15_3) & $i(all_15_4) &
% 10.35/2.21 | $i(all_15_5) & $i(all_15_6) & $i(all_15_7)
% 10.35/2.21 |
% 10.35/2.21 | ALPHA: (8) implies:
% 10.35/2.21 | (9) ~ (all_15_0 = 0)
% 10.35/2.21 | (10) $i(all_15_7)
% 10.35/2.21 | (11) $i(all_15_6)
% 10.35/2.22 | (12) $i(all_15_5)
% 10.35/2.22 | (13) $i(all_15_4)
% 10.35/2.22 | (14) $i(all_15_3)
% 10.35/2.22 | (15) $i(all_15_2)
% 10.35/2.22 | (16) $i(all_15_1)
% 10.35/2.22 | (17) equal_set(all_15_3, all_15_1) = all_15_0
% 10.35/2.22 | (18) union(all_15_7, all_15_6) = all_15_2
% 10.35/2.22 | (19) union(all_15_5, all_15_4) = all_15_3
% 10.35/2.22 | (20) sum(all_15_7) = all_15_5
% 10.35/2.22 | (21) sum(all_15_6) = all_15_4
% 10.35/2.22 | (22) sum(all_15_2) = all_15_1
% 10.35/2.22 |
% 10.35/2.22 | GROUND_INST: instantiating (2) with all_15_3, all_15_1, all_15_0, simplifying
% 10.35/2.22 | with (14), (16), (17) gives:
% 10.35/2.22 | (23) all_15_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_1,
% 10.35/2.22 | all_15_3) = v1 & subset(all_15_3, all_15_1) = v0 & ( ~ (v1 = 0) |
% 10.35/2.22 | ~ (v0 = 0)))
% 10.35/2.22 |
% 10.35/2.22 | BETA: splitting (23) gives:
% 10.35/2.22 |
% 10.35/2.22 | Case 1:
% 10.35/2.22 | |
% 10.35/2.22 | | (24) all_15_0 = 0
% 10.35/2.22 | |
% 10.35/2.22 | | REDUCE: (9), (24) imply:
% 10.35/2.22 | | (25) $false
% 10.35/2.22 | |
% 10.35/2.22 | | CLOSE: (25) is inconsistent.
% 10.35/2.22 | |
% 10.35/2.22 | Case 2:
% 10.35/2.22 | |
% 10.35/2.22 | | (26) ? [v0: any] : ? [v1: any] : (subset(all_15_1, all_15_3) = v1 &
% 10.35/2.22 | | subset(all_15_3, all_15_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 10.35/2.22 | |
% 10.35/2.22 | | DELTA: instantiating (26) with fresh symbols all_24_0, all_24_1 gives:
% 10.35/2.22 | | (27) subset(all_15_1, all_15_3) = all_24_0 & subset(all_15_3, all_15_1) =
% 10.35/2.22 | | all_24_1 & ( ~ (all_24_0 = 0) | ~ (all_24_1 = 0))
% 10.35/2.22 | |
% 10.35/2.22 | | ALPHA: (27) implies:
% 10.35/2.22 | | (28) subset(all_15_3, all_15_1) = all_24_1
% 10.35/2.22 | | (29) subset(all_15_1, all_15_3) = all_24_0
% 10.35/2.22 | | (30) ~ (all_24_0 = 0) | ~ (all_24_1 = 0)
% 10.35/2.22 | |
% 10.35/2.22 | | GROUND_INST: instantiating (1) with all_15_3, all_15_1, all_24_1,
% 10.35/2.22 | | simplifying with (14), (16), (28) gives:
% 10.35/2.22 | | (31) all_24_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 10.35/2.22 | | member(v0, all_15_1) = v1 & member(v0, all_15_3) = 0 & $i(v0))
% 10.35/2.22 | |
% 10.35/2.22 | | GROUND_INST: instantiating (1) with all_15_1, all_15_3, all_24_0,
% 10.35/2.22 | | simplifying with (14), (16), (29) gives:
% 10.35/2.22 | | (32) all_24_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 10.35/2.22 | | member(v0, all_15_1) = 0 & member(v0, all_15_3) = v1 & $i(v0))
% 10.35/2.22 | |
% 10.35/2.22 | | BETA: splitting (30) gives:
% 10.35/2.22 | |
% 10.35/2.22 | | Case 1:
% 10.35/2.22 | | |
% 10.35/2.22 | | | (33) ~ (all_24_0 = 0)
% 10.35/2.22 | | |
% 10.35/2.22 | | | BETA: splitting (32) gives:
% 10.35/2.22 | | |
% 10.35/2.22 | | | Case 1:
% 10.35/2.22 | | | |
% 10.35/2.22 | | | | (34) all_24_0 = 0
% 10.35/2.22 | | | |
% 10.35/2.22 | | | | REDUCE: (33), (34) imply:
% 10.35/2.22 | | | | (35) $false
% 10.35/2.22 | | | |
% 10.35/2.22 | | | | CLOSE: (35) is inconsistent.
% 10.35/2.22 | | | |
% 10.35/2.22 | | | Case 2:
% 10.35/2.22 | | | |
% 10.35/2.22 | | | | (36) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1)
% 10.35/2.22 | | | | = 0 & member(v0, all_15_3) = v1 & $i(v0))
% 10.35/2.22 | | | |
% 10.35/2.22 | | | | DELTA: instantiating (36) with fresh symbols all_37_0, all_37_1 gives:
% 10.35/2.22 | | | | (37) ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = 0 &
% 10.35/2.22 | | | | member(all_37_1, all_15_3) = all_37_0 & $i(all_37_1)
% 10.35/2.22 | | | |
% 10.35/2.22 | | | | ALPHA: (37) implies:
% 10.35/2.22 | | | | (38) ~ (all_37_0 = 0)
% 10.35/2.23 | | | | (39) $i(all_37_1)
% 10.35/2.23 | | | | (40) member(all_37_1, all_15_3) = all_37_0
% 10.35/2.23 | | | | (41) member(all_37_1, all_15_1) = 0
% 10.35/2.23 | | | |
% 10.35/2.23 | | | | GROUND_INST: instantiating (4) with all_37_1, all_15_5, all_15_4,
% 10.35/2.23 | | | | all_15_3, all_37_0, simplifying with (12), (13), (19),
% 10.35/2.23 | | | | (39), (40) gives:
% 10.35/2.23 | | | | (42) all_37_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~
% 10.35/2.23 | | | | (v0 = 0) & member(all_37_1, all_15_4) = v1 & member(all_37_1,
% 10.35/2.23 | | | | all_15_5) = v0)
% 10.35/2.23 | | | |
% 10.35/2.23 | | | | GROUND_INST: instantiating (5) with all_37_1, all_15_2, all_15_1,
% 10.35/2.23 | | | | simplifying with (15), (22), (39), (41) gives:
% 10.35/2.23 | | | | (43) ? [v0: $i] : (member(v0, all_15_2) = 0 & member(all_37_1, v0) =
% 10.35/2.23 | | | | 0 & $i(v0))
% 10.35/2.23 | | | |
% 10.35/2.23 | | | | DELTA: instantiating (43) with fresh symbol all_44_0 gives:
% 10.35/2.23 | | | | (44) member(all_44_0, all_15_2) = 0 & member(all_37_1, all_44_0) = 0
% 10.35/2.23 | | | | & $i(all_44_0)
% 10.35/2.23 | | | |
% 10.35/2.23 | | | | ALPHA: (44) implies:
% 10.35/2.23 | | | | (45) $i(all_44_0)
% 10.35/2.23 | | | | (46) member(all_37_1, all_44_0) = 0
% 10.35/2.23 | | | | (47) member(all_44_0, all_15_2) = 0
% 10.35/2.23 | | | |
% 10.35/2.23 | | | | BETA: splitting (42) gives:
% 10.35/2.23 | | | |
% 10.35/2.23 | | | | Case 1:
% 10.35/2.23 | | | | |
% 10.35/2.23 | | | | | (48) all_37_0 = 0
% 10.35/2.23 | | | | |
% 10.35/2.23 | | | | | REDUCE: (38), (48) imply:
% 10.35/2.23 | | | | | (49) $false
% 10.35/2.23 | | | | |
% 10.35/2.23 | | | | | CLOSE: (49) is inconsistent.
% 10.35/2.23 | | | | |
% 10.35/2.23 | | | | Case 2:
% 10.35/2.23 | | | | |
% 10.35/2.23 | | | | | (50) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) &
% 10.35/2.23 | | | | | member(all_37_1, all_15_4) = v1 & member(all_37_1, all_15_5)
% 10.35/2.23 | | | | | = v0)
% 10.35/2.23 | | | | |
% 10.35/2.23 | | | | | DELTA: instantiating (50) with fresh symbols all_50_0, all_50_1 gives:
% 10.35/2.23 | | | | | (51) ~ (all_50_0 = 0) & ~ (all_50_1 = 0) & member(all_37_1,
% 10.35/2.23 | | | | | all_15_4) = all_50_0 & member(all_37_1, all_15_5) = all_50_1
% 10.35/2.23 | | | | |
% 10.35/2.23 | | | | | ALPHA: (51) implies:
% 10.35/2.23 | | | | | (52) ~ (all_50_1 = 0)
% 10.35/2.23 | | | | | (53) ~ (all_50_0 = 0)
% 10.35/2.23 | | | | | (54) member(all_37_1, all_15_5) = all_50_1
% 10.35/2.23 | | | | | (55) member(all_37_1, all_15_4) = all_50_0
% 10.35/2.23 | | | | |
% 10.35/2.23 | | | | | GROUND_INST: instantiating (6) with all_37_1, all_15_7, all_15_5,
% 10.35/2.23 | | | | | all_50_1, simplifying with (10), (20), (39), (54) gives:
% 10.35/2.23 | | | | | (56) all_50_1 = 0 | ! [v0: $i] : ( ~ (member(all_37_1, v0) = 0) |
% 10.35/2.23 | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 10.35/2.23 | | | | | all_15_7) = v1))
% 10.35/2.23 | | | | |
% 10.35/2.23 | | | | | GROUND_INST: instantiating (6) with all_37_1, all_15_6, all_15_4,
% 10.35/2.23 | | | | | all_50_0, simplifying with (11), (21), (39), (55) gives:
% 10.35/2.23 | | | | | (57) all_50_0 = 0 | ! [v0: $i] : ( ~ (member(all_37_1, v0) = 0) |
% 10.35/2.23 | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 10.35/2.23 | | | | | all_15_6) = v1))
% 10.35/2.23 | | | | |
% 10.35/2.23 | | | | | GROUND_INST: instantiating (3) with all_44_0, all_15_7, all_15_6,
% 10.35/2.23 | | | | | all_15_2, simplifying with (10), (11), (18), (45), (47)
% 10.35/2.23 | | | | | gives:
% 10.35/2.23 | | | | | (58) ? [v0: any] : ? [v1: any] : (member(all_44_0, all_15_6) = v1
% 10.35/2.23 | | | | | & member(all_44_0, all_15_7) = v0 & (v1 = 0 | v0 = 0))
% 10.35/2.23 | | | | |
% 10.35/2.23 | | | | | DELTA: instantiating (58) with fresh symbols all_57_0, all_57_1 gives:
% 10.35/2.23 | | | | | (59) member(all_44_0, all_15_6) = all_57_0 & member(all_44_0,
% 10.35/2.23 | | | | | all_15_7) = all_57_1 & (all_57_0 = 0 | all_57_1 = 0)
% 10.35/2.23 | | | | |
% 10.35/2.23 | | | | | ALPHA: (59) implies:
% 10.35/2.24 | | | | | (60) member(all_44_0, all_15_7) = all_57_1
% 10.35/2.24 | | | | | (61) member(all_44_0, all_15_6) = all_57_0
% 10.35/2.24 | | | | | (62) all_57_0 = 0 | all_57_1 = 0
% 10.35/2.24 | | | | |
% 10.35/2.24 | | | | | BETA: splitting (56) gives:
% 10.35/2.24 | | | | |
% 10.35/2.24 | | | | | Case 1:
% 10.35/2.24 | | | | | |
% 10.35/2.24 | | | | | | (63) all_50_1 = 0
% 10.35/2.24 | | | | | |
% 10.35/2.24 | | | | | | REDUCE: (52), (63) imply:
% 10.35/2.24 | | | | | | (64) $false
% 10.35/2.24 | | | | | |
% 10.35/2.24 | | | | | | CLOSE: (64) is inconsistent.
% 10.35/2.24 | | | | | |
% 10.35/2.24 | | | | | Case 2:
% 10.35/2.24 | | | | | |
% 10.35/2.24 | | | | | | (65) ! [v0: $i] : ( ~ (member(all_37_1, v0) = 0) | ~ $i(v0) |
% 10.35/2.24 | | | | | | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_7) = v1))
% 10.35/2.24 | | | | | |
% 10.35/2.24 | | | | | | GROUND_INST: instantiating (65) with all_44_0, simplifying with
% 10.35/2.24 | | | | | | (45), (46) gives:
% 10.35/2.24 | | | | | | (66) ? [v0: int] : ( ~ (v0 = 0) & member(all_44_0, all_15_7) =
% 10.35/2.24 | | | | | | v0)
% 10.35/2.24 | | | | | |
% 10.35/2.24 | | | | | | BETA: splitting (57) gives:
% 10.35/2.24 | | | | | |
% 10.35/2.24 | | | | | | Case 1:
% 10.35/2.24 | | | | | | |
% 10.35/2.24 | | | | | | | (67) all_50_0 = 0
% 10.35/2.24 | | | | | | |
% 10.35/2.24 | | | | | | | REDUCE: (53), (67) imply:
% 10.35/2.24 | | | | | | | (68) $false
% 10.35/2.24 | | | | | | |
% 10.35/2.24 | | | | | | | CLOSE: (68) is inconsistent.
% 10.35/2.24 | | | | | | |
% 10.35/2.24 | | | | | | Case 2:
% 10.35/2.24 | | | | | | |
% 10.35/2.24 | | | | | | | (69) ! [v0: $i] : ( ~ (member(all_37_1, v0) = 0) | ~ $i(v0) |
% 10.35/2.24 | | | | | | | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_6) =
% 10.35/2.24 | | | | | | | v1))
% 10.35/2.24 | | | | | | |
% 10.35/2.24 | | | | | | | GROUND_INST: instantiating (69) with all_44_0, simplifying with
% 10.35/2.24 | | | | | | | (45), (46) gives:
% 10.35/2.24 | | | | | | | (70) ? [v0: int] : ( ~ (v0 = 0) & member(all_44_0, all_15_6) =
% 10.35/2.24 | | | | | | | v0)
% 10.35/2.24 | | | | | | |
% 10.35/2.24 | | | | | | | DELTA: instantiating (66) with fresh symbol all_68_0 gives:
% 10.35/2.24 | | | | | | | (71) ~ (all_68_0 = 0) & member(all_44_0, all_15_7) = all_68_0
% 10.35/2.24 | | | | | | |
% 10.35/2.24 | | | | | | | ALPHA: (71) implies:
% 10.35/2.24 | | | | | | | (72) ~ (all_68_0 = 0)
% 10.35/2.24 | | | | | | | (73) member(all_44_0, all_15_7) = all_68_0
% 10.35/2.24 | | | | | | |
% 10.35/2.24 | | | | | | | DELTA: instantiating (70) with fresh symbol all_72_0 gives:
% 10.35/2.24 | | | | | | | (74) ~ (all_72_0 = 0) & member(all_44_0, all_15_6) = all_72_0
% 10.35/2.24 | | | | | | |
% 10.35/2.24 | | | | | | | ALPHA: (74) implies:
% 10.35/2.24 | | | | | | | (75) ~ (all_72_0 = 0)
% 10.35/2.24 | | | | | | | (76) member(all_44_0, all_15_6) = all_72_0
% 10.35/2.24 | | | | | | |
% 10.35/2.24 | | | | | | | GROUND_INST: instantiating (7) with all_57_1, all_68_0, all_15_7,
% 10.35/2.24 | | | | | | | all_44_0, simplifying with (60), (73) gives:
% 10.35/2.24 | | | | | | | (77) all_68_0 = all_57_1
% 10.35/2.24 | | | | | | |
% 10.35/2.24 | | | | | | | GROUND_INST: instantiating (7) with all_57_0, all_72_0, all_15_6,
% 10.35/2.24 | | | | | | | all_44_0, simplifying with (61), (76) gives:
% 10.35/2.24 | | | | | | | (78) all_72_0 = all_57_0
% 10.35/2.24 | | | | | | |
% 10.35/2.24 | | | | | | | REDUCE: (75), (78) imply:
% 10.35/2.24 | | | | | | | (79) ~ (all_57_0 = 0)
% 10.35/2.24 | | | | | | |
% 10.35/2.24 | | | | | | | REDUCE: (72), (77) imply:
% 10.35/2.24 | | | | | | | (80) ~ (all_57_1 = 0)
% 10.35/2.24 | | | | | | |
% 10.35/2.24 | | | | | | | BETA: splitting (62) gives:
% 10.35/2.24 | | | | | | |
% 10.35/2.24 | | | | | | | Case 1:
% 10.35/2.24 | | | | | | | |
% 10.35/2.24 | | | | | | | | (81) all_57_0 = 0
% 10.35/2.24 | | | | | | | |
% 10.35/2.24 | | | | | | | | REDUCE: (79), (81) imply:
% 10.35/2.24 | | | | | | | | (82) $false
% 10.35/2.24 | | | | | | | |
% 10.35/2.24 | | | | | | | | CLOSE: (82) is inconsistent.
% 10.35/2.24 | | | | | | | |
% 10.35/2.24 | | | | | | | Case 2:
% 10.35/2.24 | | | | | | | |
% 10.35/2.24 | | | | | | | | (83) all_57_1 = 0
% 10.35/2.24 | | | | | | | |
% 10.35/2.24 | | | | | | | | REDUCE: (80), (83) imply:
% 10.35/2.24 | | | | | | | | (84) $false
% 10.35/2.24 | | | | | | | |
% 10.35/2.24 | | | | | | | | CLOSE: (84) is inconsistent.
% 10.35/2.24 | | | | | | | |
% 10.35/2.24 | | | | | | | End of split
% 10.35/2.24 | | | | | | |
% 10.35/2.24 | | | | | | End of split
% 10.35/2.24 | | | | | |
% 10.35/2.24 | | | | | End of split
% 10.35/2.24 | | | | |
% 10.35/2.24 | | | | End of split
% 10.35/2.24 | | | |
% 10.35/2.24 | | | End of split
% 10.35/2.24 | | |
% 10.35/2.24 | | Case 2:
% 10.35/2.24 | | |
% 10.35/2.24 | | | (85) ~ (all_24_1 = 0)
% 10.35/2.24 | | |
% 10.35/2.24 | | | BETA: splitting (31) gives:
% 10.35/2.24 | | |
% 10.35/2.24 | | | Case 1:
% 10.35/2.24 | | | |
% 10.35/2.24 | | | | (86) all_24_1 = 0
% 10.35/2.24 | | | |
% 10.35/2.24 | | | | REDUCE: (85), (86) imply:
% 10.35/2.24 | | | | (87) $false
% 10.35/2.24 | | | |
% 10.35/2.24 | | | | CLOSE: (87) is inconsistent.
% 10.35/2.24 | | | |
% 10.35/2.24 | | | Case 2:
% 10.35/2.24 | | | |
% 10.35/2.24 | | | | (88) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1)
% 10.35/2.24 | | | | = v1 & member(v0, all_15_3) = 0 & $i(v0))
% 10.35/2.24 | | | |
% 10.35/2.24 | | | | DELTA: instantiating (88) with fresh symbols all_37_0, all_37_1 gives:
% 10.35/2.25 | | | | (89) ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = all_37_0 &
% 10.35/2.25 | | | | member(all_37_1, all_15_3) = 0 & $i(all_37_1)
% 10.35/2.25 | | | |
% 10.35/2.25 | | | | ALPHA: (89) implies:
% 10.35/2.25 | | | | (90) ~ (all_37_0 = 0)
% 10.35/2.25 | | | | (91) $i(all_37_1)
% 10.35/2.25 | | | | (92) member(all_37_1, all_15_3) = 0
% 10.35/2.25 | | | | (93) member(all_37_1, all_15_1) = all_37_0
% 10.35/2.25 | | | |
% 10.35/2.25 | | | | GROUND_INST: instantiating (3) with all_37_1, all_15_5, all_15_4,
% 10.35/2.25 | | | | all_15_3, simplifying with (12), (13), (19), (91), (92)
% 10.35/2.25 | | | | gives:
% 10.35/2.25 | | | | (94) ? [v0: any] : ? [v1: any] : (member(all_37_1, all_15_4) = v1 &
% 10.35/2.25 | | | | member(all_37_1, all_15_5) = v0 & (v1 = 0 | v0 = 0))
% 10.35/2.25 | | | |
% 10.35/2.25 | | | | GROUND_INST: instantiating (6) with all_37_1, all_15_2, all_15_1,
% 10.35/2.25 | | | | all_37_0, simplifying with (15), (22), (91), (93) gives:
% 10.35/2.25 | | | | (95) all_37_0 = 0 | ! [v0: $i] : ( ~ (member(all_37_1, v0) = 0) | ~
% 10.35/2.25 | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_2) =
% 10.35/2.25 | | | | v1))
% 10.35/2.25 | | | |
% 10.35/2.25 | | | | DELTA: instantiating (94) with fresh symbols all_45_0, all_45_1 gives:
% 10.35/2.25 | | | | (96) member(all_37_1, all_15_4) = all_45_0 & member(all_37_1,
% 10.35/2.25 | | | | all_15_5) = all_45_1 & (all_45_0 = 0 | all_45_1 = 0)
% 10.35/2.25 | | | |
% 10.35/2.25 | | | | ALPHA: (96) implies:
% 10.35/2.25 | | | | (97) member(all_37_1, all_15_5) = all_45_1
% 10.35/2.25 | | | | (98) member(all_37_1, all_15_4) = all_45_0
% 10.85/2.25 | | | | (99) all_45_0 = 0 | all_45_1 = 0
% 10.85/2.25 | | | |
% 10.85/2.25 | | | | BETA: splitting (95) gives:
% 10.85/2.25 | | | |
% 10.85/2.25 | | | | Case 1:
% 10.85/2.25 | | | | |
% 10.85/2.25 | | | | | (100) all_37_0 = 0
% 10.85/2.25 | | | | |
% 10.85/2.25 | | | | | REDUCE: (90), (100) imply:
% 10.85/2.25 | | | | | (101) $false
% 10.85/2.25 | | | | |
% 10.85/2.25 | | | | | CLOSE: (101) is inconsistent.
% 10.85/2.25 | | | | |
% 10.85/2.25 | | | | Case 2:
% 10.85/2.25 | | | | |
% 10.85/2.25 | | | | | (102) ! [v0: $i] : ( ~ (member(all_37_1, v0) = 0) | ~ $i(v0) | ?
% 10.85/2.25 | | | | | [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_2) = v1))
% 10.85/2.25 | | | | |
% 10.85/2.25 | | | | | GROUND_INST: instantiating (6) with all_37_1, all_15_6, all_15_4,
% 10.85/2.25 | | | | | all_45_0, simplifying with (11), (21), (91), (98) gives:
% 10.85/2.25 | | | | | (103) all_45_0 = 0 | ! [v0: $i] : ( ~ (member(all_37_1, v0) = 0) |
% 10.85/2.25 | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 10.85/2.25 | | | | | all_15_6) = v1))
% 10.85/2.25 | | | | |
% 10.85/2.25 | | | | | BETA: splitting (99) gives:
% 10.85/2.25 | | | | |
% 10.85/2.25 | | | | | Case 1:
% 10.85/2.25 | | | | | |
% 10.85/2.25 | | | | | | (104) all_45_0 = 0
% 10.85/2.25 | | | | | |
% 10.85/2.25 | | | | | | REDUCE: (98), (104) imply:
% 10.85/2.25 | | | | | | (105) member(all_37_1, all_15_4) = 0
% 10.85/2.25 | | | | | |
% 10.85/2.25 | | | | | | GROUND_INST: instantiating (5) with all_37_1, all_15_6, all_15_4,
% 10.85/2.25 | | | | | | simplifying with (11), (21), (91), (105) gives:
% 10.85/2.25 | | | | | | (106) ? [v0: $i] : (member(v0, all_15_6) = 0 & member(all_37_1,
% 10.85/2.25 | | | | | | v0) = 0 & $i(v0))
% 10.85/2.25 | | | | | |
% 10.85/2.25 | | | | | | DELTA: instantiating (106) with fresh symbol all_74_0 gives:
% 10.85/2.25 | | | | | | (107) member(all_74_0, all_15_6) = 0 & member(all_37_1, all_74_0)
% 10.85/2.25 | | | | | | = 0 & $i(all_74_0)
% 10.85/2.25 | | | | | |
% 10.85/2.25 | | | | | | ALPHA: (107) implies:
% 10.85/2.25 | | | | | | (108) $i(all_74_0)
% 10.85/2.25 | | | | | | (109) member(all_37_1, all_74_0) = 0
% 10.85/2.25 | | | | | | (110) member(all_74_0, all_15_6) = 0
% 10.85/2.25 | | | | | |
% 10.85/2.25 | | | | | | GROUND_INST: instantiating (102) with all_74_0, simplifying with
% 10.85/2.25 | | | | | | (108), (109) gives:
% 10.85/2.25 | | | | | | (111) ? [v0: int] : ( ~ (v0 = 0) & member(all_74_0, all_15_2) =
% 10.85/2.25 | | | | | | v0)
% 10.85/2.25 | | | | | |
% 10.85/2.25 | | | | | | DELTA: instantiating (111) with fresh symbol all_81_0 gives:
% 10.85/2.25 | | | | | | (112) ~ (all_81_0 = 0) & member(all_74_0, all_15_2) = all_81_0
% 10.85/2.25 | | | | | |
% 10.85/2.25 | | | | | | ALPHA: (112) implies:
% 10.85/2.25 | | | | | | (113) ~ (all_81_0 = 0)
% 10.85/2.25 | | | | | | (114) member(all_74_0, all_15_2) = all_81_0
% 10.85/2.25 | | | | | |
% 10.85/2.26 | | | | | | GROUND_INST: instantiating (4) with all_74_0, all_15_7, all_15_6,
% 10.85/2.26 | | | | | | all_15_2, all_81_0, simplifying with (10), (11), (18),
% 10.85/2.26 | | | | | | (108), (114) gives:
% 10.85/2.26 | | | | | | (115) all_81_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) &
% 10.85/2.26 | | | | | | ~ (v0 = 0) & member(all_74_0, all_15_6) = v1 &
% 10.85/2.26 | | | | | | member(all_74_0, all_15_7) = v0)
% 10.85/2.26 | | | | | |
% 10.85/2.26 | | | | | | BETA: splitting (115) gives:
% 10.85/2.26 | | | | | |
% 10.85/2.26 | | | | | | Case 1:
% 10.85/2.26 | | | | | | |
% 10.85/2.26 | | | | | | | (116) all_81_0 = 0
% 10.85/2.26 | | | | | | |
% 10.85/2.26 | | | | | | | REDUCE: (113), (116) imply:
% 10.85/2.26 | | | | | | | (117) $false
% 10.85/2.26 | | | | | | |
% 10.85/2.26 | | | | | | | CLOSE: (117) is inconsistent.
% 10.85/2.26 | | | | | | |
% 10.85/2.26 | | | | | | Case 2:
% 10.85/2.26 | | | | | | |
% 10.85/2.26 | | | | | | | (118) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0)
% 10.85/2.26 | | | | | | | & member(all_74_0, all_15_6) = v1 & member(all_74_0,
% 10.85/2.26 | | | | | | | all_15_7) = v0)
% 10.85/2.26 | | | | | | |
% 10.85/2.26 | | | | | | | DELTA: instantiating (118) with fresh symbols all_100_0, all_100_1
% 10.85/2.26 | | | | | | | gives:
% 10.85/2.26 | | | | | | | (119) ~ (all_100_0 = 0) & ~ (all_100_1 = 0) &
% 10.85/2.26 | | | | | | | member(all_74_0, all_15_6) = all_100_0 & member(all_74_0,
% 10.85/2.26 | | | | | | | all_15_7) = all_100_1
% 10.85/2.26 | | | | | | |
% 10.85/2.26 | | | | | | | ALPHA: (119) implies:
% 10.85/2.26 | | | | | | | (120) ~ (all_100_0 = 0)
% 10.85/2.26 | | | | | | | (121) member(all_74_0, all_15_6) = all_100_0
% 10.85/2.26 | | | | | | |
% 10.85/2.26 | | | | | | | GROUND_INST: instantiating (7) with 0, all_100_0, all_15_6,
% 10.85/2.26 | | | | | | | all_74_0, simplifying with (110), (121) gives:
% 10.85/2.26 | | | | | | | (122) all_100_0 = 0
% 10.85/2.26 | | | | | | |
% 10.85/2.26 | | | | | | | REDUCE: (120), (122) imply:
% 10.85/2.26 | | | | | | | (123) $false
% 10.85/2.26 | | | | | | |
% 10.85/2.26 | | | | | | | CLOSE: (123) is inconsistent.
% 10.85/2.26 | | | | | | |
% 10.85/2.26 | | | | | | End of split
% 10.85/2.26 | | | | | |
% 10.85/2.26 | | | | | Case 2:
% 10.85/2.26 | | | | | |
% 10.85/2.26 | | | | | | (124) all_45_1 = 0
% 10.85/2.26 | | | | | | (125) ~ (all_45_0 = 0)
% 10.85/2.26 | | | | | |
% 10.85/2.26 | | | | | | REDUCE: (97), (124) imply:
% 10.85/2.26 | | | | | | (126) member(all_37_1, all_15_5) = 0
% 10.85/2.26 | | | | | |
% 10.85/2.26 | | | | | | BETA: splitting (103) gives:
% 10.85/2.26 | | | | | |
% 10.85/2.26 | | | | | | Case 1:
% 10.85/2.26 | | | | | | |
% 10.85/2.26 | | | | | | | (127) all_45_0 = 0
% 10.85/2.26 | | | | | | |
% 10.85/2.26 | | | | | | | REDUCE: (125), (127) imply:
% 10.85/2.26 | | | | | | | (128) $false
% 10.85/2.26 | | | | | | |
% 10.85/2.26 | | | | | | | CLOSE: (128) is inconsistent.
% 10.85/2.26 | | | | | | |
% 10.85/2.26 | | | | | | Case 2:
% 10.85/2.26 | | | | | | |
% 10.85/2.26 | | | | | | |
% 10.85/2.26 | | | | | | | GROUND_INST: instantiating (5) with all_37_1, all_15_7, all_15_5,
% 10.85/2.26 | | | | | | | simplifying with (10), (20), (91), (126) gives:
% 10.85/2.26 | | | | | | | (129) ? [v0: $i] : (member(v0, all_15_7) = 0 &
% 10.85/2.26 | | | | | | | member(all_37_1, v0) = 0 & $i(v0))
% 10.85/2.26 | | | | | | |
% 10.85/2.26 | | | | | | | DELTA: instantiating (129) with fresh symbol all_86_0 gives:
% 10.85/2.26 | | | | | | | (130) member(all_86_0, all_15_7) = 0 & member(all_37_1,
% 10.85/2.26 | | | | | | | all_86_0) = 0 & $i(all_86_0)
% 10.85/2.26 | | | | | | |
% 10.85/2.26 | | | | | | | ALPHA: (130) implies:
% 10.85/2.26 | | | | | | | (131) $i(all_86_0)
% 10.85/2.26 | | | | | | | (132) member(all_37_1, all_86_0) = 0
% 10.85/2.26 | | | | | | | (133) member(all_86_0, all_15_7) = 0
% 10.85/2.26 | | | | | | |
% 10.85/2.26 | | | | | | | GROUND_INST: instantiating (102) with all_86_0, simplifying with
% 10.85/2.26 | | | | | | | (131), (132) gives:
% 10.85/2.26 | | | | | | | (134) ? [v0: int] : ( ~ (v0 = 0) & member(all_86_0, all_15_2)
% 10.85/2.26 | | | | | | | = v0)
% 10.85/2.26 | | | | | | |
% 10.85/2.26 | | | | | | | DELTA: instantiating (134) with fresh symbol all_95_0 gives:
% 10.85/2.26 | | | | | | | (135) ~ (all_95_0 = 0) & member(all_86_0, all_15_2) = all_95_0
% 10.85/2.26 | | | | | | |
% 10.85/2.26 | | | | | | | ALPHA: (135) implies:
% 10.85/2.26 | | | | | | | (136) ~ (all_95_0 = 0)
% 10.85/2.26 | | | | | | | (137) member(all_86_0, all_15_2) = all_95_0
% 10.85/2.26 | | | | | | |
% 10.85/2.26 | | | | | | | GROUND_INST: instantiating (4) with all_86_0, all_15_7, all_15_6,
% 10.85/2.26 | | | | | | | all_15_2, all_95_0, simplifying with (10), (11),
% 10.85/2.26 | | | | | | | (18), (131), (137) gives:
% 10.85/2.26 | | | | | | | (138) all_95_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0)
% 10.85/2.26 | | | | | | | & ~ (v0 = 0) & member(all_86_0, all_15_6) = v1 &
% 10.85/2.26 | | | | | | | member(all_86_0, all_15_7) = v0)
% 10.85/2.26 | | | | | | |
% 10.85/2.26 | | | | | | | BETA: splitting (138) gives:
% 10.85/2.26 | | | | | | |
% 10.85/2.26 | | | | | | | Case 1:
% 10.85/2.26 | | | | | | | |
% 10.85/2.26 | | | | | | | | (139) all_95_0 = 0
% 10.85/2.26 | | | | | | | |
% 10.85/2.26 | | | | | | | | REDUCE: (136), (139) imply:
% 10.85/2.26 | | | | | | | | (140) $false
% 10.85/2.26 | | | | | | | |
% 10.85/2.26 | | | | | | | | CLOSE: (140) is inconsistent.
% 10.85/2.26 | | | | | | | |
% 10.85/2.26 | | | | | | | Case 2:
% 10.85/2.26 | | | | | | | |
% 10.85/2.26 | | | | | | | | (141) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 =
% 10.85/2.26 | | | | | | | | 0) & member(all_86_0, all_15_6) = v1 &
% 10.85/2.26 | | | | | | | | member(all_86_0, all_15_7) = v0)
% 10.85/2.26 | | | | | | | |
% 10.85/2.26 | | | | | | | | DELTA: instantiating (141) with fresh symbols all_114_0,
% 10.85/2.26 | | | | | | | | all_114_1 gives:
% 10.85/2.26 | | | | | | | | (142) ~ (all_114_0 = 0) & ~ (all_114_1 = 0) &
% 10.85/2.26 | | | | | | | | member(all_86_0, all_15_6) = all_114_0 &
% 10.85/2.26 | | | | | | | | member(all_86_0, all_15_7) = all_114_1
% 10.85/2.26 | | | | | | | |
% 10.85/2.26 | | | | | | | | ALPHA: (142) implies:
% 10.85/2.26 | | | | | | | | (143) ~ (all_114_1 = 0)
% 10.85/2.26 | | | | | | | | (144) member(all_86_0, all_15_7) = all_114_1
% 10.85/2.26 | | | | | | | |
% 10.85/2.27 | | | | | | | | GROUND_INST: instantiating (7) with 0, all_114_1, all_15_7,
% 10.85/2.27 | | | | | | | | all_86_0, simplifying with (133), (144) gives:
% 10.85/2.27 | | | | | | | | (145) all_114_1 = 0
% 10.85/2.27 | | | | | | | |
% 10.85/2.27 | | | | | | | | REDUCE: (143), (145) imply:
% 10.85/2.27 | | | | | | | | (146) $false
% 10.85/2.27 | | | | | | | |
% 10.85/2.27 | | | | | | | | CLOSE: (146) is inconsistent.
% 10.85/2.27 | | | | | | | |
% 10.85/2.27 | | | | | | | End of split
% 10.85/2.27 | | | | | | |
% 10.85/2.27 | | | | | | End of split
% 10.85/2.27 | | | | | |
% 10.85/2.27 | | | | | End of split
% 10.85/2.27 | | | | |
% 10.85/2.27 | | | | End of split
% 10.85/2.27 | | | |
% 10.85/2.27 | | | End of split
% 10.85/2.27 | | |
% 10.85/2.27 | | End of split
% 10.85/2.27 | |
% 10.85/2.27 | End of split
% 10.85/2.27 |
% 10.85/2.27 End of proof
% 10.85/2.27 % SZS output end Proof for theBenchmark
% 10.85/2.27
% 10.85/2.27 1654ms
%------------------------------------------------------------------------------