TSTP Solution File: SET603+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET603+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 : n003.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 15:25:33 EDT 2023
% Result : Theorem 6.45s 1.61s
% Output : Proof 8.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET603+4 : TPTP v8.1.2. Released v2.2.0.
% 0.14/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 13:51:39 EDT 2023
% 0.21/0.34 % CPUTime :
% 0.21/0.56 ________ _____
% 0.21/0.56 ___ __ \_________(_)________________________________
% 0.21/0.56 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.56 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.56 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.56
% 0.21/0.56 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.56 (2023-06-19)
% 0.21/0.56
% 0.21/0.56 (c) Philipp Rümmer, 2009-2023
% 0.21/0.56 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.56 Amanda Stjerna.
% 0.21/0.56 Free software under BSD-3-Clause.
% 0.21/0.56
% 0.21/0.56 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.56
% 0.21/0.56 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.57 Running up to 7 provers in parallel.
% 0.21/0.59 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.59 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.59 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.59 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.59 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.59 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.59 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.43/1.01 Prover 1: Preprocessing ...
% 2.43/1.02 Prover 4: Preprocessing ...
% 2.91/1.06 Prover 2: Preprocessing ...
% 2.91/1.06 Prover 6: Preprocessing ...
% 2.91/1.06 Prover 0: Preprocessing ...
% 2.91/1.06 Prover 3: Preprocessing ...
% 2.91/1.06 Prover 5: Preprocessing ...
% 5.50/1.43 Prover 5: Proving ...
% 5.50/1.43 Prover 6: Proving ...
% 5.50/1.43 Prover 3: Constructing countermodel ...
% 5.60/1.44 Prover 1: Constructing countermodel ...
% 5.60/1.45 Prover 2: Proving ...
% 5.60/1.46 Prover 0: Proving ...
% 5.60/1.46 Prover 4: Constructing countermodel ...
% 6.45/1.60 Prover 3: proved (1002ms)
% 6.45/1.61
% 6.45/1.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.45/1.61
% 6.45/1.61 Prover 5: stopped
% 6.45/1.61 Prover 2: stopped
% 6.45/1.61 Prover 6: stopped
% 6.45/1.61 Prover 0: stopped
% 6.45/1.61 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.45/1.61 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.45/1.61 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.45/1.61 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.45/1.62 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.06/1.65 Prover 7: Preprocessing ...
% 7.06/1.66 Prover 13: Preprocessing ...
% 7.06/1.66 Prover 8: Preprocessing ...
% 7.06/1.67 Prover 11: Preprocessing ...
% 7.30/1.69 Prover 10: Preprocessing ...
% 7.30/1.70 Prover 1: Found proof (size 47)
% 7.30/1.70 Prover 1: proved (1114ms)
% 7.30/1.70 Prover 4: stopped
% 7.30/1.70 Prover 13: stopped
% 7.30/1.71 Prover 11: stopped
% 7.30/1.72 Prover 10: stopped
% 7.30/1.72 Prover 7: Warning: ignoring some quantifiers
% 7.60/1.73 Prover 7: Constructing countermodel ...
% 7.60/1.74 Prover 7: stopped
% 7.69/1.76 Prover 8: Warning: ignoring some quantifiers
% 7.69/1.77 Prover 8: Constructing countermodel ...
% 7.69/1.78 Prover 8: stopped
% 7.69/1.78
% 7.69/1.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.69/1.78
% 7.69/1.78 % SZS output start Proof for theBenchmark
% 7.69/1.79 Assumptions after simplification:
% 7.69/1.79 ---------------------------------
% 7.69/1.79
% 7.69/1.79 (difference)
% 8.02/1.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 8.02/1.81 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~
% 8.02/1.81 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v0, v2) = v5 &
% 8.02/1.81 member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i]
% 8.02/1.81 : ! [v2: $i] : ! [v3: $i] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0,
% 8.02/1.81 v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 =
% 8.02/1.81 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 8.02/1.81
% 8.02/1.81 (empty_set)
% 8.02/1.82 $i(empty_set) & ! [v0: $i] : ( ~ (member(v0, empty_set) = 0) | ~ $i(v0))
% 8.02/1.82
% 8.02/1.82 (equal_set)
% 8.02/1.82 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) =
% 8.02/1.82 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1,
% 8.02/1.82 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0:
% 8.02/1.82 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 8.02/1.82 (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 8.02/1.82
% 8.02/1.82 (subset)
% 8.02/1.82 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 8.02/1.82 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 8.02/1.82 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 8.02/1.82 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 8.02/1.82 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 8.02/1.82
% 8.02/1.82 (thI30)
% 8.02/1.82 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 8.02/1.82 difference(v0, empty_set) = v1 & equal_set(v1, v0) = v2 & $i(v1) & $i(v0))
% 8.02/1.82
% 8.02/1.82 (function-axioms)
% 8.02/1.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.02/1.83 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 8.02/1.83 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.02/1.83 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 8.02/1.83 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 8.02/1.83 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 8.02/1.83 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 8.02/1.83 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 8.02/1.83 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 8.02/1.83 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.02/1.83 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 8.02/1.83 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 8.02/1.83 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.02/1.83 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 8.02/1.83 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 8.02/1.83 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 8.02/1.83 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 8.02/1.83 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 8.02/1.83 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 8.02/1.83 (power_set(v2) = v0))
% 8.02/1.83
% 8.02/1.83 Further assumptions not needed in the proof:
% 8.02/1.83 --------------------------------------------
% 8.02/1.83 intersection, power_set, product, singleton, sum, union, unordered_pair
% 8.02/1.83
% 8.02/1.83 Those formulas are unsatisfiable:
% 8.02/1.83 ---------------------------------
% 8.02/1.83
% 8.02/1.83 Begin of proof
% 8.02/1.83 |
% 8.02/1.83 | ALPHA: (subset) implies:
% 8.02/1.83 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 8.02/1.83 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 8.02/1.83 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 8.02/1.83 |
% 8.02/1.83 | ALPHA: (equal_set) implies:
% 8.02/1.83 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0,
% 8.02/1.83 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 8.02/1.83 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 =
% 8.02/1.83 | 0))))
% 8.02/1.83 |
% 8.02/1.83 | ALPHA: (empty_set) implies:
% 8.02/1.84 | (3) ! [v0: $i] : ( ~ (member(v0, empty_set) = 0) | ~ $i(v0))
% 8.02/1.84 |
% 8.02/1.84 | ALPHA: (difference) implies:
% 8.02/1.84 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 8.02/1.84 | (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~
% 8.02/1.84 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v0, v2) = 0
% 8.02/1.84 | & member(v0, v1) = v4))
% 8.02/1.84 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 8.02/1.84 | (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ~
% 8.02/1.84 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] :
% 8.02/1.84 | (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0)))
% 8.02/1.84 |
% 8.02/1.84 | ALPHA: (thI30) implies:
% 8.02/1.84 | (6) $i(empty_set)
% 8.02/1.84 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 8.02/1.84 | difference(v0, empty_set) = v1 & equal_set(v1, v0) = v2 & $i(v1) &
% 8.02/1.84 | $i(v0))
% 8.02/1.84 |
% 8.02/1.84 | ALPHA: (function-axioms) implies:
% 8.02/1.84 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.02/1.84 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 8.02/1.84 | = v0))
% 8.02/1.84 |
% 8.02/1.84 | DELTA: instantiating (7) with fresh symbols all_15_0, all_15_1, all_15_2
% 8.02/1.84 | gives:
% 8.02/1.84 | (9) ~ (all_15_0 = 0) & difference(all_15_2, empty_set) = all_15_1 &
% 8.02/1.84 | equal_set(all_15_1, all_15_2) = all_15_0 & $i(all_15_1) & $i(all_15_2)
% 8.02/1.84 |
% 8.02/1.84 | ALPHA: (9) implies:
% 8.02/1.84 | (10) ~ (all_15_0 = 0)
% 8.02/1.84 | (11) $i(all_15_2)
% 8.02/1.84 | (12) $i(all_15_1)
% 8.02/1.84 | (13) equal_set(all_15_1, all_15_2) = all_15_0
% 8.02/1.84 | (14) difference(all_15_2, empty_set) = all_15_1
% 8.02/1.84 |
% 8.02/1.84 | GROUND_INST: instantiating (2) with all_15_1, all_15_2, all_15_0, simplifying
% 8.02/1.84 | with (11), (12), (13) gives:
% 8.02/1.84 | (15) all_15_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_1,
% 8.02/1.84 | all_15_2) = v0 & subset(all_15_2, all_15_1) = v1 & ( ~ (v1 = 0) |
% 8.02/1.84 | ~ (v0 = 0)))
% 8.02/1.84 |
% 8.02/1.84 | BETA: splitting (15) gives:
% 8.02/1.84 |
% 8.02/1.84 | Case 1:
% 8.02/1.84 | |
% 8.02/1.84 | | (16) all_15_0 = 0
% 8.02/1.84 | |
% 8.02/1.84 | | REDUCE: (10), (16) imply:
% 8.02/1.84 | | (17) $false
% 8.02/1.85 | |
% 8.02/1.85 | | CLOSE: (17) is inconsistent.
% 8.02/1.85 | |
% 8.02/1.85 | Case 2:
% 8.02/1.85 | |
% 8.02/1.85 | | (18) ? [v0: any] : ? [v1: any] : (subset(all_15_1, all_15_2) = v0 &
% 8.02/1.85 | | subset(all_15_2, all_15_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 8.02/1.85 | |
% 8.02/1.85 | | DELTA: instantiating (18) with fresh symbols all_24_0, all_24_1 gives:
% 8.02/1.85 | | (19) subset(all_15_1, all_15_2) = all_24_1 & subset(all_15_2, all_15_1) =
% 8.02/1.85 | | all_24_0 & ( ~ (all_24_0 = 0) | ~ (all_24_1 = 0))
% 8.02/1.85 | |
% 8.02/1.85 | | ALPHA: (19) implies:
% 8.02/1.85 | | (20) subset(all_15_2, all_15_1) = all_24_0
% 8.02/1.85 | | (21) subset(all_15_1, all_15_2) = all_24_1
% 8.02/1.85 | | (22) ~ (all_24_0 = 0) | ~ (all_24_1 = 0)
% 8.02/1.85 | |
% 8.02/1.85 | | GROUND_INST: instantiating (1) with all_15_2, all_15_1, all_24_0,
% 8.02/1.85 | | simplifying with (11), (12), (20) gives:
% 8.02/1.85 | | (23) all_24_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 8.02/1.85 | | member(v0, all_15_1) = v1 & member(v0, all_15_2) = 0 & $i(v0))
% 8.02/1.85 | |
% 8.02/1.85 | | GROUND_INST: instantiating (1) with all_15_1, all_15_2, all_24_1,
% 8.02/1.85 | | simplifying with (11), (12), (21) gives:
% 8.02/1.85 | | (24) all_24_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 8.02/1.85 | | member(v0, all_15_1) = 0 & member(v0, all_15_2) = v1 & $i(v0))
% 8.02/1.85 | |
% 8.02/1.85 | | BETA: splitting (22) gives:
% 8.02/1.85 | |
% 8.02/1.85 | | Case 1:
% 8.02/1.85 | | |
% 8.02/1.85 | | | (25) ~ (all_24_0 = 0)
% 8.02/1.85 | | |
% 8.02/1.85 | | | BETA: splitting (23) gives:
% 8.02/1.85 | | |
% 8.02/1.85 | | | Case 1:
% 8.02/1.85 | | | |
% 8.02/1.85 | | | | (26) all_24_0 = 0
% 8.02/1.85 | | | |
% 8.02/1.85 | | | | REDUCE: (25), (26) imply:
% 8.02/1.85 | | | | (27) $false
% 8.02/1.85 | | | |
% 8.02/1.85 | | | | CLOSE: (27) is inconsistent.
% 8.02/1.85 | | | |
% 8.02/1.85 | | | Case 2:
% 8.02/1.85 | | | |
% 8.02/1.85 | | | | (28) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1)
% 8.02/1.85 | | | | = v1 & member(v0, all_15_2) = 0 & $i(v0))
% 8.02/1.85 | | | |
% 8.02/1.85 | | | | DELTA: instantiating (28) with fresh symbols all_37_0, all_37_1 gives:
% 8.02/1.85 | | | | (29) ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = all_37_0 &
% 8.02/1.85 | | | | member(all_37_1, all_15_2) = 0 & $i(all_37_1)
% 8.02/1.85 | | | |
% 8.02/1.85 | | | | ALPHA: (29) implies:
% 8.02/1.85 | | | | (30) ~ (all_37_0 = 0)
% 8.02/1.85 | | | | (31) $i(all_37_1)
% 8.02/1.85 | | | | (32) member(all_37_1, all_15_2) = 0
% 8.02/1.85 | | | | (33) member(all_37_1, all_15_1) = all_37_0
% 8.02/1.85 | | | |
% 8.02/1.85 | | | | GROUND_INST: instantiating (5) with all_37_1, empty_set, all_15_2,
% 8.02/1.85 | | | | all_15_1, all_37_0, simplifying with (6), (11), (14), (31),
% 8.02/1.85 | | | | (33) gives:
% 8.02/1.85 | | | | (34) all_37_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_37_1,
% 8.02/1.85 | | | | all_15_2) = v0 & member(all_37_1, empty_set) = v1 & ( ~ (v0
% 8.02/1.85 | | | | = 0) | v1 = 0))
% 8.02/1.85 | | | |
% 8.02/1.85 | | | | BETA: splitting (34) gives:
% 8.02/1.85 | | | |
% 8.02/1.85 | | | | Case 1:
% 8.02/1.85 | | | | |
% 8.02/1.85 | | | | | (35) all_37_0 = 0
% 8.02/1.85 | | | | |
% 8.02/1.85 | | | | | REDUCE: (30), (35) imply:
% 8.02/1.85 | | | | | (36) $false
% 8.02/1.85 | | | | |
% 8.02/1.85 | | | | | CLOSE: (36) is inconsistent.
% 8.02/1.85 | | | | |
% 8.02/1.85 | | | | Case 2:
% 8.02/1.85 | | | | |
% 8.02/1.85 | | | | | (37) ? [v0: any] : ? [v1: any] : (member(all_37_1, all_15_2) = v0
% 8.02/1.85 | | | | | & member(all_37_1, empty_set) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 8.02/1.85 | | | | |
% 8.02/1.85 | | | | | DELTA: instantiating (37) with fresh symbols all_52_0, all_52_1 gives:
% 8.02/1.85 | | | | | (38) member(all_37_1, all_15_2) = all_52_1 & member(all_37_1,
% 8.02/1.85 | | | | | empty_set) = all_52_0 & ( ~ (all_52_1 = 0) | all_52_0 = 0)
% 8.02/1.85 | | | | |
% 8.02/1.85 | | | | | ALPHA: (38) implies:
% 8.02/1.85 | | | | | (39) member(all_37_1, empty_set) = all_52_0
% 8.02/1.85 | | | | | (40) member(all_37_1, all_15_2) = all_52_1
% 8.02/1.85 | | | | | (41) ~ (all_52_1 = 0) | all_52_0 = 0
% 8.02/1.85 | | | | |
% 8.02/1.85 | | | | | GROUND_INST: instantiating (8) with 0, all_52_1, all_15_2, all_37_1,
% 8.02/1.85 | | | | | simplifying with (32), (40) gives:
% 8.02/1.86 | | | | | (42) all_52_1 = 0
% 8.02/1.86 | | | | |
% 8.02/1.86 | | | | | BETA: splitting (41) gives:
% 8.02/1.86 | | | | |
% 8.02/1.86 | | | | | Case 1:
% 8.02/1.86 | | | | | |
% 8.02/1.86 | | | | | | (43) ~ (all_52_1 = 0)
% 8.02/1.86 | | | | | |
% 8.02/1.86 | | | | | | REDUCE: (42), (43) imply:
% 8.02/1.86 | | | | | | (44) $false
% 8.02/1.86 | | | | | |
% 8.02/1.86 | | | | | | CLOSE: (44) is inconsistent.
% 8.02/1.86 | | | | | |
% 8.02/1.86 | | | | | Case 2:
% 8.02/1.86 | | | | | |
% 8.02/1.86 | | | | | | (45) all_52_0 = 0
% 8.02/1.86 | | | | | |
% 8.02/1.86 | | | | | | REDUCE: (39), (45) imply:
% 8.02/1.86 | | | | | | (46) member(all_37_1, empty_set) = 0
% 8.02/1.86 | | | | | |
% 8.02/1.86 | | | | | | GROUND_INST: instantiating (3) with all_37_1, simplifying with (31),
% 8.02/1.86 | | | | | | (46) gives:
% 8.02/1.86 | | | | | | (47) $false
% 8.02/1.86 | | | | | |
% 8.02/1.86 | | | | | | CLOSE: (47) is inconsistent.
% 8.02/1.86 | | | | | |
% 8.02/1.86 | | | | | End of split
% 8.02/1.86 | | | | |
% 8.02/1.86 | | | | End of split
% 8.02/1.86 | | | |
% 8.02/1.86 | | | End of split
% 8.02/1.86 | | |
% 8.02/1.86 | | Case 2:
% 8.02/1.86 | | |
% 8.02/1.86 | | | (48) ~ (all_24_1 = 0)
% 8.02/1.86 | | |
% 8.02/1.86 | | | BETA: splitting (24) gives:
% 8.02/1.86 | | |
% 8.02/1.86 | | | Case 1:
% 8.02/1.86 | | | |
% 8.02/1.86 | | | | (49) all_24_1 = 0
% 8.02/1.86 | | | |
% 8.02/1.86 | | | | REDUCE: (48), (49) imply:
% 8.02/1.86 | | | | (50) $false
% 8.02/1.86 | | | |
% 8.02/1.86 | | | | CLOSE: (50) is inconsistent.
% 8.02/1.86 | | | |
% 8.02/1.86 | | | Case 2:
% 8.02/1.86 | | | |
% 8.02/1.86 | | | | (51) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1)
% 8.02/1.86 | | | | = 0 & member(v0, all_15_2) = v1 & $i(v0))
% 8.02/1.86 | | | |
% 8.02/1.86 | | | | DELTA: instantiating (51) with fresh symbols all_37_0, all_37_1 gives:
% 8.02/1.86 | | | | (52) ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = 0 &
% 8.02/1.86 | | | | member(all_37_1, all_15_2) = all_37_0 & $i(all_37_1)
% 8.02/1.86 | | | |
% 8.02/1.86 | | | | ALPHA: (52) implies:
% 8.02/1.86 | | | | (53) ~ (all_37_0 = 0)
% 8.02/1.86 | | | | (54) $i(all_37_1)
% 8.02/1.86 | | | | (55) member(all_37_1, all_15_2) = all_37_0
% 8.02/1.86 | | | | (56) member(all_37_1, all_15_1) = 0
% 8.02/1.86 | | | |
% 8.02/1.86 | | | | GROUND_INST: instantiating (4) with all_37_1, empty_set, all_15_2,
% 8.02/1.86 | | | | all_15_1, simplifying with (6), (11), (14), (54), (56)
% 8.02/1.86 | | | | gives:
% 8.02/1.86 | | | | (57) ? [v0: int] : ( ~ (v0 = 0) & member(all_37_1, all_15_2) = 0 &
% 8.02/1.86 | | | | member(all_37_1, empty_set) = v0)
% 8.02/1.86 | | | |
% 8.02/1.86 | | | | DELTA: instantiating (57) with fresh symbol all_45_0 gives:
% 8.02/1.86 | | | | (58) ~ (all_45_0 = 0) & member(all_37_1, all_15_2) = 0 &
% 8.02/1.86 | | | | member(all_37_1, empty_set) = all_45_0
% 8.02/1.86 | | | |
% 8.02/1.86 | | | | ALPHA: (58) implies:
% 8.02/1.86 | | | | (59) member(all_37_1, all_15_2) = 0
% 8.02/1.86 | | | |
% 8.02/1.86 | | | | GROUND_INST: instantiating (8) with all_37_0, 0, all_15_2, all_37_1,
% 8.02/1.86 | | | | simplifying with (55), (59) gives:
% 8.02/1.86 | | | | (60) all_37_0 = 0
% 8.02/1.86 | | | |
% 8.02/1.86 | | | | REDUCE: (53), (60) imply:
% 8.02/1.86 | | | | (61) $false
% 8.02/1.86 | | | |
% 8.02/1.86 | | | | CLOSE: (61) is inconsistent.
% 8.02/1.86 | | | |
% 8.02/1.86 | | | End of split
% 8.02/1.86 | | |
% 8.02/1.86 | | End of split
% 8.02/1.86 | |
% 8.02/1.86 | End of split
% 8.02/1.86 |
% 8.02/1.86 End of proof
% 8.02/1.86 % SZS output end Proof for theBenchmark
% 8.02/1.86
% 8.02/1.86 1299ms
%------------------------------------------------------------------------------