TSTP Solution File: SET012+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET012+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 : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 15:23:04 EDT 2023
% Result : Theorem 7.03s 1.73s
% Output : Proof 8.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET012+4 : TPTP v8.1.2. Released v2.2.0.
% 0.10/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n005.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 08:47:38 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.60 Running up to 7 provers in parallel.
% 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.08/1.06 Prover 1: Preprocessing ...
% 2.08/1.06 Prover 4: Preprocessing ...
% 2.86/1.11 Prover 6: Preprocessing ...
% 2.86/1.11 Prover 3: Preprocessing ...
% 2.86/1.11 Prover 0: Preprocessing ...
% 2.86/1.11 Prover 2: Preprocessing ...
% 2.86/1.11 Prover 5: Preprocessing ...
% 4.95/1.47 Prover 6: Proving ...
% 4.95/1.47 Prover 5: Proving ...
% 5.54/1.47 Prover 1: Constructing countermodel ...
% 5.54/1.48 Prover 3: Constructing countermodel ...
% 5.54/1.49 Prover 2: Proving ...
% 5.73/1.52 Prover 0: Proving ...
% 5.95/1.53 Prover 4: Constructing countermodel ...
% 7.03/1.73 Prover 3: proved (1116ms)
% 7.03/1.73
% 7.03/1.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.03/1.73
% 7.03/1.73 Prover 2: stopped
% 7.03/1.73 Prover 0: stopped
% 7.03/1.73 Prover 5: stopped
% 7.03/1.74 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.03/1.74 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.03/1.74 Prover 6: stopped
% 7.03/1.74 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.03/1.74 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.03/1.74 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.76/1.77 Prover 7: Preprocessing ...
% 7.76/1.77 Prover 13: Preprocessing ...
% 7.76/1.79 Prover 8: Preprocessing ...
% 7.76/1.79 Prover 11: Preprocessing ...
% 7.76/1.79 Prover 10: Preprocessing ...
% 8.11/1.82 Prover 1: Found proof (size 61)
% 8.11/1.82 Prover 1: proved (1210ms)
% 8.13/1.82 Prover 4: stopped
% 8.13/1.83 Prover 7: stopped
% 8.13/1.84 Prover 13: stopped
% 8.13/1.85 Prover 10: Warning: ignoring some quantifiers
% 8.13/1.85 Prover 11: stopped
% 8.13/1.86 Prover 10: Constructing countermodel ...
% 8.13/1.87 Prover 10: stopped
% 8.13/1.88 Prover 8: Warning: ignoring some quantifiers
% 8.13/1.89 Prover 8: Constructing countermodel ...
% 8.13/1.90 Prover 8: stopped
% 8.13/1.90
% 8.13/1.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.13/1.90
% 8.13/1.91 % SZS output start Proof for theBenchmark
% 8.13/1.91 Assumptions after simplification:
% 8.13/1.91 ---------------------------------
% 8.13/1.91
% 8.13/1.91 (difference)
% 8.13/1.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 8.13/1.94 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~
% 8.13/1.94 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v0, v2) = v5 &
% 8.13/1.94 member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i]
% 8.13/1.94 : ! [v2: $i] : ! [v3: $i] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0,
% 8.13/1.94 v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 =
% 8.13/1.94 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 8.13/1.94
% 8.13/1.94 (equal_set)
% 8.13/1.95 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) =
% 8.13/1.95 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1,
% 8.13/1.95 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0:
% 8.13/1.95 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 8.13/1.95 (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 8.13/1.95
% 8.13/1.95 (subset)
% 8.13/1.95 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 8.13/1.95 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 8.13/1.95 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 8.13/1.95 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 8.13/1.95 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 8.13/1.95
% 8.13/1.95 (thI23)
% 8.13/1.95 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4
% 8.13/1.95 = 0) & difference(v1, v2) = v3 & difference(v1, v0) = v2 & equal_set(v3,
% 8.13/1.95 v0) = v4 & subset(v0, v1) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 8.13/1.95
% 8.13/1.95 (function-axioms)
% 8.13/1.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.13/1.96 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 8.13/1.96 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.13/1.96 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 8.13/1.96 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 8.13/1.96 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 8.13/1.96 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 8.13/1.96 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 8.13/1.96 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 8.13/1.96 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.13/1.96 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 8.13/1.96 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 8.13/1.96 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.13/1.96 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 8.13/1.96 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 8.13/1.96 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 8.13/1.96 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 8.13/1.96 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 8.13/1.96 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 8.13/1.96 (power_set(v2) = v0))
% 8.13/1.96
% 8.13/1.96 Further assumptions not needed in the proof:
% 8.13/1.96 --------------------------------------------
% 8.13/1.96 empty_set, intersection, power_set, product, singleton, sum, union,
% 8.13/1.96 unordered_pair
% 8.13/1.96
% 8.13/1.96 Those formulas are unsatisfiable:
% 8.13/1.96 ---------------------------------
% 8.13/1.96
% 8.13/1.96 Begin of proof
% 8.13/1.96 |
% 8.13/1.96 | ALPHA: (subset) implies:
% 8.13/1.97 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 8.13/1.97 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) |
% 8.13/1.97 | member(v2, v1) = 0))
% 8.13/1.97 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 8.13/1.97 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 8.13/1.97 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 8.13/1.97 |
% 8.13/1.97 | ALPHA: (equal_set) implies:
% 8.66/1.97 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0,
% 8.66/1.97 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 8.66/1.97 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 =
% 8.66/1.97 | 0))))
% 8.66/1.97 |
% 8.66/1.97 | ALPHA: (difference) implies:
% 8.66/1.97 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 8.66/1.97 | (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~
% 8.66/1.97 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v0, v2) = 0
% 8.66/1.97 | & member(v0, v1) = v4))
% 8.66/1.97 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 8.66/1.97 | (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ~
% 8.66/1.97 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] :
% 8.66/1.97 | (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0)))
% 8.66/1.97 |
% 8.66/1.97 | ALPHA: (function-axioms) implies:
% 8.66/1.97 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.66/1.97 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 8.66/1.97 | = v0))
% 8.66/1.97 |
% 8.66/1.97 | DELTA: instantiating (thI23) with fresh symbols all_15_0, all_15_1, all_15_2,
% 8.66/1.97 | all_15_3, all_15_4 gives:
% 8.66/1.97 | (7) ~ (all_15_0 = 0) & difference(all_15_3, all_15_2) = all_15_1 &
% 8.66/1.97 | difference(all_15_3, all_15_4) = all_15_2 & equal_set(all_15_1,
% 8.66/1.97 | all_15_4) = all_15_0 & subset(all_15_4, all_15_3) = 0 & $i(all_15_1)
% 8.66/1.97 | & $i(all_15_2) & $i(all_15_3) & $i(all_15_4)
% 8.66/1.97 |
% 8.66/1.97 | ALPHA: (7) implies:
% 8.66/1.97 | (8) ~ (all_15_0 = 0)
% 8.66/1.97 | (9) $i(all_15_4)
% 8.66/1.97 | (10) $i(all_15_3)
% 8.66/1.98 | (11) $i(all_15_2)
% 8.66/1.98 | (12) $i(all_15_1)
% 8.66/1.98 | (13) subset(all_15_4, all_15_3) = 0
% 8.66/1.98 | (14) equal_set(all_15_1, all_15_4) = all_15_0
% 8.66/1.98 | (15) difference(all_15_3, all_15_4) = all_15_2
% 8.66/1.98 | (16) difference(all_15_3, all_15_2) = all_15_1
% 8.66/1.98 |
% 8.66/1.98 | GROUND_INST: instantiating (1) with all_15_4, all_15_3, simplifying with (9),
% 8.66/1.98 | (10), (13) gives:
% 8.66/1.98 | (17) ! [v0: $i] : ( ~ (member(v0, all_15_4) = 0) | ~ $i(v0) | member(v0,
% 8.66/1.98 | all_15_3) = 0)
% 8.66/1.98 |
% 8.66/1.98 | GROUND_INST: instantiating (3) with all_15_1, all_15_4, all_15_0, simplifying
% 8.66/1.98 | with (9), (12), (14) gives:
% 8.66/1.98 | (18) all_15_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_1,
% 8.66/1.98 | all_15_4) = v0 & subset(all_15_4, all_15_1) = v1 & ( ~ (v1 = 0) |
% 8.66/1.98 | ~ (v0 = 0)))
% 8.66/1.98 |
% 8.66/1.98 | BETA: splitting (18) gives:
% 8.66/1.98 |
% 8.66/1.98 | Case 1:
% 8.66/1.98 | |
% 8.66/1.98 | | (19) all_15_0 = 0
% 8.66/1.98 | |
% 8.66/1.98 | | REDUCE: (8), (19) imply:
% 8.66/1.98 | | (20) $false
% 8.66/1.98 | |
% 8.66/1.98 | | CLOSE: (20) is inconsistent.
% 8.66/1.98 | |
% 8.66/1.98 | Case 2:
% 8.66/1.98 | |
% 8.66/1.98 | | (21) ? [v0: any] : ? [v1: any] : (subset(all_15_1, all_15_4) = v0 &
% 8.66/1.98 | | subset(all_15_4, all_15_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 8.66/1.98 | |
% 8.66/1.98 | | DELTA: instantiating (21) with fresh symbols all_27_0, all_27_1 gives:
% 8.66/1.98 | | (22) subset(all_15_1, all_15_4) = all_27_1 & subset(all_15_4, all_15_1) =
% 8.66/1.98 | | all_27_0 & ( ~ (all_27_0 = 0) | ~ (all_27_1 = 0))
% 8.66/1.98 | |
% 8.66/1.98 | | ALPHA: (22) implies:
% 8.66/1.98 | | (23) subset(all_15_4, all_15_1) = all_27_0
% 8.66/1.98 | | (24) subset(all_15_1, all_15_4) = all_27_1
% 8.66/1.98 | | (25) ~ (all_27_0 = 0) | ~ (all_27_1 = 0)
% 8.66/1.98 | |
% 8.66/1.98 | | GROUND_INST: instantiating (2) with all_15_4, all_15_1, all_27_0,
% 8.66/1.98 | | simplifying with (9), (12), (23) gives:
% 8.66/1.98 | | (26) all_27_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 8.66/1.98 | | member(v0, all_15_1) = v1 & member(v0, all_15_4) = 0 & $i(v0))
% 8.66/1.98 | |
% 8.66/1.98 | | GROUND_INST: instantiating (2) with all_15_1, all_15_4, all_27_1,
% 8.66/1.98 | | simplifying with (9), (12), (24) gives:
% 8.66/1.98 | | (27) all_27_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 8.66/1.98 | | member(v0, all_15_1) = 0 & member(v0, all_15_4) = v1 & $i(v0))
% 8.66/1.98 | |
% 8.66/1.98 | | BETA: splitting (25) gives:
% 8.66/1.98 | |
% 8.66/1.98 | | Case 1:
% 8.66/1.98 | | |
% 8.66/1.99 | | | (28) ~ (all_27_0 = 0)
% 8.66/1.99 | | |
% 8.66/1.99 | | | BETA: splitting (26) gives:
% 8.66/1.99 | | |
% 8.66/1.99 | | | Case 1:
% 8.66/1.99 | | | |
% 8.66/1.99 | | | | (29) all_27_0 = 0
% 8.66/1.99 | | | |
% 8.66/1.99 | | | | REDUCE: (28), (29) imply:
% 8.66/1.99 | | | | (30) $false
% 8.66/1.99 | | | |
% 8.66/1.99 | | | | CLOSE: (30) is inconsistent.
% 8.66/1.99 | | | |
% 8.66/1.99 | | | Case 2:
% 8.66/1.99 | | | |
% 8.66/1.99 | | | | (31) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1)
% 8.66/1.99 | | | | = v1 & member(v0, all_15_4) = 0 & $i(v0))
% 8.66/1.99 | | | |
% 8.66/1.99 | | | | DELTA: instantiating (31) with fresh symbols all_40_0, all_40_1 gives:
% 8.66/1.99 | | | | (32) ~ (all_40_0 = 0) & member(all_40_1, all_15_1) = all_40_0 &
% 8.66/1.99 | | | | member(all_40_1, all_15_4) = 0 & $i(all_40_1)
% 8.66/1.99 | | | |
% 8.66/1.99 | | | | ALPHA: (32) implies:
% 8.66/1.99 | | | | (33) ~ (all_40_0 = 0)
% 8.66/1.99 | | | | (34) $i(all_40_1)
% 8.66/1.99 | | | | (35) member(all_40_1, all_15_4) = 0
% 8.66/1.99 | | | | (36) member(all_40_1, all_15_1) = all_40_0
% 8.66/1.99 | | | |
% 8.66/1.99 | | | | GROUND_INST: instantiating (17) with all_40_1, simplifying with (34),
% 8.66/1.99 | | | | (35) gives:
% 8.66/1.99 | | | | (37) member(all_40_1, all_15_3) = 0
% 8.66/1.99 | | | |
% 8.66/1.99 | | | | GROUND_INST: instantiating (5) with all_40_1, all_15_2, all_15_3,
% 8.66/1.99 | | | | all_15_1, all_40_0, simplifying with (10), (11), (16),
% 8.66/1.99 | | | | (34), (36) gives:
% 8.66/1.99 | | | | (38) all_40_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_40_1,
% 8.66/1.99 | | | | all_15_2) = v1 & member(all_40_1, all_15_3) = v0 & ( ~ (v0 =
% 8.66/1.99 | | | | 0) | v1 = 0))
% 8.66/1.99 | | | |
% 8.66/1.99 | | | | BETA: splitting (38) gives:
% 8.66/1.99 | | | |
% 8.66/1.99 | | | | Case 1:
% 8.66/1.99 | | | | |
% 8.66/1.99 | | | | | (39) all_40_0 = 0
% 8.66/1.99 | | | | |
% 8.66/1.99 | | | | | REDUCE: (33), (39) imply:
% 8.66/1.99 | | | | | (40) $false
% 8.66/1.99 | | | | |
% 8.66/1.99 | | | | | CLOSE: (40) is inconsistent.
% 8.66/1.99 | | | | |
% 8.66/1.99 | | | | Case 2:
% 8.66/1.99 | | | | |
% 8.66/1.99 | | | | | (41) ? [v0: any] : ? [v1: any] : (member(all_40_1, all_15_2) = v1
% 8.66/1.99 | | | | | & member(all_40_1, all_15_3) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 8.66/1.99 | | | | |
% 8.66/1.99 | | | | | DELTA: instantiating (41) with fresh symbols all_52_0, all_52_1 gives:
% 8.66/1.99 | | | | | (42) member(all_40_1, all_15_2) = all_52_0 & member(all_40_1,
% 8.66/1.99 | | | | | all_15_3) = all_52_1 & ( ~ (all_52_1 = 0) | all_52_0 = 0)
% 8.66/1.99 | | | | |
% 8.66/1.99 | | | | | ALPHA: (42) implies:
% 8.66/1.99 | | | | | (43) member(all_40_1, all_15_3) = all_52_1
% 8.66/1.99 | | | | | (44) member(all_40_1, all_15_2) = all_52_0
% 8.66/1.99 | | | | | (45) ~ (all_52_1 = 0) | all_52_0 = 0
% 8.66/1.99 | | | | |
% 8.66/1.99 | | | | | GROUND_INST: instantiating (6) with 0, all_52_1, all_15_3, all_40_1,
% 8.66/1.99 | | | | | simplifying with (37), (43) gives:
% 8.66/1.99 | | | | | (46) all_52_1 = 0
% 8.66/1.99 | | | | |
% 8.66/1.99 | | | | | BETA: splitting (45) gives:
% 8.66/1.99 | | | | |
% 8.66/1.99 | | | | | Case 1:
% 8.66/1.99 | | | | | |
% 8.66/1.99 | | | | | | (47) ~ (all_52_1 = 0)
% 8.66/1.99 | | | | | |
% 8.66/1.99 | | | | | | REDUCE: (46), (47) imply:
% 8.66/1.99 | | | | | | (48) $false
% 8.66/1.99 | | | | | |
% 8.66/1.99 | | | | | | CLOSE: (48) is inconsistent.
% 8.66/1.99 | | | | | |
% 8.66/1.99 | | | | | Case 2:
% 8.66/1.99 | | | | | |
% 8.66/1.99 | | | | | | (49) all_52_0 = 0
% 8.66/1.99 | | | | | |
% 8.66/1.99 | | | | | | REDUCE: (44), (49) imply:
% 8.66/1.99 | | | | | | (50) member(all_40_1, all_15_2) = 0
% 8.66/1.99 | | | | | |
% 8.66/1.99 | | | | | | GROUND_INST: instantiating (4) with all_40_1, all_15_4, all_15_3,
% 8.66/1.99 | | | | | | all_15_2, simplifying with (9), (10), (15), (34), (50)
% 8.66/1.99 | | | | | | gives:
% 8.66/1.99 | | | | | | (51) ? [v0: int] : ( ~ (v0 = 0) & member(all_40_1, all_15_3) = 0
% 8.66/1.99 | | | | | | & member(all_40_1, all_15_4) = v0)
% 8.66/1.99 | | | | | |
% 8.66/1.99 | | | | | | DELTA: instantiating (51) with fresh symbol all_67_0 gives:
% 8.66/2.00 | | | | | | (52) ~ (all_67_0 = 0) & member(all_40_1, all_15_3) = 0 &
% 8.66/2.00 | | | | | | member(all_40_1, all_15_4) = all_67_0
% 8.66/2.00 | | | | | |
% 8.66/2.00 | | | | | | ALPHA: (52) implies:
% 8.66/2.00 | | | | | | (53) ~ (all_67_0 = 0)
% 8.66/2.00 | | | | | | (54) member(all_40_1, all_15_4) = all_67_0
% 8.66/2.00 | | | | | |
% 8.66/2.00 | | | | | | GROUND_INST: instantiating (6) with 0, all_67_0, all_15_4, all_40_1,
% 8.66/2.00 | | | | | | simplifying with (35), (54) gives:
% 8.66/2.00 | | | | | | (55) all_67_0 = 0
% 8.66/2.00 | | | | | |
% 8.66/2.00 | | | | | | REDUCE: (53), (55) imply:
% 8.66/2.00 | | | | | | (56) $false
% 8.66/2.00 | | | | | |
% 8.66/2.00 | | | | | | CLOSE: (56) is inconsistent.
% 8.66/2.00 | | | | | |
% 8.66/2.00 | | | | | End of split
% 8.66/2.00 | | | | |
% 8.66/2.00 | | | | End of split
% 8.66/2.00 | | | |
% 8.66/2.00 | | | End of split
% 8.66/2.00 | | |
% 8.66/2.00 | | Case 2:
% 8.66/2.00 | | |
% 8.66/2.00 | | | (57) ~ (all_27_1 = 0)
% 8.66/2.00 | | |
% 8.66/2.00 | | | BETA: splitting (27) gives:
% 8.66/2.00 | | |
% 8.66/2.00 | | | Case 1:
% 8.66/2.00 | | | |
% 8.66/2.00 | | | | (58) all_27_1 = 0
% 8.66/2.00 | | | |
% 8.66/2.00 | | | | REDUCE: (57), (58) imply:
% 8.66/2.00 | | | | (59) $false
% 8.66/2.00 | | | |
% 8.66/2.00 | | | | CLOSE: (59) is inconsistent.
% 8.66/2.00 | | | |
% 8.66/2.00 | | | Case 2:
% 8.66/2.00 | | | |
% 8.66/2.00 | | | | (60) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1)
% 8.66/2.00 | | | | = 0 & member(v0, all_15_4) = v1 & $i(v0))
% 8.66/2.00 | | | |
% 8.66/2.00 | | | | DELTA: instantiating (60) with fresh symbols all_40_0, all_40_1 gives:
% 8.66/2.00 | | | | (61) ~ (all_40_0 = 0) & member(all_40_1, all_15_1) = 0 &
% 8.66/2.00 | | | | member(all_40_1, all_15_4) = all_40_0 & $i(all_40_1)
% 8.66/2.00 | | | |
% 8.66/2.00 | | | | ALPHA: (61) implies:
% 8.66/2.00 | | | | (62) ~ (all_40_0 = 0)
% 8.66/2.00 | | | | (63) $i(all_40_1)
% 8.66/2.00 | | | | (64) member(all_40_1, all_15_4) = all_40_0
% 8.66/2.00 | | | | (65) member(all_40_1, all_15_1) = 0
% 8.66/2.00 | | | |
% 8.66/2.00 | | | | GROUND_INST: instantiating (4) with all_40_1, all_15_2, all_15_3,
% 8.66/2.00 | | | | all_15_1, simplifying with (10), (11), (16), (63), (65)
% 8.66/2.00 | | | | gives:
% 8.66/2.00 | | | | (66) ? [v0: int] : ( ~ (v0 = 0) & member(all_40_1, all_15_2) = v0 &
% 8.66/2.00 | | | | member(all_40_1, all_15_3) = 0)
% 8.66/2.00 | | | |
% 8.66/2.00 | | | | DELTA: instantiating (66) with fresh symbol all_48_0 gives:
% 8.66/2.00 | | | | (67) ~ (all_48_0 = 0) & member(all_40_1, all_15_2) = all_48_0 &
% 8.66/2.00 | | | | member(all_40_1, all_15_3) = 0
% 8.66/2.00 | | | |
% 8.66/2.00 | | | | ALPHA: (67) implies:
% 8.66/2.00 | | | | (68) ~ (all_48_0 = 0)
% 8.66/2.00 | | | | (69) member(all_40_1, all_15_3) = 0
% 8.66/2.00 | | | | (70) member(all_40_1, all_15_2) = all_48_0
% 8.66/2.00 | | | |
% 8.66/2.00 | | | | GROUND_INST: instantiating (5) with all_40_1, all_15_4, all_15_3,
% 8.66/2.00 | | | | all_15_2, all_48_0, simplifying with (9), (10), (15), (63),
% 8.66/2.00 | | | | (70) gives:
% 8.66/2.00 | | | | (71) all_48_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_40_1,
% 8.66/2.00 | | | | all_15_3) = v0 & member(all_40_1, all_15_4) = v1 & ( ~ (v0 =
% 8.66/2.00 | | | | 0) | v1 = 0))
% 8.66/2.00 | | | |
% 8.66/2.00 | | | | BETA: splitting (71) gives:
% 8.66/2.00 | | | |
% 8.66/2.00 | | | | Case 1:
% 8.66/2.00 | | | | |
% 8.66/2.00 | | | | | (72) all_48_0 = 0
% 8.66/2.00 | | | | |
% 8.66/2.00 | | | | | REDUCE: (68), (72) imply:
% 8.66/2.00 | | | | | (73) $false
% 8.66/2.00 | | | | |
% 8.66/2.00 | | | | | CLOSE: (73) is inconsistent.
% 8.66/2.00 | | | | |
% 8.66/2.00 | | | | Case 2:
% 8.66/2.00 | | | | |
% 8.66/2.00 | | | | | (74) ? [v0: any] : ? [v1: any] : (member(all_40_1, all_15_3) = v0
% 8.66/2.00 | | | | | & member(all_40_1, all_15_4) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 8.66/2.00 | | | | |
% 8.66/2.00 | | | | | DELTA: instantiating (74) with fresh symbols all_57_0, all_57_1 gives:
% 8.66/2.00 | | | | | (75) member(all_40_1, all_15_3) = all_57_1 & member(all_40_1,
% 8.66/2.00 | | | | | all_15_4) = all_57_0 & ( ~ (all_57_1 = 0) | all_57_0 = 0)
% 8.66/2.00 | | | | |
% 8.66/2.00 | | | | | ALPHA: (75) implies:
% 8.66/2.01 | | | | | (76) member(all_40_1, all_15_4) = all_57_0
% 8.66/2.01 | | | | | (77) member(all_40_1, all_15_3) = all_57_1
% 8.66/2.01 | | | | | (78) ~ (all_57_1 = 0) | all_57_0 = 0
% 8.66/2.01 | | | | |
% 8.66/2.01 | | | | | GROUND_INST: instantiating (6) with all_40_0, all_57_0, all_15_4,
% 8.66/2.01 | | | | | all_40_1, simplifying with (64), (76) gives:
% 8.66/2.01 | | | | | (79) all_57_0 = all_40_0
% 8.66/2.01 | | | | |
% 8.66/2.01 | | | | | GROUND_INST: instantiating (6) with 0, all_57_1, all_15_3, all_40_1,
% 8.66/2.01 | | | | | simplifying with (69), (77) gives:
% 8.66/2.01 | | | | | (80) all_57_1 = 0
% 8.66/2.01 | | | | |
% 8.66/2.01 | | | | | BETA: splitting (78) gives:
% 8.66/2.01 | | | | |
% 8.66/2.01 | | | | | Case 1:
% 8.66/2.01 | | | | | |
% 8.66/2.01 | | | | | | (81) ~ (all_57_1 = 0)
% 8.66/2.01 | | | | | |
% 8.66/2.01 | | | | | | REDUCE: (80), (81) imply:
% 8.66/2.01 | | | | | | (82) $false
% 8.66/2.01 | | | | | |
% 8.66/2.01 | | | | | | CLOSE: (82) is inconsistent.
% 8.66/2.01 | | | | | |
% 8.66/2.01 | | | | | Case 2:
% 8.66/2.01 | | | | | |
% 8.66/2.01 | | | | | | (83) all_57_0 = 0
% 8.66/2.01 | | | | | |
% 8.66/2.01 | | | | | | COMBINE_EQS: (79), (83) imply:
% 8.66/2.01 | | | | | | (84) all_40_0 = 0
% 8.66/2.01 | | | | | |
% 8.66/2.01 | | | | | | REDUCE: (62), (84) imply:
% 8.66/2.01 | | | | | | (85) $false
% 8.66/2.01 | | | | | |
% 8.66/2.01 | | | | | | CLOSE: (85) is inconsistent.
% 8.66/2.01 | | | | | |
% 8.66/2.01 | | | | | End of split
% 8.66/2.01 | | | | |
% 8.66/2.01 | | | | End of split
% 8.66/2.01 | | | |
% 8.66/2.01 | | | End of split
% 8.66/2.01 | | |
% 8.66/2.01 | | End of split
% 8.66/2.01 | |
% 8.66/2.01 | End of split
% 8.66/2.01 |
% 8.66/2.01 End of proof
% 8.66/2.01 % SZS output end Proof for theBenchmark
% 8.66/2.01
% 8.66/2.01 1417ms
%------------------------------------------------------------------------------