TSTP Solution File: SET807+4 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET807+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n025.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 15:26:31 EDT 2023
% Result : Theorem 9.45s 1.99s
% Output : Proof 11.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET807+4 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n025.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 16:50:53 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.58/1.08 Prover 1: Preprocessing ...
% 2.58/1.08 Prover 4: Preprocessing ...
% 3.17/1.12 Prover 5: Preprocessing ...
% 3.17/1.12 Prover 2: Preprocessing ...
% 3.17/1.12 Prover 3: Preprocessing ...
% 3.17/1.12 Prover 0: Preprocessing ...
% 3.17/1.12 Prover 6: Preprocessing ...
% 6.70/1.61 Prover 5: Proving ...
% 6.70/1.66 Prover 2: Proving ...
% 6.70/1.67 Prover 6: Proving ...
% 6.70/1.67 Prover 1: Constructing countermodel ...
% 6.70/1.67 Prover 3: Constructing countermodel ...
% 7.62/1.79 Prover 4: Constructing countermodel ...
% 8.31/1.82 Prover 0: Proving ...
% 9.45/1.99 Prover 3: proved (1356ms)
% 9.45/1.99
% 9.45/1.99 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.45/1.99
% 9.45/2.00 Prover 5: stopped
% 9.45/2.00 Prover 6: stopped
% 9.67/2.01 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.67/2.01 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.67/2.01 Prover 2: stopped
% 9.67/2.02 Prover 0: stopped
% 9.67/2.03 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.67/2.03 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.67/2.03 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.67/2.04 Prover 8: Preprocessing ...
% 9.67/2.04 Prover 7: Preprocessing ...
% 9.67/2.07 Prover 11: Preprocessing ...
% 9.67/2.07 Prover 1: Found proof (size 52)
% 9.67/2.07 Prover 1: proved (1443ms)
% 9.67/2.08 Prover 4: stopped
% 9.67/2.08 Prover 13: Preprocessing ...
% 9.67/2.09 Prover 10: Preprocessing ...
% 9.67/2.09 Prover 7: stopped
% 9.67/2.12 Prover 10: stopped
% 9.67/2.12 Prover 13: stopped
% 9.67/2.13 Prover 11: stopped
% 10.49/2.20 Prover 8: Warning: ignoring some quantifiers
% 10.49/2.21 Prover 8: Constructing countermodel ...
% 10.49/2.22 Prover 8: stopped
% 10.49/2.22
% 10.49/2.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.49/2.22
% 10.49/2.23 % SZS output start Proof for theBenchmark
% 11.03/2.23 Assumptions after simplification:
% 11.03/2.23 ---------------------------------
% 11.03/2.23
% 11.03/2.23 (pre_order)
% 11.03/2.27 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (pre_order(v0, v1) =
% 11.03/2.27 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ?
% 11.03/2.27 [v6: int] : ( ~ (v6 = 0) & apply(v0, v4, v5) = 0 & apply(v0, v3, v5) = v6 &
% 11.03/2.27 apply(v0, v3, v4) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0 &
% 11.03/2.27 member(v3, v1) = 0 & $i(v5) & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4:
% 11.03/2.27 int] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0 &
% 11.03/2.27 $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (pre_order(v0, v1) = 0) | ~
% 11.03/2.27 $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int]
% 11.03/2.27 : (v5 = 0 | ~ (apply(v0, v2, v4) = v5) | ~ (apply(v0, v2, v3) = 0) | ~
% 11.03/2.27 $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any] : ? [v8:
% 11.03/2.27 any] : ? [v9: any] : (apply(v0, v3, v4) = v9 & member(v4, v1) = v8 &
% 11.03/2.27 member(v3, v1) = v7 & member(v2, v1) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0)
% 11.03/2.27 | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v2: $i] : ! [v3: int] : (v3 =
% 11.03/2.27 0 | ~ (apply(v0, v2, v2) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 =
% 11.03/2.28 0) & member(v2, v1) = v4))))
% 11.03/2.28
% 11.03/2.28 (rel_subset)
% 11.03/2.28 $i(subset_predicate) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 11.03/2.28 (apply(subset_predicate, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 11.03/2.28 int] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] :
% 11.03/2.28 ( ~ (apply(subset_predicate, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | subset(v0,
% 11.03/2.28 v1) = 0)
% 11.03/2.28
% 11.03/2.28 (subset)
% 11.03/2.28 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 11.03/2.28 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 11.03/2.28 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 11.03/2.28 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 11.03/2.28 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 11.03/2.28
% 11.03/2.28 (thIV18a)
% 11.03/2.28 $i(subset_predicate) & ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0)
% 11.03/2.28 & pre_order(subset_predicate, v1) = v2 & power_set(v0) = v1 & $i(v1) &
% 11.03/2.28 $i(v0))
% 11.03/2.28
% 11.03/2.28 (function-axioms)
% 11.03/2.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 11.03/2.29 | ~ (equivalence_class(v4, v3, v2) = v1) | ~ (equivalence_class(v4, v3,
% 11.03/2.29 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 11.03/2.29 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) =
% 11.03/2.29 v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.03/2.29 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.03/2.29 (pre_order(v3, v2) = v1) | ~ (pre_order(v3, v2) = v0)) & ! [v0:
% 11.03/2.29 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.03/2.29 : (v1 = v0 | ~ (equivalence(v3, v2) = v1) | ~ (equivalence(v3, v2) = v0)) &
% 11.03/2.29 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 11.03/2.29 $i] : (v1 = v0 | ~ (partition(v3, v2) = v1) | ~ (partition(v3, v2) = v0))
% 11.03/2.29 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 11.03/2.29 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 11.03/2.29 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.03/2.29 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 11.03/2.29 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.03/2.29 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 11.03/2.29 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 11.03/2.29 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 11.03/2.29 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 11.03/2.29 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 11.03/2.29 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 11.03/2.29 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.03/2.29 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 11.03/2.29 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 11.03/2.29 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.03/2.29 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 11.03/2.29 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 11.03/2.29 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 11.03/2.29 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 11.03/2.29 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 11.03/2.29 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 11.03/2.29 (power_set(v2) = v0))
% 11.03/2.29
% 11.03/2.29 Further assumptions not needed in the proof:
% 11.03/2.29 --------------------------------------------
% 11.03/2.29 difference, disjoint, empty_set, equal_set, equivalence, equivalence_class,
% 11.03/2.29 intersection, partition, power_set, product, singleton, sum, union,
% 11.03/2.29 unordered_pair
% 11.03/2.29
% 11.03/2.29 Those formulas are unsatisfiable:
% 11.03/2.29 ---------------------------------
% 11.03/2.29
% 11.03/2.29 Begin of proof
% 11.03/2.29 |
% 11.03/2.29 | ALPHA: (subset) implies:
% 11.03/2.29 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 11.03/2.29 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) |
% 11.03/2.29 | member(v2, v1) = 0))
% 11.03/2.29 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 11.03/2.29 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 11.03/2.29 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 11.03/2.29 |
% 11.03/2.29 | ALPHA: (pre_order) implies:
% 11.03/2.30 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (pre_order(v0,
% 11.03/2.30 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 11.03/2.30 | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & apply(v0, v4, v5) = 0 &
% 11.03/2.30 | apply(v0, v3, v5) = v6 & apply(v0, v3, v4) = 0 & member(v5, v1) = 0
% 11.03/2.30 | & member(v4, v1) = 0 & member(v3, v1) = 0 & $i(v5) & $i(v4) &
% 11.03/2.30 | $i(v3)) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & apply(v0, v3,
% 11.03/2.30 | v3) = v4 & member(v3, v1) = 0 & $i(v3)))
% 11.03/2.30 |
% 11.03/2.30 | ALPHA: (rel_subset) implies:
% 11.03/2.30 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (apply(subset_predicate, v0, v1) = 0) |
% 11.03/2.30 | ~ $i(v1) | ~ $i(v0) | subset(v0, v1) = 0)
% 11.03/2.30 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 11.03/2.30 | (apply(subset_predicate, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 11.03/2.30 | [v3: int] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 11.03/2.30 |
% 11.03/2.30 | ALPHA: (thIV18a) implies:
% 11.03/2.30 | (6) $i(subset_predicate)
% 11.03/2.30 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 11.03/2.30 | pre_order(subset_predicate, v1) = v2 & power_set(v0) = v1 & $i(v1) &
% 11.03/2.30 | $i(v0))
% 11.03/2.30 |
% 11.03/2.30 | ALPHA: (function-axioms) implies:
% 11.03/2.30 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 11.03/2.30 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 11.03/2.30 | = v0))
% 11.03/2.30 |
% 11.03/2.30 | DELTA: instantiating (7) with fresh symbols all_21_0, all_21_1, all_21_2
% 11.03/2.30 | gives:
% 11.03/2.30 | (9) ~ (all_21_0 = 0) & pre_order(subset_predicate, all_21_1) = all_21_0 &
% 11.03/2.30 | power_set(all_21_2) = all_21_1 & $i(all_21_1) & $i(all_21_2)
% 11.03/2.30 |
% 11.03/2.30 | ALPHA: (9) implies:
% 11.03/2.30 | (10) ~ (all_21_0 = 0)
% 11.03/2.30 | (11) $i(all_21_1)
% 11.39/2.30 | (12) pre_order(subset_predicate, all_21_1) = all_21_0
% 11.39/2.30 |
% 11.39/2.30 | GROUND_INST: instantiating (3) with subset_predicate, all_21_1, all_21_0,
% 11.39/2.30 | simplifying with (6), (11), (12) gives:
% 11.39/2.31 | (13) all_21_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int]
% 11.39/2.31 | : ( ~ (v3 = 0) & apply(subset_predicate, v1, v2) = 0 &
% 11.39/2.31 | apply(subset_predicate, v0, v2) = v3 & apply(subset_predicate, v0,
% 11.39/2.31 | v1) = 0 & member(v2, all_21_1) = 0 & member(v1, all_21_1) = 0 &
% 11.39/2.31 | member(v0, all_21_1) = 0 & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] :
% 11.39/2.31 | ? [v1: int] : ( ~ (v1 = 0) & apply(subset_predicate, v0, v0) = v1 &
% 11.39/2.31 | member(v0, all_21_1) = 0 & $i(v0))
% 11.39/2.31 |
% 11.39/2.31 | BETA: splitting (13) gives:
% 11.39/2.31 |
% 11.39/2.31 | Case 1:
% 11.39/2.31 | |
% 11.39/2.31 | | (14) all_21_0 = 0
% 11.39/2.31 | |
% 11.39/2.31 | | REDUCE: (10), (14) imply:
% 11.39/2.31 | | (15) $false
% 11.39/2.31 | |
% 11.39/2.31 | | CLOSE: (15) is inconsistent.
% 11.39/2.31 | |
% 11.39/2.31 | Case 2:
% 11.39/2.31 | |
% 11.39/2.31 | | (16) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 =
% 11.39/2.31 | | 0) & apply(subset_predicate, v1, v2) = 0 &
% 11.39/2.31 | | apply(subset_predicate, v0, v2) = v3 & apply(subset_predicate, v0,
% 11.39/2.31 | | v1) = 0 & member(v2, all_21_1) = 0 & member(v1, all_21_1) = 0 &
% 11.39/2.31 | | member(v0, all_21_1) = 0 & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i]
% 11.39/2.31 | | : ? [v1: int] : ( ~ (v1 = 0) & apply(subset_predicate, v0, v0) = v1
% 11.39/2.31 | | & member(v0, all_21_1) = 0 & $i(v0))
% 11.39/2.31 | |
% 11.39/2.31 | | BETA: splitting (16) gives:
% 11.39/2.31 | |
% 11.39/2.31 | | Case 1:
% 11.39/2.31 | | |
% 11.39/2.31 | | | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 =
% 11.39/2.31 | | | 0) & apply(subset_predicate, v1, v2) = 0 &
% 11.39/2.31 | | | apply(subset_predicate, v0, v2) = v3 & apply(subset_predicate,
% 11.39/2.31 | | | v0, v1) = 0 & member(v2, all_21_1) = 0 & member(v1, all_21_1)
% 11.39/2.31 | | | = 0 & member(v0, all_21_1) = 0 & $i(v2) & $i(v1) & $i(v0))
% 11.39/2.31 | | |
% 11.39/2.31 | | | DELTA: instantiating (17) with fresh symbols all_36_0, all_36_1, all_36_2,
% 11.39/2.31 | | | all_36_3 gives:
% 11.39/2.31 | | | (18) ~ (all_36_0 = 0) & apply(subset_predicate, all_36_2, all_36_1) =
% 11.39/2.31 | | | 0 & apply(subset_predicate, all_36_3, all_36_1) = all_36_0 &
% 11.39/2.31 | | | apply(subset_predicate, all_36_3, all_36_2) = 0 & member(all_36_1,
% 11.39/2.31 | | | all_21_1) = 0 & member(all_36_2, all_21_1) = 0 &
% 11.39/2.31 | | | member(all_36_3, all_21_1) = 0 & $i(all_36_1) & $i(all_36_2) &
% 11.39/2.31 | | | $i(all_36_3)
% 11.39/2.31 | | |
% 11.39/2.31 | | | ALPHA: (18) implies:
% 11.39/2.31 | | | (19) ~ (all_36_0 = 0)
% 11.39/2.31 | | | (20) $i(all_36_3)
% 11.39/2.31 | | | (21) $i(all_36_2)
% 11.39/2.31 | | | (22) $i(all_36_1)
% 11.39/2.31 | | | (23) apply(subset_predicate, all_36_3, all_36_2) = 0
% 11.39/2.31 | | | (24) apply(subset_predicate, all_36_3, all_36_1) = all_36_0
% 11.39/2.31 | | | (25) apply(subset_predicate, all_36_2, all_36_1) = 0
% 11.39/2.31 | | |
% 11.39/2.32 | | | GROUND_INST: instantiating (4) with all_36_3, all_36_2, simplifying with
% 11.39/2.32 | | | (20), (21), (23) gives:
% 11.39/2.32 | | | (26) subset(all_36_3, all_36_2) = 0
% 11.39/2.32 | | |
% 11.39/2.32 | | | GROUND_INST: instantiating (5) with all_36_3, all_36_1, all_36_0,
% 11.39/2.32 | | | simplifying with (20), (22), (24) gives:
% 11.39/2.32 | | | (27) all_36_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_36_3,
% 11.39/2.32 | | | all_36_1) = v0)
% 11.39/2.32 | | |
% 11.39/2.32 | | | GROUND_INST: instantiating (4) with all_36_2, all_36_1, simplifying with
% 11.39/2.32 | | | (21), (22), (25) gives:
% 11.39/2.32 | | | (28) subset(all_36_2, all_36_1) = 0
% 11.39/2.32 | | |
% 11.39/2.32 | | | BETA: splitting (27) gives:
% 11.39/2.32 | | |
% 11.39/2.32 | | | Case 1:
% 11.39/2.32 | | | |
% 11.39/2.32 | | | | (29) all_36_0 = 0
% 11.39/2.32 | | | |
% 11.39/2.32 | | | | REDUCE: (19), (29) imply:
% 11.39/2.32 | | | | (30) $false
% 11.39/2.32 | | | |
% 11.39/2.32 | | | | CLOSE: (30) is inconsistent.
% 11.39/2.32 | | | |
% 11.39/2.32 | | | Case 2:
% 11.39/2.32 | | | |
% 11.39/2.32 | | | | (31) ? [v0: int] : ( ~ (v0 = 0) & subset(all_36_3, all_36_1) = v0)
% 11.39/2.32 | | | |
% 11.39/2.32 | | | | DELTA: instantiating (31) with fresh symbol all_48_0 gives:
% 11.39/2.32 | | | | (32) ~ (all_48_0 = 0) & subset(all_36_3, all_36_1) = all_48_0
% 11.39/2.32 | | | |
% 11.39/2.32 | | | | ALPHA: (32) implies:
% 11.39/2.32 | | | | (33) ~ (all_48_0 = 0)
% 11.39/2.32 | | | | (34) subset(all_36_3, all_36_1) = all_48_0
% 11.39/2.32 | | | |
% 11.39/2.32 | | | | GROUND_INST: instantiating (1) with all_36_3, all_36_2, simplifying with
% 11.39/2.32 | | | | (20), (21), (26) gives:
% 11.39/2.32 | | | | (35) ! [v0: $i] : ( ~ (member(v0, all_36_3) = 0) | ~ $i(v0) |
% 11.39/2.32 | | | | member(v0, all_36_2) = 0)
% 11.39/2.32 | | | |
% 11.39/2.32 | | | | GROUND_INST: instantiating (2) with all_36_3, all_36_1, all_48_0,
% 11.39/2.32 | | | | simplifying with (20), (22), (34) gives:
% 11.39/2.32 | | | | (36) all_48_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 11.39/2.32 | | | | member(v0, all_36_1) = v1 & member(v0, all_36_3) = 0 & $i(v0))
% 11.39/2.32 | | | |
% 11.39/2.32 | | | | GROUND_INST: instantiating (1) with all_36_2, all_36_1, simplifying with
% 11.39/2.32 | | | | (21), (22), (28) gives:
% 11.39/2.32 | | | | (37) ! [v0: $i] : ( ~ (member(v0, all_36_2) = 0) | ~ $i(v0) |
% 11.39/2.32 | | | | member(v0, all_36_1) = 0)
% 11.39/2.32 | | | |
% 11.39/2.32 | | | | BETA: splitting (36) gives:
% 11.39/2.32 | | | |
% 11.39/2.32 | | | | Case 1:
% 11.39/2.32 | | | | |
% 11.39/2.32 | | | | | (38) all_48_0 = 0
% 11.39/2.32 | | | | |
% 11.39/2.32 | | | | | REDUCE: (33), (38) imply:
% 11.39/2.32 | | | | | (39) $false
% 11.39/2.32 | | | | |
% 11.39/2.32 | | | | | CLOSE: (39) is inconsistent.
% 11.39/2.32 | | | | |
% 11.39/2.32 | | | | Case 2:
% 11.39/2.32 | | | | |
% 11.39/2.33 | | | | | (40) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 11.39/2.33 | | | | | all_36_1) = v1 & member(v0, all_36_3) = 0 & $i(v0))
% 11.39/2.33 | | | | |
% 11.39/2.33 | | | | | DELTA: instantiating (40) with fresh symbols all_63_0, all_63_1 gives:
% 11.39/2.33 | | | | | (41) ~ (all_63_0 = 0) & member(all_63_1, all_36_1) = all_63_0 &
% 11.39/2.33 | | | | | member(all_63_1, all_36_3) = 0 & $i(all_63_1)
% 11.39/2.33 | | | | |
% 11.39/2.33 | | | | | ALPHA: (41) implies:
% 11.39/2.33 | | | | | (42) ~ (all_63_0 = 0)
% 11.39/2.33 | | | | | (43) $i(all_63_1)
% 11.39/2.33 | | | | | (44) member(all_63_1, all_36_3) = 0
% 11.39/2.33 | | | | | (45) member(all_63_1, all_36_1) = all_63_0
% 11.39/2.33 | | | | |
% 11.39/2.33 | | | | | GROUND_INST: instantiating (35) with all_63_1, simplifying with (43),
% 11.39/2.33 | | | | | (44) gives:
% 11.39/2.33 | | | | | (46) member(all_63_1, all_36_2) = 0
% 11.39/2.33 | | | | |
% 11.39/2.33 | | | | | GROUND_INST: instantiating (37) with all_63_1, simplifying with (43),
% 11.39/2.33 | | | | | (46) gives:
% 11.39/2.33 | | | | | (47) member(all_63_1, all_36_1) = 0
% 11.39/2.33 | | | | |
% 11.39/2.33 | | | | | GROUND_INST: instantiating (8) with all_63_0, 0, all_36_1, all_63_1,
% 11.39/2.33 | | | | | simplifying with (45), (47) gives:
% 11.39/2.33 | | | | | (48) all_63_0 = 0
% 11.39/2.33 | | | | |
% 11.39/2.33 | | | | | REDUCE: (42), (48) imply:
% 11.39/2.33 | | | | | (49) $false
% 11.39/2.33 | | | | |
% 11.39/2.33 | | | | | CLOSE: (49) is inconsistent.
% 11.39/2.33 | | | | |
% 11.39/2.33 | | | | End of split
% 11.39/2.33 | | | |
% 11.39/2.33 | | | End of split
% 11.39/2.33 | | |
% 11.39/2.33 | | Case 2:
% 11.39/2.33 | | |
% 11.39/2.33 | | | (50) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 11.39/2.33 | | | apply(subset_predicate, v0, v0) = v1 & member(v0, all_21_1) = 0
% 11.39/2.33 | | | & $i(v0))
% 11.39/2.33 | | |
% 11.39/2.33 | | | DELTA: instantiating (50) with fresh symbols all_36_0, all_36_1 gives:
% 11.39/2.33 | | | (51) ~ (all_36_0 = 0) & apply(subset_predicate, all_36_1, all_36_1) =
% 11.39/2.33 | | | all_36_0 & member(all_36_1, all_21_1) = 0 & $i(all_36_1)
% 11.39/2.33 | | |
% 11.39/2.33 | | | ALPHA: (51) implies:
% 11.39/2.33 | | | (52) ~ (all_36_0 = 0)
% 11.39/2.33 | | | (53) $i(all_36_1)
% 11.39/2.33 | | | (54) apply(subset_predicate, all_36_1, all_36_1) = all_36_0
% 11.39/2.33 | | |
% 11.39/2.33 | | | GROUND_INST: instantiating (5) with all_36_1, all_36_1, all_36_0,
% 11.39/2.33 | | | simplifying with (53), (54) gives:
% 11.39/2.33 | | | (55) all_36_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_36_1,
% 11.39/2.33 | | | all_36_1) = v0)
% 11.39/2.33 | | |
% 11.39/2.33 | | | BETA: splitting (55) gives:
% 11.39/2.33 | | |
% 11.39/2.33 | | | Case 1:
% 11.39/2.33 | | | |
% 11.39/2.33 | | | | (56) all_36_0 = 0
% 11.39/2.33 | | | |
% 11.39/2.33 | | | | REDUCE: (52), (56) imply:
% 11.39/2.33 | | | | (57) $false
% 11.39/2.33 | | | |
% 11.39/2.33 | | | | CLOSE: (57) is inconsistent.
% 11.39/2.33 | | | |
% 11.39/2.33 | | | Case 2:
% 11.39/2.33 | | | |
% 11.39/2.33 | | | | (58) ? [v0: int] : ( ~ (v0 = 0) & subset(all_36_1, all_36_1) = v0)
% 11.39/2.33 | | | |
% 11.39/2.33 | | | | DELTA: instantiating (58) with fresh symbol all_48_0 gives:
% 11.39/2.33 | | | | (59) ~ (all_48_0 = 0) & subset(all_36_1, all_36_1) = all_48_0
% 11.39/2.33 | | | |
% 11.39/2.34 | | | | ALPHA: (59) implies:
% 11.39/2.34 | | | | (60) ~ (all_48_0 = 0)
% 11.39/2.34 | | | | (61) subset(all_36_1, all_36_1) = all_48_0
% 11.39/2.34 | | | |
% 11.39/2.34 | | | | GROUND_INST: instantiating (2) with all_36_1, all_36_1, all_48_0,
% 11.39/2.34 | | | | simplifying with (53), (61) gives:
% 11.39/2.34 | | | | (62) all_48_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 11.39/2.34 | | | | member(v0, all_36_1) = v1 & member(v0, all_36_1) = 0 & $i(v0))
% 11.39/2.34 | | | |
% 11.39/2.34 | | | | BETA: splitting (62) gives:
% 11.39/2.34 | | | |
% 11.39/2.34 | | | | Case 1:
% 11.39/2.34 | | | | |
% 11.39/2.34 | | | | | (63) all_48_0 = 0
% 11.39/2.34 | | | | |
% 11.39/2.34 | | | | | REDUCE: (60), (63) imply:
% 11.39/2.34 | | | | | (64) $false
% 11.39/2.34 | | | | |
% 11.39/2.34 | | | | | CLOSE: (64) is inconsistent.
% 11.39/2.34 | | | | |
% 11.39/2.34 | | | | Case 2:
% 11.39/2.34 | | | | |
% 11.39/2.34 | | | | | (65) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 11.39/2.34 | | | | | all_36_1) = v1 & member(v0, all_36_1) = 0 & $i(v0))
% 11.39/2.34 | | | | |
% 11.39/2.34 | | | | | DELTA: instantiating (65) with fresh symbols all_60_0, all_60_1 gives:
% 11.39/2.34 | | | | | (66) ~ (all_60_0 = 0) & member(all_60_1, all_36_1) = all_60_0 &
% 11.39/2.34 | | | | | member(all_60_1, all_36_1) = 0 & $i(all_60_1)
% 11.39/2.34 | | | | |
% 11.39/2.34 | | | | | ALPHA: (66) implies:
% 11.39/2.34 | | | | | (67) ~ (all_60_0 = 0)
% 11.39/2.34 | | | | | (68) member(all_60_1, all_36_1) = 0
% 11.39/2.34 | | | | | (69) member(all_60_1, all_36_1) = all_60_0
% 11.39/2.34 | | | | |
% 11.39/2.34 | | | | | GROUND_INST: instantiating (8) with 0, all_60_0, all_36_1, all_60_1,
% 11.39/2.34 | | | | | simplifying with (68), (69) gives:
% 11.39/2.34 | | | | | (70) all_60_0 = 0
% 11.39/2.34 | | | | |
% 11.39/2.34 | | | | | REDUCE: (67), (70) imply:
% 11.39/2.34 | | | | | (71) $false
% 11.39/2.34 | | | | |
% 11.39/2.34 | | | | | CLOSE: (71) is inconsistent.
% 11.39/2.34 | | | | |
% 11.39/2.34 | | | | End of split
% 11.39/2.34 | | | |
% 11.39/2.34 | | | End of split
% 11.39/2.34 | | |
% 11.39/2.34 | | End of split
% 11.39/2.34 | |
% 11.39/2.34 | End of split
% 11.39/2.34 |
% 11.39/2.34 End of proof
% 11.39/2.34 % SZS output end Proof for theBenchmark
% 11.39/2.34
% 11.39/2.34 1730ms
%------------------------------------------------------------------------------