TSTP Solution File: SET774+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET774+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 : n001.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 15:26:23 EDT 2023
% Result : Theorem 10.37s 2.24s
% Output : Proof 13.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET774+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.33 % Computer : n001.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Sat Aug 26 12:26:45 EDT 2023
% 0.11/0.34 % CPUTime :
% 0.17/0.62 ________ _____
% 0.17/0.62 ___ __ \_________(_)________________________________
% 0.17/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.17/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.17/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.17/0.62
% 0.17/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.17/0.62 (2023-06-19)
% 0.17/0.62
% 0.17/0.62 (c) Philipp Rümmer, 2009-2023
% 0.17/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.17/0.62 Amanda Stjerna.
% 0.17/0.62 Free software under BSD-3-Clause.
% 0.17/0.62
% 0.17/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.17/0.62
% 0.17/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.17/0.63 Running up to 7 provers in parallel.
% 0.17/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.17/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.17/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.17/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.17/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.17/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.17/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.08/1.17 Prover 4: Preprocessing ...
% 3.08/1.17 Prover 1: Preprocessing ...
% 3.08/1.22 Prover 3: Preprocessing ...
% 3.08/1.22 Prover 6: Preprocessing ...
% 3.08/1.22 Prover 2: Preprocessing ...
% 3.08/1.22 Prover 5: Preprocessing ...
% 3.08/1.22 Prover 0: Preprocessing ...
% 8.21/1.93 Prover 5: Proving ...
% 8.21/1.94 Prover 2: Proving ...
% 8.21/1.94 Prover 6: Proving ...
% 9.00/2.01 Prover 3: Constructing countermodel ...
% 9.21/2.03 Prover 1: Constructing countermodel ...
% 10.37/2.20 Prover 4: Constructing countermodel ...
% 10.37/2.24 Prover 3: proved (1599ms)
% 10.37/2.24
% 10.37/2.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.37/2.24
% 10.37/2.24 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.37/2.25 Prover 2: stopped
% 10.37/2.25 Prover 6: stopped
% 10.97/2.30 Prover 5: stopped
% 10.97/2.30 Prover 0: Proving ...
% 10.97/2.30 Prover 0: stopped
% 10.97/2.31 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.97/2.31 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.97/2.31 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.97/2.32 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.97/2.36 Prover 8: Preprocessing ...
% 10.97/2.37 Prover 7: Preprocessing ...
% 10.97/2.37 Prover 11: Preprocessing ...
% 10.97/2.38 Prover 13: Preprocessing ...
% 10.97/2.39 Prover 10: Preprocessing ...
% 10.97/2.46 Prover 1: Found proof (size 51)
% 10.97/2.46 Prover 1: proved (1821ms)
% 10.97/2.47 Prover 4: stopped
% 11.33/2.47 Prover 13: stopped
% 11.33/2.48 Prover 10: stopped
% 12.28/2.52 Prover 7: Warning: ignoring some quantifiers
% 12.28/2.53 Prover 11: stopped
% 12.28/2.54 Prover 7: Constructing countermodel ...
% 12.28/2.55 Prover 7: stopped
% 12.99/2.62 Prover 8: Warning: ignoring some quantifiers
% 12.99/2.63 Prover 8: Constructing countermodel ...
% 12.99/2.65 Prover 8: stopped
% 12.99/2.65
% 12.99/2.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.99/2.65
% 12.99/2.66 % SZS output start Proof for theBenchmark
% 12.99/2.67 Assumptions after simplification:
% 12.99/2.67 ---------------------------------
% 12.99/2.67
% 12.99/2.67 (pre_order)
% 13.45/2.72 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (pre_order(v0, v1) =
% 13.45/2.72 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ?
% 13.45/2.72 [v6: int] : ( ~ (v6 = 0) & apply(v0, v4, v5) = 0 & apply(v0, v3, v5) = v6 &
% 13.45/2.72 apply(v0, v3, v4) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0 &
% 13.45/2.72 member(v3, v1) = 0 & $i(v5) & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4:
% 13.45/2.72 int] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0 &
% 13.45/2.72 $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (pre_order(v0, v1) = 0) | ~
% 13.45/2.72 $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int]
% 13.45/2.72 : (v5 = 0 | ~ (apply(v0, v2, v4) = v5) | ~ (apply(v0, v2, v3) = 0) | ~
% 13.45/2.72 $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any] : ? [v8:
% 13.45/2.72 any] : ? [v9: any] : (apply(v0, v3, v4) = v9 & member(v4, v1) = v8 &
% 13.45/2.72 member(v3, v1) = v7 & member(v2, v1) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0)
% 13.45/2.72 | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v2: $i] : ! [v3: int] : (v3 =
% 13.45/2.72 0 | ~ (apply(v0, v2, v2) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 =
% 13.45/2.72 0) & member(v2, v1) = v4))))
% 13.45/2.72
% 13.45/2.72 (subset)
% 13.45/2.72 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 13.45/2.72 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 13.45/2.72 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 13.45/2.72 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 13.45/2.72 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 13.45/2.72
% 13.45/2.72 (thIII10)
% 13.45/2.72 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 13.45/2.72 pre_order(v2, v1) = v3 & pre_order(v2, v0) = 0 & subset(v1, v0) = 0 & $i(v2)
% 13.45/2.72 & $i(v1) & $i(v0))
% 13.45/2.72
% 13.45/2.72 (function-axioms)
% 13.45/2.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 13.45/2.73 | ~ (equivalence_class(v4, v3, v2) = v1) | ~ (equivalence_class(v4, v3,
% 13.45/2.73 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 13.45/2.73 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) =
% 13.45/2.73 v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.45/2.73 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.45/2.73 (pre_order(v3, v2) = v1) | ~ (pre_order(v3, v2) = v0)) & ! [v0:
% 13.45/2.73 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.45/2.73 : (v1 = v0 | ~ (equivalence(v3, v2) = v1) | ~ (equivalence(v3, v2) = v0)) &
% 13.45/2.73 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 13.45/2.73 $i] : (v1 = v0 | ~ (partition(v3, v2) = v1) | ~ (partition(v3, v2) = v0))
% 13.45/2.73 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 13.45/2.73 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 13.45/2.73 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.45/2.73 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 13.45/2.73 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.45/2.73 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 13.45/2.73 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 13.45/2.73 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 13.45/2.73 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 13.45/2.73 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 13.45/2.73 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 13.45/2.73 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.45/2.73 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 13.45/2.73 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 13.45/2.73 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.45/2.73 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 13.45/2.73 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 13.45/2.73 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 13.45/2.73 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 13.45/2.73 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 13.45/2.73 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 13.45/2.73 (power_set(v2) = v0))
% 13.45/2.73
% 13.45/2.73 Further assumptions not needed in the proof:
% 13.45/2.73 --------------------------------------------
% 13.45/2.73 difference, disjoint, empty_set, equal_set, equivalence, equivalence_class,
% 13.45/2.73 intersection, partition, power_set, product, singleton, sum, union,
% 13.45/2.73 unordered_pair
% 13.45/2.73
% 13.45/2.73 Those formulas are unsatisfiable:
% 13.45/2.73 ---------------------------------
% 13.45/2.73
% 13.45/2.73 Begin of proof
% 13.45/2.73 |
% 13.45/2.73 | ALPHA: (subset) implies:
% 13.45/2.73 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 13.45/2.73 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) |
% 13.45/2.73 | member(v2, v1) = 0))
% 13.45/2.73 |
% 13.45/2.73 | ALPHA: (pre_order) implies:
% 13.45/2.74 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (pre_order(v0, v1) = 0) | ~ $i(v1) |
% 13.45/2.74 | ~ $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] :
% 13.45/2.74 | (v5 = 0 | ~ (apply(v0, v2, v4) = v5) | ~ (apply(v0, v2, v3) = 0)
% 13.45/2.74 | | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any]
% 13.45/2.74 | : ? [v8: any] : ? [v9: any] : (apply(v0, v3, v4) = v9 &
% 13.45/2.74 | member(v4, v1) = v8 & member(v3, v1) = v7 & member(v2, v1) = v6
% 13.45/2.74 | & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) &
% 13.45/2.74 | ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apply(v0, v2, v2) = v3) |
% 13.45/2.74 | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) = v4))))
% 13.45/2.74 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (pre_order(v0,
% 13.45/2.74 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 13.45/2.74 | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & apply(v0, v4, v5) = 0 &
% 13.45/2.74 | apply(v0, v3, v5) = v6 & apply(v0, v3, v4) = 0 & member(v5, v1) = 0
% 13.45/2.74 | & member(v4, v1) = 0 & member(v3, v1) = 0 & $i(v5) & $i(v4) &
% 13.45/2.74 | $i(v3)) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & apply(v0, v3,
% 13.45/2.74 | v3) = v4 & member(v3, v1) = 0 & $i(v3)))
% 13.45/2.74 |
% 13.45/2.74 | ALPHA: (function-axioms) implies:
% 13.45/2.74 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 13.45/2.74 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 13.45/2.74 | = v0))
% 13.45/2.74 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 13.45/2.74 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~
% 13.45/2.74 | (apply(v4, v3, v2) = v0))
% 13.45/2.74 |
% 13.45/2.74 | DELTA: instantiating (thIII10) with fresh symbols all_20_0, all_20_1,
% 13.45/2.74 | all_20_2, all_20_3 gives:
% 13.45/2.74 | (6) ~ (all_20_0 = 0) & pre_order(all_20_1, all_20_2) = all_20_0 &
% 13.45/2.74 | pre_order(all_20_1, all_20_3) = 0 & subset(all_20_2, all_20_3) = 0 &
% 13.45/2.74 | $i(all_20_1) & $i(all_20_2) & $i(all_20_3)
% 13.45/2.74 |
% 13.45/2.74 | ALPHA: (6) implies:
% 13.45/2.74 | (7) ~ (all_20_0 = 0)
% 13.45/2.74 | (8) $i(all_20_3)
% 13.45/2.74 | (9) $i(all_20_2)
% 13.45/2.74 | (10) $i(all_20_1)
% 13.45/2.74 | (11) subset(all_20_2, all_20_3) = 0
% 13.45/2.74 | (12) pre_order(all_20_1, all_20_3) = 0
% 13.45/2.74 | (13) pre_order(all_20_1, all_20_2) = all_20_0
% 13.45/2.74 |
% 13.45/2.74 | GROUND_INST: instantiating (1) with all_20_2, all_20_3, simplifying with (8),
% 13.45/2.74 | (9), (11) gives:
% 13.45/2.74 | (14) ! [v0: $i] : ( ~ (member(v0, all_20_2) = 0) | ~ $i(v0) | member(v0,
% 13.45/2.74 | all_20_3) = 0)
% 13.45/2.74 |
% 13.45/2.74 | GROUND_INST: instantiating (2) with all_20_1, all_20_3, simplifying with (8),
% 13.45/2.74 | (10), (12) gives:
% 13.45/2.75 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 13.45/2.75 | (apply(all_20_1, v0, v2) = v3) | ~ (apply(all_20_1, v0, v1) = 0) |
% 13.45/2.75 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ?
% 13.45/2.75 | [v6: any] : ? [v7: any] : (apply(all_20_1, v1, v2) = v7 &
% 13.45/2.75 | member(v2, all_20_3) = v6 & member(v1, all_20_3) = v5 & member(v0,
% 13.45/2.75 | all_20_3) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~
% 13.45/2.75 | (v4 = 0)))) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 13.45/2.75 | (apply(all_20_1, v0, v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2
% 13.45/2.75 | = 0) & member(v0, all_20_3) = v2))
% 13.45/2.75 |
% 13.45/2.75 | ALPHA: (15) implies:
% 13.45/2.75 | (16) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (apply(all_20_1, v0, v0) =
% 13.45/2.75 | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & member(v0,
% 13.45/2.75 | all_20_3) = v2))
% 13.45/2.75 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 13.45/2.75 | (apply(all_20_1, v0, v2) = v3) | ~ (apply(all_20_1, v0, v1) = 0) |
% 13.45/2.75 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ?
% 13.45/2.75 | [v6: any] : ? [v7: any] : (apply(all_20_1, v1, v2) = v7 &
% 13.45/2.75 | member(v2, all_20_3) = v6 & member(v1, all_20_3) = v5 & member(v0,
% 13.45/2.75 | all_20_3) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~
% 13.45/2.75 | (v4 = 0))))
% 13.45/2.75 |
% 13.45/2.75 | GROUND_INST: instantiating (3) with all_20_1, all_20_2, all_20_0, simplifying
% 13.45/2.75 | with (9), (10), (13) gives:
% 13.45/2.75 | (18) all_20_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int]
% 13.45/2.75 | : ( ~ (v3 = 0) & apply(all_20_1, v1, v2) = 0 & apply(all_20_1, v0, v2)
% 13.45/2.75 | = v3 & apply(all_20_1, v0, v1) = 0 & member(v2, all_20_2) = 0 &
% 13.45/2.75 | member(v1, all_20_2) = 0 & member(v0, all_20_2) = 0 & $i(v2) &
% 13.45/2.75 | $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 13.45/2.75 | apply(all_20_1, v0, v0) = v1 & member(v0, all_20_2) = 0 & $i(v0))
% 13.45/2.75 |
% 13.45/2.75 | BETA: splitting (18) gives:
% 13.45/2.75 |
% 13.45/2.75 | Case 1:
% 13.45/2.75 | |
% 13.45/2.75 | | (19) all_20_0 = 0
% 13.45/2.75 | |
% 13.45/2.75 | | REDUCE: (7), (19) imply:
% 13.45/2.76 | | (20) $false
% 13.45/2.76 | |
% 13.45/2.76 | | CLOSE: (20) is inconsistent.
% 13.45/2.76 | |
% 13.45/2.76 | Case 2:
% 13.45/2.76 | |
% 13.45/2.76 | | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 =
% 13.45/2.76 | | 0) & apply(all_20_1, v1, v2) = 0 & apply(all_20_1, v0, v2) = v3
% 13.45/2.76 | | & apply(all_20_1, v0, v1) = 0 & member(v2, all_20_2) = 0 &
% 13.45/2.76 | | member(v1, all_20_2) = 0 & member(v0, all_20_2) = 0 & $i(v2) &
% 13.45/2.76 | | $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 13.45/2.76 | | apply(all_20_1, v0, v0) = v1 & member(v0, all_20_2) = 0 & $i(v0))
% 13.45/2.76 | |
% 13.45/2.76 | | BETA: splitting (21) gives:
% 13.45/2.76 | |
% 13.45/2.76 | | Case 1:
% 13.45/2.76 | | |
% 13.45/2.76 | | | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 =
% 13.45/2.76 | | | 0) & apply(all_20_1, v1, v2) = 0 & apply(all_20_1, v0, v2) =
% 13.45/2.76 | | | v3 & apply(all_20_1, v0, v1) = 0 & member(v2, all_20_2) = 0 &
% 13.45/2.76 | | | member(v1, all_20_2) = 0 & member(v0, all_20_2) = 0 & $i(v2) &
% 13.45/2.76 | | | $i(v1) & $i(v0))
% 13.45/2.76 | | |
% 13.45/2.76 | | | DELTA: instantiating (22) with fresh symbols all_40_0, all_40_1, all_40_2,
% 13.45/2.76 | | | all_40_3 gives:
% 13.45/2.76 | | | (23) ~ (all_40_0 = 0) & apply(all_20_1, all_40_2, all_40_1) = 0 &
% 13.45/2.76 | | | apply(all_20_1, all_40_3, all_40_1) = all_40_0 & apply(all_20_1,
% 13.45/2.76 | | | all_40_3, all_40_2) = 0 & member(all_40_1, all_20_2) = 0 &
% 13.45/2.76 | | | member(all_40_2, all_20_2) = 0 & member(all_40_3, all_20_2) = 0 &
% 13.45/2.76 | | | $i(all_40_1) & $i(all_40_2) & $i(all_40_3)
% 13.45/2.76 | | |
% 13.45/2.76 | | | ALPHA: (23) implies:
% 13.45/2.76 | | | (24) ~ (all_40_0 = 0)
% 13.45/2.76 | | | (25) $i(all_40_3)
% 13.45/2.76 | | | (26) $i(all_40_2)
% 13.45/2.76 | | | (27) $i(all_40_1)
% 13.45/2.76 | | | (28) member(all_40_3, all_20_2) = 0
% 13.45/2.76 | | | (29) member(all_40_2, all_20_2) = 0
% 13.45/2.76 | | | (30) member(all_40_1, all_20_2) = 0
% 13.45/2.76 | | | (31) apply(all_20_1, all_40_3, all_40_2) = 0
% 13.45/2.77 | | | (32) apply(all_20_1, all_40_3, all_40_1) = all_40_0
% 13.45/2.77 | | | (33) apply(all_20_1, all_40_2, all_40_1) = 0
% 13.45/2.77 | | |
% 13.45/2.77 | | | GROUND_INST: instantiating (14) with all_40_3, simplifying with (25), (28)
% 13.45/2.77 | | | gives:
% 13.45/2.77 | | | (34) member(all_40_3, all_20_3) = 0
% 13.45/2.77 | | |
% 13.45/2.77 | | | GROUND_INST: instantiating (14) with all_40_2, simplifying with (26), (29)
% 13.45/2.77 | | | gives:
% 13.45/2.77 | | | (35) member(all_40_2, all_20_3) = 0
% 13.45/2.77 | | |
% 13.45/2.77 | | | GROUND_INST: instantiating (14) with all_40_1, simplifying with (27), (30)
% 13.45/2.77 | | | gives:
% 13.45/2.77 | | | (36) member(all_40_1, all_20_3) = 0
% 13.45/2.77 | | |
% 13.45/2.77 | | | GROUND_INST: instantiating (17) with all_40_3, all_40_2, all_40_1,
% 13.45/2.77 | | | all_40_0, simplifying with (25), (26), (27), (31), (32)
% 13.45/2.77 | | | gives:
% 13.45/2.77 | | | (37) all_40_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 13.45/2.77 | | | [v3: any] : (apply(all_20_1, all_40_2, all_40_1) = v3 &
% 13.45/2.77 | | | member(all_40_1, all_20_3) = v2 & member(all_40_2, all_20_3) =
% 13.45/2.77 | | | v1 & member(all_40_3, all_20_3) = v0 & ( ~ (v3 = 0) | ~ (v2 =
% 13.45/2.77 | | | 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 13.45/2.77 | | |
% 13.45/2.77 | | | BETA: splitting (37) gives:
% 13.45/2.77 | | |
% 13.45/2.77 | | | Case 1:
% 13.45/2.77 | | | |
% 13.45/2.77 | | | | (38) all_40_0 = 0
% 13.45/2.77 | | | |
% 13.45/2.77 | | | | REDUCE: (24), (38) imply:
% 13.45/2.77 | | | | (39) $false
% 13.45/2.77 | | | |
% 13.45/2.77 | | | | CLOSE: (39) is inconsistent.
% 13.45/2.77 | | | |
% 13.45/2.77 | | | Case 2:
% 13.45/2.77 | | | |
% 13.45/2.77 | | | | (40) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 13.45/2.77 | | | | (apply(all_20_1, all_40_2, all_40_1) = v3 & member(all_40_1,
% 13.45/2.77 | | | | all_20_3) = v2 & member(all_40_2, all_20_3) = v1 &
% 13.45/2.77 | | | | member(all_40_3, all_20_3) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) |
% 13.45/2.77 | | | | ~ (v1 = 0) | ~ (v0 = 0)))
% 13.45/2.77 | | | |
% 13.45/2.77 | | | | DELTA: instantiating (40) with fresh symbols all_52_0, all_52_1,
% 13.45/2.77 | | | | all_52_2, all_52_3 gives:
% 13.45/2.77 | | | | (41) apply(all_20_1, all_40_2, all_40_1) = all_52_0 &
% 13.45/2.77 | | | | member(all_40_1, all_20_3) = all_52_1 & member(all_40_2,
% 13.45/2.77 | | | | all_20_3) = all_52_2 & member(all_40_3, all_20_3) = all_52_3 &
% 13.45/2.77 | | | | ( ~ (all_52_0 = 0) | ~ (all_52_1 = 0) | ~ (all_52_2 = 0) | ~
% 13.45/2.77 | | | | (all_52_3 = 0))
% 13.45/2.77 | | | |
% 13.45/2.77 | | | | ALPHA: (41) implies:
% 13.45/2.77 | | | | (42) member(all_40_3, all_20_3) = all_52_3
% 13.45/2.77 | | | | (43) member(all_40_2, all_20_3) = all_52_2
% 13.45/2.77 | | | | (44) member(all_40_1, all_20_3) = all_52_1
% 13.45/2.78 | | | | (45) apply(all_20_1, all_40_2, all_40_1) = all_52_0
% 13.45/2.78 | | | | (46) ~ (all_52_0 = 0) | ~ (all_52_1 = 0) | ~ (all_52_2 = 0) | ~
% 13.45/2.78 | | | | (all_52_3 = 0)
% 13.45/2.78 | | | |
% 13.45/2.78 | | | | GROUND_INST: instantiating (4) with 0, all_52_3, all_20_3, all_40_3,
% 13.45/2.78 | | | | simplifying with (34), (42) gives:
% 13.45/2.78 | | | | (47) all_52_3 = 0
% 13.45/2.78 | | | |
% 13.45/2.78 | | | | GROUND_INST: instantiating (4) with 0, all_52_2, all_20_3, all_40_2,
% 13.45/2.78 | | | | simplifying with (35), (43) gives:
% 13.45/2.78 | | | | (48) all_52_2 = 0
% 13.45/2.78 | | | |
% 13.45/2.78 | | | | GROUND_INST: instantiating (4) with 0, all_52_1, all_20_3, all_40_1,
% 13.45/2.78 | | | | simplifying with (36), (44) gives:
% 13.45/2.78 | | | | (49) all_52_1 = 0
% 13.45/2.78 | | | |
% 13.45/2.78 | | | | GROUND_INST: instantiating (5) with 0, all_52_0, all_40_1, all_40_2,
% 13.45/2.78 | | | | all_20_1, simplifying with (33), (45) gives:
% 13.45/2.78 | | | | (50) all_52_0 = 0
% 13.45/2.78 | | | |
% 13.45/2.78 | | | | BETA: splitting (46) gives:
% 13.45/2.78 | | | |
% 13.45/2.78 | | | | Case 1:
% 13.45/2.78 | | | | |
% 13.45/2.78 | | | | | (51) ~ (all_52_0 = 0)
% 13.45/2.78 | | | | |
% 13.45/2.78 | | | | | REDUCE: (50), (51) imply:
% 13.45/2.78 | | | | | (52) $false
% 13.45/2.78 | | | | |
% 13.45/2.78 | | | | | CLOSE: (52) is inconsistent.
% 13.45/2.78 | | | | |
% 13.45/2.78 | | | | Case 2:
% 13.45/2.78 | | | | |
% 13.45/2.78 | | | | | (53) ~ (all_52_1 = 0) | ~ (all_52_2 = 0) | ~ (all_52_3 = 0)
% 13.45/2.78 | | | | |
% 13.45/2.78 | | | | | BETA: splitting (53) gives:
% 13.45/2.78 | | | | |
% 13.45/2.78 | | | | | Case 1:
% 13.45/2.78 | | | | | |
% 13.45/2.78 | | | | | | (54) ~ (all_52_1 = 0)
% 13.45/2.78 | | | | | |
% 13.45/2.78 | | | | | | REDUCE: (49), (54) imply:
% 13.45/2.78 | | | | | | (55) $false
% 13.45/2.78 | | | | | |
% 13.45/2.78 | | | | | | CLOSE: (55) is inconsistent.
% 13.45/2.78 | | | | | |
% 13.45/2.78 | | | | | Case 2:
% 13.45/2.78 | | | | | |
% 13.45/2.78 | | | | | | (56) ~ (all_52_2 = 0) | ~ (all_52_3 = 0)
% 13.45/2.78 | | | | | |
% 13.45/2.78 | | | | | | BETA: splitting (56) gives:
% 13.45/2.78 | | | | | |
% 13.45/2.78 | | | | | | Case 1:
% 13.45/2.78 | | | | | | |
% 13.45/2.78 | | | | | | | (57) ~ (all_52_2 = 0)
% 13.45/2.78 | | | | | | |
% 13.45/2.78 | | | | | | | REDUCE: (48), (57) imply:
% 13.45/2.78 | | | | | | | (58) $false
% 13.45/2.78 | | | | | | |
% 13.45/2.78 | | | | | | | CLOSE: (58) is inconsistent.
% 13.45/2.78 | | | | | | |
% 13.45/2.78 | | | | | | Case 2:
% 13.45/2.78 | | | | | | |
% 13.45/2.78 | | | | | | | (59) ~ (all_52_3 = 0)
% 13.45/2.78 | | | | | | |
% 13.45/2.78 | | | | | | | REDUCE: (47), (59) imply:
% 13.45/2.78 | | | | | | | (60) $false
% 13.45/2.78 | | | | | | |
% 13.45/2.78 | | | | | | | CLOSE: (60) is inconsistent.
% 13.45/2.78 | | | | | | |
% 13.45/2.78 | | | | | | End of split
% 13.45/2.78 | | | | | |
% 13.45/2.78 | | | | | End of split
% 13.45/2.78 | | | | |
% 13.45/2.78 | | | | End of split
% 13.45/2.78 | | | |
% 13.45/2.78 | | | End of split
% 13.45/2.78 | | |
% 13.45/2.78 | | Case 2:
% 13.45/2.78 | | |
% 13.45/2.78 | | | (61) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & apply(all_20_1, v0,
% 13.45/2.78 | | | v0) = v1 & member(v0, all_20_2) = 0 & $i(v0))
% 13.45/2.78 | | |
% 13.45/2.78 | | | DELTA: instantiating (61) with fresh symbols all_40_0, all_40_1 gives:
% 13.45/2.78 | | | (62) ~ (all_40_0 = 0) & apply(all_20_1, all_40_1, all_40_1) = all_40_0
% 13.45/2.78 | | | & member(all_40_1, all_20_2) = 0 & $i(all_40_1)
% 13.45/2.78 | | |
% 13.45/2.78 | | | ALPHA: (62) implies:
% 13.45/2.78 | | | (63) ~ (all_40_0 = 0)
% 13.45/2.79 | | | (64) $i(all_40_1)
% 13.45/2.79 | | | (65) member(all_40_1, all_20_2) = 0
% 13.45/2.79 | | | (66) apply(all_20_1, all_40_1, all_40_1) = all_40_0
% 13.45/2.79 | | |
% 13.45/2.79 | | | GROUND_INST: instantiating (14) with all_40_1, simplifying with (64), (65)
% 13.45/2.79 | | | gives:
% 13.45/2.79 | | | (67) member(all_40_1, all_20_3) = 0
% 13.45/2.79 | | |
% 13.45/2.79 | | | GROUND_INST: instantiating (16) with all_40_1, all_40_0, simplifying with
% 13.45/2.79 | | | (64), (66) gives:
% 13.45/2.79 | | | (68) all_40_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_40_1,
% 13.45/2.79 | | | all_20_3) = v0)
% 13.45/2.79 | | |
% 13.45/2.79 | | | BETA: splitting (68) gives:
% 13.45/2.79 | | |
% 13.45/2.79 | | | Case 1:
% 13.45/2.79 | | | |
% 13.45/2.79 | | | | (69) all_40_0 = 0
% 13.45/2.79 | | | |
% 13.45/2.79 | | | | REDUCE: (63), (69) imply:
% 13.45/2.79 | | | | (70) $false
% 13.45/2.79 | | | |
% 13.45/2.79 | | | | CLOSE: (70) is inconsistent.
% 13.45/2.79 | | | |
% 13.45/2.79 | | | Case 2:
% 13.45/2.79 | | | |
% 13.45/2.79 | | | | (71) ? [v0: int] : ( ~ (v0 = 0) & member(all_40_1, all_20_3) = v0)
% 13.45/2.79 | | | |
% 13.45/2.79 | | | | DELTA: instantiating (71) with fresh symbol all_52_0 gives:
% 13.45/2.79 | | | | (72) ~ (all_52_0 = 0) & member(all_40_1, all_20_3) = all_52_0
% 13.45/2.79 | | | |
% 13.45/2.79 | | | | ALPHA: (72) implies:
% 13.45/2.79 | | | | (73) ~ (all_52_0 = 0)
% 13.45/2.79 | | | | (74) member(all_40_1, all_20_3) = all_52_0
% 13.45/2.79 | | | |
% 13.45/2.79 | | | | GROUND_INST: instantiating (4) with 0, all_52_0, all_20_3, all_40_1,
% 13.45/2.79 | | | | simplifying with (67), (74) gives:
% 13.45/2.79 | | | | (75) all_52_0 = 0
% 13.45/2.79 | | | |
% 13.45/2.79 | | | | REDUCE: (73), (75) imply:
% 13.45/2.79 | | | | (76) $false
% 13.85/2.79 | | | |
% 13.85/2.79 | | | | CLOSE: (76) is inconsistent.
% 13.85/2.79 | | | |
% 13.85/2.79 | | | End of split
% 13.85/2.79 | | |
% 13.85/2.79 | | End of split
% 13.85/2.79 | |
% 13.85/2.79 | End of split
% 13.85/2.79 |
% 13.85/2.79 End of proof
% 13.85/2.79 % SZS output end Proof for theBenchmark
% 13.85/2.79
% 13.85/2.79 2173ms
%------------------------------------------------------------------------------