TSTP Solution File: SET800+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET800+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 : n032.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 15:26:30 EDT 2023
% Result : Theorem 9.49s 1.97s
% Output : Proof 12.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET800+4 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.30 % Computer : n032.cluster.edu
% 0.13/0.30 % Model : x86_64 x86_64
% 0.13/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.30 % Memory : 8042.1875MB
% 0.13/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.30 % CPULimit : 300
% 0.13/0.30 % WCLimit : 300
% 0.13/0.30 % DateTime : Sat Aug 26 09:44:28 EDT 2023
% 0.13/0.30 % CPUTime :
% 0.16/0.52 ________ _____
% 0.16/0.52 ___ __ \_________(_)________________________________
% 0.16/0.52 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.16/0.52 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.16/0.52 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.16/0.52
% 0.16/0.52 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.16/0.52 (2023-06-19)
% 0.16/0.52
% 0.16/0.52 (c) Philipp Rümmer, 2009-2023
% 0.16/0.52 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.16/0.52 Amanda Stjerna.
% 0.16/0.52 Free software under BSD-3-Clause.
% 0.16/0.52
% 0.16/0.52 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.16/0.52
% 0.16/0.52 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.16/0.53 Running up to 7 provers in parallel.
% 0.16/0.54 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.16/0.54 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.16/0.54 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.16/0.54 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.16/0.54 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.16/0.54 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.16/0.54 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.40/1.02 Prover 1: Preprocessing ...
% 2.40/1.02 Prover 4: Preprocessing ...
% 2.93/1.06 Prover 2: Preprocessing ...
% 2.93/1.06 Prover 3: Preprocessing ...
% 2.93/1.06 Prover 5: Preprocessing ...
% 2.93/1.06 Prover 6: Preprocessing ...
% 2.93/1.06 Prover 0: Preprocessing ...
% 7.32/1.65 Prover 5: Proving ...
% 7.32/1.68 Prover 2: Proving ...
% 7.69/1.72 Prover 6: Proving ...
% 8.21/1.76 Prover 1: Constructing countermodel ...
% 8.21/1.79 Prover 3: Constructing countermodel ...
% 9.49/1.97 Prover 3: proved (1428ms)
% 9.49/1.97
% 9.49/1.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.49/1.97
% 9.49/1.97 Prover 6: stopped
% 9.49/1.97 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.49/1.98 Prover 2: stopped
% 9.82/1.99 Prover 5: stopped
% 9.82/1.99 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.82/1.99 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.82/1.99 Prover 0: Proving ...
% 9.82/1.99 Prover 0: stopped
% 9.82/2.01 Prover 4: Constructing countermodel ...
% 9.82/2.01 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.82/2.01 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.82/2.01 Prover 8: Preprocessing ...
% 9.82/2.03 Prover 7: Preprocessing ...
% 9.82/2.04 Prover 10: Preprocessing ...
% 10.27/2.05 Prover 13: Preprocessing ...
% 10.27/2.05 Prover 11: Preprocessing ...
% 10.38/2.09 Prover 1: Found proof (size 26)
% 10.38/2.09 Prover 1: proved (1559ms)
% 10.38/2.09 Prover 13: stopped
% 10.38/2.10 Prover 4: stopped
% 10.38/2.13 Prover 7: Warning: ignoring some quantifiers
% 10.38/2.14 Prover 11: stopped
% 10.38/2.16 Prover 7: Constructing countermodel ...
% 10.38/2.16 Prover 10: Warning: ignoring some quantifiers
% 10.38/2.17 Prover 7: stopped
% 10.38/2.18 Prover 10: Constructing countermodel ...
% 10.38/2.19 Prover 10: stopped
% 11.69/2.28 Prover 8: Warning: ignoring some quantifiers
% 11.69/2.30 Prover 8: Constructing countermodel ...
% 11.69/2.32 Prover 8: stopped
% 11.69/2.32
% 11.69/2.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.69/2.32
% 11.69/2.32 % SZS output start Proof for theBenchmark
% 11.69/2.32 Assumptions after simplification:
% 11.69/2.32 ---------------------------------
% 11.69/2.32
% 11.69/2.32 (greatest_lower_bound)
% 12.13/2.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 12.13/2.35 | ~ (greatest_lower_bound(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) |
% 12.13/2.35 ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) &
% 12.13/2.36 lower_bound(v5, v2, v1) = 0 & apply(v2, v5, v0) = v6 & member(v5, v3) = 0
% 12.13/2.36 & $i(v5)) | ? [v5: any] : ? [v6: any] : (lower_bound(v0, v2, v1) = v6 &
% 12.13/2.36 member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : !
% 12.13/2.36 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (greatest_lower_bound(v0, v1, v2,
% 12.13/2.36 v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 12.13/2.36 (lower_bound(v0, v2, v1) = 0 & member(v0, v1) = 0 & ! [v4: $i] : ( ~
% 12.13/2.36 (lower_bound(v4, v2, v1) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6: any]
% 12.13/2.36 : (apply(v2, v4, v0) = v6 & member(v4, v3) = v5 & ( ~ (v5 = 0) | v6 =
% 12.13/2.36 0)))))
% 12.13/2.36
% 12.13/2.36 (lower_bound)
% 12.13/2.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 12.13/2.36 (lower_bound(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 12.13/2.36 $i] : ? [v5: int] : ( ~ (v5 = 0) & apply(v0, v2, v4) = v5 & member(v4,
% 12.13/2.36 v1) = 0 & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 12.13/2.36 (lower_bound(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v3:
% 12.13/2.36 $i] : ! [v4: int] : (v4 = 0 | ~ (apply(v0, v2, v3) = v4) | ~ $i(v3) |
% 12.13/2.36 ? [v5: int] : ( ~ (v5 = 0) & member(v3, v1) = v5)))
% 12.13/2.36
% 12.13/2.36 (subset)
% 12.13/2.36 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 12.13/2.36 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 12.13/2.36 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 12.13/2.36 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 12.13/2.36 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 12.13/2.36
% 12.13/2.36 (thIV12)
% 12.13/2.37 ? [v0: $i] : ? [v1: $i] : (order(v0, v1) = 0 & $i(v1) & $i(v0) & ? [v2: $i]
% 12.13/2.37 : ? [v3: $i] : (subset(v3, v1) = 0 & subset(v2, v3) = 0 & subset(v2, v1) =
% 12.13/2.37 0 & $i(v3) & $i(v2) & ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ( ~ (v6 =
% 12.13/2.37 0) & greatest_lower_bound(v5, v3, v0, v1) = 0 &
% 12.13/2.37 greatest_lower_bound(v4, v2, v0, v1) = 0 & apply(v0, v5, v4) = v6 &
% 12.13/2.37 $i(v5) & $i(v4))))
% 12.13/2.37
% 12.13/2.37 (function-axioms)
% 12.13/2.37 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 12.13/2.37 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (greatest_lower_bound(v5,
% 12.13/2.37 v4, v3, v2) = v1) | ~ (greatest_lower_bound(v5, v4, v3, v2) = v0)) & !
% 12.13/2.37 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 12.13/2.37 $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (least_upper_bound(v5, v4,
% 12.13/2.37 v3, v2) = v1) | ~ (least_upper_bound(v5, v4, v3, v2) = v0)) & ! [v0:
% 12.13/2.37 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 12.13/2.37 : ! [v4: $i] : (v1 = v0 | ~ (min(v4, v3, v2) = v1) | ~ (min(v4, v3, v2) =
% 12.13/2.37 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 12.13/2.37 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (max(v4, v3, v2) = v1) | ~
% 12.13/2.37 (max(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.13/2.37 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 12.13/2.37 (least(v4, v3, v2) = v1) | ~ (least(v4, v3, v2) = v0)) & ! [v0:
% 12.13/2.37 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 12.13/2.37 : ! [v4: $i] : (v1 = v0 | ~ (greatest(v4, v3, v2) = v1) | ~ (greatest(v4,
% 12.13/2.37 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 12.13/2.37 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (lower_bound(v4, v3,
% 12.13/2.37 v2) = v1) | ~ (lower_bound(v4, v3, v2) = v0)) & ! [v0:
% 12.13/2.37 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 12.13/2.37 : ! [v4: $i] : (v1 = v0 | ~ (upper_bound(v4, v3, v2) = v1) | ~
% 12.13/2.37 (upper_bound(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.13/2.37 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 12.13/2.37 (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0:
% 12.13/2.37 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 12.13/2.37 : (v1 = v0 | ~ (total_order(v3, v2) = v1) | ~ (total_order(v3, v2) = v0)) &
% 12.13/2.37 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 12.13/2.37 $i] : (v1 = v0 | ~ (order(v3, v2) = v1) | ~ (order(v3, v2) = v0)) & !
% 12.13/2.37 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.13/2.37 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 12.13/2.38 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.13/2.38 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 12.13/2.38 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 12.13/2.38 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 12.13/2.38 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 12.13/2.38 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 12.13/2.38 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 12.13/2.38 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.13/2.38 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 12.13/2.38 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 12.13/2.38 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.13/2.38 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 12.13/2.38 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 12.13/2.38 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 12.13/2.38 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 12.13/2.38 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 12.13/2.38 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 12.13/2.38 (power_set(v2) = v0))
% 12.13/2.38
% 12.13/2.38 Further assumptions not needed in the proof:
% 12.13/2.38 --------------------------------------------
% 12.13/2.38 difference, empty_set, equal_set, greatest, intersection, least,
% 12.13/2.38 least_upper_bound, max, min, order, power_set, product, singleton, sum,
% 12.13/2.38 total_order, union, unordered_pair, upper_bound
% 12.13/2.38
% 12.13/2.38 Those formulas are unsatisfiable:
% 12.13/2.38 ---------------------------------
% 12.13/2.38
% 12.13/2.38 Begin of proof
% 12.13/2.38 |
% 12.13/2.38 | ALPHA: (subset) implies:
% 12.13/2.38 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 12.13/2.38 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) |
% 12.13/2.38 | member(v2, v1) = 0))
% 12.13/2.38 |
% 12.13/2.38 | ALPHA: (lower_bound) implies:
% 12.13/2.38 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (lower_bound(v2, v0, v1)
% 12.13/2.38 | = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ! [v4:
% 12.13/2.38 | int] : (v4 = 0 | ~ (apply(v0, v2, v3) = v4) | ~ $i(v3) | ? [v5:
% 12.13/2.38 | int] : ( ~ (v5 = 0) & member(v3, v1) = v5)))
% 12.13/2.38 |
% 12.13/2.38 | ALPHA: (greatest_lower_bound) implies:
% 12.13/2.38 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 12.13/2.38 | (greatest_lower_bound(v0, v1, v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) |
% 12.13/2.38 | ~ $i(v1) | ~ $i(v0) | (lower_bound(v0, v2, v1) = 0 & member(v0, v1)
% 12.13/2.38 | = 0 & ! [v4: $i] : ( ~ (lower_bound(v4, v2, v1) = 0) | ~ $i(v4) |
% 12.13/2.38 | ? [v5: any] : ? [v6: any] : (apply(v2, v4, v0) = v6 &
% 12.13/2.38 | member(v4, v3) = v5 & ( ~ (v5 = 0) | v6 = 0)))))
% 12.13/2.38 |
% 12.13/2.38 | ALPHA: (function-axioms) implies:
% 12.13/2.38 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 12.13/2.38 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 12.13/2.38 | = v0))
% 12.13/2.38 |
% 12.13/2.38 | DELTA: instantiating (thIV12) with fresh symbols all_25_0, all_25_1 gives:
% 12.13/2.38 | (5) order(all_25_1, all_25_0) = 0 & $i(all_25_0) & $i(all_25_1) & ? [v0:
% 12.13/2.38 | $i] : ? [v1: $i] : (subset(v1, all_25_0) = 0 & subset(v0, v1) = 0 &
% 12.13/2.38 | subset(v0, all_25_0) = 0 & $i(v1) & $i(v0) & ? [v2: $i] : ? [v3:
% 12.13/2.38 | $i] : ? [v4: int] : ( ~ (v4 = 0) & greatest_lower_bound(v3, v1,
% 12.13/2.38 | all_25_1, all_25_0) = 0 & greatest_lower_bound(v2, v0, all_25_1,
% 12.13/2.38 | all_25_0) = 0 & apply(all_25_1, v3, v2) = v4 & $i(v3) & $i(v2)))
% 12.13/2.38 |
% 12.13/2.38 | ALPHA: (5) implies:
% 12.28/2.39 | (6) $i(all_25_1)
% 12.28/2.39 | (7) $i(all_25_0)
% 12.28/2.39 | (8) ? [v0: $i] : ? [v1: $i] : (subset(v1, all_25_0) = 0 & subset(v0, v1)
% 12.28/2.39 | = 0 & subset(v0, all_25_0) = 0 & $i(v1) & $i(v0) & ? [v2: $i] : ?
% 12.28/2.39 | [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & greatest_lower_bound(v3, v1,
% 12.28/2.39 | all_25_1, all_25_0) = 0 & greatest_lower_bound(v2, v0, all_25_1,
% 12.28/2.39 | all_25_0) = 0 & apply(all_25_1, v3, v2) = v4 & $i(v3) & $i(v2)))
% 12.28/2.39 |
% 12.28/2.39 | DELTA: instantiating (8) with fresh symbols all_27_0, all_27_1 gives:
% 12.28/2.39 | (9) subset(all_27_0, all_25_0) = 0 & subset(all_27_1, all_27_0) = 0 &
% 12.28/2.39 | subset(all_27_1, all_25_0) = 0 & $i(all_27_0) & $i(all_27_1) & ? [v0:
% 12.28/2.39 | $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 12.28/2.39 | greatest_lower_bound(v1, all_27_0, all_25_1, all_25_0) = 0 &
% 12.28/2.39 | greatest_lower_bound(v0, all_27_1, all_25_1, all_25_0) = 0 &
% 12.28/2.39 | apply(all_25_1, v1, v0) = v2 & $i(v1) & $i(v0))
% 12.28/2.39 |
% 12.28/2.39 | ALPHA: (9) implies:
% 12.28/2.39 | (10) $i(all_27_1)
% 12.28/2.39 | (11) $i(all_27_0)
% 12.28/2.39 | (12) subset(all_27_1, all_27_0) = 0
% 12.28/2.39 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 12.28/2.39 | greatest_lower_bound(v1, all_27_0, all_25_1, all_25_0) = 0 &
% 12.28/2.39 | greatest_lower_bound(v0, all_27_1, all_25_1, all_25_0) = 0 &
% 12.28/2.39 | apply(all_25_1, v1, v0) = v2 & $i(v1) & $i(v0))
% 12.28/2.39 |
% 12.28/2.39 | DELTA: instantiating (13) with fresh symbols all_29_0, all_29_1, all_29_2
% 12.28/2.39 | gives:
% 12.28/2.39 | (14) ~ (all_29_0 = 0) & greatest_lower_bound(all_29_1, all_27_0, all_25_1,
% 12.28/2.39 | all_25_0) = 0 & greatest_lower_bound(all_29_2, all_27_1, all_25_1,
% 12.28/2.39 | all_25_0) = 0 & apply(all_25_1, all_29_1, all_29_2) = all_29_0 &
% 12.28/2.39 | $i(all_29_1) & $i(all_29_2)
% 12.28/2.39 |
% 12.28/2.39 | ALPHA: (14) implies:
% 12.28/2.39 | (15) ~ (all_29_0 = 0)
% 12.28/2.39 | (16) $i(all_29_2)
% 12.28/2.39 | (17) $i(all_29_1)
% 12.28/2.39 | (18) apply(all_25_1, all_29_1, all_29_2) = all_29_0
% 12.28/2.39 | (19) greatest_lower_bound(all_29_2, all_27_1, all_25_1, all_25_0) = 0
% 12.28/2.39 | (20) greatest_lower_bound(all_29_1, all_27_0, all_25_1, all_25_0) = 0
% 12.28/2.39 |
% 12.28/2.39 | GROUND_INST: instantiating (1) with all_27_1, all_27_0, simplifying with (10),
% 12.28/2.39 | (11), (12) gives:
% 12.28/2.39 | (21) ! [v0: $i] : ( ~ (member(v0, all_27_1) = 0) | ~ $i(v0) | member(v0,
% 12.28/2.39 | all_27_0) = 0)
% 12.28/2.39 |
% 12.28/2.39 | GROUND_INST: instantiating (3) with all_29_2, all_27_1, all_25_1, all_25_0,
% 12.28/2.39 | simplifying with (6), (7), (10), (16), (19) gives:
% 12.28/2.40 | (22) lower_bound(all_29_2, all_25_1, all_27_1) = 0 & member(all_29_2,
% 12.28/2.40 | all_27_1) = 0 & ! [v0: $i] : ( ~ (lower_bound(v0, all_25_1,
% 12.28/2.40 | all_27_1) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] :
% 12.28/2.40 | (apply(all_25_1, v0, all_29_2) = v2 & member(v0, all_25_0) = v1 & (
% 12.28/2.40 | ~ (v1 = 0) | v2 = 0)))
% 12.28/2.40 |
% 12.28/2.40 | ALPHA: (22) implies:
% 12.28/2.40 | (23) member(all_29_2, all_27_1) = 0
% 12.28/2.40 |
% 12.28/2.40 | GROUND_INST: instantiating (3) with all_29_1, all_27_0, all_25_1, all_25_0,
% 12.28/2.40 | simplifying with (6), (7), (11), (17), (20) gives:
% 12.28/2.40 | (24) lower_bound(all_29_1, all_25_1, all_27_0) = 0 & member(all_29_1,
% 12.28/2.40 | all_27_0) = 0 & ! [v0: $i] : ( ~ (lower_bound(v0, all_25_1,
% 12.28/2.40 | all_27_0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] :
% 12.28/2.40 | (apply(all_25_1, v0, all_29_1) = v2 & member(v0, all_25_0) = v1 & (
% 12.28/2.40 | ~ (v1 = 0) | v2 = 0)))
% 12.28/2.40 |
% 12.28/2.40 | ALPHA: (24) implies:
% 12.28/2.40 | (25) lower_bound(all_29_1, all_25_1, all_27_0) = 0
% 12.28/2.40 |
% 12.28/2.40 | GROUND_INST: instantiating (21) with all_29_2, simplifying with (16), (23)
% 12.28/2.40 | gives:
% 12.28/2.40 | (26) member(all_29_2, all_27_0) = 0
% 12.28/2.40 |
% 12.28/2.40 | GROUND_INST: instantiating (2) with all_25_1, all_27_0, all_29_1, simplifying
% 12.28/2.40 | with (6), (11), (17), (25) gives:
% 12.28/2.40 | (27) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (apply(all_25_1, all_29_1,
% 12.28/2.40 | v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & member(v0,
% 12.28/2.40 | all_27_0) = v2))
% 12.28/2.40 |
% 12.28/2.40 | GROUND_INST: instantiating (27) with all_29_2, all_29_0, simplifying with
% 12.28/2.40 | (16), (18) gives:
% 12.28/2.40 | (28) all_29_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_29_2,
% 12.28/2.40 | all_27_0) = v0)
% 12.28/2.40 |
% 12.28/2.40 | BETA: splitting (28) gives:
% 12.28/2.40 |
% 12.28/2.40 | Case 1:
% 12.28/2.40 | |
% 12.28/2.40 | | (29) all_29_0 = 0
% 12.28/2.40 | |
% 12.28/2.40 | | REDUCE: (15), (29) imply:
% 12.28/2.40 | | (30) $false
% 12.28/2.40 | |
% 12.28/2.40 | | CLOSE: (30) is inconsistent.
% 12.28/2.40 | |
% 12.28/2.40 | Case 2:
% 12.28/2.40 | |
% 12.28/2.40 | | (31) ? [v0: int] : ( ~ (v0 = 0) & member(all_29_2, all_27_0) = v0)
% 12.28/2.40 | |
% 12.28/2.40 | | DELTA: instantiating (31) with fresh symbol all_59_0 gives:
% 12.28/2.40 | | (32) ~ (all_59_0 = 0) & member(all_29_2, all_27_0) = all_59_0
% 12.28/2.40 | |
% 12.28/2.40 | | ALPHA: (32) implies:
% 12.28/2.40 | | (33) ~ (all_59_0 = 0)
% 12.28/2.40 | | (34) member(all_29_2, all_27_0) = all_59_0
% 12.28/2.40 | |
% 12.28/2.40 | | GROUND_INST: instantiating (4) with 0, all_59_0, all_27_0, all_29_2,
% 12.28/2.40 | | simplifying with (26), (34) gives:
% 12.28/2.40 | | (35) all_59_0 = 0
% 12.28/2.40 | |
% 12.28/2.40 | | REDUCE: (33), (35) imply:
% 12.28/2.40 | | (36) $false
% 12.28/2.40 | |
% 12.28/2.40 | | CLOSE: (36) is inconsistent.
% 12.28/2.40 | |
% 12.28/2.40 | End of split
% 12.28/2.40 |
% 12.28/2.40 End of proof
% 12.28/2.40 % SZS output end Proof for theBenchmark
% 12.28/2.40
% 12.28/2.40 1887ms
%------------------------------------------------------------------------------