TSTP Solution File: SET798+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET798+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 : n021.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 15:26:29 EDT 2023
% Result : Theorem 9.27s 2.07s
% Output : Proof 11.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET798+4 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 14:56:27 EDT 2023
% 0.13/0.35 % 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
% 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.73/1.17 Prover 1: Preprocessing ...
% 2.73/1.17 Prover 4: Preprocessing ...
% 3.65/1.22 Prover 2: Preprocessing ...
% 3.65/1.22 Prover 3: Preprocessing ...
% 3.65/1.22 Prover 5: Preprocessing ...
% 3.65/1.22 Prover 6: Preprocessing ...
% 3.65/1.22 Prover 0: Preprocessing ...
% 7.09/1.76 Prover 5: Proving ...
% 7.74/1.81 Prover 2: Proving ...
% 7.74/1.86 Prover 6: Proving ...
% 7.74/1.88 Prover 3: Constructing countermodel ...
% 7.74/1.88 Prover 1: Constructing countermodel ...
% 9.27/2.04 Prover 4: Constructing countermodel ...
% 9.27/2.07 Prover 3: proved (1429ms)
% 9.27/2.07
% 9.27/2.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.27/2.07
% 9.27/2.07 Prover 5: stopped
% 9.27/2.07 Prover 2: stopped
% 9.27/2.08 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.27/2.08 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.27/2.08 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.27/2.08 Prover 6: stopped
% 9.27/2.09 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.96/2.09 Prover 0: Proving ...
% 9.96/2.09 Prover 0: stopped
% 9.96/2.09 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.96/2.12 Prover 7: Preprocessing ...
% 9.96/2.13 Prover 11: Preprocessing ...
% 9.96/2.13 Prover 8: Preprocessing ...
% 9.96/2.14 Prover 13: Preprocessing ...
% 9.96/2.15 Prover 10: Preprocessing ...
% 9.96/2.15 Prover 1: Found proof (size 27)
% 9.96/2.15 Prover 1: proved (1519ms)
% 9.96/2.17 Prover 4: stopped
% 9.96/2.17 Prover 10: stopped
% 9.96/2.21 Prover 13: stopped
% 9.96/2.21 Prover 11: stopped
% 9.96/2.21 Prover 7: Warning: ignoring some quantifiers
% 9.96/2.24 Prover 7: Constructing countermodel ...
% 9.96/2.25 Prover 7: stopped
% 9.96/2.31 Prover 8: Warning: ignoring some quantifiers
% 9.96/2.32 Prover 8: Constructing countermodel ...
% 11.07/2.33 Prover 8: stopped
% 11.07/2.33
% 11.07/2.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.07/2.33
% 11.07/2.34 % SZS output start Proof for theBenchmark
% 11.52/2.34 Assumptions after simplification:
% 11.52/2.34 ---------------------------------
% 11.52/2.34
% 11.52/2.34 (lower_bound)
% 11.57/2.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 11.57/2.36 (lower_bound(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 11.57/2.36 $i] : ? [v5: int] : ( ~ (v5 = 0) & apply(v0, v2, v4) = v5 & member(v4,
% 11.57/2.36 v1) = 0 & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 11.57/2.37 (lower_bound(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v3:
% 11.57/2.37 $i] : ! [v4: int] : (v4 = 0 | ~ (apply(v0, v2, v3) = v4) | ~ $i(v3) |
% 11.57/2.37 ? [v5: int] : ( ~ (v5 = 0) & member(v3, v1) = v5)))
% 11.57/2.37
% 11.57/2.37 (subset)
% 11.57/2.37 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 11.57/2.37 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 11.57/2.37 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 11.57/2.37 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 11.57/2.37 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 11.57/2.37
% 11.57/2.37 (thIV10)
% 11.57/2.37 ? [v0: $i] : ? [v1: $i] : (order(v0, v1) = 0 & $i(v1) & $i(v0) & ? [v2: $i]
% 11.57/2.37 : ? [v3: $i] : (subset(v3, v1) = 0 & subset(v2, v3) = 0 & subset(v2, v1) =
% 11.57/2.37 0 & $i(v3) & $i(v2) & ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) &
% 11.57/2.37 lower_bound(v4, v0, v3) = 0 & lower_bound(v4, v0, v2) = v5 & $i(v4))))
% 11.57/2.37
% 11.57/2.37 (function-axioms)
% 11.57/2.38 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 11.57/2.38 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (greatest_lower_bound(v5,
% 11.57/2.38 v4, v3, v2) = v1) | ~ (greatest_lower_bound(v5, v4, v3, v2) = v0)) & !
% 11.57/2.38 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 11.57/2.38 $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (least_upper_bound(v5, v4,
% 11.57/2.38 v3, v2) = v1) | ~ (least_upper_bound(v5, v4, v3, v2) = v0)) & ! [v0:
% 11.57/2.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.57/2.38 : ! [v4: $i] : (v1 = v0 | ~ (min(v4, v3, v2) = v1) | ~ (min(v4, v3, v2) =
% 11.57/2.38 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 11.57/2.38 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (max(v4, v3, v2) = v1) | ~
% 11.57/2.38 (max(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.57/2.38 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 11.57/2.38 (least(v4, v3, v2) = v1) | ~ (least(v4, v3, v2) = v0)) & ! [v0:
% 11.57/2.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.57/2.38 : ! [v4: $i] : (v1 = v0 | ~ (greatest(v4, v3, v2) = v1) | ~ (greatest(v4,
% 11.57/2.38 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 11.57/2.38 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (lower_bound(v4, v3,
% 11.57/2.38 v2) = v1) | ~ (lower_bound(v4, v3, v2) = v0)) & ! [v0:
% 11.57/2.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.57/2.38 : ! [v4: $i] : (v1 = v0 | ~ (upper_bound(v4, v3, v2) = v1) | ~
% 11.57/2.38 (upper_bound(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.57/2.38 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 11.57/2.38 (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0:
% 11.57/2.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.57/2.38 : (v1 = v0 | ~ (total_order(v3, v2) = v1) | ~ (total_order(v3, v2) = v0)) &
% 11.57/2.38 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 11.57/2.38 $i] : (v1 = v0 | ~ (order(v3, v2) = v1) | ~ (order(v3, v2) = v0)) & !
% 11.57/2.38 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.57/2.38 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 11.57/2.38 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.57/2.38 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 11.57/2.38 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 11.57/2.38 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 11.57/2.38 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 11.57/2.39 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 11.57/2.39 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 11.57/2.39 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.57/2.39 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 11.57/2.39 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 11.57/2.39 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.57/2.39 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 11.57/2.39 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 11.57/2.39 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 11.57/2.39 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 11.57/2.39 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 11.57/2.39 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 11.57/2.39 (power_set(v2) = v0))
% 11.57/2.39
% 11.57/2.39 Further assumptions not needed in the proof:
% 11.57/2.39 --------------------------------------------
% 11.57/2.39 difference, empty_set, equal_set, greatest, greatest_lower_bound, intersection,
% 11.57/2.39 least, least_upper_bound, max, min, order, power_set, product, singleton, sum,
% 11.57/2.39 total_order, union, unordered_pair, upper_bound
% 11.57/2.39
% 11.57/2.39 Those formulas are unsatisfiable:
% 11.57/2.39 ---------------------------------
% 11.57/2.39
% 11.57/2.39 Begin of proof
% 11.57/2.39 |
% 11.57/2.39 | ALPHA: (subset) implies:
% 11.57/2.39 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 11.57/2.39 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) |
% 11.57/2.39 | member(v2, v1) = 0))
% 11.57/2.39 |
% 11.57/2.39 | ALPHA: (lower_bound) implies:
% 11.57/2.39 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (lower_bound(v2, v0, v1)
% 11.57/2.39 | = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ! [v4:
% 11.57/2.39 | int] : (v4 = 0 | ~ (apply(v0, v2, v3) = v4) | ~ $i(v3) | ? [v5:
% 11.57/2.39 | int] : ( ~ (v5 = 0) & member(v3, v1) = v5)))
% 11.57/2.39 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 11.57/2.39 | (lower_bound(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 11.57/2.39 | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & apply(v0, v2, v4) = v5 &
% 11.57/2.39 | member(v4, v1) = 0 & $i(v4)))
% 11.57/2.39 |
% 11.57/2.39 | ALPHA: (function-axioms) implies:
% 11.57/2.39 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 11.57/2.39 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 11.57/2.39 | = v0))
% 11.57/2.39 |
% 11.57/2.39 | DELTA: instantiating (thIV10) with fresh symbols all_25_0, all_25_1 gives:
% 11.57/2.39 | (5) order(all_25_1, all_25_0) = 0 & $i(all_25_0) & $i(all_25_1) & ? [v0:
% 11.57/2.39 | $i] : ? [v1: $i] : (subset(v1, all_25_0) = 0 & subset(v0, v1) = 0 &
% 11.57/2.39 | subset(v0, all_25_0) = 0 & $i(v1) & $i(v0) & ? [v2: $i] : ? [v3:
% 11.57/2.39 | int] : ( ~ (v3 = 0) & lower_bound(v2, all_25_1, v1) = 0 &
% 11.57/2.39 | lower_bound(v2, all_25_1, v0) = v3 & $i(v2)))
% 11.57/2.39 |
% 11.57/2.39 | ALPHA: (5) implies:
% 11.57/2.40 | (6) $i(all_25_1)
% 11.57/2.40 | (7) ? [v0: $i] : ? [v1: $i] : (subset(v1, all_25_0) = 0 & subset(v0, v1)
% 11.57/2.40 | = 0 & subset(v0, all_25_0) = 0 & $i(v1) & $i(v0) & ? [v2: $i] : ?
% 11.57/2.40 | [v3: int] : ( ~ (v3 = 0) & lower_bound(v2, all_25_1, v1) = 0 &
% 11.57/2.40 | lower_bound(v2, all_25_1, v0) = v3 & $i(v2)))
% 11.57/2.40 |
% 11.57/2.40 | DELTA: instantiating (7) with fresh symbols all_27_0, all_27_1 gives:
% 11.57/2.40 | (8) subset(all_27_0, all_25_0) = 0 & subset(all_27_1, all_27_0) = 0 &
% 11.57/2.40 | subset(all_27_1, all_25_0) = 0 & $i(all_27_0) & $i(all_27_1) & ? [v0:
% 11.57/2.40 | $i] : ? [v1: int] : ( ~ (v1 = 0) & lower_bound(v0, all_25_1,
% 11.57/2.40 | all_27_0) = 0 & lower_bound(v0, all_25_1, all_27_1) = v1 & $i(v0))
% 11.57/2.40 |
% 11.57/2.40 | ALPHA: (8) implies:
% 11.57/2.40 | (9) $i(all_27_1)
% 11.57/2.40 | (10) $i(all_27_0)
% 11.57/2.40 | (11) subset(all_27_1, all_27_0) = 0
% 11.57/2.40 | (12) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & lower_bound(v0, all_25_1,
% 11.57/2.40 | all_27_0) = 0 & lower_bound(v0, all_25_1, all_27_1) = v1 & $i(v0))
% 11.57/2.40 |
% 11.57/2.40 | DELTA: instantiating (12) with fresh symbols all_29_0, all_29_1 gives:
% 11.57/2.40 | (13) ~ (all_29_0 = 0) & lower_bound(all_29_1, all_25_1, all_27_0) = 0 &
% 11.57/2.40 | lower_bound(all_29_1, all_25_1, all_27_1) = all_29_0 & $i(all_29_1)
% 11.57/2.40 |
% 11.57/2.40 | ALPHA: (13) implies:
% 11.57/2.40 | (14) ~ (all_29_0 = 0)
% 11.57/2.40 | (15) $i(all_29_1)
% 11.57/2.40 | (16) lower_bound(all_29_1, all_25_1, all_27_1) = all_29_0
% 11.57/2.40 | (17) lower_bound(all_29_1, all_25_1, all_27_0) = 0
% 11.57/2.40 |
% 11.57/2.40 | GROUND_INST: instantiating (1) with all_27_1, all_27_0, simplifying with (9),
% 11.57/2.40 | (10), (11) gives:
% 11.57/2.40 | (18) ! [v0: $i] : ( ~ (member(v0, all_27_1) = 0) | ~ $i(v0) | member(v0,
% 11.57/2.40 | all_27_0) = 0)
% 11.57/2.40 |
% 11.57/2.40 | GROUND_INST: instantiating (3) with all_25_1, all_27_1, all_29_1, all_29_0,
% 11.57/2.40 | simplifying with (6), (9), (15), (16) gives:
% 11.57/2.40 | (19) all_29_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 11.57/2.40 | apply(all_25_1, all_29_1, v0) = v1 & member(v0, all_27_1) = 0 &
% 11.57/2.40 | $i(v0))
% 11.57/2.40 |
% 11.57/2.40 | GROUND_INST: instantiating (2) with all_25_1, all_27_0, all_29_1, simplifying
% 11.57/2.40 | with (6), (10), (15), (17) gives:
% 11.57/2.40 | (20) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (apply(all_25_1, all_29_1,
% 11.57/2.40 | v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & member(v0,
% 11.57/2.40 | all_27_0) = v2))
% 11.57/2.40 |
% 11.57/2.40 | BETA: splitting (19) gives:
% 11.57/2.40 |
% 11.57/2.40 | Case 1:
% 11.57/2.40 | |
% 11.57/2.40 | | (21) all_29_0 = 0
% 11.57/2.40 | |
% 11.57/2.40 | | REDUCE: (14), (21) imply:
% 11.57/2.40 | | (22) $false
% 11.57/2.41 | |
% 11.57/2.41 | | CLOSE: (22) is inconsistent.
% 11.57/2.41 | |
% 11.57/2.41 | Case 2:
% 11.57/2.41 | |
% 11.57/2.41 | | (23) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & apply(all_25_1,
% 11.57/2.41 | | all_29_1, v0) = v1 & member(v0, all_27_1) = 0 & $i(v0))
% 11.57/2.41 | |
% 11.57/2.41 | | DELTA: instantiating (23) with fresh symbols all_44_0, all_44_1 gives:
% 11.57/2.41 | | (24) ~ (all_44_0 = 0) & apply(all_25_1, all_29_1, all_44_1) = all_44_0 &
% 11.57/2.41 | | member(all_44_1, all_27_1) = 0 & $i(all_44_1)
% 11.57/2.41 | |
% 11.57/2.41 | | ALPHA: (24) implies:
% 11.57/2.41 | | (25) ~ (all_44_0 = 0)
% 11.57/2.41 | | (26) $i(all_44_1)
% 11.57/2.41 | | (27) member(all_44_1, all_27_1) = 0
% 11.57/2.41 | | (28) apply(all_25_1, all_29_1, all_44_1) = all_44_0
% 11.57/2.41 | |
% 11.57/2.41 | | GROUND_INST: instantiating (18) with all_44_1, simplifying with (26), (27)
% 11.57/2.41 | | gives:
% 11.57/2.41 | | (29) member(all_44_1, all_27_0) = 0
% 11.57/2.41 | |
% 11.57/2.41 | | GROUND_INST: instantiating (20) with all_44_1, all_44_0, simplifying with
% 11.57/2.41 | | (26), (28) gives:
% 11.87/2.41 | | (30) all_44_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_44_1,
% 11.87/2.41 | | all_27_0) = v0)
% 11.87/2.41 | |
% 11.87/2.41 | | BETA: splitting (30) gives:
% 11.87/2.41 | |
% 11.87/2.41 | | Case 1:
% 11.87/2.41 | | |
% 11.87/2.41 | | | (31) all_44_0 = 0
% 11.87/2.41 | | |
% 11.87/2.41 | | | REDUCE: (25), (31) imply:
% 11.87/2.41 | | | (32) $false
% 11.87/2.41 | | |
% 11.87/2.41 | | | CLOSE: (32) is inconsistent.
% 11.87/2.41 | | |
% 11.87/2.41 | | Case 2:
% 11.87/2.41 | | |
% 11.87/2.41 | | | (33) ? [v0: int] : ( ~ (v0 = 0) & member(all_44_1, all_27_0) = v0)
% 11.87/2.41 | | |
% 11.87/2.41 | | | DELTA: instantiating (33) with fresh symbol all_56_0 gives:
% 11.87/2.41 | | | (34) ~ (all_56_0 = 0) & member(all_44_1, all_27_0) = all_56_0
% 11.87/2.41 | | |
% 11.87/2.41 | | | ALPHA: (34) implies:
% 11.87/2.41 | | | (35) ~ (all_56_0 = 0)
% 11.87/2.41 | | | (36) member(all_44_1, all_27_0) = all_56_0
% 11.87/2.41 | | |
% 11.87/2.41 | | | GROUND_INST: instantiating (4) with 0, all_56_0, all_27_0, all_44_1,
% 11.87/2.41 | | | simplifying with (29), (36) gives:
% 11.87/2.41 | | | (37) all_56_0 = 0
% 11.87/2.41 | | |
% 11.87/2.41 | | | REDUCE: (35), (37) imply:
% 11.87/2.41 | | | (38) $false
% 11.87/2.41 | | |
% 11.87/2.41 | | | CLOSE: (38) is inconsistent.
% 11.87/2.41 | | |
% 11.87/2.41 | | End of split
% 11.87/2.41 | |
% 11.87/2.41 | End of split
% 11.87/2.41 |
% 11.87/2.41 End of proof
% 11.87/2.41 % SZS output end Proof for theBenchmark
% 11.87/2.41
% 11.87/2.41 1796ms
%------------------------------------------------------------------------------