TSTP Solution File: SET791+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET791+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 : n012.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 15:26:27 EDT 2023
% Result : Theorem 7.39s 1.76s
% Output : Proof 9.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET791+4 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 12:04:41 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.18/0.61 ________ _____
% 0.18/0.61 ___ __ \_________(_)________________________________
% 0.18/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.62
% 0.18/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.62 (2023-06-19)
% 0.18/0.62
% 0.18/0.62 (c) Philipp Rümmer, 2009-2023
% 0.18/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.62 Amanda Stjerna.
% 0.18/0.62 Free software under BSD-3-Clause.
% 0.18/0.62
% 0.18/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.62
% 0.18/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.64 Running up to 7 provers in parallel.
% 0.18/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.73/1.08 Prover 1: Preprocessing ...
% 2.73/1.09 Prover 4: Preprocessing ...
% 2.73/1.12 Prover 5: Preprocessing ...
% 2.73/1.12 Prover 6: Preprocessing ...
% 2.73/1.12 Prover 0: Preprocessing ...
% 2.73/1.12 Prover 2: Preprocessing ...
% 2.73/1.12 Prover 3: Preprocessing ...
% 5.21/1.44 Prover 5: Proving ...
% 5.21/1.46 Prover 2: Proving ...
% 6.37/1.60 Prover 6: Proving ...
% 6.74/1.63 Prover 3: Constructing countermodel ...
% 6.74/1.65 Prover 1: Constructing countermodel ...
% 7.39/1.76 Prover 3: proved (1109ms)
% 7.39/1.76
% 7.39/1.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.39/1.76
% 7.74/1.77 Prover 2: stopped
% 7.74/1.77 Prover 6: stopped
% 7.74/1.77 Prover 5: stopped
% 7.74/1.78 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.74/1.78 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.74/1.78 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.74/1.78 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.74/1.81 Prover 1: Found proof (size 46)
% 7.74/1.81 Prover 1: proved (1166ms)
% 7.74/1.83 Prover 0: Proving ...
% 7.74/1.83 Prover 4: Constructing countermodel ...
% 7.74/1.83 Prover 11: Preprocessing ...
% 7.74/1.84 Prover 7: Preprocessing ...
% 7.74/1.84 Prover 10: Preprocessing ...
% 7.74/1.84 Prover 8: Preprocessing ...
% 7.74/1.84 Prover 0: stopped
% 8.32/1.85 Prover 4: stopped
% 8.32/1.85 Prover 7: stopped
% 8.32/1.85 Prover 10: stopped
% 8.51/1.90 Prover 11: stopped
% 8.80/1.96 Prover 8: Warning: ignoring some quantifiers
% 8.80/1.97 Prover 8: Constructing countermodel ...
% 8.80/1.97 Prover 8: stopped
% 8.80/1.97
% 8.80/1.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.80/1.97
% 8.80/1.99 % SZS output start Proof for theBenchmark
% 8.80/1.99 Assumptions after simplification:
% 8.80/1.99 ---------------------------------
% 8.80/1.99
% 8.80/1.99 (greatest)
% 8.80/2.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 8.80/2.02 (greatest(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 8.80/2.02 $i] : ? [v5: int] : ( ~ (v5 = 0) & apply(v0, v4, v2) = v5 & member(v4,
% 8.80/2.02 v1) = 0 & $i(v4)) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) = v4))
% 8.80/2.02 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (greatest(v2, v0, v1) = 0) |
% 8.80/2.02 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v2, v1) = 0 & ! [v3: $i] : !
% 8.80/2.02 [v4: int] : (v4 = 0 | ~ (apply(v0, v3, v2) = v4) | ~ $i(v3) | ? [v5:
% 8.80/2.02 int] : ( ~ (v5 = 0) & member(v3, v1) = v5))))
% 8.80/2.02
% 8.80/2.02 (max)
% 8.80/2.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (max(v2,
% 8.80/2.02 v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ( ~
% 8.80/2.02 (v4 = v2) & apply(v0, v2, v4) = 0 & member(v4, v1) = 0 & $i(v4)) | ? [v4:
% 8.80/2.02 int] : ( ~ (v4 = 0) & member(v2, v1) = v4)) & ! [v0: $i] : ! [v1: $i] :
% 8.80/2.02 ! [v2: $i] : ( ~ (max(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 8.80/2.02 (member(v2, v1) = 0 & ! [v3: $i] : (v3 = v2 | ~ (apply(v0, v2, v3) = 0) |
% 8.80/2.03 ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4))))
% 8.80/2.03
% 8.80/2.03 (order)
% 8.80/2.04 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (order(v0, v1) = v2) |
% 8.80/2.04 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6:
% 8.80/2.04 int] : ( ~ (v6 = 0) & apply(v0, v4, v5) = 0 & apply(v0, v3, v5) = v6 &
% 8.80/2.04 apply(v0, v3, v4) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0 &
% 8.80/2.04 member(v3, v1) = 0 & $i(v5) & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: $i]
% 8.80/2.04 : ( ~ (v4 = v3) & apply(v0, v4, v3) = 0 & apply(v0, v3, v4) = 0 & member(v4,
% 8.80/2.04 v1) = 0 & member(v3, v1) = 0 & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4:
% 8.80/2.04 int] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0 &
% 8.80/2.04 $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (order(v0, v1) = 0) | ~ $i(v1)
% 8.80/2.04 | ~ $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5
% 8.80/2.04 = 0 | ~ (apply(v0, v2, v4) = v5) | ~ (apply(v0, v2, v3) = 0) | ~
% 8.80/2.04 $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any] : ? [v8:
% 8.80/2.04 any] : ? [v9: any] : (apply(v0, v3, v4) = v9 & member(v4, v1) = v8 &
% 8.80/2.04 member(v3, v1) = v7 & member(v2, v1) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0)
% 8.80/2.04 | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v2: $i] : ! [v3: $i] : (v3 =
% 8.80/2.04 v2 | ~ (apply(v0, v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v4: any] :
% 8.80/2.04 ? [v5: any] : ? [v6: any] : (apply(v0, v3, v2) = v6 & member(v3, v1) =
% 8.80/2.04 v5 & member(v2, v1) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))
% 8.80/2.04 & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apply(v0, v2, v2) = v3) | ~
% 8.80/2.04 $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) = v4))))
% 8.80/2.04
% 8.80/2.04 (thIV3)
% 8.80/2.04 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 8.80/2.04 max(v2, v0, v1) = v3 & greatest(v2, v0, v1) = 0 & order(v0, v1) = 0 & $i(v2)
% 8.80/2.04 & $i(v1) & $i(v0))
% 8.80/2.04
% 8.80/2.04 (function-axioms)
% 9.27/2.05 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 9.27/2.05 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (greatest_lower_bound(v5,
% 9.27/2.05 v4, v3, v2) = v1) | ~ (greatest_lower_bound(v5, v4, v3, v2) = v0)) & !
% 9.27/2.05 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 9.27/2.05 $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (least_upper_bound(v5, v4,
% 9.27/2.05 v3, v2) = v1) | ~ (least_upper_bound(v5, v4, v3, v2) = v0)) & ! [v0:
% 9.27/2.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.27/2.05 : ! [v4: $i] : (v1 = v0 | ~ (min(v4, v3, v2) = v1) | ~ (min(v4, v3, v2) =
% 9.27/2.05 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 9.27/2.05 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (max(v4, v3, v2) = v1) | ~
% 9.27/2.05 (max(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.27/2.05 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 9.27/2.05 (least(v4, v3, v2) = v1) | ~ (least(v4, v3, v2) = v0)) & ! [v0:
% 9.27/2.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.27/2.05 : ! [v4: $i] : (v1 = v0 | ~ (greatest(v4, v3, v2) = v1) | ~ (greatest(v4,
% 9.27/2.05 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 9.27/2.05 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (lower_bound(v4, v3,
% 9.27/2.05 v2) = v1) | ~ (lower_bound(v4, v3, v2) = v0)) & ! [v0:
% 9.27/2.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.27/2.05 : ! [v4: $i] : (v1 = v0 | ~ (upper_bound(v4, v3, v2) = v1) | ~
% 9.27/2.05 (upper_bound(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.27/2.05 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 9.27/2.05 (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0:
% 9.27/2.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.27/2.05 : (v1 = v0 | ~ (total_order(v3, v2) = v1) | ~ (total_order(v3, v2) = v0)) &
% 9.27/2.05 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 9.27/2.05 $i] : (v1 = v0 | ~ (order(v3, v2) = v1) | ~ (order(v3, v2) = v0)) & !
% 9.27/2.05 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 9.27/2.05 $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 9.27/2.05
% 9.27/2.05 Further assumptions not needed in the proof:
% 9.27/2.05 --------------------------------------------
% 9.27/2.05 greatest_lower_bound, least, least_upper_bound, lower_bound, min, total_order,
% 9.27/2.05 upper_bound
% 9.27/2.05
% 9.27/2.05 Those formulas are unsatisfiable:
% 9.27/2.05 ---------------------------------
% 9.27/2.05
% 9.27/2.05 Begin of proof
% 9.27/2.05 |
% 9.27/2.05 | ALPHA: (order) implies:
% 9.27/2.06 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (order(v0, v1) = 0) | ~ $i(v1) | ~
% 9.27/2.06 | $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] :
% 9.27/2.06 | (v5 = 0 | ~ (apply(v0, v2, v4) = v5) | ~ (apply(v0, v2, v3) = 0)
% 9.27/2.06 | | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any]
% 9.27/2.06 | : ? [v8: any] : ? [v9: any] : (apply(v0, v3, v4) = v9 &
% 9.27/2.06 | member(v4, v1) = v8 & member(v3, v1) = v7 & member(v2, v1) = v6
% 9.27/2.06 | & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) &
% 9.27/2.06 | ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ (apply(v0, v2, v3) = 0) |
% 9.27/2.06 | ~ $i(v3) | ~ $i(v2) | ? [v4: any] : ? [v5: any] : ? [v6: any]
% 9.27/2.06 | : (apply(v0, v3, v2) = v6 & member(v3, v1) = v5 & member(v2, v1)
% 9.27/2.06 | = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v2:
% 9.27/2.06 | $i] : ! [v3: int] : (v3 = 0 | ~ (apply(v0, v2, v2) = v3) | ~
% 9.27/2.06 | $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) = v4))))
% 9.27/2.06 |
% 9.27/2.06 | ALPHA: (greatest) implies:
% 9.27/2.06 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (greatest(v2, v0, v1) =
% 9.27/2.06 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v2, v1) = 0 & !
% 9.27/2.06 | [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (apply(v0, v3, v2) = v4) |
% 9.27/2.06 | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = 0) & member(v3, v1) = v5))))
% 9.27/2.06 |
% 9.27/2.06 | ALPHA: (max) implies:
% 9.27/2.06 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 9.27/2.06 | (max(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 9.27/2.06 | $i] : ( ~ (v4 = v2) & apply(v0, v2, v4) = 0 & member(v4, v1) = 0 &
% 9.27/2.06 | $i(v4)) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) = v4))
% 9.27/2.06 |
% 9.27/2.06 | ALPHA: (function-axioms) implies:
% 9.27/2.06 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 9.27/2.06 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 9.27/2.06 | = v0))
% 9.27/2.06 |
% 9.27/2.06 | DELTA: instantiating (thIV3) with fresh symbols all_13_0, all_13_1, all_13_2,
% 9.27/2.06 | all_13_3 gives:
% 9.27/2.06 | (5) ~ (all_13_0 = 0) & max(all_13_1, all_13_3, all_13_2) = all_13_0 &
% 9.27/2.06 | greatest(all_13_1, all_13_3, all_13_2) = 0 & order(all_13_3, all_13_2)
% 9.27/2.06 | = 0 & $i(all_13_1) & $i(all_13_2) & $i(all_13_3)
% 9.27/2.06 |
% 9.27/2.06 | ALPHA: (5) implies:
% 9.27/2.07 | (6) ~ (all_13_0 = 0)
% 9.27/2.07 | (7) $i(all_13_3)
% 9.27/2.07 | (8) $i(all_13_2)
% 9.27/2.07 | (9) $i(all_13_1)
% 9.27/2.07 | (10) order(all_13_3, all_13_2) = 0
% 9.27/2.07 | (11) greatest(all_13_1, all_13_3, all_13_2) = 0
% 9.27/2.07 | (12) max(all_13_1, all_13_3, all_13_2) = all_13_0
% 9.27/2.07 |
% 9.27/2.07 | GROUND_INST: instantiating (1) with all_13_3, all_13_2, simplifying with (7),
% 9.27/2.07 | (8), (10) gives:
% 9.27/2.07 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 9.27/2.07 | (apply(all_13_3, v0, v2) = v3) | ~ (apply(all_13_3, v0, v1) = 0) |
% 9.27/2.07 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ?
% 9.27/2.07 | [v6: any] : ? [v7: any] : (apply(all_13_3, v1, v2) = v7 &
% 9.27/2.07 | member(v2, all_13_2) = v6 & member(v1, all_13_2) = v5 & member(v0,
% 9.27/2.07 | all_13_2) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~
% 9.27/2.07 | (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~
% 9.27/2.07 | (apply(all_13_3, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any]
% 9.27/2.07 | : ? [v3: any] : ? [v4: any] : (apply(all_13_3, v1, v0) = v4 &
% 9.27/2.07 | member(v1, all_13_2) = v3 & member(v0, all_13_2) = v2 & ( ~ (v4 =
% 9.27/2.07 | 0) | ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: int]
% 9.27/2.07 | : (v1 = 0 | ~ (apply(all_13_3, v0, v0) = v1) | ~ $i(v0) | ? [v2:
% 9.27/2.07 | int] : ( ~ (v2 = 0) & member(v0, all_13_2) = v2))
% 9.27/2.07 |
% 9.27/2.07 | ALPHA: (13) implies:
% 9.27/2.07 | (14) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (apply(all_13_3, v0, v1) =
% 9.27/2.07 | 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4:
% 9.27/2.07 | any] : (apply(all_13_3, v1, v0) = v4 & member(v1, all_13_2) = v3 &
% 9.27/2.07 | member(v0, all_13_2) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 =
% 9.27/2.07 | 0))))
% 9.27/2.07 |
% 9.27/2.07 | GROUND_INST: instantiating (2) with all_13_3, all_13_2, all_13_1, simplifying
% 9.27/2.07 | with (7), (8), (9), (11) gives:
% 9.27/2.07 | (15) member(all_13_1, all_13_2) = 0 & ! [v0: $i] : ! [v1: int] : (v1 = 0
% 9.27/2.07 | | ~ (apply(all_13_3, v0, all_13_1) = v1) | ~ $i(v0) | ? [v2: int]
% 9.27/2.07 | : ( ~ (v2 = 0) & member(v0, all_13_2) = v2))
% 9.27/2.07 |
% 9.27/2.07 | ALPHA: (15) implies:
% 9.27/2.07 | (16) member(all_13_1, all_13_2) = 0
% 9.27/2.08 | (17) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (apply(all_13_3, v0,
% 9.27/2.08 | all_13_1) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 9.27/2.08 | member(v0, all_13_2) = v2))
% 9.27/2.08 |
% 9.27/2.08 | GROUND_INST: instantiating (3) with all_13_3, all_13_2, all_13_1, all_13_0,
% 9.27/2.08 | simplifying with (7), (8), (9), (12) gives:
% 9.27/2.08 | (18) all_13_0 = 0 | ? [v0: any] : ( ~ (v0 = all_13_1) & apply(all_13_3,
% 9.27/2.08 | all_13_1, v0) = 0 & member(v0, all_13_2) = 0 & $i(v0)) | ? [v0:
% 9.27/2.08 | int] : ( ~ (v0 = 0) & member(all_13_1, all_13_2) = v0)
% 9.27/2.08 |
% 9.27/2.08 | BETA: splitting (18) gives:
% 9.27/2.08 |
% 9.27/2.08 | Case 1:
% 9.27/2.08 | |
% 9.27/2.08 | | (19) all_13_0 = 0
% 9.27/2.08 | |
% 9.27/2.08 | | REDUCE: (6), (19) imply:
% 9.27/2.08 | | (20) $false
% 9.27/2.08 | |
% 9.27/2.08 | | CLOSE: (20) is inconsistent.
% 9.27/2.08 | |
% 9.27/2.08 | Case 2:
% 9.27/2.08 | |
% 9.27/2.08 | | (21) ? [v0: any] : ( ~ (v0 = all_13_1) & apply(all_13_3, all_13_1, v0) =
% 9.27/2.08 | | 0 & member(v0, all_13_2) = 0 & $i(v0)) | ? [v0: int] : ( ~ (v0 =
% 9.27/2.08 | | 0) & member(all_13_1, all_13_2) = v0)
% 9.27/2.08 | |
% 9.27/2.08 | | BETA: splitting (21) gives:
% 9.27/2.08 | |
% 9.27/2.08 | | Case 1:
% 9.27/2.08 | | |
% 9.27/2.08 | | | (22) ? [v0: any] : ( ~ (v0 = all_13_1) & apply(all_13_3, all_13_1, v0)
% 9.27/2.08 | | | = 0 & member(v0, all_13_2) = 0 & $i(v0))
% 9.27/2.08 | | |
% 9.27/2.08 | | | DELTA: instantiating (22) with fresh symbol all_30_0 gives:
% 9.27/2.08 | | | (23) ~ (all_30_0 = all_13_1) & apply(all_13_3, all_13_1, all_30_0) = 0
% 9.27/2.08 | | | & member(all_30_0, all_13_2) = 0 & $i(all_30_0)
% 9.27/2.08 | | |
% 9.27/2.08 | | | ALPHA: (23) implies:
% 9.27/2.08 | | | (24) ~ (all_30_0 = all_13_1)
% 9.27/2.08 | | | (25) $i(all_30_0)
% 9.27/2.08 | | | (26) member(all_30_0, all_13_2) = 0
% 9.27/2.08 | | | (27) apply(all_13_3, all_13_1, all_30_0) = 0
% 9.27/2.08 | | |
% 9.27/2.08 | | | GROUND_INST: instantiating (14) with all_13_1, all_30_0, simplifying with
% 9.27/2.08 | | | (9), (25), (27) gives:
% 9.27/2.08 | | | (28) all_30_0 = all_13_1 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 9.27/2.08 | | | (apply(all_13_3, all_30_0, all_13_1) = v2 & member(all_30_0,
% 9.27/2.08 | | | all_13_2) = v1 & member(all_13_1, all_13_2) = v0 & ( ~ (v2 =
% 9.27/2.08 | | | 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 9.27/2.08 | | |
% 9.27/2.08 | | | BETA: splitting (28) gives:
% 9.27/2.08 | | |
% 9.27/2.08 | | | Case 1:
% 9.27/2.08 | | | |
% 9.27/2.08 | | | | (29) all_30_0 = all_13_1
% 9.27/2.08 | | | |
% 9.27/2.08 | | | | REDUCE: (24), (29) imply:
% 9.27/2.08 | | | | (30) $false
% 9.27/2.08 | | | |
% 9.27/2.08 | | | | CLOSE: (30) is inconsistent.
% 9.27/2.08 | | | |
% 9.27/2.08 | | | Case 2:
% 9.27/2.08 | | | |
% 9.27/2.09 | | | | (31) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_13_3,
% 9.27/2.09 | | | | all_30_0, all_13_1) = v2 & member(all_30_0, all_13_2) = v1 &
% 9.27/2.09 | | | | member(all_13_1, all_13_2) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) |
% 9.27/2.09 | | | | ~ (v0 = 0)))
% 9.27/2.09 | | | |
% 9.27/2.09 | | | | DELTA: instantiating (31) with fresh symbols all_39_0, all_39_1,
% 9.27/2.09 | | | | all_39_2 gives:
% 9.27/2.09 | | | | (32) apply(all_13_3, all_30_0, all_13_1) = all_39_0 &
% 9.27/2.09 | | | | member(all_30_0, all_13_2) = all_39_1 & member(all_13_1,
% 9.27/2.09 | | | | all_13_2) = all_39_2 & ( ~ (all_39_0 = 0) | ~ (all_39_1 = 0)
% 9.27/2.09 | | | | | ~ (all_39_2 = 0))
% 9.27/2.09 | | | |
% 9.27/2.09 | | | | ALPHA: (32) implies:
% 9.27/2.09 | | | | (33) member(all_13_1, all_13_2) = all_39_2
% 9.27/2.09 | | | | (34) member(all_30_0, all_13_2) = all_39_1
% 9.27/2.09 | | | | (35) apply(all_13_3, all_30_0, all_13_1) = all_39_0
% 9.27/2.09 | | | | (36) ~ (all_39_0 = 0) | ~ (all_39_1 = 0) | ~ (all_39_2 = 0)
% 9.27/2.09 | | | |
% 9.27/2.09 | | | | GROUND_INST: instantiating (4) with 0, all_39_2, all_13_2, all_13_1,
% 9.27/2.09 | | | | simplifying with (16), (33) gives:
% 9.27/2.09 | | | | (37) all_39_2 = 0
% 9.27/2.09 | | | |
% 9.27/2.09 | | | | GROUND_INST: instantiating (4) with 0, all_39_1, all_13_2, all_30_0,
% 9.27/2.09 | | | | simplifying with (26), (34) gives:
% 9.27/2.09 | | | | (38) all_39_1 = 0
% 9.27/2.09 | | | |
% 9.27/2.09 | | | | BETA: splitting (36) gives:
% 9.27/2.09 | | | |
% 9.27/2.09 | | | | Case 1:
% 9.27/2.09 | | | | |
% 9.27/2.09 | | | | | (39) ~ (all_39_0 = 0)
% 9.27/2.09 | | | | |
% 9.27/2.09 | | | | | GROUND_INST: instantiating (17) with all_30_0, all_39_0, simplifying
% 9.27/2.09 | | | | | with (25), (35) gives:
% 9.27/2.09 | | | | | (40) all_39_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_30_0,
% 9.27/2.09 | | | | | all_13_2) = v0)
% 9.27/2.09 | | | | |
% 9.27/2.09 | | | | | BETA: splitting (40) gives:
% 9.27/2.09 | | | | |
% 9.27/2.09 | | | | | Case 1:
% 9.27/2.09 | | | | | |
% 9.27/2.09 | | | | | | (41) all_39_0 = 0
% 9.27/2.09 | | | | | |
% 9.27/2.09 | | | | | | REDUCE: (39), (41) imply:
% 9.27/2.09 | | | | | | (42) $false
% 9.27/2.09 | | | | | |
% 9.27/2.09 | | | | | | CLOSE: (42) is inconsistent.
% 9.27/2.09 | | | | | |
% 9.27/2.09 | | | | | Case 2:
% 9.27/2.09 | | | | | |
% 9.27/2.09 | | | | | | (43) ? [v0: int] : ( ~ (v0 = 0) & member(all_30_0, all_13_2) =
% 9.27/2.09 | | | | | | v0)
% 9.27/2.09 | | | | | |
% 9.27/2.09 | | | | | | DELTA: instantiating (43) with fresh symbol all_56_0 gives:
% 9.27/2.09 | | | | | | (44) ~ (all_56_0 = 0) & member(all_30_0, all_13_2) = all_56_0
% 9.27/2.09 | | | | | |
% 9.27/2.09 | | | | | | ALPHA: (44) implies:
% 9.27/2.09 | | | | | | (45) ~ (all_56_0 = 0)
% 9.27/2.09 | | | | | | (46) member(all_30_0, all_13_2) = all_56_0
% 9.27/2.09 | | | | | |
% 9.27/2.09 | | | | | | GROUND_INST: instantiating (4) with 0, all_56_0, all_13_2, all_30_0,
% 9.27/2.09 | | | | | | simplifying with (26), (46) gives:
% 9.27/2.09 | | | | | | (47) all_56_0 = 0
% 9.27/2.09 | | | | | |
% 9.27/2.09 | | | | | | REDUCE: (45), (47) imply:
% 9.27/2.09 | | | | | | (48) $false
% 9.27/2.09 | | | | | |
% 9.27/2.09 | | | | | | CLOSE: (48) is inconsistent.
% 9.27/2.09 | | | | | |
% 9.27/2.09 | | | | | End of split
% 9.27/2.09 | | | | |
% 9.27/2.09 | | | | Case 2:
% 9.27/2.09 | | | | |
% 9.27/2.09 | | | | | (49) ~ (all_39_1 = 0) | ~ (all_39_2 = 0)
% 9.27/2.09 | | | | |
% 9.27/2.09 | | | | | BETA: splitting (49) gives:
% 9.27/2.09 | | | | |
% 9.27/2.09 | | | | | Case 1:
% 9.27/2.09 | | | | | |
% 9.27/2.09 | | | | | | (50) ~ (all_39_1 = 0)
% 9.27/2.09 | | | | | |
% 9.27/2.09 | | | | | | REDUCE: (38), (50) imply:
% 9.27/2.09 | | | | | | (51) $false
% 9.27/2.09 | | | | | |
% 9.27/2.09 | | | | | | CLOSE: (51) is inconsistent.
% 9.27/2.09 | | | | | |
% 9.27/2.09 | | | | | Case 2:
% 9.27/2.09 | | | | | |
% 9.27/2.09 | | | | | | (52) ~ (all_39_2 = 0)
% 9.27/2.09 | | | | | |
% 9.27/2.09 | | | | | | REDUCE: (37), (52) imply:
% 9.27/2.09 | | | | | | (53) $false
% 9.27/2.09 | | | | | |
% 9.27/2.09 | | | | | | CLOSE: (53) is inconsistent.
% 9.27/2.09 | | | | | |
% 9.27/2.09 | | | | | End of split
% 9.27/2.09 | | | | |
% 9.27/2.09 | | | | End of split
% 9.27/2.09 | | | |
% 9.27/2.09 | | | End of split
% 9.27/2.09 | | |
% 9.27/2.09 | | Case 2:
% 9.27/2.09 | | |
% 9.27/2.09 | | | (54) ? [v0: int] : ( ~ (v0 = 0) & member(all_13_1, all_13_2) = v0)
% 9.27/2.09 | | |
% 9.27/2.09 | | | DELTA: instantiating (54) with fresh symbol all_30_0 gives:
% 9.27/2.09 | | | (55) ~ (all_30_0 = 0) & member(all_13_1, all_13_2) = all_30_0
% 9.27/2.09 | | |
% 9.27/2.09 | | | ALPHA: (55) implies:
% 9.27/2.09 | | | (56) ~ (all_30_0 = 0)
% 9.27/2.10 | | | (57) member(all_13_1, all_13_2) = all_30_0
% 9.27/2.10 | | |
% 9.27/2.10 | | | GROUND_INST: instantiating (4) with 0, all_30_0, all_13_2, all_13_1,
% 9.27/2.10 | | | simplifying with (16), (57) gives:
% 9.27/2.10 | | | (58) all_30_0 = 0
% 9.27/2.10 | | |
% 9.27/2.10 | | | REDUCE: (56), (58) imply:
% 9.27/2.10 | | | (59) $false
% 9.27/2.10 | | |
% 9.27/2.10 | | | CLOSE: (59) is inconsistent.
% 9.27/2.10 | | |
% 9.27/2.10 | | End of split
% 9.27/2.10 | |
% 9.27/2.10 | End of split
% 9.27/2.10 |
% 9.27/2.10 End of proof
% 9.27/2.10 % SZS output end Proof for theBenchmark
% 9.27/2.10
% 9.27/2.10 1479ms
%------------------------------------------------------------------------------