TSTP Solution File: KRS171+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KRS171+1 : TPTP v8.1.2. Released v3.1.0.
% 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 05:51:31 EDT 2023
% Result : Theorem 3.81s 1.32s
% Output : Proof 5.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS171+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 02:07:58 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.59 ________ _____
% 0.18/0.59 ___ __ \_________(_)________________________________
% 0.18/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.59
% 0.18/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.59 (2023-06-19)
% 0.18/0.59
% 0.18/0.59 (c) Philipp Rümmer, 2009-2023
% 0.18/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.59 Amanda Stjerna.
% 0.18/0.59 Free software under BSD-3-Clause.
% 0.18/0.59
% 0.18/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.59
% 0.18/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.60 Running up to 7 provers in parallel.
% 0.18/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.18/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 1.85/0.97 Prover 1: Preprocessing ...
% 1.85/0.98 Prover 4: Preprocessing ...
% 1.85/1.01 Prover 6: Preprocessing ...
% 1.85/1.01 Prover 3: Preprocessing ...
% 1.85/1.01 Prover 0: Preprocessing ...
% 1.85/1.01 Prover 2: Preprocessing ...
% 1.85/1.01 Prover 5: Preprocessing ...
% 2.91/1.11 Prover 5: Proving ...
% 2.91/1.12 Prover 2: Proving ...
% 2.91/1.16 Prover 6: Constructing countermodel ...
% 2.91/1.16 Prover 3: Constructing countermodel ...
% 2.91/1.16 Prover 1: Constructing countermodel ...
% 3.42/1.17 Prover 4: Constructing countermodel ...
% 3.63/1.22 Prover 0: Proving ...
% 3.81/1.31 Prover 6: proved (693ms)
% 3.81/1.32
% 3.81/1.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.81/1.32
% 3.81/1.32 Prover 3: proved (696ms)
% 3.81/1.32
% 3.81/1.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.81/1.32
% 4.51/1.32 Prover 0: stopped
% 4.51/1.32 Prover 5: stopped
% 4.51/1.32 Prover 2: stopped
% 4.51/1.33 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.51/1.33 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.51/1.33 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.51/1.33 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.51/1.33 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.51/1.34 Prover 7: Preprocessing ...
% 4.51/1.35 Prover 13: Preprocessing ...
% 4.51/1.35 Prover 8: Preprocessing ...
% 4.51/1.35 Prover 11: Preprocessing ...
% 4.51/1.36 Prover 10: Preprocessing ...
% 4.51/1.37 Prover 13: Warning: ignoring some quantifiers
% 4.51/1.37 Prover 10: Warning: ignoring some quantifiers
% 4.51/1.37 Prover 10: Constructing countermodel ...
% 4.51/1.37 Prover 7: Warning: ignoring some quantifiers
% 4.51/1.38 Prover 7: Constructing countermodel ...
% 4.51/1.38 Prover 13: Constructing countermodel ...
% 4.51/1.39 Prover 10: gave up
% 4.51/1.40 Prover 8: Warning: ignoring some quantifiers
% 4.51/1.40 Prover 13: gave up
% 4.51/1.41 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 4.51/1.41 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 4.51/1.41 Prover 8: Constructing countermodel ...
% 4.51/1.42 Prover 16: Preprocessing ...
% 4.51/1.42 Prover 4: Found proof (size 68)
% 4.51/1.42 Prover 4: proved (802ms)
% 4.51/1.42 Prover 19: Preprocessing ...
% 4.51/1.42 Prover 1: Found proof (size 54)
% 4.51/1.42 Prover 1: proved (811ms)
% 4.51/1.43 Prover 7: stopped
% 4.51/1.44 Prover 8: stopped
% 4.51/1.44 Prover 16: Warning: ignoring some quantifiers
% 4.51/1.44 Prover 16: Constructing countermodel ...
% 4.51/1.44 Prover 16: stopped
% 4.51/1.45 Prover 11: Constructing countermodel ...
% 4.51/1.45 Prover 11: stopped
% 4.51/1.46 Prover 19: Warning: ignoring some quantifiers
% 4.51/1.47 Prover 19: Constructing countermodel ...
% 4.51/1.48 Prover 19: stopped
% 4.51/1.48
% 4.51/1.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.51/1.48
% 4.51/1.49 % SZS output start Proof for theBenchmark
% 5.28/1.49 Assumptions after simplification:
% 5.28/1.49 ---------------------------------
% 5.28/1.49
% 5.28/1.50 (axiom_0)
% 5.28/1.53 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ $i(v0)) &
% 5.28/1.53 ! [v0: $i] : ( ~ (cowlNothing(v0) = 0) | ~ $i(v0))
% 5.28/1.53
% 5.28/1.53 (axiom_1)
% 5.28/1.53 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (xsd_integer(v0) = v1) | ~ $i(v0) |
% 5.28/1.53 xsd_string(v0) = 0) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 5.28/1.53 (xsd_string(v0) = v1) | ~ $i(v0) | xsd_integer(v0) = 0) & ! [v0: $i] : ( ~
% 5.28/1.53 (xsd_integer(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 5.28/1.53 xsd_string(v0) = v1)) & ! [v0: $i] : ( ~ (xsd_string(v0) = 0) | ~ $i(v0)
% 5.28/1.53 | ? [v1: int] : ( ~ (v1 = 0) & xsd_integer(v0) = v1))
% 5.28/1.53
% 5.28/1.53 (axiom_2)
% 5.28/1.54 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (rhasLeader(v0, v1) =
% 5.28/1.54 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & rhasHead(v0,
% 5.28/1.54 v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ (rhasHead(v0, v1) = 0) | ~
% 5.28/1.54 $i(v1) | ~ $i(v0) | rhasLeader(v0, v1) = 0)
% 5.28/1.54
% 5.28/1.54 (axiom_3)
% 5.28/1.54 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (rhasHead(v0, v1) =
% 5.28/1.54 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & rhasLeader(v0,
% 5.28/1.54 v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ (rhasLeader(v0, v1) = 0) |
% 5.28/1.54 ~ $i(v1) | ~ $i(v0) | rhasHead(v0, v1) = 0)
% 5.28/1.54
% 5.28/1.54 (the_axiom)
% 5.28/1.54 ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : ? [v4: $i] : ?
% 5.28/1.54 [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: any] : ($i(v7)
% 5.28/1.54 & $i(v4) & $i(v1) & $i(v0) & ((rhasLeader(v0, v1) = v2 & rhasHead(v0, v1) =
% 5.28/1.54 v3 & ((v3 = 0 & ~ (v2 = 0)) | (v2 = 0 & ~ (v3 = 0)))) |
% 5.28/1.54 (xsd_integer(v4) = v6 & xsd_string(v4) = v5 & ((v6 = 0 & v5 = 0) | ( ~ (v6
% 5.28/1.54 = 0) & ~ (v5 = 0)))) | (cowlNothing(v7) = v9 & cowlThing(v7) = v8
% 5.28/1.54 & ( ~ (v8 = 0) | v9 = 0))))
% 5.28/1.54
% 5.28/1.54 (function-axioms)
% 5.28/1.55 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 5.28/1.55 [v3: $i] : (v1 = v0 | ~ (rhasLeader(v3, v2) = v1) | ~ (rhasLeader(v3, v2) =
% 5.28/1.55 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 5.28/1.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (rhasHead(v3, v2) = v1) | ~ (rhasHead(v3,
% 5.28/1.55 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 5.28/1.55 ! [v2: $i] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0))
% 5.28/1.55 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 5.28/1.55 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) & ! [v0:
% 5.28/1.55 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 5.28/1.55 ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) & ! [v0:
% 5.28/1.55 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 5.28/1.55 ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0))
% 5.28/1.55
% 5.28/1.55 Those formulas are unsatisfiable:
% 5.28/1.55 ---------------------------------
% 5.28/1.55
% 5.28/1.55 Begin of proof
% 5.28/1.55 |
% 5.28/1.55 | ALPHA: (axiom_0) implies:
% 5.28/1.55 | (1) ! [v0: $i] : ( ~ (cowlNothing(v0) = 0) | ~ $i(v0))
% 5.28/1.55 | (2) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~
% 5.28/1.55 | $i(v0))
% 5.28/1.55 |
% 5.28/1.55 | ALPHA: (axiom_1) implies:
% 5.28/1.55 | (3) ! [v0: $i] : ( ~ (xsd_integer(v0) = 0) | ~ $i(v0) | ? [v1: int] : (
% 5.28/1.55 | ~ (v1 = 0) & xsd_string(v0) = v1))
% 5.28/1.55 | (4) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~
% 5.28/1.55 | $i(v0) | xsd_integer(v0) = 0)
% 5.28/1.56 | (5) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (xsd_integer(v0) = v1) | ~
% 5.28/1.56 | $i(v0) | xsd_string(v0) = 0)
% 5.28/1.56 |
% 5.28/1.56 | ALPHA: (axiom_2) implies:
% 5.28/1.56 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (rhasLeader(v0,
% 5.28/1.56 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 5.28/1.56 | rhasHead(v0, v1) = v3))
% 5.28/1.56 |
% 5.28/1.56 | ALPHA: (axiom_3) implies:
% 5.28/1.56 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (rhasHead(v0,
% 5.28/1.56 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 5.28/1.56 | rhasLeader(v0, v1) = v3))
% 5.28/1.56 |
% 5.28/1.56 | ALPHA: (function-axioms) implies:
% 5.28/1.56 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 5.28/1.56 | (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0))
% 5.28/1.56 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 5.28/1.56 | ! [v3: $i] : (v1 = v0 | ~ (rhasHead(v3, v2) = v1) | ~ (rhasHead(v3,
% 5.28/1.56 | v2) = v0))
% 5.28/1.56 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 5.28/1.56 | : ! [v3: $i] : (v1 = v0 | ~ (rhasLeader(v3, v2) = v1) | ~
% 5.28/1.56 | (rhasLeader(v3, v2) = v0))
% 5.28/1.56 |
% 5.28/1.56 | DELTA: instantiating (the_axiom) with fresh symbols all_7_0, all_7_1, all_7_2,
% 5.28/1.56 | all_7_3, all_7_4, all_7_5, all_7_6, all_7_7, all_7_8, all_7_9 gives:
% 5.28/1.56 | (11) $i(all_7_2) & $i(all_7_5) & $i(all_7_8) & $i(all_7_9) &
% 5.28/1.56 | ((rhasLeader(all_7_9, all_7_8) = all_7_7 & rhasHead(all_7_9, all_7_8)
% 5.28/1.56 | = all_7_6 & ((all_7_6 = 0 & ~ (all_7_7 = 0)) | (all_7_7 = 0 & ~
% 5.28/1.56 | (all_7_6 = 0)))) | (xsd_integer(all_7_5) = all_7_3 &
% 5.28/1.56 | xsd_string(all_7_5) = all_7_4 & ((all_7_3 = 0 & all_7_4 = 0) | ( ~
% 5.28/1.56 | (all_7_3 = 0) & ~ (all_7_4 = 0)))) | (cowlNothing(all_7_2) =
% 5.28/1.56 | all_7_0 & cowlThing(all_7_2) = all_7_1 & ( ~ (all_7_1 = 0) |
% 5.28/1.56 | all_7_0 = 0)))
% 5.28/1.56 |
% 5.28/1.56 | ALPHA: (11) implies:
% 5.28/1.56 | (12) $i(all_7_9)
% 5.28/1.56 | (13) $i(all_7_8)
% 5.28/1.56 | (14) $i(all_7_5)
% 5.28/1.57 | (15) $i(all_7_2)
% 5.28/1.57 | (16) (rhasLeader(all_7_9, all_7_8) = all_7_7 & rhasHead(all_7_9, all_7_8) =
% 5.28/1.57 | all_7_6 & ((all_7_6 = 0 & ~ (all_7_7 = 0)) | (all_7_7 = 0 & ~
% 5.28/1.57 | (all_7_6 = 0)))) | (xsd_integer(all_7_5) = all_7_3 &
% 5.28/1.57 | xsd_string(all_7_5) = all_7_4 & ((all_7_3 = 0 & all_7_4 = 0) | ( ~
% 5.28/1.57 | (all_7_3 = 0) & ~ (all_7_4 = 0)))) | (cowlNothing(all_7_2) =
% 5.28/1.57 | all_7_0 & cowlThing(all_7_2) = all_7_1 & ( ~ (all_7_1 = 0) | all_7_0
% 5.28/1.57 | = 0))
% 5.28/1.57 |
% 5.28/1.57 | BETA: splitting (16) gives:
% 5.93/1.57 |
% 5.93/1.57 | Case 1:
% 5.93/1.57 | |
% 5.93/1.57 | | (17) rhasLeader(all_7_9, all_7_8) = all_7_7 & rhasHead(all_7_9, all_7_8)
% 5.93/1.57 | | = all_7_6 & ((all_7_6 = 0 & ~ (all_7_7 = 0)) | (all_7_7 = 0 & ~
% 5.93/1.57 | | (all_7_6 = 0)))
% 5.93/1.57 | |
% 5.93/1.57 | | ALPHA: (17) implies:
% 5.93/1.57 | | (18) rhasHead(all_7_9, all_7_8) = all_7_6
% 5.93/1.57 | | (19) rhasLeader(all_7_9, all_7_8) = all_7_7
% 5.93/1.57 | | (20) (all_7_6 = 0 & ~ (all_7_7 = 0)) | (all_7_7 = 0 & ~ (all_7_6 = 0))
% 5.93/1.57 | |
% 5.93/1.57 | | GROUND_INST: instantiating (7) with all_7_9, all_7_8, all_7_6, simplifying
% 5.93/1.57 | | with (12), (13), (18) gives:
% 5.93/1.57 | | (21) all_7_6 = 0 | ? [v0: int] : ( ~ (v0 = 0) & rhasLeader(all_7_9,
% 5.93/1.57 | | all_7_8) = v0)
% 5.93/1.57 | |
% 5.93/1.57 | | GROUND_INST: instantiating (6) with all_7_9, all_7_8, all_7_7, simplifying
% 5.93/1.57 | | with (12), (13), (19) gives:
% 5.93/1.57 | | (22) all_7_7 = 0 | ? [v0: int] : ( ~ (v0 = 0) & rhasHead(all_7_9,
% 5.93/1.57 | | all_7_8) = v0)
% 5.93/1.57 | |
% 5.93/1.57 | | BETA: splitting (20) gives:
% 5.93/1.57 | |
% 5.93/1.57 | | Case 1:
% 5.93/1.57 | | |
% 5.93/1.57 | | | (23) all_7_6 = 0 & ~ (all_7_7 = 0)
% 5.93/1.57 | | |
% 5.93/1.57 | | | ALPHA: (23) implies:
% 5.93/1.57 | | | (24) all_7_6 = 0
% 5.93/1.57 | | | (25) ~ (all_7_7 = 0)
% 5.93/1.57 | | |
% 5.93/1.57 | | | REDUCE: (18), (24) imply:
% 5.93/1.57 | | | (26) rhasHead(all_7_9, all_7_8) = 0
% 5.93/1.57 | | |
% 5.93/1.57 | | | BETA: splitting (22) gives:
% 5.93/1.57 | | |
% 5.93/1.57 | | | Case 1:
% 5.93/1.57 | | | |
% 5.93/1.57 | | | | (27) all_7_7 = 0
% 5.93/1.57 | | | |
% 5.93/1.57 | | | | REDUCE: (25), (27) imply:
% 5.93/1.57 | | | | (28) $false
% 5.96/1.57 | | | |
% 5.96/1.57 | | | | CLOSE: (28) is inconsistent.
% 5.96/1.57 | | | |
% 5.96/1.57 | | | Case 2:
% 5.96/1.57 | | | |
% 5.96/1.57 | | | | (29) ? [v0: int] : ( ~ (v0 = 0) & rhasHead(all_7_9, all_7_8) = v0)
% 5.96/1.57 | | | |
% 5.96/1.57 | | | | DELTA: instantiating (29) with fresh symbol all_27_0 gives:
% 5.96/1.58 | | | | (30) ~ (all_27_0 = 0) & rhasHead(all_7_9, all_7_8) = all_27_0
% 5.96/1.58 | | | |
% 5.96/1.58 | | | | ALPHA: (30) implies:
% 5.96/1.58 | | | | (31) ~ (all_27_0 = 0)
% 5.96/1.58 | | | | (32) rhasHead(all_7_9, all_7_8) = all_27_0
% 5.96/1.58 | | | |
% 5.96/1.58 | | | | GROUND_INST: instantiating (9) with 0, all_27_0, all_7_8, all_7_9,
% 5.96/1.58 | | | | simplifying with (26), (32) gives:
% 5.96/1.58 | | | | (33) all_27_0 = 0
% 5.96/1.58 | | | |
% 5.96/1.58 | | | | REDUCE: (31), (33) imply:
% 5.96/1.58 | | | | (34) $false
% 5.96/1.58 | | | |
% 5.96/1.58 | | | | CLOSE: (34) is inconsistent.
% 5.96/1.58 | | | |
% 5.96/1.58 | | | End of split
% 5.96/1.58 | | |
% 5.96/1.58 | | Case 2:
% 5.96/1.58 | | |
% 5.96/1.58 | | | (35) all_7_7 = 0 & ~ (all_7_6 = 0)
% 5.96/1.58 | | |
% 5.96/1.58 | | | ALPHA: (35) implies:
% 5.96/1.58 | | | (36) all_7_7 = 0
% 5.96/1.58 | | | (37) ~ (all_7_6 = 0)
% 5.96/1.58 | | |
% 5.96/1.58 | | | REDUCE: (19), (36) imply:
% 5.96/1.58 | | | (38) rhasLeader(all_7_9, all_7_8) = 0
% 5.96/1.58 | | |
% 5.96/1.58 | | | BETA: splitting (21) gives:
% 5.96/1.58 | | |
% 5.96/1.58 | | | Case 1:
% 5.96/1.58 | | | |
% 5.96/1.58 | | | | (39) all_7_6 = 0
% 5.96/1.58 | | | |
% 5.96/1.58 | | | | REDUCE: (37), (39) imply:
% 5.96/1.58 | | | | (40) $false
% 5.96/1.58 | | | |
% 5.96/1.58 | | | | CLOSE: (40) is inconsistent.
% 5.96/1.58 | | | |
% 5.96/1.58 | | | Case 2:
% 5.96/1.58 | | | |
% 5.96/1.58 | | | | (41) ? [v0: int] : ( ~ (v0 = 0) & rhasLeader(all_7_9, all_7_8) = v0)
% 5.96/1.58 | | | |
% 5.96/1.58 | | | | DELTA: instantiating (41) with fresh symbol all_27_0 gives:
% 5.96/1.58 | | | | (42) ~ (all_27_0 = 0) & rhasLeader(all_7_9, all_7_8) = all_27_0
% 5.96/1.58 | | | |
% 5.96/1.58 | | | | ALPHA: (42) implies:
% 5.96/1.58 | | | | (43) ~ (all_27_0 = 0)
% 5.96/1.58 | | | | (44) rhasLeader(all_7_9, all_7_8) = all_27_0
% 5.96/1.58 | | | |
% 5.96/1.58 | | | | GROUND_INST: instantiating (10) with 0, all_27_0, all_7_8, all_7_9,
% 5.96/1.58 | | | | simplifying with (38), (44) gives:
% 5.96/1.58 | | | | (45) all_27_0 = 0
% 5.96/1.58 | | | |
% 5.96/1.58 | | | | REDUCE: (43), (45) imply:
% 5.96/1.58 | | | | (46) $false
% 5.96/1.58 | | | |
% 5.96/1.58 | | | | CLOSE: (46) is inconsistent.
% 5.96/1.58 | | | |
% 5.96/1.58 | | | End of split
% 5.96/1.58 | | |
% 5.96/1.58 | | End of split
% 5.96/1.58 | |
% 5.96/1.58 | Case 2:
% 5.96/1.58 | |
% 5.96/1.58 | | (47) (xsd_integer(all_7_5) = all_7_3 & xsd_string(all_7_5) = all_7_4 &
% 5.96/1.58 | | ((all_7_3 = 0 & all_7_4 = 0) | ( ~ (all_7_3 = 0) & ~ (all_7_4 =
% 5.96/1.58 | | 0)))) | (cowlNothing(all_7_2) = all_7_0 & cowlThing(all_7_2)
% 5.96/1.58 | | = all_7_1 & ( ~ (all_7_1 = 0) | all_7_0 = 0))
% 5.96/1.58 | |
% 5.96/1.58 | | BETA: splitting (47) gives:
% 5.96/1.58 | |
% 5.96/1.58 | | Case 1:
% 5.96/1.58 | | |
% 5.96/1.58 | | | (48) xsd_integer(all_7_5) = all_7_3 & xsd_string(all_7_5) = all_7_4 &
% 5.96/1.58 | | | ((all_7_3 = 0 & all_7_4 = 0) | ( ~ (all_7_3 = 0) & ~ (all_7_4 =
% 5.96/1.58 | | | 0)))
% 5.96/1.58 | | |
% 5.96/1.58 | | | ALPHA: (48) implies:
% 5.96/1.58 | | | (49) xsd_string(all_7_5) = all_7_4
% 5.96/1.58 | | | (50) xsd_integer(all_7_5) = all_7_3
% 5.96/1.58 | | | (51) (all_7_3 = 0 & all_7_4 = 0) | ( ~ (all_7_3 = 0) & ~ (all_7_4 =
% 5.96/1.58 | | | 0))
% 5.96/1.58 | | |
% 5.96/1.58 | | | GROUND_INST: instantiating (4) with all_7_5, all_7_4, simplifying with
% 5.96/1.58 | | | (14), (49) gives:
% 5.96/1.58 | | | (52) all_7_4 = 0 | xsd_integer(all_7_5) = 0
% 5.96/1.58 | | |
% 5.96/1.58 | | | GROUND_INST: instantiating (5) with all_7_5, all_7_3, simplifying with
% 5.96/1.58 | | | (14), (50) gives:
% 5.96/1.58 | | | (53) all_7_3 = 0 | xsd_string(all_7_5) = 0
% 5.96/1.58 | | |
% 5.96/1.59 | | | BETA: splitting (51) gives:
% 5.96/1.59 | | |
% 5.96/1.59 | | | Case 1:
% 5.96/1.59 | | | |
% 5.96/1.59 | | | | (54) all_7_3 = 0 & all_7_4 = 0
% 5.96/1.59 | | | |
% 5.96/1.59 | | | | ALPHA: (54) implies:
% 5.96/1.59 | | | | (55) all_7_4 = 0
% 5.96/1.59 | | | | (56) all_7_3 = 0
% 5.96/1.59 | | | |
% 5.96/1.59 | | | | REDUCE: (50), (56) imply:
% 5.96/1.59 | | | | (57) xsd_integer(all_7_5) = 0
% 5.96/1.59 | | | |
% 5.96/1.59 | | | | REDUCE: (49), (55) imply:
% 5.96/1.59 | | | | (58) xsd_string(all_7_5) = 0
% 5.96/1.59 | | | |
% 5.96/1.59 | | | | REF_CLOSE: (3), (8), (14), (57), (58) are inconsistent by sub-proof #1.
% 5.96/1.59 | | | |
% 5.96/1.59 | | | Case 2:
% 5.96/1.59 | | | |
% 5.96/1.59 | | | | (59) ~ (all_7_3 = 0) & ~ (all_7_4 = 0)
% 5.96/1.59 | | | |
% 5.96/1.59 | | | | ALPHA: (59) implies:
% 5.96/1.59 | | | | (60) ~ (all_7_4 = 0)
% 5.96/1.59 | | | | (61) ~ (all_7_3 = 0)
% 5.96/1.59 | | | |
% 5.96/1.59 | | | | BETA: splitting (53) gives:
% 5.96/1.59 | | | |
% 5.96/1.59 | | | | Case 1:
% 5.96/1.59 | | | | |
% 5.96/1.59 | | | | | (62) xsd_string(all_7_5) = 0
% 5.96/1.59 | | | | |
% 5.96/1.59 | | | | | BETA: splitting (52) gives:
% 5.96/1.59 | | | | |
% 5.96/1.59 | | | | | Case 1:
% 5.96/1.59 | | | | | |
% 5.96/1.59 | | | | | | (63) xsd_integer(all_7_5) = 0
% 5.96/1.59 | | | | | |
% 5.96/1.59 | | | | | | REF_CLOSE: (3), (8), (14), (62), (63) are inconsistent by sub-proof
% 5.96/1.59 | | | | | | #1.
% 5.96/1.59 | | | | | |
% 5.96/1.59 | | | | | Case 2:
% 5.96/1.59 | | | | | |
% 5.96/1.59 | | | | | | (64) all_7_4 = 0
% 5.96/1.59 | | | | | |
% 5.96/1.59 | | | | | | REDUCE: (60), (64) imply:
% 5.96/1.59 | | | | | | (65) $false
% 5.96/1.59 | | | | | |
% 5.96/1.59 | | | | | | CLOSE: (65) is inconsistent.
% 5.96/1.59 | | | | | |
% 5.96/1.59 | | | | | End of split
% 5.96/1.59 | | | | |
% 5.96/1.59 | | | | Case 2:
% 5.96/1.59 | | | | |
% 5.96/1.59 | | | | | (66) all_7_3 = 0
% 5.96/1.59 | | | | |
% 5.96/1.59 | | | | | REDUCE: (61), (66) imply:
% 5.96/1.59 | | | | | (67) $false
% 5.96/1.59 | | | | |
% 5.96/1.59 | | | | | CLOSE: (67) is inconsistent.
% 5.96/1.59 | | | | |
% 5.96/1.59 | | | | End of split
% 5.96/1.59 | | | |
% 5.96/1.59 | | | End of split
% 5.96/1.59 | | |
% 5.96/1.59 | | Case 2:
% 5.96/1.59 | | |
% 5.96/1.59 | | | (68) cowlNothing(all_7_2) = all_7_0 & cowlThing(all_7_2) = all_7_1 & (
% 5.96/1.59 | | | ~ (all_7_1 = 0) | all_7_0 = 0)
% 5.96/1.59 | | |
% 5.96/1.59 | | | ALPHA: (68) implies:
% 5.96/1.59 | | | (69) cowlThing(all_7_2) = all_7_1
% 5.96/1.59 | | | (70) cowlNothing(all_7_2) = all_7_0
% 5.96/1.59 | | | (71) ~ (all_7_1 = 0) | all_7_0 = 0
% 5.96/1.59 | | |
% 5.96/1.59 | | | GROUND_INST: instantiating (2) with all_7_2, all_7_1, simplifying with
% 5.96/1.59 | | | (15), (69) gives:
% 5.96/1.59 | | | (72) all_7_1 = 0
% 5.96/1.59 | | |
% 5.96/1.59 | | | BETA: splitting (71) gives:
% 5.96/1.59 | | |
% 5.96/1.59 | | | Case 1:
% 5.96/1.59 | | | |
% 5.96/1.59 | | | | (73) ~ (all_7_1 = 0)
% 5.96/1.59 | | | |
% 5.96/1.59 | | | | REDUCE: (72), (73) imply:
% 5.96/1.59 | | | | (74) $false
% 5.96/1.59 | | | |
% 5.96/1.59 | | | | CLOSE: (74) is inconsistent.
% 5.96/1.59 | | | |
% 5.96/1.59 | | | Case 2:
% 5.96/1.59 | | | |
% 5.96/1.59 | | | | (75) all_7_0 = 0
% 5.96/1.59 | | | |
% 5.96/1.59 | | | | REDUCE: (70), (75) imply:
% 5.96/1.59 | | | | (76) cowlNothing(all_7_2) = 0
% 5.96/1.59 | | | |
% 5.96/1.59 | | | | GROUND_INST: instantiating (1) with all_7_2, simplifying with (15), (76)
% 5.96/1.59 | | | | gives:
% 5.96/1.59 | | | | (77) $false
% 5.96/1.59 | | | |
% 5.96/1.59 | | | | CLOSE: (77) is inconsistent.
% 5.96/1.59 | | | |
% 5.96/1.59 | | | End of split
% 5.96/1.59 | | |
% 5.96/1.59 | | End of split
% 5.96/1.59 | |
% 5.96/1.59 | End of split
% 5.96/1.59 |
% 5.96/1.59 End of proof
% 5.96/1.59
% 5.96/1.59 Sub-proof #1 shows that the following formulas are inconsistent:
% 5.96/1.59 ----------------------------------------------------------------
% 5.96/1.59 (1) xsd_integer(all_7_5) = 0
% 5.96/1.59 (2) $i(all_7_5)
% 5.96/1.59 (3) ! [v0: $i] : ( ~ (xsd_integer(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~
% 5.96/1.59 (v1 = 0) & xsd_string(v0) = v1))
% 5.96/1.60 (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 5.96/1.60 (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0))
% 5.96/1.60 (5) xsd_string(all_7_5) = 0
% 5.96/1.60
% 5.96/1.60 Begin of proof
% 5.96/1.60 |
% 5.96/1.60 | GROUND_INST: instantiating (3) with all_7_5, simplifying with (1), (2) gives:
% 5.96/1.60 | (6) ? [v0: int] : ( ~ (v0 = 0) & xsd_string(all_7_5) = v0)
% 5.96/1.60 |
% 5.96/1.60 | DELTA: instantiating (6) with fresh symbol all_28_0 gives:
% 5.96/1.60 | (7) ~ (all_28_0 = 0) & xsd_string(all_7_5) = all_28_0
% 5.96/1.60 |
% 5.96/1.60 | ALPHA: (7) implies:
% 5.96/1.60 | (8) ~ (all_28_0 = 0)
% 5.96/1.60 | (9) xsd_string(all_7_5) = all_28_0
% 5.96/1.60 |
% 5.96/1.60 | GROUND_INST: instantiating (4) with 0, all_28_0, all_7_5, simplifying with
% 5.96/1.60 | (5), (9) gives:
% 5.96/1.60 | (10) all_28_0 = 0
% 5.96/1.60 |
% 5.96/1.60 | REDUCE: (8), (10) imply:
% 5.96/1.60 | (11) $false
% 5.96/1.60 |
% 5.96/1.60 | CLOSE: (11) is inconsistent.
% 5.96/1.60 |
% 5.96/1.60 End of proof
% 5.96/1.60 % SZS output end Proof for theBenchmark
% 5.96/1.60
% 5.96/1.60 1005ms
%------------------------------------------------------------------------------