TSTP Solution File: SWB029+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWB029+2 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n005.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 20:11:54 EDT 2023
% Result : Theorem 8.25s 2.06s
% Output : Proof 11.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11 % Problem : SWB029+2 : TPTP v8.1.2. Released v5.2.0.
% 0.05/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.10/0.32 % Computer : n005.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Sun Aug 27 06:42:08 EDT 2023
% 0.10/0.33 % CPUTime :
% 0.17/0.62 ________ _____
% 0.17/0.62 ___ __ \_________(_)________________________________
% 0.17/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.17/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.17/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.17/0.62
% 0.17/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.17/0.62 (2023-06-19)
% 0.17/0.62
% 0.17/0.62 (c) Philipp Rümmer, 2009-2023
% 0.17/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.17/0.62 Amanda Stjerna.
% 0.17/0.62 Free software under BSD-3-Clause.
% 0.17/0.62
% 0.17/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.17/0.62
% 0.17/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.17/0.63 Running up to 7 provers in parallel.
% 0.52/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.52/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.52/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.52/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.52/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.52/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.52/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.24/1.10 Prover 4: Preprocessing ...
% 2.24/1.10 Prover 1: Preprocessing ...
% 2.64/1.16 Prover 2: Preprocessing ...
% 2.64/1.16 Prover 5: Preprocessing ...
% 2.64/1.16 Prover 3: Preprocessing ...
% 2.64/1.16 Prover 0: Preprocessing ...
% 2.64/1.16 Prover 6: Preprocessing ...
% 4.64/1.51 Prover 5: Proving ...
% 4.64/1.53 Prover 2: Proving ...
% 5.19/1.62 Prover 3: Constructing countermodel ...
% 5.51/1.62 Prover 6: Proving ...
% 5.51/1.63 Prover 1: Constructing countermodel ...
% 8.25/2.05 Prover 3: proved (1397ms)
% 8.25/2.06
% 8.25/2.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.25/2.06
% 8.25/2.07 Prover 2: stopped
% 8.25/2.07 Prover 5: stopped
% 8.25/2.08 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.25/2.08 Prover 6: stopped
% 8.25/2.09 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.25/2.09 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.25/2.09 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.25/2.11 Prover 7: Preprocessing ...
% 8.25/2.12 Prover 10: Preprocessing ...
% 8.25/2.13 Prover 11: Preprocessing ...
% 8.25/2.13 Prover 8: Preprocessing ...
% 9.22/2.20 Prover 10: Warning: ignoring some quantifiers
% 9.22/2.22 Prover 7: Warning: ignoring some quantifiers
% 9.22/2.22 Prover 10: Constructing countermodel ...
% 9.22/2.24 Prover 7: Constructing countermodel ...
% 9.81/2.27 Prover 1: Found proof (size 34)
% 9.81/2.27 Prover 1: proved (1632ms)
% 9.81/2.27 Prover 8: Warning: ignoring some quantifiers
% 9.81/2.27 Prover 10: stopped
% 9.81/2.28 Prover 7: stopped
% 9.81/2.28 Prover 8: Constructing countermodel ...
% 9.81/2.28 Prover 11: stopped
% 9.81/2.29 Prover 8: stopped
% 10.32/2.38 Prover 4: Constructing countermodel ...
% 10.32/2.39 Prover 4: stopped
% 11.03/2.51 Prover 0: Proving ...
% 11.03/2.52 Prover 0: stopped
% 11.03/2.52
% 11.03/2.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.03/2.52
% 11.03/2.54 % SZS output start Proof for theBenchmark
% 11.03/2.54 Assumptions after simplification:
% 11.03/2.54 ---------------------------------
% 11.03/2.54
% 11.03/2.54 (owl_bool_complementof_class)
% 11.03/2.59 $i(uri_owl_complementOf) & ! [v0: $i] : ! [v1: $i] : ( ~
% 11.03/2.60 (iext(uri_owl_complementOf, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | (ic(v1) =
% 11.03/2.60 0 & ic(v0) = 0 & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (icext(v0, v2)
% 11.03/2.60 = v3) | ~ $i(v2) | icext(v1, v2) = 0) & ! [v2: $i] : ( ~ (icext(v0,
% 11.03/2.60 v2) = 0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & icext(v1, v2) =
% 11.03/2.60 v3))))
% 11.03/2.60
% 11.03/2.60 (owl_bool_intersectionof_class_002)
% 11.03/2.62 $i(uri_owl_intersectionOf) & $i(uri_rdf_nil) & $i(uri_rdf_rest) &
% 11.03/2.62 $i(uri_rdf_first) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 11.03/2.62 [v4: $i] : ! [v5: any] : ! [v6: any] : ( ~ (ic(v4) = v6) | ~
% 11.03/2.62 (iext(uri_owl_intersectionOf, v0, v1) = v5) | ~ (iext(uri_rdf_rest, v3,
% 11.03/2.62 uri_rdf_nil) = 0) | ~ (iext(uri_rdf_first, v1, v2) = 0) | ~ $i(v4) |
% 11.03/2.62 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] :
% 11.03/2.62 ? [v9: any] : ? [v10: any] : (ic(v2) = v10 & ic(v0) = v9 &
% 11.03/2.62 iext(uri_rdf_rest, v1, v3) = v7 & iext(uri_rdf_first, v3, v4) = v8 & ( ~
% 11.03/2.62 (v8 = 0) | ~ (v7 = 0) | (( ~ (v10 = 0) | ~ (v9 = 0) | ~ (v6 = 0) | v5
% 11.03/2.62 = 0 | ? [v11: $i] : ? [v12: any] : ? [v13: any] : ? [v14: any] :
% 11.03/2.62 (icext(v4, v11) = v14 & icext(v2, v11) = v13 & icext(v0, v11) = v12
% 11.03/2.62 & $i(v11) & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0)) & (v12 =
% 11.03/2.62 0 | (v14 = 0 & v13 = 0)))) & ( ~ (v5 = 0) | (v10 = 0 & v9 = 0 &
% 11.03/2.62 v6 = 0 & ! [v11: $i] : ! [v12: int] : (v12 = 0 | ~ (icext(v0,
% 11.03/2.62 v11) = v12) | ~ $i(v11) | ? [v13: any] : ? [v14: any] :
% 11.03/2.62 (icext(v4, v11) = v14 & icext(v2, v11) = v13 & ( ~ (v14 = 0) |
% 11.03/2.62 ~ (v13 = 0)))) & ! [v11: $i] : ( ~ (icext(v0, v11) = 0) |
% 11.03/2.62 ~ $i(v11) | (icext(v4, v11) = 0 & icext(v2, v11) = 0))))))))
% 11.03/2.62
% 11.03/2.62 (rdfs_cext_def)
% 11.03/2.62 $i(uri_rdf_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 11.03/2.62 (iext(uri_rdf_type, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : (
% 11.03/2.62 ~ (v3 = 0) & icext(v1, v0) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 11.03/2.62 (iext(uri_rdf_type, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | icext(v1, v0) =
% 11.03/2.62 0)
% 11.03/2.63
% 11.03/2.63 (testcase_conclusion_fullish_029_Ex_Falso_Quodlibet)
% 11.03/2.63 $i(uri_ex_B) & $i(uri_ex_w) & $i(uri_rdf_type) & ? [v0: int] : ( ~ (v0 = 0) &
% 11.03/2.63 iext(uri_rdf_type, uri_ex_w, uri_ex_B) = v0)
% 11.03/2.63
% 11.03/2.63 (testcase_premise_fullish_029_Ex_Falso_Quodlibet)
% 11.03/2.63 $i(uri_owl_Class) & $i(uri_ex_A) & $i(uri_ex_B) & $i(uri_ex_w) &
% 11.03/2.63 $i(uri_owl_intersectionOf) & $i(uri_rdf_nil) & $i(uri_rdf_rest) &
% 11.03/2.63 $i(uri_rdf_first) & $i(uri_owl_complementOf) & $i(uri_rdf_type) & ? [v0: any]
% 11.03/2.63 : ? [v1: any] : (iext(uri_rdf_type, uri_ex_A, uri_owl_Class) = v0 &
% 11.03/2.63 iext(uri_rdf_type, uri_ex_B, uri_owl_Class) = v1 & ? [v2: $i] : ? [v3: $i]
% 11.03/2.63 : ? [v4: $i] : ? [v5: $i] : (v1 = 0 & v0 = 0 &
% 11.03/2.63 iext(uri_owl_intersectionOf, v2, v4) = 0 & iext(uri_rdf_rest, v5,
% 11.03/2.63 uri_rdf_nil) = 0 & iext(uri_rdf_rest, v4, v5) = 0 & iext(uri_rdf_first,
% 11.03/2.63 v5, v3) = 0 & iext(uri_rdf_first, v4, uri_ex_A) = 0 &
% 11.03/2.63 iext(uri_owl_complementOf, v3, uri_ex_A) = 0 & iext(uri_rdf_type,
% 11.03/2.63 uri_ex_w, v2) = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2)))
% 11.03/2.63
% 11.03/2.63 (function-axioms)
% 11.03/2.64 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 11.03/2.64 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (iext(v4, v3, v2) = v1) | ~ (iext(v4,
% 11.03/2.64 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 11.03/2.64 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (icext(v3, v2) = v1) | ~
% 11.03/2.64 (icext(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.03/2.64 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ic(v2) = v1) | ~ (ic(v2)
% 11.03/2.64 = v0))
% 11.03/2.64
% 11.03/2.64 Those formulas are unsatisfiable:
% 11.03/2.64 ---------------------------------
% 11.03/2.64
% 11.03/2.64 Begin of proof
% 11.03/2.64 |
% 11.03/2.64 | ALPHA: (rdfs_cext_def) implies:
% 11.03/2.64 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (iext(uri_rdf_type, v0, v1) = 0) | ~
% 11.03/2.64 | $i(v1) | ~ $i(v0) | icext(v1, v0) = 0)
% 11.03/2.64 |
% 11.03/2.64 | ALPHA: (owl_bool_complementof_class) implies:
% 11.03/2.65 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (iext(uri_owl_complementOf, v0, v1) =
% 11.03/2.65 | 0) | ~ $i(v1) | ~ $i(v0) | (ic(v1) = 0 & ic(v0) = 0 & ! [v2: $i]
% 11.03/2.65 | : ! [v3: int] : (v3 = 0 | ~ (icext(v0, v2) = v3) | ~ $i(v2) |
% 11.03/2.65 | icext(v1, v2) = 0) & ! [v2: $i] : ( ~ (icext(v0, v2) = 0) | ~
% 11.03/2.65 | $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & icext(v1, v2) = v3))))
% 11.03/2.65 |
% 11.03/2.65 | ALPHA: (owl_bool_intersectionof_class_002) implies:
% 11.41/2.66 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 11.41/2.66 | ! [v5: any] : ! [v6: any] : ( ~ (ic(v4) = v6) | ~
% 11.41/2.66 | (iext(uri_owl_intersectionOf, v0, v1) = v5) | ~ (iext(uri_rdf_rest,
% 11.41/2.66 | v3, uri_rdf_nil) = 0) | ~ (iext(uri_rdf_first, v1, v2) = 0) | ~
% 11.41/2.66 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any]
% 11.41/2.66 | : ? [v8: any] : ? [v9: any] : ? [v10: any] : (ic(v2) = v10 &
% 11.41/2.66 | ic(v0) = v9 & iext(uri_rdf_rest, v1, v3) = v7 & iext(uri_rdf_first,
% 11.41/2.66 | v3, v4) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0) | (( ~ (v10 = 0) | ~
% 11.41/2.66 | (v9 = 0) | ~ (v6 = 0) | v5 = 0 | ? [v11: $i] : ? [v12:
% 11.41/2.66 | any] : ? [v13: any] : ? [v14: any] : (icext(v4, v11) =
% 11.41/2.66 | v14 & icext(v2, v11) = v13 & icext(v0, v11) = v12 & $i(v11)
% 11.41/2.66 | & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0)) & (v12 = 0 |
% 11.41/2.66 | (v14 = 0 & v13 = 0)))) & ( ~ (v5 = 0) | (v10 = 0 & v9 = 0
% 11.41/2.66 | & v6 = 0 & ! [v11: $i] : ! [v12: int] : (v12 = 0 | ~
% 11.41/2.66 | (icext(v0, v11) = v12) | ~ $i(v11) | ? [v13: any] : ?
% 11.41/2.66 | [v14: any] : (icext(v4, v11) = v14 & icext(v2, v11) = v13
% 11.41/2.66 | & ( ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v11: $i] : ( ~
% 11.41/2.66 | (icext(v0, v11) = 0) | ~ $i(v11) | (icext(v4, v11) = 0 &
% 11.41/2.66 | icext(v2, v11) = 0))))))))
% 11.41/2.66 |
% 11.41/2.66 | ALPHA: (testcase_premise_fullish_029_Ex_Falso_Quodlibet) implies:
% 11.41/2.66 | (4) $i(uri_ex_A)
% 11.41/2.66 | (5) ? [v0: any] : ? [v1: any] : (iext(uri_rdf_type, uri_ex_A,
% 11.41/2.66 | uri_owl_Class) = v0 & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) =
% 11.41/2.66 | v1 & ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (v1 = 0
% 11.41/2.66 | & v0 = 0 & iext(uri_owl_intersectionOf, v2, v4) = 0 &
% 11.41/2.66 | iext(uri_rdf_rest, v5, uri_rdf_nil) = 0 & iext(uri_rdf_rest, v4,
% 11.41/2.66 | v5) = 0 & iext(uri_rdf_first, v5, v3) = 0 & iext(uri_rdf_first,
% 11.41/2.66 | v4, uri_ex_A) = 0 & iext(uri_owl_complementOf, v3, uri_ex_A) = 0
% 11.41/2.66 | & iext(uri_rdf_type, uri_ex_w, v2) = 0 & $i(v5) & $i(v4) & $i(v3) &
% 11.41/2.66 | $i(v2)))
% 11.41/2.66 |
% 11.41/2.66 | ALPHA: (testcase_conclusion_fullish_029_Ex_Falso_Quodlibet) implies:
% 11.41/2.66 | (6) $i(uri_ex_w)
% 11.41/2.66 |
% 11.41/2.66 | ALPHA: (function-axioms) implies:
% 11.41/2.66 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 11.41/2.66 | ! [v3: $i] : (v1 = v0 | ~ (icext(v3, v2) = v1) | ~ (icext(v3, v2) =
% 11.90/2.67 | v0))
% 11.90/2.67 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 11.90/2.67 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (iext(v4, v3, v2) = v1) | ~
% 11.90/2.67 | (iext(v4, v3, v2) = v0))
% 11.90/2.67 |
% 11.90/2.67 | DELTA: instantiating (5) with fresh symbols all_9_0, all_9_1 gives:
% 11.90/2.67 | (9) iext(uri_rdf_type, uri_ex_A, uri_owl_Class) = all_9_1 &
% 11.90/2.67 | iext(uri_rdf_type, uri_ex_B, uri_owl_Class) = all_9_0 & ? [v0: $i] :
% 11.90/2.67 | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (all_9_0 = 0 & all_9_1 = 0 &
% 11.90/2.67 | iext(uri_owl_intersectionOf, v0, v2) = 0 & iext(uri_rdf_rest, v3,
% 11.90/2.67 | uri_rdf_nil) = 0 & iext(uri_rdf_rest, v2, v3) = 0 &
% 11.90/2.67 | iext(uri_rdf_first, v3, v1) = 0 & iext(uri_rdf_first, v2, uri_ex_A) =
% 11.90/2.67 | 0 & iext(uri_owl_complementOf, v1, uri_ex_A) = 0 & iext(uri_rdf_type,
% 11.90/2.67 | uri_ex_w, v0) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 11.90/2.67 |
% 11.90/2.67 | ALPHA: (9) implies:
% 11.90/2.67 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (all_9_0 = 0 &
% 11.90/2.67 | all_9_1 = 0 & iext(uri_owl_intersectionOf, v0, v2) = 0 &
% 11.90/2.67 | iext(uri_rdf_rest, v3, uri_rdf_nil) = 0 & iext(uri_rdf_rest, v2, v3)
% 11.90/2.67 | = 0 & iext(uri_rdf_first, v3, v1) = 0 & iext(uri_rdf_first, v2,
% 11.90/2.67 | uri_ex_A) = 0 & iext(uri_owl_complementOf, v1, uri_ex_A) = 0 &
% 11.90/2.67 | iext(uri_rdf_type, uri_ex_w, v0) = 0 & $i(v3) & $i(v2) & $i(v1) &
% 11.90/2.67 | $i(v0))
% 11.90/2.67 |
% 11.90/2.67 | DELTA: instantiating (10) with fresh symbols all_11_0, all_11_1, all_11_2,
% 11.90/2.67 | all_11_3 gives:
% 11.90/2.67 | (11) all_9_0 = 0 & all_9_1 = 0 & iext(uri_owl_intersectionOf, all_11_3,
% 11.90/2.67 | all_11_1) = 0 & iext(uri_rdf_rest, all_11_0, uri_rdf_nil) = 0 &
% 11.90/2.67 | iext(uri_rdf_rest, all_11_1, all_11_0) = 0 & iext(uri_rdf_first,
% 11.90/2.67 | all_11_0, all_11_2) = 0 & iext(uri_rdf_first, all_11_1, uri_ex_A) =
% 11.90/2.67 | 0 & iext(uri_owl_complementOf, all_11_2, uri_ex_A) = 0 &
% 11.90/2.67 | iext(uri_rdf_type, uri_ex_w, all_11_3) = 0 & $i(all_11_0) &
% 11.90/2.67 | $i(all_11_1) & $i(all_11_2) & $i(all_11_3)
% 11.90/2.67 |
% 11.90/2.67 | ALPHA: (11) implies:
% 11.90/2.68 | (12) $i(all_11_3)
% 11.90/2.68 | (13) $i(all_11_2)
% 11.90/2.68 | (14) $i(all_11_1)
% 11.90/2.68 | (15) $i(all_11_0)
% 11.90/2.68 | (16) iext(uri_rdf_type, uri_ex_w, all_11_3) = 0
% 11.90/2.68 | (17) iext(uri_owl_complementOf, all_11_2, uri_ex_A) = 0
% 11.90/2.68 | (18) iext(uri_rdf_first, all_11_1, uri_ex_A) = 0
% 11.90/2.68 | (19) iext(uri_rdf_first, all_11_0, all_11_2) = 0
% 11.90/2.68 | (20) iext(uri_rdf_rest, all_11_1, all_11_0) = 0
% 11.90/2.68 | (21) iext(uri_rdf_rest, all_11_0, uri_rdf_nil) = 0
% 11.90/2.68 | (22) iext(uri_owl_intersectionOf, all_11_3, all_11_1) = 0
% 11.90/2.68 |
% 11.90/2.68 | GROUND_INST: instantiating (1) with uri_ex_w, all_11_3, simplifying with (6),
% 11.90/2.68 | (12), (16) gives:
% 11.90/2.68 | (23) icext(all_11_3, uri_ex_w) = 0
% 11.90/2.68 |
% 11.90/2.68 | GROUND_INST: instantiating (2) with all_11_2, uri_ex_A, simplifying with (4),
% 11.90/2.68 | (13), (17) gives:
% 11.90/2.68 | (24) ic(all_11_2) = 0 & ic(uri_ex_A) = 0 & ! [v0: $i] : ! [v1: int] : (v1
% 11.90/2.68 | = 0 | ~ (icext(all_11_2, v0) = v1) | ~ $i(v0) | icext(uri_ex_A,
% 11.90/2.68 | v0) = 0) & ! [v0: $i] : ( ~ (icext(all_11_2, v0) = 0) | ~ $i(v0)
% 11.90/2.68 | | ? [v1: int] : ( ~ (v1 = 0) & icext(uri_ex_A, v0) = v1))
% 11.90/2.68 |
% 11.90/2.68 | ALPHA: (24) implies:
% 11.90/2.68 | (25) ic(all_11_2) = 0
% 11.90/2.68 | (26) ! [v0: $i] : ( ~ (icext(all_11_2, v0) = 0) | ~ $i(v0) | ? [v1: int]
% 11.90/2.68 | : ( ~ (v1 = 0) & icext(uri_ex_A, v0) = v1))
% 11.90/2.68 |
% 11.90/2.69 | GROUND_INST: instantiating (3) with all_11_3, all_11_1, uri_ex_A, all_11_0,
% 11.90/2.69 | all_11_2, 0, 0, simplifying with (4), (12), (13), (14), (15),
% 11.90/2.69 | (18), (21), (22), (25) gives:
% 11.90/2.69 | (27) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 11.90/2.69 | (ic(all_11_3) = v2 & ic(uri_ex_A) = v3 & iext(uri_rdf_rest, all_11_1,
% 11.90/2.69 | all_11_0) = v0 & iext(uri_rdf_first, all_11_0, all_11_2) = v1 & (
% 11.90/2.69 | ~ (v1 = 0) | ~ (v0 = 0) | (v3 = 0 & v2 = 0 & ! [v4: $i] : !
% 11.90/2.69 | [v5: int] : (v5 = 0 | ~ (icext(all_11_3, v4) = v5) | ~ $i(v4)
% 11.90/2.69 | | ? [v6: any] : ? [v7: any] : (icext(all_11_2, v4) = v7 &
% 11.90/2.69 | icext(uri_ex_A, v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) &
% 11.90/2.69 | ! [v4: $i] : ( ~ (icext(all_11_3, v4) = 0) | ~ $i(v4) |
% 11.90/2.69 | (icext(all_11_2, v4) = 0 & icext(uri_ex_A, v4) = 0)))))
% 11.90/2.69 |
% 11.90/2.69 | DELTA: instantiating (27) with fresh symbols all_33_0, all_33_1, all_33_2,
% 11.90/2.69 | all_33_3 gives:
% 11.90/2.69 | (28) ic(all_11_3) = all_33_1 & ic(uri_ex_A) = all_33_0 & iext(uri_rdf_rest,
% 11.90/2.69 | all_11_1, all_11_0) = all_33_3 & iext(uri_rdf_first, all_11_0,
% 11.90/2.69 | all_11_2) = all_33_2 & ( ~ (all_33_2 = 0) | ~ (all_33_3 = 0) |
% 11.90/2.69 | (all_33_0 = 0 & all_33_1 = 0 & ! [v0: $i] : ! [v1: int] : (v1 = 0
% 11.90/2.69 | | ~ (icext(all_11_3, v0) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 11.90/2.69 | [v3: any] : (icext(all_11_2, v0) = v3 & icext(uri_ex_A, v0) = v2
% 11.90/2.69 | & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ( ~
% 11.90/2.69 | (icext(all_11_3, v0) = 0) | ~ $i(v0) | (icext(all_11_2, v0) = 0
% 11.90/2.69 | & icext(uri_ex_A, v0) = 0))))
% 11.90/2.69 |
% 11.90/2.69 | ALPHA: (28) implies:
% 11.90/2.69 | (29) iext(uri_rdf_first, all_11_0, all_11_2) = all_33_2
% 11.90/2.69 | (30) iext(uri_rdf_rest, all_11_1, all_11_0) = all_33_3
% 11.90/2.70 | (31) ~ (all_33_2 = 0) | ~ (all_33_3 = 0) | (all_33_0 = 0 & all_33_1 = 0 &
% 11.90/2.70 | ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (icext(all_11_3, v0) = v1)
% 11.90/2.70 | | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (icext(all_11_2, v0) =
% 11.90/2.70 | v3 & icext(uri_ex_A, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) &
% 11.90/2.70 | ! [v0: $i] : ( ~ (icext(all_11_3, v0) = 0) | ~ $i(v0) |
% 11.90/2.70 | (icext(all_11_2, v0) = 0 & icext(uri_ex_A, v0) = 0)))
% 11.90/2.70 |
% 11.90/2.70 | GROUND_INST: instantiating (8) with 0, all_33_2, all_11_2, all_11_0,
% 11.90/2.70 | uri_rdf_first, simplifying with (19), (29) gives:
% 11.90/2.70 | (32) all_33_2 = 0
% 11.90/2.70 |
% 11.90/2.70 | GROUND_INST: instantiating (8) with 0, all_33_3, all_11_0, all_11_1,
% 11.90/2.70 | uri_rdf_rest, simplifying with (20), (30) gives:
% 11.90/2.70 | (33) all_33_3 = 0
% 11.90/2.70 |
% 11.90/2.70 | BETA: splitting (31) gives:
% 11.90/2.70 |
% 11.90/2.70 | Case 1:
% 11.90/2.70 | |
% 11.90/2.70 | | (34) ~ (all_33_2 = 0)
% 11.90/2.70 | |
% 11.90/2.70 | | REDUCE: (32), (34) imply:
% 11.90/2.70 | | (35) $false
% 11.90/2.70 | |
% 11.90/2.70 | | CLOSE: (35) is inconsistent.
% 11.90/2.70 | |
% 11.90/2.70 | Case 2:
% 11.90/2.70 | |
% 11.90/2.70 | | (36) ~ (all_33_3 = 0) | (all_33_0 = 0 & all_33_1 = 0 & ! [v0: $i] : !
% 11.90/2.70 | | [v1: int] : (v1 = 0 | ~ (icext(all_11_3, v0) = v1) | ~ $i(v0) |
% 11.90/2.70 | | ? [v2: any] : ? [v3: any] : (icext(all_11_2, v0) = v3 &
% 11.90/2.70 | | icext(uri_ex_A, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & !
% 11.90/2.70 | | [v0: $i] : ( ~ (icext(all_11_3, v0) = 0) | ~ $i(v0) |
% 11.90/2.70 | | (icext(all_11_2, v0) = 0 & icext(uri_ex_A, v0) = 0)))
% 11.90/2.70 | |
% 11.90/2.70 | | BETA: splitting (36) gives:
% 11.90/2.70 | |
% 11.90/2.70 | | Case 1:
% 11.90/2.70 | | |
% 11.90/2.70 | | | (37) ~ (all_33_3 = 0)
% 11.90/2.70 | | |
% 11.90/2.70 | | | REDUCE: (33), (37) imply:
% 11.90/2.70 | | | (38) $false
% 11.90/2.70 | | |
% 11.90/2.70 | | | CLOSE: (38) is inconsistent.
% 11.90/2.70 | | |
% 11.90/2.70 | | Case 2:
% 11.90/2.70 | | |
% 11.90/2.71 | | | (39) all_33_0 = 0 & all_33_1 = 0 & ! [v0: $i] : ! [v1: int] : (v1 = 0
% 11.90/2.71 | | | | ~ (icext(all_11_3, v0) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 11.90/2.71 | | | [v3: any] : (icext(all_11_2, v0) = v3 & icext(uri_ex_A, v0) = v2
% 11.90/2.71 | | | & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ( ~
% 11.90/2.71 | | | (icext(all_11_3, v0) = 0) | ~ $i(v0) | (icext(all_11_2, v0) = 0
% 11.90/2.71 | | | & icext(uri_ex_A, v0) = 0))
% 11.90/2.71 | | |
% 11.90/2.71 | | | ALPHA: (39) implies:
% 11.90/2.71 | | | (40) ! [v0: $i] : ( ~ (icext(all_11_3, v0) = 0) | ~ $i(v0) |
% 11.90/2.71 | | | (icext(all_11_2, v0) = 0 & icext(uri_ex_A, v0) = 0))
% 11.90/2.71 | | |
% 11.90/2.71 | | | GROUND_INST: instantiating (40) with uri_ex_w, simplifying with (6), (23)
% 11.90/2.71 | | | gives:
% 11.90/2.71 | | | (41) icext(all_11_2, uri_ex_w) = 0 & icext(uri_ex_A, uri_ex_w) = 0
% 11.90/2.71 | | |
% 11.90/2.71 | | | ALPHA: (41) implies:
% 11.90/2.71 | | | (42) icext(uri_ex_A, uri_ex_w) = 0
% 11.90/2.71 | | | (43) icext(all_11_2, uri_ex_w) = 0
% 11.90/2.71 | | |
% 11.90/2.71 | | | GROUND_INST: instantiating (26) with uri_ex_w, simplifying with (6), (43)
% 11.90/2.71 | | | gives:
% 11.90/2.71 | | | (44) ? [v0: int] : ( ~ (v0 = 0) & icext(uri_ex_A, uri_ex_w) = v0)
% 11.90/2.71 | | |
% 11.90/2.71 | | | DELTA: instantiating (44) with fresh symbol all_54_0 gives:
% 11.90/2.71 | | | (45) ~ (all_54_0 = 0) & icext(uri_ex_A, uri_ex_w) = all_54_0
% 11.90/2.71 | | |
% 11.90/2.71 | | | ALPHA: (45) implies:
% 11.90/2.71 | | | (46) ~ (all_54_0 = 0)
% 11.90/2.71 | | | (47) icext(uri_ex_A, uri_ex_w) = all_54_0
% 11.90/2.71 | | |
% 11.90/2.71 | | | GROUND_INST: instantiating (7) with 0, all_54_0, uri_ex_w, uri_ex_A,
% 11.90/2.71 | | | simplifying with (42), (47) gives:
% 11.90/2.71 | | | (48) all_54_0 = 0
% 11.90/2.71 | | |
% 11.90/2.71 | | | REDUCE: (46), (48) imply:
% 11.90/2.71 | | | (49) $false
% 11.90/2.71 | | |
% 11.90/2.71 | | | CLOSE: (49) is inconsistent.
% 11.90/2.71 | | |
% 11.90/2.71 | | End of split
% 11.90/2.71 | |
% 11.90/2.71 | End of split
% 11.90/2.71 |
% 11.90/2.71 End of proof
% 11.90/2.71 % SZS output end Proof for theBenchmark
% 11.90/2.71
% 11.90/2.71 2097ms
%------------------------------------------------------------------------------