%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SWB027+2 : TPTP v8.1.0. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n028.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 : 600s % DateTime : Tue Jul 19 18:59:43 EDT 2022 % Result : Theorem 15.90s 4.42s % Output : Proof 17.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SWB027+2 : TPTP v8.1.0. Released v5.2.0. % 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.33 % Computer : n028.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Wed Jun 1 13:49:52 EDT 2022 % 0.13/0.33 % CPUTime : % 0.61/0.60 ____ _ % 0.61/0.60 ___ / __ \_____(_)___ ________ __________ % 0.61/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.61/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.61/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.61/0.60 % 0.61/0.60 A Theorem Prover for First-Order Logic % 0.61/0.60 (ePrincess v.1.0) % 0.61/0.60 % 0.61/0.60 (c) Philipp Rümmer, 2009-2015 % 0.61/0.60 (c) Peter Backeman, 2014-2015 % 0.61/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.61/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.61/0.60 Bug reports to peter@backeman.se % 0.61/0.60 % 0.61/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.61/0.60 % 0.61/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.71/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.44/0.92 Prover 0: Preprocessing ... % 1.73/1.04 Prover 0: Warning: ignoring some quantifiers % 1.73/1.06 Prover 0: Constructing countermodel ... % 15.90/4.41 Prover 0: proved (3738ms) % 15.90/4.42 % 15.90/4.42 No countermodel exists, formula is valid % 15.90/4.42 % SZS status Theorem for theBenchmark % 15.90/4.42 % 15.90/4.42 Generating proof ... Warning: ignoring some quantifiers % 17.19/4.69 found it (size 26) % 17.19/4.69 % 17.19/4.69 % SZS output start Proof for theBenchmark % 17.19/4.69 Assumed formulas after preprocessing and simplification: % 17.19/4.69 | (0) ? [v0] : ? [v1] : ? [v2] : (iext(uri_owl_inverseOf, v2, uri_ex_p) & iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, v0) & iext(uri_rdf_rest, v1, uri_rdf_nil) & iext(uri_rdf_rest, v0, v1) & iext(uri_rdf_first, v1, v2) & iext(uri_rdf_first, v0, uri_ex_p) & ~ iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ iext(v7, v9, v10) | ~ iext(v5, v8, v9) | ~ iext(uri_owl_propertyChainAxiom, v3, v4) | ~ iext(uri_rdf_rest, v6, uri_rdf_nil) | ~ iext(uri_rdf_rest, v4, v6) | ~ iext(uri_rdf_first, v6, v7) | ~ iext(uri_rdf_first, v4, v5) | iext(v3, v8, v10)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ ip(v7) | ~ ip(v5) | ~ ip(v3) | ~ iext(uri_rdf_rest, v6, uri_rdf_nil) | ~ iext(uri_rdf_rest, v4, v6) | ~ iext(uri_rdf_first, v6, v7) | ~ iext(uri_rdf_first, v4, v5) | iext(uri_owl_propertyChainAxiom, v3, v4) | ? [v8] : ? [v9] : ? [v10] : (iext(v7, v9, v10) & iext(v5, v8, v9) & ~ iext(v3, v8, v10))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ iext(uri_owl_propertyChainAxiom, v3, v4) | ~ iext(uri_rdf_rest, v6, uri_rdf_nil) | ~ iext(uri_rdf_rest, v4, v6) | ~ iext(uri_rdf_first, v6, v7) | ~ iext(uri_rdf_first, v4, v5) | ip(v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ iext(uri_owl_propertyChainAxiom, v3, v4) | ~ iext(uri_rdf_rest, v6, uri_rdf_nil) | ~ iext(uri_rdf_rest, v4, v6) | ~ iext(uri_rdf_first, v6, v7) | ~ iext(uri_rdf_first, v4, v5) | ip(v5)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ iext(uri_owl_propertyChainAxiom, v3, v4) | ~ iext(uri_rdf_rest, v6, uri_rdf_nil) | ~ iext(uri_rdf_rest, v4, v6) | ~ iext(uri_rdf_first, v6, v7) | ~ iext(uri_rdf_first, v4, v5) | ip(v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ icext(uri_owl_InverseFunctionalProperty, v3) | ~ iext(v3, v5, v6) | ~ iext(v3, v4, v6)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ iext(v4, v6, v5) | ~ iext(uri_owl_inverseOf, v3, v4) | iext(v3, v5, v6)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ iext(v3, v5, v6) | ~ iext(uri_owl_inverseOf, v3, v4) | iext(v4, v6, v5)) & ! [v3] : ! [v4] : (v4 = v3 | ~ iext(uri_owl_sameAs, v3, v4)) & ! [v3] : ! [v4] : ( ~ ip(v4) | ~ ip(v3) | iext(uri_owl_inverseOf, v3, v4) | ? [v5] : ? [v6] : (( ~ iext(v4, v6, v5) | ~ iext(v3, v5, v6)) & (iext(v4, v6, v5) | iext(v3, v5, v6)))) & ! [v3] : ! [v4] : ( ~ icext(v4, v3) | iext(uri_rdf_type, v3, v4)) & ! [v3] : ! [v4] : ( ~ iext(uri_owl_inverseOf, v3, v4) | ip(v4)) & ! [v3] : ! [v4] : ( ~ iext(uri_owl_inverseOf, v3, v4) | ip(v3)) & ! [v3] : ! [v4] : ( ~ iext(uri_rdf_type, v3, v4) | icext(v4, v3)) & ! [v3] : ( ~ ip(v3) | icext(uri_owl_InverseFunctionalProperty, v3) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v5 = v4) & iext(v3, v5, v6) & iext(v3, v4, v6))) & ! [v3] : ( ~ icext(uri_owl_InverseFunctionalProperty, v3) | ip(v3)) & ? [v3] : iext(uri_owl_sameAs, v3, v3)) % 17.19/4.70 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields: % 17.19/4.70 | (1) iext(uri_owl_inverseOf, all_0_0_0, uri_ex_p) & iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, all_0_2_2) & iext(uri_rdf_rest, all_0_1_1, uri_rdf_nil) & iext(uri_rdf_rest, all_0_2_2, all_0_1_1) & iext(uri_rdf_first, all_0_1_1, all_0_0_0) & iext(uri_rdf_first, all_0_2_2, uri_ex_p) & ~ iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ iext(v4, v6, v7) | ~ iext(v2, v5, v6) | ~ iext(uri_owl_propertyChainAxiom, v0, v1) | ~ iext(uri_rdf_rest, v3, uri_rdf_nil) | ~ iext(uri_rdf_rest, v1, v3) | ~ iext(uri_rdf_first, v3, v4) | ~ iext(uri_rdf_first, v1, v2) | iext(v0, v5, v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ ip(v4) | ~ ip(v2) | ~ ip(v0) | ~ iext(uri_rdf_rest, v3, uri_rdf_nil) | ~ iext(uri_rdf_rest, v1, v3) | ~ iext(uri_rdf_first, v3, v4) | ~ iext(uri_rdf_first, v1, v2) | iext(uri_owl_propertyChainAxiom, v0, v1) | ? [v5] : ? [v6] : ? [v7] : (iext(v4, v6, v7) & iext(v2, v5, v6) & ~ iext(v0, v5, v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ iext(uri_owl_propertyChainAxiom, v0, v1) | ~ iext(uri_rdf_rest, v3, uri_rdf_nil) | ~ iext(uri_rdf_rest, v1, v3) | ~ iext(uri_rdf_first, v3, v4) | ~ iext(uri_rdf_first, v1, v2) | ip(v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ iext(uri_owl_propertyChainAxiom, v0, v1) | ~ iext(uri_rdf_rest, v3, uri_rdf_nil) | ~ iext(uri_rdf_rest, v1, v3) | ~ iext(uri_rdf_first, v3, v4) | ~ iext(uri_rdf_first, v1, v2) | ip(v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ iext(uri_owl_propertyChainAxiom, v0, v1) | ~ iext(uri_rdf_rest, v3, uri_rdf_nil) | ~ iext(uri_rdf_rest, v1, v3) | ~ iext(uri_rdf_first, v3, v4) | ~ iext(uri_rdf_first, v1, v2) | ip(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ icext(uri_owl_InverseFunctionalProperty, v0) | ~ iext(v0, v2, v3) | ~ iext(v0, v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ iext(v1, v3, v2) | ~ iext(uri_owl_inverseOf, v0, v1) | iext(v0, v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ iext(v0, v2, v3) | ~ iext(uri_owl_inverseOf, v0, v1) | iext(v1, v3, v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ iext(uri_owl_sameAs, v0, v1)) & ! [v0] : ! [v1] : ( ~ ip(v1) | ~ ip(v0) | iext(uri_owl_inverseOf, v0, v1) | ? [v2] : ? [v3] : (( ~ iext(v1, v3, v2) | ~ iext(v0, v2, v3)) & (iext(v1, v3, v2) | iext(v0, v2, v3)))) & ! [v0] : ! [v1] : ( ~ icext(v1, v0) | iext(uri_rdf_type, v0, v1)) & ! [v0] : ! [v1] : ( ~ iext(uri_owl_inverseOf, v0, v1) | ip(v1)) & ! [v0] : ! [v1] : ( ~ iext(uri_owl_inverseOf, v0, v1) | ip(v0)) & ! [v0] : ! [v1] : ( ~ iext(uri_rdf_type, v0, v1) | icext(v1, v0)) & ! [v0] : ( ~ ip(v0) | icext(uri_owl_InverseFunctionalProperty, v0) | ? [v1] : ? [v2] : ? [v3] : ( ~ (v2 = v1) & iext(v0, v2, v3) & iext(v0, v1, v3))) & ! [v0] : ( ~ icext(uri_owl_InverseFunctionalProperty, v0) | ip(v0)) & ? [v0] : iext(uri_owl_sameAs, v0, v0) % 17.35/4.71 | % 17.35/4.71 | Applying alpha-rule on (1) yields: % 17.35/4.71 | (2) ! [v0] : ( ~ icext(uri_owl_InverseFunctionalProperty, v0) | ip(v0)) % 17.35/4.71 | (3) ! [v0] : ( ~ ip(v0) | icext(uri_owl_InverseFunctionalProperty, v0) | ? [v1] : ? [v2] : ? [v3] : ( ~ (v2 = v1) & iext(v0, v2, v3) & iext(v0, v1, v3))) % 17.35/4.71 | (4) ! [v0] : ! [v1] : ( ~ iext(uri_owl_inverseOf, v0, v1) | ip(v0)) % 17.35/4.71 | (5) iext(uri_rdf_first, all_0_2_2, uri_ex_p) % 17.35/4.71 | (6) ! [v0] : ! [v1] : (v1 = v0 | ~ iext(uri_owl_sameAs, v0, v1)) % 17.35/4.71 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ iext(v0, v2, v3) | ~ iext(uri_owl_inverseOf, v0, v1) | iext(v1, v3, v2)) % 17.35/4.71 | (8) ! [v0] : ! [v1] : ( ~ iext(uri_rdf_type, v0, v1) | icext(v1, v0)) % 17.35/4.71 | (9) ! [v0] : ! [v1] : ( ~ icext(v1, v0) | iext(uri_rdf_type, v0, v1)) % 17.35/4.71 | (10) ! [v0] : ! [v1] : ( ~ iext(uri_owl_inverseOf, v0, v1) | ip(v1)) % 17.35/4.71 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ icext(uri_owl_InverseFunctionalProperty, v0) | ~ iext(v0, v2, v3) | ~ iext(v0, v1, v3)) % 17.35/4.71 | (12) iext(uri_rdf_first, all_0_1_1, all_0_0_0) % 17.35/4.71 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ iext(v1, v3, v2) | ~ iext(uri_owl_inverseOf, v0, v1) | iext(v0, v2, v3)) % 17.35/4.71 | (14) iext(uri_owl_inverseOf, all_0_0_0, uri_ex_p) % 17.35/4.71 | (15) ! [v0] : ! [v1] : ( ~ ip(v1) | ~ ip(v0) | iext(uri_owl_inverseOf, v0, v1) | ? [v2] : ? [v3] : (( ~ iext(v1, v3, v2) | ~ iext(v0, v2, v3)) & (iext(v1, v3, v2) | iext(v0, v2, v3)))) % 17.35/4.71 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ iext(uri_owl_propertyChainAxiom, v0, v1) | ~ iext(uri_rdf_rest, v3, uri_rdf_nil) | ~ iext(uri_rdf_rest, v1, v3) | ~ iext(uri_rdf_first, v3, v4) | ~ iext(uri_rdf_first, v1, v2) | ip(v0)) % 17.35/4.71 | (17) iext(uri_rdf_rest, all_0_1_1, uri_rdf_nil) % 17.35/4.71 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ iext(uri_owl_propertyChainAxiom, v0, v1) | ~ iext(uri_rdf_rest, v3, uri_rdf_nil) | ~ iext(uri_rdf_rest, v1, v3) | ~ iext(uri_rdf_first, v3, v4) | ~ iext(uri_rdf_first, v1, v2) | ip(v2)) % 17.35/4.71 | (19) iext(uri_rdf_rest, all_0_2_2, all_0_1_1) % 17.35/4.71 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ iext(uri_owl_propertyChainAxiom, v0, v1) | ~ iext(uri_rdf_rest, v3, uri_rdf_nil) | ~ iext(uri_rdf_rest, v1, v3) | ~ iext(uri_rdf_first, v3, v4) | ~ iext(uri_rdf_first, v1, v2) | ip(v4)) % 17.35/4.71 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ iext(v4, v6, v7) | ~ iext(v2, v5, v6) | ~ iext(uri_owl_propertyChainAxiom, v0, v1) | ~ iext(uri_rdf_rest, v3, uri_rdf_nil) | ~ iext(uri_rdf_rest, v1, v3) | ~ iext(uri_rdf_first, v3, v4) | ~ iext(uri_rdf_first, v1, v2) | iext(v0, v5, v7)) % 17.35/4.71 | (22) ~ iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty) % 17.35/4.71 | (23) iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, all_0_2_2) % 17.35/4.71 | (24) ? [v0] : iext(uri_owl_sameAs, v0, v0) % 17.35/4.71 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ ip(v4) | ~ ip(v2) | ~ ip(v0) | ~ iext(uri_rdf_rest, v3, uri_rdf_nil) | ~ iext(uri_rdf_rest, v1, v3) | ~ iext(uri_rdf_first, v3, v4) | ~ iext(uri_rdf_first, v1, v2) | iext(uri_owl_propertyChainAxiom, v0, v1) | ? [v5] : ? [v6] : ? [v7] : (iext(v4, v6, v7) & iext(v2, v5, v6) & ~ iext(v0, v5, v7))) % 17.35/4.71 | % 17.35/4.71 | Instantiating formula (18) with all_0_0_0, all_0_1_1, uri_ex_p, all_0_2_2, uri_owl_sameAs and discharging atoms iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, all_0_2_2), iext(uri_rdf_rest, all_0_1_1, uri_rdf_nil), iext(uri_rdf_rest, all_0_2_2, all_0_1_1), iext(uri_rdf_first, all_0_1_1, all_0_0_0), iext(uri_rdf_first, all_0_2_2, uri_ex_p), yields: % 17.35/4.71 | (26) ip(uri_ex_p) % 17.35/4.71 | % 17.35/4.71 | Instantiating formula (16) with all_0_0_0, all_0_1_1, uri_ex_p, all_0_2_2, uri_owl_sameAs and discharging atoms iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, all_0_2_2), iext(uri_rdf_rest, all_0_1_1, uri_rdf_nil), iext(uri_rdf_rest, all_0_2_2, all_0_1_1), iext(uri_rdf_first, all_0_1_1, all_0_0_0), iext(uri_rdf_first, all_0_2_2, uri_ex_p), yields: % 17.35/4.71 | (27) ip(uri_owl_sameAs) % 17.35/4.71 | % 17.35/4.71 | Instantiating formula (3) with uri_ex_p and discharging atoms ip(uri_ex_p), yields: % 17.35/4.71 | (28) icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | ? [v0] : ? [v1] : ? [v2] : ( ~ (v1 = v0) & iext(uri_ex_p, v1, v2) & iext(uri_ex_p, v0, v2)) % 17.35/4.71 | % 17.35/4.71 | Instantiating formula (3) with uri_owl_sameAs and discharging atoms ip(uri_owl_sameAs), yields: % 17.35/4.71 | (29) icext(uri_owl_InverseFunctionalProperty, uri_owl_sameAs) | ? [v0] : ? [v1] : ? [v2] : ( ~ (v1 = v0) & iext(uri_owl_sameAs, v1, v2) & iext(uri_owl_sameAs, v0, v2)) % 17.35/4.71 | % 17.35/4.71 +-Applying beta-rule and splitting (29), into two cases. % 17.35/4.71 |-Branch one: % 17.35/4.71 | (30) icext(uri_owl_InverseFunctionalProperty, uri_owl_sameAs) % 17.35/4.71 | % 17.35/4.71 +-Applying beta-rule and splitting (28), into two cases. % 17.35/4.71 |-Branch one: % 17.35/4.71 | (31) icext(uri_owl_InverseFunctionalProperty, uri_ex_p) % 17.35/4.71 | % 17.35/4.72 | Instantiating formula (9) with uri_owl_InverseFunctionalProperty, uri_ex_p and discharging atoms icext(uri_owl_InverseFunctionalProperty, uri_ex_p), ~ iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty), yields: % 17.35/4.72 | (32) $false % 17.35/4.72 | % 17.35/4.72 |-The branch is then unsatisfiable % 17.35/4.72 |-Branch two: % 17.35/4.72 | (33) ~ icext(uri_owl_InverseFunctionalProperty, uri_ex_p) % 17.35/4.72 | (34) ? [v0] : ? [v1] : ? [v2] : ( ~ (v1 = v0) & iext(uri_ex_p, v1, v2) & iext(uri_ex_p, v0, v2)) % 17.35/4.72 | % 17.35/4.72 | Instantiating (34) with all_97_0_29, all_97_1_30, all_97_2_31 yields: % 17.35/4.72 | (35) ~ (all_97_1_30 = all_97_2_31) & iext(uri_ex_p, all_97_1_30, all_97_0_29) & iext(uri_ex_p, all_97_2_31, all_97_0_29) % 17.35/4.72 | % 17.35/4.72 | Applying alpha-rule on (35) yields: % 17.35/4.72 | (36) ~ (all_97_1_30 = all_97_2_31) % 17.35/4.72 | (37) iext(uri_ex_p, all_97_1_30, all_97_0_29) % 17.35/4.72 | (38) iext(uri_ex_p, all_97_2_31, all_97_0_29) % 17.35/4.72 | % 17.35/4.72 | Instantiating formula (13) with all_97_2_31, all_97_0_29, uri_ex_p, all_0_0_0 and discharging atoms iext(uri_ex_p, all_97_2_31, all_97_0_29), iext(uri_owl_inverseOf, all_0_0_0, uri_ex_p), yields: % 17.35/4.72 | (39) iext(all_0_0_0, all_97_0_29, all_97_2_31) % 17.35/4.72 | % 17.35/4.72 | Instantiating formula (21) with all_97_2_31, all_97_0_29, all_97_1_30, all_0_0_0, all_0_1_1, uri_ex_p, all_0_2_2, uri_owl_sameAs and discharging atoms iext(all_0_0_0, all_97_0_29, all_97_2_31), iext(uri_ex_p, all_97_1_30, all_97_0_29), iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, all_0_2_2), iext(uri_rdf_rest, all_0_1_1, uri_rdf_nil), iext(uri_rdf_rest, all_0_2_2, all_0_1_1), iext(uri_rdf_first, all_0_1_1, all_0_0_0), iext(uri_rdf_first, all_0_2_2, uri_ex_p), yields: % 17.35/4.72 | (40) iext(uri_owl_sameAs, all_97_1_30, all_97_2_31) % 17.35/4.72 | % 17.35/4.72 | Instantiating formula (21) with all_97_2_31, all_97_0_29, all_97_2_31, all_0_0_0, all_0_1_1, uri_ex_p, all_0_2_2, uri_owl_sameAs and discharging atoms iext(all_0_0_0, all_97_0_29, all_97_2_31), iext(uri_ex_p, all_97_2_31, all_97_0_29), iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, all_0_2_2), iext(uri_rdf_rest, all_0_1_1, uri_rdf_nil), iext(uri_rdf_rest, all_0_2_2, all_0_1_1), iext(uri_rdf_first, all_0_1_1, all_0_0_0), iext(uri_rdf_first, all_0_2_2, uri_ex_p), yields: % 17.35/4.72 | (41) iext(uri_owl_sameAs, all_97_2_31, all_97_2_31) % 17.35/4.72 | % 17.35/4.72 | Instantiating formula (11) with all_97_2_31, all_97_2_31, all_97_1_30, uri_owl_sameAs and discharging atoms icext(uri_owl_InverseFunctionalProperty, uri_owl_sameAs), iext(uri_owl_sameAs, all_97_1_30, all_97_2_31), iext(uri_owl_sameAs, all_97_2_31, all_97_2_31), yields: % 17.35/4.72 | (42) all_97_1_30 = all_97_2_31 % 17.35/4.72 | % 17.35/4.72 | Equations (42) can reduce 36 to: % 17.35/4.72 | (43) $false % 17.35/4.72 | % 17.35/4.72 |-The branch is then unsatisfiable % 17.35/4.72 |-Branch two: % 17.35/4.72 | (44) ~ icext(uri_owl_InverseFunctionalProperty, uri_owl_sameAs) % 17.35/4.72 | (45) ? [v0] : ? [v1] : ? [v2] : ( ~ (v1 = v0) & iext(uri_owl_sameAs, v1, v2) & iext(uri_owl_sameAs, v0, v2)) % 17.35/4.72 | % 17.35/4.72 | Instantiating (45) with all_18_0_32, all_18_1_33, all_18_2_34 yields: % 17.35/4.72 | (46) ~ (all_18_1_33 = all_18_2_34) & iext(uri_owl_sameAs, all_18_1_33, all_18_0_32) & iext(uri_owl_sameAs, all_18_2_34, all_18_0_32) % 17.35/4.72 | % 17.35/4.72 | Applying alpha-rule on (46) yields: % 17.35/4.72 | (47) ~ (all_18_1_33 = all_18_2_34) % 17.35/4.72 | (48) iext(uri_owl_sameAs, all_18_1_33, all_18_0_32) % 17.35/4.72 | (49) iext(uri_owl_sameAs, all_18_2_34, all_18_0_32) % 17.35/4.72 | % 17.35/4.72 | Instantiating formula (6) with all_18_0_32, all_18_1_33 and discharging atoms iext(uri_owl_sameAs, all_18_1_33, all_18_0_32), yields: % 17.35/4.72 | (50) all_18_0_32 = all_18_1_33 % 17.35/4.72 | % 17.35/4.72 | Instantiating formula (6) with all_18_0_32, all_18_2_34 and discharging atoms iext(uri_owl_sameAs, all_18_2_34, all_18_0_32), yields: % 17.35/4.72 | (51) all_18_0_32 = all_18_2_34 % 17.35/4.72 | % 17.35/4.72 | Combining equations (50,51) yields a new equation: % 17.35/4.72 | (52) all_18_1_33 = all_18_2_34 % 17.35/4.72 | % 17.35/4.72 | Simplifying 52 yields: % 17.35/4.72 | (53) all_18_1_33 = all_18_2_34 % 17.35/4.72 | % 17.35/4.72 | Equations (53) can reduce 47 to: % 17.35/4.72 | (43) $false % 17.35/4.72 | % 17.35/4.72 |-The branch is then unsatisfiable % 17.35/4.72 % SZS output end Proof for theBenchmark % 17.35/4.72 % 17.35/4.72 4106ms %------------------------------------------------------------------------------