%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SWB023+2 : TPTP v8.1.0. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%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 : 600s % DateTime : Tue Jul 19 18:59:42 EDT 2022 % Result : Theorem 7.23s 2.33s % Output : Proof 8.32s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SWB023+2 : TPTP v8.1.0. Released v5.2.0. % 0.07/0.12 % Command : ePrincess-casc -timeout=%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 : 600 % 0.12/0.33 % DateTime : Wed Jun 1 03:23:00 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.58 ____ _ % 0.18/0.58 ___ / __ \_____(_)___ ________ __________ % 0.18/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.18/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.18/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.18/0.58 % 0.18/0.58 A Theorem Prover for First-Order Logic % 0.18/0.58 (ePrincess v.1.0) % 0.18/0.58 % 0.18/0.58 (c) Philipp Rümmer, 2009-2015 % 0.18/0.58 (c) Peter Backeman, 2014-2015 % 0.18/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.18/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.18/0.58 Bug reports to peter@backeman.se % 0.18/0.58 % 0.18/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.18/0.58 % 0.18/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.72/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.39/0.88 Prover 0: Preprocessing ... % 1.56/0.98 Prover 0: Warning: ignoring some quantifiers % 1.56/1.00 Prover 0: Constructing countermodel ... % 6.53/2.21 Prover 0: gave up % 6.53/2.21 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 6.87/2.23 Prover 1: Preprocessing ... % 7.23/2.29 Prover 1: Constructing countermodel ... % 7.23/2.33 Prover 1: proved (122ms) % 7.23/2.33 % 7.23/2.33 No countermodel exists, formula is valid % 7.23/2.33 % SZS status Theorem for theBenchmark % 7.23/2.33 % 7.23/2.33 Generating proof ... found it (size 41) % 7.88/2.52 % 7.88/2.52 % SZS output start Proof for theBenchmark % 7.88/2.52 Assumed formulas after preprocessing and simplification: % 7.88/2.52 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (iext(uri_owl_sameAs, uri_ex_w, uri_ex_v) = v1 & iext(uri_owl_sameAs, uri_ex_w, uri_ex_u) = v0 & iext(uri_owl_oneOf, v2, v3) = 0 & iext(uri_rdf_rest, v3, uri_rdf_nil) = 0 & iext(uri_rdf_first, v3, uri_ex_v) = 0 & iext(uri_rdf_first, v3, uri_ex_u) = 0 & iext(uri_rdf_type, v2, uri_owl_Class) = 0 & iext(uri_rdf_type, uri_ex_w, v2) = 0 & iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) = 0 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = v4 | ~ (iext(v8, v7, v6) = v5) | ~ (iext(v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (iext(v4, v5, v7) = 0) | ~ (iext(v4, v5, v6) = 0) | ~ (icext(uri_owl_FunctionalProperty, v4) = 0)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (icext(v7, v6) = v5) | ~ (icext(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (iext(uri_owl_oneOf, v4, v5) = v7) | ~ (iext(uri_rdf_first, v5, v6) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : (ic(v4) = v9 & iext(uri_rdf_rest, v5, uri_rdf_nil) = v8 & ( ~ (v8 = 0) | (( ~ (v9 = 0) | v7 = 0 | (icext(v4, v10) = v11 & ( ~ (v11 = 0) | ~ (v10 = v6)) & (v11 = 0 | v10 = v6))) & ( ~ (v7 = 0) | (v9 = 0 & ! [v12] : (v12 = v6 | ~ (icext(v4, v12) = 0)) & ! [v12] : (v12 = 0 | ~ (icext(v4, v6) = v12)))))))) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (iext(uri_rdf_type, v4, v5) = v6) | ? [v7] : ( ~ (v7 = 0) & icext(v5, v4) = v7)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (ip(v6) = v5) | ~ (ip(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (ic(v6) = v5) | ~ (ic(v6) = v4)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (iext(uri_owl_sameAs, v4, v5) = 0)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (iext(uri_owl_sameAs, v4, v4) = v5)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (icext(uri_owl_FunctionalProperty, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & ~ (v8 = v7) & iext(v4, v6, v8) = 0 & iext(v4, v6, v7) = 0) | ( ~ (v6 = 0) & ip(v4) = v6))) & ! [v4] : ! [v5] : ( ~ (iext(uri_rdf_type, v4, v5) = 0) | icext(v5, v4) = 0) & ! [v4] : ( ~ (icext(uri_owl_FunctionalProperty, v4) = 0) | ip(v4) = 0) & ( ~ (v1 = 0) | ~ (v0 = 0))) % 8.32/2.55 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 8.32/2.55 | (1) iext(uri_owl_sameAs, uri_ex_w, uri_ex_v) = all_0_2_2 & iext(uri_owl_sameAs, uri_ex_w, uri_ex_u) = all_0_3_3 & iext(uri_owl_oneOf, all_0_1_1, all_0_0_0) = 0 & iext(uri_rdf_rest, all_0_0_0, uri_rdf_nil) = 0 & iext(uri_rdf_first, all_0_0_0, uri_ex_v) = 0 & iext(uri_rdf_first, all_0_0_0, uri_ex_u) = 0 & iext(uri_rdf_type, all_0_1_1, uri_owl_Class) = 0 & iext(uri_rdf_type, uri_ex_w, all_0_1_1) = 0 & iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (iext(v4, v3, v2) = v1) | ~ (iext(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (iext(v0, v1, v3) = 0) | ~ (iext(v0, v1, v2) = 0) | ~ (icext(uri_owl_FunctionalProperty, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (icext(v3, v2) = v1) | ~ (icext(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (iext(uri_owl_oneOf, v0, v1) = v3) | ~ (iext(uri_rdf_first, v1, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ic(v0) = v5 & iext(uri_rdf_rest, v1, uri_rdf_nil) = v4 & ( ~ (v4 = 0) | (( ~ (v5 = 0) | v3 = 0 | (icext(v0, v6) = v7 & ( ~ (v7 = 0) | ~ (v6 = v2)) & (v7 = 0 | v6 = v2))) & ( ~ (v3 = 0) | (v5 = 0 & ! [v8] : (v8 = v2 | ~ (icext(v0, v8) = 0)) & ! [v8] : (v8 = 0 | ~ (icext(v0, v2) = v8)))))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (iext(uri_rdf_type, v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & icext(v1, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ip(v2) = v1) | ~ (ip(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ic(v2) = v1) | ~ (ic(v2) = v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (iext(uri_owl_sameAs, v0, v1) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (iext(uri_owl_sameAs, v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (icext(uri_owl_FunctionalProperty, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & ~ (v4 = v3) & iext(v0, v2, v4) = 0 & iext(v0, v2, v3) = 0) | ( ~ (v2 = 0) & ip(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (iext(uri_rdf_type, v0, v1) = 0) | icext(v1, v0) = 0) & ! [v0] : ( ~ (icext(uri_owl_FunctionalProperty, v0) = 0) | ip(v0) = 0) & ( ~ (all_0_2_2 = 0) | ~ (all_0_3_3 = 0)) % 8.32/2.56 | % 8.32/2.56 | Applying alpha-rule on (1) yields: % 8.32/2.56 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (icext(v3, v2) = v1) | ~ (icext(v3, v2) = v0)) % 8.32/2.56 | (3) iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) = 0 % 8.32/2.56 | (4) iext(uri_rdf_first, all_0_0_0, uri_ex_u) = 0 % 8.32/2.56 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (iext(v0, v1, v3) = 0) | ~ (iext(v0, v1, v2) = 0) | ~ (icext(uri_owl_FunctionalProperty, v0) = 0)) % 8.32/2.56 | (6) iext(uri_rdf_type, uri_ex_w, all_0_1_1) = 0 % 8.32/2.56 | (7) ! [v0] : ( ~ (icext(uri_owl_FunctionalProperty, v0) = 0) | ip(v0) = 0) % 8.32/2.56 | (8) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (iext(uri_rdf_type, v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & icext(v1, v0) = v3)) % 8.32/2.56 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ip(v2) = v1) | ~ (ip(v2) = v0)) % 8.32/2.56 | (10) ! [v0] : ! [v1] : (v1 = 0 | ~ (icext(uri_owl_FunctionalProperty, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & ~ (v4 = v3) & iext(v0, v2, v4) = 0 & iext(v0, v2, v3) = 0) | ( ~ (v2 = 0) & ip(v0) = v2))) % 8.32/2.56 | (11) ! [v0] : ! [v1] : (v1 = 0 | ~ (iext(uri_owl_sameAs, v0, v0) = v1)) % 8.32/2.56 | (12) ~ (all_0_2_2 = 0) | ~ (all_0_3_3 = 0) % 8.32/2.56 | (13) iext(uri_rdf_first, all_0_0_0, uri_ex_v) = 0 % 8.32/2.56 | (14) iext(uri_owl_sameAs, uri_ex_w, uri_ex_v) = all_0_2_2 % 8.32/2.56 | (15) iext(uri_rdf_type, all_0_1_1, uri_owl_Class) = 0 % 8.32/2.56 | (16) ! [v0] : ! [v1] : ( ~ (iext(uri_rdf_type, v0, v1) = 0) | icext(v1, v0) = 0) % 8.32/2.56 | (17) iext(uri_owl_oneOf, all_0_1_1, all_0_0_0) = 0 % 8.32/2.56 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (iext(v4, v3, v2) = v1) | ~ (iext(v4, v3, v2) = v0)) % 8.32/2.56 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (iext(uri_owl_oneOf, v0, v1) = v3) | ~ (iext(uri_rdf_first, v1, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ic(v0) = v5 & iext(uri_rdf_rest, v1, uri_rdf_nil) = v4 & ( ~ (v4 = 0) | (( ~ (v5 = 0) | v3 = 0 | (icext(v0, v6) = v7 & ( ~ (v7 = 0) | ~ (v6 = v2)) & (v7 = 0 | v6 = v2))) & ( ~ (v3 = 0) | (v5 = 0 & ! [v8] : (v8 = v2 | ~ (icext(v0, v8) = 0)) & ! [v8] : (v8 = 0 | ~ (icext(v0, v2) = v8)))))))) % 8.32/2.57 | (20) ! [v0] : ! [v1] : (v1 = v0 | ~ (iext(uri_owl_sameAs, v0, v1) = 0)) % 8.32/2.57 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ic(v2) = v1) | ~ (ic(v2) = v0)) % 8.32/2.57 | (22) iext(uri_rdf_rest, all_0_0_0, uri_rdf_nil) = 0 % 8.32/2.57 | (23) iext(uri_owl_sameAs, uri_ex_w, uri_ex_u) = all_0_3_3 % 8.32/2.57 | % 8.32/2.57 | Instantiating formula (11) with all_0_2_2, uri_ex_w yields: % 8.32/2.57 | (24) all_0_2_2 = 0 | ~ (iext(uri_owl_sameAs, uri_ex_w, uri_ex_w) = all_0_2_2) % 8.32/2.57 | % 8.32/2.57 | Instantiating formula (18) with uri_owl_sameAs, uri_ex_w, uri_ex_u, all_0_3_3, all_0_2_2 and discharging atoms iext(uri_owl_sameAs, uri_ex_w, uri_ex_u) = all_0_3_3, yields: % 8.32/2.57 | (25) all_0_2_2 = all_0_3_3 | ~ (iext(uri_owl_sameAs, uri_ex_w, uri_ex_u) = all_0_2_2) % 8.32/2.57 | % 8.32/2.57 | Instantiating formula (19) with 0, uri_ex_v, all_0_0_0, all_0_1_1 and discharging atoms iext(uri_owl_oneOf, all_0_1_1, all_0_0_0) = 0, iext(uri_rdf_first, all_0_0_0, uri_ex_v) = 0, yields: % 8.32/2.57 | (26) ? [v0] : ? [v1] : (ic(all_0_1_1) = v1 & iext(uri_rdf_rest, all_0_0_0, uri_rdf_nil) = v0 & ( ~ (v0 = 0) | (v1 = 0 & ! [v2] : (v2 = uri_ex_v | ~ (icext(all_0_1_1, v2) = 0)) & ! [v2] : (v2 = 0 | ~ (icext(all_0_1_1, uri_ex_v) = v2))))) % 8.32/2.57 | % 8.32/2.57 | Instantiating formula (19) with 0, uri_ex_u, all_0_0_0, all_0_1_1 and discharging atoms iext(uri_owl_oneOf, all_0_1_1, all_0_0_0) = 0, iext(uri_rdf_first, all_0_0_0, uri_ex_u) = 0, yields: % 8.32/2.57 | (27) ? [v0] : ? [v1] : (ic(all_0_1_1) = v1 & iext(uri_rdf_rest, all_0_0_0, uri_rdf_nil) = v0 & ( ~ (v0 = 0) | (v1 = 0 & ! [v2] : (v2 = uri_ex_u | ~ (icext(all_0_1_1, v2) = 0)) & ! [v2] : (v2 = 0 | ~ (icext(all_0_1_1, uri_ex_u) = v2))))) % 8.32/2.57 | % 8.32/2.57 | Instantiating formula (16) with all_0_1_1, uri_ex_w and discharging atoms iext(uri_rdf_type, uri_ex_w, all_0_1_1) = 0, yields: % 8.32/2.57 | (28) icext(all_0_1_1, uri_ex_w) = 0 % 8.32/2.57 | % 8.32/2.57 | Instantiating formula (16) with uri_owl_FunctionalProperty, uri_rdf_first and discharging atoms iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) = 0, yields: % 8.32/2.57 | (29) icext(uri_owl_FunctionalProperty, uri_rdf_first) = 0 % 8.32/2.57 | % 8.32/2.57 | Instantiating (27) with all_9_0_4, all_9_1_5 yields: % 8.32/2.57 | (30) ic(all_0_1_1) = all_9_0_4 & iext(uri_rdf_rest, all_0_0_0, uri_rdf_nil) = all_9_1_5 & ( ~ (all_9_1_5 = 0) | (all_9_0_4 = 0 & ! [v0] : (v0 = uri_ex_u | ~ (icext(all_0_1_1, v0) = 0)) & ! [v0] : (v0 = 0 | ~ (icext(all_0_1_1, uri_ex_u) = v0)))) % 8.32/2.57 | % 8.32/2.57 | Applying alpha-rule on (30) yields: % 8.32/2.57 | (31) ic(all_0_1_1) = all_9_0_4 % 8.32/2.57 | (32) iext(uri_rdf_rest, all_0_0_0, uri_rdf_nil) = all_9_1_5 % 8.32/2.57 | (33) ~ (all_9_1_5 = 0) | (all_9_0_4 = 0 & ! [v0] : (v0 = uri_ex_u | ~ (icext(all_0_1_1, v0) = 0)) & ! [v0] : (v0 = 0 | ~ (icext(all_0_1_1, uri_ex_u) = v0))) % 8.32/2.57 | % 8.32/2.57 | Instantiating (26) with all_11_0_6, all_11_1_7 yields: % 8.32/2.57 | (34) ic(all_0_1_1) = all_11_0_6 & iext(uri_rdf_rest, all_0_0_0, uri_rdf_nil) = all_11_1_7 & ( ~ (all_11_1_7 = 0) | (all_11_0_6 = 0 & ! [v0] : (v0 = uri_ex_v | ~ (icext(all_0_1_1, v0) = 0)) & ! [v0] : (v0 = 0 | ~ (icext(all_0_1_1, uri_ex_v) = v0)))) % 8.32/2.57 | % 8.32/2.57 | Applying alpha-rule on (34) yields: % 8.32/2.57 | (35) ic(all_0_1_1) = all_11_0_6 % 8.32/2.57 | (36) iext(uri_rdf_rest, all_0_0_0, uri_rdf_nil) = all_11_1_7 % 8.32/2.57 | (37) ~ (all_11_1_7 = 0) | (all_11_0_6 = 0 & ! [v0] : (v0 = uri_ex_v | ~ (icext(all_0_1_1, v0) = 0)) & ! [v0] : (v0 = 0 | ~ (icext(all_0_1_1, uri_ex_v) = v0))) % 8.32/2.57 | % 8.32/2.57 | Instantiating formula (18) with uri_rdf_rest, all_0_0_0, uri_rdf_nil, all_11_1_7, 0 and discharging atoms iext(uri_rdf_rest, all_0_0_0, uri_rdf_nil) = all_11_1_7, iext(uri_rdf_rest, all_0_0_0, uri_rdf_nil) = 0, yields: % 8.32/2.57 | (38) all_11_1_7 = 0 % 8.32/2.57 | % 8.32/2.57 | Instantiating formula (18) with uri_rdf_rest, all_0_0_0, uri_rdf_nil, all_9_1_5, all_11_1_7 and discharging atoms iext(uri_rdf_rest, all_0_0_0, uri_rdf_nil) = all_11_1_7, iext(uri_rdf_rest, all_0_0_0, uri_rdf_nil) = all_9_1_5, yields: % 8.32/2.57 | (39) all_11_1_7 = all_9_1_5 % 8.32/2.57 | % 8.32/2.57 | Instantiating formula (5) with uri_ex_v, uri_ex_u, all_0_0_0, uri_rdf_first and discharging atoms iext(uri_rdf_first, all_0_0_0, uri_ex_v) = 0, iext(uri_rdf_first, all_0_0_0, uri_ex_u) = 0, icext(uri_owl_FunctionalProperty, uri_rdf_first) = 0, yields: % 8.32/2.57 | (40) uri_ex_v = uri_ex_u % 8.32/2.57 | % 8.32/2.57 | Combining equations (39,38) yields a new equation: % 8.32/2.57 | (41) all_9_1_5 = 0 % 8.32/2.57 | % 8.32/2.57 | Simplifying 41 yields: % 8.32/2.57 | (42) all_9_1_5 = 0 % 8.32/2.57 | % 8.32/2.57 | From (40) and (14) follows: % 8.32/2.57 | (43) iext(uri_owl_sameAs, uri_ex_w, uri_ex_u) = all_0_2_2 % 8.32/2.58 | % 8.32/2.58 +-Applying beta-rule and splitting (33), into two cases. % 8.32/2.58 |-Branch one: % 8.32/2.58 | (44) ~ (all_9_1_5 = 0) % 8.32/2.58 | % 8.32/2.58 | Equations (42) can reduce 44 to: % 8.32/2.58 | (45) $false % 8.32/2.58 | % 8.32/2.58 |-The branch is then unsatisfiable % 8.32/2.58 |-Branch two: % 8.32/2.58 | (42) all_9_1_5 = 0 % 8.32/2.58 | (47) all_9_0_4 = 0 & ! [v0] : (v0 = uri_ex_u | ~ (icext(all_0_1_1, v0) = 0)) & ! [v0] : (v0 = 0 | ~ (icext(all_0_1_1, uri_ex_u) = v0)) % 8.32/2.58 | % 8.32/2.58 | Applying alpha-rule on (47) yields: % 8.32/2.58 | (48) all_9_0_4 = 0 % 8.32/2.58 | (49) ! [v0] : (v0 = uri_ex_u | ~ (icext(all_0_1_1, v0) = 0)) % 8.32/2.58 | (50) ! [v0] : (v0 = 0 | ~ (icext(all_0_1_1, uri_ex_u) = v0)) % 8.32/2.58 | % 8.32/2.58 | Instantiating formula (49) with uri_ex_w and discharging atoms icext(all_0_1_1, uri_ex_w) = 0, yields: % 8.32/2.58 | (51) uri_ex_u = uri_ex_w % 8.32/2.58 | % 8.32/2.58 | From (51) and (43) follows: % 8.32/2.58 | (52) iext(uri_owl_sameAs, uri_ex_w, uri_ex_w) = all_0_2_2 % 8.32/2.58 | % 8.32/2.58 +-Applying beta-rule and splitting (25), into two cases. % 8.32/2.58 |-Branch one: % 8.32/2.58 | (53) ~ (iext(uri_owl_sameAs, uri_ex_w, uri_ex_u) = all_0_2_2) % 8.32/2.58 | % 8.32/2.58 | From (51) and (53) follows: % 8.32/2.58 | (54) ~ (iext(uri_owl_sameAs, uri_ex_w, uri_ex_w) = all_0_2_2) % 8.32/2.58 | % 8.32/2.58 | Using (52) and (54) yields: % 8.32/2.58 | (55) $false % 8.32/2.58 | % 8.32/2.58 |-The branch is then unsatisfiable % 8.32/2.58 |-Branch two: % 8.32/2.58 | (43) iext(uri_owl_sameAs, uri_ex_w, uri_ex_u) = all_0_2_2 % 8.32/2.58 | (57) all_0_2_2 = all_0_3_3 % 8.32/2.58 | % 8.32/2.58 | From (57) and (52) follows: % 8.32/2.58 | (58) iext(uri_owl_sameAs, uri_ex_w, uri_ex_w) = all_0_3_3 % 8.32/2.58 | % 8.32/2.58 +-Applying beta-rule and splitting (12), into two cases. % 8.32/2.58 |-Branch one: % 8.32/2.58 | (59) ~ (all_0_2_2 = 0) % 8.32/2.58 | % 8.32/2.58 | Equations (57) can reduce 59 to: % 8.32/2.58 | (60) ~ (all_0_3_3 = 0) % 8.32/2.58 | % 8.32/2.58 +-Applying beta-rule and splitting (24), into two cases. % 8.32/2.58 |-Branch one: % 8.32/2.58 | (54) ~ (iext(uri_owl_sameAs, uri_ex_w, uri_ex_w) = all_0_2_2) % 8.32/2.58 | % 8.32/2.58 | From (57) and (54) follows: % 8.32/2.58 | (62) ~ (iext(uri_owl_sameAs, uri_ex_w, uri_ex_w) = all_0_3_3) % 8.32/2.58 | % 8.32/2.58 | Using (58) and (62) yields: % 8.32/2.58 | (55) $false % 8.32/2.58 | % 8.32/2.58 |-The branch is then unsatisfiable % 8.32/2.58 |-Branch two: % 8.32/2.58 | (52) iext(uri_owl_sameAs, uri_ex_w, uri_ex_w) = all_0_2_2 % 8.32/2.58 | (65) all_0_2_2 = 0 % 8.32/2.58 | % 8.32/2.58 | Combining equations (65,57) yields a new equation: % 8.32/2.58 | (66) all_0_3_3 = 0 % 8.32/2.58 | % 8.32/2.58 | Equations (66) can reduce 60 to: % 8.32/2.58 | (45) $false % 8.32/2.58 | % 8.32/2.58 |-The branch is then unsatisfiable % 8.32/2.58 |-Branch two: % 8.32/2.58 | (65) all_0_2_2 = 0 % 8.32/2.58 | (60) ~ (all_0_3_3 = 0) % 8.32/2.58 | % 8.32/2.58 | Combining equations (65,57) yields a new equation: % 8.32/2.58 | (66) all_0_3_3 = 0 % 8.32/2.58 | % 8.32/2.58 | Equations (66) can reduce 60 to: % 8.32/2.58 | (45) $false % 8.32/2.58 | % 8.32/2.58 |-The branch is then unsatisfiable % 8.32/2.58 % SZS output end Proof for theBenchmark % 8.32/2.58 % 8.32/2.58 1991ms %------------------------------------------------------------------------------