%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO080+1 : TPTP v8.1.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n019.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 : Sat Jul 16 03:47:28 EDT 2022 % Result : Theorem 20.73s 6.20s % Output : Proof 21.92s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : GEO080+1 : TPTP v8.1.0. Released v2.4.0. % 0.06/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n019.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Sat Jun 18 11:25:09 EDT 2022 % 0.12/0.34 % CPUTime : % 0.21/0.60 ____ _ % 0.21/0.60 ___ / __ \_____(_)___ ________ __________ % 0.21/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.21/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.21/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.21/0.60 % 0.21/0.60 A Theorem Prover for First-Order Logic % 0.21/0.60 (ePrincess v.1.0) % 0.21/0.60 % 0.21/0.60 (c) Philipp Rümmer, 2009-2015 % 0.21/0.60 (c) Peter Backeman, 2014-2015 % 0.21/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.21/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.21/0.60 Bug reports to peter@backeman.se % 0.21/0.60 % 0.21/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.21/0.60 % 0.21/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.72/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.76/0.95 Prover 0: Preprocessing ... % 2.12/1.15 Prover 0: Warning: ignoring some quantifiers % 2.12/1.17 Prover 0: Constructing countermodel ... % 19.54/5.94 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 19.86/5.99 Prover 1: Preprocessing ... % 20.40/6.17 Prover 1: Warning: ignoring some quantifiers % 20.40/6.18 Prover 1: Constructing countermodel ... % 20.73/6.20 Prover 1: proved (256ms) % 20.73/6.20 Prover 0: stopped % 20.73/6.20 % 20.73/6.20 No countermodel exists, formula is valid % 20.73/6.20 % SZS status Theorem for theBenchmark % 20.73/6.20 % 20.73/6.20 Generating proof ... Warning: ignoring some quantifiers % 21.46/6.37 found it (size 11) % 21.46/6.37 % 21.46/6.37 % SZS output start Proof for theBenchmark % 21.46/6.37 Assumed formulas after preprocessing and simplification: % 21.46/6.37 | (0) ? [v0] : ? [v1] : ( ~ (v1 = 0) & part_of(v0, v0) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = 0 | v6 = 0 | ~ (end_point(v8, v3) = 0) | ~ (part_of(v3, v5) = v7) | ~ (part_of(v3, v4) = v6) | ~ (part_of(v3, v2) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((end_point(v8, v5) = v10 & end_point(v8, v4) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0))) | (part_of(v5, v4) = v12 & part_of(v5, v3) = v14 & part_of(v5, v2) = v10 & part_of(v4, v5) = v11 & part_of(v4, v3) = v13 & part_of(v4, v2) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0) | v14 = 0 | v13 = 0 | v12 = 0 | v11 = 0)))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (closed(v2) = 0) | ~ (meet(v6, v3, v4) = v7) | ~ (meet(v5, v3, v4) = 0) | ? [v8] : (( ~ (v8 = v2) & sum(v3, v4) = v8) | ( ~ (v8 = 0) & end_point(v6, v3) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (sum(v3, v4) = v2) | ~ (incident_c(v5, v2) = v6) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & ~ (v7 = 0) & incident_c(v5, v4) = v8 & incident_c(v5, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v3 = v2 | ~ (meet(v6, v5, v4) = v3) | ~ (meet(v6, v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (meet(v2, v3, v4) = 0) | ~ (end_point(v5, v3) = v6) | ? [v7] : ? [v8] : ? [v9] : (end_point(v5, v4) = v9 & incident_c(v5, v4) = v8 & incident_c(v5, v3) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v9 = 0 & v6 = 0)))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | v5 = v3 | v4 = v3 | ~ (end_point(v5, v2) = 0) | ~ (end_point(v4, v2) = 0) | ~ (end_point(v3, v2) = 0)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (meet(v2, v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v8 = 0 & v7 = 0 & end_point(v6, v4) = v10 & end_point(v6, v3) = v9 & incident_c(v6, v4) = 0 & incident_c(v6, v3) = 0 & ( ~ (v10 = 0) | ~ (v9 = 0))) | (incident_c(v2, v4) = v7 & incident_c(v2, v3) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (part_of(v3, v2) = 0) | ~ (incident_c(v4, v2) = v5) | ? [v6] : ( ~ (v6 = 0) & incident_c(v4, v3) = v6)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (inner_point(v5, v4) = v3) | ~ (inner_point(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (end_point(v5, v4) = v3) | ~ (end_point(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (sum(v5, v4) = v3) | ~ (sum(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (part_of(v5, v4) = v3) | ~ (part_of(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (incident_c(v5, v4) = v3) | ~ (incident_c(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (end_point(v2, v3) = 0) | ~ (part_of(v5, v3) = 0) | ~ (part_of(v4, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (part_of(v5, v4) = v9 & part_of(v4, v5) = v8 & incident_c(v2, v5) = v7 & incident_c(v2, v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sum(v3, v4) = v2) | ~ (incident_c(v5, v2) = 0) | ? [v6] : ? [v7] : (incident_c(v5, v4) = v7 & incident_c(v5, v3) = v6 & (v7 = 0 | v6 = 0))) & ? [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v2 | ~ (sum(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (incident_c(v6, v4) = v9 & incident_c(v6, v3) = v8 & incident_c(v6, v2) = v7 & ( ~ (v7 = 0) | ( ~ (v9 = 0) & ~ (v8 = 0))) & (v9 = 0 | v8 = 0 | v7 = 0))) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (inner_point(v2, v3) = v4) | ? [v5] : ? [v6] : (end_point(v2, v3) = v6 & incident_c(v2, v3) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (end_point(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & ~ (v12 = 0) & ~ (v11 = 0) & part_of(v6, v5) = v12 & part_of(v6, v3) = 0 & part_of(v5, v6) = v11 & part_of(v5, v3) = 0 & incident_c(v2, v6) = 0 & incident_c(v2, v5) = 0) | ( ~ (v5 = 0) & incident_c(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (part_of(v3, v2) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & incident_c(v5, v3) = 0 & incident_c(v5, v2) = v6)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (open(v4) = v3) | ~ (open(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (closed(v4) = v3) | ~ (closed(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (open(v2) = v3) | ~ (end_point(v4, v2) = 0)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (meet(v2, v3, v4) = 0) | (incident_c(v2, v4) = 0 & incident_c(v2, v3) = 0)) & ! [v2] : ! [v3] : (v3 = v2 | ~ (part_of(v3, v2) = 0) | open(v3) = 0) & ! [v2] : ! [v3] : (v3 = 0 | ~ (closed(v2) = v3) | ? [v4] : end_point(v4, v2) = 0) & ! [v2] : ! [v3] : ( ~ (closed(v2) = 0) | ~ (end_point(v3, v2) = 0)) & ! [v2] : ! [v3] : ( ~ (inner_point(v3, v2) = 0) | ? [v4] : ? [v5] : (meet(v3, v4, v5) = 0 & sum(v4, v5) = v2)) & ! [v2] : ! [v3] : ( ~ (inner_point(v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & end_point(v2, v3) = v4 & incident_c(v2, v3) = 0)) & ! [v2] : ! [v3] : ( ~ (end_point(v3, v2) = 0) | ? [v4] : ( ~ (v4 = v3) & end_point(v4, v2) = 0)) & ! [v2] : ! [v3] : ( ~ (end_point(v2, v3) = 0) | incident_c(v2, v3) = 0) & ! [v2] : ( ~ (open(v2) = 0) | ? [v3] : end_point(v3, v2) = 0) & ? [v2] : ? [v3] : (v3 = v2 | ? [v4] : ? [v5] : ? [v6] : (incident_c(v4, v3) = v6 & incident_c(v4, v2) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)) & (v6 = 0 | v5 = 0))) & ? [v2] : ? [v3] : inner_point(v3, v2) = 0) % 21.46/6.41 | Instantiating (0) with all_0_0_0, all_0_1_1 yields: % 21.46/6.41 | (1) ~ (all_0_0_0 = 0) & part_of(all_0_1_1, all_0_1_1) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | v4 = 0 | ~ (end_point(v6, v1) = 0) | ~ (part_of(v1, v3) = v5) | ~ (part_of(v1, v2) = v4) | ~ (part_of(v1, v0) = 0) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((end_point(v6, v3) = v8 & end_point(v6, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))) | (part_of(v3, v2) = v10 & part_of(v3, v1) = v12 & part_of(v3, v0) = v8 & part_of(v2, v3) = v9 & part_of(v2, v1) = v11 & part_of(v2, v0) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | v12 = 0 | v11 = 0 | v10 = 0 | v9 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (closed(v0) = 0) | ~ (meet(v4, v1, v2) = v5) | ~ (meet(v3, v1, v2) = 0) | ? [v6] : (( ~ (v6 = v0) & sum(v1, v2) = v6) | ( ~ (v6 = 0) & end_point(v4, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (sum(v1, v2) = v0) | ~ (incident_c(v3, v0) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & incident_c(v3, v2) = v6 & incident_c(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (meet(v4, v3, v2) = v1) | ~ (meet(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (meet(v0, v1, v2) = 0) | ~ (end_point(v3, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : (end_point(v3, v2) = v7 & incident_c(v3, v2) = v6 & incident_c(v3, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v7 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v3 = v1 | v2 = v1 | ~ (end_point(v3, v0) = 0) | ~ (end_point(v2, v0) = 0) | ~ (end_point(v1, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (meet(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v6 = 0 & v5 = 0 & end_point(v4, v2) = v8 & end_point(v4, v1) = v7 & incident_c(v4, v2) = 0 & incident_c(v4, v1) = 0 & ( ~ (v8 = 0) | ~ (v7 = 0))) | (incident_c(v0, v2) = v5 & incident_c(v0, v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (part_of(v1, v0) = 0) | ~ (incident_c(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & incident_c(v2, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (inner_point(v3, v2) = v1) | ~ (inner_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (end_point(v3, v2) = v1) | ~ (end_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ (sum(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (part_of(v3, v2) = v1) | ~ (part_of(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_c(v3, v2) = v1) | ~ (incident_c(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (end_point(v0, v1) = 0) | ~ (part_of(v3, v1) = 0) | ~ (part_of(v2, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (part_of(v3, v2) = v7 & part_of(v2, v3) = v6 & incident_c(v0, v3) = v5 & incident_c(v0, v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v7 = 0 | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum(v1, v2) = v0) | ~ (incident_c(v3, v0) = 0) | ? [v4] : ? [v5] : (incident_c(v3, v2) = v5 & incident_c(v3, v1) = v4 & (v5 = 0 | v4 = 0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (sum(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (incident_c(v4, v2) = v7 & incident_c(v4, v1) = v6 & incident_c(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (inner_point(v0, v1) = v2) | ? [v3] : ? [v4] : (end_point(v0, v1) = v4 & incident_c(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (end_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v8 = 0 & v7 = 0 & v6 = 0 & v5 = 0 & ~ (v10 = 0) & ~ (v9 = 0) & part_of(v4, v3) = v10 & part_of(v4, v1) = 0 & part_of(v3, v4) = v9 & part_of(v3, v1) = 0 & incident_c(v0, v4) = 0 & incident_c(v0, v3) = 0) | ( ~ (v3 = 0) & incident_c(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (part_of(v1, v0) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & incident_c(v3, v1) = 0 & incident_c(v3, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (open(v2) = v1) | ~ (open(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (closed(v2) = v1) | ~ (closed(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (open(v0) = v1) | ~ (end_point(v2, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (meet(v0, v1, v2) = 0) | (incident_c(v0, v2) = 0 & incident_c(v0, v1) = 0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (part_of(v1, v0) = 0) | open(v1) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (closed(v0) = v1) | ? [v2] : end_point(v2, v0) = 0) & ! [v0] : ! [v1] : ( ~ (closed(v0) = 0) | ~ (end_point(v1, v0) = 0)) & ! [v0] : ! [v1] : ( ~ (inner_point(v1, v0) = 0) | ? [v2] : ? [v3] : (meet(v1, v2, v3) = 0 & sum(v2, v3) = v0)) & ! [v0] : ! [v1] : ( ~ (inner_point(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & end_point(v0, v1) = v2 & incident_c(v0, v1) = 0)) & ! [v0] : ! [v1] : ( ~ (end_point(v1, v0) = 0) | ? [v2] : ( ~ (v2 = v1) & end_point(v2, v0) = 0)) & ! [v0] : ! [v1] : ( ~ (end_point(v0, v1) = 0) | incident_c(v0, v1) = 0) & ! [v0] : ( ~ (open(v0) = 0) | ? [v1] : end_point(v1, v0) = 0) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (incident_c(v2, v1) = v4 & incident_c(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0))) & ? [v0] : ? [v1] : inner_point(v1, v0) = 0 % 21.46/6.42 | % 21.46/6.42 | Applying alpha-rule on (1) yields: % 21.46/6.42 | (2) ! [v0] : ! [v1] : ( ~ (inner_point(v1, v0) = 0) | ? [v2] : ? [v3] : (meet(v1, v2, v3) = 0 & sum(v2, v3) = v0)) % 21.46/6.42 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | v4 = 0 | ~ (end_point(v6, v1) = 0) | ~ (part_of(v1, v3) = v5) | ~ (part_of(v1, v2) = v4) | ~ (part_of(v1, v0) = 0) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((end_point(v6, v3) = v8 & end_point(v6, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))) | (part_of(v3, v2) = v10 & part_of(v3, v1) = v12 & part_of(v3, v0) = v8 & part_of(v2, v3) = v9 & part_of(v2, v1) = v11 & part_of(v2, v0) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | v12 = 0 | v11 = 0 | v10 = 0 | v9 = 0)))) % 21.46/6.42 | (4) part_of(all_0_1_1, all_0_1_1) = all_0_0_0 % 21.46/6.42 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (open(v0) = v1) | ~ (end_point(v2, v0) = 0)) % 21.46/6.42 | (6) ! [v0] : ! [v1] : ( ~ (inner_point(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & end_point(v0, v1) = v2 & incident_c(v0, v1) = 0)) % 21.46/6.42 | (7) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (end_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v8 = 0 & v7 = 0 & v6 = 0 & v5 = 0 & ~ (v10 = 0) & ~ (v9 = 0) & part_of(v4, v3) = v10 & part_of(v4, v1) = 0 & part_of(v3, v4) = v9 & part_of(v3, v1) = 0 & incident_c(v0, v4) = 0 & incident_c(v0, v3) = 0) | ( ~ (v3 = 0) & incident_c(v0, v1) = v3))) % 21.46/6.42 | (8) ~ (all_0_0_0 = 0) % 21.46/6.42 | (9) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (sum(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (incident_c(v4, v2) = v7 & incident_c(v4, v1) = v6 & incident_c(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) % 21.46/6.42 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (meet(v0, v1, v2) = 0) | (incident_c(v0, v2) = 0 & incident_c(v0, v1) = 0)) % 21.46/6.42 | (11) ! [v0] : ! [v1] : ( ~ (end_point(v0, v1) = 0) | incident_c(v0, v1) = 0) % 21.46/6.42 | (12) ! [v0] : ! [v1] : (v1 = 0 | ~ (closed(v0) = v1) | ? [v2] : end_point(v2, v0) = 0) % 21.46/6.42 | (13) ! [v0] : ! [v1] : (v1 = v0 | ~ (part_of(v1, v0) = 0) | open(v1) = 0) % 21.46/6.42 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v3 = v1 | v2 = v1 | ~ (end_point(v3, v0) = 0) | ~ (end_point(v2, v0) = 0) | ~ (end_point(v1, v0) = 0)) % 21.46/6.42 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (inner_point(v3, v2) = v1) | ~ (inner_point(v3, v2) = v0)) % 21.46/6.42 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_c(v3, v2) = v1) | ~ (incident_c(v3, v2) = v0)) % 21.46/6.42 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (meet(v0, v1, v2) = 0) | ~ (end_point(v3, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : (end_point(v3, v2) = v7 & incident_c(v3, v2) = v6 & incident_c(v3, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v7 = 0 & v4 = 0)))) % 21.46/6.42 | (18) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (inner_point(v0, v1) = v2) | ? [v3] : ? [v4] : (end_point(v0, v1) = v4 & incident_c(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 21.46/6.42 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ (sum(v3, v2) = v0)) % 21.46/6.42 | (20) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (incident_c(v2, v1) = v4 & incident_c(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0))) % 21.46/6.43 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum(v1, v2) = v0) | ~ (incident_c(v3, v0) = 0) | ? [v4] : ? [v5] : (incident_c(v3, v2) = v5 & incident_c(v3, v1) = v4 & (v5 = 0 | v4 = 0))) % 21.46/6.43 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (closed(v0) = 0) | ~ (meet(v4, v1, v2) = v5) | ~ (meet(v3, v1, v2) = 0) | ? [v6] : (( ~ (v6 = v0) & sum(v1, v2) = v6) | ( ~ (v6 = 0) & end_point(v4, v1) = v6))) % 21.46/6.43 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (meet(v4, v3, v2) = v1) | ~ (meet(v4, v3, v2) = v0)) % 21.46/6.43 | (24) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (part_of(v1, v0) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & incident_c(v3, v1) = 0 & incident_c(v3, v0) = v4)) % 21.46/6.43 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (end_point(v3, v2) = v1) | ~ (end_point(v3, v2) = v0)) % 21.46/6.43 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (part_of(v3, v2) = v1) | ~ (part_of(v3, v2) = v0)) % 21.46/6.43 | (27) ! [v0] : ! [v1] : ( ~ (end_point(v1, v0) = 0) | ? [v2] : ( ~ (v2 = v1) & end_point(v2, v0) = 0)) % 21.46/6.43 | (28) ! [v0] : ! [v1] : ( ~ (closed(v0) = 0) | ~ (end_point(v1, v0) = 0)) % 21.92/6.43 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (part_of(v1, v0) = 0) | ~ (incident_c(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & incident_c(v2, v1) = v4)) % 21.92/6.43 | (30) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (open(v2) = v1) | ~ (open(v2) = v0)) % 21.92/6.43 | (31) ? [v0] : ? [v1] : inner_point(v1, v0) = 0 % 21.92/6.43 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (end_point(v0, v1) = 0) | ~ (part_of(v3, v1) = 0) | ~ (part_of(v2, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (part_of(v3, v2) = v7 & part_of(v2, v3) = v6 & incident_c(v0, v3) = v5 & incident_c(v0, v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v7 = 0 | v6 = 0))) % 21.92/6.43 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (meet(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v6 = 0 & v5 = 0 & end_point(v4, v2) = v8 & end_point(v4, v1) = v7 & incident_c(v4, v2) = 0 & incident_c(v4, v1) = 0 & ( ~ (v8 = 0) | ~ (v7 = 0))) | (incident_c(v0, v2) = v5 & incident_c(v0, v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) % 21.92/6.43 | (34) ! [v0] : ( ~ (open(v0) = 0) | ? [v1] : end_point(v1, v0) = 0) % 21.92/6.43 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (sum(v1, v2) = v0) | ~ (incident_c(v3, v0) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & incident_c(v3, v2) = v6 & incident_c(v3, v1) = v5)) % 21.92/6.43 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (closed(v2) = v1) | ~ (closed(v2) = v0)) % 21.92/6.43 | % 21.92/6.43 | Instantiating formula (24) with all_0_0_0, all_0_1_1, all_0_1_1 and discharging atoms part_of(all_0_1_1, all_0_1_1) = all_0_0_0, yields: % 21.92/6.43 | (37) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & incident_c(v0, all_0_1_1) = v1 & incident_c(v0, all_0_1_1) = 0) % 21.92/6.43 | % 21.92/6.43 +-Applying beta-rule and splitting (37), into two cases. % 21.92/6.43 |-Branch one: % 21.92/6.43 | (38) all_0_0_0 = 0 % 21.92/6.43 | % 21.92/6.43 | Equations (38) can reduce 8 to: % 21.92/6.43 | (39) $false % 21.92/6.43 | % 21.92/6.43 |-The branch is then unsatisfiable % 21.92/6.43 |-Branch two: % 21.92/6.43 | (8) ~ (all_0_0_0 = 0) % 21.92/6.43 | (41) ? [v0] : ? [v1] : ( ~ (v1 = 0) & incident_c(v0, all_0_1_1) = v1 & incident_c(v0, all_0_1_1) = 0) % 21.92/6.43 | % 21.92/6.43 | Instantiating (41) with all_21_0_10, all_21_1_11 yields: % 21.92/6.43 | (42) ~ (all_21_0_10 = 0) & incident_c(all_21_1_11, all_0_1_1) = all_21_0_10 & incident_c(all_21_1_11, all_0_1_1) = 0 % 21.92/6.43 | % 21.92/6.43 | Applying alpha-rule on (42) yields: % 21.92/6.43 | (43) ~ (all_21_0_10 = 0) % 21.92/6.43 | (44) incident_c(all_21_1_11, all_0_1_1) = all_21_0_10 % 21.92/6.43 | (45) incident_c(all_21_1_11, all_0_1_1) = 0 % 21.92/6.43 | % 21.92/6.43 | Instantiating formula (16) with all_21_1_11, all_0_1_1, 0, all_21_0_10 and discharging atoms incident_c(all_21_1_11, all_0_1_1) = all_21_0_10, incident_c(all_21_1_11, all_0_1_1) = 0, yields: % 21.92/6.43 | (46) all_21_0_10 = 0 % 21.92/6.43 | % 21.92/6.43 | Equations (46) can reduce 43 to: % 21.92/6.43 | (39) $false % 21.92/6.43 | % 21.92/6.43 |-The branch is then unsatisfiable % 21.92/6.43 % SZS output end Proof for theBenchmark % 21.92/6.43 % 21.92/6.43 5822ms %------------------------------------------------------------------------------