%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO083+1 : TPTP v8.1.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n026.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 03:47:29 EDT 2022 % Result : Theorem 21.93s 6.21s % Output : Proof 23.75s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : GEO083+1 : TPTP v8.1.0. Released v2.4.0. % 0.10/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n026.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sat Jun 18 19:02:10 EDT 2022 % 0.13/0.34 % CPUTime : % 0.20/0.58 ____ _ % 0.20/0.58 ___ / __ \_____(_)___ ________ __________ % 0.20/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.20/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.20/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.20/0.58 % 0.20/0.58 A Theorem Prover for First-Order Logic % 0.20/0.59 (ePrincess v.1.0) % 0.20/0.59 % 0.20/0.59 (c) Philipp Rümmer, 2009-2015 % 0.20/0.59 (c) Peter Backeman, 2014-2015 % 0.20/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.20/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.20/0.59 Bug reports to peter@backeman.se % 0.20/0.59 % 0.20/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.20/0.59 % 0.20/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.74/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.68/0.95 Prover 0: Preprocessing ... % 2.02/1.16 Prover 0: Warning: ignoring some quantifiers % 2.30/1.18 Prover 0: Constructing countermodel ... % 20.96/5.93 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 20.96/5.97 Prover 1: Preprocessing ... % 21.85/6.12 Prover 1: Warning: ignoring some quantifiers % 21.93/6.13 Prover 1: Constructing countermodel ... % 21.93/6.21 Prover 1: proved (283ms) % 21.93/6.21 Prover 0: stopped % 21.93/6.21 % 21.93/6.21 No countermodel exists, formula is valid % 21.93/6.21 % SZS status Theorem for theBenchmark % 21.93/6.21 % 21.93/6.21 Generating proof ... Warning: ignoring some quantifiers % 23.30/6.51 found it (size 32) % 23.30/6.51 % 23.30/6.51 % SZS output start Proof for theBenchmark % 23.30/6.51 Assumed formulas after preprocessing and simplification: % 23.30/6.51 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & meet(v3, v0, v2) = 0 & meet(v3, v0, v1) = 0 & sum(v0, v2) = v5 & sum(v0, v1) = v4 & part_of(v4, v5) = v6 & part_of(v1, v2) = 0 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = 0 | v11 = 0 | ~ (end_point(v13, v8) = 0) | ~ (part_of(v8, v10) = v12) | ~ (part_of(v8, v9) = v11) | ~ (part_of(v8, v7) = 0) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((end_point(v13, v10) = v15 & end_point(v13, v9) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0))) | (part_of(v10, v9) = v17 & part_of(v10, v8) = v19 & part_of(v10, v7) = v15 & part_of(v9, v10) = v16 & part_of(v9, v8) = v18 & part_of(v9, v7) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0) | v19 = 0 | v18 = 0 | v17 = 0 | v16 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (closed(v7) = 0) | ~ (meet(v11, v8, v9) = v12) | ~ (meet(v10, v8, v9) = 0) | ? [v13] : (( ~ (v13 = v7) & sum(v8, v9) = v13) | ( ~ (v13 = 0) & end_point(v11, v8) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (sum(v8, v9) = v7) | ~ (incident_c(v10, v7) = v11) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & ~ (v12 = 0) & incident_c(v10, v9) = v13 & incident_c(v10, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (meet(v11, v10, v9) = v8) | ~ (meet(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (meet(v7, v8, v9) = 0) | ~ (end_point(v10, v8) = v11) | ? [v12] : ? [v13] : ? [v14] : (end_point(v10, v9) = v14 & incident_c(v10, v9) = v13 & incident_c(v10, v8) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0) | (v14 = 0 & v11 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | v10 = v8 | v9 = v8 | ~ (end_point(v10, v7) = 0) | ~ (end_point(v9, v7) = 0) | ~ (end_point(v8, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (meet(v7, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ((v13 = 0 & v12 = 0 & end_point(v11, v9) = v15 & end_point(v11, v8) = v14 & incident_c(v11, v9) = 0 & incident_c(v11, v8) = 0 & ( ~ (v15 = 0) | ~ (v14 = 0))) | (incident_c(v7, v9) = v12 & incident_c(v7, v8) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (part_of(v8, v7) = 0) | ~ (incident_c(v9, v7) = v10) | ? [v11] : ( ~ (v11 = 0) & incident_c(v9, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (inner_point(v10, v9) = v8) | ~ (inner_point(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (end_point(v10, v9) = v8) | ~ (end_point(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sum(v10, v9) = v8) | ~ (sum(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (part_of(v10, v9) = v8) | ~ (part_of(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (incident_c(v10, v9) = v8) | ~ (incident_c(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (end_point(v7, v8) = 0) | ~ (part_of(v10, v8) = 0) | ~ (part_of(v9, v8) = 0) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (part_of(v10, v9) = v14 & part_of(v9, v10) = v13 & incident_c(v7, v10) = v12 & incident_c(v7, v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0) | v14 = 0 | v13 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sum(v8, v9) = v7) | ~ (incident_c(v10, v7) = 0) | ? [v11] : ? [v12] : (incident_c(v10, v9) = v12 & incident_c(v10, v8) = v11 & (v12 = 0 | v11 = 0))) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (sum(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (incident_c(v11, v9) = v14 & incident_c(v11, v8) = v13 & incident_c(v11, v7) = v12 & ( ~ (v12 = 0) | ( ~ (v14 = 0) & ~ (v13 = 0))) & (v14 = 0 | v13 = 0 | v12 = 0))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (inner_point(v7, v8) = v9) | ? [v10] : ? [v11] : (end_point(v7, v8) = v11 & incident_c(v7, v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (end_point(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v15 = 0 & v14 = 0 & v13 = 0 & v12 = 0 & ~ (v17 = 0) & ~ (v16 = 0) & part_of(v11, v10) = v17 & part_of(v11, v8) = 0 & part_of(v10, v11) = v16 & part_of(v10, v8) = 0 & incident_c(v7, v11) = 0 & incident_c(v7, v10) = 0) | ( ~ (v10 = 0) & incident_c(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (part_of(v8, v7) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & incident_c(v10, v8) = 0 & incident_c(v10, v7) = v11)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (open(v9) = v8) | ~ (open(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (closed(v9) = v8) | ~ (closed(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (open(v7) = v8) | ~ (end_point(v9, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (meet(v7, v8, v9) = 0) | (incident_c(v7, v9) = 0 & incident_c(v7, v8) = 0)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (part_of(v8, v7) = 0) | open(v8) = 0) & ! [v7] : ! [v8] : (v8 = 0 | ~ (closed(v7) = v8) | ? [v9] : end_point(v9, v7) = 0) & ! [v7] : ! [v8] : ( ~ (closed(v7) = 0) | ~ (end_point(v8, v7) = 0)) & ! [v7] : ! [v8] : ( ~ (inner_point(v8, v7) = 0) | ? [v9] : ? [v10] : (meet(v8, v9, v10) = 0 & sum(v9, v10) = v7)) & ! [v7] : ! [v8] : ( ~ (inner_point(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & end_point(v7, v8) = v9 & incident_c(v7, v8) = 0)) & ! [v7] : ! [v8] : ( ~ (end_point(v8, v7) = 0) | ? [v9] : ( ~ (v9 = v8) & end_point(v9, v7) = 0)) & ! [v7] : ! [v8] : ( ~ (end_point(v7, v8) = 0) | incident_c(v7, v8) = 0) & ! [v7] : ( ~ (open(v7) = 0) | ? [v8] : end_point(v8, v7) = 0) & ? [v7] : ? [v8] : (v8 = v7 | ? [v9] : ? [v10] : ? [v11] : (incident_c(v9, v8) = v11 & incident_c(v9, v7) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)) & (v11 = 0 | v10 = 0))) & ? [v7] : ? [v8] : inner_point(v8, v7) = 0) % 23.75/6.55 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 yields: % 23.75/6.55 | (1) ~ (all_0_0_0 = 0) & meet(all_0_3_3, all_0_6_6, all_0_4_4) = 0 & meet(all_0_3_3, all_0_6_6, all_0_5_5) = 0 & sum(all_0_6_6, all_0_4_4) = all_0_1_1 & sum(all_0_6_6, all_0_5_5) = all_0_2_2 & part_of(all_0_2_2, all_0_1_1) = all_0_0_0 & part_of(all_0_5_5, all_0_4_4) = 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 % 23.75/6.56 | % 23.75/6.56 | Applying alpha-rule on (1) yields: % 23.75/6.56 | (2) ! [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))) % 23.75/6.56 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (part_of(v1, v0) = 0) | ~ (incident_c(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & incident_c(v2, v1) = v4)) % 23.75/6.57 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (meet(v4, v3, v2) = v1) | ~ (meet(v4, v3, v2) = v0)) % 23.75/6.57 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ (sum(v3, v2) = v0)) % 23.75/6.57 | (6) ! [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)))) % 23.75/6.57 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (open(v2) = v1) | ~ (open(v2) = v0)) % 23.75/6.57 | (8) ! [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))) % 23.75/6.57 | (9) ! [v0] : ( ~ (open(v0) = 0) | ? [v1] : end_point(v1, v0) = 0) % 23.75/6.57 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (closed(v2) = v1) | ~ (closed(v2) = v0)) % 23.75/6.57 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (meet(v0, v1, v2) = 0) | (incident_c(v0, v2) = 0 & incident_c(v0, v1) = 0)) % 23.75/6.57 | (12) ! [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)) % 23.75/6.57 | (13) ! [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))))) % 23.75/6.57 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (open(v0) = v1) | ~ (end_point(v2, v0) = 0)) % 23.75/6.57 | (15) ! [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))) % 23.75/6.57 | (16) ! [v0] : ! [v1] : ( ~ (inner_point(v1, v0) = 0) | ? [v2] : ? [v3] : (meet(v1, v2, v3) = 0 & sum(v2, v3) = v0)) % 23.75/6.57 | (17) part_of(all_0_2_2, all_0_1_1) = all_0_0_0 % 23.75/6.57 | (18) ~ (all_0_0_0 = 0) % 23.75/6.57 | (19) meet(all_0_3_3, all_0_6_6, all_0_5_5) = 0 % 23.75/6.57 | (20) ! [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)))) % 23.75/6.57 | (21) ! [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))) % 23.75/6.57 | (22) ! [v0] : ! [v1] : (v1 = v0 | ~ (part_of(v1, v0) = 0) | open(v1) = 0) % 23.75/6.57 | (23) meet(all_0_3_3, all_0_6_6, all_0_4_4) = 0 % 23.75/6.57 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_c(v3, v2) = v1) | ~ (incident_c(v3, v2) = v0)) % 23.75/6.57 | (25) ! [v0] : ! [v1] : ( ~ (end_point(v1, v0) = 0) | ? [v2] : ( ~ (v2 = v1) & end_point(v2, v0) = 0)) % 23.75/6.57 | (26) ! [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)) % 23.75/6.57 | (27) ! [v0] : ! [v1] : ( ~ (end_point(v0, v1) = 0) | incident_c(v0, v1) = 0) % 23.75/6.57 | (28) ! [v0] : ! [v1] : ( ~ (inner_point(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & end_point(v0, v1) = v2 & incident_c(v0, v1) = 0)) % 23.75/6.57 | (29) ! [v0] : ! [v1] : (v1 = 0 | ~ (closed(v0) = v1) | ? [v2] : end_point(v2, v0) = 0) % 23.75/6.57 | (30) ! [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))) % 23.75/6.57 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (inner_point(v3, v2) = v1) | ~ (inner_point(v3, v2) = v0)) % 23.75/6.57 | (32) sum(all_0_6_6, all_0_4_4) = all_0_1_1 % 23.75/6.57 | (33) ? [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))) % 23.75/6.57 | (34) sum(all_0_6_6, all_0_5_5) = all_0_2_2 % 23.75/6.57 | (35) ? [v0] : ? [v1] : inner_point(v1, v0) = 0 % 23.75/6.57 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (end_point(v3, v2) = v1) | ~ (end_point(v3, v2) = v0)) % 23.75/6.57 | (37) ! [v0] : ! [v1] : ( ~ (closed(v0) = 0) | ~ (end_point(v1, v0) = 0)) % 23.75/6.58 | (38) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (part_of(v1, v0) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & incident_c(v3, v1) = 0 & incident_c(v3, v0) = v4)) % 23.75/6.58 | (39) part_of(all_0_5_5, all_0_4_4) = 0 % 23.75/6.58 | (40) ? [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))) % 23.75/6.58 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (part_of(v3, v2) = v1) | ~ (part_of(v3, v2) = v0)) % 23.75/6.58 | % 23.75/6.58 | Instantiating formula (38) with all_0_0_0, all_0_2_2, all_0_1_1 and discharging atoms part_of(all_0_2_2, all_0_1_1) = all_0_0_0, yields: % 23.75/6.58 | (42) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & incident_c(v0, all_0_1_1) = v1 & incident_c(v0, all_0_2_2) = 0) % 23.75/6.58 | % 23.75/6.58 +-Applying beta-rule and splitting (42), into two cases. % 23.75/6.58 |-Branch one: % 23.75/6.58 | (43) all_0_0_0 = 0 % 23.75/6.58 | % 23.75/6.58 | Equations (43) can reduce 18 to: % 23.75/6.58 | (44) $false % 23.75/6.58 | % 23.75/6.58 |-The branch is then unsatisfiable % 23.75/6.58 |-Branch two: % 23.75/6.58 | (18) ~ (all_0_0_0 = 0) % 23.75/6.58 | (46) ? [v0] : ? [v1] : ( ~ (v1 = 0) & incident_c(v0, all_0_1_1) = v1 & incident_c(v0, all_0_2_2) = 0) % 23.75/6.58 | % 23.75/6.58 | Instantiating (46) with all_22_0_15, all_22_1_16 yields: % 23.75/6.58 | (47) ~ (all_22_0_15 = 0) & incident_c(all_22_1_16, all_0_1_1) = all_22_0_15 & incident_c(all_22_1_16, all_0_2_2) = 0 % 23.75/6.58 | % 23.75/6.58 | Applying alpha-rule on (47) yields: % 23.75/6.58 | (48) ~ (all_22_0_15 = 0) % 23.75/6.58 | (49) incident_c(all_22_1_16, all_0_1_1) = all_22_0_15 % 23.75/6.58 | (50) incident_c(all_22_1_16, all_0_2_2) = 0 % 23.75/6.58 | % 23.75/6.58 | Instantiating formula (26) with all_22_0_15, all_22_1_16, all_0_4_4, all_0_6_6, all_0_1_1 and discharging atoms sum(all_0_6_6, all_0_4_4) = all_0_1_1, incident_c(all_22_1_16, all_0_1_1) = all_22_0_15, yields: % 23.75/6.58 | (51) all_22_0_15 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & incident_c(all_22_1_16, all_0_4_4) = v1 & incident_c(all_22_1_16, all_0_6_6) = v0) % 23.75/6.58 | % 23.75/6.58 | Instantiating formula (8) with all_22_1_16, all_0_5_5, all_0_6_6, all_0_2_2 and discharging atoms sum(all_0_6_6, all_0_5_5) = all_0_2_2, incident_c(all_22_1_16, all_0_2_2) = 0, yields: % 23.75/6.58 | (52) ? [v0] : ? [v1] : (incident_c(all_22_1_16, all_0_5_5) = v1 & incident_c(all_22_1_16, all_0_6_6) = v0 & (v1 = 0 | v0 = 0)) % 23.75/6.58 | % 23.75/6.58 | Instantiating (52) with all_32_0_19, all_32_1_20 yields: % 23.75/6.58 | (53) incident_c(all_22_1_16, all_0_5_5) = all_32_0_19 & incident_c(all_22_1_16, all_0_6_6) = all_32_1_20 & (all_32_0_19 = 0 | all_32_1_20 = 0) % 23.75/6.58 | % 23.75/6.58 | Applying alpha-rule on (53) yields: % 23.75/6.58 | (54) incident_c(all_22_1_16, all_0_5_5) = all_32_0_19 % 23.75/6.58 | (55) incident_c(all_22_1_16, all_0_6_6) = all_32_1_20 % 23.75/6.58 | (56) all_32_0_19 = 0 | all_32_1_20 = 0 % 23.75/6.58 | % 23.75/6.58 +-Applying beta-rule and splitting (51), into two cases. % 23.75/6.58 |-Branch one: % 23.75/6.58 | (57) all_22_0_15 = 0 % 23.75/6.58 | % 23.75/6.58 | Equations (57) can reduce 48 to: % 23.75/6.58 | (44) $false % 23.75/6.58 | % 23.75/6.58 |-The branch is then unsatisfiable % 23.75/6.58 |-Branch two: % 23.75/6.58 | (48) ~ (all_22_0_15 = 0) % 23.75/6.58 | (60) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & incident_c(all_22_1_16, all_0_4_4) = v1 & incident_c(all_22_1_16, all_0_6_6) = v0) % 23.75/6.58 | % 23.75/6.58 | Instantiating (60) with all_42_0_29, all_42_1_30 yields: % 23.75/6.58 | (61) ~ (all_42_0_29 = 0) & ~ (all_42_1_30 = 0) & incident_c(all_22_1_16, all_0_4_4) = all_42_0_29 & incident_c(all_22_1_16, all_0_6_6) = all_42_1_30 % 23.75/6.58 | % 23.75/6.58 | Applying alpha-rule on (61) yields: % 23.75/6.58 | (62) ~ (all_42_0_29 = 0) % 23.75/6.58 | (63) ~ (all_42_1_30 = 0) % 23.75/6.58 | (64) incident_c(all_22_1_16, all_0_4_4) = all_42_0_29 % 23.75/6.58 | (65) incident_c(all_22_1_16, all_0_6_6) = all_42_1_30 % 23.75/6.58 | % 23.75/6.58 | Instantiating formula (24) with all_22_1_16, all_0_6_6, all_32_1_20, all_42_1_30 and discharging atoms incident_c(all_22_1_16, all_0_6_6) = all_42_1_30, incident_c(all_22_1_16, all_0_6_6) = all_32_1_20, yields: % 23.75/6.58 | (66) all_42_1_30 = all_32_1_20 % 23.75/6.58 | % 23.75/6.58 | Equations (66) can reduce 63 to: % 23.75/6.58 | (67) ~ (all_32_1_20 = 0) % 23.75/6.58 | % 23.75/6.58 +-Applying beta-rule and splitting (56), into two cases. % 23.75/6.58 |-Branch one: % 23.75/6.58 | (68) all_32_0_19 = 0 % 23.75/6.58 | % 23.75/6.58 | From (68) and (54) follows: % 23.75/6.58 | (69) incident_c(all_22_1_16, all_0_5_5) = 0 % 23.75/6.58 | % 23.75/6.58 | Instantiating formula (3) with all_42_0_29, all_22_1_16, all_0_5_5, all_0_4_4 and discharging atoms part_of(all_0_5_5, all_0_4_4) = 0, incident_c(all_22_1_16, all_0_4_4) = all_42_0_29, yields: % 23.75/6.58 | (70) all_42_0_29 = 0 | ? [v0] : ( ~ (v0 = 0) & incident_c(all_22_1_16, all_0_5_5) = v0) % 23.75/6.58 | % 23.75/6.58 +-Applying beta-rule and splitting (70), into two cases. % 23.75/6.58 |-Branch one: % 23.75/6.58 | (71) all_42_0_29 = 0 % 23.75/6.58 | % 23.75/6.58 | Equations (71) can reduce 62 to: % 23.75/6.58 | (44) $false % 23.75/6.58 | % 23.75/6.58 |-The branch is then unsatisfiable % 23.75/6.58 |-Branch two: % 23.75/6.58 | (62) ~ (all_42_0_29 = 0) % 23.75/6.58 | (74) ? [v0] : ( ~ (v0 = 0) & incident_c(all_22_1_16, all_0_5_5) = v0) % 23.75/6.58 | % 23.75/6.58 | Instantiating (74) with all_105_0_36 yields: % 23.75/6.58 | (75) ~ (all_105_0_36 = 0) & incident_c(all_22_1_16, all_0_5_5) = all_105_0_36 % 23.75/6.58 | % 23.75/6.58 | Applying alpha-rule on (75) yields: % 23.75/6.58 | (76) ~ (all_105_0_36 = 0) % 23.75/6.58 | (77) incident_c(all_22_1_16, all_0_5_5) = all_105_0_36 % 23.75/6.59 | % 23.75/6.59 | Instantiating formula (24) with all_22_1_16, all_0_5_5, all_105_0_36, 0 and discharging atoms incident_c(all_22_1_16, all_0_5_5) = all_105_0_36, incident_c(all_22_1_16, all_0_5_5) = 0, yields: % 23.75/6.59 | (78) all_105_0_36 = 0 % 23.75/6.59 | % 23.75/6.59 | Equations (78) can reduce 76 to: % 23.75/6.59 | (44) $false % 23.75/6.59 | % 23.75/6.59 |-The branch is then unsatisfiable % 23.75/6.59 |-Branch two: % 23.75/6.59 | (80) ~ (all_32_0_19 = 0) % 23.75/6.59 | (81) all_32_1_20 = 0 % 23.75/6.59 | % 23.75/6.59 | Equations (81) can reduce 67 to: % 23.75/6.59 | (44) $false % 23.75/6.59 | % 23.75/6.59 |-The branch is then unsatisfiable % 23.75/6.59 % SZS output end Proof for theBenchmark % 23.75/6.59 % 23.75/6.59 5991ms %------------------------------------------------------------------------------