%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO125+1 : TPTP v8.1.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n004.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 03:47:48 EDT 2022 % Result : Theorem 4.01s 1.58s % Output : Proof 6.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.14/0.14 % Problem : GEO125+1 : TPTP v8.1.0. Released v2.4.0. % 0.14/0.15 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.36 % Computer : n004.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 600 % 0.14/0.36 % DateTime : Fri Jun 17 20:44:53 EDT 2022 % 0.14/0.36 % CPUTime : % 0.52/0.62 ____ _ % 0.52/0.62 ___ / __ \_____(_)___ ________ __________ % 0.52/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.52/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.52/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.52/0.62 % 0.52/0.62 A Theorem Prover for First-Order Logic % 0.52/0.62 (ePrincess v.1.0) % 0.52/0.62 % 0.52/0.62 (c) Philipp Rümmer, 2009-2015 % 0.52/0.62 (c) Peter Backeman, 2014-2015 % 0.52/0.62 (contributions by Angelo Brillout, Peter Baumgartner) % 0.52/0.62 Free software under GNU Lesser General Public License (LGPL). % 0.52/0.62 Bug reports to peter@backeman.se % 0.52/0.62 % 0.52/0.62 For more information, visit http://user.uu.se/~petba168/breu/ % 0.52/0.62 % 0.52/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.75/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.87/1.00 Prover 0: Preprocessing ... % 2.72/1.29 Prover 0: Warning: ignoring some quantifiers % 2.97/1.32 Prover 0: Constructing countermodel ... % 4.01/1.58 Prover 0: proved (903ms) % 4.01/1.58 % 4.01/1.58 No countermodel exists, formula is valid % 4.01/1.58 % SZS status Theorem for theBenchmark % 4.01/1.58 % 4.01/1.58 Generating proof ... Warning: ignoring some quantifiers % 5.96/1.99 found it (size 18) % 5.96/1.99 % 5.96/1.99 % SZS output start Proof for theBenchmark % 5.96/1.99 Assumed formulas after preprocessing and simplification: % 5.96/1.99 | (0) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & finish_point(v2, v0) & finish_point(v1, v0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = v4 | ~ inner_point(v5, v7) | ~ end_point(v6, v7) | ~ end_point(v4, v7) | ~ part_of(v7, v3) | between_c(v3, v4, v5, v6)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (sum(v4, v5) = v3) | ~ closed(v3) | ~ meet(v6, v4, v5) | ~ end_point(v7, v4) | meet(v7, v4, v5)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ end_point(v7, v6) | ~ end_point(v7, v5) | ~ end_point(v7, v4) | ~ part_of(v6, v3) | ~ part_of(v5, v3) | ~ part_of(v4, v3) | part_of(v6, v5) | part_of(v6, v4) | part_of(v5, v6) | part_of(v5, v4) | part_of(v4, v6) | part_of(v4, v5)) & ? [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ between_c(v7, v4, v5, v6) | between_o(v3, v4, v5, v6) | ? [v8] : (( ~ incident_o(v8, v3) | ~ incident_c(v8, v7)) & (incident_o(v8, v3) | incident_c(v8, v7)))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | v6 = v4 | v5 = v4 | ~ end_point(v6, v3) | ~ end_point(v5, v3) | ~ end_point(v4, v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (sum(v6, v5) = v4) | ~ (sum(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (sum(v4, v5) = v3) | ~ incident_c(v6, v5) | incident_c(v6, v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (sum(v4, v5) = v3) | ~ incident_c(v6, v4) | incident_c(v6, v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (sum(v4, v5) = v3) | ~ incident_c(v6, v3) | incident_c(v6, v5) | incident_c(v6, v4)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ ordered_by(v3, v6, v5) | ~ ordered_by(v3, v5, v4) | between_o(v3, v4, v5, v6)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ ordered_by(v3, v5, v6) | ~ ordered_by(v3, v4, v5) | between_o(v3, v4, v5, v6)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ between_o(v6, v3, v4, v5) | ? [v7] : (between_c(v7, v3, v4, v5) & ! [v8] : ( ~ incident_o(v8, v6) | incident_c(v8, v7)) & ! [v8] : ( ~ incident_c(v8, v7) | incident_o(v8, v6)))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ between_o(v3, v4, v5, v6) | ordered_by(v3, v6, v5) | ordered_by(v3, v5, v6)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ between_o(v3, v4, v5, v6) | ordered_by(v3, v6, v5) | ordered_by(v3, v4, v5)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ between_o(v3, v4, v5, v6) | ordered_by(v3, v5, v6) | ordered_by(v3, v5, v4)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ between_o(v3, v4, v5, v6) | ordered_by(v3, v5, v4) | ordered_by(v3, v4, v5)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ between_c(v3, v4, v5, v6) | ? [v7] : (inner_point(v5, v7) & end_point(v6, v7) & end_point(v4, v7) & part_of(v7, v3))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ meet(v3, v4, v5) | ~ incident_c(v6, v5) | ~ incident_c(v6, v4) | end_point(v6, v5)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ meet(v3, v4, v5) | ~ incident_c(v6, v5) | ~ incident_c(v6, v4) | end_point(v6, v4)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ end_point(v3, v4) | ~ incident_c(v3, v6) | ~ incident_c(v3, v5) | ~ part_of(v6, v4) | ~ part_of(v5, v4) | part_of(v6, v5) | part_of(v5, v6)) & ? [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v3 | ~ (sum(v4, v5) = v6) | ? [v7] : (( ~ incident_c(v7, v3) | ( ~ incident_c(v7, v5) & ~ incident_c(v7, v4))) & (incident_c(v7, v5) | incident_c(v7, v4) | incident_c(v7, v3)))) & ! [v3] : ! [v4] : ! [v5] : (v5 = v3 | ~ finish_point(v3, v4) | ~ incident_o(v5, v4) | ordered_by(v4, v5, v3)) & ! [v3] : ! [v4] : ! [v5] : (v5 = v3 | ~ incident_o(v5, v4) | ~ start_point(v3, v4) | ordered_by(v4, v3, v5)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (underlying_curve(v5) = v4) | ~ (underlying_curve(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ open(v5) | ~ incident_c(v4, v5) | ~ incident_c(v3, v5) | ? [v6] : (ordered_by(v6, v3, v4) & ! [v7] : ( ~ incident_o(v7, v6) | incident_c(v7, v5)) & ! [v7] : ( ~ incident_c(v7, v5) | incident_o(v7, v6)))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (underlying_curve(v4) = v3) | ~ incident_o(v5, v4) | incident_c(v5, v3)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (underlying_curve(v4) = v3) | ~ incident_c(v5, v3) | incident_o(v5, v4)) & ! [v3] : ! [v4] : ! [v5] : ( ~ ordered_by(v3, v4, v5) | incident_o(v5, v3)) & ! [v3] : ! [v4] : ! [v5] : ( ~ ordered_by(v3, v4, v5) | incident_o(v4, v3)) & ! [v3] : ! [v4] : ! [v5] : ~ between_c(v3, v4, v5, v4) & ! [v3] : ! [v4] : ! [v5] : ( ~ meet(v3, v4, v5) | incident_c(v3, v5)) & ! [v3] : ! [v4] : ! [v5] : ( ~ meet(v3, v4, v5) | incident_c(v3, v4)) & ! [v3] : ! [v4] : ! [v5] : ( ~ incident_c(v5, v4) | ~ part_of(v4, v3) | incident_c(v5, v3)) & ! [v3] : ! [v4] : ! [v5] : ( ~ incident_c(v3, v5) | ~ incident_c(v3, v4) | meet(v3, v4, v5) | ? [v6] : (incident_c(v6, v5) & incident_c(v6, v4) & ( ~ end_point(v6, v5) | ~ end_point(v6, v4)))) & ? [v3] : ! [v4] : ! [v5] : (v5 = v3 | ~ (underlying_curve(v4) = v5) | ? [v6] : (( ~ incident_o(v6, v4) | ~ incident_c(v6, v3)) & (incident_o(v6, v4) | incident_c(v6, v3)))) & ! [v3] : ! [v4] : (v4 = v3 | ~ part_of(v4, v3) | open(v4)) & ! [v3] : ! [v4] : ( ~ finish_point(v3, v4) | incident_o(v3, v4)) & ! [v3] : ! [v4] : ( ~ incident_o(v3, v4) | finish_point(v3, v4) | ? [v5] : ( ~ (v5 = v3) & incident_o(v5, v4) & ~ ordered_by(v4, v5, v3))) & ! [v3] : ! [v4] : ( ~ incident_o(v3, v4) | start_point(v3, v4) | ? [v5] : ( ~ (v5 = v3) & incident_o(v5, v4) & ~ ordered_by(v4, v3, v5))) & ! [v3] : ! [v4] : ( ~ start_point(v3, v4) | incident_o(v3, v4)) & ! [v3] : ! [v4] : ( ~ closed(v3) | ~ end_point(v4, v3)) & ! [v3] : ! [v4] : ( ~ inner_point(v4, v3) | ? [v5] : ? [v6] : (sum(v5, v6) = v3 & meet(v4, v5, v6))) & ! [v3] : ! [v4] : ( ~ inner_point(v3, v4) | ~ end_point(v3, v4)) & ! [v3] : ! [v4] : ( ~ inner_point(v3, v4) | incident_c(v3, v4)) & ! [v3] : ! [v4] : ( ~ end_point(v4, v3) | open(v3)) & ! [v3] : ! [v4] : ( ~ end_point(v4, v3) | ? [v5] : ( ~ (v5 = v4) & end_point(v5, v3))) & ! [v3] : ! [v4] : ( ~ end_point(v3, v4) | incident_c(v3, v4)) & ! [v3] : ! [v4] : ( ~ incident_c(v3, v4) | inner_point(v3, v4) | end_point(v3, v4)) & ! [v3] : ! [v4] : ( ~ incident_c(v3, v4) | end_point(v3, v4) | ? [v5] : ? [v6] : (incident_c(v3, v6) & incident_c(v3, v5) & part_of(v6, v4) & part_of(v5, v4) & ~ part_of(v6, v5) & ~ part_of(v5, v6))) & ! [v3] : ( ~ open(v3) | ? [v4] : end_point(v4, v3)) & ? [v3] : ? [v4] : (v4 = v3 | ? [v5] : ? [v6] : (( ~ ordered_by(v4, v5, v6) | ~ ordered_by(v3, v5, v6)) & (ordered_by(v4, v5, v6) | ordered_by(v3, v5, v6)))) & ? [v3] : ? [v4] : (v4 = v3 | ? [v5] : (( ~ incident_c(v5, v4) | ~ incident_c(v5, v3)) & (incident_c(v5, v4) | incident_c(v5, v3)))) & ? [v3] : ? [v4] : start_point(v4, v3) & ? [v3] : ? [v4] : inner_point(v4, v3) & ? [v3] : ? [v4] : (part_of(v4, v3) | ? [v5] : (incident_c(v5, v4) & ~ incident_c(v5, v3))) & ? [v3] : ? [v4] : (open(v4) & ! [v5] : ( ~ incident_o(v5, v3) | incident_c(v5, v4)) & ! [v5] : ( ~ incident_c(v5, v4) | incident_o(v5, v3))) & ? [v3] : (closed(v3) | ? [v4] : end_point(v4, v3))) % 5.96/2.04 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields: % 5.96/2.04 | (1) ~ (all_0_0_0 = all_0_1_1) & finish_point(all_0_0_0, all_0_2_2) & finish_point(all_0_1_1, all_0_2_2) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ inner_point(v2, v4) | ~ end_point(v3, v4) | ~ end_point(v1, v4) | ~ part_of(v4, v0) | between_c(v0, v1, v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sum(v1, v2) = v0) | ~ closed(v0) | ~ meet(v3, v1, v2) | ~ end_point(v4, v1) | meet(v4, v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ end_point(v4, v3) | ~ end_point(v4, v2) | ~ end_point(v4, v1) | ~ part_of(v3, v0) | ~ part_of(v2, v0) | ~ part_of(v1, v0) | part_of(v3, v2) | part_of(v3, v1) | part_of(v2, v3) | part_of(v2, v1) | part_of(v1, v3) | part_of(v1, v2)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ between_c(v4, v1, v2, v3) | between_o(v0, v1, v2, v3) | ? [v5] : (( ~ incident_o(v5, v0) | ~ incident_c(v5, v4)) & (incident_o(v5, v0) | incident_c(v5, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v3 = v1 | v2 = v1 | ~ end_point(v3, v0) | ~ end_point(v2, v0) | ~ end_point(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ (sum(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum(v1, v2) = v0) | ~ incident_c(v3, v2) | incident_c(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum(v1, v2) = v0) | ~ incident_c(v3, v1) | incident_c(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum(v1, v2) = v0) | ~ incident_c(v3, v0) | incident_c(v3, v2) | incident_c(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ ordered_by(v0, v3, v2) | ~ ordered_by(v0, v2, v1) | between_o(v0, v1, v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ ordered_by(v0, v2, v3) | ~ ordered_by(v0, v1, v2) | between_o(v0, v1, v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_o(v3, v0, v1, v2) | ? [v4] : (between_c(v4, v0, v1, v2) & ! [v5] : ( ~ incident_o(v5, v3) | incident_c(v5, v4)) & ! [v5] : ( ~ incident_c(v5, v4) | incident_o(v5, v3)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_o(v0, v1, v2, v3) | ordered_by(v0, v3, v2) | ordered_by(v0, v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_o(v0, v1, v2, v3) | ordered_by(v0, v3, v2) | ordered_by(v0, v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_o(v0, v1, v2, v3) | ordered_by(v0, v2, v3) | ordered_by(v0, v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_o(v0, v1, v2, v3) | ordered_by(v0, v2, v1) | ordered_by(v0, v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_c(v0, v1, v2, v3) | ? [v4] : (inner_point(v2, v4) & end_point(v3, v4) & end_point(v1, v4) & part_of(v4, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ meet(v0, v1, v2) | ~ incident_c(v3, v2) | ~ incident_c(v3, v1) | end_point(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ meet(v0, v1, v2) | ~ incident_c(v3, v2) | ~ incident_c(v3, v1) | end_point(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ end_point(v0, v1) | ~ incident_c(v0, v3) | ~ incident_c(v0, v2) | ~ part_of(v3, v1) | ~ part_of(v2, v1) | part_of(v3, v2) | part_of(v2, v3)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (sum(v1, v2) = v3) | ? [v4] : (( ~ incident_c(v4, v0) | ( ~ incident_c(v4, v2) & ~ incident_c(v4, v1))) & (incident_c(v4, v2) | incident_c(v4, v1) | incident_c(v4, v0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ finish_point(v0, v1) | ~ incident_o(v2, v1) | ordered_by(v1, v2, v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ incident_o(v2, v1) | ~ start_point(v0, v1) | ordered_by(v1, v0, v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (underlying_curve(v2) = v1) | ~ (underlying_curve(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ open(v2) | ~ incident_c(v1, v2) | ~ incident_c(v0, v2) | ? [v3] : (ordered_by(v3, v0, v1) & ! [v4] : ( ~ incident_o(v4, v3) | incident_c(v4, v2)) & ! [v4] : ( ~ incident_c(v4, v2) | incident_o(v4, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (underlying_curve(v1) = v0) | ~ incident_o(v2, v1) | incident_c(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (underlying_curve(v1) = v0) | ~ incident_c(v2, v0) | incident_o(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ ordered_by(v0, v1, v2) | incident_o(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ ordered_by(v0, v1, v2) | incident_o(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ~ between_c(v0, v1, v2, v1) & ! [v0] : ! [v1] : ! [v2] : ( ~ meet(v0, v1, v2) | incident_c(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ meet(v0, v1, v2) | incident_c(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ incident_c(v2, v1) | ~ part_of(v1, v0) | incident_c(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ incident_c(v0, v2) | ~ incident_c(v0, v1) | meet(v0, v1, v2) | ? [v3] : (incident_c(v3, v2) & incident_c(v3, v1) & ( ~ end_point(v3, v2) | ~ end_point(v3, v1)))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (underlying_curve(v1) = v2) | ? [v3] : (( ~ incident_o(v3, v1) | ~ incident_c(v3, v0)) & (incident_o(v3, v1) | incident_c(v3, v0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ part_of(v1, v0) | open(v1)) & ! [v0] : ! [v1] : ( ~ finish_point(v0, v1) | incident_o(v0, v1)) & ! [v0] : ! [v1] : ( ~ incident_o(v0, v1) | finish_point(v0, v1) | ? [v2] : ( ~ (v2 = v0) & incident_o(v2, v1) & ~ ordered_by(v1, v2, v0))) & ! [v0] : ! [v1] : ( ~ incident_o(v0, v1) | start_point(v0, v1) | ? [v2] : ( ~ (v2 = v0) & incident_o(v2, v1) & ~ ordered_by(v1, v0, v2))) & ! [v0] : ! [v1] : ( ~ start_point(v0, v1) | incident_o(v0, v1)) & ! [v0] : ! [v1] : ( ~ closed(v0) | ~ end_point(v1, v0)) & ! [v0] : ! [v1] : ( ~ inner_point(v1, v0) | ? [v2] : ? [v3] : (sum(v2, v3) = v0 & meet(v1, v2, v3))) & ! [v0] : ! [v1] : ( ~ inner_point(v0, v1) | ~ end_point(v0, v1)) & ! [v0] : ! [v1] : ( ~ inner_point(v0, v1) | incident_c(v0, v1)) & ! [v0] : ! [v1] : ( ~ end_point(v1, v0) | open(v0)) & ! [v0] : ! [v1] : ( ~ end_point(v1, v0) | ? [v2] : ( ~ (v2 = v1) & end_point(v2, v0))) & ! [v0] : ! [v1] : ( ~ end_point(v0, v1) | incident_c(v0, v1)) & ! [v0] : ! [v1] : ( ~ incident_c(v0, v1) | inner_point(v0, v1) | end_point(v0, v1)) & ! [v0] : ! [v1] : ( ~ incident_c(v0, v1) | end_point(v0, v1) | ? [v2] : ? [v3] : (incident_c(v0, v3) & incident_c(v0, v2) & part_of(v3, v1) & part_of(v2, v1) & ~ part_of(v3, v2) & ~ part_of(v2, v3))) & ! [v0] : ( ~ open(v0) | ? [v1] : end_point(v1, v0)) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : (( ~ ordered_by(v1, v2, v3) | ~ ordered_by(v0, v2, v3)) & (ordered_by(v1, v2, v3) | ordered_by(v0, v2, v3)))) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ incident_c(v2, v1) | ~ incident_c(v2, v0)) & (incident_c(v2, v1) | incident_c(v2, v0)))) & ? [v0] : ? [v1] : start_point(v1, v0) & ? [v0] : ? [v1] : inner_point(v1, v0) & ? [v0] : ? [v1] : (part_of(v1, v0) | ? [v2] : (incident_c(v2, v1) & ~ incident_c(v2, v0))) & ? [v0] : ? [v1] : (open(v1) & ! [v2] : ( ~ incident_o(v2, v0) | incident_c(v2, v1)) & ! [v2] : ( ~ incident_c(v2, v1) | incident_o(v2, v0))) & ? [v0] : (closed(v0) | ? [v1] : end_point(v1, v0)) % 5.96/2.05 | % 5.96/2.06 | Applying alpha-rule on (1) yields: % 5.96/2.06 | (2) ? [v0] : ? [v1] : inner_point(v1, v0) % 5.96/2.06 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_o(v0, v1, v2, v3) | ordered_by(v0, v3, v2) | ordered_by(v0, v1, v2)) % 5.96/2.06 | (4) ! [v0] : ! [v1] : ( ~ start_point(v0, v1) | incident_o(v0, v1)) % 5.96/2.06 | (5) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (sum(v1, v2) = v3) | ? [v4] : (( ~ incident_c(v4, v0) | ( ~ incident_c(v4, v2) & ~ incident_c(v4, v1))) & (incident_c(v4, v2) | incident_c(v4, v1) | incident_c(v4, v0)))) % 5.96/2.06 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_o(v0, v1, v2, v3) | ordered_by(v0, v2, v1) | ordered_by(v0, v1, v2)) % 5.96/2.06 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ end_point(v4, v3) | ~ end_point(v4, v2) | ~ end_point(v4, v1) | ~ part_of(v3, v0) | ~ part_of(v2, v0) | ~ part_of(v1, v0) | part_of(v3, v2) | part_of(v3, v1) | part_of(v2, v3) | part_of(v2, v1) | part_of(v1, v3) | part_of(v1, v2)) % 5.96/2.06 | (8) ! [v0] : ! [v1] : ( ~ incident_c(v0, v1) | end_point(v0, v1) | ? [v2] : ? [v3] : (incident_c(v0, v3) & incident_c(v0, v2) & part_of(v3, v1) & part_of(v2, v1) & ~ part_of(v3, v2) & ~ part_of(v2, v3))) % 5.96/2.06 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ meet(v0, v1, v2) | ~ incident_c(v3, v2) | ~ incident_c(v3, v1) | end_point(v3, v1)) % 5.96/2.06 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ (sum(v3, v2) = v0)) % 5.96/2.06 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_o(v0, v1, v2, v3) | ordered_by(v0, v3, v2) | ordered_by(v0, v2, v3)) % 5.96/2.06 | (12) ! [v0] : ! [v1] : ( ~ end_point(v1, v0) | open(v0)) % 5.96/2.06 | (13) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (underlying_curve(v1) = v2) | ? [v3] : (( ~ incident_o(v3, v1) | ~ incident_c(v3, v0)) & (incident_o(v3, v1) | incident_c(v3, v0)))) % 5.96/2.06 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ incident_c(v0, v2) | ~ incident_c(v0, v1) | meet(v0, v1, v2) | ? [v3] : (incident_c(v3, v2) & incident_c(v3, v1) & ( ~ end_point(v3, v2) | ~ end_point(v3, v1)))) % 5.96/2.06 | (15) ! [v0] : ! [v1] : ( ~ end_point(v0, v1) | incident_c(v0, v1)) % 5.96/2.06 | (16) finish_point(all_0_0_0, all_0_2_2) % 5.96/2.06 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sum(v1, v2) = v0) | ~ closed(v0) | ~ meet(v3, v1, v2) | ~ end_point(v4, v1) | meet(v4, v1, v2)) % 5.96/2.06 | (18) ! [v0] : ! [v1] : ( ~ incident_o(v0, v1) | finish_point(v0, v1) | ? [v2] : ( ~ (v2 = v0) & incident_o(v2, v1) & ~ ordered_by(v1, v2, v0))) % 5.96/2.06 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ inner_point(v2, v4) | ~ end_point(v3, v4) | ~ end_point(v1, v4) | ~ part_of(v4, v0) | between_c(v0, v1, v2, v3)) % 5.96/2.06 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ ordered_by(v0, v3, v2) | ~ ordered_by(v0, v2, v1) | between_o(v0, v1, v2, v3)) % 5.96/2.06 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (underlying_curve(v2) = v1) | ~ (underlying_curve(v2) = v0)) % 5.96/2.06 | (22) ! [v0] : ! [v1] : (v1 = v0 | ~ part_of(v1, v0) | open(v1)) % 5.96/2.06 | (23) ! [v0] : ! [v1] : ( ~ incident_c(v0, v1) | inner_point(v0, v1) | end_point(v0, v1)) % 5.96/2.06 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ ordered_by(v0, v2, v3) | ~ ordered_by(v0, v1, v2) | between_o(v0, v1, v2, v3)) % 5.96/2.06 | (25) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ incident_o(v2, v1) | ~ start_point(v0, v1) | ordered_by(v1, v0, v2)) % 5.96/2.06 | (26) ! [v0] : ( ~ open(v0) | ? [v1] : end_point(v1, v0)) % 5.96/2.06 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (underlying_curve(v1) = v0) | ~ incident_c(v2, v0) | incident_o(v2, v1)) % 5.96/2.06 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (underlying_curve(v1) = v0) | ~ incident_o(v2, v1) | incident_c(v2, v0)) % 5.96/2.07 | (29) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : (( ~ ordered_by(v1, v2, v3) | ~ ordered_by(v0, v2, v3)) & (ordered_by(v1, v2, v3) | ordered_by(v0, v2, v3)))) % 5.96/2.07 | (30) ? [v0] : ? [v1] : start_point(v1, v0) % 5.96/2.07 | (31) ! [v0] : ! [v1] : ( ~ finish_point(v0, v1) | incident_o(v0, v1)) % 5.96/2.07 | (32) ! [v0] : ! [v1] : ( ~ inner_point(v1, v0) | ? [v2] : ? [v3] : (sum(v2, v3) = v0 & meet(v1, v2, v3))) % 5.96/2.07 | (33) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ finish_point(v0, v1) | ~ incident_o(v2, v1) | ordered_by(v1, v2, v0)) % 5.96/2.07 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ meet(v0, v1, v2) | incident_c(v0, v1)) % 5.96/2.07 | (35) ? [v0] : ? [v1] : (part_of(v1, v0) | ? [v2] : (incident_c(v2, v1) & ~ incident_c(v2, v0))) % 5.96/2.07 | (36) ! [v0] : ! [v1] : ( ~ incident_o(v0, v1) | start_point(v0, v1) | ? [v2] : ( ~ (v2 = v0) & incident_o(v2, v1) & ~ ordered_by(v1, v0, v2))) % 5.96/2.07 | (37) ? [v0] : (closed(v0) | ? [v1] : end_point(v1, v0)) % 5.96/2.07 | (38) ~ (all_0_0_0 = all_0_1_1) % 5.96/2.07 | (39) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ incident_c(v2, v1) | ~ incident_c(v2, v0)) & (incident_c(v2, v1) | incident_c(v2, v0)))) % 5.96/2.07 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v3 = v1 | v2 = v1 | ~ end_point(v3, v0) | ~ end_point(v2, v0) | ~ end_point(v1, v0)) % 5.96/2.07 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ ordered_by(v0, v1, v2) | incident_o(v1, v0)) % 5.96/2.07 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_o(v0, v1, v2, v3) | ordered_by(v0, v2, v3) | ordered_by(v0, v2, v1)) % 5.96/2.07 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ end_point(v0, v1) | ~ incident_c(v0, v3) | ~ incident_c(v0, v2) | ~ part_of(v3, v1) | ~ part_of(v2, v1) | part_of(v3, v2) | part_of(v2, v3)) % 5.96/2.07 | (44) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ open(v2) | ~ incident_c(v1, v2) | ~ incident_c(v0, v2) | ? [v3] : (ordered_by(v3, v0, v1) & ! [v4] : ( ~ incident_o(v4, v3) | incident_c(v4, v2)) & ! [v4] : ( ~ incident_c(v4, v2) | incident_o(v4, v3)))) % 5.96/2.07 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ meet(v0, v1, v2) | ~ incident_c(v3, v2) | ~ incident_c(v3, v1) | end_point(v3, v2)) % 5.96/2.07 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ meet(v0, v1, v2) | incident_c(v0, v2)) % 6.41/2.07 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ ordered_by(v0, v1, v2) | incident_o(v2, v0)) % 6.41/2.07 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum(v1, v2) = v0) | ~ incident_c(v3, v0) | incident_c(v3, v2) | incident_c(v3, v1)) % 6.41/2.07 | (49) ! [v0] : ! [v1] : ( ~ end_point(v1, v0) | ? [v2] : ( ~ (v2 = v1) & end_point(v2, v0))) % 6.41/2.07 | (50) ! [v0] : ! [v1] : ( ~ inner_point(v0, v1) | incident_c(v0, v1)) % 6.41/2.07 | (51) ! [v0] : ! [v1] : ! [v2] : ~ between_c(v0, v1, v2, v1) % 6.41/2.07 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_c(v0, v1, v2, v3) | ? [v4] : (inner_point(v2, v4) & end_point(v3, v4) & end_point(v1, v4) & part_of(v4, v0))) % 6.41/2.07 | (53) ? [v0] : ? [v1] : (open(v1) & ! [v2] : ( ~ incident_o(v2, v0) | incident_c(v2, v1)) & ! [v2] : ( ~ incident_c(v2, v1) | incident_o(v2, v0))) % 6.41/2.07 | (54) ! [v0] : ! [v1] : ! [v2] : ( ~ incident_c(v2, v1) | ~ part_of(v1, v0) | incident_c(v2, v0)) % 6.41/2.07 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum(v1, v2) = v0) | ~ incident_c(v3, v1) | incident_c(v3, v0)) % 6.41/2.07 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_o(v3, v0, v1, v2) | ? [v4] : (between_c(v4, v0, v1, v2) & ! [v5] : ( ~ incident_o(v5, v3) | incident_c(v5, v4)) & ! [v5] : ( ~ incident_c(v5, v4) | incident_o(v5, v3)))) % 6.41/2.07 | (57) ! [v0] : ! [v1] : ( ~ inner_point(v0, v1) | ~ end_point(v0, v1)) % 6.41/2.07 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum(v1, v2) = v0) | ~ incident_c(v3, v2) | incident_c(v3, v0)) % 6.41/2.08 | (59) finish_point(all_0_1_1, all_0_2_2) % 6.41/2.08 | (60) ! [v0] : ! [v1] : ( ~ closed(v0) | ~ end_point(v1, v0)) % 6.41/2.08 | (61) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ between_c(v4, v1, v2, v3) | between_o(v0, v1, v2, v3) | ? [v5] : (( ~ incident_o(v5, v0) | ~ incident_c(v5, v4)) & (incident_o(v5, v0) | incident_c(v5, v4)))) % 6.41/2.08 | % 6.41/2.08 | Instantiating formula (31) with all_0_2_2, all_0_0_0 and discharging atoms finish_point(all_0_0_0, all_0_2_2), yields: % 6.41/2.08 | (62) incident_o(all_0_0_0, all_0_2_2) % 6.41/2.08 | % 6.41/2.08 | Instantiating formula (31) with all_0_2_2, all_0_1_1 and discharging atoms finish_point(all_0_1_1, all_0_2_2), yields: % 6.41/2.08 | (63) incident_o(all_0_1_1, all_0_2_2) % 6.41/2.08 | % 6.41/2.08 | Instantiating formula (33) with all_0_0_0, all_0_2_2, all_0_1_1 and discharging atoms finish_point(all_0_1_1, all_0_2_2), incident_o(all_0_0_0, all_0_2_2), yields: % 6.41/2.08 | (64) all_0_0_0 = all_0_1_1 | ordered_by(all_0_2_2, all_0_0_0, all_0_1_1) % 6.41/2.08 | % 6.41/2.08 | Instantiating formula (33) with all_0_1_1, all_0_2_2, all_0_0_0 and discharging atoms finish_point(all_0_0_0, all_0_2_2), incident_o(all_0_1_1, all_0_2_2), yields: % 6.41/2.08 | (65) all_0_0_0 = all_0_1_1 | ordered_by(all_0_2_2, all_0_1_1, all_0_0_0) % 6.41/2.08 | % 6.41/2.08 +-Applying beta-rule and splitting (65), into two cases. % 6.41/2.08 |-Branch one: % 6.41/2.08 | (66) ordered_by(all_0_2_2, all_0_1_1, all_0_0_0) % 6.41/2.08 | % 6.41/2.08 +-Applying beta-rule and splitting (64), into two cases. % 6.41/2.08 |-Branch one: % 6.41/2.08 | (67) ordered_by(all_0_2_2, all_0_0_0, all_0_1_1) % 6.41/2.08 | % 6.41/2.08 | Instantiating formula (20) with all_0_1_1, all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms ordered_by(all_0_2_2, all_0_0_0, all_0_1_1), ordered_by(all_0_2_2, all_0_1_1, all_0_0_0), yields: % 6.41/2.08 | (68) between_o(all_0_2_2, all_0_1_1, all_0_0_0, all_0_1_1) % 6.41/2.08 | % 6.41/2.08 | Instantiating formula (56) with all_0_2_2, all_0_1_1, all_0_0_0, all_0_1_1 and discharging atoms between_o(all_0_2_2, all_0_1_1, all_0_0_0, all_0_1_1), yields: % 6.41/2.08 | (69) ? [v0] : (between_c(v0, all_0_1_1, all_0_0_0, all_0_1_1) & ! [v1] : ( ~ incident_o(v1, all_0_2_2) | incident_c(v1, v0)) & ! [v1] : ( ~ incident_c(v1, v0) | incident_o(v1, all_0_2_2))) % 6.41/2.08 | % 6.41/2.08 | Instantiating (69) with all_62_0_25 yields: % 6.41/2.08 | (70) between_c(all_62_0_25, all_0_1_1, all_0_0_0, all_0_1_1) & ! [v0] : ( ~ incident_o(v0, all_0_2_2) | incident_c(v0, all_62_0_25)) & ! [v0] : ( ~ incident_c(v0, all_62_0_25) | incident_o(v0, all_0_2_2)) % 6.41/2.08 | % 6.41/2.08 | Applying alpha-rule on (70) yields: % 6.41/2.08 | (71) between_c(all_62_0_25, all_0_1_1, all_0_0_0, all_0_1_1) % 6.41/2.08 | (72) ! [v0] : ( ~ incident_o(v0, all_0_2_2) | incident_c(v0, all_62_0_25)) % 6.41/2.08 | (73) ! [v0] : ( ~ incident_c(v0, all_62_0_25) | incident_o(v0, all_0_2_2)) % 6.41/2.08 | % 6.41/2.08 | Instantiating formula (51) with all_0_0_0, all_0_1_1, all_62_0_25 and discharging atoms between_c(all_62_0_25, all_0_1_1, all_0_0_0, all_0_1_1), yields: % 6.41/2.08 | (74) $false % 6.41/2.08 | % 6.41/2.08 |-The branch is then unsatisfiable % 6.41/2.08 |-Branch two: % 6.41/2.08 | (75) ~ ordered_by(all_0_2_2, all_0_0_0, all_0_1_1) % 6.41/2.08 | (76) all_0_0_0 = all_0_1_1 % 6.41/2.08 | % 6.41/2.08 | Equations (76) can reduce 38 to: % 6.41/2.08 | (77) $false % 6.41/2.08 | % 6.41/2.08 |-The branch is then unsatisfiable % 6.41/2.08 |-Branch two: % 6.41/2.08 | (78) ~ ordered_by(all_0_2_2, all_0_1_1, all_0_0_0) % 6.41/2.08 | (76) all_0_0_0 = all_0_1_1 % 6.41/2.08 | % 6.41/2.08 | Equations (76) can reduce 38 to: % 6.41/2.08 | (77) $false % 6.41/2.08 | % 6.41/2.08 |-The branch is then unsatisfiable % 6.41/2.08 % SZS output end Proof for theBenchmark % 6.41/2.08 % 6.41/2.08 1450ms %------------------------------------------------------------------------------