%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO112+1 : TPTP v8.1.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n014.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 03:47:43 EDT 2022 % Result : Theorem 2.97s 1.37s % Output : Proof 4.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GEO112+1 : TPTP v8.1.0. Released v2.4.0. % 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.33 % Computer : n014.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Fri Jun 17 23:30:34 EDT 2022 % 0.13/0.34 % CPUTime : % 0.59/0.59 ____ _ % 0.59/0.59 ___ / __ \_____(_)___ ________ __________ % 0.59/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.59/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.59/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.59/0.59 % 0.59/0.59 A Theorem Prover for First-Order Logic % 0.59/0.59 (ePrincess v.1.0) % 0.59/0.59 % 0.59/0.59 (c) Philipp Rümmer, 2009-2015 % 0.59/0.59 (c) Peter Backeman, 2014-2015 % 0.59/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.59/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.59/0.59 Bug reports to peter@backeman.se % 0.59/0.59 % 0.59/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.59/0.59 % 0.59/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.76/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.63/0.97 Prover 0: Preprocessing ... % 2.30/1.19 Prover 0: Warning: ignoring some quantifiers % 2.30/1.21 Prover 0: Constructing countermodel ... % 2.97/1.37 Prover 0: proved (727ms) % 2.97/1.37 % 2.97/1.37 No countermodel exists, formula is valid % 2.97/1.37 % SZS status Theorem for theBenchmark % 2.97/1.37 % 2.97/1.37 Generating proof ... Warning: ignoring some quantifiers % 4.04/1.64 found it (size 10) % 4.04/1.64 % 4.04/1.64 % SZS output start Proof for theBenchmark % 4.04/1.64 Assumed formulas after preprocessing and simplification: % 4.04/1.64 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (between_c(v0, v1, v2, v3) & ~ between_c(v0, v3, v2, v1) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v5 | ~ inner_point(v6, v8) | ~ end_point(v7, v8) | ~ end_point(v5, v8) | ~ part_of(v8, v4) | between_c(v4, v5, v6, v7)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sum(v5, v6) = v4) | ~ closed(v4) | ~ meet(v7, v5, v6) | ~ end_point(v8, v5) | meet(v8, v5, v6)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ end_point(v8, v7) | ~ end_point(v8, v6) | ~ end_point(v8, v5) | ~ part_of(v7, v4) | ~ part_of(v6, v4) | ~ part_of(v5, v4) | part_of(v7, v6) | part_of(v7, v5) | part_of(v6, v7) | part_of(v6, v5) | part_of(v5, v7) | part_of(v5, v6)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | v7 = v5 | v6 = v5 | ~ end_point(v7, v4) | ~ end_point(v6, v4) | ~ end_point(v5, v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (sum(v7, v6) = v5) | ~ (sum(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (sum(v5, v6) = v4) | ~ incident_c(v7, v6) | incident_c(v7, v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (sum(v5, v6) = v4) | ~ incident_c(v7, v5) | incident_c(v7, v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (sum(v5, v6) = v4) | ~ incident_c(v7, v4) | incident_c(v7, v6) | incident_c(v7, v5)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ between_c(v4, v5, v6, v7) | ? [v8] : (inner_point(v6, v8) & end_point(v7, v8) & end_point(v5, v8) & part_of(v8, v4))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ meet(v4, v5, v6) | ~ incident_c(v7, v6) | ~ incident_c(v7, v5) | end_point(v7, v6)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ meet(v4, v5, v6) | ~ incident_c(v7, v6) | ~ incident_c(v7, v5) | end_point(v7, v5)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ end_point(v4, v5) | ~ incident_c(v4, v7) | ~ incident_c(v4, v6) | ~ part_of(v7, v5) | ~ part_of(v6, v5) | part_of(v7, v6) | part_of(v6, v7)) & ? [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v4 | ~ (sum(v5, v6) = v7) | ? [v8] : (( ~ incident_c(v8, v4) | ( ~ incident_c(v8, v6) & ~ incident_c(v8, v5))) & (incident_c(v8, v6) | incident_c(v8, v5) | incident_c(v8, v4)))) & ! [v4] : ! [v5] : ! [v6] : ~ between_c(v4, v5, v6, v5) & ! [v4] : ! [v5] : ! [v6] : ( ~ meet(v4, v5, v6) | incident_c(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ meet(v4, v5, v6) | incident_c(v4, v5)) & ! [v4] : ! [v5] : ! [v6] : ( ~ incident_c(v6, v5) | ~ part_of(v5, v4) | incident_c(v6, v4)) & ! [v4] : ! [v5] : ! [v6] : ( ~ incident_c(v4, v6) | ~ incident_c(v4, v5) | meet(v4, v5, v6) | ? [v7] : (incident_c(v7, v6) & incident_c(v7, v5) & ( ~ end_point(v7, v6) | ~ end_point(v7, v5)))) & ! [v4] : ! [v5] : (v5 = v4 | ~ part_of(v5, v4) | open(v5)) & ! [v4] : ! [v5] : ( ~ closed(v4) | ~ end_point(v5, v4)) & ! [v4] : ! [v5] : ( ~ inner_point(v5, v4) | ? [v6] : ? [v7] : (sum(v6, v7) = v4 & meet(v5, v6, v7))) & ! [v4] : ! [v5] : ( ~ inner_point(v4, v5) | ~ end_point(v4, v5)) & ! [v4] : ! [v5] : ( ~ inner_point(v4, v5) | incident_c(v4, v5)) & ! [v4] : ! [v5] : ( ~ end_point(v5, v4) | open(v4)) & ! [v4] : ! [v5] : ( ~ end_point(v5, v4) | ? [v6] : ( ~ (v6 = v5) & end_point(v6, v4))) & ! [v4] : ! [v5] : ( ~ end_point(v4, v5) | incident_c(v4, v5)) & ! [v4] : ! [v5] : ( ~ incident_c(v4, v5) | inner_point(v4, v5) | end_point(v4, v5)) & ! [v4] : ! [v5] : ( ~ incident_c(v4, v5) | end_point(v4, v5) | ? [v6] : ? [v7] : (incident_c(v4, v7) & incident_c(v4, v6) & part_of(v7, v5) & part_of(v6, v5) & ~ part_of(v7, v6) & ~ part_of(v6, v7))) & ! [v4] : ( ~ open(v4) | ? [v5] : end_point(v5, v4)) & ? [v4] : ? [v5] : (v5 = v4 | ? [v6] : (( ~ incident_c(v6, v5) | ~ incident_c(v6, v4)) & (incident_c(v6, v5) | incident_c(v6, v4)))) & ? [v4] : ? [v5] : inner_point(v5, v4) & ? [v4] : ? [v5] : (part_of(v5, v4) | ? [v6] : (incident_c(v6, v5) & ~ incident_c(v6, v4))) & ? [v4] : (closed(v4) | ? [v5] : end_point(v5, v4))) % 4.04/1.68 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 4.04/1.68 | (1) between_c(all_0_3_3, all_0_2_2, all_0_1_1, all_0_0_0) & ~ between_c(all_0_3_3, all_0_0_0, 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] : (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] : ( ~ 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] : ~ 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] : (v1 = v0 | ~ part_of(v1, v0) | open(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] : (( ~ incident_c(v2, v1) | ~ incident_c(v2, v0)) & (incident_c(v2, v1) | incident_c(v2, v0)))) & ? [v0] : ? [v1] : inner_point(v1, v0) & ? [v0] : ? [v1] : (part_of(v1, v0) | ? [v2] : (incident_c(v2, v1) & ~ incident_c(v2, v0))) & ? [v0] : (closed(v0) | ? [v1] : end_point(v1, v0)) % 4.38/1.69 | % 4.38/1.69 | Applying alpha-rule on (1) yields: % 4.38/1.69 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ meet(v0, v1, v2) | ~ incident_c(v3, v2) | ~ incident_c(v3, v1) | end_point(v3, v2)) % 4.38/1.69 | (3) ~ between_c(all_0_3_3, all_0_0_0, all_0_1_1, all_0_2_2) % 4.38/1.69 | (4) ! [v0] : ! [v1] : ( ~ inner_point(v0, v1) | ~ end_point(v0, v1)) % 4.38/1.69 | (5) ? [v0] : (closed(v0) | ? [v1] : end_point(v1, v0)) % 4.38/1.69 | (6) ! [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)) % 4.38/1.70 | (7) ! [v0] : ! [v1] : ( ~ incident_c(v0, v1) | inner_point(v0, v1) | end_point(v0, v1)) % 4.38/1.70 | (8) ? [v0] : ? [v1] : (part_of(v1, v0) | ? [v2] : (incident_c(v2, v1) & ~ incident_c(v2, v0))) % 4.38/1.70 | (9) ! [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))) % 4.38/1.70 | (10) ! [v0] : ! [v1] : ( ~ inner_point(v0, v1) | incident_c(v0, v1)) % 4.38/1.70 | (11) between_c(all_0_3_3, all_0_2_2, all_0_1_1, all_0_0_0) % 4.38/1.70 | (12) ! [v0] : ! [v1] : ( ~ closed(v0) | ~ end_point(v1, v0)) % 4.38/1.70 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sum(v1, v2) = v0) | ~ closed(v0) | ~ meet(v3, v1, v2) | ~ end_point(v4, v1) | meet(v4, v1, v2)) % 4.38/1.70 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ (sum(v3, v2) = v0)) % 4.38/1.70 | (15) ! [v0] : ! [v1] : ( ~ end_point(v0, v1) | incident_c(v0, v1)) % 4.38/1.70 | (16) ! [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)) % 4.38/1.70 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ incident_c(v2, v1) | ~ part_of(v1, v0) | incident_c(v2, v0)) % 4.38/1.70 | (18) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ incident_c(v2, v1) | ~ incident_c(v2, v0)) & (incident_c(v2, v1) | incident_c(v2, v0)))) % 4.38/1.70 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ meet(v0, v1, v2) | incident_c(v0, v2)) % 4.38/1.70 | (20) ! [v0] : ! [v1] : ! [v2] : ~ between_c(v0, v1, v2, v1) % 4.38/1.70 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ meet(v0, v1, v2) | ~ incident_c(v3, v2) | ~ incident_c(v3, v1) | end_point(v3, v1)) % 4.38/1.70 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ meet(v0, v1, v2) | incident_c(v0, v1)) % 4.38/1.70 | (23) ? [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)))) % 4.38/1.70 | (24) ! [v0] : ( ~ open(v0) | ? [v1] : end_point(v1, v0)) % 4.38/1.70 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v3 = v1 | v2 = v1 | ~ end_point(v3, v0) | ~ end_point(v2, v0) | ~ end_point(v1, v0)) % 4.38/1.70 | (26) ! [v0] : ! [v1] : (v1 = v0 | ~ part_of(v1, v0) | open(v1)) % 4.38/1.70 | (27) ! [v0] : ! [v1] : ( ~ end_point(v1, v0) | ? [v2] : ( ~ (v2 = v1) & end_point(v2, v0))) % 4.38/1.70 | (28) ? [v0] : ? [v1] : inner_point(v1, v0) % 4.38/1.70 | (29) ! [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)))) % 4.38/1.70 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum(v1, v2) = v0) | ~ incident_c(v3, v0) | incident_c(v3, v2) | incident_c(v3, v1)) % 4.38/1.70 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum(v1, v2) = v0) | ~ incident_c(v3, v2) | incident_c(v3, v0)) % 4.38/1.70 | (32) ! [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)) % 4.38/1.70 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum(v1, v2) = v0) | ~ incident_c(v3, v1) | incident_c(v3, v0)) % 4.38/1.71 | (34) ! [v0] : ! [v1] : ( ~ inner_point(v1, v0) | ? [v2] : ? [v3] : (sum(v2, v3) = v0 & meet(v1, v2, v3))) % 4.38/1.71 | (35) ! [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))) % 4.38/1.71 | (36) ! [v0] : ! [v1] : ( ~ end_point(v1, v0) | open(v0)) % 4.38/1.71 | % 4.38/1.71 | Instantiating formula (35) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms between_c(all_0_3_3, all_0_2_2, all_0_1_1, all_0_0_0), yields: % 4.38/1.71 | (37) ? [v0] : (inner_point(all_0_1_1, v0) & end_point(all_0_0_0, v0) & end_point(all_0_2_2, v0) & part_of(v0, all_0_3_3)) % 4.38/1.71 | % 4.38/1.71 | Instantiating (37) with all_18_0_14 yields: % 4.38/1.71 | (38) inner_point(all_0_1_1, all_18_0_14) & end_point(all_0_0_0, all_18_0_14) & end_point(all_0_2_2, all_18_0_14) & part_of(all_18_0_14, all_0_3_3) % 4.38/1.71 | % 4.38/1.71 | Applying alpha-rule on (38) yields: % 4.38/1.71 | (39) inner_point(all_0_1_1, all_18_0_14) % 4.38/1.71 | (40) end_point(all_0_0_0, all_18_0_14) % 4.38/1.71 | (41) end_point(all_0_2_2, all_18_0_14) % 4.38/1.71 | (42) part_of(all_18_0_14, all_0_3_3) % 4.38/1.71 | % 4.38/1.71 | Instantiating formula (6) with all_18_0_14, all_0_2_2, all_0_1_1, all_0_0_0, all_0_3_3 and discharging atoms inner_point(all_0_1_1, all_18_0_14), end_point(all_0_0_0, all_18_0_14), end_point(all_0_2_2, all_18_0_14), part_of(all_18_0_14, all_0_3_3), ~ between_c(all_0_3_3, all_0_0_0, all_0_1_1, all_0_2_2), yields: % 4.38/1.71 | (43) all_0_0_0 = all_0_2_2 % 4.38/1.71 | % 4.38/1.71 | From (43) and (11) follows: % 4.38/1.71 | (44) between_c(all_0_3_3, all_0_2_2, all_0_1_1, all_0_2_2) % 4.38/1.71 | % 4.38/1.71 | From (43) and (3) follows: % 4.38/1.71 | (45) ~ between_c(all_0_3_3, all_0_2_2, all_0_1_1, all_0_2_2) % 4.38/1.71 | % 4.38/1.71 | Using (44) and (45) yields: % 4.38/1.71 | (46) $false % 4.38/1.71 | % 4.38/1.71 |-The branch is then unsatisfiable % 4.38/1.71 % SZS output end Proof for theBenchmark % 4.38/1.71 % 4.38/1.71 1109ms %------------------------------------------------------------------------------