%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO171+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n006.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 03:48:07 EDT 2022 % Result : Theorem 10.73s 3.23s % Output : Proof 12.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : GEO171+1 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.34 % Computer : n006.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Sat Jun 18 02:07:25 EDT 2022 % 0.14/0.35 % CPUTime : % 0.20/0.60 ____ _ % 0.20/0.60 ___ / __ \_____(_)___ ________ __________ % 0.20/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.20/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.20/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic % 0.20/0.60 (ePrincess v.1.0) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2015 % 0.20/0.60 (c) Peter Backeman, 2014-2015 % 0.20/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.20/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.20/0.60 Bug reports to peter@backeman.se % 0.20/0.60 % 0.20/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.71/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.68/0.94 Prover 0: Preprocessing ... % 1.84/1.06 Prover 0: Warning: ignoring some quantifiers % 1.98/1.08 Prover 0: Constructing countermodel ... % 2.53/1.30 Prover 0: gave up % 2.53/1.30 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.53/1.33 Prover 1: Preprocessing ... % 2.98/1.43 Prover 1: Constructing countermodel ... % 3.20/1.47 Prover 1: gave up % 3.20/1.47 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 3.20/1.49 Prover 2: Preprocessing ... % 3.55/1.62 Prover 2: Warning: ignoring some quantifiers % 3.55/1.63 Prover 2: Constructing countermodel ... % 4.68/1.79 Prover 2: gave up % 4.68/1.79 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 4.68/1.80 Prover 3: Preprocessing ... % 4.68/1.82 Prover 3: Warning: ignoring some quantifiers % 4.68/1.82 Prover 3: Constructing countermodel ... % 4.96/1.85 Prover 3: gave up % 4.96/1.85 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 4.96/1.87 Prover 4: Preprocessing ... % 5.31/1.94 Prover 4: Warning: ignoring some quantifiers % 5.31/1.94 Prover 4: Constructing countermodel ... % 9.91/3.07 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 9.91/3.09 Prover 5: Preprocessing ... % 10.31/3.16 Prover 5: Constructing countermodel ... % 10.73/3.22 Prover 5: proved (157ms) % 10.73/3.23 Prover 4: stopped % 10.73/3.23 % 10.73/3.23 No countermodel exists, formula is valid % 10.73/3.23 % SZS status Theorem for theBenchmark % 10.73/3.23 % 10.73/3.23 Generating proof ... found it (size 36) % 11.76/3.48 % 11.76/3.48 % SZS output start Proof for theBenchmark % 11.76/3.48 Assumed formulas after preprocessing and simplification: % 11.76/3.48 | (0) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v2) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apart_point_and_line(v1, v2) = v9 & apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v1, v3) = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v2, v1) = v4 & convergent_lines(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v2, v0) = v4 & convergent_lines(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = 0 & distinct_lines(v0, v1) = v2) % 12.24/3.52 | Applying alpha-rule on (0) yields: % 12.24/3.52 | (1) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) % 12.24/3.52 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 12.24/3.52 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) % 12.24/3.52 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 12.24/3.52 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) % 12.24/3.52 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) % 12.24/3.52 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 12.24/3.52 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) % 12.24/3.52 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) % 12.24/3.52 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v1, v3) = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) % 12.24/3.52 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) % 12.24/3.52 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) % 12.24/3.52 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v2, v0) = v4 & convergent_lines(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 12.24/3.52 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) % 12.24/3.52 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 12.24/3.52 | (16) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) % 12.24/3.52 | (17) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) % 12.24/3.52 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 12.24/3.52 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 12.24/3.53 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v2, v1) = v4 & convergent_lines(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 12.24/3.53 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) % 12.24/3.53 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 12.24/3.53 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) % 12.24/3.53 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) % 12.24/3.53 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) % 12.24/3.53 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) % 12.24/3.53 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) % 12.24/3.53 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 12.24/3.53 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 12.24/3.53 | (30) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) % 12.24/3.53 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) % 12.24/3.53 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) % 12.24/3.53 | (33) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) % 12.24/3.53 | (34) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 12.24/3.53 | (35) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 12.24/3.53 | (36) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 12.24/3.53 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 12.24/3.53 | (38) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = 0 & distinct_lines(v0, v1) = v2) % 12.24/3.53 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 12.24/3.53 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apart_point_and_line(v1, v2) = v9 & apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) % 12.24/3.53 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 12.24/3.53 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v2) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) % 12.24/3.54 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 12.24/3.54 | % 12.24/3.54 | Instantiating (38) with all_1_0_0, all_1_1_1, all_1_2_2 yields: % 12.24/3.54 | (44) ~ (all_1_0_0 = 0) & convergent_lines(all_1_2_2, all_1_1_1) = 0 & distinct_lines(all_1_2_2, all_1_1_1) = all_1_0_0 % 12.24/3.54 | % 12.24/3.54 | Applying alpha-rule on (44) yields: % 12.24/3.54 | (45) ~ (all_1_0_0 = 0) % 12.24/3.54 | (46) convergent_lines(all_1_2_2, all_1_1_1) = 0 % 12.24/3.54 | (47) distinct_lines(all_1_2_2, all_1_1_1) = all_1_0_0 % 12.24/3.54 | % 12.24/3.54 | Instantiating formula (35) with all_1_2_2 yields: % 12.24/3.54 | (48) ~ (convergent_lines(all_1_2_2, all_1_2_2) = 0) % 12.24/3.54 | % 12.24/3.54 | Instantiating formula (30) with all_1_1_1, all_1_2_2 and discharging atoms convergent_lines(all_1_2_2, all_1_1_1) = 0, yields: % 12.24/3.54 | (49) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_1_2_2, all_1_1_1) = v0 & apart_point_and_line(v0, all_1_1_1) = v1) % 12.24/3.54 | % 12.24/3.54 | Instantiating formula (33) with all_1_1_1, all_1_2_2 and discharging atoms convergent_lines(all_1_2_2, all_1_1_1) = 0, yields: % 12.24/3.54 | (50) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_1_2_2, all_1_1_1) = v0 & apart_point_and_line(v0, all_1_2_2) = v1) % 12.24/3.54 | % 12.24/3.54 | Instantiating formula (3) with all_1_0_0, all_1_0_0, all_1_1_1, all_1_2_2, all_1_2_2 and discharging atoms distinct_lines(all_1_2_2, all_1_1_1) = all_1_0_0, yields: % 12.24/3.54 | (51) all_1_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_1_2_2, all_1_2_2) = v0) % 12.24/3.54 | % 12.24/3.54 | Instantiating (50) with all_16_0_3, all_16_1_4 yields: % 12.24/3.54 | (52) ~ (all_16_0_3 = 0) & intersection_point(all_1_2_2, all_1_1_1) = all_16_1_4 & apart_point_and_line(all_16_1_4, all_1_2_2) = all_16_0_3 % 12.24/3.54 | % 12.24/3.54 | Applying alpha-rule on (52) yields: % 12.24/3.54 | (53) ~ (all_16_0_3 = 0) % 12.24/3.54 | (54) intersection_point(all_1_2_2, all_1_1_1) = all_16_1_4 % 12.24/3.54 | (55) apart_point_and_line(all_16_1_4, all_1_2_2) = all_16_0_3 % 12.24/3.54 | % 12.24/3.54 | Instantiating (49) with all_18_0_5, all_18_1_6 yields: % 12.24/3.54 | (56) ~ (all_18_0_5 = 0) & intersection_point(all_1_2_2, all_1_1_1) = all_18_1_6 & apart_point_and_line(all_18_1_6, all_1_1_1) = all_18_0_5 % 12.24/3.54 | % 12.24/3.54 | Applying alpha-rule on (56) yields: % 12.24/3.54 | (57) ~ (all_18_0_5 = 0) % 12.24/3.54 | (58) intersection_point(all_1_2_2, all_1_1_1) = all_18_1_6 % 12.24/3.54 | (59) apart_point_and_line(all_18_1_6, all_1_1_1) = all_18_0_5 % 12.24/3.54 | % 12.24/3.54 +-Applying beta-rule and splitting (51), into two cases. % 12.24/3.54 |-Branch one: % 12.24/3.54 | (60) all_1_0_0 = 0 % 12.24/3.54 | % 12.24/3.54 | Equations (60) can reduce 45 to: % 12.24/3.54 | (61) $false % 12.24/3.54 | % 12.24/3.54 |-The branch is then unsatisfiable % 12.24/3.54 |-Branch two: % 12.24/3.54 | (45) ~ (all_1_0_0 = 0) % 12.24/3.54 | (63) ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_1_2_2, all_1_2_2) = v0) % 12.24/3.54 | % 12.24/3.54 | Instantiating formula (2) with all_1_2_2, all_1_1_1, all_16_1_4, all_18_1_6 and discharging atoms intersection_point(all_1_2_2, all_1_1_1) = all_18_1_6, intersection_point(all_1_2_2, all_1_1_1) = all_16_1_4, yields: % 12.24/3.54 | (64) all_18_1_6 = all_16_1_4 % 12.24/3.54 | % 12.24/3.54 | From (64) and (59) follows: % 12.24/3.54 | (65) apart_point_and_line(all_16_1_4, all_1_1_1) = all_18_0_5 % 12.24/3.54 | % 12.24/3.54 | Instantiating formula (40) with all_18_0_5, all_18_0_5, all_1_1_1, all_1_1_1, all_16_1_4, all_16_1_4 and discharging atoms apart_point_and_line(all_16_1_4, all_1_1_1) = all_18_0_5, yields: % 12.24/3.54 | (66) all_18_0_5 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_16_1_4, all_1_1_1) = v3 & apart_point_and_line(all_16_1_4, all_1_1_1) = v2 & distinct_lines(all_1_1_1, all_1_1_1) = v1 & distinct_points(all_16_1_4, all_16_1_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 12.24/3.54 | % 12.24/3.54 +-Applying beta-rule and splitting (66), into two cases. % 12.24/3.54 |-Branch one: % 12.24/3.54 | (67) all_18_0_5 = 0 % 12.24/3.54 | % 12.24/3.54 | Equations (67) can reduce 57 to: % 12.24/3.54 | (61) $false % 12.24/3.54 | % 12.24/3.54 |-The branch is then unsatisfiable % 12.24/3.54 |-Branch two: % 12.24/3.54 | (57) ~ (all_18_0_5 = 0) % 12.24/3.55 | (70) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_16_1_4, all_1_1_1) = v3 & apart_point_and_line(all_16_1_4, all_1_1_1) = v2 & distinct_lines(all_1_1_1, all_1_1_1) = v1 & distinct_points(all_16_1_4, all_16_1_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 12.24/3.55 | % 12.24/3.55 | Instantiating (70) with all_43_0_12, all_43_1_13, all_43_2_14, all_43_3_15 yields: % 12.24/3.55 | (71) apart_point_and_line(all_16_1_4, all_1_1_1) = all_43_0_12 & apart_point_and_line(all_16_1_4, all_1_1_1) = all_43_1_13 & distinct_lines(all_1_1_1, all_1_1_1) = all_43_2_14 & distinct_points(all_16_1_4, all_16_1_4) = all_43_3_15 & ( ~ (all_43_2_14 = 0) | ~ (all_43_3_15 = 0) | all_43_0_12 = 0 | all_43_1_13 = 0) % 12.24/3.55 | % 12.24/3.55 | Applying alpha-rule on (71) yields: % 12.24/3.55 | (72) ~ (all_43_2_14 = 0) | ~ (all_43_3_15 = 0) | all_43_0_12 = 0 | all_43_1_13 = 0 % 12.24/3.55 | (73) distinct_points(all_16_1_4, all_16_1_4) = all_43_3_15 % 12.24/3.55 | (74) distinct_lines(all_1_1_1, all_1_1_1) = all_43_2_14 % 12.24/3.55 | (75) apart_point_and_line(all_16_1_4, all_1_1_1) = all_43_0_12 % 12.24/3.55 | (76) apart_point_and_line(all_16_1_4, all_1_1_1) = all_43_1_13 % 12.24/3.55 | % 12.24/3.55 | Instantiating formula (36) with all_1_1_1 yields: % 12.24/3.55 | (77) ~ (distinct_lines(all_1_1_1, all_1_1_1) = 0) % 12.24/3.55 | % 12.24/3.55 | Using (74) and (77) yields: % 12.24/3.55 | (78) ~ (all_43_2_14 = 0) % 12.24/3.55 | % 12.24/3.55 | Instantiating formula (3) with all_1_0_0, all_43_2_14, all_1_1_1, all_1_2_2, all_1_1_1 and discharging atoms distinct_lines(all_1_1_1, all_1_1_1) = all_43_2_14, distinct_lines(all_1_2_2, all_1_1_1) = all_1_0_0, yields: % 12.24/3.55 | (79) all_43_2_14 = 0 | all_1_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_1_1_1, all_1_2_2) = v0) % 12.24/3.55 | % 12.24/3.55 +-Applying beta-rule and splitting (79), into two cases. % 12.24/3.55 |-Branch one: % 12.24/3.55 | (80) all_43_2_14 = 0 % 12.24/3.55 | % 12.24/3.55 | Equations (80) can reduce 78 to: % 12.24/3.55 | (61) $false % 12.24/3.55 | % 12.24/3.55 |-The branch is then unsatisfiable % 12.24/3.55 |-Branch two: % 12.24/3.55 | (78) ~ (all_43_2_14 = 0) % 12.24/3.55 | (83) all_1_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_1_1_1, all_1_2_2) = v0) % 12.24/3.55 | % 12.24/3.55 +-Applying beta-rule and splitting (83), into two cases. % 12.24/3.55 |-Branch one: % 12.24/3.55 | (60) all_1_0_0 = 0 % 12.24/3.55 | % 12.24/3.55 | Equations (60) can reduce 45 to: % 12.24/3.55 | (61) $false % 12.24/3.55 | % 12.24/3.55 |-The branch is then unsatisfiable % 12.24/3.55 |-Branch two: % 12.24/3.55 | (45) ~ (all_1_0_0 = 0) % 12.24/3.55 | (87) ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_1_1_1, all_1_2_2) = v0) % 12.24/3.55 | % 12.24/3.55 | Instantiating (87) with all_81_0_24 yields: % 12.24/3.55 | (88) ~ (all_81_0_24 = 0) & distinct_lines(all_1_1_1, all_1_2_2) = all_81_0_24 % 12.24/3.55 | % 12.24/3.55 | Applying alpha-rule on (88) yields: % 12.24/3.55 | (89) ~ (all_81_0_24 = 0) % 12.24/3.55 | (90) distinct_lines(all_1_1_1, all_1_2_2) = all_81_0_24 % 12.24/3.55 | % 12.24/3.55 | Instantiating formula (31) with all_81_0_24, all_1_2_2, all_1_1_1, all_1_2_2 and discharging atoms convergent_lines(all_1_2_2, all_1_1_1) = 0, distinct_lines(all_1_1_1, all_1_2_2) = all_81_0_24, ~ (convergent_lines(all_1_2_2, all_1_2_2) = 0), yields: % 12.24/3.55 | (91) all_81_0_24 = 0 % 12.24/3.55 | % 12.24/3.55 | Equations (91) can reduce 89 to: % 12.24/3.55 | (61) $false % 12.24/3.55 | % 12.24/3.55 |-The branch is then unsatisfiable % 12.24/3.55 % SZS output end Proof for theBenchmark % 12.24/3.55 % 12.24/3.55 2940ms %------------------------------------------------------------------------------