TSTP Solution File: GEO179+2 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO179+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n013.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 03:48:16 EDT 2022
% Result : Theorem 3.33s 1.45s
% Output : Proof 5.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO179+2 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 18 00:55:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.49/0.57 ____ _
% 0.49/0.57 ___ / __ \_____(_)___ ________ __________
% 0.49/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.49/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.49/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.49/0.57
% 0.49/0.57 A Theorem Prover for First-Order Logic
% 0.49/0.57 (ePrincess v.1.0)
% 0.49/0.57
% 0.49/0.57 (c) Philipp Rümmer, 2009-2015
% 0.49/0.57 (c) Peter Backeman, 2014-2015
% 0.49/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.49/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.49/0.57 Bug reports to peter@backeman.se
% 0.49/0.57
% 0.49/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.49/0.57
% 0.49/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.49/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.51/0.89 Prover 0: Preprocessing ...
% 1.90/1.01 Prover 0: Warning: ignoring some quantifiers
% 1.90/1.03 Prover 0: Constructing countermodel ...
% 2.66/1.25 Prover 0: gave up
% 2.66/1.25 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.78/1.28 Prover 1: Preprocessing ...
% 3.04/1.36 Prover 1: Constructing countermodel ...
% 3.33/1.45 Prover 1: proved (199ms)
% 3.33/1.45
% 3.33/1.45 No countermodel exists, formula is valid
% 3.33/1.45 % SZS status Theorem for theBenchmark
% 3.33/1.45
% 3.33/1.45 Generating proof ... found it (size 85)
% 5.23/1.89
% 5.23/1.89 % SZS output start Proof for theBenchmark
% 5.23/1.89 Assumed formulas after preprocessing and simplification:
% 5.23/1.89 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (line_connecting(v2, v1) = v6 & line_connecting(v2, v0) = v4 & line_connecting(v0, v1) = v3 & apart_point_and_line(v2, v3) = 0 & distinct_lines(v3, v6) = v7 & distinct_lines(v3, v4) = v5 & distinct_points(v0, v1) = 0 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (intersection_point(v8, v9) = v11) | ~ (distinct_points(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : (apart_point_and_line(v10, v9) = v15 & apart_point_and_line(v10, v8) = v14 & convergent_lines(v8, v9) = v13 & ( ~ (v13 = 0) | ( ~ (v15 = 0) & ~ (v14 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (apart_point_and_line(v8, v9) = 0) | ~ (distinct_lines(v9, v10) = v11) | apart_point_and_line(v8, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (apart_point_and_line(v8, v9) = 0) | ~ (distinct_points(v8, v10) = v11) | apart_point_and_line(v10, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (convergent_lines(v8, v10) = v11) | ~ (convergent_lines(v8, v9) = 0) | convergent_lines(v9, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (distinct_lines(v8, v10) = v11) | ~ (distinct_lines(v8, v9) = 0) | distinct_lines(v9, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (distinct_points(v8, v10) = v11) | ~ (distinct_points(v8, v9) = 0) | distinct_points(v9, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (intersection_point(v11, v10) = v9) | ~ (intersection_point(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (line_connecting(v11, v10) = v9) | ~ (line_connecting(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (apart_point_and_line(v11, v10) = v9) | ~ (apart_point_and_line(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (convergent_lines(v11, v10) = v9) | ~ (convergent_lines(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (distinct_lines(v11, v10) = v9) | ~ (distinct_lines(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (distinct_points(v11, v10) = v9) | ~ (distinct_points(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (line_connecting(v8, v9) = v11) | ~ (apart_point_and_line(v10, v11) = 0) | ? [v12] : ? [v13] : ? [v14] : (distinct_points(v10, v9) = v14 & distinct_points(v10, v8) = v13 & distinct_points(v8, v9) = v12 & ( ~ (v12 = 0) | (v14 = 0 & v13 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (distinct_lines(v10, v11) = 0) | ~ (distinct_points(v8, v9) = 0) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (apart_point_and_line(v9, v11) = v15 & apart_point_and_line(v9, v10) = v14 & apart_point_and_line(v8, v11) = v13 & apart_point_and_line(v8, v10) = v12 & (v15 = 0 | v14 = 0 | v13 = 0 | v12 = 0))) & ! [v8] : ! [v9] : ( ~ (convergent_lines(v8, v9) = 0) | distinct_lines(v8, v9) = 0) & ! [v8] : ~ (convergent_lines(v8, v8) = 0) & ! [v8] : ~ (distinct_lines(v8, v8) = 0) & ! [v8] : ~ (distinct_points(v8, v8) = 0) & ( ~ (v7 = 0) | ~ (v5 = 0)))
% 5.23/1.92 | 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, all_0_7_7 yields:
% 5.23/1.92 | (1) line_connecting(all_0_5_5, all_0_6_6) = all_0_1_1 & line_connecting(all_0_5_5, all_0_7_7) = all_0_3_3 & line_connecting(all_0_7_7, all_0_6_6) = all_0_4_4 & apart_point_and_line(all_0_5_5, all_0_4_4) = 0 & distinct_lines(all_0_4_4, all_0_1_1) = all_0_0_0 & distinct_lines(all_0_4_4, all_0_3_3) = all_0_2_2 & distinct_points(all_0_7_7, all_0_6_6) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection_point(v0, v1) = v3) | ~ (distinct_points(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v1) = v7 & apart_point_and_line(v2, v0) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 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(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, 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(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] : ( ~ (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) = v5 & distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 0)))) & ! [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] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ( ~ (all_0_0_0 = 0) | ~ (all_0_2_2 = 0))
% 5.23/1.93 |
% 5.23/1.93 | Applying alpha-rule on (1) yields:
% 5.23/1.93 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 5.23/1.93 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 5.23/1.93 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 5.23/1.93 | (5) ! [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)))
% 5.23/1.93 | (6) line_connecting(all_0_5_5, all_0_7_7) = all_0_3_3
% 5.23/1.93 | (7) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0)
% 5.23/1.93 | (8) ~ (all_0_0_0 = 0) | ~ (all_0_2_2 = 0)
% 5.23/1.93 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) = v5 & distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 0))))
% 5.23/1.93 | (10) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 5.23/1.93 | (11) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 5.23/1.93 | (12) ! [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)
% 5.23/1.93 | (13) apart_point_and_line(all_0_5_5, all_0_4_4) = 0
% 5.23/1.93 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 5.23/1.94 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 5.23/1.94 | (16) line_connecting(all_0_5_5, all_0_6_6) = all_0_1_1
% 5.23/1.94 | (17) distinct_points(all_0_7_7, all_0_6_6) = 0
% 5.23/1.94 | (18) distinct_lines(all_0_4_4, all_0_1_1) = all_0_0_0
% 5.23/1.94 | (19) line_connecting(all_0_7_7, all_0_6_6) = all_0_4_4
% 5.23/1.94 | (20) distinct_lines(all_0_4_4, all_0_3_3) = all_0_2_2
% 5.23/1.94 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection_point(v0, v1) = v3) | ~ (distinct_points(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v1) = v7 & apart_point_and_line(v2, v0) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0)))))
% 5.23/1.94 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 5.23/1.94 | (23) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 5.23/1.94 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 5.62/1.94 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 5.62/1.94 | (26) ! [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)
% 5.62/1.94 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 5.62/1.94 |
% 5.62/1.94 | Instantiating formula (15) with all_0_4_4, all_0_3_3, all_0_2_2, all_0_0_0 and discharging atoms distinct_lines(all_0_4_4, all_0_3_3) = all_0_2_2, yields:
% 5.62/1.94 | (28) all_0_0_0 = all_0_2_2 | ~ (distinct_lines(all_0_4_4, all_0_3_3) = all_0_0_0)
% 5.62/1.94 |
% 5.62/1.94 | Instantiating formula (9) with all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms line_connecting(all_0_7_7, all_0_6_6) = all_0_4_4, apart_point_and_line(all_0_5_5, all_0_4_4) = 0, yields:
% 5.62/1.94 | (29) ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_0_5_5, all_0_6_6) = v2 & distinct_points(all_0_5_5, all_0_7_7) = v1 & distinct_points(all_0_7_7, all_0_6_6) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0)))
% 5.62/1.94 |
% 5.62/1.94 | Instantiating formula (26) with all_0_0_0, all_0_1_1, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_4_4) = 0, distinct_lines(all_0_4_4, all_0_1_1) = all_0_0_0, yields:
% 5.62/1.94 | (30) all_0_0_0 = 0 | apart_point_and_line(all_0_5_5, all_0_1_1) = 0
% 5.62/1.94 |
% 5.62/1.94 | Instantiating formula (26) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_4_4) = 0, distinct_lines(all_0_4_4, all_0_3_3) = all_0_2_2, yields:
% 5.62/1.94 | (31) all_0_2_2 = 0 | apart_point_and_line(all_0_5_5, all_0_3_3) = 0
% 5.62/1.94 |
% 5.62/1.94 | Instantiating (29) with all_16_0_8, all_16_1_9, all_16_2_10 yields:
% 5.62/1.94 | (32) distinct_points(all_0_5_5, all_0_6_6) = all_16_0_8 & distinct_points(all_0_5_5, all_0_7_7) = all_16_1_9 & distinct_points(all_0_7_7, all_0_6_6) = all_16_2_10 & ( ~ (all_16_2_10 = 0) | (all_16_0_8 = 0 & all_16_1_9 = 0))
% 5.62/1.94 |
% 5.62/1.94 | Applying alpha-rule on (32) yields:
% 5.62/1.94 | (33) distinct_points(all_0_5_5, all_0_6_6) = all_16_0_8
% 5.62/1.94 | (34) distinct_points(all_0_5_5, all_0_7_7) = all_16_1_9
% 5.62/1.94 | (35) distinct_points(all_0_7_7, all_0_6_6) = all_16_2_10
% 5.62/1.94 | (36) ~ (all_16_2_10 = 0) | (all_16_0_8 = 0 & all_16_1_9 = 0)
% 5.62/1.94 |
% 5.62/1.94 | Instantiating formula (3) with all_0_7_7, all_0_6_6, all_16_2_10, 0 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_16_2_10, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 5.62/1.95 | (37) all_16_2_10 = 0
% 5.62/1.95 |
% 5.62/1.95 +-Applying beta-rule and splitting (36), into two cases.
% 5.62/1.95 |-Branch one:
% 5.62/1.95 | (38) ~ (all_16_2_10 = 0)
% 5.62/1.95 |
% 5.62/1.95 | Equations (37) can reduce 38 to:
% 5.62/1.95 | (39) $false
% 5.62/1.95 |
% 5.62/1.95 |-The branch is then unsatisfiable
% 5.62/1.95 |-Branch two:
% 5.62/1.95 | (37) all_16_2_10 = 0
% 5.62/1.95 | (41) all_16_0_8 = 0 & all_16_1_9 = 0
% 5.62/1.95 |
% 5.62/1.95 | Applying alpha-rule on (41) yields:
% 5.62/1.95 | (42) all_16_0_8 = 0
% 5.62/1.95 | (43) all_16_1_9 = 0
% 5.62/1.95 |
% 5.62/1.95 | From (42) and (33) follows:
% 5.62/1.95 | (44) distinct_points(all_0_5_5, all_0_6_6) = 0
% 5.62/1.95 |
% 5.62/1.95 | From (43) and (34) follows:
% 5.62/1.95 | (45) distinct_points(all_0_5_5, all_0_7_7) = 0
% 5.62/1.95 |
% 5.62/1.95 +-Applying beta-rule and splitting (28), into two cases.
% 5.62/1.95 |-Branch one:
% 5.62/1.95 | (46) ~ (distinct_lines(all_0_4_4, all_0_3_3) = all_0_0_0)
% 5.62/1.95 |
% 5.62/1.95 | Using (20) and (46) yields:
% 5.62/1.95 | (47) ~ (all_0_0_0 = all_0_2_2)
% 5.62/1.95 |
% 5.62/1.95 +-Applying beta-rule and splitting (8), into two cases.
% 5.62/1.95 |-Branch one:
% 5.62/1.95 | (48) ~ (all_0_0_0 = 0)
% 5.62/1.95 |
% 5.62/1.95 +-Applying beta-rule and splitting (30), into two cases.
% 5.62/1.95 |-Branch one:
% 5.62/1.95 | (49) apart_point_and_line(all_0_5_5, all_0_1_1) = 0
% 5.62/1.95 |
% 5.62/1.95 | Instantiating formula (9) with all_0_1_1, all_0_5_5, all_0_6_6, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_6_6) = all_0_1_1, apart_point_and_line(all_0_5_5, all_0_1_1) = 0, yields:
% 5.62/1.95 | (50) ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_0_5_5, all_0_5_5) = v1 & distinct_points(all_0_5_5, all_0_6_6) = v2 & distinct_points(all_0_5_5, all_0_6_6) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0)))
% 5.62/1.95 |
% 5.62/1.95 | Instantiating (50) with all_61_0_11, all_61_1_12, all_61_2_13 yields:
% 5.62/1.95 | (51) distinct_points(all_0_5_5, all_0_5_5) = all_61_1_12 & distinct_points(all_0_5_5, all_0_6_6) = all_61_0_11 & distinct_points(all_0_5_5, all_0_6_6) = all_61_2_13 & ( ~ (all_61_2_13 = 0) | (all_61_0_11 = 0 & all_61_1_12 = 0))
% 5.62/1.95 |
% 5.62/1.95 | Applying alpha-rule on (51) yields:
% 5.62/1.95 | (52) distinct_points(all_0_5_5, all_0_5_5) = all_61_1_12
% 5.62/1.95 | (53) distinct_points(all_0_5_5, all_0_6_6) = all_61_0_11
% 5.62/1.95 | (54) distinct_points(all_0_5_5, all_0_6_6) = all_61_2_13
% 5.62/1.95 | (55) ~ (all_61_2_13 = 0) | (all_61_0_11 = 0 & all_61_1_12 = 0)
% 5.62/1.95 |
% 5.62/1.95 | Instantiating formula (10) with all_0_5_5 yields:
% 5.62/1.95 | (56) ~ (distinct_points(all_0_5_5, all_0_5_5) = 0)
% 5.62/1.95 |
% 5.62/1.95 | Instantiating formula (3) with all_0_5_5, all_0_6_6, all_61_0_11, 0 and discharging atoms distinct_points(all_0_5_5, all_0_6_6) = all_61_0_11, distinct_points(all_0_5_5, all_0_6_6) = 0, yields:
% 5.62/1.95 | (57) all_61_0_11 = 0
% 5.62/1.95 |
% 5.62/1.95 | Instantiating formula (3) with all_0_5_5, all_0_6_6, all_61_2_13, all_61_0_11 and discharging atoms distinct_points(all_0_5_5, all_0_6_6) = all_61_0_11, distinct_points(all_0_5_5, all_0_6_6) = all_61_2_13, yields:
% 5.62/1.95 | (58) all_61_0_11 = all_61_2_13
% 5.62/1.95 |
% 5.62/1.95 | Combining equations (57,58) yields a new equation:
% 5.62/1.95 | (59) all_61_2_13 = 0
% 5.62/1.95 |
% 5.62/1.95 +-Applying beta-rule and splitting (55), into two cases.
% 5.62/1.95 |-Branch one:
% 5.62/1.95 | (60) ~ (all_61_2_13 = 0)
% 5.62/1.95 |
% 5.62/1.95 | Equations (59) can reduce 60 to:
% 5.62/1.95 | (39) $false
% 5.62/1.95 |
% 5.62/1.95 |-The branch is then unsatisfiable
% 5.62/1.95 |-Branch two:
% 5.62/1.95 | (59) all_61_2_13 = 0
% 5.62/1.95 | (63) all_61_0_11 = 0 & all_61_1_12 = 0
% 5.62/1.95 |
% 5.62/1.95 | Applying alpha-rule on (63) yields:
% 5.62/1.95 | (57) all_61_0_11 = 0
% 5.62/1.95 | (65) all_61_1_12 = 0
% 5.62/1.95 |
% 5.62/1.95 | From (65) and (52) follows:
% 5.62/1.95 | (66) distinct_points(all_0_5_5, all_0_5_5) = 0
% 5.62/1.95 |
% 5.62/1.95 | Using (66) and (56) yields:
% 5.62/1.95 | (67) $false
% 5.62/1.95 |
% 5.62/1.95 |-The branch is then unsatisfiable
% 5.62/1.96 |-Branch two:
% 5.62/1.96 | (68) ~ (apart_point_and_line(all_0_5_5, all_0_1_1) = 0)
% 5.62/1.96 | (69) all_0_0_0 = 0
% 5.62/1.96 |
% 5.62/1.96 | Equations (69) can reduce 48 to:
% 5.62/1.96 | (39) $false
% 5.62/1.96 |
% 5.62/1.96 |-The branch is then unsatisfiable
% 5.62/1.96 |-Branch two:
% 5.62/1.96 | (69) all_0_0_0 = 0
% 5.62/1.96 | (72) ~ (all_0_2_2 = 0)
% 5.62/1.96 |
% 5.62/1.96 | Equations (69) can reduce 47 to:
% 5.62/1.96 | (73) ~ (all_0_2_2 = 0)
% 5.62/1.96 |
% 5.62/1.96 | Simplifying 73 yields:
% 5.62/1.96 | (72) ~ (all_0_2_2 = 0)
% 5.62/1.96 |
% 5.62/1.96 +-Applying beta-rule and splitting (31), into two cases.
% 5.62/1.96 |-Branch one:
% 5.62/1.96 | (75) apart_point_and_line(all_0_5_5, all_0_3_3) = 0
% 5.62/1.96 |
% 5.62/1.96 | Instantiating formula (9) with all_0_3_3, all_0_5_5, all_0_7_7, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_7_7) = all_0_3_3, apart_point_and_line(all_0_5_5, all_0_3_3) = 0, yields:
% 5.62/1.96 | (76) ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_0_5_5, all_0_5_5) = v1 & distinct_points(all_0_5_5, all_0_7_7) = v2 & distinct_points(all_0_5_5, all_0_7_7) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0)))
% 5.62/1.96 |
% 5.62/1.96 | Instantiating (76) with all_85_0_38, all_85_1_39, all_85_2_40 yields:
% 5.62/1.96 | (77) distinct_points(all_0_5_5, all_0_5_5) = all_85_1_39 & distinct_points(all_0_5_5, all_0_7_7) = all_85_0_38 & distinct_points(all_0_5_5, all_0_7_7) = all_85_2_40 & ( ~ (all_85_2_40 = 0) | (all_85_0_38 = 0 & all_85_1_39 = 0))
% 5.62/1.96 |
% 5.62/1.96 | Applying alpha-rule on (77) yields:
% 5.62/1.96 | (78) distinct_points(all_0_5_5, all_0_5_5) = all_85_1_39
% 5.62/1.96 | (79) distinct_points(all_0_5_5, all_0_7_7) = all_85_0_38
% 5.62/1.96 | (80) distinct_points(all_0_5_5, all_0_7_7) = all_85_2_40
% 5.62/1.96 | (81) ~ (all_85_2_40 = 0) | (all_85_0_38 = 0 & all_85_1_39 = 0)
% 5.62/1.96 |
% 5.62/1.96 | Instantiating formula (10) with all_0_5_5 yields:
% 5.62/1.96 | (56) ~ (distinct_points(all_0_5_5, all_0_5_5) = 0)
% 5.62/1.96 |
% 5.62/1.96 | Instantiating formula (3) with all_0_5_5, all_0_7_7, all_85_0_38, 0 and discharging atoms distinct_points(all_0_5_5, all_0_7_7) = all_85_0_38, distinct_points(all_0_5_5, all_0_7_7) = 0, yields:
% 5.62/1.96 | (83) all_85_0_38 = 0
% 5.62/1.96 |
% 5.62/1.96 | Instantiating formula (3) with all_0_5_5, all_0_7_7, all_85_2_40, all_85_0_38 and discharging atoms distinct_points(all_0_5_5, all_0_7_7) = all_85_0_38, distinct_points(all_0_5_5, all_0_7_7) = all_85_2_40, yields:
% 5.62/1.96 | (84) all_85_0_38 = all_85_2_40
% 5.62/1.96 |
% 5.62/1.96 | Combining equations (83,84) yields a new equation:
% 5.62/1.96 | (85) all_85_2_40 = 0
% 5.62/1.96 |
% 5.62/1.96 +-Applying beta-rule and splitting (81), into two cases.
% 5.62/1.96 |-Branch one:
% 5.62/1.96 | (86) ~ (all_85_2_40 = 0)
% 5.62/1.96 |
% 5.62/1.96 | Equations (85) can reduce 86 to:
% 5.62/1.96 | (39) $false
% 5.62/1.96 |
% 5.62/1.96 |-The branch is then unsatisfiable
% 5.62/1.96 |-Branch two:
% 5.62/1.96 | (85) all_85_2_40 = 0
% 5.62/1.96 | (89) all_85_0_38 = 0 & all_85_1_39 = 0
% 5.62/1.96 |
% 5.62/1.96 | Applying alpha-rule on (89) yields:
% 5.62/1.96 | (83) all_85_0_38 = 0
% 5.62/1.96 | (91) all_85_1_39 = 0
% 5.62/1.96 |
% 5.62/1.96 | From (91) and (78) follows:
% 5.62/1.96 | (66) distinct_points(all_0_5_5, all_0_5_5) = 0
% 5.62/1.96 |
% 5.62/1.96 | Using (66) and (56) yields:
% 5.62/1.96 | (67) $false
% 5.62/1.96 |
% 5.62/1.96 |-The branch is then unsatisfiable
% 5.62/1.96 |-Branch two:
% 5.62/1.96 | (94) ~ (apart_point_and_line(all_0_5_5, all_0_3_3) = 0)
% 5.62/1.96 | (95) all_0_2_2 = 0
% 5.62/1.96 |
% 5.62/1.96 | Equations (95) can reduce 72 to:
% 5.62/1.96 | (39) $false
% 5.62/1.96 |
% 5.62/1.96 |-The branch is then unsatisfiable
% 5.62/1.96 |-Branch two:
% 5.62/1.96 | (97) distinct_lines(all_0_4_4, all_0_3_3) = all_0_0_0
% 5.62/1.96 | (98) all_0_0_0 = all_0_2_2
% 5.62/1.96 |
% 5.62/1.96 +-Applying beta-rule and splitting (8), into two cases.
% 5.62/1.96 |-Branch one:
% 5.62/1.96 | (48) ~ (all_0_0_0 = 0)
% 5.62/1.96 |
% 5.62/1.96 | Equations (98) can reduce 48 to:
% 5.62/1.96 | (72) ~ (all_0_2_2 = 0)
% 5.62/1.96 |
% 5.62/1.96 +-Applying beta-rule and splitting (31), into two cases.
% 5.62/1.96 |-Branch one:
% 5.62/1.96 | (75) apart_point_and_line(all_0_5_5, all_0_3_3) = 0
% 5.62/1.97 |
% 5.62/1.97 +-Applying beta-rule and splitting (30), into two cases.
% 5.62/1.97 |-Branch one:
% 5.62/1.97 | (49) apart_point_and_line(all_0_5_5, all_0_1_1) = 0
% 5.62/1.97 |
% 5.62/1.97 | Instantiating formula (9) with all_0_1_1, all_0_5_5, all_0_6_6, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_6_6) = all_0_1_1, apart_point_and_line(all_0_5_5, all_0_1_1) = 0, yields:
% 5.62/1.97 | (50) ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_0_5_5, all_0_5_5) = v1 & distinct_points(all_0_5_5, all_0_6_6) = v2 & distinct_points(all_0_5_5, all_0_6_6) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0)))
% 5.62/1.97 |
% 5.62/1.97 | Instantiating formula (9) with all_0_3_3, all_0_5_5, all_0_7_7, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_7_7) = all_0_3_3, apart_point_and_line(all_0_5_5, all_0_3_3) = 0, yields:
% 5.62/1.97 | (76) ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_0_5_5, all_0_5_5) = v1 & distinct_points(all_0_5_5, all_0_7_7) = v2 & distinct_points(all_0_5_5, all_0_7_7) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0)))
% 5.62/1.97 |
% 5.62/1.97 | Instantiating (76) with all_58_0_41, all_58_1_42, all_58_2_43 yields:
% 5.62/1.97 | (105) distinct_points(all_0_5_5, all_0_5_5) = all_58_1_42 & distinct_points(all_0_5_5, all_0_7_7) = all_58_0_41 & distinct_points(all_0_5_5, all_0_7_7) = all_58_2_43 & ( ~ (all_58_2_43 = 0) | (all_58_0_41 = 0 & all_58_1_42 = 0))
% 5.62/1.97 |
% 5.62/1.97 | Applying alpha-rule on (105) yields:
% 5.62/1.97 | (106) distinct_points(all_0_5_5, all_0_5_5) = all_58_1_42
% 5.62/1.97 | (107) distinct_points(all_0_5_5, all_0_7_7) = all_58_0_41
% 5.62/1.97 | (108) distinct_points(all_0_5_5, all_0_7_7) = all_58_2_43
% 5.62/1.97 | (109) ~ (all_58_2_43 = 0) | (all_58_0_41 = 0 & all_58_1_42 = 0)
% 5.62/1.97 |
% 5.62/1.97 | Instantiating (50) with all_60_0_44, all_60_1_45, all_60_2_46 yields:
% 5.62/1.97 | (110) distinct_points(all_0_5_5, all_0_5_5) = all_60_1_45 & distinct_points(all_0_5_5, all_0_6_6) = all_60_0_44 & distinct_points(all_0_5_5, all_0_6_6) = all_60_2_46 & ( ~ (all_60_2_46 = 0) | (all_60_0_44 = 0 & all_60_1_45 = 0))
% 5.62/1.97 |
% 5.62/1.97 | Applying alpha-rule on (110) yields:
% 5.62/1.97 | (111) distinct_points(all_0_5_5, all_0_5_5) = all_60_1_45
% 5.62/1.97 | (112) distinct_points(all_0_5_5, all_0_6_6) = all_60_0_44
% 5.62/1.97 | (113) distinct_points(all_0_5_5, all_0_6_6) = all_60_2_46
% 5.62/1.97 | (114) ~ (all_60_2_46 = 0) | (all_60_0_44 = 0 & all_60_1_45 = 0)
% 5.62/1.97 |
% 5.62/1.97 | Instantiating formula (10) with all_0_5_5 yields:
% 5.62/1.97 | (56) ~ (distinct_points(all_0_5_5, all_0_5_5) = 0)
% 5.62/1.97 |
% 5.62/1.97 | Instantiating formula (3) with all_0_5_5, all_0_5_5, all_58_1_42, all_60_1_45 and discharging atoms distinct_points(all_0_5_5, all_0_5_5) = all_60_1_45, distinct_points(all_0_5_5, all_0_5_5) = all_58_1_42, yields:
% 5.62/1.97 | (116) all_60_1_45 = all_58_1_42
% 5.62/1.97 |
% 5.62/1.97 | Instantiating formula (3) with all_0_5_5, all_0_7_7, all_58_0_41, 0 and discharging atoms distinct_points(all_0_5_5, all_0_7_7) = all_58_0_41, distinct_points(all_0_5_5, all_0_7_7) = 0, yields:
% 5.62/1.97 | (117) all_58_0_41 = 0
% 5.62/1.97 |
% 5.62/1.97 | Instantiating formula (3) with all_0_5_5, all_0_7_7, all_58_2_43, all_58_0_41 and discharging atoms distinct_points(all_0_5_5, all_0_7_7) = all_58_0_41, distinct_points(all_0_5_5, all_0_7_7) = all_58_2_43, yields:
% 5.62/1.97 | (118) all_58_0_41 = all_58_2_43
% 5.62/1.97 |
% 5.62/1.97 | Combining equations (117,118) yields a new equation:
% 5.62/1.97 | (119) all_58_2_43 = 0
% 5.62/1.97 |
% 5.62/1.97 | From (116) and (111) follows:
% 5.62/1.97 | (106) distinct_points(all_0_5_5, all_0_5_5) = all_58_1_42
% 5.62/1.97 |
% 5.62/1.97 +-Applying beta-rule and splitting (109), into two cases.
% 5.62/1.97 |-Branch one:
% 5.62/1.97 | (121) ~ (all_58_2_43 = 0)
% 5.62/1.97 |
% 5.62/1.97 | Equations (119) can reduce 121 to:
% 5.62/1.97 | (39) $false
% 5.62/1.97 |
% 5.62/1.97 |-The branch is then unsatisfiable
% 5.62/1.97 |-Branch two:
% 5.62/1.97 | (119) all_58_2_43 = 0
% 5.62/1.97 | (124) all_58_0_41 = 0 & all_58_1_42 = 0
% 5.62/1.97 |
% 5.62/1.97 | Applying alpha-rule on (124) yields:
% 5.62/1.97 | (117) all_58_0_41 = 0
% 5.62/1.97 | (126) all_58_1_42 = 0
% 5.62/1.97 |
% 5.62/1.97 | From (126) and (106) follows:
% 5.62/1.97 | (66) distinct_points(all_0_5_5, all_0_5_5) = 0
% 5.62/1.97 |
% 5.62/1.97 | Using (66) and (56) yields:
% 5.62/1.97 | (67) $false
% 5.62/1.97 |
% 5.62/1.97 |-The branch is then unsatisfiable
% 5.62/1.97 |-Branch two:
% 5.62/1.97 | (68) ~ (apart_point_and_line(all_0_5_5, all_0_1_1) = 0)
% 5.62/1.98 | (69) all_0_0_0 = 0
% 5.62/1.98 |
% 5.62/1.98 | Combining equations (69,98) yields a new equation:
% 5.62/1.98 | (95) all_0_2_2 = 0
% 5.62/1.98 |
% 5.62/1.98 | Equations (95) can reduce 72 to:
% 5.62/1.98 | (39) $false
% 5.62/1.98 |
% 5.62/1.98 |-The branch is then unsatisfiable
% 5.62/1.98 |-Branch two:
% 5.62/1.98 | (94) ~ (apart_point_and_line(all_0_5_5, all_0_3_3) = 0)
% 5.62/1.98 | (95) all_0_2_2 = 0
% 5.62/1.98 |
% 5.62/1.98 | Equations (95) can reduce 72 to:
% 5.62/1.98 | (39) $false
% 5.62/1.98 |
% 5.62/1.98 |-The branch is then unsatisfiable
% 5.62/1.98 |-Branch two:
% 5.62/1.98 | (69) all_0_0_0 = 0
% 5.62/1.98 | (72) ~ (all_0_2_2 = 0)
% 5.62/1.98 |
% 5.62/1.98 | Combining equations (69,98) yields a new equation:
% 5.62/1.98 | (95) all_0_2_2 = 0
% 5.62/1.98 |
% 5.62/1.98 | Equations (95) can reduce 72 to:
% 5.62/1.98 | (39) $false
% 5.62/1.98 |
% 5.62/1.98 |-The branch is then unsatisfiable
% 5.62/1.98 % SZS output end Proof for theBenchmark
% 5.62/1.98
% 5.62/1.98 1395ms
%------------------------------------------------------------------------------