TSTP Solution File: GEO111+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO111+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n005.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 03:47:42 EDT 2022
% Result : Theorem 21.58s 6.21s
% Output : Proof 27.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO111+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n005.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 18:10:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.58 ____ _
% 0.19/0.58 ___ / __ \_____(_)___ ________ __________
% 0.19/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.58
% 0.19/0.58 A Theorem Prover for First-Order Logic
% 0.19/0.58 (ePrincess v.1.0)
% 0.19/0.58
% 0.19/0.58 (c) Philipp Rümmer, 2009-2015
% 0.19/0.58 (c) Peter Backeman, 2014-2015
% 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.58 Bug reports to peter@backeman.se
% 0.19/0.58
% 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.58
% 0.19/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.81/0.99 Prover 0: Preprocessing ...
% 2.44/1.24 Prover 0: Warning: ignoring some quantifiers
% 2.44/1.27 Prover 0: Constructing countermodel ...
% 20.19/5.93 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 20.28/5.98 Prover 1: Preprocessing ...
% 20.98/6.13 Prover 1: Warning: ignoring some quantifiers
% 20.98/6.13 Prover 1: Constructing countermodel ...
% 21.42/6.21 Prover 1: proved (280ms)
% 21.58/6.21 Prover 0: stopped
% 21.58/6.21
% 21.58/6.21 No countermodel exists, formula is valid
% 21.58/6.21 % SZS status Theorem for theBenchmark
% 21.58/6.21
% 21.58/6.21 Generating proof ... Warning: ignoring some quantifiers
% 26.70/7.50 found it (size 114)
% 26.70/7.50
% 26.70/7.50 % SZS output start Proof for theBenchmark
% 26.70/7.50 Assumed formulas after preprocessing and simplification:
% 26.70/7.50 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (between_c(v0, v1, v2, v3) = 0 & incident_c(v3, v0) = v6 & incident_c(v2, v0) = v5 & incident_c(v1, v0) = v4 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = 0 | v11 = 0 | ~ (end_point(v13, v8) = 0) | ~ (part_of(v8, v10) = v12) | ~ (part_of(v8, v9) = v11) | ~ (part_of(v8, v7) = 0) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((end_point(v13, v10) = v15 & end_point(v13, v9) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0))) | (part_of(v10, v9) = v17 & part_of(v10, v8) = v19 & part_of(v10, v7) = v15 & part_of(v9, v10) = v16 & part_of(v9, v8) = v18 & part_of(v9, v7) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0) | v19 = 0 | v18 = 0 | v17 = 0 | v16 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (closed(v7) = 0) | ~ (meet(v11, v8, v9) = v12) | ~ (meet(v10, v8, v9) = 0) | ? [v13] : (( ~ (v13 = v7) & sum(v8, v9) = v13) | ( ~ (v13 = 0) & end_point(v11, v8) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | v10 = v8 | ~ (between_c(v7, v8, v9, v10) = v11) | ~ (inner_point(v9, v12) = 0) | ? [v13] : ? [v14] : ? [v15] : (end_point(v10, v12) = v15 & end_point(v8, v12) = v14 & part_of(v12, v7) = v13 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v8 = v7 | ~ (between_c(v12, v11, v10, v9) = v8) | ~ (between_c(v12, v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (sum(v8, v9) = v7) | ~ (incident_c(v10, v7) = v11) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & ~ (v12 = 0) & incident_c(v10, v9) = v13 & incident_c(v10, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (meet(v11, v10, v9) = v8) | ~ (meet(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (meet(v7, v8, v9) = 0) | ~ (end_point(v10, v8) = v11) | ? [v12] : ? [v13] : ? [v14] : (end_point(v10, v9) = v14 & incident_c(v10, v9) = v13 & incident_c(v10, v8) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0) | (v14 = 0 & v11 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | v10 = v8 | v9 = v8 | ~ (end_point(v10, v7) = 0) | ~ (end_point(v9, v7) = 0) | ~ (end_point(v8, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (meet(v7, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ((v13 = 0 & v12 = 0 & end_point(v11, v9) = v15 & end_point(v11, v8) = v14 & incident_c(v11, v9) = 0 & incident_c(v11, v8) = 0 & ( ~ (v15 = 0) | ~ (v14 = 0))) | (incident_c(v7, v9) = v12 & incident_c(v7, v8) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (part_of(v8, v7) = 0) | ~ (incident_c(v9, v7) = v10) | ? [v11] : ( ~ (v11 = 0) & incident_c(v9, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (inner_point(v10, v9) = v8) | ~ (inner_point(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (end_point(v10, v9) = v8) | ~ (end_point(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sum(v10, v9) = v8) | ~ (sum(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (part_of(v10, v9) = v8) | ~ (part_of(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (incident_c(v10, v9) = v8) | ~ (incident_c(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (between_c(v7, v8, v9, v10) = 0) | ? [v11] : (inner_point(v9, v11) = 0 & end_point(v10, v11) = 0 & end_point(v8, v11) = 0 & part_of(v11, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (end_point(v7, v8) = 0) | ~ (part_of(v10, v8) = 0) | ~ (part_of(v9, v8) = 0) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (part_of(v10, v9) = v14 & part_of(v9, v10) = v13 & incident_c(v7, v10) = v12 & incident_c(v7, v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0) | v14 = 0 | v13 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sum(v8, v9) = v7) | ~ (incident_c(v10, v7) = 0) | ? [v11] : ? [v12] : (incident_c(v10, v9) = v12 & incident_c(v10, v8) = v11 & (v12 = 0 | v11 = 0))) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (sum(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (incident_c(v11, v9) = v14 & incident_c(v11, v8) = v13 & incident_c(v11, v7) = v12 & ( ~ (v12 = 0) | ( ~ (v14 = 0) & ~ (v13 = 0))) & (v14 = 0 | v13 = 0 | v12 = 0))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (inner_point(v7, v8) = v9) | ? [v10] : ? [v11] : (end_point(v7, v8) = v11 & incident_c(v7, v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (end_point(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v15 = 0 & v14 = 0 & v13 = 0 & v12 = 0 & ~ (v17 = 0) & ~ (v16 = 0) & part_of(v11, v10) = v17 & part_of(v11, v8) = 0 & part_of(v10, v11) = v16 & part_of(v10, v8) = 0 & incident_c(v7, v11) = 0 & incident_c(v7, v10) = 0) | ( ~ (v10 = 0) & incident_c(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (part_of(v8, v7) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & incident_c(v10, v8) = 0 & incident_c(v10, v7) = v11)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (open(v9) = v8) | ~ (open(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (closed(v9) = v8) | ~ (closed(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (open(v7) = v8) | ~ (end_point(v9, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : ~ (between_c(v7, v8, v9, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (meet(v7, v8, v9) = 0) | (incident_c(v7, v9) = 0 & incident_c(v7, v8) = 0)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (part_of(v8, v7) = 0) | open(v8) = 0) & ! [v7] : ! [v8] : (v8 = 0 | ~ (closed(v7) = v8) | ? [v9] : end_point(v9, v7) = 0) & ! [v7] : ! [v8] : ( ~ (closed(v7) = 0) | ~ (end_point(v8, v7) = 0)) & ! [v7] : ! [v8] : ( ~ (inner_point(v8, v7) = 0) | ? [v9] : ? [v10] : (meet(v8, v9, v10) = 0 & sum(v9, v10) = v7)) & ! [v7] : ! [v8] : ( ~ (inner_point(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & end_point(v7, v8) = v9 & incident_c(v7, v8) = 0)) & ! [v7] : ! [v8] : ( ~ (end_point(v8, v7) = 0) | ? [v9] : ( ~ (v9 = v8) & end_point(v9, v7) = 0)) & ! [v7] : ! [v8] : ( ~ (end_point(v7, v8) = 0) | incident_c(v7, v8) = 0) & ! [v7] : ( ~ (open(v7) = 0) | ? [v8] : end_point(v8, v7) = 0) & ? [v7] : ? [v8] : (v8 = v7 | ? [v9] : ? [v10] : ? [v11] : (incident_c(v9, v8) = v11 & incident_c(v9, v7) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)) & (v11 = 0 | v10 = 0))) & ? [v7] : ? [v8] : inner_point(v8, v7) = 0 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v3 = v2 | v3 = v1 | v2 = v1))
% 27.10/7.54 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 yields:
% 27.10/7.54 | (1) between_c(all_0_6_6, all_0_5_5, all_0_4_4, all_0_3_3) = 0 & incident_c(all_0_3_3, all_0_6_6) = all_0_0_0 & incident_c(all_0_4_4, all_0_6_6) = all_0_1_1 & incident_c(all_0_5_5, all_0_6_6) = all_0_2_2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | v4 = 0 | ~ (end_point(v6, v1) = 0) | ~ (part_of(v1, v3) = v5) | ~ (part_of(v1, v2) = v4) | ~ (part_of(v1, v0) = 0) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((end_point(v6, v3) = v8 & end_point(v6, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))) | (part_of(v3, v2) = v10 & part_of(v3, v1) = v12 & part_of(v3, v0) = v8 & part_of(v2, v3) = v9 & part_of(v2, v1) = v11 & part_of(v2, v0) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | v12 = 0 | v11 = 0 | v10 = 0 | v9 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (closed(v0) = 0) | ~ (meet(v4, v1, v2) = v5) | ~ (meet(v3, v1, v2) = 0) | ? [v6] : (( ~ (v6 = v0) & sum(v1, v2) = v6) | ( ~ (v6 = 0) & end_point(v4, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | v3 = v1 | ~ (between_c(v0, v1, v2, v3) = v4) | ~ (inner_point(v2, v5) = 0) | ? [v6] : ? [v7] : ? [v8] : (end_point(v3, v5) = v8 & end_point(v1, v5) = v7 & part_of(v5, v0) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (between_c(v5, v4, v3, v2) = v1) | ~ (between_c(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (sum(v1, v2) = v0) | ~ (incident_c(v3, v0) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & incident_c(v3, v2) = v6 & incident_c(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (meet(v4, v3, v2) = v1) | ~ (meet(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (meet(v0, v1, v2) = 0) | ~ (end_point(v3, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : (end_point(v3, v2) = v7 & incident_c(v3, v2) = v6 & incident_c(v3, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v7 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v3 = v1 | v2 = v1 | ~ (end_point(v3, v0) = 0) | ~ (end_point(v2, v0) = 0) | ~ (end_point(v1, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (meet(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v6 = 0 & v5 = 0 & end_point(v4, v2) = v8 & end_point(v4, v1) = v7 & incident_c(v4, v2) = 0 & incident_c(v4, v1) = 0 & ( ~ (v8 = 0) | ~ (v7 = 0))) | (incident_c(v0, v2) = v5 & incident_c(v0, v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (part_of(v1, v0) = 0) | ~ (incident_c(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & incident_c(v2, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (inner_point(v3, v2) = v1) | ~ (inner_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (end_point(v3, v2) = v1) | ~ (end_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ (sum(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (part_of(v3, v2) = v1) | ~ (part_of(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_c(v3, v2) = v1) | ~ (incident_c(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (between_c(v0, v1, v2, v3) = 0) | ? [v4] : (inner_point(v2, v4) = 0 & end_point(v3, v4) = 0 & end_point(v1, v4) = 0 & part_of(v4, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (end_point(v0, v1) = 0) | ~ (part_of(v3, v1) = 0) | ~ (part_of(v2, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (part_of(v3, v2) = v7 & part_of(v2, v3) = v6 & incident_c(v0, v3) = v5 & incident_c(v0, v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v7 = 0 | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum(v1, v2) = v0) | ~ (incident_c(v3, v0) = 0) | ? [v4] : ? [v5] : (incident_c(v3, v2) = v5 & incident_c(v3, v1) = v4 & (v5 = 0 | v4 = 0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (sum(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (incident_c(v4, v2) = v7 & incident_c(v4, v1) = v6 & incident_c(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (inner_point(v0, v1) = v2) | ? [v3] : ? [v4] : (end_point(v0, v1) = v4 & incident_c(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (end_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v8 = 0 & v7 = 0 & v6 = 0 & v5 = 0 & ~ (v10 = 0) & ~ (v9 = 0) & part_of(v4, v3) = v10 & part_of(v4, v1) = 0 & part_of(v3, v4) = v9 & part_of(v3, v1) = 0 & incident_c(v0, v4) = 0 & incident_c(v0, v3) = 0) | ( ~ (v3 = 0) & incident_c(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (part_of(v1, v0) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & incident_c(v3, v1) = 0 & incident_c(v3, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (open(v2) = v1) | ~ (open(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (closed(v2) = v1) | ~ (closed(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (open(v0) = v1) | ~ (end_point(v2, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ~ (between_c(v0, v1, v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (meet(v0, v1, v2) = 0) | (incident_c(v0, v2) = 0 & incident_c(v0, v1) = 0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (part_of(v1, v0) = 0) | open(v1) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (closed(v0) = v1) | ? [v2] : end_point(v2, v0) = 0) & ! [v0] : ! [v1] : ( ~ (closed(v0) = 0) | ~ (end_point(v1, v0) = 0)) & ! [v0] : ! [v1] : ( ~ (inner_point(v1, v0) = 0) | ? [v2] : ? [v3] : (meet(v1, v2, v3) = 0 & sum(v2, v3) = v0)) & ! [v0] : ! [v1] : ( ~ (inner_point(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & end_point(v0, v1) = v2 & incident_c(v0, v1) = 0)) & ! [v0] : ! [v1] : ( ~ (end_point(v1, v0) = 0) | ? [v2] : ( ~ (v2 = v1) & end_point(v2, v0) = 0)) & ! [v0] : ! [v1] : ( ~ (end_point(v0, v1) = 0) | incident_c(v0, v1) = 0) & ! [v0] : ( ~ (open(v0) = 0) | ? [v1] : end_point(v1, v0) = 0) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (incident_c(v2, v1) = v4 & incident_c(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0))) & ? [v0] : ? [v1] : inner_point(v1, v0) = 0 & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0) | ~ (all_0_2_2 = 0) | all_0_3_3 = all_0_4_4 | all_0_3_3 = all_0_5_5 | all_0_4_4 = all_0_5_5)
% 27.10/7.55 |
% 27.10/7.55 | Applying alpha-rule on (1) yields:
% 27.10/7.55 | (2) between_c(all_0_6_6, all_0_5_5, all_0_4_4, all_0_3_3) = 0
% 27.10/7.56 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ (sum(v3, v2) = v0))
% 27.10/7.56 | (4) incident_c(all_0_5_5, all_0_6_6) = all_0_2_2
% 27.10/7.56 | (5) ! [v0] : ! [v1] : ( ~ (end_point(v0, v1) = 0) | incident_c(v0, v1) = 0)
% 27.10/7.56 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | v4 = 0 | ~ (end_point(v6, v1) = 0) | ~ (part_of(v1, v3) = v5) | ~ (part_of(v1, v2) = v4) | ~ (part_of(v1, v0) = 0) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((end_point(v6, v3) = v8 & end_point(v6, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))) | (part_of(v3, v2) = v10 & part_of(v3, v1) = v12 & part_of(v3, v0) = v8 & part_of(v2, v3) = v9 & part_of(v2, v1) = v11 & part_of(v2, v0) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | v12 = 0 | v11 = 0 | v10 = 0 | v9 = 0))))
% 27.10/7.56 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (meet(v4, v3, v2) = v1) | ~ (meet(v4, v3, v2) = v0))
% 27.10/7.56 | (8) ! [v0] : ! [v1] : ( ~ (closed(v0) = 0) | ~ (end_point(v1, v0) = 0))
% 27.10/7.56 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (open(v2) = v1) | ~ (open(v2) = v0))
% 27.10/7.56 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (inner_point(v3, v2) = v1) | ~ (inner_point(v3, v2) = v0))
% 27.10/7.56 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (meet(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v6 = 0 & v5 = 0 & end_point(v4, v2) = v8 & end_point(v4, v1) = v7 & incident_c(v4, v2) = 0 & incident_c(v4, v1) = 0 & ( ~ (v8 = 0) | ~ (v7 = 0))) | (incident_c(v0, v2) = v5 & incident_c(v0, v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))
% 27.10/7.56 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (part_of(v3, v2) = v1) | ~ (part_of(v3, v2) = v0))
% 27.10/7.56 | (13) ? [v0] : ? [v1] : inner_point(v1, v0) = 0
% 27.10/7.56 | (14) ! [v0] : ! [v1] : (v1 = 0 | ~ (closed(v0) = v1) | ? [v2] : end_point(v2, v0) = 0)
% 27.10/7.56 | (15) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (inner_point(v0, v1) = v2) | ? [v3] : ? [v4] : (end_point(v0, v1) = v4 & incident_c(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 27.10/7.56 | (16) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (end_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v8 = 0 & v7 = 0 & v6 = 0 & v5 = 0 & ~ (v10 = 0) & ~ (v9 = 0) & part_of(v4, v3) = v10 & part_of(v4, v1) = 0 & part_of(v3, v4) = v9 & part_of(v3, v1) = 0 & incident_c(v0, v4) = 0 & incident_c(v0, v3) = 0) | ( ~ (v3 = 0) & incident_c(v0, v1) = v3)))
% 27.10/7.56 | (17) incident_c(all_0_4_4, all_0_6_6) = all_0_1_1
% 27.10/7.56 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (closed(v2) = v1) | ~ (closed(v2) = v0))
% 27.10/7.56 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (part_of(v1, v0) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & incident_c(v3, v1) = 0 & incident_c(v3, v0) = v4))
% 27.10/7.56 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_c(v3, v2) = v1) | ~ (incident_c(v3, v2) = v0))
% 27.10/7.56 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (open(v0) = v1) | ~ (end_point(v2, v0) = 0))
% 27.10/7.56 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (meet(v0, v1, v2) = 0) | (incident_c(v0, v2) = 0 & incident_c(v0, v1) = 0))
% 27.10/7.56 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (meet(v0, v1, v2) = 0) | ~ (end_point(v3, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : (end_point(v3, v2) = v7 & incident_c(v3, v2) = v6 & incident_c(v3, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v7 = 0 & v4 = 0))))
% 27.10/7.56 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (sum(v1, v2) = v0) | ~ (incident_c(v3, v0) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & incident_c(v3, v2) = v6 & incident_c(v3, v1) = v5))
% 27.10/7.56 | (25) ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0) | ~ (all_0_2_2 = 0) | all_0_3_3 = all_0_4_4 | all_0_3_3 = all_0_5_5 | all_0_4_4 = all_0_5_5
% 27.10/7.56 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum(v1, v2) = v0) | ~ (incident_c(v3, v0) = 0) | ? [v4] : ? [v5] : (incident_c(v3, v2) = v5 & incident_c(v3, v1) = v4 & (v5 = 0 | v4 = 0)))
% 27.10/7.56 | (27) incident_c(all_0_3_3, all_0_6_6) = all_0_0_0
% 27.10/7.56 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (end_point(v0, v1) = 0) | ~ (part_of(v3, v1) = 0) | ~ (part_of(v2, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (part_of(v3, v2) = v7 & part_of(v2, v3) = v6 & incident_c(v0, v3) = v5 & incident_c(v0, v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v7 = 0 | v6 = 0)))
% 27.10/7.56 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (between_c(v0, v1, v2, v3) = 0) | ? [v4] : (inner_point(v2, v4) = 0 & end_point(v3, v4) = 0 & end_point(v1, v4) = 0 & part_of(v4, v0) = 0))
% 27.10/7.56 | (30) ! [v0] : ! [v1] : ( ~ (inner_point(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & end_point(v0, v1) = v2 & incident_c(v0, v1) = 0))
% 27.10/7.56 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (end_point(v3, v2) = v1) | ~ (end_point(v3, v2) = v0))
% 27.10/7.56 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (between_c(v5, v4, v3, v2) = v1) | ~ (between_c(v5, v4, v3, v2) = v0))
% 27.10/7.56 | (33) ! [v0] : ! [v1] : ( ~ (inner_point(v1, v0) = 0) | ? [v2] : ? [v3] : (meet(v1, v2, v3) = 0 & sum(v2, v3) = v0))
% 27.10/7.56 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (part_of(v1, v0) = 0) | ~ (incident_c(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & incident_c(v2, v1) = v4))
% 27.10/7.56 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | v3 = v1 | ~ (between_c(v0, v1, v2, v3) = v4) | ~ (inner_point(v2, v5) = 0) | ? [v6] : ? [v7] : ? [v8] : (end_point(v3, v5) = v8 & end_point(v1, v5) = v7 & part_of(v5, v0) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))))
% 27.10/7.56 | (36) ! [v0] : ! [v1] : ( ~ (end_point(v1, v0) = 0) | ? [v2] : ( ~ (v2 = v1) & end_point(v2, v0) = 0))
% 27.10/7.57 | (37) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (sum(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (incident_c(v4, v2) = v7 & incident_c(v4, v1) = v6 & incident_c(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0)))
% 27.10/7.57 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v3 = v1 | v2 = v1 | ~ (end_point(v3, v0) = 0) | ~ (end_point(v2, v0) = 0) | ~ (end_point(v1, v0) = 0))
% 27.10/7.57 | (39) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (incident_c(v2, v1) = v4 & incident_c(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0)))
% 27.10/7.57 | (40) ! [v0] : ! [v1] : ! [v2] : ~ (between_c(v0, v1, v2, v1) = 0)
% 27.10/7.57 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (closed(v0) = 0) | ~ (meet(v4, v1, v2) = v5) | ~ (meet(v3, v1, v2) = 0) | ? [v6] : (( ~ (v6 = v0) & sum(v1, v2) = v6) | ( ~ (v6 = 0) & end_point(v4, v1) = v6)))
% 27.10/7.57 | (42) ! [v0] : ( ~ (open(v0) = 0) | ? [v1] : end_point(v1, v0) = 0)
% 27.10/7.57 | (43) ! [v0] : ! [v1] : (v1 = v0 | ~ (part_of(v1, v0) = 0) | open(v1) = 0)
% 27.10/7.57 |
% 27.10/7.57 | Instantiating formula (40) with all_0_4_4, all_0_5_5, all_0_6_6 yields:
% 27.10/7.57 | (44) ~ (between_c(all_0_6_6, all_0_5_5, all_0_4_4, all_0_5_5) = 0)
% 27.10/7.57 |
% 27.10/7.57 | Instantiating formula (20) with all_0_4_4, all_0_6_6, all_0_1_1, all_0_0_0 and discharging atoms incident_c(all_0_4_4, all_0_6_6) = all_0_1_1, yields:
% 27.10/7.57 | (45) all_0_0_0 = all_0_1_1 | ~ (incident_c(all_0_4_4, all_0_6_6) = all_0_0_0)
% 27.10/7.57 |
% 27.10/7.57 | Instantiating formula (20) with all_0_5_5, all_0_6_6, all_0_2_2, all_0_0_0 and discharging atoms incident_c(all_0_5_5, all_0_6_6) = all_0_2_2, yields:
% 27.10/7.57 | (46) all_0_0_0 = all_0_2_2 | ~ (incident_c(all_0_5_5, all_0_6_6) = all_0_0_0)
% 27.10/7.57 |
% 27.10/7.57 | Instantiating formula (20) with all_0_5_5, all_0_6_6, all_0_2_2, all_0_1_1 and discharging atoms incident_c(all_0_5_5, all_0_6_6) = all_0_2_2, yields:
% 27.10/7.57 | (47) all_0_1_1 = all_0_2_2 | ~ (incident_c(all_0_5_5, all_0_6_6) = all_0_1_1)
% 27.10/7.57 |
% 27.10/7.57 | Using (2) and (44) yields:
% 27.10/7.57 | (48) ~ (all_0_3_3 = all_0_5_5)
% 27.10/7.57 |
% 27.10/7.57 | Instantiating formula (29) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms between_c(all_0_6_6, all_0_5_5, all_0_4_4, all_0_3_3) = 0, yields:
% 27.10/7.57 | (49) ? [v0] : (inner_point(all_0_4_4, v0) = 0 & end_point(all_0_3_3, v0) = 0 & end_point(all_0_5_5, v0) = 0 & part_of(v0, all_0_6_6) = 0)
% 27.10/7.57 |
% 27.10/7.57 | Instantiating (49) with all_25_0_15 yields:
% 27.10/7.57 | (50) inner_point(all_0_4_4, all_25_0_15) = 0 & end_point(all_0_3_3, all_25_0_15) = 0 & end_point(all_0_5_5, all_25_0_15) = 0 & part_of(all_25_0_15, all_0_6_6) = 0
% 27.10/7.57 |
% 27.10/7.57 | Applying alpha-rule on (50) yields:
% 27.10/7.57 | (51) inner_point(all_0_4_4, all_25_0_15) = 0
% 27.10/7.57 | (52) end_point(all_0_3_3, all_25_0_15) = 0
% 27.10/7.57 | (53) end_point(all_0_5_5, all_25_0_15) = 0
% 27.10/7.57 | (54) part_of(all_25_0_15, all_0_6_6) = 0
% 27.10/7.57 |
% 27.10/7.57 | Instantiating formula (30) with all_25_0_15, all_0_4_4 and discharging atoms inner_point(all_0_4_4, all_25_0_15) = 0, yields:
% 27.10/7.57 | (55) ? [v0] : ( ~ (v0 = 0) & end_point(all_0_4_4, all_25_0_15) = v0 & incident_c(all_0_4_4, all_25_0_15) = 0)
% 27.10/7.57 |
% 27.10/7.57 | Instantiating formula (36) with all_0_3_3, all_25_0_15 and discharging atoms end_point(all_0_3_3, all_25_0_15) = 0, yields:
% 27.10/7.57 | (56) ? [v0] : ( ~ (v0 = all_0_3_3) & end_point(v0, all_25_0_15) = 0)
% 27.10/7.57 |
% 27.10/7.57 | Instantiating formula (5) with all_25_0_15, all_0_3_3 and discharging atoms end_point(all_0_3_3, all_25_0_15) = 0, yields:
% 27.10/7.57 | (57) incident_c(all_0_3_3, all_25_0_15) = 0
% 27.10/7.57 |
% 27.10/7.57 | Instantiating formula (36) with all_0_5_5, all_25_0_15 and discharging atoms end_point(all_0_5_5, all_25_0_15) = 0, yields:
% 27.10/7.57 | (58) ? [v0] : ( ~ (v0 = all_0_5_5) & end_point(v0, all_25_0_15) = 0)
% 27.10/7.57 |
% 27.10/7.57 | Instantiating formula (5) with all_25_0_15, all_0_5_5 and discharging atoms end_point(all_0_5_5, all_25_0_15) = 0, yields:
% 27.10/7.57 | (59) incident_c(all_0_5_5, all_25_0_15) = 0
% 27.10/7.57 |
% 27.10/7.57 | Instantiating formula (34) with all_0_0_0, all_0_3_3, all_25_0_15, all_0_6_6 and discharging atoms part_of(all_25_0_15, all_0_6_6) = 0, incident_c(all_0_3_3, all_0_6_6) = all_0_0_0, yields:
% 27.10/7.57 | (60) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & incident_c(all_0_3_3, all_25_0_15) = v0)
% 27.10/7.57 |
% 27.10/7.57 | Instantiating formula (34) with all_0_1_1, all_0_4_4, all_25_0_15, all_0_6_6 and discharging atoms part_of(all_25_0_15, all_0_6_6) = 0, incident_c(all_0_4_4, all_0_6_6) = all_0_1_1, yields:
% 27.10/7.57 | (61) all_0_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & incident_c(all_0_4_4, all_25_0_15) = v0)
% 27.10/7.57 |
% 27.10/7.57 | Instantiating formula (34) with all_0_2_2, all_0_5_5, all_25_0_15, all_0_6_6 and discharging atoms part_of(all_25_0_15, all_0_6_6) = 0, incident_c(all_0_5_5, all_0_6_6) = all_0_2_2, yields:
% 27.10/7.57 | (62) all_0_2_2 = 0 | ? [v0] : ( ~ (v0 = 0) & incident_c(all_0_5_5, all_25_0_15) = v0)
% 27.10/7.57 |
% 27.10/7.57 | Instantiating (55) with all_35_0_18 yields:
% 27.10/7.57 | (63) ~ (all_35_0_18 = 0) & end_point(all_0_4_4, all_25_0_15) = all_35_0_18 & incident_c(all_0_4_4, all_25_0_15) = 0
% 27.10/7.57 |
% 27.10/7.57 | Applying alpha-rule on (63) yields:
% 27.10/7.57 | (64) ~ (all_35_0_18 = 0)
% 27.10/7.57 | (65) end_point(all_0_4_4, all_25_0_15) = all_35_0_18
% 27.10/7.57 | (66) incident_c(all_0_4_4, all_25_0_15) = 0
% 27.10/7.57 |
% 27.10/7.57 | Instantiating (58) with all_37_0_19 yields:
% 27.10/7.57 | (67) ~ (all_37_0_19 = all_0_5_5) & end_point(all_37_0_19, all_25_0_15) = 0
% 27.10/7.57 |
% 27.10/7.57 | Applying alpha-rule on (67) yields:
% 27.10/7.57 | (68) ~ (all_37_0_19 = all_0_5_5)
% 27.10/7.57 | (69) end_point(all_37_0_19, all_25_0_15) = 0
% 27.10/7.57 |
% 27.10/7.57 | Instantiating (56) with all_39_0_20 yields:
% 27.10/7.57 | (70) ~ (all_39_0_20 = all_0_3_3) & end_point(all_39_0_20, all_25_0_15) = 0
% 27.10/7.57 |
% 27.10/7.57 | Applying alpha-rule on (70) yields:
% 27.10/7.57 | (71) ~ (all_39_0_20 = all_0_3_3)
% 27.10/7.57 | (72) end_point(all_39_0_20, all_25_0_15) = 0
% 27.10/7.57 |
% 27.10/7.57 +-Applying beta-rule and splitting (60), into two cases.
% 27.10/7.57 |-Branch one:
% 27.10/7.57 | (73) all_0_0_0 = 0
% 27.10/7.57 |
% 27.10/7.57 +-Applying beta-rule and splitting (62), into two cases.
% 27.10/7.57 |-Branch one:
% 27.10/7.57 | (74) all_0_2_2 = 0
% 27.10/7.57 |
% 27.10/7.57 | From (74) and (4) follows:
% 27.10/7.58 | (75) incident_c(all_0_5_5, all_0_6_6) = 0
% 27.10/7.58 |
% 27.10/7.58 +-Applying beta-rule and splitting (61), into two cases.
% 27.10/7.58 |-Branch one:
% 27.10/7.58 | (76) all_0_1_1 = 0
% 27.10/7.58 |
% 27.10/7.58 | From (76) and (17) follows:
% 27.10/7.58 | (77) incident_c(all_0_4_4, all_0_6_6) = 0
% 27.10/7.58 |
% 27.10/7.58 | Instantiating formula (38) with all_37_0_19, all_0_3_3, all_0_5_5, all_25_0_15 and discharging atoms end_point(all_37_0_19, all_25_0_15) = 0, end_point(all_0_3_3, all_25_0_15) = 0, end_point(all_0_5_5, all_25_0_15) = 0, yields:
% 27.10/7.58 | (78) all_37_0_19 = all_0_3_3 | all_37_0_19 = all_0_5_5 | all_0_3_3 = all_0_5_5
% 27.10/7.58 |
% 27.10/7.58 | Instantiating formula (38) with all_37_0_19, all_0_5_5, all_39_0_20, all_25_0_15 and discharging atoms end_point(all_39_0_20, all_25_0_15) = 0, end_point(all_37_0_19, all_25_0_15) = 0, end_point(all_0_5_5, all_25_0_15) = 0, yields:
% 27.10/7.58 | (79) all_39_0_20 = all_37_0_19 | all_39_0_20 = all_0_5_5 | all_37_0_19 = all_0_5_5
% 27.10/7.58 |
% 27.10/7.58 | Instantiating formula (31) with all_0_4_4, all_25_0_15, all_35_0_18, 0 and discharging atoms end_point(all_0_4_4, all_25_0_15) = all_35_0_18, yields:
% 27.10/7.58 | (80) all_35_0_18 = 0 | ~ (end_point(all_0_4_4, all_25_0_15) = 0)
% 27.10/7.58 |
% 27.10/7.58 | Instantiating formula (31) with all_0_5_5, all_25_0_15, all_35_0_18, 0 and discharging atoms end_point(all_0_5_5, all_25_0_15) = 0, yields:
% 27.10/7.58 | (81) all_35_0_18 = 0 | ~ (end_point(all_0_5_5, all_25_0_15) = all_35_0_18)
% 27.10/7.58 |
% 27.10/7.58 +-Applying beta-rule and splitting (78), into two cases.
% 27.10/7.58 |-Branch one:
% 27.10/7.58 | (82) all_37_0_19 = all_0_3_3
% 27.10/7.58 |
% 27.10/7.58 | Equations (82) can reduce 68 to:
% 27.10/7.58 | (48) ~ (all_0_3_3 = all_0_5_5)
% 27.10/7.58 |
% 27.10/7.58 | From (82) and (69) follows:
% 27.10/7.58 | (52) end_point(all_0_3_3, all_25_0_15) = 0
% 27.10/7.58 |
% 27.10/7.58 +-Applying beta-rule and splitting (79), into two cases.
% 27.10/7.58 |-Branch one:
% 27.10/7.58 | (85) all_39_0_20 = all_37_0_19
% 27.10/7.58 |
% 27.10/7.58 | Combining equations (82,85) yields a new equation:
% 27.10/7.58 | (86) all_39_0_20 = all_0_3_3
% 27.10/7.58 |
% 27.10/7.58 | Equations (86) can reduce 71 to:
% 27.10/7.58 | (87) $false
% 27.10/7.58 |
% 27.10/7.58 |-The branch is then unsatisfiable
% 27.10/7.58 |-Branch two:
% 27.10/7.58 | (88) ~ (all_39_0_20 = all_37_0_19)
% 27.10/7.58 | (89) all_39_0_20 = all_0_5_5 | all_37_0_19 = all_0_5_5
% 27.10/7.58 |
% 27.10/7.58 | Equations (82) can reduce 88 to:
% 27.10/7.58 | (71) ~ (all_39_0_20 = all_0_3_3)
% 27.10/7.58 |
% 27.10/7.58 +-Applying beta-rule and splitting (89), into two cases.
% 27.10/7.58 |-Branch one:
% 27.10/7.58 | (91) all_39_0_20 = all_0_5_5
% 27.10/7.58 |
% 27.10/7.58 | Equations (91) can reduce 71 to:
% 27.10/7.58 | (92) ~ (all_0_3_3 = all_0_5_5)
% 27.10/7.58 |
% 27.10/7.58 | Simplifying 92 yields:
% 27.10/7.58 | (48) ~ (all_0_3_3 = all_0_5_5)
% 27.10/7.58 |
% 27.10/7.58 | Instantiating formula (16) with all_35_0_18, all_25_0_15, all_0_4_4 and discharging atoms end_point(all_0_4_4, all_25_0_15) = all_35_0_18, yields:
% 27.10/7.58 | (94) all_35_0_18 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & ~ (v7 = 0) & ~ (v6 = 0) & part_of(v1, v0) = v7 & part_of(v1, all_25_0_15) = 0 & part_of(v0, v1) = v6 & part_of(v0, all_25_0_15) = 0 & incident_c(all_0_4_4, v1) = 0 & incident_c(all_0_4_4, v0) = 0) | ( ~ (v0 = 0) & incident_c(all_0_4_4, all_25_0_15) = v0))
% 27.10/7.58 |
% 27.10/7.58 +-Applying beta-rule and splitting (94), into two cases.
% 27.10/7.58 |-Branch one:
% 27.10/7.58 | (95) all_35_0_18 = 0
% 27.10/7.58 |
% 27.10/7.58 | Equations (95) can reduce 64 to:
% 27.10/7.58 | (87) $false
% 27.10/7.58 |
% 27.10/7.58 |-The branch is then unsatisfiable
% 27.10/7.58 |-Branch two:
% 27.10/7.58 | (64) ~ (all_35_0_18 = 0)
% 27.10/7.58 | (98) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & ~ (v7 = 0) & ~ (v6 = 0) & part_of(v1, v0) = v7 & part_of(v1, all_25_0_15) = 0 & part_of(v0, v1) = v6 & part_of(v0, all_25_0_15) = 0 & incident_c(all_0_4_4, v1) = 0 & incident_c(all_0_4_4, v0) = 0) | ( ~ (v0 = 0) & incident_c(all_0_4_4, all_25_0_15) = v0))
% 27.10/7.58 |
% 27.10/7.58 +-Applying beta-rule and splitting (47), into two cases.
% 27.10/7.58 |-Branch one:
% 27.10/7.58 | (99) ~ (incident_c(all_0_5_5, all_0_6_6) = all_0_1_1)
% 27.10/7.58 |
% 27.10/7.58 | From (76) and (99) follows:
% 27.10/7.58 | (100) ~ (incident_c(all_0_5_5, all_0_6_6) = 0)
% 27.10/7.58 |
% 27.10/7.58 | Using (75) and (100) yields:
% 27.10/7.58 | (101) $false
% 27.10/7.58 |
% 27.10/7.58 |-The branch is then unsatisfiable
% 27.10/7.58 |-Branch two:
% 27.10/7.58 | (102) incident_c(all_0_5_5, all_0_6_6) = all_0_1_1
% 27.10/7.58 | (103) all_0_1_1 = all_0_2_2
% 27.10/7.58 |
% 27.10/7.58 | From (76) and (102) follows:
% 27.10/7.58 | (75) incident_c(all_0_5_5, all_0_6_6) = 0
% 27.10/7.58 |
% 27.10/7.58 +-Applying beta-rule and splitting (45), into two cases.
% 27.10/7.58 |-Branch one:
% 27.10/7.58 | (105) ~ (incident_c(all_0_4_4, all_0_6_6) = all_0_0_0)
% 27.10/7.58 |
% 27.10/7.58 | From (73) and (105) follows:
% 27.10/7.58 | (106) ~ (incident_c(all_0_4_4, all_0_6_6) = 0)
% 27.10/7.58 |
% 27.10/7.58 | Using (77) and (106) yields:
% 27.10/7.58 | (101) $false
% 27.10/7.58 |
% 27.10/7.58 |-The branch is then unsatisfiable
% 27.10/7.58 |-Branch two:
% 27.10/7.58 | (108) incident_c(all_0_4_4, all_0_6_6) = all_0_0_0
% 27.10/7.58 | (109) all_0_0_0 = all_0_1_1
% 27.10/7.58 |
% 27.10/7.58 | Combining equations (73,109) yields a new equation:
% 27.10/7.58 | (76) all_0_1_1 = 0
% 27.10/7.58 |
% 27.10/7.58 | Combining equations (76,109) yields a new equation:
% 27.10/7.58 | (73) all_0_0_0 = 0
% 27.10/7.58 |
% 27.10/7.58 +-Applying beta-rule and splitting (46), into two cases.
% 27.10/7.58 |-Branch one:
% 27.10/7.58 | (112) ~ (incident_c(all_0_5_5, all_0_6_6) = all_0_0_0)
% 27.10/7.58 |
% 27.10/7.58 | From (73) and (112) follows:
% 27.10/7.58 | (100) ~ (incident_c(all_0_5_5, all_0_6_6) = 0)
% 27.10/7.58 |
% 27.10/7.58 | Using (75) and (100) yields:
% 27.10/7.58 | (101) $false
% 27.10/7.58 |
% 27.10/7.58 |-The branch is then unsatisfiable
% 27.10/7.58 |-Branch two:
% 27.10/7.58 | (115) incident_c(all_0_5_5, all_0_6_6) = all_0_0_0
% 27.10/7.59 | (116) all_0_0_0 = all_0_2_2
% 27.10/7.59 |
% 27.10/7.59 | Combining equations (73,116) yields a new equation:
% 27.10/7.59 | (74) all_0_2_2 = 0
% 27.10/7.59 |
% 27.10/7.59 | Combining equations (74,116) yields a new equation:
% 27.10/7.59 | (73) all_0_0_0 = 0
% 27.10/7.59 |
% 27.10/7.59 +-Applying beta-rule and splitting (25), into two cases.
% 27.10/7.59 |-Branch one:
% 27.10/7.59 | (119) ~ (all_0_0_0 = 0)
% 27.10/7.59 |
% 27.10/7.59 | Equations (73) can reduce 119 to:
% 27.10/7.59 | (87) $false
% 27.10/7.59 |
% 27.10/7.59 |-The branch is then unsatisfiable
% 27.10/7.59 |-Branch two:
% 27.10/7.59 | (73) all_0_0_0 = 0
% 27.10/7.59 | (122) ~ (all_0_1_1 = 0) | ~ (all_0_2_2 = 0) | all_0_3_3 = all_0_4_4 | all_0_3_3 = all_0_5_5 | all_0_4_4 = all_0_5_5
% 27.10/7.59 |
% 27.10/7.59 +-Applying beta-rule and splitting (81), into two cases.
% 27.10/7.59 |-Branch one:
% 27.10/7.59 | (123) ~ (end_point(all_0_5_5, all_25_0_15) = all_35_0_18)
% 27.10/7.59 |
% 27.10/7.59 | Using (65) and (123) yields:
% 27.10/7.59 | (124) ~ (all_0_4_4 = all_0_5_5)
% 27.10/7.59 |
% 27.10/7.59 +-Applying beta-rule and splitting (122), into two cases.
% 27.10/7.59 |-Branch one:
% 27.10/7.59 | (125) ~ (all_0_1_1 = 0)
% 27.10/7.59 |
% 27.10/7.59 | Equations (76) can reduce 125 to:
% 27.10/7.59 | (87) $false
% 27.10/7.59 |
% 27.10/7.59 |-The branch is then unsatisfiable
% 27.10/7.59 |-Branch two:
% 27.10/7.59 | (76) all_0_1_1 = 0
% 27.10/7.59 | (128) ~ (all_0_2_2 = 0) | all_0_3_3 = all_0_4_4 | all_0_3_3 = all_0_5_5 | all_0_4_4 = all_0_5_5
% 27.10/7.59 |
% 27.10/7.59 +-Applying beta-rule and splitting (128), into two cases.
% 27.10/7.59 |-Branch one:
% 27.10/7.59 | (129) ~ (all_0_2_2 = 0)
% 27.10/7.59 |
% 27.10/7.59 | Equations (74) can reduce 129 to:
% 27.10/7.59 | (87) $false
% 27.10/7.59 |
% 27.10/7.59 |-The branch is then unsatisfiable
% 27.10/7.59 |-Branch two:
% 27.10/7.59 | (74) all_0_2_2 = 0
% 27.10/7.59 | (132) all_0_3_3 = all_0_4_4 | all_0_3_3 = all_0_5_5 | all_0_4_4 = all_0_5_5
% 27.10/7.59 |
% 27.10/7.59 +-Applying beta-rule and splitting (132), into two cases.
% 27.10/7.59 |-Branch one:
% 27.10/7.59 | (133) all_0_3_3 = all_0_4_4
% 27.10/7.59 |
% 27.10/7.59 | From (133) and (52) follows:
% 27.10/7.59 | (134) end_point(all_0_4_4, all_25_0_15) = 0
% 27.10/7.59 |
% 27.10/7.59 +-Applying beta-rule and splitting (80), into two cases.
% 27.10/7.59 |-Branch one:
% 27.10/7.59 | (135) ~ (end_point(all_0_4_4, all_25_0_15) = 0)
% 27.10/7.59 |
% 27.10/7.59 | Using (134) and (135) yields:
% 27.10/7.59 | (101) $false
% 27.10/7.59 |
% 27.10/7.59 |-The branch is then unsatisfiable
% 27.10/7.59 |-Branch two:
% 27.10/7.59 | (134) end_point(all_0_4_4, all_25_0_15) = 0
% 27.10/7.59 | (95) all_35_0_18 = 0
% 27.10/7.59 |
% 27.10/7.59 | Equations (95) can reduce 64 to:
% 27.10/7.59 | (87) $false
% 27.10/7.59 |
% 27.10/7.59 |-The branch is then unsatisfiable
% 27.10/7.59 |-Branch two:
% 27.10/7.59 | (140) ~ (all_0_3_3 = all_0_4_4)
% 27.10/7.59 | (141) all_0_3_3 = all_0_5_5 | all_0_4_4 = all_0_5_5
% 27.10/7.59 |
% 27.10/7.59 +-Applying beta-rule and splitting (141), into two cases.
% 27.10/7.59 |-Branch one:
% 27.10/7.59 | (142) all_0_3_3 = all_0_5_5
% 27.10/7.59 |
% 27.10/7.59 | Equations (142) can reduce 48 to:
% 27.10/7.59 | (87) $false
% 27.10/7.59 |
% 27.10/7.59 |-The branch is then unsatisfiable
% 27.10/7.59 |-Branch two:
% 27.10/7.59 | (48) ~ (all_0_3_3 = all_0_5_5)
% 27.10/7.59 | (145) all_0_4_4 = all_0_5_5
% 27.10/7.59 |
% 27.10/7.59 | Equations (145) can reduce 124 to:
% 27.10/7.59 | (87) $false
% 27.10/7.59 |
% 27.10/7.59 |-The branch is then unsatisfiable
% 27.10/7.59 |-Branch two:
% 27.10/7.59 | (147) end_point(all_0_5_5, all_25_0_15) = all_35_0_18
% 27.10/7.59 | (95) all_35_0_18 = 0
% 27.10/7.59 |
% 27.10/7.59 | Equations (95) can reduce 64 to:
% 27.57/7.59 | (87) $false
% 27.57/7.59 |
% 27.57/7.59 |-The branch is then unsatisfiable
% 27.57/7.59 |-Branch two:
% 27.57/7.59 | (150) ~ (all_39_0_20 = all_0_5_5)
% 27.57/7.59 | (151) all_37_0_19 = all_0_5_5
% 27.57/7.59 |
% 27.57/7.59 | Combining equations (82,151) yields a new equation:
% 27.57/7.59 | (152) all_0_3_3 = all_0_5_5
% 27.57/7.59 |
% 27.57/7.59 | Simplifying 152 yields:
% 27.57/7.59 | (142) all_0_3_3 = all_0_5_5
% 27.57/7.59 |
% 27.57/7.59 | Equations (142) can reduce 48 to:
% 27.57/7.59 | (87) $false
% 27.57/7.59 |
% 27.57/7.59 |-The branch is then unsatisfiable
% 27.57/7.59 |-Branch two:
% 27.57/7.59 | (155) ~ (all_37_0_19 = all_0_3_3)
% 27.57/7.59 | (156) all_37_0_19 = all_0_5_5 | all_0_3_3 = all_0_5_5
% 27.57/7.59 |
% 27.57/7.59 +-Applying beta-rule and splitting (156), into two cases.
% 27.57/7.59 |-Branch one:
% 27.57/7.59 | (151) all_37_0_19 = all_0_5_5
% 27.57/7.59 |
% 27.57/7.59 | Equations (151) can reduce 68 to:
% 27.57/7.59 | (87) $false
% 27.57/7.59 |
% 27.57/7.59 |-The branch is then unsatisfiable
% 27.57/7.59 |-Branch two:
% 27.57/7.59 | (68) ~ (all_37_0_19 = all_0_5_5)
% 27.57/7.59 | (142) all_0_3_3 = all_0_5_5
% 27.57/7.59 |
% 27.57/7.59 | Equations (142) can reduce 48 to:
% 27.57/7.59 | (87) $false
% 27.57/7.59 |
% 27.57/7.59 |-The branch is then unsatisfiable
% 27.57/7.59 |-Branch two:
% 27.57/7.59 | (125) ~ (all_0_1_1 = 0)
% 27.57/7.59 | (163) ? [v0] : ( ~ (v0 = 0) & incident_c(all_0_4_4, all_25_0_15) = v0)
% 27.57/7.59 |
% 27.57/7.59 | Instantiating (163) with all_59_0_88 yields:
% 27.57/7.59 | (164) ~ (all_59_0_88 = 0) & incident_c(all_0_4_4, all_25_0_15) = all_59_0_88
% 27.57/7.59 |
% 27.57/7.59 | Applying alpha-rule on (164) yields:
% 27.57/7.59 | (165) ~ (all_59_0_88 = 0)
% 27.57/7.60 | (166) incident_c(all_0_4_4, all_25_0_15) = all_59_0_88
% 27.57/7.60 |
% 27.57/7.60 | Instantiating formula (20) with all_0_4_4, all_25_0_15, all_59_0_88, 0 and discharging atoms incident_c(all_0_4_4, all_25_0_15) = all_59_0_88, incident_c(all_0_4_4, all_25_0_15) = 0, yields:
% 27.57/7.60 | (167) all_59_0_88 = 0
% 27.57/7.60 |
% 27.57/7.60 | Equations (167) can reduce 165 to:
% 27.57/7.60 | (87) $false
% 27.57/7.60 |
% 27.57/7.60 |-The branch is then unsatisfiable
% 27.57/7.60 |-Branch two:
% 27.57/7.60 | (129) ~ (all_0_2_2 = 0)
% 27.57/7.60 | (170) ? [v0] : ( ~ (v0 = 0) & incident_c(all_0_5_5, all_25_0_15) = v0)
% 27.57/7.60 |
% 27.57/7.60 | Instantiating (170) with all_51_0_89 yields:
% 27.57/7.60 | (171) ~ (all_51_0_89 = 0) & incident_c(all_0_5_5, all_25_0_15) = all_51_0_89
% 27.57/7.60 |
% 27.57/7.60 | Applying alpha-rule on (171) yields:
% 27.57/7.60 | (172) ~ (all_51_0_89 = 0)
% 27.57/7.60 | (173) incident_c(all_0_5_5, all_25_0_15) = all_51_0_89
% 27.57/7.60 |
% 27.57/7.60 | Instantiating formula (20) with all_0_5_5, all_25_0_15, all_51_0_89, 0 and discharging atoms incident_c(all_0_5_5, all_25_0_15) = all_51_0_89, incident_c(all_0_5_5, all_25_0_15) = 0, yields:
% 27.57/7.60 | (174) all_51_0_89 = 0
% 27.57/7.60 |
% 27.57/7.60 | Equations (174) can reduce 172 to:
% 27.57/7.60 | (87) $false
% 27.57/7.60 |
% 27.57/7.60 |-The branch is then unsatisfiable
% 27.57/7.60 |-Branch two:
% 27.57/7.60 | (119) ~ (all_0_0_0 = 0)
% 27.57/7.60 | (177) ? [v0] : ( ~ (v0 = 0) & incident_c(all_0_3_3, all_25_0_15) = v0)
% 27.57/7.60 |
% 27.57/7.60 | Instantiating (177) with all_47_0_98 yields:
% 27.57/7.60 | (178) ~ (all_47_0_98 = 0) & incident_c(all_0_3_3, all_25_0_15) = all_47_0_98
% 27.57/7.60 |
% 27.57/7.60 | Applying alpha-rule on (178) yields:
% 27.57/7.60 | (179) ~ (all_47_0_98 = 0)
% 27.57/7.60 | (180) incident_c(all_0_3_3, all_25_0_15) = all_47_0_98
% 27.57/7.60 |
% 27.57/7.60 | Instantiating formula (20) with all_0_3_3, all_25_0_15, 0, all_47_0_98 and discharging atoms incident_c(all_0_3_3, all_25_0_15) = all_47_0_98, incident_c(all_0_3_3, all_25_0_15) = 0, yields:
% 27.57/7.60 | (181) all_47_0_98 = 0
% 27.57/7.60 |
% 27.57/7.60 | Equations (181) can reduce 179 to:
% 27.57/7.60 | (87) $false
% 27.57/7.60 |
% 27.57/7.60 |-The branch is then unsatisfiable
% 27.57/7.60 % SZS output end Proof for theBenchmark
% 27.57/7.60
% 27.57/7.60 7010ms
%------------------------------------------------------------------------------