TSTP Solution File: GEO084+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO084+1 : TPTP v8.1.0. Released v2.4.0.
% 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 03:47:30 EDT 2022
% Result : Theorem 21.91s 6.13s
% Output : Proof 22.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO084+1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 18 03:58:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.62/0.60 ____ _
% 0.62/0.60 ___ / __ \_____(_)___ ________ __________
% 0.62/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.62/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.62/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.62/0.60
% 0.62/0.60 A Theorem Prover for First-Order Logic
% 0.62/0.61 (ePrincess v.1.0)
% 0.62/0.61
% 0.62/0.61 (c) Philipp Rümmer, 2009-2015
% 0.62/0.61 (c) Peter Backeman, 2014-2015
% 0.62/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.62/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.62/0.61 Bug reports to peter@backeman.se
% 0.62/0.61
% 0.62/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.62/0.61
% 0.62/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.71/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.74/0.99 Prover 0: Preprocessing ...
% 2.34/1.22 Prover 0: Warning: ignoring some quantifiers
% 2.49/1.25 Prover 0: Constructing countermodel ...
% 21.08/5.95 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 21.08/5.98 Prover 1: Preprocessing ...
% 21.43/6.08 Prover 1: Warning: ignoring some quantifiers
% 21.43/6.09 Prover 1: Constructing countermodel ...
% 21.91/6.13 Prover 1: proved (183ms)
% 21.91/6.13 Prover 0: stopped
% 21.91/6.13
% 21.91/6.13 No countermodel exists, formula is valid
% 21.91/6.13 % SZS status Theorem for theBenchmark
% 21.91/6.13
% 21.91/6.13 Generating proof ... Warning: ignoring some quantifiers
% 22.89/6.33 found it (size 32)
% 22.89/6.33
% 22.89/6.33 % SZS output start Proof for theBenchmark
% 22.89/6.33 Assumed formulas after preprocessing and simplification:
% 22.89/6.33 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & meet(v3, v0, v1) = 0 & sum(v0, v1) = v4 & part_of(v4, v2) = v5 & part_of(v1, v2) = 0 & part_of(v0, v2) = 0 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | v10 = 0 | ~ (end_point(v12, v7) = 0) | ~ (part_of(v7, v9) = v11) | ~ (part_of(v7, v8) = v10) | ~ (part_of(v7, v6) = 0) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((end_point(v12, v9) = v14 & end_point(v12, v8) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0))) | (part_of(v9, v8) = v16 & part_of(v9, v7) = v18 & part_of(v9, v6) = v14 & part_of(v8, v9) = v15 & part_of(v8, v7) = v17 & part_of(v8, v6) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0) | v18 = 0 | v17 = 0 | v16 = 0 | v15 = 0)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (closed(v6) = 0) | ~ (meet(v10, v7, v8) = v11) | ~ (meet(v9, v7, v8) = 0) | ? [v12] : (( ~ (v12 = v6) & sum(v7, v8) = v12) | ( ~ (v12 = 0) & end_point(v10, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (sum(v7, v8) = v6) | ~ (incident_c(v9, v6) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & ~ (v11 = 0) & incident_c(v9, v8) = v12 & incident_c(v9, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (meet(v10, v9, v8) = v7) | ~ (meet(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (meet(v6, v7, v8) = 0) | ~ (end_point(v9, v7) = v10) | ? [v11] : ? [v12] : ? [v13] : (end_point(v9, v8) = v13 & incident_c(v9, v8) = v12 & incident_c(v9, v7) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0) | (v13 = 0 & v10 = 0)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | v9 = v7 | v8 = v7 | ~ (end_point(v9, v6) = 0) | ~ (end_point(v8, v6) = 0) | ~ (end_point(v7, v6) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (meet(v6, v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v12 = 0 & v11 = 0 & end_point(v10, v8) = v14 & end_point(v10, v7) = v13 & incident_c(v10, v8) = 0 & incident_c(v10, v7) = 0 & ( ~ (v14 = 0) | ~ (v13 = 0))) | (incident_c(v6, v8) = v11 & incident_c(v6, v7) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (part_of(v7, v6) = 0) | ~ (incident_c(v8, v6) = v9) | ? [v10] : ( ~ (v10 = 0) & incident_c(v8, v7) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (inner_point(v9, v8) = v7) | ~ (inner_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (end_point(v9, v8) = v7) | ~ (end_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sum(v9, v8) = v7) | ~ (sum(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (part_of(v9, v8) = v7) | ~ (part_of(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (incident_c(v9, v8) = v7) | ~ (incident_c(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (end_point(v6, v7) = 0) | ~ (part_of(v9, v7) = 0) | ~ (part_of(v8, v7) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (part_of(v9, v8) = v13 & part_of(v8, v9) = v12 & incident_c(v6, v9) = v11 & incident_c(v6, v8) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0) | v13 = 0 | v12 = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sum(v7, v8) = v6) | ~ (incident_c(v9, v6) = 0) | ? [v10] : ? [v11] : (incident_c(v9, v8) = v11 & incident_c(v9, v7) = v10 & (v11 = 0 | v10 = 0))) & ? [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v6 | ~ (sum(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (incident_c(v10, v8) = v13 & incident_c(v10, v7) = v12 & incident_c(v10, v6) = v11 & ( ~ (v11 = 0) | ( ~ (v13 = 0) & ~ (v12 = 0))) & (v13 = 0 | v12 = 0 | v11 = 0))) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (inner_point(v6, v7) = v8) | ? [v9] : ? [v10] : (end_point(v6, v7) = v10 & incident_c(v6, v7) = v9 & ( ~ (v9 = 0) | v10 = 0))) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (end_point(v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & ~ (v16 = 0) & ~ (v15 = 0) & part_of(v10, v9) = v16 & part_of(v10, v7) = 0 & part_of(v9, v10) = v15 & part_of(v9, v7) = 0 & incident_c(v6, v10) = 0 & incident_c(v6, v9) = 0) | ( ~ (v9 = 0) & incident_c(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (part_of(v7, v6) = v8) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & incident_c(v9, v7) = 0 & incident_c(v9, v6) = v10)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (open(v8) = v7) | ~ (open(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (closed(v8) = v7) | ~ (closed(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = 0 | ~ (open(v6) = v7) | ~ (end_point(v8, v6) = 0)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (meet(v6, v7, v8) = 0) | (incident_c(v6, v8) = 0 & incident_c(v6, v7) = 0)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (part_of(v7, v6) = 0) | open(v7) = 0) & ! [v6] : ! [v7] : (v7 = 0 | ~ (closed(v6) = v7) | ? [v8] : end_point(v8, v6) = 0) & ! [v6] : ! [v7] : ( ~ (closed(v6) = 0) | ~ (end_point(v7, v6) = 0)) & ! [v6] : ! [v7] : ( ~ (inner_point(v7, v6) = 0) | ? [v8] : ? [v9] : (meet(v7, v8, v9) = 0 & sum(v8, v9) = v6)) & ! [v6] : ! [v7] : ( ~ (inner_point(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & end_point(v6, v7) = v8 & incident_c(v6, v7) = 0)) & ! [v6] : ! [v7] : ( ~ (end_point(v7, v6) = 0) | ? [v8] : ( ~ (v8 = v7) & end_point(v8, v6) = 0)) & ! [v6] : ! [v7] : ( ~ (end_point(v6, v7) = 0) | incident_c(v6, v7) = 0) & ! [v6] : ( ~ (open(v6) = 0) | ? [v7] : end_point(v7, v6) = 0) & ? [v6] : ? [v7] : (v7 = v6 | ? [v8] : ? [v9] : ? [v10] : (incident_c(v8, v7) = v10 & incident_c(v8, v6) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)) & (v10 = 0 | v9 = 0))) & ? [v6] : ? [v7] : inner_point(v7, v6) = 0)
% 22.89/6.36 | 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 yields:
% 22.89/6.36 | (1) ~ (all_0_0_0 = 0) & meet(all_0_2_2, all_0_5_5, all_0_4_4) = 0 & sum(all_0_5_5, all_0_4_4) = all_0_1_1 & part_of(all_0_1_1, all_0_3_3) = all_0_0_0 & part_of(all_0_4_4, all_0_3_3) = 0 & part_of(all_0_5_5, all_0_3_3) = 0 & ! [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] : (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] : ( ~ (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] : ( ~ (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
% 22.89/6.37 |
% 22.89/6.37 | Applying alpha-rule on (1) yields:
% 22.89/6.37 | (2) ! [v0] : ! [v1] : ( ~ (closed(v0) = 0) | ~ (end_point(v1, v0) = 0))
% 22.89/6.37 | (3) ! [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))))
% 22.89/6.37 | (4) ! [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))))
% 22.89/6.37 | (5) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (part_of(v1, v0) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & incident_c(v3, v1) = 0 & incident_c(v3, v0) = v4))
% 22.89/6.37 | (6) ! [v0] : ! [v1] : (v1 = v0 | ~ (part_of(v1, v0) = 0) | open(v1) = 0)
% 22.89/6.37 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (part_of(v1, v0) = 0) | ~ (incident_c(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & incident_c(v2, v1) = v4))
% 22.89/6.38 | (8) ! [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))
% 22.89/6.38 | (9) ! [v0] : ! [v1] : ( ~ (inner_point(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & end_point(v0, v1) = v2 & incident_c(v0, v1) = 0))
% 22.89/6.38 | (10) ! [v0] : ! [v1] : ( ~ (end_point(v0, v1) = 0) | incident_c(v0, v1) = 0)
% 22.89/6.38 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (meet(v0, v1, v2) = 0) | (incident_c(v0, v2) = 0 & incident_c(v0, v1) = 0))
% 22.89/6.38 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (inner_point(v3, v2) = v1) | ~ (inner_point(v3, v2) = v0))
% 22.89/6.38 | (13) ! [v0] : ! [v1] : (v1 = 0 | ~ (closed(v0) = v1) | ? [v2] : end_point(v2, v0) = 0)
% 22.89/6.38 | (14) sum(all_0_5_5, all_0_4_4) = all_0_1_1
% 22.89/6.38 | (15) ! [v0] : ! [v1] : ( ~ (end_point(v1, v0) = 0) | ? [v2] : ( ~ (v2 = v1) & end_point(v2, v0) = 0))
% 22.89/6.38 | (16) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (open(v2) = v1) | ~ (open(v2) = v0))
% 22.89/6.38 | (17) ~ (all_0_0_0 = 0)
% 22.89/6.38 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_c(v3, v2) = v1) | ~ (incident_c(v3, v2) = v0))
% 22.89/6.38 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ (sum(v3, v2) = v0))
% 22.89/6.38 | (20) meet(all_0_2_2, all_0_5_5, all_0_4_4) = 0
% 22.89/6.38 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (closed(v2) = v1) | ~ (closed(v2) = v0))
% 22.89/6.38 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (end_point(v3, v2) = v1) | ~ (end_point(v3, v2) = v0))
% 22.89/6.38 | (23) ! [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)))
% 22.89/6.38 | (24) part_of(all_0_4_4, all_0_3_3) = 0
% 22.89/6.38 | (25) ? [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)))
% 22.89/6.38 | (26) ! [v0] : ! [v1] : ( ~ (inner_point(v1, v0) = 0) | ? [v2] : ? [v3] : (meet(v1, v2, v3) = 0 & sum(v2, v3) = v0))
% 22.89/6.38 | (27) ! [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))
% 22.89/6.38 | (28) ! [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)))
% 22.89/6.38 | (29) ? [v0] : ? [v1] : inner_point(v1, v0) = 0
% 22.89/6.38 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (meet(v4, v3, v2) = v1) | ~ (meet(v4, v3, v2) = v0))
% 22.89/6.38 | (31) ! [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)))
% 22.89/6.38 | (32) ! [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)))
% 22.89/6.38 | (33) ! [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)))
% 22.89/6.38 | (34) part_of(all_0_5_5, all_0_3_3) = 0
% 22.89/6.38 | (35) ! [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)))))
% 22.89/6.38 | (36) ! [v0] : ( ~ (open(v0) = 0) | ? [v1] : end_point(v1, v0) = 0)
% 22.89/6.38 | (37) ? [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)))
% 22.89/6.38 | (38) part_of(all_0_1_1, all_0_3_3) = all_0_0_0
% 22.89/6.38 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (part_of(v3, v2) = v1) | ~ (part_of(v3, v2) = v0))
% 22.89/6.38 | (40) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (open(v0) = v1) | ~ (end_point(v2, v0) = 0))
% 22.89/6.38 |
% 22.89/6.39 | Instantiating formula (5) with all_0_0_0, all_0_1_1, all_0_3_3 and discharging atoms part_of(all_0_1_1, all_0_3_3) = all_0_0_0, yields:
% 22.89/6.39 | (41) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & incident_c(v0, all_0_1_1) = 0 & incident_c(v0, all_0_3_3) = v1)
% 22.89/6.39 |
% 22.89/6.39 +-Applying beta-rule and splitting (41), into two cases.
% 22.89/6.39 |-Branch one:
% 22.89/6.39 | (42) all_0_0_0 = 0
% 22.89/6.39 |
% 22.89/6.39 | Equations (42) can reduce 17 to:
% 22.89/6.39 | (43) $false
% 22.89/6.39 |
% 22.89/6.39 |-The branch is then unsatisfiable
% 22.89/6.39 |-Branch two:
% 22.89/6.39 | (17) ~ (all_0_0_0 = 0)
% 22.89/6.39 | (45) ? [v0] : ? [v1] : ( ~ (v1 = 0) & incident_c(v0, all_0_1_1) = 0 & incident_c(v0, all_0_3_3) = v1)
% 22.89/6.39 |
% 22.89/6.39 | Instantiating (45) with all_22_0_14, all_22_1_15 yields:
% 22.89/6.39 | (46) ~ (all_22_0_14 = 0) & incident_c(all_22_1_15, all_0_1_1) = 0 & incident_c(all_22_1_15, all_0_3_3) = all_22_0_14
% 22.89/6.39 |
% 22.89/6.39 | Applying alpha-rule on (46) yields:
% 22.89/6.39 | (47) ~ (all_22_0_14 = 0)
% 22.89/6.39 | (48) incident_c(all_22_1_15, all_0_1_1) = 0
% 22.89/6.39 | (49) incident_c(all_22_1_15, all_0_3_3) = all_22_0_14
% 22.89/6.39 |
% 22.89/6.39 | Instantiating formula (32) with all_22_1_15, all_0_4_4, all_0_5_5, all_0_1_1 and discharging atoms sum(all_0_5_5, all_0_4_4) = all_0_1_1, incident_c(all_22_1_15, all_0_1_1) = 0, yields:
% 22.89/6.39 | (50) ? [v0] : ? [v1] : (incident_c(all_22_1_15, all_0_4_4) = v1 & incident_c(all_22_1_15, all_0_5_5) = v0 & (v1 = 0 | v0 = 0))
% 22.89/6.39 |
% 22.89/6.39 | Instantiating formula (7) with all_22_0_14, all_22_1_15, all_0_4_4, all_0_3_3 and discharging atoms part_of(all_0_4_4, all_0_3_3) = 0, incident_c(all_22_1_15, all_0_3_3) = all_22_0_14, yields:
% 22.89/6.39 | (51) all_22_0_14 = 0 | ? [v0] : ( ~ (v0 = 0) & incident_c(all_22_1_15, all_0_4_4) = v0)
% 22.89/6.39 |
% 22.89/6.39 | Instantiating formula (7) with all_22_0_14, all_22_1_15, all_0_5_5, all_0_3_3 and discharging atoms part_of(all_0_5_5, all_0_3_3) = 0, incident_c(all_22_1_15, all_0_3_3) = all_22_0_14, yields:
% 22.89/6.39 | (52) all_22_0_14 = 0 | ? [v0] : ( ~ (v0 = 0) & incident_c(all_22_1_15, all_0_5_5) = v0)
% 22.89/6.39 |
% 22.89/6.39 | Instantiating (50) with all_32_0_18, all_32_1_19 yields:
% 22.89/6.39 | (53) incident_c(all_22_1_15, all_0_4_4) = all_32_0_18 & incident_c(all_22_1_15, all_0_5_5) = all_32_1_19 & (all_32_0_18 = 0 | all_32_1_19 = 0)
% 22.89/6.39 |
% 22.89/6.39 | Applying alpha-rule on (53) yields:
% 22.89/6.39 | (54) incident_c(all_22_1_15, all_0_4_4) = all_32_0_18
% 22.89/6.39 | (55) incident_c(all_22_1_15, all_0_5_5) = all_32_1_19
% 22.89/6.39 | (56) all_32_0_18 = 0 | all_32_1_19 = 0
% 22.89/6.39 |
% 22.89/6.39 +-Applying beta-rule and splitting (52), into two cases.
% 22.89/6.39 |-Branch one:
% 22.89/6.39 | (57) all_22_0_14 = 0
% 22.89/6.39 |
% 22.89/6.39 | Equations (57) can reduce 47 to:
% 22.89/6.39 | (43) $false
% 22.89/6.39 |
% 22.89/6.39 |-The branch is then unsatisfiable
% 22.89/6.39 |-Branch two:
% 22.89/6.39 | (47) ~ (all_22_0_14 = 0)
% 22.89/6.39 | (60) ? [v0] : ( ~ (v0 = 0) & incident_c(all_22_1_15, all_0_5_5) = v0)
% 22.89/6.39 |
% 22.89/6.39 | Instantiating (60) with all_38_0_20 yields:
% 22.89/6.39 | (61) ~ (all_38_0_20 = 0) & incident_c(all_22_1_15, all_0_5_5) = all_38_0_20
% 22.89/6.39 |
% 22.89/6.39 | Applying alpha-rule on (61) yields:
% 22.89/6.39 | (62) ~ (all_38_0_20 = 0)
% 22.89/6.39 | (63) incident_c(all_22_1_15, all_0_5_5) = all_38_0_20
% 22.89/6.39 |
% 22.89/6.39 +-Applying beta-rule and splitting (51), into two cases.
% 22.89/6.39 |-Branch one:
% 22.89/6.39 | (57) all_22_0_14 = 0
% 22.89/6.39 |
% 22.89/6.39 | Equations (57) can reduce 47 to:
% 22.89/6.39 | (43) $false
% 22.89/6.39 |
% 22.89/6.39 |-The branch is then unsatisfiable
% 22.89/6.39 |-Branch two:
% 22.89/6.39 | (47) ~ (all_22_0_14 = 0)
% 22.89/6.39 | (67) ? [v0] : ( ~ (v0 = 0) & incident_c(all_22_1_15, all_0_4_4) = v0)
% 22.89/6.39 |
% 22.89/6.39 | Instantiating (67) with all_52_0_29 yields:
% 22.89/6.39 | (68) ~ (all_52_0_29 = 0) & incident_c(all_22_1_15, all_0_4_4) = all_52_0_29
% 22.89/6.39 |
% 22.89/6.39 | Applying alpha-rule on (68) yields:
% 22.89/6.39 | (69) ~ (all_52_0_29 = 0)
% 22.89/6.39 | (70) incident_c(all_22_1_15, all_0_4_4) = all_52_0_29
% 22.89/6.39 |
% 22.89/6.39 | Instantiating formula (18) with all_22_1_15, all_0_4_4, all_32_0_18, all_52_0_29 and discharging atoms incident_c(all_22_1_15, all_0_4_4) = all_52_0_29, incident_c(all_22_1_15, all_0_4_4) = all_32_0_18, yields:
% 22.89/6.39 | (71) all_52_0_29 = all_32_0_18
% 22.89/6.39 |
% 22.89/6.39 | Instantiating formula (18) with all_22_1_15, all_0_5_5, all_32_1_19, all_38_0_20 and discharging atoms incident_c(all_22_1_15, all_0_5_5) = all_38_0_20, incident_c(all_22_1_15, all_0_5_5) = all_32_1_19, yields:
% 22.89/6.39 | (72) all_38_0_20 = all_32_1_19
% 22.89/6.39 |
% 22.89/6.39 | Equations (71) can reduce 69 to:
% 22.89/6.39 | (73) ~ (all_32_0_18 = 0)
% 22.89/6.39 |
% 22.89/6.39 | Equations (72) can reduce 62 to:
% 22.89/6.39 | (74) ~ (all_32_1_19 = 0)
% 22.89/6.39 |
% 22.89/6.39 +-Applying beta-rule and splitting (56), into two cases.
% 22.89/6.39 |-Branch one:
% 22.89/6.39 | (75) all_32_0_18 = 0
% 22.89/6.39 |
% 22.89/6.39 | Equations (75) can reduce 73 to:
% 22.89/6.39 | (43) $false
% 22.89/6.39 |
% 22.89/6.39 |-The branch is then unsatisfiable
% 22.89/6.39 |-Branch two:
% 22.89/6.39 | (73) ~ (all_32_0_18 = 0)
% 22.89/6.39 | (78) all_32_1_19 = 0
% 22.89/6.39 |
% 22.89/6.39 | Equations (78) can reduce 74 to:
% 22.89/6.39 | (43) $false
% 22.89/6.39 |
% 22.89/6.39 |-The branch is then unsatisfiable
% 22.89/6.39 % SZS output end Proof for theBenchmark
% 22.89/6.39
% 22.89/6.39 5779ms
%------------------------------------------------------------------------------