TSTP Solution File: LAT310+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : LAT310+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n029.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 : Sun Jul 17 04:32:49 EDT 2022
% Result : Theorem 3.72s 1.54s
% Output : Proof 6.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : LAT310+1 : TPTP v8.1.0. Released v3.4.0.
% 0.09/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n029.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 : Wed Jun 29 02:48:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.58 ____ _
% 0.18/0.58 ___ / __ \_____(_)___ ________ __________
% 0.18/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.58
% 0.18/0.58 A Theorem Prover for First-Order Logic
% 0.58/0.58 (ePrincess v.1.0)
% 0.58/0.58
% 0.58/0.58 (c) Philipp Rümmer, 2009-2015
% 0.58/0.58 (c) Peter Backeman, 2014-2015
% 0.58/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.58 Bug reports to peter@backeman.se
% 0.58/0.58
% 0.58/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.58
% 0.58/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.68/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.65/0.97 Prover 0: Preprocessing ...
% 2.38/1.21 Prover 0: Warning: ignoring some quantifiers
% 2.47/1.23 Prover 0: Constructing countermodel ...
% 3.72/1.54 Prover 0: proved (878ms)
% 3.72/1.54
% 3.72/1.54 No countermodel exists, formula is valid
% 3.72/1.54 % SZS status Theorem for theBenchmark
% 3.72/1.54
% 3.72/1.54 Generating proof ... Warning: ignoring some quantifiers
% 5.82/2.06 found it (size 99)
% 5.82/2.06
% 5.82/2.06 % SZS output start Proof for theBenchmark
% 5.82/2.06 Assumed formulas after preprocessing and simplification:
% 5.82/2.06 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (u1_struct_0(v0) = v1 & k1_zfmisc_1(v1) = v2 & k19_filter_2(v0, v8) = v9 & k19_filter_2(v0, v6) = v7 & k19_filter_2(v0, v4) = v5 & k19_filter_2(v0, v3) = v4 & l2_lattices(v14) & l1_struct_0(v15) & l1_struct_0(v10) & l1_lattices(v16) & m1_subset_1(v8, v2) & m1_subset_1(v6, v2) & m1_subset_1(v3, v2) & v1_xboole_0(v12) & v1_xboole_0(k1_xboole_0) & l3_lattices(v13) & l3_lattices(v0) & v10_lattices(v0) & ~ v1_xboole_0(v11) & ~ v1_xboole_0(v8) & ~ v1_xboole_0(v6) & ~ v1_xboole_0(v3) & ~ v3_struct_0(v10) & ~ v3_struct_0(v0) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (k19_filter_2(v20, v19) = v18) | ~ (k19_filter_2(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (k1_zfmisc_1(v19) = v20) | ~ r2_hidden(v17, v18) | ~ m1_subset_1(v18, v20) | ~ v1_xboole_0(v19)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (k1_zfmisc_1(v19) = v20) | ~ r2_hidden(v17, v18) | ~ m1_subset_1(v18, v20) | m1_subset_1(v17, v19)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (u1_struct_0(v19) = v18) | ~ (u1_struct_0(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (k1_zfmisc_1(v19) = v18) | ~ (k1_zfmisc_1(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (k1_zfmisc_1(v18) = v19) | ~ r1_tarski(v17, v18) | m1_subset_1(v17, v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (k1_zfmisc_1(v18) = v19) | ~ m1_subset_1(v17, v19) | r1_tarski(v17, v18)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (k19_filter_2(v17, v18) = v19) | ~ l3_lattices(v17) | ~ v10_lattices(v17) | m2_filter_2(v19, v17) | v1_xboole_0(v18) | v3_struct_0(v17) | ? [v20] : ? [v21] : (u1_struct_0(v17) = v20 & k1_zfmisc_1(v20) = v21 & ~ m1_subset_1(v18, v21))) & ! [v17] : ! [v18] : ! [v19] : ( ~ r1_tarski(v18, v19) | ~ r1_tarski(v17, v18) | r1_tarski(v17, v19)) & ! [v17] : ! [v18] : (v18 = v17 | ~ v1_xboole_0(v18) | ~ v1_xboole_0(v17)) & ! [v17] : ! [v18] : ( ~ (u1_struct_0(v17) = v18) | ~ l1_struct_0(v17) | ~ v1_xboole_0(v18) | v3_struct_0(v17)) & ! [v17] : ! [v18] : ( ~ (u1_struct_0(v17) = v18) | ~ l1_struct_0(v17) | v3_struct_0(v17) | ? [v19] : ? [v20] : (k1_zfmisc_1(v18) = v19 & m1_subset_1(v20, v19) & ~ v1_xboole_0(v20))) & ! [v17] : ! [v18] : ( ~ (u1_struct_0(v17) = v18) | ~ l3_lattices(v17) | ~ v10_lattices(v17) | v3_struct_0(v17) | ? [v19] : (k1_zfmisc_1(v18) = v19 & ! [v20] : ! [v21] : ! [v22] : (v22 = v21 | ~ (k19_filter_2(v17, v20) = v21) | ~ m2_filter_2(v22, v17) | ~ r1_tarski(v20, v22) | ~ m1_subset_1(v20, v19) | v1_xboole_0(v20) | ? [v23] : (m2_filter_2(v23, v17) & r1_tarski(v20, v23) & ~ r1_tarski(v22, v23))) & ! [v20] : ! [v21] : ! [v22] : ( ~ (k19_filter_2(v17, v20) = v21) | ~ m2_filter_2(v22, v17) | ~ m2_filter_2(v21, v17) | ~ r1_tarski(v20, v22) | ~ m1_subset_1(v20, v19) | r1_tarski(v21, v22) | v1_xboole_0(v20)) & ! [v20] : ! [v21] : ( ~ (k19_filter_2(v17, v20) = v21) | ~ m2_filter_2(v21, v17) | ~ m1_subset_1(v20, v19) | r1_tarski(v20, v21) | v1_xboole_0(v20)))) & ! [v17] : ! [v18] : ( ~ (u1_struct_0(v17) = v18) | ~ l3_lattices(v17) | ~ v10_lattices(v17) | v3_struct_0(v17) | ? [v19] : (k1_zfmisc_1(v18) = v19 & ! [v20] : ( ~ m2_lattice4(v20, v17) | m1_subset_1(v20, v19)))) & ! [v17] : ! [v18] : ( ~ (k1_zfmisc_1(v17) = v18) | ~ v1_xboole_0(v18)) & ! [v17] : ! [v18] : ( ~ (k1_zfmisc_1(v17) = v18) | v1_xboole_0(v17) | ? [v19] : (m1_subset_1(v19, v18) & ~ v1_xboole_0(v19))) & ! [v17] : ! [v18] : ( ~ (k1_zfmisc_1(v17) = v18) | ? [v19] : (m1_subset_1(v19, v18) & v1_xboole_0(v19))) & ! [v17] : ! [v18] : ( ~ m2_filter_2(v18, v17) | ~ v1_xboole_0(v18) | ~ l3_lattices(v17) | ~ v10_lattices(v17) | v3_struct_0(v17)) & ! [v17] : ! [v18] : ( ~ m2_filter_2(v18, v17) | ~ l3_lattices(v17) | ~ v10_lattices(v17) | m2_lattice4(v18, v17) | v3_struct_0(v17)) & ! [v17] : ! [v18] : ( ~ r2_hidden(v18, v17) | ~ r2_hidden(v17, v18)) & ! [v17] : ! [v18] : ( ~ r2_hidden(v17, v18) | ~ v1_xboole_0(v18)) & ! [v17] : ! [v18] : ( ~ r2_hidden(v17, v18) | m1_subset_1(v17, v18)) & ! [v17] : ! [v18] : ( ~ m1_subset_1(v17, v18) | r2_hidden(v17, v18) | v1_xboole_0(v18)) & ! [v17] : (v17 = k1_xboole_0 | ~ v1_xboole_0(v17)) & ! [v17] : ( ~ l2_lattices(v17) | l1_struct_0(v17)) & ! [v17] : ( ~ l1_lattices(v17) | l1_struct_0(v17)) & ! [v17] : ( ~ v9_lattices(v17) | ~ v8_lattices(v17) | ~ v7_lattices(v17) | ~ v6_lattices(v17) | ~ v5_lattices(v17) | ~ v4_lattices(v17) | ~ l3_lattices(v17) | v10_lattices(v17) | v3_struct_0(v17)) & ! [v17] : ( ~ v1_xboole_0(v17) | v1_funct_1(v17)) & ! [v17] : ( ~ l3_lattices(v17) | ~ v10_lattices(v17) | v9_lattices(v17) | v3_struct_0(v17)) & ! [v17] : ( ~ l3_lattices(v17) | ~ v10_lattices(v17) | v8_lattices(v17) | v3_struct_0(v17)) & ! [v17] : ( ~ l3_lattices(v17) | ~ v10_lattices(v17) | v7_lattices(v17) | v3_struct_0(v17)) & ! [v17] : ( ~ l3_lattices(v17) | ~ v10_lattices(v17) | v6_lattices(v17) | v3_struct_0(v17)) & ! [v17] : ( ~ l3_lattices(v17) | ~ v10_lattices(v17) | v5_lattices(v17) | v3_struct_0(v17)) & ! [v17] : ( ~ l3_lattices(v17) | ~ v10_lattices(v17) | v4_lattices(v17) | v3_struct_0(v17)) & ! [v17] : ( ~ l3_lattices(v17) | ~ v10_lattices(v17) | v3_struct_0(v17) | ? [v18] : (m2_lattice4(v18, v17) & ~ v1_xboole_0(v18))) & ! [v17] : ( ~ l3_lattices(v17) | ~ v10_lattices(v17) | v3_struct_0(v17) | ? [v18] : m2_lattice4(v18, v17)) & ! [v17] : ( ~ l3_lattices(v17) | ~ v10_lattices(v17) | v3_struct_0(v17) | ? [v18] : m2_filter_2(v18, v17)) & ! [v17] : ( ~ l3_lattices(v17) | l2_lattices(v17)) & ! [v17] : ( ~ l3_lattices(v17) | l1_lattices(v17)) & ? [v17] : ? [v18] : m1_subset_1(v18, v17) & ? [v17] : r1_tarski(v17, v17) & ( ~ r1_tarski(v5, v4) | (r1_tarski(v6, v8) & ~ r1_tarski(v7, v9))))
% 6.27/2.10 | 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, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15, all_0_16_16 yields:
% 6.27/2.10 | (1) u1_struct_0(all_0_16_16) = all_0_15_15 & k1_zfmisc_1(all_0_15_15) = all_0_14_14 & k19_filter_2(all_0_16_16, all_0_8_8) = all_0_7_7 & k19_filter_2(all_0_16_16, all_0_10_10) = all_0_9_9 & k19_filter_2(all_0_16_16, all_0_12_12) = all_0_11_11 & k19_filter_2(all_0_16_16, all_0_13_13) = all_0_12_12 & l2_lattices(all_0_2_2) & l1_struct_0(all_0_1_1) & l1_struct_0(all_0_6_6) & l1_lattices(all_0_0_0) & m1_subset_1(all_0_8_8, all_0_14_14) & m1_subset_1(all_0_10_10, all_0_14_14) & m1_subset_1(all_0_13_13, all_0_14_14) & v1_xboole_0(all_0_4_4) & v1_xboole_0(k1_xboole_0) & l3_lattices(all_0_3_3) & l3_lattices(all_0_16_16) & v10_lattices(all_0_16_16) & ~ v1_xboole_0(all_0_5_5) & ~ v1_xboole_0(all_0_8_8) & ~ v1_xboole_0(all_0_10_10) & ~ v1_xboole_0(all_0_13_13) & ~ v3_struct_0(all_0_6_6) & ~ v3_struct_0(all_0_16_16) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k19_filter_2(v3, v2) = v1) | ~ (k19_filter_2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ r2_hidden(v0, v1) | ~ m1_subset_1(v1, v3) | ~ v1_xboole_0(v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ r2_hidden(v0, v1) | ~ m1_subset_1(v1, v3) | m1_subset_1(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_zfmisc_1(v1) = v2) | ~ r1_tarski(v0, v1) | m1_subset_1(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_zfmisc_1(v1) = v2) | ~ m1_subset_1(v0, v2) | r1_tarski(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k19_filter_2(v0, v1) = v2) | ~ l3_lattices(v0) | ~ v10_lattices(v0) | m2_filter_2(v2, v0) | v1_xboole_0(v1) | v3_struct_0(v0) | ? [v3] : ? [v4] : (u1_struct_0(v0) = v3 & k1_zfmisc_1(v3) = v4 & ~ m1_subset_1(v1, v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ r1_tarski(v1, v2) | ~ r1_tarski(v0, v1) | r1_tarski(v0, v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ v1_xboole_0(v1) | ~ v1_xboole_0(v0)) & ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l1_struct_0(v0) | ~ v1_xboole_0(v1) | v3_struct_0(v0)) & ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l1_struct_0(v0) | v3_struct_0(v0) | ? [v2] : ? [v3] : (k1_zfmisc_1(v1) = v2 & m1_subset_1(v3, v2) & ~ v1_xboole_0(v3))) & ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l3_lattices(v0) | ~ v10_lattices(v0) | v3_struct_0(v0) | ? [v2] : (k1_zfmisc_1(v1) = v2 & ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (k19_filter_2(v0, v3) = v4) | ~ m2_filter_2(v5, v0) | ~ r1_tarski(v3, v5) | ~ m1_subset_1(v3, v2) | v1_xboole_0(v3) | ? [v6] : (m2_filter_2(v6, v0) & r1_tarski(v3, v6) & ~ r1_tarski(v5, v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (k19_filter_2(v0, v3) = v4) | ~ m2_filter_2(v5, v0) | ~ m2_filter_2(v4, v0) | ~ r1_tarski(v3, v5) | ~ m1_subset_1(v3, v2) | r1_tarski(v4, v5) | v1_xboole_0(v3)) & ! [v3] : ! [v4] : ( ~ (k19_filter_2(v0, v3) = v4) | ~ m2_filter_2(v4, v0) | ~ m1_subset_1(v3, v2) | r1_tarski(v3, v4) | v1_xboole_0(v3)))) & ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l3_lattices(v0) | ~ v10_lattices(v0) | v3_struct_0(v0) | ? [v2] : (k1_zfmisc_1(v1) = v2 & ! [v3] : ( ~ m2_lattice4(v3, v0) | m1_subset_1(v3, v2)))) & ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ~ v1_xboole_0(v1)) & ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | v1_xboole_0(v0) | ? [v2] : (m1_subset_1(v2, v1) & ~ v1_xboole_0(v2))) & ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ? [v2] : (m1_subset_1(v2, v1) & v1_xboole_0(v2))) & ! [v0] : ! [v1] : ( ~ m2_filter_2(v1, v0) | ~ v1_xboole_0(v1) | ~ l3_lattices(v0) | ~ v10_lattices(v0) | v3_struct_0(v0)) & ! [v0] : ! [v1] : ( ~ m2_filter_2(v1, v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) | m2_lattice4(v1, v0) | v3_struct_0(v0)) & ! [v0] : ! [v1] : ( ~ r2_hidden(v1, v0) | ~ r2_hidden(v0, v1)) & ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | ~ v1_xboole_0(v1)) & ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | m1_subset_1(v0, v1)) & ! [v0] : ! [v1] : ( ~ m1_subset_1(v0, v1) | r2_hidden(v0, v1) | v1_xboole_0(v1)) & ! [v0] : (v0 = k1_xboole_0 | ~ v1_xboole_0(v0)) & ! [v0] : ( ~ l2_lattices(v0) | l1_struct_0(v0)) & ! [v0] : ( ~ l1_lattices(v0) | l1_struct_0(v0)) & ! [v0] : ( ~ v9_lattices(v0) | ~ v8_lattices(v0) | ~ v7_lattices(v0) | ~ v6_lattices(v0) | ~ v5_lattices(v0) | ~ v4_lattices(v0) | ~ l3_lattices(v0) | v10_lattices(v0) | v3_struct_0(v0)) & ! [v0] : ( ~ v1_xboole_0(v0) | v1_funct_1(v0)) & ! [v0] : ( ~ l3_lattices(v0) | ~ v10_lattices(v0) | v9_lattices(v0) | v3_struct_0(v0)) & ! [v0] : ( ~ l3_lattices(v0) | ~ v10_lattices(v0) | v8_lattices(v0) | v3_struct_0(v0)) & ! [v0] : ( ~ l3_lattices(v0) | ~ v10_lattices(v0) | v7_lattices(v0) | v3_struct_0(v0)) & ! [v0] : ( ~ l3_lattices(v0) | ~ v10_lattices(v0) | v6_lattices(v0) | v3_struct_0(v0)) & ! [v0] : ( ~ l3_lattices(v0) | ~ v10_lattices(v0) | v5_lattices(v0) | v3_struct_0(v0)) & ! [v0] : ( ~ l3_lattices(v0) | ~ v10_lattices(v0) | v4_lattices(v0) | v3_struct_0(v0)) & ! [v0] : ( ~ l3_lattices(v0) | ~ v10_lattices(v0) | v3_struct_0(v0) | ? [v1] : (m2_lattice4(v1, v0) & ~ v1_xboole_0(v1))) & ! [v0] : ( ~ l3_lattices(v0) | ~ v10_lattices(v0) | v3_struct_0(v0) | ? [v1] : m2_lattice4(v1, v0)) & ! [v0] : ( ~ l3_lattices(v0) | ~ v10_lattices(v0) | v3_struct_0(v0) | ? [v1] : m2_filter_2(v1, v0)) & ! [v0] : ( ~ l3_lattices(v0) | l2_lattices(v0)) & ! [v0] : ( ~ l3_lattices(v0) | l1_lattices(v0)) & ? [v0] : ? [v1] : m1_subset_1(v1, v0) & ? [v0] : r1_tarski(v0, v0) & ( ~ r1_tarski(all_0_11_11, all_0_12_12) | (r1_tarski(all_0_10_10, all_0_8_8) & ~ r1_tarski(all_0_9_9, all_0_7_7)))
% 6.36/2.11 |
% 6.36/2.11 | Applying alpha-rule on (1) yields:
% 6.36/2.11 | (2) k19_filter_2(all_0_16_16, all_0_12_12) = all_0_11_11
% 6.36/2.11 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_zfmisc_1(v1) = v2) | ~ m1_subset_1(v0, v2) | r1_tarski(v0, v1))
% 6.36/2.12 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_zfmisc_1(v1) = v2) | ~ r1_tarski(v0, v1) | m1_subset_1(v0, v2))
% 6.36/2.12 | (5) ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l3_lattices(v0) | ~ v10_lattices(v0) | v3_struct_0(v0) | ? [v2] : (k1_zfmisc_1(v1) = v2 & ! [v3] : ( ~ m2_lattice4(v3, v0) | m1_subset_1(v3, v2))))
% 6.41/2.12 | (6) l1_struct_0(all_0_1_1)
% 6.41/2.12 | (7) ~ v3_struct_0(all_0_16_16)
% 6.41/2.12 | (8) v1_xboole_0(k1_xboole_0)
% 6.41/2.12 | (9) v10_lattices(all_0_16_16)
% 6.41/2.12 | (10) ~ v1_xboole_0(all_0_10_10)
% 6.41/2.12 | (11) l1_lattices(all_0_0_0)
% 6.41/2.12 | (12) ! [v0] : ( ~ l2_lattices(v0) | l1_struct_0(v0))
% 6.41/2.12 | (13) ? [v0] : r1_tarski(v0, v0)
% 6.41/2.12 | (14) ! [v0] : ( ~ l3_lattices(v0) | ~ v10_lattices(v0) | v5_lattices(v0) | v3_struct_0(v0))
% 6.41/2.12 | (15) ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | v1_xboole_0(v0) | ? [v2] : (m1_subset_1(v2, v1) & ~ v1_xboole_0(v2)))
% 6.41/2.12 | (16) ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | m1_subset_1(v0, v1))
% 6.41/2.12 | (17) ! [v0] : ( ~ l3_lattices(v0) | ~ v10_lattices(v0) | v8_lattices(v0) | v3_struct_0(v0))
% 6.41/2.12 | (18) m1_subset_1(all_0_10_10, all_0_14_14)
% 6.41/2.12 | (19) k19_filter_2(all_0_16_16, all_0_10_10) = all_0_9_9
% 6.41/2.12 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (k19_filter_2(v0, v1) = v2) | ~ l3_lattices(v0) | ~ v10_lattices(v0) | m2_filter_2(v2, v0) | v1_xboole_0(v1) | v3_struct_0(v0) | ? [v3] : ? [v4] : (u1_struct_0(v0) = v3 & k1_zfmisc_1(v3) = v4 & ~ m1_subset_1(v1, v4)))
% 6.41/2.12 | (21) m1_subset_1(all_0_13_13, all_0_14_14)
% 6.41/2.12 | (22) k19_filter_2(all_0_16_16, all_0_8_8) = all_0_7_7
% 6.41/2.12 | (23) ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l1_struct_0(v0) | ~ v1_xboole_0(v1) | v3_struct_0(v0))
% 6.41/2.12 | (24) ! [v0] : ( ~ l3_lattices(v0) | l1_lattices(v0))
% 6.41/2.12 | (25) ! [v0] : ! [v1] : ( ~ r2_hidden(v1, v0) | ~ r2_hidden(v0, v1))
% 6.41/2.12 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ r1_tarski(v1, v2) | ~ r1_tarski(v0, v1) | r1_tarski(v0, v2))
% 6.41/2.12 | (27) ! [v0] : ( ~ l3_lattices(v0) | ~ v10_lattices(v0) | v3_struct_0(v0) | ? [v1] : m2_filter_2(v1, v0))
% 6.41/2.12 | (28) ! [v0] : ! [v1] : ( ~ m2_filter_2(v1, v0) | ~ v1_xboole_0(v1) | ~ l3_lattices(v0) | ~ v10_lattices(v0) | v3_struct_0(v0))
% 6.41/2.12 | (29) ~ v3_struct_0(all_0_6_6)
% 6.41/2.12 | (30) ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ? [v2] : (m1_subset_1(v2, v1) & v1_xboole_0(v2)))
% 6.41/2.12 | (31) ! [v0] : (v0 = k1_xboole_0 | ~ v1_xboole_0(v0))
% 6.41/2.12 | (32) ~ v1_xboole_0(all_0_5_5)
% 6.41/2.12 | (33) m1_subset_1(all_0_8_8, all_0_14_14)
% 6.41/2.12 | (34) ! [v0] : ( ~ v1_xboole_0(v0) | v1_funct_1(v0))
% 6.41/2.12 | (35) ! [v0] : ! [v1] : (v1 = v0 | ~ v1_xboole_0(v1) | ~ v1_xboole_0(v0))
% 6.41/2.12 | (36) ! [v0] : ( ~ l3_lattices(v0) | ~ v10_lattices(v0) | v7_lattices(v0) | v3_struct_0(v0))
% 6.41/2.12 | (37) ! [v0] : ! [v1] : ( ~ m1_subset_1(v0, v1) | r2_hidden(v0, v1) | v1_xboole_0(v1))
% 6.41/2.12 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0))
% 6.41/2.12 | (39) l2_lattices(all_0_2_2)
% 6.41/2.12 | (40) ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ~ v1_xboole_0(v1))
% 6.41/2.12 | (41) ! [v0] : ( ~ l3_lattices(v0) | ~ v10_lattices(v0) | v4_lattices(v0) | v3_struct_0(v0))
% 6.41/2.13 | (42) ? [v0] : ? [v1] : m1_subset_1(v1, v0)
% 6.41/2.13 | (43) ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l3_lattices(v0) | ~ v10_lattices(v0) | v3_struct_0(v0) | ? [v2] : (k1_zfmisc_1(v1) = v2 & ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (k19_filter_2(v0, v3) = v4) | ~ m2_filter_2(v5, v0) | ~ r1_tarski(v3, v5) | ~ m1_subset_1(v3, v2) | v1_xboole_0(v3) | ? [v6] : (m2_filter_2(v6, v0) & r1_tarski(v3, v6) & ~ r1_tarski(v5, v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (k19_filter_2(v0, v3) = v4) | ~ m2_filter_2(v5, v0) | ~ m2_filter_2(v4, v0) | ~ r1_tarski(v3, v5) | ~ m1_subset_1(v3, v2) | r1_tarski(v4, v5) | v1_xboole_0(v3)) & ! [v3] : ! [v4] : ( ~ (k19_filter_2(v0, v3) = v4) | ~ m2_filter_2(v4, v0) | ~ m1_subset_1(v3, v2) | r1_tarski(v3, v4) | v1_xboole_0(v3))))
% 6.41/2.13 | (44) ! [v0] : ! [v1] : ( ~ m2_filter_2(v1, v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) | m2_lattice4(v1, v0) | v3_struct_0(v0))
% 6.41/2.13 | (45) l1_struct_0(all_0_6_6)
% 6.41/2.13 | (46) ! [v0] : ( ~ l3_lattices(v0) | ~ v10_lattices(v0) | v3_struct_0(v0) | ? [v1] : (m2_lattice4(v1, v0) & ~ v1_xboole_0(v1)))
% 6.41/2.13 | (47) l3_lattices(all_0_3_3)
% 6.41/2.13 | (48) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0))
% 6.41/2.13 | (49) v1_xboole_0(all_0_4_4)
% 6.41/2.13 | (50) ! [v0] : ( ~ l3_lattices(v0) | ~ v10_lattices(v0) | v9_lattices(v0) | v3_struct_0(v0))
% 6.41/2.13 | (51) k1_zfmisc_1(all_0_15_15) = all_0_14_14
% 6.41/2.13 | (52) u1_struct_0(all_0_16_16) = all_0_15_15
% 6.41/2.13 | (53) ~ v1_xboole_0(all_0_13_13)
% 6.41/2.13 | (54) k19_filter_2(all_0_16_16, all_0_13_13) = all_0_12_12
% 6.41/2.13 | (55) ~ r1_tarski(all_0_11_11, all_0_12_12) | (r1_tarski(all_0_10_10, all_0_8_8) & ~ r1_tarski(all_0_9_9, all_0_7_7))
% 6.41/2.13 | (56) ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l1_struct_0(v0) | v3_struct_0(v0) | ? [v2] : ? [v3] : (k1_zfmisc_1(v1) = v2 & m1_subset_1(v3, v2) & ~ v1_xboole_0(v3)))
% 6.41/2.13 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ r2_hidden(v0, v1) | ~ m1_subset_1(v1, v3) | m1_subset_1(v0, v2))
% 6.41/2.13 | (58) ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | ~ v1_xboole_0(v1))
% 6.41/2.13 | (59) ! [v0] : ( ~ l1_lattices(v0) | l1_struct_0(v0))
% 6.41/2.13 | (60) ~ v1_xboole_0(all_0_8_8)
% 6.41/2.13 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k19_filter_2(v3, v2) = v1) | ~ (k19_filter_2(v3, v2) = v0))
% 6.41/2.13 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ r2_hidden(v0, v1) | ~ m1_subset_1(v1, v3) | ~ v1_xboole_0(v2))
% 6.41/2.13 | (63) ! [v0] : ( ~ l3_lattices(v0) | ~ v10_lattices(v0) | v3_struct_0(v0) | ? [v1] : m2_lattice4(v1, v0))
% 6.41/2.13 | (64) ! [v0] : ( ~ l3_lattices(v0) | ~ v10_lattices(v0) | v6_lattices(v0) | v3_struct_0(v0))
% 6.41/2.13 | (65) l3_lattices(all_0_16_16)
% 6.41/2.13 | (66) ! [v0] : ( ~ v9_lattices(v0) | ~ v8_lattices(v0) | ~ v7_lattices(v0) | ~ v6_lattices(v0) | ~ v5_lattices(v0) | ~ v4_lattices(v0) | ~ l3_lattices(v0) | v10_lattices(v0) | v3_struct_0(v0))
% 6.41/2.13 | (67) ! [v0] : ( ~ l3_lattices(v0) | l2_lattices(v0))
% 6.41/2.13 |
% 6.41/2.13 | Instantiating formula (20) with all_0_7_7, all_0_8_8, all_0_16_16 and discharging atoms k19_filter_2(all_0_16_16, all_0_8_8) = all_0_7_7, l3_lattices(all_0_16_16), v10_lattices(all_0_16_16), ~ v1_xboole_0(all_0_8_8), ~ v3_struct_0(all_0_16_16), yields:
% 6.41/2.13 | (68) m2_filter_2(all_0_7_7, all_0_16_16) | ? [v0] : ? [v1] : (u1_struct_0(all_0_16_16) = v0 & k1_zfmisc_1(v0) = v1 & ~ m1_subset_1(all_0_8_8, v1))
% 6.41/2.14 |
% 6.41/2.14 | Instantiating formula (20) with all_0_9_9, all_0_10_10, all_0_16_16 and discharging atoms k19_filter_2(all_0_16_16, all_0_10_10) = all_0_9_9, l3_lattices(all_0_16_16), v10_lattices(all_0_16_16), ~ v1_xboole_0(all_0_10_10), ~ v3_struct_0(all_0_16_16), yields:
% 6.41/2.14 | (69) m2_filter_2(all_0_9_9, all_0_16_16) | ? [v0] : ? [v1] : (u1_struct_0(all_0_16_16) = v0 & k1_zfmisc_1(v0) = v1 & ~ m1_subset_1(all_0_10_10, v1))
% 6.41/2.14 |
% 6.41/2.14 | Instantiating formula (20) with all_0_11_11, all_0_12_12, all_0_16_16 and discharging atoms k19_filter_2(all_0_16_16, all_0_12_12) = all_0_11_11, l3_lattices(all_0_16_16), v10_lattices(all_0_16_16), ~ v3_struct_0(all_0_16_16), yields:
% 6.41/2.14 | (70) m2_filter_2(all_0_11_11, all_0_16_16) | v1_xboole_0(all_0_12_12) | ? [v0] : ? [v1] : (u1_struct_0(all_0_16_16) = v0 & k1_zfmisc_1(v0) = v1 & ~ m1_subset_1(all_0_12_12, v1))
% 6.41/2.14 |
% 6.41/2.14 | Instantiating formula (20) with all_0_12_12, all_0_13_13, all_0_16_16 and discharging atoms k19_filter_2(all_0_16_16, all_0_13_13) = all_0_12_12, l3_lattices(all_0_16_16), v10_lattices(all_0_16_16), ~ v1_xboole_0(all_0_13_13), ~ v3_struct_0(all_0_16_16), yields:
% 6.41/2.14 | (71) m2_filter_2(all_0_12_12, all_0_16_16) | ? [v0] : ? [v1] : (u1_struct_0(all_0_16_16) = v0 & k1_zfmisc_1(v0) = v1 & ~ m1_subset_1(all_0_13_13, v1))
% 6.41/2.14 |
% 6.41/2.14 | Instantiating formula (43) with all_0_15_15, all_0_16_16 and discharging atoms u1_struct_0(all_0_16_16) = all_0_15_15, l3_lattices(all_0_16_16), v10_lattices(all_0_16_16), ~ v3_struct_0(all_0_16_16), yields:
% 6.41/2.14 | (72) ? [v0] : (k1_zfmisc_1(all_0_15_15) = v0 & ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (k19_filter_2(all_0_16_16, v1) = v2) | ~ m2_filter_2(v3, all_0_16_16) | ~ r1_tarski(v1, v3) | ~ m1_subset_1(v1, v0) | v1_xboole_0(v1) | ? [v4] : (m2_filter_2(v4, all_0_16_16) & r1_tarski(v1, v4) & ~ r1_tarski(v3, v4))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (k19_filter_2(all_0_16_16, v1) = v2) | ~ m2_filter_2(v3, all_0_16_16) | ~ m2_filter_2(v2, all_0_16_16) | ~ r1_tarski(v1, v3) | ~ m1_subset_1(v1, v0) | r1_tarski(v2, v3) | v1_xboole_0(v1)) & ! [v1] : ! [v2] : ( ~ (k19_filter_2(all_0_16_16, v1) = v2) | ~ m2_filter_2(v2, all_0_16_16) | ~ m1_subset_1(v1, v0) | r1_tarski(v1, v2) | v1_xboole_0(v1)))
% 6.41/2.14 |
% 6.41/2.14 | Instantiating formula (5) with all_0_15_15, all_0_16_16 and discharging atoms u1_struct_0(all_0_16_16) = all_0_15_15, l3_lattices(all_0_16_16), v10_lattices(all_0_16_16), ~ v3_struct_0(all_0_16_16), yields:
% 6.41/2.14 | (73) ? [v0] : (k1_zfmisc_1(all_0_15_15) = v0 & ! [v1] : ( ~ m2_lattice4(v1, all_0_16_16) | m1_subset_1(v1, v0)))
% 6.41/2.14 |
% 6.41/2.14 | Instantiating (73) with all_17_0_20 yields:
% 6.41/2.14 | (74) k1_zfmisc_1(all_0_15_15) = all_17_0_20 & ! [v0] : ( ~ m2_lattice4(v0, all_0_16_16) | m1_subset_1(v0, all_17_0_20))
% 6.41/2.14 |
% 6.41/2.14 | Applying alpha-rule on (74) yields:
% 6.41/2.14 | (75) k1_zfmisc_1(all_0_15_15) = all_17_0_20
% 6.41/2.14 | (76) ! [v0] : ( ~ m2_lattice4(v0, all_0_16_16) | m1_subset_1(v0, all_17_0_20))
% 6.41/2.14 |
% 6.41/2.14 | Instantiating (72) with all_24_0_23 yields:
% 6.41/2.14 | (77) k1_zfmisc_1(all_0_15_15) = all_24_0_23 & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (k19_filter_2(all_0_16_16, v0) = v1) | ~ m2_filter_2(v2, all_0_16_16) | ~ r1_tarski(v0, v2) | ~ m1_subset_1(v0, all_24_0_23) | v1_xboole_0(v0) | ? [v3] : (m2_filter_2(v3, all_0_16_16) & r1_tarski(v0, v3) & ~ r1_tarski(v2, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k19_filter_2(all_0_16_16, v0) = v1) | ~ m2_filter_2(v2, all_0_16_16) | ~ m2_filter_2(v1, all_0_16_16) | ~ r1_tarski(v0, v2) | ~ m1_subset_1(v0, all_24_0_23) | r1_tarski(v1, v2) | v1_xboole_0(v0)) & ! [v0] : ! [v1] : ( ~ (k19_filter_2(all_0_16_16, v0) = v1) | ~ m2_filter_2(v1, all_0_16_16) | ~ m1_subset_1(v0, all_24_0_23) | r1_tarski(v0, v1) | v1_xboole_0(v0))
% 6.41/2.14 |
% 6.41/2.14 | Applying alpha-rule on (77) yields:
% 6.41/2.14 | (78) k1_zfmisc_1(all_0_15_15) = all_24_0_23
% 6.41/2.14 | (79) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (k19_filter_2(all_0_16_16, v0) = v1) | ~ m2_filter_2(v2, all_0_16_16) | ~ r1_tarski(v0, v2) | ~ m1_subset_1(v0, all_24_0_23) | v1_xboole_0(v0) | ? [v3] : (m2_filter_2(v3, all_0_16_16) & r1_tarski(v0, v3) & ~ r1_tarski(v2, v3)))
% 6.41/2.14 | (80) ! [v0] : ! [v1] : ! [v2] : ( ~ (k19_filter_2(all_0_16_16, v0) = v1) | ~ m2_filter_2(v2, all_0_16_16) | ~ m2_filter_2(v1, all_0_16_16) | ~ r1_tarski(v0, v2) | ~ m1_subset_1(v0, all_24_0_23) | r1_tarski(v1, v2) | v1_xboole_0(v0))
% 6.41/2.14 | (81) ! [v0] : ! [v1] : ( ~ (k19_filter_2(all_0_16_16, v0) = v1) | ~ m2_filter_2(v1, all_0_16_16) | ~ m1_subset_1(v0, all_24_0_23) | r1_tarski(v0, v1) | v1_xboole_0(v0))
% 6.41/2.14 |
% 6.41/2.14 | Instantiating formula (38) with all_0_15_15, all_24_0_23, all_0_14_14 and discharging atoms k1_zfmisc_1(all_0_15_15) = all_24_0_23, k1_zfmisc_1(all_0_15_15) = all_0_14_14, yields:
% 6.41/2.14 | (82) all_24_0_23 = all_0_14_14
% 6.41/2.15 |
% 6.41/2.15 | Instantiating formula (38) with all_0_15_15, all_17_0_20, all_24_0_23 and discharging atoms k1_zfmisc_1(all_0_15_15) = all_24_0_23, k1_zfmisc_1(all_0_15_15) = all_17_0_20, yields:
% 6.41/2.15 | (83) all_24_0_23 = all_17_0_20
% 6.41/2.15 |
% 6.41/2.15 | Combining equations (82,83) yields a new equation:
% 6.41/2.15 | (84) all_17_0_20 = all_0_14_14
% 6.41/2.15 |
% 6.41/2.15 | Combining equations (84,83) yields a new equation:
% 6.41/2.15 | (82) all_24_0_23 = all_0_14_14
% 6.41/2.15 |
% 6.41/2.15 | From (84) and (75) follows:
% 6.41/2.15 | (51) k1_zfmisc_1(all_0_15_15) = all_0_14_14
% 6.41/2.15 |
% 6.41/2.15 +-Applying beta-rule and splitting (71), into two cases.
% 6.41/2.15 |-Branch one:
% 6.41/2.15 | (87) m2_filter_2(all_0_12_12, all_0_16_16)
% 6.41/2.15 |
% 6.41/2.15 +-Applying beta-rule and splitting (69), into two cases.
% 6.41/2.15 |-Branch one:
% 6.41/2.15 | (88) m2_filter_2(all_0_9_9, all_0_16_16)
% 6.41/2.15 |
% 6.41/2.15 +-Applying beta-rule and splitting (68), into two cases.
% 6.41/2.15 |-Branch one:
% 6.41/2.15 | (89) m2_filter_2(all_0_7_7, all_0_16_16)
% 6.41/2.15 |
% 6.41/2.15 | Instantiating formula (81) with all_0_7_7, all_0_8_8 and discharging atoms k19_filter_2(all_0_16_16, all_0_8_8) = all_0_7_7, m2_filter_2(all_0_7_7, all_0_16_16), ~ v1_xboole_0(all_0_8_8), yields:
% 6.41/2.15 | (90) ~ m1_subset_1(all_0_8_8, all_24_0_23) | r1_tarski(all_0_8_8, all_0_7_7)
% 6.41/2.15 |
% 6.41/2.15 | Instantiating formula (81) with all_0_9_9, all_0_10_10 and discharging atoms k19_filter_2(all_0_16_16, all_0_10_10) = all_0_9_9, m2_filter_2(all_0_9_9, all_0_16_16), ~ v1_xboole_0(all_0_10_10), yields:
% 6.41/2.15 | (91) ~ m1_subset_1(all_0_10_10, all_24_0_23) | r1_tarski(all_0_10_10, all_0_9_9)
% 6.41/2.15 |
% 6.41/2.15 | Instantiating formula (44) with all_0_12_12, all_0_16_16 and discharging atoms m2_filter_2(all_0_12_12, all_0_16_16), l3_lattices(all_0_16_16), v10_lattices(all_0_16_16), ~ v3_struct_0(all_0_16_16), yields:
% 6.41/2.15 | (92) m2_lattice4(all_0_12_12, all_0_16_16)
% 6.41/2.15 |
% 6.41/2.15 | Instantiating formula (81) with all_0_12_12, all_0_13_13 and discharging atoms k19_filter_2(all_0_16_16, all_0_13_13) = all_0_12_12, m2_filter_2(all_0_12_12, all_0_16_16), ~ v1_xboole_0(all_0_13_13), yields:
% 6.41/2.15 | (93) ~ m1_subset_1(all_0_13_13, all_24_0_23) | r1_tarski(all_0_13_13, all_0_12_12)
% 6.41/2.15 |
% 6.41/2.15 +-Applying beta-rule and splitting (91), into two cases.
% 6.41/2.15 |-Branch one:
% 6.41/2.15 | (94) ~ m1_subset_1(all_0_10_10, all_24_0_23)
% 6.41/2.15 |
% 6.41/2.15 | From (82) and (94) follows:
% 6.41/2.15 | (95) ~ m1_subset_1(all_0_10_10, all_0_14_14)
% 6.41/2.15 |
% 6.41/2.15 | Using (18) and (95) yields:
% 6.41/2.15 | (96) $false
% 6.41/2.15 |
% 6.41/2.15 |-The branch is then unsatisfiable
% 6.41/2.15 |-Branch two:
% 6.41/2.15 | (97) m1_subset_1(all_0_10_10, all_24_0_23)
% 6.41/2.15 | (98) r1_tarski(all_0_10_10, all_0_9_9)
% 6.41/2.15 |
% 6.41/2.15 | From (82) and (97) follows:
% 6.41/2.15 | (18) m1_subset_1(all_0_10_10, all_0_14_14)
% 6.41/2.15 |
% 6.41/2.15 +-Applying beta-rule and splitting (90), into two cases.
% 6.41/2.15 |-Branch one:
% 6.41/2.15 | (100) ~ m1_subset_1(all_0_8_8, all_24_0_23)
% 6.41/2.15 |
% 6.41/2.15 | From (82) and (100) follows:
% 6.41/2.15 | (101) ~ m1_subset_1(all_0_8_8, all_0_14_14)
% 6.41/2.15 |
% 6.41/2.15 | Using (33) and (101) yields:
% 6.41/2.15 | (96) $false
% 6.41/2.15 |
% 6.41/2.15 |-The branch is then unsatisfiable
% 6.41/2.15 |-Branch two:
% 6.41/2.15 | (103) m1_subset_1(all_0_8_8, all_24_0_23)
% 6.41/2.15 | (104) r1_tarski(all_0_8_8, all_0_7_7)
% 6.41/2.15 |
% 6.41/2.15 +-Applying beta-rule and splitting (93), into two cases.
% 6.41/2.15 |-Branch one:
% 6.41/2.15 | (105) ~ m1_subset_1(all_0_13_13, all_24_0_23)
% 6.41/2.15 |
% 6.41/2.15 | From (82) and (105) follows:
% 6.41/2.15 | (106) ~ m1_subset_1(all_0_13_13, all_0_14_14)
% 6.41/2.15 |
% 6.41/2.15 | Using (21) and (106) yields:
% 6.41/2.15 | (96) $false
% 6.41/2.15 |
% 6.41/2.15 |-The branch is then unsatisfiable
% 6.41/2.15 |-Branch two:
% 6.41/2.15 | (108) m1_subset_1(all_0_13_13, all_24_0_23)
% 6.41/2.15 | (109) r1_tarski(all_0_13_13, all_0_12_12)
% 6.41/2.15 |
% 6.41/2.15 | From (82) and (108) follows:
% 6.41/2.15 | (21) m1_subset_1(all_0_13_13, all_0_14_14)
% 6.41/2.15 |
% 6.41/2.15 | Instantiating formula (76) with all_0_12_12 and discharging atoms m2_lattice4(all_0_12_12, all_0_16_16), yields:
% 6.41/2.15 | (111) m1_subset_1(all_0_12_12, all_17_0_20)
% 6.41/2.15 |
% 6.41/2.15 | Instantiating formula (80) with all_0_9_9, all_0_9_9, all_0_10_10 and discharging atoms k19_filter_2(all_0_16_16, all_0_10_10) = all_0_9_9, m2_filter_2(all_0_9_9, all_0_16_16), r1_tarski(all_0_10_10, all_0_9_9), ~ v1_xboole_0(all_0_10_10), yields:
% 6.41/2.16 | (112) ~ m1_subset_1(all_0_10_10, all_24_0_23) | r1_tarski(all_0_9_9, all_0_9_9)
% 6.41/2.16 |
% 6.41/2.16 | Instantiating formula (80) with all_0_12_12, all_0_12_12, all_0_13_13 and discharging atoms k19_filter_2(all_0_16_16, all_0_13_13) = all_0_12_12, m2_filter_2(all_0_12_12, all_0_16_16), r1_tarski(all_0_13_13, all_0_12_12), ~ v1_xboole_0(all_0_13_13), yields:
% 6.41/2.16 | (113) ~ m1_subset_1(all_0_13_13, all_24_0_23) | r1_tarski(all_0_12_12, all_0_12_12)
% 6.41/2.16 |
% 6.41/2.16 | From (84) and (111) follows:
% 6.41/2.16 | (114) m1_subset_1(all_0_12_12, all_0_14_14)
% 6.41/2.16 |
% 6.41/2.16 +-Applying beta-rule and splitting (113), into two cases.
% 6.41/2.16 |-Branch one:
% 6.41/2.16 | (105) ~ m1_subset_1(all_0_13_13, all_24_0_23)
% 6.41/2.16 |
% 6.41/2.16 | From (82) and (105) follows:
% 6.41/2.16 | (106) ~ m1_subset_1(all_0_13_13, all_0_14_14)
% 6.41/2.16 |
% 6.41/2.16 | Using (21) and (106) yields:
% 6.41/2.16 | (96) $false
% 6.41/2.16 |
% 6.41/2.16 |-The branch is then unsatisfiable
% 6.41/2.16 |-Branch two:
% 6.41/2.16 | (108) m1_subset_1(all_0_13_13, all_24_0_23)
% 6.41/2.16 | (119) r1_tarski(all_0_12_12, all_0_12_12)
% 6.41/2.16 |
% 6.41/2.16 +-Applying beta-rule and splitting (112), into two cases.
% 6.41/2.16 |-Branch one:
% 6.41/2.16 | (94) ~ m1_subset_1(all_0_10_10, all_24_0_23)
% 6.41/2.16 |
% 6.41/2.16 | From (82) and (94) follows:
% 6.41/2.16 | (95) ~ m1_subset_1(all_0_10_10, all_0_14_14)
% 6.41/2.16 |
% 6.41/2.16 | Using (18) and (95) yields:
% 6.41/2.16 | (96) $false
% 6.41/2.16 |
% 6.41/2.16 |-The branch is then unsatisfiable
% 6.41/2.16 |-Branch two:
% 6.41/2.16 | (97) m1_subset_1(all_0_10_10, all_24_0_23)
% 6.41/2.16 | (124) r1_tarski(all_0_9_9, all_0_9_9)
% 6.41/2.16 |
% 6.41/2.16 | From (82) and (97) follows:
% 6.41/2.16 | (18) m1_subset_1(all_0_10_10, all_0_14_14)
% 6.41/2.16 |
% 6.41/2.16 | Instantiating formula (79) with all_0_12_12, all_0_11_11, all_0_12_12 and discharging atoms k19_filter_2(all_0_16_16, all_0_12_12) = all_0_11_11, m2_filter_2(all_0_12_12, all_0_16_16), r1_tarski(all_0_12_12, all_0_12_12), yields:
% 6.41/2.16 | (126) all_0_11_11 = all_0_12_12 | ~ m1_subset_1(all_0_12_12, all_24_0_23) | v1_xboole_0(all_0_12_12)
% 6.41/2.16 |
% 6.41/2.16 +-Applying beta-rule and splitting (55), into two cases.
% 6.41/2.16 |-Branch one:
% 6.41/2.16 | (127) ~ r1_tarski(all_0_11_11, all_0_12_12)
% 6.41/2.16 |
% 6.41/2.16 +-Applying beta-rule and splitting (70), into two cases.
% 6.41/2.16 |-Branch one:
% 6.41/2.16 | (128) v1_xboole_0(all_0_12_12)
% 6.41/2.16 |
% 6.41/2.16 | Instantiating formula (31) with all_0_12_12 and discharging atoms v1_xboole_0(all_0_12_12), yields:
% 6.41/2.16 | (129) all_0_12_12 = k1_xboole_0
% 6.41/2.16 |
% 6.41/2.16 | From (129) and (87) follows:
% 6.41/2.16 | (130) m2_filter_2(k1_xboole_0, all_0_16_16)
% 6.41/2.16 |
% 6.41/2.16 | From (129) and (128) follows:
% 6.41/2.16 | (8) v1_xboole_0(k1_xboole_0)
% 6.41/2.16 |
% 6.41/2.16 | Instantiating formula (28) with k1_xboole_0, all_0_16_16 and discharging atoms m2_filter_2(k1_xboole_0, all_0_16_16), v1_xboole_0(k1_xboole_0), l3_lattices(all_0_16_16), v10_lattices(all_0_16_16), ~ v3_struct_0(all_0_16_16), yields:
% 6.41/2.16 | (96) $false
% 6.41/2.16 |
% 6.41/2.16 |-The branch is then unsatisfiable
% 6.41/2.16 |-Branch two:
% 6.41/2.16 | (133) ~ v1_xboole_0(all_0_12_12)
% 6.41/2.16 | (134) m2_filter_2(all_0_11_11, all_0_16_16) | ? [v0] : ? [v1] : (u1_struct_0(all_0_16_16) = v0 & k1_zfmisc_1(v0) = v1 & ~ m1_subset_1(all_0_12_12, v1))
% 6.41/2.16 |
% 6.41/2.16 +-Applying beta-rule and splitting (126), into two cases.
% 6.41/2.16 |-Branch one:
% 6.41/2.16 | (128) v1_xboole_0(all_0_12_12)
% 6.41/2.16 |
% 6.41/2.16 | Using (128) and (133) yields:
% 6.41/2.16 | (96) $false
% 6.41/2.16 |
% 6.41/2.16 |-The branch is then unsatisfiable
% 6.41/2.16 |-Branch two:
% 6.41/2.16 | (133) ~ v1_xboole_0(all_0_12_12)
% 6.41/2.16 | (138) all_0_11_11 = all_0_12_12 | ~ m1_subset_1(all_0_12_12, all_24_0_23)
% 6.41/2.16 |
% 6.41/2.16 +-Applying beta-rule and splitting (138), into two cases.
% 6.41/2.16 |-Branch one:
% 6.41/2.16 | (139) ~ m1_subset_1(all_0_12_12, all_24_0_23)
% 6.41/2.16 |
% 6.41/2.16 | From (82) and (139) follows:
% 6.41/2.16 | (140) ~ m1_subset_1(all_0_12_12, all_0_14_14)
% 6.41/2.16 |
% 6.41/2.16 | Using (114) and (140) yields:
% 6.41/2.16 | (96) $false
% 6.41/2.16 |
% 6.41/2.16 |-The branch is then unsatisfiable
% 6.41/2.16 |-Branch two:
% 6.41/2.16 | (142) m1_subset_1(all_0_12_12, all_24_0_23)
% 6.41/2.17 | (143) all_0_11_11 = all_0_12_12
% 6.41/2.17 |
% 6.41/2.17 | From (143) and (127) follows:
% 6.41/2.17 | (144) ~ r1_tarski(all_0_12_12, all_0_12_12)
% 6.41/2.17 |
% 6.41/2.17 | Using (119) and (144) yields:
% 6.41/2.17 | (96) $false
% 6.41/2.17 |
% 6.41/2.17 |-The branch is then unsatisfiable
% 6.41/2.17 |-Branch two:
% 6.41/2.17 | (146) r1_tarski(all_0_11_11, all_0_12_12)
% 6.41/2.17 | (147) r1_tarski(all_0_10_10, all_0_8_8) & ~ r1_tarski(all_0_9_9, all_0_7_7)
% 6.41/2.17 |
% 6.41/2.17 | Applying alpha-rule on (147) yields:
% 6.41/2.17 | (148) r1_tarski(all_0_10_10, all_0_8_8)
% 6.41/2.17 | (149) ~ r1_tarski(all_0_9_9, all_0_7_7)
% 6.41/2.17 |
% 6.41/2.17 | Instantiating formula (26) with all_0_7_7, all_0_8_8, all_0_10_10 and discharging atoms r1_tarski(all_0_8_8, all_0_7_7), r1_tarski(all_0_10_10, all_0_8_8), yields:
% 6.41/2.17 | (150) r1_tarski(all_0_10_10, all_0_7_7)
% 6.41/2.17 |
% 6.41/2.17 | Instantiating formula (80) with all_0_7_7, all_0_9_9, all_0_10_10 and discharging atoms k19_filter_2(all_0_16_16, all_0_10_10) = all_0_9_9, m2_filter_2(all_0_7_7, all_0_16_16), m2_filter_2(all_0_9_9, all_0_16_16), r1_tarski(all_0_10_10, all_0_7_7), ~ r1_tarski(all_0_9_9, all_0_7_7), ~ v1_xboole_0(all_0_10_10), yields:
% 6.41/2.17 | (94) ~ m1_subset_1(all_0_10_10, all_24_0_23)
% 6.41/2.17 |
% 6.41/2.17 | From (82) and (94) follows:
% 6.41/2.17 | (95) ~ m1_subset_1(all_0_10_10, all_0_14_14)
% 6.41/2.17 |
% 6.41/2.17 | Using (18) and (95) yields:
% 6.41/2.17 | (96) $false
% 6.41/2.17 |
% 6.41/2.17 |-The branch is then unsatisfiable
% 6.41/2.17 |-Branch two:
% 6.41/2.17 | (154) ~ m2_filter_2(all_0_7_7, all_0_16_16)
% 6.41/2.17 | (155) ? [v0] : ? [v1] : (u1_struct_0(all_0_16_16) = v0 & k1_zfmisc_1(v0) = v1 & ~ m1_subset_1(all_0_8_8, v1))
% 6.41/2.17 |
% 6.41/2.17 | Instantiating (155) with all_47_0_29, all_47_1_30 yields:
% 6.41/2.17 | (156) u1_struct_0(all_0_16_16) = all_47_1_30 & k1_zfmisc_1(all_47_1_30) = all_47_0_29 & ~ m1_subset_1(all_0_8_8, all_47_0_29)
% 6.41/2.17 |
% 6.41/2.17 | Applying alpha-rule on (156) yields:
% 6.41/2.17 | (157) u1_struct_0(all_0_16_16) = all_47_1_30
% 6.41/2.17 | (158) k1_zfmisc_1(all_47_1_30) = all_47_0_29
% 6.41/2.17 | (159) ~ m1_subset_1(all_0_8_8, all_47_0_29)
% 6.41/2.17 |
% 6.41/2.17 | Instantiating formula (48) with all_0_16_16, all_47_1_30, all_0_15_15 and discharging atoms u1_struct_0(all_0_16_16) = all_47_1_30, u1_struct_0(all_0_16_16) = all_0_15_15, yields:
% 6.41/2.17 | (160) all_47_1_30 = all_0_15_15
% 6.41/2.17 |
% 6.41/2.17 | From (160) and (158) follows:
% 6.41/2.17 | (161) k1_zfmisc_1(all_0_15_15) = all_47_0_29
% 6.41/2.17 |
% 6.41/2.17 | Instantiating formula (38) with all_0_15_15, all_47_0_29, all_0_14_14 and discharging atoms k1_zfmisc_1(all_0_15_15) = all_47_0_29, k1_zfmisc_1(all_0_15_15) = all_0_14_14, yields:
% 6.41/2.17 | (162) all_47_0_29 = all_0_14_14
% 6.41/2.17 |
% 6.41/2.17 | From (162) and (159) follows:
% 6.41/2.17 | (101) ~ m1_subset_1(all_0_8_8, all_0_14_14)
% 6.41/2.17 |
% 6.41/2.17 | Using (33) and (101) yields:
% 6.41/2.17 | (96) $false
% 6.41/2.17 |
% 6.41/2.17 |-The branch is then unsatisfiable
% 6.41/2.17 |-Branch two:
% 6.41/2.17 | (165) ~ m2_filter_2(all_0_9_9, all_0_16_16)
% 6.41/2.17 | (166) ? [v0] : ? [v1] : (u1_struct_0(all_0_16_16) = v0 & k1_zfmisc_1(v0) = v1 & ~ m1_subset_1(all_0_10_10, v1))
% 6.41/2.17 |
% 6.41/2.17 | Instantiating (166) with all_43_0_31, all_43_1_32 yields:
% 6.41/2.17 | (167) u1_struct_0(all_0_16_16) = all_43_1_32 & k1_zfmisc_1(all_43_1_32) = all_43_0_31 & ~ m1_subset_1(all_0_10_10, all_43_0_31)
% 6.41/2.17 |
% 6.41/2.17 | Applying alpha-rule on (167) yields:
% 6.41/2.17 | (168) u1_struct_0(all_0_16_16) = all_43_1_32
% 6.41/2.17 | (169) k1_zfmisc_1(all_43_1_32) = all_43_0_31
% 6.41/2.17 | (170) ~ m1_subset_1(all_0_10_10, all_43_0_31)
% 6.41/2.17 |
% 6.41/2.17 | Instantiating formula (48) with all_0_16_16, all_43_1_32, all_0_15_15 and discharging atoms u1_struct_0(all_0_16_16) = all_43_1_32, u1_struct_0(all_0_16_16) = all_0_15_15, yields:
% 6.41/2.17 | (171) all_43_1_32 = all_0_15_15
% 6.41/2.17 |
% 6.41/2.17 | From (171) and (169) follows:
% 6.41/2.17 | (172) k1_zfmisc_1(all_0_15_15) = all_43_0_31
% 6.41/2.17 |
% 6.41/2.17 | Instantiating formula (38) with all_0_15_15, all_43_0_31, all_0_14_14 and discharging atoms k1_zfmisc_1(all_0_15_15) = all_43_0_31, k1_zfmisc_1(all_0_15_15) = all_0_14_14, yields:
% 6.41/2.17 | (173) all_43_0_31 = all_0_14_14
% 6.41/2.17 |
% 6.41/2.17 | From (173) and (170) follows:
% 6.41/2.17 | (95) ~ m1_subset_1(all_0_10_10, all_0_14_14)
% 6.41/2.17 |
% 6.41/2.17 | Using (18) and (95) yields:
% 6.41/2.17 | (96) $false
% 6.41/2.17 |
% 6.41/2.17 |-The branch is then unsatisfiable
% 6.41/2.17 |-Branch two:
% 6.41/2.17 | (176) ~ m2_filter_2(all_0_12_12, all_0_16_16)
% 6.41/2.17 | (177) ? [v0] : ? [v1] : (u1_struct_0(all_0_16_16) = v0 & k1_zfmisc_1(v0) = v1 & ~ m1_subset_1(all_0_13_13, v1))
% 6.41/2.17 |
% 6.41/2.17 | Instantiating (177) with all_39_0_33, all_39_1_34 yields:
% 6.41/2.17 | (178) u1_struct_0(all_0_16_16) = all_39_1_34 & k1_zfmisc_1(all_39_1_34) = all_39_0_33 & ~ m1_subset_1(all_0_13_13, all_39_0_33)
% 6.41/2.17 |
% 6.41/2.17 | Applying alpha-rule on (178) yields:
% 6.41/2.17 | (179) u1_struct_0(all_0_16_16) = all_39_1_34
% 6.41/2.17 | (180) k1_zfmisc_1(all_39_1_34) = all_39_0_33
% 6.41/2.17 | (181) ~ m1_subset_1(all_0_13_13, all_39_0_33)
% 6.41/2.17 |
% 6.41/2.17 | Instantiating formula (48) with all_0_16_16, all_39_1_34, all_0_15_15 and discharging atoms u1_struct_0(all_0_16_16) = all_39_1_34, u1_struct_0(all_0_16_16) = all_0_15_15, yields:
% 6.41/2.17 | (182) all_39_1_34 = all_0_15_15
% 6.41/2.17 |
% 6.41/2.17 | From (182) and (180) follows:
% 6.41/2.17 | (183) k1_zfmisc_1(all_0_15_15) = all_39_0_33
% 6.41/2.17 |
% 6.41/2.17 | Instantiating formula (38) with all_0_15_15, all_39_0_33, all_0_14_14 and discharging atoms k1_zfmisc_1(all_0_15_15) = all_39_0_33, k1_zfmisc_1(all_0_15_15) = all_0_14_14, yields:
% 6.41/2.17 | (184) all_39_0_33 = all_0_14_14
% 6.41/2.17 |
% 6.41/2.17 | From (184) and (181) follows:
% 6.41/2.17 | (106) ~ m1_subset_1(all_0_13_13, all_0_14_14)
% 6.41/2.17 |
% 6.41/2.17 | Using (21) and (106) yields:
% 6.41/2.17 | (96) $false
% 6.41/2.18 |
% 6.41/2.18 |-The branch is then unsatisfiable
% 6.41/2.18 % SZS output end Proof for theBenchmark
% 6.41/2.18
% 6.41/2.18 1576ms
%------------------------------------------------------------------------------