TSTP Solution File: GRP641+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GRP641+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n009.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 08:43:15 EDT 2022
% Result : Theorem 5.32s 1.87s
% Output : Proof 7.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP641+1 : TPTP v8.1.0. Released v3.4.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % 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 : Mon Jun 13 13:24:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.58/0.59 ____ _
% 0.58/0.59 ___ / __ \_____(_)___ ________ __________
% 0.58/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.58/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.58/0.59
% 0.58/0.59 A Theorem Prover for First-Order Logic
% 0.58/0.59 (ePrincess v.1.0)
% 0.58/0.59
% 0.58/0.59 (c) Philipp Rümmer, 2009-2015
% 0.58/0.59 (c) Peter Backeman, 2014-2015
% 0.58/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.59 Bug reports to peter@backeman.se
% 0.58/0.59
% 0.58/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.59
% 0.58/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.73/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.83/0.97 Prover 0: Preprocessing ...
% 2.84/1.29 Prover 0: Warning: ignoring some quantifiers
% 3.12/1.33 Prover 0: Constructing countermodel ...
% 5.32/1.86 Prover 0: proved (1230ms)
% 5.32/1.87
% 5.32/1.87 No countermodel exists, formula is valid
% 5.32/1.87 % SZS status Theorem for theBenchmark
% 5.32/1.87
% 5.32/1.87 Generating proof ... Warning: ignoring some quantifiers
% 7.77/2.37 found it (size 53)
% 7.77/2.37
% 7.77/2.37 % SZS output start Proof for theBenchmark
% 7.77/2.37 Assumed formulas after preprocessing and simplification:
% 7.77/2.37 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (k2_group_1(v0) = v1 & k1_latsubgr(v0) = v2 & k1_funct_1(v2, v3) = v4 & l1_struct_0(v8) & l1_struct_0(v5) & v1_xboole_0(v7) & v1_xboole_0(k1_xboole_0) & m1_group_2(v3, v0) & v1_group_1(v3) & l1_group_1(v9) & l1_group_1(v0) & v4_group_1(v0) & v3_group_1(v0) & ~ v1_xboole_0(v6) & ~ r2_hidden(v1, v4) & ~ v3_struct_0(v5) & ~ v3_struct_0(v0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v11 | ~ (g1_group_1(v13, v14) = v12) | ~ (g1_group_1(v10, v11) = v12) | ~ v1_funct_1(v11) | ? [v15] : (k2_zfmisc_1(v10, v10) = v15 & ( ~ v1_funct_2(v11, v15, v10) | ~ m1_relset_1(v11, v15, v10)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = v10 | ~ (g1_group_1(v13, v14) = v12) | ~ (g1_group_1(v10, v11) = v12) | ~ v1_funct_1(v11) | ? [v15] : (k2_zfmisc_1(v10, v10) = v15 & ( ~ v1_funct_2(v11, v15, v10) | ~ m1_relset_1(v11, v15, v10)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (k2_group_1(v12) = v13) | ~ (k2_group_1(v10) = v11) | ~ m1_group_2(v12, v10) | ~ l1_group_1(v10) | ~ v4_group_1(v10) | ~ v3_group_1(v10) | v3_struct_0(v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v10 | ~ (u1_struct_0(v10) = v11) | ~ (u1_group_1(v10) = v12) | ~ (g1_group_1(v11, v12) = v13) | ~ v1_group_1(v10) | ~ l1_group_1(v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (k1_funct_1(v13, v12) = v11) | ~ (k1_funct_1(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (k2_zfmisc_1(v13, v12) = v11) | ~ (k2_zfmisc_1(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (g1_group_1(v13, v12) = v11) | ~ (g1_group_1(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (k2_zfmisc_1(v10, v11) = v13) | ~ m2_relset_1(v12, v10, v11) | ? [v14] : (k1_zfmisc_1(v13) = v14 & m1_subset_1(v12, v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (k1_zfmisc_1(v12) = v13) | ~ v1_xboole_0(v12) | ~ m1_subset_1(v11, v13) | ~ r2_hidden(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (k1_zfmisc_1(v12) = v13) | ~ m1_subset_1(v11, v13) | ~ r2_hidden(v10, v11) | m1_subset_1(v10, v12)) & ? [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (k2_zfmisc_1(v11, v12) = v13) | v1_relat_1(v10) | ? [v14] : (k1_zfmisc_1(v13) = v14 & ~ m1_subset_1(v10, v14))) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (k2_group_1(v12) = v11) | ~ (k2_group_1(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (k1_latsubgr(v12) = v11) | ~ (k1_latsubgr(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (k1_group_3(v12) = v11) | ~ (k1_group_3(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (k1_zfmisc_1(v12) = v11) | ~ (k1_zfmisc_1(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (u1_struct_0(v12) = v11) | ~ (u1_struct_0(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (u1_group_1(v12) = v11) | ~ (u1_group_1(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (k2_zfmisc_1(v11, v11) = v12) | ~ (u1_struct_0(v10) = v11) | ~ l1_group_1(v10) | ? [v13] : (u1_group_1(v10) = v13 & m2_relset_1(v13, v12, v11) & v1_funct_2(v13, v12, v11) & v1_funct_1(v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (k2_zfmisc_1(v10, v11) = v12) | ~ v1_xboole_0(v12) | v1_xboole_0(v11) | v1_xboole_0(v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (k1_zfmisc_1(v11) = v12) | ~ r1_tarski(v10, v11) | m1_subset_1(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (k1_zfmisc_1(v11) = v12) | ~ m1_subset_1(v10, v12) | r1_tarski(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (g1_group_1(v10, v11) = v12) | ~ v1_funct_1(v11) | v1_group_1(v12) | ? [v13] : (k2_zfmisc_1(v10, v10) = v13 & ( ~ v1_funct_2(v11, v13, v10) | ~ m1_relset_1(v11, v13, v10)))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (g1_group_1(v10, v11) = v12) | ~ v1_funct_1(v11) | l1_group_1(v12) | ? [v13] : (k2_zfmisc_1(v10, v10) = v13 & ( ~ v1_funct_2(v11, v13, v10) | ~ m1_relset_1(v11, v13, v10)))) & ! [v10] : ! [v11] : ! [v12] : ( ~ m2_relset_1(v12, v10, v11) | m1_relset_1(v12, v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ( ~ v1_xboole_0(v12) | ~ v1_funct_2(v12, v10, v11) | ~ v1_funct_1(v12) | ~ m1_relset_1(v12, v10, v11) | v1_xboole_0(v11) | v1_xboole_0(v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ v1_funct_2(v12, v10, v11) | ~ v1_funct_1(v12) | ~ m1_relset_1(v12, v10, v11) | v1_xboole_0(v11) | v1_xboole_0(v10) | v1_partfun1(v12, v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ( ~ v1_funct_2(v12, v10, v11) | ~ v1_funct_1(v12) | ~ m1_relset_1(v12, v10, v11) | v1_xboole_0(v11) | v1_partfun1(v12, v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ( ~ v1_partfun1(v12, v10, v11) | ~ v1_funct_1(v12) | ~ m1_relset_1(v12, v10, v11) | v1_funct_2(v12, v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ( ~ m1_relset_1(v12, v10, v11) | m2_relset_1(v12, v10, v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ v1_xboole_0(v11) | ~ v1_xboole_0(v10)) & ! [v10] : ! [v11] : ( ~ (k2_group_1(v10) = v11) | ~ l1_group_1(v10) | v3_struct_0(v10) | ? [v12] : (u1_struct_0(v10) = v12 & m1_subset_1(v11, v12))) & ! [v10] : ! [v11] : ( ~ (k1_latsubgr(v10) = v11) | ~ l1_group_1(v10) | ~ v4_group_1(v10) | ~ v3_group_1(v10) | v1_funct_1(v11) | v3_struct_0(v10)) & ! [v10] : ! [v11] : ( ~ (k1_latsubgr(v10) = v11) | ~ l1_group_1(v10) | ~ v4_group_1(v10) | ~ v3_group_1(v10) | v3_struct_0(v10) | ? [v12] : ? [v13] : ? [v14] : (k1_group_3(v10) = v12 & k1_zfmisc_1(v13) = v14 & u1_struct_0(v10) = v13 & m2_relset_1(v11, v12, v14) & v1_funct_2(v11, v12, v14))) & ! [v10] : ! [v11] : ( ~ (k1_latsubgr(v10) = v11) | ~ l1_group_1(v10) | ~ v4_group_1(v10) | ~ v3_group_1(v10) | v3_struct_0(v10) | ? [v12] : ? [v13] : ? [v14] : (k1_group_3(v10) = v12 & k1_zfmisc_1(v13) = v14 & u1_struct_0(v10) = v13 & ! [v15] : ! [v16] : ( ~ (k1_funct_1(v11, v15) = v16) | ~ m2_relset_1(v11, v12, v14) | ~ v1_funct_2(v11, v12, v14) | ~ v1_funct_1(v11) | ~ m1_group_2(v15, v10) | ~ v1_group_1(v15) | u1_struct_0(v15) = v16) & ! [v15] : ! [v16] : ( ~ (u1_struct_0(v15) = v16) | ~ m2_relset_1(v11, v12, v14) | ~ v1_funct_2(v11, v12, v14) | ~ v1_funct_1(v11) | ~ m1_group_2(v15, v10) | ~ v1_group_1(v15) | k1_funct_1(v11, v15) = v16) & ! [v15] : (v15 = v11 | ~ m2_relset_1(v15, v12, v14) | ~ v1_funct_2(v15, v12, v14) | ~ v1_funct_1(v15) | ? [v16] : ? [v17] : ? [v18] : ( ~ (v18 = v17) & k1_funct_1(v15, v16) = v17 & u1_struct_0(v16) = v18 & m1_group_2(v16, v10) & v1_group_1(v16))))) & ! [v10] : ! [v11] : ( ~ (k1_group_3(v10) = v11) | ~ v1_xboole_0(v11) | ~ l1_group_1(v10) | ~ v4_group_1(v10) | ~ v3_group_1(v10) | v3_struct_0(v10)) & ! [v10] : ! [v11] : ( ~ (k1_group_3(v10) = v11) | ~ l1_group_1(v10) | ~ v4_group_1(v10) | ~ v3_group_1(v10) | v3_struct_0(v10) | ? [v12] : ? [v13] : ? [v14] : (k1_latsubgr(v10) = v14 & k1_zfmisc_1(v12) = v13 & u1_struct_0(v10) = v12 & ! [v15] : ! [v16] : ( ~ (k1_funct_1(v14, v15) = v16) | ~ m2_relset_1(v14, v11, v13) | ~ v1_funct_2(v14, v11, v13) | ~ v1_funct_1(v14) | ~ m1_group_2(v15, v10) | ~ v1_group_1(v15) | u1_struct_0(v15) = v16) & ! [v15] : ! [v16] : ( ~ (u1_struct_0(v15) = v16) | ~ m2_relset_1(v14, v11, v13) | ~ v1_funct_2(v14, v11, v13) | ~ v1_funct_1(v14) | ~ m1_group_2(v15, v10) | ~ v1_group_1(v15) | k1_funct_1(v14, v15) = v16) & ! [v15] : (v15 = v14 | ~ m2_relset_1(v15, v11, v13) | ~ v1_funct_2(v15, v11, v13) | ~ v1_funct_1(v15) | ? [v16] : ? [v17] : ? [v18] : ( ~ (v18 = v17) & k1_funct_1(v15, v16) = v17 & u1_struct_0(v16) = v18 & m1_group_2(v16, v10) & v1_group_1(v16))))) & ! [v10] : ! [v11] : ( ~ (k1_group_3(v10) = v11) | ~ l1_group_1(v10) | ~ v4_group_1(v10) | ~ v3_group_1(v10) | v3_struct_0(v10) | ? [v12] : ? [v13] : ? [v14] : (k1_latsubgr(v10) = v12 & k1_zfmisc_1(v13) = v14 & u1_struct_0(v10) = v13 & m2_relset_1(v12, v11, v14) & v1_funct_2(v12, v11, v14) & v1_funct_1(v12))) & ! [v10] : ! [v11] : ( ~ (k1_zfmisc_1(v10) = v11) | ~ v1_xboole_0(v11)) & ! [v10] : ! [v11] : ( ~ (k1_zfmisc_1(v10) = v11) | v1_xboole_0(v10) | ? [v12] : (m1_subset_1(v12, v11) & ~ v1_xboole_0(v12))) & ! [v10] : ! [v11] : ( ~ (k1_zfmisc_1(v10) = v11) | ? [v12] : (v1_xboole_0(v12) & m1_subset_1(v12, v11))) & ! [v10] : ! [v11] : ( ~ (u1_struct_0(v10) = v11) | ~ l1_struct_0(v10) | ~ v1_xboole_0(v11) | v3_struct_0(v10)) & ! [v10] : ! [v11] : ( ~ (u1_struct_0(v10) = v11) | ~ l1_struct_0(v10) | v3_struct_0(v10) | ? [v12] : ? [v13] : (k1_zfmisc_1(v11) = v12 & m1_subset_1(v13, v12) & ~ v1_xboole_0(v13))) & ! [v10] : ! [v11] : ( ~ (u1_struct_0(v10) = v11) | ~ l1_group_1(v10) | ~ v4_group_1(v10) | ~ v3_group_1(v10) | v3_struct_0(v10) | ? [v12] : ? [v13] : ? [v14] : (k1_latsubgr(v10) = v14 & k1_group_3(v10) = v12 & k1_zfmisc_1(v11) = v13 & ! [v15] : ! [v16] : ( ~ (k1_funct_1(v14, v15) = v16) | ~ m2_relset_1(v14, v12, v13) | ~ v1_funct_2(v14, v12, v13) | ~ v1_funct_1(v14) | ~ m1_group_2(v15, v10) | ~ v1_group_1(v15) | u1_struct_0(v15) = v16) & ! [v15] : ! [v16] : ( ~ (u1_struct_0(v15) = v16) | ~ m2_relset_1(v14, v12, v13) | ~ v1_funct_2(v14, v12, v13) | ~ v1_funct_1(v14) | ~ m1_group_2(v15, v10) | ~ v1_group_1(v15) | k1_funct_1(v14, v15) = v16) & ! [v15] : (v15 = v14 | ~ m2_relset_1(v15, v12, v13) | ~ v1_funct_2(v15, v12, v13) | ~ v1_funct_1(v15) | ? [v16] : ? [v17] : ? [v18] : ( ~ (v18 = v17) & k1_funct_1(v15, v16) = v17 & u1_struct_0(v16) = v18 & m1_group_2(v16, v10) & v1_group_1(v16))))) & ! [v10] : ! [v11] : ( ~ (u1_struct_0(v10) = v11) | ~ l1_group_1(v10) | ~ v4_group_1(v10) | ~ v3_group_1(v10) | v3_struct_0(v10) | ? [v12] : ? [v13] : ? [v14] : (k1_latsubgr(v10) = v12 & k1_group_3(v10) = v13 & k1_zfmisc_1(v11) = v14 & m2_relset_1(v12, v13, v14) & v1_funct_2(v12, v13, v14) & v1_funct_1(v12))) & ! [v10] : ! [v11] : ( ~ (u1_struct_0(v10) = v11) | ~ l1_group_1(v10) | v3_struct_0(v10) | ? [v12] : (k2_group_1(v10) = v12 & m1_subset_1(v12, v11))) & ! [v10] : ! [v11] : ( ~ (u1_struct_0(v10) = v11) | ~ l1_group_1(v10) | ? [v12] : ? [v13] : (k2_zfmisc_1(v11, v11) = v13 & u1_group_1(v10) = v12 & m2_relset_1(v12, v13, v11) & v1_funct_2(v12, v13, v11) & v1_funct_1(v12))) & ! [v10] : ! [v11] : ( ~ (u1_group_1(v10) = v11) | ~ l1_group_1(v10) | v1_funct_1(v11)) & ! [v10] : ! [v11] : ( ~ (u1_group_1(v10) = v11) | ~ l1_group_1(v10) | ? [v12] : ? [v13] : (k2_zfmisc_1(v12, v12) = v13 & u1_struct_0(v10) = v12 & m2_relset_1(v11, v13, v12) & v1_funct_2(v11, v13, v12))) & ! [v10] : ! [v11] : ( ~ v1_xboole_0(v11) | ~ r2_hidden(v10, v11)) & ! [v10] : ! [v11] : ( ~ m1_subset_1(v10, v11) | v1_xboole_0(v11) | r2_hidden(v10, v11)) & ! [v10] : ! [v11] : ( ~ r2_hidden(v11, v10) | ~ r2_hidden(v10, v11)) & ! [v10] : ! [v11] : ( ~ r2_hidden(v10, v11) | m1_subset_1(v10, v11)) & ! [v10] : ! [v11] : ( ~ m1_group_2(v11, v10) | ~ l1_group_1(v10) | ~ v3_group_1(v10) | ~ v3_struct_0(v11) | v3_struct_0(v10)) & ! [v10] : ! [v11] : ( ~ m1_group_2(v11, v10) | ~ l1_group_1(v10) | ~ v3_group_1(v10) | l1_group_1(v11) | v3_struct_0(v10)) & ! [v10] : ! [v11] : ( ~ m1_group_2(v11, v10) | ~ l1_group_1(v10) | ~ v3_group_1(v10) | v3_group_1(v11) | v3_struct_0(v10)) & ! [v10] : (v10 = k1_xboole_0 | ~ v1_xboole_0(v10)) & ! [v10] : ( ~ l1_group_1(v10) | ~ v3_group_1(v10) | v3_struct_0(v10) | ? [v11] : m1_group_2(v11, v10)) & ! [v10] : ( ~ l1_group_1(v10) | l1_struct_0(v10)) & ? [v10] : ? [v11] : ? [v12] : m2_relset_1(v12, v10, v11) & ? [v10] : ? [v11] : ? [v12] : m1_relset_1(v12, v10, v11) & ? [v10] : ? [v11] : ? [v12] : (v1_relat_1(v12) & v1_funct_2(v12, v10, v11) & v1_funct_1(v12) & m1_relset_1(v12, v10, v11)) & ? [v10] : ? [v11] : ? [v12] : (v1_relat_1(v12) & v1_funct_1(v12) & m1_relset_1(v12, v10, v11)) & ? [v10] : ? [v11] : m1_subset_1(v11, v10) & ? [v10] : r1_tarski(v10, v10))
% 7.98/2.43 | 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 yields:
% 7.98/2.43 | (1) k2_group_1(all_0_9_9) = all_0_8_8 & k1_latsubgr(all_0_9_9) = all_0_7_7 & k1_funct_1(all_0_7_7, all_0_6_6) = all_0_5_5 & l1_struct_0(all_0_1_1) & l1_struct_0(all_0_4_4) & v1_xboole_0(all_0_2_2) & v1_xboole_0(k1_xboole_0) & m1_group_2(all_0_6_6, all_0_9_9) & v1_group_1(all_0_6_6) & l1_group_1(all_0_0_0) & l1_group_1(all_0_9_9) & v4_group_1(all_0_9_9) & v3_group_1(all_0_9_9) & ~ v1_xboole_0(all_0_3_3) & ~ r2_hidden(all_0_8_8, all_0_5_5) & ~ v3_struct_0(all_0_4_4) & ~ v3_struct_0(all_0_9_9) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v1 | ~ (g1_group_1(v3, v4) = v2) | ~ (g1_group_1(v0, v1) = v2) | ~ v1_funct_1(v1) | ? [v5] : (k2_zfmisc_1(v0, v0) = v5 & ( ~ v1_funct_2(v1, v5, v0) | ~ m1_relset_1(v1, v5, v0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | ~ (g1_group_1(v3, v4) = v2) | ~ (g1_group_1(v0, v1) = v2) | ~ v1_funct_1(v1) | ? [v5] : (k2_zfmisc_1(v0, v0) = v5 & ( ~ v1_funct_2(v1, v5, v0) | ~ m1_relset_1(v1, v5, v0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (k2_group_1(v2) = v3) | ~ (k2_group_1(v0) = v1) | ~ m1_group_2(v2, v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (u1_struct_0(v0) = v1) | ~ (u1_group_1(v0) = v2) | ~ (g1_group_1(v1, v2) = v3) | ~ v1_group_1(v0) | ~ l1_group_1(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k1_funct_1(v3, v2) = v1) | ~ (k1_funct_1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k2_zfmisc_1(v3, v2) = v1) | ~ (k2_zfmisc_1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (g1_group_1(v3, v2) = v1) | ~ (g1_group_1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k2_zfmisc_1(v0, v1) = v3) | ~ m2_relset_1(v2, v0, v1) | ? [v4] : (k1_zfmisc_1(v3) = v4 & m1_subset_1(v2, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ v1_xboole_0(v2) | ~ m1_subset_1(v1, v3) | ~ r2_hidden(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ m1_subset_1(v1, v3) | ~ r2_hidden(v0, v1) | m1_subset_1(v0, v2)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k2_zfmisc_1(v1, v2) = v3) | v1_relat_1(v0) | ? [v4] : (k1_zfmisc_1(v3) = v4 & ~ m1_subset_1(v0, v4))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k2_group_1(v2) = v1) | ~ (k2_group_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_latsubgr(v2) = v1) | ~ (k1_latsubgr(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_group_3(v2) = v1) | ~ (k1_group_3(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (u1_group_1(v2) = v1) | ~ (u1_group_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_zfmisc_1(v1, v1) = v2) | ~ (u1_struct_0(v0) = v1) | ~ l1_group_1(v0) | ? [v3] : (u1_group_1(v0) = v3 & m2_relset_1(v3, v2, v1) & v1_funct_2(v3, v2, v1) & v1_funct_1(v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_zfmisc_1(v0, v1) = v2) | ~ v1_xboole_0(v2) | v1_xboole_0(v1) | v1_xboole_0(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] : ( ~ (g1_group_1(v0, v1) = v2) | ~ v1_funct_1(v1) | v1_group_1(v2) | ? [v3] : (k2_zfmisc_1(v0, v0) = v3 & ( ~ v1_funct_2(v1, v3, v0) | ~ m1_relset_1(v1, v3, v0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (g1_group_1(v0, v1) = v2) | ~ v1_funct_1(v1) | l1_group_1(v2) | ? [v3] : (k2_zfmisc_1(v0, v0) = v3 & ( ~ v1_funct_2(v1, v3, v0) | ~ m1_relset_1(v1, v3, v0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ m2_relset_1(v2, v0, v1) | m1_relset_1(v2, v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ v1_xboole_0(v2) | ~ v1_funct_2(v2, v0, v1) | ~ v1_funct_1(v2) | ~ m1_relset_1(v2, v0, v1) | v1_xboole_0(v1) | v1_xboole_0(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ v1_funct_2(v2, v0, v1) | ~ v1_funct_1(v2) | ~ m1_relset_1(v2, v0, v1) | v1_xboole_0(v1) | v1_xboole_0(v0) | v1_partfun1(v2, v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ v1_funct_2(v2, v0, v1) | ~ v1_funct_1(v2) | ~ m1_relset_1(v2, v0, v1) | v1_xboole_0(v1) | v1_partfun1(v2, v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ v1_partfun1(v2, v0, v1) | ~ v1_funct_1(v2) | ~ m1_relset_1(v2, v0, v1) | v1_funct_2(v2, v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ m1_relset_1(v2, v0, v1) | m2_relset_1(v2, v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ v1_xboole_0(v1) | ~ v1_xboole_0(v0)) & ! [v0] : ! [v1] : ( ~ (k2_group_1(v0) = v1) | ~ l1_group_1(v0) | v3_struct_0(v0) | ? [v2] : (u1_struct_0(v0) = v2 & m1_subset_1(v1, v2))) & ! [v0] : ! [v1] : ( ~ (k1_latsubgr(v0) = v1) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v1_funct_1(v1) | v3_struct_0(v0)) & ! [v0] : ! [v1] : ( ~ (k1_latsubgr(v0) = v1) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v2] : ? [v3] : ? [v4] : (k1_group_3(v0) = v2 & k1_zfmisc_1(v3) = v4 & u1_struct_0(v0) = v3 & m2_relset_1(v1, v2, v4) & v1_funct_2(v1, v2, v4))) & ! [v0] : ! [v1] : ( ~ (k1_latsubgr(v0) = v1) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v2] : ? [v3] : ? [v4] : (k1_group_3(v0) = v2 & k1_zfmisc_1(v3) = v4 & u1_struct_0(v0) = v3 & ! [v5] : ! [v6] : ( ~ (k1_funct_1(v1, v5) = v6) | ~ m2_relset_1(v1, v2, v4) | ~ v1_funct_2(v1, v2, v4) | ~ v1_funct_1(v1) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) | u1_struct_0(v5) = v6) & ! [v5] : ! [v6] : ( ~ (u1_struct_0(v5) = v6) | ~ m2_relset_1(v1, v2, v4) | ~ v1_funct_2(v1, v2, v4) | ~ v1_funct_1(v1) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) | k1_funct_1(v1, v5) = v6) & ! [v5] : (v5 = v1 | ~ m2_relset_1(v5, v2, v4) | ~ v1_funct_2(v5, v2, v4) | ~ v1_funct_1(v5) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = v7) & k1_funct_1(v5, v6) = v7 & u1_struct_0(v6) = v8 & m1_group_2(v6, v0) & v1_group_1(v6))))) & ! [v0] : ! [v1] : ( ~ (k1_group_3(v0) = v1) | ~ v1_xboole_0(v1) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0)) & ! [v0] : ! [v1] : ( ~ (k1_group_3(v0) = v1) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v2] : ? [v3] : ? [v4] : (k1_latsubgr(v0) = v4 & k1_zfmisc_1(v2) = v3 & u1_struct_0(v0) = v2 & ! [v5] : ! [v6] : ( ~ (k1_funct_1(v4, v5) = v6) | ~ m2_relset_1(v4, v1, v3) | ~ v1_funct_2(v4, v1, v3) | ~ v1_funct_1(v4) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) | u1_struct_0(v5) = v6) & ! [v5] : ! [v6] : ( ~ (u1_struct_0(v5) = v6) | ~ m2_relset_1(v4, v1, v3) | ~ v1_funct_2(v4, v1, v3) | ~ v1_funct_1(v4) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) | k1_funct_1(v4, v5) = v6) & ! [v5] : (v5 = v4 | ~ m2_relset_1(v5, v1, v3) | ~ v1_funct_2(v5, v1, v3) | ~ v1_funct_1(v5) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = v7) & k1_funct_1(v5, v6) = v7 & u1_struct_0(v6) = v8 & m1_group_2(v6, v0) & v1_group_1(v6))))) & ! [v0] : ! [v1] : ( ~ (k1_group_3(v0) = v1) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v2] : ? [v3] : ? [v4] : (k1_latsubgr(v0) = v2 & k1_zfmisc_1(v3) = v4 & u1_struct_0(v0) = v3 & m2_relset_1(v2, v1, v4) & v1_funct_2(v2, v1, v4) & v1_funct_1(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] : (v1_xboole_0(v2) & m1_subset_1(v2, v1))) & ! [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) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v2] : ? [v3] : ? [v4] : (k1_latsubgr(v0) = v4 & k1_group_3(v0) = v2 & k1_zfmisc_1(v1) = v3 & ! [v5] : ! [v6] : ( ~ (k1_funct_1(v4, v5) = v6) | ~ m2_relset_1(v4, v2, v3) | ~ v1_funct_2(v4, v2, v3) | ~ v1_funct_1(v4) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) | u1_struct_0(v5) = v6) & ! [v5] : ! [v6] : ( ~ (u1_struct_0(v5) = v6) | ~ m2_relset_1(v4, v2, v3) | ~ v1_funct_2(v4, v2, v3) | ~ v1_funct_1(v4) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) | k1_funct_1(v4, v5) = v6) & ! [v5] : (v5 = v4 | ~ m2_relset_1(v5, v2, v3) | ~ v1_funct_2(v5, v2, v3) | ~ v1_funct_1(v5) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = v7) & k1_funct_1(v5, v6) = v7 & u1_struct_0(v6) = v8 & m1_group_2(v6, v0) & v1_group_1(v6))))) & ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v2] : ? [v3] : ? [v4] : (k1_latsubgr(v0) = v2 & k1_group_3(v0) = v3 & k1_zfmisc_1(v1) = v4 & m2_relset_1(v2, v3, v4) & v1_funct_2(v2, v3, v4) & v1_funct_1(v2))) & ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l1_group_1(v0) | v3_struct_0(v0) | ? [v2] : (k2_group_1(v0) = v2 & m1_subset_1(v2, v1))) & ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l1_group_1(v0) | ? [v2] : ? [v3] : (k2_zfmisc_1(v1, v1) = v3 & u1_group_1(v0) = v2 & m2_relset_1(v2, v3, v1) & v1_funct_2(v2, v3, v1) & v1_funct_1(v2))) & ! [v0] : ! [v1] : ( ~ (u1_group_1(v0) = v1) | ~ l1_group_1(v0) | v1_funct_1(v1)) & ! [v0] : ! [v1] : ( ~ (u1_group_1(v0) = v1) | ~ l1_group_1(v0) | ? [v2] : ? [v3] : (k2_zfmisc_1(v2, v2) = v3 & u1_struct_0(v0) = v2 & m2_relset_1(v1, v3, v2) & v1_funct_2(v1, v3, v2))) & ! [v0] : ! [v1] : ( ~ v1_xboole_0(v1) | ~ r2_hidden(v0, v1)) & ! [v0] : ! [v1] : ( ~ m1_subset_1(v0, v1) | v1_xboole_0(v1) | r2_hidden(v0, v1)) & ! [v0] : ! [v1] : ( ~ r2_hidden(v1, v0) | ~ r2_hidden(v0, v1)) & ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | m1_subset_1(v0, v1)) & ! [v0] : ! [v1] : ( ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v3_group_1(v0) | ~ v3_struct_0(v1) | v3_struct_0(v0)) & ! [v0] : ! [v1] : ( ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v3_group_1(v0) | l1_group_1(v1) | v3_struct_0(v0)) & ! [v0] : ! [v1] : ( ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v3_group_1(v0) | v3_group_1(v1) | v3_struct_0(v0)) & ! [v0] : (v0 = k1_xboole_0 | ~ v1_xboole_0(v0)) & ! [v0] : ( ~ l1_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v1] : m1_group_2(v1, v0)) & ! [v0] : ( ~ l1_group_1(v0) | l1_struct_0(v0)) & ? [v0] : ? [v1] : ? [v2] : m2_relset_1(v2, v0, v1) & ? [v0] : ? [v1] : ? [v2] : m1_relset_1(v2, v0, v1) & ? [v0] : ? [v1] : ? [v2] : (v1_relat_1(v2) & v1_funct_2(v2, v0, v1) & v1_funct_1(v2) & m1_relset_1(v2, v0, v1)) & ? [v0] : ? [v1] : ? [v2] : (v1_relat_1(v2) & v1_funct_1(v2) & m1_relset_1(v2, v0, v1)) & ? [v0] : ? [v1] : m1_subset_1(v1, v0) & ? [v0] : r1_tarski(v0, v0)
% 7.98/2.45 |
% 7.98/2.45 | Applying alpha-rule on (1) yields:
% 7.98/2.45 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_zfmisc_1(v1) = v2) | ~ m1_subset_1(v0, v2) | r1_tarski(v0, v1))
% 7.98/2.45 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_zfmisc_1(v1) = v2) | ~ r1_tarski(v0, v1) | m1_subset_1(v0, v2))
% 7.98/2.45 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ v1_xboole_0(v2) | ~ v1_funct_2(v2, v0, v1) | ~ v1_funct_1(v2) | ~ m1_relset_1(v2, v0, v1) | v1_xboole_0(v1) | v1_xboole_0(v0))
% 7.98/2.45 | (5) ! [v0] : ! [v1] : ( ~ (k2_group_1(v0) = v1) | ~ l1_group_1(v0) | v3_struct_0(v0) | ? [v2] : (u1_struct_0(v0) = v2 & m1_subset_1(v1, v2)))
% 7.98/2.45 | (6) ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l1_group_1(v0) | ? [v2] : ? [v3] : (k2_zfmisc_1(v1, v1) = v3 & u1_group_1(v0) = v2 & m2_relset_1(v2, v3, v1) & v1_funct_2(v2, v3, v1) & v1_funct_1(v2)))
% 7.98/2.45 | (7) k1_funct_1(all_0_7_7, all_0_6_6) = all_0_5_5
% 7.98/2.45 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v1 | ~ (g1_group_1(v3, v4) = v2) | ~ (g1_group_1(v0, v1) = v2) | ~ v1_funct_1(v1) | ? [v5] : (k2_zfmisc_1(v0, v0) = v5 & ( ~ v1_funct_2(v1, v5, v0) | ~ m1_relset_1(v1, v5, v0))))
% 7.98/2.45 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k2_zfmisc_1(v3, v2) = v1) | ~ (k2_zfmisc_1(v3, v2) = v0))
% 7.98/2.45 | (10) ! [v0] : ! [v1] : ( ~ (k1_latsubgr(v0) = v1) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v1_funct_1(v1) | v3_struct_0(v0))
% 7.98/2.45 | (11) k2_group_1(all_0_9_9) = all_0_8_8
% 7.98/2.45 | (12) ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v2] : ? [v3] : ? [v4] : (k1_latsubgr(v0) = v4 & k1_group_3(v0) = v2 & k1_zfmisc_1(v1) = v3 & ! [v5] : ! [v6] : ( ~ (k1_funct_1(v4, v5) = v6) | ~ m2_relset_1(v4, v2, v3) | ~ v1_funct_2(v4, v2, v3) | ~ v1_funct_1(v4) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) | u1_struct_0(v5) = v6) & ! [v5] : ! [v6] : ( ~ (u1_struct_0(v5) = v6) | ~ m2_relset_1(v4, v2, v3) | ~ v1_funct_2(v4, v2, v3) | ~ v1_funct_1(v4) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) | k1_funct_1(v4, v5) = v6) & ! [v5] : (v5 = v4 | ~ m2_relset_1(v5, v2, v3) | ~ v1_funct_2(v5, v2, v3) | ~ v1_funct_1(v5) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = v7) & k1_funct_1(v5, v6) = v7 & u1_struct_0(v6) = v8 & m1_group_2(v6, v0) & v1_group_1(v6)))))
% 7.98/2.45 | (13) ! [v0] : ! [v1] : ( ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v3_group_1(v0) | v3_group_1(v1) | v3_struct_0(v0))
% 7.98/2.45 | (14) m1_group_2(all_0_6_6, all_0_9_9)
% 7.98/2.45 | (15) ! [v0] : ! [v1] : ( ~ (k1_latsubgr(v0) = v1) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v2] : ? [v3] : ? [v4] : (k1_group_3(v0) = v2 & k1_zfmisc_1(v3) = v4 & u1_struct_0(v0) = v3 & ! [v5] : ! [v6] : ( ~ (k1_funct_1(v1, v5) = v6) | ~ m2_relset_1(v1, v2, v4) | ~ v1_funct_2(v1, v2, v4) | ~ v1_funct_1(v1) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) | u1_struct_0(v5) = v6) & ! [v5] : ! [v6] : ( ~ (u1_struct_0(v5) = v6) | ~ m2_relset_1(v1, v2, v4) | ~ v1_funct_2(v1, v2, v4) | ~ v1_funct_1(v1) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) | k1_funct_1(v1, v5) = v6) & ! [v5] : (v5 = v1 | ~ m2_relset_1(v5, v2, v4) | ~ v1_funct_2(v5, v2, v4) | ~ v1_funct_1(v5) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = v7) & k1_funct_1(v5, v6) = v7 & u1_struct_0(v6) = v8 & m1_group_2(v6, v0) & v1_group_1(v6)))))
% 7.98/2.45 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ v1_partfun1(v2, v0, v1) | ~ v1_funct_1(v2) | ~ m1_relset_1(v2, v0, v1) | v1_funct_2(v2, v0, v1))
% 7.98/2.45 | (17) ~ v3_struct_0(all_0_9_9)
% 7.98/2.45 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | ~ (g1_group_1(v3, v4) = v2) | ~ (g1_group_1(v0, v1) = v2) | ~ v1_funct_1(v1) | ? [v5] : (k2_zfmisc_1(v0, v0) = v5 & ( ~ v1_funct_2(v1, v5, v0) | ~ m1_relset_1(v1, v5, v0))))
% 7.98/2.45 | (19) ! [v0] : ( ~ l1_group_1(v0) | l1_struct_0(v0))
% 7.98/2.45 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (k2_group_1(v2) = v3) | ~ (k2_group_1(v0) = v1) | ~ m1_group_2(v2, v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0))
% 7.98/2.45 | (21) k1_latsubgr(all_0_9_9) = all_0_7_7
% 7.98/2.45 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (g1_group_1(v0, v1) = v2) | ~ v1_funct_1(v1) | l1_group_1(v2) | ? [v3] : (k2_zfmisc_1(v0, v0) = v3 & ( ~ v1_funct_2(v1, v3, v0) | ~ m1_relset_1(v1, v3, v0))))
% 7.98/2.46 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ v1_funct_2(v2, v0, v1) | ~ v1_funct_1(v2) | ~ m1_relset_1(v2, v0, v1) | v1_xboole_0(v1) | v1_xboole_0(v0) | v1_partfun1(v2, v0, v1))
% 7.98/2.46 | (24) v3_group_1(all_0_9_9)
% 7.98/2.46 | (25) ! [v0] : ! [v1] : ( ~ (k1_group_3(v0) = v1) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v2] : ? [v3] : ? [v4] : (k1_latsubgr(v0) = v2 & k1_zfmisc_1(v3) = v4 & u1_struct_0(v0) = v3 & m2_relset_1(v2, v1, v4) & v1_funct_2(v2, v1, v4) & v1_funct_1(v2)))
% 7.98/2.46 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0))
% 7.98/2.46 | (27) ? [v0] : ? [v1] : ? [v2] : m2_relset_1(v2, v0, v1)
% 7.98/2.46 | (28) ! [v0] : ! [v1] : ( ~ r2_hidden(v1, v0) | ~ r2_hidden(v0, v1))
% 7.98/2.46 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ v1_xboole_0(v2) | ~ m1_subset_1(v1, v3) | ~ r2_hidden(v0, v1))
% 7.98/2.46 | (30) ! [v0] : ! [v1] : ( ~ (k1_latsubgr(v0) = v1) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v2] : ? [v3] : ? [v4] : (k1_group_3(v0) = v2 & k1_zfmisc_1(v3) = v4 & u1_struct_0(v0) = v3 & m2_relset_1(v1, v2, v4) & v1_funct_2(v1, v2, v4)))
% 7.98/2.46 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (u1_group_1(v2) = v1) | ~ (u1_group_1(v2) = v0))
% 7.98/2.46 | (32) ! [v0] : (v0 = k1_xboole_0 | ~ v1_xboole_0(v0))
% 7.98/2.46 | (33) ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v2] : ? [v3] : ? [v4] : (k1_latsubgr(v0) = v2 & k1_group_3(v0) = v3 & k1_zfmisc_1(v1) = v4 & m2_relset_1(v2, v3, v4) & v1_funct_2(v2, v3, v4) & v1_funct_1(v2)))
% 7.98/2.46 | (34) ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ? [v2] : (v1_xboole_0(v2) & m1_subset_1(v2, v1)))
% 7.98/2.46 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_zfmisc_1(v1, v1) = v2) | ~ (u1_struct_0(v0) = v1) | ~ l1_group_1(v0) | ? [v3] : (u1_group_1(v0) = v3 & m2_relset_1(v3, v2, v1) & v1_funct_2(v3, v2, v1) & v1_funct_1(v3)))
% 7.98/2.46 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_latsubgr(v2) = v1) | ~ (k1_latsubgr(v2) = v0))
% 7.98/2.46 | (37) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_group_3(v2) = v1) | ~ (k1_group_3(v2) = v0))
% 7.98/2.46 | (38) l1_group_1(all_0_9_9)
% 7.98/2.46 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ m1_relset_1(v2, v0, v1) | m2_relset_1(v2, v0, v1))
% 7.98/2.46 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ m2_relset_1(v2, v0, v1) | m1_relset_1(v2, v0, v1))
% 7.98/2.46 | (41) ~ v1_xboole_0(all_0_3_3)
% 7.98/2.46 | (42) ? [v0] : ? [v1] : ? [v2] : (v1_relat_1(v2) & v1_funct_2(v2, v0, v1) & v1_funct_1(v2) & m1_relset_1(v2, v0, v1))
% 7.98/2.46 | (43) ! [v0] : ! [v1] : ( ~ (u1_group_1(v0) = v1) | ~ l1_group_1(v0) | ? [v2] : ? [v3] : (k2_zfmisc_1(v2, v2) = v3 & u1_struct_0(v0) = v2 & m2_relset_1(v1, v3, v2) & v1_funct_2(v1, v3, v2)))
% 7.98/2.46 | (44) ! [v0] : ! [v1] : (v1 = v0 | ~ v1_xboole_0(v1) | ~ v1_xboole_0(v0))
% 7.98/2.46 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (u1_struct_0(v0) = v1) | ~ (u1_group_1(v0) = v2) | ~ (g1_group_1(v1, v2) = v3) | ~ v1_group_1(v0) | ~ l1_group_1(v0))
% 7.98/2.46 | (46) ? [v0] : ? [v1] : ? [v2] : (v1_relat_1(v2) & v1_funct_1(v2) & m1_relset_1(v2, v0, v1))
% 7.98/2.46 | (47) v1_xboole_0(all_0_2_2)
% 7.98/2.46 | (48) v4_group_1(all_0_9_9)
% 7.98/2.46 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k2_zfmisc_1(v0, v1) = v3) | ~ m2_relset_1(v2, v0, v1) | ? [v4] : (k1_zfmisc_1(v3) = v4 & m1_subset_1(v2, v4)))
% 7.98/2.46 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ v1_funct_2(v2, v0, v1) | ~ v1_funct_1(v2) | ~ m1_relset_1(v2, v0, v1) | v1_xboole_0(v1) | v1_partfun1(v2, v0, v1))
% 7.98/2.46 | (51) ! [v0] : ! [v1] : ( ~ v1_xboole_0(v1) | ~ r2_hidden(v0, v1))
% 7.98/2.46 | (52) l1_struct_0(all_0_4_4)
% 7.98/2.46 | (53) l1_struct_0(all_0_1_1)
% 7.98/2.46 | (54) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k2_zfmisc_1(v1, v2) = v3) | v1_relat_1(v0) | ? [v4] : (k1_zfmisc_1(v3) = v4 & ~ m1_subset_1(v0, v4)))
% 7.98/2.46 | (55) ~ v3_struct_0(all_0_4_4)
% 7.98/2.46 | (56) v1_xboole_0(k1_xboole_0)
% 7.98/2.46 | (57) ! [v0] : ! [v1] : ( ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v3_group_1(v0) | ~ v3_struct_0(v1) | v3_struct_0(v0))
% 7.98/2.46 | (58) ! [v0] : ! [v1] : ( ~ (u1_group_1(v0) = v1) | ~ l1_group_1(v0) | v1_funct_1(v1))
% 7.98/2.46 | (59) ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l1_struct_0(v0) | ~ v1_xboole_0(v1) | v3_struct_0(v0))
% 7.98/2.46 | (60) ! [v0] : ! [v1] : ( ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v3_group_1(v0) | l1_group_1(v1) | v3_struct_0(v0))
% 7.98/2.47 | (61) ! [v0] : ! [v1] : ( ~ m1_subset_1(v0, v1) | v1_xboole_0(v1) | r2_hidden(v0, v1))
% 7.98/2.47 | (62) ! [v0] : ! [v1] : ! [v2] : ( ~ (g1_group_1(v0, v1) = v2) | ~ v1_funct_1(v1) | v1_group_1(v2) | ? [v3] : (k2_zfmisc_1(v0, v0) = v3 & ( ~ v1_funct_2(v1, v3, v0) | ~ m1_relset_1(v1, v3, v0))))
% 7.98/2.47 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ m1_subset_1(v1, v3) | ~ r2_hidden(v0, v1) | m1_subset_1(v0, v2))
% 7.98/2.47 | (64) l1_group_1(all_0_0_0)
% 7.98/2.47 | (65) ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | m1_subset_1(v0, v1))
% 7.98/2.47 | (66) ~ r2_hidden(all_0_8_8, all_0_5_5)
% 7.98/2.47 | (67) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0))
% 7.98/2.47 | (68) v1_group_1(all_0_6_6)
% 7.98/2.47 | (69) ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l1_group_1(v0) | v3_struct_0(v0) | ? [v2] : (k2_group_1(v0) = v2 & m1_subset_1(v2, v1)))
% 7.98/2.47 | (70) ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ~ v1_xboole_0(v1))
% 7.98/2.47 | (71) ! [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)))
% 7.98/2.47 | (72) ! [v0] : ( ~ l1_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v1] : m1_group_2(v1, v0))
% 7.98/2.47 | (73) ? [v0] : r1_tarski(v0, v0)
% 7.98/2.47 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_zfmisc_1(v0, v1) = v2) | ~ v1_xboole_0(v2) | v1_xboole_0(v1) | v1_xboole_0(v0))
% 7.98/2.47 | (75) ! [v0] : ! [v1] : ( ~ (k1_group_3(v0) = v1) | ~ v1_xboole_0(v1) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0))
% 7.98/2.47 | (76) ! [v0] : ! [v1] : ( ~ (k1_group_3(v0) = v1) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v2] : ? [v3] : ? [v4] : (k1_latsubgr(v0) = v4 & k1_zfmisc_1(v2) = v3 & u1_struct_0(v0) = v2 & ! [v5] : ! [v6] : ( ~ (k1_funct_1(v4, v5) = v6) | ~ m2_relset_1(v4, v1, v3) | ~ v1_funct_2(v4, v1, v3) | ~ v1_funct_1(v4) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) | u1_struct_0(v5) = v6) & ! [v5] : ! [v6] : ( ~ (u1_struct_0(v5) = v6) | ~ m2_relset_1(v4, v1, v3) | ~ v1_funct_2(v4, v1, v3) | ~ v1_funct_1(v4) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) | k1_funct_1(v4, v5) = v6) & ! [v5] : (v5 = v4 | ~ m2_relset_1(v5, v1, v3) | ~ v1_funct_2(v5, v1, v3) | ~ v1_funct_1(v5) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = v7) & k1_funct_1(v5, v6) = v7 & u1_struct_0(v6) = v8 & m1_group_2(v6, v0) & v1_group_1(v6)))))
% 7.98/2.47 | (77) ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | v1_xboole_0(v0) | ? [v2] : (m1_subset_1(v2, v1) & ~ v1_xboole_0(v2)))
% 7.98/2.47 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (g1_group_1(v3, v2) = v1) | ~ (g1_group_1(v3, v2) = v0))
% 7.98/2.47 | (79) ? [v0] : ? [v1] : m1_subset_1(v1, v0)
% 7.98/2.47 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k1_funct_1(v3, v2) = v1) | ~ (k1_funct_1(v3, v2) = v0))
% 7.98/2.47 | (81) ? [v0] : ? [v1] : ? [v2] : m1_relset_1(v2, v0, v1)
% 7.98/2.47 | (82) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k2_group_1(v2) = v1) | ~ (k2_group_1(v2) = v0))
% 7.98/2.47 |
% 7.98/2.47 | Instantiating formula (10) with all_0_7_7, all_0_9_9 and discharging atoms k1_latsubgr(all_0_9_9) = all_0_7_7, l1_group_1(all_0_9_9), v4_group_1(all_0_9_9), v3_group_1(all_0_9_9), ~ v3_struct_0(all_0_9_9), yields:
% 7.98/2.47 | (83) v1_funct_1(all_0_7_7)
% 7.98/2.47 |
% 7.98/2.47 | Instantiating formula (30) with all_0_7_7, all_0_9_9 and discharging atoms k1_latsubgr(all_0_9_9) = all_0_7_7, l1_group_1(all_0_9_9), v4_group_1(all_0_9_9), v3_group_1(all_0_9_9), ~ v3_struct_0(all_0_9_9), yields:
% 7.98/2.47 | (84) ? [v0] : ? [v1] : ? [v2] : (k1_group_3(all_0_9_9) = v0 & k1_zfmisc_1(v1) = v2 & u1_struct_0(all_0_9_9) = v1 & m2_relset_1(all_0_7_7, v0, v2) & v1_funct_2(all_0_7_7, v0, v2))
% 7.98/2.47 |
% 7.98/2.47 | Instantiating formula (15) with all_0_7_7, all_0_9_9 and discharging atoms k1_latsubgr(all_0_9_9) = all_0_7_7, l1_group_1(all_0_9_9), v4_group_1(all_0_9_9), v3_group_1(all_0_9_9), ~ v3_struct_0(all_0_9_9), yields:
% 7.98/2.47 | (85) ? [v0] : ? [v1] : ? [v2] : (k1_group_3(all_0_9_9) = v0 & k1_zfmisc_1(v1) = v2 & u1_struct_0(all_0_9_9) = v1 & ! [v3] : ! [v4] : ( ~ (k1_funct_1(all_0_7_7, v3) = v4) | ~ m2_relset_1(all_0_7_7, v0, v2) | ~ v1_funct_2(all_0_7_7, v0, v2) | ~ v1_funct_1(all_0_7_7) | ~ m1_group_2(v3, all_0_9_9) | ~ v1_group_1(v3) | u1_struct_0(v3) = v4) & ! [v3] : ! [v4] : ( ~ (u1_struct_0(v3) = v4) | ~ m2_relset_1(all_0_7_7, v0, v2) | ~ v1_funct_2(all_0_7_7, v0, v2) | ~ v1_funct_1(all_0_7_7) | ~ m1_group_2(v3, all_0_9_9) | ~ v1_group_1(v3) | k1_funct_1(all_0_7_7, v3) = v4) & ! [v3] : (v3 = all_0_7_7 | ~ m2_relset_1(v3, v0, v2) | ~ v1_funct_2(v3, v0, v2) | ~ v1_funct_1(v3) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & k1_funct_1(v3, v4) = v5 & u1_struct_0(v4) = v6 & m1_group_2(v4, all_0_9_9) & v1_group_1(v4))))
% 7.98/2.48 |
% 7.98/2.48 | Instantiating formula (60) with all_0_6_6, all_0_9_9 and discharging atoms m1_group_2(all_0_6_6, all_0_9_9), l1_group_1(all_0_9_9), v3_group_1(all_0_9_9), ~ v3_struct_0(all_0_9_9), yields:
% 7.98/2.48 | (86) l1_group_1(all_0_6_6)
% 7.98/2.48 |
% 7.98/2.48 | Instantiating formula (13) with all_0_6_6, all_0_9_9 and discharging atoms m1_group_2(all_0_6_6, all_0_9_9), l1_group_1(all_0_9_9), v3_group_1(all_0_9_9), ~ v3_struct_0(all_0_9_9), yields:
% 7.98/2.48 | (87) v3_group_1(all_0_6_6)
% 7.98/2.48 |
% 7.98/2.48 | Instantiating (85) with all_27_0_26, all_27_1_27, all_27_2_28 yields:
% 7.98/2.48 | (88) k1_group_3(all_0_9_9) = all_27_2_28 & k1_zfmisc_1(all_27_1_27) = all_27_0_26 & u1_struct_0(all_0_9_9) = all_27_1_27 & ! [v0] : ! [v1] : ( ~ (k1_funct_1(all_0_7_7, v0) = v1) | ~ m2_relset_1(all_0_7_7, all_27_2_28, all_27_0_26) | ~ v1_funct_2(all_0_7_7, all_27_2_28, all_27_0_26) | ~ v1_funct_1(all_0_7_7) | ~ m1_group_2(v0, all_0_9_9) | ~ v1_group_1(v0) | u1_struct_0(v0) = v1) & ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ m2_relset_1(all_0_7_7, all_27_2_28, all_27_0_26) | ~ v1_funct_2(all_0_7_7, all_27_2_28, all_27_0_26) | ~ v1_funct_1(all_0_7_7) | ~ m1_group_2(v0, all_0_9_9) | ~ v1_group_1(v0) | k1_funct_1(all_0_7_7, v0) = v1) & ! [v0] : (v0 = all_0_7_7 | ~ m2_relset_1(v0, all_27_2_28, all_27_0_26) | ~ v1_funct_2(v0, all_27_2_28, all_27_0_26) | ~ v1_funct_1(v0) | ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & k1_funct_1(v0, v1) = v2 & u1_struct_0(v1) = v3 & m1_group_2(v1, all_0_9_9) & v1_group_1(v1)))
% 7.98/2.48 |
% 7.98/2.48 | Applying alpha-rule on (88) yields:
% 7.98/2.48 | (89) ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ m2_relset_1(all_0_7_7, all_27_2_28, all_27_0_26) | ~ v1_funct_2(all_0_7_7, all_27_2_28, all_27_0_26) | ~ v1_funct_1(all_0_7_7) | ~ m1_group_2(v0, all_0_9_9) | ~ v1_group_1(v0) | k1_funct_1(all_0_7_7, v0) = v1)
% 7.98/2.48 | (90) k1_zfmisc_1(all_27_1_27) = all_27_0_26
% 7.98/2.48 | (91) u1_struct_0(all_0_9_9) = all_27_1_27
% 7.98/2.48 | (92) k1_group_3(all_0_9_9) = all_27_2_28
% 7.98/2.48 | (93) ! [v0] : (v0 = all_0_7_7 | ~ m2_relset_1(v0, all_27_2_28, all_27_0_26) | ~ v1_funct_2(v0, all_27_2_28, all_27_0_26) | ~ v1_funct_1(v0) | ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & k1_funct_1(v0, v1) = v2 & u1_struct_0(v1) = v3 & m1_group_2(v1, all_0_9_9) & v1_group_1(v1)))
% 7.98/2.48 | (94) ! [v0] : ! [v1] : ( ~ (k1_funct_1(all_0_7_7, v0) = v1) | ~ m2_relset_1(all_0_7_7, all_27_2_28, all_27_0_26) | ~ v1_funct_2(all_0_7_7, all_27_2_28, all_27_0_26) | ~ v1_funct_1(all_0_7_7) | ~ m1_group_2(v0, all_0_9_9) | ~ v1_group_1(v0) | u1_struct_0(v0) = v1)
% 7.98/2.48 |
% 7.98/2.48 | Instantiating (84) with all_34_0_31, all_34_1_32, all_34_2_33 yields:
% 7.98/2.48 | (95) k1_group_3(all_0_9_9) = all_34_2_33 & k1_zfmisc_1(all_34_1_32) = all_34_0_31 & u1_struct_0(all_0_9_9) = all_34_1_32 & m2_relset_1(all_0_7_7, all_34_2_33, all_34_0_31) & v1_funct_2(all_0_7_7, all_34_2_33, all_34_0_31)
% 7.98/2.48 |
% 7.98/2.48 | Applying alpha-rule on (95) yields:
% 7.98/2.48 | (96) u1_struct_0(all_0_9_9) = all_34_1_32
% 7.98/2.48 | (97) v1_funct_2(all_0_7_7, all_34_2_33, all_34_0_31)
% 7.98/2.48 | (98) k1_group_3(all_0_9_9) = all_34_2_33
% 7.98/2.48 | (99) k1_zfmisc_1(all_34_1_32) = all_34_0_31
% 7.98/2.48 | (100) m2_relset_1(all_0_7_7, all_34_2_33, all_34_0_31)
% 7.98/2.48 |
% 7.98/2.48 | Instantiating formula (37) with all_0_9_9, all_27_2_28, all_34_2_33 and discharging atoms k1_group_3(all_0_9_9) = all_34_2_33, k1_group_3(all_0_9_9) = all_27_2_28, yields:
% 7.98/2.48 | (101) all_34_2_33 = all_27_2_28
% 7.98/2.48 |
% 7.98/2.48 | Instantiating formula (26) with all_0_9_9, all_27_1_27, all_34_1_32 and discharging atoms u1_struct_0(all_0_9_9) = all_34_1_32, u1_struct_0(all_0_9_9) = all_27_1_27, yields:
% 7.98/2.48 | (102) all_34_1_32 = all_27_1_27
% 7.98/2.48 |
% 7.98/2.48 | From (102) and (99) follows:
% 7.98/2.48 | (103) k1_zfmisc_1(all_27_1_27) = all_34_0_31
% 7.98/2.48 |
% 7.98/2.48 | From (101) and (100) follows:
% 7.98/2.48 | (104) m2_relset_1(all_0_7_7, all_27_2_28, all_34_0_31)
% 7.98/2.48 |
% 7.98/2.48 | From (101) and (97) follows:
% 7.98/2.48 | (105) v1_funct_2(all_0_7_7, all_27_2_28, all_34_0_31)
% 7.98/2.48 |
% 7.98/2.48 | Instantiating formula (67) with all_27_1_27, all_34_0_31, all_27_0_26 and discharging atoms k1_zfmisc_1(all_27_1_27) = all_34_0_31, k1_zfmisc_1(all_27_1_27) = all_27_0_26, yields:
% 7.98/2.48 | (106) all_34_0_31 = all_27_0_26
% 7.98/2.48 |
% 7.98/2.48 | From (106) and (104) follows:
% 7.98/2.48 | (107) m2_relset_1(all_0_7_7, all_27_2_28, all_27_0_26)
% 7.98/2.48 |
% 7.98/2.48 | From (106) and (105) follows:
% 7.98/2.48 | (108) v1_funct_2(all_0_7_7, all_27_2_28, all_27_0_26)
% 7.98/2.48 |
% 7.98/2.49 | Instantiating formula (94) with all_0_5_5, all_0_6_6 and discharging atoms k1_funct_1(all_0_7_7, all_0_6_6) = all_0_5_5, m2_relset_1(all_0_7_7, all_27_2_28, all_27_0_26), v1_funct_2(all_0_7_7, all_27_2_28, all_27_0_26), v1_funct_1(all_0_7_7), m1_group_2(all_0_6_6, all_0_9_9), v1_group_1(all_0_6_6), yields:
% 7.98/2.49 | (109) u1_struct_0(all_0_6_6) = all_0_5_5
% 7.98/2.49 |
% 7.98/2.49 | Instantiating formula (19) with all_0_6_6 and discharging atoms l1_group_1(all_0_6_6), yields:
% 7.98/2.49 | (110) l1_struct_0(all_0_6_6)
% 7.98/2.49 |
% 7.98/2.49 | Instantiating formula (72) with all_0_6_6 and discharging atoms l1_group_1(all_0_6_6), v3_group_1(all_0_6_6), yields:
% 7.98/2.49 | (111) v3_struct_0(all_0_6_6) | ? [v0] : m1_group_2(v0, all_0_6_6)
% 7.98/2.49 |
% 7.98/2.49 | Instantiating formula (69) with all_0_5_5, all_0_6_6 and discharging atoms u1_struct_0(all_0_6_6) = all_0_5_5, l1_group_1(all_0_6_6), yields:
% 7.98/2.49 | (112) v3_struct_0(all_0_6_6) | ? [v0] : (k2_group_1(all_0_6_6) = v0 & m1_subset_1(v0, all_0_5_5))
% 7.98/2.49 |
% 7.98/2.49 | Instantiating formula (71) with all_0_5_5, all_0_6_6 and discharging atoms u1_struct_0(all_0_6_6) = all_0_5_5, l1_struct_0(all_0_6_6), yields:
% 7.98/2.49 | (113) v3_struct_0(all_0_6_6) | ? [v0] : ? [v1] : (k1_zfmisc_1(all_0_5_5) = v0 & m1_subset_1(v1, v0) & ~ v1_xboole_0(v1))
% 7.98/2.49 |
% 7.98/2.49 +-Applying beta-rule and splitting (111), into two cases.
% 7.98/2.49 |-Branch one:
% 7.98/2.49 | (114) v3_struct_0(all_0_6_6)
% 7.98/2.49 |
% 7.98/2.49 | Instantiating formula (57) with all_0_6_6, all_0_9_9 and discharging atoms m1_group_2(all_0_6_6, all_0_9_9), l1_group_1(all_0_9_9), v3_group_1(all_0_9_9), v3_struct_0(all_0_6_6), ~ v3_struct_0(all_0_9_9), yields:
% 7.98/2.49 | (115) $false
% 7.98/2.49 |
% 7.98/2.49 |-The branch is then unsatisfiable
% 7.98/2.49 |-Branch two:
% 7.98/2.49 | (116) ~ v3_struct_0(all_0_6_6)
% 7.98/2.49 | (117) ? [v0] : m1_group_2(v0, all_0_6_6)
% 7.98/2.49 |
% 7.98/2.49 +-Applying beta-rule and splitting (113), into two cases.
% 7.98/2.49 |-Branch one:
% 7.98/2.49 | (114) v3_struct_0(all_0_6_6)
% 7.98/2.49 |
% 7.98/2.49 | Using (114) and (116) yields:
% 7.98/2.49 | (115) $false
% 7.98/2.49 |
% 7.98/2.49 |-The branch is then unsatisfiable
% 7.98/2.49 |-Branch two:
% 7.98/2.49 | (116) ~ v3_struct_0(all_0_6_6)
% 7.98/2.49 | (121) ? [v0] : ? [v1] : (k1_zfmisc_1(all_0_5_5) = v0 & m1_subset_1(v1, v0) & ~ v1_xboole_0(v1))
% 7.98/2.49 |
% 7.98/2.49 | Instantiating (121) with all_141_0_49, all_141_1_50 yields:
% 7.98/2.49 | (122) k1_zfmisc_1(all_0_5_5) = all_141_1_50 & m1_subset_1(all_141_0_49, all_141_1_50) & ~ v1_xboole_0(all_141_0_49)
% 7.98/2.49 |
% 7.98/2.49 | Applying alpha-rule on (122) yields:
% 7.98/2.49 | (123) k1_zfmisc_1(all_0_5_5) = all_141_1_50
% 7.98/2.49 | (124) m1_subset_1(all_141_0_49, all_141_1_50)
% 7.98/2.49 | (125) ~ v1_xboole_0(all_141_0_49)
% 7.98/2.49 |
% 7.98/2.49 +-Applying beta-rule and splitting (112), into two cases.
% 7.98/2.49 |-Branch one:
% 7.98/2.49 | (114) v3_struct_0(all_0_6_6)
% 7.98/2.49 |
% 7.98/2.49 | Using (114) and (116) yields:
% 7.98/2.49 | (115) $false
% 7.98/2.49 |
% 7.98/2.49 |-The branch is then unsatisfiable
% 7.98/2.49 |-Branch two:
% 7.98/2.49 | (116) ~ v3_struct_0(all_0_6_6)
% 7.98/2.49 | (129) ? [v0] : (k2_group_1(all_0_6_6) = v0 & m1_subset_1(v0, all_0_5_5))
% 7.98/2.49 |
% 7.98/2.49 | Instantiating (129) with all_146_0_51 yields:
% 7.98/2.49 | (130) k2_group_1(all_0_6_6) = all_146_0_51 & m1_subset_1(all_146_0_51, all_0_5_5)
% 7.98/2.49 |
% 7.98/2.49 | Applying alpha-rule on (130) yields:
% 7.98/2.49 | (131) k2_group_1(all_0_6_6) = all_146_0_51
% 7.98/2.49 | (132) m1_subset_1(all_146_0_51, all_0_5_5)
% 7.98/2.49 |
% 7.98/2.49 | Instantiating formula (20) with all_146_0_51, all_0_6_6, all_0_8_8, all_0_9_9 and discharging atoms k2_group_1(all_0_6_6) = all_146_0_51, k2_group_1(all_0_9_9) = all_0_8_8, m1_group_2(all_0_6_6, all_0_9_9), l1_group_1(all_0_9_9), v4_group_1(all_0_9_9), v3_group_1(all_0_9_9), ~ v3_struct_0(all_0_9_9), yields:
% 7.98/2.49 | (133) all_146_0_51 = all_0_8_8
% 7.98/2.49 |
% 7.98/2.49 | Instantiating formula (34) with all_141_1_50, all_0_5_5 and discharging atoms k1_zfmisc_1(all_0_5_5) = all_141_1_50, yields:
% 7.98/2.49 | (134) ? [v0] : (v1_xboole_0(v0) & m1_subset_1(v0, all_141_1_50))
% 7.98/2.49 |
% 7.98/2.49 | Instantiating formula (61) with all_0_5_5, all_146_0_51 and discharging atoms m1_subset_1(all_146_0_51, all_0_5_5), yields:
% 7.98/2.49 | (135) v1_xboole_0(all_0_5_5) | r2_hidden(all_146_0_51, all_0_5_5)
% 7.98/2.49 |
% 7.98/2.49 | Instantiating (134) with all_154_0_52 yields:
% 7.98/2.49 | (136) v1_xboole_0(all_154_0_52) & m1_subset_1(all_154_0_52, all_141_1_50)
% 7.98/2.49 |
% 7.98/2.49 | Applying alpha-rule on (136) yields:
% 7.98/2.49 | (137) v1_xboole_0(all_154_0_52)
% 7.98/2.49 | (138) m1_subset_1(all_154_0_52, all_141_1_50)
% 7.98/2.49 |
% 7.98/2.49 +-Applying beta-rule and splitting (135), into two cases.
% 7.98/2.49 |-Branch one:
% 7.98/2.49 | (139) v1_xboole_0(all_0_5_5)
% 7.98/2.49 |
% 7.98/2.49 | Instantiating formula (32) with all_154_0_52 and discharging atoms v1_xboole_0(all_154_0_52), yields:
% 7.98/2.49 | (140) all_154_0_52 = k1_xboole_0
% 7.98/2.49 |
% 7.98/2.49 | Instantiating formula (44) with all_0_5_5, all_154_0_52 and discharging atoms v1_xboole_0(all_154_0_52), v1_xboole_0(all_0_5_5), yields:
% 7.98/2.49 | (141) all_154_0_52 = all_0_5_5
% 7.98/2.49 |
% 7.98/2.49 | Combining equations (140,141) yields a new equation:
% 7.98/2.49 | (142) all_0_5_5 = k1_xboole_0
% 7.98/2.49 |
% 7.98/2.49 | From (142) and (109) follows:
% 7.98/2.49 | (143) u1_struct_0(all_0_6_6) = k1_xboole_0
% 7.98/2.49 |
% 7.98/2.49 | From (142) and (139) follows:
% 7.98/2.49 | (56) v1_xboole_0(k1_xboole_0)
% 7.98/2.49 |
% 7.98/2.49 | Instantiating formula (59) with k1_xboole_0, all_0_6_6 and discharging atoms u1_struct_0(all_0_6_6) = k1_xboole_0, l1_struct_0(all_0_6_6), v1_xboole_0(k1_xboole_0), ~ v3_struct_0(all_0_6_6), yields:
% 7.98/2.49 | (115) $false
% 7.98/2.49 |
% 7.98/2.49 |-The branch is then unsatisfiable
% 7.98/2.49 |-Branch two:
% 7.98/2.49 | (146) ~ v1_xboole_0(all_0_5_5)
% 7.98/2.49 | (147) r2_hidden(all_146_0_51, all_0_5_5)
% 7.98/2.49 |
% 7.98/2.49 | From (133) and (147) follows:
% 7.98/2.49 | (148) r2_hidden(all_0_8_8, all_0_5_5)
% 7.98/2.49 |
% 7.98/2.49 | Using (148) and (66) yields:
% 7.98/2.49 | (115) $false
% 7.98/2.49 |
% 7.98/2.49 |-The branch is then unsatisfiable
% 7.98/2.49 % SZS output end Proof for theBenchmark
% 7.98/2.49
% 7.98/2.49 1896ms
%------------------------------------------------------------------------------