TSTP Solution File: GRP645+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GRP645+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n022.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 08:43:18 EDT 2022
% Result : Theorem 4.95s 1.86s
% Output : Proof 7.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP645+1 : TPTP v8.1.0. Released v3.4.0.
% 0.07/0.14 % Command : ePrincess-casc -timeout=%d %s
% 0.15/0.35 % Computer : n022.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Mon Jun 13 22:35:48 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.60/0.63 ____ _
% 0.60/0.63 ___ / __ \_____(_)___ ________ __________
% 0.60/0.63 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.60/0.63 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.60/0.63 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.60/0.63
% 0.60/0.63 A Theorem Prover for First-Order Logic
% 0.60/0.63 (ePrincess v.1.0)
% 0.60/0.63
% 0.60/0.63 (c) Philipp Rümmer, 2009-2015
% 0.66/0.63 (c) Peter Backeman, 2014-2015
% 0.66/0.63 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.66/0.63 Free software under GNU Lesser General Public License (LGPL).
% 0.66/0.63 Bug reports to peter@backeman.se
% 0.66/0.63
% 0.66/0.63 For more information, visit http://user.uu.se/~petba168/breu/
% 0.66/0.63
% 0.66/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.66/0.70 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.95/1.09 Prover 0: Preprocessing ...
% 3.49/1.47 Prover 0: Warning: ignoring some quantifiers
% 3.57/1.50 Prover 0: Constructing countermodel ...
% 4.95/1.86 Prover 0: proved (1161ms)
% 4.95/1.86
% 4.95/1.86 No countermodel exists, formula is valid
% 4.95/1.86 % SZS status Theorem for theBenchmark
% 4.95/1.86
% 4.95/1.86 Generating proof ... Warning: ignoring some quantifiers
% 6.71/2.27 found it (size 33)
% 6.71/2.27
% 6.71/2.27 % SZS output start Proof for theBenchmark
% 6.71/2.27 Assumed formulas after preprocessing and simplification:
% 6.71/2.27 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ( ~ (v8 = v6) & k1_latsubgr(v0) = v1 & k1_funct_1(v1, v5) = v6 & k1_funct_1(v1, v4) = v7 & k1_funct_1(v1, v2) = v3 & k9_group_2(v0, v2, v4) = v5 & k3_xboole_0(v3, v7) = v8 & l1_struct_0(v12) & l1_struct_0(v9) & v1_xboole_0(v11) & v1_xboole_0(k1_xboole_0) & m1_group_2(v4, v0) & m1_group_2(v2, v0) & v1_group_1(v4) & v1_group_1(v2) & l1_group_1(v13) & l1_group_1(v0) & v4_group_1(v0) & v3_group_1(v0) & ~ v1_xboole_0(v10) & ~ v3_struct_0(v9) & ~ v3_struct_0(v0) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (k1_latsubgr(v14) = v15) | ~ (k1_funct_1(v15, v18) = v19) | ~ (k1_funct_1(v15, v16) = v17) | ~ (k3_xboole_0(v17, v19) = v20) | ~ m1_group_2(v18, v14) | ~ m1_group_2(v16, v14) | ~ v1_group_1(v18) | ~ v1_group_1(v16) | ~ l1_group_1(v14) | ~ v4_group_1(v14) | ~ v3_group_1(v14) | v3_struct_0(v14) | ? [v21] : (k9_group_2(v14, v16, v18) = v21 & u1_struct_0(v21) = v20)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (k1_latsubgr(v14) = v15) | ~ (k1_funct_1(v15, v16) = v17) | ~ (k9_group_2(v14, v16, v18) = v19) | ~ m1_group_2(v18, v14) | ~ m1_group_2(v16, v14) | ~ v1_group_1(v18) | ~ v1_group_1(v16) | ~ l1_group_1(v14) | ~ v4_group_1(v14) | ~ v3_group_1(v14) | v3_struct_0(v14) | ? [v20] : ? [v21] : (k1_funct_1(v15, v18) = v21 & k3_xboole_0(v17, v21) = v20 & u1_struct_0(v19) = v20)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v15 | ~ (g1_group_1(v17, v18) = v16) | ~ (g1_group_1(v14, v15) = v16) | ~ v1_funct_1(v15) | ? [v19] : (k2_zfmisc_1(v14, v14) = v19 & ( ~ v1_funct_2(v15, v19, v14) | ~ m1_relset_1(v15, v19, v14)))) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v17 = v14 | ~ (g1_group_1(v17, v18) = v16) | ~ (g1_group_1(v14, v15) = v16) | ~ v1_funct_1(v15) | ? [v19] : (k2_zfmisc_1(v14, v14) = v19 & ( ~ v1_funct_2(v15, v19, v14) | ~ m1_relset_1(v15, v19, v14)))) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v15 = v14 | ~ (k8_group_2(v18, v17, v16) = v15) | ~ (k8_group_2(v18, v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v15 = v14 | ~ (k9_group_2(v18, v17, v16) = v15) | ~ (k9_group_2(v18, v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = v14 | ~ (u1_struct_0(v14) = v15) | ~ (u1_group_1(v14) = v16) | ~ (g1_group_1(v15, v16) = v17) | ~ v1_group_1(v14) | ~ l1_group_1(v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (k1_funct_1(v17, v16) = v15) | ~ (k1_funct_1(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (k3_xboole_0(v17, v16) = v15) | ~ (k3_xboole_0(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (k2_zfmisc_1(v17, v16) = v15) | ~ (k2_zfmisc_1(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (g1_group_1(v17, v16) = v15) | ~ (g1_group_1(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (k8_group_2(v14, v15, v16) = v17) | ~ m1_group_2(v16, v14) | ~ m1_group_2(v15, v14) | ~ l1_group_1(v14) | ~ v4_group_1(v14) | ~ v3_group_1(v14) | k9_group_2(v14, v15, v16) = v17 | v3_struct_0(v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (k8_group_2(v14, v15, v16) = v17) | ~ m1_group_2(v16, v14) | ~ m1_group_2(v15, v14) | ~ l1_group_1(v14) | ~ v4_group_1(v14) | ~ v3_group_1(v14) | m1_group_2(v17, v14) | v3_struct_0(v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (k8_group_2(v14, v15, v16) = v17) | ~ m1_group_2(v16, v14) | ~ m1_group_2(v15, v14) | ~ l1_group_1(v14) | ~ v4_group_1(v14) | ~ v3_group_1(v14) | v1_group_1(v17) | v3_struct_0(v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (k9_group_2(v14, v16, v15) = v17) | ~ m1_group_2(v16, v14) | ~ m1_group_2(v15, v14) | ~ l1_group_1(v14) | ~ v4_group_1(v14) | ~ v3_group_1(v14) | k9_group_2(v14, v15, v16) = v17 | v3_struct_0(v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (k9_group_2(v14, v15, v16) = v17) | ~ m1_group_2(v16, v14) | ~ m1_group_2(v15, v14) | ~ l1_group_1(v14) | ~ v4_group_1(v14) | ~ v3_group_1(v14) | k8_group_2(v14, v15, v16) = v17 | v3_struct_0(v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (k9_group_2(v14, v15, v16) = v17) | ~ m1_group_2(v16, v14) | ~ m1_group_2(v15, v14) | ~ l1_group_1(v14) | ~ v4_group_1(v14) | ~ v3_group_1(v14) | k9_group_2(v14, v16, v15) = v17 | v3_struct_0(v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (k9_group_2(v14, v15, v16) = v17) | ~ m1_group_2(v16, v14) | ~ m1_group_2(v15, v14) | ~ l1_group_1(v14) | ~ v4_group_1(v14) | ~ v3_group_1(v14) | m1_group_2(v17, v14) | v3_struct_0(v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (k9_group_2(v14, v15, v16) = v17) | ~ m1_group_2(v16, v14) | ~ m1_group_2(v15, v14) | ~ l1_group_1(v14) | ~ v4_group_1(v14) | ~ v3_group_1(v14) | v1_group_1(v17) | v3_struct_0(v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (k2_zfmisc_1(v14, v15) = v17) | ~ m2_relset_1(v16, v14, v15) | ? [v18] : (k1_zfmisc_1(v17) = v18 & m1_subset_1(v16, v18))) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (k1_zfmisc_1(v16) = v17) | ~ v1_xboole_0(v16) | ~ m1_subset_1(v15, v17) | ~ r2_hidden(v14, v15)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (k1_zfmisc_1(v16) = v17) | ~ m1_subset_1(v15, v17) | ~ r2_hidden(v14, v15) | m1_subset_1(v14, v16)) & ? [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (k2_zfmisc_1(v15, v16) = v17) | v1_relat_1(v14) | ? [v18] : (k1_zfmisc_1(v17) = v18 & ~ m1_subset_1(v14, v18))) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (k1_latsubgr(v16) = v15) | ~ (k1_latsubgr(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (k1_group_3(v16) = v15) | ~ (k1_group_3(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (k1_zfmisc_1(v16) = v15) | ~ (k1_zfmisc_1(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (u1_struct_0(v16) = v15) | ~ (u1_struct_0(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (u1_group_1(v16) = v15) | ~ (u1_group_1(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (k3_xboole_0(v15, v14) = v16) | k3_xboole_0(v14, v15) = v16) & ! [v14] : ! [v15] : ! [v16] : ( ~ (k3_xboole_0(v14, v15) = v16) | k3_xboole_0(v15, v14) = v16) & ! [v14] : ! [v15] : ! [v16] : ( ~ (k2_zfmisc_1(v15, v15) = v16) | ~ (u1_struct_0(v14) = v15) | ~ l1_group_1(v14) | ? [v17] : (u1_group_1(v14) = v17 & m2_relset_1(v17, v16, v15) & v1_funct_2(v17, v16, v15) & v1_funct_1(v17))) & ! [v14] : ! [v15] : ! [v16] : ( ~ (k2_zfmisc_1(v14, v15) = v16) | ~ v1_xboole_0(v16) | v1_xboole_0(v15) | v1_xboole_0(v14)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (k1_zfmisc_1(v15) = v16) | ~ r1_tarski(v14, v15) | m1_subset_1(v14, v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (k1_zfmisc_1(v15) = v16) | ~ m1_subset_1(v14, v16) | r1_tarski(v14, v15)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (g1_group_1(v14, v15) = v16) | ~ v1_funct_1(v15) | v1_group_1(v16) | ? [v17] : (k2_zfmisc_1(v14, v14) = v17 & ( ~ v1_funct_2(v15, v17, v14) | ~ m1_relset_1(v15, v17, v14)))) & ! [v14] : ! [v15] : ! [v16] : ( ~ (g1_group_1(v14, v15) = v16) | ~ v1_funct_1(v15) | l1_group_1(v16) | ? [v17] : (k2_zfmisc_1(v14, v14) = v17 & ( ~ v1_funct_2(v15, v17, v14) | ~ m1_relset_1(v15, v17, v14)))) & ! [v14] : ! [v15] : ! [v16] : ( ~ m2_relset_1(v16, v14, v15) | m1_relset_1(v16, v14, v15)) & ! [v14] : ! [v15] : ! [v16] : ( ~ v1_xboole_0(v16) | ~ v1_funct_2(v16, v14, v15) | ~ v1_funct_1(v16) | ~ m1_relset_1(v16, v14, v15) | v1_xboole_0(v15) | v1_xboole_0(v14)) & ! [v14] : ! [v15] : ! [v16] : ( ~ v1_funct_2(v16, v14, v15) | ~ v1_funct_1(v16) | ~ m1_relset_1(v16, v14, v15) | v1_xboole_0(v15) | v1_xboole_0(v14) | v1_partfun1(v16, v14, v15)) & ! [v14] : ! [v15] : ! [v16] : ( ~ v1_funct_2(v16, v14, v15) | ~ v1_funct_1(v16) | ~ m1_relset_1(v16, v14, v15) | v1_xboole_0(v15) | v1_partfun1(v16, v14, v15)) & ! [v14] : ! [v15] : ! [v16] : ( ~ v1_partfun1(v16, v14, v15) | ~ v1_funct_1(v16) | ~ m1_relset_1(v16, v14, v15) | v1_funct_2(v16, v14, v15)) & ! [v14] : ! [v15] : ! [v16] : ( ~ m1_relset_1(v16, v14, v15) | m2_relset_1(v16, v14, v15)) & ! [v14] : ! [v15] : (v15 = v14 | ~ (k3_xboole_0(v14, v14) = v15)) & ! [v14] : ! [v15] : (v15 = v14 | ~ v1_xboole_0(v15) | ~ v1_xboole_0(v14)) & ! [v14] : ! [v15] : (v15 = k1_xboole_0 | ~ (k3_xboole_0(v14, k1_xboole_0) = v15)) & ! [v14] : ! [v15] : ( ~ (k1_latsubgr(v14) = v15) | ~ l1_group_1(v14) | ~ v4_group_1(v14) | ~ v3_group_1(v14) | v1_funct_1(v15) | v3_struct_0(v14)) & ! [v14] : ! [v15] : ( ~ (k1_latsubgr(v14) = v15) | ~ l1_group_1(v14) | ~ v4_group_1(v14) | ~ v3_group_1(v14) | v3_struct_0(v14) | ? [v16] : ? [v17] : ? [v18] : (k1_group_3(v14) = v16 & k1_zfmisc_1(v17) = v18 & u1_struct_0(v14) = v17 & m2_relset_1(v15, v16, v18) & v1_funct_2(v15, v16, v18))) & ! [v14] : ! [v15] : ( ~ (k1_latsubgr(v14) = v15) | ~ l1_group_1(v14) | ~ v4_group_1(v14) | ~ v3_group_1(v14) | v3_struct_0(v14) | ? [v16] : ? [v17] : ? [v18] : (k1_group_3(v14) = v16 & k1_zfmisc_1(v17) = v18 & u1_struct_0(v14) = v17 & ! [v19] : ! [v20] : ( ~ (k1_funct_1(v15, v19) = v20) | ~ m2_relset_1(v15, v16, v18) | ~ v1_funct_2(v15, v16, v18) | ~ v1_funct_1(v15) | ~ m1_group_2(v19, v14) | ~ v1_group_1(v19) | u1_struct_0(v19) = v20) & ! [v19] : ! [v20] : ( ~ (u1_struct_0(v19) = v20) | ~ m2_relset_1(v15, v16, v18) | ~ v1_funct_2(v15, v16, v18) | ~ v1_funct_1(v15) | ~ m1_group_2(v19, v14) | ~ v1_group_1(v19) | k1_funct_1(v15, v19) = v20) & ! [v19] : (v19 = v15 | ~ m2_relset_1(v19, v16, v18) | ~ v1_funct_2(v19, v16, v18) | ~ v1_funct_1(v19) | ? [v20] : ? [v21] : ? [v22] : ( ~ (v22 = v21) & k1_funct_1(v19, v20) = v21 & u1_struct_0(v20) = v22 & m1_group_2(v20, v14) & v1_group_1(v20))))) & ! [v14] : ! [v15] : ( ~ (k1_group_3(v14) = v15) | ~ v1_xboole_0(v15) | ~ l1_group_1(v14) | ~ v4_group_1(v14) | ~ v3_group_1(v14) | v3_struct_0(v14)) & ! [v14] : ! [v15] : ( ~ (k1_group_3(v14) = v15) | ~ l1_group_1(v14) | ~ v4_group_1(v14) | ~ v3_group_1(v14) | v3_struct_0(v14) | ? [v16] : ? [v17] : ? [v18] : (k1_latsubgr(v14) = v18 & k1_zfmisc_1(v16) = v17 & u1_struct_0(v14) = v16 & ! [v19] : ! [v20] : ( ~ (k1_funct_1(v18, v19) = v20) | ~ m2_relset_1(v18, v15, v17) | ~ v1_funct_2(v18, v15, v17) | ~ v1_funct_1(v18) | ~ m1_group_2(v19, v14) | ~ v1_group_1(v19) | u1_struct_0(v19) = v20) & ! [v19] : ! [v20] : ( ~ (u1_struct_0(v19) = v20) | ~ m2_relset_1(v18, v15, v17) | ~ v1_funct_2(v18, v15, v17) | ~ v1_funct_1(v18) | ~ m1_group_2(v19, v14) | ~ v1_group_1(v19) | k1_funct_1(v18, v19) = v20) & ! [v19] : (v19 = v18 | ~ m2_relset_1(v19, v15, v17) | ~ v1_funct_2(v19, v15, v17) | ~ v1_funct_1(v19) | ? [v20] : ? [v21] : ? [v22] : ( ~ (v22 = v21) & k1_funct_1(v19, v20) = v21 & u1_struct_0(v20) = v22 & m1_group_2(v20, v14) & v1_group_1(v20))))) & ! [v14] : ! [v15] : ( ~ (k1_group_3(v14) = v15) | ~ l1_group_1(v14) | ~ v4_group_1(v14) | ~ v3_group_1(v14) | v3_struct_0(v14) | ? [v16] : ? [v17] : ? [v18] : (k1_latsubgr(v14) = v16 & k1_zfmisc_1(v17) = v18 & u1_struct_0(v14) = v17 & m2_relset_1(v16, v15, v18) & v1_funct_2(v16, v15, v18) & v1_funct_1(v16))) & ! [v14] : ! [v15] : ( ~ (k1_zfmisc_1(v14) = v15) | ~ v1_xboole_0(v15)) & ! [v14] : ! [v15] : ( ~ (k1_zfmisc_1(v14) = v15) | v1_xboole_0(v14) | ? [v16] : (m1_subset_1(v16, v15) & ~ v1_xboole_0(v16))) & ! [v14] : ! [v15] : ( ~ (k1_zfmisc_1(v14) = v15) | ? [v16] : (v1_xboole_0(v16) & m1_subset_1(v16, v15))) & ! [v14] : ! [v15] : ( ~ (u1_struct_0(v14) = v15) | ~ l1_struct_0(v14) | ~ v1_xboole_0(v15) | v3_struct_0(v14)) & ! [v14] : ! [v15] : ( ~ (u1_struct_0(v14) = v15) | ~ l1_struct_0(v14) | v3_struct_0(v14) | ? [v16] : ? [v17] : (k1_zfmisc_1(v15) = v16 & m1_subset_1(v17, v16) & ~ v1_xboole_0(v17))) & ! [v14] : ! [v15] : ( ~ (u1_struct_0(v14) = v15) | ~ l1_group_1(v14) | ~ v4_group_1(v14) | ~ v3_group_1(v14) | v3_struct_0(v14) | ? [v16] : ? [v17] : ? [v18] : (k1_latsubgr(v14) = v18 & k1_group_3(v14) = v16 & k1_zfmisc_1(v15) = v17 & ! [v19] : ! [v20] : ( ~ (k1_funct_1(v18, v19) = v20) | ~ m2_relset_1(v18, v16, v17) | ~ v1_funct_2(v18, v16, v17) | ~ v1_funct_1(v18) | ~ m1_group_2(v19, v14) | ~ v1_group_1(v19) | u1_struct_0(v19) = v20) & ! [v19] : ! [v20] : ( ~ (u1_struct_0(v19) = v20) | ~ m2_relset_1(v18, v16, v17) | ~ v1_funct_2(v18, v16, v17) | ~ v1_funct_1(v18) | ~ m1_group_2(v19, v14) | ~ v1_group_1(v19) | k1_funct_1(v18, v19) = v20) & ! [v19] : (v19 = v18 | ~ m2_relset_1(v19, v16, v17) | ~ v1_funct_2(v19, v16, v17) | ~ v1_funct_1(v19) | ? [v20] : ? [v21] : ? [v22] : ( ~ (v22 = v21) & k1_funct_1(v19, v20) = v21 & u1_struct_0(v20) = v22 & m1_group_2(v20, v14) & v1_group_1(v20))))) & ! [v14] : ! [v15] : ( ~ (u1_struct_0(v14) = v15) | ~ l1_group_1(v14) | ~ v4_group_1(v14) | ~ v3_group_1(v14) | v3_struct_0(v14) | ? [v16] : ? [v17] : ? [v18] : (k1_latsubgr(v14) = v16 & k1_group_3(v14) = v17 & k1_zfmisc_1(v15) = v18 & m2_relset_1(v16, v17, v18) & v1_funct_2(v16, v17, v18) & v1_funct_1(v16))) & ! [v14] : ! [v15] : ( ~ (u1_struct_0(v14) = v15) | ~ l1_group_1(v14) | ? [v16] : ? [v17] : (k2_zfmisc_1(v15, v15) = v17 & u1_group_1(v14) = v16 & m2_relset_1(v16, v17, v15) & v1_funct_2(v16, v17, v15) & v1_funct_1(v16))) & ! [v14] : ! [v15] : ( ~ (u1_group_1(v14) = v15) | ~ l1_group_1(v14) | v1_funct_1(v15)) & ! [v14] : ! [v15] : ( ~ (u1_group_1(v14) = v15) | ~ l1_group_1(v14) | ? [v16] : ? [v17] : (k2_zfmisc_1(v16, v16) = v17 & u1_struct_0(v14) = v16 & m2_relset_1(v15, v17, v16) & v1_funct_2(v15, v17, v16))) & ! [v14] : ! [v15] : ( ~ v1_xboole_0(v15) | ~ r2_hidden(v14, v15)) & ! [v14] : ! [v15] : ( ~ m1_subset_1(v14, v15) | v1_xboole_0(v15) | r2_hidden(v14, v15)) & ! [v14] : ! [v15] : ( ~ r2_hidden(v15, v14) | ~ r2_hidden(v14, v15)) & ! [v14] : ! [v15] : ( ~ r2_hidden(v14, v15) | m1_subset_1(v14, v15)) & ! [v14] : ! [v15] : ( ~ m1_group_2(v15, v14) | ~ l1_group_1(v14) | ~ v3_group_1(v14) | ~ v3_struct_0(v15) | v3_struct_0(v14)) & ! [v14] : ! [v15] : ( ~ m1_group_2(v15, v14) | ~ l1_group_1(v14) | ~ v3_group_1(v14) | l1_group_1(v15) | v3_struct_0(v14)) & ! [v14] : ! [v15] : ( ~ m1_group_2(v15, v14) | ~ l1_group_1(v14) | ~ v3_group_1(v14) | v3_group_1(v15) | v3_struct_0(v14)) & ! [v14] : (v14 = k1_xboole_0 | ~ v1_xboole_0(v14)) & ! [v14] : ( ~ l1_group_1(v14) | ~ v3_group_1(v14) | v3_struct_0(v14) | ? [v15] : m1_group_2(v15, v14)) & ! [v14] : ( ~ l1_group_1(v14) | l1_struct_0(v14)) & ? [v14] : ? [v15] : ? [v16] : m2_relset_1(v16, v14, v15) & ? [v14] : ? [v15] : ? [v16] : m1_relset_1(v16, v14, v15) & ? [v14] : ? [v15] : ? [v16] : (v1_relat_1(v16) & v1_funct_2(v16, v14, v15) & v1_funct_1(v16) & m1_relset_1(v16, v14, v15)) & ? [v14] : ? [v15] : ? [v16] : (v1_relat_1(v16) & v1_funct_1(v16) & m1_relset_1(v16, v14, v15)) & ? [v14] : ? [v15] : m1_subset_1(v15, v14) & ? [v14] : r1_tarski(v14, v14))
% 7.13/2.32 | 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 yields:
% 7.13/2.32 | (1) ~ (all_0_5_5 = all_0_7_7) & k1_latsubgr(all_0_13_13) = all_0_12_12 & k1_funct_1(all_0_12_12, all_0_8_8) = all_0_7_7 & k1_funct_1(all_0_12_12, all_0_9_9) = all_0_6_6 & k1_funct_1(all_0_12_12, all_0_11_11) = all_0_10_10 & k9_group_2(all_0_13_13, all_0_11_11, all_0_9_9) = all_0_8_8 & k3_xboole_0(all_0_10_10, 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_9_9, all_0_13_13) & m1_group_2(all_0_11_11, all_0_13_13) & v1_group_1(all_0_9_9) & v1_group_1(all_0_11_11) & l1_group_1(all_0_0_0) & l1_group_1(all_0_13_13) & v4_group_1(all_0_13_13) & v3_group_1(all_0_13_13) & ~ v1_xboole_0(all_0_3_3) & ~ v3_struct_0(all_0_4_4) & ~ v3_struct_0(all_0_13_13) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (k1_latsubgr(v0) = v1) | ~ (k1_funct_1(v1, v4) = v5) | ~ (k1_funct_1(v1, v2) = v3) | ~ (k3_xboole_0(v3, v5) = v6) | ~ m1_group_2(v4, v0) | ~ m1_group_2(v2, v0) | ~ v1_group_1(v4) | ~ v1_group_1(v2) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v7] : (k9_group_2(v0, v2, v4) = v7 & u1_struct_0(v7) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (k1_latsubgr(v0) = v1) | ~ (k1_funct_1(v1, v2) = v3) | ~ (k9_group_2(v0, v2, v4) = v5) | ~ m1_group_2(v4, v0) | ~ m1_group_2(v2, v0) | ~ v1_group_1(v4) | ~ v1_group_1(v2) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v6] : ? [v7] : (k1_funct_1(v1, v4) = v7 & k3_xboole_0(v3, v7) = v6 & u1_struct_0(v5) = v6)) & ! [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] : ! [v4] : (v1 = v0 | ~ (k8_group_2(v4, v3, v2) = v1) | ~ (k8_group_2(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (k9_group_2(v4, v3, v2) = v1) | ~ (k9_group_2(v4, v3, v2) = 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 | ~ (k3_xboole_0(v3, v2) = v1) | ~ (k3_xboole_0(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] : ( ~ (k8_group_2(v0, v1, v2) = v3) | ~ m1_group_2(v2, v0) | ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | k9_group_2(v0, v1, v2) = v3 | v3_struct_0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k8_group_2(v0, v1, v2) = v3) | ~ m1_group_2(v2, v0) | ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | m1_group_2(v3, v0) | v3_struct_0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k8_group_2(v0, v1, v2) = v3) | ~ m1_group_2(v2, v0) | ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v1_group_1(v3) | v3_struct_0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k9_group_2(v0, v2, v1) = v3) | ~ m1_group_2(v2, v0) | ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | k9_group_2(v0, v1, v2) = v3 | v3_struct_0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k9_group_2(v0, v1, v2) = v3) | ~ m1_group_2(v2, v0) | ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | k8_group_2(v0, v1, v2) = v3 | v3_struct_0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k9_group_2(v0, v1, v2) = v3) | ~ m1_group_2(v2, v0) | ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | k9_group_2(v0, v2, v1) = v3 | v3_struct_0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k9_group_2(v0, v1, v2) = v3) | ~ m1_group_2(v2, v0) | ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | m1_group_2(v3, v0) | v3_struct_0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k9_group_2(v0, v1, v2) = v3) | ~ m1_group_2(v2, v0) | ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v1_group_1(v3) | v3_struct_0(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 | ~ (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] : ( ~ (k3_xboole_0(v1, v0) = v2) | k3_xboole_0(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k3_xboole_0(v0, v1) = v2) | k3_xboole_0(v1, v0) = v2) & ! [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 | ~ (k3_xboole_0(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ v1_xboole_0(v1) | ~ v1_xboole_0(v0)) & ! [v0] : ! [v1] : (v1 = k1_xboole_0 | ~ (k3_xboole_0(v0, k1_xboole_0) = v1)) & ! [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) | ? [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)
% 7.13/2.35 |
% 7.13/2.35 | Applying alpha-rule on (1) yields:
% 7.13/2.35 | (2) ! [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)))
% 7.13/2.35 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (k3_xboole_0(v0, v1) = v2) | k3_xboole_0(v1, v0) = v2)
% 7.13/2.35 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (k3_xboole_0(v1, v0) = v2) | k3_xboole_0(v0, v1) = v2)
% 7.13/2.35 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_zfmisc_1(v1) = v2) | ~ m1_subset_1(v0, v2) | r1_tarski(v0, v1))
% 7.13/2.35 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_zfmisc_1(v1) = v2) | ~ r1_tarski(v0, v1) | m1_subset_1(v0, v2))
% 7.13/2.35 | (7) ! [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))
% 7.13/2.35 | (8) ! [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)))
% 7.13/2.35 | (9) ~ v3_struct_0(all_0_13_13)
% 7.13/2.35 | (10) ! [v0] : ! [v1] : ( ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v3_group_1(v0) | ~ v3_struct_0(v1) | v3_struct_0(v0))
% 7.13/2.35 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (k1_latsubgr(v0) = v1) | ~ (k1_funct_1(v1, v4) = v5) | ~ (k1_funct_1(v1, v2) = v3) | ~ (k3_xboole_0(v3, v5) = v6) | ~ m1_group_2(v4, v0) | ~ m1_group_2(v2, v0) | ~ v1_group_1(v4) | ~ v1_group_1(v2) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v7] : (k9_group_2(v0, v2, v4) = v7 & u1_struct_0(v7) = v6))
% 7.13/2.35 | (12) l1_struct_0(all_0_4_4)
% 7.13/2.35 | (13) ? [v0] : ? [v1] : m1_subset_1(v1, v0)
% 7.13/2.35 | (14) k1_funct_1(all_0_12_12, all_0_8_8) = all_0_7_7
% 7.13/2.35 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k9_group_2(v0, v1, v2) = v3) | ~ m1_group_2(v2, v0) | ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | m1_group_2(v3, v0) | v3_struct_0(v0))
% 7.13/2.35 | (16) ! [v0] : ( ~ l1_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v1] : m1_group_2(v1, v0))
% 7.13/2.36 | (17) ! [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)))
% 7.13/2.36 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (k9_group_2(v4, v3, v2) = v1) | ~ (k9_group_2(v4, v3, v2) = v0))
% 7.13/2.36 | (19) ! [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)))
% 7.13/2.36 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k8_group_2(v0, v1, v2) = v3) | ~ m1_group_2(v2, v0) | ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v1_group_1(v3) | v3_struct_0(v0))
% 7.13/2.36 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (u1_group_1(v2) = v1) | ~ (u1_group_1(v2) = v0))
% 7.13/2.36 | (22) ! [v0] : ! [v1] : ( ~ v1_xboole_0(v1) | ~ r2_hidden(v0, v1))
% 7.13/2.36 | (23) ! [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)))))
% 7.13/2.36 | (24) l1_group_1(all_0_13_13)
% 7.13/2.36 | (25) ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | m1_subset_1(v0, v1))
% 7.13/2.36 | (26) ? [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)))
% 7.13/2.36 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k9_group_2(v0, v1, v2) = v3) | ~ m1_group_2(v2, v0) | ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | k8_group_2(v0, v1, v2) = v3 | v3_struct_0(v0))
% 7.13/2.36 | (28) v3_group_1(all_0_13_13)
% 7.13/2.36 | (29) ! [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))
% 7.13/2.36 | (30) ! [v0] : ( ~ l1_group_1(v0) | l1_struct_0(v0))
% 7.13/2.36 | (31) ~ v1_xboole_0(all_0_3_3)
% 7.13/2.36 | (32) m1_group_2(all_0_11_11, all_0_13_13)
% 7.13/2.36 | (33) ! [v0] : ! [v1] : ( ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v3_group_1(v0) | l1_group_1(v1) | v3_struct_0(v0))
% 7.13/2.36 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ m1_relset_1(v2, v0, v1) | m2_relset_1(v2, v0, v1))
% 7.13/2.36 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ m2_relset_1(v2, v0, v1) | m1_relset_1(v2, v0, v1))
% 7.13/2.36 | (36) ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ? [v2] : (v1_xboole_0(v2) & m1_subset_1(v2, v1)))
% 7.13/2.36 | (37) ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | v1_xboole_0(v0) | ? [v2] : (m1_subset_1(v2, v1) & ~ v1_xboole_0(v2)))
% 7.13/2.36 | (38) k1_funct_1(all_0_12_12, all_0_11_11) = all_0_10_10
% 7.13/2.36 | (39) ! [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)))
% 7.13/2.36 | (40) ~ (all_0_5_5 = all_0_7_7)
% 7.13/2.36 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ v1_xboole_0(v2) | ~ m1_subset_1(v1, v3) | ~ r2_hidden(v0, v1))
% 7.13/2.36 | (42) v1_xboole_0(k1_xboole_0)
% 7.13/2.36 | (43) k9_group_2(all_0_13_13, all_0_11_11, all_0_9_9) = all_0_8_8
% 7.13/2.36 | (44) l1_group_1(all_0_0_0)
% 7.13/2.36 | (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))
% 7.13/2.36 | (46) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0))
% 7.13/2.37 | (47) ? [v0] : ? [v1] : ? [v2] : m2_relset_1(v2, v0, v1)
% 7.13/2.37 | (48) ? [v0] : ? [v1] : ? [v2] : (v1_relat_1(v2) & v1_funct_2(v2, v0, v1) & v1_funct_1(v2) & m1_relset_1(v2, v0, v1))
% 7.13/2.37 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (g1_group_1(v3, v2) = v1) | ~ (g1_group_1(v3, v2) = v0))
% 7.13/2.37 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ m1_subset_1(v1, v3) | ~ r2_hidden(v0, v1) | m1_subset_1(v0, v2))
% 7.13/2.37 | (51) ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ~ v1_xboole_0(v1))
% 7.13/2.37 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k1_funct_1(v3, v2) = v1) | ~ (k1_funct_1(v3, v2) = v0))
% 7.13/2.37 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k9_group_2(v0, v1, v2) = v3) | ~ m1_group_2(v2, v0) | ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | k9_group_2(v0, v2, v1) = v3 | v3_struct_0(v0))
% 7.13/2.37 | (54) k1_latsubgr(all_0_13_13) = all_0_12_12
% 7.13/2.37 | (55) l1_struct_0(all_0_1_1)
% 7.13/2.37 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (k1_latsubgr(v0) = v1) | ~ (k1_funct_1(v1, v2) = v3) | ~ (k9_group_2(v0, v2, v4) = v5) | ~ m1_group_2(v4, v0) | ~ m1_group_2(v2, v0) | ~ v1_group_1(v4) | ~ v1_group_1(v2) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v6] : ? [v7] : (k1_funct_1(v1, v4) = v7 & k3_xboole_0(v3, v7) = v6 & u1_struct_0(v5) = v6))
% 7.13/2.37 | (57) k3_xboole_0(all_0_10_10, all_0_6_6) = all_0_5_5
% 7.13/2.37 | (58) ! [v0] : ! [v1] : (v1 = v0 | ~ v1_xboole_0(v1) | ~ v1_xboole_0(v0))
% 7.13/2.37 | (59) ? [v0] : ? [v1] : ? [v2] : m1_relset_1(v2, v0, v1)
% 7.13/2.37 | (60) ! [v0] : ! [v1] : ( ~ m1_subset_1(v0, v1) | v1_xboole_0(v1) | r2_hidden(v0, v1))
% 7.13/2.37 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k9_group_2(v0, v2, v1) = v3) | ~ m1_group_2(v2, v0) | ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | k9_group_2(v0, v1, v2) = v3 | v3_struct_0(v0))
% 7.13/2.37 | (62) ? [v0] : ? [v1] : ? [v2] : (v1_relat_1(v2) & v1_funct_1(v2) & m1_relset_1(v2, v0, v1))
% 7.13/2.37 | (63) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_latsubgr(v2) = v1) | ~ (k1_latsubgr(v2) = v0))
% 7.13/2.37 | (64) ! [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))
% 7.13/2.37 | (65) ! [v0] : ! [v1] : (v1 = k1_xboole_0 | ~ (k3_xboole_0(v0, k1_xboole_0) = v1))
% 7.13/2.37 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k9_group_2(v0, v1, v2) = v3) | ~ m1_group_2(v2, v0) | ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v1_group_1(v3) | v3_struct_0(v0))
% 7.13/2.37 | (67) ! [v0] : ! [v1] : (v1 = v0 | ~ (k3_xboole_0(v0, v0) = v1))
% 7.13/2.37 | (68) ! [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))))
% 7.13/2.37 | (69) v1_group_1(all_0_11_11)
% 7.13/2.37 | (70) ! [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)))
% 7.13/2.37 | (71) ! [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)))
% 7.13/2.37 | (72) ! [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)))
% 7.13/2.37 | (73) ? [v0] : r1_tarski(v0, v0)
% 7.13/2.37 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_zfmisc_1(v0, v1) = v2) | ~ v1_xboole_0(v2) | v1_xboole_0(v1) | v1_xboole_0(v0))
% 7.13/2.37 | (75) ! [v0] : ! [v1] : ( ~ (u1_group_1(v0) = v1) | ~ l1_group_1(v0) | v1_funct_1(v1))
% 7.13/2.37 | (76) ! [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))
% 7.13/2.37 | (77) ! [v0] : ! [v1] : ( ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v3_group_1(v0) | v3_group_1(v1) | v3_struct_0(v0))
% 7.13/2.37 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k3_xboole_0(v3, v2) = v1) | ~ (k3_xboole_0(v3, v2) = v0))
% 7.13/2.38 | (79) ! [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))))
% 7.13/2.38 | (80) ~ v3_struct_0(all_0_4_4)
% 7.13/2.38 | (81) v1_group_1(all_0_9_9)
% 7.13/2.38 | (82) v1_xboole_0(all_0_2_2)
% 7.13/2.38 | (83) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0))
% 7.13/2.38 | (84) ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l1_struct_0(v0) | ~ v1_xboole_0(v1) | v3_struct_0(v0))
% 7.13/2.38 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (k8_group_2(v4, v3, v2) = v1) | ~ (k8_group_2(v4, v3, v2) = v0))
% 7.13/2.38 | (86) ! [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))
% 7.13/2.38 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k2_zfmisc_1(v3, v2) = v1) | ~ (k2_zfmisc_1(v3, v2) = v0))
% 7.13/2.38 | (88) ! [v0] : ! [v1] : ! [v2] : ( ~ v1_partfun1(v2, v0, v1) | ~ v1_funct_1(v2) | ~ m1_relset_1(v2, v0, v1) | v1_funct_2(v2, v0, v1))
% 7.13/2.38 | (89) ! [v0] : (v0 = k1_xboole_0 | ~ v1_xboole_0(v0))
% 7.13/2.38 | (90) ! [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))))
% 7.13/2.38 | (91) m1_group_2(all_0_9_9, all_0_13_13)
% 7.13/2.38 | (92) ! [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))))
% 7.13/2.38 | (93) ! [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)))))
% 7.13/2.38 | (94) ! [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)))))
% 7.13/2.38 | (95) ! [v0] : ! [v1] : ( ~ r2_hidden(v1, v0) | ~ r2_hidden(v0, v1))
% 7.13/2.38 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k8_group_2(v0, v1, v2) = v3) | ~ m1_group_2(v2, v0) | ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | m1_group_2(v3, v0) | v3_struct_0(v0))
% 7.13/2.38 | (97) k1_funct_1(all_0_12_12, all_0_9_9) = all_0_6_6
% 7.13/2.38 | (98) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_group_3(v2) = v1) | ~ (k1_group_3(v2) = v0))
% 7.13/2.38 | (99) v4_group_1(all_0_13_13)
% 7.13/2.38 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k8_group_2(v0, v1, v2) = v3) | ~ m1_group_2(v2, v0) | ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | k9_group_2(v0, v1, v2) = v3 | v3_struct_0(v0))
% 7.13/2.38 |
% 7.13/2.39 | Instantiating formula (11) with all_0_5_5, all_0_6_6, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13 and discharging atoms k1_latsubgr(all_0_13_13) = all_0_12_12, k1_funct_1(all_0_12_12, all_0_9_9) = all_0_6_6, k1_funct_1(all_0_12_12, all_0_11_11) = all_0_10_10, k3_xboole_0(all_0_10_10, all_0_6_6) = all_0_5_5, m1_group_2(all_0_9_9, all_0_13_13), m1_group_2(all_0_11_11, all_0_13_13), v1_group_1(all_0_9_9), v1_group_1(all_0_11_11), l1_group_1(all_0_13_13), v4_group_1(all_0_13_13), v3_group_1(all_0_13_13), ~ v3_struct_0(all_0_13_13), yields:
% 7.13/2.39 | (101) ? [v0] : (k9_group_2(all_0_13_13, all_0_11_11, all_0_9_9) = v0 & u1_struct_0(v0) = all_0_5_5)
% 7.13/2.39 |
% 7.13/2.39 | Instantiating formula (56) with all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13 and discharging atoms k1_latsubgr(all_0_13_13) = all_0_12_12, k1_funct_1(all_0_12_12, all_0_11_11) = all_0_10_10, k9_group_2(all_0_13_13, all_0_11_11, all_0_9_9) = all_0_8_8, m1_group_2(all_0_9_9, all_0_13_13), m1_group_2(all_0_11_11, all_0_13_13), v1_group_1(all_0_9_9), v1_group_1(all_0_11_11), l1_group_1(all_0_13_13), v4_group_1(all_0_13_13), v3_group_1(all_0_13_13), ~ v3_struct_0(all_0_13_13), yields:
% 7.13/2.39 | (102) ? [v0] : ? [v1] : (k1_funct_1(all_0_12_12, all_0_9_9) = v1 & k3_xboole_0(all_0_10_10, v1) = v0 & u1_struct_0(all_0_8_8) = v0)
% 7.13/2.39 |
% 7.13/2.39 | Instantiating formula (7) with all_0_12_12, all_0_13_13 and discharging atoms k1_latsubgr(all_0_13_13) = all_0_12_12, l1_group_1(all_0_13_13), v4_group_1(all_0_13_13), v3_group_1(all_0_13_13), ~ v3_struct_0(all_0_13_13), yields:
% 7.13/2.39 | (103) v1_funct_1(all_0_12_12)
% 7.13/2.39 |
% 7.13/2.39 | Instantiating formula (8) with all_0_12_12, all_0_13_13 and discharging atoms k1_latsubgr(all_0_13_13) = all_0_12_12, l1_group_1(all_0_13_13), v4_group_1(all_0_13_13), v3_group_1(all_0_13_13), ~ v3_struct_0(all_0_13_13), yields:
% 7.13/2.39 | (104) ? [v0] : ? [v1] : ? [v2] : (k1_group_3(all_0_13_13) = v0 & k1_zfmisc_1(v1) = v2 & u1_struct_0(all_0_13_13) = v1 & m2_relset_1(all_0_12_12, v0, v2) & v1_funct_2(all_0_12_12, v0, v2))
% 7.13/2.39 |
% 7.13/2.39 | Instantiating formula (23) with all_0_12_12, all_0_13_13 and discharging atoms k1_latsubgr(all_0_13_13) = all_0_12_12, l1_group_1(all_0_13_13), v4_group_1(all_0_13_13), v3_group_1(all_0_13_13), ~ v3_struct_0(all_0_13_13), yields:
% 7.13/2.39 | (105) ? [v0] : ? [v1] : ? [v2] : (k1_group_3(all_0_13_13) = v0 & k1_zfmisc_1(v1) = v2 & u1_struct_0(all_0_13_13) = v1 & ! [v3] : ! [v4] : ( ~ (k1_funct_1(all_0_12_12, v3) = v4) | ~ m2_relset_1(all_0_12_12, v0, v2) | ~ v1_funct_2(all_0_12_12, v0, v2) | ~ v1_funct_1(all_0_12_12) | ~ m1_group_2(v3, all_0_13_13) | ~ v1_group_1(v3) | u1_struct_0(v3) = v4) & ! [v3] : ! [v4] : ( ~ (u1_struct_0(v3) = v4) | ~ m2_relset_1(all_0_12_12, v0, v2) | ~ v1_funct_2(all_0_12_12, v0, v2) | ~ v1_funct_1(all_0_12_12) | ~ m1_group_2(v3, all_0_13_13) | ~ v1_group_1(v3) | k1_funct_1(all_0_12_12, v3) = v4) & ! [v3] : (v3 = all_0_12_12 | ~ 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_13_13) & v1_group_1(v4))))
% 7.13/2.39 |
% 7.13/2.39 | Instantiating formula (15) with all_0_8_8, all_0_9_9, all_0_11_11, all_0_13_13 and discharging atoms k9_group_2(all_0_13_13, all_0_11_11, all_0_9_9) = all_0_8_8, m1_group_2(all_0_9_9, all_0_13_13), m1_group_2(all_0_11_11, all_0_13_13), l1_group_1(all_0_13_13), v4_group_1(all_0_13_13), v3_group_1(all_0_13_13), ~ v3_struct_0(all_0_13_13), yields:
% 7.13/2.39 | (106) m1_group_2(all_0_8_8, all_0_13_13)
% 7.13/2.39 |
% 7.13/2.39 | Instantiating formula (66) with all_0_8_8, all_0_9_9, all_0_11_11, all_0_13_13 and discharging atoms k9_group_2(all_0_13_13, all_0_11_11, all_0_9_9) = all_0_8_8, m1_group_2(all_0_9_9, all_0_13_13), m1_group_2(all_0_11_11, all_0_13_13), l1_group_1(all_0_13_13), v4_group_1(all_0_13_13), v3_group_1(all_0_13_13), ~ v3_struct_0(all_0_13_13), yields:
% 7.13/2.39 | (107) v1_group_1(all_0_8_8)
% 7.13/2.39 |
% 7.13/2.39 | Instantiating (105) with all_27_0_30, all_27_1_31, all_27_2_32 yields:
% 7.13/2.39 | (108) k1_group_3(all_0_13_13) = all_27_2_32 & k1_zfmisc_1(all_27_1_31) = all_27_0_30 & u1_struct_0(all_0_13_13) = all_27_1_31 & ! [v0] : ! [v1] : ( ~ (k1_funct_1(all_0_12_12, v0) = v1) | ~ m2_relset_1(all_0_12_12, all_27_2_32, all_27_0_30) | ~ v1_funct_2(all_0_12_12, all_27_2_32, all_27_0_30) | ~ v1_funct_1(all_0_12_12) | ~ m1_group_2(v0, all_0_13_13) | ~ v1_group_1(v0) | u1_struct_0(v0) = v1) & ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ m2_relset_1(all_0_12_12, all_27_2_32, all_27_0_30) | ~ v1_funct_2(all_0_12_12, all_27_2_32, all_27_0_30) | ~ v1_funct_1(all_0_12_12) | ~ m1_group_2(v0, all_0_13_13) | ~ v1_group_1(v0) | k1_funct_1(all_0_12_12, v0) = v1) & ! [v0] : (v0 = all_0_12_12 | ~ m2_relset_1(v0, all_27_2_32, all_27_0_30) | ~ v1_funct_2(v0, all_27_2_32, all_27_0_30) | ~ 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_13_13) & v1_group_1(v1)))
% 7.13/2.39 |
% 7.13/2.39 | Applying alpha-rule on (108) yields:
% 7.13/2.39 | (109) ! [v0] : (v0 = all_0_12_12 | ~ m2_relset_1(v0, all_27_2_32, all_27_0_30) | ~ v1_funct_2(v0, all_27_2_32, all_27_0_30) | ~ 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_13_13) & v1_group_1(v1)))
% 7.57/2.39 | (110) ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ m2_relset_1(all_0_12_12, all_27_2_32, all_27_0_30) | ~ v1_funct_2(all_0_12_12, all_27_2_32, all_27_0_30) | ~ v1_funct_1(all_0_12_12) | ~ m1_group_2(v0, all_0_13_13) | ~ v1_group_1(v0) | k1_funct_1(all_0_12_12, v0) = v1)
% 7.57/2.39 | (111) k1_zfmisc_1(all_27_1_31) = all_27_0_30
% 7.57/2.39 | (112) u1_struct_0(all_0_13_13) = all_27_1_31
% 7.57/2.39 | (113) k1_group_3(all_0_13_13) = all_27_2_32
% 7.57/2.39 | (114) ! [v0] : ! [v1] : ( ~ (k1_funct_1(all_0_12_12, v0) = v1) | ~ m2_relset_1(all_0_12_12, all_27_2_32, all_27_0_30) | ~ v1_funct_2(all_0_12_12, all_27_2_32, all_27_0_30) | ~ v1_funct_1(all_0_12_12) | ~ m1_group_2(v0, all_0_13_13) | ~ v1_group_1(v0) | u1_struct_0(v0) = v1)
% 7.57/2.39 |
% 7.57/2.39 | Instantiating (102) with all_30_0_33, all_30_1_34 yields:
% 7.57/2.39 | (115) k1_funct_1(all_0_12_12, all_0_9_9) = all_30_0_33 & k3_xboole_0(all_0_10_10, all_30_0_33) = all_30_1_34 & u1_struct_0(all_0_8_8) = all_30_1_34
% 7.57/2.39 |
% 7.57/2.39 | Applying alpha-rule on (115) yields:
% 7.57/2.39 | (116) k1_funct_1(all_0_12_12, all_0_9_9) = all_30_0_33
% 7.57/2.39 | (117) k3_xboole_0(all_0_10_10, all_30_0_33) = all_30_1_34
% 7.57/2.39 | (118) u1_struct_0(all_0_8_8) = all_30_1_34
% 7.57/2.39 |
% 7.57/2.39 | Instantiating (101) with all_34_0_36 yields:
% 7.57/2.39 | (119) k9_group_2(all_0_13_13, all_0_11_11, all_0_9_9) = all_34_0_36 & u1_struct_0(all_34_0_36) = all_0_5_5
% 7.57/2.39 |
% 7.57/2.39 | Applying alpha-rule on (119) yields:
% 7.57/2.39 | (120) k9_group_2(all_0_13_13, all_0_11_11, all_0_9_9) = all_34_0_36
% 7.57/2.39 | (121) u1_struct_0(all_34_0_36) = all_0_5_5
% 7.57/2.39 |
% 7.57/2.39 | Instantiating (104) with all_36_0_37, all_36_1_38, all_36_2_39 yields:
% 7.57/2.39 | (122) k1_group_3(all_0_13_13) = all_36_2_39 & k1_zfmisc_1(all_36_1_38) = all_36_0_37 & u1_struct_0(all_0_13_13) = all_36_1_38 & m2_relset_1(all_0_12_12, all_36_2_39, all_36_0_37) & v1_funct_2(all_0_12_12, all_36_2_39, all_36_0_37)
% 7.57/2.39 |
% 7.57/2.39 | Applying alpha-rule on (122) yields:
% 7.57/2.39 | (123) k1_zfmisc_1(all_36_1_38) = all_36_0_37
% 7.57/2.39 | (124) m2_relset_1(all_0_12_12, all_36_2_39, all_36_0_37)
% 7.57/2.39 | (125) k1_group_3(all_0_13_13) = all_36_2_39
% 7.57/2.39 | (126) v1_funct_2(all_0_12_12, all_36_2_39, all_36_0_37)
% 7.57/2.40 | (127) u1_struct_0(all_0_13_13) = all_36_1_38
% 7.57/2.40 |
% 7.57/2.40 | Instantiating formula (98) with all_0_13_13, all_27_2_32, all_36_2_39 and discharging atoms k1_group_3(all_0_13_13) = all_36_2_39, k1_group_3(all_0_13_13) = all_27_2_32, yields:
% 7.57/2.40 | (128) all_36_2_39 = all_27_2_32
% 7.57/2.40 |
% 7.57/2.40 | Instantiating formula (18) with all_0_13_13, all_0_11_11, all_0_9_9, all_34_0_36, all_0_8_8 and discharging atoms k9_group_2(all_0_13_13, all_0_11_11, all_0_9_9) = all_34_0_36, k9_group_2(all_0_13_13, all_0_11_11, all_0_9_9) = all_0_8_8, yields:
% 7.57/2.40 | (129) all_34_0_36 = all_0_8_8
% 7.57/2.40 |
% 7.57/2.40 | Instantiating formula (83) with all_0_13_13, all_27_1_31, all_36_1_38 and discharging atoms u1_struct_0(all_0_13_13) = all_36_1_38, u1_struct_0(all_0_13_13) = all_27_1_31, yields:
% 7.57/2.40 | (130) all_36_1_38 = all_27_1_31
% 7.57/2.40 |
% 7.57/2.40 | From (130) and (123) follows:
% 7.57/2.40 | (131) k1_zfmisc_1(all_27_1_31) = all_36_0_37
% 7.57/2.40 |
% 7.57/2.40 | From (129) and (121) follows:
% 7.57/2.40 | (132) u1_struct_0(all_0_8_8) = all_0_5_5
% 7.57/2.40 |
% 7.57/2.40 | From (128) and (124) follows:
% 7.57/2.40 | (133) m2_relset_1(all_0_12_12, all_27_2_32, all_36_0_37)
% 7.57/2.40 |
% 7.57/2.40 | From (128) and (126) follows:
% 7.57/2.40 | (134) v1_funct_2(all_0_12_12, all_27_2_32, all_36_0_37)
% 7.57/2.40 |
% 7.57/2.40 | Instantiating formula (46) with all_27_1_31, all_36_0_37, all_27_0_30 and discharging atoms k1_zfmisc_1(all_27_1_31) = all_36_0_37, k1_zfmisc_1(all_27_1_31) = all_27_0_30, yields:
% 7.57/2.40 | (135) all_36_0_37 = all_27_0_30
% 7.57/2.40 |
% 7.57/2.40 | Instantiating formula (83) with all_0_8_8, all_0_5_5, all_30_1_34 and discharging atoms u1_struct_0(all_0_8_8) = all_30_1_34, u1_struct_0(all_0_8_8) = all_0_5_5, yields:
% 7.57/2.40 | (136) all_30_1_34 = all_0_5_5
% 7.57/2.40 |
% 7.57/2.40 | From (136) and (118) follows:
% 7.57/2.40 | (132) u1_struct_0(all_0_8_8) = all_0_5_5
% 7.57/2.40 |
% 7.57/2.40 | From (135) and (133) follows:
% 7.57/2.40 | (138) m2_relset_1(all_0_12_12, all_27_2_32, all_27_0_30)
% 7.57/2.40 |
% 7.57/2.40 | From (135) and (134) follows:
% 7.57/2.40 | (139) v1_funct_2(all_0_12_12, all_27_2_32, all_27_0_30)
% 7.57/2.40 |
% 7.57/2.40 | Instantiating formula (114) with all_0_7_7, all_0_8_8 and discharging atoms k1_funct_1(all_0_12_12, all_0_8_8) = all_0_7_7, m2_relset_1(all_0_12_12, all_27_2_32, all_27_0_30), v1_funct_2(all_0_12_12, all_27_2_32, all_27_0_30), v1_funct_1(all_0_12_12), m1_group_2(all_0_8_8, all_0_13_13), v1_group_1(all_0_8_8), yields:
% 7.57/2.40 | (140) u1_struct_0(all_0_8_8) = all_0_7_7
% 7.57/2.40 |
% 7.57/2.40 | Instantiating formula (83) with all_0_8_8, all_0_7_7, all_0_5_5 and discharging atoms u1_struct_0(all_0_8_8) = all_0_5_5, u1_struct_0(all_0_8_8) = all_0_7_7, yields:
% 7.57/2.40 | (141) all_0_5_5 = all_0_7_7
% 7.57/2.40 |
% 7.57/2.40 | Equations (141) can reduce 40 to:
% 7.57/2.40 | (142) $false
% 7.57/2.40 |
% 7.57/2.40 |-The branch is then unsatisfiable
% 7.57/2.40 % SZS output end Proof for theBenchmark
% 7.57/2.40
% 7.57/2.40 1755ms
%------------------------------------------------------------------------------