TSTP Solution File: CAT026+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : CAT026+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n027.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 : Thu Jul 14 23:59:08 EDT 2022
% Result : Theorem 5.20s 1.94s
% Output : Proof 8.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : CAT026+1 : TPTP v8.1.0. Released v3.4.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun May 29 19:19:15 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.49/0.59 ____ _
% 0.49/0.59 ___ / __ \_____(_)___ ________ __________
% 0.49/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.49/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.49/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.49/0.59
% 0.49/0.59 A Theorem Prover for First-Order Logic
% 0.49/0.59 (ePrincess v.1.0)
% 0.49/0.59
% 0.49/0.59 (c) Philipp Rümmer, 2009-2015
% 0.49/0.59 (c) Peter Backeman, 2014-2015
% 0.49/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.49/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.49/0.59 Bug reports to peter@backeman.se
% 0.49/0.59
% 0.49/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.49/0.59
% 0.49/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.74/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.87/1.03 Prover 0: Preprocessing ...
% 3.29/1.45 Prover 0: Warning: ignoring some quantifiers
% 3.29/1.49 Prover 0: Constructing countermodel ...
% 5.20/1.94 Prover 0: proved (1294ms)
% 5.20/1.94
% 5.20/1.94 No countermodel exists, formula is valid
% 5.20/1.94 % SZS status Theorem for theBenchmark
% 5.20/1.94
% 5.20/1.94 Generating proof ... Warning: ignoring some quantifiers
% 7.61/2.47 found it (size 84)
% 7.61/2.47
% 7.61/2.47 % SZS output start Proof for theBenchmark
% 7.61/2.47 Assumed formulas after preprocessing and simplification:
% 7.61/2.47 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (k12_isocat_2(v0, v1, v2, v7) = v9 & k12_isocat_2(v0, v1, v2, v4) = v6 & k11_isocat_2(v0, v1, v2, v7) = v8 & k11_isocat_2(v0, v1, v2, v4) = v5 & k11_cat_2(v1, v2) = v3 & v1_xboole_0(v12) & v1_xboole_0(k1_xboole_0) & r2_nattra_1(v0, v3, v4, v7) & m2_cat_1(v7, v0, v3) & m2_cat_1(v4, v0, v3) & l1_cat_1(v10) & l1_cat_1(v2) & l1_cat_1(v1) & l1_cat_1(v0) & v2_cat_1(v2) & v2_cat_1(v1) & v2_cat_1(v0) & ~ v1_xboole_0(v11) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (k2_isocat_1(v13, v14, v15, v17, v20) = v21) | ~ (k2_isocat_1(v13, v14, v15, v16, v18) = v19) | ~ r2_nattra_1(v14, v15, v18, v20) | ~ r2_nattra_1(v13, v14, v16, v17) | ~ m2_cat_1(v20, v14, v15) | ~ m2_cat_1(v18, v14, v15) | ~ m2_cat_1(v17, v13, v14) | ~ m2_cat_1(v16, v13, v14) | ~ l1_cat_1(v15) | ~ l1_cat_1(v14) | ~ l1_cat_1(v13) | ~ v2_cat_1(v15) | ~ v2_cat_1(v14) | ~ v2_cat_1(v13) | r2_nattra_1(v13, v15, v19, v21)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v14 = v13 | ~ (k2_isocat_1(v19, v18, v17, v16, v15) = v14) | ~ (k2_isocat_1(v19, v18, v17, v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v14 = v13 | ~ (k12_isocat_2(v18, v17, v16, v15) = v14) | ~ (k12_isocat_2(v18, v17, v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v14 = v13 | ~ (k11_isocat_2(v18, v17, v16, v15) = v14) | ~ (k11_isocat_2(v18, v17, v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (k2_isocat_1(v13, v14, v15, v16, v17) = v18) | ~ m2_cat_1(v17, v14, v15) | ~ m2_cat_1(v16, v13, v14) | ~ l1_cat_1(v15) | ~ l1_cat_1(v14) | ~ l1_cat_1(v13) | ~ v2_cat_1(v15) | ~ v2_cat_1(v14) | ~ v2_cat_1(v13) | k5_relat_1(v16, v17) = v18) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (k2_isocat_1(v13, v14, v15, v16, v17) = v18) | ~ m2_cat_1(v17, v14, v15) | ~ m2_cat_1(v16, v13, v14) | ~ l1_cat_1(v15) | ~ l1_cat_1(v14) | ~ l1_cat_1(v13) | ~ v2_cat_1(v15) | ~ v2_cat_1(v14) | ~ v2_cat_1(v13) | m2_cat_1(v18, v13, v15)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (k12_isocat_2(v13, v14, v15, v16) = v17) | ~ l1_cat_1(v15) | ~ l1_cat_1(v14) | ~ l1_cat_1(v13) | ~ v2_cat_1(v15) | ~ v2_cat_1(v14) | ~ v2_cat_1(v13) | m2_cat_1(v17, v13, v15) | ? [v18] : (k11_cat_2(v14, v15) = v18 & ~ m2_cat_1(v16, v13, v18))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (k11_isocat_2(v13, v14, v15, v16) = v17) | ~ l1_cat_1(v15) | ~ l1_cat_1(v14) | ~ l1_cat_1(v13) | ~ v2_cat_1(v15) | ~ v2_cat_1(v14) | ~ v2_cat_1(v13) | m2_cat_1(v17, v13, v14) | ? [v18] : (k11_cat_2(v14, v15) = v18 & ~ m2_cat_1(v16, v13, v18))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (u2_cat_1(v14) = v16) | ~ (u2_cat_1(v13) = v15) | ~ m2_cat_1(v17, v13, v14) | ~ l1_cat_1(v14) | ~ l1_cat_1(v13) | ~ v2_cat_1(v14) | ~ v2_cat_1(v13) | v1_funct_2(v17, v15, v16)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (u2_cat_1(v14) = v16) | ~ (u2_cat_1(v13) = v15) | ~ m2_cat_1(v17, v13, v14) | ~ l1_cat_1(v14) | ~ l1_cat_1(v13) | ~ v2_cat_1(v14) | ~ v2_cat_1(v13) | v1_funct_1(v17)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (u2_cat_1(v14) = v16) | ~ (u2_cat_1(v13) = v15) | ~ m2_cat_1(v17, v13, v14) | ~ l1_cat_1(v14) | ~ l1_cat_1(v13) | ~ v2_cat_1(v14) | ~ v2_cat_1(v13) | m2_relset_1(v17, v15, v16)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (k5_relat_1(v16, v15) = v14) | ~ (k5_relat_1(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (k9_isocat_2(v16, v15) = v14) | ~ (k9_isocat_2(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (k8_isocat_2(v16, v15) = v14) | ~ (k8_isocat_2(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (k2_zfmisc_1(v16, v15) = v14) | ~ (k2_zfmisc_1(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (k17_cat_2(v16, v15) = v14) | ~ (k17_cat_2(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (k11_cat_2(v16, v15) = v14) | ~ (k11_cat_2(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (k16_cat_2(v16, v15) = v14) | ~ (k16_cat_2(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (k9_isocat_2(v14, v15) = v16) | ~ l1_cat_1(v15) | ~ l1_cat_1(v14) | ~ l1_cat_1(v13) | ~ v2_cat_1(v15) | ~ v2_cat_1(v14) | ~ v2_cat_1(v13) | ? [v17] : (k11_cat_2(v14, v15) = v17 & ! [v18] : ! [v19] : ( ~ (k12_isocat_2(v13, v14, v15, v18) = v19) | ~ m2_cat_1(v18, v13, v17) | k2_isocat_1(v13, v17, v15, v18, v16) = v19) & ! [v18] : ! [v19] : ( ~ (k2_isocat_1(v13, v17, v15, v18, v16) = v19) | ~ m2_cat_1(v18, v13, v17) | k12_isocat_2(v13, v14, v15, v18) = v19))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (k8_isocat_2(v14, v15) = v16) | ~ l1_cat_1(v15) | ~ l1_cat_1(v14) | ~ l1_cat_1(v13) | ~ v2_cat_1(v15) | ~ v2_cat_1(v14) | ~ v2_cat_1(v13) | ? [v17] : (k11_cat_2(v14, v15) = v17 & ! [v18] : ! [v19] : ( ~ (k11_isocat_2(v13, v14, v15, v18) = v19) | ~ m2_cat_1(v18, v13, v17) | k2_isocat_1(v13, v17, v14, v18, v16) = v19) & ! [v18] : ! [v19] : ( ~ (k2_isocat_1(v13, v17, v14, v18, v16) = v19) | ~ m2_cat_1(v18, v13, v17) | k11_isocat_2(v13, v14, v15, v18) = v19))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (k2_zfmisc_1(v13, v14) = v16) | ~ m2_relset_1(v15, v13, v14) | ? [v17] : (k1_zfmisc_1(v16) = v17 & m1_subset_1(v15, v17))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (k11_cat_2(v14, v15) = v16) | ~ l1_cat_1(v15) | ~ l1_cat_1(v14) | ~ l1_cat_1(v13) | ~ v2_cat_1(v15) | ~ v2_cat_1(v14) | ~ v2_cat_1(v13) | ? [v17] : (k9_isocat_2(v14, v15) = v17 & ! [v18] : ! [v19] : ( ~ (k12_isocat_2(v13, v14, v15, v18) = v19) | ~ m2_cat_1(v18, v13, v16) | k2_isocat_1(v13, v16, v15, v18, v17) = v19) & ! [v18] : ! [v19] : ( ~ (k2_isocat_1(v13, v16, v15, v18, v17) = v19) | ~ m2_cat_1(v18, v13, v16) | k12_isocat_2(v13, v14, v15, v18) = v19))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (k11_cat_2(v14, v15) = v16) | ~ l1_cat_1(v15) | ~ l1_cat_1(v14) | ~ l1_cat_1(v13) | ~ v2_cat_1(v15) | ~ v2_cat_1(v14) | ~ v2_cat_1(v13) | ? [v17] : (k8_isocat_2(v14, v15) = v17 & ! [v18] : ! [v19] : ( ~ (k11_isocat_2(v13, v14, v15, v18) = v19) | ~ m2_cat_1(v18, v13, v16) | k2_isocat_1(v13, v16, v14, v18, v17) = v19) & ! [v18] : ! [v19] : ( ~ (k2_isocat_1(v13, v16, v14, v18, v17) = v19) | ~ m2_cat_1(v18, v13, v16) | k11_isocat_2(v13, v14, v15, v18) = v19))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (k1_zfmisc_1(v15) = v16) | ~ m1_subset_1(v14, v16) | ~ v1_xboole_0(v15) | ~ r2_hidden(v13, v14)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (k1_zfmisc_1(v15) = v16) | ~ m1_subset_1(v14, v16) | ~ r2_hidden(v13, v14) | m1_subset_1(v13, v15)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ m2_cat_1(v16, v13, v14) | ~ m2_cat_1(v15, v13, v14) | ~ l1_cat_1(v14) | ~ l1_cat_1(v13) | ~ v2_cat_1(v14) | ~ v2_cat_1(v13) | r2_nattra_1(v13, v14, v15, v15)) & ? [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (k2_zfmisc_1(v14, v15) = v16) | v1_relat_1(v13) | ? [v17] : (k1_zfmisc_1(v16) = v17 & ~ m1_subset_1(v13, v17))) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (u2_cat_1(v15) = v14) | ~ (u2_cat_1(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (k1_zfmisc_1(v15) = v14) | ~ (k1_zfmisc_1(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (k5_relat_1(v13, v14) = v15) | ~ v1_relat_1(v14) | ~ v1_relat_1(v13) | v1_relat_1(v15)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (k9_isocat_2(v13, v14) = v15) | ~ l1_cat_1(v14) | ~ l1_cat_1(v13) | ~ v2_cat_1(v14) | ~ v2_cat_1(v13) | k17_cat_2(v13, v14) = v15) & ! [v13] : ! [v14] : ! [v15] : ( ~ (k9_isocat_2(v13, v14) = v15) | ~ l1_cat_1(v14) | ~ l1_cat_1(v13) | ~ v2_cat_1(v14) | ~ v2_cat_1(v13) | ? [v16] : (k11_cat_2(v13, v14) = v16 & m2_cat_1(v15, v16, v14))) & ! [v13] : ! [v14] : ! [v15] : ( ~ (k8_isocat_2(v13, v14) = v15) | ~ l1_cat_1(v14) | ~ l1_cat_1(v13) | ~ v2_cat_1(v14) | ~ v2_cat_1(v13) | k16_cat_2(v13, v14) = v15) & ! [v13] : ! [v14] : ! [v15] : ( ~ (k8_isocat_2(v13, v14) = v15) | ~ l1_cat_1(v14) | ~ l1_cat_1(v13) | ~ v2_cat_1(v14) | ~ v2_cat_1(v13) | ? [v16] : (k11_cat_2(v13, v14) = v16 & m2_cat_1(v15, v16, v13))) & ! [v13] : ! [v14] : ! [v15] : ( ~ (k2_zfmisc_1(v13, v14) = v15) | ~ v1_xboole_0(v15) | v1_xboole_0(v14) | v1_xboole_0(v13)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (k17_cat_2(v13, v14) = v15) | ~ l1_cat_1(v14) | ~ l1_cat_1(v13) | ~ v2_cat_1(v14) | ~ v2_cat_1(v13) | k9_isocat_2(v13, v14) = v15) & ! [v13] : ! [v14] : ! [v15] : ( ~ (k17_cat_2(v13, v14) = v15) | ~ l1_cat_1(v14) | ~ l1_cat_1(v13) | ~ v2_cat_1(v14) | ~ v2_cat_1(v13) | ? [v16] : (k11_cat_2(v13, v14) = v16 & m2_cat_1(v15, v16, v14))) & ! [v13] : ! [v14] : ! [v15] : ( ~ (k11_cat_2(v13, v14) = v15) | ~ l1_cat_1(v14) | ~ l1_cat_1(v13) | ~ v2_cat_1(v14) | ~ v2_cat_1(v13) | l1_cat_1(v15)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (k11_cat_2(v13, v14) = v15) | ~ l1_cat_1(v14) | ~ l1_cat_1(v13) | ~ v2_cat_1(v14) | ~ v2_cat_1(v13) | v2_cat_1(v15)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (k11_cat_2(v13, v14) = v15) | ~ l1_cat_1(v14) | ~ l1_cat_1(v13) | ~ v2_cat_1(v14) | ~ v2_cat_1(v13) | ? [v16] : (k9_isocat_2(v13, v14) = v16 & m2_cat_1(v16, v15, v14))) & ! [v13] : ! [v14] : ! [v15] : ( ~ (k11_cat_2(v13, v14) = v15) | ~ l1_cat_1(v14) | ~ l1_cat_1(v13) | ~ v2_cat_1(v14) | ~ v2_cat_1(v13) | ? [v16] : (k8_isocat_2(v13, v14) = v16 & m2_cat_1(v16, v15, v13))) & ! [v13] : ! [v14] : ! [v15] : ( ~ (k11_cat_2(v13, v14) = v15) | ~ l1_cat_1(v14) | ~ l1_cat_1(v13) | ~ v2_cat_1(v14) | ~ v2_cat_1(v13) | ? [v16] : (k17_cat_2(v13, v14) = v16 & m2_cat_1(v16, v15, v14))) & ! [v13] : ! [v14] : ! [v15] : ( ~ (k11_cat_2(v13, v14) = v15) | ~ l1_cat_1(v14) | ~ l1_cat_1(v13) | ~ v2_cat_1(v14) | ~ v2_cat_1(v13) | ? [v16] : (k16_cat_2(v13, v14) = v16 & m2_cat_1(v16, v15, v13))) & ! [v13] : ! [v14] : ! [v15] : ( ~ (k16_cat_2(v13, v14) = v15) | ~ l1_cat_1(v14) | ~ l1_cat_1(v13) | ~ v2_cat_1(v14) | ~ v2_cat_1(v13) | k8_isocat_2(v13, v14) = v15) & ! [v13] : ! [v14] : ! [v15] : ( ~ (k16_cat_2(v13, v14) = v15) | ~ l1_cat_1(v14) | ~ l1_cat_1(v13) | ~ v2_cat_1(v14) | ~ v2_cat_1(v13) | ? [v16] : (k11_cat_2(v13, v14) = v16 & m2_cat_1(v15, v16, v13))) & ! [v13] : ! [v14] : ! [v15] : ( ~ (k1_zfmisc_1(v14) = v15) | ~ m1_subset_1(v13, v15) | r1_tarski(v13, v14)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (k1_zfmisc_1(v14) = v15) | ~ r1_tarski(v13, v14) | m1_subset_1(v13, v15)) & ! [v13] : ! [v14] : ! [v15] : ( ~ m2_relset_1(v15, v13, v14) | m1_relset_1(v15, v13, v14)) & ! [v13] : ! [v14] : ! [v15] : ( ~ m1_relset_1(v15, v13, v14) | m2_relset_1(v15, v13, v14)) & ! [v13] : ! [v14] : (v14 = v13 | ~ v1_xboole_0(v14) | ~ v1_xboole_0(v13)) & ! [v13] : ! [v14] : ( ~ (u2_cat_1(v13) = v14) | ~ v1_xboole_0(v14) | ~ l1_cat_1(v13)) & ! [v13] : ! [v14] : ( ~ (k1_zfmisc_1(v13) = v14) | ~ v1_xboole_0(v14)) & ! [v13] : ! [v14] : ( ~ (k1_zfmisc_1(v13) = v14) | v1_xboole_0(v13) | ? [v15] : (m1_subset_1(v15, v14) & ~ v1_xboole_0(v15))) & ! [v13] : ! [v14] : ( ~ (k1_zfmisc_1(v13) = v14) | ? [v15] : (m1_subset_1(v15, v14) & v1_xboole_0(v15))) & ! [v13] : ! [v14] : ( ~ m1_subset_1(v13, v14) | v1_xboole_0(v14) | r2_hidden(v13, v14)) & ! [v13] : ! [v14] : ( ~ v1_xboole_0(v14) | ~ r2_hidden(v13, v14)) & ! [v13] : ! [v14] : ( ~ r2_hidden(v14, v13) | ~ r2_hidden(v13, v14)) & ! [v13] : ! [v14] : ( ~ r2_hidden(v13, v14) | m1_subset_1(v13, v14)) & ! [v13] : ! [v14] : ( ~ l1_cat_1(v14) | ~ l1_cat_1(v13) | ~ v2_cat_1(v14) | ~ v2_cat_1(v13) | ? [v15] : m2_cat_1(v15, v13, v14)) & ! [v13] : (v13 = k1_xboole_0 | ~ v1_xboole_0(v13)) & ? [v13] : ? [v14] : ? [v15] : m2_relset_1(v15, v13, v14) & ? [v13] : ? [v14] : ? [v15] : m1_relset_1(v15, v13, v14) & ? [v13] : ? [v14] : m1_subset_1(v14, v13) & ? [v13] : r1_tarski(v13, v13) & ( ~ r2_nattra_1(v0, v2, v6, v9) | ~ r2_nattra_1(v0, v1, v5, v8)))
% 7.90/2.52 | 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 yields:
% 7.90/2.52 | (1) k12_isocat_2(all_0_12_12, all_0_11_11, all_0_10_10, all_0_5_5) = all_0_3_3 & k12_isocat_2(all_0_12_12, all_0_11_11, all_0_10_10, all_0_8_8) = all_0_6_6 & k11_isocat_2(all_0_12_12, all_0_11_11, all_0_10_10, all_0_5_5) = all_0_4_4 & k11_isocat_2(all_0_12_12, all_0_11_11, all_0_10_10, all_0_8_8) = all_0_7_7 & k11_cat_2(all_0_11_11, all_0_10_10) = all_0_9_9 & v1_xboole_0(all_0_0_0) & v1_xboole_0(k1_xboole_0) & r2_nattra_1(all_0_12_12, all_0_9_9, all_0_8_8, all_0_5_5) & m2_cat_1(all_0_5_5, all_0_12_12, all_0_9_9) & m2_cat_1(all_0_8_8, all_0_12_12, all_0_9_9) & l1_cat_1(all_0_2_2) & l1_cat_1(all_0_10_10) & l1_cat_1(all_0_11_11) & l1_cat_1(all_0_12_12) & v2_cat_1(all_0_10_10) & v2_cat_1(all_0_11_11) & v2_cat_1(all_0_12_12) & ~ v1_xboole_0(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (k2_isocat_1(v0, v1, v2, v4, v7) = v8) | ~ (k2_isocat_1(v0, v1, v2, v3, v5) = v6) | ~ r2_nattra_1(v1, v2, v5, v7) | ~ r2_nattra_1(v0, v1, v3, v4) | ~ m2_cat_1(v7, v1, v2) | ~ m2_cat_1(v5, v1, v2) | ~ m2_cat_1(v4, v0, v1) | ~ m2_cat_1(v3, v0, v1) | ~ l1_cat_1(v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v2) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | r2_nattra_1(v0, v2, v6, v8)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (k2_isocat_1(v6, v5, v4, v3, v2) = v1) | ~ (k2_isocat_1(v6, v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (k12_isocat_2(v5, v4, v3, v2) = v1) | ~ (k12_isocat_2(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (k11_isocat_2(v5, v4, v3, v2) = v1) | ~ (k11_isocat_2(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (k2_isocat_1(v0, v1, v2, v3, v4) = v5) | ~ m2_cat_1(v4, v1, v2) | ~ m2_cat_1(v3, v0, v1) | ~ l1_cat_1(v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v2) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | k5_relat_1(v3, v4) = v5) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (k2_isocat_1(v0, v1, v2, v3, v4) = v5) | ~ m2_cat_1(v4, v1, v2) | ~ m2_cat_1(v3, v0, v1) | ~ l1_cat_1(v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v2) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | m2_cat_1(v5, v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k12_isocat_2(v0, v1, v2, v3) = v4) | ~ l1_cat_1(v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v2) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | m2_cat_1(v4, v0, v2) | ? [v5] : (k11_cat_2(v1, v2) = v5 & ~ m2_cat_1(v3, v0, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k11_isocat_2(v0, v1, v2, v3) = v4) | ~ l1_cat_1(v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v2) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | m2_cat_1(v4, v0, v1) | ? [v5] : (k11_cat_2(v1, v2) = v5 & ~ m2_cat_1(v3, v0, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (u2_cat_1(v1) = v3) | ~ (u2_cat_1(v0) = v2) | ~ m2_cat_1(v4, v0, v1) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | v1_funct_2(v4, v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (u2_cat_1(v1) = v3) | ~ (u2_cat_1(v0) = v2) | ~ m2_cat_1(v4, v0, v1) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | v1_funct_1(v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (u2_cat_1(v1) = v3) | ~ (u2_cat_1(v0) = v2) | ~ m2_cat_1(v4, v0, v1) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | m2_relset_1(v4, v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k5_relat_1(v3, v2) = v1) | ~ (k5_relat_1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k9_isocat_2(v3, v2) = v1) | ~ (k9_isocat_2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k8_isocat_2(v3, v2) = v1) | ~ (k8_isocat_2(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 | ~ (k17_cat_2(v3, v2) = v1) | ~ (k17_cat_2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k11_cat_2(v3, v2) = v1) | ~ (k11_cat_2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k16_cat_2(v3, v2) = v1) | ~ (k16_cat_2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k9_isocat_2(v1, v2) = v3) | ~ l1_cat_1(v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v2) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v4] : (k11_cat_2(v1, v2) = v4 & ! [v5] : ! [v6] : ( ~ (k12_isocat_2(v0, v1, v2, v5) = v6) | ~ m2_cat_1(v5, v0, v4) | k2_isocat_1(v0, v4, v2, v5, v3) = v6) & ! [v5] : ! [v6] : ( ~ (k2_isocat_1(v0, v4, v2, v5, v3) = v6) | ~ m2_cat_1(v5, v0, v4) | k12_isocat_2(v0, v1, v2, v5) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k8_isocat_2(v1, v2) = v3) | ~ l1_cat_1(v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v2) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v4] : (k11_cat_2(v1, v2) = v4 & ! [v5] : ! [v6] : ( ~ (k11_isocat_2(v0, v1, v2, v5) = v6) | ~ m2_cat_1(v5, v0, v4) | k2_isocat_1(v0, v4, v1, v5, v3) = v6) & ! [v5] : ! [v6] : ( ~ (k2_isocat_1(v0, v4, v1, v5, v3) = v6) | ~ m2_cat_1(v5, v0, v4) | k11_isocat_2(v0, v1, v2, v5) = v6))) & ! [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] : ( ~ (k11_cat_2(v1, v2) = v3) | ~ l1_cat_1(v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v2) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v4] : (k9_isocat_2(v1, v2) = v4 & ! [v5] : ! [v6] : ( ~ (k12_isocat_2(v0, v1, v2, v5) = v6) | ~ m2_cat_1(v5, v0, v3) | k2_isocat_1(v0, v3, v2, v5, v4) = v6) & ! [v5] : ! [v6] : ( ~ (k2_isocat_1(v0, v3, v2, v5, v4) = v6) | ~ m2_cat_1(v5, v0, v3) | k12_isocat_2(v0, v1, v2, v5) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k11_cat_2(v1, v2) = v3) | ~ l1_cat_1(v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v2) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v4] : (k8_isocat_2(v1, v2) = v4 & ! [v5] : ! [v6] : ( ~ (k11_isocat_2(v0, v1, v2, v5) = v6) | ~ m2_cat_1(v5, v0, v3) | k2_isocat_1(v0, v3, v1, v5, v4) = v6) & ! [v5] : ! [v6] : ( ~ (k2_isocat_1(v0, v3, v1, v5, v4) = v6) | ~ m2_cat_1(v5, v0, v3) | k11_isocat_2(v0, v1, v2, v5) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ m1_subset_1(v1, v3) | ~ v1_xboole_0(v2) | ~ 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] : ( ~ m2_cat_1(v3, v0, v1) | ~ m2_cat_1(v2, v0, v1) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | r2_nattra_1(v0, v1, v2, 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 | ~ (u2_cat_1(v2) = v1) | ~ (u2_cat_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k5_relat_1(v0, v1) = v2) | ~ v1_relat_1(v1) | ~ v1_relat_1(v0) | v1_relat_1(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k9_isocat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | k17_cat_2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k9_isocat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v3] : (k11_cat_2(v0, v1) = v3 & m2_cat_1(v2, v3, v1))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k8_isocat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | k16_cat_2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k8_isocat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v3] : (k11_cat_2(v0, v1) = v3 & m2_cat_1(v2, v3, v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_zfmisc_1(v0, v1) = v2) | ~ v1_xboole_0(v2) | v1_xboole_0(v1) | v1_xboole_0(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k17_cat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | k9_isocat_2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k17_cat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v3] : (k11_cat_2(v0, v1) = v3 & m2_cat_1(v2, v3, v1))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k11_cat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | l1_cat_1(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k11_cat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | v2_cat_1(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k11_cat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v3] : (k9_isocat_2(v0, v1) = v3 & m2_cat_1(v3, v2, v1))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k11_cat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v3] : (k8_isocat_2(v0, v1) = v3 & m2_cat_1(v3, v2, v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k11_cat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v3] : (k17_cat_2(v0, v1) = v3 & m2_cat_1(v3, v2, v1))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k11_cat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v3] : (k16_cat_2(v0, v1) = v3 & m2_cat_1(v3, v2, v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k16_cat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | k8_isocat_2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k16_cat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v3] : (k11_cat_2(v0, v1) = v3 & m2_cat_1(v2, v3, v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_zfmisc_1(v1) = v2) | ~ m1_subset_1(v0, v2) | r1_tarski(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_zfmisc_1(v1) = v2) | ~ r1_tarski(v0, v1) | m1_subset_1(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ m2_relset_1(v2, v0, v1) | m1_relset_1(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] : ( ~ (u2_cat_1(v0) = v1) | ~ v1_xboole_0(v1) | ~ l1_cat_1(v0)) & ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ~ v1_xboole_0(v1)) & ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | v1_xboole_0(v0) | ? [v2] : (m1_subset_1(v2, v1) & ~ v1_xboole_0(v2))) & ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ? [v2] : (m1_subset_1(v2, v1) & v1_xboole_0(v2))) & ! [v0] : ! [v1] : ( ~ m1_subset_1(v0, v1) | v1_xboole_0(v1) | r2_hidden(v0, v1)) & ! [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] : ( ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v2] : m2_cat_1(v2, v0, v1)) & ! [v0] : (v0 = k1_xboole_0 | ~ v1_xboole_0(v0)) & ? [v0] : ? [v1] : ? [v2] : m2_relset_1(v2, v0, v1) & ? [v0] : ? [v1] : ? [v2] : m1_relset_1(v2, v0, v1) & ? [v0] : ? [v1] : m1_subset_1(v1, v0) & ? [v0] : r1_tarski(v0, v0) & ( ~ r2_nattra_1(all_0_12_12, all_0_10_10, all_0_6_6, all_0_3_3) | ~ r2_nattra_1(all_0_12_12, all_0_11_11, all_0_7_7, all_0_4_4))
% 7.90/2.54 |
% 7.90/2.54 | Applying alpha-rule on (1) yields:
% 7.90/2.54 | (2) v2_cat_1(all_0_10_10)
% 7.90/2.54 | (3) v2_cat_1(all_0_11_11)
% 7.90/2.54 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k9_isocat_2(v1, v2) = v3) | ~ l1_cat_1(v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v2) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v4] : (k11_cat_2(v1, v2) = v4 & ! [v5] : ! [v6] : ( ~ (k12_isocat_2(v0, v1, v2, v5) = v6) | ~ m2_cat_1(v5, v0, v4) | k2_isocat_1(v0, v4, v2, v5, v3) = v6) & ! [v5] : ! [v6] : ( ~ (k2_isocat_1(v0, v4, v2, v5, v3) = v6) | ~ m2_cat_1(v5, v0, v4) | k12_isocat_2(v0, v1, v2, v5) = v6)))
% 7.90/2.54 | (5) ! [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)))
% 7.90/2.54 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_zfmisc_1(v0, v1) = v2) | ~ v1_xboole_0(v2) | v1_xboole_0(v1) | v1_xboole_0(v0))
% 7.90/2.54 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (k17_cat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v3] : (k11_cat_2(v0, v1) = v3 & m2_cat_1(v2, v3, v1)))
% 7.90/2.54 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k12_isocat_2(v0, v1, v2, v3) = v4) | ~ l1_cat_1(v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v2) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | m2_cat_1(v4, v0, v2) | ? [v5] : (k11_cat_2(v1, v2) = v5 & ~ m2_cat_1(v3, v0, v5)))
% 7.90/2.54 | (9) k12_isocat_2(all_0_12_12, all_0_11_11, all_0_10_10, all_0_8_8) = all_0_6_6
% 7.90/2.54 | (10) ? [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)))
% 7.90/2.55 | (11) ! [v0] : ! [v1] : ( ~ (u2_cat_1(v0) = v1) | ~ v1_xboole_0(v1) | ~ l1_cat_1(v0))
% 7.90/2.55 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (k11_cat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v3] : (k17_cat_2(v0, v1) = v3 & m2_cat_1(v3, v2, v1)))
% 7.90/2.55 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (k2_isocat_1(v0, v1, v2, v3, v4) = v5) | ~ m2_cat_1(v4, v1, v2) | ~ m2_cat_1(v3, v0, v1) | ~ l1_cat_1(v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v2) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | k5_relat_1(v3, v4) = v5)
% 7.90/2.55 | (14) ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | m1_subset_1(v0, v1))
% 7.90/2.55 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k5_relat_1(v3, v2) = v1) | ~ (k5_relat_1(v3, v2) = v0))
% 7.90/2.55 | (16) ! [v0] : ! [v1] : (v1 = v0 | ~ v1_xboole_0(v1) | ~ v1_xboole_0(v0))
% 7.90/2.55 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (k8_isocat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v3] : (k11_cat_2(v0, v1) = v3 & m2_cat_1(v2, v3, v0)))
% 7.90/2.55 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k11_cat_2(v1, v2) = v3) | ~ l1_cat_1(v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v2) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v4] : (k9_isocat_2(v1, v2) = v4 & ! [v5] : ! [v6] : ( ~ (k12_isocat_2(v0, v1, v2, v5) = v6) | ~ m2_cat_1(v5, v0, v3) | k2_isocat_1(v0, v3, v2, v5, v4) = v6) & ! [v5] : ! [v6] : ( ~ (k2_isocat_1(v0, v3, v2, v5, v4) = v6) | ~ m2_cat_1(v5, v0, v3) | k12_isocat_2(v0, v1, v2, v5) = v6)))
% 7.90/2.55 | (19) ! [v0] : ! [v1] : ( ~ m1_subset_1(v0, v1) | v1_xboole_0(v1) | r2_hidden(v0, v1))
% 7.90/2.55 | (20) k12_isocat_2(all_0_12_12, all_0_11_11, all_0_10_10, all_0_5_5) = all_0_3_3
% 7.90/2.55 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k2_zfmisc_1(v3, v2) = v1) | ~ (k2_zfmisc_1(v3, v2) = v0))
% 7.90/2.55 | (22) r2_nattra_1(all_0_12_12, all_0_9_9, all_0_8_8, all_0_5_5)
% 7.90/2.55 | (23) v1_xboole_0(all_0_0_0)
% 7.90/2.55 | (24) ? [v0] : ? [v1] : ? [v2] : m2_relset_1(v2, v0, v1)
% 7.90/2.55 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (k2_isocat_1(v0, v1, v2, v4, v7) = v8) | ~ (k2_isocat_1(v0, v1, v2, v3, v5) = v6) | ~ r2_nattra_1(v1, v2, v5, v7) | ~ r2_nattra_1(v0, v1, v3, v4) | ~ m2_cat_1(v7, v1, v2) | ~ m2_cat_1(v5, v1, v2) | ~ m2_cat_1(v4, v0, v1) | ~ m2_cat_1(v3, v0, v1) | ~ l1_cat_1(v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v2) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | r2_nattra_1(v0, v2, v6, v8))
% 7.90/2.55 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (k5_relat_1(v0, v1) = v2) | ~ v1_relat_1(v1) | ~ v1_relat_1(v0) | v1_relat_1(v2))
% 7.90/2.55 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (k8_isocat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | k16_cat_2(v0, v1) = v2)
% 7.90/2.55 | (28) ? [v0] : r1_tarski(v0, v0)
% 7.90/2.55 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ m1_subset_1(v1, v3) | ~ v1_xboole_0(v2) | ~ r2_hidden(v0, v1))
% 7.90/2.55 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (k2_isocat_1(v0, v1, v2, v3, v4) = v5) | ~ m2_cat_1(v4, v1, v2) | ~ m2_cat_1(v3, v0, v1) | ~ l1_cat_1(v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v2) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | m2_cat_1(v5, v0, v2))
% 7.90/2.55 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (k11_cat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v3] : (k16_cat_2(v0, v1) = v3 & m2_cat_1(v3, v2, v0)))
% 7.90/2.55 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (k9_isocat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v3] : (k11_cat_2(v0, v1) = v3 & m2_cat_1(v2, v3, v1)))
% 7.90/2.55 | (33) ? [v0] : ? [v1] : m1_subset_1(v1, v0)
% 7.90/2.55 | (34) v1_xboole_0(k1_xboole_0)
% 7.90/2.55 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k8_isocat_2(v3, v2) = v1) | ~ (k8_isocat_2(v3, v2) = v0))
% 7.90/2.55 | (36) l1_cat_1(all_0_10_10)
% 7.90/2.55 | (37) ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ~ v1_xboole_0(v1))
% 7.90/2.55 | (38) ! [v0] : ! [v1] : ( ~ r2_hidden(v1, v0) | ~ r2_hidden(v0, v1))
% 7.90/2.55 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k8_isocat_2(v1, v2) = v3) | ~ l1_cat_1(v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v2) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v4] : (k11_cat_2(v1, v2) = v4 & ! [v5] : ! [v6] : ( ~ (k11_isocat_2(v0, v1, v2, v5) = v6) | ~ m2_cat_1(v5, v0, v4) | k2_isocat_1(v0, v4, v1, v5, v3) = v6) & ! [v5] : ! [v6] : ( ~ (k2_isocat_1(v0, v4, v1, v5, v3) = v6) | ~ m2_cat_1(v5, v0, v4) | k11_isocat_2(v0, v1, v2, v5) = v6)))
% 7.90/2.55 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (u2_cat_1(v1) = v3) | ~ (u2_cat_1(v0) = v2) | ~ m2_cat_1(v4, v0, v1) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | v1_funct_2(v4, v2, v3))
% 7.90/2.55 | (41) ~ v1_xboole_0(all_0_1_1)
% 7.90/2.55 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ m1_subset_1(v1, v3) | ~ r2_hidden(v0, v1) | m1_subset_1(v0, v2))
% 7.90/2.56 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k11_cat_2(v3, v2) = v1) | ~ (k11_cat_2(v3, v2) = v0))
% 7.90/2.56 | (44) m2_cat_1(all_0_5_5, all_0_12_12, all_0_9_9)
% 7.90/2.56 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_zfmisc_1(v1) = v2) | ~ r1_tarski(v0, v1) | m1_subset_1(v0, v2))
% 7.90/2.56 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_zfmisc_1(v1) = v2) | ~ m1_subset_1(v0, v2) | r1_tarski(v0, v1))
% 7.90/2.56 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k9_isocat_2(v3, v2) = v1) | ~ (k9_isocat_2(v3, v2) = v0))
% 7.90/2.56 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k17_cat_2(v3, v2) = v1) | ~ (k17_cat_2(v3, v2) = v0))
% 7.90/2.56 | (49) ~ r2_nattra_1(all_0_12_12, all_0_10_10, all_0_6_6, all_0_3_3) | ~ r2_nattra_1(all_0_12_12, all_0_11_11, all_0_7_7, all_0_4_4)
% 7.90/2.56 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (k11_isocat_2(v5, v4, v3, v2) = v1) | ~ (k11_isocat_2(v5, v4, v3, v2) = v0))
% 7.90/2.56 | (51) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (u2_cat_1(v2) = v1) | ~ (u2_cat_1(v2) = v0))
% 7.90/2.56 | (52) ! [v0] : ! [v1] : ! [v2] : ( ~ (k11_cat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v3] : (k9_isocat_2(v0, v1) = v3 & m2_cat_1(v3, v2, v1)))
% 7.90/2.56 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ m2_cat_1(v3, v0, v1) | ~ m2_cat_1(v2, v0, v1) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | r2_nattra_1(v0, v1, v2, v2))
% 7.90/2.56 | (54) l1_cat_1(all_0_12_12)
% 7.90/2.56 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (u2_cat_1(v1) = v3) | ~ (u2_cat_1(v0) = v2) | ~ m2_cat_1(v4, v0, v1) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | v1_funct_1(v4))
% 7.90/2.56 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (k17_cat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | k9_isocat_2(v0, v1) = v2)
% 7.90/2.56 | (57) l1_cat_1(all_0_2_2)
% 7.90/2.56 | (58) ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ? [v2] : (m1_subset_1(v2, v1) & v1_xboole_0(v2)))
% 7.90/2.56 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k11_isocat_2(v0, v1, v2, v3) = v4) | ~ l1_cat_1(v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v2) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | m2_cat_1(v4, v0, v1) | ? [v5] : (k11_cat_2(v1, v2) = v5 & ~ m2_cat_1(v3, v0, v5)))
% 7.90/2.56 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ (k16_cat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v3] : (k11_cat_2(v0, v1) = v3 & m2_cat_1(v2, v3, v0)))
% 7.90/2.56 | (61) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0))
% 7.90/2.56 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (u2_cat_1(v1) = v3) | ~ (u2_cat_1(v0) = v2) | ~ m2_cat_1(v4, v0, v1) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | m2_relset_1(v4, v2, v3))
% 7.90/2.56 | (63) k11_isocat_2(all_0_12_12, all_0_11_11, all_0_10_10, all_0_5_5) = all_0_4_4
% 7.90/2.56 | (64) ! [v0] : ! [v1] : ( ~ v1_xboole_0(v1) | ~ r2_hidden(v0, v1))
% 7.90/2.56 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k11_cat_2(v1, v2) = v3) | ~ l1_cat_1(v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v2) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v4] : (k8_isocat_2(v1, v2) = v4 & ! [v5] : ! [v6] : ( ~ (k11_isocat_2(v0, v1, v2, v5) = v6) | ~ m2_cat_1(v5, v0, v3) | k2_isocat_1(v0, v3, v1, v5, v4) = v6) & ! [v5] : ! [v6] : ( ~ (k2_isocat_1(v0, v3, v1, v5, v4) = v6) | ~ m2_cat_1(v5, v0, v3) | k11_isocat_2(v0, v1, v2, v5) = v6)))
% 7.90/2.56 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (k12_isocat_2(v5, v4, v3, v2) = v1) | ~ (k12_isocat_2(v5, v4, v3, v2) = v0))
% 7.90/2.56 | (67) ! [v0] : ! [v1] : ! [v2] : ( ~ (k9_isocat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | k17_cat_2(v0, v1) = v2)
% 8.34/2.56 | (68) k11_isocat_2(all_0_12_12, all_0_11_11, all_0_10_10, all_0_8_8) = all_0_7_7
% 8.34/2.56 | (69) l1_cat_1(all_0_11_11)
% 8.34/2.56 | (70) ! [v0] : ! [v1] : ! [v2] : ( ~ m1_relset_1(v2, v0, v1) | m2_relset_1(v2, v0, v1))
% 8.34/2.56 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ m2_relset_1(v2, v0, v1) | m1_relset_1(v2, v0, v1))
% 8.34/2.56 | (72) ! [v0] : ! [v1] : ! [v2] : ( ~ (k11_cat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | l1_cat_1(v2))
% 8.34/2.56 | (73) ! [v0] : ! [v1] : ( ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v2] : m2_cat_1(v2, v0, v1))
% 8.34/2.56 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (k11_cat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | v2_cat_1(v2))
% 8.34/2.57 | (75) v2_cat_1(all_0_12_12)
% 8.34/2.57 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k16_cat_2(v3, v2) = v1) | ~ (k16_cat_2(v3, v2) = v0))
% 8.34/2.57 | (77) ! [v0] : ! [v1] : ! [v2] : ( ~ (k16_cat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | k8_isocat_2(v0, v1) = v2)
% 8.34/2.57 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (k2_isocat_1(v6, v5, v4, v3, v2) = v1) | ~ (k2_isocat_1(v6, v5, v4, v3, v2) = v0))
% 8.34/2.57 | (79) ! [v0] : ! [v1] : ! [v2] : ( ~ (k11_cat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v3] : (k8_isocat_2(v0, v1) = v3 & m2_cat_1(v3, v2, v0)))
% 8.34/2.57 | (80) ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | v1_xboole_0(v0) | ? [v2] : (m1_subset_1(v2, v1) & ~ v1_xboole_0(v2)))
% 8.34/2.57 | (81) m2_cat_1(all_0_8_8, all_0_12_12, all_0_9_9)
% 8.34/2.57 | (82) ! [v0] : (v0 = k1_xboole_0 | ~ v1_xboole_0(v0))
% 8.34/2.57 | (83) k11_cat_2(all_0_11_11, all_0_10_10) = all_0_9_9
% 8.34/2.57 | (84) ? [v0] : ? [v1] : ? [v2] : m1_relset_1(v2, v0, v1)
% 8.34/2.57 |
% 8.34/2.57 | Instantiating formula (18) with all_0_9_9, all_0_10_10, all_0_11_11, all_0_11_11 and discharging atoms k11_cat_2(all_0_11_11, all_0_10_10) = all_0_9_9, l1_cat_1(all_0_10_10), l1_cat_1(all_0_11_11), v2_cat_1(all_0_10_10), v2_cat_1(all_0_11_11), yields:
% 8.34/2.57 | (85) ? [v0] : (k9_isocat_2(all_0_11_11, all_0_10_10) = v0 & ! [v1] : ! [v2] : ( ~ (k12_isocat_2(all_0_11_11, all_0_11_11, all_0_10_10, v1) = v2) | ~ m2_cat_1(v1, all_0_11_11, all_0_9_9) | k2_isocat_1(all_0_11_11, all_0_9_9, all_0_10_10, v1, v0) = v2) & ! [v1] : ! [v2] : ( ~ (k2_isocat_1(all_0_11_11, all_0_9_9, all_0_10_10, v1, v0) = v2) | ~ m2_cat_1(v1, all_0_11_11, all_0_9_9) | k12_isocat_2(all_0_11_11, all_0_11_11, all_0_10_10, v1) = v2))
% 8.34/2.57 |
% 8.34/2.57 | Instantiating formula (65) with all_0_9_9, all_0_10_10, all_0_11_11, all_0_11_11 and discharging atoms k11_cat_2(all_0_11_11, all_0_10_10) = all_0_9_9, l1_cat_1(all_0_10_10), l1_cat_1(all_0_11_11), v2_cat_1(all_0_10_10), v2_cat_1(all_0_11_11), yields:
% 8.34/2.57 | (86) ? [v0] : (k8_isocat_2(all_0_11_11, all_0_10_10) = v0 & ! [v1] : ! [v2] : ( ~ (k11_isocat_2(all_0_11_11, all_0_11_11, all_0_10_10, v1) = v2) | ~ m2_cat_1(v1, all_0_11_11, all_0_9_9) | k2_isocat_1(all_0_11_11, all_0_9_9, all_0_11_11, v1, v0) = v2) & ! [v1] : ! [v2] : ( ~ (k2_isocat_1(all_0_11_11, all_0_9_9, all_0_11_11, v1, v0) = v2) | ~ m2_cat_1(v1, all_0_11_11, all_0_9_9) | k11_isocat_2(all_0_11_11, all_0_11_11, all_0_10_10, v1) = v2))
% 8.34/2.57 |
% 8.34/2.57 | Instantiating formula (18) with all_0_9_9, all_0_10_10, all_0_11_11, all_0_10_10 and discharging atoms k11_cat_2(all_0_11_11, all_0_10_10) = all_0_9_9, l1_cat_1(all_0_10_10), l1_cat_1(all_0_11_11), v2_cat_1(all_0_10_10), v2_cat_1(all_0_11_11), yields:
% 8.34/2.57 | (87) ? [v0] : (k9_isocat_2(all_0_11_11, all_0_10_10) = v0 & ! [v1] : ! [v2] : ( ~ (k12_isocat_2(all_0_10_10, all_0_11_11, all_0_10_10, v1) = v2) | ~ m2_cat_1(v1, all_0_10_10, all_0_9_9) | k2_isocat_1(all_0_10_10, all_0_9_9, all_0_10_10, v1, v0) = v2) & ! [v1] : ! [v2] : ( ~ (k2_isocat_1(all_0_10_10, all_0_9_9, all_0_10_10, v1, v0) = v2) | ~ m2_cat_1(v1, all_0_10_10, all_0_9_9) | k12_isocat_2(all_0_10_10, all_0_11_11, all_0_10_10, v1) = v2))
% 8.34/2.57 |
% 8.34/2.57 | Instantiating formula (65) with all_0_9_9, all_0_10_10, all_0_11_11, all_0_10_10 and discharging atoms k11_cat_2(all_0_11_11, all_0_10_10) = all_0_9_9, l1_cat_1(all_0_10_10), l1_cat_1(all_0_11_11), v2_cat_1(all_0_10_10), v2_cat_1(all_0_11_11), yields:
% 8.34/2.57 | (88) ? [v0] : (k8_isocat_2(all_0_11_11, all_0_10_10) = v0 & ! [v1] : ! [v2] : ( ~ (k11_isocat_2(all_0_10_10, all_0_11_11, all_0_10_10, v1) = v2) | ~ m2_cat_1(v1, all_0_10_10, all_0_9_9) | k2_isocat_1(all_0_10_10, all_0_9_9, all_0_11_11, v1, v0) = v2) & ! [v1] : ! [v2] : ( ~ (k2_isocat_1(all_0_10_10, all_0_9_9, all_0_11_11, v1, v0) = v2) | ~ m2_cat_1(v1, all_0_10_10, all_0_9_9) | k11_isocat_2(all_0_10_10, all_0_11_11, all_0_10_10, v1) = v2))
% 8.34/2.57 |
% 8.34/2.57 | Instantiating formula (72) with all_0_9_9, all_0_10_10, all_0_11_11 and discharging atoms k11_cat_2(all_0_11_11, all_0_10_10) = all_0_9_9, l1_cat_1(all_0_10_10), l1_cat_1(all_0_11_11), v2_cat_1(all_0_10_10), v2_cat_1(all_0_11_11), yields:
% 8.34/2.57 | (89) l1_cat_1(all_0_9_9)
% 8.34/2.57 |
% 8.34/2.57 | Instantiating formula (74) with all_0_9_9, all_0_10_10, all_0_11_11 and discharging atoms k11_cat_2(all_0_11_11, all_0_10_10) = all_0_9_9, l1_cat_1(all_0_10_10), l1_cat_1(all_0_11_11), v2_cat_1(all_0_10_10), v2_cat_1(all_0_11_11), yields:
% 8.34/2.57 | (90) v2_cat_1(all_0_9_9)
% 8.34/2.57 |
% 8.34/2.57 | Instantiating formula (52) with all_0_9_9, all_0_10_10, all_0_11_11 and discharging atoms k11_cat_2(all_0_11_11, all_0_10_10) = all_0_9_9, l1_cat_1(all_0_10_10), l1_cat_1(all_0_11_11), v2_cat_1(all_0_10_10), v2_cat_1(all_0_11_11), yields:
% 8.34/2.57 | (91) ? [v0] : (k9_isocat_2(all_0_11_11, all_0_10_10) = v0 & m2_cat_1(v0, all_0_9_9, all_0_10_10))
% 8.34/2.57 |
% 8.34/2.57 | Instantiating formula (79) with all_0_9_9, all_0_10_10, all_0_11_11 and discharging atoms k11_cat_2(all_0_11_11, all_0_10_10) = all_0_9_9, l1_cat_1(all_0_10_10), l1_cat_1(all_0_11_11), v2_cat_1(all_0_10_10), v2_cat_1(all_0_11_11), yields:
% 8.34/2.58 | (92) ? [v0] : (k8_isocat_2(all_0_11_11, all_0_10_10) = v0 & m2_cat_1(v0, all_0_9_9, all_0_11_11))
% 8.34/2.58 |
% 8.34/2.58 | Instantiating formula (12) with all_0_9_9, all_0_10_10, all_0_11_11 and discharging atoms k11_cat_2(all_0_11_11, all_0_10_10) = all_0_9_9, l1_cat_1(all_0_10_10), l1_cat_1(all_0_11_11), v2_cat_1(all_0_10_10), v2_cat_1(all_0_11_11), yields:
% 8.34/2.58 | (93) ? [v0] : (k17_cat_2(all_0_11_11, all_0_10_10) = v0 & m2_cat_1(v0, all_0_9_9, all_0_10_10))
% 8.34/2.58 |
% 8.34/2.58 | Instantiating formula (31) with all_0_9_9, all_0_10_10, all_0_11_11 and discharging atoms k11_cat_2(all_0_11_11, all_0_10_10) = all_0_9_9, l1_cat_1(all_0_10_10), l1_cat_1(all_0_11_11), v2_cat_1(all_0_10_10), v2_cat_1(all_0_11_11), yields:
% 8.34/2.58 | (94) ? [v0] : (k16_cat_2(all_0_11_11, all_0_10_10) = v0 & m2_cat_1(v0, all_0_9_9, all_0_11_11))
% 8.34/2.58 |
% 8.34/2.58 | Instantiating formula (18) with all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12 and discharging atoms k11_cat_2(all_0_11_11, all_0_10_10) = all_0_9_9, l1_cat_1(all_0_10_10), l1_cat_1(all_0_11_11), l1_cat_1(all_0_12_12), v2_cat_1(all_0_10_10), v2_cat_1(all_0_11_11), v2_cat_1(all_0_12_12), yields:
% 8.34/2.58 | (95) ? [v0] : (k9_isocat_2(all_0_11_11, all_0_10_10) = v0 & ! [v1] : ! [v2] : ( ~ (k12_isocat_2(all_0_12_12, all_0_11_11, all_0_10_10, v1) = v2) | ~ m2_cat_1(v1, all_0_12_12, all_0_9_9) | k2_isocat_1(all_0_12_12, all_0_9_9, all_0_10_10, v1, v0) = v2) & ! [v1] : ! [v2] : ( ~ (k2_isocat_1(all_0_12_12, all_0_9_9, all_0_10_10, v1, v0) = v2) | ~ m2_cat_1(v1, all_0_12_12, all_0_9_9) | k12_isocat_2(all_0_12_12, all_0_11_11, all_0_10_10, v1) = v2))
% 8.34/2.58 |
% 8.34/2.58 | Instantiating formula (65) with all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12 and discharging atoms k11_cat_2(all_0_11_11, all_0_10_10) = all_0_9_9, l1_cat_1(all_0_10_10), l1_cat_1(all_0_11_11), l1_cat_1(all_0_12_12), v2_cat_1(all_0_10_10), v2_cat_1(all_0_11_11), v2_cat_1(all_0_12_12), yields:
% 8.34/2.58 | (96) ? [v0] : (k8_isocat_2(all_0_11_11, all_0_10_10) = v0 & ! [v1] : ! [v2] : ( ~ (k11_isocat_2(all_0_12_12, all_0_11_11, all_0_10_10, v1) = v2) | ~ m2_cat_1(v1, all_0_12_12, all_0_9_9) | k2_isocat_1(all_0_12_12, all_0_9_9, all_0_11_11, v1, v0) = v2) & ! [v1] : ! [v2] : ( ~ (k2_isocat_1(all_0_12_12, all_0_9_9, all_0_11_11, v1, v0) = v2) | ~ m2_cat_1(v1, all_0_12_12, all_0_9_9) | k11_isocat_2(all_0_12_12, all_0_11_11, all_0_10_10, v1) = v2))
% 8.34/2.58 |
% 8.34/2.58 | Instantiating (96) with all_25_0_24 yields:
% 8.34/2.58 | (97) k8_isocat_2(all_0_11_11, all_0_10_10) = all_25_0_24 & ! [v0] : ! [v1] : ( ~ (k11_isocat_2(all_0_12_12, all_0_11_11, all_0_10_10, v0) = v1) | ~ m2_cat_1(v0, all_0_12_12, all_0_9_9) | k2_isocat_1(all_0_12_12, all_0_9_9, all_0_11_11, v0, all_25_0_24) = v1) & ! [v0] : ! [v1] : ( ~ (k2_isocat_1(all_0_12_12, all_0_9_9, all_0_11_11, v0, all_25_0_24) = v1) | ~ m2_cat_1(v0, all_0_12_12, all_0_9_9) | k11_isocat_2(all_0_12_12, all_0_11_11, all_0_10_10, v0) = v1)
% 8.34/2.58 |
% 8.34/2.58 | Applying alpha-rule on (97) yields:
% 8.34/2.58 | (98) k8_isocat_2(all_0_11_11, all_0_10_10) = all_25_0_24
% 8.34/2.58 | (99) ! [v0] : ! [v1] : ( ~ (k11_isocat_2(all_0_12_12, all_0_11_11, all_0_10_10, v0) = v1) | ~ m2_cat_1(v0, all_0_12_12, all_0_9_9) | k2_isocat_1(all_0_12_12, all_0_9_9, all_0_11_11, v0, all_25_0_24) = v1)
% 8.34/2.58 | (100) ! [v0] : ! [v1] : ( ~ (k2_isocat_1(all_0_12_12, all_0_9_9, all_0_11_11, v0, all_25_0_24) = v1) | ~ m2_cat_1(v0, all_0_12_12, all_0_9_9) | k11_isocat_2(all_0_12_12, all_0_11_11, all_0_10_10, v0) = v1)
% 8.34/2.58 |
% 8.34/2.58 | Instantiating formula (99) with all_0_4_4, all_0_5_5 and discharging atoms k11_isocat_2(all_0_12_12, all_0_11_11, all_0_10_10, all_0_5_5) = all_0_4_4, m2_cat_1(all_0_5_5, all_0_12_12, all_0_9_9), yields:
% 8.34/2.58 | (101) k2_isocat_1(all_0_12_12, all_0_9_9, all_0_11_11, all_0_5_5, all_25_0_24) = all_0_4_4
% 8.34/2.58 |
% 8.34/2.58 | Instantiating formula (99) with all_0_7_7, all_0_8_8 and discharging atoms k11_isocat_2(all_0_12_12, all_0_11_11, all_0_10_10, all_0_8_8) = all_0_7_7, m2_cat_1(all_0_8_8, all_0_12_12, all_0_9_9), yields:
% 8.34/2.58 | (102) k2_isocat_1(all_0_12_12, all_0_9_9, all_0_11_11, all_0_8_8, all_25_0_24) = all_0_7_7
% 8.34/2.58 |
% 8.34/2.58 | Instantiating (88) with all_29_0_25 yields:
% 8.34/2.58 | (103) k8_isocat_2(all_0_11_11, all_0_10_10) = all_29_0_25 & ! [v0] : ! [v1] : ( ~ (k11_isocat_2(all_0_10_10, all_0_11_11, all_0_10_10, v0) = v1) | ~ m2_cat_1(v0, all_0_10_10, all_0_9_9) | k2_isocat_1(all_0_10_10, all_0_9_9, all_0_11_11, v0, all_29_0_25) = v1) & ! [v0] : ! [v1] : ( ~ (k2_isocat_1(all_0_10_10, all_0_9_9, all_0_11_11, v0, all_29_0_25) = v1) | ~ m2_cat_1(v0, all_0_10_10, all_0_9_9) | k11_isocat_2(all_0_10_10, all_0_11_11, all_0_10_10, v0) = v1)
% 8.34/2.58 |
% 8.34/2.58 | Applying alpha-rule on (103) yields:
% 8.34/2.58 | (104) k8_isocat_2(all_0_11_11, all_0_10_10) = all_29_0_25
% 8.34/2.58 | (105) ! [v0] : ! [v1] : ( ~ (k11_isocat_2(all_0_10_10, all_0_11_11, all_0_10_10, v0) = v1) | ~ m2_cat_1(v0, all_0_10_10, all_0_9_9) | k2_isocat_1(all_0_10_10, all_0_9_9, all_0_11_11, v0, all_29_0_25) = v1)
% 8.34/2.59 | (106) ! [v0] : ! [v1] : ( ~ (k2_isocat_1(all_0_10_10, all_0_9_9, all_0_11_11, v0, all_29_0_25) = v1) | ~ m2_cat_1(v0, all_0_10_10, all_0_9_9) | k11_isocat_2(all_0_10_10, all_0_11_11, all_0_10_10, v0) = v1)
% 8.34/2.59 |
% 8.34/2.59 | Instantiating (95) with all_32_0_26 yields:
% 8.34/2.59 | (107) k9_isocat_2(all_0_11_11, all_0_10_10) = all_32_0_26 & ! [v0] : ! [v1] : ( ~ (k12_isocat_2(all_0_12_12, all_0_11_11, all_0_10_10, v0) = v1) | ~ m2_cat_1(v0, all_0_12_12, all_0_9_9) | k2_isocat_1(all_0_12_12, all_0_9_9, all_0_10_10, v0, all_32_0_26) = v1) & ! [v0] : ! [v1] : ( ~ (k2_isocat_1(all_0_12_12, all_0_9_9, all_0_10_10, v0, all_32_0_26) = v1) | ~ m2_cat_1(v0, all_0_12_12, all_0_9_9) | k12_isocat_2(all_0_12_12, all_0_11_11, all_0_10_10, v0) = v1)
% 8.34/2.59 |
% 8.34/2.59 | Applying alpha-rule on (107) yields:
% 8.34/2.59 | (108) k9_isocat_2(all_0_11_11, all_0_10_10) = all_32_0_26
% 8.34/2.59 | (109) ! [v0] : ! [v1] : ( ~ (k12_isocat_2(all_0_12_12, all_0_11_11, all_0_10_10, v0) = v1) | ~ m2_cat_1(v0, all_0_12_12, all_0_9_9) | k2_isocat_1(all_0_12_12, all_0_9_9, all_0_10_10, v0, all_32_0_26) = v1)
% 8.34/2.59 | (110) ! [v0] : ! [v1] : ( ~ (k2_isocat_1(all_0_12_12, all_0_9_9, all_0_10_10, v0, all_32_0_26) = v1) | ~ m2_cat_1(v0, all_0_12_12, all_0_9_9) | k12_isocat_2(all_0_12_12, all_0_11_11, all_0_10_10, v0) = v1)
% 8.34/2.59 |
% 8.34/2.59 | Instantiating formula (109) with all_0_3_3, all_0_5_5 and discharging atoms k12_isocat_2(all_0_12_12, all_0_11_11, all_0_10_10, all_0_5_5) = all_0_3_3, m2_cat_1(all_0_5_5, all_0_12_12, all_0_9_9), yields:
% 8.34/2.59 | (111) k2_isocat_1(all_0_12_12, all_0_9_9, all_0_10_10, all_0_5_5, all_32_0_26) = all_0_3_3
% 8.34/2.59 |
% 8.34/2.59 | Instantiating formula (109) with all_0_6_6, all_0_8_8 and discharging atoms k12_isocat_2(all_0_12_12, all_0_11_11, all_0_10_10, all_0_8_8) = all_0_6_6, m2_cat_1(all_0_8_8, all_0_12_12, all_0_9_9), yields:
% 8.34/2.59 | (112) k2_isocat_1(all_0_12_12, all_0_9_9, all_0_10_10, all_0_8_8, all_32_0_26) = all_0_6_6
% 8.34/2.59 |
% 8.34/2.59 | Instantiating (94) with all_48_0_33 yields:
% 8.34/2.59 | (113) k16_cat_2(all_0_11_11, all_0_10_10) = all_48_0_33 & m2_cat_1(all_48_0_33, all_0_9_9, all_0_11_11)
% 8.34/2.59 |
% 8.34/2.59 | Applying alpha-rule on (113) yields:
% 8.34/2.59 | (114) k16_cat_2(all_0_11_11, all_0_10_10) = all_48_0_33
% 8.34/2.59 | (115) m2_cat_1(all_48_0_33, all_0_9_9, all_0_11_11)
% 8.34/2.59 |
% 8.34/2.59 | Instantiating (91) with all_50_0_34 yields:
% 8.34/2.59 | (116) k9_isocat_2(all_0_11_11, all_0_10_10) = all_50_0_34 & m2_cat_1(all_50_0_34, all_0_9_9, all_0_10_10)
% 8.34/2.59 |
% 8.34/2.59 | Applying alpha-rule on (116) yields:
% 8.34/2.59 | (117) k9_isocat_2(all_0_11_11, all_0_10_10) = all_50_0_34
% 8.34/2.59 | (118) m2_cat_1(all_50_0_34, all_0_9_9, all_0_10_10)
% 8.34/2.59 |
% 8.34/2.59 | Instantiating (93) with all_52_0_35 yields:
% 8.34/2.59 | (119) k17_cat_2(all_0_11_11, all_0_10_10) = all_52_0_35 & m2_cat_1(all_52_0_35, all_0_9_9, all_0_10_10)
% 8.34/2.59 |
% 8.34/2.59 | Applying alpha-rule on (119) yields:
% 8.34/2.59 | (120) k17_cat_2(all_0_11_11, all_0_10_10) = all_52_0_35
% 8.34/2.59 | (121) m2_cat_1(all_52_0_35, all_0_9_9, all_0_10_10)
% 8.34/2.59 |
% 8.34/2.59 | Instantiating (92) with all_54_0_36 yields:
% 8.34/2.59 | (122) k8_isocat_2(all_0_11_11, all_0_10_10) = all_54_0_36 & m2_cat_1(all_54_0_36, all_0_9_9, all_0_11_11)
% 8.47/2.59 |
% 8.47/2.59 | Applying alpha-rule on (122) yields:
% 8.47/2.59 | (123) k8_isocat_2(all_0_11_11, all_0_10_10) = all_54_0_36
% 8.47/2.59 | (124) m2_cat_1(all_54_0_36, all_0_9_9, all_0_11_11)
% 8.47/2.59 |
% 8.47/2.59 | Instantiating (87) with all_58_0_38 yields:
% 8.47/2.59 | (125) k9_isocat_2(all_0_11_11, all_0_10_10) = all_58_0_38 & ! [v0] : ! [v1] : ( ~ (k12_isocat_2(all_0_10_10, all_0_11_11, all_0_10_10, v0) = v1) | ~ m2_cat_1(v0, all_0_10_10, all_0_9_9) | k2_isocat_1(all_0_10_10, all_0_9_9, all_0_10_10, v0, all_58_0_38) = v1) & ! [v0] : ! [v1] : ( ~ (k2_isocat_1(all_0_10_10, all_0_9_9, all_0_10_10, v0, all_58_0_38) = v1) | ~ m2_cat_1(v0, all_0_10_10, all_0_9_9) | k12_isocat_2(all_0_10_10, all_0_11_11, all_0_10_10, v0) = v1)
% 8.47/2.59 |
% 8.47/2.59 | Applying alpha-rule on (125) yields:
% 8.47/2.59 | (126) k9_isocat_2(all_0_11_11, all_0_10_10) = all_58_0_38
% 8.47/2.59 | (127) ! [v0] : ! [v1] : ( ~ (k12_isocat_2(all_0_10_10, all_0_11_11, all_0_10_10, v0) = v1) | ~ m2_cat_1(v0, all_0_10_10, all_0_9_9) | k2_isocat_1(all_0_10_10, all_0_9_9, all_0_10_10, v0, all_58_0_38) = v1)
% 8.47/2.59 | (128) ! [v0] : ! [v1] : ( ~ (k2_isocat_1(all_0_10_10, all_0_9_9, all_0_10_10, v0, all_58_0_38) = v1) | ~ m2_cat_1(v0, all_0_10_10, all_0_9_9) | k12_isocat_2(all_0_10_10, all_0_11_11, all_0_10_10, v0) = v1)
% 8.47/2.59 |
% 8.47/2.59 | Instantiating (86) with all_61_0_39 yields:
% 8.47/2.59 | (129) k8_isocat_2(all_0_11_11, all_0_10_10) = all_61_0_39 & ! [v0] : ! [v1] : ( ~ (k11_isocat_2(all_0_11_11, all_0_11_11, all_0_10_10, v0) = v1) | ~ m2_cat_1(v0, all_0_11_11, all_0_9_9) | k2_isocat_1(all_0_11_11, all_0_9_9, all_0_11_11, v0, all_61_0_39) = v1) & ! [v0] : ! [v1] : ( ~ (k2_isocat_1(all_0_11_11, all_0_9_9, all_0_11_11, v0, all_61_0_39) = v1) | ~ m2_cat_1(v0, all_0_11_11, all_0_9_9) | k11_isocat_2(all_0_11_11, all_0_11_11, all_0_10_10, v0) = v1)
% 8.47/2.59 |
% 8.47/2.59 | Applying alpha-rule on (129) yields:
% 8.47/2.59 | (130) k8_isocat_2(all_0_11_11, all_0_10_10) = all_61_0_39
% 8.47/2.59 | (131) ! [v0] : ! [v1] : ( ~ (k11_isocat_2(all_0_11_11, all_0_11_11, all_0_10_10, v0) = v1) | ~ m2_cat_1(v0, all_0_11_11, all_0_9_9) | k2_isocat_1(all_0_11_11, all_0_9_9, all_0_11_11, v0, all_61_0_39) = v1)
% 8.47/2.59 | (132) ! [v0] : ! [v1] : ( ~ (k2_isocat_1(all_0_11_11, all_0_9_9, all_0_11_11, v0, all_61_0_39) = v1) | ~ m2_cat_1(v0, all_0_11_11, all_0_9_9) | k11_isocat_2(all_0_11_11, all_0_11_11, all_0_10_10, v0) = v1)
% 8.47/2.59 |
% 8.47/2.59 | Instantiating (85) with all_64_0_40 yields:
% 8.47/2.59 | (133) k9_isocat_2(all_0_11_11, all_0_10_10) = all_64_0_40 & ! [v0] : ! [v1] : ( ~ (k12_isocat_2(all_0_11_11, all_0_11_11, all_0_10_10, v0) = v1) | ~ m2_cat_1(v0, all_0_11_11, all_0_9_9) | k2_isocat_1(all_0_11_11, all_0_9_9, all_0_10_10, v0, all_64_0_40) = v1) & ! [v0] : ! [v1] : ( ~ (k2_isocat_1(all_0_11_11, all_0_9_9, all_0_10_10, v0, all_64_0_40) = v1) | ~ m2_cat_1(v0, all_0_11_11, all_0_9_9) | k12_isocat_2(all_0_11_11, all_0_11_11, all_0_10_10, v0) = v1)
% 8.47/2.59 |
% 8.47/2.59 | Applying alpha-rule on (133) yields:
% 8.47/2.59 | (134) k9_isocat_2(all_0_11_11, all_0_10_10) = all_64_0_40
% 8.47/2.59 | (135) ! [v0] : ! [v1] : ( ~ (k12_isocat_2(all_0_11_11, all_0_11_11, all_0_10_10, v0) = v1) | ~ m2_cat_1(v0, all_0_11_11, all_0_9_9) | k2_isocat_1(all_0_11_11, all_0_9_9, all_0_10_10, v0, all_64_0_40) = v1)
% 8.47/2.59 | (136) ! [v0] : ! [v1] : ( ~ (k2_isocat_1(all_0_11_11, all_0_9_9, all_0_10_10, v0, all_64_0_40) = v1) | ~ m2_cat_1(v0, all_0_11_11, all_0_9_9) | k12_isocat_2(all_0_11_11, all_0_11_11, all_0_10_10, v0) = v1)
% 8.47/2.59 |
% 8.47/2.59 | Instantiating formula (47) with all_0_11_11, all_0_10_10, all_58_0_38, all_64_0_40 and discharging atoms k9_isocat_2(all_0_11_11, all_0_10_10) = all_64_0_40, k9_isocat_2(all_0_11_11, all_0_10_10) = all_58_0_38, yields:
% 8.47/2.59 | (137) all_64_0_40 = all_58_0_38
% 8.47/2.59 |
% 8.47/2.59 | Instantiating formula (47) with all_0_11_11, all_0_10_10, all_50_0_34, all_58_0_38 and discharging atoms k9_isocat_2(all_0_11_11, all_0_10_10) = all_58_0_38, k9_isocat_2(all_0_11_11, all_0_10_10) = all_50_0_34, yields:
% 8.47/2.59 | (138) all_58_0_38 = all_50_0_34
% 8.47/2.59 |
% 8.47/2.59 | Instantiating formula (47) with all_0_11_11, all_0_10_10, all_32_0_26, all_64_0_40 and discharging atoms k9_isocat_2(all_0_11_11, all_0_10_10) = all_64_0_40, k9_isocat_2(all_0_11_11, all_0_10_10) = all_32_0_26, yields:
% 8.47/2.59 | (139) all_64_0_40 = all_32_0_26
% 8.47/2.59 |
% 8.47/2.59 | Instantiating formula (35) with all_0_11_11, all_0_10_10, all_54_0_36, all_61_0_39 and discharging atoms k8_isocat_2(all_0_11_11, all_0_10_10) = all_61_0_39, k8_isocat_2(all_0_11_11, all_0_10_10) = all_54_0_36, yields:
% 8.47/2.59 | (140) all_61_0_39 = all_54_0_36
% 8.47/2.59 |
% 8.47/2.59 | Instantiating formula (35) with all_0_11_11, all_0_10_10, all_29_0_25, all_61_0_39 and discharging atoms k8_isocat_2(all_0_11_11, all_0_10_10) = all_61_0_39, k8_isocat_2(all_0_11_11, all_0_10_10) = all_29_0_25, yields:
% 8.47/2.59 | (141) all_61_0_39 = all_29_0_25
% 8.47/2.59 |
% 8.47/2.59 | Instantiating formula (35) with all_0_11_11, all_0_10_10, all_25_0_24, all_54_0_36 and discharging atoms k8_isocat_2(all_0_11_11, all_0_10_10) = all_54_0_36, k8_isocat_2(all_0_11_11, all_0_10_10) = all_25_0_24, yields:
% 8.47/2.59 | (142) all_54_0_36 = all_25_0_24
% 8.47/2.59 |
% 8.47/2.59 | Combining equations (137,139) yields a new equation:
% 8.47/2.59 | (143) all_58_0_38 = all_32_0_26
% 8.47/2.59 |
% 8.47/2.59 | Simplifying 143 yields:
% 8.47/2.59 | (144) all_58_0_38 = all_32_0_26
% 8.47/2.59 |
% 8.47/2.59 | Combining equations (140,141) yields a new equation:
% 8.47/2.59 | (145) all_54_0_36 = all_29_0_25
% 8.47/2.59 |
% 8.47/2.59 | Simplifying 145 yields:
% 8.47/2.59 | (146) all_54_0_36 = all_29_0_25
% 8.47/2.59 |
% 8.47/2.60 | Combining equations (138,144) yields a new equation:
% 8.47/2.60 | (147) all_50_0_34 = all_32_0_26
% 8.47/2.60 |
% 8.47/2.60 | Simplifying 147 yields:
% 8.47/2.60 | (148) all_50_0_34 = all_32_0_26
% 8.47/2.60 |
% 8.47/2.60 | Combining equations (146,142) yields a new equation:
% 8.47/2.60 | (149) all_29_0_25 = all_25_0_24
% 8.47/2.60 |
% 8.47/2.60 | Simplifying 149 yields:
% 8.47/2.60 | (150) all_29_0_25 = all_25_0_24
% 8.47/2.60 |
% 8.47/2.60 | From (148) and (117) follows:
% 8.47/2.60 | (108) k9_isocat_2(all_0_11_11, all_0_10_10) = all_32_0_26
% 8.47/2.60 |
% 8.47/2.60 | From (150) and (104) follows:
% 8.47/2.60 | (98) k8_isocat_2(all_0_11_11, all_0_10_10) = all_25_0_24
% 8.47/2.60 |
% 8.47/2.60 | From (142) and (124) follows:
% 8.47/2.60 | (153) m2_cat_1(all_25_0_24, all_0_9_9, all_0_11_11)
% 8.47/2.60 |
% 8.47/2.60 | From (148) and (118) follows:
% 8.47/2.60 | (154) m2_cat_1(all_32_0_26, all_0_9_9, all_0_10_10)
% 8.47/2.60 |
% 8.47/2.60 | Instantiating formula (56) with all_52_0_35, all_0_10_10, all_0_11_11 and discharging atoms k17_cat_2(all_0_11_11, all_0_10_10) = all_52_0_35, l1_cat_1(all_0_10_10), l1_cat_1(all_0_11_11), v2_cat_1(all_0_10_10), v2_cat_1(all_0_11_11), yields:
% 8.47/2.60 | (155) k9_isocat_2(all_0_11_11, all_0_10_10) = all_52_0_35
% 8.47/2.60 |
% 8.47/2.60 | Instantiating formula (77) with all_48_0_33, all_0_10_10, all_0_11_11 and discharging atoms k16_cat_2(all_0_11_11, all_0_10_10) = all_48_0_33, l1_cat_1(all_0_10_10), l1_cat_1(all_0_11_11), v2_cat_1(all_0_10_10), v2_cat_1(all_0_11_11), yields:
% 8.47/2.60 | (156) k8_isocat_2(all_0_11_11, all_0_10_10) = all_48_0_33
% 8.47/2.60 |
% 8.47/2.60 | Instantiating formula (18) with all_0_9_9, all_0_10_10, all_0_11_11, all_0_9_9 and discharging atoms k11_cat_2(all_0_11_11, all_0_10_10) = all_0_9_9, l1_cat_1(all_0_9_9), l1_cat_1(all_0_10_10), l1_cat_1(all_0_11_11), v2_cat_1(all_0_9_9), v2_cat_1(all_0_10_10), v2_cat_1(all_0_11_11), yields:
% 8.47/2.60 | (157) ? [v0] : (k9_isocat_2(all_0_11_11, all_0_10_10) = v0 & ! [v1] : ! [v2] : ( ~ (k12_isocat_2(all_0_9_9, all_0_11_11, all_0_10_10, v1) = v2) | ~ m2_cat_1(v1, all_0_9_9, all_0_9_9) | k2_isocat_1(all_0_9_9, all_0_9_9, all_0_10_10, v1, v0) = v2) & ! [v1] : ! [v2] : ( ~ (k2_isocat_1(all_0_9_9, all_0_9_9, all_0_10_10, v1, v0) = v2) | ~ m2_cat_1(v1, all_0_9_9, all_0_9_9) | k12_isocat_2(all_0_9_9, all_0_11_11, all_0_10_10, v1) = v2))
% 8.47/2.60 |
% 8.47/2.60 | Instantiating formula (65) with all_0_9_9, all_0_10_10, all_0_11_11, all_0_9_9 and discharging atoms k11_cat_2(all_0_11_11, all_0_10_10) = all_0_9_9, l1_cat_1(all_0_9_9), l1_cat_1(all_0_10_10), l1_cat_1(all_0_11_11), v2_cat_1(all_0_9_9), v2_cat_1(all_0_10_10), v2_cat_1(all_0_11_11), yields:
% 8.47/2.60 | (158) ? [v0] : (k8_isocat_2(all_0_11_11, all_0_10_10) = v0 & ! [v1] : ! [v2] : ( ~ (k11_isocat_2(all_0_9_9, all_0_11_11, all_0_10_10, v1) = v2) | ~ m2_cat_1(v1, all_0_9_9, all_0_9_9) | k2_isocat_1(all_0_9_9, all_0_9_9, all_0_11_11, v1, v0) = v2) & ! [v1] : ! [v2] : ( ~ (k2_isocat_1(all_0_9_9, all_0_9_9, all_0_11_11, v1, v0) = v2) | ~ m2_cat_1(v1, all_0_9_9, all_0_9_9) | k11_isocat_2(all_0_9_9, all_0_11_11, all_0_10_10, v1) = v2))
% 8.47/2.60 |
% 8.47/2.60 | Instantiating formula (53) with all_32_0_26, all_52_0_35, all_0_10_10, all_0_9_9 and discharging atoms m2_cat_1(all_52_0_35, all_0_9_9, all_0_10_10), m2_cat_1(all_32_0_26, all_0_9_9, all_0_10_10), l1_cat_1(all_0_9_9), l1_cat_1(all_0_10_10), v2_cat_1(all_0_9_9), v2_cat_1(all_0_10_10), yields:
% 8.47/2.60 | (159) r2_nattra_1(all_0_9_9, all_0_10_10, all_52_0_35, all_52_0_35)
% 8.47/2.60 |
% 8.47/2.60 | Instantiating formula (53) with all_25_0_24, all_48_0_33, all_0_11_11, all_0_9_9 and discharging atoms m2_cat_1(all_48_0_33, all_0_9_9, all_0_11_11), m2_cat_1(all_25_0_24, all_0_9_9, all_0_11_11), l1_cat_1(all_0_9_9), l1_cat_1(all_0_11_11), v2_cat_1(all_0_9_9), v2_cat_1(all_0_11_11), yields:
% 8.47/2.60 | (160) r2_nattra_1(all_0_9_9, all_0_11_11, all_48_0_33, all_48_0_33)
% 8.47/2.60 |
% 8.47/2.60 | Instantiating (158) with all_97_0_43 yields:
% 8.47/2.60 | (161) k8_isocat_2(all_0_11_11, all_0_10_10) = all_97_0_43 & ! [v0] : ! [v1] : ( ~ (k11_isocat_2(all_0_9_9, all_0_11_11, all_0_10_10, v0) = v1) | ~ m2_cat_1(v0, all_0_9_9, all_0_9_9) | k2_isocat_1(all_0_9_9, all_0_9_9, all_0_11_11, v0, all_97_0_43) = v1) & ! [v0] : ! [v1] : ( ~ (k2_isocat_1(all_0_9_9, all_0_9_9, all_0_11_11, v0, all_97_0_43) = v1) | ~ m2_cat_1(v0, all_0_9_9, all_0_9_9) | k11_isocat_2(all_0_9_9, all_0_11_11, all_0_10_10, v0) = v1)
% 8.47/2.60 |
% 8.47/2.60 | Applying alpha-rule on (161) yields:
% 8.47/2.60 | (162) k8_isocat_2(all_0_11_11, all_0_10_10) = all_97_0_43
% 8.47/2.60 | (163) ! [v0] : ! [v1] : ( ~ (k11_isocat_2(all_0_9_9, all_0_11_11, all_0_10_10, v0) = v1) | ~ m2_cat_1(v0, all_0_9_9, all_0_9_9) | k2_isocat_1(all_0_9_9, all_0_9_9, all_0_11_11, v0, all_97_0_43) = v1)
% 8.47/2.60 | (164) ! [v0] : ! [v1] : ( ~ (k2_isocat_1(all_0_9_9, all_0_9_9, all_0_11_11, v0, all_97_0_43) = v1) | ~ m2_cat_1(v0, all_0_9_9, all_0_9_9) | k11_isocat_2(all_0_9_9, all_0_11_11, all_0_10_10, v0) = v1)
% 8.47/2.60 |
% 8.47/2.60 | Instantiating (157) with all_119_0_51 yields:
% 8.47/2.60 | (165) k9_isocat_2(all_0_11_11, all_0_10_10) = all_119_0_51 & ! [v0] : ! [v1] : ( ~ (k12_isocat_2(all_0_9_9, all_0_11_11, all_0_10_10, v0) = v1) | ~ m2_cat_1(v0, all_0_9_9, all_0_9_9) | k2_isocat_1(all_0_9_9, all_0_9_9, all_0_10_10, v0, all_119_0_51) = v1) & ! [v0] : ! [v1] : ( ~ (k2_isocat_1(all_0_9_9, all_0_9_9, all_0_10_10, v0, all_119_0_51) = v1) | ~ m2_cat_1(v0, all_0_9_9, all_0_9_9) | k12_isocat_2(all_0_9_9, all_0_11_11, all_0_10_10, v0) = v1)
% 8.47/2.60 |
% 8.47/2.60 | Applying alpha-rule on (165) yields:
% 8.47/2.60 | (166) k9_isocat_2(all_0_11_11, all_0_10_10) = all_119_0_51
% 8.47/2.60 | (167) ! [v0] : ! [v1] : ( ~ (k12_isocat_2(all_0_9_9, all_0_11_11, all_0_10_10, v0) = v1) | ~ m2_cat_1(v0, all_0_9_9, all_0_9_9) | k2_isocat_1(all_0_9_9, all_0_9_9, all_0_10_10, v0, all_119_0_51) = v1)
% 8.47/2.60 | (168) ! [v0] : ! [v1] : ( ~ (k2_isocat_1(all_0_9_9, all_0_9_9, all_0_10_10, v0, all_119_0_51) = v1) | ~ m2_cat_1(v0, all_0_9_9, all_0_9_9) | k12_isocat_2(all_0_9_9, all_0_11_11, all_0_10_10, v0) = v1)
% 8.47/2.60 |
% 8.47/2.60 | Instantiating formula (47) with all_0_11_11, all_0_10_10, all_119_0_51, all_32_0_26 and discharging atoms k9_isocat_2(all_0_11_11, all_0_10_10) = all_119_0_51, k9_isocat_2(all_0_11_11, all_0_10_10) = all_32_0_26, yields:
% 8.47/2.60 | (169) all_119_0_51 = all_32_0_26
% 8.47/2.60 |
% 8.47/2.60 | Instantiating formula (47) with all_0_11_11, all_0_10_10, all_52_0_35, all_119_0_51 and discharging atoms k9_isocat_2(all_0_11_11, all_0_10_10) = all_119_0_51, k9_isocat_2(all_0_11_11, all_0_10_10) = all_52_0_35, yields:
% 8.47/2.60 | (170) all_119_0_51 = all_52_0_35
% 8.47/2.60 |
% 8.47/2.60 | Instantiating formula (35) with all_0_11_11, all_0_10_10, all_97_0_43, all_25_0_24 and discharging atoms k8_isocat_2(all_0_11_11, all_0_10_10) = all_97_0_43, k8_isocat_2(all_0_11_11, all_0_10_10) = all_25_0_24, yields:
% 8.47/2.60 | (171) all_97_0_43 = all_25_0_24
% 8.47/2.60 |
% 8.47/2.60 | Instantiating formula (35) with all_0_11_11, all_0_10_10, all_48_0_33, all_97_0_43 and discharging atoms k8_isocat_2(all_0_11_11, all_0_10_10) = all_97_0_43, k8_isocat_2(all_0_11_11, all_0_10_10) = all_48_0_33, yields:
% 8.47/2.60 | (172) all_97_0_43 = all_48_0_33
% 8.47/2.60 |
% 8.47/2.60 | Combining equations (170,169) yields a new equation:
% 8.47/2.60 | (173) all_52_0_35 = all_32_0_26
% 8.47/2.60 |
% 8.47/2.60 | Simplifying 173 yields:
% 8.47/2.60 | (174) all_52_0_35 = all_32_0_26
% 8.47/2.60 |
% 8.47/2.60 | Combining equations (171,172) yields a new equation:
% 8.47/2.60 | (175) all_48_0_33 = all_25_0_24
% 8.47/2.60 |
% 8.47/2.60 | From (174)(174) and (159) follows:
% 8.47/2.60 | (176) r2_nattra_1(all_0_9_9, all_0_10_10, all_32_0_26, all_32_0_26)
% 8.47/2.60 |
% 8.47/2.60 | From (175)(175) and (160) follows:
% 8.47/2.60 | (177) r2_nattra_1(all_0_9_9, all_0_11_11, all_25_0_24, all_25_0_24)
% 8.47/2.60 |
% 8.47/2.60 | From (174) and (121) follows:
% 8.47/2.60 | (154) m2_cat_1(all_32_0_26, all_0_9_9, all_0_10_10)
% 8.47/2.60 |
% 8.47/2.60 | From (175) and (115) follows:
% 8.47/2.60 | (153) m2_cat_1(all_25_0_24, all_0_9_9, all_0_11_11)
% 8.47/2.60 |
% 8.47/2.60 | Instantiating formula (25) with all_0_3_3, all_32_0_26, all_0_6_6, all_32_0_26, all_0_5_5, all_0_8_8, all_0_10_10, all_0_9_9, all_0_12_12 and discharging atoms k2_isocat_1(all_0_12_12, all_0_9_9, all_0_10_10, all_0_5_5, all_32_0_26) = all_0_3_3, k2_isocat_1(all_0_12_12, all_0_9_9, all_0_10_10, all_0_8_8, all_32_0_26) = all_0_6_6, r2_nattra_1(all_0_9_9, all_0_10_10, all_32_0_26, all_32_0_26), r2_nattra_1(all_0_12_12, all_0_9_9, all_0_8_8, all_0_5_5), m2_cat_1(all_32_0_26, all_0_9_9, all_0_10_10), m2_cat_1(all_0_5_5, all_0_12_12, all_0_9_9), m2_cat_1(all_0_8_8, all_0_12_12, all_0_9_9), l1_cat_1(all_0_9_9), l1_cat_1(all_0_10_10), l1_cat_1(all_0_12_12), v2_cat_1(all_0_9_9), v2_cat_1(all_0_10_10), v2_cat_1(all_0_12_12), yields:
% 8.47/2.60 | (180) r2_nattra_1(all_0_12_12, all_0_10_10, all_0_6_6, all_0_3_3)
% 8.47/2.60 |
% 8.47/2.60 | Instantiating formula (25) with all_0_4_4, all_25_0_24, all_0_7_7, all_25_0_24, all_0_5_5, all_0_8_8, all_0_11_11, all_0_9_9, all_0_12_12 and discharging atoms k2_isocat_1(all_0_12_12, all_0_9_9, all_0_11_11, all_0_5_5, all_25_0_24) = all_0_4_4, k2_isocat_1(all_0_12_12, all_0_9_9, all_0_11_11, all_0_8_8, all_25_0_24) = all_0_7_7, r2_nattra_1(all_0_9_9, all_0_11_11, all_25_0_24, all_25_0_24), r2_nattra_1(all_0_12_12, all_0_9_9, all_0_8_8, all_0_5_5), m2_cat_1(all_25_0_24, all_0_9_9, all_0_11_11), m2_cat_1(all_0_5_5, all_0_12_12, all_0_9_9), m2_cat_1(all_0_8_8, all_0_12_12, all_0_9_9), l1_cat_1(all_0_9_9), l1_cat_1(all_0_11_11), l1_cat_1(all_0_12_12), v2_cat_1(all_0_9_9), v2_cat_1(all_0_11_11), v2_cat_1(all_0_12_12), yields:
% 8.47/2.60 | (181) r2_nattra_1(all_0_12_12, all_0_11_11, all_0_7_7, all_0_4_4)
% 8.47/2.60 |
% 8.47/2.60 +-Applying beta-rule and splitting (49), into two cases.
% 8.47/2.60 |-Branch one:
% 8.47/2.60 | (182) ~ r2_nattra_1(all_0_12_12, all_0_10_10, all_0_6_6, all_0_3_3)
% 8.47/2.60 |
% 8.47/2.60 | Using (180) and (182) yields:
% 8.47/2.60 | (183) $false
% 8.47/2.60 |
% 8.47/2.61 |-The branch is then unsatisfiable
% 8.47/2.61 |-Branch two:
% 8.47/2.61 | (180) r2_nattra_1(all_0_12_12, all_0_10_10, all_0_6_6, all_0_3_3)
% 8.47/2.61 | (185) ~ r2_nattra_1(all_0_12_12, all_0_11_11, all_0_7_7, all_0_4_4)
% 8.47/2.61 |
% 8.47/2.61 | Using (181) and (185) yields:
% 8.47/2.61 | (183) $false
% 8.47/2.61 |
% 8.47/2.61 |-The branch is then unsatisfiable
% 8.47/2.61 % SZS output end Proof for theBenchmark
% 8.47/2.61
% 8.47/2.61 2001ms
%------------------------------------------------------------------------------