TSTP Solution File: LAT294+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : LAT294+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 04:32:33 EDT 2022
% Result : Theorem 3.92s 1.61s
% Output : Proof 6.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT294+1 : TPTP v8.1.0. Released v3.4.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 29 07:49:28 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.55/0.57 ____ _
% 0.55/0.57 ___ / __ \_____(_)___ ________ __________
% 0.55/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.57
% 0.55/0.57 A Theorem Prover for First-Order Logic
% 0.55/0.57 (ePrincess v.1.0)
% 0.55/0.57
% 0.55/0.57 (c) Philipp Rümmer, 2009-2015
% 0.55/0.57 (c) Peter Backeman, 2014-2015
% 0.55/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.57 Bug reports to peter@backeman.se
% 0.55/0.57
% 0.55/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.57
% 0.55/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.55/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.69/1.00 Prover 0: Preprocessing ...
% 2.59/1.30 Prover 0: Warning: ignoring some quantifiers
% 2.86/1.33 Prover 0: Constructing countermodel ...
% 3.92/1.61 Prover 0: proved (987ms)
% 3.92/1.61
% 3.92/1.61 No countermodel exists, formula is valid
% 3.92/1.61 % SZS status Theorem for theBenchmark
% 3.92/1.61
% 3.92/1.61 Generating proof ... Warning: ignoring some quantifiers
% 6.28/2.09 found it (size 29)
% 6.28/2.09
% 6.28/2.09 % SZS output start Proof for theBenchmark
% 6.28/2.09 Assumed formulas after preprocessing and simplification:
% 6.28/2.09 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (k1_realset1(v7, v3) = v8 & k1_realset1(v5, v3) = v6 & k2_zfmisc_1(v3, v3) = v4 & k2_zfmisc_1(v0, v0) = v2 & k1_zfmisc_1(v0) = v1 & v2_funct_1(v9) & v1_relat_1(v13) & v1_relat_1(v11) & v1_relat_1(v9) & r6_binop_1(v0, v5, v7) & m2_relset_1(v8, v4, v3) & m2_relset_1(v7, v2, v0) & m2_relset_1(v6, v4, v3) & m2_relset_1(v5, v2, v0) & v1_funct_2(v8, v4, v3) & v1_funct_2(v7, v2, v0) & v1_funct_2(v6, v4, v3) & v1_funct_2(v5, v2, v0) & v1_funct_1(v13) & v1_funct_1(v11) & v1_funct_1(v9) & v1_funct_1(v8) & v1_funct_1(v7) & v1_funct_1(v6) & v1_funct_1(v5) & m1_subset_1(v3, v1) & v1_xboole_0(v12) & v1_xboole_0(v11) & v1_xboole_0(k1_xboole_0) & ~ r6_binop_1(v3, v6, v8) & ~ v1_xboole_0(v10) & ~ v1_xboole_0(v3) & ~ v1_xboole_0(v0) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (k7_relat_1(v17, v16) = v15) | ~ (k7_relat_1(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (k1_realset1(v17, v16) = v15) | ~ (k1_realset1(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] : ( ~ (k7_relat_1(v14, v16) = v17) | ~ (k2_zfmisc_1(v15, v15) = v16) | ~ v1_relat_1(v14) | k1_realset1(v14, v15) = v17) & ! [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] : ( ~ (k2_zfmisc_1(v14, v14) = v16) | ~ r5_binop_1(v14, v15, v17) | ~ r4_binop_1(v14, v15, v17) | ~ m2_relset_1(v17, v16, v14) | ~ m2_relset_1(v15, v16, v14) | ~ v1_funct_2(v17, v16, v14) | ~ v1_funct_2(v15, v16, v14) | ~ v1_funct_1(v17) | ~ v1_funct_1(v15) | r6_binop_1(v14, v15, v17)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (k2_zfmisc_1(v14, v14) = v16) | ~ r6_binop_1(v14, v15, v17) | ~ m2_relset_1(v17, v16, v14) | ~ m2_relset_1(v15, v16, v14) | ~ v1_funct_2(v17, v16, v14) | ~ v1_funct_2(v15, v16, v14) | ~ v1_funct_1(v17) | ~ v1_funct_1(v15) | r5_binop_1(v14, v15, v17)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (k2_zfmisc_1(v14, v14) = v16) | ~ r6_binop_1(v14, v15, v17) | ~ m2_relset_1(v17, v16, v14) | ~ m2_relset_1(v15, v16, v14) | ~ v1_funct_2(v17, v16, v14) | ~ v1_funct_2(v15, v16, v14) | ~ v1_funct_1(v17) | ~ v1_funct_1(v15) | r4_binop_1(v14, v15, v17)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (k1_zfmisc_1(v16) = v17) | ~ r2_hidden(v14, v15) | ~ m1_subset_1(v15, v17) | ~ v1_xboole_0(v16)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (k1_zfmisc_1(v16) = v17) | ~ r2_hidden(v14, v15) | ~ m1_subset_1(v15, v17) | 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_zfmisc_1(v16) = v15) | ~ (k1_zfmisc_1(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (k7_relat_1(v14, v15) = v16) | ~ v1_relat_1(v14) | ~ v1_funct_1(v14) | v1_relat_1(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (k7_relat_1(v14, v15) = v16) | ~ v1_relat_1(v14) | ~ v1_funct_1(v14) | v1_funct_1(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (k7_relat_1(v14, v15) = v16) | ~ v1_relat_1(v14) | v1_relat_1(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (k1_realset1(v14, v15) = v16) | ~ v1_relat_1(v14) | ~ v1_funct_1(v14) | v1_relat_1(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (k1_realset1(v14, v15) = v16) | ~ v1_relat_1(v14) | ~ v1_funct_1(v14) | v1_funct_1(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (k1_realset1(v14, v15) = v16) | ~ v1_relat_1(v14) | v1_relat_1(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (k1_realset1(v14, v15) = v16) | ~ v1_relat_1(v14) | ? [v17] : (k7_relat_1(v14, v17) = v16 & k2_zfmisc_1(v15, v15) = 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] : ( ~ m1_relset_1(v16, v14, v15) | m2_relset_1(v16, v14, v15)) & ! [v14] : ! [v15] : ! [v16] : ( ~ m2_relset_1(v16, v14, v15) | m1_relset_1(v16, v14, v15)) & ! [v14] : ! [v15] : (v15 = v14 | ~ v1_xboole_0(v15) | ~ v1_xboole_0(v14)) & ! [v14] : ! [v15] : ( ~ (k2_zfmisc_1(v14, v14) = v15) | v1_xboole_0(v14) | ? [v16] : (k1_zfmisc_1(v14) = v16 & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (k1_realset1(v21, v17) = v22) | ~ (k1_realset1(v19, v17) = v20) | ~ (k2_zfmisc_1(v17, v17) = v18) | ~ r5_binop_1(v14, v19, v21) | ~ m2_relset_1(v22, v18, v17) | ~ m2_relset_1(v21, v15, v14) | ~ m2_relset_1(v20, v18, v17) | ~ m2_relset_1(v19, v15, v14) | ~ v1_funct_2(v22, v18, v17) | ~ v1_funct_2(v21, v15, v14) | ~ v1_funct_2(v20, v18, v17) | ~ v1_funct_2(v19, v15, v14) | ~ v1_funct_1(v22) | ~ v1_funct_1(v21) | ~ v1_funct_1(v20) | ~ v1_funct_1(v19) | ~ m1_subset_1(v17, v16) | r5_binop_1(v17, v20, v22) | v1_xboole_0(v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (k1_realset1(v21, v17) = v22) | ~ (k1_realset1(v19, v17) = v20) | ~ (k2_zfmisc_1(v17, v17) = v18) | ~ r4_binop_1(v14, v19, v21) | ~ m2_relset_1(v22, v18, v17) | ~ m2_relset_1(v21, v15, v14) | ~ m2_relset_1(v20, v18, v17) | ~ m2_relset_1(v19, v15, v14) | ~ v1_funct_2(v22, v18, v17) | ~ v1_funct_2(v21, v15, v14) | ~ v1_funct_2(v20, v18, v17) | ~ v1_funct_2(v19, v15, v14) | ~ v1_funct_1(v22) | ~ v1_funct_1(v21) | ~ v1_funct_1(v20) | ~ v1_funct_1(v19) | ~ m1_subset_1(v17, v16) | r4_binop_1(v17, v20, v22) | v1_xboole_0(v17)))) & ! [v14] : ! [v15] : ( ~ (k1_zfmisc_1(v14) = v15) | ~ v1_xboole_0(v15)) & ! [v14] : ! [v15] : ( ~ (k1_zfmisc_1(v14) = v15) | v1_xboole_0(v14) | ? [v16] : (k2_zfmisc_1(v14, v14) = v16 & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (k1_realset1(v21, v17) = v22) | ~ (k1_realset1(v19, v17) = v20) | ~ (k2_zfmisc_1(v17, v17) = v18) | ~ r5_binop_1(v14, v19, v21) | ~ m2_relset_1(v22, v18, v17) | ~ m2_relset_1(v21, v16, v14) | ~ m2_relset_1(v20, v18, v17) | ~ m2_relset_1(v19, v16, v14) | ~ v1_funct_2(v22, v18, v17) | ~ v1_funct_2(v21, v16, v14) | ~ v1_funct_2(v20, v18, v17) | ~ v1_funct_2(v19, v16, v14) | ~ v1_funct_1(v22) | ~ v1_funct_1(v21) | ~ v1_funct_1(v20) | ~ v1_funct_1(v19) | ~ m1_subset_1(v17, v15) | r5_binop_1(v17, v20, v22) | v1_xboole_0(v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (k1_realset1(v21, v17) = v22) | ~ (k1_realset1(v19, v17) = v20) | ~ (k2_zfmisc_1(v17, v17) = v18) | ~ r4_binop_1(v14, v19, v21) | ~ m2_relset_1(v22, v18, v17) | ~ m2_relset_1(v21, v16, v14) | ~ m2_relset_1(v20, v18, v17) | ~ m2_relset_1(v19, v16, v14) | ~ v1_funct_2(v22, v18, v17) | ~ v1_funct_2(v21, v16, v14) | ~ v1_funct_2(v20, v18, v17) | ~ v1_funct_2(v19, v16, v14) | ~ v1_funct_1(v22) | ~ v1_funct_1(v21) | ~ v1_funct_1(v20) | ~ v1_funct_1(v19) | ~ m1_subset_1(v17, v15) | r4_binop_1(v17, v20, v22) | v1_xboole_0(v17)))) & ! [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] : (m1_subset_1(v16, v15) & v1_xboole_0(v16))) & ! [v14] : ! [v15] : ( ~ r2_hidden(v15, v14) | ~ r2_hidden(v14, v15)) & ! [v14] : ! [v15] : ( ~ r2_hidden(v14, v15) | ~ v1_xboole_0(v15)) & ! [v14] : ! [v15] : ( ~ r2_hidden(v14, v15) | m1_subset_1(v14, v15)) & ! [v14] : ! [v15] : ( ~ m1_subset_1(v14, v15) | r2_hidden(v14, v15) | v1_xboole_0(v15)) & ! [v14] : (v14 = k1_xboole_0 | ~ v1_xboole_0(v14)) & ! [v14] : ( ~ v1_relat_1(v14) | ~ v1_funct_1(v14) | ~ v1_xboole_0(v14) | v2_funct_1(v14)) & ! [v14] : ( ~ v1_xboole_0(v14) | v1_funct_1(v14)) & ? [v14] : ? [v15] : ? [v16] : m1_relset_1(v16, v14, v15) & ? [v14] : ? [v15] : ? [v16] : m2_relset_1(v16, v14, v15) & ? [v14] : ? [v15] : m1_subset_1(v15, v14) & ? [v14] : r1_tarski(v14, v14))
% 6.41/2.14 | 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:
% 6.41/2.14 | (1) k1_realset1(all_0_6_6, all_0_10_10) = all_0_5_5 & k1_realset1(all_0_8_8, all_0_10_10) = all_0_7_7 & k2_zfmisc_1(all_0_10_10, all_0_10_10) = all_0_9_9 & k2_zfmisc_1(all_0_13_13, all_0_13_13) = all_0_11_11 & k1_zfmisc_1(all_0_13_13) = all_0_12_12 & v2_funct_1(all_0_4_4) & v1_relat_1(all_0_0_0) & v1_relat_1(all_0_2_2) & v1_relat_1(all_0_4_4) & r6_binop_1(all_0_13_13, all_0_8_8, all_0_6_6) & m2_relset_1(all_0_5_5, all_0_9_9, all_0_10_10) & m2_relset_1(all_0_6_6, all_0_11_11, all_0_13_13) & m2_relset_1(all_0_7_7, all_0_9_9, all_0_10_10) & m2_relset_1(all_0_8_8, all_0_11_11, all_0_13_13) & v1_funct_2(all_0_5_5, all_0_9_9, all_0_10_10) & v1_funct_2(all_0_6_6, all_0_11_11, all_0_13_13) & v1_funct_2(all_0_7_7, all_0_9_9, all_0_10_10) & v1_funct_2(all_0_8_8, all_0_11_11, all_0_13_13) & v1_funct_1(all_0_0_0) & v1_funct_1(all_0_2_2) & v1_funct_1(all_0_4_4) & v1_funct_1(all_0_5_5) & v1_funct_1(all_0_6_6) & v1_funct_1(all_0_7_7) & v1_funct_1(all_0_8_8) & m1_subset_1(all_0_10_10, all_0_12_12) & v1_xboole_0(all_0_1_1) & v1_xboole_0(all_0_2_2) & v1_xboole_0(k1_xboole_0) & ~ r6_binop_1(all_0_10_10, all_0_7_7, all_0_5_5) & ~ v1_xboole_0(all_0_3_3) & ~ v1_xboole_0(all_0_10_10) & ~ v1_xboole_0(all_0_13_13) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k7_relat_1(v3, v2) = v1) | ~ (k7_relat_1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k1_realset1(v3, v2) = v1) | ~ (k1_realset1(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] : ( ~ (k7_relat_1(v0, v2) = v3) | ~ (k2_zfmisc_1(v1, v1) = v2) | ~ v1_relat_1(v0) | k1_realset1(v0, v1) = v3) & ! [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] : ( ~ (k2_zfmisc_1(v0, v0) = v2) | ~ r5_binop_1(v0, v1, v3) | ~ r4_binop_1(v0, v1, v3) | ~ m2_relset_1(v3, v2, v0) | ~ m2_relset_1(v1, v2, v0) | ~ v1_funct_2(v3, v2, v0) | ~ v1_funct_2(v1, v2, v0) | ~ v1_funct_1(v3) | ~ v1_funct_1(v1) | r6_binop_1(v0, v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k2_zfmisc_1(v0, v0) = v2) | ~ r6_binop_1(v0, v1, v3) | ~ m2_relset_1(v3, v2, v0) | ~ m2_relset_1(v1, v2, v0) | ~ v1_funct_2(v3, v2, v0) | ~ v1_funct_2(v1, v2, v0) | ~ v1_funct_1(v3) | ~ v1_funct_1(v1) | r5_binop_1(v0, v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k2_zfmisc_1(v0, v0) = v2) | ~ r6_binop_1(v0, v1, v3) | ~ m2_relset_1(v3, v2, v0) | ~ m2_relset_1(v1, v2, v0) | ~ v1_funct_2(v3, v2, v0) | ~ v1_funct_2(v1, v2, v0) | ~ v1_funct_1(v3) | ~ v1_funct_1(v1) | r4_binop_1(v0, v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ r2_hidden(v0, v1) | ~ m1_subset_1(v1, v3) | ~ v1_xboole_0(v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ r2_hidden(v0, v1) | ~ m1_subset_1(v1, v3) | m1_subset_1(v0, v2)) & ? [v0] : ! [v1] : ! [v2] : ! [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_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k7_relat_1(v0, v1) = v2) | ~ v1_relat_1(v0) | ~ v1_funct_1(v0) | v1_relat_1(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k7_relat_1(v0, v1) = v2) | ~ v1_relat_1(v0) | ~ v1_funct_1(v0) | v1_funct_1(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k7_relat_1(v0, v1) = v2) | ~ v1_relat_1(v0) | v1_relat_1(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_realset1(v0, v1) = v2) | ~ v1_relat_1(v0) | ~ v1_funct_1(v0) | v1_relat_1(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_realset1(v0, v1) = v2) | ~ v1_relat_1(v0) | ~ v1_funct_1(v0) | v1_funct_1(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_realset1(v0, v1) = v2) | ~ v1_relat_1(v0) | v1_relat_1(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_realset1(v0, v1) = v2) | ~ v1_relat_1(v0) | ? [v3] : (k7_relat_1(v0, v3) = v2 & k2_zfmisc_1(v1, v1) = 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] : ( ~ m1_relset_1(v2, v0, v1) | m2_relset_1(v2, v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ m2_relset_1(v2, v0, v1) | m1_relset_1(v2, v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ v1_xboole_0(v1) | ~ v1_xboole_0(v0)) & ! [v0] : ! [v1] : ( ~ (k2_zfmisc_1(v0, v0) = v1) | v1_xboole_0(v0) | ? [v2] : (k1_zfmisc_1(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (k1_realset1(v7, v3) = v8) | ~ (k1_realset1(v5, v3) = v6) | ~ (k2_zfmisc_1(v3, v3) = v4) | ~ r5_binop_1(v0, v5, v7) | ~ m2_relset_1(v8, v4, v3) | ~ m2_relset_1(v7, v1, v0) | ~ m2_relset_1(v6, v4, v3) | ~ m2_relset_1(v5, v1, v0) | ~ v1_funct_2(v8, v4, v3) | ~ v1_funct_2(v7, v1, v0) | ~ v1_funct_2(v6, v4, v3) | ~ v1_funct_2(v5, v1, v0) | ~ v1_funct_1(v8) | ~ v1_funct_1(v7) | ~ v1_funct_1(v6) | ~ v1_funct_1(v5) | ~ m1_subset_1(v3, v2) | r5_binop_1(v3, v6, v8) | v1_xboole_0(v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (k1_realset1(v7, v3) = v8) | ~ (k1_realset1(v5, v3) = v6) | ~ (k2_zfmisc_1(v3, v3) = v4) | ~ r4_binop_1(v0, v5, v7) | ~ m2_relset_1(v8, v4, v3) | ~ m2_relset_1(v7, v1, v0) | ~ m2_relset_1(v6, v4, v3) | ~ m2_relset_1(v5, v1, v0) | ~ v1_funct_2(v8, v4, v3) | ~ v1_funct_2(v7, v1, v0) | ~ v1_funct_2(v6, v4, v3) | ~ v1_funct_2(v5, v1, v0) | ~ v1_funct_1(v8) | ~ v1_funct_1(v7) | ~ v1_funct_1(v6) | ~ v1_funct_1(v5) | ~ m1_subset_1(v3, v2) | r4_binop_1(v3, v6, v8) | v1_xboole_0(v3)))) & ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ~ v1_xboole_0(v1)) & ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | v1_xboole_0(v0) | ? [v2] : (k2_zfmisc_1(v0, v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (k1_realset1(v7, v3) = v8) | ~ (k1_realset1(v5, v3) = v6) | ~ (k2_zfmisc_1(v3, v3) = v4) | ~ r5_binop_1(v0, v5, v7) | ~ m2_relset_1(v8, v4, v3) | ~ m2_relset_1(v7, v2, v0) | ~ m2_relset_1(v6, v4, v3) | ~ m2_relset_1(v5, v2, v0) | ~ v1_funct_2(v8, v4, v3) | ~ v1_funct_2(v7, v2, v0) | ~ v1_funct_2(v6, v4, v3) | ~ v1_funct_2(v5, v2, v0) | ~ v1_funct_1(v8) | ~ v1_funct_1(v7) | ~ v1_funct_1(v6) | ~ v1_funct_1(v5) | ~ m1_subset_1(v3, v1) | r5_binop_1(v3, v6, v8) | v1_xboole_0(v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (k1_realset1(v7, v3) = v8) | ~ (k1_realset1(v5, v3) = v6) | ~ (k2_zfmisc_1(v3, v3) = v4) | ~ r4_binop_1(v0, v5, v7) | ~ m2_relset_1(v8, v4, v3) | ~ m2_relset_1(v7, v2, v0) | ~ m2_relset_1(v6, v4, v3) | ~ m2_relset_1(v5, v2, v0) | ~ v1_funct_2(v8, v4, v3) | ~ v1_funct_2(v7, v2, v0) | ~ v1_funct_2(v6, v4, v3) | ~ v1_funct_2(v5, v2, v0) | ~ v1_funct_1(v8) | ~ v1_funct_1(v7) | ~ v1_funct_1(v6) | ~ v1_funct_1(v5) | ~ m1_subset_1(v3, v1) | r4_binop_1(v3, v6, v8) | v1_xboole_0(v3)))) & ! [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] : ( ~ r2_hidden(v1, v0) | ~ r2_hidden(v0, v1)) & ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | ~ v1_xboole_0(v1)) & ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | m1_subset_1(v0, v1)) & ! [v0] : ! [v1] : ( ~ m1_subset_1(v0, v1) | r2_hidden(v0, v1) | v1_xboole_0(v1)) & ! [v0] : (v0 = k1_xboole_0 | ~ v1_xboole_0(v0)) & ! [v0] : ( ~ v1_relat_1(v0) | ~ v1_funct_1(v0) | ~ v1_xboole_0(v0) | v2_funct_1(v0)) & ! [v0] : ( ~ v1_xboole_0(v0) | v1_funct_1(v0)) & ? [v0] : ? [v1] : ? [v2] : m1_relset_1(v2, v0, v1) & ? [v0] : ? [v1] : ? [v2] : m2_relset_1(v2, v0, v1) & ? [v0] : ? [v1] : m1_subset_1(v1, v0) & ? [v0] : r1_tarski(v0, v0)
% 6.58/2.15 |
% 6.58/2.15 | Applying alpha-rule on (1) yields:
% 6.58/2.16 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k2_zfmisc_1(v3, v2) = v1) | ~ (k2_zfmisc_1(v3, v2) = v0))
% 6.58/2.16 | (3) ? [v0] : r1_tarski(v0, v0)
% 6.58/2.16 | (4) ! [v0] : (v0 = k1_xboole_0 | ~ v1_xboole_0(v0))
% 6.58/2.16 | (5) ! [v0] : ! [v1] : ( ~ (k2_zfmisc_1(v0, v0) = v1) | v1_xboole_0(v0) | ? [v2] : (k1_zfmisc_1(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (k1_realset1(v7, v3) = v8) | ~ (k1_realset1(v5, v3) = v6) | ~ (k2_zfmisc_1(v3, v3) = v4) | ~ r5_binop_1(v0, v5, v7) | ~ m2_relset_1(v8, v4, v3) | ~ m2_relset_1(v7, v1, v0) | ~ m2_relset_1(v6, v4, v3) | ~ m2_relset_1(v5, v1, v0) | ~ v1_funct_2(v8, v4, v3) | ~ v1_funct_2(v7, v1, v0) | ~ v1_funct_2(v6, v4, v3) | ~ v1_funct_2(v5, v1, v0) | ~ v1_funct_1(v8) | ~ v1_funct_1(v7) | ~ v1_funct_1(v6) | ~ v1_funct_1(v5) | ~ m1_subset_1(v3, v2) | r5_binop_1(v3, v6, v8) | v1_xboole_0(v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (k1_realset1(v7, v3) = v8) | ~ (k1_realset1(v5, v3) = v6) | ~ (k2_zfmisc_1(v3, v3) = v4) | ~ r4_binop_1(v0, v5, v7) | ~ m2_relset_1(v8, v4, v3) | ~ m2_relset_1(v7, v1, v0) | ~ m2_relset_1(v6, v4, v3) | ~ m2_relset_1(v5, v1, v0) | ~ v1_funct_2(v8, v4, v3) | ~ v1_funct_2(v7, v1, v0) | ~ v1_funct_2(v6, v4, v3) | ~ v1_funct_2(v5, v1, v0) | ~ v1_funct_1(v8) | ~ v1_funct_1(v7) | ~ v1_funct_1(v6) | ~ v1_funct_1(v5) | ~ m1_subset_1(v3, v2) | r4_binop_1(v3, v6, v8) | v1_xboole_0(v3))))
% 6.58/2.16 | (6) v2_funct_1(all_0_4_4)
% 6.58/2.16 | (7) ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ? [v2] : (m1_subset_1(v2, v1) & v1_xboole_0(v2)))
% 6.58/2.16 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ r2_hidden(v0, v1) | ~ m1_subset_1(v1, v3) | ~ v1_xboole_0(v2))
% 6.58/2.16 | (9) k2_zfmisc_1(all_0_13_13, all_0_13_13) = all_0_11_11
% 6.58/2.16 | (10) ! [v0] : ! [v1] : ( ~ r2_hidden(v1, v0) | ~ r2_hidden(v0, v1))
% 6.58/2.16 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k7_relat_1(v3, v2) = v1) | ~ (k7_relat_1(v3, v2) = v0))
% 6.58/2.16 | (12) v1_funct_1(all_0_5_5)
% 6.58/2.16 | (13) k1_zfmisc_1(all_0_13_13) = all_0_12_12
% 6.58/2.16 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_realset1(v0, v1) = v2) | ~ v1_relat_1(v0) | ~ v1_funct_1(v0) | v1_funct_1(v2))
% 6.58/2.16 | (15) v1_funct_1(all_0_0_0)
% 6.58/2.16 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k2_zfmisc_1(v0, v0) = v2) | ~ r5_binop_1(v0, v1, v3) | ~ r4_binop_1(v0, v1, v3) | ~ m2_relset_1(v3, v2, v0) | ~ m2_relset_1(v1, v2, v0) | ~ v1_funct_2(v3, v2, v0) | ~ v1_funct_2(v1, v2, v0) | ~ v1_funct_1(v3) | ~ v1_funct_1(v1) | r6_binop_1(v0, v1, v3))
% 6.58/2.16 | (17) v1_funct_1(all_0_7_7)
% 6.58/2.16 | (18) r6_binop_1(all_0_13_13, all_0_8_8, all_0_6_6)
% 6.58/2.16 | (19) k1_realset1(all_0_6_6, all_0_10_10) = all_0_5_5
% 6.58/2.16 | (20) v1_funct_1(all_0_2_2)
% 6.58/2.16 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ m2_relset_1(v2, v0, v1) | m1_relset_1(v2, v0, v1))
% 6.58/2.16 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ m1_relset_1(v2, v0, v1) | m2_relset_1(v2, v0, v1))
% 6.58/2.16 | (23) ! [v0] : ( ~ v1_relat_1(v0) | ~ v1_funct_1(v0) | ~ v1_xboole_0(v0) | v2_funct_1(v0))
% 6.58/2.16 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_zfmisc_1(v1) = v2) | ~ m1_subset_1(v0, v2) | r1_tarski(v0, v1))
% 6.58/2.16 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_zfmisc_1(v1) = v2) | ~ r1_tarski(v0, v1) | m1_subset_1(v0, v2))
% 6.58/2.16 | (26) m2_relset_1(all_0_8_8, all_0_11_11, all_0_13_13)
% 6.58/2.16 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_zfmisc_1(v0, v1) = v2) | ~ v1_xboole_0(v2) | v1_xboole_0(v1) | v1_xboole_0(v0))
% 6.58/2.16 | (28) ! [v0] : ! [v1] : ( ~ m1_subset_1(v0, v1) | r2_hidden(v0, v1) | v1_xboole_0(v1))
% 6.58/2.16 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_realset1(v0, v1) = v2) | ~ v1_relat_1(v0) | ? [v3] : (k7_relat_1(v0, v3) = v2 & k2_zfmisc_1(v1, v1) = v3))
% 6.58/2.16 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_realset1(v0, v1) = v2) | ~ v1_relat_1(v0) | ~ v1_funct_1(v0) | v1_relat_1(v2))
% 6.58/2.17 | (31) m2_relset_1(all_0_6_6, all_0_11_11, all_0_13_13)
% 6.58/2.17 | (32) ! [v0] : ! [v1] : (v1 = v0 | ~ v1_xboole_0(v1) | ~ v1_xboole_0(v0))
% 6.58/2.17 | (33) ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ~ v1_xboole_0(v1))
% 6.58/2.17 | (34) ? [v0] : ? [v1] : m1_subset_1(v1, v0)
% 6.58/2.17 | (35) ~ r6_binop_1(all_0_10_10, all_0_7_7, all_0_5_5)
% 6.58/2.17 | (36) ! [v0] : ( ~ v1_xboole_0(v0) | v1_funct_1(v0))
% 6.58/2.17 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (k7_relat_1(v0, v1) = v2) | ~ v1_relat_1(v0) | v1_relat_1(v2))
% 6.58/2.17 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (k7_relat_1(v0, v1) = v2) | ~ v1_relat_1(v0) | ~ v1_funct_1(v0) | v1_funct_1(v2))
% 6.58/2.17 | (39) ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | ~ v1_xboole_0(v1))
% 6.58/2.17 | (40) v1_funct_1(all_0_6_6)
% 6.58/2.17 | (41) m2_relset_1(all_0_7_7, all_0_9_9, all_0_10_10)
% 6.58/2.17 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k7_relat_1(v0, v2) = v3) | ~ (k2_zfmisc_1(v1, v1) = v2) | ~ v1_relat_1(v0) | k1_realset1(v0, v1) = v3)
% 6.58/2.17 | (43) ~ v1_xboole_0(all_0_13_13)
% 6.58/2.17 | (44) k2_zfmisc_1(all_0_10_10, all_0_10_10) = all_0_9_9
% 6.58/2.17 | (45) v1_relat_1(all_0_2_2)
% 6.58/2.17 | (46) ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | v1_xboole_0(v0) | ? [v2] : (k2_zfmisc_1(v0, v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (k1_realset1(v7, v3) = v8) | ~ (k1_realset1(v5, v3) = v6) | ~ (k2_zfmisc_1(v3, v3) = v4) | ~ r5_binop_1(v0, v5, v7) | ~ m2_relset_1(v8, v4, v3) | ~ m2_relset_1(v7, v2, v0) | ~ m2_relset_1(v6, v4, v3) | ~ m2_relset_1(v5, v2, v0) | ~ v1_funct_2(v8, v4, v3) | ~ v1_funct_2(v7, v2, v0) | ~ v1_funct_2(v6, v4, v3) | ~ v1_funct_2(v5, v2, v0) | ~ v1_funct_1(v8) | ~ v1_funct_1(v7) | ~ v1_funct_1(v6) | ~ v1_funct_1(v5) | ~ m1_subset_1(v3, v1) | r5_binop_1(v3, v6, v8) | v1_xboole_0(v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (k1_realset1(v7, v3) = v8) | ~ (k1_realset1(v5, v3) = v6) | ~ (k2_zfmisc_1(v3, v3) = v4) | ~ r4_binop_1(v0, v5, v7) | ~ m2_relset_1(v8, v4, v3) | ~ m2_relset_1(v7, v2, v0) | ~ m2_relset_1(v6, v4, v3) | ~ m2_relset_1(v5, v2, v0) | ~ v1_funct_2(v8, v4, v3) | ~ v1_funct_2(v7, v2, v0) | ~ v1_funct_2(v6, v4, v3) | ~ v1_funct_2(v5, v2, v0) | ~ v1_funct_1(v8) | ~ v1_funct_1(v7) | ~ v1_funct_1(v6) | ~ v1_funct_1(v5) | ~ m1_subset_1(v3, v1) | r4_binop_1(v3, v6, v8) | v1_xboole_0(v3))))
% 6.58/2.17 | (47) v1_funct_2(all_0_6_6, all_0_11_11, all_0_13_13)
% 6.58/2.17 | (48) v1_relat_1(all_0_0_0)
% 6.58/2.17 | (49) v1_xboole_0(k1_xboole_0)
% 6.58/2.17 | (50) ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | v1_xboole_0(v0) | ? [v2] : (m1_subset_1(v2, v1) & ~ v1_xboole_0(v2)))
% 6.58/2.17 | (51) ! [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)))
% 6.58/2.17 | (52) ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | m1_subset_1(v0, v1))
% 6.58/2.17 | (53) ~ v1_xboole_0(all_0_10_10)
% 6.58/2.17 | (54) ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_realset1(v0, v1) = v2) | ~ v1_relat_1(v0) | v1_relat_1(v2))
% 6.58/2.17 | (55) m2_relset_1(all_0_5_5, all_0_9_9, all_0_10_10)
% 6.58/2.17 | (56) v1_funct_1(all_0_4_4)
% 6.58/2.17 | (57) v1_funct_2(all_0_8_8, all_0_11_11, all_0_13_13)
% 6.58/2.17 | (58) v1_relat_1(all_0_4_4)
% 6.58/2.17 | (59) v1_funct_1(all_0_8_8)
% 6.58/2.17 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k2_zfmisc_1(v0, v0) = v2) | ~ r6_binop_1(v0, v1, v3) | ~ m2_relset_1(v3, v2, v0) | ~ m2_relset_1(v1, v2, v0) | ~ v1_funct_2(v3, v2, v0) | ~ v1_funct_2(v1, v2, v0) | ~ v1_funct_1(v3) | ~ v1_funct_1(v1) | r4_binop_1(v0, v1, v3))
% 6.58/2.17 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k2_zfmisc_1(v0, v0) = v2) | ~ r6_binop_1(v0, v1, v3) | ~ m2_relset_1(v3, v2, v0) | ~ m2_relset_1(v1, v2, v0) | ~ v1_funct_2(v3, v2, v0) | ~ v1_funct_2(v1, v2, v0) | ~ v1_funct_1(v3) | ~ v1_funct_1(v1) | r5_binop_1(v0, v1, v3))
% 6.58/2.18 | (62) m1_subset_1(all_0_10_10, all_0_12_12)
% 6.58/2.18 | (63) ? [v0] : ? [v1] : ? [v2] : m1_relset_1(v2, v0, v1)
% 6.58/2.18 | (64) v1_funct_2(all_0_5_5, all_0_9_9, all_0_10_10)
% 6.58/2.18 | (65) v1_xboole_0(all_0_1_1)
% 6.58/2.18 | (66) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0))
% 6.58/2.18 | (67) k1_realset1(all_0_8_8, all_0_10_10) = all_0_7_7
% 6.58/2.18 | (68) ? [v0] : ? [v1] : ? [v2] : m2_relset_1(v2, v0, v1)
% 6.58/2.18 | (69) ? [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)))
% 6.58/2.18 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ r2_hidden(v0, v1) | ~ m1_subset_1(v1, v3) | m1_subset_1(v0, v2))
% 6.58/2.18 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k1_realset1(v3, v2) = v1) | ~ (k1_realset1(v3, v2) = v0))
% 6.58/2.18 | (72) ~ v1_xboole_0(all_0_3_3)
% 6.58/2.18 | (73) v1_xboole_0(all_0_2_2)
% 6.58/2.18 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (k7_relat_1(v0, v1) = v2) | ~ v1_relat_1(v0) | ~ v1_funct_1(v0) | v1_relat_1(v2))
% 6.58/2.18 | (75) v1_funct_2(all_0_7_7, all_0_9_9, all_0_10_10)
% 6.58/2.18 |
% 6.58/2.18 | Instantiating formula (5) with all_0_9_9, all_0_10_10 and discharging atoms k2_zfmisc_1(all_0_10_10, all_0_10_10) = all_0_9_9, ~ v1_xboole_0(all_0_10_10), yields:
% 6.58/2.18 | (76) ? [v0] : (k1_zfmisc_1(all_0_10_10) = v0 & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (k1_realset1(v5, v1) = v6) | ~ (k1_realset1(v3, v1) = v4) | ~ (k2_zfmisc_1(v1, v1) = v2) | ~ r5_binop_1(all_0_10_10, v3, v5) | ~ m2_relset_1(v6, v2, v1) | ~ m2_relset_1(v5, all_0_9_9, all_0_10_10) | ~ m2_relset_1(v4, v2, v1) | ~ m2_relset_1(v3, all_0_9_9, all_0_10_10) | ~ v1_funct_2(v6, v2, v1) | ~ v1_funct_2(v5, all_0_9_9, all_0_10_10) | ~ v1_funct_2(v4, v2, v1) | ~ v1_funct_2(v3, all_0_9_9, all_0_10_10) | ~ v1_funct_1(v6) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ m1_subset_1(v1, v0) | r5_binop_1(v1, v4, v6) | v1_xboole_0(v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (k1_realset1(v5, v1) = v6) | ~ (k1_realset1(v3, v1) = v4) | ~ (k2_zfmisc_1(v1, v1) = v2) | ~ r4_binop_1(all_0_10_10, v3, v5) | ~ m2_relset_1(v6, v2, v1) | ~ m2_relset_1(v5, all_0_9_9, all_0_10_10) | ~ m2_relset_1(v4, v2, v1) | ~ m2_relset_1(v3, all_0_9_9, all_0_10_10) | ~ v1_funct_2(v6, v2, v1) | ~ v1_funct_2(v5, all_0_9_9, all_0_10_10) | ~ v1_funct_2(v4, v2, v1) | ~ v1_funct_2(v3, all_0_9_9, all_0_10_10) | ~ v1_funct_1(v6) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ m1_subset_1(v1, v0) | r4_binop_1(v1, v4, v6) | v1_xboole_0(v1)))
% 6.58/2.18 |
% 6.58/2.18 | Instantiating formula (5) with all_0_11_11, all_0_13_13 and discharging atoms k2_zfmisc_1(all_0_13_13, all_0_13_13) = all_0_11_11, ~ v1_xboole_0(all_0_13_13), yields:
% 6.58/2.18 | (77) ? [v0] : (k1_zfmisc_1(all_0_13_13) = v0 & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (k1_realset1(v5, v1) = v6) | ~ (k1_realset1(v3, v1) = v4) | ~ (k2_zfmisc_1(v1, v1) = v2) | ~ r5_binop_1(all_0_13_13, v3, v5) | ~ m2_relset_1(v6, v2, v1) | ~ m2_relset_1(v5, all_0_11_11, all_0_13_13) | ~ m2_relset_1(v4, v2, v1) | ~ m2_relset_1(v3, all_0_11_11, all_0_13_13) | ~ v1_funct_2(v6, v2, v1) | ~ v1_funct_2(v5, all_0_11_11, all_0_13_13) | ~ v1_funct_2(v4, v2, v1) | ~ v1_funct_2(v3, all_0_11_11, all_0_13_13) | ~ v1_funct_1(v6) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ m1_subset_1(v1, v0) | r5_binop_1(v1, v4, v6) | v1_xboole_0(v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (k1_realset1(v5, v1) = v6) | ~ (k1_realset1(v3, v1) = v4) | ~ (k2_zfmisc_1(v1, v1) = v2) | ~ r4_binop_1(all_0_13_13, v3, v5) | ~ m2_relset_1(v6, v2, v1) | ~ m2_relset_1(v5, all_0_11_11, all_0_13_13) | ~ m2_relset_1(v4, v2, v1) | ~ m2_relset_1(v3, all_0_11_11, all_0_13_13) | ~ v1_funct_2(v6, v2, v1) | ~ v1_funct_2(v5, all_0_11_11, all_0_13_13) | ~ v1_funct_2(v4, v2, v1) | ~ v1_funct_2(v3, all_0_11_11, all_0_13_13) | ~ v1_funct_1(v6) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ m1_subset_1(v1, v0) | r4_binop_1(v1, v4, v6) | v1_xboole_0(v1)))
% 6.58/2.19 |
% 6.58/2.19 | Instantiating formula (61) with all_0_6_6, all_0_11_11, all_0_8_8, all_0_13_13 and discharging atoms k2_zfmisc_1(all_0_13_13, all_0_13_13) = all_0_11_11, r6_binop_1(all_0_13_13, all_0_8_8, all_0_6_6), m2_relset_1(all_0_6_6, all_0_11_11, all_0_13_13), m2_relset_1(all_0_8_8, all_0_11_11, all_0_13_13), v1_funct_2(all_0_6_6, all_0_11_11, all_0_13_13), v1_funct_2(all_0_8_8, all_0_11_11, all_0_13_13), v1_funct_1(all_0_6_6), v1_funct_1(all_0_8_8), yields:
% 6.58/2.19 | (78) r5_binop_1(all_0_13_13, all_0_8_8, all_0_6_6)
% 6.58/2.19 |
% 6.58/2.19 | Instantiating formula (60) with all_0_6_6, all_0_11_11, all_0_8_8, all_0_13_13 and discharging atoms k2_zfmisc_1(all_0_13_13, all_0_13_13) = all_0_11_11, r6_binop_1(all_0_13_13, all_0_8_8, all_0_6_6), m2_relset_1(all_0_6_6, all_0_11_11, all_0_13_13), m2_relset_1(all_0_8_8, all_0_11_11, all_0_13_13), v1_funct_2(all_0_6_6, all_0_11_11, all_0_13_13), v1_funct_2(all_0_8_8, all_0_11_11, all_0_13_13), v1_funct_1(all_0_6_6), v1_funct_1(all_0_8_8), yields:
% 6.58/2.19 | (79) r4_binop_1(all_0_13_13, all_0_8_8, all_0_6_6)
% 6.58/2.19 |
% 6.58/2.19 | Instantiating (77) with all_25_0_25 yields:
% 6.58/2.19 | (80) k1_zfmisc_1(all_0_13_13) = all_25_0_25 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (k1_realset1(v4, v0) = v5) | ~ (k1_realset1(v2, v0) = v3) | ~ (k2_zfmisc_1(v0, v0) = v1) | ~ r5_binop_1(all_0_13_13, v2, v4) | ~ m2_relset_1(v5, v1, v0) | ~ m2_relset_1(v4, all_0_11_11, all_0_13_13) | ~ m2_relset_1(v3, v1, v0) | ~ m2_relset_1(v2, all_0_11_11, all_0_13_13) | ~ v1_funct_2(v5, v1, v0) | ~ v1_funct_2(v4, all_0_11_11, all_0_13_13) | ~ v1_funct_2(v3, v1, v0) | ~ v1_funct_2(v2, all_0_11_11, all_0_13_13) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ v1_funct_1(v2) | ~ m1_subset_1(v0, all_25_0_25) | r5_binop_1(v0, v3, v5) | v1_xboole_0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (k1_realset1(v4, v0) = v5) | ~ (k1_realset1(v2, v0) = v3) | ~ (k2_zfmisc_1(v0, v0) = v1) | ~ r4_binop_1(all_0_13_13, v2, v4) | ~ m2_relset_1(v5, v1, v0) | ~ m2_relset_1(v4, all_0_11_11, all_0_13_13) | ~ m2_relset_1(v3, v1, v0) | ~ m2_relset_1(v2, all_0_11_11, all_0_13_13) | ~ v1_funct_2(v5, v1, v0) | ~ v1_funct_2(v4, all_0_11_11, all_0_13_13) | ~ v1_funct_2(v3, v1, v0) | ~ v1_funct_2(v2, all_0_11_11, all_0_13_13) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ v1_funct_1(v2) | ~ m1_subset_1(v0, all_25_0_25) | r4_binop_1(v0, v3, v5) | v1_xboole_0(v0))
% 6.58/2.19 |
% 6.58/2.19 | Applying alpha-rule on (80) yields:
% 6.58/2.19 | (81) k1_zfmisc_1(all_0_13_13) = all_25_0_25
% 6.58/2.19 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (k1_realset1(v4, v0) = v5) | ~ (k1_realset1(v2, v0) = v3) | ~ (k2_zfmisc_1(v0, v0) = v1) | ~ r5_binop_1(all_0_13_13, v2, v4) | ~ m2_relset_1(v5, v1, v0) | ~ m2_relset_1(v4, all_0_11_11, all_0_13_13) | ~ m2_relset_1(v3, v1, v0) | ~ m2_relset_1(v2, all_0_11_11, all_0_13_13) | ~ v1_funct_2(v5, v1, v0) | ~ v1_funct_2(v4, all_0_11_11, all_0_13_13) | ~ v1_funct_2(v3, v1, v0) | ~ v1_funct_2(v2, all_0_11_11, all_0_13_13) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ v1_funct_1(v2) | ~ m1_subset_1(v0, all_25_0_25) | r5_binop_1(v0, v3, v5) | v1_xboole_0(v0))
% 6.58/2.19 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (k1_realset1(v4, v0) = v5) | ~ (k1_realset1(v2, v0) = v3) | ~ (k2_zfmisc_1(v0, v0) = v1) | ~ r4_binop_1(all_0_13_13, v2, v4) | ~ m2_relset_1(v5, v1, v0) | ~ m2_relset_1(v4, all_0_11_11, all_0_13_13) | ~ m2_relset_1(v3, v1, v0) | ~ m2_relset_1(v2, all_0_11_11, all_0_13_13) | ~ v1_funct_2(v5, v1, v0) | ~ v1_funct_2(v4, all_0_11_11, all_0_13_13) | ~ v1_funct_2(v3, v1, v0) | ~ v1_funct_2(v2, all_0_11_11, all_0_13_13) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ v1_funct_1(v2) | ~ m1_subset_1(v0, all_25_0_25) | r4_binop_1(v0, v3, v5) | v1_xboole_0(v0))
% 6.58/2.19 |
% 6.58/2.19 | Instantiating (76) with all_28_0_26 yields:
% 6.58/2.19 | (84) k1_zfmisc_1(all_0_10_10) = all_28_0_26 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (k1_realset1(v4, v0) = v5) | ~ (k1_realset1(v2, v0) = v3) | ~ (k2_zfmisc_1(v0, v0) = v1) | ~ r5_binop_1(all_0_10_10, v2, v4) | ~ m2_relset_1(v5, v1, v0) | ~ m2_relset_1(v4, all_0_9_9, all_0_10_10) | ~ m2_relset_1(v3, v1, v0) | ~ m2_relset_1(v2, all_0_9_9, all_0_10_10) | ~ v1_funct_2(v5, v1, v0) | ~ v1_funct_2(v4, all_0_9_9, all_0_10_10) | ~ v1_funct_2(v3, v1, v0) | ~ v1_funct_2(v2, all_0_9_9, all_0_10_10) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ v1_funct_1(v2) | ~ m1_subset_1(v0, all_28_0_26) | r5_binop_1(v0, v3, v5) | v1_xboole_0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (k1_realset1(v4, v0) = v5) | ~ (k1_realset1(v2, v0) = v3) | ~ (k2_zfmisc_1(v0, v0) = v1) | ~ r4_binop_1(all_0_10_10, v2, v4) | ~ m2_relset_1(v5, v1, v0) | ~ m2_relset_1(v4, all_0_9_9, all_0_10_10) | ~ m2_relset_1(v3, v1, v0) | ~ m2_relset_1(v2, all_0_9_9, all_0_10_10) | ~ v1_funct_2(v5, v1, v0) | ~ v1_funct_2(v4, all_0_9_9, all_0_10_10) | ~ v1_funct_2(v3, v1, v0) | ~ v1_funct_2(v2, all_0_9_9, all_0_10_10) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ v1_funct_1(v2) | ~ m1_subset_1(v0, all_28_0_26) | r4_binop_1(v0, v3, v5) | v1_xboole_0(v0))
% 6.58/2.20 |
% 6.58/2.20 | Applying alpha-rule on (84) yields:
% 6.58/2.20 | (85) k1_zfmisc_1(all_0_10_10) = all_28_0_26
% 6.58/2.20 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (k1_realset1(v4, v0) = v5) | ~ (k1_realset1(v2, v0) = v3) | ~ (k2_zfmisc_1(v0, v0) = v1) | ~ r5_binop_1(all_0_10_10, v2, v4) | ~ m2_relset_1(v5, v1, v0) | ~ m2_relset_1(v4, all_0_9_9, all_0_10_10) | ~ m2_relset_1(v3, v1, v0) | ~ m2_relset_1(v2, all_0_9_9, all_0_10_10) | ~ v1_funct_2(v5, v1, v0) | ~ v1_funct_2(v4, all_0_9_9, all_0_10_10) | ~ v1_funct_2(v3, v1, v0) | ~ v1_funct_2(v2, all_0_9_9, all_0_10_10) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ v1_funct_1(v2) | ~ m1_subset_1(v0, all_28_0_26) | r5_binop_1(v0, v3, v5) | v1_xboole_0(v0))
% 6.58/2.20 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (k1_realset1(v4, v0) = v5) | ~ (k1_realset1(v2, v0) = v3) | ~ (k2_zfmisc_1(v0, v0) = v1) | ~ r4_binop_1(all_0_10_10, v2, v4) | ~ m2_relset_1(v5, v1, v0) | ~ m2_relset_1(v4, all_0_9_9, all_0_10_10) | ~ m2_relset_1(v3, v1, v0) | ~ m2_relset_1(v2, all_0_9_9, all_0_10_10) | ~ v1_funct_2(v5, v1, v0) | ~ v1_funct_2(v4, all_0_9_9, all_0_10_10) | ~ v1_funct_2(v3, v1, v0) | ~ v1_funct_2(v2, all_0_9_9, all_0_10_10) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ v1_funct_1(v2) | ~ m1_subset_1(v0, all_28_0_26) | r4_binop_1(v0, v3, v5) | v1_xboole_0(v0))
% 6.58/2.20 |
% 6.58/2.20 | Instantiating formula (66) with all_0_13_13, all_25_0_25, all_0_12_12 and discharging atoms k1_zfmisc_1(all_0_13_13) = all_25_0_25, k1_zfmisc_1(all_0_13_13) = all_0_12_12, yields:
% 6.58/2.20 | (88) all_25_0_25 = all_0_12_12
% 6.58/2.20 |
% 6.58/2.20 | Instantiating formula (46) with all_28_0_26, all_0_10_10 and discharging atoms k1_zfmisc_1(all_0_10_10) = all_28_0_26, ~ v1_xboole_0(all_0_10_10), yields:
% 6.58/2.20 | (89) ? [v0] : (k2_zfmisc_1(all_0_10_10, all_0_10_10) = v0 & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (k1_realset1(v5, v1) = v6) | ~ (k1_realset1(v3, v1) = v4) | ~ (k2_zfmisc_1(v1, v1) = v2) | ~ r5_binop_1(all_0_10_10, v3, v5) | ~ m2_relset_1(v6, v2, v1) | ~ m2_relset_1(v5, v0, all_0_10_10) | ~ m2_relset_1(v4, v2, v1) | ~ m2_relset_1(v3, v0, all_0_10_10) | ~ v1_funct_2(v6, v2, v1) | ~ v1_funct_2(v5, v0, all_0_10_10) | ~ v1_funct_2(v4, v2, v1) | ~ v1_funct_2(v3, v0, all_0_10_10) | ~ v1_funct_1(v6) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ m1_subset_1(v1, all_28_0_26) | r5_binop_1(v1, v4, v6) | v1_xboole_0(v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (k1_realset1(v5, v1) = v6) | ~ (k1_realset1(v3, v1) = v4) | ~ (k2_zfmisc_1(v1, v1) = v2) | ~ r4_binop_1(all_0_10_10, v3, v5) | ~ m2_relset_1(v6, v2, v1) | ~ m2_relset_1(v5, v0, all_0_10_10) | ~ m2_relset_1(v4, v2, v1) | ~ m2_relset_1(v3, v0, all_0_10_10) | ~ v1_funct_2(v6, v2, v1) | ~ v1_funct_2(v5, v0, all_0_10_10) | ~ v1_funct_2(v4, v2, v1) | ~ v1_funct_2(v3, v0, all_0_10_10) | ~ v1_funct_1(v6) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ m1_subset_1(v1, all_28_0_26) | r4_binop_1(v1, v4, v6) | v1_xboole_0(v1)))
% 6.58/2.20 |
% 6.58/2.20 | Instantiating formula (82) with all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10 and discharging atoms k1_realset1(all_0_6_6, all_0_10_10) = all_0_5_5, k1_realset1(all_0_8_8, all_0_10_10) = all_0_7_7, k2_zfmisc_1(all_0_10_10, all_0_10_10) = all_0_9_9, r5_binop_1(all_0_13_13, all_0_8_8, all_0_6_6), m2_relset_1(all_0_5_5, all_0_9_9, all_0_10_10), m2_relset_1(all_0_6_6, all_0_11_11, all_0_13_13), m2_relset_1(all_0_7_7, all_0_9_9, all_0_10_10), m2_relset_1(all_0_8_8, all_0_11_11, all_0_13_13), v1_funct_2(all_0_5_5, all_0_9_9, all_0_10_10), v1_funct_2(all_0_6_6, all_0_11_11, all_0_13_13), v1_funct_2(all_0_7_7, all_0_9_9, all_0_10_10), v1_funct_2(all_0_8_8, all_0_11_11, all_0_13_13), v1_funct_1(all_0_5_5), v1_funct_1(all_0_6_6), v1_funct_1(all_0_7_7), v1_funct_1(all_0_8_8), ~ v1_xboole_0(all_0_10_10), yields:
% 6.58/2.20 | (90) ~ m1_subset_1(all_0_10_10, all_25_0_25) | r5_binop_1(all_0_10_10, all_0_7_7, all_0_5_5)
% 6.58/2.20 |
% 6.58/2.20 | Instantiating formula (83) with all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10 and discharging atoms k1_realset1(all_0_6_6, all_0_10_10) = all_0_5_5, k1_realset1(all_0_8_8, all_0_10_10) = all_0_7_7, k2_zfmisc_1(all_0_10_10, all_0_10_10) = all_0_9_9, r4_binop_1(all_0_13_13, all_0_8_8, all_0_6_6), m2_relset_1(all_0_5_5, all_0_9_9, all_0_10_10), m2_relset_1(all_0_6_6, all_0_11_11, all_0_13_13), m2_relset_1(all_0_7_7, all_0_9_9, all_0_10_10), m2_relset_1(all_0_8_8, all_0_11_11, all_0_13_13), v1_funct_2(all_0_5_5, all_0_9_9, all_0_10_10), v1_funct_2(all_0_6_6, all_0_11_11, all_0_13_13), v1_funct_2(all_0_7_7, all_0_9_9, all_0_10_10), v1_funct_2(all_0_8_8, all_0_11_11, all_0_13_13), v1_funct_1(all_0_5_5), v1_funct_1(all_0_6_6), v1_funct_1(all_0_7_7), v1_funct_1(all_0_8_8), ~ v1_xboole_0(all_0_10_10), yields:
% 6.58/2.20 | (91) ~ m1_subset_1(all_0_10_10, all_25_0_25) | r4_binop_1(all_0_10_10, all_0_7_7, all_0_5_5)
% 6.58/2.20 |
% 6.58/2.20 | Instantiating (89) with all_50_0_31 yields:
% 6.58/2.20 | (92) k2_zfmisc_1(all_0_10_10, all_0_10_10) = all_50_0_31 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (k1_realset1(v4, v0) = v5) | ~ (k1_realset1(v2, v0) = v3) | ~ (k2_zfmisc_1(v0, v0) = v1) | ~ r5_binop_1(all_0_10_10, v2, v4) | ~ m2_relset_1(v5, v1, v0) | ~ m2_relset_1(v4, all_50_0_31, all_0_10_10) | ~ m2_relset_1(v3, v1, v0) | ~ m2_relset_1(v2, all_50_0_31, all_0_10_10) | ~ v1_funct_2(v5, v1, v0) | ~ v1_funct_2(v4, all_50_0_31, all_0_10_10) | ~ v1_funct_2(v3, v1, v0) | ~ v1_funct_2(v2, all_50_0_31, all_0_10_10) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ v1_funct_1(v2) | ~ m1_subset_1(v0, all_28_0_26) | r5_binop_1(v0, v3, v5) | v1_xboole_0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (k1_realset1(v4, v0) = v5) | ~ (k1_realset1(v2, v0) = v3) | ~ (k2_zfmisc_1(v0, v0) = v1) | ~ r4_binop_1(all_0_10_10, v2, v4) | ~ m2_relset_1(v5, v1, v0) | ~ m2_relset_1(v4, all_50_0_31, all_0_10_10) | ~ m2_relset_1(v3, v1, v0) | ~ m2_relset_1(v2, all_50_0_31, all_0_10_10) | ~ v1_funct_2(v5, v1, v0) | ~ v1_funct_2(v4, all_50_0_31, all_0_10_10) | ~ v1_funct_2(v3, v1, v0) | ~ v1_funct_2(v2, all_50_0_31, all_0_10_10) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ v1_funct_1(v2) | ~ m1_subset_1(v0, all_28_0_26) | r4_binop_1(v0, v3, v5) | v1_xboole_0(v0))
% 6.58/2.20 |
% 6.58/2.20 | Applying alpha-rule on (92) yields:
% 6.58/2.20 | (93) k2_zfmisc_1(all_0_10_10, all_0_10_10) = all_50_0_31
% 6.58/2.20 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (k1_realset1(v4, v0) = v5) | ~ (k1_realset1(v2, v0) = v3) | ~ (k2_zfmisc_1(v0, v0) = v1) | ~ r5_binop_1(all_0_10_10, v2, v4) | ~ m2_relset_1(v5, v1, v0) | ~ m2_relset_1(v4, all_50_0_31, all_0_10_10) | ~ m2_relset_1(v3, v1, v0) | ~ m2_relset_1(v2, all_50_0_31, all_0_10_10) | ~ v1_funct_2(v5, v1, v0) | ~ v1_funct_2(v4, all_50_0_31, all_0_10_10) | ~ v1_funct_2(v3, v1, v0) | ~ v1_funct_2(v2, all_50_0_31, all_0_10_10) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ v1_funct_1(v2) | ~ m1_subset_1(v0, all_28_0_26) | r5_binop_1(v0, v3, v5) | v1_xboole_0(v0))
% 6.58/2.20 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (k1_realset1(v4, v0) = v5) | ~ (k1_realset1(v2, v0) = v3) | ~ (k2_zfmisc_1(v0, v0) = v1) | ~ r4_binop_1(all_0_10_10, v2, v4) | ~ m2_relset_1(v5, v1, v0) | ~ m2_relset_1(v4, all_50_0_31, all_0_10_10) | ~ m2_relset_1(v3, v1, v0) | ~ m2_relset_1(v2, all_50_0_31, all_0_10_10) | ~ v1_funct_2(v5, v1, v0) | ~ v1_funct_2(v4, all_50_0_31, all_0_10_10) | ~ v1_funct_2(v3, v1, v0) | ~ v1_funct_2(v2, all_50_0_31, all_0_10_10) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ v1_funct_1(v2) | ~ m1_subset_1(v0, all_28_0_26) | r4_binop_1(v0, v3, v5) | v1_xboole_0(v0))
% 6.58/2.20 |
% 6.58/2.20 +-Applying beta-rule and splitting (91), into two cases.
% 6.58/2.20 |-Branch one:
% 6.58/2.21 | (96) ~ m1_subset_1(all_0_10_10, all_25_0_25)
% 6.58/2.21 |
% 6.58/2.21 | From (88) and (96) follows:
% 6.58/2.21 | (97) ~ m1_subset_1(all_0_10_10, all_0_12_12)
% 6.58/2.21 |
% 6.58/2.21 | Using (62) and (97) yields:
% 6.58/2.21 | (98) $false
% 6.58/2.21 |
% 6.58/2.21 |-The branch is then unsatisfiable
% 6.58/2.21 |-Branch two:
% 6.58/2.21 | (99) m1_subset_1(all_0_10_10, all_25_0_25)
% 6.58/2.21 | (100) r4_binop_1(all_0_10_10, all_0_7_7, all_0_5_5)
% 6.58/2.21 |
% 6.58/2.21 | From (88) and (99) follows:
% 6.58/2.21 | (62) m1_subset_1(all_0_10_10, all_0_12_12)
% 6.58/2.21 |
% 6.58/2.21 +-Applying beta-rule and splitting (90), into two cases.
% 6.58/2.21 |-Branch one:
% 6.58/2.21 | (96) ~ m1_subset_1(all_0_10_10, all_25_0_25)
% 6.58/2.21 |
% 6.58/2.21 | From (88) and (96) follows:
% 6.58/2.21 | (97) ~ m1_subset_1(all_0_10_10, all_0_12_12)
% 6.58/2.21 |
% 6.58/2.21 | Using (62) and (97) yields:
% 6.58/2.21 | (98) $false
% 6.58/2.21 |
% 6.58/2.21 |-The branch is then unsatisfiable
% 6.58/2.21 |-Branch two:
% 6.58/2.21 | (99) m1_subset_1(all_0_10_10, all_25_0_25)
% 6.58/2.21 | (106) r5_binop_1(all_0_10_10, all_0_7_7, all_0_5_5)
% 6.58/2.21 |
% 6.58/2.21 | Instantiating formula (2) with all_0_10_10, all_0_10_10, all_50_0_31, all_0_9_9 and discharging atoms k2_zfmisc_1(all_0_10_10, all_0_10_10) = all_50_0_31, k2_zfmisc_1(all_0_10_10, all_0_10_10) = all_0_9_9, yields:
% 6.58/2.21 | (107) all_50_0_31 = all_0_9_9
% 6.58/2.21 |
% 6.58/2.21 | From (107) and (93) follows:
% 6.58/2.21 | (44) k2_zfmisc_1(all_0_10_10, all_0_10_10) = all_0_9_9
% 6.58/2.21 |
% 6.58/2.21 | Instantiating formula (16) with all_0_5_5, all_0_9_9, all_0_7_7, all_0_10_10 and discharging atoms k2_zfmisc_1(all_0_10_10, all_0_10_10) = all_0_9_9, r5_binop_1(all_0_10_10, all_0_7_7, all_0_5_5), r4_binop_1(all_0_10_10, all_0_7_7, all_0_5_5), m2_relset_1(all_0_5_5, all_0_9_9, all_0_10_10), m2_relset_1(all_0_7_7, all_0_9_9, all_0_10_10), v1_funct_2(all_0_5_5, all_0_9_9, all_0_10_10), v1_funct_2(all_0_7_7, all_0_9_9, all_0_10_10), v1_funct_1(all_0_5_5), v1_funct_1(all_0_7_7), ~ r6_binop_1(all_0_10_10, all_0_7_7, all_0_5_5), yields:
% 6.58/2.21 | (98) $false
% 6.58/2.21 |
% 6.58/2.21 |-The branch is then unsatisfiable
% 6.58/2.21 % SZS output end Proof for theBenchmark
% 6.58/2.21
% 6.58/2.21 1625ms
%------------------------------------------------------------------------------