TSTP Solution File: SEU435+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU435+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n013.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 : Tue Jul 19 08:50:00 EDT 2022
% Result : Theorem 3.24s 1.44s
% Output : Proof 5.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU435+1 : TPTP v8.1.0. Released v3.4.0.
% 0.10/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 19 21:41:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.58 ____ _
% 0.19/0.58 ___ / __ \_____(_)___ ________ __________
% 0.19/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.58
% 0.19/0.58 A Theorem Prover for First-Order Logic
% 0.19/0.58 (ePrincess v.1.0)
% 0.19/0.58
% 0.19/0.58 (c) Philipp Rümmer, 2009-2015
% 0.19/0.58 (c) Peter Backeman, 2014-2015
% 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.58 Bug reports to peter@backeman.se
% 0.19/0.58
% 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.58
% 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.76/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.69/0.97 Prover 0: Preprocessing ...
% 2.67/1.27 Prover 0: Warning: ignoring some quantifiers
% 2.67/1.29 Prover 0: Constructing countermodel ...
% 3.24/1.44 Prover 0: proved (804ms)
% 3.24/1.44
% 3.24/1.44 No countermodel exists, formula is valid
% 3.24/1.44 % SZS status Theorem for theBenchmark
% 3.24/1.44
% 3.24/1.44 Generating proof ... Warning: ignoring some quantifiers
% 5.31/1.84 found it (size 36)
% 5.31/1.84
% 5.31/1.84 % SZS output start Proof for theBenchmark
% 5.31/1.84 Assumed formulas after preprocessing and simplification:
% 5.31/1.84 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (a_6_0_relset_2(v0, v1, v2, v6, v7, v8) = v10 & k2_zfmisc_1(v0, v1) = v3 & k1_zfmisc_1(v11) = v12 & k1_zfmisc_1(v7) = v11 & k1_zfmisc_1(v6) = v9 & k1_zfmisc_1(v4) = v5 & k1_zfmisc_1(v3) = v4 & v3_relat_1(v13) & v3_relat_1(k1_xboole_0) & v1_relat_1(v15) & v1_relat_1(v14) & v1_relat_1(v13) & v1_relat_1(k1_xboole_0) & v1_xboole_0(v15) & v1_xboole_0(k1_xboole_0) & m1_subset_1(v8, v9) & m1_subset_1(v2, v5) & ~ v1_xboole_0(v14) & ~ m1_subset_1(v10, v12) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v17 = v16 | ~ (a_6_0_relset_2(v23, v22, v21, v20, v19, v18) = v17) | ~ (a_6_0_relset_2(v23, v22, v21, v20, v19, v18) = v16)) & ? [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (a_6_0_relset_2(v17, v18, v19, v20, v21, v22) = v23) | ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : ? [v31] : (k2_zfmisc_1(v20, v21) = v28 & k2_zfmisc_1(v17, v18) = v24 & k1_zfmisc_1(v28) = v29 & k1_zfmisc_1(v25) = v26 & k1_zfmisc_1(v24) = v25 & k1_zfmisc_1(v20) = v27 & ( ~ m1_subset_1(v22, v27) | ~ m1_subset_1(v19, v26) | (( ~ r2_hidden(v16, v23) | (v31 = v16 & k8_relset_2(v20, v21, v22, v30) = v16 & r2_hidden(v30, v19) & m1_subset_1(v30, v29))) & (r2_hidden(v16, v23) | ! [v32] : ( ~ (k8_relset_2(v20, v21, v22, v32) = v16) | ~ r2_hidden(v32, v19) | ~ m1_subset_1(v32, v29))))))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (k9_relat_1(v18, v19) = v22) | ~ (k2_zfmisc_1(v16, v20) = v21) | ~ (k1_zfmisc_1(v17) = v20) | ? [v23] : ? [v24] : (k4_relset_2(v16, v17, v18, v19) = v24 & k1_zfmisc_1(v21) = v23 & (v24 = v22 | ~ m1_subset_1(v18, v23)))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (a_6_0_relset_2(v16, v17, v18, v19, v20, v21) = v22) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : (k2_zfmisc_1(v16, v17) = v23 & k1_zfmisc_1(v27) = v28 & k1_zfmisc_1(v24) = v25 & k1_zfmisc_1(v23) = v24 & k1_zfmisc_1(v20) = v27 & k1_zfmisc_1(v19) = v26 & ( ~ m1_subset_1(v21, v26) | ~ m1_subset_1(v18, v25) | m1_subset_1(v22, v28)))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v17 = v16 | ~ (k8_relset_2(v21, v20, v19, v18) = v17) | ~ (k8_relset_2(v21, v20, v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v17 = v16 | ~ (k7_relset_2(v21, v20, v19, v18) = v17) | ~ (k7_relset_2(v21, v20, v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v17 = v16 | ~ (k4_relset_2(v21, v20, v19, v18) = v17) | ~ (k4_relset_2(v21, v20, v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v17 = v16 | ~ (k6_relset_2(v20, v19, v18) = v17) | ~ (k6_relset_2(v20, v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (k8_relset_2(v16, v17, v18, v19) = v20) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : (k7_relset_2(v16, v17, v18, v19) = v24 & k2_zfmisc_1(v16, v17) = v22 & k1_zfmisc_1(v22) = v23 & k1_zfmisc_1(v16) = v21 & (v24 = v20 | ~ m1_subset_1(v19, v23) | ~ m1_subset_1(v18, v21)))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (k8_relset_2(v16, v17, v18, v19) = v20) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : (k2_zfmisc_1(v16, v17) = v22 & k1_zfmisc_1(v22) = v23 & k1_zfmisc_1(v17) = v24 & k1_zfmisc_1(v16) = v21 & ( ~ m1_subset_1(v19, v23) | ~ m1_subset_1(v18, v21) | m1_subset_1(v20, v24)))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (k5_relset_2(v17, v18) = v20) | ~ (k2_zfmisc_1(v17, v16) = v19) | ? [v21] : ? [v22] : (k6_relset_2(v16, v17, v18) = v22 & k1_zfmisc_1(v19) = v21 & (v22 = v20 | ~ m1_subset_1(v18, v21)))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (k3_pua2mss1(v18) = v20) | ~ (k2_zfmisc_1(v16, v17) = v19) | ? [v21] : ? [v22] : (k1_zfmisc_1(v19) = v22 & k1_zfmisc_1(v16) = v21 & ( ~ m1_subset_1(v18, v21) | ( ! [v23] : ! [v24] : ! [v25] : ! [v26] : ( ~ (k6_relset_2(v17, v16, v23) = v24) | ~ (k4_relset_2(v21, v17, v24, v20) = v25) | ~ (k8_setfam_1(v17, v25) = v26) | ~ m1_subset_1(v23, v22) | k7_relset_2(v16, v17, v18, v23) = v26) & ! [v23] : ! [v24] : ( ~ (k7_relset_2(v16, v17, v18, v23) = v24) | ~ m1_subset_1(v23, v22) | ? [v25] : ? [v26] : (k6_relset_2(v17, v16, v23) = v25 & k4_relset_2(v21, v17, v25, v20) = v26 & k8_setfam_1(v17, v26) = v24)))))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (k7_relset_2(v16, v17, v18, v19) = v20) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : (k8_relset_2(v16, v17, v18, v19) = v24 & k2_zfmisc_1(v16, v17) = v22 & k1_zfmisc_1(v22) = v23 & k1_zfmisc_1(v16) = v21 & (v24 = v20 | ~ m1_subset_1(v19, v23) | ~ m1_subset_1(v18, v21)))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (k4_relset_2(v16, v17, v18, v19) = v20) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : (k9_relat_1(v18, v19) = v24 & k2_zfmisc_1(v16, v21) = v22 & k1_zfmisc_1(v22) = v23 & k1_zfmisc_1(v17) = v21 & (v24 = v20 | ~ m1_subset_1(v18, v23)))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (k4_relset_2(v16, v17, v18, v19) = v20) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : (k2_zfmisc_1(v16, v21) = v22 & k1_zfmisc_1(v22) = v23 & k1_zfmisc_1(v21) = v24 & k1_zfmisc_1(v17) = v21 & ( ~ m1_subset_1(v18, v23) | m1_subset_1(v20, v24)))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (k9_relat_1(v19, v18) = v17) | ~ (k9_relat_1(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (k5_relset_2(v19, v18) = v17) | ~ (k5_relset_2(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (k8_setfam_1(v19, v18) = v17) | ~ (k8_setfam_1(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (k2_zfmisc_1(v19, v18) = v17) | ~ (k2_zfmisc_1(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (k6_relset_2(v16, v17, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (k2_zfmisc_1(v17, v16) = v20 & k1_zfmisc_1(v20) = v21 & k1_zfmisc_1(v17) = v22 & k1_zfmisc_1(v16) = v23 & ( ~ m1_subset_1(v18, v21) | (m2_relset_1(v19, v22, v23) & v1_funct_2(v19, v22, v23) & v1_funct_1(v19))))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (k6_relset_2(v16, v17, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : (k5_relset_2(v17, v18) = v22 & k2_zfmisc_1(v17, v16) = v20 & k1_zfmisc_1(v20) = v21 & (v22 = v19 | ~ m1_subset_1(v18, v21)))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (k2_zfmisc_1(v16, v17) = v19) | ~ m2_relset_1(v18, v16, v17) | ? [v20] : (k1_zfmisc_1(v19) = v20 & m1_subset_1(v18, v20))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (k1_zfmisc_1(v18) = v19) | ~ v1_xboole_0(v18) | ~ r2_hidden(v16, v17) | ~ m1_subset_1(v17, v19)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (k1_zfmisc_1(v18) = v19) | ~ r2_hidden(v16, v17) | ~ m1_subset_1(v17, v19) | m1_subset_1(v16, v18)) & ? [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (k2_zfmisc_1(v17, v18) = v19) | v1_relat_1(v16) | ? [v20] : (k1_zfmisc_1(v19) = v20 & ~ m1_subset_1(v16, v20))) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (k3_pua2mss1(v18) = v17) | ~ (k3_pua2mss1(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (k1_zfmisc_1(v18) = v17) | ~ (k1_zfmisc_1(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (k5_relset_2(v16, v17) = v18) | ~ v1_relat_1(v17) | v1_funct_1(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (k5_relset_2(v16, v17) = v18) | ~ v1_relat_1(v17) | v1_relat_1(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (k8_setfam_1(v16, v17) = v18) | ? [v19] : ? [v20] : (k1_zfmisc_1(v19) = v20 & k1_zfmisc_1(v16) = v19 & ( ~ m1_subset_1(v17, v20) | m1_subset_1(v18, v19)))) & ! [v16] : ! [v17] : ! [v18] : ( ~ (k2_zfmisc_1(v16, v17) = v18) | ~ v1_xboole_0(v18) | v1_xboole_0(v17) | v1_xboole_0(v16)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (k2_zfmisc_1(v16, v17) = v18) | v1_relat_1(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (k1_zfmisc_1(v17) = v18) | ~ r1_tarski(v16, v17) | m1_subset_1(v16, v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (k1_zfmisc_1(v17) = v18) | ~ m1_subset_1(v16, v18) | r1_tarski(v16, v17)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (k1_zfmisc_1(v16) = v18) | ~ m1_eqrel_1(v17, v16) | ? [v19] : (k1_zfmisc_1(v18) = v19 & m1_subset_1(v17, v19))) & ! [v16] : ! [v17] : ! [v18] : ( ~ m1_relset_1(v18, v16, v17) | m2_relset_1(v18, v16, v17)) & ! [v16] : ! [v17] : ! [v18] : ( ~ m2_relset_1(v18, v16, v17) | m1_relset_1(v18, v16, v17)) & ! [v16] : ! [v17] : (v17 = v16 | ~ v1_xboole_0(v17) | ~ v1_xboole_0(v16)) & ! [v16] : ! [v17] : ( ~ (k3_pua2mss1(v16) = v17) | m1_eqrel_1(v17, v16)) & ! [v16] : ! [v17] : ( ~ (k1_zfmisc_1(v16) = v17) | ~ v1_xboole_0(v17)) & ! [v16] : ! [v17] : ( ~ (k1_zfmisc_1(v16) = v17) | v1_xboole_0(v16) | ? [v18] : (m1_subset_1(v18, v17) & ~ v1_xboole_0(v18))) & ! [v16] : ! [v17] : ( ~ (k1_zfmisc_1(v16) = v17) | ? [v18] : (v1_xboole_0(v18) & m1_subset_1(v18, v17))) & ! [v16] : ! [v17] : ( ~ v1_xboole_0(v17) | ~ r2_hidden(v16, v17)) & ! [v16] : ! [v17] : ( ~ r2_hidden(v17, v16) | ~ r2_hidden(v16, v17)) & ! [v16] : ! [v17] : ( ~ r2_hidden(v16, v17) | m1_subset_1(v16, v17)) & ! [v16] : ! [v17] : ( ~ m1_subset_1(v16, v17) | v1_xboole_0(v17) | r2_hidden(v16, v17)) & ! [v16] : (v16 = k1_xboole_0 | ~ v1_xboole_0(v16)) & ! [v16] : ( ~ v1_xboole_0(v16) | v1_relat_1(v16)) & ? [v16] : ? [v17] : ? [v18] : m1_relset_1(v18, v16, v17) & ? [v16] : ? [v17] : ? [v18] : m2_relset_1(v18, v16, v17) & ? [v16] : ? [v17] : ? [v18] : (m1_relset_1(v18, v16, v17) & v1_funct_1(v18) & v1_relat_1(v18)) & ? [v16] : ? [v17] : (v17 = v16 | ? [v18] : (( ~ r2_hidden(v18, v17) | ~ r2_hidden(v18, v16)) & (r2_hidden(v18, v17) | r2_hidden(v18, v16)))) & ? [v16] : ? [v17] : m1_eqrel_1(v17, v16) & ? [v16] : ? [v17] : m1_subset_1(v17, v16) & ? [v16] : r1_tarski(v16, v16))
% 5.31/1.89 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15 yields:
% 5.31/1.89 | (1) a_6_0_relset_2(all_0_15_15, all_0_14_14, all_0_13_13, all_0_9_9, all_0_8_8, all_0_7_7) = all_0_5_5 & k2_zfmisc_1(all_0_15_15, all_0_14_14) = all_0_12_12 & k1_zfmisc_1(all_0_4_4) = all_0_3_3 & k1_zfmisc_1(all_0_8_8) = all_0_4_4 & k1_zfmisc_1(all_0_9_9) = all_0_6_6 & k1_zfmisc_1(all_0_11_11) = all_0_10_10 & k1_zfmisc_1(all_0_12_12) = all_0_11_11 & v3_relat_1(all_0_2_2) & v3_relat_1(k1_xboole_0) & v1_relat_1(all_0_0_0) & v1_relat_1(all_0_1_1) & v1_relat_1(all_0_2_2) & v1_relat_1(k1_xboole_0) & v1_xboole_0(all_0_0_0) & v1_xboole_0(k1_xboole_0) & m1_subset_1(all_0_7_7, all_0_6_6) & m1_subset_1(all_0_13_13, all_0_10_10) & ~ v1_xboole_0(all_0_1_1) & ~ m1_subset_1(all_0_5_5, all_0_3_3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v1 = v0 | ~ (a_6_0_relset_2(v7, v6, v5, v4, v3, v2) = v1) | ~ (a_6_0_relset_2(v7, v6, v5, v4, v3, v2) = v0)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (a_6_0_relset_2(v1, v2, v3, v4, v5, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (k2_zfmisc_1(v4, v5) = v12 & k2_zfmisc_1(v1, v2) = v8 & k1_zfmisc_1(v12) = v13 & k1_zfmisc_1(v9) = v10 & k1_zfmisc_1(v8) = v9 & k1_zfmisc_1(v4) = v11 & ( ~ m1_subset_1(v6, v11) | ~ m1_subset_1(v3, v10) | (( ~ r2_hidden(v0, v7) | (v15 = v0 & k8_relset_2(v4, v5, v6, v14) = v0 & r2_hidden(v14, v3) & m1_subset_1(v14, v13))) & (r2_hidden(v0, v7) | ! [v16] : ( ~ (k8_relset_2(v4, v5, v6, v16) = v0) | ~ r2_hidden(v16, v3) | ~ m1_subset_1(v16, v13))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (k9_relat_1(v2, v3) = v6) | ~ (k2_zfmisc_1(v0, v4) = v5) | ~ (k1_zfmisc_1(v1) = v4) | ? [v7] : ? [v8] : (k4_relset_2(v0, v1, v2, v3) = v8 & k1_zfmisc_1(v5) = v7 & (v8 = v6 | ~ m1_subset_1(v2, v7)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (a_6_0_relset_2(v0, v1, v2, v3, v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (k2_zfmisc_1(v0, v1) = v7 & k1_zfmisc_1(v11) = v12 & k1_zfmisc_1(v8) = v9 & k1_zfmisc_1(v7) = v8 & k1_zfmisc_1(v4) = v11 & k1_zfmisc_1(v3) = v10 & ( ~ m1_subset_1(v5, v10) | ~ m1_subset_1(v2, v9) | m1_subset_1(v6, v12)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (k8_relset_2(v5, v4, v3, v2) = v1) | ~ (k8_relset_2(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (k7_relset_2(v5, v4, v3, v2) = v1) | ~ (k7_relset_2(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (k4_relset_2(v5, v4, v3, v2) = v1) | ~ (k4_relset_2(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (k6_relset_2(v4, v3, v2) = v1) | ~ (k6_relset_2(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k8_relset_2(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (k7_relset_2(v0, v1, v2, v3) = v8 & k2_zfmisc_1(v0, v1) = v6 & k1_zfmisc_1(v6) = v7 & k1_zfmisc_1(v0) = v5 & (v8 = v4 | ~ m1_subset_1(v3, v7) | ~ m1_subset_1(v2, v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k8_relset_2(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (k2_zfmisc_1(v0, v1) = v6 & k1_zfmisc_1(v6) = v7 & k1_zfmisc_1(v1) = v8 & k1_zfmisc_1(v0) = v5 & ( ~ m1_subset_1(v3, v7) | ~ m1_subset_1(v2, v5) | m1_subset_1(v4, v8)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k5_relset_2(v1, v2) = v4) | ~ (k2_zfmisc_1(v1, v0) = v3) | ? [v5] : ? [v6] : (k6_relset_2(v0, v1, v2) = v6 & k1_zfmisc_1(v3) = v5 & (v6 = v4 | ~ m1_subset_1(v2, v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k3_pua2mss1(v2) = v4) | ~ (k2_zfmisc_1(v0, v1) = v3) | ? [v5] : ? [v6] : (k1_zfmisc_1(v3) = v6 & k1_zfmisc_1(v0) = v5 & ( ~ m1_subset_1(v2, v5) | ( ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (k6_relset_2(v1, v0, v7) = v8) | ~ (k4_relset_2(v5, v1, v8, v4) = v9) | ~ (k8_setfam_1(v1, v9) = v10) | ~ m1_subset_1(v7, v6) | k7_relset_2(v0, v1, v2, v7) = v10) & ! [v7] : ! [v8] : ( ~ (k7_relset_2(v0, v1, v2, v7) = v8) | ~ m1_subset_1(v7, v6) | ? [v9] : ? [v10] : (k6_relset_2(v1, v0, v7) = v9 & k4_relset_2(v5, v1, v9, v4) = v10 & k8_setfam_1(v1, v10) = v8)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k7_relset_2(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (k8_relset_2(v0, v1, v2, v3) = v8 & k2_zfmisc_1(v0, v1) = v6 & k1_zfmisc_1(v6) = v7 & k1_zfmisc_1(v0) = v5 & (v8 = v4 | ~ m1_subset_1(v3, v7) | ~ m1_subset_1(v2, v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k4_relset_2(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (k9_relat_1(v2, v3) = v8 & k2_zfmisc_1(v0, v5) = v6 & k1_zfmisc_1(v6) = v7 & k1_zfmisc_1(v1) = v5 & (v8 = v4 | ~ m1_subset_1(v2, v7)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k4_relset_2(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (k2_zfmisc_1(v0, v5) = v6 & k1_zfmisc_1(v6) = v7 & k1_zfmisc_1(v5) = v8 & k1_zfmisc_1(v1) = v5 & ( ~ m1_subset_1(v2, v7) | m1_subset_1(v4, v8)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k9_relat_1(v3, v2) = v1) | ~ (k9_relat_1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k5_relset_2(v3, v2) = v1) | ~ (k5_relset_2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k8_setfam_1(v3, v2) = v1) | ~ (k8_setfam_1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k2_zfmisc_1(v3, v2) = v1) | ~ (k2_zfmisc_1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k6_relset_2(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (k2_zfmisc_1(v1, v0) = v4 & k1_zfmisc_1(v4) = v5 & k1_zfmisc_1(v1) = v6 & k1_zfmisc_1(v0) = v7 & ( ~ m1_subset_1(v2, v5) | (m2_relset_1(v3, v6, v7) & v1_funct_2(v3, v6, v7) & v1_funct_1(v3))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k6_relset_2(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (k5_relset_2(v1, v2) = v6 & k2_zfmisc_1(v1, v0) = v4 & k1_zfmisc_1(v4) = v5 & (v6 = v3 | ~ m1_subset_1(v2, v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k2_zfmisc_1(v0, v1) = v3) | ~ m2_relset_1(v2, v0, v1) | ? [v4] : (k1_zfmisc_1(v3) = v4 & m1_subset_1(v2, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ v1_xboole_0(v2) | ~ r2_hidden(v0, v1) | ~ m1_subset_1(v1, v3)) & ! [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 | ~ (k3_pua2mss1(v2) = v1) | ~ (k3_pua2mss1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k5_relset_2(v0, v1) = v2) | ~ v1_relat_1(v1) | v1_funct_1(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k5_relset_2(v0, v1) = v2) | ~ v1_relat_1(v1) | v1_relat_1(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k8_setfam_1(v0, v1) = v2) | ? [v3] : ? [v4] : (k1_zfmisc_1(v3) = v4 & k1_zfmisc_1(v0) = v3 & ( ~ m1_subset_1(v1, v4) | m1_subset_1(v2, 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] : ( ~ (k2_zfmisc_1(v0, v1) = v2) | v1_relat_1(v2)) & ! [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] : ( ~ (k1_zfmisc_1(v0) = v2) | ~ m1_eqrel_1(v1, v0) | ? [v3] : (k1_zfmisc_1(v2) = v3 & m1_subset_1(v1, v3))) & ! [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] : ( ~ (k3_pua2mss1(v0) = v1) | m1_eqrel_1(v1, 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] : (v1_xboole_0(v2) & m1_subset_1(v2, 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] : ( ~ m1_subset_1(v0, v1) | v1_xboole_0(v1) | r2_hidden(v0, v1)) & ! [v0] : (v0 = k1_xboole_0 | ~ v1_xboole_0(v0)) & ! [v0] : ( ~ v1_xboole_0(v0) | v1_relat_1(v0)) & ? [v0] : ? [v1] : ? [v2] : m1_relset_1(v2, v0, v1) & ? [v0] : ? [v1] : ? [v2] : m2_relset_1(v2, v0, v1) & ? [v0] : ? [v1] : ? [v2] : (m1_relset_1(v2, v0, v1) & v1_funct_1(v2) & v1_relat_1(v2)) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ r2_hidden(v2, v1) | ~ r2_hidden(v2, v0)) & (r2_hidden(v2, v1) | r2_hidden(v2, v0)))) & ? [v0] : ? [v1] : m1_eqrel_1(v1, v0) & ? [v0] : ? [v1] : m1_subset_1(v1, v0) & ? [v0] : r1_tarski(v0, v0)
% 5.31/1.91 |
% 5.31/1.91 | Applying alpha-rule on (1) yields:
% 5.31/1.91 | (2) v1_relat_1(all_0_1_1)
% 5.31/1.91 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k6_relset_2(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (k2_zfmisc_1(v1, v0) = v4 & k1_zfmisc_1(v4) = v5 & k1_zfmisc_1(v1) = v6 & k1_zfmisc_1(v0) = v7 & ( ~ m1_subset_1(v2, v5) | (m2_relset_1(v3, v6, v7) & v1_funct_2(v3, v6, v7) & v1_funct_1(v3)))))
% 5.31/1.91 | (4) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ r2_hidden(v2, v1) | ~ r2_hidden(v2, v0)) & (r2_hidden(v2, v1) | r2_hidden(v2, v0))))
% 5.31/1.91 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v1 = v0 | ~ (a_6_0_relset_2(v7, v6, v5, v4, v3, v2) = v1) | ~ (a_6_0_relset_2(v7, v6, v5, v4, v3, v2) = v0))
% 5.31/1.91 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k5_relset_2(v3, v2) = v1) | ~ (k5_relset_2(v3, v2) = v0))
% 5.31/1.91 | (7) ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ~ v1_xboole_0(v1))
% 5.31/1.91 | (8) m1_subset_1(all_0_13_13, all_0_10_10)
% 5.31/1.91 | (9) ? [v0] : ? [v1] : ? [v2] : (m1_relset_1(v2, v0, v1) & v1_funct_1(v2) & v1_relat_1(v2))
% 5.31/1.91 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k4_relset_2(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (k9_relat_1(v2, v3) = v8 & k2_zfmisc_1(v0, v5) = v6 & k1_zfmisc_1(v6) = v7 & k1_zfmisc_1(v1) = v5 & (v8 = v4 | ~ m1_subset_1(v2, v7))))
% 5.31/1.91 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_zfmisc_1(v1) = v2) | ~ m1_subset_1(v0, v2) | r1_tarski(v0, v1))
% 5.31/1.91 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_zfmisc_1(v1) = v2) | ~ r1_tarski(v0, v1) | m1_subset_1(v0, v2))
% 5.31/1.91 | (13) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (a_6_0_relset_2(v1, v2, v3, v4, v5, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (k2_zfmisc_1(v4, v5) = v12 & k2_zfmisc_1(v1, v2) = v8 & k1_zfmisc_1(v12) = v13 & k1_zfmisc_1(v9) = v10 & k1_zfmisc_1(v8) = v9 & k1_zfmisc_1(v4) = v11 & ( ~ m1_subset_1(v6, v11) | ~ m1_subset_1(v3, v10) | (( ~ r2_hidden(v0, v7) | (v15 = v0 & k8_relset_2(v4, v5, v6, v14) = v0 & r2_hidden(v14, v3) & m1_subset_1(v14, v13))) & (r2_hidden(v0, v7) | ! [v16] : ( ~ (k8_relset_2(v4, v5, v6, v16) = v0) | ~ r2_hidden(v16, v3) | ~ m1_subset_1(v16, v13)))))))
% 5.72/1.92 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k8_relset_2(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (k7_relset_2(v0, v1, v2, v3) = v8 & k2_zfmisc_1(v0, v1) = v6 & k1_zfmisc_1(v6) = v7 & k1_zfmisc_1(v0) = v5 & (v8 = v4 | ~ m1_subset_1(v3, v7) | ~ m1_subset_1(v2, v5))))
% 5.72/1.92 | (15) ! [v0] : ! [v1] : (v1 = v0 | ~ v1_xboole_0(v1) | ~ v1_xboole_0(v0))
% 5.72/1.92 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k4_relset_2(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (k2_zfmisc_1(v0, v5) = v6 & k1_zfmisc_1(v6) = v7 & k1_zfmisc_1(v5) = v8 & k1_zfmisc_1(v1) = v5 & ( ~ m1_subset_1(v2, v7) | m1_subset_1(v4, v8))))
% 5.72/1.92 | (17) v3_relat_1(k1_xboole_0)
% 5.72/1.92 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k8_setfam_1(v3, v2) = v1) | ~ (k8_setfam_1(v3, v2) = v0))
% 5.72/1.92 | (19) ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | v1_xboole_0(v0) | ? [v2] : (m1_subset_1(v2, v1) & ~ v1_xboole_0(v2)))
% 5.72/1.92 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (k6_relset_2(v4, v3, v2) = v1) | ~ (k6_relset_2(v4, v3, v2) = v0))
% 5.72/1.92 | (21) ! [v0] : ! [v1] : ( ~ r2_hidden(v1, v0) | ~ r2_hidden(v0, v1))
% 5.72/1.92 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_zfmisc_1(v0, v1) = v2) | ~ v1_xboole_0(v2) | v1_xboole_0(v1) | v1_xboole_0(v0))
% 5.72/1.92 | (23) a_6_0_relset_2(all_0_15_15, all_0_14_14, all_0_13_13, all_0_9_9, all_0_8_8, all_0_7_7) = all_0_5_5
% 5.72/1.92 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ v1_xboole_0(v2) | ~ r2_hidden(v0, v1) | ~ m1_subset_1(v1, v3))
% 5.72/1.92 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (k5_relset_2(v0, v1) = v2) | ~ v1_relat_1(v1) | v1_relat_1(v2))
% 5.72/1.92 | (26) ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | m1_subset_1(v0, v1))
% 5.72/1.92 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_zfmisc_1(v0) = v2) | ~ m1_eqrel_1(v1, v0) | ? [v3] : (k1_zfmisc_1(v2) = v3 & m1_subset_1(v1, v3)))
% 5.72/1.92 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k7_relset_2(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (k8_relset_2(v0, v1, v2, v3) = v8 & k2_zfmisc_1(v0, v1) = v6 & k1_zfmisc_1(v6) = v7 & k1_zfmisc_1(v0) = v5 & (v8 = v4 | ~ m1_subset_1(v3, v7) | ~ m1_subset_1(v2, v5))))
% 5.72/1.92 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (k5_relset_2(v0, v1) = v2) | ~ v1_relat_1(v1) | v1_funct_1(v2))
% 5.72/1.92 | (30) v1_relat_1(all_0_0_0)
% 5.72/1.92 | (31) k2_zfmisc_1(all_0_15_15, all_0_14_14) = all_0_12_12
% 5.72/1.92 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k8_relset_2(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (k2_zfmisc_1(v0, v1) = v6 & k1_zfmisc_1(v6) = v7 & k1_zfmisc_1(v1) = v8 & k1_zfmisc_1(v0) = v5 & ( ~ m1_subset_1(v3, v7) | ~ m1_subset_1(v2, v5) | m1_subset_1(v4, v8))))
% 5.72/1.92 | (33) ? [v0] : ? [v1] : m1_eqrel_1(v1, v0)
% 5.72/1.92 | (34) ~ m1_subset_1(all_0_5_5, all_0_3_3)
% 5.72/1.92 | (35) ! [v0] : ( ~ v1_xboole_0(v0) | v1_relat_1(v0))
% 5.72/1.92 | (36) ? [v0] : ? [v1] : ? [v2] : m1_relset_1(v2, v0, v1)
% 5.72/1.92 | (37) ! [v0] : ! [v1] : ( ~ m1_subset_1(v0, v1) | v1_xboole_0(v1) | r2_hidden(v0, v1))
% 5.72/1.92 | (38) ? [v0] : ? [v1] : m1_subset_1(v1, v0)
% 5.72/1.92 | (39) k1_zfmisc_1(all_0_4_4) = all_0_3_3
% 5.72/1.92 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (k8_setfam_1(v0, v1) = v2) | ? [v3] : ? [v4] : (k1_zfmisc_1(v3) = v4 & k1_zfmisc_1(v0) = v3 & ( ~ m1_subset_1(v1, v4) | m1_subset_1(v2, v3))))
% 5.72/1.92 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k3_pua2mss1(v2) = v4) | ~ (k2_zfmisc_1(v0, v1) = v3) | ? [v5] : ? [v6] : (k1_zfmisc_1(v3) = v6 & k1_zfmisc_1(v0) = v5 & ( ~ m1_subset_1(v2, v5) | ( ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (k6_relset_2(v1, v0, v7) = v8) | ~ (k4_relset_2(v5, v1, v8, v4) = v9) | ~ (k8_setfam_1(v1, v9) = v10) | ~ m1_subset_1(v7, v6) | k7_relset_2(v0, v1, v2, v7) = v10) & ! [v7] : ! [v8] : ( ~ (k7_relset_2(v0, v1, v2, v7) = v8) | ~ m1_subset_1(v7, v6) | ? [v9] : ? [v10] : (k6_relset_2(v1, v0, v7) = v9 & k4_relset_2(v5, v1, v9, v4) = v10 & k8_setfam_1(v1, v10) = v8))))))
% 5.72/1.92 | (42) ! [v0] : ! [v1] : ( ~ (k3_pua2mss1(v0) = v1) | m1_eqrel_1(v1, v0))
% 5.72/1.92 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ r2_hidden(v0, v1) | ~ m1_subset_1(v1, v3) | m1_subset_1(v0, v2))
% 5.72/1.92 | (44) ~ v1_xboole_0(all_0_1_1)
% 5.72/1.92 | (45) m1_subset_1(all_0_7_7, all_0_6_6)
% 5.72/1.92 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (a_6_0_relset_2(v0, v1, v2, v3, v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (k2_zfmisc_1(v0, v1) = v7 & k1_zfmisc_1(v11) = v12 & k1_zfmisc_1(v8) = v9 & k1_zfmisc_1(v7) = v8 & k1_zfmisc_1(v4) = v11 & k1_zfmisc_1(v3) = v10 & ( ~ m1_subset_1(v5, v10) | ~ m1_subset_1(v2, v9) | m1_subset_1(v6, v12))))
% 5.72/1.92 | (47) k1_zfmisc_1(all_0_9_9) = all_0_6_6
% 5.72/1.92 | (48) k1_zfmisc_1(all_0_8_8) = all_0_4_4
% 5.72/1.92 | (49) k1_zfmisc_1(all_0_12_12) = all_0_11_11
% 5.72/1.93 | (50) v1_xboole_0(all_0_0_0)
% 5.72/1.93 | (51) ? [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)))
% 5.72/1.93 | (52) v1_relat_1(all_0_2_2)
% 5.72/1.93 | (53) v1_relat_1(k1_xboole_0)
% 5.72/1.93 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (k4_relset_2(v5, v4, v3, v2) = v1) | ~ (k4_relset_2(v5, v4, v3, v2) = v0))
% 5.72/1.93 | (55) ! [v0] : (v0 = k1_xboole_0 | ~ v1_xboole_0(v0))
% 5.72/1.93 | (56) v3_relat_1(all_0_2_2)
% 5.72/1.93 | (57) ? [v0] : r1_tarski(v0, v0)
% 5.72/1.93 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (k7_relset_2(v5, v4, v3, v2) = v1) | ~ (k7_relset_2(v5, v4, v3, v2) = v0))
% 5.72/1.93 | (59) ! [v0] : ! [v1] : ( ~ v1_xboole_0(v1) | ~ r2_hidden(v0, v1))
% 5.72/1.93 | (60) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k3_pua2mss1(v2) = v1) | ~ (k3_pua2mss1(v2) = v0))
% 5.72/1.93 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k9_relat_1(v3, v2) = v1) | ~ (k9_relat_1(v3, v2) = v0))
% 5.72/1.93 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (k8_relset_2(v5, v4, v3, v2) = v1) | ~ (k8_relset_2(v5, v4, v3, v2) = v0))
% 5.72/1.93 | (63) k1_zfmisc_1(all_0_11_11) = all_0_10_10
% 5.72/1.93 | (64) ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_zfmisc_1(v0, v1) = v2) | v1_relat_1(v2))
% 5.72/1.93 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k6_relset_2(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (k5_relset_2(v1, v2) = v6 & k2_zfmisc_1(v1, v0) = v4 & k1_zfmisc_1(v4) = v5 & (v6 = v3 | ~ m1_subset_1(v2, v5))))
% 5.72/1.93 | (66) ! [v0] : ! [v1] : ! [v2] : ( ~ m2_relset_1(v2, v0, v1) | m1_relset_1(v2, v0, v1))
% 5.72/1.93 | (67) ! [v0] : ! [v1] : ! [v2] : ( ~ m1_relset_1(v2, v0, v1) | m2_relset_1(v2, v0, v1))
% 5.72/1.93 | (68) ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ? [v2] : (v1_xboole_0(v2) & m1_subset_1(v2, v1)))
% 5.72/1.93 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k2_zfmisc_1(v3, v2) = v1) | ~ (k2_zfmisc_1(v3, v2) = v0))
% 5.72/1.93 | (70) v1_xboole_0(k1_xboole_0)
% 5.72/1.93 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k5_relset_2(v1, v2) = v4) | ~ (k2_zfmisc_1(v1, v0) = v3) | ? [v5] : ? [v6] : (k6_relset_2(v0, v1, v2) = v6 & k1_zfmisc_1(v3) = v5 & (v6 = v4 | ~ m1_subset_1(v2, v5))))
% 5.72/1.93 | (72) ? [v0] : ? [v1] : ? [v2] : m2_relset_1(v2, v0, v1)
% 5.72/1.93 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (k9_relat_1(v2, v3) = v6) | ~ (k2_zfmisc_1(v0, v4) = v5) | ~ (k1_zfmisc_1(v1) = v4) | ? [v7] : ? [v8] : (k4_relset_2(v0, v1, v2, v3) = v8 & k1_zfmisc_1(v5) = v7 & (v8 = v6 | ~ m1_subset_1(v2, v7))))
% 5.72/1.93 | (74) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0))
% 5.72/1.93 | (75) ! [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)))
% 5.72/1.93 |
% 5.72/1.93 | Instantiating (13) with all_16_0_30 yields:
% 5.72/1.93 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (a_6_0_relset_2(v0, v1, v2, v3, v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (k2_zfmisc_1(v3, v4) = v11 & k2_zfmisc_1(v0, v1) = v7 & k1_zfmisc_1(v11) = v12 & k1_zfmisc_1(v8) = v9 & k1_zfmisc_1(v7) = v8 & k1_zfmisc_1(v3) = v10 & ( ~ m1_subset_1(v5, v10) | ~ m1_subset_1(v2, v9) | (( ~ r2_hidden(all_16_0_30, v6) | (v14 = all_16_0_30 & k8_relset_2(v3, v4, v5, v13) = all_16_0_30 & r2_hidden(v13, v2) & m1_subset_1(v13, v12))) & (r2_hidden(all_16_0_30, v6) | ! [v15] : ( ~ (k8_relset_2(v3, v4, v5, v15) = all_16_0_30) | ~ r2_hidden(v15, v2) | ~ m1_subset_1(v15, v12)))))))
% 5.72/1.93 |
% 5.72/1.93 | Instantiating formula (76) with all_0_5_5, all_0_7_7, all_0_8_8, all_0_9_9, all_0_13_13, all_0_14_14, all_0_15_15 and discharging atoms a_6_0_relset_2(all_0_15_15, all_0_14_14, all_0_13_13, all_0_9_9, all_0_8_8, all_0_7_7) = all_0_5_5, yields:
% 5.72/1.93 | (77) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (k2_zfmisc_1(all_0_9_9, all_0_8_8) = v4 & k2_zfmisc_1(all_0_15_15, all_0_14_14) = v0 & k1_zfmisc_1(v4) = v5 & k1_zfmisc_1(v1) = v2 & k1_zfmisc_1(v0) = v1 & k1_zfmisc_1(all_0_9_9) = v3 & ( ~ m1_subset_1(all_0_7_7, v3) | ~ m1_subset_1(all_0_13_13, v2) | (( ~ r2_hidden(all_16_0_30, all_0_5_5) | (v7 = all_16_0_30 & k8_relset_2(all_0_9_9, all_0_8_8, all_0_7_7, v6) = all_16_0_30 & r2_hidden(v6, all_0_13_13) & m1_subset_1(v6, v5))) & (r2_hidden(all_16_0_30, all_0_5_5) | ! [v8] : ( ~ (k8_relset_2(all_0_9_9, all_0_8_8, all_0_7_7, v8) = all_16_0_30) | ~ r2_hidden(v8, all_0_13_13) | ~ m1_subset_1(v8, v5))))))
% 5.72/1.93 |
% 5.72/1.93 | Instantiating formula (46) with all_0_5_5, all_0_7_7, all_0_8_8, all_0_9_9, all_0_13_13, all_0_14_14, all_0_15_15 and discharging atoms a_6_0_relset_2(all_0_15_15, all_0_14_14, all_0_13_13, all_0_9_9, all_0_8_8, all_0_7_7) = all_0_5_5, yields:
% 5.72/1.93 | (78) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (k2_zfmisc_1(all_0_15_15, all_0_14_14) = v0 & k1_zfmisc_1(v4) = v5 & k1_zfmisc_1(v1) = v2 & k1_zfmisc_1(v0) = v1 & k1_zfmisc_1(all_0_8_8) = v4 & k1_zfmisc_1(all_0_9_9) = v3 & ( ~ m1_subset_1(all_0_7_7, v3) | ~ m1_subset_1(all_0_13_13, v2) | m1_subset_1(all_0_5_5, v5)))
% 5.72/1.93 |
% 5.72/1.93 | Instantiating (77) with all_34_0_36, all_34_1_37, all_34_2_38, all_34_3_39, all_34_4_40, all_34_5_41, all_34_6_42, all_34_7_43 yields:
% 5.72/1.93 | (79) k2_zfmisc_1(all_0_9_9, all_0_8_8) = all_34_3_39 & k2_zfmisc_1(all_0_15_15, all_0_14_14) = all_34_7_43 & k1_zfmisc_1(all_34_3_39) = all_34_2_38 & k1_zfmisc_1(all_34_6_42) = all_34_5_41 & k1_zfmisc_1(all_34_7_43) = all_34_6_42 & k1_zfmisc_1(all_0_9_9) = all_34_4_40 & ( ~ m1_subset_1(all_0_7_7, all_34_4_40) | ~ m1_subset_1(all_0_13_13, all_34_5_41) | (( ~ r2_hidden(all_16_0_30, all_0_5_5) | (all_34_0_36 = all_16_0_30 & k8_relset_2(all_0_9_9, all_0_8_8, all_0_7_7, all_34_1_37) = all_16_0_30 & r2_hidden(all_34_1_37, all_0_13_13) & m1_subset_1(all_34_1_37, all_34_2_38))) & (r2_hidden(all_16_0_30, all_0_5_5) | ! [v0] : ( ~ (k8_relset_2(all_0_9_9, all_0_8_8, all_0_7_7, v0) = all_16_0_30) | ~ r2_hidden(v0, all_0_13_13) | ~ m1_subset_1(v0, all_34_2_38)))))
% 5.72/1.94 |
% 5.72/1.94 | Applying alpha-rule on (79) yields:
% 5.72/1.94 | (80) k1_zfmisc_1(all_34_7_43) = all_34_6_42
% 5.72/1.94 | (81) k1_zfmisc_1(all_34_6_42) = all_34_5_41
% 5.72/1.94 | (82) k1_zfmisc_1(all_34_3_39) = all_34_2_38
% 5.72/1.94 | (83) ~ m1_subset_1(all_0_7_7, all_34_4_40) | ~ m1_subset_1(all_0_13_13, all_34_5_41) | (( ~ r2_hidden(all_16_0_30, all_0_5_5) | (all_34_0_36 = all_16_0_30 & k8_relset_2(all_0_9_9, all_0_8_8, all_0_7_7, all_34_1_37) = all_16_0_30 & r2_hidden(all_34_1_37, all_0_13_13) & m1_subset_1(all_34_1_37, all_34_2_38))) & (r2_hidden(all_16_0_30, all_0_5_5) | ! [v0] : ( ~ (k8_relset_2(all_0_9_9, all_0_8_8, all_0_7_7, v0) = all_16_0_30) | ~ r2_hidden(v0, all_0_13_13) | ~ m1_subset_1(v0, all_34_2_38))))
% 5.72/1.94 | (84) k1_zfmisc_1(all_0_9_9) = all_34_4_40
% 5.72/1.94 | (85) k2_zfmisc_1(all_0_15_15, all_0_14_14) = all_34_7_43
% 5.72/1.94 | (86) k2_zfmisc_1(all_0_9_9, all_0_8_8) = all_34_3_39
% 5.72/1.94 |
% 5.72/1.94 | Instantiating (78) with all_38_0_45, all_38_1_46, all_38_2_47, all_38_3_48, all_38_4_49, all_38_5_50 yields:
% 5.72/1.94 | (87) k2_zfmisc_1(all_0_15_15, all_0_14_14) = all_38_5_50 & k1_zfmisc_1(all_38_1_46) = all_38_0_45 & k1_zfmisc_1(all_38_4_49) = all_38_3_48 & k1_zfmisc_1(all_38_5_50) = all_38_4_49 & k1_zfmisc_1(all_0_8_8) = all_38_1_46 & k1_zfmisc_1(all_0_9_9) = all_38_2_47 & ( ~ m1_subset_1(all_0_7_7, all_38_2_47) | ~ m1_subset_1(all_0_13_13, all_38_3_48) | m1_subset_1(all_0_5_5, all_38_0_45))
% 5.72/1.94 |
% 5.72/1.94 | Applying alpha-rule on (87) yields:
% 5.72/1.94 | (88) k1_zfmisc_1(all_38_5_50) = all_38_4_49
% 5.72/1.94 | (89) k1_zfmisc_1(all_0_8_8) = all_38_1_46
% 5.72/1.94 | (90) k2_zfmisc_1(all_0_15_15, all_0_14_14) = all_38_5_50
% 5.72/1.94 | (91) k1_zfmisc_1(all_38_4_49) = all_38_3_48
% 5.72/1.94 | (92) ~ m1_subset_1(all_0_7_7, all_38_2_47) | ~ m1_subset_1(all_0_13_13, all_38_3_48) | m1_subset_1(all_0_5_5, all_38_0_45)
% 5.72/1.94 | (93) k1_zfmisc_1(all_0_9_9) = all_38_2_47
% 5.72/1.94 | (94) k1_zfmisc_1(all_38_1_46) = all_38_0_45
% 5.72/1.94 |
% 5.72/1.94 | Instantiating formula (69) with all_0_15_15, all_0_14_14, all_38_5_50, all_0_12_12 and discharging atoms k2_zfmisc_1(all_0_15_15, all_0_14_14) = all_38_5_50, k2_zfmisc_1(all_0_15_15, all_0_14_14) = all_0_12_12, yields:
% 5.72/1.94 | (95) all_38_5_50 = all_0_12_12
% 5.72/1.94 |
% 5.72/1.94 | Instantiating formula (69) with all_0_15_15, all_0_14_14, all_34_7_43, all_38_5_50 and discharging atoms k2_zfmisc_1(all_0_15_15, all_0_14_14) = all_38_5_50, k2_zfmisc_1(all_0_15_15, all_0_14_14) = all_34_7_43, yields:
% 5.72/1.94 | (96) all_38_5_50 = all_34_7_43
% 5.72/1.94 |
% 5.72/1.94 | Instantiating formula (74) with all_0_8_8, all_38_1_46, all_0_4_4 and discharging atoms k1_zfmisc_1(all_0_8_8) = all_38_1_46, k1_zfmisc_1(all_0_8_8) = all_0_4_4, yields:
% 5.72/1.94 | (97) all_38_1_46 = all_0_4_4
% 5.72/1.94 |
% 5.72/1.94 | Instantiating formula (74) with all_0_9_9, all_38_2_47, all_0_6_6 and discharging atoms k1_zfmisc_1(all_0_9_9) = all_38_2_47, k1_zfmisc_1(all_0_9_9) = all_0_6_6, yields:
% 5.72/1.94 | (98) all_38_2_47 = all_0_6_6
% 5.72/1.94 |
% 5.72/1.94 | Combining equations (95,96) yields a new equation:
% 5.72/1.94 | (99) all_34_7_43 = all_0_12_12
% 5.72/1.94 |
% 5.72/1.94 | Combining equations (99,96) yields a new equation:
% 5.72/1.94 | (95) all_38_5_50 = all_0_12_12
% 5.72/1.94 |
% 5.72/1.94 | From (97) and (94) follows:
% 5.72/1.94 | (101) k1_zfmisc_1(all_0_4_4) = all_38_0_45
% 5.72/1.94 |
% 5.72/1.94 | From (95) and (88) follows:
% 5.72/1.94 | (102) k1_zfmisc_1(all_0_12_12) = all_38_4_49
% 5.72/1.94 |
% 5.72/1.94 | From (99) and (80) follows:
% 5.72/1.94 | (103) k1_zfmisc_1(all_0_12_12) = all_34_6_42
% 5.72/1.94 |
% 5.72/1.94 | Instantiating formula (74) with all_0_4_4, all_38_0_45, all_0_3_3 and discharging atoms k1_zfmisc_1(all_0_4_4) = all_38_0_45, k1_zfmisc_1(all_0_4_4) = all_0_3_3, yields:
% 5.72/1.94 | (104) all_38_0_45 = all_0_3_3
% 5.72/1.94 |
% 5.72/1.94 | Instantiating formula (74) with all_0_12_12, all_38_4_49, all_0_11_11 and discharging atoms k1_zfmisc_1(all_0_12_12) = all_38_4_49, k1_zfmisc_1(all_0_12_12) = all_0_11_11, yields:
% 5.72/1.94 | (105) all_38_4_49 = all_0_11_11
% 5.72/1.94 |
% 5.72/1.94 | Instantiating formula (74) with all_0_12_12, all_34_6_42, all_38_4_49 and discharging atoms k1_zfmisc_1(all_0_12_12) = all_38_4_49, k1_zfmisc_1(all_0_12_12) = all_34_6_42, yields:
% 5.72/1.94 | (106) all_38_4_49 = all_34_6_42
% 5.72/1.94 |
% 5.72/1.94 | Combining equations (105,106) yields a new equation:
% 5.72/1.94 | (107) all_34_6_42 = all_0_11_11
% 5.72/1.94 |
% 5.72/1.94 | Combining equations (107,106) yields a new equation:
% 5.72/1.94 | (105) all_38_4_49 = all_0_11_11
% 5.72/1.94 |
% 5.72/1.94 | From (105) and (91) follows:
% 5.72/1.94 | (109) k1_zfmisc_1(all_0_11_11) = all_38_3_48
% 5.72/1.95 |
% 5.72/1.95 +-Applying beta-rule and splitting (92), into two cases.
% 5.72/1.95 |-Branch one:
% 5.72/1.95 | (110) ~ m1_subset_1(all_0_7_7, all_38_2_47)
% 5.72/1.95 |
% 5.72/1.95 | From (98) and (110) follows:
% 5.72/1.95 | (111) ~ m1_subset_1(all_0_7_7, all_0_6_6)
% 5.72/1.95 |
% 5.72/1.95 | Using (45) and (111) yields:
% 5.72/1.95 | (112) $false
% 5.72/1.95 |
% 5.72/1.95 |-The branch is then unsatisfiable
% 5.72/1.95 |-Branch two:
% 5.72/1.95 | (113) m1_subset_1(all_0_7_7, all_38_2_47)
% 5.72/1.95 | (114) ~ m1_subset_1(all_0_13_13, all_38_3_48) | m1_subset_1(all_0_5_5, all_38_0_45)
% 5.72/1.95 |
% 5.72/1.95 +-Applying beta-rule and splitting (114), into two cases.
% 5.72/1.95 |-Branch one:
% 5.72/1.95 | (115) ~ m1_subset_1(all_0_13_13, all_38_3_48)
% 5.72/1.95 |
% 5.72/1.95 | Instantiating formula (74) with all_0_11_11, all_38_3_48, all_0_10_10 and discharging atoms k1_zfmisc_1(all_0_11_11) = all_38_3_48, k1_zfmisc_1(all_0_11_11) = all_0_10_10, yields:
% 5.72/1.95 | (116) all_38_3_48 = all_0_10_10
% 5.72/1.95 |
% 5.72/1.95 | From (116) and (115) follows:
% 5.72/1.95 | (117) ~ m1_subset_1(all_0_13_13, all_0_10_10)
% 5.72/1.95 |
% 5.72/1.95 | Using (8) and (117) yields:
% 5.72/1.95 | (112) $false
% 5.72/1.95 |
% 5.72/1.95 |-The branch is then unsatisfiable
% 5.72/1.95 |-Branch two:
% 5.72/1.95 | (119) m1_subset_1(all_0_13_13, all_38_3_48)
% 5.72/1.95 | (120) m1_subset_1(all_0_5_5, all_38_0_45)
% 5.72/1.95 |
% 5.72/1.95 | From (104) and (120) follows:
% 5.72/1.95 | (121) m1_subset_1(all_0_5_5, all_0_3_3)
% 5.72/1.95 |
% 5.72/1.95 | Using (121) and (34) yields:
% 5.72/1.95 | (112) $false
% 5.72/1.95 |
% 5.72/1.95 |-The branch is then unsatisfiable
% 5.72/1.95 % SZS output end Proof for theBenchmark
% 5.72/1.95
% 5.72/1.95 1354ms
%------------------------------------------------------------------------------