TSTP Solution File: SEU420+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU420+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n017.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 08:49:46 EDT 2022
% Result : Theorem 85.37s 53.18s
% Output : Proof 89.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU420+1 : TPTP v8.1.0. Released v3.4.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 19 21:31:13 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.48/0.58 ____ _
% 0.48/0.58 ___ / __ \_____(_)___ ________ __________
% 0.48/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.48/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.48/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.48/0.58
% 0.48/0.58 A Theorem Prover for First-Order Logic
% 0.48/0.59 (ePrincess v.1.0)
% 0.48/0.59
% 0.48/0.59 (c) Philipp Rümmer, 2009-2015
% 0.48/0.59 (c) Peter Backeman, 2014-2015
% 0.48/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.48/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.48/0.59 Bug reports to peter@backeman.se
% 0.48/0.59
% 0.48/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.48/0.59
% 0.48/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.75/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.58/0.96 Prover 0: Preprocessing ...
% 2.20/1.23 Prover 0: Warning: ignoring some quantifiers
% 2.20/1.26 Prover 0: Constructing countermodel ...
% 19.99/5.92 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 20.41/5.98 Prover 1: Preprocessing ...
% 20.70/6.12 Prover 1: Warning: ignoring some quantifiers
% 20.70/6.12 Prover 1: Constructing countermodel ...
% 30.92/8.54 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 30.92/8.58 Prover 2: Preprocessing ...
% 31.54/8.66 Prover 2: Warning: ignoring some quantifiers
% 31.54/8.66 Prover 2: Constructing countermodel ...
% 38.16/10.99 Prover 0: stopped
% 38.60/11.19 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 38.81/11.22 Prover 3: Preprocessing ...
% 38.81/11.26 Prover 3: Warning: ignoring some quantifiers
% 38.81/11.26 Prover 3: Constructing countermodel ...
% 84.07/52.72 Prover 3: stopped
% 84.29/52.92 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 84.29/52.95 Prover 4: Preprocessing ...
% 84.68/53.04 Prover 4: Warning: ignoring some quantifiers
% 84.68/53.04 Prover 4: Constructing countermodel ...
% 85.37/53.18 Prover 4: proved (257ms)
% 85.37/53.18 Prover 2: stopped
% 85.37/53.18 Prover 1: stopped
% 85.37/53.18
% 85.37/53.18 No countermodel exists, formula is valid
% 85.37/53.18 % SZS status Theorem for theBenchmark
% 85.37/53.18
% 85.37/53.18 Generating proof ... Warning: ignoring some quantifiers
% 88.83/54.09 found it (size 83)
% 88.83/54.09
% 88.83/54.09 % SZS output start Proof for theBenchmark
% 88.83/54.09 Assumed formulas after preprocessing and simplification:
% 88.83/54.09 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ( ~ (v12 = 0) & ~ (v9 = 0) & v3_relat_1(v10) = 0 & v3_relat_1(k1_xboole_0) = 0 & k3_pua2mss1(v0) = v2 & r1_tarski(v6, v8) = v9 & k9_relat_1(v5, v2) = v6 & k9_relat_1(v4, v2) = v7 & k9_relat_1(v1, v2) = v3 & k3_xboole_0(v3, v7) = v8 & k3_xboole_0(v1, v4) = v5 & v1_xboole_0(v13) = 0 & v1_xboole_0(v11) = v12 & v1_xboole_0(k1_xboole_0) = 0 & v1_relat_1(v13) = 0 & v1_relat_1(v11) = 0 & v1_relat_1(v10) = 0 & v1_relat_1(v4) = 0 & v1_relat_1(v1) = 0 & v1_relat_1(k1_xboole_0) = 0 & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = 0 | ~ (k9_relat_1(v14, v15) = v16) | ~ (k4_tarski(v19, v17) = v20) | ~ (v1_relat_1(v14) = 0) | ~ (r2_hidden(v17, v16) = v18) | ? [v21] : ? [v22] : (r2_hidden(v20, v14) = v21 & r2_hidden(v19, v15) = v22 & ( ~ (v22 = 0) | ~ (v21 = 0)))) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v18 = 0 | ~ (k9_relat_1(v14, v15) = v16) | ~ (v1_relat_1(v14) = 0) | ~ (r2_hidden(v19, v15) = 0) | ~ (r2_hidden(v17, v16) = v18) | ? [v20] : ? [v21] : ( ~ (v21 = 0) & k4_tarski(v19, v17) = v20 & r2_hidden(v20, v14) = v21)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (k1_zfmisc_1(v16) = v17) | ~ (k1_zfmisc_1(v14) = v16) | ~ (m1_subset_1(v15, v17) = v18) | ? [v19] : ( ~ (v19 = 0) & m1_eqrel_1(v15, v14) = v19)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (k1_zfmisc_1(v16) = v17) | ~ (m1_subset_1(v15, v17) = 0) | ~ (m1_subset_1(v14, v16) = v18) | ? [v19] : ( ~ (v19 = 0) & r2_hidden(v14, v15) = v19)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (k3_xboole_0(v14, v15) = v16) | ~ (r2_hidden(v17, v16) = v18) | ? [v19] : ? [v20] : (r2_hidden(v17, v15) = v20 & r2_hidden(v17, v14) = v19 & ( ~ (v20 = 0) | ~ (v19 = 0)))) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (k3_xboole_0(v14, v15) = v16) | ~ (r2_hidden(v17, v15) = v18) | ? [v19] : ? [v20] : (r2_hidden(v17, v16) = v19 & r2_hidden(v17, v14) = v20 & ( ~ (v19 = 0) | (v20 = 0 & v18 = 0)))) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (k3_xboole_0(v14, v15) = v16) | ~ (r2_hidden(v17, v14) = v18) | ? [v19] : ? [v20] : (r2_hidden(v17, v16) = v19 & r2_hidden(v17, v15) = v20 & ( ~ (v19 = 0) | (v20 = 0 & v18 = 0)))) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (k1_zfmisc_1(v15) = v16) | ~ (m1_subset_1(v14, v16) = v17) | ? [v18] : ( ~ (v18 = 0) & r1_tarski(v14, v15) = v18)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (m1_subset_1(v14, v16) = v17) | ~ (r2_hidden(v14, v15) = 0) | ? [v18] : ? [v19] : ( ~ (v19 = 0) & k1_zfmisc_1(v16) = v18 & m1_subset_1(v15, v18) = v19)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (r1_tarski(v14, v15) = 0) | ~ (r2_hidden(v16, v15) = v17) | ? [v18] : ( ~ (v18 = 0) & r2_hidden(v16, v14) = v18)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (m1_subset_1(v17, v16) = v15) | ~ (m1_subset_1(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (m1_eqrel_1(v17, v16) = v15) | ~ (m1_eqrel_1(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (r1_tarski(v17, v16) = v15) | ~ (r1_tarski(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (k9_relat_1(v17, v16) = v15) | ~ (k9_relat_1(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (k4_tarski(v17, v16) = v15) | ~ (k4_tarski(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (k3_xboole_0(v17, v16) = v15) | ~ (k3_xboole_0(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (k2_tarski(v17, v16) = v15) | ~ (k2_tarski(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (r2_hidden(v17, v16) = v15) | ~ (r2_hidden(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (k1_zfmisc_1(v16) = v17) | ~ (m1_subset_1(v15, v17) = 0) | ~ (r2_hidden(v14, v15) = 0) | m1_subset_1(v14, v16) = 0) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (k1_zfmisc_1(v16) = v17) | ~ (m1_subset_1(v15, v17) = 0) | ~ (r2_hidden(v14, v15) = 0) | ? [v18] : ( ~ (v18 = 0) & v1_xboole_0(v16) = v18)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (k9_relat_1(v14, v15) = v16) | ~ (v1_relat_1(v14) = 0) | ~ (r2_hidden(v17, v16) = 0) | ? [v18] : ? [v19] : (k4_tarski(v18, v17) = v19 & r2_hidden(v19, v14) = 0 & r2_hidden(v18, v15) = 0)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (k3_xboole_0(v14, v15) = v16) | ~ (r2_hidden(v17, v16) = 0) | (r2_hidden(v17, v15) = 0 & r2_hidden(v17, v14) = 0)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (k3_xboole_0(v14, v15) = v16) | ~ (r2_hidden(v17, v15) = 0) | ? [v18] : ? [v19] : (r2_hidden(v17, v16) = v19 & r2_hidden(v17, v14) = v18 & ( ~ (v18 = 0) | v19 = 0))) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (k3_xboole_0(v14, v15) = v16) | ~ (r2_hidden(v17, v14) = 0) | ? [v18] : ? [v19] : (r2_hidden(v17, v16) = v19 & r2_hidden(v17, v15) = v18 & ( ~ (v18 = 0) | v19 = 0))) & ? [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = v14 | ~ (k9_relat_1(v15, v16) = v17) | ~ (v1_relat_1(v15) = 0) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (r2_hidden(v18, v14) = v19 & ( ~ (v19 = 0) | ( ! [v24] : ! [v25] : ( ~ (k4_tarski(v24, v18) = v25) | ? [v26] : ? [v27] : (r2_hidden(v25, v15) = v26 & r2_hidden(v24, v16) = v27 & ( ~ (v27 = 0) | ~ (v26 = 0)))) & ! [v24] : ( ~ (r2_hidden(v24, v16) = 0) | ? [v25] : ? [v26] : ( ~ (v26 = 0) & k4_tarski(v24, v18) = v25 & r2_hidden(v25, v15) = v26)))) & (v19 = 0 | (v23 = 0 & v22 = 0 & k4_tarski(v20, v18) = v21 & r2_hidden(v21, v15) = 0 & r2_hidden(v20, v16) = 0)))) & ? [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = v14 | ~ (k3_xboole_0(v15, v16) = v17) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : (r2_hidden(v18, v16) = v21 & r2_hidden(v18, v15) = v20 & r2_hidden(v18, v14) = v19 & ( ~ (v21 = 0) | ~ (v20 = 0) | ~ (v19 = 0)) & (v19 = 0 | (v21 = 0 & v20 = 0)))) & ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (m1_subset_1(v14, v15) = v16) | ? [v17] : ( ~ (v17 = 0) & r2_hidden(v14, v15) = v17)) & ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (r1_tarski(v14, v15) = v16) | ? [v17] : ? [v18] : ( ~ (v18 = 0) & k1_zfmisc_1(v15) = v17 & m1_subset_1(v14, v17) = v18)) & ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (r1_tarski(v14, v15) = v16) | ? [v17] : ? [v18] : ( ~ (v18 = 0) & r2_hidden(v17, v15) = v18 & r2_hidden(v17, v14) = 0)) & ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (r2_hidden(v14, v15) = v16) | ? [v17] : ? [v18] : (m1_subset_1(v14, v15) = v17 & v1_xboole_0(v15) = v18 & ( ~ (v17 = 0) | v18 = 0))) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (v3_relat_1(v16) = v15) | ~ (v3_relat_1(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (k1_zfmisc_1(v16) = v15) | ~ (k1_zfmisc_1(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (k3_pua2mss1(v16) = v15) | ~ (k3_pua2mss1(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (k1_tarski(v16) = v15) | ~ (k1_tarski(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (v1_xboole_0(v16) = v15) | ~ (v1_xboole_0(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (v1_relat_1(v16) = v15) | ~ (v1_relat_1(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (k1_zfmisc_1(v15) = v16) | ~ (m1_subset_1(v14, v16) = 0) | r1_tarski(v14, v15) = 0) & ! [v14] : ! [v15] : ! [v16] : ( ~ (r1_tarski(v14, v15) = 0) | ~ (r2_hidden(v16, v14) = 0) | r2_hidden(v16, v15) = 0) & ! [v14] : ! [v15] : ! [v16] : ( ~ (k4_tarski(v14, v15) = v16) | ? [v17] : ? [v18] : (k1_tarski(v14) = v18 & k2_tarski(v17, v18) = v16 & k2_tarski(v14, v15) = v17)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (k3_xboole_0(v15, v14) = v16) | k3_xboole_0(v14, v15) = v16) & ! [v14] : ! [v15] : ! [v16] : ( ~ (k3_xboole_0(v14, v15) = v16) | k3_xboole_0(v15, v14) = v16) & ! [v14] : ! [v15] : ! [v16] : ( ~ (k3_xboole_0(v14, v15) = v16) | ? [v17] : ? [v18] : ? [v19] : (v1_relat_1(v16) = v19 & v1_relat_1(v15) = v18 & v1_relat_1(v14) = v17 & ( ~ (v18 = 0) | ~ (v17 = 0) | v19 = 0))) & ! [v14] : ! [v15] : ! [v16] : ( ~ (k2_tarski(v15, v14) = v16) | k2_tarski(v14, v15) = v16) & ! [v14] : ! [v15] : ! [v16] : ( ~ (k2_tarski(v14, v15) = v16) | k2_tarski(v15, v14) = v16) & ! [v14] : ! [v15] : ! [v16] : ( ~ (k2_tarski(v14, v15) = v16) | ? [v17] : ? [v18] : (k1_tarski(v14) = v18 & k4_tarski(v14, v15) = v17 & k2_tarski(v16, v18) = v17)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (k2_tarski(v14, v15) = v16) | ? [v17] : ( ~ (v17 = 0) & v1_xboole_0(v16) = v17)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (v1_xboole_0(v16) = 0) | ~ (r2_hidden(v14, v15) = 0) | ? [v17] : ? [v18] : ( ~ (v18 = 0) & k1_zfmisc_1(v16) = v17 & m1_subset_1(v15, v17) = v18)) & ! [v14] : ! [v15] : (v15 = v14 | ~ (k3_xboole_0(v14, v14) = v15)) & ! [v14] : ! [v15] : (v15 = v14 | ~ (v1_xboole_0(v15) = 0) | ~ (v1_xboole_0(v14) = 0)) & ! [v14] : ! [v15] : (v15 = k1_xboole_0 | ~ (k3_xboole_0(v14, k1_xboole_0) = v15)) & ! [v14] : ! [v15] : (v15 = 0 | ~ (r1_tarski(v14, v14) = v15)) & ! [v14] : ! [v15] : (v15 = 0 | ~ (v1_xboole_0(v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ( ~ (v18 = 0) & k1_zfmisc_1(v14) = v16 & m1_subset_1(v17, v16) = 0 & v1_xboole_0(v17) = v18)) & ! [v14] : ! [v15] : (v15 = 0 | ~ (v1_relat_1(v14) = v15) | ? [v16] : ( ~ (v16 = 0) & v1_xboole_0(v14) = v16)) & ! [v14] : ! [v15] : ( ~ (k1_zfmisc_1(v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ((v17 = 0 & ~ (v18 = 0) & m1_subset_1(v16, v15) = 0 & v1_xboole_0(v16) = v18) | (v16 = 0 & v1_xboole_0(v14) = 0))) & ! [v14] : ! [v15] : ( ~ (k1_zfmisc_1(v14) = v15) | ? [v16] : ( ~ (v16 = 0) & v1_xboole_0(v15) = v16)) & ! [v14] : ! [v15] : ( ~ (k1_zfmisc_1(v14) = v15) | ? [v16] : (m1_subset_1(v16, v15) = 0 & v1_xboole_0(v16) = 0)) & ! [v14] : ! [v15] : ( ~ (m1_subset_1(v14, v15) = 0) | ? [v16] : ? [v17] : (v1_xboole_0(v15) = v16 & r2_hidden(v14, v15) = v17 & (v17 = 0 | v16 = 0))) & ! [v14] : ! [v15] : ( ~ (k3_pua2mss1(v14) = v15) | m1_eqrel_1(v15, v14) = 0) & ! [v14] : ! [v15] : ( ~ (m1_eqrel_1(v15, v14) = 0) | ? [v16] : ? [v17] : (k1_zfmisc_1(v16) = v17 & k1_zfmisc_1(v14) = v16 & m1_subset_1(v15, v17) = 0)) & ! [v14] : ! [v15] : ( ~ (k1_tarski(v14) = v15) | ? [v16] : ( ~ (v16 = 0) & v1_xboole_0(v15) = v16)) & ! [v14] : ! [v15] : ( ~ (r1_tarski(v14, v15) = 0) | ? [v16] : (k1_zfmisc_1(v15) = v16 & m1_subset_1(v14, v16) = 0)) & ! [v14] : ! [v15] : ( ~ (r2_hidden(v15, v14) = 0) | ? [v16] : ( ~ (v16 = 0) & r2_hidden(v14, v15) = v16)) & ! [v14] : ! [v15] : ( ~ (r2_hidden(v14, v15) = 0) | m1_subset_1(v14, v15) = 0) & ! [v14] : ! [v15] : ( ~ (r2_hidden(v14, v15) = 0) | ? [v16] : ( ~ (v16 = 0) & v1_xboole_0(v15) = v16)) & ! [v14] : ! [v15] : ( ~ (r2_hidden(v14, v15) = 0) | ? [v16] : ( ~ (v16 = 0) & r2_hidden(v15, v14) = v16)) & ! [v14] : (v14 = k1_xboole_0 | ~ (v1_xboole_0(v14) = 0)) & ! [v14] : ( ~ (v1_xboole_0(v14) = 0) | v1_relat_1(v14) = 0) & ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ((v17 = v16 & k9_relat_1(v14, v15) = v16) | ( ~ (v17 = 0) & v1_relat_1(v14) = v17) | (r2_hidden(v17, v16) = v18 & ( ~ (v18 = 0) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : (k4_tarski(v23, v17) = v24 & r2_hidden(v24, v14) = v25 & r2_hidden(v23, v15) = v26 & ( ~ (v26 = 0) | ~ (v25 = 0)))) & (v18 = 0 | (v22 = 0 & v21 = 0 & k4_tarski(v19, v17) = v20 & r2_hidden(v20, v14) = 0 & r2_hidden(v19, v15) = 0)))) & ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ((v21 = 0 & v20 = 0 & k4_tarski(v18, v17) = v19 & r2_hidden(v19, v14) = 0 & r2_hidden(v18, v15) = 0) | ( ~ (v18 = v16) & k9_relat_1(v14, v15) = v18) | ( ~ (v18 = 0) & v1_relat_1(v14) = v18) | ( ~ (v18 = 0) & r2_hidden(v17, v16) = v18)) & ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ((v19 = 0 & r2_hidden(v17, v16) = 0) | ( ~ (v19 = v16) & k9_relat_1(v14, v15) = v19) | ( ~ (v19 = 0) & v1_relat_1(v14) = v19) | (k4_tarski(v18, v17) = v19 & r2_hidden(v19, v14) = v20 & r2_hidden(v18, v15) = v21 & ( ~ (v21 = 0) | ~ (v20 = 0)))) & ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : (k1_zfmisc_1(v16) = v18 & m1_subset_1(v15, v18) = v19 & m1_subset_1(v14, v16) = v20 & r2_hidden(v14, v15) = v17 & ( ~ (v19 = 0) | ~ (v17 = 0) | v20 = 0)) & ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (k1_zfmisc_1(v17) = v18 & k1_zfmisc_1(v14) = v17 & m1_subset_1(v15, v18) = v19 & m1_eqrel_1(v15, v14) = v16 & ( ~ (v16 = 0) | v19 = 0)) & ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (k3_xboole_0(v14, v15) = v18 & v1_relat_1(v18) = v19 & v1_relat_1(v15) = v17 & v1_relat_1(v14) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0) | v19 = 0)) & ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (k1_zfmisc_1(v15) = v17 & m1_subset_1(v14, v17) = v18 & r1_tarski(v14, v15) = v16 & ( ~ (v16 = 0) | v18 = 0)) & ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (k1_tarski(v14) = v18 & k4_tarski(v14, v15) = v16 & k2_tarski(v17, v18) = v16 & k2_tarski(v14, v15) = v17) & ? [v14] : ? [v15] : ? [v16] : ? [v17] : (v1_xboole_0(v15) = v17 & r2_hidden(v14, v15) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0))) & ? [v14] : ? [v15] : m1_subset_1(v15, v14) = 0 & ? [v14] : ? [v15] : m1_eqrel_1(v15, v14) = 0 & ? [v14] : ? [v15] : (k3_pua2mss1(v14) = v15 & m1_eqrel_1(v15, v14) = 0))
% 89.22/54.15 | 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:
% 89.22/54.15 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_4_4 = 0) & v3_relat_1(all_0_3_3) = 0 & v3_relat_1(k1_xboole_0) = 0 & k3_pua2mss1(all_0_13_13) = all_0_11_11 & r1_tarski(all_0_7_7, all_0_5_5) = all_0_4_4 & k9_relat_1(all_0_8_8, all_0_11_11) = all_0_7_7 & k9_relat_1(all_0_9_9, all_0_11_11) = all_0_6_6 & k9_relat_1(all_0_12_12, all_0_11_11) = all_0_10_10 & k3_xboole_0(all_0_10_10, all_0_6_6) = all_0_5_5 & k3_xboole_0(all_0_12_12, all_0_9_9) = all_0_8_8 & v1_xboole_0(all_0_0_0) = 0 & v1_xboole_0(all_0_2_2) = all_0_1_1 & v1_xboole_0(k1_xboole_0) = 0 & v1_relat_1(all_0_0_0) = 0 & v1_relat_1(all_0_2_2) = 0 & v1_relat_1(all_0_3_3) = 0 & v1_relat_1(all_0_9_9) = 0 & v1_relat_1(all_0_12_12) = 0 & v1_relat_1(k1_xboole_0) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (k9_relat_1(v0, v1) = v2) | ~ (k4_tarski(v5, v3) = v6) | ~ (v1_relat_1(v0) = 0) | ~ (r2_hidden(v3, v2) = v4) | ? [v7] : ? [v8] : (r2_hidden(v6, v0) = v7 & r2_hidden(v5, v1) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (k9_relat_1(v0, v1) = v2) | ~ (v1_relat_1(v0) = 0) | ~ (r2_hidden(v5, v1) = 0) | ~ (r2_hidden(v3, v2) = v4) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & k4_tarski(v5, v3) = v6 & r2_hidden(v6, v0) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (k1_zfmisc_1(v2) = v3) | ~ (k1_zfmisc_1(v0) = v2) | ~ (m1_subset_1(v1, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & m1_eqrel_1(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (k1_zfmisc_1(v2) = v3) | ~ (m1_subset_1(v1, v3) = 0) | ~ (m1_subset_1(v0, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & r2_hidden(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (k3_xboole_0(v0, v1) = v2) | ~ (r2_hidden(v3, v2) = v4) | ? [v5] : ? [v6] : (r2_hidden(v3, v1) = v6 & r2_hidden(v3, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k3_xboole_0(v0, v1) = v2) | ~ (r2_hidden(v3, v1) = v4) | ? [v5] : ? [v6] : (r2_hidden(v3, v2) = v5 & r2_hidden(v3, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k3_xboole_0(v0, v1) = v2) | ~ (r2_hidden(v3, v0) = v4) | ? [v5] : ? [v6] : (r2_hidden(v3, v2) = v5 & r2_hidden(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (k1_zfmisc_1(v1) = v2) | ~ (m1_subset_1(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & r1_tarski(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (m1_subset_1(v0, v2) = v3) | ~ (r2_hidden(v0, v1) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & k1_zfmisc_1(v2) = v4 & m1_subset_1(v1, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (r1_tarski(v0, v1) = 0) | ~ (r2_hidden(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & r2_hidden(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (m1_subset_1(v3, v2) = v1) | ~ (m1_subset_1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (m1_eqrel_1(v3, v2) = v1) | ~ (m1_eqrel_1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (r1_tarski(v3, v2) = v1) | ~ (r1_tarski(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k9_relat_1(v3, v2) = v1) | ~ (k9_relat_1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k4_tarski(v3, v2) = v1) | ~ (k4_tarski(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k3_xboole_0(v3, v2) = v1) | ~ (k3_xboole_0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k2_tarski(v3, v2) = v1) | ~ (k2_tarski(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (r2_hidden(v3, v2) = v1) | ~ (r2_hidden(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ (m1_subset_1(v1, v3) = 0) | ~ (r2_hidden(v0, v1) = 0) | m1_subset_1(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ (m1_subset_1(v1, v3) = 0) | ~ (r2_hidden(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & v1_xboole_0(v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k9_relat_1(v0, v1) = v2) | ~ (v1_relat_1(v0) = 0) | ~ (r2_hidden(v3, v2) = 0) | ? [v4] : ? [v5] : (k4_tarski(v4, v3) = v5 & r2_hidden(v5, v0) = 0 & r2_hidden(v4, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k3_xboole_0(v0, v1) = v2) | ~ (r2_hidden(v3, v2) = 0) | (r2_hidden(v3, v1) = 0 & r2_hidden(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k3_xboole_0(v0, v1) = v2) | ~ (r2_hidden(v3, v1) = 0) | ? [v4] : ? [v5] : (r2_hidden(v3, v2) = v5 & r2_hidden(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k3_xboole_0(v0, v1) = v2) | ~ (r2_hidden(v3, v0) = 0) | ? [v4] : ? [v5] : (r2_hidden(v3, v2) = v5 & r2_hidden(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (k9_relat_1(v1, v2) = v3) | ~ (v1_relat_1(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (r2_hidden(v4, v0) = v5 & ( ~ (v5 = 0) | ( ! [v10] : ! [v11] : ( ~ (k4_tarski(v10, v4) = v11) | ? [v12] : ? [v13] : (r2_hidden(v11, v1) = v12 & r2_hidden(v10, v2) = v13 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v10] : ( ~ (r2_hidden(v10, v2) = 0) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & k4_tarski(v10, v4) = v11 & r2_hidden(v11, v1) = v12)))) & (v5 = 0 | (v9 = 0 & v8 = 0 & k4_tarski(v6, v4) = v7 & r2_hidden(v7, v1) = 0 & r2_hidden(v6, v2) = 0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (k3_xboole_0(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (r2_hidden(v4, v2) = v7 & r2_hidden(v4, v1) = v6 & r2_hidden(v4, v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (m1_subset_1(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & r2_hidden(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (r1_tarski(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & k1_zfmisc_1(v1) = v3 & m1_subset_1(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (r1_tarski(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & r2_hidden(v3, v1) = v4 & r2_hidden(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (r2_hidden(v0, v1) = v2) | ? [v3] : ? [v4] : (m1_subset_1(v0, v1) = v3 & v1_xboole_0(v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v3_relat_1(v2) = v1) | ~ (v3_relat_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k3_pua2mss1(v2) = v1) | ~ (k3_pua2mss1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_tarski(v2) = v1) | ~ (k1_tarski(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_xboole_0(v2) = v1) | ~ (v1_xboole_0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_relat_1(v2) = v1) | ~ (v1_relat_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_zfmisc_1(v1) = v2) | ~ (m1_subset_1(v0, v2) = 0) | r1_tarski(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (r1_tarski(v0, v1) = 0) | ~ (r2_hidden(v2, v0) = 0) | r2_hidden(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k4_tarski(v0, v1) = v2) | ? [v3] : ? [v4] : (k1_tarski(v0) = v4 & k2_tarski(v3, v4) = v2 & k2_tarski(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k3_xboole_0(v1, v0) = v2) | k3_xboole_0(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k3_xboole_0(v0, v1) = v2) | k3_xboole_0(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k3_xboole_0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (v1_relat_1(v2) = v5 & v1_relat_1(v1) = v4 & v1_relat_1(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_tarski(v1, v0) = v2) | k2_tarski(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_tarski(v0, v1) = v2) | k2_tarski(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_tarski(v0, v1) = v2) | ? [v3] : ? [v4] : (k1_tarski(v0) = v4 & k4_tarski(v0, v1) = v3 & k2_tarski(v2, v4) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_tarski(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & v1_xboole_0(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (v1_xboole_0(v2) = 0) | ~ (r2_hidden(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & k1_zfmisc_1(v2) = v3 & m1_subset_1(v1, v3) = v4)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (k3_xboole_0(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (v1_xboole_0(v1) = 0) | ~ (v1_xboole_0(v0) = 0)) & ! [v0] : ! [v1] : (v1 = k1_xboole_0 | ~ (k3_xboole_0(v0, k1_xboole_0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (r1_tarski(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (v1_xboole_0(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & k1_zfmisc_1(v0) = v2 & m1_subset_1(v3, v2) = 0 & v1_xboole_0(v3) = v4)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (v1_relat_1(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & v1_xboole_0(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & m1_subset_1(v2, v1) = 0 & v1_xboole_0(v2) = v4) | (v2 = 0 & v1_xboole_0(v0) = 0))) & ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & v1_xboole_0(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ? [v2] : (m1_subset_1(v2, v1) = 0 & v1_xboole_0(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (m1_subset_1(v0, v1) = 0) | ? [v2] : ? [v3] : (v1_xboole_0(v1) = v2 & r2_hidden(v0, v1) = v3 & (v3 = 0 | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (k3_pua2mss1(v0) = v1) | m1_eqrel_1(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (m1_eqrel_1(v1, v0) = 0) | ? [v2] : ? [v3] : (k1_zfmisc_1(v2) = v3 & k1_zfmisc_1(v0) = v2 & m1_subset_1(v1, v3) = 0)) & ! [v0] : ! [v1] : ( ~ (k1_tarski(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & v1_xboole_0(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (r1_tarski(v0, v1) = 0) | ? [v2] : (k1_zfmisc_1(v1) = v2 & m1_subset_1(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (r2_hidden(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & r2_hidden(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (r2_hidden(v0, v1) = 0) | m1_subset_1(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (r2_hidden(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & v1_xboole_0(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (r2_hidden(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & r2_hidden(v1, v0) = v2)) & ! [v0] : (v0 = k1_xboole_0 | ~ (v1_xboole_0(v0) = 0)) & ! [v0] : ( ~ (v1_xboole_0(v0) = 0) | v1_relat_1(v0) = 0) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v3 = v2 & k9_relat_1(v0, v1) = v2) | ( ~ (v3 = 0) & v1_relat_1(v0) = v3) | (r2_hidden(v3, v2) = v4 & ( ~ (v4 = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : (k4_tarski(v9, v3) = v10 & r2_hidden(v10, v0) = v11 & r2_hidden(v9, v1) = v12 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & (v4 = 0 | (v8 = 0 & v7 = 0 & k4_tarski(v5, v3) = v6 & r2_hidden(v6, v0) = 0 & r2_hidden(v5, v1) = 0)))) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & k4_tarski(v4, v3) = v5 & r2_hidden(v5, v0) = 0 & r2_hidden(v4, v1) = 0) | ( ~ (v4 = v2) & k9_relat_1(v0, v1) = v4) | ( ~ (v4 = 0) & v1_relat_1(v0) = v4) | ( ~ (v4 = 0) & r2_hidden(v3, v2) = v4)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v5 = 0 & r2_hidden(v3, v2) = 0) | ( ~ (v5 = v2) & k9_relat_1(v0, v1) = v5) | ( ~ (v5 = 0) & v1_relat_1(v0) = v5) | (k4_tarski(v4, v3) = v5 & r2_hidden(v5, v0) = v6 & r2_hidden(v4, v1) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (k1_zfmisc_1(v2) = v4 & m1_subset_1(v1, v4) = v5 & m1_subset_1(v0, v2) = v6 & r2_hidden(v0, v1) = v3 & ( ~ (v5 = 0) | ~ (v3 = 0) | v6 = 0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (k1_zfmisc_1(v3) = v4 & k1_zfmisc_1(v0) = v3 & m1_subset_1(v1, v4) = v5 & m1_eqrel_1(v1, v0) = v2 & ( ~ (v2 = 0) | v5 = 0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (k3_xboole_0(v0, v1) = v4 & v1_relat_1(v4) = v5 & v1_relat_1(v1) = v3 & v1_relat_1(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = 0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (k1_zfmisc_1(v1) = v3 & m1_subset_1(v0, v3) = v4 & r1_tarski(v0, v1) = v2 & ( ~ (v2 = 0) | v4 = 0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (k1_tarski(v0) = v4 & k4_tarski(v0, v1) = v2 & k2_tarski(v3, v4) = v2 & k2_tarski(v0, v1) = v3) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : (v1_xboole_0(v1) = v3 & r2_hidden(v0, v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))) & ? [v0] : ? [v1] : m1_subset_1(v1, v0) = 0 & ? [v0] : ? [v1] : m1_eqrel_1(v1, v0) = 0 & ? [v0] : ? [v1] : (k3_pua2mss1(v0) = v1 & m1_eqrel_1(v1, v0) = 0)
% 89.22/54.17 |
% 89.22/54.17 | Applying alpha-rule on (1) yields:
% 89.22/54.17 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (k3_xboole_0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (v1_relat_1(v2) = v5 & v1_relat_1(v1) = v4 & v1_relat_1(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 89.22/54.17 | (3) k9_relat_1(all_0_9_9, all_0_11_11) = all_0_6_6
% 89.22/54.17 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (k4_tarski(v0, v1) = v2) | ? [v3] : ? [v4] : (k1_tarski(v0) = v4 & k2_tarski(v3, v4) = v2 & k2_tarski(v0, v1) = v3))
% 89.22/54.17 | (5) ! [v0] : ! [v1] : ( ~ (r2_hidden(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & v1_xboole_0(v1) = v2))
% 89.22/54.18 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0))
% 89.22/54.18 | (7) ! [v0] : ! [v1] : ( ~ (r2_hidden(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & r2_hidden(v0, v1) = v2))
% 89.22/54.18 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (k9_relat_1(v0, v1) = v2) | ~ (v1_relat_1(v0) = 0) | ~ (r2_hidden(v5, v1) = 0) | ~ (r2_hidden(v3, v2) = v4) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & k4_tarski(v5, v3) = v6 & r2_hidden(v6, v0) = v7))
% 89.22/54.18 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_xboole_0(v2) = v1) | ~ (v1_xboole_0(v2) = v0))
% 89.22/54.18 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (m1_subset_1(v0, v2) = v3) | ~ (r2_hidden(v0, v1) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & k1_zfmisc_1(v2) = v4 & m1_subset_1(v1, v4) = v5))
% 89.22/54.18 | (11) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (k1_zfmisc_1(v2) = v4 & m1_subset_1(v1, v4) = v5 & m1_subset_1(v0, v2) = v6 & r2_hidden(v0, v1) = v3 & ( ~ (v5 = 0) | ~ (v3 = 0) | v6 = 0))
% 89.22/54.18 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (k1_zfmisc_1(v2) = v3) | ~ (m1_subset_1(v1, v3) = 0) | ~ (m1_subset_1(v0, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & r2_hidden(v0, v1) = v5))
% 89.22/54.18 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k3_xboole_0(v0, v1) = v2) | ~ (r2_hidden(v3, v0) = v4) | ? [v5] : ? [v6] : (r2_hidden(v3, v2) = v5 & r2_hidden(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0))))
% 89.22/54.18 | (14) ! [v0] : ! [v1] : (v1 = 0 | ~ (r1_tarski(v0, v0) = v1))
% 89.22/54.18 | (15) ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & v1_xboole_0(v1) = v2))
% 89.22/54.18 | (16) k3_xboole_0(all_0_12_12, all_0_9_9) = all_0_8_8
% 89.22/54.18 | (17) ! [v0] : ! [v1] : ( ~ (k1_tarski(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & v1_xboole_0(v1) = v2))
% 89.22/54.18 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k9_relat_1(v0, v1) = v2) | ~ (v1_relat_1(v0) = 0) | ~ (r2_hidden(v3, v2) = 0) | ? [v4] : ? [v5] : (k4_tarski(v4, v3) = v5 & r2_hidden(v5, v0) = 0 & r2_hidden(v4, v1) = 0))
% 89.22/54.18 | (19) v1_relat_1(all_0_9_9) = 0
% 89.22/54.18 | (20) k9_relat_1(all_0_12_12, all_0_11_11) = all_0_10_10
% 89.22/54.18 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_tarski(v0, v1) = v2) | k2_tarski(v1, v0) = v2)
% 89.22/54.18 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_tarski(v1, v0) = v2) | k2_tarski(v0, v1) = v2)
% 89.22/54.18 | (23) v1_relat_1(all_0_3_3) = 0
% 89.22/54.18 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ (m1_subset_1(v1, v3) = 0) | ~ (r2_hidden(v0, v1) = 0) | m1_subset_1(v0, v2) = 0)
% 89.22/54.18 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_tarski(v0, v1) = v2) | ? [v3] : ? [v4] : (k1_tarski(v0) = v4 & k4_tarski(v0, v1) = v3 & k2_tarski(v2, v4) = v3))
% 89.22/54.18 | (26) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (k1_tarski(v0) = v4 & k4_tarski(v0, v1) = v2 & k2_tarski(v3, v4) = v2 & k2_tarski(v0, v1) = v3)
% 89.22/54.18 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k3_xboole_0(v0, v1) = v2) | ~ (r2_hidden(v3, v1) = v4) | ? [v5] : ? [v6] : (r2_hidden(v3, v2) = v5 & r2_hidden(v3, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0))))
% 89.22/54.18 | (28) ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & m1_subset_1(v2, v1) = 0 & v1_xboole_0(v2) = v4) | (v2 = 0 & v1_xboole_0(v0) = 0)))
% 89.22/54.18 | (29) k3_xboole_0(all_0_10_10, all_0_6_6) = all_0_5_5
% 89.22/54.18 | (30) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (r1_tarski(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & r2_hidden(v3, v1) = v4 & r2_hidden(v3, v0) = 0))
% 89.22/54.18 | (31) ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ? [v2] : (m1_subset_1(v2, v1) = 0 & v1_xboole_0(v2) = 0))
% 89.22/54.18 | (32) ! [v0] : ! [v1] : ( ~ (r2_hidden(v0, v1) = 0) | m1_subset_1(v0, v1) = 0)
% 89.22/54.18 | (33) v1_xboole_0(all_0_0_0) = 0
% 89.22/54.18 | (34) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (r2_hidden(v0, v1) = v2) | ? [v3] : ? [v4] : (m1_subset_1(v0, v1) = v3 & v1_xboole_0(v1) = v4 & ( ~ (v3 = 0) | v4 = 0)))
% 89.22/54.18 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ (m1_subset_1(v1, v3) = 0) | ~ (r2_hidden(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & v1_xboole_0(v2) = v4))
% 89.22/54.18 | (36) ! [v0] : ! [v1] : (v1 = v0 | ~ (k3_xboole_0(v0, v0) = v1))
% 89.22/54.18 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k3_xboole_0(v0, v1) = v2) | ~ (r2_hidden(v3, v2) = 0) | (r2_hidden(v3, v1) = 0 & r2_hidden(v3, v0) = 0))
% 89.22/54.18 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (r1_tarski(v0, v1) = 0) | ~ (r2_hidden(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & r2_hidden(v2, v0) = v4))
% 89.22/54.19 | (39) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (v1_xboole_0(v1) = v3 & r2_hidden(v0, v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))
% 89.22/54.19 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (k1_zfmisc_1(v1) = v2) | ~ (m1_subset_1(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & r1_tarski(v0, v1) = v4))
% 89.22/54.19 | (41) ! [v0] : ! [v1] : ( ~ (m1_subset_1(v0, v1) = 0) | ? [v2] : ? [v3] : (v1_xboole_0(v1) = v2 & r2_hidden(v0, v1) = v3 & (v3 = 0 | v2 = 0)))
% 89.22/54.19 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k3_xboole_0(v0, v1) = v2) | ~ (r2_hidden(v3, v0) = 0) | ? [v4] : ? [v5] : (r2_hidden(v3, v2) = v5 & r2_hidden(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0)))
% 89.22/54.19 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k9_relat_1(v3, v2) = v1) | ~ (k9_relat_1(v3, v2) = v0))
% 89.22/54.19 | (44) ! [v0] : ! [v1] : ( ~ (k3_pua2mss1(v0) = v1) | m1_eqrel_1(v1, v0) = 0)
% 89.22/54.19 | (45) r1_tarski(all_0_7_7, all_0_5_5) = all_0_4_4
% 89.22/54.19 | (46) ! [v0] : ! [v1] : (v1 = 0 | ~ (v1_relat_1(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & v1_xboole_0(v0) = v2))
% 89.22/54.19 | (47) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k3_pua2mss1(v2) = v1) | ~ (k3_pua2mss1(v2) = v0))
% 89.22/54.19 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (r1_tarski(v3, v2) = v1) | ~ (r1_tarski(v3, v2) = v0))
% 89.22/54.19 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (m1_eqrel_1(v3, v2) = v1) | ~ (m1_eqrel_1(v3, v2) = v0))
% 89.22/54.19 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k3_xboole_0(v3, v2) = v1) | ~ (k3_xboole_0(v3, v2) = v0))
% 89.22/54.19 | (51) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (k3_xboole_0(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (r2_hidden(v4, v2) = v7 & r2_hidden(v4, v1) = v6 & r2_hidden(v4, v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0))))
% 89.22/54.19 | (52) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_tarski(v2) = v1) | ~ (k1_tarski(v2) = v0))
% 89.22/54.19 | (53) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v3_relat_1(v2) = v1) | ~ (v3_relat_1(v2) = v0))
% 89.22/54.19 | (54) ? [v0] : ? [v1] : m1_eqrel_1(v1, v0) = 0
% 89.22/54.19 | (55) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v3 = v2 & k9_relat_1(v0, v1) = v2) | ( ~ (v3 = 0) & v1_relat_1(v0) = v3) | (r2_hidden(v3, v2) = v4 & ( ~ (v4 = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : (k4_tarski(v9, v3) = v10 & r2_hidden(v10, v0) = v11 & r2_hidden(v9, v1) = v12 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & (v4 = 0 | (v8 = 0 & v7 = 0 & k4_tarski(v5, v3) = v6 & r2_hidden(v6, v0) = 0 & r2_hidden(v5, v1) = 0))))
% 89.22/54.19 | (56) v1_xboole_0(all_0_2_2) = all_0_1_1
% 89.22/54.19 | (57) v1_relat_1(k1_xboole_0) = 0
% 89.22/54.19 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (k1_zfmisc_1(v2) = v3) | ~ (k1_zfmisc_1(v0) = v2) | ~ (m1_subset_1(v1, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & m1_eqrel_1(v1, v0) = v5))
% 89.22/54.19 | (59) ! [v0] : ! [v1] : ( ~ (r1_tarski(v0, v1) = 0) | ? [v2] : (k1_zfmisc_1(v1) = v2 & m1_subset_1(v0, v2) = 0))
% 89.22/54.19 | (60) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (k3_xboole_0(v0, v1) = v4 & v1_relat_1(v4) = v5 & v1_relat_1(v1) = v3 & v1_relat_1(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = 0))
% 89.22/54.19 | (61) ! [v0] : ! [v1] : (v1 = 0 | ~ (v1_xboole_0(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & k1_zfmisc_1(v0) = v2 & m1_subset_1(v3, v2) = 0 & v1_xboole_0(v3) = v4))
% 89.22/54.19 | (62) k9_relat_1(all_0_8_8, all_0_11_11) = all_0_7_7
% 89.22/54.19 | (63) ! [v0] : ! [v1] : ! [v2] : ( ~ (r1_tarski(v0, v1) = 0) | ~ (r2_hidden(v2, v0) = 0) | r2_hidden(v2, v1) = 0)
% 89.22/54.19 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (m1_subset_1(v3, v2) = v1) | ~ (m1_subset_1(v3, v2) = v0))
% 89.22/54.19 | (65) v1_xboole_0(k1_xboole_0) = 0
% 89.22/54.19 | (66) ! [v0] : ! [v1] : ( ~ (m1_eqrel_1(v1, v0) = 0) | ? [v2] : ? [v3] : (k1_zfmisc_1(v2) = v3 & k1_zfmisc_1(v0) = v2 & m1_subset_1(v1, v3) = 0))
% 89.22/54.19 | (67) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (k1_zfmisc_1(v3) = v4 & k1_zfmisc_1(v0) = v3 & m1_subset_1(v1, v4) = v5 & m1_eqrel_1(v1, v0) = v2 & ( ~ (v2 = 0) | v5 = 0))
% 89.22/54.19 | (68) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (k9_relat_1(v1, v2) = v3) | ~ (v1_relat_1(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (r2_hidden(v4, v0) = v5 & ( ~ (v5 = 0) | ( ! [v10] : ! [v11] : ( ~ (k4_tarski(v10, v4) = v11) | ? [v12] : ? [v13] : (r2_hidden(v11, v1) = v12 & r2_hidden(v10, v2) = v13 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v10] : ( ~ (r2_hidden(v10, v2) = 0) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & k4_tarski(v10, v4) = v11 & r2_hidden(v11, v1) = v12)))) & (v5 = 0 | (v9 = 0 & v8 = 0 & k4_tarski(v6, v4) = v7 & r2_hidden(v7, v1) = 0 & r2_hidden(v6, v2) = 0))))
% 89.22/54.20 | (69) ? [v0] : ? [v1] : m1_subset_1(v1, v0) = 0
% 89.22/54.20 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k2_tarski(v3, v2) = v1) | ~ (k2_tarski(v3, v2) = v0))
% 89.22/54.20 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k4_tarski(v3, v2) = v1) | ~ (k4_tarski(v3, v2) = v0))
% 89.22/54.20 | (72) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & k4_tarski(v4, v3) = v5 & r2_hidden(v5, v0) = 0 & r2_hidden(v4, v1) = 0) | ( ~ (v4 = v2) & k9_relat_1(v0, v1) = v4) | ( ~ (v4 = 0) & v1_relat_1(v0) = v4) | ( ~ (v4 = 0) & r2_hidden(v3, v2) = v4))
% 89.22/54.20 | (73) ! [v0] : ! [v1] : ! [v2] : ( ~ (v1_xboole_0(v2) = 0) | ~ (r2_hidden(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & k1_zfmisc_1(v2) = v3 & m1_subset_1(v1, v3) = v4))
% 89.22/54.20 | (74) ! [v0] : ! [v1] : ( ~ (r2_hidden(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & r2_hidden(v1, v0) = v2))
% 89.22/54.20 | (75) ! [v0] : ( ~ (v1_xboole_0(v0) = 0) | v1_relat_1(v0) = 0)
% 89.22/54.20 | (76) ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_zfmisc_1(v1) = v2) | ~ (m1_subset_1(v0, v2) = 0) | r1_tarski(v0, v1) = 0)
% 89.22/54.20 | (77) ! [v0] : (v0 = k1_xboole_0 | ~ (v1_xboole_0(v0) = 0))
% 89.22/54.20 | (78) v3_relat_1(all_0_3_3) = 0
% 89.22/54.20 | (79) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_relat_1(v2) = v1) | ~ (v1_relat_1(v2) = v0))
% 89.22/54.20 | (80) ? [v0] : ? [v1] : (k3_pua2mss1(v0) = v1 & m1_eqrel_1(v1, v0) = 0)
% 89.22/54.20 | (81) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (k1_zfmisc_1(v1) = v3 & m1_subset_1(v0, v3) = v4 & r1_tarski(v0, v1) = v2 & ( ~ (v2 = 0) | v4 = 0))
% 89.22/54.20 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (k3_xboole_0(v0, v1) = v2) | ~ (r2_hidden(v3, v2) = v4) | ? [v5] : ? [v6] : (r2_hidden(v3, v1) = v6 & r2_hidden(v3, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 89.22/54.20 | (83) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v5 = 0 & r2_hidden(v3, v2) = 0) | ( ~ (v5 = v2) & k9_relat_1(v0, v1) = v5) | ( ~ (v5 = 0) & v1_relat_1(v0) = v5) | (k4_tarski(v4, v3) = v5 & r2_hidden(v5, v0) = v6 & r2_hidden(v4, v1) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0))))
% 89.70/54.20 | (84) ~ (all_0_1_1 = 0)
% 89.70/54.20 | (85) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (m1_subset_1(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & r2_hidden(v0, v1) = v3))
% 89.70/54.20 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (k9_relat_1(v0, v1) = v2) | ~ (k4_tarski(v5, v3) = v6) | ~ (v1_relat_1(v0) = 0) | ~ (r2_hidden(v3, v2) = v4) | ? [v7] : ? [v8] : (r2_hidden(v6, v0) = v7 & r2_hidden(v5, v1) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0))))
% 89.70/54.20 | (87) ! [v0] : ! [v1] : (v1 = k1_xboole_0 | ~ (k3_xboole_0(v0, k1_xboole_0) = v1))
% 89.70/54.20 | (88) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (r1_tarski(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & k1_zfmisc_1(v1) = v3 & m1_subset_1(v0, v3) = v4))
% 89.70/54.20 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k3_xboole_0(v0, v1) = v2) | ~ (r2_hidden(v3, v1) = 0) | ? [v4] : ? [v5] : (r2_hidden(v3, v2) = v5 & r2_hidden(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0)))
% 89.70/54.20 | (90) v1_relat_1(all_0_0_0) = 0
% 89.70/54.20 | (91) k3_pua2mss1(all_0_13_13) = all_0_11_11
% 89.70/54.20 | (92) ! [v0] : ! [v1] : (v1 = v0 | ~ (v1_xboole_0(v1) = 0) | ~ (v1_xboole_0(v0) = 0))
% 89.70/54.20 | (93) v3_relat_1(k1_xboole_0) = 0
% 89.70/54.20 | (94) ~ (all_0_4_4 = 0)
% 89.70/54.20 | (95) v1_relat_1(all_0_12_12) = 0
% 89.70/54.20 | (96) ! [v0] : ! [v1] : ! [v2] : ( ~ (k3_xboole_0(v0, v1) = v2) | k3_xboole_0(v1, v0) = v2)
% 89.70/54.20 | (97) ! [v0] : ! [v1] : ! [v2] : ( ~ (k3_xboole_0(v1, v0) = v2) | k3_xboole_0(v0, v1) = v2)
% 89.70/54.20 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (r2_hidden(v3, v2) = v1) | ~ (r2_hidden(v3, v2) = v0))
% 89.70/54.20 | (99) ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_tarski(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & v1_xboole_0(v2) = v3))
% 89.70/54.20 | (100) v1_relat_1(all_0_2_2) = 0
% 89.70/54.21 |
% 89.70/54.21 | Instantiating formula (30) with all_0_4_4, all_0_5_5, all_0_7_7 and discharging atoms r1_tarski(all_0_7_7, all_0_5_5) = all_0_4_4, yields:
% 89.70/54.21 | (101) all_0_4_4 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & r2_hidden(v0, all_0_5_5) = v1 & r2_hidden(v0, all_0_7_7) = 0)
% 89.70/54.21 |
% 89.70/54.21 | Instantiating formula (97) with all_0_5_5, all_0_10_10, all_0_6_6 and discharging atoms k3_xboole_0(all_0_10_10, all_0_6_6) = all_0_5_5, yields:
% 89.70/54.21 | (102) k3_xboole_0(all_0_6_6, all_0_10_10) = all_0_5_5
% 89.70/54.21 |
% 89.70/54.21 | Instantiating formula (2) with all_0_8_8, all_0_9_9, all_0_12_12 and discharging atoms k3_xboole_0(all_0_12_12, all_0_9_9) = all_0_8_8, yields:
% 89.70/54.21 | (103) ? [v0] : ? [v1] : ? [v2] : (v1_relat_1(all_0_8_8) = v2 & v1_relat_1(all_0_9_9) = v1 & v1_relat_1(all_0_12_12) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 89.70/54.21 |
% 89.70/54.21 | Instantiating (103) with all_49_0_91, all_49_1_92, all_49_2_93 yields:
% 89.70/54.21 | (104) v1_relat_1(all_0_8_8) = all_49_0_91 & v1_relat_1(all_0_9_9) = all_49_1_92 & v1_relat_1(all_0_12_12) = all_49_2_93 & ( ~ (all_49_1_92 = 0) | ~ (all_49_2_93 = 0) | all_49_0_91 = 0)
% 89.70/54.21 |
% 89.70/54.21 | Applying alpha-rule on (104) yields:
% 89.70/54.21 | (105) v1_relat_1(all_0_8_8) = all_49_0_91
% 89.70/54.21 | (106) v1_relat_1(all_0_9_9) = all_49_1_92
% 89.70/54.21 | (107) v1_relat_1(all_0_12_12) = all_49_2_93
% 89.70/54.21 | (108) ~ (all_49_1_92 = 0) | ~ (all_49_2_93 = 0) | all_49_0_91 = 0
% 89.70/54.21 |
% 89.70/54.21 +-Applying beta-rule and splitting (101), into two cases.
% 89.70/54.21 |-Branch one:
% 89.70/54.21 | (109) all_0_4_4 = 0
% 89.70/54.21 |
% 89.70/54.21 | Equations (109) can reduce 94 to:
% 89.70/54.21 | (110) $false
% 89.70/54.21 |
% 89.70/54.21 |-The branch is then unsatisfiable
% 89.70/54.21 |-Branch two:
% 89.70/54.21 | (94) ~ (all_0_4_4 = 0)
% 89.70/54.21 | (112) ? [v0] : ? [v1] : ( ~ (v1 = 0) & r2_hidden(v0, all_0_5_5) = v1 & r2_hidden(v0, all_0_7_7) = 0)
% 89.70/54.21 |
% 89.70/54.21 | Instantiating (112) with all_85_0_120, all_85_1_121 yields:
% 89.70/54.21 | (113) ~ (all_85_0_120 = 0) & r2_hidden(all_85_1_121, all_0_5_5) = all_85_0_120 & r2_hidden(all_85_1_121, all_0_7_7) = 0
% 89.70/54.21 |
% 89.70/54.21 | Applying alpha-rule on (113) yields:
% 89.70/54.21 | (114) ~ (all_85_0_120 = 0)
% 89.70/54.21 | (115) r2_hidden(all_85_1_121, all_0_5_5) = all_85_0_120
% 89.70/54.21 | (116) r2_hidden(all_85_1_121, all_0_7_7) = 0
% 89.70/54.21 |
% 89.70/54.21 | Instantiating formula (79) with all_0_9_9, all_49_1_92, 0 and discharging atoms v1_relat_1(all_0_9_9) = all_49_1_92, v1_relat_1(all_0_9_9) = 0, yields:
% 89.70/54.21 | (117) all_49_1_92 = 0
% 89.70/54.21 |
% 89.70/54.21 | Instantiating formula (79) with all_0_12_12, all_49_2_93, 0 and discharging atoms v1_relat_1(all_0_12_12) = all_49_2_93, v1_relat_1(all_0_12_12) = 0, yields:
% 89.70/54.21 | (118) all_49_2_93 = 0
% 89.70/54.21 |
% 89.70/54.21 | From (117) and (106) follows:
% 89.70/54.21 | (19) v1_relat_1(all_0_9_9) = 0
% 89.70/54.21 |
% 89.70/54.21 | From (118) and (107) follows:
% 89.70/54.21 | (95) v1_relat_1(all_0_12_12) = 0
% 89.70/54.21 |
% 89.70/54.21 +-Applying beta-rule and splitting (108), into two cases.
% 89.70/54.21 |-Branch one:
% 89.70/54.21 | (121) ~ (all_49_1_92 = 0)
% 89.70/54.21 |
% 89.70/54.21 | Equations (117) can reduce 121 to:
% 89.70/54.21 | (110) $false
% 89.70/54.21 |
% 89.70/54.21 |-The branch is then unsatisfiable
% 89.70/54.21 |-Branch two:
% 89.70/54.21 | (117) all_49_1_92 = 0
% 89.70/54.21 | (124) ~ (all_49_2_93 = 0) | all_49_0_91 = 0
% 89.70/54.21 |
% 89.70/54.21 +-Applying beta-rule and splitting (124), into two cases.
% 89.70/54.21 |-Branch one:
% 89.70/54.21 | (125) ~ (all_49_2_93 = 0)
% 89.70/54.21 |
% 89.70/54.21 | Equations (118) can reduce 125 to:
% 89.70/54.21 | (110) $false
% 89.70/54.21 |
% 89.70/54.21 |-The branch is then unsatisfiable
% 89.70/54.21 |-Branch two:
% 89.70/54.21 | (118) all_49_2_93 = 0
% 89.70/54.21 | (128) all_49_0_91 = 0
% 89.70/54.21 |
% 89.70/54.21 | From (128) and (105) follows:
% 89.70/54.21 | (129) v1_relat_1(all_0_8_8) = 0
% 89.70/54.21 |
% 89.70/54.21 | Instantiating formula (82) with all_85_0_120, all_85_1_121, all_0_5_5, all_0_6_6, all_0_10_10 and discharging atoms k3_xboole_0(all_0_10_10, all_0_6_6) = all_0_5_5, r2_hidden(all_85_1_121, all_0_5_5) = all_85_0_120, yields:
% 89.70/54.21 | (130) all_85_0_120 = 0 | ? [v0] : ? [v1] : (r2_hidden(all_85_1_121, all_0_6_6) = v1 & r2_hidden(all_85_1_121, all_0_10_10) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 89.70/54.22 |
% 89.70/54.22 | Instantiating formula (82) with all_85_0_120, all_85_1_121, all_0_5_5, all_0_10_10, all_0_6_6 and discharging atoms k3_xboole_0(all_0_6_6, all_0_10_10) = all_0_5_5, r2_hidden(all_85_1_121, all_0_5_5) = all_85_0_120, yields:
% 89.70/54.22 | (131) all_85_0_120 = 0 | ? [v0] : ? [v1] : (r2_hidden(all_85_1_121, all_0_6_6) = v0 & r2_hidden(all_85_1_121, all_0_10_10) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 89.70/54.22 |
% 89.70/54.22 | Instantiating formula (18) with all_85_1_121, all_0_7_7, all_0_11_11, all_0_8_8 and discharging atoms k9_relat_1(all_0_8_8, all_0_11_11) = all_0_7_7, v1_relat_1(all_0_8_8) = 0, r2_hidden(all_85_1_121, all_0_7_7) = 0, yields:
% 89.70/54.22 | (132) ? [v0] : ? [v1] : (k4_tarski(v0, all_85_1_121) = v1 & r2_hidden(v1, all_0_8_8) = 0 & r2_hidden(v0, all_0_11_11) = 0)
% 89.70/54.22 |
% 89.70/54.22 | Instantiating (132) with all_132_0_142, all_132_1_143 yields:
% 89.70/54.22 | (133) k4_tarski(all_132_1_143, all_85_1_121) = all_132_0_142 & r2_hidden(all_132_0_142, all_0_8_8) = 0 & r2_hidden(all_132_1_143, all_0_11_11) = 0
% 89.70/54.22 |
% 89.70/54.22 | Applying alpha-rule on (133) yields:
% 89.70/54.22 | (134) k4_tarski(all_132_1_143, all_85_1_121) = all_132_0_142
% 89.70/54.22 | (135) r2_hidden(all_132_0_142, all_0_8_8) = 0
% 89.70/54.22 | (136) r2_hidden(all_132_1_143, all_0_11_11) = 0
% 89.70/54.22 |
% 89.70/54.22 +-Applying beta-rule and splitting (130), into two cases.
% 89.70/54.22 |-Branch one:
% 89.70/54.22 | (137) all_85_0_120 = 0
% 89.70/54.22 |
% 89.70/54.22 | Equations (137) can reduce 114 to:
% 89.70/54.22 | (110) $false
% 89.70/54.22 |
% 89.70/54.22 |-The branch is then unsatisfiable
% 89.70/54.22 |-Branch two:
% 89.70/54.22 | (114) ~ (all_85_0_120 = 0)
% 89.70/54.22 | (140) ? [v0] : ? [v1] : (r2_hidden(all_85_1_121, all_0_6_6) = v1 & r2_hidden(all_85_1_121, all_0_10_10) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 89.70/54.22 |
% 89.70/54.22 | Instantiating (140) with all_202_0_195, all_202_1_196 yields:
% 89.70/54.22 | (141) r2_hidden(all_85_1_121, all_0_6_6) = all_202_0_195 & r2_hidden(all_85_1_121, all_0_10_10) = all_202_1_196 & ( ~ (all_202_0_195 = 0) | ~ (all_202_1_196 = 0))
% 89.70/54.22 |
% 89.70/54.22 | Applying alpha-rule on (141) yields:
% 89.70/54.22 | (142) r2_hidden(all_85_1_121, all_0_6_6) = all_202_0_195
% 89.70/54.22 | (143) r2_hidden(all_85_1_121, all_0_10_10) = all_202_1_196
% 89.70/54.22 | (144) ~ (all_202_0_195 = 0) | ~ (all_202_1_196 = 0)
% 89.70/54.22 |
% 89.70/54.22 +-Applying beta-rule and splitting (131), into two cases.
% 89.70/54.22 |-Branch one:
% 89.70/54.22 | (137) all_85_0_120 = 0
% 89.70/54.22 |
% 89.70/54.22 | Equations (137) can reduce 114 to:
% 89.70/54.22 | (110) $false
% 89.70/54.22 |
% 89.70/54.22 |-The branch is then unsatisfiable
% 89.70/54.22 |-Branch two:
% 89.70/54.22 | (114) ~ (all_85_0_120 = 0)
% 89.70/54.22 | (148) ? [v0] : ? [v1] : (r2_hidden(all_85_1_121, all_0_6_6) = v0 & r2_hidden(all_85_1_121, all_0_10_10) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 89.70/54.22 |
% 89.70/54.22 | Instantiating (148) with all_207_0_197, all_207_1_198 yields:
% 89.70/54.22 | (149) r2_hidden(all_85_1_121, all_0_6_6) = all_207_1_198 & r2_hidden(all_85_1_121, all_0_10_10) = all_207_0_197 & ( ~ (all_207_0_197 = 0) | ~ (all_207_1_198 = 0))
% 89.70/54.22 |
% 89.70/54.22 | Applying alpha-rule on (149) yields:
% 89.70/54.22 | (150) r2_hidden(all_85_1_121, all_0_6_6) = all_207_1_198
% 89.70/54.22 | (151) r2_hidden(all_85_1_121, all_0_10_10) = all_207_0_197
% 89.70/54.22 | (152) ~ (all_207_0_197 = 0) | ~ (all_207_1_198 = 0)
% 89.70/54.22 |
% 89.70/54.22 | Instantiating formula (98) with all_85_1_121, all_0_6_6, all_202_0_195, all_207_1_198 and discharging atoms r2_hidden(all_85_1_121, all_0_6_6) = all_207_1_198, r2_hidden(all_85_1_121, all_0_6_6) = all_202_0_195, yields:
% 89.70/54.22 | (153) all_207_1_198 = all_202_0_195
% 89.70/54.22 |
% 89.70/54.22 | Instantiating formula (98) with all_85_1_121, all_0_10_10, all_202_1_196, all_207_0_197 and discharging atoms r2_hidden(all_85_1_121, all_0_10_10) = all_207_0_197, r2_hidden(all_85_1_121, all_0_10_10) = all_202_1_196, yields:
% 89.70/54.22 | (154) all_207_0_197 = all_202_1_196
% 89.70/54.22 |
% 89.70/54.22 | From (153) and (150) follows:
% 89.70/54.22 | (142) r2_hidden(all_85_1_121, all_0_6_6) = all_202_0_195
% 89.70/54.22 |
% 89.70/54.22 | From (154) and (151) follows:
% 89.70/54.22 | (143) r2_hidden(all_85_1_121, all_0_10_10) = all_202_1_196
% 89.70/54.22 |
% 89.70/54.22 | Instantiating formula (37) with all_132_0_142, all_0_8_8, all_0_9_9, all_0_12_12 and discharging atoms k3_xboole_0(all_0_12_12, all_0_9_9) = all_0_8_8, r2_hidden(all_132_0_142, all_0_8_8) = 0, yields:
% 89.70/54.22 | (157) r2_hidden(all_132_0_142, all_0_9_9) = 0 & r2_hidden(all_132_0_142, all_0_12_12) = 0
% 89.70/54.22 |
% 89.70/54.22 | Applying alpha-rule on (157) yields:
% 89.70/54.22 | (158) r2_hidden(all_132_0_142, all_0_9_9) = 0
% 89.70/54.22 | (159) r2_hidden(all_132_0_142, all_0_12_12) = 0
% 89.70/54.22 |
% 89.70/54.22 | Instantiating formula (86) with all_132_0_142, all_132_1_143, all_202_0_195, all_85_1_121, all_0_6_6, all_0_11_11, all_0_9_9 and discharging atoms k9_relat_1(all_0_9_9, all_0_11_11) = all_0_6_6, k4_tarski(all_132_1_143, all_85_1_121) = all_132_0_142, v1_relat_1(all_0_9_9) = 0, r2_hidden(all_85_1_121, all_0_6_6) = all_202_0_195, yields:
% 89.70/54.22 | (160) all_202_0_195 = 0 | ? [v0] : ? [v1] : (r2_hidden(all_132_0_142, all_0_9_9) = v0 & r2_hidden(all_132_1_143, all_0_11_11) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 89.70/54.22 |
% 89.70/54.22 | Instantiating formula (8) with all_132_1_143, all_202_0_195, all_85_1_121, all_0_6_6, all_0_11_11, all_0_9_9 and discharging atoms k9_relat_1(all_0_9_9, all_0_11_11) = all_0_6_6, v1_relat_1(all_0_9_9) = 0, r2_hidden(all_132_1_143, all_0_11_11) = 0, r2_hidden(all_85_1_121, all_0_6_6) = all_202_0_195, yields:
% 89.70/54.22 | (161) all_202_0_195 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & k4_tarski(all_132_1_143, all_85_1_121) = v0 & r2_hidden(v0, all_0_9_9) = v1)
% 89.70/54.22 |
% 89.70/54.22 | Instantiating formula (86) with all_132_0_142, all_132_1_143, all_202_1_196, all_85_1_121, all_0_10_10, all_0_11_11, all_0_12_12 and discharging atoms k9_relat_1(all_0_12_12, all_0_11_11) = all_0_10_10, k4_tarski(all_132_1_143, all_85_1_121) = all_132_0_142, v1_relat_1(all_0_12_12) = 0, r2_hidden(all_85_1_121, all_0_10_10) = all_202_1_196, yields:
% 89.70/54.22 | (162) all_202_1_196 = 0 | ? [v0] : ? [v1] : (r2_hidden(all_132_0_142, all_0_12_12) = v0 & r2_hidden(all_132_1_143, all_0_11_11) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 89.70/54.22 |
% 89.70/54.22 | Instantiating formula (8) with all_132_1_143, all_202_1_196, all_85_1_121, all_0_10_10, all_0_11_11, all_0_12_12 and discharging atoms k9_relat_1(all_0_12_12, all_0_11_11) = all_0_10_10, v1_relat_1(all_0_12_12) = 0, r2_hidden(all_132_1_143, all_0_11_11) = 0, r2_hidden(all_85_1_121, all_0_10_10) = all_202_1_196, yields:
% 89.70/54.22 | (163) all_202_1_196 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & k4_tarski(all_132_1_143, all_85_1_121) = v0 & r2_hidden(v0, all_0_12_12) = v1)
% 89.70/54.22 |
% 89.70/54.22 | Instantiating formula (34) with all_202_1_196, all_0_10_10, all_85_1_121 and discharging atoms r2_hidden(all_85_1_121, all_0_10_10) = all_202_1_196, yields:
% 89.70/54.22 | (164) all_202_1_196 = 0 | ? [v0] : ? [v1] : (m1_subset_1(all_85_1_121, all_0_10_10) = v0 & v1_xboole_0(all_0_10_10) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 89.70/54.22 |
% 89.70/54.22 +-Applying beta-rule and splitting (161), into two cases.
% 89.70/54.22 |-Branch one:
% 89.70/54.22 | (165) all_202_0_195 = 0
% 89.70/54.22 |
% 89.70/54.22 +-Applying beta-rule and splitting (144), into two cases.
% 89.70/54.22 |-Branch one:
% 89.70/54.22 | (166) ~ (all_202_0_195 = 0)
% 89.70/54.22 |
% 89.70/54.22 | Equations (165) can reduce 166 to:
% 89.70/54.22 | (110) $false
% 89.70/54.22 |
% 89.70/54.22 |-The branch is then unsatisfiable
% 89.70/54.22 |-Branch two:
% 89.70/54.22 | (165) all_202_0_195 = 0
% 89.70/54.22 | (169) ~ (all_202_1_196 = 0)
% 89.70/54.22 |
% 89.70/54.22 +-Applying beta-rule and splitting (164), into two cases.
% 89.70/54.22 |-Branch one:
% 89.70/54.23 | (170) all_202_1_196 = 0
% 89.70/54.23 |
% 89.70/54.23 | Equations (170) can reduce 169 to:
% 89.70/54.23 | (110) $false
% 89.70/54.23 |
% 89.70/54.23 |-The branch is then unsatisfiable
% 89.70/54.23 |-Branch two:
% 89.70/54.23 | (169) ~ (all_202_1_196 = 0)
% 89.70/54.23 | (173) ? [v0] : ? [v1] : (m1_subset_1(all_85_1_121, all_0_10_10) = v0 & v1_xboole_0(all_0_10_10) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 89.70/54.23 |
% 89.70/54.23 +-Applying beta-rule and splitting (163), into two cases.
% 89.70/54.23 |-Branch one:
% 89.70/54.23 | (170) all_202_1_196 = 0
% 89.70/54.23 |
% 89.70/54.23 | Equations (170) can reduce 169 to:
% 89.70/54.23 | (110) $false
% 89.70/54.23 |
% 89.70/54.23 |-The branch is then unsatisfiable
% 89.70/54.23 |-Branch two:
% 89.70/54.23 | (169) ~ (all_202_1_196 = 0)
% 89.70/54.23 | (177) ? [v0] : ? [v1] : ( ~ (v1 = 0) & k4_tarski(all_132_1_143, all_85_1_121) = v0 & r2_hidden(v0, all_0_12_12) = v1)
% 89.70/54.23 |
% 89.70/54.23 +-Applying beta-rule and splitting (162), into two cases.
% 89.70/54.23 |-Branch one:
% 89.70/54.23 | (170) all_202_1_196 = 0
% 89.70/54.23 |
% 89.70/54.23 | Equations (170) can reduce 169 to:
% 89.70/54.23 | (110) $false
% 89.70/54.23 |
% 89.70/54.23 |-The branch is then unsatisfiable
% 89.70/54.23 |-Branch two:
% 89.70/54.23 | (169) ~ (all_202_1_196 = 0)
% 89.70/54.23 | (181) ? [v0] : ? [v1] : (r2_hidden(all_132_0_142, all_0_12_12) = v0 & r2_hidden(all_132_1_143, all_0_11_11) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 89.70/54.23 |
% 89.70/54.23 | Instantiating (181) with all_519_0_387, all_519_1_388 yields:
% 89.70/54.23 | (182) r2_hidden(all_132_0_142, all_0_12_12) = all_519_1_388 & r2_hidden(all_132_1_143, all_0_11_11) = all_519_0_387 & ( ~ (all_519_0_387 = 0) | ~ (all_519_1_388 = 0))
% 89.70/54.23 |
% 89.70/54.23 | Applying alpha-rule on (182) yields:
% 89.70/54.23 | (183) r2_hidden(all_132_0_142, all_0_12_12) = all_519_1_388
% 89.70/54.23 | (184) r2_hidden(all_132_1_143, all_0_11_11) = all_519_0_387
% 89.70/54.23 | (185) ~ (all_519_0_387 = 0) | ~ (all_519_1_388 = 0)
% 89.70/54.23 |
% 89.70/54.23 | Instantiating formula (98) with all_132_0_142, all_0_12_12, 0, all_519_1_388 and discharging atoms r2_hidden(all_132_0_142, all_0_12_12) = all_519_1_388, r2_hidden(all_132_0_142, all_0_12_12) = 0, yields:
% 89.70/54.23 | (186) all_519_1_388 = 0
% 89.70/54.23 |
% 89.70/54.23 | Instantiating formula (98) with all_132_1_143, all_0_11_11, all_519_0_387, 0 and discharging atoms r2_hidden(all_132_1_143, all_0_11_11) = all_519_0_387, r2_hidden(all_132_1_143, all_0_11_11) = 0, yields:
% 89.70/54.23 | (187) all_519_0_387 = 0
% 89.70/54.23 |
% 89.70/54.23 +-Applying beta-rule and splitting (185), into two cases.
% 89.70/54.23 |-Branch one:
% 89.70/54.23 | (188) ~ (all_519_0_387 = 0)
% 89.70/54.23 |
% 89.70/54.23 | Equations (187) can reduce 188 to:
% 89.70/54.23 | (110) $false
% 89.70/54.23 |
% 89.70/54.23 |-The branch is then unsatisfiable
% 89.70/54.23 |-Branch two:
% 89.70/54.23 | (187) all_519_0_387 = 0
% 89.70/54.23 | (191) ~ (all_519_1_388 = 0)
% 89.70/54.23 |
% 89.70/54.23 | Equations (186) can reduce 191 to:
% 89.70/54.23 | (110) $false
% 89.70/54.23 |
% 89.70/54.23 |-The branch is then unsatisfiable
% 89.70/54.23 |-Branch two:
% 89.70/54.23 | (166) ~ (all_202_0_195 = 0)
% 89.70/54.23 | (194) ? [v0] : ? [v1] : ( ~ (v1 = 0) & k4_tarski(all_132_1_143, all_85_1_121) = v0 & r2_hidden(v0, all_0_9_9) = v1)
% 89.70/54.23 |
% 89.70/54.23 +-Applying beta-rule and splitting (160), into two cases.
% 89.70/54.23 |-Branch one:
% 89.70/54.23 | (165) all_202_0_195 = 0
% 89.70/54.23 |
% 89.70/54.23 | Equations (165) can reduce 166 to:
% 89.70/54.23 | (110) $false
% 89.70/54.23 |
% 89.70/54.23 |-The branch is then unsatisfiable
% 89.70/54.23 |-Branch two:
% 89.70/54.23 | (166) ~ (all_202_0_195 = 0)
% 89.70/54.23 | (198) ? [v0] : ? [v1] : (r2_hidden(all_132_0_142, all_0_9_9) = v0 & r2_hidden(all_132_1_143, all_0_11_11) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 89.70/54.23 |
% 89.70/54.23 | Instantiating (198) with all_502_0_443, all_502_1_444 yields:
% 89.70/54.23 | (199) r2_hidden(all_132_0_142, all_0_9_9) = all_502_1_444 & r2_hidden(all_132_1_143, all_0_11_11) = all_502_0_443 & ( ~ (all_502_0_443 = 0) | ~ (all_502_1_444 = 0))
% 89.70/54.23 |
% 89.70/54.23 | Applying alpha-rule on (199) yields:
% 89.70/54.23 | (200) r2_hidden(all_132_0_142, all_0_9_9) = all_502_1_444
% 89.70/54.23 | (201) r2_hidden(all_132_1_143, all_0_11_11) = all_502_0_443
% 89.70/54.23 | (202) ~ (all_502_0_443 = 0) | ~ (all_502_1_444 = 0)
% 89.70/54.23 |
% 89.70/54.23 | Instantiating formula (98) with all_132_0_142, all_0_9_9, 0, all_502_1_444 and discharging atoms r2_hidden(all_132_0_142, all_0_9_9) = all_502_1_444, r2_hidden(all_132_0_142, all_0_9_9) = 0, yields:
% 89.70/54.23 | (203) all_502_1_444 = 0
% 89.70/54.23 |
% 89.70/54.23 | Instantiating formula (98) with all_132_1_143, all_0_11_11, all_502_0_443, 0 and discharging atoms r2_hidden(all_132_1_143, all_0_11_11) = all_502_0_443, r2_hidden(all_132_1_143, all_0_11_11) = 0, yields:
% 89.70/54.23 | (204) all_502_0_443 = 0
% 89.70/54.23 |
% 89.70/54.23 +-Applying beta-rule and splitting (202), into two cases.
% 89.70/54.23 |-Branch one:
% 89.70/54.23 | (205) ~ (all_502_0_443 = 0)
% 89.70/54.23 |
% 89.70/54.23 | Equations (204) can reduce 205 to:
% 89.70/54.23 | (110) $false
% 89.70/54.23 |
% 89.70/54.23 |-The branch is then unsatisfiable
% 89.70/54.23 |-Branch two:
% 89.70/54.23 | (204) all_502_0_443 = 0
% 89.70/54.23 | (208) ~ (all_502_1_444 = 0)
% 89.70/54.23 |
% 89.70/54.23 | Equations (203) can reduce 208 to:
% 89.70/54.23 | (110) $false
% 89.70/54.23 |
% 89.70/54.23 |-The branch is then unsatisfiable
% 89.70/54.23 % SZS output end Proof for theBenchmark
% 89.70/54.23
% 89.70/54.23 53636ms
%------------------------------------------------------------------------------