TSTP Solution File: ALG226+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : ALG226+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 15:37:39 EDT 2022
% Result : Theorem 12.22s 3.50s
% Output : Proof 14.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG226+1 : TPTP v8.1.0. Released v3.4.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 8 22:13:36 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.55/0.58 ____ _
% 0.55/0.58 ___ / __ \_____(_)___ ________ __________
% 0.55/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.58
% 0.55/0.58 A Theorem Prover for First-Order Logic
% 0.55/0.58 (ePrincess v.1.0)
% 0.55/0.58
% 0.55/0.58 (c) Philipp Rümmer, 2009-2015
% 0.55/0.58 (c) Peter Backeman, 2014-2015
% 0.55/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.58 Bug reports to peter@backeman.se
% 0.55/0.58
% 0.55/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.58
% 0.55/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.60/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.68/0.97 Prover 0: Preprocessing ...
% 2.68/1.30 Prover 0: Warning: ignoring some quantifiers
% 2.68/1.32 Prover 0: Constructing countermodel ...
% 12.22/3.50 Prover 0: proved (2871ms)
% 12.22/3.50
% 12.22/3.50 No countermodel exists, formula is valid
% 12.22/3.50 % SZS status Theorem for theBenchmark
% 12.22/3.50
% 12.22/3.50 Generating proof ... Warning: ignoring some quantifiers
% 14.20/3.93 found it (size 86)
% 14.20/3.93
% 14.20/3.93 % SZS output start Proof for theBenchmark
% 14.20/3.93 Assumed formulas after preprocessing and simplification:
% 14.20/3.93 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (k7_relat_1(v4, v2) = v3 & k7_relat_1(v1, v2) = v3 & k1_closure3(v0, v4) = v2 & k1_closure3(v0, v1) = v2 & v2_funct_1(v14) & v2_funct_1(v7) & v1_relat_1(v14) & v1_relat_1(v12) & v1_relat_1(v11) & v1_relat_1(v9) & v1_relat_1(v7) & v1_relat_1(v6) & v1_relat_1(v5) & v3_relat_1(v11) & v3_relat_1(v6) & v1_funct_1(v14) & v1_funct_1(v12) & v1_funct_1(v11) & v1_funct_1(v9) & v1_funct_1(v7) & v1_funct_1(v6) & v1_funct_1(v5) & v1_finset_1(v14) & v1_finset_1(v13) & v1_fraenkel(v14) & m1_pboole(v4, v0) & m1_pboole(v1, v0) & v2_relat_1(v5) & v2_relat_1(v4) & v2_relat_1(v1) & v1_xboole_0(v14) & v1_xboole_0(v10) & v1_xboole_0(v9) & v1_xboole_0(k1_xboole_0) & ~ r6_pboole(v0, v1, v4) & ~ v1_xboole_0(v13) & ~ v1_xboole_0(v8) & ~ v1_xboole_0(v0) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = k1_xboole_0 | ~ (a_2_1_closure3(v16, v17) = v18) | ~ (k1_funct_1(v17, v15) = v19) | ~ m1_subset_1(v15, v16) | ~ m1_pboole(v17, v16) | ~ v2_relat_1(v17) | r2_hidden(v15, v18) | v1_xboole_0(v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = k1_xboole_0 | ~ (a_2_0_closure3(v16, v17) = v18) | ~ (k1_funct_1(v17, v15) = v19) | ~ m1_subset_1(v15, v16) | ~ m1_pboole(v17, v16) | r2_hidden(v15, v18) | v1_xboole_0(v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (k7_relat_1(v17, v15) = v18) | ~ (k1_funct_1(v18, v16) = v19) | ~ v1_relat_1(v17) | ~ v1_funct_1(v17) | ? [v20] : ? [v21] : (k1_relat_1(v18) = v20 & k1_funct_1(v17, v16) = v21 & (v21 = v19 | ~ r2_hidden(v16, v20)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (k7_relat_1(v17, v15) = v18) | ~ (k1_funct_1(v17, v16) = v19) | ~ v1_relat_1(v17) | ~ v1_funct_1(v17) | ? [v20] : ? [v21] : (k1_relat_1(v18) = v20 & k1_funct_1(v18, v16) = v21 & (v21 = v19 | ~ r2_hidden(v16, v20)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (a_2_1_closure3(v18, v17) = v16) | ~ (a_2_1_closure3(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (k7_relat_1(v18, v17) = v16) | ~ (k7_relat_1(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (k1_closure3(v18, v17) = v16) | ~ (k1_closure3(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (a_2_0_closure3(v18, v17) = v16) | ~ (a_2_0_closure3(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (k1_funct_1(v18, v17) = v16) | ~ (k1_funct_1(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (k3_xboole_0(v18, v17) = v16) | ~ (k3_xboole_0(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (a_2_1_closure3(v16, v17) = v18) | ~ r2_hidden(v15, v18) | ~ m1_pboole(v17, v16) | ~ v2_relat_1(v17) | v1_xboole_0(v16) | ? [v19] : ( ~ (v19 = k1_xboole_0) & k1_funct_1(v17, v15) = v19 & m1_subset_1(v15, v16))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (k1_relat_1(v16) = v17) | ~ (k3_xboole_0(v17, v15) = v18) | ~ v1_relat_1(v16) | ? [v19] : (k7_relat_1(v16, v15) = v19 & k1_relat_1(v19) = v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (a_2_0_closure3(v16, v17) = v18) | ~ r2_hidden(v15, v18) | ~ m1_pboole(v17, v16) | v1_xboole_0(v16) | ? [v19] : ( ~ (v19 = k1_xboole_0) & k1_funct_1(v17, v15) = v19 & m1_subset_1(v15, v16))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (k1_funct_1(v16, v17) = v18) | ~ m1_subset_1(v17, v15) | ~ m1_pboole(v16, v15) | ~ v2_relat_1(v16) | ~ v1_xboole_0(v18) | v1_xboole_0(v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (k1_funct_1(v16, v17) = v18) | ~ r2_hidden(v17, v15) | ~ m1_pboole(v16, v15) | ~ v2_relat_1(v16) | ~ v1_xboole_0(v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (k3_xboole_0(v15, v16) = v17) | ~ r2_hidden(v18, v17) | r2_hidden(v18, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (k3_xboole_0(v15, v16) = v17) | ~ r2_hidden(v18, v17) | r2_hidden(v18, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (k3_xboole_0(v15, v16) = v17) | ~ r2_hidden(v18, v16) | ~ r2_hidden(v18, v15) | r2_hidden(v18, v17)) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v15 | ~ (k3_xboole_0(v16, v17) = v18) | ? [v19] : (( ~ r2_hidden(v19, v17) | ~ r2_hidden(v19, v16) | ~ r2_hidden(v19, v15)) & (r2_hidden(v19, v15) | (r2_hidden(v19, v17) & r2_hidden(v19, v16))))) & ! [v15] : ! [v16] : ! [v17] : (v17 = v16 | ~ r6_pboole(v15, v16, v17) | ~ m1_pboole(v17, v15) | ~ m1_pboole(v16, v15)) & ! [v15] : ! [v16] : ! [v17] : (v17 = v15 | ~ (k1_relat_1(v17) = v16) | ~ (k1_relat_1(v15) = v16) | ~ v1_relat_1(v17) | ~ v1_relat_1(v15) | ~ v1_funct_1(v17) | ~ v1_funct_1(v15) | ? [v18] : ? [v19] : ? [v20] : ( ~ (v20 = v19) & k1_funct_1(v17, v18) = v20 & k1_funct_1(v15, v18) = v19 & r2_hidden(v18, v16))) & ! [v15] : ! [v16] : ! [v17] : (v17 = v15 | ~ (k1_relat_1(v16) = v17) | ~ v1_relat_1(v16) | ~ v1_funct_1(v16) | ~ m1_pboole(v16, v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (k1_relat_1(v17) = v16) | ~ (k1_relat_1(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (k7_relat_1(v16, v15) = v17) | ~ v1_relat_1(v16) | ? [v18] : ? [v19] : (k1_relat_1(v17) = v18 & k1_relat_1(v16) = v19 & k3_xboole_0(v19, v15) = v18)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (k7_relat_1(v15, v16) = v17) | ~ v1_relat_1(v15) | ~ v1_funct_1(v15) | v1_relat_1(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (k7_relat_1(v15, v16) = v17) | ~ v1_relat_1(v15) | ~ v1_funct_1(v15) | v1_funct_1(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (k7_relat_1(v15, v16) = v17) | ~ v1_relat_1(v15) | v1_relat_1(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (k1_closure3(v15, v16) = v17) | ~ m1_pboole(v16, v15) | a_2_0_closure3(v15, v16) = v17 | v1_xboole_0(v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (a_2_0_closure3(v15, v16) = v17) | ~ m1_pboole(v16, v15) | k1_closure3(v15, v16) = v17 | v1_xboole_0(v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (k3_xboole_0(v16, v15) = v17) | k3_xboole_0(v15, v16) = v17) & ! [v15] : ! [v16] : ! [v17] : ( ~ (k3_xboole_0(v15, v16) = v17) | ~ v1_finset_1(v16) | v1_finset_1(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (k3_xboole_0(v15, v16) = v17) | ~ v1_finset_1(v15) | v1_finset_1(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (k3_xboole_0(v15, v16) = v17) | k3_xboole_0(v16, v15) = v17) & ! [v15] : ! [v16] : ! [v17] : ( ~ r6_pboole(v15, v16, v17) | ~ m1_pboole(v17, v15) | ~ m1_pboole(v16, v15) | r6_pboole(v15, v17, v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ m1_pboole(v17, v15) | ~ m1_pboole(v16, v15) | r6_pboole(v15, v16, v16)) & ! [v15] : ! [v16] : (v16 = v15 | ~ (k3_xboole_0(v15, v15) = v16)) & ! [v15] : ! [v16] : (v16 = v15 | ~ v1_xboole_0(v16) | ~ v1_xboole_0(v15)) & ! [v15] : ! [v16] : (v16 = k1_xboole_0 | ~ (k3_xboole_0(v15, k1_xboole_0) = v16)) & ! [v15] : ! [v16] : ( ~ (k1_relat_1(v16) = v15) | ~ v1_relat_1(v16) | ~ v1_funct_1(v16) | m1_pboole(v16, v15)) & ! [v15] : ! [v16] : ( ~ m1_subset_1(v15, v16) | r2_hidden(v15, v16) | v1_xboole_0(v16)) & ! [v15] : ! [v16] : ( ~ v3_relat_1(v16) | ~ m1_pboole(v16, v15) | ~ v2_relat_1(v16) | v1_xboole_0(v15)) & ! [v15] : ! [v16] : ( ~ v3_relat_1(v16) | ~ m1_pboole(v16, v15) | v1_pre_circ(v16, v15)) & ! [v15] : ! [v16] : ( ~ r2_hidden(v16, v15) | ~ r2_hidden(v15, v16)) & ! [v15] : ! [v16] : ( ~ r2_hidden(v15, v16) | ~ v1_xboole_0(v16)) & ! [v15] : ! [v16] : ( ~ r2_hidden(v15, v16) | m1_subset_1(v15, v16)) & ! [v15] : ! [v16] : ( ~ m1_pboole(v16, v15) | v1_relat_1(v16)) & ! [v15] : ! [v16] : ( ~ m1_pboole(v16, v15) | v1_funct_1(v16)) & ! [v15] : ! [v16] : ( ~ m1_pboole(v16, v15) | r6_pboole(v15, v16, v16)) & ! [v15] : ! [v16] : ( ~ m1_pboole(v16, v15) | v2_relat_1(v16) | ? [v17] : ? [v18] : (k1_funct_1(v16, v17) = v18 & r2_hidden(v17, v15) & v1_xboole_0(v18))) & ! [v15] : (v15 = k1_xboole_0 | ~ v1_xboole_0(v15)) & ! [v15] : ( ~ v1_relat_1(v15) | ~ v1_funct_1(v15) | ~ v1_xboole_0(v15) | v2_funct_1(v15)) & ! [v15] : ( ~ v1_xboole_0(v15) | v1_funct_1(v15)) & ! [v15] : ( ~ v1_xboole_0(v15) | v1_finset_1(v15)) & ! [v15] : ( ~ v1_xboole_0(v15) | v1_fraenkel(v15)) & ? [v15] : ? [v16] : (v16 = v15 | ? [v17] : (( ~ r2_hidden(v17, v16) | ~ r2_hidden(v17, v15)) & (r2_hidden(v17, v16) | r2_hidden(v17, v15)))) & ? [v15] : ? [v16] : m1_subset_1(v16, v15) & ? [v15] : ? [v16] : m1_pboole(v16, v15) & ? [v15] : ? [v16] : (v1_relat_1(v16) & v3_relat_1(v16) & v1_funct_1(v16) & m1_pboole(v16, v15)) & ? [v15] : ? [v16] : (v1_relat_1(v16) & v1_funct_1(v16) & m1_pboole(v16, v15) & v2_relat_1(v16)))
% 14.41/3.99 | 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 yields:
% 14.41/3.99 | (1) k7_relat_1(all_0_10_10, all_0_12_12) = all_0_11_11 & k7_relat_1(all_0_13_13, all_0_12_12) = all_0_11_11 & k1_closure3(all_0_14_14, all_0_10_10) = all_0_12_12 & k1_closure3(all_0_14_14, all_0_13_13) = all_0_12_12 & v2_funct_1(all_0_0_0) & v2_funct_1(all_0_7_7) & v1_relat_1(all_0_0_0) & v1_relat_1(all_0_2_2) & v1_relat_1(all_0_3_3) & v1_relat_1(all_0_5_5) & v1_relat_1(all_0_7_7) & v1_relat_1(all_0_8_8) & v1_relat_1(all_0_9_9) & v3_relat_1(all_0_3_3) & v3_relat_1(all_0_8_8) & v1_funct_1(all_0_0_0) & v1_funct_1(all_0_2_2) & v1_funct_1(all_0_3_3) & v1_funct_1(all_0_5_5) & v1_funct_1(all_0_7_7) & v1_funct_1(all_0_8_8) & v1_funct_1(all_0_9_9) & v1_finset_1(all_0_0_0) & v1_finset_1(all_0_1_1) & v1_fraenkel(all_0_0_0) & m1_pboole(all_0_10_10, all_0_14_14) & m1_pboole(all_0_13_13, all_0_14_14) & v2_relat_1(all_0_9_9) & v2_relat_1(all_0_10_10) & v2_relat_1(all_0_13_13) & v1_xboole_0(all_0_0_0) & v1_xboole_0(all_0_4_4) & v1_xboole_0(all_0_5_5) & v1_xboole_0(k1_xboole_0) & ~ r6_pboole(all_0_14_14, all_0_13_13, all_0_10_10) & ~ v1_xboole_0(all_0_1_1) & ~ v1_xboole_0(all_0_6_6) & ~ v1_xboole_0(all_0_14_14) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = k1_xboole_0 | ~ (a_2_1_closure3(v1, v2) = v3) | ~ (k1_funct_1(v2, v0) = v4) | ~ m1_subset_1(v0, v1) | ~ m1_pboole(v2, v1) | ~ v2_relat_1(v2) | r2_hidden(v0, v3) | v1_xboole_0(v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = k1_xboole_0 | ~ (a_2_0_closure3(v1, v2) = v3) | ~ (k1_funct_1(v2, v0) = v4) | ~ m1_subset_1(v0, v1) | ~ m1_pboole(v2, v1) | r2_hidden(v0, v3) | v1_xboole_0(v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k7_relat_1(v2, v0) = v3) | ~ (k1_funct_1(v3, v1) = v4) | ~ v1_relat_1(v2) | ~ v1_funct_1(v2) | ? [v5] : ? [v6] : (k1_relat_1(v3) = v5 & k1_funct_1(v2, v1) = v6 & (v6 = v4 | ~ r2_hidden(v1, v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k7_relat_1(v2, v0) = v3) | ~ (k1_funct_1(v2, v1) = v4) | ~ v1_relat_1(v2) | ~ v1_funct_1(v2) | ? [v5] : ? [v6] : (k1_relat_1(v3) = v5 & k1_funct_1(v3, v1) = v6 & (v6 = v4 | ~ r2_hidden(v1, v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (a_2_1_closure3(v3, v2) = v1) | ~ (a_2_1_closure3(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k7_relat_1(v3, v2) = v1) | ~ (k7_relat_1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k1_closure3(v3, v2) = v1) | ~ (k1_closure3(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (a_2_0_closure3(v3, v2) = v1) | ~ (a_2_0_closure3(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k1_funct_1(v3, v2) = v1) | ~ (k1_funct_1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k3_xboole_0(v3, v2) = v1) | ~ (k3_xboole_0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (a_2_1_closure3(v1, v2) = v3) | ~ r2_hidden(v0, v3) | ~ m1_pboole(v2, v1) | ~ v2_relat_1(v2) | v1_xboole_0(v1) | ? [v4] : ( ~ (v4 = k1_xboole_0) & k1_funct_1(v2, v0) = v4 & m1_subset_1(v0, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_relat_1(v1) = v2) | ~ (k3_xboole_0(v2, v0) = v3) | ~ v1_relat_1(v1) | ? [v4] : (k7_relat_1(v1, v0) = v4 & k1_relat_1(v4) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (a_2_0_closure3(v1, v2) = v3) | ~ r2_hidden(v0, v3) | ~ m1_pboole(v2, v1) | v1_xboole_0(v1) | ? [v4] : ( ~ (v4 = k1_xboole_0) & k1_funct_1(v2, v0) = v4 & m1_subset_1(v0, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_funct_1(v1, v2) = v3) | ~ m1_subset_1(v2, v0) | ~ m1_pboole(v1, v0) | ~ v2_relat_1(v1) | ~ v1_xboole_0(v3) | v1_xboole_0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_funct_1(v1, v2) = v3) | ~ r2_hidden(v2, v0) | ~ m1_pboole(v1, v0) | ~ v2_relat_1(v1) | ~ v1_xboole_0(v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k3_xboole_0(v0, v1) = v2) | ~ r2_hidden(v3, v2) | r2_hidden(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k3_xboole_0(v0, v1) = v2) | ~ r2_hidden(v3, v2) | r2_hidden(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k3_xboole_0(v0, v1) = v2) | ~ r2_hidden(v3, v1) | ~ r2_hidden(v3, v0) | r2_hidden(v3, v2)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (k3_xboole_0(v1, v2) = v3) | ? [v4] : (( ~ r2_hidden(v4, v2) | ~ r2_hidden(v4, v1) | ~ r2_hidden(v4, v0)) & (r2_hidden(v4, v0) | (r2_hidden(v4, v2) & r2_hidden(v4, v1))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ r6_pboole(v0, v1, v2) | ~ m1_pboole(v2, v0) | ~ m1_pboole(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (k1_relat_1(v2) = v1) | ~ (k1_relat_1(v0) = v1) | ~ v1_relat_1(v2) | ~ v1_relat_1(v0) | ~ v1_funct_1(v2) | ~ v1_funct_1(v0) | ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = v4) & k1_funct_1(v2, v3) = v5 & k1_funct_1(v0, v3) = v4 & r2_hidden(v3, v1))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (k1_relat_1(v1) = v2) | ~ v1_relat_1(v1) | ~ v1_funct_1(v1) | ~ m1_pboole(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_relat_1(v2) = v1) | ~ (k1_relat_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k7_relat_1(v1, v0) = v2) | ~ v1_relat_1(v1) | ? [v3] : ? [v4] : (k1_relat_1(v2) = v3 & k1_relat_1(v1) = v4 & k3_xboole_0(v4, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k7_relat_1(v0, v1) = v2) | ~ v1_relat_1(v0) | ~ v1_funct_1(v0) | v1_relat_1(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k7_relat_1(v0, v1) = v2) | ~ v1_relat_1(v0) | ~ v1_funct_1(v0) | v1_funct_1(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k7_relat_1(v0, v1) = v2) | ~ v1_relat_1(v0) | v1_relat_1(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_closure3(v0, v1) = v2) | ~ m1_pboole(v1, v0) | a_2_0_closure3(v0, v1) = v2 | v1_xboole_0(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (a_2_0_closure3(v0, v1) = v2) | ~ m1_pboole(v1, v0) | k1_closure3(v0, v1) = v2 | v1_xboole_0(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k3_xboole_0(v1, v0) = v2) | k3_xboole_0(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k3_xboole_0(v0, v1) = v2) | ~ v1_finset_1(v1) | v1_finset_1(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k3_xboole_0(v0, v1) = v2) | ~ v1_finset_1(v0) | v1_finset_1(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k3_xboole_0(v0, v1) = v2) | k3_xboole_0(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ r6_pboole(v0, v1, v2) | ~ m1_pboole(v2, v0) | ~ m1_pboole(v1, v0) | r6_pboole(v0, v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ m1_pboole(v2, v0) | ~ m1_pboole(v1, v0) | r6_pboole(v0, v1, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (k3_xboole_0(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ v1_xboole_0(v1) | ~ v1_xboole_0(v0)) & ! [v0] : ! [v1] : (v1 = k1_xboole_0 | ~ (k3_xboole_0(v0, k1_xboole_0) = v1)) & ! [v0] : ! [v1] : ( ~ (k1_relat_1(v1) = v0) | ~ v1_relat_1(v1) | ~ v1_funct_1(v1) | m1_pboole(v1, v0)) & ! [v0] : ! [v1] : ( ~ m1_subset_1(v0, v1) | r2_hidden(v0, v1) | v1_xboole_0(v1)) & ! [v0] : ! [v1] : ( ~ v3_relat_1(v1) | ~ m1_pboole(v1, v0) | ~ v2_relat_1(v1) | v1_xboole_0(v0)) & ! [v0] : ! [v1] : ( ~ v3_relat_1(v1) | ~ m1_pboole(v1, v0) | v1_pre_circ(v1, v0)) & ! [v0] : ! [v1] : ( ~ r2_hidden(v1, v0) | ~ r2_hidden(v0, v1)) & ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | ~ v1_xboole_0(v1)) & ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | m1_subset_1(v0, v1)) & ! [v0] : ! [v1] : ( ~ m1_pboole(v1, v0) | v1_relat_1(v1)) & ! [v0] : ! [v1] : ( ~ m1_pboole(v1, v0) | v1_funct_1(v1)) & ! [v0] : ! [v1] : ( ~ m1_pboole(v1, v0) | r6_pboole(v0, v1, v1)) & ! [v0] : ! [v1] : ( ~ m1_pboole(v1, v0) | v2_relat_1(v1) | ? [v2] : ? [v3] : (k1_funct_1(v1, v2) = v3 & r2_hidden(v2, v0) & v1_xboole_0(v3))) & ! [v0] : (v0 = k1_xboole_0 | ~ v1_xboole_0(v0)) & ! [v0] : ( ~ v1_relat_1(v0) | ~ v1_funct_1(v0) | ~ v1_xboole_0(v0) | v2_funct_1(v0)) & ! [v0] : ( ~ v1_xboole_0(v0) | v1_funct_1(v0)) & ! [v0] : ( ~ v1_xboole_0(v0) | v1_finset_1(v0)) & ! [v0] : ( ~ v1_xboole_0(v0) | v1_fraenkel(v0)) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ r2_hidden(v2, v1) | ~ r2_hidden(v2, v0)) & (r2_hidden(v2, v1) | r2_hidden(v2, v0)))) & ? [v0] : ? [v1] : m1_subset_1(v1, v0) & ? [v0] : ? [v1] : m1_pboole(v1, v0) & ? [v0] : ? [v1] : (v1_relat_1(v1) & v3_relat_1(v1) & v1_funct_1(v1) & m1_pboole(v1, v0)) & ? [v0] : ? [v1] : (v1_relat_1(v1) & v1_funct_1(v1) & m1_pboole(v1, v0) & v2_relat_1(v1))
% 14.41/4.01 |
% 14.41/4.01 | Applying alpha-rule on (1) yields:
% 14.41/4.01 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k1_closure3(v3, v2) = v1) | ~ (k1_closure3(v3, v2) = v0))
% 14.41/4.01 | (3) ! [v0] : ! [v1] : (v1 = v0 | ~ (k3_xboole_0(v0, v0) = v1))
% 14.41/4.01 | (4) v1_xboole_0(k1_xboole_0)
% 14.41/4.01 | (5) ! [v0] : ! [v1] : ( ~ m1_pboole(v1, v0) | v1_funct_1(v1))
% 14.41/4.01 | (6) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ r6_pboole(v0, v1, v2) | ~ m1_pboole(v2, v0) | ~ m1_pboole(v1, v0))
% 14.41/4.01 | (7) k7_relat_1(all_0_10_10, all_0_12_12) = all_0_11_11
% 14.41/4.01 | (8) v1_funct_1(all_0_3_3)
% 14.41/4.01 | (9) ! [v0] : ! [v1] : ( ~ v3_relat_1(v1) | ~ m1_pboole(v1, v0) | ~ v2_relat_1(v1) | v1_xboole_0(v0))
% 14.41/4.01 | (10) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ r2_hidden(v2, v1) | ~ r2_hidden(v2, v0)) & (r2_hidden(v2, v1) | r2_hidden(v2, v0))))
% 14.41/4.01 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (a_2_0_closure3(v1, v2) = v3) | ~ r2_hidden(v0, v3) | ~ m1_pboole(v2, v1) | v1_xboole_0(v1) | ? [v4] : ( ~ (v4 = k1_xboole_0) & k1_funct_1(v2, v0) = v4 & m1_subset_1(v0, v1)))
% 14.41/4.01 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k7_relat_1(v2, v0) = v3) | ~ (k1_funct_1(v2, v1) = v4) | ~ v1_relat_1(v2) | ~ v1_funct_1(v2) | ? [v5] : ? [v6] : (k1_relat_1(v3) = v5 & k1_funct_1(v3, v1) = v6 & (v6 = v4 | ~ r2_hidden(v1, v5))))
% 14.41/4.01 | (13) v1_fraenkel(all_0_0_0)
% 14.41/4.01 | (14) ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | m1_subset_1(v0, v1))
% 14.41/4.01 | (15) v1_relat_1(all_0_2_2)
% 14.41/4.01 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (k7_relat_1(v1, v0) = v2) | ~ v1_relat_1(v1) | ? [v3] : ? [v4] : (k1_relat_1(v2) = v3 & k1_relat_1(v1) = v4 & k3_xboole_0(v4, v0) = v3))
% 14.41/4.01 | (17) ? [v0] : ? [v1] : (v1_relat_1(v1) & v1_funct_1(v1) & m1_pboole(v1, v0) & v2_relat_1(v1))
% 14.41/4.01 | (18) m1_pboole(all_0_10_10, all_0_14_14)
% 14.41/4.01 | (19) v1_xboole_0(all_0_5_5)
% 14.41/4.01 | (20) ! [v0] : (v0 = k1_xboole_0 | ~ v1_xboole_0(v0))
% 14.41/4.01 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k3_xboole_0(v0, v1) = v2) | ~ r2_hidden(v3, v2) | r2_hidden(v3, v0))
% 14.41/4.01 | (22) v1_xboole_0(all_0_4_4)
% 14.41/4.01 | (23) v1_finset_1(all_0_1_1)
% 14.41/4.01 | (24) ? [v0] : ? [v1] : m1_subset_1(v1, v0)
% 14.41/4.01 | (25) ? [v0] : ? [v1] : (v1_relat_1(v1) & v3_relat_1(v1) & v1_funct_1(v1) & m1_pboole(v1, v0))
% 14.41/4.01 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (a_2_0_closure3(v3, v2) = v1) | ~ (a_2_0_closure3(v3, v2) = v0))
% 14.41/4.01 | (27) ! [v0] : ! [v1] : ( ~ (k1_relat_1(v1) = v0) | ~ v1_relat_1(v1) | ~ v1_funct_1(v1) | m1_pboole(v1, v0))
% 14.41/4.01 | (28) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (k1_relat_1(v2) = v1) | ~ (k1_relat_1(v0) = v1) | ~ v1_relat_1(v2) | ~ v1_relat_1(v0) | ~ v1_funct_1(v2) | ~ v1_funct_1(v0) | ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = v4) & k1_funct_1(v2, v3) = v5 & k1_funct_1(v0, v3) = v4 & r2_hidden(v3, v1)))
% 14.41/4.01 | (29) ! [v0] : ! [v1] : ( ~ r2_hidden(v1, v0) | ~ r2_hidden(v0, v1))
% 14.41/4.01 | (30) ! [v0] : ( ~ v1_xboole_0(v0) | v1_fraenkel(v0))
% 14.41/4.01 | (31) v1_finset_1(all_0_0_0)
% 14.41/4.01 | (32) v2_funct_1(all_0_0_0)
% 14.41/4.01 | (33) ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | ~ v1_xboole_0(v1))
% 14.41/4.01 | (34) v2_relat_1(all_0_9_9)
% 14.41/4.01 | (35) v3_relat_1(all_0_3_3)
% 14.41/4.01 | (36) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (k1_relat_1(v1) = v2) | ~ v1_relat_1(v1) | ~ v1_funct_1(v1) | ~ m1_pboole(v1, v0))
% 14.41/4.01 | (37) v1_funct_1(all_0_8_8)
% 14.41/4.01 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k7_relat_1(v3, v2) = v1) | ~ (k7_relat_1(v3, v2) = v0))
% 14.41/4.02 | (39) ! [v0] : ( ~ v1_xboole_0(v0) | v1_funct_1(v0))
% 14.41/4.02 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (a_2_1_closure3(v3, v2) = v1) | ~ (a_2_1_closure3(v3, v2) = v0))
% 14.41/4.02 | (41) v1_relat_1(all_0_7_7)
% 14.41/4.02 | (42) ~ v1_xboole_0(all_0_1_1)
% 14.41/4.02 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ r6_pboole(v0, v1, v2) | ~ m1_pboole(v2, v0) | ~ m1_pboole(v1, v0) | r6_pboole(v0, v2, v1))
% 14.41/4.02 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = k1_xboole_0 | ~ (a_2_0_closure3(v1, v2) = v3) | ~ (k1_funct_1(v2, v0) = v4) | ~ m1_subset_1(v0, v1) | ~ m1_pboole(v2, v1) | r2_hidden(v0, v3) | v1_xboole_0(v1))
% 14.41/4.02 | (45) v1_funct_1(all_0_5_5)
% 14.41/4.02 | (46) v1_relat_1(all_0_8_8)
% 14.41/4.02 | (47) v1_relat_1(all_0_5_5)
% 14.41/4.02 | (48) k1_closure3(all_0_14_14, all_0_10_10) = all_0_12_12
% 14.41/4.02 | (49) ? [v0] : ? [v1] : m1_pboole(v1, v0)
% 14.41/4.02 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ m1_pboole(v2, v0) | ~ m1_pboole(v1, v0) | r6_pboole(v0, v1, v1))
% 14.41/4.02 | (51) ! [v0] : ( ~ v1_xboole_0(v0) | v1_finset_1(v0))
% 14.41/4.02 | (52) ! [v0] : ! [v1] : ! [v2] : ( ~ (k7_relat_1(v0, v1) = v2) | ~ v1_relat_1(v0) | ~ v1_funct_1(v0) | v1_funct_1(v2))
% 14.41/4.02 | (53) ! [v0] : ! [v1] : ! [v2] : ( ~ (k7_relat_1(v0, v1) = v2) | ~ v1_relat_1(v0) | ~ v1_funct_1(v0) | v1_relat_1(v2))
% 14.41/4.02 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_funct_1(v1, v2) = v3) | ~ m1_subset_1(v2, v0) | ~ m1_pboole(v1, v0) | ~ v2_relat_1(v1) | ~ v1_xboole_0(v3) | v1_xboole_0(v0))
% 14.41/4.02 | (55) ! [v0] : ! [v1] : ( ~ m1_pboole(v1, v0) | r6_pboole(v0, v1, v1))
% 14.41/4.02 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = k1_xboole_0 | ~ (a_2_1_closure3(v1, v2) = v3) | ~ (k1_funct_1(v2, v0) = v4) | ~ m1_subset_1(v0, v1) | ~ m1_pboole(v2, v1) | ~ v2_relat_1(v2) | r2_hidden(v0, v3) | v1_xboole_0(v1))
% 14.41/4.02 | (57) k1_closure3(all_0_14_14, all_0_13_13) = all_0_12_12
% 14.41/4.02 | (58) v1_funct_1(all_0_0_0)
% 14.41/4.02 | (59) ~ r6_pboole(all_0_14_14, all_0_13_13, all_0_10_10)
% 14.41/4.02 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k1_funct_1(v3, v2) = v1) | ~ (k1_funct_1(v3, v2) = v0))
% 14.41/4.02 | (61) ! [v0] : ! [v1] : ! [v2] : ( ~ (k7_relat_1(v0, v1) = v2) | ~ v1_relat_1(v0) | v1_relat_1(v2))
% 14.41/4.02 | (62) v1_xboole_0(all_0_0_0)
% 14.41/4.02 | (63) v1_funct_1(all_0_7_7)
% 14.41/4.02 | (64) ! [v0] : ! [v1] : (v1 = k1_xboole_0 | ~ (k3_xboole_0(v0, k1_xboole_0) = v1))
% 14.41/4.02 | (65) v2_relat_1(all_0_10_10)
% 14.41/4.02 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k3_xboole_0(v3, v2) = v1) | ~ (k3_xboole_0(v3, v2) = v0))
% 14.41/4.02 | (67) ! [v0] : ! [v1] : ! [v2] : ( ~ (k3_xboole_0(v0, v1) = v2) | k3_xboole_0(v1, v0) = v2)
% 14.41/4.02 | (68) ! [v0] : ! [v1] : ! [v2] : ( ~ (k3_xboole_0(v1, v0) = v2) | k3_xboole_0(v0, v1) = v2)
% 14.41/4.02 | (69) ! [v0] : ( ~ v1_relat_1(v0) | ~ v1_funct_1(v0) | ~ v1_xboole_0(v0) | v2_funct_1(v0))
% 14.41/4.02 | (70) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_relat_1(v2) = v1) | ~ (k1_relat_1(v2) = v0))
% 14.41/4.02 | (71) v2_funct_1(all_0_7_7)
% 14.41/4.02 | (72) ! [v0] : ! [v1] : ( ~ m1_pboole(v1, v0) | v1_relat_1(v1))
% 14.41/4.02 | (73) m1_pboole(all_0_13_13, all_0_14_14)
% 14.41/4.02 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k3_xboole_0(v0, v1) = v2) | ~ r2_hidden(v3, v2) | r2_hidden(v3, v1))
% 14.41/4.02 | (75) ! [v0] : ! [v1] : (v1 = v0 | ~ v1_xboole_0(v1) | ~ v1_xboole_0(v0))
% 14.41/4.02 | (76) ~ v1_xboole_0(all_0_14_14)
% 14.41/4.02 | (77) v1_funct_1(all_0_2_2)
% 14.41/4.02 | (78) v3_relat_1(all_0_8_8)
% 14.41/4.02 | (79) ! [v0] : ! [v1] : ! [v2] : ( ~ (k3_xboole_0(v0, v1) = v2) | ~ v1_finset_1(v1) | v1_finset_1(v2))
% 14.41/4.03 | (80) ! [v0] : ! [v1] : ! [v2] : ( ~ (k3_xboole_0(v0, v1) = v2) | ~ v1_finset_1(v0) | v1_finset_1(v2))
% 14.41/4.03 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_relat_1(v1) = v2) | ~ (k3_xboole_0(v2, v0) = v3) | ~ v1_relat_1(v1) | ? [v4] : (k7_relat_1(v1, v0) = v4 & k1_relat_1(v4) = v3))
% 14.41/4.03 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (a_2_1_closure3(v1, v2) = v3) | ~ r2_hidden(v0, v3) | ~ m1_pboole(v2, v1) | ~ v2_relat_1(v2) | v1_xboole_0(v1) | ? [v4] : ( ~ (v4 = k1_xboole_0) & k1_funct_1(v2, v0) = v4 & m1_subset_1(v0, v1)))
% 14.41/4.03 | (83) v1_funct_1(all_0_9_9)
% 14.41/4.03 | (84) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (k3_xboole_0(v1, v2) = v3) | ? [v4] : (( ~ r2_hidden(v4, v2) | ~ r2_hidden(v4, v1) | ~ r2_hidden(v4, v0)) & (r2_hidden(v4, v0) | (r2_hidden(v4, v2) & r2_hidden(v4, v1)))))
% 14.41/4.03 | (85) ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_closure3(v0, v1) = v2) | ~ m1_pboole(v1, v0) | a_2_0_closure3(v0, v1) = v2 | v1_xboole_0(v0))
% 14.41/4.03 | (86) v2_relat_1(all_0_13_13)
% 14.41/4.03 | (87) ! [v0] : ! [v1] : ! [v2] : ( ~ (a_2_0_closure3(v0, v1) = v2) | ~ m1_pboole(v1, v0) | k1_closure3(v0, v1) = v2 | v1_xboole_0(v0))
% 14.41/4.03 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k7_relat_1(v2, v0) = v3) | ~ (k1_funct_1(v3, v1) = v4) | ~ v1_relat_1(v2) | ~ v1_funct_1(v2) | ? [v5] : ? [v6] : (k1_relat_1(v3) = v5 & k1_funct_1(v2, v1) = v6 & (v6 = v4 | ~ r2_hidden(v1, v5))))
% 14.41/4.03 | (89) v1_relat_1(all_0_0_0)
% 14.41/4.03 | (90) ! [v0] : ! [v1] : ( ~ v3_relat_1(v1) | ~ m1_pboole(v1, v0) | v1_pre_circ(v1, v0))
% 14.41/4.03 | (91) ~ v1_xboole_0(all_0_6_6)
% 14.41/4.03 | (92) v1_relat_1(all_0_3_3)
% 14.41/4.03 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_funct_1(v1, v2) = v3) | ~ r2_hidden(v2, v0) | ~ m1_pboole(v1, v0) | ~ v2_relat_1(v1) | ~ v1_xboole_0(v3))
% 14.41/4.03 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k3_xboole_0(v0, v1) = v2) | ~ r2_hidden(v3, v1) | ~ r2_hidden(v3, v0) | r2_hidden(v3, v2))
% 14.41/4.03 | (95) k7_relat_1(all_0_13_13, all_0_12_12) = all_0_11_11
% 14.41/4.03 | (96) v1_relat_1(all_0_9_9)
% 14.41/4.03 | (97) ! [v0] : ! [v1] : ( ~ m1_subset_1(v0, v1) | r2_hidden(v0, v1) | v1_xboole_0(v1))
% 14.41/4.03 | (98) ! [v0] : ! [v1] : ( ~ m1_pboole(v1, v0) | v2_relat_1(v1) | ? [v2] : ? [v3] : (k1_funct_1(v1, v2) = v3 & r2_hidden(v2, v0) & v1_xboole_0(v3)))
% 14.41/4.03 |
% 14.41/4.03 | Instantiating formula (85) with all_0_12_12, all_0_10_10, all_0_14_14 and discharging atoms k1_closure3(all_0_14_14, all_0_10_10) = all_0_12_12, m1_pboole(all_0_10_10, all_0_14_14), ~ v1_xboole_0(all_0_14_14), yields:
% 14.41/4.03 | (99) a_2_0_closure3(all_0_14_14, all_0_10_10) = all_0_12_12
% 14.41/4.03 |
% 14.41/4.03 | Instantiating formula (72) with all_0_10_10, all_0_14_14 and discharging atoms m1_pboole(all_0_10_10, all_0_14_14), yields:
% 14.41/4.03 | (100) v1_relat_1(all_0_10_10)
% 14.41/4.03 |
% 14.41/4.03 | Instantiating formula (5) with all_0_10_10, all_0_14_14 and discharging atoms m1_pboole(all_0_10_10, all_0_14_14), yields:
% 14.41/4.03 | (101) v1_funct_1(all_0_10_10)
% 14.41/4.03 |
% 14.41/4.03 | Instantiating formula (85) with all_0_12_12, all_0_13_13, all_0_14_14 and discharging atoms k1_closure3(all_0_14_14, all_0_13_13) = all_0_12_12, m1_pboole(all_0_13_13, all_0_14_14), ~ v1_xboole_0(all_0_14_14), yields:
% 14.41/4.03 | (102) a_2_0_closure3(all_0_14_14, all_0_13_13) = all_0_12_12
% 14.41/4.03 |
% 14.41/4.03 | Instantiating formula (50) with all_0_13_13, all_0_10_10, all_0_14_14 and discharging atoms m1_pboole(all_0_10_10, all_0_14_14), m1_pboole(all_0_13_13, all_0_14_14), yields:
% 14.41/4.03 | (103) r6_pboole(all_0_14_14, all_0_10_10, all_0_10_10)
% 14.41/4.03 |
% 14.41/4.03 | Instantiating formula (72) with all_0_13_13, all_0_14_14 and discharging atoms m1_pboole(all_0_13_13, all_0_14_14), yields:
% 14.41/4.03 | (104) v1_relat_1(all_0_13_13)
% 14.41/4.03 |
% 14.41/4.03 | Instantiating formula (5) with all_0_13_13, all_0_14_14 and discharging atoms m1_pboole(all_0_13_13, all_0_14_14), yields:
% 14.41/4.03 | (105) v1_funct_1(all_0_13_13)
% 14.41/4.03 |
% 14.41/4.03 | Instantiating formula (16) with all_0_11_11, all_0_10_10, all_0_12_12 and discharging atoms k7_relat_1(all_0_10_10, all_0_12_12) = all_0_11_11, v1_relat_1(all_0_10_10), yields:
% 14.41/4.04 | (106) ? [v0] : ? [v1] : (k1_relat_1(all_0_10_10) = v1 & k1_relat_1(all_0_11_11) = v0 & k3_xboole_0(v1, all_0_12_12) = v0)
% 14.41/4.04 |
% 14.41/4.04 | Instantiating formula (16) with all_0_11_11, all_0_13_13, all_0_12_12 and discharging atoms k7_relat_1(all_0_13_13, all_0_12_12) = all_0_11_11, v1_relat_1(all_0_13_13), yields:
% 14.41/4.04 | (107) ? [v0] : ? [v1] : (k1_relat_1(all_0_11_11) = v0 & k1_relat_1(all_0_13_13) = v1 & k3_xboole_0(v1, all_0_12_12) = v0)
% 14.41/4.04 |
% 14.41/4.04 | Instantiating (107) with all_30_0_26, all_30_1_27 yields:
% 14.41/4.04 | (108) k1_relat_1(all_0_11_11) = all_30_1_27 & k1_relat_1(all_0_13_13) = all_30_0_26 & k3_xboole_0(all_30_0_26, all_0_12_12) = all_30_1_27
% 14.41/4.04 |
% 14.41/4.04 | Applying alpha-rule on (108) yields:
% 14.41/4.04 | (109) k1_relat_1(all_0_11_11) = all_30_1_27
% 14.41/4.04 | (110) k1_relat_1(all_0_13_13) = all_30_0_26
% 14.41/4.04 | (111) k3_xboole_0(all_30_0_26, all_0_12_12) = all_30_1_27
% 14.41/4.04 |
% 14.41/4.04 | Instantiating (106) with all_32_0_28, all_32_1_29 yields:
% 14.41/4.04 | (112) k1_relat_1(all_0_10_10) = all_32_0_28 & k1_relat_1(all_0_11_11) = all_32_1_29 & k3_xboole_0(all_32_0_28, all_0_12_12) = all_32_1_29
% 14.41/4.04 |
% 14.41/4.04 | Applying alpha-rule on (112) yields:
% 14.41/4.04 | (113) k1_relat_1(all_0_10_10) = all_32_0_28
% 14.41/4.04 | (114) k1_relat_1(all_0_11_11) = all_32_1_29
% 14.41/4.04 | (115) k3_xboole_0(all_32_0_28, all_0_12_12) = all_32_1_29
% 14.41/4.04 |
% 14.41/4.04 | Instantiating formula (36) with all_32_0_28, all_0_10_10, all_0_14_14 and discharging atoms k1_relat_1(all_0_10_10) = all_32_0_28, v1_relat_1(all_0_10_10), v1_funct_1(all_0_10_10), m1_pboole(all_0_10_10, all_0_14_14), yields:
% 14.41/4.04 | (116) all_32_0_28 = all_0_14_14
% 14.41/4.04 |
% 14.41/4.04 | Instantiating formula (70) with all_0_11_11, all_30_1_27, all_32_1_29 and discharging atoms k1_relat_1(all_0_11_11) = all_32_1_29, k1_relat_1(all_0_11_11) = all_30_1_27, yields:
% 14.41/4.04 | (117) all_32_1_29 = all_30_1_27
% 14.41/4.04 |
% 14.41/4.04 | Instantiating formula (36) with all_30_0_26, all_0_13_13, all_0_14_14 and discharging atoms k1_relat_1(all_0_13_13) = all_30_0_26, v1_relat_1(all_0_13_13), v1_funct_1(all_0_13_13), m1_pboole(all_0_13_13, all_0_14_14), yields:
% 14.41/4.04 | (118) all_30_0_26 = all_0_14_14
% 14.41/4.04 |
% 14.41/4.04 | From (116) and (113) follows:
% 14.41/4.04 | (119) k1_relat_1(all_0_10_10) = all_0_14_14
% 14.41/4.04 |
% 14.41/4.04 | From (117) and (114) follows:
% 14.41/4.04 | (109) k1_relat_1(all_0_11_11) = all_30_1_27
% 14.41/4.04 |
% 14.41/4.04 | From (118) and (110) follows:
% 14.41/4.04 | (121) k1_relat_1(all_0_13_13) = all_0_14_14
% 14.41/4.04 |
% 14.41/4.04 | From (118) and (111) follows:
% 14.41/4.04 | (122) k3_xboole_0(all_0_14_14, all_0_12_12) = all_30_1_27
% 14.41/4.04 |
% 14.41/4.04 | Instantiating formula (28) with all_0_10_10, all_0_14_14, all_0_13_13 and discharging atoms k1_relat_1(all_0_10_10) = all_0_14_14, k1_relat_1(all_0_13_13) = all_0_14_14, v1_relat_1(all_0_10_10), v1_relat_1(all_0_13_13), v1_funct_1(all_0_10_10), v1_funct_1(all_0_13_13), yields:
% 14.41/4.04 | (123) all_0_10_10 = all_0_13_13 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & k1_funct_1(all_0_10_10, v0) = v2 & k1_funct_1(all_0_13_13, v0) = v1 & r2_hidden(v0, all_0_14_14))
% 14.41/4.04 |
% 14.41/4.04 | Instantiating formula (28) with all_0_13_13, all_0_14_14, all_0_10_10 and discharging atoms k1_relat_1(all_0_10_10) = all_0_14_14, k1_relat_1(all_0_13_13) = all_0_14_14, v1_relat_1(all_0_10_10), v1_relat_1(all_0_13_13), v1_funct_1(all_0_10_10), v1_funct_1(all_0_13_13), yields:
% 14.41/4.04 | (124) all_0_10_10 = all_0_13_13 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & k1_funct_1(all_0_10_10, v0) = v1 & k1_funct_1(all_0_13_13, v0) = v2 & r2_hidden(v0, all_0_14_14))
% 14.41/4.04 |
% 14.41/4.04 +-Applying beta-rule and splitting (123), into two cases.
% 14.41/4.04 |-Branch one:
% 14.41/4.04 | (125) all_0_10_10 = all_0_13_13
% 14.41/4.04 |
% 14.41/4.04 | From (125)(125) and (103) follows:
% 14.41/4.04 | (126) r6_pboole(all_0_14_14, all_0_13_13, all_0_13_13)
% 14.41/4.04 |
% 14.41/4.04 | From (125) and (59) follows:
% 14.41/4.04 | (127) ~ r6_pboole(all_0_14_14, all_0_13_13, all_0_13_13)
% 14.41/4.04 |
% 14.41/4.04 | Using (126) and (127) yields:
% 14.41/4.04 | (128) $false
% 14.41/4.04 |
% 14.41/4.04 |-The branch is then unsatisfiable
% 14.41/4.04 |-Branch two:
% 14.41/4.04 | (129) ~ (all_0_10_10 = all_0_13_13)
% 14.41/4.04 | (130) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & k1_funct_1(all_0_10_10, v0) = v2 & k1_funct_1(all_0_13_13, v0) = v1 & r2_hidden(v0, all_0_14_14))
% 14.41/4.04 |
% 14.41/4.04 | Instantiating (130) with all_95_0_30, all_95_1_31, all_95_2_32 yields:
% 14.41/4.04 | (131) ~ (all_95_0_30 = all_95_1_31) & k1_funct_1(all_0_10_10, all_95_2_32) = all_95_0_30 & k1_funct_1(all_0_13_13, all_95_2_32) = all_95_1_31 & r2_hidden(all_95_2_32, all_0_14_14)
% 14.41/4.04 |
% 14.41/4.04 | Applying alpha-rule on (131) yields:
% 14.41/4.04 | (132) ~ (all_95_0_30 = all_95_1_31)
% 14.41/4.04 | (133) k1_funct_1(all_0_10_10, all_95_2_32) = all_95_0_30
% 14.41/4.04 | (134) k1_funct_1(all_0_13_13, all_95_2_32) = all_95_1_31
% 14.41/4.04 | (135) r2_hidden(all_95_2_32, all_0_14_14)
% 14.41/4.04 |
% 14.41/4.04 +-Applying beta-rule and splitting (124), into two cases.
% 14.41/4.04 |-Branch one:
% 14.41/4.04 | (125) all_0_10_10 = all_0_13_13
% 14.41/4.04 |
% 14.41/4.04 | Equations (125) can reduce 129 to:
% 14.41/4.04 | (137) $false
% 14.41/4.04 |
% 14.41/4.04 |-The branch is then unsatisfiable
% 14.41/4.04 |-Branch two:
% 14.41/4.04 | (129) ~ (all_0_10_10 = all_0_13_13)
% 14.41/4.04 | (139) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & k1_funct_1(all_0_10_10, v0) = v1 & k1_funct_1(all_0_13_13, v0) = v2 & r2_hidden(v0, all_0_14_14))
% 14.41/4.04 |
% 14.41/4.04 | Instantiating (139) with all_101_0_33, all_101_1_34, all_101_2_35 yields:
% 14.41/4.04 | (140) ~ (all_101_0_33 = all_101_1_34) & k1_funct_1(all_0_10_10, all_101_2_35) = all_101_1_34 & k1_funct_1(all_0_13_13, all_101_2_35) = all_101_0_33 & r2_hidden(all_101_2_35, all_0_14_14)
% 14.41/4.04 |
% 14.41/4.04 | Applying alpha-rule on (140) yields:
% 14.41/4.04 | (141) ~ (all_101_0_33 = all_101_1_34)
% 14.41/4.04 | (142) k1_funct_1(all_0_10_10, all_101_2_35) = all_101_1_34
% 14.41/4.04 | (143) k1_funct_1(all_0_13_13, all_101_2_35) = all_101_0_33
% 14.41/4.04 | (144) r2_hidden(all_101_2_35, all_0_14_14)
% 14.41/4.04 |
% 14.41/4.04 | Instantiating formula (12) with all_101_1_34, all_0_11_11, all_0_10_10, all_101_2_35, all_0_12_12 and discharging atoms k7_relat_1(all_0_10_10, all_0_12_12) = all_0_11_11, k1_funct_1(all_0_10_10, all_101_2_35) = all_101_1_34, v1_relat_1(all_0_10_10), v1_funct_1(all_0_10_10), yields:
% 14.41/4.04 | (145) ? [v0] : ? [v1] : (k1_relat_1(all_0_11_11) = v0 & k1_funct_1(all_0_11_11, all_101_2_35) = v1 & (v1 = all_101_1_34 | ~ r2_hidden(all_101_2_35, v0)))
% 14.41/4.05 |
% 14.41/4.05 | Instantiating formula (12) with all_95_0_30, all_0_11_11, all_0_10_10, all_95_2_32, all_0_12_12 and discharging atoms k7_relat_1(all_0_10_10, all_0_12_12) = all_0_11_11, k1_funct_1(all_0_10_10, all_95_2_32) = all_95_0_30, v1_relat_1(all_0_10_10), v1_funct_1(all_0_10_10), yields:
% 14.41/4.05 | (146) ? [v0] : ? [v1] : (k1_relat_1(all_0_11_11) = v0 & k1_funct_1(all_0_11_11, all_95_2_32) = v1 & (v1 = all_95_0_30 | ~ r2_hidden(all_95_2_32, v0)))
% 14.41/4.05 |
% 14.41/4.05 | Instantiating formula (12) with all_101_0_33, all_0_11_11, all_0_13_13, all_101_2_35, all_0_12_12 and discharging atoms k7_relat_1(all_0_13_13, all_0_12_12) = all_0_11_11, k1_funct_1(all_0_13_13, all_101_2_35) = all_101_0_33, v1_relat_1(all_0_13_13), v1_funct_1(all_0_13_13), yields:
% 14.41/4.05 | (147) ? [v0] : ? [v1] : (k1_relat_1(all_0_11_11) = v0 & k1_funct_1(all_0_11_11, all_101_2_35) = v1 & (v1 = all_101_0_33 | ~ r2_hidden(all_101_2_35, v0)))
% 14.41/4.05 |
% 14.41/4.05 | Instantiating formula (12) with all_95_1_31, all_0_11_11, all_0_13_13, all_95_2_32, all_0_12_12 and discharging atoms k7_relat_1(all_0_13_13, all_0_12_12) = all_0_11_11, k1_funct_1(all_0_13_13, all_95_2_32) = all_95_1_31, v1_relat_1(all_0_13_13), v1_funct_1(all_0_13_13), yields:
% 14.41/4.05 | (148) ? [v0] : ? [v1] : (k1_relat_1(all_0_11_11) = v0 & k1_funct_1(all_0_11_11, all_95_2_32) = v1 & (v1 = all_95_1_31 | ~ r2_hidden(all_95_2_32, v0)))
% 14.41/4.05 |
% 14.41/4.05 | Instantiating formula (14) with all_0_14_14, all_101_2_35 and discharging atoms r2_hidden(all_101_2_35, all_0_14_14), yields:
% 14.41/4.05 | (149) m1_subset_1(all_101_2_35, all_0_14_14)
% 14.41/4.05 |
% 14.41/4.05 | Instantiating (148) with all_109_0_36, all_109_1_37 yields:
% 14.41/4.05 | (150) k1_relat_1(all_0_11_11) = all_109_1_37 & k1_funct_1(all_0_11_11, all_95_2_32) = all_109_0_36 & (all_109_0_36 = all_95_1_31 | ~ r2_hidden(all_95_2_32, all_109_1_37))
% 14.41/4.05 |
% 14.41/4.05 | Applying alpha-rule on (150) yields:
% 14.41/4.05 | (151) k1_relat_1(all_0_11_11) = all_109_1_37
% 14.41/4.05 | (152) k1_funct_1(all_0_11_11, all_95_2_32) = all_109_0_36
% 14.41/4.05 | (153) all_109_0_36 = all_95_1_31 | ~ r2_hidden(all_95_2_32, all_109_1_37)
% 14.41/4.05 |
% 14.41/4.05 | Instantiating (146) with all_111_0_38, all_111_1_39 yields:
% 14.41/4.05 | (154) k1_relat_1(all_0_11_11) = all_111_1_39 & k1_funct_1(all_0_11_11, all_95_2_32) = all_111_0_38 & (all_111_0_38 = all_95_0_30 | ~ r2_hidden(all_95_2_32, all_111_1_39))
% 14.41/4.05 |
% 14.41/4.05 | Applying alpha-rule on (154) yields:
% 14.41/4.05 | (155) k1_relat_1(all_0_11_11) = all_111_1_39
% 14.41/4.05 | (156) k1_funct_1(all_0_11_11, all_95_2_32) = all_111_0_38
% 14.41/4.05 | (157) all_111_0_38 = all_95_0_30 | ~ r2_hidden(all_95_2_32, all_111_1_39)
% 14.41/4.05 |
% 14.41/4.05 | Instantiating (145) with all_113_0_40, all_113_1_41 yields:
% 14.41/4.05 | (158) k1_relat_1(all_0_11_11) = all_113_1_41 & k1_funct_1(all_0_11_11, all_101_2_35) = all_113_0_40 & (all_113_0_40 = all_101_1_34 | ~ r2_hidden(all_101_2_35, all_113_1_41))
% 14.41/4.05 |
% 14.41/4.05 | Applying alpha-rule on (158) yields:
% 14.41/4.05 | (159) k1_relat_1(all_0_11_11) = all_113_1_41
% 14.41/4.05 | (160) k1_funct_1(all_0_11_11, all_101_2_35) = all_113_0_40
% 14.41/4.05 | (161) all_113_0_40 = all_101_1_34 | ~ r2_hidden(all_101_2_35, all_113_1_41)
% 14.41/4.05 |
% 14.41/4.05 | Instantiating (147) with all_115_0_42, all_115_1_43 yields:
% 14.41/4.05 | (162) k1_relat_1(all_0_11_11) = all_115_1_43 & k1_funct_1(all_0_11_11, all_101_2_35) = all_115_0_42 & (all_115_0_42 = all_101_0_33 | ~ r2_hidden(all_101_2_35, all_115_1_43))
% 14.41/4.05 |
% 14.41/4.05 | Applying alpha-rule on (162) yields:
% 14.41/4.05 | (163) k1_relat_1(all_0_11_11) = all_115_1_43
% 14.41/4.05 | (164) k1_funct_1(all_0_11_11, all_101_2_35) = all_115_0_42
% 14.41/4.05 | (165) all_115_0_42 = all_101_0_33 | ~ r2_hidden(all_101_2_35, all_115_1_43)
% 14.41/4.05 |
% 14.41/4.05 | Instantiating formula (70) with all_0_11_11, all_115_1_43, all_30_1_27 and discharging atoms k1_relat_1(all_0_11_11) = all_115_1_43, k1_relat_1(all_0_11_11) = all_30_1_27, yields:
% 14.41/4.05 | (166) all_115_1_43 = all_30_1_27
% 14.41/4.05 |
% 14.41/4.05 | Instantiating formula (70) with all_0_11_11, all_113_1_41, all_115_1_43 and discharging atoms k1_relat_1(all_0_11_11) = all_115_1_43, k1_relat_1(all_0_11_11) = all_113_1_41, yields:
% 14.41/4.05 | (167) all_115_1_43 = all_113_1_41
% 14.41/4.05 |
% 14.41/4.05 | Instantiating formula (70) with all_0_11_11, all_111_1_39, all_115_1_43 and discharging atoms k1_relat_1(all_0_11_11) = all_115_1_43, k1_relat_1(all_0_11_11) = all_111_1_39, yields:
% 14.41/4.05 | (168) all_115_1_43 = all_111_1_39
% 14.41/4.05 |
% 14.41/4.05 | Instantiating formula (70) with all_0_11_11, all_109_1_37, all_115_1_43 and discharging atoms k1_relat_1(all_0_11_11) = all_115_1_43, k1_relat_1(all_0_11_11) = all_109_1_37, yields:
% 14.41/4.05 | (169) all_115_1_43 = all_109_1_37
% 14.41/4.05 |
% 14.41/4.05 | Instantiating formula (60) with all_0_11_11, all_101_2_35, all_113_0_40, all_115_0_42 and discharging atoms k1_funct_1(all_0_11_11, all_101_2_35) = all_115_0_42, k1_funct_1(all_0_11_11, all_101_2_35) = all_113_0_40, yields:
% 14.41/4.05 | (170) all_115_0_42 = all_113_0_40
% 14.41/4.05 |
% 14.41/4.05 | Combining equations (169,167) yields a new equation:
% 14.41/4.05 | (171) all_113_1_41 = all_109_1_37
% 14.41/4.05 |
% 14.41/4.05 | Combining equations (166,167) yields a new equation:
% 14.41/4.05 | (172) all_113_1_41 = all_30_1_27
% 14.41/4.05 |
% 14.41/4.05 | Combining equations (168,167) yields a new equation:
% 14.41/4.05 | (173) all_113_1_41 = all_111_1_39
% 14.41/4.05 |
% 14.41/4.05 | Combining equations (171,173) yields a new equation:
% 14.41/4.05 | (174) all_111_1_39 = all_109_1_37
% 14.41/4.05 |
% 14.41/4.05 | Combining equations (172,173) yields a new equation:
% 14.41/4.05 | (175) all_111_1_39 = all_30_1_27
% 14.41/4.05 |
% 14.41/4.05 | Combining equations (175,174) yields a new equation:
% 14.41/4.05 | (176) all_109_1_37 = all_30_1_27
% 14.41/4.05 |
% 14.41/4.05 | Combining equations (176,174) yields a new equation:
% 14.41/4.05 | (175) all_111_1_39 = all_30_1_27
% 14.41/4.05 |
% 14.41/4.05 | Combining equations (175,173) yields a new equation:
% 14.41/4.05 | (172) all_113_1_41 = all_30_1_27
% 14.41/4.05 |
% 14.41/4.05 | Combining equations (172,167) yields a new equation:
% 14.41/4.05 | (166) all_115_1_43 = all_30_1_27
% 14.41/4.05 |
% 14.41/4.05 | Instantiating formula (44) with all_101_1_34, all_0_12_12, all_0_10_10, all_0_14_14, all_101_2_35 and discharging atoms a_2_0_closure3(all_0_14_14, all_0_10_10) = all_0_12_12, k1_funct_1(all_0_10_10, all_101_2_35) = all_101_1_34, m1_subset_1(all_101_2_35, all_0_14_14), m1_pboole(all_0_10_10, all_0_14_14), ~ v1_xboole_0(all_0_14_14), yields:
% 14.41/4.05 | (180) all_101_1_34 = k1_xboole_0 | r2_hidden(all_101_2_35, all_0_12_12)
% 14.41/4.05 |
% 14.41/4.05 | Instantiating formula (44) with all_101_0_33, all_0_12_12, all_0_13_13, all_0_14_14, all_101_2_35 and discharging atoms a_2_0_closure3(all_0_14_14, all_0_13_13) = all_0_12_12, k1_funct_1(all_0_13_13, all_101_2_35) = all_101_0_33, m1_subset_1(all_101_2_35, all_0_14_14), m1_pboole(all_0_13_13, all_0_14_14), ~ v1_xboole_0(all_0_14_14), yields:
% 14.41/4.05 | (181) all_101_0_33 = k1_xboole_0 | r2_hidden(all_101_2_35, all_0_12_12)
% 14.41/4.05 |
% 14.41/4.05 +-Applying beta-rule and splitting (161), into two cases.
% 14.41/4.05 |-Branch one:
% 14.41/4.05 | (182) ~ r2_hidden(all_101_2_35, all_113_1_41)
% 14.41/4.05 |
% 14.41/4.05 | From (172) and (182) follows:
% 14.41/4.05 | (183) ~ r2_hidden(all_101_2_35, all_30_1_27)
% 14.41/4.05 |
% 14.41/4.05 +-Applying beta-rule and splitting (181), into two cases.
% 14.41/4.05 |-Branch one:
% 14.41/4.05 | (184) r2_hidden(all_101_2_35, all_0_12_12)
% 14.41/4.05 |
% 14.41/4.05 | Instantiating formula (94) with all_101_2_35, all_30_1_27, all_0_12_12, all_0_14_14 and discharging atoms k3_xboole_0(all_0_14_14, all_0_12_12) = all_30_1_27, r2_hidden(all_101_2_35, all_0_12_12), r2_hidden(all_101_2_35, all_0_14_14), ~ r2_hidden(all_101_2_35, all_30_1_27), yields:
% 14.41/4.05 | (128) $false
% 14.41/4.05 |
% 14.41/4.05 |-The branch is then unsatisfiable
% 14.41/4.05 |-Branch two:
% 14.41/4.05 | (186) ~ r2_hidden(all_101_2_35, all_0_12_12)
% 14.41/4.05 | (187) all_101_0_33 = k1_xboole_0
% 14.41/4.05 |
% 14.41/4.05 | Equations (187) can reduce 141 to:
% 14.41/4.05 | (188) ~ (all_101_1_34 = k1_xboole_0)
% 14.41/4.05 |
% 14.41/4.05 | Simplifying 188 yields:
% 14.41/4.05 | (189) ~ (all_101_1_34 = k1_xboole_0)
% 14.41/4.05 |
% 14.41/4.05 +-Applying beta-rule and splitting (180), into two cases.
% 14.41/4.05 |-Branch one:
% 14.41/4.05 | (184) r2_hidden(all_101_2_35, all_0_12_12)
% 14.41/4.05 |
% 14.41/4.05 | Using (184) and (186) yields:
% 14.41/4.05 | (128) $false
% 14.41/4.05 |
% 14.41/4.05 |-The branch is then unsatisfiable
% 14.41/4.05 |-Branch two:
% 14.41/4.05 | (186) ~ r2_hidden(all_101_2_35, all_0_12_12)
% 14.41/4.05 | (193) all_101_1_34 = k1_xboole_0
% 14.41/4.05 |
% 14.41/4.05 | Equations (193) can reduce 189 to:
% 14.41/4.05 | (137) $false
% 14.41/4.05 |
% 14.41/4.05 |-The branch is then unsatisfiable
% 14.41/4.05 |-Branch two:
% 14.41/4.05 | (195) r2_hidden(all_101_2_35, all_113_1_41)
% 14.41/4.05 | (196) all_113_0_40 = all_101_1_34
% 14.41/4.05 |
% 14.41/4.05 | Combining equations (196,170) yields a new equation:
% 14.41/4.05 | (197) all_115_0_42 = all_101_1_34
% 14.41/4.05 |
% 14.41/4.05 | From (172) and (195) follows:
% 14.41/4.05 | (198) r2_hidden(all_101_2_35, all_30_1_27)
% 14.41/4.05 |
% 14.41/4.05 +-Applying beta-rule and splitting (165), into two cases.
% 14.41/4.05 |-Branch one:
% 14.41/4.05 | (199) ~ r2_hidden(all_101_2_35, all_115_1_43)
% 14.41/4.05 |
% 14.41/4.05 | From (166) and (199) follows:
% 14.41/4.05 | (183) ~ r2_hidden(all_101_2_35, all_30_1_27)
% 14.41/4.05 |
% 14.41/4.05 | Using (198) and (183) yields:
% 14.41/4.05 | (128) $false
% 14.41/4.05 |
% 14.41/4.05 |-The branch is then unsatisfiable
% 14.41/4.05 |-Branch two:
% 14.41/4.05 | (202) r2_hidden(all_101_2_35, all_115_1_43)
% 14.41/4.05 | (203) all_115_0_42 = all_101_0_33
% 14.41/4.05 |
% 14.41/4.05 | Combining equations (197,203) yields a new equation:
% 14.41/4.05 | (204) all_101_0_33 = all_101_1_34
% 14.41/4.05 |
% 14.41/4.05 | Equations (204) can reduce 141 to:
% 14.41/4.05 | (137) $false
% 14.41/4.05 |
% 14.41/4.05 |-The branch is then unsatisfiable
% 14.41/4.05 % SZS output end Proof for theBenchmark
% 14.41/4.05
% 14.41/4.05 3464ms
%------------------------------------------------------------------------------