TSTP Solution File: SEU110+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU110+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n024.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 08:46:39 EDT 2022
% Result : Theorem 7.39s 2.37s
% Output : Proof 30.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU110+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n024.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 : Sun Jun 19 20:44:02 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.51/0.57 ____ _
% 0.51/0.57 ___ / __ \_____(_)___ ________ __________
% 0.51/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.51/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.51/0.57
% 0.51/0.57 A Theorem Prover for First-Order Logic
% 0.51/0.58 (ePrincess v.1.0)
% 0.51/0.58
% 0.51/0.58 (c) Philipp Rümmer, 2009-2015
% 0.51/0.58 (c) Peter Backeman, 2014-2015
% 0.51/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.58 Bug reports to peter@backeman.se
% 0.51/0.58
% 0.51/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.58
% 0.51/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.51/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.52/0.92 Prover 0: Preprocessing ...
% 2.24/1.13 Prover 0: Warning: ignoring some quantifiers
% 2.24/1.16 Prover 0: Constructing countermodel ...
% 4.71/1.75 Prover 0: gave up
% 4.71/1.75 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.78/1.78 Prover 1: Preprocessing ...
% 5.23/1.90 Prover 1: Warning: ignoring some quantifiers
% 5.23/1.90 Prover 1: Constructing countermodel ...
% 7.39/2.37 Prover 1: proved (625ms)
% 7.39/2.37
% 7.39/2.37 No countermodel exists, formula is valid
% 7.39/2.37 % SZS status Theorem for theBenchmark
% 7.39/2.37
% 7.39/2.37 Generating proof ... Warning: ignoring some quantifiers
% 30.44/8.83 found it (size 141)
% 30.44/8.83
% 30.44/8.83 % SZS output start Proof for theBenchmark
% 30.44/8.83 Assumed formulas after preprocessing and simplification:
% 30.44/8.83 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ( ~ (v11 = 0) & ~ (v9 = 0) & ~ (v6 = 0) & ~ (v4 = 0) & cap_closed(v8) = 0 & subset(v2, v3) = v4 & subset(v0, v1) = 0 & finite_subsets(v1) = v3 & finite_subsets(v0) = v2 & diff_closed(v8) = 0 & preboolean(v8) = 0 & cup_closed(v8) = 0 & finite(v10) = 0 & empty(v10) = v11 & empty(v8) = v9 & empty(v7) = 0 & empty(v5) = v6 & empty(empty_set) = 0 & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (subset(v12, v14) = v15) | ~ (subset(v12, v13) = 0) | ? [v16] : ( ~ (v16 = 0) & subset(v13, v14) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (powerset(v13) = v14) | ~ (element(v12, v14) = v15) | ? [v16] : ( ~ (v16 = 0) & subset(v12, v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (subset(v15, v14) = v13) | ~ (subset(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (element(v15, v14) = v13) | ~ (element(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (in(v15, v14) = v13) | ~ (in(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (finite_subsets(v12) = v13) | ~ (preboolean(v13) = 0) | ~ (finite(v14) = v15) | ? [v16] : ? [v17] : (subset(v14, v12) = v17 & in(v14, v13) = v16 & ( ~ (v16 = 0) | (v17 = 0 & v15 = 0)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ~ (element(v13, v15) = 0) | ~ (in(v12, v13) = 0) | element(v12, v14) = 0) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ~ (element(v13, v15) = 0) | ~ (in(v12, v13) = 0) | ? [v16] : ( ~ (v16 = 0) & empty(v14) = v16)) & ! [v12] : ! [v13] : ! [v14] : (v14 = v13 | ~ (finite_subsets(v12) = v14) | ~ (preboolean(v13) = 0) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (subset(v15, v12) = v17 & finite(v15) = v18 & in(v15, v13) = v16 & ( ~ (v18 = 0) | ~ (v17 = 0) | ~ (v16 = 0)) & (v16 = 0 | (v18 = 0 & v17 = 0)))) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v12, v13) = v14) | ? [v15] : ? [v16] : ( ~ (v16 = 0) & in(v15, v13) = v16 & in(v15, v12) = 0)) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (in(v12, v13) = v14) | ? [v15] : ? [v16] : (element(v12, v13) = v15 & empty(v13) = v16 & ( ~ (v15 = 0) | v16 = 0))) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (relation(v14) = v13) | ~ (relation(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (function(v14) = v13) | ~ (function(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (one_to_one(v14) = v13) | ~ (one_to_one(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (epsilon_transitive(v14) = v13) | ~ (epsilon_transitive(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (epsilon_connected(v14) = v13) | ~ (epsilon_connected(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (ordinal(v14) = v13) | ~ (ordinal(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (natural(v14) = v13) | ~ (natural(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (cap_closed(v14) = v13) | ~ (cap_closed(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (finite_subsets(v14) = v13) | ~ (finite_subsets(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (powerset(v14) = v13) | ~ (powerset(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (diff_closed(v14) = v13) | ~ (diff_closed(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (preboolean(v14) = v13) | ~ (preboolean(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (cup_closed(v14) = v13) | ~ (cup_closed(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (finite(v14) = v13) | ~ (finite(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (empty(v14) = v13) | ~ (empty(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (subset(v12, v13) = 0) | ~ (in(v14, v12) = 0) | in(v14, v13) = 0) & ! [v12] : ! [v13] : ! [v14] : ( ~ (finite_subsets(v12) = v14) | ~ (element(v13, v14) = 0) | finite(v13) = 0) & ! [v12] : ! [v13] : ! [v14] : ( ~ (finite_subsets(v12) = v13) | ~ (preboolean(v13) = 0) | ~ (finite(v14) = 0) | ? [v15] : ? [v16] : (subset(v14, v12) = v15 & in(v14, v13) = v16 & ( ~ (v15 = 0) | v16 = 0))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ~ (element(v12, v14) = 0) | subset(v12, v13) = 0) & ! [v12] : ! [v13] : (v13 = v12 | ~ (empty(v13) = 0) | ~ (empty(v12) = 0)) & ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v12, v12) = v13)) & ! [v12] : ! [v13] : (v13 = 0 | ~ (finite(v12) = v13) | ? [v14] : ( ~ (v14 = 0) & empty(v12) = v14)) & ! [v12] : ! [v13] : ( ~ (finite_subsets(v12) = v13) | diff_closed(v13) = 0) & ! [v12] : ! [v13] : ( ~ (finite_subsets(v12) = v13) | preboolean(v13) = 0) & ! [v12] : ! [v13] : ( ~ (finite_subsets(v12) = v13) | cup_closed(v13) = 0) & ! [v12] : ! [v13] : ( ~ (finite_subsets(v12) = v13) | ? [v14] : ( ~ (v14 = 0) & empty(v13) = v14)) & ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | diff_closed(v13) = 0) & ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | preboolean(v13) = 0) & ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | cup_closed(v13) = 0) & ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & v15 = 0 & ~ (v16 = 0) & element(v14, v13) = 0 & finite(v14) = 0 & empty(v14) = v16) | (v14 = 0 & empty(v12) = 0))) & ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ((v15 = 0 & ~ (v16 = 0) & element(v14, v13) = 0 & empty(v14) = v16) | (v14 = 0 & empty(v12) = 0))) & ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ? [v14] : ( ~ (v14 = 0) & empty(v13) = v14)) & ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ? [v14] : (relation(v14) = 0 & function(v14) = 0 & one_to_one(v14) = 0 & epsilon_transitive(v14) = 0 & epsilon_connected(v14) = 0 & ordinal(v14) = 0 & natural(v14) = 0 & element(v14, v13) = 0 & finite(v14) = 0 & empty(v14) = 0)) & ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ? [v14] : (element(v14, v13) = 0 & empty(v14) = 0)) & ! [v12] : ! [v13] : ( ~ (diff_closed(v12) = v13) | ? [v14] : ? [v15] : (preboolean(v12) = v14 & cup_closed(v12) = v15 & ( ~ (v14 = 0) | (v15 = 0 & v13 = 0)))) & ! [v12] : ! [v13] : ( ~ (in(v12, v13) = 0) | element(v12, v13) = 0) & ! [v12] : ! [v13] : ( ~ (in(v12, v13) = 0) | ? [v14] : ( ~ (v14 = 0) & empty(v13) = v14)) & ! [v12] : ! [v13] : ( ~ (in(v12, v13) = 0) | ? [v14] : ( ~ (v14 = 0) & in(v13, v12) = v14)) & ! [v12] : (v12 = empty_set | ~ (empty(v12) = 0)) & ! [v12] : ( ~ (diff_closed(v12) = 0) | ? [v13] : ? [v14] : (preboolean(v12) = v14 & cup_closed(v12) = v13 & ( ~ (v13 = 0) | v14 = 0))) & ! [v12] : ( ~ (finite(v12) = 0) | ? [v13] : (powerset(v12) = v13 & ! [v14] : ( ~ (element(v14, v13) = 0) | finite(v14) = 0))) & ? [v12] : ? [v13] : element(v13, v12) = 0)
% 30.57/8.88 | 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 yields:
% 30.57/8.88 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_2_2 = 0) & ~ (all_0_5_5 = 0) & ~ (all_0_7_7 = 0) & cap_closed(all_0_3_3) = 0 & subset(all_0_9_9, all_0_8_8) = all_0_7_7 & subset(all_0_11_11, all_0_10_10) = 0 & finite_subsets(all_0_10_10) = all_0_8_8 & finite_subsets(all_0_11_11) = all_0_9_9 & diff_closed(all_0_3_3) = 0 & preboolean(all_0_3_3) = 0 & cup_closed(all_0_3_3) = 0 & finite(all_0_1_1) = 0 & empty(all_0_1_1) = all_0_0_0 & empty(all_0_3_3) = all_0_2_2 & empty(all_0_4_4) = 0 & empty(all_0_6_6) = all_0_5_5 & empty(empty_set) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (finite_subsets(v0) = v1) | ~ (preboolean(v1) = 0) | ~ (finite(v2) = v3) | ? [v4] : ? [v5] : (subset(v2, v0) = v5 & in(v2, v1) = v4 & ( ~ (v4 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (finite_subsets(v0) = v2) | ~ (preboolean(v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (subset(v3, v0) = v5 & finite(v3) = v6 & in(v3, v1) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) & (v4 = 0 | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : (element(v0, v1) = v3 & empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_connected(v2) = v1) | ~ (epsilon_connected(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (natural(v2) = v1) | ~ (natural(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cap_closed(v2) = v1) | ~ (cap_closed(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (finite_subsets(v2) = v1) | ~ (finite_subsets(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (diff_closed(v2) = v1) | ~ (diff_closed(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (preboolean(v2) = v1) | ~ (preboolean(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cup_closed(v2) = v1) | ~ (cup_closed(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (finite(v2) = v1) | ~ (finite(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (finite_subsets(v0) = v2) | ~ (element(v1, v2) = 0) | finite(v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (finite_subsets(v0) = v1) | ~ (preboolean(v1) = 0) | ~ (finite(v2) = 0) | ? [v3] : ? [v4] : (subset(v2, v0) = v3 & in(v2, v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (finite(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | diff_closed(v1) = 0) & ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | preboolean(v1) = 0) & ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | cup_closed(v1) = 0) & ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | diff_closed(v1) = 0) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | preboolean(v1) = 0) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | cup_closed(v1) = 0) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & finite(v2) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (relation(v2) = 0 & function(v2) = 0 & one_to_one(v2) = 0 & epsilon_transitive(v2) = 0 & epsilon_connected(v2) = 0 & ordinal(v2) = 0 & natural(v2) = 0 & element(v2, v1) = 0 & finite(v2) = 0 & empty(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (diff_closed(v0) = v1) | ? [v2] : ? [v3] : (preboolean(v0) = v2 & cup_closed(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ! [v0] : ( ~ (diff_closed(v0) = 0) | ? [v1] : ? [v2] : (preboolean(v0) = v2 & cup_closed(v0) = v1 & ( ~ (v1 = 0) | v2 = 0))) & ! [v0] : ( ~ (finite(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ( ~ (element(v2, v1) = 0) | finite(v2) = 0))) & ? [v0] : ? [v1] : element(v1, v0) = 0
% 30.57/8.90 |
% 30.57/8.90 | Applying alpha-rule on (1) yields:
% 30.57/8.90 | (2) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 30.57/8.90 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 30.57/8.90 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (preboolean(v2) = v1) | ~ (preboolean(v2) = v0))
% 30.57/8.90 | (5) empty(empty_set) = 0
% 30.57/8.90 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 30.57/8.90 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (finite_subsets(v0) = v2) | ~ (element(v1, v2) = 0) | finite(v1) = 0)
% 30.57/8.90 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0))
% 30.57/8.90 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4))
% 30.57/8.90 | (10) finite(all_0_1_1) = 0
% 30.57/8.90 | (11) ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | cup_closed(v1) = 0)
% 30.57/8.90 | (12) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | preboolean(v1) = 0)
% 30.57/8.90 | (13) ~ (all_0_7_7 = 0)
% 30.57/8.90 | (14) ! [v0] : ( ~ (finite(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ( ~ (element(v2, v1) = 0) | finite(v2) = 0)))
% 30.57/8.90 | (15) cap_closed(all_0_3_3) = 0
% 30.57/8.90 | (16) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 30.57/8.90 | (17) subset(all_0_11_11, all_0_10_10) = 0
% 30.57/8.90 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0))
% 30.57/8.90 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 30.57/8.90 | (20) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 30.57/8.90 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cap_closed(v2) = v1) | ~ (cap_closed(v2) = v0))
% 30.57/8.90 | (22) ? [v0] : ? [v1] : element(v1, v0) = 0
% 30.57/8.90 | (23) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & finite(v2) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0)))
% 30.57/8.90 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 30.57/8.90 | (25) ~ (all_0_2_2 = 0)
% 30.57/8.90 | (26) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : (element(v0, v1) = v3 & empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0)))
% 30.57/8.90 | (27) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 30.57/8.90 | (28) cup_closed(all_0_3_3) = 0
% 30.57/8.90 | (29) finite_subsets(all_0_11_11) = all_0_9_9
% 30.57/8.90 | (30) ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | diff_closed(v1) = 0)
% 30.57/8.90 | (31) ! [v0] : ( ~ (diff_closed(v0) = 0) | ? [v1] : ? [v2] : (preboolean(v0) = v2 & cup_closed(v0) = v1 & ( ~ (v1 = 0) | v2 = 0)))
% 30.57/8.90 | (32) ~ (all_0_0_0 = 0)
% 30.57/8.90 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 30.57/8.90 | (34) preboolean(all_0_3_3) = 0
% 30.57/8.90 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (diff_closed(v2) = v1) | ~ (diff_closed(v2) = v0))
% 30.57/8.90 | (36) finite_subsets(all_0_10_10) = all_0_8_8
% 30.57/8.91 | (37) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (natural(v2) = v1) | ~ (natural(v2) = v0))
% 30.57/8.91 | (38) ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 30.57/8.91 | (39) ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | preboolean(v1) = 0)
% 30.57/8.91 | (40) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cup_closed(v2) = v1) | ~ (cup_closed(v2) = v0))
% 30.57/8.91 | (41) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (finite_subsets(v0) = v2) | ~ (preboolean(v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (subset(v3, v0) = v5 & finite(v3) = v6 & in(v3, v1) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) & (v4 = 0 | (v6 = 0 & v5 = 0))))
% 30.57/8.91 | (42) diff_closed(all_0_3_3) = 0
% 30.57/8.91 | (43) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | diff_closed(v1) = 0)
% 30.57/8.91 | (44) empty(all_0_6_6) = all_0_5_5
% 30.57/8.91 | (45) ! [v0] : ! [v1] : (v1 = 0 | ~ (finite(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 30.57/8.91 | (46) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (finite_subsets(v2) = v1) | ~ (finite_subsets(v2) = v0))
% 30.57/8.91 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 30.57/8.91 | (48) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 30.57/8.91 | (49) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (relation(v2) = 0 & function(v2) = 0 & one_to_one(v2) = 0 & epsilon_transitive(v2) = 0 & epsilon_connected(v2) = 0 & ordinal(v2) = 0 & natural(v2) = 0 & element(v2, v1) = 0 & finite(v2) = 0 & empty(v2) = 0))
% 30.57/8.91 | (50) subset(all_0_9_9, all_0_8_8) = all_0_7_7
% 30.57/8.91 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 30.57/8.91 | (52) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 30.57/8.91 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (finite_subsets(v0) = v1) | ~ (preboolean(v1) = 0) | ~ (finite(v2) = v3) | ? [v4] : ? [v5] : (subset(v2, v0) = v5 & in(v2, v1) = v4 & ( ~ (v4 = 0) | (v5 = 0 & v3 = 0))))
% 30.57/8.91 | (54) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0)))
% 30.57/8.91 | (55) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 30.57/8.91 | (56) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_connected(v2) = v1) | ~ (epsilon_connected(v2) = v0))
% 30.57/8.91 | (57) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0))
% 30.57/8.91 | (58) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 30.57/8.91 | (59) empty(all_0_3_3) = all_0_2_2
% 30.57/8.91 | (60) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (finite(v2) = v1) | ~ (finite(v2) = v0))
% 30.57/8.91 | (61) empty(all_0_1_1) = all_0_0_0
% 30.57/8.91 | (62) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | cup_closed(v1) = 0)
% 30.57/8.91 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 30.57/8.91 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0)
% 30.57/8.91 | (65) ! [v0] : ! [v1] : ! [v2] : ( ~ (finite_subsets(v0) = v1) | ~ (preboolean(v1) = 0) | ~ (finite(v2) = 0) | ? [v3] : ? [v4] : (subset(v2, v0) = v3 & in(v2, v1) = v4 & ( ~ (v3 = 0) | v4 = 0)))
% 30.57/8.91 | (66) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 30.57/8.91 | (67) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 30.57/8.91 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 30.57/8.91 | (69) ! [v0] : ! [v1] : ( ~ (diff_closed(v0) = v1) | ? [v2] : ? [v3] : (preboolean(v0) = v2 & cup_closed(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0))))
% 30.57/8.91 | (70) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0))
% 30.57/8.91 | (71) empty(all_0_4_4) = 0
% 30.57/8.91 | (72) ~ (all_0_5_5 = 0)
% 30.57/8.91 |
% 30.57/8.92 | Instantiating formula (27) with all_0_7_7, all_0_9_9 yields:
% 30.57/8.92 | (73) all_0_7_7 = 0 | ~ (subset(all_0_9_9, all_0_9_9) = all_0_7_7)
% 30.57/8.92 |
% 30.57/8.92 +-Applying beta-rule and splitting (73), into two cases.
% 30.57/8.92 |-Branch one:
% 30.57/8.92 | (74) ~ (subset(all_0_9_9, all_0_9_9) = all_0_7_7)
% 30.57/8.92 |
% 30.57/8.92 | Using (50) and (74) yields:
% 30.57/8.92 | (75) ~ (all_0_8_8 = all_0_9_9)
% 30.57/8.92 |
% 30.57/8.92 | Instantiating formula (16) with all_0_7_7, all_0_8_8, all_0_9_9 and discharging atoms subset(all_0_9_9, all_0_8_8) = all_0_7_7, yields:
% 30.57/8.92 | (76) all_0_7_7 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_8_8) = v1 & in(v0, all_0_9_9) = 0)
% 30.57/8.92 |
% 30.57/8.92 | Instantiating formula (39) with all_0_8_8, all_0_10_10 and discharging atoms finite_subsets(all_0_10_10) = all_0_8_8, yields:
% 30.57/8.92 | (77) preboolean(all_0_8_8) = 0
% 30.57/8.92 |
% 30.57/8.92 | Instantiating formula (39) with all_0_9_9, all_0_11_11 and discharging atoms finite_subsets(all_0_11_11) = all_0_9_9, yields:
% 30.57/8.92 | (78) preboolean(all_0_9_9) = 0
% 30.57/8.92 |
% 30.57/8.92 | Instantiating formula (53) with 0, all_0_1_1, all_0_8_8, all_0_10_10 and discharging atoms finite_subsets(all_0_10_10) = all_0_8_8, finite(all_0_1_1) = 0, yields:
% 30.57/8.92 | (79) ~ (preboolean(all_0_8_8) = 0) | ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_10_10) = v1 & in(all_0_1_1, all_0_8_8) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 30.57/8.92 |
% 30.57/8.92 | Instantiating formula (53) with 0, all_0_1_1, all_0_9_9, all_0_11_11 and discharging atoms finite_subsets(all_0_11_11) = all_0_9_9, finite(all_0_1_1) = 0, yields:
% 30.57/8.92 | (80) ~ (preboolean(all_0_9_9) = 0) | ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_11_11) = v1 & in(all_0_1_1, all_0_9_9) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 30.57/8.92 |
% 30.57/8.92 | Instantiating formula (65) with all_0_1_1, all_0_8_8, all_0_10_10 and discharging atoms finite_subsets(all_0_10_10) = all_0_8_8, finite(all_0_1_1) = 0, yields:
% 30.57/8.92 | (81) ~ (preboolean(all_0_8_8) = 0) | ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_10_10) = v0 & in(all_0_1_1, all_0_8_8) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 30.57/8.92 |
% 30.57/8.92 | Instantiating formula (65) with all_0_1_1, all_0_9_9, all_0_11_11 and discharging atoms finite_subsets(all_0_11_11) = all_0_9_9, finite(all_0_1_1) = 0, yields:
% 30.57/8.92 | (82) ~ (preboolean(all_0_9_9) = 0) | ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_11_11) = v0 & in(all_0_1_1, all_0_9_9) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 30.57/8.92 |
% 30.57/8.92 +-Applying beta-rule and splitting (79), into two cases.
% 30.57/8.92 |-Branch one:
% 30.57/8.92 | (83) ~ (preboolean(all_0_8_8) = 0)
% 30.57/8.92 |
% 30.57/8.92 | Using (77) and (83) yields:
% 30.57/8.92 | (84) $false
% 30.57/8.92 |
% 30.57/8.92 |-The branch is then unsatisfiable
% 30.57/8.92 |-Branch two:
% 30.57/8.92 | (77) preboolean(all_0_8_8) = 0
% 30.57/8.92 | (86) ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_10_10) = v1 & in(all_0_1_1, all_0_8_8) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 30.57/8.92 |
% 30.57/8.92 +-Applying beta-rule and splitting (80), into two cases.
% 30.57/8.92 |-Branch one:
% 30.57/8.92 | (87) ~ (preboolean(all_0_9_9) = 0)
% 30.57/8.92 |
% 30.57/8.92 | Using (78) and (87) yields:
% 30.57/8.92 | (84) $false
% 30.57/8.92 |
% 30.57/8.92 |-The branch is then unsatisfiable
% 30.57/8.92 |-Branch two:
% 30.57/8.92 | (78) preboolean(all_0_9_9) = 0
% 30.57/8.92 | (90) ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_11_11) = v1 & in(all_0_1_1, all_0_9_9) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 30.57/8.92 |
% 30.57/8.92 +-Applying beta-rule and splitting (81), into two cases.
% 30.57/8.92 |-Branch one:
% 30.57/8.92 | (83) ~ (preboolean(all_0_8_8) = 0)
% 30.57/8.92 |
% 30.57/8.92 | Using (77) and (83) yields:
% 30.57/8.92 | (84) $false
% 30.57/8.92 |
% 30.57/8.92 |-The branch is then unsatisfiable
% 30.57/8.92 |-Branch two:
% 30.57/8.92 | (77) preboolean(all_0_8_8) = 0
% 30.57/8.92 | (94) ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_10_10) = v0 & in(all_0_1_1, all_0_8_8) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 30.57/8.92 |
% 30.57/8.92 +-Applying beta-rule and splitting (82), into two cases.
% 30.57/8.92 |-Branch one:
% 30.57/8.92 | (87) ~ (preboolean(all_0_9_9) = 0)
% 30.57/8.92 |
% 30.57/8.92 | Using (78) and (87) yields:
% 30.57/8.92 | (84) $false
% 30.57/8.92 |
% 30.57/8.92 |-The branch is then unsatisfiable
% 30.57/8.92 |-Branch two:
% 30.57/8.92 | (78) preboolean(all_0_9_9) = 0
% 30.57/8.92 | (98) ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_11_11) = v0 & in(all_0_1_1, all_0_9_9) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 30.57/8.92 |
% 30.57/8.92 +-Applying beta-rule and splitting (76), into two cases.
% 30.57/8.92 |-Branch one:
% 30.57/8.92 | (99) all_0_7_7 = 0
% 30.57/8.92 |
% 30.57/8.92 | Equations (99) can reduce 13 to:
% 30.57/8.92 | (100) $false
% 30.57/8.92 |
% 30.57/8.92 |-The branch is then unsatisfiable
% 30.57/8.92 |-Branch two:
% 30.57/8.92 | (13) ~ (all_0_7_7 = 0)
% 30.57/8.92 | (102) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_8_8) = v1 & in(v0, all_0_9_9) = 0)
% 30.57/8.92 |
% 30.57/8.92 | Instantiating (102) with all_54_0_25, all_54_1_26 yields:
% 30.57/8.92 | (103) ~ (all_54_0_25 = 0) & in(all_54_1_26, all_0_8_8) = all_54_0_25 & in(all_54_1_26, all_0_9_9) = 0
% 30.57/8.92 |
% 30.57/8.92 | Applying alpha-rule on (103) yields:
% 30.57/8.92 | (104) ~ (all_54_0_25 = 0)
% 30.57/8.92 | (105) in(all_54_1_26, all_0_8_8) = all_54_0_25
% 30.57/8.93 | (106) in(all_54_1_26, all_0_9_9) = 0
% 30.57/8.93 |
% 30.57/8.93 | Instantiating formula (41) with all_0_9_9, all_0_8_8, all_0_11_11 and discharging atoms finite_subsets(all_0_11_11) = all_0_9_9, preboolean(all_0_8_8) = 0, yields:
% 30.57/8.93 | (107) all_0_8_8 = all_0_9_9 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (subset(v0, all_0_11_11) = v2 & finite(v0) = v3 & in(v0, all_0_8_8) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0)) & (v1 = 0 | (v3 = 0 & v2 = 0)))
% 30.57/8.93 |
% 30.57/8.93 | Instantiating formula (41) with all_0_8_8, all_0_9_9, all_0_10_10 and discharging atoms finite_subsets(all_0_10_10) = all_0_8_8, preboolean(all_0_9_9) = 0, yields:
% 30.57/8.93 | (108) all_0_8_8 = all_0_9_9 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (subset(v0, all_0_10_10) = v2 & finite(v0) = v3 & in(v0, all_0_9_9) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0)) & (v1 = 0 | (v3 = 0 & v2 = 0)))
% 30.57/8.93 |
% 30.57/8.93 | Instantiating formula (26) with all_54_0_25, all_0_8_8, all_54_1_26 and discharging atoms in(all_54_1_26, all_0_8_8) = all_54_0_25, yields:
% 30.57/8.93 | (109) all_54_0_25 = 0 | ? [v0] : ? [v1] : (element(all_54_1_26, all_0_8_8) = v0 & empty(all_0_8_8) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 30.57/8.93 |
% 30.57/8.93 | Instantiating formula (55) with all_0_9_9, all_54_1_26 and discharging atoms in(all_54_1_26, all_0_9_9) = 0, yields:
% 30.57/8.93 | (110) element(all_54_1_26, all_0_9_9) = 0
% 30.57/8.93 |
% 30.93/8.93 +-Applying beta-rule and splitting (107), into two cases.
% 30.93/8.93 |-Branch one:
% 30.93/8.93 | (111) all_0_8_8 = all_0_9_9
% 30.93/8.93 |
% 30.93/8.93 | Equations (111) can reduce 75 to:
% 30.93/8.93 | (100) $false
% 30.93/8.93 |
% 30.93/8.93 |-The branch is then unsatisfiable
% 30.93/8.93 |-Branch two:
% 30.93/8.93 | (75) ~ (all_0_8_8 = all_0_9_9)
% 30.93/8.93 | (114) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (subset(v0, all_0_11_11) = v2 & finite(v0) = v3 & in(v0, all_0_8_8) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0)) & (v1 = 0 | (v3 = 0 & v2 = 0)))
% 30.93/8.93 |
% 30.93/8.93 +-Applying beta-rule and splitting (109), into two cases.
% 30.93/8.93 |-Branch one:
% 30.93/8.93 | (115) all_54_0_25 = 0
% 30.93/8.93 |
% 30.93/8.93 | Equations (115) can reduce 104 to:
% 30.93/8.93 | (100) $false
% 30.93/8.93 |
% 30.93/8.93 |-The branch is then unsatisfiable
% 30.93/8.93 |-Branch two:
% 30.93/8.93 | (104) ~ (all_54_0_25 = 0)
% 30.93/8.93 | (118) ? [v0] : ? [v1] : (element(all_54_1_26, all_0_8_8) = v0 & empty(all_0_8_8) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 30.93/8.93 |
% 30.93/8.93 +-Applying beta-rule and splitting (108), into two cases.
% 30.93/8.93 |-Branch one:
% 30.93/8.93 | (111) all_0_8_8 = all_0_9_9
% 30.93/8.93 |
% 30.93/8.93 | Equations (111) can reduce 75 to:
% 30.93/8.93 | (100) $false
% 30.93/8.93 |
% 30.93/8.93 |-The branch is then unsatisfiable
% 30.93/8.93 |-Branch two:
% 30.93/8.93 | (75) ~ (all_0_8_8 = all_0_9_9)
% 30.93/8.93 | (122) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (subset(v0, all_0_10_10) = v2 & finite(v0) = v3 & in(v0, all_0_9_9) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0)) & (v1 = 0 | (v3 = 0 & v2 = 0)))
% 30.93/8.93 |
% 30.93/8.93 | Instantiating (122) with all_98_0_44, all_98_1_45, all_98_2_46, all_98_3_47 yields:
% 30.93/8.93 | (123) subset(all_98_3_47, all_0_10_10) = all_98_1_45 & finite(all_98_3_47) = all_98_0_44 & in(all_98_3_47, all_0_9_9) = all_98_2_46 & ( ~ (all_98_0_44 = 0) | ~ (all_98_1_45 = 0) | ~ (all_98_2_46 = 0)) & (all_98_2_46 = 0 | (all_98_0_44 = 0 & all_98_1_45 = 0))
% 30.93/8.93 |
% 30.93/8.93 | Applying alpha-rule on (123) yields:
% 30.93/8.93 | (124) in(all_98_3_47, all_0_9_9) = all_98_2_46
% 30.93/8.93 | (125) subset(all_98_3_47, all_0_10_10) = all_98_1_45
% 30.93/8.93 | (126) ~ (all_98_0_44 = 0) | ~ (all_98_1_45 = 0) | ~ (all_98_2_46 = 0)
% 30.93/8.93 | (127) all_98_2_46 = 0 | (all_98_0_44 = 0 & all_98_1_45 = 0)
% 30.93/8.93 | (128) finite(all_98_3_47) = all_98_0_44
% 30.93/8.93 |
% 30.93/8.93 | Instantiating formula (63) with all_0_11_11, all_0_10_10, all_98_1_45, 0 and discharging atoms subset(all_0_11_11, all_0_10_10) = 0, yields:
% 30.93/8.93 | (129) all_98_1_45 = 0 | ~ (subset(all_0_11_11, all_0_10_10) = all_98_1_45)
% 30.93/8.93 |
% 30.93/8.93 | Instantiating formula (68) with all_54_1_26, all_0_9_9, all_98_2_46, 0 and discharging atoms in(all_54_1_26, all_0_9_9) = 0, yields:
% 30.93/8.93 | (130) all_98_2_46 = 0 | ~ (in(all_54_1_26, all_0_9_9) = all_98_2_46)
% 30.93/8.93 |
% 30.93/8.93 | Instantiating formula (7) with all_0_9_9, all_54_1_26, all_0_11_11 and discharging atoms finite_subsets(all_0_11_11) = all_0_9_9, element(all_54_1_26, all_0_9_9) = 0, yields:
% 30.93/8.93 | (131) finite(all_54_1_26) = 0
% 30.93/8.93 |
% 30.93/8.93 | Instantiating formula (53) with all_98_0_44, all_98_3_47, all_0_8_8, all_0_10_10 and discharging atoms finite_subsets(all_0_10_10) = all_0_8_8, preboolean(all_0_8_8) = 0, finite(all_98_3_47) = all_98_0_44, yields:
% 30.93/8.93 | (132) ? [v0] : ? [v1] : (subset(all_98_3_47, all_0_10_10) = v1 & in(all_98_3_47, all_0_8_8) = v0 & ( ~ (v0 = 0) | (v1 = 0 & all_98_0_44 = 0)))
% 30.93/8.93 |
% 30.93/8.93 | Instantiating formula (53) with all_98_0_44, all_98_3_47, all_0_9_9, all_0_11_11 and discharging atoms finite_subsets(all_0_11_11) = all_0_9_9, preboolean(all_0_9_9) = 0, finite(all_98_3_47) = all_98_0_44, yields:
% 30.93/8.93 | (133) ? [v0] : ? [v1] : (subset(all_98_3_47, all_0_11_11) = v1 & in(all_98_3_47, all_0_9_9) = v0 & ( ~ (v0 = 0) | (v1 = 0 & all_98_0_44 = 0)))
% 30.93/8.93 |
% 30.93/8.93 | Instantiating (133) with all_140_0_70, all_140_1_71 yields:
% 30.93/8.93 | (134) subset(all_98_3_47, all_0_11_11) = all_140_0_70 & in(all_98_3_47, all_0_9_9) = all_140_1_71 & ( ~ (all_140_1_71 = 0) | (all_140_0_70 = 0 & all_98_0_44 = 0))
% 30.93/8.93 |
% 30.93/8.93 | Applying alpha-rule on (134) yields:
% 30.93/8.93 | (135) subset(all_98_3_47, all_0_11_11) = all_140_0_70
% 30.93/8.93 | (136) in(all_98_3_47, all_0_9_9) = all_140_1_71
% 30.93/8.93 | (137) ~ (all_140_1_71 = 0) | (all_140_0_70 = 0 & all_98_0_44 = 0)
% 30.93/8.93 |
% 30.93/8.94 | Instantiating (132) with all_142_0_72, all_142_1_73 yields:
% 30.93/8.94 | (138) subset(all_98_3_47, all_0_10_10) = all_142_0_72 & in(all_98_3_47, all_0_8_8) = all_142_1_73 & ( ~ (all_142_1_73 = 0) | (all_142_0_72 = 0 & all_98_0_44 = 0))
% 30.93/8.94 |
% 30.93/8.94 | Applying alpha-rule on (138) yields:
% 30.93/8.94 | (139) subset(all_98_3_47, all_0_10_10) = all_142_0_72
% 30.93/8.94 | (140) in(all_98_3_47, all_0_8_8) = all_142_1_73
% 30.93/8.94 | (141) ~ (all_142_1_73 = 0) | (all_142_0_72 = 0 & all_98_0_44 = 0)
% 30.93/8.94 |
% 30.93/8.94 | Instantiating formula (63) with all_98_3_47, all_0_10_10, all_142_0_72, all_98_1_45 and discharging atoms subset(all_98_3_47, all_0_10_10) = all_142_0_72, subset(all_98_3_47, all_0_10_10) = all_98_1_45, yields:
% 30.93/8.94 | (142) all_142_0_72 = all_98_1_45
% 30.93/8.94 |
% 30.93/8.94 | Instantiating formula (68) with all_98_3_47, all_0_9_9, all_140_1_71, all_98_2_46 and discharging atoms in(all_98_3_47, all_0_9_9) = all_140_1_71, in(all_98_3_47, all_0_9_9) = all_98_2_46, yields:
% 30.93/8.94 | (143) all_140_1_71 = all_98_2_46
% 30.93/8.94 |
% 30.93/8.94 | From (142) and (139) follows:
% 30.93/8.94 | (125) subset(all_98_3_47, all_0_10_10) = all_98_1_45
% 30.93/8.94 |
% 30.93/8.94 | Instantiating formula (9) with all_98_1_45, all_0_10_10, all_0_11_11, all_98_3_47 and discharging atoms subset(all_98_3_47, all_0_10_10) = all_98_1_45, yields:
% 30.93/8.94 | (145) all_98_1_45 = 0 | ~ (subset(all_98_3_47, all_0_11_11) = 0) | ? [v0] : ( ~ (v0 = 0) & subset(all_0_11_11, all_0_10_10) = v0)
% 30.93/8.94 |
% 30.93/8.94 | Instantiating formula (53) with 0, all_54_1_26, all_0_8_8, all_0_10_10 and discharging atoms finite_subsets(all_0_10_10) = all_0_8_8, preboolean(all_0_8_8) = 0, finite(all_54_1_26) = 0, yields:
% 30.93/8.94 | (146) ? [v0] : ? [v1] : (subset(all_54_1_26, all_0_10_10) = v1 & in(all_54_1_26, all_0_8_8) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 30.93/8.94 |
% 30.93/8.94 | Instantiating formula (53) with 0, all_54_1_26, all_0_9_9, all_0_11_11 and discharging atoms finite_subsets(all_0_11_11) = all_0_9_9, preboolean(all_0_9_9) = 0, finite(all_54_1_26) = 0, yields:
% 30.93/8.94 | (147) ? [v0] : ? [v1] : (subset(all_54_1_26, all_0_11_11) = v1 & in(all_54_1_26, all_0_9_9) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 30.93/8.94 |
% 30.93/8.94 | Instantiating formula (65) with all_54_1_26, all_0_8_8, all_0_10_10 and discharging atoms finite_subsets(all_0_10_10) = all_0_8_8, preboolean(all_0_8_8) = 0, finite(all_54_1_26) = 0, yields:
% 30.93/8.94 | (148) ? [v0] : ? [v1] : (subset(all_54_1_26, all_0_10_10) = v0 & in(all_54_1_26, all_0_8_8) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 30.93/8.94 |
% 30.93/8.94 | Instantiating formula (65) with all_54_1_26, all_0_9_9, all_0_11_11 and discharging atoms finite_subsets(all_0_11_11) = all_0_9_9, preboolean(all_0_9_9) = 0, finite(all_54_1_26) = 0, yields:
% 30.93/8.94 | (149) ? [v0] : ? [v1] : (subset(all_54_1_26, all_0_11_11) = v0 & in(all_54_1_26, all_0_9_9) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 30.93/8.94 |
% 30.93/8.94 | Instantiating (149) with all_260_0_84, all_260_1_85 yields:
% 30.93/8.94 | (150) subset(all_54_1_26, all_0_11_11) = all_260_1_85 & in(all_54_1_26, all_0_9_9) = all_260_0_84 & ( ~ (all_260_1_85 = 0) | all_260_0_84 = 0)
% 30.93/8.94 |
% 30.93/8.94 | Applying alpha-rule on (150) yields:
% 30.93/8.94 | (151) subset(all_54_1_26, all_0_11_11) = all_260_1_85
% 30.93/8.94 | (152) in(all_54_1_26, all_0_9_9) = all_260_0_84
% 30.93/8.94 | (153) ~ (all_260_1_85 = 0) | all_260_0_84 = 0
% 30.93/8.94 |
% 30.93/8.94 | Instantiating (148) with all_262_0_86, all_262_1_87 yields:
% 30.93/8.94 | (154) subset(all_54_1_26, all_0_10_10) = all_262_1_87 & in(all_54_1_26, all_0_8_8) = all_262_0_86 & ( ~ (all_262_1_87 = 0) | all_262_0_86 = 0)
% 30.93/8.94 |
% 30.93/8.94 | Applying alpha-rule on (154) yields:
% 30.93/8.94 | (155) subset(all_54_1_26, all_0_10_10) = all_262_1_87
% 30.93/8.94 | (156) in(all_54_1_26, all_0_8_8) = all_262_0_86
% 30.93/8.94 | (157) ~ (all_262_1_87 = 0) | all_262_0_86 = 0
% 30.93/8.94 |
% 30.93/8.94 | Instantiating (147) with all_264_0_88, all_264_1_89 yields:
% 30.93/8.94 | (158) subset(all_54_1_26, all_0_11_11) = all_264_0_88 & in(all_54_1_26, all_0_9_9) = all_264_1_89 & ( ~ (all_264_1_89 = 0) | all_264_0_88 = 0)
% 30.93/8.94 |
% 30.93/8.94 | Applying alpha-rule on (158) yields:
% 30.93/8.94 | (159) subset(all_54_1_26, all_0_11_11) = all_264_0_88
% 30.93/8.94 | (160) in(all_54_1_26, all_0_9_9) = all_264_1_89
% 30.93/8.94 | (161) ~ (all_264_1_89 = 0) | all_264_0_88 = 0
% 30.93/8.94 |
% 30.93/8.94 | Instantiating (146) with all_266_0_90, all_266_1_91 yields:
% 30.93/8.94 | (162) subset(all_54_1_26, all_0_10_10) = all_266_0_90 & in(all_54_1_26, all_0_8_8) = all_266_1_91 & ( ~ (all_266_1_91 = 0) | all_266_0_90 = 0)
% 30.93/8.94 |
% 30.93/8.94 | Applying alpha-rule on (162) yields:
% 30.93/8.94 | (163) subset(all_54_1_26, all_0_10_10) = all_266_0_90
% 30.93/8.94 | (164) in(all_54_1_26, all_0_8_8) = all_266_1_91
% 30.93/8.94 | (165) ~ (all_266_1_91 = 0) | all_266_0_90 = 0
% 30.93/8.94 |
% 30.93/8.94 | Instantiating formula (63) with all_54_1_26, all_0_10_10, all_262_1_87, all_266_0_90 and discharging atoms subset(all_54_1_26, all_0_10_10) = all_266_0_90, subset(all_54_1_26, all_0_10_10) = all_262_1_87, yields:
% 30.93/8.94 | (166) all_266_0_90 = all_262_1_87
% 30.93/8.95 |
% 30.93/8.95 | Instantiating formula (63) with all_54_1_26, all_0_11_11, all_260_1_85, all_264_0_88 and discharging atoms subset(all_54_1_26, all_0_11_11) = all_264_0_88, subset(all_54_1_26, all_0_11_11) = all_260_1_85, yields:
% 30.93/8.95 | (167) all_264_0_88 = all_260_1_85
% 30.93/8.95 |
% 30.93/8.95 | Instantiating formula (68) with all_54_1_26, all_0_8_8, all_266_1_91, all_54_0_25 and discharging atoms in(all_54_1_26, all_0_8_8) = all_266_1_91, in(all_54_1_26, all_0_8_8) = all_54_0_25, yields:
% 30.93/8.95 | (168) all_266_1_91 = all_54_0_25
% 30.93/8.95 |
% 30.93/8.95 | Instantiating formula (68) with all_54_1_26, all_0_8_8, all_262_0_86, all_266_1_91 and discharging atoms in(all_54_1_26, all_0_8_8) = all_266_1_91, in(all_54_1_26, all_0_8_8) = all_262_0_86, yields:
% 30.93/8.95 | (169) all_266_1_91 = all_262_0_86
% 30.93/8.95 |
% 30.93/8.95 | Instantiating formula (68) with all_54_1_26, all_0_9_9, all_264_1_89, 0 and discharging atoms in(all_54_1_26, all_0_9_9) = all_264_1_89, in(all_54_1_26, all_0_9_9) = 0, yields:
% 30.93/8.95 | (170) all_264_1_89 = 0
% 30.93/8.95 |
% 30.93/8.95 | Instantiating formula (68) with all_54_1_26, all_0_9_9, all_260_0_84, all_264_1_89 and discharging atoms in(all_54_1_26, all_0_9_9) = all_264_1_89, in(all_54_1_26, all_0_9_9) = all_260_0_84, yields:
% 30.93/8.95 | (171) all_264_1_89 = all_260_0_84
% 30.93/8.95 |
% 30.93/8.95 | Combining equations (168,169) yields a new equation:
% 30.93/8.95 | (172) all_262_0_86 = all_54_0_25
% 30.93/8.95 |
% 30.93/8.95 | Combining equations (170,171) yields a new equation:
% 30.93/8.95 | (173) all_260_0_84 = 0
% 30.93/8.95 |
% 30.93/8.95 | Combining equations (173,171) yields a new equation:
% 30.93/8.95 | (170) all_264_1_89 = 0
% 30.93/8.95 |
% 30.93/8.95 | From (166) and (163) follows:
% 30.93/8.95 | (155) subset(all_54_1_26, all_0_10_10) = all_262_1_87
% 30.93/8.95 |
% 30.93/8.95 | From (167) and (159) follows:
% 30.93/8.95 | (151) subset(all_54_1_26, all_0_11_11) = all_260_1_85
% 30.93/8.95 |
% 30.93/8.95 | From (173) and (152) follows:
% 30.93/8.95 | (106) in(all_54_1_26, all_0_9_9) = 0
% 30.93/8.95 |
% 30.93/8.95 +-Applying beta-rule and splitting (157), into two cases.
% 30.93/8.95 |-Branch one:
% 30.93/8.95 | (178) ~ (all_262_1_87 = 0)
% 30.93/8.95 |
% 30.93/8.95 +-Applying beta-rule and splitting (161), into two cases.
% 30.93/8.95 |-Branch one:
% 30.93/8.95 | (179) ~ (all_264_1_89 = 0)
% 30.93/8.95 |
% 30.93/8.95 | Equations (170) can reduce 179 to:
% 30.93/8.95 | (100) $false
% 30.93/8.95 |
% 30.93/8.95 |-The branch is then unsatisfiable
% 30.93/8.95 |-Branch two:
% 30.93/8.95 | (170) all_264_1_89 = 0
% 30.93/8.95 | (182) all_264_0_88 = 0
% 30.93/8.95 |
% 30.93/8.95 | Combining equations (167,182) yields a new equation:
% 30.93/8.95 | (183) all_260_1_85 = 0
% 30.93/8.95 |
% 30.93/8.95 | Simplifying 183 yields:
% 30.93/8.95 | (184) all_260_1_85 = 0
% 30.93/8.95 |
% 30.93/8.95 | From (184) and (151) follows:
% 30.93/8.95 | (185) subset(all_54_1_26, all_0_11_11) = 0
% 30.93/8.95 |
% 30.93/8.95 +-Applying beta-rule and splitting (130), into two cases.
% 30.93/8.95 |-Branch one:
% 30.93/8.95 | (186) ~ (in(all_54_1_26, all_0_9_9) = all_98_2_46)
% 30.93/8.95 |
% 30.93/8.95 | Using (106) and (186) yields:
% 30.93/8.95 | (187) ~ (all_98_2_46 = 0)
% 30.93/8.95 |
% 30.93/8.95 +-Applying beta-rule and splitting (127), into two cases.
% 30.93/8.95 |-Branch one:
% 30.93/8.95 | (188) all_98_2_46 = 0
% 30.93/8.95 |
% 30.93/8.95 | Equations (188) can reduce 187 to:
% 30.93/8.95 | (100) $false
% 30.93/8.95 |
% 30.93/8.95 |-The branch is then unsatisfiable
% 30.93/8.95 |-Branch two:
% 30.93/8.95 | (187) ~ (all_98_2_46 = 0)
% 30.93/8.95 | (191) all_98_0_44 = 0 & all_98_1_45 = 0
% 30.93/8.95 |
% 30.93/8.95 | Applying alpha-rule on (191) yields:
% 30.93/8.95 | (192) all_98_0_44 = 0
% 30.93/8.95 | (193) all_98_1_45 = 0
% 30.93/8.95 |
% 30.93/8.95 +-Applying beta-rule and splitting (129), into two cases.
% 30.93/8.95 |-Branch one:
% 30.93/8.95 | (194) ~ (subset(all_0_11_11, all_0_10_10) = all_98_1_45)
% 30.93/8.95 |
% 30.93/8.95 | From (193) and (194) follows:
% 30.93/8.95 | (195) ~ (subset(all_0_11_11, all_0_10_10) = 0)
% 30.93/8.95 |
% 30.93/8.95 | Using (17) and (195) yields:
% 30.93/8.95 | (84) $false
% 30.93/8.95 |
% 30.93/8.95 |-The branch is then unsatisfiable
% 30.93/8.95 |-Branch two:
% 30.93/8.95 | (197) subset(all_0_11_11, all_0_10_10) = all_98_1_45
% 30.93/8.95 | (193) all_98_1_45 = 0
% 30.93/8.95 |
% 30.93/8.95 | From (193) and (197) follows:
% 30.93/8.95 | (17) subset(all_0_11_11, all_0_10_10) = 0
% 30.93/8.96 |
% 30.93/8.96 | Instantiating formula (16) with all_262_1_87, all_0_10_10, all_54_1_26 and discharging atoms subset(all_54_1_26, all_0_10_10) = all_262_1_87, yields:
% 30.93/8.96 | (200) all_262_1_87 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_54_1_26) = 0 & in(v0, all_0_10_10) = v1)
% 30.93/8.96 |
% 30.93/8.96 | Instantiating formula (9) with all_262_1_87, all_0_10_10, all_0_11_11, all_54_1_26 and discharging atoms subset(all_54_1_26, all_0_10_10) = all_262_1_87, subset(all_54_1_26, all_0_11_11) = 0, yields:
% 30.93/8.96 | (201) all_262_1_87 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_0_11_11, all_0_10_10) = v0)
% 30.93/8.96 |
% 30.93/8.96 +-Applying beta-rule and splitting (200), into two cases.
% 30.93/8.96 |-Branch one:
% 30.93/8.96 | (202) all_262_1_87 = 0
% 30.93/8.96 |
% 30.93/8.96 | Equations (202) can reduce 178 to:
% 30.93/8.96 | (100) $false
% 30.93/8.96 |
% 30.93/8.96 |-The branch is then unsatisfiable
% 30.93/8.96 |-Branch two:
% 30.93/8.96 | (178) ~ (all_262_1_87 = 0)
% 30.93/8.96 | (205) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_54_1_26) = 0 & in(v0, all_0_10_10) = v1)
% 30.93/8.96 |
% 30.93/8.96 +-Applying beta-rule and splitting (201), into two cases.
% 30.93/8.96 |-Branch one:
% 30.93/8.96 | (202) all_262_1_87 = 0
% 30.93/8.96 |
% 30.93/8.96 | Equations (202) can reduce 178 to:
% 30.93/8.96 | (100) $false
% 30.93/8.96 |
% 30.93/8.96 |-The branch is then unsatisfiable
% 30.93/8.96 |-Branch two:
% 30.93/8.96 | (178) ~ (all_262_1_87 = 0)
% 30.93/8.96 | (209) ? [v0] : ( ~ (v0 = 0) & subset(all_0_11_11, all_0_10_10) = v0)
% 30.93/8.96 |
% 30.93/8.96 | Instantiating (209) with all_1412_0_452 yields:
% 30.93/8.96 | (210) ~ (all_1412_0_452 = 0) & subset(all_0_11_11, all_0_10_10) = all_1412_0_452
% 30.93/8.96 |
% 30.93/8.96 | Applying alpha-rule on (210) yields:
% 30.93/8.96 | (211) ~ (all_1412_0_452 = 0)
% 30.93/8.96 | (212) subset(all_0_11_11, all_0_10_10) = all_1412_0_452
% 30.93/8.96 |
% 30.93/8.96 | Instantiating formula (63) with all_0_11_11, all_0_10_10, all_1412_0_452, 0 and discharging atoms subset(all_0_11_11, all_0_10_10) = all_1412_0_452, subset(all_0_11_11, all_0_10_10) = 0, yields:
% 30.93/8.96 | (213) all_1412_0_452 = 0
% 30.93/8.96 |
% 30.93/8.96 | Equations (213) can reduce 211 to:
% 30.93/8.96 | (100) $false
% 30.93/8.96 |
% 30.93/8.96 |-The branch is then unsatisfiable
% 30.93/8.96 |-Branch two:
% 30.93/8.96 | (215) in(all_54_1_26, all_0_9_9) = all_98_2_46
% 30.93/8.96 | (188) all_98_2_46 = 0
% 30.93/8.96 |
% 30.93/8.96 | Combining equations (188,143) yields a new equation:
% 30.93/8.96 | (217) all_140_1_71 = 0
% 30.93/8.96 |
% 30.93/8.96 +-Applying beta-rule and splitting (137), into two cases.
% 30.93/8.96 |-Branch one:
% 30.93/8.96 | (218) ~ (all_140_1_71 = 0)
% 30.93/8.96 |
% 30.93/8.96 | Equations (217) can reduce 218 to:
% 30.93/8.96 | (100) $false
% 30.93/8.96 |
% 30.93/8.96 |-The branch is then unsatisfiable
% 30.93/8.96 |-Branch two:
% 30.93/8.96 | (217) all_140_1_71 = 0
% 30.93/8.96 | (221) all_140_0_70 = 0 & all_98_0_44 = 0
% 30.93/8.96 |
% 30.93/8.96 | Applying alpha-rule on (221) yields:
% 30.93/8.96 | (222) all_140_0_70 = 0
% 30.93/8.96 | (192) all_98_0_44 = 0
% 30.93/8.96 |
% 30.93/8.96 | From (222) and (135) follows:
% 30.93/8.96 | (224) subset(all_98_3_47, all_0_11_11) = 0
% 30.93/8.96 |
% 30.93/8.96 +-Applying beta-rule and splitting (126), into two cases.
% 30.93/8.96 |-Branch one:
% 30.93/8.96 | (225) ~ (all_98_0_44 = 0)
% 30.93/8.96 |
% 30.93/8.96 | Equations (192) can reduce 225 to:
% 30.93/8.96 | (100) $false
% 30.93/8.96 |
% 30.93/8.96 |-The branch is then unsatisfiable
% 30.93/8.96 |-Branch two:
% 30.93/8.96 | (192) all_98_0_44 = 0
% 30.93/8.96 | (228) ~ (all_98_1_45 = 0) | ~ (all_98_2_46 = 0)
% 30.93/8.96 |
% 30.93/8.96 +-Applying beta-rule and splitting (145), into two cases.
% 30.93/8.96 |-Branch one:
% 30.93/8.96 | (229) ~ (subset(all_98_3_47, all_0_11_11) = 0)
% 30.93/8.96 |
% 30.93/8.96 | Using (224) and (229) yields:
% 30.93/8.96 | (84) $false
% 30.93/8.96 |
% 30.93/8.96 |-The branch is then unsatisfiable
% 30.93/8.96 |-Branch two:
% 30.93/8.96 | (224) subset(all_98_3_47, all_0_11_11) = 0
% 30.93/8.96 | (232) all_98_1_45 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_0_11_11, all_0_10_10) = v0)
% 30.93/8.97 |
% 30.93/8.97 +-Applying beta-rule and splitting (228), into two cases.
% 30.93/8.97 |-Branch one:
% 30.93/8.97 | (233) ~ (all_98_1_45 = 0)
% 30.93/8.97 |
% 30.93/8.97 +-Applying beta-rule and splitting (232), into two cases.
% 30.93/8.97 |-Branch one:
% 30.93/8.97 | (193) all_98_1_45 = 0
% 30.93/8.97 |
% 30.93/8.97 | Equations (193) can reduce 233 to:
% 30.93/8.97 | (100) $false
% 30.93/8.97 |
% 30.93/8.97 |-The branch is then unsatisfiable
% 30.93/8.97 |-Branch two:
% 30.93/8.97 | (233) ~ (all_98_1_45 = 0)
% 30.93/8.97 | (209) ? [v0] : ( ~ (v0 = 0) & subset(all_0_11_11, all_0_10_10) = v0)
% 30.93/8.97 |
% 30.93/8.97 | Instantiating (209) with all_1013_0_457 yields:
% 30.93/8.97 | (238) ~ (all_1013_0_457 = 0) & subset(all_0_11_11, all_0_10_10) = all_1013_0_457
% 30.93/8.97 |
% 30.93/8.97 | Applying alpha-rule on (238) yields:
% 30.93/8.97 | (239) ~ (all_1013_0_457 = 0)
% 30.93/8.97 | (240) subset(all_0_11_11, all_0_10_10) = all_1013_0_457
% 30.93/8.97 |
% 30.93/8.97 | Instantiating formula (63) with all_0_11_11, all_0_10_10, all_1013_0_457, 0 and discharging atoms subset(all_0_11_11, all_0_10_10) = all_1013_0_457, subset(all_0_11_11, all_0_10_10) = 0, yields:
% 30.93/8.97 | (241) all_1013_0_457 = 0
% 30.93/8.97 |
% 30.93/8.97 | Equations (241) can reduce 239 to:
% 30.93/8.97 | (100) $false
% 30.93/8.97 |
% 30.93/8.97 |-The branch is then unsatisfiable
% 30.93/8.97 |-Branch two:
% 30.93/8.97 | (193) all_98_1_45 = 0
% 30.93/8.97 | (187) ~ (all_98_2_46 = 0)
% 30.93/8.97 |
% 30.93/8.97 | Equations (188) can reduce 187 to:
% 30.93/8.97 | (100) $false
% 30.93/8.97 |
% 30.93/8.97 |-The branch is then unsatisfiable
% 30.93/8.97 |-Branch two:
% 30.93/8.97 | (202) all_262_1_87 = 0
% 30.93/8.97 | (247) all_262_0_86 = 0
% 30.93/8.97 |
% 30.93/8.97 | Combining equations (172,247) yields a new equation:
% 30.93/8.97 | (248) all_54_0_25 = 0
% 30.93/8.97 |
% 30.93/8.97 | Simplifying 248 yields:
% 30.93/8.97 | (115) all_54_0_25 = 0
% 30.93/8.97 |
% 30.93/8.97 | Equations (115) can reduce 104 to:
% 30.93/8.97 | (100) $false
% 30.93/8.97 |
% 30.93/8.97 |-The branch is then unsatisfiable
% 30.93/8.97 |-Branch two:
% 30.93/8.97 | (251) subset(all_0_9_9, all_0_9_9) = all_0_7_7
% 30.93/8.97 | (99) all_0_7_7 = 0
% 30.93/8.97 |
% 30.93/8.97 | Equations (99) can reduce 13 to:
% 30.93/8.97 | (100) $false
% 30.93/8.97 |
% 30.93/8.97 |-The branch is then unsatisfiable
% 30.93/8.97 % SZS output end Proof for theBenchmark
% 30.93/8.97
% 30.93/8.97 8388ms
%------------------------------------------------------------------------------