TSTP Solution File: SEU167+2 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU167+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n023.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 08:47:14 EDT 2022
% Result : Theorem 9.47s 2.80s
% Output : Proof 12.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU167+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 20 10:21:48 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.47/0.58 ____ _
% 0.47/0.58 ___ / __ \_____(_)___ ________ __________
% 0.47/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.47/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.47/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.47/0.58
% 0.47/0.58 A Theorem Prover for First-Order Logic
% 0.47/0.58 (ePrincess v.1.0)
% 0.47/0.58
% 0.47/0.58 (c) Philipp Rümmer, 2009-2015
% 0.47/0.58 (c) Peter Backeman, 2014-2015
% 0.47/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.47/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.47/0.58 Bug reports to peter@backeman.se
% 0.47/0.58
% 0.47/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.47/0.58
% 0.47/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.75/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.74/1.02 Prover 0: Preprocessing ...
% 3.66/1.51 Prover 0: Warning: ignoring some quantifiers
% 3.66/1.54 Prover 0: Constructing countermodel ...
% 7.60/2.44 Prover 0: gave up
% 7.60/2.44 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 8.12/2.50 Prover 1: Preprocessing ...
% 8.90/2.69 Prover 1: Warning: ignoring some quantifiers
% 8.90/2.70 Prover 1: Constructing countermodel ...
% 9.47/2.80 Prover 1: proved (358ms)
% 9.47/2.80
% 9.47/2.80 No countermodel exists, formula is valid
% 9.47/2.80 % SZS status Theorem for theBenchmark
% 9.47/2.80
% 9.47/2.80 Generating proof ... Warning: ignoring some quantifiers
% 11.69/3.34 found it (size 26)
% 11.69/3.34
% 11.69/3.34 % SZS output start Proof for theBenchmark
% 11.69/3.34 Assumed formulas after preprocessing and simplification:
% 11.69/3.34 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v9 = 0) & ~ (v7 = 0) & empty(v10) = 0 & empty(v8) = v9 & empty(empty_set) = 0 & cartesian_product2(v2, v4) = v6 & cartesian_product2(v1, v3) = v5 & powerset(empty_set) = v0 & singleton(empty_set) = v0 & subset(v5, v6) = v7 & subset(v3, v4) = 0 & subset(v1, v2) = 0 & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (cartesian_product2(v13, v14) = v16) | ~ (ordered_pair(v11, v12) = v15) | ~ (in(v15, v16) = v17) | ? [v18] : ? [v19] : (in(v12, v14) = v19 & in(v11, v13) = v18 & ( ~ (v19 = 0) | ~ (v18 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = 0 | ~ (cartesian_product2(v11, v12) = v13) | ~ (ordered_pair(v16, v17) = v14) | ~ (in(v14, v13) = v15) | ? [v18] : ? [v19] : (in(v17, v12) = v19 & in(v16, v11) = v18 & ( ~ (v19 = 0) | ~ (v18 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (set_difference(v12, v14) = v15) | ~ (singleton(v13) = v14) | ~ (subset(v11, v15) = v16) | ? [v17] : ? [v18] : (subset(v11, v12) = v17 & in(v13, v11) = v18 & ( ~ (v17 = 0) | v18 = 0))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (set_difference(v12, v13) = v15) | ~ (set_difference(v11, v13) = v14) | ~ (subset(v14, v15) = v16) | ? [v17] : ( ~ (v17 = 0) & subset(v11, v12) = v17)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (subset(v14, v15) = v16) | ~ (set_intersection2(v12, v13) = v15) | ~ (set_intersection2(v11, v13) = v14) | ? [v17] : ( ~ (v17 = 0) & subset(v11, v12) = v17)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (cartesian_product2(v13, v14) = v16) | ~ (ordered_pair(v11, v12) = v15) | ~ (in(v15, v16) = 0) | (in(v12, v14) = 0 & in(v11, v13) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (cartesian_product2(v12, v13) = v15) | ~ (cartesian_product2(v11, v13) = v14) | ~ (subset(v14, v15) = v16) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : (cartesian_product2(v13, v12) = v19 & cartesian_product2(v13, v11) = v18 & subset(v18, v19) = v20 & subset(v11, v12) = v17 & ( ~ (v17 = 0) | (v20 = 0 & v16 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (subset(v14, v13) = v15) | ~ (unordered_pair(v11, v12) = v14) | ? [v16] : ? [v17] : (in(v12, v13) = v17 & in(v11, v13) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (subset(v14, v12) = v15) | ~ (set_union2(v11, v13) = v14) | ? [v16] : ? [v17] : (subset(v13, v12) = v17 & subset(v11, v12) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (subset(v11, v14) = v15) | ~ (set_intersection2(v12, v13) = v14) | ? [v16] : ? [v17] : (subset(v11, v13) = v17 & subset(v11, v12) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (set_union2(v11, v12) = v13) | ~ (in(v14, v11) = v15) | ? [v16] : ? [v17] : (in(v14, v13) = v16 & in(v14, v12) = v17 & ( ~ (v16 = 0) | v17 = 0))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = v12 | ~ (ordered_pair(v13, v14) = v15) | ~ (ordered_pair(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = v11 | v13 = v11 | ~ (unordered_pair(v13, v14) = v15) | ~ (unordered_pair(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (union(v11) = v12) | ~ (in(v13, v15) = 0) | ~ (in(v13, v12) = v14) | ? [v16] : ( ~ (v16 = 0) & in(v15, v11) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v11 | ~ (ordered_pair(v13, v14) = v15) | ~ (ordered_pair(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_difference(v11, v12) = v13) | ~ (in(v14, v11) = v15) | ? [v16] : ? [v17] : (in(v14, v13) = v16 & in(v14, v12) = v17 & ( ~ (v16 = 0) | (v15 = 0 & ~ (v17 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (singleton(v11) = v14) | ~ (unordered_pair(v13, v14) = v15) | ~ (unordered_pair(v11, v12) = v13) | ordered_pair(v11, v12) = v15) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_intersection2(v11, v12) = v13) | ~ (in(v14, v11) = v15) | ? [v16] : ? [v17] : (in(v14, v13) = v16 & in(v14, v12) = v17 & ( ~ (v16 = 0) | (v17 = 0 & v15 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_union2(v11, v12) = v13) | ~ (in(v14, v11) = v15) | ? [v16] : ? [v17] : (in(v14, v13) = v17 & in(v14, v12) = v16 & (v17 = 0 | ( ~ (v16 = 0) & ~ (v15 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v12 | v14 = v11 | ~ (unordered_pair(v11, v12) = v13) | ~ (in(v14, v13) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (set_difference(v12, v11) = v13) | ~ (set_union2(v11, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & subset(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (singleton(v11) = v13) | ~ (set_union2(v13, v12) = v14) | ? [v15] : ( ~ (v15 = 0) & in(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v11 | ~ (set_difference(v11, v13) = v14) | ~ (singleton(v12) = v13) | in(v12, v11) = 0) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (disjoint(v13, v12) = v14) | ~ (singleton(v11) = v13) | in(v11, v12) = 0) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (disjoint(v12, v13) = 0) | ~ (disjoint(v11, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & subset(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (set_difference(v11, v12) = v13) | ~ (subset(v13, v11) = v14)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (union(v12) = v13) | ~ (subset(v11, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & in(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (powerset(v11) = v12) | ~ (subset(v13, v11) = v14) | ? [v15] : ( ~ (v15 = 0) & in(v13, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (singleton(v11) = v13) | ~ (subset(v13, v12) = v14) | ? [v15] : ( ~ (v15 = 0) & in(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v13, v11) = v14) | ~ (set_intersection2(v11, v12) = v13)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v11, v13) = v14) | ~ (subset(v11, v12) = 0) | ? [v15] : ( ~ (v15 = 0) & subset(v12, v13) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v11, v13) = v14) | ~ (set_union2(v11, v12) = v13)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (unordered_pair(v11, v12) = v13) | ~ (in(v12, v13) = v14)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (unordered_pair(v11, v12) = v13) | ~ (in(v11, v13) = v14)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (singleton(v11) = v14) | ~ (unordered_pair(v12, v13) = v14)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (disjoint(v14, v13) = v12) | ~ (disjoint(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (set_difference(v14, v13) = v12) | ~ (set_difference(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (cartesian_product2(v14, v13) = v12) | ~ (cartesian_product2(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (ordered_pair(v14, v13) = v12) | ~ (ordered_pair(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (singleton(v12) = v14) | ~ (singleton(v11) = v13) | ~ (subset(v13, v14) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (singleton(v11) = v14) | ~ (unordered_pair(v12, v13) = v14)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (subset(v14, v13) = v12) | ~ (subset(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (set_intersection2(v14, v13) = v12) | ~ (set_intersection2(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (set_union2(v14, v13) = v12) | ~ (set_union2(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (unordered_pair(v14, v13) = v12) | ~ (unordered_pair(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (proper_subset(v14, v13) = v12) | ~ (proper_subset(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (in(v14, v13) = v12) | ~ (in(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_difference(v13, v12) = v14) | ~ (set_union2(v11, v12) = v13) | set_difference(v11, v12) = v14) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_difference(v12, v11) = v13) | ~ (set_union2(v11, v13) = v14) | set_union2(v11, v12) = v14) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_difference(v11, v13) = v14) | ~ (set_difference(v11, v12) = v13) | set_intersection2(v11, v12) = v14) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_difference(v11, v12) = v13) | ~ (in(v14, v11) = 0) | ? [v15] : ? [v16] : (in(v14, v13) = v16 & in(v14, v12) = v15 & (v16 = 0 | v15 = 0))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (cartesian_product2(v11, v12) = v13) | ~ (in(v14, v13) = 0) | ? [v15] : ? [v16] : (ordered_pair(v15, v16) = v14 & in(v16, v12) = 0 & in(v15, v11) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (subset(v14, v13) = 0) | ~ (unordered_pair(v11, v12) = v14) | (in(v12, v13) = 0 & in(v11, v13) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_intersection2(v11, v12) = v13) | ~ (in(v14, v11) = 0) | ? [v15] : ? [v16] : (in(v14, v13) = v16 & in(v14, v12) = v15 & ( ~ (v15 = 0) | v16 = 0))) & ? [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v11 | ~ (set_difference(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (in(v15, v13) = v18 & in(v15, v12) = v17 & in(v15, v11) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0) | v18 = 0) & (v16 = 0 | (v17 = 0 & ~ (v18 = 0))))) & ? [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v11 | ~ (cartesian_product2(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (in(v15, v11) = v16 & ( ~ (v16 = 0) | ! [v22] : ! [v23] : ( ~ (ordered_pair(v22, v23) = v15) | ? [v24] : ? [v25] : (in(v23, v13) = v25 & in(v22, v12) = v24 & ( ~ (v25 = 0) | ~ (v24 = 0))))) & (v16 = 0 | (v21 = v15 & v20 = 0 & v19 = 0 & ordered_pair(v17, v18) = v15 & in(v18, v13) = 0 & in(v17, v12) = 0)))) & ? [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v11 | ~ (set_intersection2(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (in(v15, v13) = v18 & in(v15, v12) = v17 & in(v15, v11) = v16 & ( ~ (v18 = 0) | ~ (v17 = 0) | ~ (v16 = 0)) & (v16 = 0 | (v18 = 0 & v17 = 0)))) & ? [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v11 | ~ (set_union2(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (in(v15, v13) = v18 & in(v15, v12) = v17 & in(v15, v11) = v16 & ( ~ (v16 = 0) | ( ~ (v18 = 0) & ~ (v17 = 0))) & (v18 = 0 | v17 = 0 | v16 = 0))) & ? [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v11 | ~ (unordered_pair(v12, v13) = v14) | ? [v15] : ? [v16] : (in(v15, v11) = v16 & ( ~ (v16 = 0) | ( ~ (v15 = v13) & ~ (v15 = v12))) & (v16 = 0 | v15 = v13 | v15 = v12))) & ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (set_union2(v11, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & subset(v11, v12) = v14)) & ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | v11 = empty_set | ~ (singleton(v12) = v13) | ~ (subset(v11, v13) = 0)) & ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (singleton(v11) = v12) | ~ (in(v13, v12) = 0)) & ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (set_intersection2(v11, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & subset(v11, v12) = v14)) & ! [v11] : ! [v12] : ! [v13] : (v13 = empty_set | ~ (set_difference(v11, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & subset(v11, v12) = v14)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | v12 = v11 | ~ (proper_subset(v11, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & subset(v11, v12) = v14)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (disjoint(v11, v12) = v13) | ? [v14] : ? [v15] : (set_intersection2(v11, v12) = v14 & in(v15, v14) = 0)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (disjoint(v11, v12) = v13) | ? [v14] : ( ~ (v14 = v11) & set_difference(v11, v12) = v14)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (disjoint(v11, v12) = v13) | ? [v14] : ( ~ (v14 = empty_set) & set_intersection2(v11, v12) = v14)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (disjoint(v11, v12) = v13) | ? [v14] : (in(v14, v12) = 0 & in(v14, v11) = 0)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (singleton(v12) = v11) | ~ (subset(v11, v11) = v13)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (singleton(v11) = v12) | ~ (subset(empty_set, v12) = v13)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (singleton(v11) = v12) | ~ (in(v11, v12) = v13)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v11, v12) = v13) | ? [v14] : ? [v15] : ( ~ (v15 = 0) & in(v14, v12) = v15 & in(v14, v11) = 0)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (empty(v13) = v12) | ~ (empty(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (union(v13) = v12) | ~ (union(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (powerset(v13) = v12) | ~ (powerset(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (singleton(v13) = v12) | ~ (singleton(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (disjoint(v13, v12) = 0) | ~ (singleton(v11) = v13) | ? [v14] : ( ~ (v14 = 0) & in(v11, v12) = v14)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (disjoint(v11, v12) = 0) | ~ (in(v13, v11) = 0) | ? [v14] : ( ~ (v14 = 0) & in(v13, v12) = v14)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_difference(v11, v13) = v11) | ~ (singleton(v12) = v13) | ? [v14] : ( ~ (v14 = 0) & in(v12, v11) = v14)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (union(v11) = v12) | ~ (in(v13, v12) = 0) | ? [v14] : (in(v14, v11) = 0 & in(v13, v14) = 0)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (ordered_pair(v11, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & empty(v13) = v14)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v11) = v12) | ~ (subset(v13, v11) = 0) | in(v13, v12) = 0) & ! [v11] : ! [v12] : ! [v13] : ( ~ (singleton(v11) = v13) | ~ (subset(v13, v12) = 0) | in(v11, v12) = 0) & ! [v11] : ! [v12] : ! [v13] : ( ~ (subset(v11, v12) = 0) | ~ (in(v13, v11) = 0) | in(v13, v12) = 0) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v11, v12) = v13) | set_intersection2(v12, v11) = v13) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v12, v11) = v13) | ? [v14] : ? [v15] : (empty(v13) = v15 & empty(v11) = v14 & ( ~ (v15 = 0) | v14 = 0))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v11, v12) = v13) | set_union2(v12, v11) = v13) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v11, v12) = v13) | ? [v14] : ? [v15] : (empty(v13) = v15 & empty(v11) = v14 & ( ~ (v15 = 0) | v14 = 0))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (unordered_pair(v11, v12) = v13) | unordered_pair(v12, v11) = v13) & ? [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (union(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (in(v14, v11) = v15 & ( ~ (v15 = 0) | ! [v19] : ( ~ (in(v14, v19) = 0) | ? [v20] : ( ~ (v20 = 0) & in(v19, v12) = v20))) & (v15 = 0 | (v18 = 0 & v17 = 0 & in(v16, v12) = 0 & in(v14, v16) = 0)))) & ? [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (powerset(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : (subset(v14, v12) = v16 & in(v14, v11) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0)) & (v16 = 0 | v15 = 0))) & ? [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (singleton(v12) = v13) | ? [v14] : ? [v15] : (in(v14, v11) = v15 & ( ~ (v15 = 0) | ~ (v14 = v12)) & (v15 = 0 | v14 = v12))) & ! [v11] : ! [v12] : (v12 = v11 | ~ (empty(v12) = 0) | ~ (empty(v11) = 0)) & ! [v11] : ! [v12] : (v12 = v11 | ~ (set_difference(v11, empty_set) = v12)) & ! [v11] : ! [v12] : (v12 = v11 | ~ (subset(v11, v12) = 0) | ? [v13] : ( ~ (v13 = 0) & subset(v12, v11) = v13)) & ! [v11] : ! [v12] : (v12 = v11 | ~ (set_intersection2(v11, v11) = v12)) & ! [v11] : ! [v12] : (v12 = v11 | ~ (set_union2(v11, v11) = v12)) & ! [v11] : ! [v12] : (v12 = v11 | ~ (set_union2(v11, empty_set) = v12)) & ! [v11] : ! [v12] : (v12 = empty_set | ~ (set_difference(empty_set, v11) = v12)) & ! [v11] : ! [v12] : (v12 = empty_set | ~ (set_intersection2(v11, empty_set) = v12)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v11, v11) = v12)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(empty_set, v11) = v12)) & ! [v11] : ! [v12] : ( ~ (disjoint(v11, v12) = 0) | disjoint(v12, v11) = 0) & ! [v11] : ! [v12] : ( ~ (disjoint(v11, v12) = 0) | set_difference(v11, v12) = v11) & ! [v11] : ! [v12] : ( ~ (disjoint(v11, v12) = 0) | set_intersection2(v11, v12) = empty_set) & ! [v11] : ! [v12] : ( ~ (disjoint(v11, v12) = 0) | ? [v13] : (set_intersection2(v11, v12) = v13 & ! [v14] : ~ (in(v14, v13) = 0))) & ! [v11] : ! [v12] : ( ~ (set_difference(v11, v12) = empty_set) | subset(v11, v12) = 0) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | union(v12) = v11) & ! [v11] : ! [v12] : ( ~ (unordered_pair(v11, v11) = v12) | singleton(v11) = v12) & ! [v11] : ! [v12] : ( ~ (proper_subset(v12, v11) = 0) | ? [v13] : ( ~ (v13 = 0) & subset(v11, v12) = v13)) & ! [v11] : ! [v12] : ( ~ (proper_subset(v11, v12) = 0) | subset(v11, v12) = 0) & ! [v11] : ! [v12] : ( ~ (proper_subset(v11, v12) = 0) | ? [v13] : ( ~ (v13 = 0) & proper_subset(v12, v11) = v13)) & ! [v11] : ! [v12] : ( ~ (in(v11, v12) = 0) | ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) & ! [v11] : ! [v12] : ( ~ (in(v11, v12) = 0) | ? [v13] : ( ~ (v13 = 0) & in(v12, v11) = v13)) & ! [v11] : (v11 = empty_set | ~ (empty(v11) = 0)) & ! [v11] : (v11 = empty_set | ~ (subset(v11, empty_set) = 0)) & ! [v11] : ~ (singleton(v11) = empty_set) & ! [v11] : ~ (proper_subset(v11, v11) = 0) & ! [v11] : ~ (in(v11, empty_set) = 0) & ? [v11] : ? [v12] : (v12 = v11 | ? [v13] : ? [v14] : ? [v15] : (in(v13, v12) = v15 & in(v13, v11) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0)) & (v15 = 0 | v14 = 0))) & ? [v11] : (v11 = empty_set | ? [v12] : in(v12, v11) = 0))
% 12.33/3.43 | 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 yields:
% 12.33/3.43 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_3_3 = 0) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & empty(empty_set) = 0 & cartesian_product2(all_0_8_8, all_0_6_6) = all_0_4_4 & cartesian_product2(all_0_9_9, all_0_7_7) = all_0_5_5 & powerset(empty_set) = all_0_10_10 & singleton(empty_set) = all_0_10_10 & subset(all_0_5_5, all_0_4_4) = all_0_3_3 & subset(all_0_7_7, all_0_6_6) = 0 & subset(all_0_9_9, all_0_8_8) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = v6) | ? [v7] : ? [v8] : (in(v1, v3) = v8 & in(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (cartesian_product2(v0, v1) = v2) | ~ (ordered_pair(v5, v6) = v3) | ~ (in(v3, v2) = v4) | ? [v7] : ? [v8] : (in(v6, v1) = v8 & in(v5, v0) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ (subset(v0, v4) = v5) | ? [v6] : ? [v7] : (subset(v0, v1) = v6 & in(v2, v0) = v7 & ( ~ (v6 = 0) | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (subset(v3, v4) = v5) | ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = 0) | (in(v1, v3) = 0 & in(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (cartesian_product2(v2, v1) = v8 & cartesian_product2(v2, v0) = v7 & subset(v7, v8) = v9 & subset(v0, v1) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ? [v5] : ? [v6] : (in(v1, v2) = v6 & in(v0, v2) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v1) = v4) | ~ (set_union2(v0, v2) = v3) | ? [v5] : ? [v6] : (subset(v2, v1) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v0, v3) = v4) | ~ (set_intersection2(v1, v2) = v3) | ? [v5] : ? [v6] : (subset(v0, v2) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v2, v4) = 0) | ~ (in(v2, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v4, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 = 0 & ~ (v6 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v2, v1) = v3) | ~ (singleton(v0) = v2) | in(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v1, v2) = 0) | ~ (disjoint(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (subset(v2, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (union(v1) = v2) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v2, v0) = v3) | ~ (set_intersection2(v0, v1) = v2)) & ! [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 | ~ (subset(v0, v2) = v3) | ~ (set_union2(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ (subset(v2, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ~ (unordered_pair(v0, v1) = v3) | (in(v1, v2) = 0 & in(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0) & (v5 = 0 | (v6 = 0 & ~ (v7 = 0))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (cartesian_product2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ! [v11] : ! [v12] : ( ~ (ordered_pair(v11, v12) = v4) | ? [v13] : ? [v14] : (in(v12, v2) = v14 & in(v11, v1) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0))))) & (v5 = 0 | (v10 = v4 & v9 = 0 & v8 = 0 & ordered_pair(v6, v7) = v4 & in(v7, v2) = 0 & in(v6, v1) = 0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ? [v5] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v4 = v2) & ~ (v4 = v1))) & (v5 = 0 | v4 = v2 | v4 = v1))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ (subset(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (proper_subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v0) & set_difference(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v1) = v0) | ~ (subset(v0, v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (subset(empty_set, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v2, v1) = 0) | ~ (singleton(v0) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v2) = v0) | ~ (singleton(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v1, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v0) = 0 & in(v2, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = 0) | in(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (union(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ! [v8] : ( ~ (in(v3, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v1) = v9))) & (v4 = 0 | (v7 = 0 & v6 = 0 & in(v5, v1) = 0 & in(v3, v5) = 0)))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (subset(v3, v1) = v5 & in(v3, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_difference(v0, v1) = v0) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0))) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0) & ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) & ! [v0] : ! [v1] : ( ~ (proper_subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2)) & ! [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] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0)) & ! [v0] : ~ (singleton(v0) = empty_set) & ! [v0] : ~ (proper_subset(v0, v0) = 0) & ! [v0] : ~ (in(v0, empty_set) = 0) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (in(v2, v1) = v4 & in(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0))) & ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0)
% 12.42/3.45 |
% 12.42/3.45 | Applying alpha-rule on (1) yields:
% 12.42/3.45 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v2, v1) = v3) | ~ (singleton(v0) = v2) | in(v0, v1) = 0)
% 12.42/3.45 | (3) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 12.42/3.45 | (4) subset(all_0_7_7, all_0_6_6) = 0
% 12.42/3.45 | (5) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2))
% 12.42/3.45 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 12.42/3.45 | (7) subset(all_0_9_9, all_0_8_8) = 0
% 12.42/3.45 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v2) = v0) | ~ (singleton(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v1, v0) = v3))
% 12.42/3.46 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4))
% 12.42/3.46 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3))
% 12.42/3.46 | (11) ! [v0] : ~ (proper_subset(v0, v0) = 0)
% 12.42/3.46 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (subset(v3, v4) = v5) | ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6))
% 12.42/3.46 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v2, v0) = v3) | ~ (set_intersection2(v0, v1) = v2))
% 12.42/3.46 | (14) ! [v0] : ~ (singleton(v0) = empty_set)
% 12.42/3.46 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3)
% 12.42/3.46 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (cartesian_product2(v2, v1) = v8 & cartesian_product2(v2, v0) = v7 & subset(v7, v8) = v9 & subset(v0, v1) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v5 = 0))))
% 12.42/3.46 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0))
% 12.42/3.46 | (18) ! [v0] : ! [v1] : ( ~ (proper_subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2))
% 12.42/3.46 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 12.42/3.46 | (20) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 12.42/3.46 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0)))
% 12.42/3.46 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v0) = 0 & in(v2, v3) = 0))
% 12.42/3.46 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (cartesian_product2(v0, v1) = v2) | ~ (ordered_pair(v5, v6) = v3) | ~ (in(v3, v2) = v4) | ? [v7] : ? [v8] : (in(v6, v1) = v8 & in(v5, v0) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))))
% 12.42/3.46 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 12.42/3.46 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4))
% 12.42/3.46 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0))))
% 12.42/3.46 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0))
% 12.42/3.46 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 12.42/3.46 | (29) ~ (all_0_3_3 = 0)
% 12.42/3.46 | (30) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0)
% 12.42/3.46 | (31) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (subset(v3, v1) = v5 & in(v3, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0)))
% 12.42/3.46 | (32) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1))
% 12.42/3.46 | (33) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 12.42/3.46 | (34) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1)
% 12.42/3.46 | (35) ~ (all_0_1_1 = 0)
% 12.42/3.46 | (36) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_difference(v0, v1) = v0)
% 12.42/3.46 | (37) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2))
% 12.42/3.46 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ (subset(v0, v4) = v5) | ? [v6] : ? [v7] : (subset(v0, v1) = v6 & in(v2, v0) = v7 & ( ~ (v6 = 0) | v7 = 0)))
% 12.42/3.47 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 12.42/3.47 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 = 0 & ~ (v6 = 0)))))
% 12.42/3.47 | (41) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0))
% 12.42/3.47 | (42) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 12.42/3.47 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 12.42/3.47 | (44) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0))
% 12.42/3.47 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4))
% 12.42/3.47 | (46) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v1) = v0) | ~ (subset(v0, v0) = v2))
% 12.42/3.47 | (47) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (cartesian_product2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ! [v11] : ! [v12] : ( ~ (ordered_pair(v11, v12) = v4) | ? [v13] : ? [v14] : (in(v12, v2) = v14 & in(v11, v1) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0))))) & (v5 = 0 | (v10 = v4 & v9 = 0 & v8 = 0 & ordered_pair(v6, v7) = v4 & in(v7, v2) = 0 & in(v6, v1) = 0))))
% 12.42/3.47 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0)))))
% 12.42/3.47 | (49) cartesian_product2(all_0_9_9, all_0_7_7) = all_0_5_5
% 12.42/3.47 | (50) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 12.42/3.47 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v2, v1) = 0) | ~ (singleton(v0) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 12.42/3.47 | (52) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 12.42/3.47 | (53) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0)))
% 12.42/3.47 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | v6 = 0)))
% 12.42/3.47 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 12.42/3.47 | (56) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set)
% 12.42/3.47 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 12.42/3.47 | (58) subset(all_0_5_5, all_0_4_4) = all_0_3_3
% 12.42/3.47 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3)
% 12.42/3.47 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v2, v4) = 0) | ~ (in(v2, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v4, v0) = v5))
% 12.42/3.47 | (61) powerset(empty_set) = all_0_10_10
% 12.42/3.47 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (set_union2(v0, v1) = v2))
% 12.42/3.47 | (63) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0)
% 12.42/3.47 | (64) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3))
% 12.42/3.47 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (union(v1) = v2) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 12.42/3.47 | (66) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1))
% 12.42/3.47 | (67) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 12.42/3.47 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3)
% 12.42/3.48 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 12.42/3.48 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0) = 0)
% 12.42/3.48 | (71) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 12.42/3.48 | (72) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0))))
% 12.42/3.48 | (73) ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0))
% 12.42/3.48 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 12.42/3.48 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0))
% 12.42/3.48 | (76) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 12.42/3.48 | (77) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 12.42/3.48 | (78) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1))
% 12.42/3.48 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6))
% 12.42/3.48 | (80) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0)
% 12.42/3.48 | (81) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0))
% 12.42/3.48 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4))
% 12.42/3.48 | (83) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 12.42/3.48 | (84) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (subset(empty_set, v1) = v2))
% 12.42/3.48 | (85) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ (subset(v0, v2) = 0))
% 12.42/3.48 | (86) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = 0) | in(v0, v1) = 0)
% 12.42/3.48 | (87) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 12.42/3.48 | (88) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0)))
% 12.42/3.48 | (89) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 12.42/3.48 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0)))
% 12.42/3.48 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 12.42/3.48 | (92) empty(empty_set) = 0
% 12.42/3.48 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = v6) | ? [v7] : ? [v8] : (in(v1, v3) = v8 & in(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))))
% 12.42/3.48 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 12.42/3.48 | (95) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | in(v2, v1) = 0)
% 12.42/3.48 | (96) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 12.42/3.48 | (97) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (in(v2, v1) = v4 & in(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0)))
% 12.42/3.48 | (98) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 12.42/3.48 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 12.42/3.48 | (100) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0) & (v5 = 0 | (v6 = 0 & ~ (v7 = 0)))))
% 12.42/3.49 | (101) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3))
% 12.42/3.49 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = 0) | (in(v1, v3) = 0 & in(v0, v2) = 0))
% 12.42/3.49 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 12.42/3.49 | (104) empty(all_0_2_2) = all_0_1_1
% 12.42/3.49 | (105) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 12.42/3.49 | (106) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ (subset(v2, v3) = 0))
% 12.42/3.49 | (107) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | subset(v0, v1) = 0)
% 12.42/3.49 | (108) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2))
% 12.42/3.49 | (109) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (proper_subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 12.42/3.49 | (110) singleton(empty_set) = all_0_10_10
% 12.42/3.49 | (111) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1))
% 12.42/3.49 | (112) empty(all_0_0_0) = 0
% 12.42/3.49 | (113) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 12.42/3.49 | (114) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ? [v5] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v4 = v2) & ~ (v4 = v1))) & (v5 = 0 | v4 = v2 | v4 = v1)))
% 12.42/3.49 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v1, v2) = 0) | ~ (disjoint(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 12.42/3.49 | (116) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1)))
% 12.42/3.49 | (117) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3))
% 12.42/3.49 | (118) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 12.42/3.49 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v0, v3) = v4) | ~ (set_intersection2(v1, v2) = v3) | ? [v5] : ? [v6] : (subset(v0, v2) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 12.42/3.49 | (120) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v0) & set_difference(v0, v1) = v3))
% 12.42/3.49 | (121) ! [v0] : ~ (in(v0, empty_set) = 0)
% 12.42/3.49 | (122) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0))
% 12.42/3.49 | (123) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 12.42/3.49 | (124) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 12.42/3.49 | (125) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (subset(v2, v0) = v3))
% 12.42/3.49 | (126) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4))
% 12.42/3.49 | (127) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 12.42/3.49 | (128) cartesian_product2(all_0_8_8, all_0_6_6) = all_0_4_4
% 12.42/3.49 | (129) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 12.42/3.49 | (130) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0)
% 12.42/3.49 | (131) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v1) = v4) | ~ (set_union2(v0, v2) = v3) | ? [v5] : ? [v6] : (subset(v2, v1) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 12.42/3.50 | (132) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ? [v5] : ? [v6] : (in(v1, v2) = v6 & in(v0, v2) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 12.42/3.50 | (133) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ~ (unordered_pair(v0, v1) = v3) | (in(v1, v2) = 0 & in(v0, v2) = 0))
% 12.42/3.50 | (134) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (union(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ! [v8] : ( ~ (in(v3, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v1) = v9))) & (v4 = 0 | (v7 = 0 & v6 = 0 & in(v5, v1) = 0 & in(v3, v5) = 0))))
% 12.42/3.50 | (135) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 12.42/3.50 |
% 12.42/3.50 | Instantiating formula (3) with all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms subset(all_0_5_5, all_0_4_4) = all_0_3_3, yields:
% 12.42/3.50 | (136) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_5_5) = 0)
% 12.42/3.50 |
% 12.42/3.50 +-Applying beta-rule and splitting (136), into two cases.
% 12.42/3.50 |-Branch one:
% 12.42/3.50 | (137) all_0_3_3 = 0
% 12.42/3.50 |
% 12.42/3.50 | Equations (137) can reduce 29 to:
% 12.42/3.50 | (138) $false
% 12.42/3.50 |
% 12.42/3.50 |-The branch is then unsatisfiable
% 12.42/3.50 |-Branch two:
% 12.42/3.50 | (29) ~ (all_0_3_3 = 0)
% 12.42/3.50 | (140) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_5_5) = 0)
% 12.42/3.50 |
% 12.42/3.50 | Instantiating (140) with all_50_0_22, all_50_1_23 yields:
% 12.42/3.50 | (141) ~ (all_50_0_22 = 0) & in(all_50_1_23, all_0_4_4) = all_50_0_22 & in(all_50_1_23, all_0_5_5) = 0
% 12.42/3.50 |
% 12.42/3.50 | Applying alpha-rule on (141) yields:
% 12.42/3.50 | (142) ~ (all_50_0_22 = 0)
% 12.42/3.50 | (143) in(all_50_1_23, all_0_4_4) = all_50_0_22
% 12.42/3.50 | (144) in(all_50_1_23, all_0_5_5) = 0
% 12.42/3.50 |
% 12.42/3.50 | Instantiating formula (17) with all_50_1_23, all_0_5_5, all_0_7_7, all_0_9_9 and discharging atoms cartesian_product2(all_0_9_9, all_0_7_7) = all_0_5_5, in(all_50_1_23, all_0_5_5) = 0, yields:
% 12.42/3.50 | (145) ? [v0] : ? [v1] : (ordered_pair(v0, v1) = all_50_1_23 & in(v1, all_0_7_7) = 0 & in(v0, all_0_9_9) = 0)
% 12.42/3.50 |
% 12.42/3.50 | Instantiating (145) with all_71_0_27, all_71_1_28 yields:
% 12.42/3.50 | (146) ordered_pair(all_71_1_28, all_71_0_27) = all_50_1_23 & in(all_71_0_27, all_0_7_7) = 0 & in(all_71_1_28, all_0_9_9) = 0
% 12.42/3.50 |
% 12.42/3.50 | Applying alpha-rule on (146) yields:
% 12.42/3.50 | (147) ordered_pair(all_71_1_28, all_71_0_27) = all_50_1_23
% 12.42/3.50 | (148) in(all_71_0_27, all_0_7_7) = 0
% 12.42/3.50 | (149) in(all_71_1_28, all_0_9_9) = 0
% 12.42/3.50 |
% 12.42/3.50 | Instantiating formula (93) with all_50_0_22, all_0_4_4, all_50_1_23, all_0_6_6, all_0_8_8, all_71_0_27, all_71_1_28 and discharging atoms cartesian_product2(all_0_8_8, all_0_6_6) = all_0_4_4, ordered_pair(all_71_1_28, all_71_0_27) = all_50_1_23, in(all_50_1_23, all_0_4_4) = all_50_0_22, yields:
% 12.42/3.50 | (150) all_50_0_22 = 0 | ? [v0] : ? [v1] : (in(all_71_0_27, all_0_6_6) = v1 & in(all_71_1_28, all_0_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 12.42/3.50 |
% 12.42/3.50 | Instantiating formula (96) with all_71_0_27, all_0_6_6, all_0_7_7 and discharging atoms subset(all_0_7_7, all_0_6_6) = 0, in(all_71_0_27, all_0_7_7) = 0, yields:
% 12.42/3.50 | (151) in(all_71_0_27, all_0_6_6) = 0
% 12.42/3.50 |
% 12.42/3.50 | Instantiating formula (96) with all_71_1_28, all_0_8_8, all_0_9_9 and discharging atoms subset(all_0_9_9, all_0_8_8) = 0, in(all_71_1_28, all_0_9_9) = 0, yields:
% 12.42/3.50 | (152) in(all_71_1_28, all_0_8_8) = 0
% 12.42/3.50 |
% 12.42/3.50 +-Applying beta-rule and splitting (150), into two cases.
% 12.42/3.50 |-Branch one:
% 12.42/3.50 | (153) all_50_0_22 = 0
% 12.42/3.50 |
% 12.42/3.50 | Equations (153) can reduce 142 to:
% 12.42/3.50 | (138) $false
% 12.42/3.50 |
% 12.42/3.50 |-The branch is then unsatisfiable
% 12.42/3.50 |-Branch two:
% 12.42/3.50 | (142) ~ (all_50_0_22 = 0)
% 12.42/3.50 | (156) ? [v0] : ? [v1] : (in(all_71_0_27, all_0_6_6) = v1 & in(all_71_1_28, all_0_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 12.42/3.50 |
% 12.42/3.50 | Instantiating (156) with all_126_0_38, all_126_1_39 yields:
% 12.42/3.50 | (157) in(all_71_0_27, all_0_6_6) = all_126_0_38 & in(all_71_1_28, all_0_8_8) = all_126_1_39 & ( ~ (all_126_0_38 = 0) | ~ (all_126_1_39 = 0))
% 12.42/3.50 |
% 12.42/3.50 | Applying alpha-rule on (157) yields:
% 12.42/3.50 | (158) in(all_71_0_27, all_0_6_6) = all_126_0_38
% 12.42/3.50 | (159) in(all_71_1_28, all_0_8_8) = all_126_1_39
% 12.42/3.50 | (160) ~ (all_126_0_38 = 0) | ~ (all_126_1_39 = 0)
% 12.42/3.50 |
% 12.42/3.50 | Instantiating formula (127) with all_71_0_27, all_0_6_6, all_126_0_38, 0 and discharging atoms in(all_71_0_27, all_0_6_6) = all_126_0_38, in(all_71_0_27, all_0_6_6) = 0, yields:
% 12.42/3.50 | (161) all_126_0_38 = 0
% 12.42/3.50 |
% 12.42/3.50 | Instantiating formula (127) with all_71_1_28, all_0_8_8, 0, all_126_1_39 and discharging atoms in(all_71_1_28, all_0_8_8) = all_126_1_39, in(all_71_1_28, all_0_8_8) = 0, yields:
% 12.42/3.50 | (162) all_126_1_39 = 0
% 12.42/3.50 |
% 12.42/3.50 +-Applying beta-rule and splitting (160), into two cases.
% 12.42/3.50 |-Branch one:
% 12.42/3.50 | (163) ~ (all_126_0_38 = 0)
% 12.42/3.50 |
% 12.42/3.50 | Equations (161) can reduce 163 to:
% 12.42/3.50 | (138) $false
% 12.42/3.50 |
% 12.42/3.50 |-The branch is then unsatisfiable
% 12.42/3.50 |-Branch two:
% 12.42/3.50 | (161) all_126_0_38 = 0
% 12.42/3.51 | (166) ~ (all_126_1_39 = 0)
% 12.42/3.51 |
% 12.42/3.51 | Equations (162) can reduce 166 to:
% 12.42/3.51 | (138) $false
% 12.42/3.51 |
% 12.42/3.51 |-The branch is then unsatisfiable
% 12.42/3.51 % SZS output end Proof for theBenchmark
% 12.42/3.51
% 12.42/3.51 2911ms
%------------------------------------------------------------------------------